LMFDB - Embedded newform 6014.2.a.k.1.19

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.277622 q^{3} +1.00000 q^{4} -0.233184 q^{5} +0.277622 q^{6} -0.765476 q^{7} +1.00000 q^{8} -2.92293 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.277622 q^{3} +1.00000 q^{4} -0.233184 q^{5} +0.277622 q^{6} -0.765476 q^{7} +1.00000 q^{8} -2.92293 q^{9} -0.233184 q^{10} +4.25014 q^{11} +0.277622 q^{12} -1.31476 q^{13} -0.765476 q^{14} -0.0647369 q^{15} +1.00000 q^{16} +1.66493 q^{17} -2.92293 q^{18} +0.920687 q^{19} -0.233184 q^{20} -0.212513 q^{21} +4.25014 q^{22} -2.79564 q^{23} +0.277622 q^{24} -4.94563 q^{25} -1.31476 q^{26} -1.64433 q^{27} -0.765476 q^{28} +1.28532 q^{29} -0.0647369 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.17993 q^{33} +1.66493 q^{34} +0.178497 q^{35} -2.92293 q^{36} +6.05375 q^{37} +0.920687 q^{38} -0.365006 q^{39} -0.233184 q^{40} +5.39118 q^{41} -0.212513 q^{42} +8.19585 q^{43} +4.25014 q^{44} +0.681578 q^{45} -2.79564 q^{46} +2.48500 q^{47} +0.277622 q^{48} -6.41405 q^{49} -4.94563 q^{50} +0.462222 q^{51} -1.31476 q^{52} +7.70934 q^{53} -1.64433 q^{54} -0.991062 q^{55} -0.765476 q^{56} +0.255603 q^{57} +1.28532 q^{58} +9.36973 q^{59} -0.0647369 q^{60} +9.19377 q^{61} +1.00000 q^{62} +2.23743 q^{63} +1.00000 q^{64} +0.306580 q^{65} +1.17993 q^{66} +1.57485 q^{67} +1.66493 q^{68} -0.776132 q^{69} +0.178497 q^{70} +13.5427 q^{71} -2.92293 q^{72} -0.834333 q^{73} +6.05375 q^{74} -1.37301 q^{75} +0.920687 q^{76} -3.25338 q^{77} -0.365006 q^{78} -9.36797 q^{79} -0.233184 q^{80} +8.31227 q^{81} +5.39118 q^{82} -13.0674 q^{83} -0.212513 q^{84} -0.388235 q^{85} +8.19585 q^{86} +0.356832 q^{87} +4.25014 q^{88} +12.9933 q^{89} +0.681578 q^{90} +1.00642 q^{91} -2.79564 q^{92} +0.277622 q^{93} +2.48500 q^{94} -0.214689 q^{95} +0.277622 q^{96} +1.00000 q^{97} -6.41405 q^{98} -12.4228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * 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
$3$	0.277622	0.160285	0.0801426	−	0.996783i	$-0.474462\pi$
$3$	0.277622	0.160285	0.0801426	+	0.996783i	$0.474462\pi$
$4$	1.00000	0.500000
$5$	−0.233184	−0.104283	−0.0521414	−	0.998640i	$-0.516605\pi$
$5$	−0.233184	−0.104283	−0.0521414	+	0.998640i	$0.516605\pi$
$6$	0.277622	0.113339
$7$	−0.765476	−0.289323	−0.144661	−	0.989481i	$-0.546209\pi$
$7$	−0.765476	−0.289323	−0.144661	+	0.989481i	$0.546209\pi$
$8$	1.00000	0.353553
$9$	−2.92293	−0.974309
$10$	−0.233184	−0.0737391
$11$	4.25014	1.28146	0.640732	−	0.767764i	$-0.278631\pi$
$11$	4.25014	1.28146	0.640732	+	0.767764i	$0.278631\pi$
$12$	0.277622	0.0801426
$13$	−1.31476	−0.364649	−0.182324	−	0.983238i	$-0.558362\pi$
$13$	−1.31476	−0.364649	−0.182324	+	0.983238i	$0.558362\pi$
$14$	−0.765476	−0.204582
$15$	−0.0647369	−0.0167150
$16$	1.00000	0.250000
$17$	1.66493	0.403806	0.201903	−	0.979406i	$-0.435287\pi$
$17$	1.66493	0.403806	0.201903	+	0.979406i	$0.435287\pi$
$18$	−2.92293	−0.688940
$19$	0.920687	0.211220	0.105610	−	0.994408i	$-0.466320\pi$
$19$	0.920687	0.211220	0.105610	+	0.994408i	$0.466320\pi$
$20$	−0.233184	−0.0521414
$21$	−0.212513	−0.0463742
$22$	4.25014	0.906132
$23$	−2.79564	−0.582932	−0.291466	−	0.956581i	$-0.594143\pi$
$23$	−2.79564	−0.582932	−0.291466	+	0.956581i	$0.594143\pi$
$24$	0.277622	0.0566694
$25$	−4.94563	−0.989125
$26$	−1.31476	−0.257845
$27$	−1.64433	−0.316452
$28$	−0.765476	−0.144661
$29$	1.28532	0.238677	0.119339	−	0.992854i	$-0.461923\pi$
$29$	1.28532	0.238677	0.119339	+	0.992854i	$0.461923\pi$
$30$	−0.0647369	−0.0118193
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	1.17993	0.205400
$34$	1.66493	0.285534
$35$	0.178497	0.0301714
$36$	−2.92293	−0.487154
$37$	6.05375	0.995231	0.497615	−	0.867398i	$-0.334209\pi$
$37$	6.05375	0.995231	0.497615	+	0.867398i	$0.334209\pi$
$38$	0.920687	0.149355
$39$	−0.365006	−0.0584478
$40$	−0.233184	−0.0368696
$41$	5.39118	0.841960	0.420980	−	0.907070i	$-0.361686\pi$
$41$	5.39118	0.841960	0.420980	+	0.907070i	$0.361686\pi$
$42$	−0.212513	−0.0327915
$43$	8.19585	1.24986	0.624928	−	0.780682i	$-0.285128\pi$
$43$	8.19585	1.24986	0.624928	+	0.780682i	$0.285128\pi$
$44$	4.25014	0.640732
$45$	0.681578	0.101604
$46$	−2.79564	−0.412195
$47$	2.48500	0.362475	0.181237	−	0.983439i	$-0.441990\pi$
$47$	2.48500	0.362475	0.181237	+	0.983439i	$0.441990\pi$
$48$	0.277622	0.0400713
$49$	−6.41405	−0.916292
$50$	−4.94563	−0.699417
$51$	0.462222	0.0647241
$52$	−1.31476	−0.182324
$53$	7.70934	1.05896	0.529480	−	0.848323i	$-0.322387\pi$
$53$	7.70934	1.05896	0.529480	+	0.848323i	$0.322387\pi$
$54$	−1.64433	−0.223766
$55$	−0.991062	−0.133635
$56$	−0.765476	−0.102291
$57$	0.255603	0.0338554
$58$	1.28532	0.168770
$59$	9.36973	1.21983	0.609917	−	0.792465i	$-0.291203\pi$
$59$	9.36973	1.21983	0.609917	+	0.792465i	$0.291203\pi$
$60$	−0.0647369	−0.00835750
$61$	9.19377	1.17714	0.588571	−	0.808446i	$-0.299691\pi$
$61$	9.19377	1.17714	0.588571	+	0.808446i	$0.299691\pi$
$62$	1.00000	0.127000
$63$	2.23743	0.281890
$64$	1.00000	0.125000
$65$	0.306580	0.0380266
$66$	1.17993	0.145240
$67$	1.57485	0.192399	0.0961993	−	0.995362i	$-0.469331\pi$
$67$	1.57485	0.192399	0.0961993	+	0.995362i	$0.469331\pi$
$68$	1.66493	0.201903
$69$	−0.776132	−0.0934353
$70$	0.178497	0.0213344
$71$	13.5427	1.60723	0.803613	−	0.595152i	$-0.202908\pi$
$71$	13.5427	1.60723	0.803613	+	0.595152i	$0.202908\pi$
$72$	−2.92293	−0.344470
$73$	−0.834333	−0.0976513	−0.0488257	−	0.998807i	$-0.515548\pi$
$73$	−0.834333	−0.0976513	−0.0488257	+	0.998807i	$0.515548\pi$
$74$	6.05375	0.703734
$75$	−1.37301	−0.158542
$76$	0.920687	0.105610
$77$	−3.25338	−0.370757
$78$	−0.365006	−0.0413288
$79$	−9.36797	−1.05398	−0.526989	−	0.849872i	$-0.676679\pi$
$79$	−9.36797	−1.05398	−0.526989	+	0.849872i	$0.676679\pi$
$80$	−0.233184	−0.0260707
$81$	8.31227	0.923586
$82$	5.39118	0.595356
$83$	−13.0674	−1.43434	−0.717169	−	0.696899i	$-0.754563\pi$
$83$	−13.0674	−1.43434	−0.717169	+	0.696899i	$0.754563\pi$
$84$	−0.212513	−0.0231871
$85$	−0.388235	−0.0421100
$86$	8.19585	0.883782
$87$	0.356832	0.0382564
$88$	4.25014	0.453066
$89$	12.9933	1.37729	0.688643	−	0.725100i	$-0.258207\pi$
$89$	12.9933	1.37729	0.688643	+	0.725100i	$0.258207\pi$
$90$	0.681578	0.0718447
$91$	1.00642	0.105501
$92$	−2.79564	−0.291466
$93$	0.277622	0.0287881
$94$	2.48500	0.256308
$95$	−0.214689	−0.0220266
$96$	0.277622	0.0283347
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−6.41405	−0.647916
$99$	−12.4228	−1.24854
$100$	−4.94563	−0.494563
$101$	−1.05787	−0.105262	−0.0526309	−	0.998614i	$-0.516761\pi$
$101$	−1.05787	−0.105262	−0.0526309	+	0.998614i	$0.516761\pi$
$102$	0.462222	0.0457668
$103$	−5.63779	−0.555508	−0.277754	−	0.960652i	$-0.589590\pi$
$103$	−5.63779	−0.555508	−0.277754	+	0.960652i	$0.589590\pi$
$104$	−1.31476	−0.128923
$105$	0.0495546	0.00483603
$106$	7.70934	0.748797
$107$	−7.81814	−0.755808	−0.377904	−	0.925845i	$-0.623355\pi$
$107$	−7.81814	−0.755808	−0.377904	+	0.925845i	$0.623355\pi$
$108$	−1.64433	−0.158226
$109$	−6.22462	−0.596210	−0.298105	−	0.954533i	$-0.596355\pi$
$109$	−6.22462	−0.596210	−0.298105	+	0.954533i	$0.596355\pi$
$110$	−0.991062	−0.0944941
$111$	1.68065	0.159521
$112$	−0.765476	−0.0723307
$113$	13.3871	1.25935	0.629677	−	0.776857i	$-0.283187\pi$
$113$	13.3871	1.25935	0.629677	+	0.776857i	$0.283187\pi$
$114$	0.255603	0.0239394
$115$	0.651898	0.0607898
$116$	1.28532	0.119339
$117$	3.84294	0.355280
$118$	9.36973	0.862553
$119$	−1.27447	−0.116830
$120$	−0.0647369	−0.00590964
$121$	7.06367	0.642152
$122$	9.19377	0.832365
$123$	1.49671	0.134954
$124$	1.00000	0.0898027
$125$	2.31916	0.207432
$126$	2.23743	0.199326
$127$	7.79018	0.691266	0.345633	−	0.938370i	$-0.387664\pi$
$127$	7.79018	0.691266	0.345633	+	0.938370i	$0.387664\pi$
$128$	1.00000	0.0883883
$129$	2.27535	0.200333
$130$	0.306580	0.0268889
$131$	−20.1681	−1.76210	−0.881048	−	0.473026i	$-0.843162\pi$
$131$	−20.1681	−1.76210	−0.881048	+	0.473026i	$0.843162\pi$
$132$	1.17993	0.102700
$133$	−0.704764	−0.0611108
$134$	1.57485	0.136046
$135$	0.383432	0.0330006
$136$	1.66493	0.142767
$137$	9.05297	0.773447	0.386724	−	0.922196i	$-0.373607\pi$
$137$	9.05297	0.773447	0.386724	+	0.922196i	$0.373607\pi$
$138$	−0.776132	−0.0660687
$139$	17.7524	1.50574	0.752870	−	0.658170i	$-0.228669\pi$
$139$	17.7524	1.50574	0.752870	+	0.658170i	$0.228669\pi$
$140$	0.178497	0.0150857
$141$	0.689891	0.0580993
$142$	13.5427	1.13648
$143$	−5.58791	−0.467284
$144$	−2.92293	−0.243577
$145$	−0.299715	−0.0248900
$146$	−0.834333	−0.0690499
$147$	−1.78068	−0.146868
$148$	6.05375	0.497615
$149$	12.2160	1.00077	0.500385	−	0.865803i	$-0.333192\pi$
$149$	12.2160	1.00077	0.500385	+	0.865803i	$0.333192\pi$
$150$	−1.37301	−0.112106
$151$	−7.28156	−0.592565	−0.296282	−	0.955100i	$-0.595747\pi$
$151$	−7.28156	−0.592565	−0.296282	+	0.955100i	$0.595747\pi$
$152$	0.920687	0.0746776
$153$	−4.86648	−0.393432
$154$	−3.25338	−0.262165
$155$	−0.233184	−0.0187298
$156$	−0.365006	−0.0292239
$157$	−18.8096	−1.50117	−0.750585	−	0.660774i	$-0.770228\pi$
$157$	−18.8096	−1.50117	−0.750585	+	0.660774i	$0.770228\pi$
$158$	−9.36797	−0.745276
$159$	2.14028	0.169735
$160$	−0.233184	−0.0184348
$161$	2.14000	0.168655
$162$	8.31227	0.653074
$163$	−2.51234	−0.196782	−0.0983908	−	0.995148i	$-0.531370\pi$
$163$	−2.51234	−0.196782	−0.0983908	+	0.995148i	$0.531370\pi$
$164$	5.39118	0.420980
$165$	−0.275141	−0.0214197
$166$	−13.0674	−1.01423
$167$	11.7122	0.906315	0.453157	−	0.891431i	$-0.350298\pi$
$167$	11.7122	0.906315	0.453157	+	0.891431i	$0.350298\pi$
$168$	−0.212513	−0.0163957
$169$	−11.2714	−0.867031
$170$	−0.388235	−0.0297763
$171$	−2.69110	−0.205793
$172$	8.19585	0.624928
$173$	6.73206	0.511829	0.255915	−	0.966699i	$-0.417623\pi$
$173$	6.73206	0.511829	0.255915	+	0.966699i	$0.417623\pi$
$174$	0.356832	0.0270514
$175$	3.78576	0.286176
$176$	4.25014	0.320366
$177$	2.60124	0.195521
$178$	12.9933	0.973888
$179$	−4.09518	−0.306088	−0.153044	−	0.988219i	$-0.548908\pi$
$179$	−4.09518	−0.306088	−0.153044	+	0.988219i	$0.548908\pi$
$180$	0.681578	0.0508019
$181$	9.15220	0.680277	0.340139	−	0.940375i	$-0.389526\pi$
$181$	9.15220	0.680277	0.340139	+	0.940375i	$0.389526\pi$
$182$	1.00642	0.0746006
$183$	2.55239	0.188678
$184$	−2.79564	−0.206097
$185$	−1.41164	−0.103786
$186$	0.277622	0.0203562
$187$	7.07620	0.517463
$188$	2.48500	0.181237
$189$	1.25870	0.0915569
$190$	−0.214689	−0.0155752
$191$	18.1452	1.31294	0.656471	−	0.754351i	$-0.272049\pi$
$191$	18.1452	1.31294	0.656471	+	0.754351i	$0.272049\pi$
$192$	0.277622	0.0200356
$193$	−0.706840	−0.0508794	−0.0254397	−	0.999676i	$-0.508099\pi$
$193$	−0.706840	−0.0508794	−0.0254397	+	0.999676i	$0.508099\pi$
$194$	1.00000	0.0717958
$195$	0.0851134	0.00609510
$196$	−6.41405	−0.458146
$197$	−13.9460	−0.993609	−0.496804	−	0.867863i	$-0.665493\pi$
$197$	−13.9460	−0.993609	−0.496804	+	0.867863i	$0.665493\pi$
$198$	−12.4228	−0.882853
$199$	−2.34959	−0.166558	−0.0832790	−	0.996526i	$-0.526539\pi$
$199$	−2.34959	−0.166558	−0.0832790	+	0.996526i	$0.526539\pi$
$200$	−4.94563	−0.349709
$201$	0.437213	0.0308386
$202$	−1.05787	−0.0744313
$203$	−0.983880	−0.0690548
$204$	0.462222	0.0323620
$205$	−1.25713	−0.0878021
$206$	−5.63779	−0.392804
$207$	8.17145	0.567955
$208$	−1.31476	−0.0911621
$209$	3.91305	0.270671
$210$	0.0495546	0.00341959
$211$	10.1094	0.695961	0.347980	−	0.937502i	$-0.386868\pi$
$211$	10.1094	0.695961	0.347980	+	0.937502i	$0.386868\pi$
$212$	7.70934	0.529480
$213$	3.75976	0.257615
$214$	−7.81814	−0.534437
$215$	−1.91114	−0.130339
$216$	−1.64433	−0.111883
$217$	−0.765476	−0.0519639
$218$	−6.22462	−0.421584
$219$	−0.231629	−0.0156521
$220$	−0.991062	−0.0668174
$221$	−2.18899	−0.147247
$222$	1.68065	0.112798
$223$	11.6646	0.781120	0.390560	−	0.920577i	$-0.372281\pi$
$223$	11.6646	0.781120	0.390560	+	0.920577i	$0.372281\pi$
$224$	−0.765476	−0.0511455
$225$	14.4557	0.963713
$226$	13.3871	0.890498
$227$	16.0182	1.06316	0.531582	−	0.847007i	$-0.321598\pi$
$227$	16.0182	1.06316	0.531582	+	0.847007i	$0.321598\pi$
$228$	0.255603	0.0169277
$229$	28.6460	1.89298	0.946490	−	0.322733i	$-0.104602\pi$
$229$	28.6460	1.89298	0.946490	+	0.322733i	$0.104602\pi$
$230$	0.651898	0.0429849
$231$	−0.903210	−0.0594269
$232$	1.28532	0.0843852
$233$	−15.5426	−1.01823	−0.509114	−	0.860699i	$-0.670027\pi$
$233$	−15.5426	−1.01823	−0.509114	+	0.860699i	$0.670027\pi$
$234$	3.84294	0.251221
$235$	−0.579461	−0.0377999
$236$	9.36973	0.609917
$237$	−2.60075	−0.168937
$238$	−1.27447	−0.0826115
$239$	−12.1434	−0.785489	−0.392745	−	0.919648i	$-0.628474\pi$
$239$	−12.1434	−0.785489	−0.392745	+	0.919648i	$0.628474\pi$
$240$	−0.0647369	−0.00417875
$241$	19.2802	1.24194	0.620972	−	0.783833i	$-0.286738\pi$
$241$	19.2802	1.24194	0.620972	+	0.783833i	$0.286738\pi$
$242$	7.06367	0.454070
$243$	7.24068	0.464490
$244$	9.19377	0.588571
$245$	1.49565	0.0955536
$246$	1.49671	0.0954267
$247$	−1.21048	−0.0770211
$248$	1.00000	0.0635001
$249$	−3.62781	−0.229903
$250$	2.31916	0.146676
$251$	11.9964	0.757203	0.378602	−	0.925560i	$-0.376405\pi$
$251$	11.9964	0.757203	0.378602	+	0.925560i	$0.376405\pi$
$252$	2.23743	0.140945
$253$	−11.8819	−0.747006
$254$	7.79018	0.488799
$255$	−0.107783	−0.00674961
$256$	1.00000	0.0625000
$257$	27.7523	1.73114	0.865572	−	0.500785i	$-0.166955\pi$
$257$	27.7523	1.73114	0.865572	+	0.500785i	$0.166955\pi$
$258$	2.27535	0.141657
$259$	−4.63400	−0.287943
$260$	0.306580	0.0190133
$261$	−3.75689	−0.232545
$262$	−20.1681	−1.24599
$263$	2.52524	0.155713	0.0778564	−	0.996965i	$-0.475192\pi$
$263$	2.52524	0.155713	0.0778564	+	0.996965i	$0.475192\pi$
$264$	1.17993	0.0726198
$265$	−1.79769	−0.110431
$266$	−0.704764	−0.0432118
$267$	3.60722	0.220759
$268$	1.57485	0.0961993
$269$	−5.19962	−0.317027	−0.158513	−	0.987357i	$-0.550670\pi$
$269$	−5.19962	−0.317027	−0.158513	+	0.987357i	$0.550670\pi$
$270$	0.383432	0.0233349
$271$	19.0950	1.15994	0.579969	−	0.814638i	$-0.303065\pi$
$271$	19.0950	1.15994	0.579969	+	0.814638i	$0.303065\pi$
$272$	1.66493	0.100951
$273$	0.279404	0.0169103
$274$	9.05297	0.546910
$275$	−21.0196	−1.26753
$276$	−0.776132	−0.0467176
$277$	−6.92767	−0.416243	−0.208122	−	0.978103i	$-0.566735\pi$
$277$	−6.92767	−0.416243	−0.208122	+	0.978103i	$0.566735\pi$
$278$	17.7524	1.06472
$279$	−2.92293	−0.174991
$280$	0.178497	0.0106672
$281$	−4.41943	−0.263641	−0.131820	−	0.991274i	$-0.542082\pi$
$281$	−4.41943	−0.263641	−0.131820	+	0.991274i	$0.542082\pi$
$282$	0.689891	0.0410824
$283$	−7.33708	−0.436144	−0.218072	−	0.975933i	$-0.569977\pi$
$283$	−7.33708	−0.436144	−0.218072	+	0.975933i	$0.569977\pi$
$284$	13.5427	0.803613
$285$	−0.0596024	−0.00353054
$286$	−5.58791	−0.330420
$287$	−4.12682	−0.243598
$288$	−2.92293	−0.172235
$289$	−14.2280	−0.836941
$290$	−0.299715	−0.0175999
$291$	0.277622	0.0162745
$292$	−0.834333	−0.0488257
$293$	−17.7885	−1.03921	−0.519607	−	0.854406i	$-0.673922\pi$
$293$	−17.7885	−1.03921	−0.519607	+	0.854406i	$0.673922\pi$
$294$	−1.78068	−0.103851
$295$	−2.18487	−0.127208
$296$	6.05375	0.351867
$297$	−6.98865	−0.405523
$298$	12.2160	0.707651
$299$	3.67559	0.212565
$300$	−1.37301	−0.0792710
$301$	−6.27373	−0.361612
$302$	−7.28156	−0.419006
$303$	−0.293687	−0.0168719
$304$	0.920687	0.0528050
$305$	−2.14384	−0.122756
$306$	−4.86648	−0.278198
$307$	−25.3033	−1.44413	−0.722067	−	0.691824i	$-0.756808\pi$
$307$	−25.3033	−1.44413	−0.722067	+	0.691824i	$0.756808\pi$
$308$	−3.25338	−0.185379
$309$	−1.56518	−0.0890398
$310$	−0.233184	−0.0132439
$311$	−0.462242	−0.0262113	−0.0131057	−	0.999914i	$-0.504172\pi$
$311$	−0.462242	−0.0262113	−0.0131057	+	0.999914i	$0.504172\pi$
$312$	−0.365006	−0.0206644
$313$	30.7629	1.73882	0.869412	−	0.494088i	$-0.164498\pi$
$313$	30.7629	1.73882	0.869412	+	0.494088i	$0.164498\pi$
$314$	−18.8096	−1.06149
$315$	−0.521732	−0.0293963
$316$	−9.36797	−0.526989
$317$	3.25574	0.182861	0.0914303	−	0.995811i	$-0.470856\pi$
$317$	3.25574	0.182861	0.0914303	+	0.995811i	$0.470856\pi$
$318$	2.14028	0.120021
$319$	5.46277	0.305857
$320$	−0.233184	−0.0130354
$321$	−2.17049	−0.121145
$322$	2.14000	0.119257
$323$	1.53288	0.0852919
$324$	8.31227	0.461793
$325$	6.50231	0.360683
$326$	−2.51234	−0.139146
$327$	−1.72809	−0.0955637
$328$	5.39118	0.297678
$329$	−1.90221	−0.104872
$330$	−0.275141	−0.0151460
$331$	−2.86844	−0.157664	−0.0788319	−	0.996888i	$-0.525119\pi$
$331$	−2.86844	−0.157664	−0.0788319	+	0.996888i	$0.525119\pi$
$332$	−13.0674	−0.717169
$333$	−17.6947	−0.969662
$334$	11.7122	0.640861
$335$	−0.367229	−0.0200639
$336$	−0.212513	−0.0115935
$337$	6.49596	0.353858	0.176929	−	0.984224i	$-0.443384\pi$
$337$	6.49596	0.353858	0.176929	+	0.984224i	$0.443384\pi$
$338$	−11.2714	−0.613084
$339$	3.71656	0.201856
$340$	−0.388235	−0.0210550
$341$	4.25014	0.230158
$342$	−2.69110	−0.145518
$343$	10.2681	0.554427
$344$	8.19585	0.441891
$345$	0.180981	0.00974370
$346$	6.73206	0.361918
$347$	−5.84129	−0.313577	−0.156788	−	0.987632i	$-0.550114\pi$
$347$	−5.84129	−0.313577	−0.156788	+	0.987632i	$0.550114\pi$
$348$	0.356832	0.0191282
$349$	−36.4292	−1.95001	−0.975006	−	0.222181i	$-0.928683\pi$
$349$	−36.4292	−1.95001	−0.975006	+	0.222181i	$0.928683\pi$
$350$	3.78576	0.202357
$351$	2.16190	0.115394
$352$	4.25014	0.226533
$353$	21.5967	1.14948	0.574739	−	0.818337i	$-0.305104\pi$
$353$	21.5967	1.14948	0.574739	+	0.818337i	$0.305104\pi$
$354$	2.60124	0.138255
$355$	−3.15794	−0.167606
$356$	12.9933	0.688643
$357$	−0.353820	−0.0187262
$358$	−4.09518	−0.216437
$359$	16.1232	0.850950	0.425475	−	0.904970i	$-0.360107\pi$
$359$	16.1232	0.850950	0.425475	+	0.904970i	$0.360107\pi$
$360$	0.681578	0.0359223
$361$	−18.1523	−0.955386
$362$	9.15220	0.481029
$363$	1.96103	0.102927
$364$	1.00642	0.0527506
$365$	0.194553	0.0101834
$366$	2.55239	0.133416
$367$	−13.1823	−0.688109	−0.344055	−	0.938950i	$-0.611801\pi$
$367$	−13.1823	−0.688109	−0.344055	+	0.938950i	$0.611801\pi$
$368$	−2.79564	−0.145733
$369$	−15.7580	−0.820329
$370$	−1.41164	−0.0733874
$371$	−5.90132	−0.306381
$372$	0.277622	0.0143940
$373$	28.7421	1.48821	0.744105	−	0.668063i	$-0.232876\pi$
$373$	28.7421	1.48821	0.744105	+	0.668063i	$0.232876\pi$
$374$	7.07620	0.365902
$375$	0.643849	0.0332482
$376$	2.48500	0.128154
$377$	−1.68988	−0.0870334
$378$	1.25870	0.0647405
$379$	−38.4714	−1.97614	−0.988071	−	0.153998i	$-0.950785\pi$
$379$	−38.4714	−1.97614	−0.988071	+	0.153998i	$0.950785\pi$
$380$	−0.214689	−0.0110133
$381$	2.16273	0.110800
$382$	18.1452	0.928390
$383$	−23.9813	−1.22539	−0.612694	−	0.790320i	$-0.709914\pi$
$383$	−23.9813	−1.22539	−0.612694	+	0.790320i	$0.709914\pi$
$384$	0.277622	0.0141673
$385$	0.758635	0.0386636
$386$	−0.706840	−0.0359772
$387$	−23.9559	−1.21775
$388$	1.00000	0.0507673
$389$	21.2442	1.07712	0.538561	−	0.842586i	$-0.318968\pi$
$389$	21.2442	1.07712	0.538561	+	0.842586i	$0.318968\pi$
$390$	0.0851134	0.00430989
$391$	−4.65456	−0.235391
$392$	−6.41405	−0.323958
$393$	−5.59911	−0.282438
$394$	−13.9460	−0.702587
$395$	2.18446	0.109912
$396$	−12.4228	−0.624271
$397$	−8.85722	−0.444531	−0.222265	−	0.974986i	$-0.571345\pi$
$397$	−8.85722	−0.444531	−0.222265	+	0.974986i	$0.571345\pi$
$398$	−2.34959	−0.117774
$399$	−0.195658	−0.00979515
$400$	−4.94563	−0.247281
$401$	5.98005	0.298630	0.149315	−	0.988790i	$-0.452293\pi$
$401$	5.98005	0.298630	0.149315	+	0.988790i	$0.452293\pi$
$402$	0.437213	0.0218062
$403$	−1.31476	−0.0654928
$404$	−1.05787	−0.0526309
$405$	−1.93829	−0.0963142
$406$	−0.983880	−0.0488291
$407$	25.7293	1.27535
$408$	0.462222	0.0228834
$409$	−13.1972	−0.652560	−0.326280	−	0.945273i	$-0.605795\pi$
$409$	−13.1972	−0.652560	−0.326280	+	0.945273i	$0.605795\pi$
$410$	−1.25713	−0.0620854
$411$	2.51330	0.123972
$412$	−5.63779	−0.277754
$413$	−7.17231	−0.352926
$414$	8.17145	0.401605
$415$	3.04711	0.149577
$416$	−1.31476	−0.0644614
$417$	4.92846	0.241348
$418$	3.91305	0.191393
$419$	−21.9081	−1.07028	−0.535140	−	0.844763i	$-0.679741\pi$
$419$	−21.9081	−1.07028	−0.535140	+	0.844763i	$0.679741\pi$
$420$	0.0495546	0.00241802
$421$	9.39667	0.457966	0.228983	−	0.973430i	$-0.426460\pi$
$421$	9.39667	0.457966	0.228983	+	0.973430i	$0.426460\pi$
$422$	10.1094	0.492119
$423$	−7.26347	−0.353162
$424$	7.70934	0.374399
$425$	−8.23414	−0.399414
$426$	3.75976	0.182161
$427$	−7.03762	−0.340574
$428$	−7.81814	−0.377904
$429$	−1.55133	−0.0748987
$430$	−1.91114	−0.0921633
$431$	8.35419	0.402407	0.201204	−	0.979549i	$-0.435515\pi$
$431$	8.35419	0.402407	0.201204	+	0.979549i	$0.435515\pi$
$432$	−1.64433	−0.0791131
$433$	−8.28874	−0.398331	−0.199166	−	0.979966i	$-0.563823\pi$
$433$	−8.28874	−0.398331	−0.199166	+	0.979966i	$0.563823\pi$
$434$	−0.765476	−0.0367440
$435$	−0.0832075	−0.00398949
$436$	−6.22462	−0.298105
$437$	−2.57391	−0.123127
$438$	−0.231629	−0.0110677
$439$	−29.3664	−1.40158	−0.700792	−	0.713366i	$-0.747170\pi$
$439$	−29.3664	−1.40158	−0.700792	+	0.713366i	$0.747170\pi$
$440$	−0.991062	−0.0472470
$441$	18.7478	0.892752
$442$	−2.18899	−0.104120
$443$	−39.8120	−1.89152	−0.945762	−	0.324861i	$-0.894683\pi$
$443$	−39.8120	−1.89152	−0.945762	+	0.324861i	$0.894683\pi$
$444$	1.68065	0.0797603
$445$	−3.02982	−0.143627
$446$	11.6646	0.552335
$447$	3.39142	0.160409
$448$	−0.765476	−0.0361654
$449$	23.4908	1.10860	0.554300	−	0.832317i	$-0.312986\pi$
$449$	23.4908	1.10860	0.554300	+	0.832317i	$0.312986\pi$
$450$	14.4557	0.681448
$451$	22.9132	1.07894
$452$	13.3871	0.629677
$453$	−2.02152	−0.0949793
$454$	16.0182	0.751770
$455$	−0.234680	−0.0110020
$456$	0.255603	0.0119697
$457$	−5.06070	−0.236730	−0.118365	−	0.992970i	$-0.537765\pi$
$457$	−5.06070	−0.236730	−0.118365	+	0.992970i	$0.537765\pi$
$458$	28.6460	1.33854
$459$	−2.73771	−0.127785
$460$	0.651898	0.0303949
$461$	11.5655	0.538658	0.269329	−	0.963048i	$-0.413198\pi$
$461$	11.5655	0.538658	0.269329	+	0.963048i	$0.413198\pi$
$462$	−0.903210	−0.0420211
$463$	21.8949	1.01754	0.508772	−	0.860901i	$-0.330100\pi$
$463$	21.8949	1.01754	0.508772	+	0.860901i	$0.330100\pi$
$464$	1.28532	0.0596693
$465$	−0.0647369	−0.00300210
$466$	−15.5426	−0.719996
$467$	10.9783	0.508016	0.254008	−	0.967202i	$-0.418251\pi$
$467$	10.9783	0.508016	0.254008	+	0.967202i	$0.418251\pi$
$468$	3.84294	0.177640
$469$	−1.20551	−0.0556653
$470$	−0.579461	−0.0267286
$471$	−5.22196	−0.240615
$472$	9.36973	0.431277
$473$	34.8335	1.60165
$474$	−2.60075	−0.119457
$475$	−4.55337	−0.208923
$476$	−1.27447	−0.0584151
$477$	−22.5338	−1.03175
$478$	−12.1434	−0.555425
$479$	−32.3907	−1.47997	−0.739984	−	0.672625i	$-0.765167\pi$
$479$	−32.3907	−1.47997	−0.739984	+	0.672625i	$0.765167\pi$
$480$	−0.0647369	−0.00295482
$481$	−7.95922	−0.362909
$482$	19.2802	0.878187
$483$	0.594110	0.0270330
$484$	7.06367	0.321076
$485$	−0.233184	−0.0105883
$486$	7.24068	0.328444
$487$	20.3623	0.922702	0.461351	−	0.887218i	$-0.347365\pi$
$487$	20.3623	0.922702	0.461351	+	0.887218i	$0.347365\pi$
$488$	9.19377	0.416183
$489$	−0.697481	−0.0315412
$490$	1.49565	0.0675666
$491$	22.3632	1.00924	0.504618	−	0.863343i	$-0.331633\pi$
$491$	22.3632	1.00924	0.504618	+	0.863343i	$0.331633\pi$
$492$	1.49671	0.0674769
$493$	2.13997	0.0963793
$494$	−1.21048	−0.0544621
$495$	2.89680	0.130202
$496$	1.00000	0.0449013
$497$	−10.3666	−0.465007
$498$	−3.62781	−0.162566
$499$	−32.4898	−1.45444	−0.727222	−	0.686402i	$-0.759189\pi$
$499$	−32.4898	−1.45444	−0.727222	+	0.686402i	$0.759189\pi$
$500$	2.31916	0.103716
$501$	3.25156	0.145269
$502$	11.9964	0.535423
$503$	37.1365	1.65584	0.827918	−	0.560849i	$-0.189525\pi$
$503$	37.1365	1.65584	0.827918	+	0.560849i	$0.189525\pi$
$504$	2.23743	0.0996631
$505$	0.246677	0.0109770
$506$	−11.8819	−0.528213
$507$	−3.12919	−0.138972
$508$	7.79018	0.345633
$509$	−5.72826	−0.253900	−0.126950	−	0.991909i	$-0.540519\pi$
$509$	−5.72826	−0.253900	−0.126950	+	0.991909i	$0.540519\pi$
$510$	−0.107783	−0.00477270
$511$	0.638662	0.0282528
$512$	1.00000	0.0441942
$513$	−1.51392	−0.0668411
$514$	27.7523	1.22410
$515$	1.31464	0.0579300
$516$	2.27535	0.100167
$517$	10.5616	0.464498
$518$	−4.63400	−0.203606
$519$	1.86897	0.0820386
$520$	0.306580	0.0134444
$521$	−25.3238	−1.10946	−0.554729	−	0.832031i	$-0.687178\pi$
$521$	−25.3238	−1.10946	−0.554729	+	0.832031i	$0.687178\pi$
$522$	−3.75689	−0.164434
$523$	−22.3774	−0.978496	−0.489248	−	0.872145i	$-0.662729\pi$
$523$	−22.3774	−0.978496	−0.489248	+	0.872145i	$0.662729\pi$
$524$	−20.1681	−0.881048
$525$	1.05101	0.0458698
$526$	2.52524	0.110106
$527$	1.66493	0.0725257
$528$	1.17993	0.0513499
$529$	−15.1844	−0.660191
$530$	−1.79769	−0.0780867
$531$	−27.3870	−1.18850
$532$	−0.704764	−0.0305554
$533$	−7.08810	−0.307020
$534$	3.60722	0.156100
$535$	1.82306	0.0788178
$536$	1.57485	0.0680232
$537$	−1.13691	−0.0490614
$538$	−5.19962	−0.224172
$539$	−27.2606	−1.17420
$540$	0.383432	0.0165003
$541$	13.6257	0.585813	0.292906	−	0.956141i	$-0.405378\pi$
$541$	13.6257	0.585813	0.292906	+	0.956141i	$0.405378\pi$
$542$	19.0950	0.820200
$543$	2.54085	0.109038
$544$	1.66493	0.0713835
$545$	1.45148	0.0621745
$546$	0.279404	0.0119574
$547$	21.0951	0.901960	0.450980	−	0.892534i	$-0.351075\pi$
$547$	21.0951	0.901960	0.450980	+	0.892534i	$0.351075\pi$
$548$	9.05297	0.386724
$549$	−26.8727	−1.14690
$550$	−21.0196	−0.896278
$551$	1.18337	0.0504134
$552$	−0.776132	−0.0330344
$553$	7.17096	0.304940
$554$	−6.92767	−0.294328
$555$	−0.391901	−0.0166353
$556$	17.7524	0.752870
$557$	−35.7256	−1.51374	−0.756870	−	0.653565i	$-0.773272\pi$
$557$	−35.7256	−1.51374	−0.756870	+	0.653565i	$0.773272\pi$
$558$	−2.92293	−0.123737
$559$	−10.7756	−0.455758
$560$	0.178497	0.00754285
$561$	1.96451	0.0829416
$562$	−4.41943	−0.186422
$563$	30.2231	1.27375	0.636875	−	0.770967i	$-0.280227\pi$
$563$	30.2231	1.27375	0.636875	+	0.770967i	$0.280227\pi$
$564$	0.689891	0.0290497
$565$	−3.12166	−0.131329
$566$	−7.33708	−0.308400
$567$	−6.36285	−0.267215
$568$	13.5427	0.568240
$569$	−18.4462	−0.773305	−0.386652	−	0.922226i	$-0.626369\pi$
$569$	−18.4462	−0.773305	−0.386652	+	0.922226i	$0.626369\pi$
$570$	−0.0596024	−0.00249647
$571$	9.36910	0.392085	0.196042	−	0.980595i	$-0.437191\pi$
$571$	9.36910	0.392085	0.196042	+	0.980595i	$0.437191\pi$
$572$	−5.58791	−0.233642
$573$	5.03751	0.210445
$574$	−4.12682	−0.172250
$575$	13.8262	0.576592
$576$	−2.92293	−0.121789
$577$	−23.2758	−0.968985	−0.484493	−	0.874795i	$-0.660996\pi$
$577$	−23.2758	−0.968985	−0.484493	+	0.874795i	$0.660996\pi$
$578$	−14.2280	−0.591807
$579$	−0.196234	−0.00815522
$580$	−0.299715	−0.0124450
$581$	10.0028	0.414987
$582$	0.277622	0.0115078
$583$	32.7658	1.35702
$584$	−0.834333	−0.0345250
$585$	−0.896111	−0.0370496
$586$	−17.7885	−0.734835
$587$	−13.6490	−0.563354	−0.281677	−	0.959509i	$-0.590891\pi$
$587$	−13.6490	−0.563354	−0.281677	+	0.959509i	$0.590891\pi$
$588$	−1.78068	−0.0734340
$589$	0.920687	0.0379362
$590$	−2.18487	−0.0899496
$591$	−3.87171	−0.159261
$592$	6.05375	0.248808
$593$	−16.4656	−0.676160	−0.338080	−	0.941117i	$-0.609777\pi$
$593$	−16.4656	−0.676160	−0.338080	+	0.941117i	$0.609777\pi$
$594$	−6.98865	−0.286748
$595$	0.297185	0.0121834
$596$	12.2160	0.500385
$597$	−0.652298	−0.0266968
$598$	3.67559	0.150306
$599$	34.4013	1.40560	0.702800	−	0.711387i	$-0.251933\pi$
$599$	34.4013	1.40560	0.702800	+	0.711387i	$0.251933\pi$
$600$	−1.37301	−0.0560531
$601$	−32.8483	−1.33991	−0.669954	−	0.742403i	$-0.733686\pi$
$601$	−32.8483	−1.33991	−0.669954	+	0.742403i	$0.733686\pi$
$602$	−6.27373	−0.255698
$603$	−4.60317	−0.187456
$604$	−7.28156	−0.296282
$605$	−1.64713	−0.0669654
$606$	−0.293687	−0.0119302
$607$	−8.82490	−0.358191	−0.179096	−	0.983832i	$-0.557317\pi$
$607$	−8.82490	−0.358191	−0.179096	+	0.983832i	$0.557317\pi$
$608$	0.920687	0.0373388
$609$	−0.273147	−0.0110685
$610$	−2.14384	−0.0868014
$611$	−3.26718	−0.132176
$612$	−4.86648	−0.196716
$613$	−45.5951	−1.84157	−0.920785	−	0.390070i	$-0.872451\pi$
$613$	−45.5951	−1.84157	−0.920785	+	0.390070i	$0.872451\pi$
$614$	−25.3033	−1.02116
$615$	−0.349008	−0.0140734
$616$	−3.25338	−0.131082
$617$	1.19206	0.0479906	0.0239953	−	0.999712i	$-0.492361\pi$
$617$	1.19206	0.0479906	0.0239953	+	0.999712i	$0.492361\pi$
$618$	−1.56518	−0.0629606
$619$	46.2377	1.85845	0.929225	−	0.369514i	$-0.120476\pi$
$619$	46.2377	1.85845	0.929225	+	0.369514i	$0.120476\pi$
$620$	−0.233184	−0.00936488
$621$	4.59697	0.184470
$622$	−0.462242	−0.0185342
$623$	−9.94606	−0.398480
$624$	−0.365006	−0.0146119
$625$	24.1873	0.967494
$626$	30.7629	1.22953
$627$	1.08635	0.0433845
$628$	−18.8096	−0.750585
$629$	10.0791	0.401880
$630$	−0.521732	−0.0207863
$631$	−27.2400	−1.08441	−0.542204	−	0.840247i	$-0.682410\pi$
$631$	−27.2400	−1.08441	−0.542204	+	0.840247i	$0.682410\pi$
$632$	−9.36797	−0.372638
$633$	2.80660	0.111552
$634$	3.25574	0.129302
$635$	−1.81654	−0.0720873
$636$	2.14028	0.0848677
$637$	8.43293	0.334125
$638$	5.46277	0.216273
$639$	−39.5844	−1.56593
$640$	−0.233184	−0.00921739
$641$	−6.64589	−0.262497	−0.131249	−	0.991349i	$-0.541899\pi$
$641$	−6.64589	−0.262497	−0.131249	+	0.991349i	$0.541899\pi$
$642$	−2.17049	−0.0856623
$643$	−14.5429	−0.573517	−0.286759	−	0.958003i	$-0.592578\pi$
$643$	−14.5429	−0.573517	−0.286759	+	0.958003i	$0.592578\pi$
$644$	2.14000	0.0843277
$645$	−0.530574	−0.0208913
$646$	1.53288	0.0603105
$647$	−37.7650	−1.48469	−0.742347	−	0.670016i	$-0.766287\pi$
$647$	−37.7650	−1.48469	−0.742347	+	0.670016i	$0.766287\pi$
$648$	8.31227	0.326537
$649$	39.8226	1.56318
$650$	6.50231	0.255041
$651$	−0.212513	−0.00832905
$652$	−2.51234	−0.0983908
$653$	−38.8726	−1.52120	−0.760602	−	0.649218i	$-0.775096\pi$
$653$	−38.8726	−1.52120	−0.760602	+	0.649218i	$0.775096\pi$
$654$	−1.72809	−0.0675737
$655$	4.70287	0.183757
$656$	5.39118	0.210490
$657$	2.43869	0.0951425
$658$	−1.90221	−0.0741558
$659$	34.5115	1.34438	0.672189	−	0.740380i	$-0.265354\pi$
$659$	34.5115	1.34438	0.672189	+	0.740380i	$0.265354\pi$
$660$	−0.275141	−0.0107098
$661$	−48.9678	−1.90463	−0.952313	−	0.305123i	$-0.901302\pi$
$661$	−48.9678	−1.90463	−0.952313	+	0.305123i	$0.901302\pi$
$662$	−2.86844	−0.111485
$663$	−0.607711	−0.0236015
$664$	−13.0674	−0.507115
$665$	0.164339	0.00637281
$666$	−17.6947	−0.685654
$667$	−3.59329	−0.139133
$668$	11.7122	0.453157
$669$	3.23835	0.125202
$670$	−0.367229	−0.0141873
$671$	39.0748	1.50847
$672$	−0.212513	−0.00819787
$673$	−5.23978	−0.201978	−0.100989	−	0.994888i	$-0.532201\pi$
$673$	−5.23978	−0.201978	−0.100989	+	0.994888i	$0.532201\pi$
$674$	6.49596	0.250215
$675$	8.13226	0.313011
$676$	−11.2714	−0.433516
$677$	−4.63868	−0.178279	−0.0891394	−	0.996019i	$-0.528412\pi$
$677$	−4.63868	−0.178279	−0.0891394	+	0.996019i	$0.528412\pi$
$678$	3.71656	0.142734
$679$	−0.765476	−0.0293763
$680$	−0.388235	−0.0148881
$681$	4.44700	0.170409
$682$	4.25014	0.162746
$683$	−33.2526	−1.27238	−0.636188	−	0.771534i	$-0.719490\pi$
$683$	−33.2526	−1.27238	−0.636188	+	0.771534i	$0.719490\pi$
$684$	−2.69110	−0.102897
$685$	−2.11100	−0.0806573
$686$	10.2681	0.392039
$687$	7.95276	0.303417
$688$	8.19585	0.312464
$689$	−10.1359	−0.386148
$690$	0.180981	0.00688984
$691$	41.8087	1.59048	0.795238	−	0.606297i	$-0.207346\pi$
$691$	41.8087	1.59048	0.795238	+	0.606297i	$0.207346\pi$
$692$	6.73206	0.255915
$693$	9.50939	0.361232
$694$	−5.84129	−0.221732
$695$	−4.13957	−0.157023
$696$	0.356832	0.0135257
$697$	8.97595	0.339989
$698$	−36.4292	−1.37887
$699$	−4.31496	−0.163207
$700$	3.78576	0.143088
$701$	3.71413	0.140281	0.0701403	−	0.997537i	$-0.477655\pi$
$701$	3.71413	0.140281	0.0701403	+	0.997537i	$0.477655\pi$
$702$	2.16190	0.0815958
$703$	5.57361	0.210213
$704$	4.25014	0.160183
$705$	−0.160871	−0.00605876
$706$	21.5967	0.812804
$707$	0.809772	0.0304546
$708$	2.60124	0.0977607
$709$	39.0429	1.46629	0.733143	−	0.680074i	$-0.238052\pi$
$709$	39.0429	1.46629	0.733143	+	0.680074i	$0.238052\pi$
$710$	−3.15794	−0.118515
$711$	27.3819	1.02690
$712$	12.9933	0.486944
$713$	−2.79564	−0.104698
$714$	−0.353820	−0.0132414
$715$	1.30301	0.0487297
$716$	−4.09518	−0.153044
$717$	−3.37127	−0.125902
$718$	16.1232	0.601712
$719$	29.9022	1.11516	0.557582	−	0.830122i	$-0.311729\pi$
$719$	29.9022	1.11516	0.557582	+	0.830122i	$0.311729\pi$
$720$	0.681578	0.0254009
$721$	4.31560	0.160721
$722$	−18.1523	−0.675560
$723$	5.35260	0.199065
$724$	9.15220	0.340139
$725$	−6.35670	−0.236082
$726$	1.96103	0.0727807
$727$	−26.7335	−0.991489	−0.495745	−	0.868468i	$-0.665105\pi$
$727$	−26.7335	−0.991489	−0.495745	+	0.868468i	$0.665105\pi$
$728$	1.00642	0.0373003
$729$	−22.9267	−0.849135
$730$	0.194553	0.00720072
$731$	13.6456	0.504699
$732$	2.55239	0.0943392
$733$	6.75526	0.249511	0.124756	−	0.992188i	$-0.460185\pi$
$733$	6.75526	0.249511	0.124756	+	0.992188i	$0.460185\pi$
$734$	−13.1823	−0.486567
$735$	0.415226	0.0153158
$736$	−2.79564	−0.103049
$737$	6.69333	0.246552
$738$	−15.7580	−0.580060
$739$	40.0811	1.47441	0.737204	−	0.675670i	$-0.236146\pi$
$739$	40.0811	1.47441	0.737204	+	0.675670i	$0.236146\pi$
$740$	−1.41164	−0.0518928
$741$	−0.336056	−0.0123453
$742$	−5.90132	−0.216644
$743$	−2.96039	−0.108606	−0.0543030	−	0.998525i	$-0.517294\pi$
$743$	−2.96039	−0.108606	−0.0543030	+	0.998525i	$0.517294\pi$
$744$	0.277622	0.0101781
$745$	−2.84856	−0.104363
$746$	28.7421	1.05232
$747$	38.1952	1.39749
$748$	7.07620	0.258731
$749$	5.98460	0.218672
$750$	0.643849	0.0235100
$751$	51.3976	1.87552	0.937762	−	0.347279i	$-0.112894\pi$
$751$	51.3976	1.87552	0.937762	+	0.347279i	$0.112894\pi$
$752$	2.48500	0.0906187
$753$	3.33045	0.121368
$754$	−1.68988	−0.0615419
$755$	1.69794	0.0617943
$756$	1.25870	0.0457785
$757$	31.7334	1.15337	0.576685	−	0.816966i	$-0.304346\pi$
$757$	31.7334	1.15337	0.576685	+	0.816966i	$0.304346\pi$
$758$	−38.4714	−1.39734
$759$	−3.29867	−0.119734
$760$	−0.214689	−0.00778759
$761$	−32.7469	−1.18707	−0.593537	−	0.804807i	$-0.702269\pi$
$761$	−32.7469	−1.18707	−0.593537	+	0.804807i	$0.702269\pi$
$762$	2.16273	0.0783473
$763$	4.76480	0.172497
$764$	18.1452	0.656471
$765$	1.13478	0.0410282
$766$	−23.9813	−0.866481
$767$	−12.3189	−0.444811
$768$	0.277622	0.0100178
$769$	−8.76290	−0.315998	−0.157999	−	0.987439i	$-0.550504\pi$
$769$	−8.76290	−0.315998	−0.157999	+	0.987439i	$0.550504\pi$
$770$	0.758635	0.0273393
$771$	7.70466	0.277477
$772$	−0.706840	−0.0254397
$773$	−54.3748	−1.95573	−0.977863	−	0.209247i	$-0.932899\pi$
$773$	−54.3748	−1.95573	−0.977863	+	0.209247i	$0.932899\pi$
$774$	−23.9559	−0.861076
$775$	−4.94563	−0.177652
$776$	1.00000	0.0358979
$777$	−1.28650	−0.0461530
$778$	21.2442	0.761641
$779$	4.96359	0.177839
$780$	0.0851134	0.00304755
$781$	57.5585	2.05960
$782$	−4.65456	−0.166447
$783$	−2.11349	−0.0755300
$784$	−6.41405	−0.229073
$785$	4.38609	0.156546
$786$	−5.59911	−0.199714
$787$	−8.82724	−0.314657	−0.157328	−	0.987546i	$-0.550288\pi$
$787$	−8.82724	−0.314657	−0.157328	+	0.987546i	$0.550288\pi$
$788$	−13.9460	−0.496804
$789$	0.701062	0.0249585
$790$	2.18446	0.0777195
$791$	−10.2475	−0.364360
$792$	−12.4228	−0.441426
$793$	−12.0876	−0.429243
$794$	−8.85722	−0.314331
$795$	−0.499079	−0.0177005
$796$	−2.34959	−0.0832790
$797$	37.8008	1.33897	0.669487	−	0.742824i	$-0.266514\pi$
$797$	37.8008	1.33897	0.669487	+	0.742824i	$0.266514\pi$
$798$	−0.195658	−0.00692622
$799$	4.13736	0.146369
$800$	−4.94563	−0.174854
$801$	−37.9784	−1.34190
$802$	5.98005	0.211163
$803$	−3.54603	−0.125137
$804$	0.437213	0.0154193
$805$	−0.499012	−0.0175879
$806$	−1.31476	−0.0463104
$807$	−1.44353	−0.0508147
$808$	−1.05787	−0.0372156
$809$	−53.4002	−1.87745	−0.938725	−	0.344668i	$-0.887992\pi$
$809$	−53.4002	−1.87745	−0.938725	+	0.344668i	$0.887992\pi$
$810$	−1.93829	−0.0681044
$811$	−23.6811	−0.831555	−0.415778	−	0.909466i	$-0.636491\pi$
$811$	−23.6811	−0.831555	−0.415778	+	0.909466i	$0.636491\pi$
$812$	−0.983880	−0.0345274
$813$	5.30119	0.185921
$814$	25.7293	0.901811
$815$	0.585836	0.0205209
$816$	0.462222	0.0161810
$817$	7.54581	0.263995
$818$	−13.1972	−0.461429
$819$	−2.94168	−0.102791
$820$	−1.25713	−0.0439010
$821$	−28.0466	−0.978834	−0.489417	−	0.872050i	$-0.662790\pi$
$821$	−28.0466	−0.978834	−0.489417	+	0.872050i	$0.662790\pi$
$822$	2.51330	0.0876615
$823$	−30.2495	−1.05443	−0.527216	−	0.849731i	$-0.676764\pi$
$823$	−30.2495	−1.05443	−0.527216	+	0.849731i	$0.676764\pi$
$824$	−5.63779	−0.196402
$825$	−5.83550	−0.203166
$826$	−7.17231	−0.249556
$827$	−13.0685	−0.454437	−0.227219	−	0.973844i	$-0.572963\pi$
$827$	−13.0685	−0.454437	−0.227219	+	0.973844i	$0.572963\pi$
$828$	8.17145	0.283978
$829$	−24.6541	−0.856273	−0.428137	−	0.903714i	$-0.640830\pi$
$829$	−24.6541	−0.856273	−0.428137	+	0.903714i	$0.640830\pi$
$830$	3.04711	0.105767
$831$	−1.92327	−0.0667176
$832$	−1.31476	−0.0455811
$833$	−10.6790	−0.370004
$834$	4.92846	0.170659
$835$	−2.73109	−0.0945131
$836$	3.91305	0.135336
$837$	−1.64433	−0.0568365
$838$	−21.9081	−0.756803
$839$	31.9305	1.10236	0.551182	−	0.834385i	$-0.314177\pi$
$839$	31.9305	1.10236	0.551182	+	0.834385i	$0.314177\pi$
$840$	0.0495546	0.00170980
$841$	−27.3480	−0.943033
$842$	9.39667	0.323831
$843$	−1.22693	−0.0422577
$844$	10.1094	0.347980
$845$	2.62831	0.0904165
$846$	−7.26347	−0.249723
$847$	−5.40707	−0.185789
$848$	7.70934	0.264740
$849$	−2.03693	−0.0699074
$850$	−8.23414	−0.282429
$851$	−16.9241	−0.580151
$852$	3.75976	0.128807
$853$	36.4084	1.24660	0.623300	−	0.781983i	$-0.285792\pi$
$853$	36.4084	1.24660	0.623300	+	0.781983i	$0.285792\pi$
$854$	−7.03762	−0.240822
$855$	0.627520	0.0214607
$856$	−7.81814	−0.267218
$857$	−11.9711	−0.408926	−0.204463	−	0.978874i	$-0.565545\pi$
$857$	−11.9711	−0.408926	−0.204463	+	0.978874i	$0.565545\pi$
$858$	−1.55133	−0.0529614
$859$	−16.9348	−0.577807	−0.288903	−	0.957358i	$-0.593291\pi$
$859$	−16.9348	−0.577807	−0.288903	+	0.957358i	$0.593291\pi$
$860$	−1.91114	−0.0651693
$861$	−1.14570	−0.0390452
$862$	8.35419	0.284545
$863$	56.7587	1.93209	0.966044	−	0.258378i	$-0.0831878\pi$
$863$	56.7587	1.93209	0.966044	+	0.258378i	$0.0831878\pi$
$864$	−1.64433	−0.0559414
$865$	−1.56981	−0.0533750
$866$	−8.28874	−0.281663
$867$	−3.95001	−0.134149
$868$	−0.765476	−0.0259820
$869$	−39.8152	−1.35064
$870$	−0.0832075	−0.00282100
$871$	−2.07055	−0.0701579
$872$	−6.22462	−0.210792
$873$	−2.92293	−0.0989261
$874$	−2.57391	−0.0870638
$875$	−1.77526	−0.0600147
$876$	−0.231629	−0.00782603
$877$	−2.21051	−0.0746437	−0.0373219	−	0.999303i	$-0.511883\pi$
$877$	−2.21051	−0.0746437	−0.0373219	+	0.999303i	$0.511883\pi$
$878$	−29.3664	−0.991070
$879$	−4.93847	−0.166571
$880$	−0.991062	−0.0334087
$881$	54.8820	1.84902	0.924511	−	0.381155i	$-0.124474\pi$
$881$	54.8820	1.84902	0.924511	+	0.381155i	$0.124474\pi$
$882$	18.7478	0.631271
$883$	−39.8071	−1.33961	−0.669807	−	0.742535i	$-0.733623\pi$
$883$	−39.8071	−1.33961	−0.669807	+	0.742535i	$0.733623\pi$
$884$	−2.18899	−0.0736236
$885$	−0.606567	−0.0203895
$886$	−39.8120	−1.33751
$887$	53.3560	1.79152	0.895760	−	0.444538i	$-0.146632\pi$
$887$	53.3560	1.79152	0.895760	+	0.444538i	$0.146632\pi$
$888$	1.68065	0.0563991
$889$	−5.96320	−0.199999
$890$	−3.02982	−0.101560
$891$	35.3283	1.18354
$892$	11.6646	0.390560
$893$	2.28791	0.0765619
$894$	3.39142	0.113426
$895$	0.954930	0.0319198
$896$	−0.765476	−0.0255728
$897$	1.02043	0.0340710
$898$	23.4908	0.783899
$899$	1.28532	0.0428677
$900$	14.4557	0.481857
$901$	12.8355	0.427614
$902$	22.9132	0.762928
$903$	−1.74173	−0.0579610
$904$	13.3871	0.445249
$905$	−2.13414	−0.0709413
$906$	−2.02152	−0.0671605
$907$	37.8485	1.25674	0.628369	−	0.777916i	$-0.283723\pi$
$907$	37.8485	1.25674	0.628369	+	0.777916i	$0.283723\pi$
$908$	16.0182	0.531582
$909$	3.09207	0.102557
$910$	−0.234680	−0.00777956
$911$	−3.87191	−0.128282	−0.0641410	−	0.997941i	$-0.520431\pi$
$911$	−3.87191	−0.128282	−0.0641410	+	0.997941i	$0.520431\pi$
$912$	0.255603	0.00846386
$913$	−55.5384	−1.83805
$914$	−5.06070	−0.167393
$915$	−0.595177	−0.0196759
$916$	28.6460	0.946490
$917$	15.4382	0.509815
$918$	−2.73771	−0.0903579
$919$	−1.26627	−0.0417704	−0.0208852	−	0.999782i	$-0.506648\pi$
$919$	−1.26627	−0.0417704	−0.0208852	+	0.999782i	$0.506648\pi$
$920$	0.651898	0.0214924
$921$	−7.02474	−0.231473
$922$	11.5655	0.380889
$923$	−17.8054	−0.586073
$924$	−0.903210	−0.0297134
$925$	−29.9396	−0.984407
$926$	21.8949	0.719512
$927$	16.4789	0.541237
$928$	1.28532	0.0421926
$929$	26.4819	0.868844	0.434422	−	0.900709i	$-0.356953\pi$
$929$	26.4819	0.868844	0.434422	+	0.900709i	$0.356953\pi$
$930$	−0.0647369	−0.00212281
$931$	−5.90533	−0.193539
$932$	−15.5426	−0.509114
$933$	−0.128329	−0.00420129
$934$	10.9783	0.359221
$935$	−1.65005	−0.0539625
$936$	3.84294	0.125611
$937$	−3.70125	−0.120915	−0.0604573	−	0.998171i	$-0.519256\pi$
$937$	−3.70125	−0.120915	−0.0604573	+	0.998171i	$0.519256\pi$
$938$	−1.20551	−0.0393613
$939$	8.54047	0.278708
$940$	−0.579461	−0.0188999
$941$	28.6115	0.932707	0.466354	−	0.884598i	$-0.345567\pi$
$941$	28.6115	0.932707	0.466354	+	0.884598i	$0.345567\pi$
$942$	−5.22196	−0.170141
$943$	−15.0718	−0.490805
$944$	9.36973	0.304959
$945$	−0.293508	−0.00954782
$946$	34.8335	1.13254
$947$	−59.7725	−1.94235	−0.971173	−	0.238378i	$-0.923384\pi$
$947$	−59.7725	−1.94235	−0.971173	+	0.238378i	$0.923384\pi$
$948$	−2.60075	−0.0844686
$949$	1.09695	0.0356084
$950$	−4.55337	−0.147731
$951$	0.903865	0.0293098
$952$	−1.27447	−0.0413057
$953$	−29.1310	−0.943645	−0.471822	−	0.881694i	$-0.656404\pi$
$953$	−29.1310	−0.943645	−0.471822	+	0.881694i	$0.656404\pi$
$954$	−22.5338	−0.729560
$955$	−4.23117	−0.136917
$956$	−12.1434	−0.392745
$957$	1.51659	0.0490243
$958$	−32.3907	−1.04649
$959$	−6.92983	−0.223776
$960$	−0.0647369	−0.00208937
$961$	1.00000	0.0322581
$962$	−7.95922	−0.256616
$963$	22.8518	0.736390
$964$	19.2802	0.620972
$965$	0.164823	0.00530586
$966$	0.594110	0.0191152
$967$	−16.9611	−0.545431	−0.272715	−	0.962095i	$-0.587922\pi$
$967$	−16.9611	−0.545431	−0.272715	+	0.962095i	$0.587922\pi$
$968$	7.06367	0.227035
$969$	0.425562	0.0136710
$970$	−0.233184	−0.00748707
$971$	25.7156	0.825254	0.412627	−	0.910900i	$-0.364611\pi$
$971$	25.7156	0.825254	0.412627	+	0.910900i	$0.364611\pi$
$972$	7.24068	0.232245
$973$	−13.5890	−0.435645
$974$	20.3623	0.652449
$975$	1.80518	0.0578121
$976$	9.19377	0.294286
$977$	−46.0679	−1.47384	−0.736922	−	0.675978i	$-0.763721\pi$
$977$	−46.0679	−1.47384	−0.736922	+	0.675978i	$0.763721\pi$
$978$	−0.697481	−0.0223030
$979$	55.2233	1.76494
$980$	1.49565	0.0477768
$981$	18.1941	0.580893
$982$	22.3632	0.713638
$983$	−18.3171	−0.584224	−0.292112	−	0.956384i	$-0.594358\pi$
$983$	−18.3171	−0.584224	−0.292112	+	0.956384i	$0.594358\pi$
$984$	1.49671	0.0477134
$985$	3.25197	0.103616
$986$	2.13997	0.0681505
$987$	−0.528095	−0.0168095
$988$	−1.21048	−0.0385105
$989$	−22.9127	−0.728581
$990$	2.89680	0.0920664
$991$	17.6832	0.561724	0.280862	−	0.959748i	$-0.409380\pi$
$991$	17.6832	0.561724	0.280862	+	0.959748i	$0.409380\pi$
$992$	1.00000	0.0317500
$993$	−0.796342	−0.0252712
$994$	−10.3666	−0.328810
$995$	0.547886	0.0173692
$996$	−3.62781	−0.114952
$997$	35.5325	1.12532	0.562662	−	0.826687i	$-0.309777\pi$
$997$	35.5325	1.12532	0.562662	+	0.826687i	$0.309777\pi$
$998$	−32.4898	−1.02845
$999$	−9.95439	−0.314943

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.19	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.19	✓	37	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.277622 q^{3} +1.00000 q^{4} -0.233184 q^{5} +0.277622 q^{6} -0.765476 q^{7} +1.00000 q^{8} -2.92293 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.277622 q^{3} +1.00000 q^{4} -0.233184 q^{5} +0.277622 q^{6} -0.765476 q^{7} +1.00000 q^{8} -2.92293 q^{9} -0.233184 q^{10} +4.25014 q^{11} +0.277622 q^{12} -1.31476 q^{13} -0.765476 q^{14} -0.0647369 q^{15} +1.00000 q^{16} +1.66493 q^{17} -2.92293 q^{18} +0.920687 q^{19} -0.233184 q^{20} -0.212513 q^{21} +4.25014 q^{22} -2.79564 q^{23} +0.277622 q^{24} -4.94563 q^{25} -1.31476 q^{26} -1.64433 q^{27} -0.765476 q^{28} +1.28532 q^{29} -0.0647369 q^{30} +1.00000 q^{31} +1.00000 q^{32} +1.17993 q^{33} +1.66493 q^{34} +0.178497 q^{35} -2.92293 q^{36} +6.05375 q^{37} +0.920687 q^{38} -0.365006 q^{39} -0.233184 q^{40} +5.39118 q^{41} -0.212513 q^{42} +8.19585 q^{43} +4.25014 q^{44} +0.681578 q^{45} -2.79564 q^{46} +2.48500 q^{47} +0.277622 q^{48} -6.41405 q^{49} -4.94563 q^{50} +0.462222 q^{51} -1.31476 q^{52} +7.70934 q^{53} -1.64433 q^{54} -0.991062 q^{55} -0.765476 q^{56} +0.255603 q^{57} +1.28532 q^{58} +9.36973 q^{59} -0.0647369 q^{60} +9.19377 q^{61} +1.00000 q^{62} +2.23743 q^{63} +1.00000 q^{64} +0.306580 q^{65} +1.17993 q^{66} +1.57485 q^{67} +1.66493 q^{68} -0.776132 q^{69} +0.178497 q^{70} +13.5427 q^{71} -2.92293 q^{72} -0.834333 q^{73} +6.05375 q^{74} -1.37301 q^{75} +0.920687 q^{76} -3.25338 q^{77} -0.365006 q^{78} -9.36797 q^{79} -0.233184 q^{80} +8.31227 q^{81} +5.39118 q^{82} -13.0674 q^{83} -0.212513 q^{84} -0.388235 q^{85} +8.19585 q^{86} +0.356832 q^{87} +4.25014 q^{88} +12.9933 q^{89} +0.681578 q^{90} +1.00642 q^{91} -2.79564 q^{92} +0.277622 q^{93} +2.48500 q^{94} -0.214689 q^{95} +0.277622 q^{96} +1.00000 q^{97} -6.41405 q^{98} -12.4228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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