LMFDB - Embedded newform 6002.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.64063 q^{3} +1.00000 q^{4} -2.79431 q^{5} +1.64063 q^{6} +2.69140 q^{7} -1.00000 q^{8} -0.308341 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.64063 q^{3} +1.00000 q^{4} -2.79431 q^{5} +1.64063 q^{6} +2.69140 q^{7} -1.00000 q^{8} -0.308341 q^{9} +2.79431 q^{10} +2.16871 q^{11} -1.64063 q^{12} -0.202704 q^{13} -2.69140 q^{14} +4.58443 q^{15} +1.00000 q^{16} +2.39744 q^{17} +0.308341 q^{18} -1.78233 q^{19} -2.79431 q^{20} -4.41558 q^{21} -2.16871 q^{22} +2.26624 q^{23} +1.64063 q^{24} +2.80818 q^{25} +0.202704 q^{26} +5.42776 q^{27} +2.69140 q^{28} -5.49504 q^{29} -4.58443 q^{30} -3.51619 q^{31} -1.00000 q^{32} -3.55805 q^{33} -2.39744 q^{34} -7.52061 q^{35} -0.308341 q^{36} -4.06345 q^{37} +1.78233 q^{38} +0.332561 q^{39} +2.79431 q^{40} -4.20212 q^{41} +4.41558 q^{42} -3.16312 q^{43} +2.16871 q^{44} +0.861601 q^{45} -2.26624 q^{46} -0.914343 q^{47} -1.64063 q^{48} +0.243620 q^{49} -2.80818 q^{50} -3.93330 q^{51} -0.202704 q^{52} +8.04923 q^{53} -5.42776 q^{54} -6.06006 q^{55} -2.69140 q^{56} +2.92414 q^{57} +5.49504 q^{58} +4.15593 q^{59} +4.58443 q^{60} -6.51314 q^{61} +3.51619 q^{62} -0.829868 q^{63} +1.00000 q^{64} +0.566417 q^{65} +3.55805 q^{66} +14.2084 q^{67} +2.39744 q^{68} -3.71805 q^{69} +7.52061 q^{70} +10.2099 q^{71} +0.308341 q^{72} +3.58618 q^{73} +4.06345 q^{74} -4.60718 q^{75} -1.78233 q^{76} +5.83687 q^{77} -0.332561 q^{78} -11.6911 q^{79} -2.79431 q^{80} -7.97990 q^{81} +4.20212 q^{82} +9.11282 q^{83} -4.41558 q^{84} -6.69919 q^{85} +3.16312 q^{86} +9.01531 q^{87} -2.16871 q^{88} +15.6798 q^{89} -0.861601 q^{90} -0.545556 q^{91} +2.26624 q^{92} +5.76876 q^{93} +0.914343 q^{94} +4.98039 q^{95} +1.64063 q^{96} -6.21075 q^{97} -0.243620 q^{98} -0.668702 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * 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
$3$	−1.64063	−0.947217	−0.473608	−	0.880736i	$-0.657049\pi$
$3$	−1.64063	−0.947217	−0.473608	+	0.880736i	$0.657049\pi$
$4$	1.00000	0.500000
$5$	−2.79431	−1.24965	−0.624827	−	0.780763i	$-0.714831\pi$
$5$	−2.79431	−1.24965	−0.624827	+	0.780763i	$0.714831\pi$
$6$	1.64063	0.669783
$7$	2.69140	1.01725	0.508626	−	0.860987i	$-0.330153\pi$
$7$	2.69140	1.01725	0.508626	+	0.860987i	$0.330153\pi$
$8$	−1.00000	−0.353553
$9$	−0.308341	−0.102780
$10$	2.79431	0.883639
$11$	2.16871	0.653891	0.326946	−	0.945043i	$-0.393981\pi$
$11$	2.16871	0.653891	0.326946	+	0.945043i	$0.393981\pi$
$12$	−1.64063	−0.473608
$13$	−0.202704	−0.0562199	−0.0281099	−	0.999605i	$-0.508949\pi$
$13$	−0.202704	−0.0562199	−0.0281099	+	0.999605i	$0.508949\pi$
$14$	−2.69140	−0.719306
$15$	4.58443	1.18369
$16$	1.00000	0.250000
$17$	2.39744	0.581464	0.290732	−	0.956805i	$-0.406101\pi$
$17$	2.39744	0.581464	0.290732	+	0.956805i	$0.406101\pi$
$18$	0.308341	0.0726766
$19$	−1.78233	−0.408894	−0.204447	−	0.978878i	$-0.565540\pi$
$19$	−1.78233	−0.408894	−0.204447	+	0.978878i	$0.565540\pi$
$20$	−2.79431	−0.624827
$21$	−4.41558	−0.963559
$22$	−2.16871	−0.462371
$23$	2.26624	0.472544	0.236272	−	0.971687i	$-0.424074\pi$
$23$	2.26624	0.472544	0.236272	+	0.971687i	$0.424074\pi$
$24$	1.64063	0.334892
$25$	2.80818	0.561637
$26$	0.202704	0.0397534
$27$	5.42776	1.04457
$28$	2.69140	0.508626
$29$	−5.49504	−1.02040	−0.510201	−	0.860055i	$-0.670429\pi$
$29$	−5.49504	−1.02040	−0.510201	+	0.860055i	$0.670429\pi$
$30$	−4.58443	−0.836998
$31$	−3.51619	−0.631526	−0.315763	−	0.948838i	$-0.602260\pi$
$31$	−3.51619	−0.631526	−0.315763	+	0.948838i	$0.602260\pi$
$32$	−1.00000	−0.176777
$33$	−3.55805	−0.619377
$34$	−2.39744	−0.411157
$35$	−7.52061	−1.27121
$36$	−0.308341	−0.0513901
$37$	−4.06345	−0.668027	−0.334013	−	0.942568i	$-0.608403\pi$
$37$	−4.06345	−0.668027	−0.334013	+	0.942568i	$0.608403\pi$
$38$	1.78233	0.289132
$39$	0.332561	0.0532524
$40$	2.79431	0.441820
$41$	−4.20212	−0.656260	−0.328130	−	0.944633i	$-0.606418\pi$
$41$	−4.20212	−0.656260	−0.328130	+	0.944633i	$0.606418\pi$
$42$	4.41558	0.681339
$43$	−3.16312	−0.482372	−0.241186	−	0.970479i	$-0.577536\pi$
$43$	−3.16312	−0.482372	−0.241186	+	0.970479i	$0.577536\pi$
$44$	2.16871	0.326946
$45$	0.861601	0.128440
$46$	−2.26624	−0.334139
$47$	−0.914343	−0.133371	−0.0666853	−	0.997774i	$-0.521242\pi$
$47$	−0.914343	−0.133371	−0.0666853	+	0.997774i	$0.521242\pi$
$48$	−1.64063	−0.236804
$49$	0.243620	0.0348029
$50$	−2.80818	−0.397137
$51$	−3.93330	−0.550772
$52$	−0.202704	−0.0281099
$53$	8.04923	1.10565	0.552823	−	0.833298i	$-0.313550\pi$
$53$	8.04923	1.10565	0.552823	+	0.833298i	$0.313550\pi$
$54$	−5.42776	−0.738624
$55$	−6.06006	−0.817138
$56$	−2.69140	−0.359653
$57$	2.92414	0.387312
$58$	5.49504	0.721534
$59$	4.15593	0.541056	0.270528	−	0.962712i	$-0.412802\pi$
$59$	4.15593	0.541056	0.270528	+	0.962712i	$0.412802\pi$
$60$	4.58443	0.591847
$61$	−6.51314	−0.833922	−0.416961	−	0.908924i	$-0.636905\pi$
$61$	−6.51314	−0.833922	−0.416961	+	0.908924i	$0.636905\pi$
$62$	3.51619	0.446556
$63$	−0.829868	−0.104554
$64$	1.00000	0.125000
$65$	0.566417	0.0702554
$66$	3.55805	0.437965
$67$	14.2084	1.73583	0.867916	−	0.496710i	$-0.165459\pi$
$67$	14.2084	1.73583	0.867916	+	0.496710i	$0.165459\pi$
$68$	2.39744	0.290732
$69$	−3.71805	−0.447601
$70$	7.52061	0.898884
$71$	10.2099	1.21170	0.605848	−	0.795580i	$-0.292834\pi$
$71$	10.2099	1.21170	0.605848	+	0.795580i	$0.292834\pi$
$72$	0.308341	0.0363383
$73$	3.58618	0.419731	0.209866	−	0.977730i	$-0.432697\pi$
$73$	3.58618	0.419731	0.209866	+	0.977730i	$0.432697\pi$
$74$	4.06345	0.472366
$75$	−4.60718	−0.531992
$76$	−1.78233	−0.204447
$77$	5.83687	0.665173
$78$	−0.332561	−0.0376551
$79$	−11.6911	−1.31535	−0.657675	−	0.753302i	$-0.728460\pi$
$79$	−11.6911	−1.31535	−0.657675	+	0.753302i	$0.728460\pi$
$80$	−2.79431	−0.312414
$81$	−7.97990	−0.886656
$82$	4.20212	0.464046
$83$	9.11282	1.00026	0.500131	−	0.865950i	$-0.333285\pi$
$83$	9.11282	1.00026	0.500131	+	0.865950i	$0.333285\pi$
$84$	−4.41558	−0.481779
$85$	−6.69919	−0.726629
$86$	3.16312	0.341088
$87$	9.01531	0.966542
$88$	−2.16871	−0.231185
$89$	15.6798	1.66205	0.831025	−	0.556235i	$-0.187754\pi$
$89$	15.6798	1.66205	0.831025	+	0.556235i	$0.187754\pi$
$90$	−0.861601	−0.0908207
$91$	−0.545556	−0.0571898
$92$	2.26624	0.236272
$93$	5.76876	0.598192
$94$	0.914343	0.0943073
$95$	4.98039	0.510977
$96$	1.64063	0.167446
$97$	−6.21075	−0.630606	−0.315303	−	0.948991i	$-0.602106\pi$
$97$	−6.21075	−0.630606	−0.315303	+	0.948991i	$0.602106\pi$
$98$	−0.243620	−0.0246094
$99$	−0.668702	−0.0672071
$100$	2.80818	0.280818
$101$	2.64257	0.262945	0.131473	−	0.991320i	$-0.458029\pi$
$101$	2.64257	0.262945	0.131473	+	0.991320i	$0.458029\pi$
$102$	3.93330	0.389455
$103$	−5.95437	−0.586701	−0.293351	−	0.956005i	$-0.594770\pi$
$103$	−5.95437	−0.586701	−0.293351	+	0.956005i	$0.594770\pi$
$104$	0.202704	0.0198767
$105$	12.3385	1.20412
$106$	−8.04923	−0.781810
$107$	10.6756	1.03205	0.516023	−	0.856575i	$-0.327412\pi$
$107$	10.6756	1.03205	0.516023	+	0.856575i	$0.327412\pi$
$108$	5.42776	0.522286
$109$	−15.6211	−1.49623	−0.748117	−	0.663567i	$-0.769042\pi$
$109$	−15.6211	−1.49623	−0.748117	+	0.663567i	$0.769042\pi$
$110$	6.06006	0.577804
$111$	6.66660	0.632766
$112$	2.69140	0.254313
$113$	−12.0787	−1.13627	−0.568136	−	0.822935i	$-0.692335\pi$
$113$	−12.0787	−1.13627	−0.568136	+	0.822935i	$0.692335\pi$
$114$	−2.92414	−0.273871
$115$	−6.33258	−0.590516
$116$	−5.49504	−0.510201
$117$	0.0625018	0.00577829
$118$	−4.15593	−0.382585
$119$	6.45245	0.591495
$120$	−4.58443	−0.418499
$121$	−6.29669	−0.572426
$122$	6.51314	0.589672
$123$	6.89411	0.621621
$124$	−3.51619	−0.315763
$125$	6.12462	0.547803
$126$	0.829868	0.0739305
$127$	−9.84604	−0.873695	−0.436847	−	0.899536i	$-0.643905\pi$
$127$	−9.84604	−0.873695	−0.436847	+	0.899536i	$0.643905\pi$
$128$	−1.00000	−0.0883883
$129$	5.18951	0.456911
$130$	−0.566417	−0.0496781
$131$	20.1982	1.76472	0.882362	−	0.470571i	$-0.155952\pi$
$131$	20.1982	1.76472	0.882362	+	0.470571i	$0.155952\pi$
$132$	−3.55805	−0.309688
$133$	−4.79696	−0.415949
$134$	−14.2084	−1.22742
$135$	−15.1668	−1.30535
$136$	−2.39744	−0.205578
$137$	5.04566	0.431080	0.215540	−	0.976495i	$-0.430849\pi$
$137$	5.04566	0.431080	0.215540	+	0.976495i	$0.430849\pi$
$138$	3.71805	0.316502
$139$	21.1009	1.78976	0.894878	−	0.446310i	$-0.147262\pi$
$139$	21.1009	1.78976	0.894878	+	0.446310i	$0.147262\pi$
$140$	−7.52061	−0.635607
$141$	1.50010	0.126331
$142$	−10.2099	−0.856798
$143$	−0.439606	−0.0367617
$144$	−0.308341	−0.0256951
$145$	15.3548	1.27515
$146$	−3.58618	−0.296795
$147$	−0.399690	−0.0329659
$148$	−4.06345	−0.334013
$149$	−13.9208	−1.14043	−0.570217	−	0.821494i	$-0.693141\pi$
$149$	−13.9208	−1.14043	−0.570217	+	0.821494i	$0.693141\pi$
$150$	4.60718	0.376175
$151$	−5.09400	−0.414544	−0.207272	−	0.978283i	$-0.566459\pi$
$151$	−5.09400	−0.414544	−0.207272	+	0.978283i	$0.566459\pi$
$152$	1.78233	0.144566
$153$	−0.739228	−0.0597630
$154$	−5.83687	−0.470348
$155$	9.82533	0.789189
$156$	0.332561	0.0266262
$157$	3.39658	0.271076	0.135538	−	0.990772i	$-0.456724\pi$
$157$	3.39658	0.271076	0.135538	+	0.990772i	$0.456724\pi$
$158$	11.6911	0.930093
$159$	−13.2058	−1.04729
$160$	2.79431	0.220910
$161$	6.09935	0.480696
$162$	7.97990	0.626960
$163$	9.03326	0.707539	0.353770	−	0.935333i	$-0.384900\pi$
$163$	9.03326	0.707539	0.353770	+	0.935333i	$0.384900\pi$
$164$	−4.20212	−0.328130
$165$	9.94230	0.774007
$166$	−9.11282	−0.707292
$167$	−20.1977	−1.56294	−0.781471	−	0.623942i	$-0.785530\pi$
$167$	−20.1977	−1.56294	−0.781471	+	0.623942i	$0.785530\pi$
$168$	4.41558	0.340669
$169$	−12.9589	−0.996839
$170$	6.69919	0.513804
$171$	0.549565	0.0420263
$172$	−3.16312	−0.241186
$173$	−4.43748	−0.337375	−0.168688	−	0.985670i	$-0.553953\pi$
$173$	−4.43748	−0.337375	−0.168688	+	0.985670i	$0.553953\pi$
$174$	−9.01531	−0.683449
$175$	7.55794	0.571326
$176$	2.16871	0.163473
$177$	−6.81834	−0.512498
$178$	−15.6798	−1.17525
$179$	14.8959	1.11338	0.556688	−	0.830722i	$-0.312072\pi$
$179$	14.8959	1.11338	0.556688	+	0.830722i	$0.312072\pi$
$180$	0.861601	0.0642199
$181$	−14.9076	−1.10808	−0.554038	−	0.832491i	$-0.686914\pi$
$181$	−14.9076	−1.10808	−0.554038	+	0.832491i	$0.686914\pi$
$182$	0.545556	0.0404393
$183$	10.6856	0.789905
$184$	−2.26624	−0.167069
$185$	11.3545	0.834802
$186$	−5.76876	−0.422986
$187$	5.19935	0.380214
$188$	−0.914343	−0.0666853
$189$	14.6082	1.06259
$190$	−4.98039	−0.361315
$191$	−9.75291	−0.705696	−0.352848	−	0.935681i	$-0.614787\pi$
$191$	−9.75291	−0.705696	−0.352848	+	0.935681i	$0.614787\pi$
$192$	−1.64063	−0.118402
$193$	−11.0002	−0.791813	−0.395907	−	0.918291i	$-0.629570\pi$
$193$	−11.0002	−0.791813	−0.395907	+	0.918291i	$0.629570\pi$
$194$	6.21075	0.445906
$195$	−0.929280	−0.0665471
$196$	0.243620	0.0174015
$197$	25.8925	1.84476	0.922382	−	0.386279i	$-0.126240\pi$
$197$	25.8925	1.84476	0.922382	+	0.386279i	$0.126240\pi$
$198$	0.668702	0.0475226
$199$	17.3856	1.23243	0.616217	−	0.787576i	$-0.288664\pi$
$199$	17.3856	1.23243	0.616217	+	0.787576i	$0.288664\pi$
$200$	−2.80818	−0.198569
$201$	−23.3107	−1.64421
$202$	−2.64257	−0.185930
$203$	−14.7893	−1.03801
$204$	−3.93330	−0.275386
$205$	11.7420	0.820099
$206$	5.95437	0.414860
$207$	−0.698774	−0.0485682
$208$	−0.202704	−0.0140550
$209$	−3.86536	−0.267372
$210$	−12.3385	−0.851438
$211$	19.4074	1.33606	0.668030	−	0.744135i	$-0.267138\pi$
$211$	19.4074	1.33606	0.668030	+	0.744135i	$0.267138\pi$
$212$	8.04923	0.552823
$213$	−16.7507	−1.14774
$214$	−10.6756	−0.729766
$215$	8.83876	0.602798
$216$	−5.42776	−0.369312
$217$	−9.46346	−0.642422
$218$	15.6211	1.05800
$219$	−5.88359	−0.397576
$220$	−6.06006	−0.408569
$221$	−0.485969	−0.0326898
$222$	−6.66660	−0.447433
$223$	−1.21580	−0.0814159	−0.0407079	−	0.999171i	$-0.512961\pi$
$223$	−1.21580	−0.0814159	−0.0407079	+	0.999171i	$0.512961\pi$
$224$	−2.69140	−0.179827
$225$	−0.865878	−0.0577252
$226$	12.0787	0.803465
$227$	−18.9198	−1.25575	−0.627874	−	0.778315i	$-0.716075\pi$
$227$	−18.9198	−1.25575	−0.627874	+	0.778315i	$0.716075\pi$
$228$	2.92414	0.193656
$229$	3.29209	0.217548	0.108774	−	0.994067i	$-0.465308\pi$
$229$	3.29209	0.217548	0.108774	+	0.994067i	$0.465308\pi$
$230$	6.33258	0.417558
$231$	−9.57612	−0.630063
$232$	5.49504	0.360767
$233$	−12.3914	−0.811791	−0.405895	−	0.913920i	$-0.633040\pi$
$233$	−12.3914	−0.811791	−0.405895	+	0.913920i	$0.633040\pi$
$234$	−0.0625018	−0.00408587
$235$	2.55496	0.166667
$236$	4.15593	0.270528
$237$	19.1807	1.24592
$238$	−6.45245	−0.418250
$239$	26.7189	1.72830	0.864150	−	0.503235i	$-0.167857\pi$
$239$	26.7189	1.72830	0.864150	+	0.503235i	$0.167857\pi$
$240$	4.58443	0.295923
$241$	2.20943	0.142322	0.0711608	−	0.997465i	$-0.477330\pi$
$241$	2.20943	0.142322	0.0711608	+	0.997465i	$0.477330\pi$
$242$	6.29669	0.404767
$243$	−3.19122	−0.204717
$244$	−6.51314	−0.416961
$245$	−0.680751	−0.0434916
$246$	−6.89411	−0.439552
$247$	0.361285	0.0229880
$248$	3.51619	0.223278
$249$	−14.9507	−0.947465
$250$	−6.12462	−0.387355
$251$	12.2412	0.772658	0.386329	−	0.922361i	$-0.373743\pi$
$251$	12.2412	0.772658	0.386329	+	0.922361i	$0.373743\pi$
$252$	−0.829868	−0.0522768
$253$	4.91482	0.308992
$254$	9.84604	0.617795
$255$	10.9909	0.688275
$256$	1.00000	0.0625000
$257$	−16.5057	−1.02960	−0.514798	−	0.857312i	$-0.672133\pi$
$257$	−16.5057	−1.02960	−0.514798	+	0.857312i	$0.672133\pi$
$258$	−5.18951	−0.323085
$259$	−10.9364	−0.679552
$260$	0.566417	0.0351277
$261$	1.69434	0.104877
$262$	−20.1982	−1.24785
$263$	−9.26594	−0.571363	−0.285681	−	0.958325i	$-0.592220\pi$
$263$	−9.26594	−0.571363	−0.285681	+	0.958325i	$0.592220\pi$
$264$	3.55805	0.218983
$265$	−22.4921	−1.38168
$266$	4.79696	0.294120
$267$	−25.7246	−1.57432
$268$	14.2084	0.867916
$269$	−12.0325	−0.733632	−0.366816	−	0.930293i	$-0.619552\pi$
$269$	−12.0325	−0.733632	−0.366816	+	0.930293i	$0.619552\pi$
$270$	15.1668	0.923025
$271$	−21.6181	−1.31321	−0.656603	−	0.754236i	$-0.728007\pi$
$271$	−21.6181	−1.31321	−0.656603	+	0.754236i	$0.728007\pi$
$272$	2.39744	0.145366
$273$	0.895054	0.0541711
$274$	−5.04566	−0.304820
$275$	6.09014	0.367249
$276$	−3.71805	−0.223801
$277$	33.2343	1.99685	0.998427	−	0.0560675i	$-0.0178562\pi$
$277$	33.2343	1.99685	0.998427	+	0.0560675i	$0.0178562\pi$
$278$	−21.1009	−1.26555
$279$	1.08418	0.0649084
$280$	7.52061	0.449442
$281$	−22.3202	−1.33151	−0.665755	−	0.746170i	$-0.731890\pi$
$281$	−22.3202	−1.33151	−0.665755	+	0.746170i	$0.731890\pi$
$282$	−1.50010	−0.0893294
$283$	5.65009	0.335863	0.167931	−	0.985799i	$-0.446291\pi$
$283$	5.65009	0.335863	0.167931	+	0.985799i	$0.446291\pi$
$284$	10.2099	0.605848
$285$	−8.17096	−0.484006
$286$	0.439606	0.0259944
$287$	−11.3096	−0.667582
$288$	0.308341	0.0181692
$289$	−11.2523	−0.661900
$290$	−15.3548	−0.901668
$291$	10.1895	0.597321
$292$	3.58618	0.209866
$293$	−9.59687	−0.560655	−0.280328	−	0.959904i	$-0.590443\pi$
$293$	−9.59687	−0.560655	−0.280328	+	0.959904i	$0.590443\pi$
$294$	0.399690	0.0233104
$295$	−11.6130	−0.676134
$296$	4.06345	0.236183
$297$	11.7712	0.683036
$298$	13.9208	0.806409
$299$	−0.459375	−0.0265663
$300$	−4.60718	−0.265996
$301$	−8.51322	−0.490694
$302$	5.09400	0.293127
$303$	−4.33547	−0.249066
$304$	−1.78233	−0.102224
$305$	18.1998	1.04211
$306$	0.739228	0.0422588
$307$	−24.0670	−1.37358	−0.686788	−	0.726858i	$-0.740980\pi$
$307$	−24.0670	−1.37358	−0.686788	+	0.726858i	$0.740980\pi$
$308$	5.83687	0.332586
$309$	9.76890	0.555733
$310$	−9.82533	−0.558041
$311$	10.5946	0.600767	0.300384	−	0.953818i	$-0.402885\pi$
$311$	10.5946	0.600767	0.300384	+	0.953818i	$0.402885\pi$
$312$	−0.332561	−0.0188276
$313$	−5.09643	−0.288067	−0.144034	−	0.989573i	$-0.546007\pi$
$313$	−5.09643	−0.288067	−0.144034	+	0.989573i	$0.546007\pi$
$314$	−3.39658	−0.191680
$315$	2.31891	0.130656
$316$	−11.6911	−0.657675
$317$	−29.8202	−1.67487	−0.837435	−	0.546536i	$-0.815946\pi$
$317$	−29.8202	−1.67487	−0.837435	+	0.546536i	$0.815946\pi$
$318$	13.2058	0.740544
$319$	−11.9171	−0.667232
$320$	−2.79431	−0.156207
$321$	−17.5146	−0.977571
$322$	−6.09935	−0.339904
$323$	−4.27302	−0.237757
$324$	−7.97990	−0.443328
$325$	−0.569229	−0.0315751
$326$	−9.03326	−0.500306
$327$	25.6285	1.41726
$328$	4.20212	0.232023
$329$	−2.46086	−0.135672
$330$	−9.94230	−0.547306
$331$	19.9156	1.09466	0.547330	−	0.836917i	$-0.315644\pi$
$331$	19.9156	1.09466	0.547330	+	0.836917i	$0.315644\pi$
$332$	9.11282	0.500131
$333$	1.25293	0.0686600
$334$	20.1977	1.10517
$335$	−39.7027	−2.16919
$336$	−4.41558	−0.240890
$337$	5.89549	0.321148	0.160574	−	0.987024i	$-0.448666\pi$
$337$	5.89549	0.321148	0.160574	+	0.987024i	$0.448666\pi$
$338$	12.9589	0.704872
$339$	19.8167	1.07630
$340$	−6.69919	−0.363314
$341$	−7.62560	−0.412949
$342$	−0.549565	−0.0297171
$343$	−18.1841	−0.981849
$344$	3.16312	0.170544
$345$	10.3894	0.559347
$346$	4.43748	0.238560
$347$	−26.3191	−1.41289	−0.706443	−	0.707770i	$-0.749701\pi$
$347$	−26.3191	−1.41289	−0.706443	+	0.707770i	$0.749701\pi$
$348$	9.01531	0.483271
$349$	−33.7660	−1.80745	−0.903726	−	0.428111i	$-0.859179\pi$
$349$	−33.7660	−1.80745	−0.903726	+	0.428111i	$0.859179\pi$
$350$	−7.55794	−0.403989
$351$	−1.10023	−0.0587257
$352$	−2.16871	−0.115593
$353$	10.7503	0.572179	0.286090	−	0.958203i	$-0.407644\pi$
$353$	10.7503	0.572179	0.286090	+	0.958203i	$0.407644\pi$
$354$	6.81834	0.362391
$355$	−28.5297	−1.51420
$356$	15.6798	0.831025
$357$	−10.5861	−0.560274
$358$	−14.8959	−0.787275
$359$	2.86523	0.151221	0.0756105	−	0.997137i	$-0.475909\pi$
$359$	2.86523	0.151221	0.0756105	+	0.997137i	$0.475909\pi$
$360$	−0.861601	−0.0454104
$361$	−15.8233	−0.832805
$362$	14.9076	0.783529
$363$	10.3305	0.542212
$364$	−0.545556	−0.0285949
$365$	−10.0209	−0.524519
$366$	−10.6856	−0.558547
$367$	0.282643	0.0147538	0.00737691	−	0.999973i	$-0.497652\pi$
$367$	0.282643	0.0147538	0.00737691	+	0.999973i	$0.497652\pi$
$368$	2.26624	0.118136
$369$	1.29568	0.0674506
$370$	−11.3545	−0.590294
$371$	21.6637	1.12472
$372$	5.76876	0.299096
$373$	36.3290	1.88104	0.940521	−	0.339735i	$-0.110337\pi$
$373$	36.3290	1.88104	0.940521	+	0.339735i	$0.110337\pi$
$374$	−5.19935	−0.268852
$375$	−10.0482	−0.518888
$376$	0.914343	0.0471536
$377$	1.11386	0.0573669
$378$	−14.6082	−0.751367
$379$	−3.22386	−0.165599	−0.0827993	−	0.996566i	$-0.526386\pi$
$379$	−3.22386	−0.165599	−0.0827993	+	0.996566i	$0.526386\pi$
$380$	4.98039	0.255488
$381$	16.1537	0.827578
$382$	9.75291	0.499002
$383$	−37.8689	−1.93501	−0.967506	−	0.252849i	$-0.918632\pi$
$383$	−37.8689	−1.93501	−0.967506	+	0.252849i	$0.918632\pi$
$384$	1.64063	0.0837229
$385$	−16.3100	−0.831236
$386$	11.0002	0.559897
$387$	0.975320	0.0495783
$388$	−6.21075	−0.315303
$389$	28.9046	1.46552	0.732760	−	0.680488i	$-0.238232\pi$
$389$	28.9046	1.46552	0.732760	+	0.680488i	$0.238232\pi$
$390$	0.929280	0.0470559
$391$	5.43316	0.274767
$392$	−0.243620	−0.0123047
$393$	−33.1377	−1.67158
$394$	−25.8925	−1.30444
$395$	32.6686	1.64373
$396$	−0.668702	−0.0336036
$397$	−8.10040	−0.406547	−0.203274	−	0.979122i	$-0.565158\pi$
$397$	−8.10040	−0.406547	−0.203274	+	0.979122i	$0.565158\pi$
$398$	−17.3856	−0.871462
$399$	7.87002	0.393994
$400$	2.80818	0.140409
$401$	−5.07244	−0.253305	−0.126653	−	0.991947i	$-0.540423\pi$
$401$	−5.07244	−0.253305	−0.126653	+	0.991947i	$0.540423\pi$
$402$	23.3107	1.16263
$403$	0.712744	0.0355043
$404$	2.64257	0.131473
$405$	22.2983	1.10801
$406$	14.7893	0.733982
$407$	−8.81244	−0.436817
$408$	3.93330	0.194727
$409$	−11.2336	−0.555468	−0.277734	−	0.960658i	$-0.589583\pi$
$409$	−11.2336	−0.555468	−0.277734	+	0.960658i	$0.589583\pi$
$410$	−11.7420	−0.579897
$411$	−8.27805	−0.408326
$412$	−5.95437	−0.293351
$413$	11.1853	0.550391
$414$	0.698774	0.0343429
$415$	−25.4641	−1.24998
$416$	0.202704	0.00993836
$417$	−34.6187	−1.69529
$418$	3.86536	0.189061
$419$	−30.3699	−1.48367	−0.741834	−	0.670583i	$-0.766044\pi$
$419$	−30.3699	−1.48367	−0.741834	+	0.670583i	$0.766044\pi$
$420$	12.3385	0.602058
$421$	−20.8075	−1.01409	−0.507047	−	0.861918i	$-0.669263\pi$
$421$	−20.8075	−1.01409	−0.507047	+	0.861918i	$0.669263\pi$
$422$	−19.4074	−0.944737
$423$	0.281929	0.0137079
$424$	−8.04923	−0.390905
$425$	6.73244	0.326571
$426$	16.7507	0.811574
$427$	−17.5295	−0.848310
$428$	10.6756	0.516023
$429$	0.721229	0.0348213
$430$	−8.83876	−0.426243
$431$	−24.4985	−1.18005	−0.590024	−	0.807385i	$-0.700882\pi$
$431$	−24.4985	−1.18005	−0.590024	+	0.807385i	$0.700882\pi$
$432$	5.42776	0.261143
$433$	−7.27547	−0.349637	−0.174818	−	0.984601i	$-0.555934\pi$
$433$	−7.27547	−0.349637	−0.174818	+	0.984601i	$0.555934\pi$
$434$	9.46346	0.454261
$435$	−25.1916	−1.20784
$436$	−15.6211	−0.748117
$437$	−4.03919	−0.193220
$438$	5.88359	0.281129
$439$	21.8354	1.04215	0.521074	−	0.853512i	$-0.325532\pi$
$439$	21.8354	1.04215	0.521074	+	0.853512i	$0.325532\pi$
$440$	6.06006	0.288902
$441$	−0.0751181	−0.00357705
$442$	0.485969	0.0231152
$443$	−35.7061	−1.69645	−0.848225	−	0.529636i	$-0.822329\pi$
$443$	−35.7061	−1.69645	−0.848225	+	0.529636i	$0.822329\pi$
$444$	6.66660	0.316383
$445$	−43.8141	−2.07699
$446$	1.21580	0.0575697
$447$	22.8388	1.08024
$448$	2.69140	0.127157
$449$	2.52791	0.119299	0.0596496	−	0.998219i	$-0.481002\pi$
$449$	2.52791	0.119299	0.0596496	+	0.998219i	$0.481002\pi$
$450$	0.865878	0.0408179
$451$	−9.11318	−0.429123
$452$	−12.0787	−0.568136
$453$	8.35736	0.392663
$454$	18.9198	0.887948
$455$	1.52445	0.0714675
$456$	−2.92414	−0.136935
$457$	20.9531	0.980145	0.490072	−	0.871682i	$-0.336970\pi$
$457$	20.9531	0.980145	0.490072	+	0.871682i	$0.336970\pi$
$458$	−3.29209	−0.153829
$459$	13.0127	0.607381
$460$	−6.33258	−0.295258
$461$	0.0356760	0.00166160	0.000830799	−	1.00000i	$-0.499736\pi$
$461$	0.0356760	0.00166160	0.000830799		1.00000i	$0.499736\pi$
$462$	9.57612	0.445522
$463$	−38.4074	−1.78494	−0.892472	−	0.451103i	$-0.851031\pi$
$463$	−38.4074	−1.78494	−0.892472	+	0.451103i	$0.851031\pi$
$464$	−5.49504	−0.255101
$465$	−16.1197	−0.747534
$466$	12.3914	0.574023
$467$	−20.7336	−0.959438	−0.479719	−	0.877422i	$-0.659261\pi$
$467$	−20.7336	−0.959438	−0.479719	+	0.877422i	$0.659261\pi$
$468$	0.0625018	0.00288915
$469$	38.2405	1.76578
$470$	−2.55496	−0.117851
$471$	−5.57252	−0.256768
$472$	−4.15593	−0.191292
$473$	−6.85990	−0.315419
$474$	−19.1807	−0.881000
$475$	−5.00511	−0.229650
$476$	6.45245	0.295748
$477$	−2.48191	−0.113639
$478$	−26.7189	−1.22209
$479$	26.3796	1.20531	0.602657	−	0.798000i	$-0.294109\pi$
$479$	26.3796	1.20531	0.602657	+	0.798000i	$0.294109\pi$
$480$	−4.58443	−0.209249
$481$	0.823675	0.0375564
$482$	−2.20943	−0.100637
$483$	−10.0068	−0.455323
$484$	−6.29669	−0.286213
$485$	17.3548	0.788040
$486$	3.19122	0.144757
$487$	7.07968	0.320811	0.160405	−	0.987051i	$-0.448720\pi$
$487$	7.07968	0.320811	0.160405	+	0.987051i	$0.448720\pi$
$488$	6.51314	0.294836
$489$	−14.8202	−0.670193
$490$	0.680751	0.0307532
$491$	0.221219	0.00998346	0.00499173	−	0.999988i	$-0.498411\pi$
$491$	0.221219	0.00998346	0.00499173	+	0.999988i	$0.498411\pi$
$492$	6.89411	0.310810
$493$	−13.1740	−0.593327
$494$	−0.361285	−0.0162550
$495$	1.86856	0.0839857
$496$	−3.51619	−0.157882
$497$	27.4790	1.23260
$498$	14.9507	0.669959
$499$	15.8660	0.710260	0.355130	−	0.934817i	$-0.384437\pi$
$499$	15.8660	0.710260	0.355130	+	0.934817i	$0.384437\pi$
$500$	6.12462	0.273901
$501$	33.1368	1.48044
$502$	−12.2412	−0.546352
$503$	−28.4635	−1.26912	−0.634562	−	0.772872i	$-0.718819\pi$
$503$	−28.4635	−1.26912	−0.634562	+	0.772872i	$0.718819\pi$
$504$	0.829868	0.0369653
$505$	−7.38416	−0.328591
$506$	−4.91482	−0.218490
$507$	21.2607	0.944223
$508$	−9.84604	−0.436847
$509$	14.3081	0.634194	0.317097	−	0.948393i	$-0.397292\pi$
$509$	14.3081	0.634194	0.317097	+	0.948393i	$0.397292\pi$
$510$	−10.9909	−0.486684
$511$	9.65185	0.426973
$512$	−1.00000	−0.0441942
$513$	−9.67405	−0.427120
$514$	16.5057	0.728034
$515$	16.6384	0.733174
$516$	5.18951	0.228455
$517$	−1.98295	−0.0872099
$518$	10.9364	0.480516
$519$	7.28025	0.319567
$520$	−0.566417	−0.0248390
$521$	42.1708	1.84754	0.923769	−	0.382951i	$-0.125092\pi$
$521$	42.1708	1.84754	0.923769	+	0.382951i	$0.125092\pi$
$522$	−1.69434	−0.0741594
$523$	−34.6900	−1.51689	−0.758444	−	0.651738i	$-0.774040\pi$
$523$	−34.6900	−1.51689	−0.758444	+	0.651738i	$0.774040\pi$
$524$	20.1982	0.882362
$525$	−12.3998	−0.541170
$526$	9.26594	0.404014
$527$	−8.42984	−0.367209
$528$	−3.55805	−0.154844
$529$	−17.8642	−0.776703
$530$	22.4921	0.976993
$531$	−1.28144	−0.0556099
$532$	−4.79696	−0.207974
$533$	0.851784	0.0368949
$534$	25.7246	1.11321
$535$	−29.8309	−1.28970
$536$	−14.2084	−0.613710
$537$	−24.4387	−1.05461
$538$	12.0325	0.518756
$539$	0.528342	0.0227573
$540$	−15.1668	−0.652677
$541$	−17.2153	−0.740145	−0.370072	−	0.929003i	$-0.620667\pi$
$541$	−17.2153	−0.740145	−0.370072	+	0.929003i	$0.620667\pi$
$542$	21.6181	0.928578
$543$	24.4579	1.04959
$544$	−2.39744	−0.102789
$545$	43.6504	1.86978
$546$	−0.895054	−0.0383048
$547$	−12.4841	−0.533783	−0.266892	−	0.963727i	$-0.585997\pi$
$547$	−12.4841	−0.533783	−0.266892	+	0.963727i	$0.585997\pi$
$548$	5.04566	0.215540
$549$	2.00827	0.0857108
$550$	−6.09014	−0.259684
$551$	9.79397	0.417237
$552$	3.71805	0.158251
$553$	−31.4654	−1.33804
$554$	−33.2343	−1.41199
$555$	−18.6286	−0.790739
$556$	21.1009	0.894878
$557$	1.15461	0.0489225	0.0244612	−	0.999701i	$-0.492213\pi$
$557$	1.15461	0.0489225	0.0244612	+	0.999701i	$0.492213\pi$
$558$	−1.08418	−0.0458972
$559$	0.641176	0.0271189
$560$	−7.52061	−0.317804
$561$	−8.53019	−0.360145
$562$	22.3202	0.941520
$563$	39.0634	1.64633	0.823163	−	0.567805i	$-0.192207\pi$
$563$	39.0634	1.64633	0.823163	+	0.567805i	$0.192207\pi$
$564$	1.50010	0.0631654
$565$	33.7517	1.41995
$566$	−5.65009	−0.237491
$567$	−21.4771	−0.901953
$568$	−10.2099	−0.428399
$569$	4.68833	0.196545	0.0982725	−	0.995160i	$-0.468668\pi$
$569$	4.68833	0.196545	0.0982725	+	0.995160i	$0.468668\pi$
$570$	8.17096	0.342244
$571$	−37.4571	−1.56753	−0.783766	−	0.621056i	$-0.786704\pi$
$571$	−37.4571	−1.56753	−0.783766	+	0.621056i	$0.786704\pi$
$572$	−0.439606	−0.0183808
$573$	16.0009	0.668447
$574$	11.3096	0.472052
$575$	6.36401	0.265398
$576$	−0.308341	−0.0128475
$577$	13.9130	0.579205	0.289603	−	0.957147i	$-0.406477\pi$
$577$	13.9130	0.579205	0.289603	+	0.957147i	$0.406477\pi$
$578$	11.2523	0.468034
$579$	18.0473	0.750019
$580$	15.3548	0.637575
$581$	24.5262	1.01752
$582$	−10.1895	−0.422369
$583$	17.4565	0.722973
$584$	−3.58618	−0.148397
$585$	−0.174650	−0.00722087
$586$	9.59687	0.396443
$587$	5.35929	0.221202	0.110601	−	0.993865i	$-0.464723\pi$
$587$	5.35929	0.221202	0.110601	+	0.993865i	$0.464723\pi$
$588$	−0.399690	−0.0164829
$589$	6.26701	0.258228
$590$	11.6130	0.478099
$591$	−42.4799	−1.74739
$592$	−4.06345	−0.167007
$593$	−45.3060	−1.86049	−0.930246	−	0.366936i	$-0.880407\pi$
$593$	−45.3060	−1.86049	−0.930246	+	0.366936i	$0.880407\pi$
$594$	−11.7712	−0.482980
$595$	−18.0302	−0.739165
$596$	−13.9208	−0.570217
$597$	−28.5233	−1.16738
$598$	0.459375	0.0187852
$599$	−7.38124	−0.301589	−0.150795	−	0.988565i	$-0.548183\pi$
$599$	−7.38124	−0.301589	−0.150795	+	0.988565i	$0.548183\pi$
$600$	4.60718	0.188087
$601$	16.2897	0.664471	0.332236	−	0.943196i	$-0.392197\pi$
$601$	16.2897	0.664471	0.332236	+	0.943196i	$0.392197\pi$
$602$	8.51322	0.346973
$603$	−4.38103	−0.178409
$604$	−5.09400	−0.207272
$605$	17.5949	0.715335
$606$	4.33547	0.176116
$607$	19.7887	0.803198	0.401599	−	0.915816i	$-0.368455\pi$
$607$	19.7887	0.803198	0.401599	+	0.915816i	$0.368455\pi$
$608$	1.78233	0.0722830
$609$	24.2638	0.983218
$610$	−18.1998	−0.736887
$611$	0.185341	0.00749808
$612$	−0.739228	−0.0298815
$613$	−22.2172	−0.897346	−0.448673	−	0.893696i	$-0.648103\pi$
$613$	−22.2172	−0.897346	−0.448673	+	0.893696i	$0.648103\pi$
$614$	24.0670	0.971265
$615$	−19.2643	−0.776811
$616$	−5.83687	−0.235174
$617$	9.88127	0.397805	0.198902	−	0.980019i	$-0.436262\pi$
$617$	9.88127	0.397805	0.198902	+	0.980019i	$0.436262\pi$
$618$	−9.76890	−0.392963
$619$	−17.3118	−0.695820	−0.347910	−	0.937528i	$-0.613108\pi$
$619$	−17.3118	−0.695820	−0.347910	+	0.937528i	$0.613108\pi$
$620$	9.82533	0.394595
$621$	12.3006	0.493606
$622$	−10.5946	−0.424807
$623$	42.2004	1.69073
$624$	0.332561	0.0133131
$625$	−31.1550	−1.24620
$626$	5.09643	0.203694
$627$	6.34162	0.253260
$628$	3.39658	0.135538
$629$	−9.74185	−0.388433
$630$	−2.31891	−0.0923876
$631$	−48.2788	−1.92195	−0.960974	−	0.276639i	$-0.910779\pi$
$631$	−48.2788	−1.92195	−0.960974	+	0.276639i	$0.910779\pi$
$632$	11.6911	0.465047
$633$	−31.8403	−1.26554
$634$	29.8202	1.18431
$635$	27.5129	1.09182
$636$	−13.2058	−0.523644
$637$	−0.0493827	−0.00195661
$638$	11.9171	0.471804
$639$	−3.14814	−0.124538
$640$	2.79431	0.110455
$641$	−20.0957	−0.793734	−0.396867	−	0.917876i	$-0.629903\pi$
$641$	−20.0957	−0.793734	−0.396867	+	0.917876i	$0.629903\pi$
$642$	17.5146	0.691247
$643$	35.6047	1.40411	0.702056	−	0.712122i	$-0.252266\pi$
$643$	35.6047	1.40411	0.702056	+	0.712122i	$0.252266\pi$
$644$	6.09935	0.240348
$645$	−14.5011	−0.570981
$646$	4.27302	0.168120
$647$	−39.5179	−1.55361	−0.776805	−	0.629742i	$-0.783161\pi$
$647$	−39.5179	−1.55361	−0.776805	+	0.629742i	$0.783161\pi$
$648$	7.97990	0.313480
$649$	9.01302	0.353792
$650$	0.569229	0.0223270
$651$	15.5260	0.608512
$652$	9.03326	0.353770
$653$	−27.0969	−1.06039	−0.530193	−	0.847877i	$-0.677880\pi$
$653$	−27.0969	−1.06039	−0.530193	+	0.847877i	$0.677880\pi$
$654$	−25.6285	−1.00215
$655$	−56.4401	−2.20530
$656$	−4.20212	−0.164065
$657$	−1.10577	−0.0431401
$658$	2.46086	0.0959343
$659$	−26.3379	−1.02598	−0.512989	−	0.858395i	$-0.671462\pi$
$659$	−26.3379	−1.02598	−0.512989	+	0.858395i	$0.671462\pi$
$660$	9.94230	0.387003
$661$	−8.32794	−0.323919	−0.161960	−	0.986797i	$-0.551781\pi$
$661$	−8.32794	−0.323919	−0.161960	+	0.986797i	$0.551781\pi$
$662$	−19.9156	−0.774042
$663$	0.797294	0.0309643
$664$	−9.11282	−0.353646
$665$	13.4042	0.519793
$666$	−1.25293	−0.0485499
$667$	−12.4531	−0.482185
$668$	−20.1977	−0.781471
$669$	1.99467	0.0771185
$670$	39.7027	1.53385
$671$	−14.1251	−0.545294
$672$	4.41558	0.170335
$673$	−37.9578	−1.46317	−0.731583	−	0.681752i	$-0.761218\pi$
$673$	−37.9578	−1.46317	−0.731583	+	0.681752i	$0.761218\pi$
$674$	−5.89549	−0.227086
$675$	15.2421	0.586670
$676$	−12.9589	−0.498420
$677$	14.4624	0.555835	0.277917	−	0.960605i	$-0.410356\pi$
$677$	14.4624	0.555835	0.277917	+	0.960605i	$0.410356\pi$
$678$	−19.8167	−0.761056
$679$	−16.7156	−0.641486
$680$	6.69919	0.256902
$681$	31.0403	1.18947
$682$	7.62560	0.291999
$683$	−41.2042	−1.57663	−0.788317	−	0.615270i	$-0.789047\pi$
$683$	−41.2042	−1.57663	−0.788317	+	0.615270i	$0.789047\pi$
$684$	0.549565	0.0210131
$685$	−14.0992	−0.538701
$686$	18.1841	0.694272
$687$	−5.40110	−0.206065
$688$	−3.16312	−0.120593
$689$	−1.63161	−0.0621593
$690$	−10.3894	−0.395518
$691$	−46.1328	−1.75497	−0.877487	−	0.479600i	$-0.840782\pi$
$691$	−46.1328	−1.75497	−0.877487	+	0.479600i	$0.840782\pi$
$692$	−4.43748	−0.168688
$693$	−1.79974	−0.0683666
$694$	26.3191	0.999061
$695$	−58.9626	−2.23658
$696$	−9.01531	−0.341724
$697$	−10.0743	−0.381591
$698$	33.7660	1.27806
$699$	20.3297	0.768942
$700$	7.55794	0.285663
$701$	−46.4008	−1.75253	−0.876267	−	0.481827i	$-0.839974\pi$
$701$	−46.4008	−1.75253	−0.876267	+	0.481827i	$0.839974\pi$
$702$	1.10023	0.0415253
$703$	7.24240	0.273152
$704$	2.16871	0.0817364
$705$	−4.19174	−0.157870
$706$	−10.7503	−0.404592
$707$	7.11220	0.267482
$708$	−6.81834	−0.256249
$709$	−25.5760	−0.960525	−0.480263	−	0.877125i	$-0.659459\pi$
$709$	−25.5760	−0.960525	−0.480263	+	0.877125i	$0.659459\pi$
$710$	28.5297	1.07070
$711$	3.60484	0.135192
$712$	−15.6798	−0.587624
$713$	−7.96852	−0.298424
$714$	10.5861	0.396174
$715$	1.22840	0.0459394
$716$	14.8959	0.556688
$717$	−43.8357	−1.63707
$718$	−2.86523	−0.106929
$719$	2.06987	0.0771933	0.0385966	−	0.999255i	$-0.487711\pi$
$719$	2.06987	0.0771933	0.0385966	+	0.999255i	$0.487711\pi$
$720$	0.861601	0.0321100
$721$	−16.0256	−0.596823
$722$	15.8233	0.588882
$723$	−3.62485	−0.134809
$724$	−14.9076	−0.554038
$725$	−15.4311	−0.573095
$726$	−10.3305	−0.383402
$727$	26.2637	0.974067	0.487033	−	0.873383i	$-0.338079\pi$
$727$	26.2637	0.974067	0.487033	+	0.873383i	$0.338079\pi$
$728$	0.545556	0.0202196
$729$	29.1753	1.08057
$730$	10.0209	0.370891
$731$	−7.58339	−0.280482
$732$	10.6856	0.394953
$733$	40.8698	1.50956	0.754780	−	0.655979i	$-0.227744\pi$
$733$	40.8698	1.50956	0.754780	+	0.655979i	$0.227744\pi$
$734$	−0.282643	−0.0104325
$735$	1.11686	0.0411960
$736$	−2.26624	−0.0835347
$737$	30.8139	1.13505
$738$	−1.29568	−0.0476948
$739$	23.3838	0.860187	0.430094	−	0.902784i	$-0.358481\pi$
$739$	23.3838	0.860187	0.430094	+	0.902784i	$0.358481\pi$
$740$	11.3545	0.417401
$741$	−0.592733	−0.0217746
$742$	−21.6637	−0.795299
$743$	25.2697	0.927055	0.463527	−	0.886083i	$-0.346584\pi$
$743$	25.2697	0.927055	0.463527	+	0.886083i	$0.346584\pi$
$744$	−5.76876	−0.211493
$745$	38.8990	1.42515
$746$	−36.3290	−1.33010
$747$	−2.80985	−0.102807
$748$	5.19935	0.190107
$749$	28.7322	1.04985
$750$	10.0482	0.366909
$751$	43.0057	1.56930	0.784649	−	0.619940i	$-0.212843\pi$
$751$	43.0057	1.56930	0.784649	+	0.619940i	$0.212843\pi$
$752$	−0.914343	−0.0333426
$753$	−20.0833	−0.731875
$754$	−1.11386	−0.0405645
$755$	14.2342	0.518037
$756$	14.6082	0.531297
$757$	12.8085	0.465532	0.232766	−	0.972533i	$-0.425222\pi$
$757$	12.8085	0.465532	0.232766	+	0.972533i	$0.425222\pi$
$758$	3.22386	0.117096
$759$	−8.06339	−0.292682
$760$	−4.98039	−0.180658
$761$	33.0698	1.19878	0.599389	−	0.800458i	$-0.295410\pi$
$761$	33.0698	1.19878	0.599389	+	0.800458i	$0.295410\pi$
$762$	−16.1537	−0.585186
$763$	−42.0427	−1.52205
$764$	−9.75291	−0.352848
$765$	2.06563	0.0746831
$766$	37.8689	1.36826
$767$	−0.842422	−0.0304181
$768$	−1.64063	−0.0592011
$769$	51.9583	1.87366	0.936832	−	0.349781i	$-0.113744\pi$
$769$	51.9583	1.87366	0.936832	+	0.349781i	$0.113744\pi$
$770$	16.3100	0.587773
$771$	27.0797	0.975250
$772$	−11.0002	−0.395907
$773$	3.50883	0.126204	0.0631019	−	0.998007i	$-0.479901\pi$
$773$	3.50883	0.126204	0.0631019	+	0.998007i	$0.479901\pi$
$774$	−0.975320	−0.0350572
$775$	−9.87410	−0.354688
$776$	6.21075	0.222953
$777$	17.9425	0.643683
$778$	−28.9046	−1.03628
$779$	7.48956	0.268341
$780$	−0.929280	−0.0332735
$781$	22.1424	0.792317
$782$	−5.43316	−0.194290
$783$	−29.8257	−1.06588
$784$	0.243620	0.00870073
$785$	−9.49109	−0.338752
$786$	33.1377	1.18198
$787$	18.0649	0.643943	0.321972	−	0.946749i	$-0.395654\pi$
$787$	18.0649	0.643943	0.321972	+	0.946749i	$0.395654\pi$
$788$	25.8925	0.922382
$789$	15.2020	0.541204
$790$	−32.6686	−1.16230
$791$	−32.5087	−1.15588
$792$	0.668702	0.0237613
$793$	1.32024	0.0468830
$794$	8.10040	0.287472
$795$	36.9011	1.30875
$796$	17.3856	0.616217
$797$	−41.3612	−1.46509	−0.732545	−	0.680719i	$-0.761667\pi$
$797$	−41.3612	−1.46509	−0.732545	+	0.680719i	$0.761667\pi$
$798$	−7.87002	−0.278596
$799$	−2.19208	−0.0775501
$800$	−2.80818	−0.0992843
$801$	−4.83471	−0.170826
$802$	5.07244	0.179114
$803$	7.77740	0.274458
$804$	−23.3107	−0.822105
$805$	−17.0435	−0.600704
$806$	−0.712744	−0.0251053
$807$	19.7408	0.694909
$808$	−2.64257	−0.0929652
$809$	−6.46817	−0.227409	−0.113704	−	0.993515i	$-0.536272\pi$
$809$	−6.46817	−0.227409	−0.113704	+	0.993515i	$0.536272\pi$
$810$	−22.2983	−0.783484
$811$	24.7324	0.868472	0.434236	−	0.900799i	$-0.357018\pi$
$811$	24.7324	0.868472	0.434236	+	0.900799i	$0.357018\pi$
$812$	−14.7893	−0.519004
$813$	35.4673	1.24389
$814$	8.81244	0.308876
$815$	−25.2417	−0.884180
$816$	−3.93330	−0.137693
$817$	5.63773	0.197239
$818$	11.2336	0.392775
$819$	0.168217	0.00587798
$820$	11.7420	0.410049
$821$	18.1363	0.632961	0.316480	−	0.948599i	$-0.397499\pi$
$821$	18.1363	0.632961	0.316480	+	0.948599i	$0.397499\pi$
$822$	8.27805	0.288730
$823$	−27.8121	−0.969468	−0.484734	−	0.874662i	$-0.661084\pi$
$823$	−27.8121	−0.969468	−0.484734	+	0.874662i	$0.661084\pi$
$824$	5.95437	0.207430
$825$	−9.99165	−0.347865
$826$	−11.1853	−0.389185
$827$	12.4876	0.434236	0.217118	−	0.976145i	$-0.430334\pi$
$827$	12.4876	0.434236	0.217118	+	0.976145i	$0.430334\pi$
$828$	−0.698774	−0.0242841
$829$	−7.70544	−0.267621	−0.133811	−	0.991007i	$-0.542721\pi$
$829$	−7.70544	−0.267621	−0.133811	+	0.991007i	$0.542721\pi$
$830$	25.4641	0.883870
$831$	−54.5251	−1.89145
$832$	−0.202704	−0.00702748
$833$	0.584064	0.0202366
$834$	34.6187	1.19875
$835$	56.4386	1.95314
$836$	−3.86536	−0.133686
$837$	−19.0850	−0.659674
$838$	30.3699	1.04911
$839$	11.0308	0.380825	0.190413	−	0.981704i	$-0.439017\pi$
$839$	11.0308	0.380825	0.190413	+	0.981704i	$0.439017\pi$
$840$	−12.3385	−0.425719
$841$	1.19542	0.0412214
$842$	20.8075	0.717073
$843$	36.6191	1.26123
$844$	19.4074	0.668030
$845$	36.2112	1.24570
$846$	−0.281929	−0.00969293
$847$	−16.9469	−0.582302
$848$	8.04923	0.276412
$849$	−9.26969	−0.318135
$850$	−6.73244	−0.230921
$851$	−9.20874	−0.315672
$852$	−16.7507	−0.573869
$853$	−45.0896	−1.54384	−0.771918	−	0.635722i	$-0.780703\pi$
$853$	−45.0896	−1.54384	−0.771918	+	0.635722i	$0.780703\pi$
$854$	17.5295	0.599846
$855$	−1.53566	−0.0525184
$856$	−10.6756	−0.364883
$857$	27.4988	0.939340	0.469670	−	0.882842i	$-0.344373\pi$
$857$	27.4988	0.939340	0.469670	+	0.882842i	$0.344373\pi$
$858$	−0.721229	−0.0246224
$859$	26.9075	0.918071	0.459035	−	0.888418i	$-0.348195\pi$
$859$	26.9075	0.918071	0.459035	+	0.888418i	$0.348195\pi$
$860$	8.83876	0.301399
$861$	18.5548	0.632345
$862$	24.4985	0.834421
$863$	−46.8299	−1.59411	−0.797054	−	0.603907i	$-0.793610\pi$
$863$	−46.8299	−1.59411	−0.797054	+	0.603907i	$0.793610\pi$
$864$	−5.42776	−0.184656
$865$	12.3997	0.421602
$866$	7.27547	0.247230
$867$	18.4608	0.626963
$868$	−9.46346	−0.321211
$869$	−25.3546	−0.860096
$870$	25.1916	0.854075
$871$	−2.88009	−0.0975883
$872$	15.6211	0.528999
$873$	1.91503	0.0648139
$874$	4.03919	0.136627
$875$	16.4838	0.557254
$876$	−5.88359	−0.198788
$877$	24.0596	0.812434	0.406217	−	0.913777i	$-0.366848\pi$
$877$	24.0596	0.812434	0.406217	+	0.913777i	$0.366848\pi$
$878$	−21.8354	−0.736909
$879$	15.7449	0.531062
$880$	−6.06006	−0.204285
$881$	17.3302	0.583870	0.291935	−	0.956438i	$-0.405701\pi$
$881$	17.3302	0.583870	0.291935	+	0.956438i	$0.405701\pi$
$882$	0.0751181	0.00252936
$883$	−23.3113	−0.784489	−0.392244	−	0.919861i	$-0.628301\pi$
$883$	−23.3113	−0.784489	−0.392244	+	0.919861i	$0.628301\pi$
$884$	−0.485969	−0.0163449
$885$	19.0526	0.640445
$886$	35.7061	1.19957
$887$	53.2207	1.78698	0.893489	−	0.449085i	$-0.148250\pi$
$887$	53.2207	1.78698	0.893489	+	0.449085i	$0.148250\pi$
$888$	−6.66660	−0.223717
$889$	−26.4996	−0.888768
$890$	43.8141	1.46865
$891$	−17.3061	−0.579776
$892$	−1.21580	−0.0407079
$893$	1.62966	0.0545345
$894$	−22.8388	−0.763844
$895$	−41.6239	−1.39133
$896$	−2.69140	−0.0899133
$897$	0.753663	0.0251641
$898$	−2.52791	−0.0843573
$899$	19.3216	0.644411
$900$	−0.865878	−0.0288626
$901$	19.2975	0.642893
$902$	9.11318	0.303436
$903$	13.9670	0.464794
$904$	12.0787	0.401733
$905$	41.6566	1.38471
$906$	−8.35736	−0.277655
$907$	−15.5055	−0.514853	−0.257427	−	0.966298i	$-0.582875\pi$
$907$	−15.5055	−0.514853	−0.257427	+	0.966298i	$0.582875\pi$
$908$	−18.9198	−0.627874
$909$	−0.814812	−0.0270256
$910$	−1.52445	−0.0505351
$911$	−48.1562	−1.59549	−0.797744	−	0.602997i	$-0.793973\pi$
$911$	−48.1562	−1.59549	−0.797744	+	0.602997i	$0.793973\pi$
$912$	2.92414	0.0968279
$913$	19.7631	0.654062
$914$	−20.9531	−0.693067
$915$	−29.8590	−0.987109
$916$	3.29209	0.108774
$917$	54.3614	1.79517
$918$	−13.0127	−0.429483
$919$	−14.8233	−0.488974	−0.244487	−	0.969653i	$-0.578620\pi$
$919$	−14.8233	−0.488974	−0.244487	+	0.969653i	$0.578620\pi$
$920$	6.33258	0.208779
$921$	39.4850	1.30107
$922$	−0.0356760	−0.00117493
$923$	−2.06959	−0.0681214
$924$	−9.57612	−0.315031
$925$	−11.4109	−0.375188
$926$	38.4074	1.26215
$927$	1.83597	0.0603013
$928$	5.49504	0.180383
$929$	30.8389	1.01179	0.505896	−	0.862595i	$-0.331162\pi$
$929$	30.8389	1.01179	0.505896	+	0.862595i	$0.331162\pi$
$930$	16.1197	0.528586
$931$	−0.434212	−0.0142307
$932$	−12.3914	−0.405895
$933$	−17.3819	−0.569057
$934$	20.7336	0.678425
$935$	−14.5286	−0.475136
$936$	−0.0625018	−0.00204294
$937$	−20.0918	−0.656369	−0.328185	−	0.944614i	$-0.606437\pi$
$937$	−20.0918	−0.656369	−0.328185	+	0.944614i	$0.606437\pi$
$938$	−38.2405	−1.24860
$939$	8.36135	0.272862
$940$	2.55496	0.0833336
$941$	−22.3404	−0.728278	−0.364139	−	0.931345i	$-0.618637\pi$
$941$	−22.3404	−0.728278	−0.364139	+	0.931345i	$0.618637\pi$
$942$	5.57252	0.181562
$943$	−9.52300	−0.310112
$944$	4.15593	0.135264
$945$	−40.8200	−1.32788
$946$	6.85990	0.223035
$947$	26.7460	0.869127	0.434564	−	0.900641i	$-0.356903\pi$
$947$	26.7460	0.869127	0.434564	+	0.900641i	$0.356903\pi$
$948$	19.1807	0.622961
$949$	−0.726932	−0.0235972
$950$	5.00511	0.162387
$951$	48.9239	1.58647
$952$	−6.45245	−0.209125
$953$	2.85968	0.0926341	0.0463171	−	0.998927i	$-0.485252\pi$
$953$	2.85968	0.0926341	0.0463171	+	0.998927i	$0.485252\pi$
$954$	2.48191	0.0803547
$955$	27.2527	0.881876
$956$	26.7189	0.864150
$957$	19.5516	0.632014
$958$	−26.3796	−0.852286
$959$	13.5799	0.438517
$960$	4.58443	0.147962
$961$	−18.6364	−0.601175
$962$	−0.823675	−0.0265564
$963$	−3.29171	−0.106074
$964$	2.20943	0.0711608
$965$	30.7381	0.989493
$966$	10.0068	0.321962
$967$	22.4644	0.722406	0.361203	−	0.932487i	$-0.382366\pi$
$967$	22.4644	0.722406	0.361203	+	0.932487i	$0.382366\pi$
$968$	6.29669	0.202383
$969$	7.01044	0.225208
$970$	−17.3548	−0.557228
$971$	−0.635447	−0.0203925	−0.0101962	−	0.999948i	$-0.503246\pi$
$971$	−0.635447	−0.0203925	−0.0101962	+	0.999948i	$0.503246\pi$
$972$	−3.19122	−0.102358
$973$	56.7910	1.82063
$974$	−7.07968	−0.226848
$975$	0.933892	0.0299085
$976$	−6.51314	−0.208481
$977$	−10.6914	−0.342047	−0.171024	−	0.985267i	$-0.554707\pi$
$977$	−10.6914	−0.342047	−0.171024	+	0.985267i	$0.554707\pi$
$978$	14.8202	0.473898
$979$	34.0049	1.08680
$980$	−0.680751	−0.0217458
$981$	4.81664	0.153783
$982$	−0.221219	−0.00705937
$983$	−26.4390	−0.843275	−0.421637	−	0.906765i	$-0.638544\pi$
$983$	−26.4390	−0.843275	−0.421637	+	0.906765i	$0.638544\pi$
$984$	−6.89411	−0.219776
$985$	−72.3517	−2.30532
$986$	13.1740	0.419546
$987$	4.03735	0.128510
$988$	0.361285	0.0114940
$989$	−7.16840	−0.227942
$990$	−1.86856	−0.0593869
$991$	31.9486	1.01488	0.507441	−	0.861687i	$-0.330592\pi$
$991$	31.9486	1.01488	0.507441	+	0.861687i	$0.330592\pi$
$992$	3.51619	0.111639
$993$	−32.6741	−1.03688
$994$	−27.4790	−0.871580
$995$	−48.5809	−1.54012
$996$	−14.9507	−0.473732
$997$	−38.3699	−1.21519	−0.607594	−	0.794248i	$-0.707865\pi$
$997$	−38.3699	−1.21519	−0.607594	+	0.794248i	$0.707865\pi$
$998$	−15.8660	−0.502230
$999$	−22.0554	−0.697802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.18	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.18	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.64063 q^{3} +1.00000 q^{4} -2.79431 q^{5} +1.64063 q^{6} +2.69140 q^{7} -1.00000 q^{8} -0.308341 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.64063 q^{3} +1.00000 q^{4} -2.79431 q^{5} +1.64063 q^{6} +2.69140 q^{7} -1.00000 q^{8} -0.308341 q^{9} +2.79431 q^{10} +2.16871 q^{11} -1.64063 q^{12} -0.202704 q^{13} -2.69140 q^{14} +4.58443 q^{15} +1.00000 q^{16} +2.39744 q^{17} +0.308341 q^{18} -1.78233 q^{19} -2.79431 q^{20} -4.41558 q^{21} -2.16871 q^{22} +2.26624 q^{23} +1.64063 q^{24} +2.80818 q^{25} +0.202704 q^{26} +5.42776 q^{27} +2.69140 q^{28} -5.49504 q^{29} -4.58443 q^{30} -3.51619 q^{31} -1.00000 q^{32} -3.55805 q^{33} -2.39744 q^{34} -7.52061 q^{35} -0.308341 q^{36} -4.06345 q^{37} +1.78233 q^{38} +0.332561 q^{39} +2.79431 q^{40} -4.20212 q^{41} +4.41558 q^{42} -3.16312 q^{43} +2.16871 q^{44} +0.861601 q^{45} -2.26624 q^{46} -0.914343 q^{47} -1.64063 q^{48} +0.243620 q^{49} -2.80818 q^{50} -3.93330 q^{51} -0.202704 q^{52} +8.04923 q^{53} -5.42776 q^{54} -6.06006 q^{55} -2.69140 q^{56} +2.92414 q^{57} +5.49504 q^{58} +4.15593 q^{59} +4.58443 q^{60} -6.51314 q^{61} +3.51619 q^{62} -0.829868 q^{63} +1.00000 q^{64} +0.566417 q^{65} +3.55805 q^{66} +14.2084 q^{67} +2.39744 q^{68} -3.71805 q^{69} +7.52061 q^{70} +10.2099 q^{71} +0.308341 q^{72} +3.58618 q^{73} +4.06345 q^{74} -4.60718 q^{75} -1.78233 q^{76} +5.83687 q^{77} -0.332561 q^{78} -11.6911 q^{79} -2.79431 q^{80} -7.97990 q^{81} +4.20212 q^{82} +9.11282 q^{83} -4.41558 q^{84} -6.69919 q^{85} +3.16312 q^{86} +9.01531 q^{87} -2.16871 q^{88} +15.6798 q^{89} -0.861601 q^{90} -0.545556 q^{91} +2.26624 q^{92} +5.76876 q^{93} +0.914343 q^{94} +4.98039 q^{95} +1.64063 q^{96} -6.21075 q^{97} -0.243620 q^{98} -0.668702 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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