LMFDB - Embedded newform 6042.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.48689336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 6x^{4} + 7x^{3} + 9x^{2} - 5x - 2 $ x^6 - 2x^5 - 6x^4 + 7x^3 + 9x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.290197$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.709803 q^{5} +1.00000 q^{6} +0.335393 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.709803 q^{5} +1.00000 q^{6} +0.335393 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.709803 q^{10} -1.82920 q^{11} +1.00000 q^{12} -1.79639 q^{13} +0.335393 q^{14} -0.709803 q^{15} +1.00000 q^{16} -1.87183 q^{17} +1.00000 q^{18} -1.00000 q^{19} -0.709803 q^{20} +0.335393 q^{21} -1.82920 q^{22} +2.28960 q^{23} +1.00000 q^{24} -4.49618 q^{25} -1.79639 q^{26} +1.00000 q^{27} +0.335393 q^{28} -5.51807 q^{29} -0.709803 q^{30} -8.89188 q^{31} +1.00000 q^{32} -1.82920 q^{33} -1.87183 q^{34} -0.238063 q^{35} +1.00000 q^{36} -3.68230 q^{37} -1.00000 q^{38} -1.79639 q^{39} -0.709803 q^{40} -4.65583 q^{41} +0.335393 q^{42} -5.40625 q^{43} -1.82920 q^{44} -0.709803 q^{45} +2.28960 q^{46} -2.35252 q^{47} +1.00000 q^{48} -6.88751 q^{49} -4.49618 q^{50} -1.87183 q^{51} -1.79639 q^{52} -1.00000 q^{53} +1.00000 q^{54} +1.29837 q^{55} +0.335393 q^{56} -1.00000 q^{57} -5.51807 q^{58} -7.36599 q^{59} -0.709803 q^{60} +14.9287 q^{61} -8.89188 q^{62} +0.335393 q^{63} +1.00000 q^{64} +1.27508 q^{65} -1.82920 q^{66} +13.8012 q^{67} -1.87183 q^{68} +2.28960 q^{69} -0.238063 q^{70} -5.26505 q^{71} +1.00000 q^{72} -0.853957 q^{73} -3.68230 q^{74} -4.49618 q^{75} -1.00000 q^{76} -0.613500 q^{77} -1.79639 q^{78} +6.28178 q^{79} -0.709803 q^{80} +1.00000 q^{81} -4.65583 q^{82} +5.74077 q^{83} +0.335393 q^{84} +1.32863 q^{85} -5.40625 q^{86} -5.51807 q^{87} -1.82920 q^{88} +7.74438 q^{89} -0.709803 q^{90} -0.602496 q^{91} +2.28960 q^{92} -8.89188 q^{93} -2.35252 q^{94} +0.709803 q^{95} +1.00000 q^{96} +18.1735 q^{97} -6.88751 q^{98} -1.82920 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} - 8 q^{10} + 3 q^{11} + 6 q^{12} - 13 q^{13} - 6 q^{14} - 8 q^{15} + 6 q^{16} - 5 q^{17} + 6 q^{18} - 6 q^{19} - 8 q^{20} - 6 q^{21} + 3 q^{22} - 12 q^{23} + 6 q^{24} - 4 q^{25} - 13 q^{26} + 6 q^{27} - 6 q^{28} - 7 q^{29} - 8 q^{30} - 17 q^{31} + 6 q^{32} + 3 q^{33} - 5 q^{34} - 5 q^{35} + 6 q^{36} - 15 q^{37} - 6 q^{38} - 13 q^{39} - 8 q^{40} - 12 q^{41} - 6 q^{42} - 4 q^{43} + 3 q^{44} - 8 q^{45} - 12 q^{46} - 29 q^{47} + 6 q^{48} + 4 q^{49} - 4 q^{50} - 5 q^{51} - 13 q^{52} - 6 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 7 q^{58} + 9 q^{59} - 8 q^{60} - 16 q^{61} - 17 q^{62} - 6 q^{63} + 6 q^{64} + 5 q^{65} + 3 q^{66} - 8 q^{67} - 5 q^{68} - 12 q^{69} - 5 q^{70} - 2 q^{71} + 6 q^{72} - 17 q^{73} - 15 q^{74} - 4 q^{75} - 6 q^{76} - 21 q^{77} - 13 q^{78} - 31 q^{79} - 8 q^{80} + 6 q^{81} - 12 q^{82} - 5 q^{83} - 6 q^{84} - 4 q^{86} - 7 q^{87} + 3 q^{88} - 5 q^{89} - 8 q^{90} + 4 q^{91} - 12 q^{92} - 17 q^{93} - 29 q^{94} + 8 q^{95} + 6 q^{96} + 7 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9 - 8 * q^10 + 3 * q^11 + 6 * q^12 - 13 * q^13 - 6 * q^14 - 8 * q^15 + 6 * q^16 - 5 * q^17 + 6 * q^18 - 6 * q^19 - 8 * q^20 - 6 * q^21 + 3 * q^22 - 12 * q^23 + 6 * q^24 - 4 * q^25 - 13 * q^26 + 6 * q^27 - 6 * q^28 - 7 * q^29 - 8 * q^30 - 17 * q^31 + 6 * q^32 + 3 * q^33 - 5 * q^34 - 5 * q^35 + 6 * q^36 - 15 * q^37 - 6 * q^38 - 13 * q^39 - 8 * q^40 - 12 * q^41 - 6 * q^42 - 4 * q^43 + 3 * q^44 - 8 * q^45 - 12 * q^46 - 29 * q^47 + 6 * q^48 + 4 * q^49 - 4 * q^50 - 5 * q^51 - 13 * q^52 - 6 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 7 * q^58 + 9 * q^59 - 8 * q^60 - 16 * q^61 - 17 * q^62 - 6 * q^63 + 6 * q^64 + 5 * q^65 + 3 * q^66 - 8 * q^67 - 5 * q^68 - 12 * q^69 - 5 * q^70 - 2 * q^71 + 6 * q^72 - 17 * q^73 - 15 * q^74 - 4 * q^75 - 6 * q^76 - 21 * q^77 - 13 * q^78 - 31 * q^79 - 8 * q^80 + 6 * q^81 - 12 * q^82 - 5 * q^83 - 6 * q^84 - 4 * q^86 - 7 * q^87 + 3 * q^88 - 5 * q^89 - 8 * q^90 + 4 * q^91 - 12 * q^92 - 17 * q^93 - 29 * q^94 + 8 * q^95 + 6 * q^96 + 7 * q^97 + 4 * q^98 + 3 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.709803	−0.317434	−0.158717	−	0.987324i	$-0.550736\pi$
$5$	−0.709803	−0.317434	−0.158717	+	0.987324i	$0.550736\pi$
$6$	1.00000	0.408248
$7$	0.335393	0.126767	0.0633833	−	0.997989i	$-0.479811\pi$
$7$	0.335393	0.126767	0.0633833	+	0.997989i	$0.479811\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.709803	−0.224460
$11$	−1.82920	−0.551524	−0.275762	−	0.961226i	$-0.588930\pi$
$11$	−1.82920	−0.551524	−0.275762	+	0.961226i	$0.588930\pi$
$12$	1.00000	0.288675
$13$	−1.79639	−0.498229	−0.249114	−	0.968474i	$-0.580140\pi$
$13$	−1.79639	−0.498229	−0.249114	+	0.968474i	$0.580140\pi$
$14$	0.335393	0.0896375
$15$	−0.709803	−0.183270
$16$	1.00000	0.250000
$17$	−1.87183	−0.453985	−0.226992	−	0.973897i	$-0.572889\pi$
$17$	−1.87183	−0.453985	−0.226992	+	0.973897i	$0.572889\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−0.709803	−0.158717
$21$	0.335393	0.0731887
$22$	−1.82920	−0.389987
$23$	2.28960	0.477414	0.238707	−	0.971092i	$-0.423276\pi$
$23$	2.28960	0.477414	0.238707	+	0.971092i	$0.423276\pi$
$24$	1.00000	0.204124
$25$	−4.49618	−0.899236
$26$	−1.79639	−0.352301
$27$	1.00000	0.192450
$28$	0.335393	0.0633833
$29$	−5.51807	−1.02468	−0.512340	−	0.858783i	$-0.671221\pi$
$29$	−5.51807	−1.02468	−0.512340	+	0.858783i	$0.671221\pi$
$30$	−0.709803	−0.129592
$31$	−8.89188	−1.59703	−0.798514	−	0.601976i	$-0.794380\pi$
$31$	−8.89188	−1.59703	−0.798514	+	0.601976i	$0.794380\pi$
$32$	1.00000	0.176777
$33$	−1.82920	−0.318423
$34$	−1.87183	−0.321016
$35$	−0.238063	−0.0402400
$36$	1.00000	0.166667
$37$	−3.68230	−0.605367	−0.302684	−	0.953091i	$-0.597883\pi$
$37$	−3.68230	−0.605367	−0.302684	+	0.953091i	$0.597883\pi$
$38$	−1.00000	−0.162221
$39$	−1.79639	−0.287653
$40$	−0.709803	−0.112230
$41$	−4.65583	−0.727119	−0.363559	−	0.931571i	$-0.618439\pi$
$41$	−4.65583	−0.727119	−0.363559	+	0.931571i	$0.618439\pi$
$42$	0.335393	0.0517522
$43$	−5.40625	−0.824445	−0.412223	−	0.911083i	$-0.635247\pi$
$43$	−5.40625	−0.824445	−0.412223	+	0.911083i	$0.635247\pi$
$44$	−1.82920	−0.275762
$45$	−0.709803	−0.105811
$46$	2.28960	0.337583
$47$	−2.35252	−0.343150	−0.171575	−	0.985171i	$-0.554886\pi$
$47$	−2.35252	−0.343150	−0.171575	+	0.985171i	$0.554886\pi$
$48$	1.00000	0.144338
$49$	−6.88751	−0.983930
$50$	−4.49618	−0.635856
$51$	−1.87183	−0.262108
$52$	−1.79639	−0.249114
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	1.29837	0.175072
$56$	0.335393	0.0448188
$57$	−1.00000	−0.132453
$58$	−5.51807	−0.724558
$59$	−7.36599	−0.958971	−0.479485	−	0.877550i	$-0.659177\pi$
$59$	−7.36599	−0.958971	−0.479485	+	0.877550i	$0.659177\pi$
$60$	−0.709803	−0.0916352
$61$	14.9287	1.91142	0.955710	−	0.294311i	$-0.0950903\pi$
$61$	14.9287	1.91142	0.955710	+	0.294311i	$0.0950903\pi$
$62$	−8.89188	−1.12927
$63$	0.335393	0.0422555
$64$	1.00000	0.125000
$65$	1.27508	0.158155
$66$	−1.82920	−0.225159
$67$	13.8012	1.68609	0.843045	−	0.537842i	$-0.180760\pi$
$67$	13.8012	1.68609	0.843045	+	0.537842i	$0.180760\pi$
$68$	−1.87183	−0.226992
$69$	2.28960	0.275635
$70$	−0.238063	−0.0284540
$71$	−5.26505	−0.624847	−0.312423	−	0.949943i	$-0.601141\pi$
$71$	−5.26505	−0.624847	−0.312423	+	0.949943i	$0.601141\pi$
$72$	1.00000	0.117851
$73$	−0.853957	−0.0999481	−0.0499741	−	0.998751i	$-0.515914\pi$
$73$	−0.853957	−0.0999481	−0.0499741	+	0.998751i	$0.515914\pi$
$74$	−3.68230	−0.428059
$75$	−4.49618	−0.519174
$76$	−1.00000	−0.114708
$77$	−0.613500	−0.0699149
$78$	−1.79639	−0.203401
$79$	6.28178	0.706755	0.353378	−	0.935481i	$-0.385033\pi$
$79$	6.28178	0.706755	0.353378	+	0.935481i	$0.385033\pi$
$80$	−0.709803	−0.0793584
$81$	1.00000	0.111111
$82$	−4.65583	−0.514151
$83$	5.74077	0.630132	0.315066	−	0.949070i	$-0.397973\pi$
$83$	5.74077	0.630132	0.315066	+	0.949070i	$0.397973\pi$
$84$	0.335393	0.0365944
$85$	1.32863	0.144110
$86$	−5.40625	−0.582971
$87$	−5.51807	−0.591599
$88$	−1.82920	−0.194993
$89$	7.74438	0.820903	0.410452	−	0.911882i	$-0.365371\pi$
$89$	7.74438	0.820903	0.410452	+	0.911882i	$0.365371\pi$
$90$	−0.709803	−0.0748199
$91$	−0.602496	−0.0631588
$92$	2.28960	0.238707
$93$	−8.89188	−0.922045
$94$	−2.35252	−0.242644
$95$	0.709803	0.0728243
$96$	1.00000	0.102062
$97$	18.1735	1.84524	0.922619	−	0.385713i	$-0.126044\pi$
$97$	18.1735	1.84524	0.922619	+	0.385713i	$0.126044\pi$
$98$	−6.88751	−0.695744
$99$	−1.82920	−0.183841
$100$	−4.49618	−0.449618
$101$	9.30033	0.925417	0.462709	−	0.886510i	$-0.346878\pi$
$101$	9.30033	0.925417	0.462709	+	0.886510i	$0.346878\pi$
$102$	−1.87183	−0.185339
$103$	−15.2452	−1.50216	−0.751078	−	0.660213i	$-0.770466\pi$
$103$	−15.2452	−1.50216	−0.751078	+	0.660213i	$0.770466\pi$
$104$	−1.79639	−0.176151
$105$	−0.238063	−0.0232326
$106$	−1.00000	−0.0971286
$107$	4.43826	0.429063	0.214532	−	0.976717i	$-0.431178\pi$
$107$	4.43826	0.429063	0.214532	+	0.976717i	$0.431178\pi$
$108$	1.00000	0.0962250
$109$	−19.0575	−1.82537	−0.912687	−	0.408660i	$-0.865996\pi$
$109$	−19.0575	−1.82537	−0.912687	+	0.408660i	$0.865996\pi$
$110$	1.29837	0.123795
$111$	−3.68230	−0.349509
$112$	0.335393	0.0316916
$113$	2.94663	0.277195	0.138598	−	0.990349i	$-0.455740\pi$
$113$	2.94663	0.277195	0.138598	+	0.990349i	$0.455740\pi$
$114$	−1.00000	−0.0936586
$115$	−1.62516	−0.151547
$116$	−5.51807	−0.512340
$117$	−1.79639	−0.166076
$118$	−7.36599	−0.678095
$119$	−0.627798	−0.0575501
$120$	−0.709803	−0.0647959
$121$	−7.65403	−0.695821
$122$	14.9287	1.35158
$123$	−4.65583	−0.419802
$124$	−8.89188	−0.798514
$125$	6.74042	0.602882
$126$	0.335393	0.0298792
$127$	1.11738	0.0991517	0.0495758	−	0.998770i	$-0.484213\pi$
$127$	1.11738	0.0991517	0.0495758	+	0.998770i	$0.484213\pi$
$128$	1.00000	0.0883883
$129$	−5.40625	−0.475994
$130$	1.27508	0.111832
$131$	−15.5092	−1.35504	−0.677521	−	0.735504i	$-0.736946\pi$
$131$	−15.5092	−1.35504	−0.677521	+	0.735504i	$0.736946\pi$
$132$	−1.82920	−0.159211
$133$	−0.335393	−0.0290823
$134$	13.8012	1.19225
$135$	−0.709803	−0.0610902
$136$	−1.87183	−0.160508
$137$	11.3495	0.969656	0.484828	−	0.874609i	$-0.338882\pi$
$137$	11.3495	0.969656	0.484828	+	0.874609i	$0.338882\pi$
$138$	2.28960	0.194903
$139$	−16.8602	−1.43006	−0.715030	−	0.699094i	$-0.753587\pi$
$139$	−16.8602	−1.43006	−0.715030	+	0.699094i	$0.753587\pi$
$140$	−0.238063	−0.0201200
$141$	−2.35252	−0.198118
$142$	−5.26505	−0.441833
$143$	3.28596	0.274785
$144$	1.00000	0.0833333
$145$	3.91675	0.325268
$146$	−0.853957	−0.0706740
$147$	−6.88751	−0.568072
$148$	−3.68230	−0.302684
$149$	−4.91772	−0.402875	−0.201437	−	0.979501i	$-0.564561\pi$
$149$	−4.91772	−0.402875	−0.201437	+	0.979501i	$0.564561\pi$
$150$	−4.49618	−0.367111
$151$	−4.72465	−0.384487	−0.192243	−	0.981347i	$-0.561576\pi$
$151$	−4.72465	−0.384487	−0.192243	+	0.981347i	$0.561576\pi$
$152$	−1.00000	−0.0811107
$153$	−1.87183	−0.151328
$154$	−0.613500	−0.0494373
$155$	6.31149	0.506951
$156$	−1.79639	−0.143826
$157$	−5.22293	−0.416836	−0.208418	−	0.978040i	$-0.566831\pi$
$157$	−5.22293	−0.416836	−0.208418	+	0.978040i	$0.566831\pi$
$158$	6.28178	0.499752
$159$	−1.00000	−0.0793052
$160$	−0.709803	−0.0561149
$161$	0.767914	0.0605201
$162$	1.00000	0.0785674
$163$	−4.22906	−0.331245	−0.165623	−	0.986189i	$-0.552963\pi$
$163$	−4.22906	−0.331245	−0.165623	+	0.986189i	$0.552963\pi$
$164$	−4.65583	−0.363559
$165$	1.29837	0.101078
$166$	5.74077	0.445570
$167$	−6.61090	−0.511567	−0.255784	−	0.966734i	$-0.582333\pi$
$167$	−6.61090	−0.511567	−0.255784	+	0.966734i	$0.582333\pi$
$168$	0.335393	0.0258761
$169$	−9.77298	−0.751768
$170$	1.32863	0.101901
$171$	−1.00000	−0.0764719
$172$	−5.40625	−0.412223
$173$	−0.306886	−0.0233321	−0.0116660	−	0.999932i	$-0.503714\pi$
$173$	−0.306886	−0.0233321	−0.0116660	+	0.999932i	$0.503714\pi$
$174$	−5.51807	−0.418324
$175$	−1.50799	−0.113993
$176$	−1.82920	−0.137881
$177$	−7.36599	−0.553662
$178$	7.74438	0.580466
$179$	18.8224	1.40685	0.703425	−	0.710769i	$-0.251653\pi$
$179$	18.8224	1.40685	0.703425	+	0.710769i	$0.251653\pi$
$180$	−0.709803	−0.0529056
$181$	−11.6919	−0.869050	−0.434525	−	0.900660i	$-0.643084\pi$
$181$	−11.6919	−0.869050	−0.434525	+	0.900660i	$0.643084\pi$
$182$	−0.602496	−0.0446600
$183$	14.9287	1.10356
$184$	2.28960	0.168791
$185$	2.61371	0.192164
$186$	−8.89188	−0.651984
$187$	3.42395	0.250384
$188$	−2.35252	−0.171575
$189$	0.335393	0.0243962
$190$	0.709803	0.0514946
$191$	−11.2036	−0.810666	−0.405333	−	0.914169i	$-0.632844\pi$
$191$	−11.2036	−0.810666	−0.405333	+	0.914169i	$0.632844\pi$
$192$	1.00000	0.0721688
$193$	7.34308	0.528566	0.264283	−	0.964445i	$-0.414865\pi$
$193$	7.34308	0.528566	0.264283	+	0.964445i	$0.414865\pi$
$194$	18.1735	1.30478
$195$	1.27508	0.0913107
$196$	−6.88751	−0.491965
$197$	−19.8966	−1.41757	−0.708786	−	0.705423i	$-0.750757\pi$
$197$	−19.8966	−1.41757	−0.708786	+	0.705423i	$0.750757\pi$
$198$	−1.82920	−0.129996
$199$	5.90613	0.418674	0.209337	−	0.977844i	$-0.432869\pi$
$199$	5.90613	0.418674	0.209337	+	0.977844i	$0.432869\pi$
$200$	−4.49618	−0.317928
$201$	13.8012	0.973465
$202$	9.30033	0.654369
$203$	−1.85072	−0.129895
$204$	−1.87183	−0.131054
$205$	3.30473	0.230812
$206$	−15.2452	−1.06219
$207$	2.28960	0.159138
$208$	−1.79639	−0.124557
$209$	1.82920	0.126528
$210$	−0.238063	−0.0164279
$211$	−0.474220	−0.0326467	−0.0163233	−	0.999867i	$-0.505196\pi$
$211$	−0.474220	−0.0326467	−0.0163233	+	0.999867i	$0.505196\pi$
$212$	−1.00000	−0.0686803
$213$	−5.26505	−0.360755
$214$	4.43826	0.303393
$215$	3.83737	0.261707
$216$	1.00000	0.0680414
$217$	−2.98227	−0.202450
$218$	−19.0575	−1.29073
$219$	−0.853957	−0.0577051
$220$	1.29837	0.0875362
$221$	3.36253	0.226188
$222$	−3.68230	−0.247140
$223$	9.20078	0.616130	0.308065	−	0.951365i	$-0.400319\pi$
$223$	9.20078	0.616130	0.308065	+	0.951365i	$0.400319\pi$
$224$	0.335393	0.0224094
$225$	−4.49618	−0.299745
$226$	2.94663	0.196007
$227$	−6.61163	−0.438829	−0.219415	−	0.975632i	$-0.570415\pi$
$227$	−6.61163	−0.438829	−0.219415	+	0.975632i	$0.570415\pi$
$228$	−1.00000	−0.0662266
$229$	4.23491	0.279850	0.139925	−	0.990162i	$-0.455314\pi$
$229$	4.23491	0.279850	0.139925	+	0.990162i	$0.455314\pi$
$230$	−1.62516	−0.107160
$231$	−0.613500	−0.0403654
$232$	−5.51807	−0.362279
$233$	−0.175472	−0.0114956	−0.00574779	−	0.999983i	$-0.501830\pi$
$233$	−0.175472	−0.0114956	−0.00574779	+	0.999983i	$0.501830\pi$
$234$	−1.79639	−0.117434
$235$	1.66983	0.108927
$236$	−7.36599	−0.479485
$237$	6.28178	0.408045
$238$	−0.627798	−0.0406941
$239$	8.56302	0.553896	0.276948	−	0.960885i	$-0.410677\pi$
$239$	8.56302	0.553896	0.276948	+	0.960885i	$0.410677\pi$
$240$	−0.709803	−0.0458176
$241$	−18.7941	−1.21064	−0.605318	−	0.795983i	$-0.706954\pi$
$241$	−18.7941	−1.21064	−0.605318	+	0.795983i	$0.706954\pi$
$242$	−7.65403	−0.492020
$243$	1.00000	0.0641500
$244$	14.9287	0.955710
$245$	4.88878	0.312333
$246$	−4.65583	−0.296845
$247$	1.79639	0.114302
$248$	−8.89188	−0.564635
$249$	5.74077	0.363807
$250$	6.74042	0.426302
$251$	4.24907	0.268199	0.134100	−	0.990968i	$-0.457186\pi$
$251$	4.24907	0.268199	0.134100	+	0.990968i	$0.457186\pi$
$252$	0.335393	0.0211278
$253$	−4.18813	−0.263305
$254$	1.11738	0.0701108
$255$	1.32863	0.0832020
$256$	1.00000	0.0625000
$257$	−6.34627	−0.395870	−0.197935	−	0.980215i	$-0.563423\pi$
$257$	−6.34627	−0.395870	−0.197935	+	0.980215i	$0.563423\pi$
$258$	−5.40625	−0.336578
$259$	−1.23502	−0.0767403
$260$	1.27508	0.0790773
$261$	−5.51807	−0.341560
$262$	−15.5092	−0.958159
$263$	1.49064	0.0919167	0.0459583	−	0.998943i	$-0.485366\pi$
$263$	1.49064	0.0919167	0.0459583	+	0.998943i	$0.485366\pi$
$264$	−1.82920	−0.112579
$265$	0.709803	0.0436029
$266$	−0.335393	−0.0205643
$267$	7.74438	0.473949
$268$	13.8012	0.843045
$269$	20.8588	1.27179	0.635893	−	0.771777i	$-0.280632\pi$
$269$	20.8588	1.27179	0.635893	+	0.771777i	$0.280632\pi$
$270$	−0.709803	−0.0431973
$271$	15.2680	0.927468	0.463734	−	0.885975i	$-0.346509\pi$
$271$	15.2680	0.927468	0.463734	+	0.885975i	$0.346509\pi$
$272$	−1.87183	−0.113496
$273$	−0.602496	−0.0364647
$274$	11.3495	0.685651
$275$	8.22441	0.495950
$276$	2.28960	0.137817
$277$	−5.97836	−0.359205	−0.179602	−	0.983739i	$-0.557481\pi$
$277$	−5.97836	−0.359205	−0.179602	+	0.983739i	$0.557481\pi$
$278$	−16.8602	−1.01121
$279$	−8.89188	−0.532343
$280$	−0.238063	−0.0142270
$281$	3.10450	0.185199	0.0925994	−	0.995703i	$-0.470482\pi$
$281$	3.10450	0.185199	0.0925994	+	0.995703i	$0.470482\pi$
$282$	−2.35252	−0.140090
$283$	−8.07228	−0.479847	−0.239924	−	0.970792i	$-0.577122\pi$
$283$	−8.07228	−0.479847	−0.239924	+	0.970792i	$0.577122\pi$
$284$	−5.26505	−0.312423
$285$	0.709803	0.0420451
$286$	3.28596	0.194303
$287$	−1.56153	−0.0921744
$288$	1.00000	0.0589256
$289$	−13.4963	−0.793898
$290$	3.91675	0.229999
$291$	18.1735	1.06535
$292$	−0.853957	−0.0499741
$293$	22.3014	1.30286	0.651431	−	0.758708i	$-0.274169\pi$
$293$	22.3014	1.30286	0.651431	+	0.758708i	$0.274169\pi$
$294$	−6.88751	−0.401688
$295$	5.22841	0.304410
$296$	−3.68230	−0.214030
$297$	−1.82920	−0.106141
$298$	−4.91772	−0.284876
$299$	−4.11301	−0.237861
$300$	−4.49618	−0.259587
$301$	−1.81322	−0.104512
$302$	−4.72465	−0.271873
$303$	9.30033	0.534290
$304$	−1.00000	−0.0573539
$305$	−10.5964	−0.606749
$306$	−1.87183	−0.107005
$307$	−19.1655	−1.09383	−0.546916	−	0.837188i	$-0.684198\pi$
$307$	−19.1655	−1.09383	−0.546916	+	0.837188i	$0.684198\pi$
$308$	−0.613500	−0.0349574
$309$	−15.2452	−0.867270
$310$	6.31149	0.358468
$311$	6.04777	0.342937	0.171469	−	0.985190i	$-0.445149\pi$
$311$	6.04777	0.342937	0.171469	+	0.985190i	$0.445149\pi$
$312$	−1.79639	−0.101701
$313$	5.59485	0.316240	0.158120	−	0.987420i	$-0.449457\pi$
$313$	5.59485	0.316240	0.158120	+	0.987420i	$0.449457\pi$
$314$	−5.22293	−0.294747
$315$	−0.238063	−0.0134133
$316$	6.28178	0.353378
$317$	9.01084	0.506099	0.253050	−	0.967453i	$-0.418566\pi$
$317$	9.01084	0.506099	0.253050	+	0.967453i	$0.418566\pi$
$318$	−1.00000	−0.0560772
$319$	10.0937	0.565136
$320$	−0.709803	−0.0396792
$321$	4.43826	0.247720
$322$	0.767914	0.0427942
$323$	1.87183	0.104151
$324$	1.00000	0.0555556
$325$	8.07689	0.448025
$326$	−4.22906	−0.234226
$327$	−19.0575	−1.05388
$328$	−4.65583	−0.257075
$329$	−0.789018	−0.0435000
$330$	1.29837	0.0714730
$331$	5.47570	0.300972	0.150486	−	0.988612i	$-0.451916\pi$
$331$	5.47570	0.300972	0.150486	+	0.988612i	$0.451916\pi$
$332$	5.74077	0.315066
$333$	−3.68230	−0.201789
$334$	−6.61090	−0.361733
$335$	−9.79617	−0.535222
$336$	0.335393	0.0182972
$337$	33.8886	1.84603	0.923014	−	0.384766i	$-0.125718\pi$
$337$	33.8886	1.84603	0.923014	+	0.384766i	$0.125718\pi$
$338$	−9.77298	−0.531580
$339$	2.94663	0.160039
$340$	1.32863	0.0720551
$341$	16.2650	0.880800
$342$	−1.00000	−0.0540738
$343$	−4.65777	−0.251496
$344$	−5.40625	−0.291485
$345$	−1.62516	−0.0874958
$346$	−0.306886	−0.0164983
$347$	−15.5892	−0.836873	−0.418436	−	0.908246i	$-0.637422\pi$
$347$	−15.5892	−0.836873	−0.418436	+	0.908246i	$0.637422\pi$
$348$	−5.51807	−0.295800
$349$	−26.9374	−1.44193	−0.720963	−	0.692974i	$-0.756300\pi$
$349$	−26.9374	−1.44193	−0.720963	+	0.692974i	$0.756300\pi$
$350$	−1.50799	−0.0806053
$351$	−1.79639	−0.0958842
$352$	−1.82920	−0.0974967
$353$	−13.8313	−0.736167	−0.368083	−	0.929793i	$-0.619986\pi$
$353$	−13.8313	−0.736167	−0.368083	+	0.929793i	$0.619986\pi$
$354$	−7.36599	−0.391498
$355$	3.73715	0.198347
$356$	7.74438	0.410452
$357$	−0.627798	−0.0332266
$358$	18.8224	0.994794
$359$	27.8267	1.46864	0.734318	−	0.678806i	$-0.237502\pi$
$359$	27.8267	1.46864	0.734318	+	0.678806i	$0.237502\pi$
$360$	−0.709803	−0.0374099
$361$	1.00000	0.0526316
$362$	−11.6919	−0.614511
$363$	−7.65403	−0.401732
$364$	−0.602496	−0.0315794
$365$	0.606142	0.0317269
$366$	14.9287	0.780334
$367$	−10.6055	−0.553602	−0.276801	−	0.960927i	$-0.589274\pi$
$367$	−10.6055	−0.553602	−0.276801	+	0.960927i	$0.589274\pi$
$368$	2.28960	0.119353
$369$	−4.65583	−0.242373
$370$	2.61371	0.135880
$371$	−0.335393	−0.0174127
$372$	−8.89188	−0.461023
$373$	20.6051	1.06689	0.533445	−	0.845835i	$-0.320897\pi$
$373$	20.6051	1.06689	0.533445	+	0.845835i	$0.320897\pi$
$374$	3.42395	0.177048
$375$	6.74042	0.348074
$376$	−2.35252	−0.121322
$377$	9.91261	0.510525
$378$	0.335393	0.0172507
$379$	−26.0897	−1.34014	−0.670069	−	0.742299i	$-0.733735\pi$
$379$	−26.0897	−1.34014	−0.670069	+	0.742299i	$0.733735\pi$
$380$	0.709803	0.0364121
$381$	1.11738	0.0572453
$382$	−11.2036	−0.573227
$383$	29.8832	1.52696	0.763480	−	0.645831i	$-0.223489\pi$
$383$	29.8832	1.52696	0.763480	+	0.645831i	$0.223489\pi$
$384$	1.00000	0.0510310
$385$	0.435465	0.0221933
$386$	7.34308	0.373753
$387$	−5.40625	−0.274815
$388$	18.1735	0.922619
$389$	10.9287	0.554106	0.277053	−	0.960855i	$-0.410642\pi$
$389$	10.9287	0.554106	0.277053	+	0.960855i	$0.410642\pi$
$390$	1.27508	0.0645664
$391$	−4.28573	−0.216739
$392$	−6.88751	−0.347872
$393$	−15.5092	−0.782334
$394$	−19.8966	−1.00237
$395$	−4.45883	−0.224348
$396$	−1.82920	−0.0919207
$397$	12.9723	0.651062	0.325531	−	0.945531i	$-0.394457\pi$
$397$	12.9723	0.651062	0.325531	+	0.945531i	$0.394457\pi$
$398$	5.90613	0.296047
$399$	−0.335393	−0.0167906
$400$	−4.49618	−0.224809
$401$	14.0412	0.701183	0.350592	−	0.936528i	$-0.385981\pi$
$401$	14.0412	0.701183	0.350592	+	0.936528i	$0.385981\pi$
$402$	13.8012	0.688344
$403$	15.9733	0.795686
$404$	9.30033	0.462709
$405$	−0.709803	−0.0352704
$406$	−1.85072	−0.0918498
$407$	6.73567	0.333875
$408$	−1.87183	−0.0926693
$409$	−27.1033	−1.34017	−0.670086	−	0.742284i	$-0.733743\pi$
$409$	−27.1033	−1.34017	−0.670086	+	0.742284i	$0.733743\pi$
$410$	3.30473	0.163209
$411$	11.3495	0.559831
$412$	−15.2452	−0.751078
$413$	−2.47050	−0.121565
$414$	2.28960	0.112528
$415$	−4.07482	−0.200025
$416$	−1.79639	−0.0880753
$417$	−16.8602	−0.825646
$418$	1.82920	0.0894691
$419$	−3.12380	−0.152608	−0.0763039	−	0.997085i	$-0.524312\pi$
$419$	−3.12380	−0.152608	−0.0763039	+	0.997085i	$0.524312\pi$
$420$	−0.238063	−0.0116163
$421$	−40.2226	−1.96033	−0.980164	−	0.198186i	$-0.936495\pi$
$421$	−40.2226	−1.96033	−0.980164	+	0.198186i	$0.936495\pi$
$422$	−0.474220	−0.0230847
$423$	−2.35252	−0.114383
$424$	−1.00000	−0.0485643
$425$	8.41607	0.408240
$426$	−5.26505	−0.255093
$427$	5.00697	0.242304
$428$	4.43826	0.214532
$429$	3.28596	0.158647
$430$	3.83737	0.185055
$431$	−0.635594	−0.0306155	−0.0153077	−	0.999883i	$-0.504873\pi$
$431$	−0.635594	−0.0306155	−0.0153077	+	0.999883i	$0.504873\pi$
$432$	1.00000	0.0481125
$433$	−8.90063	−0.427737	−0.213868	−	0.976862i	$-0.568606\pi$
$433$	−8.90063	−0.427737	−0.213868	+	0.976862i	$0.568606\pi$
$434$	−2.98227	−0.143154
$435$	3.91675	0.187794
$436$	−19.0575	−0.912687
$437$	−2.28960	−0.109526
$438$	−0.853957	−0.0408036
$439$	1.53473	0.0732488	0.0366244	−	0.999329i	$-0.488339\pi$
$439$	1.53473	0.0732488	0.0366244	+	0.999329i	$0.488339\pi$
$440$	1.29837	0.0618975
$441$	−6.88751	−0.327977
$442$	3.36253	0.159939
$443$	−6.01214	−0.285645	−0.142823	−	0.989748i	$-0.545618\pi$
$443$	−6.01214	−0.285645	−0.142823	+	0.989748i	$0.545618\pi$
$444$	−3.68230	−0.174754
$445$	−5.49699	−0.260582
$446$	9.20078	0.435670
$447$	−4.91772	−0.232600
$448$	0.335393	0.0158458
$449$	13.0869	0.617609	0.308804	−	0.951126i	$-0.400071\pi$
$449$	13.0869	0.617609	0.308804	+	0.951126i	$0.400071\pi$
$450$	−4.49618	−0.211952
$451$	8.51644	0.401024
$452$	2.94663	0.138598
$453$	−4.72465	−0.221984
$454$	−6.61163	−0.310299
$455$	0.427654	0.0200487
$456$	−1.00000	−0.0468293
$457$	16.2792	0.761508	0.380754	−	0.924676i	$-0.375664\pi$
$457$	16.2792	0.761508	0.380754	+	0.924676i	$0.375664\pi$
$458$	4.23491	0.197884
$459$	−1.87183	−0.0873694
$460$	−1.62516	−0.0757736
$461$	−32.0630	−1.49332	−0.746661	−	0.665205i	$-0.768344\pi$
$461$	−32.0630	−1.49332	−0.746661	+	0.665205i	$0.768344\pi$
$462$	−0.613500	−0.0285426
$463$	36.8701	1.71350	0.856749	−	0.515733i	$-0.172481\pi$
$463$	36.8701	1.71350	0.856749	+	0.515733i	$0.172481\pi$
$464$	−5.51807	−0.256170
$465$	6.31149	0.292688
$466$	−0.175472	−0.00812860
$467$	−24.2682	−1.12300	−0.561499	−	0.827477i	$-0.689775\pi$
$467$	−24.2682	−1.12300	−0.561499	+	0.827477i	$0.689775\pi$
$468$	−1.79639	−0.0830382
$469$	4.62884	0.213740
$470$	1.66983	0.0770233
$471$	−5.22293	−0.240660
$472$	−7.36599	−0.339047
$473$	9.88911	0.454702
$474$	6.28178	0.288532
$475$	4.49618	0.206299
$476$	−0.627798	−0.0287751
$477$	−1.00000	−0.0457869
$478$	8.56302	0.391663
$479$	−24.4097	−1.11531	−0.557653	−	0.830074i	$-0.688298\pi$
$479$	−24.4097	−1.11531	−0.557653	+	0.830074i	$0.688298\pi$
$480$	−0.709803	−0.0323979
$481$	6.61485	0.301611
$482$	−18.7941	−0.856049
$483$	0.767914	0.0349413
$484$	−7.65403	−0.347910
$485$	−12.8996	−0.585741
$486$	1.00000	0.0453609
$487$	−28.4709	−1.29014	−0.645069	−	0.764124i	$-0.723171\pi$
$487$	−28.4709	−1.29014	−0.645069	+	0.764124i	$0.723171\pi$
$488$	14.9287	0.675789
$489$	−4.22906	−0.191245
$490$	4.88878	0.220853
$491$	10.2696	0.463460	0.231730	−	0.972780i	$-0.425561\pi$
$491$	10.2696	0.463460	0.231730	+	0.972780i	$0.425561\pi$
$492$	−4.65583	−0.209901
$493$	10.3289	0.465189
$494$	1.79639	0.0808234
$495$	1.29837	0.0583575
$496$	−8.89188	−0.399257
$497$	−1.76586	−0.0792097
$498$	5.74077	0.257250
$499$	10.4507	0.467836	0.233918	−	0.972256i	$-0.424845\pi$
$499$	10.4507	0.467836	0.233918	+	0.972256i	$0.424845\pi$
$500$	6.74042	0.301441
$501$	−6.61090	−0.295353
$502$	4.24907	0.189645
$503$	1.50999	0.0673271	0.0336636	−	0.999433i	$-0.489283\pi$
$503$	1.50999	0.0673271	0.0336636	+	0.999433i	$0.489283\pi$
$504$	0.335393	0.0149396
$505$	−6.60141	−0.293759
$506$	−4.18813	−0.186185
$507$	−9.77298	−0.434033
$508$	1.11738	0.0495758
$509$	12.1430	0.538228	0.269114	−	0.963108i	$-0.413269\pi$
$509$	12.1430	0.538228	0.269114	+	0.963108i	$0.413269\pi$
$510$	1.32863	0.0588327
$511$	−0.286411	−0.0126701
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	−6.34627	−0.279922
$515$	10.8211	0.476835
$516$	−5.40625	−0.237997
$517$	4.30323	0.189256
$518$	−1.23502	−0.0542636
$519$	−0.306886	−0.0134708
$520$	1.27508	0.0559161
$521$	−12.4233	−0.544275	−0.272137	−	0.962258i	$-0.587731\pi$
$521$	−12.4233	−0.544275	−0.272137	+	0.962258i	$0.587731\pi$
$522$	−5.51807	−0.241519
$523$	−7.03352	−0.307554	−0.153777	−	0.988106i	$-0.549144\pi$
$523$	−7.03352	−0.307554	−0.153777	+	0.988106i	$0.549144\pi$
$524$	−15.5092	−0.677521
$525$	−1.50799	−0.0658139
$526$	1.49064	0.0649949
$527$	16.6441	0.725027
$528$	−1.82920	−0.0796057
$529$	−17.7577	−0.772076
$530$	0.709803	0.0308319
$531$	−7.36599	−0.319657
$532$	−0.335393	−0.0145411
$533$	8.36369	0.362272
$534$	7.74438	0.335132
$535$	−3.15029	−0.136199
$536$	13.8012	0.596123
$537$	18.8224	0.812246
$538$	20.8588	0.899289
$539$	12.5986	0.542662
$540$	−0.709803	−0.0305451
$541$	−1.72153	−0.0740143	−0.0370071	−	0.999315i	$-0.511782\pi$
$541$	−1.72153	−0.0740143	−0.0370071	+	0.999315i	$0.511782\pi$
$542$	15.2680	0.655819
$543$	−11.6919	−0.501746
$544$	−1.87183	−0.0802540
$545$	13.5270	0.579435
$546$	−0.602496	−0.0257845
$547$	12.1974	0.521525	0.260762	−	0.965403i	$-0.416026\pi$
$547$	12.1974	0.521525	0.260762	+	0.965403i	$0.416026\pi$
$548$	11.3495	0.484828
$549$	14.9287	0.637140
$550$	8.22441	0.350690
$551$	5.51807	0.235078
$552$	2.28960	0.0974517
$553$	2.10686	0.0895930
$554$	−5.97836	−0.253996
$555$	2.61371	0.110946
$556$	−16.8602	−0.715030
$557$	12.5913	0.533510	0.266755	−	0.963764i	$-0.414049\pi$
$557$	12.5913	0.533510	0.266755	+	0.963764i	$0.414049\pi$
$558$	−8.89188	−0.376423
$559$	9.71173	0.410763
$560$	−0.238063	−0.0100600
$561$	3.42395	0.144559
$562$	3.10450	0.130955
$563$	27.6123	1.16372	0.581860	−	0.813289i	$-0.302325\pi$
$563$	27.6123	1.16372	0.581860	+	0.813289i	$0.302325\pi$
$564$	−2.35252	−0.0990589
$565$	−2.09153	−0.0879912
$566$	−8.07228	−0.339303
$567$	0.335393	0.0140852
$568$	−5.26505	−0.220917
$569$	−7.80711	−0.327291	−0.163646	−	0.986519i	$-0.552325\pi$
$569$	−7.80711	−0.327291	−0.163646	+	0.986519i	$0.552325\pi$
$570$	0.709803	0.0297304
$571$	22.1183	0.925621	0.462811	−	0.886457i	$-0.346841\pi$
$571$	22.1183	0.925621	0.462811	+	0.886457i	$0.346841\pi$
$572$	3.28596	0.137393
$573$	−11.2036	−0.468038
$574$	−1.56153	−0.0651771
$575$	−10.2944	−0.429308
$576$	1.00000	0.0416667
$577$	−7.86917	−0.327598	−0.163799	−	0.986494i	$-0.552375\pi$
$577$	−7.86917	−0.327598	−0.163799	+	0.986494i	$0.552375\pi$
$578$	−13.4963	−0.561370
$579$	7.34308	0.305168
$580$	3.91675	0.162634
$581$	1.92541	0.0798797
$582$	18.1735	0.753315
$583$	1.82920	0.0757577
$584$	−0.853957	−0.0353370
$585$	1.27508	0.0527182
$586$	22.3014	0.921262
$587$	46.8965	1.93563	0.967813	−	0.251670i	$-0.0809797\pi$
$587$	46.8965	1.93563	0.967813	+	0.251670i	$0.0809797\pi$
$588$	−6.88751	−0.284036
$589$	8.89188	0.366384
$590$	5.22841	0.215250
$591$	−19.8966	−0.818436
$592$	−3.68230	−0.151342
$593$	−14.0945	−0.578791	−0.289396	−	0.957210i	$-0.593454\pi$
$593$	−14.0945	−0.578791	−0.289396	+	0.957210i	$0.593454\pi$
$594$	−1.82920	−0.0750530
$595$	0.445613	0.0182684
$596$	−4.91772	−0.201437
$597$	5.90613	0.241722
$598$	−4.11301	−0.168193
$599$	−36.4361	−1.48874	−0.744370	−	0.667768i	$-0.767250\pi$
$599$	−36.4361	−1.48874	−0.744370	+	0.667768i	$0.767250\pi$
$600$	−4.49618	−0.183556
$601$	30.0432	1.22549	0.612744	−	0.790281i	$-0.290066\pi$
$601$	30.0432	1.22549	0.612744	+	0.790281i	$0.290066\pi$
$602$	−1.81322	−0.0739012
$603$	13.8012	0.562030
$604$	−4.72465	−0.192243
$605$	5.43286	0.220877
$606$	9.30033	0.377800
$607$	10.6341	0.431627	0.215813	−	0.976435i	$-0.430760\pi$
$607$	10.6341	0.431627	0.215813	+	0.976435i	$0.430760\pi$
$608$	−1.00000	−0.0405554
$609$	−1.85072	−0.0749950
$610$	−10.5964	−0.429036
$611$	4.22604	0.170967
$612$	−1.87183	−0.0756642
$613$	−7.85895	−0.317420	−0.158710	−	0.987325i	$-0.550733\pi$
$613$	−7.85895	−0.317420	−0.158710	+	0.987325i	$0.550733\pi$
$614$	−19.1655	−0.773456
$615$	3.30473	0.133259
$616$	−0.613500	−0.0247186
$617$	1.01209	0.0407453	0.0203726	−	0.999792i	$-0.493515\pi$
$617$	1.01209	0.0407453	0.0203726	+	0.999792i	$0.493515\pi$
$618$	−15.2452	−0.613253
$619$	−8.88095	−0.356956	−0.178478	−	0.983944i	$-0.557117\pi$
$619$	−8.88095	−0.356956	−0.178478	+	0.983944i	$0.557117\pi$
$620$	6.31149	0.253475
$621$	2.28960	0.0918783
$622$	6.04777	0.242493
$623$	2.59741	0.104063
$624$	−1.79639	−0.0719132
$625$	17.6965	0.707861
$626$	5.59485	0.223615
$627$	1.82920	0.0730512
$628$	−5.22293	−0.208418
$629$	6.89264	0.274828
$630$	−0.238063	−0.00948466
$631$	19.3139	0.768873	0.384436	−	0.923151i	$-0.374396\pi$
$631$	19.3139	0.768873	0.384436	+	0.923151i	$0.374396\pi$
$632$	6.28178	0.249876
$633$	−0.474220	−0.0188486
$634$	9.01084	0.357866
$635$	−0.793122	−0.0314741
$636$	−1.00000	−0.0396526
$637$	12.3727	0.490223
$638$	10.0937	0.399612
$639$	−5.26505	−0.208282
$640$	−0.709803	−0.0280574
$641$	−6.45009	−0.254763	−0.127382	−	0.991854i	$-0.540657\pi$
$641$	−6.45009	−0.254763	−0.127382	+	0.991854i	$0.540657\pi$
$642$	4.43826	0.175164
$643$	−4.56471	−0.180015	−0.0900074	−	0.995941i	$-0.528689\pi$
$643$	−4.56471	−0.180015	−0.0900074	+	0.995941i	$0.528689\pi$
$644$	0.767914	0.0302601
$645$	3.83737	0.151096
$646$	1.87183	0.0736461
$647$	−32.1326	−1.26326	−0.631631	−	0.775269i	$-0.717614\pi$
$647$	−32.1326	−1.26326	−0.631631	+	0.775269i	$0.717614\pi$
$648$	1.00000	0.0392837
$649$	13.4739	0.528896
$650$	8.07689	0.316802
$651$	−2.98227	−0.116885
$652$	−4.22906	−0.165623
$653$	10.7163	0.419362	0.209681	−	0.977770i	$-0.432757\pi$
$653$	10.7163	0.419362	0.209681	+	0.977770i	$0.432757\pi$
$654$	−19.0575	−0.745205
$655$	11.0085	0.430136
$656$	−4.65583	−0.181780
$657$	−0.853957	−0.0333160
$658$	−0.789018	−0.0307591
$659$	40.3413	1.57147	0.785737	−	0.618561i	$-0.212284\pi$
$659$	40.3413	1.57147	0.785737	+	0.618561i	$0.212284\pi$
$660$	1.29837	0.0505391
$661$	−21.3912	−0.832021	−0.416010	−	0.909360i	$-0.636572\pi$
$661$	−21.3912	−0.832021	−0.416010	+	0.909360i	$0.636572\pi$
$662$	5.47570	0.212819
$663$	3.36253	0.130590
$664$	5.74077	0.222785
$665$	0.238063	0.00923169
$666$	−3.68230	−0.142686
$667$	−12.6342	−0.489196
$668$	−6.61090	−0.255784
$669$	9.20078	0.355723
$670$	−9.79617	−0.378459
$671$	−27.3075	−1.05419
$672$	0.335393	0.0129381
$673$	−20.1457	−0.776558	−0.388279	−	0.921542i	$-0.626930\pi$
$673$	−20.1457	−0.776558	−0.388279	+	0.921542i	$0.626930\pi$
$674$	33.8886	1.30534
$675$	−4.49618	−0.173058
$676$	−9.77298	−0.375884
$677$	25.1621	0.967059	0.483530	−	0.875328i	$-0.339355\pi$
$677$	25.1621	0.967059	0.483530	+	0.875328i	$0.339355\pi$
$678$	2.94663	0.113165
$679$	6.09526	0.233915
$680$	1.32863	0.0509506
$681$	−6.61163	−0.253358
$682$	16.2650	0.622820
$683$	35.7408	1.36758	0.683791	−	0.729678i	$-0.260330\pi$
$683$	35.7408	1.36758	0.683791	+	0.729678i	$0.260330\pi$
$684$	−1.00000	−0.0382360
$685$	−8.05594	−0.307802
$686$	−4.65777	−0.177835
$687$	4.23491	0.161572
$688$	−5.40625	−0.206111
$689$	1.79639	0.0684370
$690$	−1.62516	−0.0618689
$691$	2.22906	0.0847976	0.0423988	−	0.999101i	$-0.486500\pi$
$691$	2.22906	0.0847976	0.0423988	+	0.999101i	$0.486500\pi$
$692$	−0.306886	−0.0116660
$693$	−0.613500	−0.0233050
$694$	−15.5892	−0.591758
$695$	11.9674	0.453949
$696$	−5.51807	−0.209162
$697$	8.71492	0.330101
$698$	−26.9374	−1.01960
$699$	−0.175472	−0.00663698
$700$	−1.50799	−0.0569965
$701$	−36.6996	−1.38612	−0.693062	−	0.720878i	$-0.743739\pi$
$701$	−36.6996	−1.38612	−0.693062	+	0.720878i	$0.743739\pi$
$702$	−1.79639	−0.0678004
$703$	3.68230	0.138881
$704$	−1.82920	−0.0689405
$705$	1.66983	0.0628893
$706$	−13.8313	−0.520548
$707$	3.11926	0.117312
$708$	−7.36599	−0.276831
$709$	8.07393	0.303223	0.151611	−	0.988440i	$-0.451554\pi$
$709$	8.07393	0.303223	0.151611	+	0.988440i	$0.451554\pi$
$710$	3.73715	0.140253
$711$	6.28178	0.235585
$712$	7.74438	0.290233
$713$	−20.3588	−0.762444
$714$	−0.627798	−0.0234947
$715$	−2.33238	−0.0872262
$716$	18.8224	0.703425
$717$	8.56302	0.319792
$718$	27.8267	1.03848
$719$	17.4120	0.649358	0.324679	−	0.945824i	$-0.394744\pi$
$719$	17.4120	0.649358	0.324679	+	0.945824i	$0.394744\pi$
$720$	−0.709803	−0.0264528
$721$	−5.11314	−0.190423
$722$	1.00000	0.0372161
$723$	−18.7941	−0.698961
$724$	−11.6919	−0.434525
$725$	24.8102	0.921429
$726$	−7.65403	−0.284068
$727$	−39.2428	−1.45544	−0.727718	−	0.685876i	$-0.759419\pi$
$727$	−39.2428	−1.45544	−0.727718	+	0.685876i	$0.759419\pi$
$728$	−0.602496	−0.0223300
$729$	1.00000	0.0370370
$730$	0.606142	0.0224343
$731$	10.1196	0.374286
$732$	14.9287	0.551779
$733$	−0.351801	−0.0129941	−0.00649703	−	0.999979i	$-0.502068\pi$
$733$	−0.351801	−0.0129941	−0.00649703	+	0.999979i	$0.502068\pi$
$734$	−10.6055	−0.391455
$735$	4.88878	0.180325
$736$	2.28960	0.0843956
$737$	−25.2452	−0.929920
$738$	−4.65583	−0.171384
$739$	42.8804	1.57738	0.788690	−	0.614791i	$-0.210760\pi$
$739$	42.8804	1.57738	0.788690	+	0.614791i	$0.210760\pi$
$740$	2.61371	0.0960820
$741$	1.79639	0.0659920
$742$	−0.335393	−0.0123127
$743$	−41.4162	−1.51941	−0.759707	−	0.650265i	$-0.774658\pi$
$743$	−41.4162	−1.51941	−0.759707	+	0.650265i	$0.774658\pi$
$744$	−8.89188	−0.325992
$745$	3.49061	0.127886
$746$	20.6051	0.754405
$747$	5.74077	0.210044
$748$	3.42395	0.125192
$749$	1.48856	0.0543909
$750$	6.74042	0.246125
$751$	−10.6485	−0.388569	−0.194285	−	0.980945i	$-0.562239\pi$
$751$	−10.6485	−0.388569	−0.194285	+	0.980945i	$0.562239\pi$
$752$	−2.35252	−0.0857875
$753$	4.24907	0.154845
$754$	9.91261	0.360996
$755$	3.35358	0.122049
$756$	0.335393	0.0121981
$757$	13.5307	0.491782	0.245891	−	0.969298i	$-0.420920\pi$
$757$	13.5307	0.491782	0.245891	+	0.969298i	$0.420920\pi$
$758$	−26.0897	−0.947621
$759$	−4.18813	−0.152019
$760$	0.709803	0.0257473
$761$	51.1323	1.85354	0.926772	−	0.375625i	$-0.122572\pi$
$761$	51.1323	1.85354	0.926772	+	0.375625i	$0.122572\pi$
$762$	1.11738	0.0404785
$763$	−6.39173	−0.231396
$764$	−11.2036	−0.405333
$765$	1.32863	0.0480367
$766$	29.8832	1.07972
$767$	13.2322	0.477787
$768$	1.00000	0.0360844
$769$	−10.8548	−0.391433	−0.195717	−	0.980661i	$-0.562703\pi$
$769$	−10.8548	−0.391433	−0.195717	+	0.980661i	$0.562703\pi$
$770$	0.435465	0.0156931
$771$	−6.34627	−0.228555
$772$	7.34308	0.264283
$773$	−17.1140	−0.615549	−0.307775	−	0.951459i	$-0.599584\pi$
$773$	−17.1140	−0.615549	−0.307775	+	0.951459i	$0.599584\pi$
$774$	−5.40625	−0.194324
$775$	39.9795	1.43611
$776$	18.1735	0.652390
$777$	−1.23502	−0.0443060
$778$	10.9287	0.391812
$779$	4.65583	0.166812
$780$	1.27508	0.0456553
$781$	9.63083	0.344618
$782$	−4.28573	−0.153257
$783$	−5.51807	−0.197200
$784$	−6.88751	−0.245983
$785$	3.70726	0.132318
$786$	−15.5092	−0.553193
$787$	−23.6795	−0.844083	−0.422041	−	0.906577i	$-0.638686\pi$
$787$	−23.6795	−0.844083	−0.422041	+	0.906577i	$0.638686\pi$
$788$	−19.8966	−0.708786
$789$	1.49064	0.0530681
$790$	−4.45883	−0.158638
$791$	0.988278	0.0351391
$792$	−1.82920	−0.0649978
$793$	−26.8177	−0.952324
$794$	12.9723	0.460371
$795$	0.709803	0.0251741
$796$	5.90613	0.209337
$797$	51.6884	1.83090	0.915448	−	0.402435i	$-0.131836\pi$
$797$	51.6884	1.83090	0.915448	+	0.402435i	$0.131836\pi$
$798$	−0.335393	−0.0118728
$799$	4.40351	0.155785
$800$	−4.49618	−0.158964
$801$	7.74438	0.273634
$802$	14.0412	0.495812
$803$	1.56206	0.0551238
$804$	13.8012	0.486732
$805$	−0.545068	−0.0192111
$806$	15.9733	0.562635
$807$	20.8588	0.734266
$808$	9.30033	0.327184
$809$	−47.6933	−1.67681	−0.838404	−	0.545050i	$-0.816511\pi$
$809$	−47.6933	−1.67681	−0.838404	+	0.545050i	$0.816511\pi$
$810$	−0.709803	−0.0249400
$811$	−43.4546	−1.52590	−0.762948	−	0.646459i	$-0.776249\pi$
$811$	−43.4546	−1.52590	−0.762948	+	0.646459i	$0.776249\pi$
$812$	−1.85072	−0.0649476
$813$	15.2680	0.535474
$814$	6.73567	0.236085
$815$	3.00180	0.105148
$816$	−1.87183	−0.0655271
$817$	5.40625	0.189141
$818$	−27.1033	−0.947644
$819$	−0.602496	−0.0210529
$820$	3.30473	0.115406
$821$	30.9354	1.07965	0.539826	−	0.841777i	$-0.318490\pi$
$821$	30.9354	1.07965	0.539826	+	0.841777i	$0.318490\pi$
$822$	11.3495	0.395861
$823$	−38.5671	−1.34437	−0.672183	−	0.740385i	$-0.734643\pi$
$823$	−38.5671	−1.34437	−0.672183	+	0.740385i	$0.734643\pi$
$824$	−15.2452	−0.531093
$825$	8.22441	0.286337
$826$	−2.47050	−0.0859598
$827$	37.6023	1.30756	0.653780	−	0.756685i	$-0.273182\pi$
$827$	37.6023	1.30756	0.653780	+	0.756685i	$0.273182\pi$
$828$	2.28960	0.0795690
$829$	−6.01196	−0.208804	−0.104402	−	0.994535i	$-0.533293\pi$
$829$	−6.01196	−0.208804	−0.104402	+	0.994535i	$0.533293\pi$
$830$	−4.07482	−0.141439
$831$	−5.97836	−0.207387
$832$	−1.79639	−0.0622786
$833$	12.8922	0.446690
$834$	−16.8602	−0.583820
$835$	4.69244	0.162389
$836$	1.82920	0.0632642
$837$	−8.89188	−0.307348
$838$	−3.12380	−0.107910
$839$	14.4189	0.497797	0.248899	−	0.968530i	$-0.419931\pi$
$839$	14.4189	0.497797	0.248899	+	0.968530i	$0.419931\pi$
$840$	−0.238063	−0.00821396
$841$	1.44911	0.0499692
$842$	−40.2226	−1.38616
$843$	3.10450	0.106925
$844$	−0.474220	−0.0163233
$845$	6.93690	0.238637
$846$	−2.35252	−0.0808813
$847$	−2.56711	−0.0882068
$848$	−1.00000	−0.0343401
$849$	−8.07228	−0.277040
$850$	8.41607	0.288669
$851$	−8.43099	−0.289011
$852$	−5.26505	−0.180378
$853$	−11.5298	−0.394774	−0.197387	−	0.980326i	$-0.563245\pi$
$853$	−11.5298	−0.394774	−0.197387	+	0.980326i	$0.563245\pi$
$854$	5.00697	0.171335
$855$	0.709803	0.0242748
$856$	4.43826	0.151697
$857$	43.2149	1.47619	0.738097	−	0.674695i	$-0.235725\pi$
$857$	43.2149	1.47619	0.738097	+	0.674695i	$0.235725\pi$
$858$	3.28596	0.112181
$859$	9.93685	0.339041	0.169520	−	0.985527i	$-0.445778\pi$
$859$	9.93685	0.339041	0.169520	+	0.985527i	$0.445778\pi$
$860$	3.83737	0.130853
$861$	−1.56153	−0.0532169
$862$	−0.635594	−0.0216484
$863$	−6.03179	−0.205325	−0.102662	−	0.994716i	$-0.532736\pi$
$863$	−6.03179	−0.205325	−0.102662	+	0.994716i	$0.532736\pi$
$864$	1.00000	0.0340207
$865$	0.217829	0.00740640
$866$	−8.90063	−0.302456
$867$	−13.4963	−0.458357
$868$	−2.98227	−0.101225
$869$	−11.4906	−0.389793
$870$	3.91675	0.132790
$871$	−24.7924	−0.840059
$872$	−19.0575	−0.645367
$873$	18.1735	0.615079
$874$	−2.28960	−0.0774467
$875$	2.26069	0.0764252
$876$	−0.853957	−0.0288525
$877$	18.3343	0.619104	0.309552	−	0.950883i	$-0.399821\pi$
$877$	18.3343	0.619104	0.309552	+	0.950883i	$0.399821\pi$
$878$	1.53473	0.0517947
$879$	22.3014	0.752207
$880$	1.29837	0.0437681
$881$	19.7961	0.666949	0.333475	−	0.942759i	$-0.391779\pi$
$881$	19.7961	0.666949	0.333475	+	0.942759i	$0.391779\pi$
$882$	−6.88751	−0.231915
$883$	33.7857	1.13698	0.568489	−	0.822691i	$-0.307528\pi$
$883$	33.7857	1.13698	0.568489	+	0.822691i	$0.307528\pi$
$884$	3.36253	0.113094
$885$	5.22841	0.175751
$886$	−6.01214	−0.201982
$887$	−49.0422	−1.64668	−0.823338	−	0.567551i	$-0.807891\pi$
$887$	−49.0422	−1.64668	−0.823338	+	0.567551i	$0.807891\pi$
$888$	−3.68230	−0.123570
$889$	0.374762	0.0125691
$890$	−5.49699	−0.184260
$891$	−1.82920	−0.0612805
$892$	9.20078	0.308065
$893$	2.35252	0.0787240
$894$	−4.91772	−0.164473
$895$	−13.3602	−0.446582
$896$	0.335393	0.0112047
$897$	−4.11301	−0.137329
$898$	13.0869	0.436715
$899$	49.0660	1.63644
$900$	−4.49618	−0.149873
$901$	1.87183	0.0623596
$902$	8.51644	0.283567
$903$	−1.81322	−0.0603401
$904$	2.94663	0.0980034
$905$	8.29893	0.275866
$906$	−4.72465	−0.156966
$907$	−42.1057	−1.39810	−0.699048	−	0.715075i	$-0.746393\pi$
$907$	−42.1057	−1.39810	−0.699048	+	0.715075i	$0.746393\pi$
$908$	−6.61163	−0.219415
$909$	9.30033	0.308472
$910$	0.427654	0.0141766
$911$	21.3304	0.706708	0.353354	−	0.935490i	$-0.385041\pi$
$911$	21.3304	0.706708	0.353354	+	0.935490i	$0.385041\pi$
$912$	−1.00000	−0.0331133
$913$	−10.5010	−0.347533
$914$	16.2792	0.538467
$915$	−10.5964	−0.350307
$916$	4.23491	0.139925
$917$	−5.20166	−0.171774
$918$	−1.87183	−0.0617795
$919$	20.0291	0.660698	0.330349	−	0.943859i	$-0.392833\pi$
$919$	20.0291	0.660698	0.330349	+	0.943859i	$0.392833\pi$
$920$	−1.62516	−0.0535800
$921$	−19.1655	−0.631524
$922$	−32.0630	−1.05594
$923$	9.45809	0.311317
$924$	−0.613500	−0.0201827
$925$	16.5563	0.544368
$926$	36.8701	1.21163
$927$	−15.2452	−0.500719
$928$	−5.51807	−0.181140
$929$	−29.7986	−0.977662	−0.488831	−	0.872379i	$-0.662576\pi$
$929$	−29.7986	−0.977662	−0.488831	+	0.872379i	$0.662576\pi$
$930$	6.31149	0.206962
$931$	6.88751	0.225729
$932$	−0.175472	−0.00574779
$933$	6.04777	0.197995
$934$	−24.2682	−0.794079
$935$	−2.43033	−0.0794803
$936$	−1.79639	−0.0587168
$937$	36.4270	1.19002	0.595009	−	0.803719i	$-0.297148\pi$
$937$	36.4270	1.19002	0.595009	+	0.803719i	$0.297148\pi$
$938$	4.62884	0.151137
$939$	5.59485	0.182581
$940$	1.66983	0.0544637
$941$	−26.2513	−0.855768	−0.427884	−	0.903834i	$-0.640741\pi$
$941$	−26.2513	−0.855768	−0.427884	+	0.903834i	$0.640741\pi$
$942$	−5.22293	−0.170172
$943$	−10.6600	−0.347136
$944$	−7.36599	−0.239743
$945$	−0.238063	−0.00774419
$946$	9.88911	0.321523
$947$	25.5290	0.829582	0.414791	−	0.909917i	$-0.363855\pi$
$947$	25.5290	0.829582	0.414791	+	0.909917i	$0.363855\pi$
$948$	6.28178	0.204023
$949$	1.53404	0.0497970
$950$	4.49618	0.145875
$951$	9.01084	0.292197
$952$	−0.627798	−0.0203470
$953$	20.4221	0.661538	0.330769	−	0.943712i	$-0.392692\pi$
$953$	20.4221	0.661538	0.330769	+	0.943712i	$0.392692\pi$
$954$	−1.00000	−0.0323762
$955$	7.95237	0.257333
$956$	8.56302	0.276948
$957$	10.0937	0.326281
$958$	−24.4097	−0.788641
$959$	3.80655	0.122920
$960$	−0.709803	−0.0229088
$961$	48.0655	1.55050
$962$	6.61485	0.213271
$963$	4.43826	0.143021
$964$	−18.7941	−0.605318
$965$	−5.21214	−0.167785
$966$	0.767914	0.0247072
$967$	−39.8169	−1.28042	−0.640212	−	0.768198i	$-0.721153\pi$
$967$	−39.8169	−1.28042	−0.640212	+	0.768198i	$0.721153\pi$
$968$	−7.65403	−0.246010
$969$	1.87183	0.0601318
$970$	−12.8996	−0.414181
$971$	33.3493	1.07023	0.535115	−	0.844779i	$-0.320268\pi$
$971$	33.3493	1.07023	0.535115	+	0.844779i	$0.320268\pi$
$972$	1.00000	0.0320750
$973$	−5.65478	−0.181284
$974$	−28.4709	−0.912265
$975$	8.07689	0.258668
$976$	14.9287	0.477855
$977$	−26.1402	−0.836300	−0.418150	−	0.908378i	$-0.637321\pi$
$977$	−26.1402	−0.836300	−0.418150	+	0.908378i	$0.637321\pi$
$978$	−4.22906	−0.135230
$979$	−14.1660	−0.452748
$980$	4.88878	0.156166
$981$	−19.0575	−0.608458
$982$	10.2696	0.327716
$983$	0.346922	0.0110651	0.00553255	−	0.999985i	$-0.498239\pi$
$983$	0.346922	0.0110651	0.00553255	+	0.999985i	$0.498239\pi$
$984$	−4.65583	−0.148422
$985$	14.1227	0.449985
$986$	10.3289	0.328939
$987$	−0.789018	−0.0251147
$988$	1.79639	0.0571508
$989$	−12.3781	−0.393602
$990$	1.29837	0.0412650
$991$	5.27592	0.167595	0.0837976	−	0.996483i	$-0.473295\pi$
$991$	5.27592	0.167595	0.0837976	+	0.996483i	$0.473295\pi$
$992$	−8.89188	−0.282318
$993$	5.47570	0.173766
$994$	−1.76586	−0.0560097
$995$	−4.19219	−0.132901
$996$	5.74077	0.181903
$997$	35.0103	1.10879	0.554393	−	0.832255i	$-0.312950\pi$
$997$	35.0103	1.10879	0.554393	+	0.832255i	$0.312950\pi$
$998$	10.4507	0.330810
$999$	−3.68230	−0.116503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.x.1.4	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.x.1.4	✓	6	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:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.709803 q^{5} +1.00000 q^{6} +0.335393 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.709803 q^{5} +1.00000 q^{6} +0.335393 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.709803 q^{10} -1.82920 q^{11} +1.00000 q^{12} -1.79639 q^{13} +0.335393 q^{14} -0.709803 q^{15} +1.00000 q^{16} -1.87183 q^{17} +1.00000 q^{18} -1.00000 q^{19} -0.709803 q^{20} +0.335393 q^{21} -1.82920 q^{22} +2.28960 q^{23} +1.00000 q^{24} -4.49618 q^{25} -1.79639 q^{26} +1.00000 q^{27} +0.335393 q^{28} -5.51807 q^{29} -0.709803 q^{30} -8.89188 q^{31} +1.00000 q^{32} -1.82920 q^{33} -1.87183 q^{34} -0.238063 q^{35} +1.00000 q^{36} -3.68230 q^{37} -1.00000 q^{38} -1.79639 q^{39} -0.709803 q^{40} -4.65583 q^{41} +0.335393 q^{42} -5.40625 q^{43} -1.82920 q^{44} -0.709803 q^{45} +2.28960 q^{46} -2.35252 q^{47} +1.00000 q^{48} -6.88751 q^{49} -4.49618 q^{50} -1.87183 q^{51} -1.79639 q^{52} -1.00000 q^{53} +1.00000 q^{54} +1.29837 q^{55} +0.335393 q^{56} -1.00000 q^{57} -5.51807 q^{58} -7.36599 q^{59} -0.709803 q^{60} +14.9287 q^{61} -8.89188 q^{62} +0.335393 q^{63} +1.00000 q^{64} +1.27508 q^{65} -1.82920 q^{66} +13.8012 q^{67} -1.87183 q^{68} +2.28960 q^{69} -0.238063 q^{70} -5.26505 q^{71} +1.00000 q^{72} -0.853957 q^{73} -3.68230 q^{74} -4.49618 q^{75} -1.00000 q^{76} -0.613500 q^{77} -1.79639 q^{78} +6.28178 q^{79} -0.709803 q^{80} +1.00000 q^{81} -4.65583 q^{82} +5.74077 q^{83} +0.335393 q^{84} +1.32863 q^{85} -5.40625 q^{86} -5.51807 q^{87} -1.82920 q^{88} +7.74438 q^{89} -0.709803 q^{90} -0.602496 q^{91} +2.28960 q^{92} -8.89188 q^{93} -2.35252 q^{94} +0.709803 q^{95} +1.00000 q^{96} +18.1735 q^{97} -6.88751 q^{98} -1.82920 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 6 q^{7} + 6 q^{8} + 6 q^{9} - 8 q^{10} + 3 q^{11} + 6 q^{12} - 13 q^{13} - 6 q^{14} - 8 q^{15} + 6 q^{16} - 5 q^{17} + 6 q^{18} - 6 q^{19} - 8 q^{20} - 6 q^{21} + 3 q^{22} - 12 q^{23} + 6 q^{24} - 4 q^{25} - 13 q^{26} + 6 q^{27} - 6 q^{28} - 7 q^{29} - 8 q^{30} - 17 q^{31} + 6 q^{32} + 3 q^{33} - 5 q^{34} - 5 q^{35} + 6 q^{36} - 15 q^{37} - 6 q^{38} - 13 q^{39} - 8 q^{40} - 12 q^{41} - 6 q^{42} - 4 q^{43} + 3 q^{44} - 8 q^{45} - 12 q^{46} - 29 q^{47} + 6 q^{48} + 4 q^{49} - 4 q^{50} - 5 q^{51} - 13 q^{52} - 6 q^{53} + 6 q^{54} + 6 q^{55} - 6 q^{56} - 6 q^{57} - 7 q^{58} + 9 q^{59} - 8 q^{60} - 16 q^{61} - 17 q^{62} - 6 q^{63} + 6 q^{64} + 5 q^{65} + 3 q^{66} - 8 q^{67} - 5 q^{68} - 12 q^{69} - 5 q^{70} - 2 q^{71} + 6 q^{72} - 17 q^{73} - 15 q^{74} - 4 q^{75} - 6 q^{76} - 21 q^{77} - 13 q^{78} - 31 q^{79} - 8 q^{80} + 6 q^{81} - 12 q^{82} - 5 q^{83} - 6 q^{84} - 4 q^{86} - 7 q^{87} + 3 q^{88} - 5 q^{89} - 8 q^{90} + 4 q^{91} - 12 q^{92} - 17 q^{93} - 29 q^{94} + 8 q^{95} + 6 q^{96} + 7 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 6 * q^7 + 6 * q^8 + 6 * q^9 - 8 * q^10 + 3 * q^11 + 6 * q^12 - 13 * q^13 - 6 * q^14 - 8 * q^15 + 6 * q^16 - 5 * q^17 + 6 * q^18 - 6 * q^19 - 8 * q^20 - 6 * q^21 + 3 * q^22 - 12 * q^23 + 6 * q^24 - 4 * q^25 - 13 * q^26 + 6 * q^27 - 6 * q^28 - 7 * q^29 - 8 * q^30 - 17 * q^31 + 6 * q^32 + 3 * q^33 - 5 * q^34 - 5 * q^35 + 6 * q^36 - 15 * q^37 - 6 * q^38 - 13 * q^39 - 8 * q^40 - 12 * q^41 - 6 * q^42 - 4 * q^43 + 3 * q^44 - 8 * q^45 - 12 * q^46 - 29 * q^47 + 6 * q^48 + 4 * q^49 - 4 * q^50 - 5 * q^51 - 13 * q^52 - 6 * q^53 + 6 * q^54 + 6 * q^55 - 6 * q^56 - 6 * q^57 - 7 * q^58 + 9 * q^59 - 8 * q^60 - 16 * q^61 - 17 * q^62 - 6 * q^63 + 6 * q^64 + 5 * q^65 + 3 * q^66 - 8 * q^67 - 5 * q^68 - 12 * q^69 - 5 * q^70 - 2 * q^71 + 6 * q^72 - 17 * q^73 - 15 * q^74 - 4 * q^75 - 6 * q^76 - 21 * q^77 - 13 * q^78 - 31 * q^79 - 8 * q^80 + 6 * q^81 - 12 * q^82 - 5 * q^83 - 6 * q^84 - 4 * q^86 - 7 * q^87 + 3 * q^88 - 5 * q^89 - 8 * q^90 + 4 * q^91 - 12 * q^92 - 17 * q^93 - 29 * q^94 + 8 * q^95 + 6 * q^96 + 7 * q^97 + 4 * q^98 + 3 * q^99

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