LMFDB - Embedded newform 6042.2.a.be.1.8

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 36 x^{10} + 105 x^{9} + 465 x^{8} - 1287 x^{7} - 2668 x^{6} + 6443 x^{5} + \cdots + 1496 $ x^12 - 3x^11 - 36x^10 + 105x^9 + 465x^8 - 1287x^7 - 2668x^6 + 6443x^5 + 7140x^4 - 10858x^3 - 10086x^2 + 2072*x + 1496
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.11996$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.11996 q^{5} +1.00000 q^{6} +0.414381 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.11996 q^{5} +1.00000 q^{6} +0.414381 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.11996 q^{10} +1.07426 q^{11} -1.00000 q^{12} +4.69865 q^{13} -0.414381 q^{14} -1.11996 q^{15} +1.00000 q^{16} -2.07982 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.11996 q^{20} -0.414381 q^{21} -1.07426 q^{22} +0.442517 q^{23} +1.00000 q^{24} -3.74569 q^{25} -4.69865 q^{26} -1.00000 q^{27} +0.414381 q^{28} -5.42550 q^{29} +1.11996 q^{30} +6.58106 q^{31} -1.00000 q^{32} -1.07426 q^{33} +2.07982 q^{34} +0.464090 q^{35} +1.00000 q^{36} -5.30061 q^{37} +1.00000 q^{38} -4.69865 q^{39} -1.11996 q^{40} -5.21985 q^{41} +0.414381 q^{42} -6.51709 q^{43} +1.07426 q^{44} +1.11996 q^{45} -0.442517 q^{46} -4.83494 q^{47} -1.00000 q^{48} -6.82829 q^{49} +3.74569 q^{50} +2.07982 q^{51} +4.69865 q^{52} -1.00000 q^{53} +1.00000 q^{54} +1.20312 q^{55} -0.414381 q^{56} +1.00000 q^{57} +5.42550 q^{58} +1.71044 q^{59} -1.11996 q^{60} +1.28641 q^{61} -6.58106 q^{62} +0.414381 q^{63} +1.00000 q^{64} +5.26230 q^{65} +1.07426 q^{66} -0.633661 q^{67} -2.07982 q^{68} -0.442517 q^{69} -0.464090 q^{70} -12.8057 q^{71} -1.00000 q^{72} -0.429813 q^{73} +5.30061 q^{74} +3.74569 q^{75} -1.00000 q^{76} +0.445152 q^{77} +4.69865 q^{78} -4.95804 q^{79} +1.11996 q^{80} +1.00000 q^{81} +5.21985 q^{82} +1.90178 q^{83} -0.414381 q^{84} -2.32931 q^{85} +6.51709 q^{86} +5.42550 q^{87} -1.07426 q^{88} -12.4686 q^{89} -1.11996 q^{90} +1.94703 q^{91} +0.442517 q^{92} -6.58106 q^{93} +4.83494 q^{94} -1.11996 q^{95} +1.00000 q^{96} +15.2292 q^{97} +6.82829 q^{98} +1.07426 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9} + 3 q^{10} - 7 q^{11} - 12 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} + 12 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} - 18 q^{23} + 12 q^{24} + 21 q^{25} - 4 q^{26} - 12 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} + 4 q^{34} - 19 q^{35} + 12 q^{36} + 14 q^{37} + 12 q^{38} - 4 q^{39} + 3 q^{40} - 9 q^{41} - q^{42} - 4 q^{43} - 7 q^{44} - 3 q^{45} + 18 q^{46} - 14 q^{47} - 12 q^{48} + 37 q^{49} - 21 q^{50} + 4 q^{51} + 4 q^{52} - 12 q^{53} + 12 q^{54} - 4 q^{55} + q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 3 q^{60} - 7 q^{61} - 14 q^{62} - q^{63} + 12 q^{64} + 3 q^{65} - 7 q^{66} + 8 q^{67} - 4 q^{68} + 18 q^{69} + 19 q^{70} - q^{71} - 12 q^{72} - 31 q^{73} - 14 q^{74} - 21 q^{75} - 12 q^{76} - 25 q^{77} + 4 q^{78} - 3 q^{80} + 12 q^{81} + 9 q^{82} - 48 q^{83} + q^{84} + 4 q^{85} + 4 q^{86} - 10 q^{87} + 7 q^{88} + 13 q^{89} + 3 q^{90} + 9 q^{91} - 18 q^{92} - 14 q^{93} + 14 q^{94} + 3 q^{95} + 12 q^{96} + 25 q^{97} - 37 q^{98} - 7 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9 + 3 * q^10 - 7 * q^11 - 12 * q^12 + 4 * q^13 + q^14 + 3 * q^15 + 12 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^19 - 3 * q^20 + q^21 + 7 * q^22 - 18 * q^23 + 12 * q^24 + 21 * q^25 - 4 * q^26 - 12 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 + 4 * q^34 - 19 * q^35 + 12 * q^36 + 14 * q^37 + 12 * q^38 - 4 * q^39 + 3 * q^40 - 9 * q^41 - q^42 - 4 * q^43 - 7 * q^44 - 3 * q^45 + 18 * q^46 - 14 * q^47 - 12 * q^48 + 37 * q^49 - 21 * q^50 + 4 * q^51 + 4 * q^52 - 12 * q^53 + 12 * q^54 - 4 * q^55 + q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 3 * q^60 - 7 * q^61 - 14 * q^62 - q^63 + 12 * q^64 + 3 * q^65 - 7 * q^66 + 8 * q^67 - 4 * q^68 + 18 * q^69 + 19 * q^70 - q^71 - 12 * q^72 - 31 * q^73 - 14 * q^74 - 21 * q^75 - 12 * q^76 - 25 * q^77 + 4 * q^78 - 3 * q^80 + 12 * q^81 + 9 * q^82 - 48 * q^83 + q^84 + 4 * q^85 + 4 * q^86 - 10 * q^87 + 7 * q^88 + 13 * q^89 + 3 * q^90 + 9 * q^91 - 18 * q^92 - 14 * q^93 + 14 * q^94 + 3 * q^95 + 12 * q^96 + 25 * q^97 - 37 * q^98 - 7 * 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
$5$	1.11996	0.500861	0.250431	−	0.968135i	$-0.419428\pi$
$5$	1.11996	0.500861	0.250431	+	0.968135i	$0.419428\pi$
$6$	1.00000	0.408248
$7$	0.414381	0.156621	0.0783106	−	0.996929i	$-0.475047\pi$
$7$	0.414381	0.156621	0.0783106	+	0.996929i	$0.475047\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.11996	−0.354162
$11$	1.07426	0.323901	0.161950	−	0.986799i	$-0.448222\pi$
$11$	1.07426	0.323901	0.161950	+	0.986799i	$0.448222\pi$
$12$	−1.00000	−0.288675
$13$	4.69865	1.30317	0.651586	−	0.758575i	$-0.274104\pi$
$13$	4.69865	1.30317	0.651586	+	0.758575i	$0.274104\pi$
$14$	−0.414381	−0.110748
$15$	−1.11996	−0.289172
$16$	1.00000	0.250000
$17$	−2.07982	−0.504430	−0.252215	−	0.967671i	$-0.581159\pi$
$17$	−2.07982	−0.504430	−0.252215	+	0.967671i	$0.581159\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.11996	0.250431
$21$	−0.414381	−0.0904253
$22$	−1.07426	−0.229032
$23$	0.442517	0.0922712	0.0461356	−	0.998935i	$-0.485309\pi$
$23$	0.442517	0.0922712	0.0461356	+	0.998935i	$0.485309\pi$
$24$	1.00000	0.204124
$25$	−3.74569	−0.749138
$26$	−4.69865	−0.921481
$27$	−1.00000	−0.192450
$28$	0.414381	0.0783106
$29$	−5.42550	−1.00749	−0.503745	−	0.863853i	$-0.668045\pi$
$29$	−5.42550	−1.00749	−0.503745	+	0.863853i	$0.668045\pi$
$30$	1.11996	0.204476
$31$	6.58106	1.18199	0.590996	−	0.806674i	$-0.298735\pi$
$31$	6.58106	1.18199	0.590996	+	0.806674i	$0.298735\pi$
$32$	−1.00000	−0.176777
$33$	−1.07426	−0.187004
$34$	2.07982	0.356686
$35$	0.464090	0.0784455
$36$	1.00000	0.166667
$37$	−5.30061	−0.871416	−0.435708	−	0.900088i	$-0.643502\pi$
$37$	−5.30061	−0.871416	−0.435708	+	0.900088i	$0.643502\pi$
$38$	1.00000	0.162221
$39$	−4.69865	−0.752386
$40$	−1.11996	−0.177081
$41$	−5.21985	−0.815204	−0.407602	−	0.913160i	$-0.633635\pi$
$41$	−5.21985	−0.815204	−0.407602	+	0.913160i	$0.633635\pi$
$42$	0.414381	0.0639404
$43$	−6.51709	−0.993847	−0.496924	−	0.867794i	$-0.665537\pi$
$43$	−6.51709	−0.993847	−0.496924	+	0.867794i	$0.665537\pi$
$44$	1.07426	0.161950
$45$	1.11996	0.166954
$46$	−0.442517	−0.0652456
$47$	−4.83494	−0.705248	−0.352624	−	0.935765i	$-0.614711\pi$
$47$	−4.83494	−0.705248	−0.352624	+	0.935765i	$0.614711\pi$
$48$	−1.00000	−0.144338
$49$	−6.82829	−0.975470
$50$	3.74569	0.529721
$51$	2.07982	0.291233
$52$	4.69865	0.651586
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	1.20312	0.162229
$56$	−0.414381	−0.0553740
$57$	1.00000	0.132453
$58$	5.42550	0.712403
$59$	1.71044	0.222681	0.111340	−	0.993782i	$-0.464486\pi$
$59$	1.71044	0.222681	0.111340	+	0.993782i	$0.464486\pi$
$60$	−1.11996	−0.144586
$61$	1.28641	0.164708	0.0823538	−	0.996603i	$-0.473756\pi$
$61$	1.28641	0.164708	0.0823538	+	0.996603i	$0.473756\pi$
$62$	−6.58106	−0.835795
$63$	0.414381	0.0522071
$64$	1.00000	0.125000
$65$	5.26230	0.652708
$66$	1.07426	0.132232
$67$	−0.633661	−0.0774140	−0.0387070	−	0.999251i	$-0.512324\pi$
$67$	−0.633661	−0.0774140	−0.0387070	+	0.999251i	$0.512324\pi$
$68$	−2.07982	−0.252215
$69$	−0.442517	−0.0532728
$70$	−0.464090	−0.0554694
$71$	−12.8057	−1.51976	−0.759881	−	0.650062i	$-0.774743\pi$
$71$	−12.8057	−1.51976	−0.759881	+	0.650062i	$0.774743\pi$
$72$	−1.00000	−0.117851
$73$	−0.429813	−0.0503058	−0.0251529	−	0.999684i	$-0.508007\pi$
$73$	−0.429813	−0.0503058	−0.0251529	+	0.999684i	$0.508007\pi$
$74$	5.30061	0.616184
$75$	3.74569	0.432515
$76$	−1.00000	−0.114708
$77$	0.445152	0.0507297
$78$	4.69865	0.532017
$79$	−4.95804	−0.557823	−0.278912	−	0.960317i	$-0.589974\pi$
$79$	−4.95804	−0.557823	−0.278912	+	0.960317i	$0.589974\pi$
$80$	1.11996	0.125215
$81$	1.00000	0.111111
$82$	5.21985	0.576436
$83$	1.90178	0.208747	0.104373	−	0.994538i	$-0.466716\pi$
$83$	1.90178	0.208747	0.104373	+	0.994538i	$0.466716\pi$
$84$	−0.414381	−0.0452127
$85$	−2.32931	−0.252649
$86$	6.51709	0.702756
$87$	5.42550	0.581674
$88$	−1.07426	−0.114516
$89$	−12.4686	−1.32167	−0.660836	−	0.750531i	$-0.729798\pi$
$89$	−12.4686	−1.32167	−0.660836	+	0.750531i	$0.729798\pi$
$90$	−1.11996	−0.118054
$91$	1.94703	0.204104
$92$	0.442517	0.0461356
$93$	−6.58106	−0.682424
$94$	4.83494	0.498686
$95$	−1.11996	−0.114905
$96$	1.00000	0.102062
$97$	15.2292	1.54629	0.773147	−	0.634227i	$-0.218682\pi$
$97$	15.2292	1.54629	0.773147	+	0.634227i	$0.218682\pi$
$98$	6.82829	0.689761
$99$	1.07426	0.107967
$100$	−3.74569	−0.374569
$101$	1.59554	0.158762	0.0793812	−	0.996844i	$-0.474706\pi$
$101$	1.59554	0.158762	0.0793812	+	0.996844i	$0.474706\pi$
$102$	−2.07982	−0.205933
$103$	−4.54676	−0.448006	−0.224003	−	0.974588i	$-0.571913\pi$
$103$	−4.54676	−0.448006	−0.224003	+	0.974588i	$0.571913\pi$
$104$	−4.69865	−0.460741
$105$	−0.464090	−0.0452905
$106$	1.00000	0.0971286
$107$	−18.1239	−1.75210	−0.876052	−	0.482217i	$-0.839832\pi$
$107$	−18.1239	−1.75210	−0.876052	+	0.482217i	$0.839832\pi$
$108$	−1.00000	−0.0962250
$109$	12.8271	1.22861	0.614306	−	0.789068i	$-0.289436\pi$
$109$	12.8271	1.22861	0.614306	+	0.789068i	$0.289436\pi$
$110$	−1.20312	−0.114713
$111$	5.30061	0.503112
$112$	0.414381	0.0391553
$113$	13.8844	1.30614	0.653069	−	0.757299i	$-0.273481\pi$
$113$	13.8844	1.30614	0.653069	+	0.757299i	$0.273481\pi$
$114$	−1.00000	−0.0936586
$115$	0.495601	0.0462151
$116$	−5.42550	−0.503745
$117$	4.69865	0.434390
$118$	−1.71044	−0.157459
$119$	−0.861837	−0.0790045
$120$	1.11996	0.102238
$121$	−9.84597	−0.895088
$122$	−1.28641	−0.116466
$123$	5.21985	0.470658
$124$	6.58106	0.590996
$125$	−9.79482	−0.876075
$126$	−0.414381	−0.0369160
$127$	−0.191244	−0.0169702	−0.00848509	−	0.999964i	$-0.502701\pi$
$127$	−0.191244	−0.0169702	−0.00848509	+	0.999964i	$0.502701\pi$
$128$	−1.00000	−0.0883883
$129$	6.51709	0.573798
$130$	−5.26230	−0.461534
$131$	−5.98910	−0.523270	−0.261635	−	0.965167i	$-0.584262\pi$
$131$	−5.98910	−0.523270	−0.261635	+	0.965167i	$0.584262\pi$
$132$	−1.07426	−0.0935021
$133$	−0.414381	−0.0359314
$134$	0.633661	0.0547399
$135$	−1.11996	−0.0963908
$136$	2.07982	0.178343
$137$	−15.4908	−1.32347	−0.661734	−	0.749739i	$-0.730179\pi$
$137$	−15.4908	−1.32347	−0.661734	+	0.749739i	$0.730179\pi$
$138$	0.442517	0.0376696
$139$	20.3956	1.72994	0.864968	−	0.501828i	$-0.167339\pi$
$139$	20.3956	1.72994	0.864968	+	0.501828i	$0.167339\pi$
$140$	0.464090	0.0392228
$141$	4.83494	0.407175
$142$	12.8057	1.07463
$143$	5.04756	0.422098
$144$	1.00000	0.0833333
$145$	−6.07634	−0.504612
$146$	0.429813	0.0355716
$147$	6.82829	0.563188
$148$	−5.30061	−0.435708
$149$	11.4678	0.939482	0.469741	−	0.882804i	$-0.344347\pi$
$149$	11.4678	0.939482	0.469741	+	0.882804i	$0.344347\pi$
$150$	−3.74569	−0.305834
$151$	−21.1846	−1.72398	−0.861988	−	0.506929i	$-0.830781\pi$
$151$	−21.1846	−1.72398	−0.861988	+	0.506929i	$0.830781\pi$
$152$	1.00000	0.0811107
$153$	−2.07982	−0.168143
$154$	−0.445152	−0.0358713
$155$	7.37052	0.592014
$156$	−4.69865	−0.376193
$157$	−16.3639	−1.30598	−0.652989	−	0.757367i	$-0.726485\pi$
$157$	−16.3639	−1.30598	−0.652989	+	0.757367i	$0.726485\pi$
$158$	4.95804	0.394440
$159$	1.00000	0.0793052
$160$	−1.11996	−0.0885406
$161$	0.183371	0.0144516
$162$	−1.00000	−0.0785674
$163$	−7.80612	−0.611422	−0.305711	−	0.952124i	$-0.598894\pi$
$163$	−7.80612	−0.611422	−0.305711	+	0.952124i	$0.598894\pi$
$164$	−5.21985	−0.407602
$165$	−1.20312	−0.0936631
$166$	−1.90178	−0.147606
$167$	7.23291	0.559699	0.279850	−	0.960044i	$-0.409715\pi$
$167$	7.23291	0.559699	0.279850	+	0.960044i	$0.409715\pi$
$168$	0.414381	0.0319702
$169$	9.07732	0.698256
$170$	2.32931	0.178650
$171$	−1.00000	−0.0764719
$172$	−6.51709	−0.496924
$173$	13.3026	1.01138	0.505689	−	0.862716i	$-0.331238\pi$
$173$	13.3026	1.01138	0.505689	+	0.862716i	$0.331238\pi$
$174$	−5.42550	−0.411306
$175$	−1.55214	−0.117331
$176$	1.07426	0.0809752
$177$	−1.71044	−0.128565
$178$	12.4686	0.934563
$179$	7.63427	0.570612	0.285306	−	0.958437i	$-0.407905\pi$
$179$	7.63427	0.570612	0.285306	+	0.958437i	$0.407905\pi$
$180$	1.11996	0.0834769
$181$	−2.67830	−0.199077	−0.0995384	−	0.995034i	$-0.531737\pi$
$181$	−2.67830	−0.199077	−0.0995384	+	0.995034i	$0.531737\pi$
$182$	−1.94703	−0.144324
$183$	−1.28641	−0.0950940
$184$	−0.442517	−0.0326228
$185$	−5.93647	−0.436458
$186$	6.58106	0.482546
$187$	−2.23426	−0.163385
$188$	−4.83494	−0.352624
$189$	−0.414381	−0.0301418
$190$	1.11996	0.0812504
$191$	5.64261	0.408285	0.204142	−	0.978941i	$-0.434559\pi$
$191$	5.64261	0.408285	0.204142	+	0.978941i	$0.434559\pi$
$192$	−1.00000	−0.0721688
$193$	−4.86025	−0.349848	−0.174924	−	0.984582i	$-0.555968\pi$
$193$	−4.86025	−0.349848	−0.174924	+	0.984582i	$0.555968\pi$
$194$	−15.2292	−1.09339
$195$	−5.26230	−0.376841
$196$	−6.82829	−0.487735
$197$	6.45088	0.459606	0.229803	−	0.973237i	$-0.426192\pi$
$197$	6.45088	0.459606	0.229803	+	0.973237i	$0.426192\pi$
$198$	−1.07426	−0.0763441
$199$	12.1704	0.862736	0.431368	−	0.902176i	$-0.358031\pi$
$199$	12.1704	0.862736	0.431368	+	0.902176i	$0.358031\pi$
$200$	3.74569	0.264860
$201$	0.633661	0.0446950
$202$	−1.59554	−0.112262
$203$	−2.24822	−0.157794
$204$	2.07982	0.145616
$205$	−5.84603	−0.408304
$206$	4.54676	0.316788
$207$	0.442517	0.0307571
$208$	4.69865	0.325793
$209$	−1.07426	−0.0743079
$210$	0.464090	0.0320253
$211$	7.54566	0.519465	0.259732	−	0.965681i	$-0.416366\pi$
$211$	7.54566	0.519465	0.259732	+	0.965681i	$0.416366\pi$
$212$	−1.00000	−0.0686803
$213$	12.8057	0.877435
$214$	18.1239	1.23892
$215$	−7.29888	−0.497780
$216$	1.00000	0.0680414
$217$	2.72706	0.185125
$218$	−12.8271	−0.868760
$219$	0.429813	0.0290441
$220$	1.20312	0.0811146
$221$	−9.77234	−0.657359
$222$	−5.30061	−0.355754
$223$	−13.8813	−0.929558	−0.464779	−	0.885427i	$-0.653866\pi$
$223$	−13.8813	−0.929558	−0.464779	+	0.885427i	$0.653866\pi$
$224$	−0.414381	−0.0276870
$225$	−3.74569	−0.249713
$226$	−13.8844	−0.923578
$227$	−11.2878	−0.749194	−0.374597	−	0.927188i	$-0.622219\pi$
$227$	−11.2878	−0.749194	−0.374597	+	0.927188i	$0.622219\pi$
$228$	1.00000	0.0662266
$229$	27.4562	1.81436	0.907178	−	0.420747i	$-0.138232\pi$
$229$	27.4562	1.81436	0.907178	+	0.420747i	$0.138232\pi$
$230$	−0.495601	−0.0326790
$231$	−0.445152	−0.0292888
$232$	5.42550	0.356201
$233$	1.63814	0.107318	0.0536591	−	0.998559i	$-0.482912\pi$
$233$	1.63814	0.107318	0.0536591	+	0.998559i	$0.482912\pi$
$234$	−4.69865	−0.307160
$235$	−5.41493	−0.353231
$236$	1.71044	0.111340
$237$	4.95804	0.322059
$238$	0.861837	0.0558646
$239$	−19.8796	−1.28590	−0.642951	−	0.765907i	$-0.722290\pi$
$239$	−19.8796	−1.28590	−0.642951	+	0.765907i	$0.722290\pi$
$240$	−1.11996	−0.0722931
$241$	30.0258	1.93413	0.967066	−	0.254527i	$-0.0819198\pi$
$241$	30.0258	1.93413	0.967066	+	0.254527i	$0.0819198\pi$
$242$	9.84597	0.632923
$243$	−1.00000	−0.0641500
$244$	1.28641	0.0823538
$245$	−7.64741	−0.488575
$246$	−5.21985	−0.332806
$247$	−4.69865	−0.298968
$248$	−6.58106	−0.417897
$249$	−1.90178	−0.120520
$250$	9.79482	0.619479
$251$	−25.6800	−1.62091	−0.810454	−	0.585802i	$-0.800780\pi$
$251$	−25.6800	−1.62091	−0.810454	+	0.585802i	$0.800780\pi$
$252$	0.414381	0.0261035
$253$	0.475377	0.0298867
$254$	0.191244	0.0119997
$255$	2.32931	0.145867
$256$	1.00000	0.0625000
$257$	28.0707	1.75100	0.875500	−	0.483218i	$-0.160532\pi$
$257$	28.0707	1.75100	0.875500	+	0.483218i	$0.160532\pi$
$258$	−6.51709	−0.405737
$259$	−2.19647	−0.136482
$260$	5.26230	0.326354
$261$	−5.42550	−0.335830
$262$	5.98910	0.370008
$263$	−17.6616	−1.08906	−0.544530	−	0.838742i	$-0.683292\pi$
$263$	−17.6616	−1.08906	−0.544530	+	0.838742i	$0.683292\pi$
$264$	1.07426	0.0661159
$265$	−1.11996	−0.0687986
$266$	0.414381	0.0254073
$267$	12.4686	0.763067
$268$	−0.633661	−0.0387070
$269$	−6.19768	−0.377879	−0.188940	−	0.981989i	$-0.560505\pi$
$269$	−6.19768	−0.377879	−0.188940	+	0.981989i	$0.560505\pi$
$270$	1.11996	0.0681586
$271$	−2.76949	−0.168235	−0.0841174	−	0.996456i	$-0.526807\pi$
$271$	−2.76949	−0.168235	−0.0841174	+	0.996456i	$0.526807\pi$
$272$	−2.07982	−0.126107
$273$	−1.94703	−0.117840
$274$	15.4908	0.935833
$275$	−4.02383	−0.242646
$276$	−0.442517	−0.0266364
$277$	−6.62257	−0.397912	−0.198956	−	0.980008i	$-0.563755\pi$
$277$	−6.62257	−0.397912	−0.198956	+	0.980008i	$0.563755\pi$
$278$	−20.3956	−1.22325
$279$	6.58106	0.393998
$280$	−0.464090	−0.0277347
$281$	19.4572	1.16072	0.580361	−	0.814359i	$-0.302911\pi$
$281$	19.4572	1.16072	0.580361	+	0.814359i	$0.302911\pi$
$282$	−4.83494	−0.287916
$283$	−7.92876	−0.471316	−0.235658	−	0.971836i	$-0.575724\pi$
$283$	−7.92876	−0.471316	−0.235658	+	0.971836i	$0.575724\pi$
$284$	−12.8057	−0.759881
$285$	1.11996	0.0663407
$286$	−5.04756	−0.298468
$287$	−2.16301	−0.127678
$288$	−1.00000	−0.0589256
$289$	−12.6744	−0.745550
$290$	6.07634	0.356815
$291$	−15.2292	−0.892753
$292$	−0.429813	−0.0251529
$293$	7.10688	0.415189	0.207594	−	0.978215i	$-0.433437\pi$
$293$	7.10688	0.415189	0.207594	+	0.978215i	$0.433437\pi$
$294$	−6.82829	−0.398234
$295$	1.91563	0.111532
$296$	5.30061	0.308092
$297$	−1.07426	−0.0623347
$298$	−11.4678	−0.664314
$299$	2.07923	0.120245
$300$	3.74569	0.216258
$301$	−2.70056	−0.155658
$302$	21.1846	1.21903
$303$	−1.59554	−0.0916615
$304$	−1.00000	−0.0573539
$305$	1.44072	0.0824957
$306$	2.07982	0.118895
$307$	−31.2053	−1.78098	−0.890490	−	0.455003i	$-0.849638\pi$
$307$	−31.2053	−1.78098	−0.890490	+	0.455003i	$0.849638\pi$
$308$	0.445152	0.0253649
$309$	4.54676	0.258656
$310$	−7.37052	−0.418617
$311$	−15.2071	−0.862315	−0.431158	−	0.902277i	$-0.641895\pi$
$311$	−15.2071	−0.862315	−0.431158	+	0.902277i	$0.641895\pi$
$312$	4.69865	0.266009
$313$	6.26851	0.354317	0.177159	−	0.984182i	$-0.443309\pi$
$313$	6.26851	0.354317	0.177159	+	0.984182i	$0.443309\pi$
$314$	16.3639	0.923466
$315$	0.464090	0.0261485
$316$	−4.95804	−0.278912
$317$	−30.6940	−1.72395	−0.861974	−	0.506952i	$-0.830772\pi$
$317$	−30.6940	−1.72395	−0.861974	+	0.506952i	$0.830772\pi$
$318$	−1.00000	−0.0560772
$319$	−5.82838	−0.326326
$320$	1.11996	0.0626076
$321$	18.1239	1.01158
$322$	−0.183371	−0.0102189
$323$	2.07982	0.115724
$324$	1.00000	0.0555556
$325$	−17.5997	−0.976255
$326$	7.80612	0.432341
$327$	−12.8271	−0.709339
$328$	5.21985	0.288218
$329$	−2.00351	−0.110457
$330$	1.20312	0.0662298
$331$	11.4351	0.628531	0.314265	−	0.949335i	$-0.398242\pi$
$331$	11.4351	0.628531	0.314265	+	0.949335i	$0.398242\pi$
$332$	1.90178	0.104373
$333$	−5.30061	−0.290472
$334$	−7.23291	−0.395767
$335$	−0.709674	−0.0387736
$336$	−0.414381	−0.0226063
$337$	14.2608	0.776833	0.388417	−	0.921484i	$-0.373022\pi$
$337$	14.2608	0.776833	0.388417	+	0.921484i	$0.373022\pi$
$338$	−9.07732	−0.493741
$339$	−13.8844	−0.754099
$340$	−2.32931	−0.126325
$341$	7.06975	0.382848
$342$	1.00000	0.0540738
$343$	−5.73018	−0.309401
$344$	6.51709	0.351378
$345$	−0.495601	−0.0266823
$346$	−13.3026	−0.715152
$347$	−30.7758	−1.65213	−0.826066	−	0.563574i	$-0.809426\pi$
$347$	−30.7758	−1.65213	−0.826066	+	0.563574i	$0.809426\pi$
$348$	5.42550	0.290837
$349$	31.0773	1.66353	0.831764	−	0.555130i	$-0.187331\pi$
$349$	31.0773	1.66353	0.831764	+	0.555130i	$0.187331\pi$
$350$	1.55214	0.0829655
$351$	−4.69865	−0.250795
$352$	−1.07426	−0.0572581
$353$	−10.2429	−0.545173	−0.272586	−	0.962131i	$-0.587879\pi$
$353$	−10.2429	−0.545173	−0.272586	+	0.962131i	$0.587879\pi$
$354$	1.71044	0.0909090
$355$	−14.3419	−0.761190
$356$	−12.4686	−0.660836
$357$	0.861837	0.0456133
$358$	−7.63427	−0.403483
$359$	−12.8429	−0.677823	−0.338911	−	0.940818i	$-0.610059\pi$
$359$	−12.8429	−0.677823	−0.338911	+	0.940818i	$0.610059\pi$
$360$	−1.11996	−0.0590271
$361$	1.00000	0.0526316
$362$	2.67830	0.140769
$363$	9.84597	0.516779
$364$	1.94703	0.102052
$365$	−0.481373	−0.0251962
$366$	1.28641	0.0672416
$367$	32.1983	1.68074	0.840369	−	0.542015i	$-0.182338\pi$
$367$	32.1983	1.68074	0.840369	+	0.542015i	$0.182338\pi$
$368$	0.442517	0.0230678
$369$	−5.21985	−0.271735
$370$	5.93647	0.308623
$371$	−0.414381	−0.0215136
$372$	−6.58106	−0.341212
$373$	20.2458	1.04829	0.524144	−	0.851629i	$-0.324385\pi$
$373$	20.2458	1.04829	0.524144	+	0.851629i	$0.324385\pi$
$374$	2.23426	0.115531
$375$	9.79482	0.505802
$376$	4.83494	0.249343
$377$	−25.4925	−1.31293
$378$	0.414381	0.0213135
$379$	17.0255	0.874539	0.437270	−	0.899330i	$-0.355946\pi$
$379$	17.0255	0.874539	0.437270	+	0.899330i	$0.355946\pi$
$380$	−1.11996	−0.0574527
$381$	0.191244	0.00979774
$382$	−5.64261	−0.288701
$383$	−10.5466	−0.538906	−0.269453	−	0.963014i	$-0.586843\pi$
$383$	−10.5466	−0.538906	−0.269453	+	0.963014i	$0.586843\pi$
$384$	1.00000	0.0510310
$385$	0.498552	0.0254086
$386$	4.86025	0.247380
$387$	−6.51709	−0.331282
$388$	15.2292	0.773147
$389$	6.58782	0.334016	0.167008	−	0.985956i	$-0.446589\pi$
$389$	6.58782	0.334016	0.167008	+	0.985956i	$0.446589\pi$
$390$	5.26230	0.266467
$391$	−0.920355	−0.0465444
$392$	6.82829	0.344881
$393$	5.98910	0.302110
$394$	−6.45088	−0.324991
$395$	−5.55280	−0.279392
$396$	1.07426	0.0539834
$397$	−9.44960	−0.474262	−0.237131	−	0.971478i	$-0.576207\pi$
$397$	−9.44960	−0.474262	−0.237131	+	0.971478i	$0.576207\pi$
$398$	−12.1704	−0.610046
$399$	0.414381	0.0207450
$400$	−3.74569	−0.187285
$401$	21.0080	1.04909	0.524544	−	0.851383i	$-0.324236\pi$
$401$	21.0080	1.04909	0.524544	+	0.851383i	$0.324236\pi$
$402$	−0.633661	−0.0316041
$403$	30.9221	1.54034
$404$	1.59554	0.0793812
$405$	1.11996	0.0556512
$406$	2.24822	0.111577
$407$	−5.69422	−0.282252
$408$	−2.07982	−0.102966
$409$	25.3697	1.25445	0.627224	−	0.778839i	$-0.284191\pi$
$409$	25.3697	1.25445	0.627224	+	0.778839i	$0.284191\pi$
$410$	5.84603	0.288715
$411$	15.4908	0.764105
$412$	−4.54676	−0.224003
$413$	0.708775	0.0348765
$414$	−0.442517	−0.0217485
$415$	2.12991	0.104553
$416$	−4.69865	−0.230370
$417$	−20.3956	−0.998779
$418$	1.07426	0.0525436
$419$	−14.9257	−0.729169	−0.364585	−	0.931170i	$-0.618789\pi$
$419$	−14.9257	−0.729169	−0.364585	+	0.931170i	$0.618789\pi$
$420$	−0.464090	−0.0226453
$421$	−28.3912	−1.38370	−0.691852	−	0.722039i	$-0.743205\pi$
$421$	−28.3912	−1.38370	−0.691852	+	0.722039i	$0.743205\pi$
$422$	−7.54566	−0.367317
$423$	−4.83494	−0.235083
$424$	1.00000	0.0485643
$425$	7.79035	0.377888
$426$	−12.8057	−0.620440
$427$	0.533063	0.0257967
$428$	−18.1239	−0.876052
$429$	−5.04756	−0.243698
$430$	7.29888	0.351983
$431$	1.97971	0.0953592	0.0476796	−	0.998863i	$-0.484817\pi$
$431$	1.97971	0.0953592	0.0476796	+	0.998863i	$0.484817\pi$
$432$	−1.00000	−0.0481125
$433$	1.14752	0.0551465	0.0275732	−	0.999620i	$-0.491222\pi$
$433$	1.14752	0.0551465	0.0275732	+	0.999620i	$0.491222\pi$
$434$	−2.72706	−0.130903
$435$	6.07634	0.291338
$436$	12.8271	0.614306
$437$	−0.442517	−0.0211685
$438$	−0.429813	−0.0205372
$439$	−2.31753	−0.110610	−0.0553048	−	0.998470i	$-0.517613\pi$
$439$	−2.31753	−0.110610	−0.0553048	+	0.998470i	$0.517613\pi$
$440$	−1.20312	−0.0573567
$441$	−6.82829	−0.325157
$442$	9.77234	0.464823
$443$	0.543528	0.0258238	0.0129119	−	0.999917i	$-0.495890\pi$
$443$	0.543528	0.0258238	0.0129119	+	0.999917i	$0.495890\pi$
$444$	5.30061	0.251556
$445$	−13.9644	−0.661974
$446$	13.8813	0.657297
$447$	−11.4678	−0.542410
$448$	0.414381	0.0195777
$449$	25.5434	1.20547	0.602734	−	0.797942i	$-0.294078\pi$
$449$	25.5434	1.20547	0.602734	+	0.797942i	$0.294078\pi$
$450$	3.74569	0.176574
$451$	−5.60747	−0.264045
$452$	13.8844	0.653069
$453$	21.1846	0.995338
$454$	11.2878	0.529760
$455$	2.18060	0.102228
$456$	−1.00000	−0.0468293
$457$	−0.955007	−0.0446733	−0.0223367	−	0.999751i	$-0.507111\pi$
$457$	−0.955007	−0.0446733	−0.0223367	+	0.999751i	$0.507111\pi$
$458$	−27.4562	−1.28294
$459$	2.07982	0.0970776
$460$	0.495601	0.0231075
$461$	−19.9060	−0.927115	−0.463557	−	0.886067i	$-0.653427\pi$
$461$	−19.9060	−0.927115	−0.463557	+	0.886067i	$0.653427\pi$
$462$	0.445152	0.0207103
$463$	−24.1051	−1.12026	−0.560129	−	0.828405i	$-0.689248\pi$
$463$	−24.1051	−1.12026	−0.560129	+	0.828405i	$0.689248\pi$
$464$	−5.42550	−0.251872
$465$	−7.37052	−0.341800
$466$	−1.63814	−0.0758854
$467$	16.6305	0.769570	0.384785	−	0.923006i	$-0.374276\pi$
$467$	16.6305	0.769570	0.384785	+	0.923006i	$0.374276\pi$
$468$	4.69865	0.217195
$469$	−0.262577	−0.0121247
$470$	5.41493	0.249772
$471$	16.3639	0.754007
$472$	−1.71044	−0.0787295
$473$	−7.00103	−0.321908
$474$	−4.95804	−0.227730
$475$	3.74569	0.171864
$476$	−0.861837	−0.0395022
$477$	−1.00000	−0.0457869
$478$	19.8796	0.909270
$479$	−6.31504	−0.288542	−0.144271	−	0.989538i	$-0.546084\pi$
$479$	−6.31504	−0.288542	−0.144271	+	0.989538i	$0.546084\pi$
$480$	1.11996	0.0511189
$481$	−24.9057	−1.13560
$482$	−30.0258	−1.36764
$483$	−0.183371	−0.00834366
$484$	−9.84597	−0.447544
$485$	17.0561	0.774479
$486$	1.00000	0.0453609
$487$	−19.4356	−0.880712	−0.440356	−	0.897823i	$-0.645148\pi$
$487$	−19.4356	−0.880712	−0.440356	+	0.897823i	$0.645148\pi$
$488$	−1.28641	−0.0582329
$489$	7.80612	0.353005
$490$	7.64741	0.345475
$491$	−42.5307	−1.91938	−0.959691	−	0.281057i	$-0.909315\pi$
$491$	−42.5307	−1.91938	−0.959691	+	0.281057i	$0.909315\pi$
$492$	5.21985	0.235329
$493$	11.2840	0.508208
$494$	4.69865	0.211402
$495$	1.20312	0.0540764
$496$	6.58106	0.295498
$497$	−5.30646	−0.238027
$498$	1.90178	0.0852206
$499$	4.68008	0.209509	0.104755	−	0.994498i	$-0.466594\pi$
$499$	4.68008	0.209509	0.104755	+	0.994498i	$0.466594\pi$
$500$	−9.79482	−0.438038
$501$	−7.23291	−0.323142
$502$	25.6800	1.14616
$503$	−29.4650	−1.31378	−0.656889	−	0.753988i	$-0.728128\pi$
$503$	−29.4650	−1.31378	−0.656889	+	0.753988i	$0.728128\pi$
$504$	−0.414381	−0.0184580
$505$	1.78694	0.0795179
$506$	−0.475377	−0.0211331
$507$	−9.07732	−0.403138
$508$	−0.191244	−0.00848509
$509$	−26.8002	−1.18790	−0.593950	−	0.804502i	$-0.702432\pi$
$509$	−26.8002	−1.18790	−0.593950	+	0.804502i	$0.702432\pi$
$510$	−2.32931	−0.103144
$511$	−0.178106	−0.00787896
$512$	−1.00000	−0.0441942
$513$	1.00000	0.0441511
$514$	−28.0707	−1.23814
$515$	−5.09219	−0.224389
$516$	6.51709	0.286899
$517$	−5.19396	−0.228430
$518$	2.19647	0.0965075
$519$	−13.3026	−0.583919
$520$	−5.26230	−0.230767
$521$	20.4705	0.896831	0.448415	−	0.893825i	$-0.351989\pi$
$521$	20.4705	0.896831	0.448415	+	0.893825i	$0.351989\pi$
$522$	5.42550	0.237468
$523$	17.4789	0.764299	0.382149	−	0.924101i	$-0.375184\pi$
$523$	17.4789	0.764299	0.382149	+	0.924101i	$0.375184\pi$
$524$	−5.98910	−0.261635
$525$	1.55214	0.0677411
$526$	17.6616	0.770081
$527$	−13.6874	−0.596232
$528$	−1.07426	−0.0467510
$529$	−22.8042	−0.991486
$530$	1.11996	0.0486479
$531$	1.71044	0.0742269
$532$	−0.414381	−0.0179657
$533$	−24.5263	−1.06235
$534$	−12.4686	−0.539570
$535$	−20.2980	−0.877561
$536$	0.633661	0.0273700
$537$	−7.63427	−0.329443
$538$	6.19768	0.267201
$539$	−7.33534	−0.315955
$540$	−1.11996	−0.0481954
$541$	−10.6989	−0.459982	−0.229991	−	0.973193i	$-0.573870\pi$
$541$	−10.6989	−0.459982	−0.229991	+	0.973193i	$0.573870\pi$
$542$	2.76949	0.118960
$543$	2.67830	0.114937
$544$	2.07982	0.0891715
$545$	14.3658	0.615364
$546$	1.94703	0.0833253
$547$	−44.5921	−1.90662	−0.953310	−	0.301993i	$-0.902348\pi$
$547$	−44.5921	−1.90662	−0.953310	+	0.301993i	$0.902348\pi$
$548$	−15.4908	−0.661734
$549$	1.28641	0.0549025
$550$	4.02383	0.171577
$551$	5.42550	0.231134
$552$	0.442517	0.0188348
$553$	−2.05452	−0.0873670
$554$	6.62257	0.281366
$555$	5.93647	0.251989
$556$	20.3956	0.864968
$557$	−2.82402	−0.119658	−0.0598288	−	0.998209i	$-0.519055\pi$
$557$	−2.82402	−0.119658	−0.0598288	+	0.998209i	$0.519055\pi$
$558$	−6.58106	−0.278598
$559$	−30.6215	−1.29515
$560$	0.464090	0.0196114
$561$	2.23426	0.0943305
$562$	−19.4572	−0.820754
$563$	5.86191	0.247050	0.123525	−	0.992341i	$-0.460580\pi$
$563$	5.86191	0.247050	0.123525	+	0.992341i	$0.460580\pi$
$564$	4.83494	0.203588
$565$	15.5500	0.654193
$566$	7.92876	0.333271
$567$	0.414381	0.0174024
$568$	12.8057	0.537317
$569$	−28.3074	−1.18671	−0.593353	−	0.804942i	$-0.702196\pi$
$569$	−28.3074	−1.18671	−0.593353	+	0.804942i	$0.702196\pi$
$570$	−1.11996	−0.0469099
$571$	−16.4541	−0.688584	−0.344292	−	0.938863i	$-0.611881\pi$
$571$	−16.4541	−0.688584	−0.344292	+	0.938863i	$0.611881\pi$
$572$	5.04756	0.211049
$573$	−5.64261	−0.235723
$574$	2.16301	0.0902822
$575$	−1.65753	−0.0691239
$576$	1.00000	0.0416667
$577$	1.84690	0.0768873	0.0384436	−	0.999261i	$-0.487760\pi$
$577$	1.84690	0.0768873	0.0384436	+	0.999261i	$0.487760\pi$
$578$	12.6744	0.527184
$579$	4.86025	0.201985
$580$	−6.07634	−0.252306
$581$	0.788060	0.0326942
$582$	15.2292	0.631272
$583$	−1.07426	−0.0444912
$584$	0.429813	0.0177858
$585$	5.26230	0.217569
$586$	−7.10688	−0.293583
$587$	−22.2344	−0.917710	−0.458855	−	0.888511i	$-0.651740\pi$
$587$	−22.2344	−0.917710	−0.458855	+	0.888511i	$0.651740\pi$
$588$	6.82829	0.281594
$589$	−6.58106	−0.271168
$590$	−1.91563	−0.0788651
$591$	−6.45088	−0.265354
$592$	−5.30061	−0.217854
$593$	−36.4801	−1.49806	−0.749030	−	0.662536i	$-0.769480\pi$
$593$	−36.4801	−1.49806	−0.749030	+	0.662536i	$0.769480\pi$
$594$	1.07426	0.0440773
$595$	−0.965223	−0.0395703
$596$	11.4678	0.469741
$597$	−12.1704	−0.498101
$598$	−2.07923	−0.0850262
$599$	7.33975	0.299894	0.149947	−	0.988694i	$-0.452090\pi$
$599$	7.33975	0.299894	0.149947	+	0.988694i	$0.452090\pi$
$600$	−3.74569	−0.152917
$601$	−15.4216	−0.629058	−0.314529	−	0.949248i	$-0.601847\pi$
$601$	−15.4216	−0.629058	−0.314529	+	0.949248i	$0.601847\pi$
$602$	2.70056	0.110067
$603$	−0.633661	−0.0258047
$604$	−21.1846	−0.861988
$605$	−11.0271	−0.448315
$606$	1.59554	0.0648145
$607$	−25.4169	−1.03164	−0.515820	−	0.856697i	$-0.672512\pi$
$607$	−25.4169	−1.03164	−0.515820	+	0.856697i	$0.672512\pi$
$608$	1.00000	0.0405554
$609$	2.24822	0.0911026
$610$	−1.44072	−0.0583332
$611$	−22.7177	−0.919059
$612$	−2.07982	−0.0840717
$613$	−8.79762	−0.355332	−0.177666	−	0.984091i	$-0.556855\pi$
$613$	−8.79762	−0.355332	−0.177666	+	0.984091i	$0.556855\pi$
$614$	31.2053	1.25934
$615$	5.84603	0.235735
$616$	−0.445152	−0.0179357
$617$	−11.1952	−0.450701	−0.225350	−	0.974278i	$-0.572353\pi$
$617$	−11.1952	−0.450701	−0.225350	+	0.974278i	$0.572353\pi$
$618$	−4.54676	−0.182898
$619$	37.5674	1.50996	0.754980	−	0.655748i	$-0.227646\pi$
$619$	37.5674	1.50996	0.754980	+	0.655748i	$0.227646\pi$
$620$	7.37052	0.296007
$621$	−0.442517	−0.0177576
$622$	15.2071	0.609749
$623$	−5.16676	−0.207002
$624$	−4.69865	−0.188097
$625$	7.75865	0.310346
$626$	−6.26851	−0.250540
$627$	1.07426	0.0429017
$628$	−16.3639	−0.652989
$629$	11.0243	0.439568
$630$	−0.464090	−0.0184898
$631$	−2.80410	−0.111629	−0.0558147	−	0.998441i	$-0.517776\pi$
$631$	−2.80410	−0.111629	−0.0558147	+	0.998441i	$0.517776\pi$
$632$	4.95804	0.197220
$633$	−7.54566	−0.299913
$634$	30.6940	1.21902
$635$	−0.214186	−0.00849970
$636$	1.00000	0.0396526
$637$	−32.0837	−1.27120
$638$	5.82838	0.230748
$639$	−12.8057	−0.506587
$640$	−1.11996	−0.0442703
$641$	−22.3746	−0.883743	−0.441872	−	0.897078i	$-0.645685\pi$
$641$	−22.3746	−0.883743	−0.441872	+	0.897078i	$0.645685\pi$
$642$	−18.1239	−0.715293
$643$	23.8410	0.940197	0.470099	−	0.882614i	$-0.344218\pi$
$643$	23.8410	0.940197	0.470099	+	0.882614i	$0.344218\pi$
$644$	0.183371	0.00722582
$645$	7.29888	0.287393
$646$	−2.07982	−0.0818293
$647$	−42.2770	−1.66208	−0.831039	−	0.556214i	$-0.812254\pi$
$647$	−42.2770	−1.66208	−0.831039	+	0.556214i	$0.812254\pi$
$648$	−1.00000	−0.0392837
$649$	1.83746	0.0721264
$650$	17.5997	0.690317
$651$	−2.72706	−0.106882
$652$	−7.80612	−0.305711
$653$	40.2192	1.57390	0.786950	−	0.617017i	$-0.211659\pi$
$653$	40.2192	1.57390	0.786950	+	0.617017i	$0.211659\pi$
$654$	12.8271	0.501579
$655$	−6.70755	−0.262086
$656$	−5.21985	−0.203801
$657$	−0.429813	−0.0167686
$658$	2.00351	0.0781048
$659$	20.1793	0.786073	0.393037	−	0.919523i	$-0.371425\pi$
$659$	20.1793	0.786073	0.393037	+	0.919523i	$0.371425\pi$
$660$	−1.20312	−0.0468316
$661$	41.3843	1.60966	0.804832	−	0.593503i	$-0.202255\pi$
$661$	41.3843	1.60966	0.804832	+	0.593503i	$0.202255\pi$
$662$	−11.4351	−0.444438
$663$	9.77234	0.379526
$664$	−1.90178	−0.0738032
$665$	−0.464090	−0.0179966
$666$	5.30061	0.205395
$667$	−2.40088	−0.0929623
$668$	7.23291	0.279850
$669$	13.8813	0.536681
$670$	0.709674	0.0274171
$671$	1.38193	0.0533489
$672$	0.414381	0.0159851
$673$	37.6174	1.45005	0.725023	−	0.688725i	$-0.241829\pi$
$673$	37.6174	1.45005	0.725023	+	0.688725i	$0.241829\pi$
$674$	−14.2608	−0.549304
$675$	3.74569	0.144172
$676$	9.07732	0.349128
$677$	−12.1463	−0.466819	−0.233409	−	0.972379i	$-0.574988\pi$
$677$	−12.1463	−0.466819	−0.233409	+	0.972379i	$0.574988\pi$
$678$	13.8844	0.533228
$679$	6.31070	0.242183
$680$	2.32931	0.0893250
$681$	11.2878	0.432548
$682$	−7.06975	−0.270715
$683$	−39.2370	−1.50136	−0.750680	−	0.660665i	$-0.770274\pi$
$683$	−39.2370	−1.50136	−0.750680	+	0.660665i	$0.770274\pi$
$684$	−1.00000	−0.0382360
$685$	−17.3491	−0.662874
$686$	5.73018	0.218779
$687$	−27.4562	−1.04752
$688$	−6.51709	−0.248462
$689$	−4.69865	−0.179004
$690$	0.495601	0.0188672
$691$	4.83337	0.183870	0.0919349	−	0.995765i	$-0.470695\pi$
$691$	4.83337	0.183870	0.0919349	+	0.995765i	$0.470695\pi$
$692$	13.3026	0.505689
$693$	0.445152	0.0169099
$694$	30.7758	1.16823
$695$	22.8423	0.866457
$696$	−5.42550	−0.205653
$697$	10.8563	0.411213
$698$	−31.0773	−1.17629
$699$	−1.63814	−0.0619602
$700$	−1.55214	−0.0586655
$701$	10.1038	0.381616	0.190808	−	0.981627i	$-0.438889\pi$
$701$	10.1038	0.381616	0.190808	+	0.981627i	$0.438889\pi$
$702$	4.69865	0.177339
$703$	5.30061	0.199916
$704$	1.07426	0.0404876
$705$	5.41493	0.203938
$706$	10.2429	0.385495
$707$	0.661163	0.0248656
$708$	−1.71044	−0.0642824
$709$	−38.2215	−1.43544	−0.717718	−	0.696333i	$-0.754813\pi$
$709$	−38.2215	−1.43544	−0.717718	+	0.696333i	$0.754813\pi$
$710$	14.3419	0.538242
$711$	−4.95804	−0.185941
$712$	12.4686	0.467281
$713$	2.91223	0.109064
$714$	−0.861837	−0.0322534
$715$	5.65306	0.211413
$716$	7.63427	0.285306
$717$	19.8796	0.742416
$718$	12.8429	0.479293
$719$	−14.3412	−0.534835	−0.267418	−	0.963581i	$-0.586170\pi$
$719$	−14.3412	−0.534835	−0.267418	+	0.963581i	$0.586170\pi$
$720$	1.11996	0.0417384
$721$	−1.88409	−0.0701673
$722$	−1.00000	−0.0372161
$723$	−30.0258	−1.11667
$724$	−2.67830	−0.0995384
$725$	20.3222	0.754749
$726$	−9.84597	−0.365418
$727$	1.45227	0.0538615	0.0269308	−	0.999637i	$-0.491427\pi$
$727$	1.45227	0.0538615	0.0269308	+	0.999637i	$0.491427\pi$
$728$	−1.94703	−0.0721618
$729$	1.00000	0.0370370
$730$	0.481373	0.0178164
$731$	13.5544	0.501326
$732$	−1.28641	−0.0475470
$733$	−41.5039	−1.53298	−0.766490	−	0.642256i	$-0.777998\pi$
$733$	−41.5039	−1.53298	−0.766490	+	0.642256i	$0.777998\pi$
$734$	−32.1983	−1.18846
$735$	7.64741	0.282079
$736$	−0.442517	−0.0163114
$737$	−0.680714	−0.0250744
$738$	5.21985	0.192145
$739$	28.1207	1.03444	0.517218	−	0.855854i	$-0.326968\pi$
$739$	28.1207	1.03444	0.517218	+	0.855854i	$0.326968\pi$
$740$	−5.93647	−0.218229
$741$	4.69865	0.172609
$742$	0.414381	0.0152124
$743$	−14.7024	−0.539380	−0.269690	−	0.962947i	$-0.586921\pi$
$743$	−14.7024	−0.539380	−0.269690	+	0.962947i	$0.586921\pi$
$744$	6.58106	0.241273
$745$	12.8435	0.470550
$746$	−20.2458	−0.741252
$747$	1.90178	0.0695823
$748$	−2.23426	−0.0816926
$749$	−7.51020	−0.274417
$750$	−9.79482	−0.357656
$751$	20.3889	0.744003	0.372002	−	0.928232i	$-0.378672\pi$
$751$	20.3889	0.744003	0.372002	+	0.928232i	$0.378672\pi$
$752$	−4.83494	−0.176312
$753$	25.6800	0.935832
$754$	25.4925	0.928383
$755$	−23.7259	−0.863472
$756$	−0.414381	−0.0150709
$757$	−2.81834	−0.102434	−0.0512172	−	0.998688i	$-0.516310\pi$
$757$	−2.81834	−0.102434	−0.0512172	+	0.998688i	$0.516310\pi$
$758$	−17.0255	−0.618393
$759$	−0.475377	−0.0172551
$760$	1.11996	0.0406252
$761$	11.0317	0.399898	0.199949	−	0.979806i	$-0.435922\pi$
$761$	11.0317	0.399898	0.199949	+	0.979806i	$0.435922\pi$
$762$	−0.191244	−0.00692805
$763$	5.31530	0.192427
$764$	5.64261	0.204142
$765$	−2.32931	−0.0842165
$766$	10.5466	0.381064
$767$	8.03677	0.290191
$768$	−1.00000	−0.0360844
$769$	−42.2476	−1.52349	−0.761744	−	0.647879i	$-0.775656\pi$
$769$	−42.2476	−1.52349	−0.761744	+	0.647879i	$0.775656\pi$
$770$	−0.498552	−0.0179666
$771$	−28.0707	−1.01094
$772$	−4.86025	−0.174924
$773$	−12.8314	−0.461513	−0.230756	−	0.973012i	$-0.574120\pi$
$773$	−12.8314	−0.461513	−0.230756	+	0.973012i	$0.574120\pi$
$774$	6.51709	0.234252
$775$	−24.6506	−0.885476
$776$	−15.2292	−0.546697
$777$	2.19647	0.0787981
$778$	−6.58782	−0.236185
$779$	5.21985	0.187021
$780$	−5.26230	−0.188421
$781$	−13.7567	−0.492252
$782$	0.920355	0.0329118
$783$	5.42550	0.193891
$784$	−6.82829	−0.243867
$785$	−18.3269	−0.654114
$786$	−5.98910	−0.213624
$787$	5.31264	0.189375	0.0946876	−	0.995507i	$-0.469815\pi$
$787$	5.31264	0.189375	0.0946876	+	0.995507i	$0.469815\pi$
$788$	6.45088	0.229803
$789$	17.6616	0.628769
$790$	5.55280	0.197560
$791$	5.75344	0.204569
$792$	−1.07426	−0.0381721
$793$	6.04438	0.214642
$794$	9.44960	0.335354
$795$	1.11996	0.0397209
$796$	12.1704	0.431368
$797$	16.7831	0.594489	0.297245	−	0.954801i	$-0.403932\pi$
$797$	16.7831	0.594489	0.297245	+	0.954801i	$0.403932\pi$
$798$	−0.414381	−0.0146689
$799$	10.0558	0.355748
$800$	3.74569	0.132430
$801$	−12.4686	−0.440557
$802$	−21.0080	−0.741817
$803$	−0.461729	−0.0162941
$804$	0.633661	0.0223475
$805$	0.205368	0.00723827
$806$	−30.9221	−1.08918
$807$	6.19768	0.218169
$808$	−1.59554	−0.0561310
$809$	−36.6521	−1.28862	−0.644310	−	0.764765i	$-0.722855\pi$
$809$	−36.6521	−1.28862	−0.644310	+	0.764765i	$0.722855\pi$
$810$	−1.11996	−0.0393514
$811$	27.3061	0.958848	0.479424	−	0.877584i	$-0.340846\pi$
$811$	27.3061	0.958848	0.479424	+	0.877584i	$0.340846\pi$
$812$	−2.24822	−0.0788971
$813$	2.76949	0.0971304
$814$	5.69422	0.199582
$815$	−8.74254	−0.306238
$816$	2.07982	0.0728082
$817$	6.51709	0.228004
$818$	−25.3697	−0.887029
$819$	1.94703	0.0680348
$820$	−5.84603	−0.204152
$821$	−49.9945	−1.74482	−0.872411	−	0.488774i	$-0.837444\pi$
$821$	−49.9945	−1.74482	−0.872411	+	0.488774i	$0.837444\pi$
$822$	−15.4908	−0.540303
$823$	8.48972	0.295933	0.147967	−	0.988992i	$-0.452727\pi$
$823$	8.48972	0.295933	0.147967	+	0.988992i	$0.452727\pi$
$824$	4.54676	0.158394
$825$	4.02383	0.140092
$826$	−0.708775	−0.0246614
$827$	19.1545	0.666068	0.333034	−	0.942915i	$-0.391928\pi$
$827$	19.1545	0.666068	0.333034	+	0.942915i	$0.391928\pi$
$828$	0.442517	0.0153785
$829$	−33.6923	−1.17018	−0.585091	−	0.810967i	$-0.698941\pi$
$829$	−33.6923	−1.17018	−0.585091	+	0.810967i	$0.698941\pi$
$830$	−2.12991	−0.0739303
$831$	6.62257	0.229734
$832$	4.69865	0.162896
$833$	14.2016	0.492056
$834$	20.3956	0.706243
$835$	8.10056	0.280332
$836$	−1.07426	−0.0371540
$837$	−6.58106	−0.227475
$838$	14.9257	0.515600
$839$	46.7094	1.61259	0.806293	−	0.591516i	$-0.201470\pi$
$839$	46.7094	1.61259	0.806293	+	0.591516i	$0.201470\pi$
$840$	0.464090	0.0160126
$841$	0.436005	0.0150347
$842$	28.3912	0.978426
$843$	−19.4572	−0.670143
$844$	7.54566	0.259732
$845$	10.1662	0.349729
$846$	4.83494	0.166229
$847$	−4.07998	−0.140190
$848$	−1.00000	−0.0343401
$849$	7.92876	0.272114
$850$	−7.79035	−0.267207
$851$	−2.34561	−0.0804066
$852$	12.8057	0.438718
$853$	−18.6645	−0.639061	−0.319531	−	0.947576i	$-0.603525\pi$
$853$	−18.6645	−0.639061	−0.319531	+	0.947576i	$0.603525\pi$
$854$	−0.533063	−0.0182410
$855$	−1.11996	−0.0383018
$856$	18.1239	0.619462
$857$	30.7604	1.05076	0.525378	−	0.850869i	$-0.323924\pi$
$857$	30.7604	1.05076	0.525378	+	0.850869i	$0.323924\pi$
$858$	5.04756	0.172321
$859$	51.3224	1.75110	0.875549	−	0.483130i	$-0.160500\pi$
$859$	51.3224	1.75110	0.875549	+	0.483130i	$0.160500\pi$
$860$	−7.29888	−0.248890
$861$	2.16301	0.0737151
$862$	−1.97971	−0.0674291
$863$	−25.8111	−0.878621	−0.439311	−	0.898335i	$-0.644777\pi$
$863$	−25.8111	−0.878621	−0.439311	+	0.898335i	$0.644777\pi$
$864$	1.00000	0.0340207
$865$	14.8984	0.506560
$866$	−1.14752	−0.0389945
$867$	12.6744	0.430444
$868$	2.72706	0.0925626
$869$	−5.32621	−0.180679
$870$	−6.07634	−0.206007
$871$	−2.97735	−0.100884
$872$	−12.8271	−0.434380
$873$	15.2292	0.515431
$874$	0.442517	0.0149684
$875$	−4.05879	−0.137212
$876$	0.429813	0.0145220
$877$	30.6715	1.03570	0.517852	−	0.855470i	$-0.326732\pi$
$877$	30.6715	1.03570	0.517852	+	0.855470i	$0.326732\pi$
$878$	2.31753	0.0782128
$879$	−7.10688	−0.239709
$880$	1.20312	0.0405573
$881$	−51.2097	−1.72530	−0.862649	−	0.505803i	$-0.831196\pi$
$881$	−51.2097	−1.72530	−0.862649	+	0.505803i	$0.831196\pi$
$882$	6.82829	0.229920
$883$	−14.3969	−0.484494	−0.242247	−	0.970215i	$-0.577884\pi$
$883$	−14.3969	−0.484494	−0.242247	+	0.970215i	$0.577884\pi$
$884$	−9.77234	−0.328679
$885$	−1.91563	−0.0643931
$886$	−0.543528	−0.0182602
$887$	52.9445	1.77770	0.888851	−	0.458197i	$-0.151504\pi$
$887$	52.9445	1.77770	0.888851	+	0.458197i	$0.151504\pi$
$888$	−5.30061	−0.177877
$889$	−0.0792480	−0.00265789
$890$	13.9644	0.468086
$891$	1.07426	0.0359890
$892$	−13.8813	−0.464779
$893$	4.83494	0.161795
$894$	11.4678	0.383542
$895$	8.55007	0.285797
$896$	−0.414381	−0.0138435
$897$	−2.07923	−0.0694236
$898$	−25.5434	−0.852394
$899$	−35.7055	−1.19084
$900$	−3.74569	−0.124856
$901$	2.07982	0.0692888
$902$	5.60747	0.186708
$903$	2.70056	0.0898690
$904$	−13.8844	−0.461789
$905$	−2.99959	−0.0997098
$906$	−21.1846	−0.703810
$907$	49.4848	1.64311	0.821557	−	0.570126i	$-0.193106\pi$
$907$	49.4848	1.64311	0.821557	+	0.570126i	$0.193106\pi$
$908$	−11.2878	−0.374597
$909$	1.59554	0.0529208
$910$	−2.18060	−0.0722861
$911$	16.4759	0.545872	0.272936	−	0.962032i	$-0.412005\pi$
$911$	16.4759	0.545872	0.272936	+	0.962032i	$0.412005\pi$
$912$	1.00000	0.0331133
$913$	2.04300	0.0676133
$914$	0.955007	0.0315888
$915$	−1.44072	−0.0476289
$916$	27.4562	0.907178
$917$	−2.48177	−0.0819553
$918$	−2.07982	−0.0686442
$919$	−47.3816	−1.56297	−0.781487	−	0.623922i	$-0.785538\pi$
$919$	−47.3816	−1.56297	−0.781487	+	0.623922i	$0.785538\pi$
$920$	−0.495601	−0.0163395
$921$	31.2053	1.02825
$922$	19.9060	0.655569
$923$	−60.1697	−1.98051
$924$	−0.445152	−0.0146444
$925$	19.8545	0.652811
$926$	24.1051	0.792142
$927$	−4.54676	−0.149335
$928$	5.42550	0.178101
$929$	−24.8094	−0.813969	−0.406984	−	0.913435i	$-0.633420\pi$
$929$	−24.8094	−0.813969	−0.406984	+	0.913435i	$0.633420\pi$
$930$	7.37052	0.241689
$931$	6.82829	0.223788
$932$	1.63814	0.0536591
$933$	15.2071	0.497858
$934$	−16.6305	−0.544168
$935$	−2.50228	−0.0818333
$936$	−4.69865	−0.153580
$937$	9.48123	0.309738	0.154869	−	0.987935i	$-0.450504\pi$
$937$	9.48123	0.309738	0.154869	+	0.987935i	$0.450504\pi$
$938$	0.262577	0.00857344
$939$	−6.26851	−0.204565
$940$	−5.41493	−0.176616
$941$	−11.9359	−0.389100	−0.194550	−	0.980893i	$-0.562325\pi$
$941$	−11.9359	−0.389100	−0.194550	+	0.980893i	$0.562325\pi$
$942$	−16.3639	−0.533163
$943$	−2.30988	−0.0752199
$944$	1.71044	0.0556702
$945$	−0.464090	−0.0150968
$946$	7.00103	0.227623
$947$	23.8381	0.774633	0.387317	−	0.921947i	$-0.373402\pi$
$947$	23.8381	0.774633	0.387317	+	0.921947i	$0.373402\pi$
$948$	4.95804	0.161030
$949$	−2.01954	−0.0655570
$950$	−3.74569	−0.121526
$951$	30.6940	0.995322
$952$	0.861837	0.0279323
$953$	−23.4850	−0.760754	−0.380377	−	0.924831i	$-0.624206\pi$
$953$	−23.4850	−0.760754	−0.380377	+	0.924831i	$0.624206\pi$
$954$	1.00000	0.0323762
$955$	6.31949	0.204494
$956$	−19.8796	−0.642951
$957$	5.82838	0.188405
$958$	6.31504	0.204030
$959$	−6.41909	−0.207283
$960$	−1.11996	−0.0361465
$961$	12.3103	0.397106
$962$	24.9057	0.802993
$963$	−18.1239	−0.584035
$964$	30.0258	0.967066
$965$	−5.44328	−0.175225
$966$	0.183371	0.00589986
$967$	−26.9973	−0.868174	−0.434087	−	0.900871i	$-0.642929\pi$
$967$	−26.9973	−0.868174	−0.434087	+	0.900871i	$0.642929\pi$
$968$	9.84597	0.316462
$969$	−2.07982	−0.0668134
$970$	−17.0561	−0.547639
$971$	14.4317	0.463134	0.231567	−	0.972819i	$-0.425615\pi$
$971$	14.4317	0.463134	0.231567	+	0.972819i	$0.425615\pi$
$972$	−1.00000	−0.0320750
$973$	8.45156	0.270945
$974$	19.4356	0.622757
$975$	17.5997	0.563641
$976$	1.28641	0.0411769
$977$	−6.71026	−0.214680	−0.107340	−	0.994222i	$-0.534233\pi$
$977$	−6.71026	−0.214680	−0.107340	+	0.994222i	$0.534233\pi$
$978$	−7.80612	−0.249612
$979$	−13.3945	−0.428090
$980$	−7.64741	−0.244287
$981$	12.8271	0.409537
$982$	42.5307	1.35721
$983$	−37.0926	−1.18307	−0.591535	−	0.806279i	$-0.701478\pi$
$983$	−37.0926	−1.18307	−0.591535	+	0.806279i	$0.701478\pi$
$984$	−5.21985	−0.166403
$985$	7.22473	0.230199
$986$	−11.2840	−0.359357
$987$	2.00351	0.0637723
$988$	−4.69865	−0.149484
$989$	−2.88393	−0.0917035
$990$	−1.20312	−0.0382378
$991$	39.1857	1.24478	0.622388	−	0.782709i	$-0.286163\pi$
$991$	39.1857	1.24478	0.622388	+	0.782709i	$0.286163\pi$
$992$	−6.58106	−0.208949
$993$	−11.4351	−0.362882
$994$	5.30646	0.168311
$995$	13.6303	0.432111
$996$	−1.90178	−0.0602601
$997$	31.8595	1.00900	0.504500	−	0.863412i	$-0.331677\pi$
$997$	31.8595	1.00900	0.504500	+	0.863412i	$0.331677\pi$
$998$	−4.68008	−0.148145
$999$	5.30061	0.167704

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.be.1.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.be.1.8	✓	12	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.11996 q^{5} +1.00000 q^{6} +0.414381 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.11996 q^{5} +1.00000 q^{6} +0.414381 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.11996 q^{10} +1.07426 q^{11} -1.00000 q^{12} +4.69865 q^{13} -0.414381 q^{14} -1.11996 q^{15} +1.00000 q^{16} -2.07982 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.11996 q^{20} -0.414381 q^{21} -1.07426 q^{22} +0.442517 q^{23} +1.00000 q^{24} -3.74569 q^{25} -4.69865 q^{26} -1.00000 q^{27} +0.414381 q^{28} -5.42550 q^{29} +1.11996 q^{30} +6.58106 q^{31} -1.00000 q^{32} -1.07426 q^{33} +2.07982 q^{34} +0.464090 q^{35} +1.00000 q^{36} -5.30061 q^{37} +1.00000 q^{38} -4.69865 q^{39} -1.11996 q^{40} -5.21985 q^{41} +0.414381 q^{42} -6.51709 q^{43} +1.07426 q^{44} +1.11996 q^{45} -0.442517 q^{46} -4.83494 q^{47} -1.00000 q^{48} -6.82829 q^{49} +3.74569 q^{50} +2.07982 q^{51} +4.69865 q^{52} -1.00000 q^{53} +1.00000 q^{54} +1.20312 q^{55} -0.414381 q^{56} +1.00000 q^{57} +5.42550 q^{58} +1.71044 q^{59} -1.11996 q^{60} +1.28641 q^{61} -6.58106 q^{62} +0.414381 q^{63} +1.00000 q^{64} +5.26230 q^{65} +1.07426 q^{66} -0.633661 q^{67} -2.07982 q^{68} -0.442517 q^{69} -0.464090 q^{70} -12.8057 q^{71} -1.00000 q^{72} -0.429813 q^{73} +5.30061 q^{74} +3.74569 q^{75} -1.00000 q^{76} +0.445152 q^{77} +4.69865 q^{78} -4.95804 q^{79} +1.11996 q^{80} +1.00000 q^{81} +5.21985 q^{82} +1.90178 q^{83} -0.414381 q^{84} -2.32931 q^{85} +6.51709 q^{86} +5.42550 q^{87} -1.07426 q^{88} -12.4686 q^{89} -1.11996 q^{90} +1.94703 q^{91} +0.442517 q^{92} -6.58106 q^{93} +4.83494 q^{94} -1.11996 q^{95} +1.00000 q^{96} +15.2292 q^{97} +6.82829 q^{98} +1.07426 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} - 12 q^{3} + 12 q^{4} - 3 q^{5} + 12 q^{6} - q^{7} - 12 q^{8} + 12 q^{9} + 3 q^{10} - 7 q^{11} - 12 q^{12} + 4 q^{13} + q^{14} + 3 q^{15} + 12 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{19} - 3 q^{20} + q^{21} + 7 q^{22} - 18 q^{23} + 12 q^{24} + 21 q^{25} - 4 q^{26} - 12 q^{27} - q^{28} + 10 q^{29} - 3 q^{30} + 14 q^{31} - 12 q^{32} + 7 q^{33} + 4 q^{34} - 19 q^{35} + 12 q^{36} + 14 q^{37} + 12 q^{38} - 4 q^{39} + 3 q^{40} - 9 q^{41} - q^{42} - 4 q^{43} - 7 q^{44} - 3 q^{45} + 18 q^{46} - 14 q^{47} - 12 q^{48} + 37 q^{49} - 21 q^{50} + 4 q^{51} + 4 q^{52} - 12 q^{53} + 12 q^{54} - 4 q^{55} + q^{56} + 12 q^{57} - 10 q^{58} - 18 q^{59} + 3 q^{60} - 7 q^{61} - 14 q^{62} - q^{63} + 12 q^{64} + 3 q^{65} - 7 q^{66} + 8 q^{67} - 4 q^{68} + 18 q^{69} + 19 q^{70} - q^{71} - 12 q^{72} - 31 q^{73} - 14 q^{74} - 21 q^{75} - 12 q^{76} - 25 q^{77} + 4 q^{78} - 3 q^{80} + 12 q^{81} + 9 q^{82} - 48 q^{83} + q^{84} + 4 q^{85} + 4 q^{86} - 10 q^{87} + 7 q^{88} + 13 q^{89} + 3 q^{90} + 9 q^{91} - 18 q^{92} - 14 q^{93} + 14 q^{94} + 3 q^{95} + 12 q^{96} + 25 q^{97} - 37 q^{98} - 7 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 12 * q^3 + 12 * q^4 - 3 * q^5 + 12 * q^6 - q^7 - 12 * q^8 + 12 * q^9 + 3 * q^10 - 7 * q^11 - 12 * q^12 + 4 * q^13 + q^14 + 3 * q^15 + 12 * q^16 - 4 * q^17 - 12 * q^18 - 12 * q^19 - 3 * q^20 + q^21 + 7 * q^22 - 18 * q^23 + 12 * q^24 + 21 * q^25 - 4 * q^26 - 12 * q^27 - q^28 + 10 * q^29 - 3 * q^30 + 14 * q^31 - 12 * q^32 + 7 * q^33 + 4 * q^34 - 19 * q^35 + 12 * q^36 + 14 * q^37 + 12 * q^38 - 4 * q^39 + 3 * q^40 - 9 * q^41 - q^42 - 4 * q^43 - 7 * q^44 - 3 * q^45 + 18 * q^46 - 14 * q^47 - 12 * q^48 + 37 * q^49 - 21 * q^50 + 4 * q^51 + 4 * q^52 - 12 * q^53 + 12 * q^54 - 4 * q^55 + q^56 + 12 * q^57 - 10 * q^58 - 18 * q^59 + 3 * q^60 - 7 * q^61 - 14 * q^62 - q^63 + 12 * q^64 + 3 * q^65 - 7 * q^66 + 8 * q^67 - 4 * q^68 + 18 * q^69 + 19 * q^70 - q^71 - 12 * q^72 - 31 * q^73 - 14 * q^74 - 21 * q^75 - 12 * q^76 - 25 * q^77 + 4 * q^78 - 3 * q^80 + 12 * q^81 + 9 * q^82 - 48 * q^83 + q^84 + 4 * q^85 + 4 * q^86 - 10 * q^87 + 7 * q^88 + 13 * q^89 + 3 * q^90 + 9 * q^91 - 18 * q^92 - 14 * q^93 + 14 * q^94 + 3 * q^95 + 12 * q^96 + 25 * q^97 - 37 * q^98 - 7 * q^99

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