LMFDB - Embedded newform 6042.2.a.t.1.1

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.17609.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 7x^{2} + 10x - 1 $ x^4 - x^3 - 7x^2 + 10x - 1
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			1.1
Root			$0.108328$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.35130 q^{5} -1.00000 q^{6} -2.98827 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.35130 q^{5} -1.00000 q^{6} -2.98827 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.35130 q^{10} +0.528633 q^{11} -1.00000 q^{12} -2.16559 q^{13} -2.98827 q^{14} +1.35130 q^{15} +1.00000 q^{16} -5.01459 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.35130 q^{20} +2.98827 q^{21} +0.528633 q^{22} -0.879937 q^{23} -1.00000 q^{24} -3.17398 q^{25} -2.16559 q^{26} -1.00000 q^{27} -2.98827 q^{28} -4.13465 q^{29} +1.35130 q^{30} +2.45963 q^{31} +1.00000 q^{32} -0.528633 q^{33} -5.01459 q^{34} +4.03806 q^{35} +1.00000 q^{36} +3.93100 q^{37} -1.00000 q^{38} +2.16559 q^{39} -1.35130 q^{40} +5.66328 q^{41} +2.98827 q^{42} +3.23459 q^{43} +0.528633 q^{44} -1.35130 q^{45} -0.879937 q^{46} +9.72893 q^{47} -1.00000 q^{48} +1.92973 q^{49} -3.17398 q^{50} +5.01459 q^{51} -2.16559 q^{52} -1.00000 q^{53} -1.00000 q^{54} -0.714344 q^{55} -2.98827 q^{56} +1.00000 q^{57} -4.13465 q^{58} -3.89167 q^{59} +1.35130 q^{60} -7.77999 q^{61} +2.45963 q^{62} -2.98827 q^{63} +1.00000 q^{64} +2.92638 q^{65} -0.528633 q^{66} +11.0849 q^{67} -5.01459 q^{68} +0.879937 q^{69} +4.03806 q^{70} -7.75987 q^{71} +1.00000 q^{72} +6.77161 q^{73} +3.93100 q^{74} +3.17398 q^{75} -1.00000 q^{76} -1.57969 q^{77} +2.16559 q^{78} -7.58255 q^{79} -1.35130 q^{80} +1.00000 q^{81} +5.66328 q^{82} +7.33957 q^{83} +2.98827 q^{84} +6.77623 q^{85} +3.23459 q^{86} +4.13465 q^{87} +0.528633 q^{88} +7.98827 q^{89} -1.35130 q^{90} +6.47137 q^{91} -0.879937 q^{92} -2.45963 q^{93} +9.72893 q^{94} +1.35130 q^{95} -1.00000 q^{96} -4.09197 q^{97} +1.92973 q^{98} +0.528633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 2 q^{11} - 4 q^{12} - q^{13} + 3 q^{14} - 6 q^{15} + 4 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 6 q^{20} - 3 q^{21} - 2 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - q^{26} - 4 q^{27} + 3 q^{28} - 4 q^{29} - 6 q^{30} - q^{31} + 4 q^{32} + 2 q^{33} + 8 q^{34} + 18 q^{35} + 4 q^{36} + 9 q^{37} - 4 q^{38} + q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 2 q^{44} + 6 q^{45} + 12 q^{46} + 3 q^{47} - 4 q^{48} + 9 q^{49} + 6 q^{50} - 8 q^{51} - q^{52} - 4 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 4 q^{57} - 4 q^{58} - 15 q^{59} - 6 q^{60} - 4 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} - 13 q^{65} + 2 q^{66} + 15 q^{67} + 8 q^{68} - 12 q^{69} + 18 q^{70} + 4 q^{72} + 11 q^{73} + 9 q^{74} - 6 q^{75} - 4 q^{76} - 11 q^{77} + q^{78} + 8 q^{79} + 6 q^{80} + 4 q^{81} + 6 q^{82} + 3 q^{83} - 3 q^{84} + 29 q^{85} + 12 q^{86} + 4 q^{87} - 2 q^{88} + 17 q^{89} + 6 q^{90} + 30 q^{91} + 12 q^{92} + q^{93} + 3 q^{94} - 6 q^{95} - 4 q^{96} + 16 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 2 * q^11 - 4 * q^12 - q^13 + 3 * q^14 - 6 * q^15 + 4 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 6 * q^20 - 3 * q^21 - 2 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - q^26 - 4 * q^27 + 3 * q^28 - 4 * q^29 - 6 * q^30 - q^31 + 4 * q^32 + 2 * q^33 + 8 * q^34 + 18 * q^35 + 4 * q^36 + 9 * q^37 - 4 * q^38 + q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 2 * q^44 + 6 * q^45 + 12 * q^46 + 3 * q^47 - 4 * q^48 + 9 * q^49 + 6 * q^50 - 8 * q^51 - q^52 - 4 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 4 * q^57 - 4 * q^58 - 15 * q^59 - 6 * q^60 - 4 * q^61 - q^62 + 3 * q^63 + 4 * q^64 - 13 * q^65 + 2 * q^66 + 15 * q^67 + 8 * q^68 - 12 * q^69 + 18 * q^70 + 4 * q^72 + 11 * q^73 + 9 * q^74 - 6 * q^75 - 4 * q^76 - 11 * q^77 + q^78 + 8 * q^79 + 6 * q^80 + 4 * q^81 + 6 * q^82 + 3 * q^83 - 3 * q^84 + 29 * q^85 + 12 * q^86 + 4 * q^87 - 2 * q^88 + 17 * q^89 + 6 * q^90 + 30 * q^91 + 12 * q^92 + q^93 + 3 * q^94 - 6 * q^95 - 4 * q^96 + 16 * q^97 + 9 * q^98 - 2 * 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
$5$	−1.35130	−0.604322	−0.302161	−	0.953257i	$-0.597708\pi$
$5$	−1.35130	−0.604322	−0.302161	+	0.953257i	$0.597708\pi$
$6$	−1.00000	−0.408248
$7$	−2.98827	−1.12946	−0.564729	−	0.825276i	$-0.691019\pi$
$7$	−2.98827	−1.12946	−0.564729	+	0.825276i	$0.691019\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.35130	−0.427320
$11$	0.528633	0.159389	0.0796944	−	0.996819i	$-0.474606\pi$
$11$	0.528633	0.159389	0.0796944	+	0.996819i	$0.474606\pi$
$12$	−1.00000	−0.288675
$13$	−2.16559	−0.600628	−0.300314	−	0.953840i	$-0.597091\pi$
$13$	−2.16559	−0.600628	−0.300314	+	0.953840i	$0.597091\pi$
$14$	−2.98827	−0.798647
$15$	1.35130	0.348905
$16$	1.00000	0.250000
$17$	−5.01459	−1.21622	−0.608108	−	0.793854i	$-0.708071\pi$
$17$	−5.01459	−1.21622	−0.608108	+	0.793854i	$0.708071\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.35130	−0.302161
$21$	2.98827	0.652093
$22$	0.528633	0.112705
$23$	−0.879937	−0.183480	−0.0917398	−	0.995783i	$-0.529243\pi$
$23$	−0.879937	−0.183480	−0.0917398	+	0.995783i	$0.529243\pi$
$24$	−1.00000	−0.204124
$25$	−3.17398	−0.634795
$26$	−2.16559	−0.424708
$27$	−1.00000	−0.192450
$28$	−2.98827	−0.564729
$29$	−4.13465	−0.767785	−0.383893	−	0.923378i	$-0.625417\pi$
$29$	−4.13465	−0.767785	−0.383893	+	0.923378i	$0.625417\pi$
$30$	1.35130	0.246713
$31$	2.45963	0.441763	0.220881	−	0.975301i	$-0.429107\pi$
$31$	2.45963	0.441763	0.220881	+	0.975301i	$0.429107\pi$
$32$	1.00000	0.176777
$33$	−0.528633	−0.0920232
$34$	−5.01459	−0.859994
$35$	4.03806	0.682556
$36$	1.00000	0.166667
$37$	3.93100	0.646252	0.323126	−	0.946356i	$-0.395266\pi$
$37$	3.93100	0.646252	0.323126	+	0.946356i	$0.395266\pi$
$38$	−1.00000	−0.162221
$39$	2.16559	0.346772
$40$	−1.35130	−0.213660
$41$	5.66328	0.884456	0.442228	−	0.896903i	$-0.354188\pi$
$41$	5.66328	0.884456	0.442228	+	0.896903i	$0.354188\pi$
$42$	2.98827	0.461099
$43$	3.23459	0.493271	0.246635	−	0.969108i	$-0.420675\pi$
$43$	3.23459	0.493271	0.246635	+	0.969108i	$0.420675\pi$
$44$	0.528633	0.0796944
$45$	−1.35130	−0.201441
$46$	−0.879937	−0.129740
$47$	9.72893	1.41911	0.709555	−	0.704650i	$-0.248896\pi$
$47$	9.72893	1.41911	0.709555	+	0.704650i	$0.248896\pi$
$48$	−1.00000	−0.144338
$49$	1.92973	0.275675
$50$	−3.17398	−0.448868
$51$	5.01459	0.702183
$52$	−2.16559	−0.300314
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	−1.00000	−0.136083
$55$	−0.714344	−0.0963221
$56$	−2.98827	−0.399324
$57$	1.00000	0.132453
$58$	−4.13465	−0.542906
$59$	−3.89167	−0.506653	−0.253326	−	0.967381i	$-0.581525\pi$
$59$	−3.89167	−0.506653	−0.253326	+	0.967381i	$0.581525\pi$
$60$	1.35130	0.174453
$61$	−7.77999	−0.996126	−0.498063	−	0.867141i	$-0.665955\pi$
$61$	−7.77999	−0.996126	−0.498063	+	0.867141i	$0.665955\pi$
$62$	2.45963	0.312374
$63$	−2.98827	−0.376486
$64$	1.00000	0.125000
$65$	2.92638	0.362972
$66$	−0.528633	−0.0650702
$67$	11.0849	1.35423	0.677115	−	0.735877i	$-0.263230\pi$
$67$	11.0849	1.35423	0.677115	+	0.735877i	$0.263230\pi$
$68$	−5.01459	−0.608108
$69$	0.879937	0.105932
$70$	4.03806	0.482640
$71$	−7.75987	−0.920928	−0.460464	−	0.887678i	$-0.652317\pi$
$71$	−7.75987	−0.920928	−0.460464	+	0.887678i	$0.652317\pi$
$72$	1.00000	0.117851
$73$	6.77161	0.792557	0.396278	−	0.918130i	$-0.370301\pi$
$73$	6.77161	0.792557	0.396278	+	0.918130i	$0.370301\pi$
$74$	3.93100	0.456969
$75$	3.17398	0.366499
$76$	−1.00000	−0.114708
$77$	−1.57969	−0.180023
$78$	2.16559	0.245205
$79$	−7.58255	−0.853103	−0.426552	−	0.904463i	$-0.640272\pi$
$79$	−7.58255	−0.853103	−0.426552	+	0.904463i	$0.640272\pi$
$80$	−1.35130	−0.151080
$81$	1.00000	0.111111
$82$	5.66328	0.625405
$83$	7.33957	0.805622	0.402811	−	0.915283i	$-0.368033\pi$
$83$	7.33957	0.805622	0.402811	+	0.915283i	$0.368033\pi$
$84$	2.98827	0.326046
$85$	6.77623	0.734986
$86$	3.23459	0.348795
$87$	4.13465	0.443281
$88$	0.528633	0.0563524
$89$	7.98827	0.846754	0.423377	−	0.905953i	$-0.360845\pi$
$89$	7.98827	0.846754	0.423377	+	0.905953i	$0.360845\pi$
$90$	−1.35130	−0.142440
$91$	6.47137	0.678384
$92$	−0.879937	−0.0917398
$93$	−2.45963	−0.255052
$94$	9.72893	1.00346
$95$	1.35130	0.138641
$96$	−1.00000	−0.102062
$97$	−4.09197	−0.415477	−0.207738	−	0.978184i	$-0.566610\pi$
$97$	−4.09197	−0.415477	−0.207738	+	0.978184i	$0.566610\pi$
$98$	1.92973	0.194932
$99$	0.528633	0.0531296
$100$	−3.17398	−0.317398
$101$	8.83441	0.879056	0.439528	−	0.898229i	$-0.355146\pi$
$101$	8.83441	0.879056	0.439528	+	0.898229i	$0.355146\pi$
$102$	5.01459	0.496518
$103$	11.9385	1.17633	0.588166	−	0.808740i	$-0.299850\pi$
$103$	11.9385	1.17633	0.588166	+	0.808740i	$0.299850\pi$
$104$	−2.16559	−0.212354
$105$	−4.03806	−0.394074
$106$	−1.00000	−0.0971286
$107$	0.165593	0.0160085	0.00800426	−	0.999968i	$-0.497452\pi$
$107$	0.165593	0.0160085	0.00800426	+	0.999968i	$0.497452\pi$
$108$	−1.00000	−0.0962250
$109$	7.66455	0.734131	0.367066	−	0.930195i	$-0.380362\pi$
$109$	7.66455	0.734131	0.367066	+	0.930195i	$0.380362\pi$
$110$	−0.714344	−0.0681100
$111$	−3.93100	−0.373114
$112$	−2.98827	−0.282365
$113$	10.6453	1.00143	0.500715	−	0.865612i	$-0.333071\pi$
$113$	10.6453	1.00143	0.500715	+	0.865612i	$0.333071\pi$
$114$	1.00000	0.0936586
$115$	1.18906	0.110881
$116$	−4.13465	−0.383893
$117$	−2.16559	−0.200209
$118$	−3.89167	−0.358257
$119$	14.9849	1.37366
$120$	1.35130	0.123357
$121$	−10.7205	−0.974595
$122$	−7.77999	−0.704367
$123$	−5.66328	−0.510641
$124$	2.45963	0.220881
$125$	11.0455	0.987942
$126$	−2.98827	−0.266216
$127$	−16.2049	−1.43795	−0.718977	−	0.695034i	$-0.755389\pi$
$127$	−16.2049	−1.43795	−0.718977	+	0.695034i	$0.755389\pi$
$128$	1.00000	0.0883883
$129$	−3.23459	−0.284790
$130$	2.92638	0.256660
$131$	−2.90626	−0.253921	−0.126960	−	0.991908i	$-0.540522\pi$
$131$	−2.90626	−0.253921	−0.126960	+	0.991908i	$0.540522\pi$
$132$	−0.528633	−0.0460116
$133$	2.98827	0.259115
$134$	11.0849	0.957586
$135$	1.35130	0.116302
$136$	−5.01459	−0.429997
$137$	−17.0484	−1.45654	−0.728271	−	0.685289i	$-0.759676\pi$
$137$	−17.0484	−1.45654	−0.728271	+	0.685289i	$0.759676\pi$
$138$	0.879937	0.0749052
$139$	−0.309126	−0.0262197	−0.0131099	−	0.999914i	$-0.504173\pi$
$139$	−0.309126	−0.0262197	−0.0131099	+	0.999914i	$0.504173\pi$
$140$	4.03806	0.341278
$141$	−9.72893	−0.819324
$142$	−7.75987	−0.651194
$143$	−1.14480	−0.0957333
$144$	1.00000	0.0833333
$145$	5.58717	0.463989
$146$	6.77161	0.560422
$147$	−1.92973	−0.159161
$148$	3.93100	0.323126
$149$	4.18571	0.342907	0.171453	−	0.985192i	$-0.445154\pi$
$149$	4.18571	0.342907	0.171453	+	0.985192i	$0.445154\pi$
$150$	3.17398	0.259154
$151$	2.99538	0.243760	0.121880	−	0.992545i	$-0.461108\pi$
$151$	2.99538	0.243760	0.121880	+	0.992545i	$0.461108\pi$
$152$	−1.00000	−0.0811107
$153$	−5.01459	−0.405405
$154$	−1.57969	−0.127295
$155$	−3.32371	−0.266967
$156$	2.16559	0.173386
$157$	4.65617	0.371603	0.185801	−	0.982587i	$-0.440512\pi$
$157$	4.65617	0.371603	0.185801	+	0.982587i	$0.440512\pi$
$158$	−7.58255	−0.603235
$159$	1.00000	0.0793052
$160$	−1.35130	−0.106830
$161$	2.62949	0.207233
$162$	1.00000	0.0785674
$163$	0.00285131	0.000223332 0	0.000111666	−	1.00000i	$-0.499964\pi$
$163$	0.00285131	0.000223332 0	0.000111666		1.00000i	$0.499964\pi$
$164$	5.66328	0.442228
$165$	0.714344	0.0556116
$166$	7.33957	0.569661
$167$	−6.46711	−0.500440	−0.250220	−	0.968189i	$-0.580503\pi$
$167$	−6.46711	−0.500440	−0.250220	+	0.968189i	$0.580503\pi$
$168$	2.98827	0.230550
$169$	−8.31021	−0.639247
$170$	6.77623	0.519713
$171$	−1.00000	−0.0764719
$172$	3.23459	0.246635
$173$	12.5708	0.955741	0.477871	−	0.878430i	$-0.341409\pi$
$173$	12.5708	0.955741	0.477871	+	0.878430i	$0.341409\pi$
$174$	4.13465	0.313447
$175$	9.48468	0.716975
$176$	0.528633	0.0398472
$177$	3.89167	0.292516
$178$	7.98827	0.598746
$179$	−25.4963	−1.90568	−0.952841	−	0.303471i	$-0.901854\pi$
$179$	−25.4963	−1.90568	−0.952841	+	0.303471i	$0.901854\pi$
$180$	−1.35130	−0.100720
$181$	16.5624	1.23108	0.615538	−	0.788107i	$-0.288939\pi$
$181$	16.5624	1.23108	0.615538	+	0.788107i	$0.288939\pi$
$182$	6.47137	0.479690
$183$	7.77999	0.575114
$184$	−0.879937	−0.0648698
$185$	−5.31198	−0.390544
$186$	−2.45963	−0.180349
$187$	−2.65087	−0.193851
$188$	9.72893	0.709555
$189$	2.98827	0.217364
$190$	1.35130	0.0980339
$191$	6.40522	0.463465	0.231733	−	0.972780i	$-0.425561\pi$
$191$	6.40522	0.463465	0.231733	+	0.972780i	$0.425561\pi$
$192$	−1.00000	−0.0721688
$193$	14.7553	1.06211	0.531053	−	0.847339i	$-0.321796\pi$
$193$	14.7553	1.06211	0.531053	+	0.847339i	$0.321796\pi$
$194$	−4.09197	−0.293786
$195$	−2.92638	−0.209562
$196$	1.92973	0.137838
$197$	2.58590	0.184238	0.0921188	−	0.995748i	$-0.470636\pi$
$197$	2.58590	0.184238	0.0921188	+	0.995748i	$0.470636\pi$
$198$	0.528633	0.0375683
$199$	23.8271	1.68906	0.844529	−	0.535509i	$-0.179880\pi$
$199$	23.8271	1.68906	0.844529	+	0.535509i	$0.179880\pi$
$200$	−3.17398	−0.224434
$201$	−11.0849	−0.781866
$202$	8.83441	0.621587
$203$	12.3554	0.867181
$204$	5.01459	0.351091
$205$	−7.65282	−0.534496
$206$	11.9385	0.831793
$207$	−0.879937	−0.0611599
$208$	−2.16559	−0.150157
$209$	−0.528633	−0.0365663
$210$	−4.03806	−0.278652
$211$	15.0388	1.03532	0.517658	−	0.855588i	$-0.326804\pi$
$211$	15.0388	1.03532	0.517658	+	0.855588i	$0.326804\pi$
$212$	−1.00000	−0.0686803
$213$	7.75987	0.531698
$214$	0.165593	0.0113197
$215$	−4.37092	−0.298094
$216$	−1.00000	−0.0680414
$217$	−7.35003	−0.498953
$218$	7.66455	0.519109
$219$	−6.77161	−0.457583
$220$	−0.714344	−0.0481611
$221$	10.8596	0.730493
$222$	−3.93100	−0.263831
$223$	22.6352	1.51576	0.757882	−	0.652391i	$-0.226234\pi$
$223$	22.6352	1.51576	0.757882	+	0.652391i	$0.226234\pi$
$224$	−2.98827	−0.199662
$225$	−3.17398	−0.211598
$226$	10.6453	0.708118
$227$	7.53611	0.500189	0.250095	−	0.968221i	$-0.419538\pi$
$227$	7.53611	0.500189	0.250095	+	0.968221i	$0.419538\pi$
$228$	1.00000	0.0662266
$229$	−1.80758	−0.119449	−0.0597243	−	0.998215i	$-0.519022\pi$
$229$	−1.80758	−0.119449	−0.0597243	+	0.998215i	$0.519022\pi$
$230$	1.18906	0.0784045
$231$	1.57969	0.103936
$232$	−4.13465	−0.271453
$233$	10.6135	0.695313	0.347656	−	0.937622i	$-0.386978\pi$
$233$	10.6135	0.695313	0.347656	+	0.937622i	$0.386978\pi$
$234$	−2.16559	−0.141569
$235$	−13.1467	−0.857599
$236$	−3.89167	−0.253326
$237$	7.58255	0.492539
$238$	14.9849	0.971328
$239$	13.7227	0.887649	0.443825	−	0.896114i	$-0.353621\pi$
$239$	13.7227	0.887649	0.443825	+	0.896114i	$0.353621\pi$
$240$	1.35130	0.0872263
$241$	29.2500	1.88415	0.942077	−	0.335395i	$-0.108870\pi$
$241$	29.2500	1.88415	0.942077	+	0.335395i	$0.108870\pi$
$242$	−10.7205	−0.689143
$243$	−1.00000	−0.0641500
$244$	−7.77999	−0.498063
$245$	−2.60765	−0.166597
$246$	−5.66328	−0.361078
$247$	2.16559	0.137793
$248$	2.45963	0.156187
$249$	−7.33957	−0.465126
$250$	11.0455	0.698581
$251$	−5.04268	−0.318291	−0.159146	−	0.987255i	$-0.550874\pi$
$251$	−5.04268	−0.318291	−0.159146	+	0.987255i	$0.550874\pi$
$252$	−2.98827	−0.188243
$253$	−0.465164	−0.0292446
$254$	−16.2049	−1.01679
$255$	−6.77623	−0.424344
$256$	1.00000	0.0625000
$257$	16.3513	1.01997	0.509983	−	0.860184i	$-0.329652\pi$
$257$	16.3513	1.01997	0.509983	+	0.860184i	$0.329652\pi$
$258$	−3.23459	−0.201377
$259$	−11.7469	−0.729915
$260$	2.92638	0.181486
$261$	−4.13465	−0.255928
$262$	−2.90626	−0.179549
$263$	−14.4303	−0.889808	−0.444904	−	0.895578i	$-0.646762\pi$
$263$	−14.4303	−0.889808	−0.444904	+	0.895578i	$0.646762\pi$
$264$	−0.528633	−0.0325351
$265$	1.35130	0.0830100
$266$	2.98827	0.183222
$267$	−7.98827	−0.488874
$268$	11.0849	0.677115
$269$	18.7716	1.14453	0.572263	−	0.820070i	$-0.306066\pi$
$269$	18.7716	1.14453	0.572263	+	0.820070i	$0.306066\pi$
$270$	1.35130	0.0822378
$271$	11.7729	0.715152	0.357576	−	0.933884i	$-0.383603\pi$
$271$	11.7729	0.715152	0.357576	+	0.933884i	$0.383603\pi$
$272$	−5.01459	−0.304054
$273$	−6.47137	−0.391665
$274$	−17.0484	−1.02993
$275$	−1.67787	−0.101179
$276$	0.879937	0.0529660
$277$	24.6256	1.47961	0.739805	−	0.672821i	$-0.234918\pi$
$277$	24.6256	1.47961	0.739805	+	0.672821i	$0.234918\pi$
$278$	−0.309126	−0.0185401
$279$	2.45963	0.147254
$280$	4.03806	0.241320
$281$	15.2111	0.907420	0.453710	−	0.891149i	$-0.350100\pi$
$281$	15.2111	0.907420	0.453710	+	0.891149i	$0.350100\pi$
$282$	−9.72893	−0.579349
$283$	−18.1713	−1.08017	−0.540086	−	0.841610i	$-0.681608\pi$
$283$	−18.1713	−1.08017	−0.540086	+	0.841610i	$0.681608\pi$
$284$	−7.75987	−0.460464
$285$	−1.35130	−0.0800444
$286$	−1.14480	−0.0676937
$287$	−16.9234	−0.998956
$288$	1.00000	0.0589256
$289$	8.14607	0.479181
$290$	5.58717	0.328090
$291$	4.09197	0.239876
$292$	6.77161	0.396278
$293$	25.2852	1.47717	0.738587	−	0.674158i	$-0.235493\pi$
$293$	25.2852	1.47717	0.738587	+	0.674158i	$0.235493\pi$
$294$	−1.92973	−0.112544
$295$	5.25883	0.306181
$296$	3.93100	0.228485
$297$	−0.528633	−0.0306744
$298$	4.18571	0.242472
$299$	1.90559	0.110203
$300$	3.17398	0.183250
$301$	−9.66582	−0.557129
$302$	2.99538	0.172365
$303$	−8.83441	−0.507523
$304$	−1.00000	−0.0573539
$305$	10.5131	0.601981
$306$	−5.01459	−0.286665
$307$	−30.3851	−1.73417	−0.867085	−	0.498161i	$-0.834009\pi$
$307$	−30.3851	−1.73417	−0.867085	+	0.498161i	$0.834009\pi$
$308$	−1.57969	−0.0900115
$309$	−11.9385	−0.679156
$310$	−3.32371	−0.188774
$311$	4.35878	0.247164	0.123582	−	0.992334i	$-0.460562\pi$
$311$	4.35878	0.247164	0.123582	+	0.992334i	$0.460562\pi$
$312$	2.16559	0.122603
$313$	−15.0886	−0.852859	−0.426430	−	0.904521i	$-0.640229\pi$
$313$	−15.0886	−0.852859	−0.426430	+	0.904521i	$0.640229\pi$
$314$	4.65617	0.262763
$315$	4.03806	0.227519
$316$	−7.58255	−0.426552
$317$	23.2286	1.30465	0.652323	−	0.757941i	$-0.273795\pi$
$317$	23.2286	1.30465	0.652323	+	0.757941i	$0.273795\pi$
$318$	1.00000	0.0560772
$319$	−2.18571	−0.122376
$320$	−1.35130	−0.0755402
$321$	−0.165593	−0.00924252
$322$	2.62949	0.146536
$323$	5.01459	0.279019
$324$	1.00000	0.0555556
$325$	6.87354	0.381276
$326$	0.00285131	0.000157919 0
$327$	−7.66455	−0.423851
$328$	5.66328	0.312702
$329$	−29.0726	−1.60283
$330$	0.714344	0.0393233
$331$	−27.6999	−1.52253	−0.761263	−	0.648443i	$-0.775420\pi$
$331$	−27.6999	−1.52253	−0.761263	+	0.648443i	$0.775420\pi$
$332$	7.33957	0.402811
$333$	3.93100	0.215417
$334$	−6.46711	−0.353864
$335$	−14.9790	−0.818391
$336$	2.98827	0.163023
$337$	−21.4340	−1.16758	−0.583792	−	0.811903i	$-0.698432\pi$
$337$	−21.4340	−1.16758	−0.583792	+	0.811903i	$0.698432\pi$
$338$	−8.31021	−0.452016
$339$	−10.6453	−0.578176
$340$	6.77623	0.367493
$341$	1.30024	0.0704121
$342$	−1.00000	−0.0540738
$343$	15.1513	0.818094
$344$	3.23459	0.174398
$345$	−1.18906	−0.0640170
$346$	12.5708	0.675811
$347$	33.4428	1.79530	0.897651	−	0.440707i	$-0.145272\pi$
$347$	33.4428	1.79530	0.897651	+	0.440707i	$0.145272\pi$
$348$	4.13465	0.221640
$349$	5.06153	0.270937	0.135469	−	0.990782i	$-0.456746\pi$
$349$	5.06153	0.270937	0.135469	+	0.990782i	$0.456746\pi$
$350$	9.48468	0.506978
$351$	2.16559	0.115591
$352$	0.528633	0.0281762
$353$	6.06347	0.322726	0.161363	−	0.986895i	$-0.448411\pi$
$353$	6.06347	0.322726	0.161363	+	0.986895i	$0.448411\pi$
$354$	3.89167	0.206840
$355$	10.4860	0.556537
$356$	7.98827	0.423377
$357$	−14.9849	−0.793086
$358$	−25.4963	−1.34752
$359$	−0.359687	−0.0189836	−0.00949178	−	0.999955i	$-0.503021\pi$
$359$	−0.359687	−0.0189836	−0.00949178	+	0.999955i	$0.503021\pi$
$360$	−1.35130	−0.0712200
$361$	1.00000	0.0526316
$362$	16.5624	0.870502
$363$	10.7205	0.562683
$364$	6.47137	0.339192
$365$	−9.15051	−0.478959
$366$	7.77999	0.406667
$367$	0.800974	0.0418105	0.0209052	−	0.999781i	$-0.493345\pi$
$367$	0.800974	0.0418105	0.0209052	+	0.999781i	$0.493345\pi$
$368$	−0.879937	−0.0458699
$369$	5.66328	0.294819
$370$	−5.31198	−0.276157
$371$	2.98827	0.155143
$372$	−2.45963	−0.127526
$373$	−36.6712	−1.89876	−0.949380	−	0.314129i	$-0.898288\pi$
$373$	−36.6712	−1.89876	−0.949380	+	0.314129i	$0.898288\pi$
$374$	−2.65087	−0.137073
$375$	−11.0455	−0.570389
$376$	9.72893	0.501731
$377$	8.95397	0.461153
$378$	2.98827	0.153700
$379$	13.6178	0.699497	0.349748	−	0.936844i	$-0.386267\pi$
$379$	13.6178	0.699497	0.349748	+	0.936844i	$0.386267\pi$
$380$	1.35130	0.0693205
$381$	16.2049	0.830203
$382$	6.40522	0.327719
$383$	0.918356	0.0469258	0.0234629	−	0.999725i	$-0.492531\pi$
$383$	0.918356	0.0469258	0.0234629	+	0.999725i	$0.492531\pi$
$384$	−1.00000	−0.0510310
$385$	2.13465	0.108792
$386$	14.7553	0.751023
$387$	3.23459	0.164424
$388$	−4.09197	−0.207738
$389$	−33.9120	−1.71940	−0.859702	−	0.510795i	$-0.829351\pi$
$389$	−33.9120	−1.71940	−0.859702	+	0.510795i	$0.829351\pi$
$390$	−2.92638	−0.148183
$391$	4.41252	0.223151
$392$	1.92973	0.0974660
$393$	2.90626	0.146601
$394$	2.58590	0.130276
$395$	10.2463	0.515549
$396$	0.528633	0.0265648
$397$	−12.9113	−0.647999	−0.324000	−	0.946057i	$-0.605028\pi$
$397$	−12.9113	−0.647999	−0.324000	+	0.946057i	$0.605028\pi$
$398$	23.8271	1.19434
$399$	−2.98827	−0.149600
$400$	−3.17398	−0.158699
$401$	6.56760	0.327970	0.163985	−	0.986463i	$-0.447565\pi$
$401$	6.56760	0.327970	0.163985	+	0.986463i	$0.447565\pi$
$402$	−11.0849	−0.552862
$403$	−5.32656	−0.265335
$404$	8.83441	0.439528
$405$	−1.35130	−0.0671469
$406$	12.3554	0.613190
$407$	2.07806	0.103005
$408$	5.01459	0.248259
$409$	4.64870	0.229863	0.114932	−	0.993373i	$-0.463335\pi$
$409$	4.64870	0.229863	0.114932	+	0.993373i	$0.463335\pi$
$410$	−7.65282	−0.377946
$411$	17.0484	0.840935
$412$	11.9385	0.588166
$413$	11.6293	0.572243
$414$	−0.879937	−0.0432466
$415$	−9.91799	−0.486855
$416$	−2.16559	−0.106177
$417$	0.309126	0.0151380
$418$	−0.528633	−0.0258563
$419$	−18.6590	−0.911553	−0.455776	−	0.890094i	$-0.650638\pi$
$419$	−18.6590	−0.911553	−0.455776	+	0.890094i	$0.650638\pi$
$420$	−4.03806	−0.197037
$421$	−23.5646	−1.14847	−0.574234	−	0.818691i	$-0.694700\pi$
$421$	−23.5646	−1.14847	−0.574234	+	0.818691i	$0.694700\pi$
$422$	15.0388	0.732079
$423$	9.72893	0.473037
$424$	−1.00000	−0.0485643
$425$	15.9162	0.772048
$426$	7.75987	0.375967
$427$	23.2487	1.12508
$428$	0.165593	0.00800426
$429$	1.14480	0.0552716
$430$	−4.37092	−0.210785
$431$	−29.1229	−1.40280	−0.701401	−	0.712767i	$-0.747442\pi$
$431$	−29.1229	−1.40280	−0.701401	+	0.712767i	$0.747442\pi$
$432$	−1.00000	−0.0481125
$433$	14.6131	0.702262	0.351131	−	0.936326i	$-0.385797\pi$
$433$	14.6131	0.702262	0.351131	+	0.936326i	$0.385797\pi$
$434$	−7.35003	−0.352813
$435$	−5.58717	−0.267884
$436$	7.66455	0.367066
$437$	0.879937	0.0420931
$438$	−6.77161	−0.323560
$439$	−34.8485	−1.66323	−0.831614	−	0.555354i	$-0.812583\pi$
$439$	−34.8485	−1.66323	−0.831614	+	0.555354i	$0.812583\pi$
$440$	−0.714344	−0.0340550
$441$	1.92973	0.0918918
$442$	10.8596	0.516536
$443$	−4.44632	−0.211251	−0.105625	−	0.994406i	$-0.533684\pi$
$443$	−4.44632	−0.211251	−0.105625	+	0.994406i	$0.533684\pi$
$444$	−3.93100	−0.186557
$445$	−10.7946	−0.511712
$446$	22.6352	1.07181
$447$	−4.18571	−0.197977
$448$	−2.98827	−0.141182
$449$	33.3703	1.57484	0.787421	−	0.616415i	$-0.211416\pi$
$449$	33.3703	1.57484	0.787421	+	0.616415i	$0.211416\pi$
$450$	−3.17398	−0.149623
$451$	2.99380	0.140972
$452$	10.6453	0.500715
$453$	−2.99538	−0.140735
$454$	7.53611	0.353687
$455$	−8.74479	−0.409962
$456$	1.00000	0.0468293
$457$	30.4081	1.42243	0.711215	−	0.702975i	$-0.248145\pi$
$457$	30.4081	1.42243	0.711215	+	0.702975i	$0.248145\pi$
$458$	−1.80758	−0.0844629
$459$	5.01459	0.234061
$460$	1.18906	0.0554404
$461$	11.1610	0.519818	0.259909	−	0.965633i	$-0.416307\pi$
$461$	11.1610	0.519818	0.259909	+	0.965633i	$0.416307\pi$
$462$	1.57969	0.0734941
$463$	−8.57045	−0.398303	−0.199151	−	0.979969i	$-0.563819\pi$
$463$	−8.57045	−0.398303	−0.199151	+	0.979969i	$0.563819\pi$
$464$	−4.13465	−0.191946
$465$	3.32371	0.154133
$466$	10.6135	0.491660
$467$	−23.1158	−1.06967	−0.534836	−	0.844956i	$-0.679627\pi$
$467$	−23.1158	−1.06967	−0.534836	+	0.844956i	$0.679627\pi$
$468$	−2.16559	−0.100105
$469$	−33.1245	−1.52955
$470$	−13.1467	−0.606414
$471$	−4.65617	−0.214545
$472$	−3.89167	−0.179129
$473$	1.70991	0.0786219
$474$	7.58255	0.348278
$475$	3.17398	0.145632
$476$	14.9849	0.686832
$477$	−1.00000	−0.0457869
$478$	13.7227	0.627663
$479$	13.4835	0.616075	0.308038	−	0.951374i	$-0.400328\pi$
$479$	13.4835	0.616075	0.308038	+	0.951374i	$0.400328\pi$
$480$	1.35130	0.0616783
$481$	−8.51295	−0.388157
$482$	29.2500	1.33230
$483$	−2.62949	−0.119646
$484$	−10.7205	−0.487298
$485$	5.52950	0.251082
$486$	−1.00000	−0.0453609
$487$	3.51247	0.159165	0.0795825	−	0.996828i	$-0.474641\pi$
$487$	3.51247	0.159165	0.0795825	+	0.996828i	$0.474641\pi$
$488$	−7.77999	−0.352184
$489$	−0.00285131	−0.000128941 0
$490$	−2.60765	−0.117802
$491$	−28.6882	−1.29468	−0.647340	−	0.762201i	$-0.724119\pi$
$491$	−28.6882	−1.29468	−0.647340	+	0.762201i	$0.724119\pi$
$492$	−5.66328	−0.255320
$493$	20.7336	0.933792
$494$	2.16559	0.0974347
$495$	−0.714344	−0.0321074
$496$	2.45963	0.110441
$497$	23.1886	1.04015
$498$	−7.33957	−0.328894
$499$	−33.8565	−1.51562	−0.757812	−	0.652473i	$-0.773732\pi$
$499$	−33.8565	−1.51562	−0.757812	+	0.652473i	$0.773732\pi$
$500$	11.0455	0.493971
$501$	6.46711	0.288929
$502$	−5.04268	−0.225066
$503$	−0.283884	−0.0126578	−0.00632888	−	0.999980i	$-0.502015\pi$
$503$	−0.283884	−0.0126578	−0.00632888	+	0.999980i	$0.502015\pi$
$504$	−2.98827	−0.133108
$505$	−11.9380	−0.531233
$506$	−0.465164	−0.0206791
$507$	8.31021	0.369069
$508$	−16.2049	−0.718977
$509$	20.3190	0.900622	0.450311	−	0.892872i	$-0.351313\pi$
$509$	20.3190	0.900622	0.450311	+	0.892872i	$0.351313\pi$
$510$	−6.77623	−0.300057
$511$	−20.2354	−0.895160
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	16.3513	0.721225
$515$	−16.1325	−0.710883
$516$	−3.23459	−0.142395
$517$	5.14303	0.226190
$518$	−11.7469	−0.516128
$519$	−12.5708	−0.551797
$520$	2.92638	0.128330
$521$	−14.9038	−0.652946	−0.326473	−	0.945207i	$-0.605860\pi$
$521$	−14.9038	−0.652946	−0.326473	+	0.945207i	$0.605860\pi$
$522$	−4.13465	−0.180969
$523$	−18.2519	−0.798098	−0.399049	−	0.916930i	$-0.630660\pi$
$523$	−18.2519	−0.798098	−0.399049	+	0.916930i	$0.630660\pi$
$524$	−2.90626	−0.126960
$525$	−9.48468	−0.413945
$526$	−14.4303	−0.629190
$527$	−12.3340	−0.537279
$528$	−0.528633	−0.0230058
$529$	−22.2257	−0.966335
$530$	1.35130	0.0586969
$531$	−3.89167	−0.168884
$532$	2.98827	0.129558
$533$	−12.2644	−0.531229
$534$	−7.98827	−0.345686
$535$	−0.223767	−0.00967430
$536$	11.0849	0.478793
$537$	25.4963	1.10025
$538$	18.7716	0.809302
$539$	1.02012	0.0439396
$540$	1.35130	0.0581509
$541$	−7.73700	−0.332640	−0.166320	−	0.986072i	$-0.553188\pi$
$541$	−7.73700	−0.332640	−0.166320	+	0.986072i	$0.553188\pi$
$542$	11.7729	0.505689
$543$	−16.5624	−0.710762
$544$	−5.01459	−0.214999
$545$	−10.3571	−0.443651
$546$	−6.47137	−0.276949
$547$	−5.58839	−0.238942	−0.119471	−	0.992838i	$-0.538120\pi$
$547$	−5.58839	−0.238942	−0.119471	+	0.992838i	$0.538120\pi$
$548$	−17.0484	−0.728271
$549$	−7.77999	−0.332042
$550$	−1.67787	−0.0715445
$551$	4.13465	0.176142
$552$	0.879937	0.0374526
$553$	22.6587	0.963544
$554$	24.6256	1.04624
$555$	5.31198	0.225481
$556$	−0.309126	−0.0131099
$557$	10.6670	0.451977	0.225989	−	0.974130i	$-0.427439\pi$
$557$	10.6670	0.451977	0.225989	+	0.974130i	$0.427439\pi$
$558$	2.45963	0.104125
$559$	−7.00482	−0.296272
$560$	4.03806	0.170639
$561$	2.65087	0.111920
$562$	15.2111	0.641643
$563$	36.5719	1.54132	0.770661	−	0.637246i	$-0.219926\pi$
$563$	36.5719	1.54132	0.770661	+	0.637246i	$0.219926\pi$
$564$	−9.72893	−0.409662
$565$	−14.3851	−0.605186
$566$	−18.1713	−0.763797
$567$	−2.98827	−0.125495
$568$	−7.75987	−0.325597
$569$	19.4541	0.815558	0.407779	−	0.913081i	$-0.366303\pi$
$569$	19.4541	0.815558	0.407779	+	0.913081i	$0.366303\pi$
$570$	−1.35130	−0.0565999
$571$	−23.5838	−0.986952	−0.493476	−	0.869759i	$-0.664274\pi$
$571$	−23.5838	−0.986952	−0.493476	+	0.869759i	$0.664274\pi$
$572$	−1.14480	−0.0478666
$573$	−6.40522	−0.267582
$574$	−16.9234	−0.706369
$575$	2.79290	0.116472
$576$	1.00000	0.0416667
$577$	−6.97435	−0.290346	−0.145173	−	0.989406i	$-0.546374\pi$
$577$	−6.97435	−0.290346	−0.145173	+	0.989406i	$0.546374\pi$
$578$	8.14607	0.338832
$579$	−14.7553	−0.613207
$580$	5.58717	0.231995
$581$	−21.9326	−0.909917
$582$	4.09197	0.169618
$583$	−0.528633	−0.0218937
$584$	6.77161	0.280211
$585$	2.92638	0.120991
$586$	25.2852	1.04452
$587$	14.7825	0.610141	0.305070	−	0.952330i	$-0.401320\pi$
$587$	14.7825	0.610141	0.305070	+	0.952330i	$0.401320\pi$
$588$	−1.92973	−0.0795807
$589$	−2.45963	−0.101347
$590$	5.25883	0.216503
$591$	−2.58590	−0.106370
$592$	3.93100	0.161563
$593$	−33.1562	−1.36156	−0.680781	−	0.732487i	$-0.738360\pi$
$593$	−33.1562	−1.36156	−0.680781	+	0.732487i	$0.738360\pi$
$594$	−0.528633	−0.0216901
$595$	−20.2492	−0.830135
$596$	4.18571	0.171453
$597$	−23.8271	−0.975178
$598$	1.90559	0.0779252
$599$	−2.51726	−0.102852	−0.0514262	−	0.998677i	$-0.516377\pi$
$599$	−2.51726	−0.102852	−0.0514262	+	0.998677i	$0.516377\pi$
$600$	3.17398	0.129577
$601$	−17.5491	−0.715843	−0.357922	−	0.933752i	$-0.616515\pi$
$601$	−17.5491	−0.715843	−0.357922	+	0.933752i	$0.616515\pi$
$602$	−9.66582	−0.393950
$603$	11.0849	0.451410
$604$	2.99538	0.121880
$605$	14.4867	0.588969
$606$	−8.83441	−0.358873
$607$	44.8520	1.82049	0.910244	−	0.414073i	$-0.135894\pi$
$607$	44.8520	1.82049	0.910244	+	0.414073i	$0.135894\pi$
$608$	−1.00000	−0.0405554
$609$	−12.3554	−0.500667
$610$	10.5131	0.425665
$611$	−21.0689	−0.852357
$612$	−5.01459	−0.202703
$613$	1.95986	0.0791581	0.0395791	−	0.999216i	$-0.487398\pi$
$613$	1.95986	0.0791581	0.0395791	+	0.999216i	$0.487398\pi$
$614$	−30.3851	−1.22624
$615$	7.65282	0.308591
$616$	−1.57969	−0.0636477
$617$	−10.1350	−0.408020	−0.204010	−	0.978969i	$-0.565398\pi$
$617$	−10.1350	−0.408020	−0.204010	+	0.978969i	$0.565398\pi$
$618$	−11.9385	−0.480236
$619$	−26.6368	−1.07062	−0.535312	−	0.844654i	$-0.679806\pi$
$619$	−26.6368	−1.07062	−0.535312	+	0.844654i	$0.679806\pi$
$620$	−3.32371	−0.133483
$621$	0.879937	0.0353107
$622$	4.35878	0.174771
$623$	−23.8711	−0.956374
$624$	2.16559	0.0866931
$625$	0.944006	0.0377602
$626$	−15.0886	−0.603062
$627$	0.528633	0.0211116
$628$	4.65617	0.185801
$629$	−19.7123	−0.785982
$630$	4.03806	0.160880
$631$	−31.9840	−1.27326	−0.636632	−	0.771168i	$-0.719673\pi$
$631$	−31.9840	−1.27326	−0.636632	+	0.771168i	$0.719673\pi$
$632$	−7.58255	−0.301617
$633$	−15.0388	−0.597740
$634$	23.2286	0.922524
$635$	21.8978	0.868987
$636$	1.00000	0.0396526
$637$	−4.17901	−0.165578
$638$	−2.18571	−0.0865331
$639$	−7.75987	−0.306976
$640$	−1.35130	−0.0534150
$641$	25.9275	1.02407	0.512036	−	0.858964i	$-0.328891\pi$
$641$	25.9275	1.02407	0.512036	+	0.858964i	$0.328891\pi$
$642$	−0.165593	−0.00653545
$643$	37.8814	1.49390	0.746948	−	0.664883i	$-0.231518\pi$
$643$	37.8814	1.49390	0.746948	+	0.664883i	$0.231518\pi$
$644$	2.62949	0.103616
$645$	4.37092	0.172105
$646$	5.01459	0.197296
$647$	6.05817	0.238171	0.119086	−	0.992884i	$-0.462004\pi$
$647$	6.05817	0.238171	0.119086	+	0.992884i	$0.462004\pi$
$648$	1.00000	0.0392837
$649$	−2.05727	−0.0807547
$650$	6.87354	0.269602
$651$	7.35003	0.288071
$652$	0.00285131	0.000111666 0
$653$	−6.42208	−0.251315	−0.125658	−	0.992074i	$-0.540104\pi$
$653$	−6.42208	−0.251315	−0.125658	+	0.992074i	$0.540104\pi$
$654$	−7.66455	−0.299708
$655$	3.92724	0.153450
$656$	5.66328	0.221114
$657$	6.77161	0.264186
$658$	−29.0726	−1.13337
$659$	24.6776	0.961301	0.480651	−	0.876912i	$-0.340401\pi$
$659$	24.6776	0.961301	0.480651	+	0.876912i	$0.340401\pi$
$660$	0.714344	0.0278058
$661$	−40.5583	−1.57753	−0.788767	−	0.614692i	$-0.789280\pi$
$661$	−40.5583	−1.57753	−0.788767	+	0.614692i	$0.789280\pi$
$662$	−27.6999	−1.07659
$663$	−10.8596	−0.421750
$664$	7.33957	0.284831
$665$	−4.03806	−0.156589
$666$	3.93100	0.152323
$667$	3.63823	0.140873
$668$	−6.46711	−0.250220
$669$	−22.6352	−0.875127
$670$	−14.9790	−0.578690
$671$	−4.11276	−0.158771
$672$	2.98827	0.115275
$673$	−6.12133	−0.235960	−0.117980	−	0.993016i	$-0.537642\pi$
$673$	−6.12133	−0.235960	−0.117980	+	0.993016i	$0.537642\pi$
$674$	−21.4340	−0.825606
$675$	3.17398	0.122166
$676$	−8.31021	−0.319623
$677$	49.7920	1.91366	0.956831	−	0.290645i	$-0.0938699\pi$
$677$	49.7920	1.91366	0.956831	+	0.290645i	$0.0938699\pi$
$678$	−10.6453	−0.408832
$679$	12.2279	0.469263
$680$	6.77623	0.259857
$681$	−7.53611	−0.288784
$682$	1.30024	0.0497889
$683$	13.8041	0.528201	0.264100	−	0.964495i	$-0.414925\pi$
$683$	13.8041	0.528201	0.264100	+	0.964495i	$0.414925\pi$
$684$	−1.00000	−0.0382360
$685$	23.0376	0.880220
$686$	15.1513	0.578480
$687$	1.80758	0.0689637
$688$	3.23459	0.123318
$689$	2.16559	0.0825025
$690$	−1.18906	−0.0452669
$691$	−21.9586	−0.835344	−0.417672	−	0.908598i	$-0.637154\pi$
$691$	−21.9586	−0.835344	−0.417672	+	0.908598i	$0.637154\pi$
$692$	12.5708	0.477871
$693$	−1.57969	−0.0600077
$694$	33.4428	1.26947
$695$	0.417723	0.0158451
$696$	4.13465	0.156723
$697$	−28.3990	−1.07569
$698$	5.06153	0.191582
$699$	−10.6135	−0.401439
$700$	9.48468	0.358487
$701$	22.4189	0.846750	0.423375	−	0.905955i	$-0.360845\pi$
$701$	22.4189	0.846750	0.423375	+	0.905955i	$0.360845\pi$
$702$	2.16559	0.0817351
$703$	−3.93100	−0.148260
$704$	0.528633	0.0199236
$705$	13.1467	0.495135
$706$	6.06347	0.228202
$707$	−26.3995	−0.992857
$708$	3.89167	0.146258
$709$	−24.8247	−0.932312	−0.466156	−	0.884703i	$-0.654361\pi$
$709$	−24.8247	−0.932312	−0.466156	+	0.884703i	$0.654361\pi$
$710$	10.4860	0.393531
$711$	−7.58255	−0.284368
$712$	7.98827	0.299373
$713$	−2.16432	−0.0810545
$714$	−14.9849	−0.560796
$715$	1.54698	0.0578537
$716$	−25.4963	−0.952841
$717$	−13.7227	−0.512485
$718$	−0.359687	−0.0134234
$719$	−21.1830	−0.789994	−0.394997	−	0.918682i	$-0.629254\pi$
$719$	−21.1830	−0.789994	−0.394997	+	0.918682i	$0.629254\pi$
$720$	−1.35130	−0.0503601
$721$	−35.6753	−1.32862
$722$	1.00000	0.0372161
$723$	−29.2500	−1.08782
$724$	16.5624	0.615538
$725$	13.1233	0.487386
$726$	10.7205	0.397877
$727$	41.2479	1.52980	0.764899	−	0.644150i	$-0.222789\pi$
$727$	41.2479	1.52980	0.764899	+	0.644150i	$0.222789\pi$
$728$	6.47137	0.239845
$729$	1.00000	0.0370370
$730$	−9.15051	−0.338675
$731$	−16.2202	−0.599924
$732$	7.77999	0.287557
$733$	9.19446	0.339605	0.169803	−	0.985478i	$-0.445687\pi$
$733$	9.19446	0.339605	0.169803	+	0.985478i	$0.445687\pi$
$734$	0.800974	0.0295645
$735$	2.60765	0.0961846
$736$	−0.879937	−0.0324349
$737$	5.85982	0.215849
$738$	5.66328	0.208468
$739$	41.8328	1.53884	0.769422	−	0.638740i	$-0.220544\pi$
$739$	41.8328	1.53884	0.769422	+	0.638740i	$0.220544\pi$
$740$	−5.31198	−0.195272
$741$	−2.16559	−0.0795551
$742$	2.98827	0.109703
$743$	−14.3706	−0.527207	−0.263603	−	0.964631i	$-0.584911\pi$
$743$	−14.3706	−0.527207	−0.263603	+	0.964631i	$0.584911\pi$
$744$	−2.45963	−0.0901745
$745$	−5.65617	−0.207226
$746$	−36.6712	−1.34263
$747$	7.33957	0.268541
$748$	−2.65087	−0.0969256
$749$	−0.494837	−0.0180810
$750$	−11.0455	−0.403326
$751$	−26.1418	−0.953926	−0.476963	−	0.878923i	$-0.658263\pi$
$751$	−26.1418	−0.953926	−0.476963	+	0.878923i	$0.658263\pi$
$752$	9.72893	0.354778
$753$	5.04268	0.183765
$754$	8.95397	0.326084
$755$	−4.04767	−0.147310
$756$	2.98827	0.108682
$757$	−1.12255	−0.0407998	−0.0203999	−	0.999792i	$-0.506494\pi$
$757$	−1.12255	−0.0407998	−0.0203999	+	0.999792i	$0.506494\pi$
$758$	13.6178	0.494619
$759$	0.465164	0.0168844
$760$	1.35130	0.0490170
$761$	21.7188	0.787307	0.393653	−	0.919259i	$-0.371211\pi$
$761$	21.7188	0.787307	0.393653	+	0.919259i	$0.371211\pi$
$762$	16.2049	0.587042
$763$	−22.9037	−0.829170
$764$	6.40522	0.231733
$765$	6.77623	0.244995
$766$	0.918356	0.0331816
$767$	8.42778	0.304309
$768$	−1.00000	−0.0360844
$769$	−21.6664	−0.781312	−0.390656	−	0.920537i	$-0.627752\pi$
$769$	−21.6664	−0.781312	−0.390656	+	0.920537i	$0.627752\pi$
$770$	2.13465	0.0769274
$771$	−16.3513	−0.588878
$772$	14.7553	0.531053
$773$	−5.18825	−0.186609	−0.0933043	−	0.995638i	$-0.529743\pi$
$773$	−5.18825	−0.186609	−0.0933043	+	0.995638i	$0.529743\pi$
$774$	3.23459	0.116265
$775$	−7.80681	−0.280429
$776$	−4.09197	−0.146893
$777$	11.7469	0.421417
$778$	−33.9120	−1.21580
$779$	−5.66328	−0.202908
$780$	−2.92638	−0.104781
$781$	−4.10212	−0.146786
$782$	4.41252	0.157791
$783$	4.13465	0.147760
$784$	1.92973	0.0689189
$785$	−6.29190	−0.224568
$786$	2.90626	0.103663
$787$	−2.59773	−0.0925991	−0.0462996	−	0.998928i	$-0.514743\pi$
$787$	−2.59773	−0.0925991	−0.0462996	+	0.998928i	$0.514743\pi$
$788$	2.58590	0.0921188
$789$	14.4303	0.513731
$790$	10.2463	0.364548
$791$	−31.8111	−1.13107
$792$	0.528633	0.0187841
$793$	16.8483	0.598301
$794$	−12.9113	−0.458205
$795$	−1.35130	−0.0479258
$796$	23.8271	0.844529
$797$	8.08680	0.286449	0.143225	−	0.989690i	$-0.454253\pi$
$797$	8.08680	0.286449	0.143225	+	0.989690i	$0.454253\pi$
$798$	−2.98827	−0.105783
$799$	−48.7866	−1.72594
$800$	−3.17398	−0.112217
$801$	7.98827	0.282251
$802$	6.56760	0.231910
$803$	3.57969	0.126325
$804$	−11.0849	−0.390933
$805$	−3.55324	−0.125235
$806$	−5.32656	−0.187620
$807$	−18.7716	−0.660792
$808$	8.83441	0.310793
$809$	22.5188	0.791720	0.395860	−	0.918311i	$-0.370447\pi$
$809$	22.5188	0.791720	0.395860	+	0.918311i	$0.370447\pi$
$810$	−1.35130	−0.0474800
$811$	−10.8143	−0.379741	−0.189871	−	0.981809i	$-0.560807\pi$
$811$	−10.8143	−0.379741	−0.189871	+	0.981809i	$0.560807\pi$
$812$	12.3554	0.433590
$813$	−11.7729	−0.412893
$814$	2.07806	0.0728358
$815$	−0.00385299	−0.000134964 0
$816$	5.01459	0.175546
$817$	−3.23459	−0.113164
$818$	4.64870	0.162538
$819$	6.47137	0.226128
$820$	−7.65282	−0.267248
$821$	22.0904	0.770960	0.385480	−	0.922716i	$-0.374036\pi$
$821$	22.0904	0.770960	0.385480	+	0.922716i	$0.374036\pi$
$822$	17.0484	0.594631
$823$	−2.97191	−0.103594	−0.0517971	−	0.998658i	$-0.516495\pi$
$823$	−2.97191	−0.103594	−0.0517971	+	0.998658i	$0.516495\pi$
$824$	11.9385	0.415896
$825$	1.67787	0.0584159
$826$	11.6293	0.404637
$827$	8.22119	0.285879	0.142939	−	0.989731i	$-0.454345\pi$
$827$	8.22119	0.285879	0.142939	+	0.989731i	$0.454345\pi$
$828$	−0.879937	−0.0305799
$829$	−8.70958	−0.302496	−0.151248	−	0.988496i	$-0.548329\pi$
$829$	−8.70958	−0.302496	−0.151248	+	0.988496i	$0.548329\pi$
$830$	−9.91799	−0.344259
$831$	−24.6256	−0.854254
$832$	−2.16559	−0.0750784
$833$	−9.67679	−0.335281
$834$	0.309126	0.0107042
$835$	8.73903	0.302427
$836$	−0.528633	−0.0182831
$837$	−2.45963	−0.0850173
$838$	−18.6590	−0.644565
$839$	5.80504	0.200412	0.100206	−	0.994967i	$-0.468050\pi$
$839$	5.80504	0.200412	0.100206	+	0.994967i	$0.468050\pi$
$840$	−4.03806	−0.139326
$841$	−11.9047	−0.410506
$842$	−23.5646	−0.812090
$843$	−15.2111	−0.523899
$844$	15.0388	0.517658
$845$	11.2296	0.386311
$846$	9.72893	0.334488
$847$	32.0358	1.10076
$848$	−1.00000	−0.0343401
$849$	18.1713	0.623637
$850$	15.9162	0.545920
$851$	−3.45903	−0.118574
$852$	7.75987	0.265849
$853$	46.9107	1.60619	0.803097	−	0.595849i	$-0.203184\pi$
$853$	46.9107	1.60619	0.803097	+	0.595849i	$0.203184\pi$
$854$	23.2487	0.795553
$855$	1.35130	0.0462136
$856$	0.165593	0.00565987
$857$	−45.4798	−1.55356	−0.776780	−	0.629772i	$-0.783148\pi$
$857$	−45.4798	−1.55356	−0.776780	+	0.629772i	$0.783148\pi$
$858$	1.14480	0.0390830
$859$	−12.5336	−0.427640	−0.213820	−	0.976873i	$-0.568591\pi$
$859$	−12.5336	−0.427640	−0.213820	+	0.976873i	$0.568591\pi$
$860$	−4.37092	−0.149047
$861$	16.9234	0.576747
$862$	−29.1229	−0.991930
$863$	−15.9952	−0.544484	−0.272242	−	0.962229i	$-0.587765\pi$
$863$	−15.9952	−0.544484	−0.272242	+	0.962229i	$0.587765\pi$
$864$	−1.00000	−0.0340207
$865$	−16.9870	−0.577575
$866$	14.6131	0.496574
$867$	−8.14607	−0.276655
$868$	−7.35003	−0.249476
$869$	−4.00838	−0.135975
$870$	−5.58717	−0.189423
$871$	−24.0053	−0.813388
$872$	7.66455	0.259555
$873$	−4.09197	−0.138492
$874$	0.879937	0.0297643
$875$	−33.0070	−1.11584
$876$	−6.77161	−0.228791
$877$	37.2982	1.25947	0.629735	−	0.776810i	$-0.283164\pi$
$877$	37.2982	1.25947	0.629735	+	0.776810i	$0.283164\pi$
$878$	−34.8485	−1.17608
$879$	−25.2852	−0.852847
$880$	−0.714344	−0.0240805
$881$	33.6984	1.13533	0.567664	−	0.823260i	$-0.307847\pi$
$881$	33.6984	1.13533	0.567664	+	0.823260i	$0.307847\pi$
$882$	1.92973	0.0649773
$883$	38.4154	1.29278	0.646390	−	0.763007i	$-0.276278\pi$
$883$	38.4154	1.29278	0.646390	+	0.763007i	$0.276278\pi$
$884$	10.8596	0.365246
$885$	−5.25883	−0.176774
$886$	−4.44632	−0.149377
$887$	−0.337219	−0.0113227	−0.00566135	−	0.999984i	$-0.501802\pi$
$887$	−0.337219	−0.0113227	−0.00566135	+	0.999984i	$0.501802\pi$
$888$	−3.93100	−0.131916
$889$	48.4246	1.62411
$890$	−10.7946	−0.361835
$891$	0.528633	0.0177099
$892$	22.6352	0.757882
$893$	−9.72893	−0.325566
$894$	−4.18571	−0.139991
$895$	34.4532	1.15164
$896$	−2.98827	−0.0998309
$897$	−1.90559	−0.0636257
$898$	33.3703	1.11358
$899$	−10.1697	−0.339179
$900$	−3.17398	−0.105799
$901$	5.01459	0.167060
$902$	2.99380	0.0996825
$903$	9.66582	0.321658
$904$	10.6453	0.354059
$905$	−22.3809	−0.743966
$906$	−2.99538	−0.0995147
$907$	−45.8806	−1.52344	−0.761720	−	0.647906i	$-0.775645\pi$
$907$	−45.8806	−1.52344	−0.761720	+	0.647906i	$0.775645\pi$
$908$	7.53611	0.250095
$909$	8.83441	0.293019
$910$	−8.74479	−0.289887
$911$	36.9540	1.22434	0.612170	−	0.790726i	$-0.290297\pi$
$911$	36.9540	1.22434	0.612170	+	0.790726i	$0.290297\pi$
$912$	1.00000	0.0331133
$913$	3.87994	0.128407
$914$	30.4081	1.00581
$915$	−10.5131	−0.347554
$916$	−1.80758	−0.0597243
$917$	8.68467	0.286793
$918$	5.01459	0.165506
$919$	−29.7132	−0.980149	−0.490075	−	0.871680i	$-0.663031\pi$
$919$	−29.7132	−0.980149	−0.490075	+	0.871680i	$0.663031\pi$
$920$	1.18906	0.0392023
$921$	30.3851	1.00122
$922$	11.1610	0.367567
$923$	16.8047	0.553135
$924$	1.57969	0.0519681
$925$	−12.4769	−0.410238
$926$	−8.57045	−0.281642
$927$	11.9385	0.392111
$928$	−4.13465	−0.135727
$929$	−7.28036	−0.238861	−0.119430	−	0.992843i	$-0.538107\pi$
$929$	−7.28036	−0.238861	−0.119430	+	0.992843i	$0.538107\pi$
$930$	3.32371	0.108989
$931$	−1.92973	−0.0632443
$932$	10.6135	0.347656
$933$	−4.35878	−0.142700
$934$	−23.1158	−0.756372
$935$	3.58214	0.117148
$936$	−2.16559	−0.0707846
$937$	−21.8138	−0.712625	−0.356313	−	0.934367i	$-0.615966\pi$
$937$	−21.8138	−0.712625	−0.356313	+	0.934367i	$0.615966\pi$
$938$	−33.1245	−1.08155
$939$	15.0886	0.492398
$940$	−13.1467	−0.428800
$941$	17.2834	0.563422	0.281711	−	0.959499i	$-0.409098\pi$
$941$	17.2834	0.563422	0.281711	+	0.959499i	$0.409098\pi$
$942$	−4.65617	−0.151706
$943$	−4.98333	−0.162280
$944$	−3.89167	−0.126663
$945$	−4.03806	−0.131358
$946$	1.70991	0.0555941
$947$	30.5334	0.992203	0.496102	−	0.868265i	$-0.334764\pi$
$947$	30.5334	0.992203	0.496102	+	0.868265i	$0.334764\pi$
$948$	7.58255	0.246270
$949$	−14.6646	−0.476032
$950$	3.17398	0.102977
$951$	−23.2286	−0.753238
$952$	14.9849	0.485664
$953$	53.7549	1.74129	0.870646	−	0.491909i	$-0.163701\pi$
$953$	53.7549	1.74129	0.870646	+	0.491909i	$0.163701\pi$
$954$	−1.00000	−0.0323762
$955$	−8.65540	−0.280082
$956$	13.7227	0.443825
$957$	2.18571	0.0706540
$958$	13.4835	0.435631
$959$	50.9451	1.64510
$960$	1.35130	0.0436132
$961$	−24.9502	−0.804845
$962$	−8.51295	−0.274468
$963$	0.165593	0.00533617
$964$	29.2500	0.942077
$965$	−19.9388	−0.641854
$966$	−2.62949	−0.0846023
$967$	−14.9879	−0.481978	−0.240989	−	0.970528i	$-0.577472\pi$
$967$	−14.9879	−0.481978	−0.240989	+	0.970528i	$0.577472\pi$
$968$	−10.7205	−0.344571
$969$	−5.01459	−0.161092
$970$	5.52950	0.177541
$971$	−17.9573	−0.576278	−0.288139	−	0.957589i	$-0.593036\pi$
$971$	−17.9573	−0.576278	−0.288139	+	0.957589i	$0.593036\pi$
$972$	−1.00000	−0.0320750
$973$	0.923750	0.0296141
$974$	3.51247	0.112547
$975$	−6.87354	−0.220130
$976$	−7.77999	−0.249031
$977$	−47.7983	−1.52920	−0.764602	−	0.644503i	$-0.777065\pi$
$977$	−47.7983	−1.52920	−0.764602	+	0.644503i	$0.777065\pi$
$978$	−0.00285131	−9.11748e−5 0
$979$	4.22286	0.134963
$980$	−2.60765	−0.0832983
$981$	7.66455	0.244710
$982$	−28.6882	−0.915477
$983$	4.53879	0.144765	0.0723824	−	0.997377i	$-0.476940\pi$
$983$	4.53879	0.144765	0.0723824	+	0.997377i	$0.476940\pi$
$984$	−5.66328	−0.180539
$985$	−3.49434	−0.111339
$986$	20.7336	0.660291
$987$	29.0726	0.925392
$988$	2.16559	0.0688967
$989$	−2.84624	−0.0905052
$990$	−0.714344	−0.0227033
$991$	12.4376	0.395094	0.197547	−	0.980293i	$-0.436703\pi$
$991$	12.4376	0.395094	0.197547	+	0.980293i	$0.436703\pi$
$992$	2.45963	0.0780934
$993$	27.6999	0.879031
$994$	23.1886	0.735497
$995$	−32.1977	−1.02073
$996$	−7.33957	−0.232563
$997$	38.0611	1.20541	0.602703	−	0.797966i	$-0.294090\pi$
$997$	38.0611	1.20541	0.602703	+	0.797966i	$0.294090\pi$
$998$	−33.8565	−1.07171
$999$	−3.93100	−0.124371

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.t.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.t.1.1	✓	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.35130 q^{5} -1.00000 q^{6} -2.98827 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.35130 q^{5} -1.00000 q^{6} -2.98827 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.35130 q^{10} +0.528633 q^{11} -1.00000 q^{12} -2.16559 q^{13} -2.98827 q^{14} +1.35130 q^{15} +1.00000 q^{16} -5.01459 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.35130 q^{20} +2.98827 q^{21} +0.528633 q^{22} -0.879937 q^{23} -1.00000 q^{24} -3.17398 q^{25} -2.16559 q^{26} -1.00000 q^{27} -2.98827 q^{28} -4.13465 q^{29} +1.35130 q^{30} +2.45963 q^{31} +1.00000 q^{32} -0.528633 q^{33} -5.01459 q^{34} +4.03806 q^{35} +1.00000 q^{36} +3.93100 q^{37} -1.00000 q^{38} +2.16559 q^{39} -1.35130 q^{40} +5.66328 q^{41} +2.98827 q^{42} +3.23459 q^{43} +0.528633 q^{44} -1.35130 q^{45} -0.879937 q^{46} +9.72893 q^{47} -1.00000 q^{48} +1.92973 q^{49} -3.17398 q^{50} +5.01459 q^{51} -2.16559 q^{52} -1.00000 q^{53} -1.00000 q^{54} -0.714344 q^{55} -2.98827 q^{56} +1.00000 q^{57} -4.13465 q^{58} -3.89167 q^{59} +1.35130 q^{60} -7.77999 q^{61} +2.45963 q^{62} -2.98827 q^{63} +1.00000 q^{64} +2.92638 q^{65} -0.528633 q^{66} +11.0849 q^{67} -5.01459 q^{68} +0.879937 q^{69} +4.03806 q^{70} -7.75987 q^{71} +1.00000 q^{72} +6.77161 q^{73} +3.93100 q^{74} +3.17398 q^{75} -1.00000 q^{76} -1.57969 q^{77} +2.16559 q^{78} -7.58255 q^{79} -1.35130 q^{80} +1.00000 q^{81} +5.66328 q^{82} +7.33957 q^{83} +2.98827 q^{84} +6.77623 q^{85} +3.23459 q^{86} +4.13465 q^{87} +0.528633 q^{88} +7.98827 q^{89} -1.35130 q^{90} +6.47137 q^{91} -0.879937 q^{92} -2.45963 q^{93} +9.72893 q^{94} +1.35130 q^{95} -1.00000 q^{96} -4.09197 q^{97} +1.92973 q^{98} +0.528633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 6 q^{5} - 4 q^{6} + 3 q^{7} + 4 q^{8} + 4 q^{9} + 6 q^{10} - 2 q^{11} - 4 q^{12} - q^{13} + 3 q^{14} - 6 q^{15} + 4 q^{16} + 8 q^{17} + 4 q^{18} - 4 q^{19} + 6 q^{20} - 3 q^{21} - 2 q^{22} + 12 q^{23} - 4 q^{24} + 6 q^{25} - q^{26} - 4 q^{27} + 3 q^{28} - 4 q^{29} - 6 q^{30} - q^{31} + 4 q^{32} + 2 q^{33} + 8 q^{34} + 18 q^{35} + 4 q^{36} + 9 q^{37} - 4 q^{38} + q^{39} + 6 q^{40} + 6 q^{41} - 3 q^{42} + 12 q^{43} - 2 q^{44} + 6 q^{45} + 12 q^{46} + 3 q^{47} - 4 q^{48} + 9 q^{49} + 6 q^{50} - 8 q^{51} - q^{52} - 4 q^{53} - 4 q^{54} + 5 q^{55} + 3 q^{56} + 4 q^{57} - 4 q^{58} - 15 q^{59} - 6 q^{60} - 4 q^{61} - q^{62} + 3 q^{63} + 4 q^{64} - 13 q^{65} + 2 q^{66} + 15 q^{67} + 8 q^{68} - 12 q^{69} + 18 q^{70} + 4 q^{72} + 11 q^{73} + 9 q^{74} - 6 q^{75} - 4 q^{76} - 11 q^{77} + q^{78} + 8 q^{79} + 6 q^{80} + 4 q^{81} + 6 q^{82} + 3 q^{83} - 3 q^{84} + 29 q^{85} + 12 q^{86} + 4 q^{87} - 2 q^{88} + 17 q^{89} + 6 q^{90} + 30 q^{91} + 12 q^{92} + q^{93} + 3 q^{94} - 6 q^{95} - 4 q^{96} + 16 q^{97} + 9 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 6 * q^5 - 4 * q^6 + 3 * q^7 + 4 * q^8 + 4 * q^9 + 6 * q^10 - 2 * q^11 - 4 * q^12 - q^13 + 3 * q^14 - 6 * q^15 + 4 * q^16 + 8 * q^17 + 4 * q^18 - 4 * q^19 + 6 * q^20 - 3 * q^21 - 2 * q^22 + 12 * q^23 - 4 * q^24 + 6 * q^25 - q^26 - 4 * q^27 + 3 * q^28 - 4 * q^29 - 6 * q^30 - q^31 + 4 * q^32 + 2 * q^33 + 8 * q^34 + 18 * q^35 + 4 * q^36 + 9 * q^37 - 4 * q^38 + q^39 + 6 * q^40 + 6 * q^41 - 3 * q^42 + 12 * q^43 - 2 * q^44 + 6 * q^45 + 12 * q^46 + 3 * q^47 - 4 * q^48 + 9 * q^49 + 6 * q^50 - 8 * q^51 - q^52 - 4 * q^53 - 4 * q^54 + 5 * q^55 + 3 * q^56 + 4 * q^57 - 4 * q^58 - 15 * q^59 - 6 * q^60 - 4 * q^61 - q^62 + 3 * q^63 + 4 * q^64 - 13 * q^65 + 2 * q^66 + 15 * q^67 + 8 * q^68 - 12 * q^69 + 18 * q^70 + 4 * q^72 + 11 * q^73 + 9 * q^74 - 6 * q^75 - 4 * q^76 - 11 * q^77 + q^78 + 8 * q^79 + 6 * q^80 + 4 * q^81 + 6 * q^82 + 3 * q^83 - 3 * q^84 + 29 * q^85 + 12 * q^86 + 4 * q^87 - 2 * q^88 + 17 * q^89 + 6 * q^90 + 30 * q^91 + 12 * q^92 + q^93 + 3 * q^94 - 6 * q^95 - 4 * q^96 + 16 * q^97 + 9 * q^98 - 2 * q^99

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