LMFDB - Embedded newform 4026.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.30998405.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9x^{4} + 8x^{3} + 16x^{2} - 13x + 2 $ x^6 - x^5 - 9x^4 + 8x^3 + 16x^2 - 13x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.58506$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.713913 q^{5} +1.00000 q^{6} +2.21640 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.713913 q^{5} +1.00000 q^{6} +2.21640 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.713913 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.89395 q^{13} -2.21640 q^{14} +0.713913 q^{15} +1.00000 q^{16} -3.80146 q^{17} -1.00000 q^{18} +6.51811 q^{19} -0.713913 q^{20} -2.21640 q^{21} -1.00000 q^{22} -6.69541 q^{23} +1.00000 q^{24} -4.49033 q^{25} -2.89395 q^{26} -1.00000 q^{27} +2.21640 q^{28} -5.22906 q^{29} -0.713913 q^{30} -7.71218 q^{31} -1.00000 q^{32} -1.00000 q^{33} +3.80146 q^{34} -1.58232 q^{35} +1.00000 q^{36} +9.84176 q^{37} -6.51811 q^{38} -2.89395 q^{39} +0.713913 q^{40} -3.13964 q^{41} +2.21640 q^{42} -8.89965 q^{43} +1.00000 q^{44} -0.713913 q^{45} +6.69541 q^{46} -6.11140 q^{47} -1.00000 q^{48} -2.08755 q^{49} +4.49033 q^{50} +3.80146 q^{51} +2.89395 q^{52} +5.41618 q^{53} +1.00000 q^{54} -0.713913 q^{55} -2.21640 q^{56} -6.51811 q^{57} +5.22906 q^{58} +4.87463 q^{59} +0.713913 q^{60} +1.00000 q^{61} +7.71218 q^{62} +2.21640 q^{63} +1.00000 q^{64} -2.06603 q^{65} +1.00000 q^{66} +12.1708 q^{67} -3.80146 q^{68} +6.69541 q^{69} +1.58232 q^{70} +4.11519 q^{71} -1.00000 q^{72} -2.29949 q^{73} -9.84176 q^{74} +4.49033 q^{75} +6.51811 q^{76} +2.21640 q^{77} +2.89395 q^{78} -13.6015 q^{79} -0.713913 q^{80} +1.00000 q^{81} +3.13964 q^{82} -7.12488 q^{83} -2.21640 q^{84} +2.71391 q^{85} +8.89965 q^{86} +5.22906 q^{87} -1.00000 q^{88} -2.53058 q^{89} +0.713913 q^{90} +6.41416 q^{91} -6.69541 q^{92} +7.71218 q^{93} +6.11140 q^{94} -4.65336 q^{95} +1.00000 q^{96} -14.8503 q^{97} +2.08755 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 6 q^{11} - 6 q^{12} + 2 q^{13} - 5 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 5 q^{19} - q^{20} - 5 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} - q^{25} - 2 q^{26} - 6 q^{27} + 5 q^{28} - 10 q^{29} - q^{30} - 15 q^{31} - 6 q^{32} - 6 q^{33} + 4 q^{34} - 21 q^{35} + 6 q^{36} - 3 q^{37} + 5 q^{38} - 2 q^{39} + q^{40} - 9 q^{41} + 5 q^{42} + 10 q^{43} + 6 q^{44} - q^{45} + 6 q^{46} - 14 q^{47} - 6 q^{48} + 3 q^{49} + q^{50} + 4 q^{51} + 2 q^{52} - 11 q^{53} + 6 q^{54} - q^{55} - 5 q^{56} + 5 q^{57} + 10 q^{58} - 20 q^{59} + q^{60} + 6 q^{61} + 15 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} + 6 q^{66} + 14 q^{67} - 4 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 6 q^{72} + 16 q^{73} + 3 q^{74} + q^{75} - 5 q^{76} + 5 q^{77} + 2 q^{78} - 6 q^{79} - q^{80} + 6 q^{81} + 9 q^{82} - 10 q^{83} - 5 q^{84} + 13 q^{85} - 10 q^{86} + 10 q^{87} - 6 q^{88} - 11 q^{89} + q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} + 14 q^{94} + 9 q^{95} + 6 q^{96} + 2 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 6 * q^11 - 6 * q^12 + 2 * q^13 - 5 * q^14 + q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 5 * q^19 - q^20 - 5 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 - q^25 - 2 * q^26 - 6 * q^27 + 5 * q^28 - 10 * q^29 - q^30 - 15 * q^31 - 6 * q^32 - 6 * q^33 + 4 * q^34 - 21 * q^35 + 6 * q^36 - 3 * q^37 + 5 * q^38 - 2 * q^39 + q^40 - 9 * q^41 + 5 * q^42 + 10 * q^43 + 6 * q^44 - q^45 + 6 * q^46 - 14 * q^47 - 6 * q^48 + 3 * q^49 + q^50 + 4 * q^51 + 2 * q^52 - 11 * q^53 + 6 * q^54 - q^55 - 5 * q^56 + 5 * q^57 + 10 * q^58 - 20 * q^59 + q^60 + 6 * q^61 + 15 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 + 6 * q^66 + 14 * q^67 - 4 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 6 * q^72 + 16 * q^73 + 3 * q^74 + q^75 - 5 * q^76 + 5 * q^77 + 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 9 * q^82 - 10 * q^83 - 5 * q^84 + 13 * q^85 - 10 * q^86 + 10 * q^87 - 6 * q^88 - 11 * q^89 + q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 + 14 * q^94 + 9 * q^95 + 6 * q^96 + 2 * q^97 - 3 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.713913	−0.319271	−0.159636	−	0.987176i	$-0.551032\pi$
$5$	−0.713913	−0.319271	−0.159636	+	0.987176i	$0.551032\pi$
$6$	1.00000	0.408248
$7$	2.21640	0.837722	0.418861	−	0.908050i	$-0.362429\pi$
$7$	2.21640	0.837722	0.418861	+	0.908050i	$0.362429\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.713913	0.225759
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	2.89395	0.802637	0.401318	−	0.915939i	$-0.368552\pi$
$13$	2.89395	0.802637	0.401318	+	0.915939i	$0.368552\pi$
$14$	−2.21640	−0.592359
$15$	0.713913	0.184331
$16$	1.00000	0.250000
$17$	−3.80146	−0.921990	−0.460995	−	0.887403i	$-0.652507\pi$
$17$	−3.80146	−0.921990	−0.460995	+	0.887403i	$0.652507\pi$
$18$	−1.00000	−0.235702
$19$	6.51811	1.49536	0.747679	−	0.664060i	$-0.231168\pi$
$19$	6.51811	1.49536	0.747679	+	0.664060i	$0.231168\pi$
$20$	−0.713913	−0.159636
$21$	−2.21640	−0.483659
$22$	−1.00000	−0.213201
$23$	−6.69541	−1.39609	−0.698045	−	0.716054i	$-0.745946\pi$
$23$	−6.69541	−1.39609	−0.698045	+	0.716054i	$0.745946\pi$
$24$	1.00000	0.204124
$25$	−4.49033	−0.898066
$26$	−2.89395	−0.567550
$27$	−1.00000	−0.192450
$28$	2.21640	0.418861
$29$	−5.22906	−0.971012	−0.485506	−	0.874233i	$-0.661365\pi$
$29$	−5.22906	−0.971012	−0.485506	+	0.874233i	$0.661365\pi$
$30$	−0.713913	−0.130342
$31$	−7.71218	−1.38515	−0.692575	−	0.721346i	$-0.743524\pi$
$31$	−7.71218	−1.38515	−0.692575	+	0.721346i	$0.743524\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	3.80146	0.651946
$35$	−1.58232	−0.267461
$36$	1.00000	0.166667
$37$	9.84176	1.61798	0.808988	−	0.587826i	$-0.200016\pi$
$37$	9.84176	1.61798	0.808988	+	0.587826i	$0.200016\pi$
$38$	−6.51811	−1.05738
$39$	−2.89395	−0.463403
$40$	0.713913	0.112880
$41$	−3.13964	−0.490330	−0.245165	−	0.969481i	$-0.578842\pi$
$41$	−3.13964	−0.490330	−0.245165	+	0.969481i	$0.578842\pi$
$42$	2.21640	0.341999
$43$	−8.89965	−1.35718	−0.678592	−	0.734515i	$-0.737410\pi$
$43$	−8.89965	−1.35718	−0.678592	+	0.734515i	$0.737410\pi$
$44$	1.00000	0.150756
$45$	−0.713913	−0.106424
$46$	6.69541	0.987185
$47$	−6.11140	−0.891440	−0.445720	−	0.895172i	$-0.647052\pi$
$47$	−6.11140	−0.891440	−0.445720	+	0.895172i	$0.647052\pi$
$48$	−1.00000	−0.144338
$49$	−2.08755	−0.298221
$50$	4.49033	0.635028
$51$	3.80146	0.532311
$52$	2.89395	0.401318
$53$	5.41618	0.743969	0.371985	−	0.928239i	$-0.378677\pi$
$53$	5.41618	0.743969	0.371985	+	0.928239i	$0.378677\pi$
$54$	1.00000	0.136083
$55$	−0.713913	−0.0962640
$56$	−2.21640	−0.296180
$57$	−6.51811	−0.863345
$58$	5.22906	0.686610
$59$	4.87463	0.634622	0.317311	−	0.948321i	$-0.397220\pi$
$59$	4.87463	0.634622	0.317311	+	0.948321i	$0.397220\pi$
$60$	0.713913	0.0921657
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	7.71218	0.979448
$63$	2.21640	0.279241
$64$	1.00000	0.125000
$65$	−2.06603	−0.256259
$66$	1.00000	0.123091
$67$	12.1708	1.48690	0.743452	−	0.668789i	$-0.233187\pi$
$67$	12.1708	1.48690	0.743452	+	0.668789i	$0.233187\pi$
$68$	−3.80146	−0.460995
$69$	6.69541	0.806033
$70$	1.58232	0.189123
$71$	4.11519	0.488383	0.244192	−	0.969727i	$-0.421477\pi$
$71$	4.11519	0.488383	0.244192	+	0.969727i	$0.421477\pi$
$72$	−1.00000	−0.117851
$73$	−2.29949	−0.269135	−0.134567	−	0.990904i	$-0.542964\pi$
$73$	−2.29949	−0.269135	−0.134567	+	0.990904i	$0.542964\pi$
$74$	−9.84176	−1.14408
$75$	4.49033	0.518498
$76$	6.51811	0.747679
$77$	2.21640	0.252583
$78$	2.89395	0.327675
$79$	−13.6015	−1.53029	−0.765147	−	0.643856i	$-0.777334\pi$
$79$	−13.6015	−1.53029	−0.765147	+	0.643856i	$0.777334\pi$
$80$	−0.713913	−0.0798179
$81$	1.00000	0.111111
$82$	3.13964	0.346715
$83$	−7.12488	−0.782057	−0.391029	−	0.920379i	$-0.627881\pi$
$83$	−7.12488	−0.782057	−0.391029	+	0.920379i	$0.627881\pi$
$84$	−2.21640	−0.241830
$85$	2.71391	0.294365
$86$	8.89965	0.959674
$87$	5.22906	0.560614
$88$	−1.00000	−0.106600
$89$	−2.53058	−0.268241	−0.134120	−	0.990965i	$-0.542821\pi$
$89$	−2.53058	−0.268241	−0.134120	+	0.990965i	$0.542821\pi$
$90$	0.713913	0.0752530
$91$	6.41416	0.672387
$92$	−6.69541	−0.698045
$93$	7.71218	0.799716
$94$	6.11140	0.630343
$95$	−4.65336	−0.477425
$96$	1.00000	0.102062
$97$	−14.8503	−1.50782	−0.753910	−	0.656978i	$-0.771834\pi$
$97$	−14.8503	−1.50782	−0.753910	+	0.656978i	$0.771834\pi$
$98$	2.08755	0.210874
$99$	1.00000	0.100504
$100$	−4.49033	−0.449033
$101$	1.62632	0.161825	0.0809125	−	0.996721i	$-0.474217\pi$
$101$	1.62632	0.161825	0.0809125	+	0.996721i	$0.474217\pi$
$102$	−3.80146	−0.376401
$103$	15.7623	1.55311	0.776553	−	0.630052i	$-0.216966\pi$
$103$	15.7623	1.55311	0.776553	+	0.630052i	$0.216966\pi$
$104$	−2.89395	−0.283775
$105$	1.58232	0.154419
$106$	−5.41618	−0.526066
$107$	4.50955	0.435955	0.217977	−	0.975954i	$-0.430054\pi$
$107$	4.50955	0.435955	0.217977	+	0.975954i	$0.430054\pi$
$108$	−1.00000	−0.0962250
$109$	−18.0320	−1.72715	−0.863576	−	0.504219i	$-0.831780\pi$
$109$	−18.0320	−1.72715	−0.863576	+	0.504219i	$0.831780\pi$
$110$	0.713913	0.0680689
$111$	−9.84176	−0.934138
$112$	2.21640	0.209431
$113$	8.73608	0.821821	0.410911	−	0.911676i	$-0.365211\pi$
$113$	8.73608	0.821821	0.410911	+	0.911676i	$0.365211\pi$
$114$	6.51811	0.610477
$115$	4.77994	0.445732
$116$	−5.22906	−0.485506
$117$	2.89395	0.267546
$118$	−4.87463	−0.448746
$119$	−8.42558	−0.772372
$120$	−0.713913	−0.0651710
$121$	1.00000	0.0909091
$122$	−1.00000	−0.0905357
$123$	3.13964	0.283092
$124$	−7.71218	−0.692575
$125$	6.77527	0.605998
$126$	−2.21640	−0.197453
$127$	4.51189	0.400366	0.200183	−	0.979759i	$-0.435846\pi$
$127$	4.51189	0.400366	0.200183	+	0.979759i	$0.435846\pi$
$128$	−1.00000	−0.0883883
$129$	8.89965	0.783571
$130$	2.06603	0.181202
$131$	2.28747	0.199857	0.0999287	−	0.994995i	$-0.468139\pi$
$131$	2.28747	0.199857	0.0999287	+	0.994995i	$0.468139\pi$
$132$	−1.00000	−0.0870388
$133$	14.4468	1.25269
$134$	−12.1708	−1.05140
$135$	0.713913	0.0614438
$136$	3.80146	0.325973
$137$	−7.21660	−0.616555	−0.308278	−	0.951296i	$-0.599753\pi$
$137$	−7.21660	−0.616555	−0.308278	+	0.951296i	$0.599753\pi$
$138$	−6.69541	−0.569951
$139$	−9.00891	−0.764126	−0.382063	−	0.924136i	$-0.624786\pi$
$139$	−9.00891	−0.764126	−0.382063	+	0.924136i	$0.624786\pi$
$140$	−1.58232	−0.133730
$141$	6.11140	0.514673
$142$	−4.11519	−0.345339
$143$	2.89395	0.242004
$144$	1.00000	0.0833333
$145$	3.73309	0.310017
$146$	2.29949	0.190307
$147$	2.08755	0.172178
$148$	9.84176	0.808988
$149$	−24.2824	−1.98929	−0.994647	−	0.103331i	$-0.967050\pi$
$149$	−24.2824	−1.98929	−0.994647	+	0.103331i	$0.967050\pi$
$150$	−4.49033	−0.366634
$151$	2.59194	0.210929	0.105464	−	0.994423i	$-0.466367\pi$
$151$	2.59194	0.210929	0.105464	+	0.994423i	$0.466367\pi$
$152$	−6.51811	−0.528689
$153$	−3.80146	−0.307330
$154$	−2.21640	−0.178603
$155$	5.50583	0.442239
$156$	−2.89395	−0.231701
$157$	−11.2129	−0.894884	−0.447442	−	0.894313i	$-0.647665\pi$
$157$	−11.2129	−0.894884	−0.447442	+	0.894313i	$0.647665\pi$
$158$	13.6015	1.08208
$159$	−5.41618	−0.429531
$160$	0.713913	0.0564398
$161$	−14.8397	−1.16954
$162$	−1.00000	−0.0785674
$163$	−1.32328	−0.103647	−0.0518235	−	0.998656i	$-0.516503\pi$
$163$	−1.32328	−0.103647	−0.0518235	+	0.998656i	$0.516503\pi$
$164$	−3.13964	−0.245165
$165$	0.713913	0.0555780
$166$	7.12488	0.552998
$167$	10.9233	0.845273	0.422636	−	0.906299i	$-0.361105\pi$
$167$	10.9233	0.845273	0.422636	+	0.906299i	$0.361105\pi$
$168$	2.21640	0.170999
$169$	−4.62506	−0.355774
$170$	−2.71391	−0.208148
$171$	6.51811	0.498453
$172$	−8.89965	−0.678592
$173$	15.6601	1.19061	0.595306	−	0.803499i	$-0.297031\pi$
$173$	15.6601	1.19061	0.595306	+	0.803499i	$0.297031\pi$
$174$	−5.22906	−0.396414
$175$	−9.95239	−0.752330
$176$	1.00000	0.0753778
$177$	−4.87463	−0.366399
$178$	2.53058	0.189675
$179$	4.64098	0.346883	0.173441	−	0.984844i	$-0.444511\pi$
$179$	4.64098	0.346883	0.173441	+	0.984844i	$0.444511\pi$
$180$	−0.713913	−0.0532119
$181$	−8.69230	−0.646093	−0.323047	−	0.946383i	$-0.604707\pi$
$181$	−8.69230	−0.646093	−0.323047	+	0.946383i	$0.604707\pi$
$182$	−6.41416	−0.475449
$183$	−1.00000	−0.0739221
$184$	6.69541	0.493592
$185$	−7.02616	−0.516573
$186$	−7.71218	−0.565485
$187$	−3.80146	−0.277991
$188$	−6.11140	−0.445720
$189$	−2.21640	−0.161220
$190$	4.65336	0.337591
$191$	−13.6763	−0.989585	−0.494792	−	0.869011i	$-0.664756\pi$
$191$	−13.6763	−0.989585	−0.494792	+	0.869011i	$0.664756\pi$
$192$	−1.00000	−0.0721688
$193$	21.5860	1.55379	0.776896	−	0.629629i	$-0.216793\pi$
$193$	21.5860	1.55379	0.776896	+	0.629629i	$0.216793\pi$
$194$	14.8503	1.06619
$195$	2.06603	0.147951
$196$	−2.08755	−0.149111
$197$	−5.87387	−0.418496	−0.209248	−	0.977863i	$-0.567102\pi$
$197$	−5.87387	−0.418496	−0.209248	+	0.977863i	$0.567102\pi$
$198$	−1.00000	−0.0710669
$199$	0.0192795	0.00136669	0.000683343	−	1.00000i	$-0.499782\pi$
$199$	0.0192795	0.00136669	0.000683343		1.00000i	$0.499782\pi$
$200$	4.49033	0.317514
$201$	−12.1708	−0.858465
$202$	−1.62632	−0.114428
$203$	−11.5897	−0.813439
$204$	3.80146	0.266156
$205$	2.24143	0.156548
$206$	−15.7623	−1.09821
$207$	−6.69541	−0.465363
$208$	2.89395	0.200659
$209$	6.51811	0.450867
$210$	−1.58232	−0.109190
$211$	11.6694	0.803352	0.401676	−	0.915782i	$-0.368428\pi$
$211$	11.6694	0.803352	0.401676	+	0.915782i	$0.368428\pi$
$212$	5.41618	0.371985
$213$	−4.11519	−0.281968
$214$	−4.50955	−0.308267
$215$	6.35357	0.433310
$216$	1.00000	0.0680414
$217$	−17.0933	−1.16037
$218$	18.0320	1.22128
$219$	2.29949	0.155385
$220$	−0.713913	−0.0481320
$221$	−11.0012	−0.740023
$222$	9.84176	0.660536
$223$	−15.7792	−1.05665	−0.528326	−	0.849042i	$-0.677180\pi$
$223$	−15.7792	−1.05665	−0.528326	+	0.849042i	$0.677180\pi$
$224$	−2.21640	−0.148090
$225$	−4.49033	−0.299355
$226$	−8.73608	−0.581115
$227$	−6.03088	−0.400283	−0.200142	−	0.979767i	$-0.564140\pi$
$227$	−6.03088	−0.400283	−0.200142	+	0.979767i	$0.564140\pi$
$228$	−6.51811	−0.431673
$229$	17.0456	1.12641	0.563203	−	0.826319i	$-0.309569\pi$
$229$	17.0456	1.12641	0.563203	+	0.826319i	$0.309569\pi$
$230$	−4.77994	−0.315180
$231$	−2.21640	−0.145829
$232$	5.22906	0.343305
$233$	−7.96519	−0.521817	−0.260909	−	0.965364i	$-0.584022\pi$
$233$	−7.96519	−0.521817	−0.260909	+	0.965364i	$0.584022\pi$
$234$	−2.89395	−0.189183
$235$	4.36301	0.284611
$236$	4.87463	0.317311
$237$	13.6015	0.883516
$238$	8.42558	0.546149
$239$	−22.6053	−1.46222	−0.731109	−	0.682261i	$-0.760997\pi$
$239$	−22.6053	−1.46222	−0.731109	+	0.682261i	$0.760997\pi$
$240$	0.713913	0.0460829
$241$	11.2728	0.726143	0.363071	−	0.931761i	$-0.381728\pi$
$241$	11.2728	0.726143	0.363071	+	0.931761i	$0.381728\pi$
$242$	−1.00000	−0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	1.49033	0.0952136
$246$	−3.13964	−0.200176
$247$	18.8631	1.20023
$248$	7.71218	0.489724
$249$	7.12488	0.451521
$250$	−6.77527	−0.428505
$251$	−29.0422	−1.83313	−0.916564	−	0.399889i	$-0.869049\pi$
$251$	−29.0422	−1.83313	−0.916564	+	0.399889i	$0.869049\pi$
$252$	2.21640	0.139620
$253$	−6.69541	−0.420937
$254$	−4.51189	−0.283101
$255$	−2.71391	−0.169952
$256$	1.00000	0.0625000
$257$	−12.7886	−0.797732	−0.398866	−	0.917009i	$-0.630596\pi$
$257$	−12.7886	−0.797732	−0.398866	+	0.917009i	$0.630596\pi$
$258$	−8.89965	−0.554068
$259$	21.8133	1.35541
$260$	−2.06603	−0.128130
$261$	−5.22906	−0.323671
$262$	−2.28747	−0.141321
$263$	15.0466	0.927811	0.463906	−	0.885885i	$-0.346448\pi$
$263$	15.0466	0.927811	0.463906	+	0.885885i	$0.346448\pi$
$264$	1.00000	0.0615457
$265$	−3.86668	−0.237528
$266$	−14.4468	−0.885789
$267$	2.53058	0.154869
$268$	12.1708	0.743452
$269$	11.4706	0.699378	0.349689	−	0.936866i	$-0.386287\pi$
$269$	11.4706	0.699378	0.349689	+	0.936866i	$0.386287\pi$
$270$	−0.713913	−0.0434473
$271$	15.9187	0.966993	0.483497	−	0.875346i	$-0.339367\pi$
$271$	15.9187	0.966993	0.483497	+	0.875346i	$0.339367\pi$
$272$	−3.80146	−0.230498
$273$	−6.41416	−0.388203
$274$	7.21660	0.435971
$275$	−4.49033	−0.270777
$276$	6.69541	0.403016
$277$	−31.5070	−1.89307	−0.946535	−	0.322601i	$-0.895443\pi$
$277$	−31.5070	−1.89307	−0.946535	+	0.322601i	$0.895443\pi$
$278$	9.00891	0.540319
$279$	−7.71218	−0.461716
$280$	1.58232	0.0945617
$281$	9.32257	0.556138	0.278069	−	0.960561i	$-0.410306\pi$
$281$	9.32257	0.556138	0.278069	+	0.960561i	$0.410306\pi$
$282$	−6.11140	−0.363929
$283$	−13.6198	−0.809612	−0.404806	−	0.914403i	$-0.632661\pi$
$283$	−13.6198	−0.809612	−0.404806	+	0.914403i	$0.632661\pi$
$284$	4.11519	0.244192
$285$	4.65336	0.275642
$286$	−2.89395	−0.171123
$287$	−6.95871	−0.410760
$288$	−1.00000	−0.0589256
$289$	−2.54888	−0.149934
$290$	−3.73309	−0.219215
$291$	14.8503	0.870540
$292$	−2.29949	−0.134567
$293$	16.5857	0.968945	0.484472	−	0.874807i	$-0.339012\pi$
$293$	16.5857	0.968945	0.484472	+	0.874807i	$0.339012\pi$
$294$	−2.08755	−0.121748
$295$	−3.48006	−0.202617
$296$	−9.84176	−0.572041
$297$	−1.00000	−0.0580259
$298$	24.2824	1.40664
$299$	−19.3762	−1.12055
$300$	4.49033	0.259249
$301$	−19.7252	−1.13694
$302$	−2.59194	−0.149149
$303$	−1.62632	−0.0934297
$304$	6.51811	0.373840
$305$	−0.713913	−0.0408785
$306$	3.80146	0.217315
$307$	−29.6050	−1.68964	−0.844822	−	0.535048i	$-0.820294\pi$
$307$	−29.6050	−1.68964	−0.844822	+	0.535048i	$0.820294\pi$
$308$	2.21640	0.126291
$309$	−15.7623	−0.896686
$310$	−5.50583	−0.312710
$311$	−31.1110	−1.76414	−0.882072	−	0.471115i	$-0.843852\pi$
$311$	−31.1110	−1.76414	−0.882072	+	0.471115i	$0.843852\pi$
$312$	2.89395	0.163838
$313$	−1.58625	−0.0896599	−0.0448300	−	0.998995i	$-0.514275\pi$
$313$	−1.58625	−0.0896599	−0.0448300	+	0.998995i	$0.514275\pi$
$314$	11.2129	0.632778
$315$	−1.58232	−0.0891536
$316$	−13.6015	−0.765147
$317$	2.30994	0.129739	0.0648696	−	0.997894i	$-0.479337\pi$
$317$	2.30994	0.129739	0.0648696	+	0.997894i	$0.479337\pi$
$318$	5.41618	0.303724
$319$	−5.22906	−0.292771
$320$	−0.713913	−0.0399089
$321$	−4.50955	−0.251699
$322$	14.8397	0.826986
$323$	−24.7784	−1.37871
$324$	1.00000	0.0555556
$325$	−12.9948	−0.720821
$326$	1.32328	0.0732894
$327$	18.0320	0.997171
$328$	3.13964	0.173358
$329$	−13.5453	−0.746779
$330$	−0.713913	−0.0392996
$331$	−20.4018	−1.12139	−0.560694	−	0.828023i	$-0.689465\pi$
$331$	−20.4018	−1.12139	−0.560694	+	0.828023i	$0.689465\pi$
$332$	−7.12488	−0.391029
$333$	9.84176	0.539325
$334$	−10.9233	−0.597698
$335$	−8.68892	−0.474726
$336$	−2.21640	−0.120915
$337$	8.00437	0.436026	0.218013	−	0.975946i	$-0.430043\pi$
$337$	8.00437	0.436026	0.218013	+	0.975946i	$0.430043\pi$
$338$	4.62506	0.251570
$339$	−8.73608	−0.474479
$340$	2.71391	0.147183
$341$	−7.71218	−0.417638
$342$	−6.51811	−0.352459
$343$	−20.1417	−1.08755
$344$	8.89965	0.479837
$345$	−4.77994	−0.257343
$346$	−15.6601	−0.841890
$347$	18.8063	1.00958	0.504788	−	0.863244i	$-0.331571\pi$
$347$	18.8063	1.00958	0.504788	+	0.863244i	$0.331571\pi$
$348$	5.22906	0.280307
$349$	7.81741	0.418456	0.209228	−	0.977867i	$-0.432905\pi$
$349$	7.81741	0.418456	0.209228	+	0.977867i	$0.432905\pi$
$350$	9.95239	0.531977
$351$	−2.89395	−0.154468
$352$	−1.00000	−0.0533002
$353$	−21.5546	−1.14724	−0.573618	−	0.819123i	$-0.694461\pi$
$353$	−21.5546	−1.14724	−0.573618	+	0.819123i	$0.694461\pi$
$354$	4.87463	0.259084
$355$	−2.93789	−0.155927
$356$	−2.53058	−0.134120
$357$	8.42558	0.445929
$358$	−4.64098	−0.245283
$359$	−30.6478	−1.61753	−0.808765	−	0.588133i	$-0.799863\pi$
$359$	−30.6478	−1.61753	−0.808765	+	0.588133i	$0.799863\pi$
$360$	0.713913	0.0376265
$361$	23.4858	1.23610
$362$	8.69230	0.456857
$363$	−1.00000	−0.0524864
$364$	6.41416	0.336193
$365$	1.64163	0.0859270
$366$	1.00000	0.0522708
$367$	12.3449	0.644397	0.322198	−	0.946672i	$-0.395578\pi$
$367$	12.3449	0.644397	0.322198	+	0.946672i	$0.395578\pi$
$368$	−6.69541	−0.349022
$369$	−3.13964	−0.163443
$370$	7.02616	0.365272
$371$	12.0044	0.623240
$372$	7.71218	0.399858
$373$	−7.41919	−0.384151	−0.192076	−	0.981380i	$-0.561522\pi$
$373$	−7.41919	−0.384151	−0.192076	+	0.981380i	$0.561522\pi$
$374$	3.80146	0.196569
$375$	−6.77527	−0.349873
$376$	6.11140	0.315172
$377$	−15.1326	−0.779370
$378$	2.21640	0.114000
$379$	−24.1855	−1.24233	−0.621164	−	0.783681i	$-0.713340\pi$
$379$	−24.1855	−1.24233	−0.621164	+	0.783681i	$0.713340\pi$
$380$	−4.65336	−0.238713
$381$	−4.51189	−0.231151
$382$	13.6763	0.699742
$383$	−8.72811	−0.445986	−0.222993	−	0.974820i	$-0.571583\pi$
$383$	−8.72811	−0.445986	−0.222993	+	0.974820i	$0.571583\pi$
$384$	1.00000	0.0510310
$385$	−1.58232	−0.0806425
$386$	−21.5860	−1.09870
$387$	−8.89965	−0.452395
$388$	−14.8503	−0.753910
$389$	28.8618	1.46335	0.731675	−	0.681654i	$-0.238739\pi$
$389$	28.8618	1.46335	0.731675	+	0.681654i	$0.238739\pi$
$390$	−2.06603	−0.104617
$391$	25.4524	1.28718
$392$	2.08755	0.105437
$393$	−2.28747	−0.115388
$394$	5.87387	0.295921
$395$	9.71032	0.488579
$396$	1.00000	0.0502519
$397$	5.41691	0.271867	0.135933	−	0.990718i	$-0.456597\pi$
$397$	5.41691	0.271867	0.135933	+	0.990718i	$0.456597\pi$
$398$	−0.0192795	−0.000966393 0
$399$	−14.4468	−0.723244
$400$	−4.49033	−0.224516
$401$	−1.28475	−0.0641573	−0.0320786	−	0.999485i	$-0.510213\pi$
$401$	−1.28475	−0.0641573	−0.0320786	+	0.999485i	$0.510213\pi$
$402$	12.1708	0.607026
$403$	−22.3187	−1.11177
$404$	1.62632	0.0809125
$405$	−0.713913	−0.0354746
$406$	11.5897	0.575188
$407$	9.84176	0.487838
$408$	−3.80146	−0.188200
$409$	11.5704	0.572122	0.286061	−	0.958211i	$-0.407654\pi$
$409$	11.5704	0.572122	0.286061	+	0.958211i	$0.407654\pi$
$410$	−2.24143	−0.110696
$411$	7.21660	0.355968
$412$	15.7623	0.776553
$413$	10.8041	0.531637
$414$	6.69541	0.329062
$415$	5.08654	0.249689
$416$	−2.89395	−0.141887
$417$	9.00891	0.441168
$418$	−6.51811	−0.318811
$419$	−39.0153	−1.90602	−0.953011	−	0.302934i	$-0.902034\pi$
$419$	−39.0153	−1.90602	−0.953011	+	0.302934i	$0.902034\pi$
$420$	1.58232	0.0772093
$421$	27.8409	1.35688	0.678442	−	0.734654i	$-0.262656\pi$
$421$	27.8409	1.35688	0.678442	+	0.734654i	$0.262656\pi$
$422$	−11.6694	−0.568055
$423$	−6.11140	−0.297147
$424$	−5.41618	−0.263033
$425$	17.0698	0.828008
$426$	4.11519	0.199382
$427$	2.21640	0.107259
$428$	4.50955	0.217977
$429$	−2.89395	−0.139721
$430$	−6.35357	−0.306397
$431$	−21.1699	−1.01972	−0.509859	−	0.860258i	$-0.670302\pi$
$431$	−21.1699	−1.01972	−0.509859	+	0.860258i	$0.670302\pi$
$432$	−1.00000	−0.0481125
$433$	7.93697	0.381426	0.190713	−	0.981646i	$-0.438920\pi$
$433$	7.93697	0.381426	0.190713	+	0.981646i	$0.438920\pi$
$434$	17.0933	0.820506
$435$	−3.73309	−0.178988
$436$	−18.0320	−0.863576
$437$	−43.6415	−2.08765
$438$	−2.29949	−0.109874
$439$	−3.02163	−0.144215	−0.0721073	−	0.997397i	$-0.522972\pi$
$439$	−3.02163	−0.144215	−0.0721073	+	0.997397i	$0.522972\pi$
$440$	0.713913	0.0340345
$441$	−2.08755	−0.0994072
$442$	11.0012	0.523275
$443$	−29.6543	−1.40892	−0.704459	−	0.709744i	$-0.748810\pi$
$443$	−29.6543	−1.40892	−0.704459	+	0.709744i	$0.748810\pi$
$444$	−9.84176	−0.467069
$445$	1.80661	0.0856417
$446$	15.7792	0.747166
$447$	24.2824	1.14852
$448$	2.21640	0.104715
$449$	34.2834	1.61793	0.808966	−	0.587855i	$-0.200027\pi$
$449$	34.2834	1.61793	0.808966	+	0.587855i	$0.200027\pi$
$450$	4.49033	0.211676
$451$	−3.13964	−0.147840
$452$	8.73608	0.410911
$453$	−2.59194	−0.121780
$454$	6.03088	0.283043
$455$	−4.57915	−0.214674
$456$	6.51811	0.305239
$457$	18.5375	0.867148	0.433574	−	0.901118i	$-0.357252\pi$
$457$	18.5375	0.867148	0.433574	+	0.901118i	$0.357252\pi$
$458$	−17.0456	−0.796489
$459$	3.80146	0.177437
$460$	4.77994	0.222866
$461$	−21.4403	−0.998576	−0.499288	−	0.866436i	$-0.666405\pi$
$461$	−21.4403	−0.998576	−0.499288	+	0.866436i	$0.666405\pi$
$462$	2.21640	0.103116
$463$	−21.6531	−1.00630	−0.503152	−	0.864198i	$-0.667826\pi$
$463$	−21.6531	−1.00630	−0.503152	+	0.864198i	$0.667826\pi$
$464$	−5.22906	−0.242753
$465$	−5.50583	−0.255327
$466$	7.96519	0.368980
$467$	−5.34296	−0.247243	−0.123621	−	0.992329i	$-0.539451\pi$
$467$	−5.34296	−0.247243	−0.123621	+	0.992329i	$0.539451\pi$
$468$	2.89395	0.133773
$469$	26.9755	1.24561
$470$	−4.36301	−0.201251
$471$	11.2129	0.516661
$472$	−4.87463	−0.224373
$473$	−8.89965	−0.409206
$474$	−13.6015	−0.624740
$475$	−29.2685	−1.34293
$476$	−8.42558	−0.386186
$477$	5.41618	0.247990
$478$	22.6053	1.03394
$479$	42.6730	1.94978	0.974889	−	0.222690i	$-0.0714836\pi$
$479$	42.6730	1.94978	0.974889	+	0.222690i	$0.0714836\pi$
$480$	−0.713913	−0.0325855
$481$	28.4815	1.29865
$482$	−11.2728	−0.513461
$483$	14.8397	0.675232
$484$	1.00000	0.0454545
$485$	10.6018	0.481404
$486$	1.00000	0.0453609
$487$	−31.1213	−1.41024	−0.705121	−	0.709087i	$-0.749107\pi$
$487$	−31.1213	−1.41024	−0.705121	+	0.709087i	$0.749107\pi$
$488$	−1.00000	−0.0452679
$489$	1.32328	0.0598406
$490$	−1.49033	−0.0673262
$491$	7.59198	0.342621	0.171311	−	0.985217i	$-0.445200\pi$
$491$	7.59198	0.342621	0.171311	+	0.985217i	$0.445200\pi$
$492$	3.13964	0.141546
$493$	19.8781	0.895264
$494$	−18.8631	−0.848690
$495$	−0.713913	−0.0320880
$496$	−7.71218	−0.346287
$497$	9.12092	0.409129
$498$	−7.12488	−0.319274
$499$	−6.47997	−0.290083	−0.145042	−	0.989426i	$-0.546332\pi$
$499$	−6.47997	−0.290083	−0.145042	+	0.989426i	$0.546332\pi$
$500$	6.77527	0.302999
$501$	−10.9233	−0.488018
$502$	29.0422	1.29622
$503$	20.6903	0.922534	0.461267	−	0.887261i	$-0.347395\pi$
$503$	20.6903	0.922534	0.461267	+	0.887261i	$0.347395\pi$
$504$	−2.21640	−0.0987265
$505$	−1.16105	−0.0516661
$506$	6.69541	0.297647
$507$	4.62506	0.205406
$508$	4.51189	0.200183
$509$	−16.4900	−0.730905	−0.365453	−	0.930830i	$-0.619086\pi$
$509$	−16.4900	−0.730905	−0.365453	+	0.930830i	$0.619086\pi$
$510$	2.71391	0.120174
$511$	−5.09660	−0.225460
$512$	−1.00000	−0.0441942
$513$	−6.51811	−0.287782
$514$	12.7886	0.564082
$515$	−11.2529	−0.495862
$516$	8.89965	0.391785
$517$	−6.11140	−0.268779
$518$	−21.8133	−0.958422
$519$	−15.6601	−0.687400
$520$	2.06603	0.0906012
$521$	−0.382346	−0.0167509	−0.00837545	−	0.999965i	$-0.502666\pi$
$521$	−0.382346	−0.0167509	−0.00837545	+	0.999965i	$0.502666\pi$
$522$	5.22906	0.228870
$523$	6.36122	0.278157	0.139078	−	0.990281i	$-0.455586\pi$
$523$	6.36122	0.278157	0.139078	+	0.990281i	$0.455586\pi$
$524$	2.28747	0.0999287
$525$	9.95239	0.434358
$526$	−15.0466	−0.656061
$527$	29.3176	1.27709
$528$	−1.00000	−0.0435194
$529$	21.8285	0.949067
$530$	3.86668	0.167958
$531$	4.87463	0.211541
$532$	14.4468	0.626347
$533$	−9.08596	−0.393557
$534$	−2.53058	−0.109509
$535$	−3.21943	−0.139188
$536$	−12.1708	−0.525700
$537$	−4.64098	−0.200273
$538$	−11.4706	−0.494535
$539$	−2.08755	−0.0899172
$540$	0.713913	0.0307219
$541$	−4.37160	−0.187950	−0.0939748	−	0.995575i	$-0.529957\pi$
$541$	−4.37160	−0.187950	−0.0939748	+	0.995575i	$0.529957\pi$
$542$	−15.9187	−0.683767
$543$	8.69230	0.373022
$544$	3.80146	0.162986
$545$	12.8733	0.551430
$546$	6.41416	0.274501
$547$	−28.9470	−1.23768	−0.618842	−	0.785516i	$-0.712398\pi$
$547$	−28.9470	−1.23768	−0.618842	+	0.785516i	$0.712398\pi$
$548$	−7.21660	−0.308278
$549$	1.00000	0.0426790
$550$	4.49033	0.191468
$551$	−34.0836	−1.45201
$552$	−6.69541	−0.284976
$553$	−30.1465	−1.28196
$554$	31.5070	1.33860
$555$	7.02616	0.298244
$556$	−9.00891	−0.382063
$557$	37.2433	1.57805	0.789025	−	0.614361i	$-0.210586\pi$
$557$	37.2433	1.57805	0.789025	+	0.614361i	$0.210586\pi$
$558$	7.71218	0.326483
$559$	−25.7551	−1.08933
$560$	−1.58232	−0.0668652
$561$	3.80146	0.160498
$562$	−9.32257	−0.393249
$563$	17.2006	0.724918	0.362459	−	0.932000i	$-0.381937\pi$
$563$	17.2006	0.724918	0.362459	+	0.932000i	$0.381937\pi$
$564$	6.11140	0.257337
$565$	−6.23680	−0.262384
$566$	13.6198	0.572482
$567$	2.21640	0.0930802
$568$	−4.11519	−0.172669
$569$	−5.70366	−0.239110	−0.119555	−	0.992828i	$-0.538147\pi$
$569$	−5.70366	−0.239110	−0.119555	+	0.992828i	$0.538147\pi$
$570$	−4.65336	−0.194908
$571$	7.84061	0.328119	0.164060	−	0.986450i	$-0.447541\pi$
$571$	7.84061	0.328119	0.164060	+	0.986450i	$0.447541\pi$
$572$	2.89395	0.121002
$573$	13.6763	0.571337
$574$	6.95871	0.290451
$575$	30.0646	1.25378
$576$	1.00000	0.0416667
$577$	27.6766	1.15219	0.576097	−	0.817381i	$-0.304575\pi$
$577$	27.6766	1.15219	0.576097	+	0.817381i	$0.304575\pi$
$578$	2.54888	0.106019
$579$	−21.5860	−0.897082
$580$	3.73309	0.155008
$581$	−15.7916	−0.655147
$582$	−14.8503	−0.615565
$583$	5.41618	0.224315
$584$	2.29949	0.0951535
$585$	−2.06603	−0.0854197
$586$	−16.5857	−0.685147
$587$	−30.9500	−1.27744	−0.638721	−	0.769438i	$-0.720536\pi$
$587$	−30.9500	−1.27744	−0.638721	+	0.769438i	$0.720536\pi$
$588$	2.08755	0.0860891
$589$	−50.2689	−2.07129
$590$	3.48006	0.143272
$591$	5.87387	0.241619
$592$	9.84176	0.404494
$593$	−25.6271	−1.05238	−0.526189	−	0.850368i	$-0.676380\pi$
$593$	−25.6271	−1.05238	−0.526189	+	0.850368i	$0.676380\pi$
$594$	1.00000	0.0410305
$595$	6.01513	0.246596
$596$	−24.2824	−0.994647
$597$	−0.0192795	−0.000789057 0
$598$	19.3762	0.792351
$599$	32.5122	1.32841	0.664207	−	0.747549i	$-0.268769\pi$
$599$	32.5122	1.32841	0.664207	+	0.747549i	$0.268769\pi$
$600$	−4.49033	−0.183317
$601$	−7.06661	−0.288253	−0.144126	−	0.989559i	$-0.546037\pi$
$601$	−7.06661	−0.288253	−0.144126	+	0.989559i	$0.546037\pi$
$602$	19.7252	0.803940
$603$	12.1708	0.495635
$604$	2.59194	0.105464
$605$	−0.713913	−0.0290247
$606$	1.62632	0.0660648
$607$	−23.9113	−0.970531	−0.485266	−	0.874367i	$-0.661277\pi$
$607$	−23.9113	−0.970531	−0.485266	+	0.874367i	$0.661277\pi$
$608$	−6.51811	−0.264344
$609$	11.5897	0.469639
$610$	0.713913	0.0289055
$611$	−17.6861	−0.715503
$612$	−3.80146	−0.153665
$613$	14.1877	0.573036	0.286518	−	0.958075i	$-0.407502\pi$
$613$	14.1877	0.573036	0.286518	+	0.958075i	$0.407502\pi$
$614$	29.6050	1.19476
$615$	−2.24143	−0.0903832
$616$	−2.21640	−0.0893015
$617$	23.4289	0.943213	0.471607	−	0.881809i	$-0.343674\pi$
$617$	23.4289	0.943213	0.471607	+	0.881809i	$0.343674\pi$
$618$	15.7623	0.634053
$619$	−16.2840	−0.654507	−0.327254	−	0.944937i	$-0.606123\pi$
$619$	−16.2840	−0.654507	−0.327254	+	0.944937i	$0.606123\pi$
$620$	5.50583	0.221119
$621$	6.69541	0.268678
$622$	31.1110	1.24744
$623$	−5.60879	−0.224711
$624$	−2.89395	−0.115851
$625$	17.6147	0.704588
$626$	1.58625	0.0633992
$627$	−6.51811	−0.260308
$628$	−11.2129	−0.447442
$629$	−37.4131	−1.49176
$630$	1.58232	0.0630411
$631$	−11.0402	−0.439505	−0.219752	−	0.975556i	$-0.570525\pi$
$631$	−11.0402	−0.439505	−0.219752	+	0.975556i	$0.570525\pi$
$632$	13.6015	0.541041
$633$	−11.6694	−0.463815
$634$	−2.30994	−0.0917395
$635$	−3.22110	−0.127825
$636$	−5.41618	−0.214765
$637$	−6.04126	−0.239364
$638$	5.22906	0.207021
$639$	4.11519	0.162794
$640$	0.713913	0.0282199
$641$	−31.2732	−1.23522	−0.617609	−	0.786485i	$-0.711899\pi$
$641$	−31.2732	−1.23522	−0.617609	+	0.786485i	$0.711899\pi$
$642$	4.50955	0.177978
$643$	15.5759	0.614252	0.307126	−	0.951669i	$-0.400633\pi$
$643$	15.5759	0.614252	0.307126	+	0.951669i	$0.400633\pi$
$644$	−14.8397	−0.584768
$645$	−6.35357	−0.250172
$646$	24.7784	0.974892
$647$	0.117094	0.00460343	0.00230172	−	0.999997i	$-0.499267\pi$
$647$	0.117094	0.00460343	0.00230172	+	0.999997i	$0.499267\pi$
$648$	−1.00000	−0.0392837
$649$	4.87463	0.191346
$650$	12.9948	0.509697
$651$	17.0933	0.669940
$652$	−1.32328	−0.0518235
$653$	−4.21209	−0.164832	−0.0824160	−	0.996598i	$-0.526264\pi$
$653$	−4.21209	−0.164832	−0.0824160	+	0.996598i	$0.526264\pi$
$654$	−18.0320	−0.705107
$655$	−1.63306	−0.0638088
$656$	−3.13964	−0.122582
$657$	−2.29949	−0.0897116
$658$	13.5453	0.528053
$659$	−18.7171	−0.729115	−0.364557	−	0.931181i	$-0.618780\pi$
$659$	−18.7171	−0.729115	−0.364557	+	0.931181i	$0.618780\pi$
$660$	0.713913	0.0277890
$661$	−10.6520	−0.414314	−0.207157	−	0.978308i	$-0.566421\pi$
$661$	−10.6520	−0.414314	−0.207157	+	0.978308i	$0.566421\pi$
$662$	20.4018	0.792940
$663$	11.0012	0.427253
$664$	7.12488	0.276499
$665$	−10.3137	−0.399950
$666$	−9.84176	−0.381360
$667$	35.0107	1.35562
$668$	10.9233	0.422636
$669$	15.7792	0.610058
$670$	8.68892	0.335682
$671$	1.00000	0.0386046
$672$	2.21640	0.0854997
$673$	−31.9898	−1.23311	−0.616557	−	0.787310i	$-0.711473\pi$
$673$	−31.9898	−1.23311	−0.616557	+	0.787310i	$0.711473\pi$
$674$	−8.00437	−0.308317
$675$	4.49033	0.172833
$676$	−4.62506	−0.177887
$677$	15.0685	0.579128	0.289564	−	0.957159i	$-0.406490\pi$
$677$	15.0685	0.579128	0.289564	+	0.957159i	$0.406490\pi$
$678$	8.73608	0.335507
$679$	−32.9143	−1.26313
$680$	−2.71391	−0.104074
$681$	6.03088	0.231104
$682$	7.71218	0.295315
$683$	−3.87060	−0.148104	−0.0740522	−	0.997254i	$-0.523593\pi$
$683$	−3.87060	−0.148104	−0.0740522	+	0.997254i	$0.523593\pi$
$684$	6.51811	0.249226
$685$	5.15202	0.196849
$686$	20.1417	0.769013
$687$	−17.0456	−0.650331
$688$	−8.89965	−0.339296
$689$	15.6741	0.597137
$690$	4.77994	0.181969
$691$	8.07032	0.307010	0.153505	−	0.988148i	$-0.450944\pi$
$691$	8.07032	0.307010	0.153505	+	0.988148i	$0.450944\pi$
$692$	15.6601	0.595306
$693$	2.21640	0.0841943
$694$	−18.8063	−0.713877
$695$	6.43158	0.243964
$696$	−5.22906	−0.198207
$697$	11.9352	0.452079
$698$	−7.81741	−0.295893
$699$	7.96519	0.301271
$700$	−9.95239	−0.376165
$701$	23.7261	0.896123	0.448062	−	0.894003i	$-0.352115\pi$
$701$	23.7261	0.896123	0.448062	+	0.894003i	$0.352115\pi$
$702$	2.89395	0.109225
$703$	64.1497	2.41945
$704$	1.00000	0.0376889
$705$	−4.36301	−0.164320
$706$	21.5546	0.811218
$707$	3.60459	0.135564
$708$	−4.87463	−0.183200
$709$	−19.6207	−0.736870	−0.368435	−	0.929654i	$-0.620106\pi$
$709$	−19.6207	−0.736870	−0.368435	+	0.929654i	$0.620106\pi$
$710$	2.93789	0.110257
$711$	−13.6015	−0.510098
$712$	2.53058	0.0948375
$713$	51.6362	1.93379
$714$	−8.42558	−0.315319
$715$	−2.06603	−0.0772650
$716$	4.64098	0.173441
$717$	22.6053	0.844212
$718$	30.6478	1.14377
$719$	15.2560	0.568954	0.284477	−	0.958683i	$-0.408180\pi$
$719$	15.2560	0.568954	0.284477	+	0.958683i	$0.408180\pi$
$720$	−0.713913	−0.0266060
$721$	34.9356	1.30107
$722$	−23.4858	−0.874052
$723$	−11.2728	−0.419239
$724$	−8.69230	−0.323047
$725$	23.4802	0.872033
$726$	1.00000	0.0371135
$727$	31.5993	1.17195	0.585977	−	0.810328i	$-0.300711\pi$
$727$	31.5993	1.17195	0.585977	+	0.810328i	$0.300711\pi$
$728$	−6.41416	−0.237725
$729$	1.00000	0.0370370
$730$	−1.64163	−0.0607596
$731$	33.8317	1.25131
$732$	−1.00000	−0.0369611
$733$	−29.6837	−1.09639	−0.548196	−	0.836350i	$-0.684685\pi$
$733$	−29.6837	−1.09639	−0.548196	+	0.836350i	$0.684685\pi$
$734$	−12.3449	−0.455657
$735$	−1.49033	−0.0549716
$736$	6.69541	0.246796
$737$	12.1708	0.448319
$738$	3.13964	0.115572
$739$	−25.6925	−0.945113	−0.472557	−	0.881300i	$-0.656669\pi$
$739$	−25.6925	−0.945113	−0.472557	+	0.881300i	$0.656669\pi$
$740$	−7.02616	−0.258287
$741$	−18.8631	−0.692953
$742$	−12.0044	−0.440697
$743$	8.71977	0.319897	0.159949	−	0.987125i	$-0.448867\pi$
$743$	8.71977	0.319897	0.159949	+	0.987125i	$0.448867\pi$
$744$	−7.71218	−0.282742
$745$	17.3355	0.635125
$746$	7.41919	0.271636
$747$	−7.12488	−0.260686
$748$	−3.80146	−0.138995
$749$	9.99499	0.365209
$750$	6.77527	0.247398
$751$	−48.9387	−1.78580	−0.892898	−	0.450258i	$-0.851332\pi$
$751$	−48.9387	−1.78580	−0.892898	+	0.450258i	$0.851332\pi$
$752$	−6.11140	−0.222860
$753$	29.0422	1.05836
$754$	15.1326	0.551098
$755$	−1.85042	−0.0673435
$756$	−2.21640	−0.0806099
$757$	4.63477	0.168454	0.0842268	−	0.996447i	$-0.473158\pi$
$757$	4.63477	0.168454	0.0842268	+	0.996447i	$0.473158\pi$
$758$	24.1855	0.878458
$759$	6.69541	0.243028
$760$	4.65336	0.168795
$761$	27.0101	0.979116	0.489558	−	0.871971i	$-0.337158\pi$
$761$	27.0101	0.979116	0.489558	+	0.871971i	$0.337158\pi$
$762$	4.51189	0.163449
$763$	−39.9662	−1.44687
$764$	−13.6763	−0.494792
$765$	2.71391	0.0981217
$766$	8.72811	0.315359
$767$	14.1069	0.509371
$768$	−1.00000	−0.0360844
$769$	−2.18856	−0.0789214	−0.0394607	−	0.999221i	$-0.512564\pi$
$769$	−2.18856	−0.0789214	−0.0394607	+	0.999221i	$0.512564\pi$
$770$	1.58232	0.0570228
$771$	12.7886	0.460571
$772$	21.5860	0.776896
$773$	−27.1259	−0.975651	−0.487825	−	0.872941i	$-0.662210\pi$
$773$	−27.1259	−0.975651	−0.487825	+	0.872941i	$0.662210\pi$
$774$	8.89965	0.319891
$775$	34.6302	1.24396
$776$	14.8503	0.533095
$777$	−21.8133	−0.782549
$778$	−28.8618	−1.03474
$779$	−20.4645	−0.733218
$780$	2.06603	0.0739756
$781$	4.11519	0.147253
$782$	−25.4524	−0.910175
$783$	5.22906	0.186871
$784$	−2.08755	−0.0745554
$785$	8.00500	0.285711
$786$	2.28747	0.0815914
$787$	10.0043	0.356615	0.178307	−	0.983975i	$-0.442938\pi$
$787$	10.0043	0.356615	0.178307	+	0.983975i	$0.442938\pi$
$788$	−5.87387	−0.209248
$789$	−15.0466	−0.535672
$790$	−9.71032	−0.345478
$791$	19.3627	0.688458
$792$	−1.00000	−0.0355335
$793$	2.89395	0.102767
$794$	−5.41691	−0.192239
$795$	3.86668	0.137137
$796$	0.0192795	0.000683343 0
$797$	40.6209	1.43887	0.719433	−	0.694562i	$-0.244402\pi$
$797$	40.6209	1.43887	0.719433	+	0.694562i	$0.244402\pi$
$798$	14.4468	0.511410
$799$	23.2323	0.821899
$800$	4.49033	0.158757
$801$	−2.53058	−0.0894137
$802$	1.28475	0.0453660
$803$	−2.29949	−0.0811472
$804$	−12.1708	−0.429232
$805$	10.5943	0.373399
$806$	22.3187	0.786141
$807$	−11.4706	−0.403786
$808$	−1.62632	−0.0572138
$809$	27.2668	0.958648	0.479324	−	0.877638i	$-0.340882\pi$
$809$	27.2668	0.958648	0.479324	+	0.877638i	$0.340882\pi$
$810$	0.713913	0.0250843
$811$	−9.15496	−0.321474	−0.160737	−	0.986997i	$-0.551387\pi$
$811$	−9.15496	−0.321474	−0.160737	+	0.986997i	$0.551387\pi$
$812$	−11.5897	−0.406719
$813$	−15.9187	−0.558294
$814$	−9.84176	−0.344953
$815$	0.944703	0.0330915
$816$	3.80146	0.133078
$817$	−58.0090	−2.02948
$818$	−11.5704	−0.404551
$819$	6.41416	0.224129
$820$	2.24143	0.0782741
$821$	−12.7000	−0.443232	−0.221616	−	0.975134i	$-0.571133\pi$
$821$	−12.7000	−0.443232	−0.221616	+	0.975134i	$0.571133\pi$
$822$	−7.21660	−0.251708
$823$	29.4235	1.02564	0.512820	−	0.858496i	$-0.328601\pi$
$823$	29.4235	1.02564	0.512820	+	0.858496i	$0.328601\pi$
$824$	−15.7623	−0.549106
$825$	4.49033	0.156333
$826$	−10.8041	−0.375924
$827$	31.9129	1.10972	0.554859	−	0.831944i	$-0.312772\pi$
$827$	31.9129	1.10972	0.554859	+	0.831944i	$0.312772\pi$
$828$	−6.69541	−0.232682
$829$	−10.4195	−0.361884	−0.180942	−	0.983494i	$-0.557915\pi$
$829$	−10.4195	−0.361884	−0.180942	+	0.983494i	$0.557915\pi$
$830$	−5.08654	−0.176556
$831$	31.5070	1.09296
$832$	2.89395	0.100330
$833$	7.93575	0.274957
$834$	−9.00891	−0.311953
$835$	−7.79830	−0.269871
$836$	6.51811	0.225434
$837$	7.71218	0.266572
$838$	39.0153	1.34776
$839$	−46.2265	−1.59592	−0.797958	−	0.602713i	$-0.794086\pi$
$839$	−46.2265	−1.59592	−0.797958	+	0.602713i	$0.794086\pi$
$840$	−1.58232	−0.0545952
$841$	−1.65691	−0.0571347
$842$	−27.8409	−0.959462
$843$	−9.32257	−0.321086
$844$	11.6694	0.401676
$845$	3.30189	0.113589
$846$	6.11140	0.210114
$847$	2.21640	0.0761566
$848$	5.41618	0.185992
$849$	13.6198	0.467430
$850$	−17.0698	−0.585490
$851$	−65.8946	−2.25884
$852$	−4.11519	−0.140984
$853$	42.6329	1.45972	0.729861	−	0.683596i	$-0.239585\pi$
$853$	42.6329	1.45972	0.729861	+	0.683596i	$0.239585\pi$
$854$	−2.21640	−0.0758438
$855$	−4.65336	−0.159142
$856$	−4.50955	−0.154133
$857$	−6.20846	−0.212077	−0.106039	−	0.994362i	$-0.533817\pi$
$857$	−6.20846	−0.212077	−0.106039	+	0.994362i	$0.533817\pi$
$858$	2.89395	0.0987978
$859$	50.4441	1.72113	0.860565	−	0.509341i	$-0.170111\pi$
$859$	50.4441	1.72113	0.860565	+	0.509341i	$0.170111\pi$
$860$	6.35357	0.216655
$861$	6.95871	0.237152
$862$	21.1699	0.721049
$863$	−35.5015	−1.20849	−0.604243	−	0.796800i	$-0.706524\pi$
$863$	−35.5015	−1.20849	−0.604243	+	0.796800i	$0.706524\pi$
$864$	1.00000	0.0340207
$865$	−11.1799	−0.380128
$866$	−7.93697	−0.269709
$867$	2.54888	0.0865644
$868$	−17.0933	−0.580185
$869$	−13.6015	−0.461401
$870$	3.73309	0.126564
$871$	35.2218	1.19344
$872$	18.0320	0.610640
$873$	−14.8503	−0.502607
$874$	43.6415	1.47619
$875$	15.0167	0.507658
$876$	2.29949	0.0776925
$877$	1.88450	0.0636349	0.0318174	−	0.999494i	$-0.489870\pi$
$877$	1.88450	0.0636349	0.0318174	+	0.999494i	$0.489870\pi$
$878$	3.02163	0.101975
$879$	−16.5857	−0.559420
$880$	−0.713913	−0.0240660
$881$	8.19166	0.275984	0.137992	−	0.990433i	$-0.455935\pi$
$881$	8.19166	0.275984	0.137992	+	0.990433i	$0.455935\pi$
$882$	2.08755	0.0702915
$883$	48.7025	1.63897	0.819484	−	0.573102i	$-0.194260\pi$
$883$	48.7025	1.63897	0.819484	+	0.573102i	$0.194260\pi$
$884$	−11.0012	−0.370012
$885$	3.48006	0.116981
$886$	29.6543	0.996256
$887$	−1.24923	−0.0419450	−0.0209725	−	0.999780i	$-0.506676\pi$
$887$	−1.24923	−0.0419450	−0.0209725	+	0.999780i	$0.506676\pi$
$888$	9.84176	0.330268
$889$	10.0002	0.335395
$890$	−1.80661	−0.0605578
$891$	1.00000	0.0335013
$892$	−15.7792	−0.528326
$893$	−39.8348	−1.33302
$894$	−24.2824	−0.812126
$895$	−3.31325	−0.110750
$896$	−2.21640	−0.0740449
$897$	19.3762	0.646952
$898$	−34.2834	−1.14405
$899$	40.3275	1.34500
$900$	−4.49033	−0.149678
$901$	−20.5894	−0.685932
$902$	3.13964	0.104539
$903$	19.7252	0.656415
$904$	−8.73608	−0.290558
$905$	6.20554	0.206279
$906$	2.59194	0.0861113
$907$	32.6530	1.08422	0.542112	−	0.840306i	$-0.317625\pi$
$907$	32.6530	1.08422	0.542112	+	0.840306i	$0.317625\pi$
$908$	−6.03088	−0.200142
$909$	1.62632	0.0539417
$910$	4.57915	0.151797
$911$	−20.9096	−0.692768	−0.346384	−	0.938093i	$-0.612590\pi$
$911$	−20.9096	−0.692768	−0.346384	+	0.938093i	$0.612590\pi$
$912$	−6.51811	−0.215836
$913$	−7.12488	−0.235799
$914$	−18.5375	−0.613166
$915$	0.713913	0.0236012
$916$	17.0456	0.563203
$917$	5.06996	0.167425
$918$	−3.80146	−0.125467
$919$	36.1275	1.19174	0.595868	−	0.803082i	$-0.296808\pi$
$919$	36.1275	1.19174	0.595868	+	0.803082i	$0.296808\pi$
$920$	−4.77994	−0.157590
$921$	29.6050	0.975516
$922$	21.4403	0.706100
$923$	11.9091	0.391994
$924$	−2.21640	−0.0729144
$925$	−44.1927	−1.45305
$926$	21.6531	0.711565
$927$	15.7623	0.517702
$928$	5.22906	0.171652
$929$	−16.1266	−0.529098	−0.264549	−	0.964372i	$-0.585223\pi$
$929$	−16.1266	−0.529098	−0.264549	+	0.964372i	$0.585223\pi$
$930$	5.50583	0.180543
$931$	−13.6069	−0.445948
$932$	−7.96519	−0.260909
$933$	31.1110	1.01853
$934$	5.34296	0.174827
$935$	2.71391	0.0887544
$936$	−2.89395	−0.0945917
$937$	−0.666220	−0.0217644	−0.0108822	−	0.999941i	$-0.503464\pi$
$937$	−0.666220	−0.0217644	−0.0108822	+	0.999941i	$0.503464\pi$
$938$	−26.9755	−0.880781
$939$	1.58625	0.0517652
$940$	4.36301	0.142306
$941$	0.130212	0.00424479	0.00212240	−	0.999998i	$-0.499324\pi$
$941$	0.130212	0.00424479	0.00212240	+	0.999998i	$0.499324\pi$
$942$	−11.2129	−0.365335
$943$	21.0212	0.684544
$944$	4.87463	0.158656
$945$	1.58232	0.0514729
$946$	8.89965	0.289353
$947$	28.1476	0.914675	0.457337	−	0.889293i	$-0.348803\pi$
$947$	28.1476	0.914675	0.457337	+	0.889293i	$0.348803\pi$
$948$	13.6015	0.441758
$949$	−6.65460	−0.216017
$950$	29.2685	0.949595
$951$	−2.30994	−0.0749050
$952$	8.42558	0.273075
$953$	22.0488	0.714229	0.357115	−	0.934061i	$-0.383761\pi$
$953$	22.0488	0.714229	0.357115	+	0.934061i	$0.383761\pi$
$954$	−5.41618	−0.175355
$955$	9.76371	0.315946
$956$	−22.6053	−0.731109
$957$	5.22906	0.169032
$958$	−42.6730	−1.37870
$959$	−15.9949	−0.516502
$960$	0.713913	0.0230414
$961$	28.4778	0.918638
$962$	−28.4815	−0.918282
$963$	4.50955	0.145318
$964$	11.2728	0.363071
$965$	−15.4105	−0.496081
$966$	−14.8397	−0.477461
$967$	57.6350	1.85342	0.926709	−	0.375780i	$-0.122625\pi$
$967$	57.6350	1.85342	0.926709	+	0.375780i	$0.122625\pi$
$968$	−1.00000	−0.0321412
$969$	24.7784	0.795996
$970$	−10.6018	−0.340404
$971$	14.7249	0.472543	0.236272	−	0.971687i	$-0.424074\pi$
$971$	14.7249	0.472543	0.236272	+	0.971687i	$0.424074\pi$
$972$	−1.00000	−0.0320750
$973$	−19.9674	−0.640125
$974$	31.1213	0.997191
$975$	12.9948	0.416166
$976$	1.00000	0.0320092
$977$	22.8628	0.731445	0.365722	−	0.930724i	$-0.380822\pi$
$977$	22.8628	0.731445	0.365722	+	0.930724i	$0.380822\pi$
$978$	−1.32328	−0.0423137
$979$	−2.53058	−0.0808777
$980$	1.49033	0.0476068
$981$	−18.0320	−0.575717
$982$	−7.59198	−0.242270
$983$	−27.5071	−0.877339	−0.438670	−	0.898648i	$-0.644550\pi$
$983$	−27.5071	−0.877339	−0.438670	+	0.898648i	$0.644550\pi$
$984$	−3.13964	−0.100088
$985$	4.19343	0.133614
$986$	−19.8781	−0.633047
$987$	13.5453	0.431153
$988$	18.8631	0.600115
$989$	59.5868	1.89475
$990$	0.713913	0.0226896
$991$	−29.5785	−0.939593	−0.469797	−	0.882775i	$-0.655673\pi$
$991$	−29.5785	−0.939593	−0.469797	+	0.882775i	$0.655673\pi$
$992$	7.71218	0.244862
$993$	20.4018	0.647433
$994$	−9.12092	−0.289298
$995$	−0.0137639	−0.000436344 0
$996$	7.12488	0.225761
$997$	11.7007	0.370566	0.185283	−	0.982685i	$-0.440680\pi$
$997$	11.7007	0.370566	0.185283	+	0.982685i	$0.440680\pi$
$998$	6.47997	0.205120
$999$	−9.84176	−0.311379

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.w.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.w.1.3	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.713913 q^{5} +1.00000 q^{6} +2.21640 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.713913 q^{5} +1.00000 q^{6} +2.21640 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.713913 q^{10} +1.00000 q^{11} -1.00000 q^{12} +2.89395 q^{13} -2.21640 q^{14} +0.713913 q^{15} +1.00000 q^{16} -3.80146 q^{17} -1.00000 q^{18} +6.51811 q^{19} -0.713913 q^{20} -2.21640 q^{21} -1.00000 q^{22} -6.69541 q^{23} +1.00000 q^{24} -4.49033 q^{25} -2.89395 q^{26} -1.00000 q^{27} +2.21640 q^{28} -5.22906 q^{29} -0.713913 q^{30} -7.71218 q^{31} -1.00000 q^{32} -1.00000 q^{33} +3.80146 q^{34} -1.58232 q^{35} +1.00000 q^{36} +9.84176 q^{37} -6.51811 q^{38} -2.89395 q^{39} +0.713913 q^{40} -3.13964 q^{41} +2.21640 q^{42} -8.89965 q^{43} +1.00000 q^{44} -0.713913 q^{45} +6.69541 q^{46} -6.11140 q^{47} -1.00000 q^{48} -2.08755 q^{49} +4.49033 q^{50} +3.80146 q^{51} +2.89395 q^{52} +5.41618 q^{53} +1.00000 q^{54} -0.713913 q^{55} -2.21640 q^{56} -6.51811 q^{57} +5.22906 q^{58} +4.87463 q^{59} +0.713913 q^{60} +1.00000 q^{61} +7.71218 q^{62} +2.21640 q^{63} +1.00000 q^{64} -2.06603 q^{65} +1.00000 q^{66} +12.1708 q^{67} -3.80146 q^{68} +6.69541 q^{69} +1.58232 q^{70} +4.11519 q^{71} -1.00000 q^{72} -2.29949 q^{73} -9.84176 q^{74} +4.49033 q^{75} +6.51811 q^{76} +2.21640 q^{77} +2.89395 q^{78} -13.6015 q^{79} -0.713913 q^{80} +1.00000 q^{81} +3.13964 q^{82} -7.12488 q^{83} -2.21640 q^{84} +2.71391 q^{85} +8.89965 q^{86} +5.22906 q^{87} -1.00000 q^{88} -2.53058 q^{89} +0.713913 q^{90} +6.41416 q^{91} -6.69541 q^{92} +7.71218 q^{93} +6.11140 q^{94} -4.65336 q^{95} +1.00000 q^{96} -14.8503 q^{97} +2.08755 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} - q^{5} + 6 q^{6} + 5 q^{7} - 6 q^{8} + 6 q^{9} + q^{10} + 6 q^{11} - 6 q^{12} + 2 q^{13} - 5 q^{14} + q^{15} + 6 q^{16} - 4 q^{17} - 6 q^{18} - 5 q^{19} - q^{20} - 5 q^{21} - 6 q^{22} - 6 q^{23} + 6 q^{24} - q^{25} - 2 q^{26} - 6 q^{27} + 5 q^{28} - 10 q^{29} - q^{30} - 15 q^{31} - 6 q^{32} - 6 q^{33} + 4 q^{34} - 21 q^{35} + 6 q^{36} - 3 q^{37} + 5 q^{38} - 2 q^{39} + q^{40} - 9 q^{41} + 5 q^{42} + 10 q^{43} + 6 q^{44} - q^{45} + 6 q^{46} - 14 q^{47} - 6 q^{48} + 3 q^{49} + q^{50} + 4 q^{51} + 2 q^{52} - 11 q^{53} + 6 q^{54} - q^{55} - 5 q^{56} + 5 q^{57} + 10 q^{58} - 20 q^{59} + q^{60} + 6 q^{61} + 15 q^{62} + 5 q^{63} + 6 q^{64} - 2 q^{65} + 6 q^{66} + 14 q^{67} - 4 q^{68} + 6 q^{69} + 21 q^{70} - 21 q^{71} - 6 q^{72} + 16 q^{73} + 3 q^{74} + q^{75} - 5 q^{76} + 5 q^{77} + 2 q^{78} - 6 q^{79} - q^{80} + 6 q^{81} + 9 q^{82} - 10 q^{83} - 5 q^{84} + 13 q^{85} - 10 q^{86} + 10 q^{87} - 6 q^{88} - 11 q^{89} + q^{90} - 21 q^{91} - 6 q^{92} + 15 q^{93} + 14 q^{94} + 9 q^{95} + 6 q^{96} + 2 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 - q^5 + 6 * q^6 + 5 * q^7 - 6 * q^8 + 6 * q^9 + q^10 + 6 * q^11 - 6 * q^12 + 2 * q^13 - 5 * q^14 + q^15 + 6 * q^16 - 4 * q^17 - 6 * q^18 - 5 * q^19 - q^20 - 5 * q^21 - 6 * q^22 - 6 * q^23 + 6 * q^24 - q^25 - 2 * q^26 - 6 * q^27 + 5 * q^28 - 10 * q^29 - q^30 - 15 * q^31 - 6 * q^32 - 6 * q^33 + 4 * q^34 - 21 * q^35 + 6 * q^36 - 3 * q^37 + 5 * q^38 - 2 * q^39 + q^40 - 9 * q^41 + 5 * q^42 + 10 * q^43 + 6 * q^44 - q^45 + 6 * q^46 - 14 * q^47 - 6 * q^48 + 3 * q^49 + q^50 + 4 * q^51 + 2 * q^52 - 11 * q^53 + 6 * q^54 - q^55 - 5 * q^56 + 5 * q^57 + 10 * q^58 - 20 * q^59 + q^60 + 6 * q^61 + 15 * q^62 + 5 * q^63 + 6 * q^64 - 2 * q^65 + 6 * q^66 + 14 * q^67 - 4 * q^68 + 6 * q^69 + 21 * q^70 - 21 * q^71 - 6 * q^72 + 16 * q^73 + 3 * q^74 + q^75 - 5 * q^76 + 5 * q^77 + 2 * q^78 - 6 * q^79 - q^80 + 6 * q^81 + 9 * q^82 - 10 * q^83 - 5 * q^84 + 13 * q^85 - 10 * q^86 + 10 * q^87 - 6 * q^88 - 11 * q^89 + q^90 - 21 * q^91 - 6 * q^92 + 15 * q^93 + 14 * q^94 + 9 * q^95 + 6 * q^96 + 2 * q^97 - 3 * q^98 + 6 * q^99

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