LMFDB - Embedded newform 4026.2.a.p.1.2

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:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 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			1.2
Root			$-1.24698$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.55496 q^{5} +1.00000 q^{6} -0.643104 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.55496 q^{5} +1.00000 q^{6} -0.643104 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.55496 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.30798 q^{13} -0.643104 q^{14} -1.55496 q^{15} +1.00000 q^{16} -2.60388 q^{17} +1.00000 q^{18} -7.78986 q^{19} -1.55496 q^{20} -0.643104 q^{21} +1.00000 q^{22} -6.18598 q^{23} +1.00000 q^{24} -2.58211 q^{25} -1.30798 q^{26} +1.00000 q^{27} -0.643104 q^{28} +0.740939 q^{29} -1.55496 q^{30} +6.45473 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.60388 q^{34} +1.00000 q^{35} +1.00000 q^{36} -0.307979 q^{37} -7.78986 q^{38} -1.30798 q^{39} -1.55496 q^{40} +5.31767 q^{41} -0.643104 q^{42} -3.26875 q^{43} +1.00000 q^{44} -1.55496 q^{45} -6.18598 q^{46} -1.06100 q^{47} +1.00000 q^{48} -6.58642 q^{49} -2.58211 q^{50} -2.60388 q^{51} -1.30798 q^{52} -12.2131 q^{53} +1.00000 q^{54} -1.55496 q^{55} -0.643104 q^{56} -7.78986 q^{57} +0.740939 q^{58} -5.64310 q^{59} -1.55496 q^{60} +1.00000 q^{61} +6.45473 q^{62} -0.643104 q^{63} +1.00000 q^{64} +2.03385 q^{65} +1.00000 q^{66} +4.63102 q^{67} -2.60388 q^{68} -6.18598 q^{69} +1.00000 q^{70} +2.45473 q^{71} +1.00000 q^{72} -1.25906 q^{73} -0.307979 q^{74} -2.58211 q^{75} -7.78986 q^{76} -0.643104 q^{77} -1.30798 q^{78} -10.5157 q^{79} -1.55496 q^{80} +1.00000 q^{81} +5.31767 q^{82} -4.29052 q^{83} -0.643104 q^{84} +4.04892 q^{85} -3.26875 q^{86} +0.740939 q^{87} +1.00000 q^{88} -9.69633 q^{89} -1.55496 q^{90} +0.841166 q^{91} -6.18598 q^{92} +6.45473 q^{93} -1.06100 q^{94} +12.1129 q^{95} +1.00000 q^{96} +1.46681 q^{97} -6.58642 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 5 q^{10} + 3 q^{11} + 3 q^{12} - 9 q^{13} - 6 q^{14} - 5 q^{15} + 3 q^{16} + q^{17} + 3 q^{18} - 5 q^{20} - 6 q^{21} + 3 q^{22} - 4 q^{23} + 3 q^{24} - 2 q^{25} - 9 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} - 5 q^{30} - 3 q^{31} + 3 q^{32} + 3 q^{33} + q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} - 9 q^{39} - 5 q^{40} - q^{41} - 6 q^{42} - 2 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} - 13 q^{47} + 3 q^{48} + 5 q^{49} - 2 q^{50} + q^{51} - 9 q^{52} - 16 q^{53} + 3 q^{54} - 5 q^{55} - 6 q^{56} - 12 q^{58} - 21 q^{59} - 5 q^{60} + 3 q^{61} - 3 q^{62} - 6 q^{63} + 3 q^{64} + 22 q^{65} + 3 q^{66} - q^{67} + q^{68} - 4 q^{69} + 3 q^{70} - 15 q^{71} + 3 q^{72} - 18 q^{73} - 6 q^{74} - 2 q^{75} - 6 q^{77} - 9 q^{78} - 19 q^{79} - 5 q^{80} + 3 q^{81} - q^{82} - 2 q^{83} - 6 q^{84} + 3 q^{85} - 2 q^{86} - 12 q^{87} + 3 q^{88} - 5 q^{89} - 5 q^{90} + 11 q^{91} - 4 q^{92} - 3 q^{93} - 13 q^{94} - 7 q^{95} + 3 q^{96} + q^{97} + 5 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 5 * q^10 + 3 * q^11 + 3 * q^12 - 9 * q^13 - 6 * q^14 - 5 * q^15 + 3 * q^16 + q^17 + 3 * q^18 - 5 * q^20 - 6 * q^21 + 3 * q^22 - 4 * q^23 + 3 * q^24 - 2 * q^25 - 9 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 - 5 * q^30 - 3 * q^31 + 3 * q^32 + 3 * q^33 + q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 - 9 * q^39 - 5 * q^40 - q^41 - 6 * q^42 - 2 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 - 13 * q^47 + 3 * q^48 + 5 * q^49 - 2 * q^50 + q^51 - 9 * q^52 - 16 * q^53 + 3 * q^54 - 5 * q^55 - 6 * q^56 - 12 * q^58 - 21 * q^59 - 5 * q^60 + 3 * q^61 - 3 * q^62 - 6 * q^63 + 3 * q^64 + 22 * q^65 + 3 * q^66 - q^67 + q^68 - 4 * q^69 + 3 * q^70 - 15 * q^71 + 3 * q^72 - 18 * q^73 - 6 * q^74 - 2 * q^75 - 6 * q^77 - 9 * q^78 - 19 * q^79 - 5 * q^80 + 3 * q^81 - q^82 - 2 * q^83 - 6 * q^84 + 3 * q^85 - 2 * q^86 - 12 * q^87 + 3 * q^88 - 5 * q^89 - 5 * q^90 + 11 * q^91 - 4 * q^92 - 3 * q^93 - 13 * q^94 - 7 * q^95 + 3 * q^96 + q^97 + 5 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.55496	−0.695398	−0.347699	−	0.937606i	$-0.613037\pi$
$5$	−1.55496	−0.695398	−0.347699	+	0.937606i	$0.613037\pi$
$6$	1.00000	0.408248
$7$	−0.643104	−0.243071	−0.121535	−	0.992587i	$-0.538782\pi$
$7$	−0.643104	−0.243071	−0.121535	+	0.992587i	$0.538782\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.55496	−0.491721
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	−1.30798	−0.362768	−0.181384	−	0.983412i	$-0.558058\pi$
$13$	−1.30798	−0.362768	−0.181384	+	0.983412i	$0.558058\pi$
$14$	−0.643104	−0.171877
$15$	−1.55496	−0.401488
$16$	1.00000	0.250000
$17$	−2.60388	−0.631533	−0.315766	−	0.948837i	$-0.602262\pi$
$17$	−2.60388	−0.631533	−0.315766	+	0.948837i	$0.602262\pi$
$18$	1.00000	0.235702
$19$	−7.78986	−1.78712	−0.893558	−	0.448948i	$-0.851799\pi$
$19$	−7.78986	−1.78712	−0.893558	+	0.448948i	$0.851799\pi$
$20$	−1.55496	−0.347699
$21$	−0.643104	−0.140337
$22$	1.00000	0.213201
$23$	−6.18598	−1.28987	−0.644933	−	0.764239i	$-0.723115\pi$
$23$	−6.18598	−1.28987	−0.644933	+	0.764239i	$0.723115\pi$
$24$	1.00000	0.204124
$25$	−2.58211	−0.516421
$26$	−1.30798	−0.256516
$27$	1.00000	0.192450
$28$	−0.643104	−0.121535
$29$	0.740939	0.137589	0.0687944	−	0.997631i	$-0.478085\pi$
$29$	0.740939	0.137589	0.0687944	+	0.997631i	$0.478085\pi$
$30$	−1.55496	−0.283895
$31$	6.45473	1.15930	0.579652	−	0.814864i	$-0.303189\pi$
$31$	6.45473	1.15930	0.579652	+	0.814864i	$0.303189\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−2.60388	−0.446561
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−0.307979	−0.0506314	−0.0253157	−	0.999680i	$-0.508059\pi$
$37$	−0.307979	−0.0506314	−0.0253157	+	0.999680i	$0.508059\pi$
$38$	−7.78986	−1.26368
$39$	−1.30798	−0.209444
$40$	−1.55496	−0.245860
$41$	5.31767	0.830480	0.415240	−	0.909712i	$-0.363698\pi$
$41$	5.31767	0.830480	0.415240	+	0.909712i	$0.363698\pi$
$42$	−0.643104	−0.0992331
$43$	−3.26875	−0.498480	−0.249240	−	0.968442i	$-0.580181\pi$
$43$	−3.26875	−0.498480	−0.249240	+	0.968442i	$0.580181\pi$
$44$	1.00000	0.150756
$45$	−1.55496	−0.231799
$46$	−6.18598	−0.912073
$47$	−1.06100	−0.154763	−0.0773813	−	0.997002i	$-0.524656\pi$
$47$	−1.06100	−0.154763	−0.0773813	+	0.997002i	$0.524656\pi$
$48$	1.00000	0.144338
$49$	−6.58642	−0.940917
$50$	−2.58211	−0.365165
$51$	−2.60388	−0.364615
$52$	−1.30798	−0.181384
$53$	−12.2131	−1.67760	−0.838801	−	0.544438i	$-0.816743\pi$
$53$	−12.2131	−1.67760	−0.838801	+	0.544438i	$0.816743\pi$
$54$	1.00000	0.136083
$55$	−1.55496	−0.209671
$56$	−0.643104	−0.0859384
$57$	−7.78986	−1.03179
$58$	0.740939	0.0972900
$59$	−5.64310	−0.734670	−0.367335	−	0.930089i	$-0.619730\pi$
$59$	−5.64310	−0.734670	−0.367335	+	0.930089i	$0.619730\pi$
$60$	−1.55496	−0.200744
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	6.45473	0.819752
$63$	−0.643104	−0.0810235
$64$	1.00000	0.125000
$65$	2.03385	0.252268
$66$	1.00000	0.123091
$67$	4.63102	0.565769	0.282885	−	0.959154i	$-0.408709\pi$
$67$	4.63102	0.565769	0.282885	+	0.959154i	$0.408709\pi$
$68$	−2.60388	−0.315766
$69$	−6.18598	−0.744705
$70$	1.00000	0.119523
$71$	2.45473	0.291323	0.145661	−	0.989334i	$-0.453469\pi$
$71$	2.45473	0.291323	0.145661	+	0.989334i	$0.453469\pi$
$72$	1.00000	0.117851
$73$	−1.25906	−0.147362	−0.0736810	−	0.997282i	$-0.523475\pi$
$73$	−1.25906	−0.147362	−0.0736810	+	0.997282i	$0.523475\pi$
$74$	−0.307979	−0.0358018
$75$	−2.58211	−0.298156
$76$	−7.78986	−0.893558
$77$	−0.643104	−0.0732885
$78$	−1.30798	−0.148099
$79$	−10.5157	−1.18311	−0.591556	−	0.806264i	$-0.701486\pi$
$79$	−10.5157	−1.18311	−0.591556	+	0.806264i	$0.701486\pi$
$80$	−1.55496	−0.173850
$81$	1.00000	0.111111
$82$	5.31767	0.587238
$83$	−4.29052	−0.470946	−0.235473	−	0.971881i	$-0.575664\pi$
$83$	−4.29052	−0.470946	−0.235473	+	0.971881i	$0.575664\pi$
$84$	−0.643104	−0.0701684
$85$	4.04892	0.439167
$86$	−3.26875	−0.352478
$87$	0.740939	0.0794370
$88$	1.00000	0.106600
$89$	−9.69633	−1.02781	−0.513905	−	0.857847i	$-0.671801\pi$
$89$	−9.69633	−1.02781	−0.513905	+	0.857847i	$0.671801\pi$
$90$	−1.55496	−0.163907
$91$	0.841166	0.0881782
$92$	−6.18598	−0.644933
$93$	6.45473	0.669324
$94$	−1.06100	−0.109434
$95$	12.1129	1.24276
$96$	1.00000	0.102062
$97$	1.46681	0.148932	0.0744661	−	0.997224i	$-0.476275\pi$
$97$	1.46681	0.148932	0.0744661	+	0.997224i	$0.476275\pi$
$98$	−6.58642	−0.665329
$99$	1.00000	0.100504
$100$	−2.58211	−0.258211
$101$	10.2446	1.01937	0.509687	−	0.860360i	$-0.329761\pi$
$101$	10.2446	1.01937	0.509687	+	0.860360i	$0.329761\pi$
$102$	−2.60388	−0.257822
$103$	2.22521	0.219256	0.109628	−	0.993973i	$-0.465034\pi$
$103$	2.22521	0.219256	0.109628	+	0.993973i	$0.465034\pi$
$104$	−1.30798	−0.128258
$105$	1.00000	0.0975900
$106$	−12.2131	−1.18624
$107$	7.30798	0.706489	0.353244	−	0.935531i	$-0.385078\pi$
$107$	7.30798	0.706489	0.353244	+	0.935531i	$0.385078\pi$
$108$	1.00000	0.0962250
$109$	−9.46011	−0.906114	−0.453057	−	0.891482i	$-0.649667\pi$
$109$	−9.46011	−0.906114	−0.453057	+	0.891482i	$0.649667\pi$
$110$	−1.55496	−0.148259
$111$	−0.307979	−0.0292320
$112$	−0.643104	−0.0607676
$113$	8.03684	0.756042	0.378021	−	0.925797i	$-0.376605\pi$
$113$	8.03684	0.756042	0.378021	+	0.925797i	$0.376605\pi$
$114$	−7.78986	−0.729587
$115$	9.61894	0.896971
$116$	0.740939	0.0687944
$117$	−1.30798	−0.120923
$118$	−5.64310	−0.519490
$119$	1.67456	0.153507
$120$	−1.55496	−0.141948
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	5.31767	0.479478
$124$	6.45473	0.579652
$125$	11.7899	1.05452
$126$	−0.643104	−0.0572923
$127$	2.92154	0.259245	0.129622	−	0.991563i	$-0.458623\pi$
$127$	2.92154	0.259245	0.129622	+	0.991563i	$0.458623\pi$
$128$	1.00000	0.0883883
$129$	−3.26875	−0.287797
$130$	2.03385	0.178381
$131$	10.6963	0.934543	0.467271	−	0.884114i	$-0.345237\pi$
$131$	10.6963	0.934543	0.467271	+	0.884114i	$0.345237\pi$
$132$	1.00000	0.0870388
$133$	5.00969	0.434395
$134$	4.63102	0.400059
$135$	−1.55496	−0.133829
$136$	−2.60388	−0.223280
$137$	−6.65817	−0.568846	−0.284423	−	0.958699i	$-0.591802\pi$
$137$	−6.65817	−0.568846	−0.284423	+	0.958699i	$0.591802\pi$
$138$	−6.18598	−0.526586
$139$	3.50365	0.297176	0.148588	−	0.988899i	$-0.452527\pi$
$139$	3.50365	0.297176	0.148588	+	0.988899i	$0.452527\pi$
$140$	1.00000	0.0845154
$141$	−1.06100	−0.0893522
$142$	2.45473	0.205996
$143$	−1.30798	−0.109379
$144$	1.00000	0.0833333
$145$	−1.15213	−0.0956791
$146$	−1.25906	−0.104201
$147$	−6.58642	−0.543239
$148$	−0.307979	−0.0253157
$149$	−13.6896	−1.12150	−0.560749	−	0.827986i	$-0.689487\pi$
$149$	−13.6896	−1.12150	−0.560749	+	0.827986i	$0.689487\pi$
$150$	−2.58211	−0.210828
$151$	3.34050	0.271846	0.135923	−	0.990719i	$-0.456600\pi$
$151$	3.34050	0.271846	0.135923	+	0.990719i	$0.456600\pi$
$152$	−7.78986	−0.631841
$153$	−2.60388	−0.210511
$154$	−0.643104	−0.0518228
$155$	−10.0368	−0.806178
$156$	−1.30798	−0.104722
$157$	4.38835	0.350229	0.175114	−	0.984548i	$-0.443970\pi$
$157$	4.38835	0.350229	0.175114	+	0.984548i	$0.443970\pi$
$158$	−10.5157	−0.836587
$159$	−12.2131	−0.968564
$160$	−1.55496	−0.122930
$161$	3.97823	0.313528
$162$	1.00000	0.0785674
$163$	−4.66248	−0.365194	−0.182597	−	0.983188i	$-0.558450\pi$
$163$	−4.66248	−0.365194	−0.182597	+	0.983188i	$0.558450\pi$
$164$	5.31767	0.415240
$165$	−1.55496	−0.121053
$166$	−4.29052	−0.333009
$167$	−20.3110	−1.57171	−0.785855	−	0.618411i	$-0.787777\pi$
$167$	−20.3110	−1.57171	−0.785855	+	0.618411i	$0.787777\pi$
$168$	−0.643104	−0.0496166
$169$	−11.2892	−0.868399
$170$	4.04892	0.310538
$171$	−7.78986	−0.595705
$172$	−3.26875	−0.249240
$173$	11.5332	0.876852	0.438426	−	0.898767i	$-0.355536\pi$
$173$	11.5332	0.876852	0.438426	+	0.898767i	$0.355536\pi$
$174$	0.740939	0.0561704
$175$	1.66056	0.125527
$176$	1.00000	0.0753778
$177$	−5.64310	−0.424162
$178$	−9.69633	−0.726771
$179$	−1.23729	−0.0924795	−0.0462397	−	0.998930i	$-0.514724\pi$
$179$	−1.23729	−0.0924795	−0.0462397	+	0.998930i	$0.514724\pi$
$180$	−1.55496	−0.115900
$181$	−11.3961	−0.847067	−0.423534	−	0.905880i	$-0.639210\pi$
$181$	−11.3961	−0.847067	−0.423534	+	0.905880i	$0.639210\pi$
$182$	0.841166	0.0623514
$183$	1.00000	0.0739221
$184$	−6.18598	−0.456037
$185$	0.478894	0.0352090
$186$	6.45473	0.473284
$187$	−2.60388	−0.190414
$188$	−1.06100	−0.0773813
$189$	−0.643104	−0.0467789
$190$	12.1129	0.878762
$191$	−4.91185	−0.355409	−0.177705	−	0.984084i	$-0.556867\pi$
$191$	−4.91185	−0.355409	−0.177705	+	0.984084i	$0.556867\pi$
$192$	1.00000	0.0721688
$193$	0.454731	0.0327322	0.0163661	−	0.999866i	$-0.494790\pi$
$193$	0.454731	0.0327322	0.0163661	+	0.999866i	$0.494790\pi$
$194$	1.46681	0.105311
$195$	2.03385	0.145647
$196$	−6.58642	−0.470458
$197$	8.90648	0.634560	0.317280	−	0.948332i	$-0.397230\pi$
$197$	8.90648	0.634560	0.317280	+	0.948332i	$0.397230\pi$
$198$	1.00000	0.0710669
$199$	−16.1414	−1.14423	−0.572116	−	0.820173i	$-0.693877\pi$
$199$	−16.1414	−1.14423	−0.572116	+	0.820173i	$0.693877\pi$
$200$	−2.58211	−0.182582
$201$	4.63102	0.326647
$202$	10.2446	0.720807
$203$	−0.476501	−0.0334438
$204$	−2.60388	−0.182308
$205$	−8.26875	−0.577515
$206$	2.22521	0.155038
$207$	−6.18598	−0.429955
$208$	−1.30798	−0.0906920
$209$	−7.78986	−0.538836
$210$	1.00000	0.0690066
$211$	−0.493959	−0.0340056	−0.0170028	−	0.999855i	$-0.505412\pi$
$211$	−0.493959	−0.0340056	−0.0170028	+	0.999855i	$0.505412\pi$
$212$	−12.2131	−0.838801
$213$	2.45473	0.168195
$214$	7.30798	0.499563
$215$	5.08277	0.346642
$216$	1.00000	0.0680414
$217$	−4.15106	−0.281793
$218$	−9.46011	−0.640719
$219$	−1.25906	−0.0850795
$220$	−1.55496	−0.104835
$221$	3.40581	0.229100
$222$	−0.307979	−0.0206702
$223$	−26.3545	−1.76483	−0.882414	−	0.470474i	$-0.844083\pi$
$223$	−26.3545	−1.76483	−0.882414	+	0.470474i	$0.844083\pi$
$224$	−0.643104	−0.0429692
$225$	−2.58211	−0.172140
$226$	8.03684	0.534602
$227$	12.4668	0.827451	0.413726	−	0.910402i	$-0.364227\pi$
$227$	12.4668	0.827451	0.413726	+	0.910402i	$0.364227\pi$
$228$	−7.78986	−0.515896
$229$	−20.3032	−1.34167	−0.670836	−	0.741605i	$-0.734065\pi$
$229$	−20.3032	−1.34167	−0.670836	+	0.741605i	$0.734065\pi$
$230$	9.61894	0.634254
$231$	−0.643104	−0.0423131
$232$	0.740939	0.0486450
$233$	12.8901	0.844457	0.422229	−	0.906489i	$-0.361248\pi$
$233$	12.8901	0.844457	0.422229	+	0.906489i	$0.361248\pi$
$234$	−1.30798	−0.0855052
$235$	1.64981	0.107622
$236$	−5.64310	−0.367335
$237$	−10.5157	−0.683070
$238$	1.67456	0.108546
$239$	26.3230	1.70270	0.851348	−	0.524601i	$-0.175786\pi$
$239$	26.3230	1.70270	0.851348	+	0.524601i	$0.175786\pi$
$240$	−1.55496	−0.100372
$241$	−4.35152	−0.280306	−0.140153	−	0.990130i	$-0.544759\pi$
$241$	−4.35152	−0.280306	−0.140153	+	0.990130i	$0.544759\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	10.2416	0.654312
$246$	5.31767	0.339042
$247$	10.1890	0.648308
$248$	6.45473	0.409876
$249$	−4.29052	−0.271901
$250$	11.7899	0.745656
$251$	0.0513102	0.00323867	0.00161934	−	0.999999i	$-0.499485\pi$
$251$	0.0513102	0.00323867	0.00161934	+	0.999999i	$0.499485\pi$
$252$	−0.643104	−0.0405118
$253$	−6.18598	−0.388909
$254$	2.92154	0.183314
$255$	4.04892	0.253553
$256$	1.00000	0.0625000
$257$	15.8146	0.986488	0.493244	−	0.869891i	$-0.335811\pi$
$257$	15.8146	0.986488	0.493244	+	0.869891i	$0.335811\pi$
$258$	−3.26875	−0.203503
$259$	0.198062	0.0123070
$260$	2.03385	0.126134
$261$	0.740939	0.0458630
$262$	10.6963	0.660822
$263$	16.5754	1.02208	0.511041	−	0.859556i	$-0.329260\pi$
$263$	16.5754	1.02208	0.511041	+	0.859556i	$0.329260\pi$
$264$	1.00000	0.0615457
$265$	18.9909	1.16660
$266$	5.00969	0.307164
$267$	−9.69633	−0.593406
$268$	4.63102	0.282885
$269$	11.4504	0.698144	0.349072	−	0.937096i	$-0.386497\pi$
$269$	11.4504	0.698144	0.349072	+	0.937096i	$0.386497\pi$
$270$	−1.55496	−0.0946317
$271$	−26.6558	−1.61922	−0.809612	−	0.586966i	$-0.800322\pi$
$271$	−26.6558	−1.61922	−0.809612	+	0.586966i	$0.800322\pi$
$272$	−2.60388	−0.157883
$273$	0.841166	0.0509097
$274$	−6.65817	−0.402235
$275$	−2.58211	−0.155707
$276$	−6.18598	−0.372352
$277$	11.8756	0.713536	0.356768	−	0.934193i	$-0.383879\pi$
$277$	11.8756	0.713536	0.356768	+	0.934193i	$0.383879\pi$
$278$	3.50365	0.210135
$279$	6.45473	0.386435
$280$	1.00000	0.0597614
$281$	−16.5405	−0.986723	−0.493361	−	0.869825i	$-0.664232\pi$
$281$	−16.5405	−0.986723	−0.493361	+	0.869825i	$0.664232\pi$
$282$	−1.06100	−0.0631816
$283$	13.3123	0.791334	0.395667	−	0.918394i	$-0.370514\pi$
$283$	13.3123	0.791334	0.395667	+	0.918394i	$0.370514\pi$
$284$	2.45473	0.145661
$285$	12.1129	0.717506
$286$	−1.30798	−0.0773424
$287$	−3.41981	−0.201865
$288$	1.00000	0.0589256
$289$	−10.2198	−0.601167
$290$	−1.15213	−0.0676553
$291$	1.46681	0.0859860
$292$	−1.25906	−0.0736810
$293$	−15.3773	−0.898354	−0.449177	−	0.893443i	$-0.648283\pi$
$293$	−15.3773	−0.898354	−0.449177	+	0.893443i	$0.648283\pi$
$294$	−6.58642	−0.384128
$295$	8.77479	0.510888
$296$	−0.307979	−0.0179009
$297$	1.00000	0.0580259
$298$	−13.6896	−0.793019
$299$	8.09113	0.467922
$300$	−2.58211	−0.149078
$301$	2.10215	0.121166
$302$	3.34050	0.192224
$303$	10.2446	0.588536
$304$	−7.78986	−0.446779
$305$	−1.55496	−0.0890366
$306$	−2.60388	−0.148854
$307$	19.0084	1.08486	0.542432	−	0.840100i	$-0.317504\pi$
$307$	19.0084	1.08486	0.542432	+	0.840100i	$0.317504\pi$
$308$	−0.643104	−0.0366443
$309$	2.22521	0.126588
$310$	−10.0368	−0.570054
$311$	−26.4252	−1.49844	−0.749218	−	0.662324i	$-0.769570\pi$
$311$	−26.4252	−1.49844	−0.749218	+	0.662324i	$0.769570\pi$
$312$	−1.30798	−0.0740497
$313$	5.33944	0.301803	0.150901	−	0.988549i	$-0.451782\pi$
$313$	5.33944	0.301803	0.150901	+	0.988549i	$0.451782\pi$
$314$	4.38835	0.247649
$315$	1.00000	0.0563436
$316$	−10.5157	−0.591556
$317$	25.0790	1.40858	0.704290	−	0.709913i	$-0.251266\pi$
$317$	25.0790	1.40858	0.704290	+	0.709913i	$0.251266\pi$
$318$	−12.2131	−0.684878
$319$	0.740939	0.0414846
$320$	−1.55496	−0.0869248
$321$	7.30798	0.407892
$322$	3.97823	0.221698
$323$	20.2838	1.12862
$324$	1.00000	0.0555556
$325$	3.37734	0.187341
$326$	−4.66248	−0.258231
$327$	−9.46011	−0.523145
$328$	5.31767	0.293619
$329$	0.682333	0.0376182
$330$	−1.55496	−0.0855976
$331$	−15.4969	−0.851789	−0.425895	−	0.904773i	$-0.640041\pi$
$331$	−15.4969	−0.851789	−0.425895	+	0.904773i	$0.640041\pi$
$332$	−4.29052	−0.235473
$333$	−0.307979	−0.0168771
$334$	−20.3110	−1.11137
$335$	−7.20105	−0.393435
$336$	−0.643104	−0.0350842
$337$	20.6112	1.12276	0.561381	−	0.827557i	$-0.310270\pi$
$337$	20.6112	1.12276	0.561381	+	0.827557i	$0.310270\pi$
$338$	−11.2892	−0.614051
$339$	8.03684	0.436501
$340$	4.04892	0.219583
$341$	6.45473	0.349543
$342$	−7.78986	−0.421227
$343$	8.73748	0.471780
$344$	−3.26875	−0.176239
$345$	9.61894	0.517866
$346$	11.5332	0.620028
$347$	5.57912	0.299503	0.149751	−	0.988724i	$-0.452153\pi$
$347$	5.57912	0.299503	0.149751	+	0.988724i	$0.452153\pi$
$348$	0.740939	0.0397185
$349$	2.87071	0.153665	0.0768327	−	0.997044i	$-0.475519\pi$
$349$	2.87071	0.153665	0.0768327	+	0.997044i	$0.475519\pi$
$350$	1.66056	0.0887608
$351$	−1.30798	−0.0698147
$352$	1.00000	0.0533002
$353$	11.6692	0.621088	0.310544	−	0.950559i	$-0.399489\pi$
$353$	11.6692	0.621088	0.310544	+	0.950559i	$0.399489\pi$
$354$	−5.64310	−0.299928
$355$	−3.81700	−0.202585
$356$	−9.69633	−0.513905
$357$	1.67456	0.0886273
$358$	−1.23729	−0.0653929
$359$	9.27413	0.489470	0.244735	−	0.969590i	$-0.421299\pi$
$359$	9.27413	0.489470	0.244735	+	0.969590i	$0.421299\pi$
$360$	−1.55496	−0.0819535
$361$	41.6819	2.19378
$362$	−11.3961	−0.598967
$363$	1.00000	0.0524864
$364$	0.841166	0.0440891
$365$	1.95779	0.102475
$366$	1.00000	0.0522708
$367$	−8.34913	−0.435821	−0.217910	−	0.975969i	$-0.569924\pi$
$367$	−8.34913	−0.435821	−0.217910	+	0.975969i	$0.569924\pi$
$368$	−6.18598	−0.322467
$369$	5.31767	0.276827
$370$	0.478894	0.0248965
$371$	7.85431	0.407776
$372$	6.45473	0.334662
$373$	−26.3327	−1.36346	−0.681729	−	0.731605i	$-0.738772\pi$
$373$	−26.3327	−1.36346	−0.681729	+	0.731605i	$0.738772\pi$
$374$	−2.60388	−0.134643
$375$	11.7899	0.608826
$376$	−1.06100	−0.0547168
$377$	−0.969132	−0.0499128
$378$	−0.643104	−0.0330777
$379$	10.1099	0.519312	0.259656	−	0.965701i	$-0.416391\pi$
$379$	10.1099	0.519312	0.259656	+	0.965701i	$0.416391\pi$
$380$	12.1129	0.621379
$381$	2.92154	0.149675
$382$	−4.91185	−0.251312
$383$	7.76809	0.396931	0.198465	−	0.980108i	$-0.436404\pi$
$383$	7.76809	0.396931	0.198465	+	0.980108i	$0.436404\pi$
$384$	1.00000	0.0510310
$385$	1.00000	0.0509647
$386$	0.454731	0.0231452
$387$	−3.26875	−0.166160
$388$	1.46681	0.0744661
$389$	9.89440	0.501666	0.250833	−	0.968030i	$-0.419296\pi$
$389$	9.89440	0.501666	0.250833	+	0.968030i	$0.419296\pi$
$390$	2.03385	0.102988
$391$	16.1075	0.814592
$392$	−6.58642	−0.332664
$393$	10.6963	0.539559
$394$	8.90648	0.448702
$395$	16.3515	0.822734
$396$	1.00000	0.0502519
$397$	−7.90648	−0.396815	−0.198407	−	0.980120i	$-0.563577\pi$
$397$	−7.90648	−0.396815	−0.198407	+	0.980120i	$0.563577\pi$
$398$	−16.1414	−0.809094
$399$	5.00969	0.250798
$400$	−2.58211	−0.129105
$401$	11.5060	0.574584	0.287292	−	0.957843i	$-0.407245\pi$
$401$	11.5060	0.574584	0.287292	+	0.957843i	$0.407245\pi$
$402$	4.63102	0.230974
$403$	−8.44265	−0.420558
$404$	10.2446	0.509687
$405$	−1.55496	−0.0772665
$406$	−0.476501	−0.0236483
$407$	−0.307979	−0.0152659
$408$	−2.60388	−0.128911
$409$	13.5319	0.669107	0.334554	−	0.942377i	$-0.391414\pi$
$409$	13.5319	0.669107	0.334554	+	0.942377i	$0.391414\pi$
$410$	−8.26875	−0.408364
$411$	−6.65817	−0.328423
$412$	2.22521	0.109628
$413$	3.62910	0.178577
$414$	−6.18598	−0.304024
$415$	6.67158	0.327495
$416$	−1.30798	−0.0641289
$417$	3.50365	0.171574
$418$	−7.78986	−0.381014
$419$	−39.6122	−1.93518	−0.967592	−	0.252518i	$-0.918741\pi$
$419$	−39.6122	−1.93518	−0.967592	+	0.252518i	$0.918741\pi$
$420$	1.00000	0.0487950
$421$	−5.15452	−0.251216	−0.125608	−	0.992080i	$-0.540088\pi$
$421$	−5.15452	−0.251216	−0.125608	+	0.992080i	$0.540088\pi$
$422$	−0.493959	−0.0240456
$423$	−1.06100	−0.0515875
$424$	−12.2131	−0.593122
$425$	6.72348	0.326137
$426$	2.45473	0.118932
$427$	−0.643104	−0.0311220
$428$	7.30798	0.353244
$429$	−1.30798	−0.0631498
$430$	5.08277	0.245113
$431$	5.10859	0.246072	0.123036	−	0.992402i	$-0.460737\pi$
$431$	5.10859	0.246072	0.123036	+	0.992402i	$0.460737\pi$
$432$	1.00000	0.0481125
$433$	−39.1038	−1.87921	−0.939604	−	0.342262i	$-0.888807\pi$
$433$	−39.1038	−1.87921	−0.939604	+	0.342262i	$0.888807\pi$
$434$	−4.15106	−0.199257
$435$	−1.15213	−0.0552403
$436$	−9.46011	−0.453057
$437$	48.1879	2.30514
$438$	−1.25906	−0.0601603
$439$	−15.2731	−0.728943	−0.364472	−	0.931214i	$-0.618750\pi$
$439$	−15.2731	−0.728943	−0.364472	+	0.931214i	$0.618750\pi$
$440$	−1.55496	−0.0741297
$441$	−6.58642	−0.313639
$442$	3.40581	0.161998
$443$	−20.2000	−0.959730	−0.479865	−	0.877342i	$-0.659314\pi$
$443$	−20.2000	−0.959730	−0.479865	+	0.877342i	$0.659314\pi$
$444$	−0.307979	−0.0146160
$445$	15.0774	0.714737
$446$	−26.3545	−1.24792
$447$	−13.6896	−0.647497
$448$	−0.643104	−0.0303838
$449$	27.5327	1.29935	0.649675	−	0.760212i	$-0.274905\pi$
$449$	27.5327	1.29935	0.649675	+	0.760212i	$0.274905\pi$
$450$	−2.58211	−0.121722
$451$	5.31767	0.250399
$452$	8.03684	0.378021
$453$	3.34050	0.156950
$454$	12.4668	0.585096
$455$	−1.30798	−0.0613190
$456$	−7.78986	−0.364793
$457$	−15.1879	−0.710460	−0.355230	−	0.934779i	$-0.615597\pi$
$457$	−15.1879	−0.710460	−0.355230	+	0.934779i	$0.615597\pi$
$458$	−20.3032	−0.948706
$459$	−2.60388	−0.121538
$460$	9.61894	0.448485
$461$	−20.4892	−0.954276	−0.477138	−	0.878828i	$-0.658326\pi$
$461$	−20.4892	−0.954276	−0.477138	+	0.878828i	$0.658326\pi$
$462$	−0.643104	−0.0299199
$463$	0.868313	0.0403539	0.0201770	−	0.999796i	$-0.493577\pi$
$463$	0.868313	0.0403539	0.0201770	+	0.999796i	$0.493577\pi$
$464$	0.740939	0.0343972
$465$	−10.0368	−0.465447
$466$	12.8901	0.597122
$467$	8.49289	0.393004	0.196502	−	0.980503i	$-0.437042\pi$
$467$	8.49289	0.393004	0.196502	+	0.980503i	$0.437042\pi$
$468$	−1.30798	−0.0604613
$469$	−2.97823	−0.137522
$470$	1.64981	0.0761000
$471$	4.38835	0.202205
$472$	−5.64310	−0.259745
$473$	−3.26875	−0.150297
$474$	−10.5157	−0.483003
$475$	20.1142	0.922904
$476$	1.67456	0.0767535
$477$	−12.2131	−0.559201
$478$	26.3230	1.20399
$479$	−7.68904	−0.351321	−0.175661	−	0.984451i	$-0.556206\pi$
$479$	−7.68904	−0.351321	−0.175661	+	0.984451i	$0.556206\pi$
$480$	−1.55496	−0.0709738
$481$	0.402829	0.0183674
$482$	−4.35152	−0.198206
$483$	3.97823	0.181016
$484$	1.00000	0.0454545
$485$	−2.28083	−0.103567
$486$	1.00000	0.0453609
$487$	15.4896	0.701903	0.350951	−	0.936394i	$-0.385858\pi$
$487$	15.4896	0.701903	0.350951	+	0.936394i	$0.385858\pi$
$488$	1.00000	0.0452679
$489$	−4.66248	−0.210845
$490$	10.2416	0.462668
$491$	−4.67696	−0.211068	−0.105534	−	0.994416i	$-0.533655\pi$
$491$	−4.67696	−0.211068	−0.105534	+	0.994416i	$0.533655\pi$
$492$	5.31767	0.239739
$493$	−1.92931	−0.0868919
$494$	10.1890	0.458423
$495$	−1.55496	−0.0698902
$496$	6.45473	0.289826
$497$	−1.57865	−0.0708120
$498$	−4.29052	−0.192263
$499$	31.4687	1.40873	0.704367	−	0.709836i	$-0.251231\pi$
$499$	31.4687	1.40873	0.704367	+	0.709836i	$0.251231\pi$
$500$	11.7899	0.527258
$501$	−20.3110	−0.907427
$502$	0.0513102	0.00229009
$503$	34.2000	1.52490	0.762451	−	0.647046i	$-0.223996\pi$
$503$	34.2000	1.52490	0.762451	+	0.647046i	$0.223996\pi$
$504$	−0.643104	−0.0286461
$505$	−15.9299	−0.708871
$506$	−6.18598	−0.275000
$507$	−11.2892	−0.501371
$508$	2.92154	0.129622
$509$	25.5109	1.13075	0.565376	−	0.824833i	$-0.308731\pi$
$509$	25.5109	1.13075	0.565376	+	0.824833i	$0.308731\pi$
$510$	4.04892	0.179289
$511$	0.809707	0.0358193
$512$	1.00000	0.0441942
$513$	−7.78986	−0.343931
$514$	15.8146	0.697553
$515$	−3.46011	−0.152471
$516$	−3.26875	−0.143899
$517$	−1.06100	−0.0466627
$518$	0.198062	0.00870236
$519$	11.5332	0.506251
$520$	2.03385	0.0891903
$521$	−16.5840	−0.726559	−0.363280	−	0.931680i	$-0.618343\pi$
$521$	−16.5840	−0.726559	−0.363280	+	0.931680i	$0.618343\pi$
$522$	0.740939	0.0324300
$523$	18.9898	0.830368	0.415184	−	0.909738i	$-0.363717\pi$
$523$	18.9898	0.830368	0.415184	+	0.909738i	$0.363717\pi$
$524$	10.6963	0.467271
$525$	1.66056	0.0724729
$526$	16.5754	0.722722
$527$	−16.8073	−0.732138
$528$	1.00000	0.0435194
$529$	15.2664	0.663755
$530$	18.9909	0.824912
$531$	−5.64310	−0.244890
$532$	5.00969	0.217198
$533$	−6.95539	−0.301272
$534$	−9.69633	−0.419601
$535$	−11.3636	−0.491291
$536$	4.63102	0.200030
$537$	−1.23729	−0.0533930
$538$	11.4504	0.493663
$539$	−6.58642	−0.283697
$540$	−1.55496	−0.0669147
$541$	15.7928	0.678987	0.339494	−	0.940608i	$-0.389744\pi$
$541$	15.7928	0.678987	0.339494	+	0.940608i	$0.389744\pi$
$542$	−26.6558	−1.14496
$543$	−11.3961	−0.489055
$544$	−2.60388	−0.111640
$545$	14.7101	0.630110
$546$	0.841166	0.0359986
$547$	19.0640	0.815117	0.407559	−	0.913179i	$-0.366380\pi$
$547$	19.0640	0.815117	0.407559	+	0.913179i	$0.366380\pi$
$548$	−6.65817	−0.284423
$549$	1.00000	0.0426790
$550$	−2.58211	−0.110101
$551$	−5.77181	−0.245887
$552$	−6.18598	−0.263293
$553$	6.76271	0.287580
$554$	11.8756	0.504546
$555$	0.478894	0.0203279
$556$	3.50365	0.148588
$557$	−9.95599	−0.421849	−0.210924	−	0.977502i	$-0.567647\pi$
$557$	−9.95599	−0.421849	−0.210924	+	0.977502i	$0.567647\pi$
$558$	6.45473	0.273251
$559$	4.27545	0.180832
$560$	1.00000	0.0422577
$561$	−2.60388	−0.109936
$562$	−16.5405	−0.697718
$563$	−11.8552	−0.499636	−0.249818	−	0.968293i	$-0.580371\pi$
$563$	−11.8552	−0.499636	−0.249818	+	0.968293i	$0.580371\pi$
$564$	−1.06100	−0.0446761
$565$	−12.4969	−0.525750
$566$	13.3123	0.559557
$567$	−0.643104	−0.0270078
$568$	2.45473	0.102998
$569$	33.6625	1.41120	0.705602	−	0.708608i	$-0.250677\pi$
$569$	33.6625	1.41120	0.705602	+	0.708608i	$0.250677\pi$
$570$	12.1129	0.507354
$571$	38.6795	1.61869	0.809343	−	0.587337i	$-0.199824\pi$
$571$	38.6795	1.61869	0.809343	+	0.587337i	$0.199824\pi$
$572$	−1.30798	−0.0546893
$573$	−4.91185	−0.205196
$574$	−3.41981	−0.142740
$575$	15.9729	0.666114
$576$	1.00000	0.0416667
$577$	6.99761	0.291314	0.145657	−	0.989335i	$-0.453470\pi$
$577$	6.99761	0.291314	0.145657	+	0.989335i	$0.453470\pi$
$578$	−10.2198	−0.425089
$579$	0.454731	0.0188980
$580$	−1.15213	−0.0478395
$581$	2.75925	0.114473
$582$	1.46681	0.0608013
$583$	−12.2131	−0.505816
$584$	−1.25906	−0.0521003
$585$	2.03385	0.0840894
$586$	−15.3773	−0.635232
$587$	35.3943	1.46088	0.730440	−	0.682977i	$-0.239315\pi$
$587$	35.3943	1.46088	0.730440	+	0.682977i	$0.239315\pi$
$588$	−6.58642	−0.271619
$589$	−50.2814	−2.07181
$590$	8.77479	0.361252
$591$	8.90648	0.366364
$592$	−0.307979	−0.0126578
$593$	−9.51871	−0.390887	−0.195443	−	0.980715i	$-0.562615\pi$
$593$	−9.51871	−0.390887	−0.195443	+	0.980715i	$0.562615\pi$
$594$	1.00000	0.0410305
$595$	−2.60388	−0.106748
$596$	−13.6896	−0.560749
$597$	−16.1414	−0.660623
$598$	8.09113	0.330871
$599$	30.4868	1.24566	0.622828	−	0.782359i	$-0.285984\pi$
$599$	30.4868	1.24566	0.622828	+	0.782359i	$0.285984\pi$
$600$	−2.58211	−0.105414
$601$	−24.7888	−1.01116	−0.505578	−	0.862781i	$-0.668721\pi$
$601$	−24.7888	−1.01116	−0.505578	+	0.862781i	$0.668721\pi$
$602$	2.10215	0.0856771
$603$	4.63102	0.188590
$604$	3.34050	0.135923
$605$	−1.55496	−0.0632180
$606$	10.2446	0.416158
$607$	−28.8122	−1.16945	−0.584726	−	0.811231i	$-0.698798\pi$
$607$	−28.8122	−1.16945	−0.584726	+	0.811231i	$0.698798\pi$
$608$	−7.78986	−0.315920
$609$	−0.476501	−0.0193088
$610$	−1.55496	−0.0629584
$611$	1.38776	0.0561429
$612$	−2.60388	−0.105255
$613$	−2.98898	−0.120724	−0.0603620	−	0.998177i	$-0.519225\pi$
$613$	−2.98898	−0.120724	−0.0603620	+	0.998177i	$0.519225\pi$
$614$	19.0084	0.767115
$615$	−8.26875	−0.333428
$616$	−0.643104	−0.0259114
$617$	20.4620	0.823770	0.411885	−	0.911236i	$-0.364871\pi$
$617$	20.4620	0.823770	0.411885	+	0.911236i	$0.364871\pi$
$618$	2.22521	0.0895110
$619$	−8.27950	−0.332781	−0.166391	−	0.986060i	$-0.553211\pi$
$619$	−8.27950	−0.332781	−0.166391	+	0.986060i	$0.553211\pi$
$620$	−10.0368	−0.403089
$621$	−6.18598	−0.248235
$622$	−26.4252	−1.05955
$623$	6.23575	0.249830
$624$	−1.30798	−0.0523610
$625$	−5.42221	−0.216888
$626$	5.33944	0.213407
$627$	−7.78986	−0.311097
$628$	4.38835	0.175114
$629$	0.801938	0.0319754
$630$	1.00000	0.0398410
$631$	6.27844	0.249941	0.124970	−	0.992160i	$-0.460116\pi$
$631$	6.27844	0.249941	0.124970	+	0.992160i	$0.460116\pi$
$632$	−10.5157	−0.418293
$633$	−0.493959	−0.0196331
$634$	25.0790	0.996016
$635$	−4.54288	−0.180279
$636$	−12.2131	−0.484282
$637$	8.61489	0.341334
$638$	0.740939	0.0293340
$639$	2.45473	0.0971076
$640$	−1.55496	−0.0614651
$641$	30.8418	1.21818	0.609088	−	0.793103i	$-0.291536\pi$
$641$	30.8418	1.21818	0.609088	+	0.793103i	$0.291536\pi$
$642$	7.30798	0.288423
$643$	21.3980	0.843856	0.421928	−	0.906629i	$-0.361353\pi$
$643$	21.3980	0.843856	0.421928	+	0.906629i	$0.361353\pi$
$644$	3.97823	0.156764
$645$	5.08277	0.200134
$646$	20.2838	0.798056
$647$	−0.432960	−0.0170214	−0.00851071	−	0.999964i	$-0.502709\pi$
$647$	−0.432960	−0.0170214	−0.00851071	+	0.999964i	$0.502709\pi$
$648$	1.00000	0.0392837
$649$	−5.64310	−0.221511
$650$	3.37734	0.132470
$651$	−4.15106	−0.162693
$652$	−4.66248	−0.182597
$653$	−2.85862	−0.111867	−0.0559333	−	0.998435i	$-0.517813\pi$
$653$	−2.85862	−0.111867	−0.0559333	+	0.998435i	$0.517813\pi$
$654$	−9.46011	−0.369919
$655$	−16.6324	−0.649880
$656$	5.31767	0.207620
$657$	−1.25906	−0.0491207
$658$	0.682333	0.0266001
$659$	−24.9965	−0.973727	−0.486864	−	0.873478i	$-0.661859\pi$
$659$	−24.9965	−0.973727	−0.486864	+	0.873478i	$0.661859\pi$
$660$	−1.55496	−0.0605267
$661$	−20.2101	−0.786083	−0.393042	−	0.919521i	$-0.628577\pi$
$661$	−20.2101	−0.786083	−0.393042	+	0.919521i	$0.628577\pi$
$662$	−15.4969	−0.602306
$663$	3.40581	0.132271
$664$	−4.29052	−0.166504
$665$	−7.78986	−0.302078
$666$	−0.307979	−0.0119339
$667$	−4.58343	−0.177471
$668$	−20.3110	−0.785855
$669$	−26.3545	−1.01892
$670$	−7.20105	−0.278201
$671$	1.00000	0.0386046
$672$	−0.643104	−0.0248083
$673$	9.54420	0.367902	0.183951	−	0.982935i	$-0.441111\pi$
$673$	9.54420	0.367902	0.183951	+	0.982935i	$0.441111\pi$
$674$	20.6112	0.793913
$675$	−2.58211	−0.0993853
$676$	−11.2892	−0.434200
$677$	−27.1588	−1.04380	−0.521899	−	0.853007i	$-0.674776\pi$
$677$	−27.1588	−1.04380	−0.521899	+	0.853007i	$0.674776\pi$
$678$	8.03684	0.308653
$679$	−0.943313	−0.0362010
$680$	4.04892	0.155269
$681$	12.4668	0.477729
$682$	6.45473	0.247164
$683$	−18.9202	−0.723962	−0.361981	−	0.932185i	$-0.617899\pi$
$683$	−18.9202	−0.723962	−0.361981	+	0.932185i	$0.617899\pi$
$684$	−7.78986	−0.297853
$685$	10.3532	0.395574
$686$	8.73748	0.333599
$687$	−20.3032	−0.774615
$688$	−3.26875	−0.124620
$689$	15.9745	0.608580
$690$	9.61894	0.366187
$691$	11.9280	0.453762	0.226881	−	0.973922i	$-0.427147\pi$
$691$	11.9280	0.453762	0.226881	+	0.973922i	$0.427147\pi$
$692$	11.5332	0.438426
$693$	−0.643104	−0.0244295
$694$	5.57912	0.211781
$695$	−5.44803	−0.206655
$696$	0.740939	0.0280852
$697$	−13.8465	−0.524475
$698$	2.87071	0.108658
$699$	12.8901	0.487548
$700$	1.66056	0.0627634
$701$	24.7826	0.936024	0.468012	−	0.883722i	$-0.344970\pi$
$701$	24.7826	0.936024	0.468012	+	0.883722i	$0.344970\pi$
$702$	−1.30798	−0.0493665
$703$	2.39911	0.0904841
$704$	1.00000	0.0376889
$705$	1.64981	0.0621354
$706$	11.6692	0.439176
$707$	−6.58834	−0.247780
$708$	−5.64310	−0.212081
$709$	−19.4470	−0.730346	−0.365173	−	0.930940i	$-0.618990\pi$
$709$	−19.4470	−0.730346	−0.365173	+	0.930940i	$0.618990\pi$
$710$	−3.81700	−0.143250
$711$	−10.5157	−0.394371
$712$	−9.69633	−0.363385
$713$	−39.9288	−1.49535
$714$	1.67456	0.0626689
$715$	2.03385	0.0760617
$716$	−1.23729	−0.0462397
$717$	26.3230	0.983052
$718$	9.27413	0.346107
$719$	−26.6002	−0.992018	−0.496009	−	0.868317i	$-0.665202\pi$
$719$	−26.6002	−0.992018	−0.496009	+	0.868317i	$0.665202\pi$
$720$	−1.55496	−0.0579499
$721$	−1.43104	−0.0532948
$722$	41.6819	1.55124
$723$	−4.35152	−0.161835
$724$	−11.3961	−0.423534
$725$	−1.91318	−0.0710538
$726$	1.00000	0.0371135
$727$	10.5332	0.390654	0.195327	−	0.980738i	$-0.437423\pi$
$727$	10.5332	0.390654	0.195327	+	0.980738i	$0.437423\pi$
$728$	0.841166	0.0311757
$729$	1.00000	0.0370370
$730$	1.95779	0.0724610
$731$	8.51142	0.314806
$732$	1.00000	0.0369611
$733$	−49.6819	−1.83504	−0.917521	−	0.397688i	$-0.869813\pi$
$733$	−49.6819	−1.83504	−0.917521	+	0.397688i	$0.869813\pi$
$734$	−8.34913	−0.308172
$735$	10.2416	0.377767
$736$	−6.18598	−0.228018
$737$	4.63102	0.170586
$738$	5.31767	0.195746
$739$	13.4252	0.493854	0.246927	−	0.969034i	$-0.420579\pi$
$739$	13.4252	0.493854	0.246927	+	0.969034i	$0.420579\pi$
$740$	0.478894	0.0176045
$741$	10.1890	0.374301
$742$	7.85431	0.288341
$743$	23.2728	0.853796	0.426898	−	0.904300i	$-0.359606\pi$
$743$	23.2728	0.853796	0.426898	+	0.904300i	$0.359606\pi$
$744$	6.45473	0.236642
$745$	21.2868	0.779888
$746$	−26.3327	−0.964110
$747$	−4.29052	−0.156982
$748$	−2.60388	−0.0952071
$749$	−4.69979	−0.171727
$750$	11.7899	0.430505
$751$	8.68425	0.316893	0.158446	−	0.987368i	$-0.449351\pi$
$751$	8.68425	0.316893	0.158446	+	0.987368i	$0.449351\pi$
$752$	−1.06100	−0.0386906
$753$	0.0513102	0.00186985
$754$	−0.969132	−0.0352937
$755$	−5.19434	−0.189041
$756$	−0.643104	−0.0233895
$757$	43.0586	1.56499	0.782496	−	0.622656i	$-0.213946\pi$
$757$	43.0586	1.56499	0.782496	+	0.622656i	$0.213946\pi$
$758$	10.1099	0.367209
$759$	−6.18598	−0.224537
$760$	12.1129	0.439381
$761$	−24.6786	−0.894599	−0.447299	−	0.894384i	$-0.647614\pi$
$761$	−24.6786	−0.894599	−0.447299	+	0.894384i	$0.647614\pi$
$762$	2.92154	0.105836
$763$	6.08383	0.220250
$764$	−4.91185	−0.177705
$765$	4.04892	0.146389
$766$	7.76809	0.280672
$767$	7.38106	0.266515
$768$	1.00000	0.0360844
$769$	−26.2403	−0.946249	−0.473124	−	0.880996i	$-0.656874\pi$
$769$	−26.2403	−0.946249	−0.473124	+	0.880996i	$0.656874\pi$
$770$	1.00000	0.0360375
$771$	15.8146	0.569549
$772$	0.454731	0.0163661
$773$	17.0774	0.614231	0.307116	−	0.951672i	$-0.400636\pi$
$773$	17.0774	0.614231	0.307116	+	0.951672i	$0.400636\pi$
$774$	−3.26875	−0.117493
$775$	−16.6668	−0.598689
$776$	1.46681	0.0526555
$777$	0.198062	0.00710544
$778$	9.89440	0.354731
$779$	−41.4239	−1.48416
$780$	2.03385	0.0728236
$781$	2.45473	0.0878372
$782$	16.1075	0.576004
$783$	0.740939	0.0264790
$784$	−6.58642	−0.235229
$785$	−6.82371	−0.243549
$786$	10.6963	0.381526
$787$	−6.21446	−0.221521	−0.110761	−	0.993847i	$-0.535329\pi$
$787$	−6.21446	−0.221521	−0.110761	+	0.993847i	$0.535329\pi$
$788$	8.90648	0.317280
$789$	16.5754	0.590100
$790$	16.3515	0.581761
$791$	−5.16852	−0.183771
$792$	1.00000	0.0355335
$793$	−1.30798	−0.0464477
$794$	−7.90648	−0.280590
$795$	18.9909	0.673538
$796$	−16.1414	−0.572116
$797$	−12.6464	−0.447957	−0.223978	−	0.974594i	$-0.571904\pi$
$797$	−12.6464	−0.447957	−0.223978	+	0.974594i	$0.571904\pi$
$798$	5.00969	0.177341
$799$	2.76271	0.0977376
$800$	−2.58211	−0.0912912
$801$	−9.69633	−0.342603
$802$	11.5060	0.406292
$803$	−1.25906	−0.0444313
$804$	4.63102	0.163324
$805$	−6.18598	−0.218027
$806$	−8.44265	−0.297380
$807$	11.4504	0.403074
$808$	10.2446	0.360403
$809$	21.0616	0.740486	0.370243	−	0.928935i	$-0.379274\pi$
$809$	21.0616	0.740486	0.370243	+	0.928935i	$0.379274\pi$
$810$	−1.55496	−0.0546357
$811$	−18.8629	−0.662367	−0.331184	−	0.943566i	$-0.607448\pi$
$811$	−18.8629	−0.662367	−0.331184	+	0.943566i	$0.607448\pi$
$812$	−0.476501	−0.0167219
$813$	−26.6558	−0.934859
$814$	−0.307979	−0.0107946
$815$	7.24996	0.253955
$816$	−2.60388	−0.0911539
$817$	25.4631	0.890841
$818$	13.5319	0.473130
$819$	0.841166	0.0293927
$820$	−8.26875	−0.288757
$821$	−24.1400	−0.842493	−0.421247	−	0.906946i	$-0.638407\pi$
$821$	−24.1400	−0.842493	−0.421247	+	0.906946i	$0.638407\pi$
$822$	−6.65817	−0.232230
$823$	20.5864	0.717597	0.358799	−	0.933415i	$-0.383186\pi$
$823$	20.5864	0.717597	0.358799	+	0.933415i	$0.383186\pi$
$824$	2.22521	0.0775188
$825$	−2.58211	−0.0898974
$826$	3.62910	0.126273
$827$	51.7972	1.80116	0.900582	−	0.434687i	$-0.143141\pi$
$827$	51.7972	1.80116	0.900582	+	0.434687i	$0.143141\pi$
$828$	−6.18598	−0.214978
$829$	−1.69143	−0.0587458	−0.0293729	−	0.999569i	$-0.509351\pi$
$829$	−1.69143	−0.0587458	−0.0293729	+	0.999569i	$0.509351\pi$
$830$	6.67158	0.231574
$831$	11.8756	0.411960
$832$	−1.30798	−0.0453460
$833$	17.1502	0.594220
$834$	3.50365	0.121321
$835$	31.5827	1.09296
$836$	−7.78986	−0.269418
$837$	6.45473	0.223108
$838$	−39.6122	−1.36838
$839$	−1.98062	−0.0683787	−0.0341893	−	0.999415i	$-0.510885\pi$
$839$	−1.98062	−0.0683787	−0.0341893	+	0.999415i	$0.510885\pi$
$840$	1.00000	0.0345033
$841$	−28.4510	−0.981069
$842$	−5.15452	−0.177637
$843$	−16.5405	−0.569685
$844$	−0.493959	−0.0170028
$845$	17.5542	0.603884
$846$	−1.06100	−0.0364779
$847$	−0.643104	−0.0220973
$848$	−12.2131	−0.419401
$849$	13.3123	0.456877
$850$	6.72348	0.230613
$851$	1.90515	0.0653077
$852$	2.45473	0.0840977
$853$	18.0291	0.617303	0.308652	−	0.951175i	$-0.400122\pi$
$853$	18.0291	0.617303	0.308652	+	0.951175i	$0.400122\pi$
$854$	−0.643104	−0.0220066
$855$	12.1129	0.414252
$856$	7.30798	0.249782
$857$	0.542877	0.0185443	0.00927215	−	0.999957i	$-0.497049\pi$
$857$	0.542877	0.0185443	0.00927215	+	0.999957i	$0.497049\pi$
$858$	−1.30798	−0.0446537
$859$	−30.7356	−1.04868	−0.524342	−	0.851508i	$-0.675689\pi$
$859$	−30.7356	−1.04868	−0.524342	+	0.851508i	$0.675689\pi$
$860$	5.08277	0.173321
$861$	−3.41981	−0.116547
$862$	5.10859	0.173999
$863$	3.69633	0.125825	0.0629123	−	0.998019i	$-0.479961\pi$
$863$	3.69633	0.125825	0.0629123	+	0.998019i	$0.479961\pi$
$864$	1.00000	0.0340207
$865$	−17.9336	−0.609762
$866$	−39.1038	−1.32880
$867$	−10.2198	−0.347084
$868$	−4.15106	−0.140896
$869$	−10.5157	−0.356722
$870$	−1.15213	−0.0390608
$871$	−6.05728	−0.205243
$872$	−9.46011	−0.320360
$873$	1.46681	0.0496441
$874$	48.1879	1.62998
$875$	−7.58211	−0.256322
$876$	−1.25906	−0.0425397
$877$	−28.2833	−0.955061	−0.477530	−	0.878615i	$-0.658468\pi$
$877$	−28.2833	−0.955061	−0.477530	+	0.878615i	$0.658468\pi$
$878$	−15.2731	−0.515441
$879$	−15.3773	−0.518665
$880$	−1.55496	−0.0524176
$881$	−18.0054	−0.606617	−0.303308	−	0.952892i	$-0.598091\pi$
$881$	−18.0054	−0.606617	−0.303308	+	0.952892i	$0.598091\pi$
$882$	−6.58642	−0.221776
$883$	35.1497	1.18288	0.591441	−	0.806348i	$-0.298559\pi$
$883$	35.1497	1.18288	0.591441	+	0.806348i	$0.298559\pi$
$884$	3.40581	0.114550
$885$	8.77479	0.294961
$886$	−20.2000	−0.678632
$887$	−12.8635	−0.431915	−0.215957	−	0.976403i	$-0.569287\pi$
$887$	−12.8635	−0.431915	−0.215957	+	0.976403i	$0.569287\pi$
$888$	−0.307979	−0.0103351
$889$	−1.87886	−0.0630148
$890$	15.0774	0.505395
$891$	1.00000	0.0335013
$892$	−26.3545	−0.882414
$893$	8.26503	0.276579
$894$	−13.6896	−0.457850
$895$	1.92394	0.0643101
$896$	−0.643104	−0.0214846
$897$	8.09113	0.270155
$898$	27.5327	0.918779
$899$	4.78256	0.159507
$900$	−2.58211	−0.0860702
$901$	31.8015	1.05946
$902$	5.31767	0.177059
$903$	2.10215	0.0699551
$904$	8.03684	0.267301
$905$	17.7205	0.589049
$906$	3.34050	0.110981
$907$	21.7864	0.723405	0.361703	−	0.932293i	$-0.382196\pi$
$907$	21.7864	0.723405	0.361703	+	0.932293i	$0.382196\pi$
$908$	12.4668	0.413726
$909$	10.2446	0.339791
$910$	−1.30798	−0.0433591
$911$	−19.8653	−0.658168	−0.329084	−	0.944301i	$-0.606740\pi$
$911$	−19.8653	−0.658168	−0.329084	+	0.944301i	$0.606740\pi$
$912$	−7.78986	−0.257948
$913$	−4.29052	−0.141995
$914$	−15.1879	−0.502371
$915$	−1.55496	−0.0514053
$916$	−20.3032	−0.670836
$917$	−6.87886	−0.227160
$918$	−2.60388	−0.0859407
$919$	0.334061	0.0110196	0.00550982	−	0.999985i	$-0.498246\pi$
$919$	0.334061	0.0110196	0.00550982	+	0.999985i	$0.498246\pi$
$920$	9.61894	0.317127
$921$	19.0084	0.626347
$922$	−20.4892	−0.674775
$923$	−3.21073	−0.105683
$924$	−0.643104	−0.0211566
$925$	0.795233	0.0261471
$926$	0.868313	0.0285346
$927$	2.22521	0.0730855
$928$	0.740939	0.0243225
$929$	23.9422	0.785520	0.392760	−	0.919641i	$-0.371520\pi$
$929$	23.9422	0.785520	0.392760	+	0.919641i	$0.371520\pi$
$930$	−10.0368	−0.329121
$931$	51.3072	1.68153
$932$	12.8901	0.422229
$933$	−26.4252	−0.865122
$934$	8.49289	0.277896
$935$	4.04892	0.132414
$936$	−1.30798	−0.0427526
$937$	−46.1992	−1.50926	−0.754632	−	0.656149i	$-0.772184\pi$
$937$	−46.1992	−1.50926	−0.754632	+	0.656149i	$0.772184\pi$
$938$	−2.97823	−0.0972426
$939$	5.33944	0.174246
$940$	1.64981	0.0538108
$941$	−20.8345	−0.679184	−0.339592	−	0.940573i	$-0.610289\pi$
$941$	−20.8345	−0.679184	−0.339592	+	0.940573i	$0.610289\pi$
$942$	4.38835	0.142980
$943$	−32.8950	−1.07121
$944$	−5.64310	−0.183667
$945$	1.00000	0.0325300
$946$	−3.26875	−0.106276
$947$	−44.1450	−1.43452	−0.717259	−	0.696807i	$-0.754604\pi$
$947$	−44.1450	−1.43452	−0.717259	+	0.696807i	$0.754604\pi$
$948$	−10.5157	−0.341535
$949$	1.64683	0.0534582
$950$	20.1142	0.652592
$951$	25.0790	0.813244
$952$	1.67456	0.0542729
$953$	0.537974	0.0174267	0.00871334	−	0.999962i	$-0.497226\pi$
$953$	0.537974	0.0174267	0.00871334	+	0.999962i	$0.497226\pi$
$954$	−12.2131	−0.395415
$955$	7.63773	0.247151
$956$	26.3230	0.851348
$957$	0.740939	0.0239512
$958$	−7.68904	−0.248422
$959$	4.28190	0.138270
$960$	−1.55496	−0.0501861
$961$	10.6635	0.343985
$962$	0.402829	0.0129877
$963$	7.30798	0.235496
$964$	−4.35152	−0.140153
$965$	−0.707087	−0.0227619
$966$	3.97823	0.127997
$967$	−6.12020	−0.196812	−0.0984061	−	0.995146i	$-0.531374\pi$
$967$	−6.12020	−0.196812	−0.0984061	+	0.995146i	$0.531374\pi$
$968$	1.00000	0.0321412
$969$	20.2838	0.651610
$970$	−2.28083	−0.0732331
$971$	34.3327	1.10179	0.550895	−	0.834575i	$-0.314287\pi$
$971$	34.3327	1.10179	0.550895	+	0.834575i	$0.314287\pi$
$972$	1.00000	0.0320750
$973$	−2.25321	−0.0722346
$974$	15.4896	0.496320
$975$	3.37734	0.108161
$976$	1.00000	0.0320092
$977$	−26.1118	−0.835392	−0.417696	−	0.908587i	$-0.637162\pi$
$977$	−26.1118	−0.835392	−0.417696	+	0.908587i	$0.637162\pi$
$978$	−4.66248	−0.149090
$979$	−9.69633	−0.309896
$980$	10.2416	0.327156
$981$	−9.46011	−0.302038
$982$	−4.67696	−0.149248
$983$	−7.29722	−0.232745	−0.116373	−	0.993206i	$-0.537127\pi$
$983$	−7.29722	−0.232745	−0.116373	+	0.993206i	$0.537127\pi$
$984$	5.31767	0.169521
$985$	−13.8492	−0.441272
$986$	−1.92931	−0.0614418
$987$	0.682333	0.0217189
$988$	10.1890	0.324154
$989$	20.2204	0.642972
$990$	−1.55496	−0.0494198
$991$	−58.7803	−1.86722	−0.933609	−	0.358294i	$-0.883358\pi$
$991$	−58.7803	−1.86722	−0.933609	+	0.358294i	$0.883358\pi$
$992$	6.45473	0.204938
$993$	−15.4969	−0.491781
$994$	−1.57865	−0.0500717
$995$	25.0992	0.795697
$996$	−4.29052	−0.135950
$997$	−42.2107	−1.33683	−0.668414	−	0.743790i	$-0.733026\pi$
$997$	−42.2107	−1.33683	−0.668414	+	0.743790i	$0.733026\pi$
$998$	31.4687	0.996125
$999$	−0.307979	−0.00974401

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.p.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.p.1.2	✓	3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.55496 q^{5} +1.00000 q^{6} -0.643104 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.55496 q^{5} +1.00000 q^{6} -0.643104 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.55496 q^{10} +1.00000 q^{11} +1.00000 q^{12} -1.30798 q^{13} -0.643104 q^{14} -1.55496 q^{15} +1.00000 q^{16} -2.60388 q^{17} +1.00000 q^{18} -7.78986 q^{19} -1.55496 q^{20} -0.643104 q^{21} +1.00000 q^{22} -6.18598 q^{23} +1.00000 q^{24} -2.58211 q^{25} -1.30798 q^{26} +1.00000 q^{27} -0.643104 q^{28} +0.740939 q^{29} -1.55496 q^{30} +6.45473 q^{31} +1.00000 q^{32} +1.00000 q^{33} -2.60388 q^{34} +1.00000 q^{35} +1.00000 q^{36} -0.307979 q^{37} -7.78986 q^{38} -1.30798 q^{39} -1.55496 q^{40} +5.31767 q^{41} -0.643104 q^{42} -3.26875 q^{43} +1.00000 q^{44} -1.55496 q^{45} -6.18598 q^{46} -1.06100 q^{47} +1.00000 q^{48} -6.58642 q^{49} -2.58211 q^{50} -2.60388 q^{51} -1.30798 q^{52} -12.2131 q^{53} +1.00000 q^{54} -1.55496 q^{55} -0.643104 q^{56} -7.78986 q^{57} +0.740939 q^{58} -5.64310 q^{59} -1.55496 q^{60} +1.00000 q^{61} +6.45473 q^{62} -0.643104 q^{63} +1.00000 q^{64} +2.03385 q^{65} +1.00000 q^{66} +4.63102 q^{67} -2.60388 q^{68} -6.18598 q^{69} +1.00000 q^{70} +2.45473 q^{71} +1.00000 q^{72} -1.25906 q^{73} -0.307979 q^{74} -2.58211 q^{75} -7.78986 q^{76} -0.643104 q^{77} -1.30798 q^{78} -10.5157 q^{79} -1.55496 q^{80} +1.00000 q^{81} +5.31767 q^{82} -4.29052 q^{83} -0.643104 q^{84} +4.04892 q^{85} -3.26875 q^{86} +0.740939 q^{87} +1.00000 q^{88} -9.69633 q^{89} -1.55496 q^{90} +0.841166 q^{91} -6.18598 q^{92} +6.45473 q^{93} -1.06100 q^{94} +12.1129 q^{95} +1.00000 q^{96} +1.46681 q^{97} -6.58642 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 5 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 5 q^{10} + 3 q^{11} + 3 q^{12} - 9 q^{13} - 6 q^{14} - 5 q^{15} + 3 q^{16} + q^{17} + 3 q^{18} - 5 q^{20} - 6 q^{21} + 3 q^{22} - 4 q^{23} + 3 q^{24} - 2 q^{25} - 9 q^{26} + 3 q^{27} - 6 q^{28} - 12 q^{29} - 5 q^{30} - 3 q^{31} + 3 q^{32} + 3 q^{33} + q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} - 9 q^{39} - 5 q^{40} - q^{41} - 6 q^{42} - 2 q^{43} + 3 q^{44} - 5 q^{45} - 4 q^{46} - 13 q^{47} + 3 q^{48} + 5 q^{49} - 2 q^{50} + q^{51} - 9 q^{52} - 16 q^{53} + 3 q^{54} - 5 q^{55} - 6 q^{56} - 12 q^{58} - 21 q^{59} - 5 q^{60} + 3 q^{61} - 3 q^{62} - 6 q^{63} + 3 q^{64} + 22 q^{65} + 3 q^{66} - q^{67} + q^{68} - 4 q^{69} + 3 q^{70} - 15 q^{71} + 3 q^{72} - 18 q^{73} - 6 q^{74} - 2 q^{75} - 6 q^{77} - 9 q^{78} - 19 q^{79} - 5 q^{80} + 3 q^{81} - q^{82} - 2 q^{83} - 6 q^{84} + 3 q^{85} - 2 q^{86} - 12 q^{87} + 3 q^{88} - 5 q^{89} - 5 q^{90} + 11 q^{91} - 4 q^{92} - 3 q^{93} - 13 q^{94} - 7 q^{95} + 3 q^{96} + q^{97} + 5 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 5 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 5 * q^10 + 3 * q^11 + 3 * q^12 - 9 * q^13 - 6 * q^14 - 5 * q^15 + 3 * q^16 + q^17 + 3 * q^18 - 5 * q^20 - 6 * q^21 + 3 * q^22 - 4 * q^23 + 3 * q^24 - 2 * q^25 - 9 * q^26 + 3 * q^27 - 6 * q^28 - 12 * q^29 - 5 * q^30 - 3 * q^31 + 3 * q^32 + 3 * q^33 + q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 - 9 * q^39 - 5 * q^40 - q^41 - 6 * q^42 - 2 * q^43 + 3 * q^44 - 5 * q^45 - 4 * q^46 - 13 * q^47 + 3 * q^48 + 5 * q^49 - 2 * q^50 + q^51 - 9 * q^52 - 16 * q^53 + 3 * q^54 - 5 * q^55 - 6 * q^56 - 12 * q^58 - 21 * q^59 - 5 * q^60 + 3 * q^61 - 3 * q^62 - 6 * q^63 + 3 * q^64 + 22 * q^65 + 3 * q^66 - q^67 + q^68 - 4 * q^69 + 3 * q^70 - 15 * q^71 + 3 * q^72 - 18 * q^73 - 6 * q^74 - 2 * q^75 - 6 * q^77 - 9 * q^78 - 19 * q^79 - 5 * q^80 + 3 * q^81 - q^82 - 2 * q^83 - 6 * q^84 + 3 * q^85 - 2 * q^86 - 12 * q^87 + 3 * q^88 - 5 * q^89 - 5 * q^90 + 11 * q^91 - 4 * q^92 - 3 * q^93 - 13 * q^94 - 7 * q^95 + 3 * q^96 + q^97 + 5 * q^98 + 3 * q^99

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