LMFDB - Embedded newform 4029.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.67513 q^{2} -1.00000 q^{3} +0.806063 q^{4} -3.48119 q^{5} -1.67513 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.67513 q^{2} -1.00000 q^{3} +0.806063 q^{4} -3.48119 q^{5} -1.67513 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} -5.83146 q^{10} +1.61213 q^{11} -0.806063 q^{12} +3.19394 q^{13} +1.67513 q^{14} +3.48119 q^{15} -4.96239 q^{16} +1.00000 q^{17} +1.67513 q^{18} -0.193937 q^{19} -2.80606 q^{20} -1.00000 q^{21} +2.70052 q^{22} +5.63752 q^{23} +2.00000 q^{24} +7.11871 q^{25} +5.35026 q^{26} -1.00000 q^{27} +0.806063 q^{28} +1.61213 q^{29} +5.83146 q^{30} -5.61213 q^{31} -4.31265 q^{32} -1.61213 q^{33} +1.67513 q^{34} -3.48119 q^{35} +0.806063 q^{36} -9.96239 q^{37} -0.324869 q^{38} -3.19394 q^{39} +6.96239 q^{40} -1.22425 q^{41} -1.67513 q^{42} +7.73813 q^{43} +1.29948 q^{44} -3.48119 q^{45} +9.44358 q^{46} +4.67513 q^{47} +4.96239 q^{48} -6.00000 q^{49} +11.9248 q^{50} -1.00000 q^{51} +2.57452 q^{52} -10.1065 q^{53} -1.67513 q^{54} -5.61213 q^{55} -2.00000 q^{56} +0.193937 q^{57} +2.70052 q^{58} -2.28726 q^{59} +2.80606 q^{60} +1.31265 q^{61} -9.40105 q^{62} +1.00000 q^{63} +2.70052 q^{64} -11.1187 q^{65} -2.70052 q^{66} -6.93207 q^{67} +0.806063 q^{68} -5.63752 q^{69} -5.83146 q^{70} -0.712742 q^{71} -2.00000 q^{72} -9.83146 q^{73} -16.6883 q^{74} -7.11871 q^{75} -0.156325 q^{76} +1.61213 q^{77} -5.35026 q^{78} +1.00000 q^{79} +17.2750 q^{80} +1.00000 q^{81} -2.05079 q^{82} -0.249646 q^{83} -0.806063 q^{84} -3.48119 q^{85} +12.9624 q^{86} -1.61213 q^{87} -3.22425 q^{88} +5.08840 q^{89} -5.83146 q^{90} +3.19394 q^{91} +4.54420 q^{92} +5.61213 q^{93} +7.83146 q^{94} +0.675131 q^{95} +4.31265 q^{96} -2.86907 q^{97} -10.0508 q^{98} +1.61213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9	$ 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 10 q^{13} + 5 q^{15} - 4 q^{16} + 3 q^{17} - q^{19} - 8 q^{20} - 3 q^{21} - 12 q^{22} + q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 2 q^{28} + 4 q^{29} + 2 q^{30} - 16 q^{31} + 8 q^{32} - 4 q^{33} - 5 q^{35} + 2 q^{36} - 19 q^{37} - 6 q^{38} - 10 q^{39} + 10 q^{40} - 2 q^{41} + 14 q^{43} + 24 q^{44} - 5 q^{45} + 12 q^{46} + 9 q^{47} + 4 q^{48} - 18 q^{49} + 14 q^{50} - 3 q^{51} - 4 q^{52} + 17 q^{53} - 16 q^{55} - 6 q^{56} + q^{57} - 12 q^{58} - q^{59} + 8 q^{60} - 17 q^{61} + 12 q^{62} + 3 q^{63} - 12 q^{64} - 12 q^{65} + 12 q^{66} - 12 q^{67} + 2 q^{68} - q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} - 14 q^{73} - 4 q^{74} + 10 q^{76} + 4 q^{77} - 6 q^{78} + 3 q^{79} + 20 q^{80} + 3 q^{81} + 24 q^{82} + 16 q^{83} - 2 q^{84} - 5 q^{85} + 28 q^{86} - 4 q^{87} - 8 q^{88} - 4 q^{89} - 2 q^{90} + 10 q^{91} + 4 q^{92} + 16 q^{93} + 8 q^{94} - 3 q^{95} - 8 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 10 * q^13 + 5 * q^15 - 4 * q^16 + 3 * q^17 - q^19 - 8 * q^20 - 3 * q^21 - 12 * q^22 + q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 2 * q^28 + 4 * q^29 + 2 * q^30 - 16 * q^31 + 8 * q^32 - 4 * q^33 - 5 * q^35 + 2 * q^36 - 19 * q^37 - 6 * q^38 - 10 * q^39 + 10 * q^40 - 2 * q^41 + 14 * q^43 + 24 * q^44 - 5 * q^45 + 12 * q^46 + 9 * q^47 + 4 * q^48 - 18 * q^49 + 14 * q^50 - 3 * q^51 - 4 * q^52 + 17 * q^53 - 16 * q^55 - 6 * q^56 + q^57 - 12 * q^58 - q^59 + 8 * q^60 - 17 * q^61 + 12 * q^62 + 3 * q^63 - 12 * q^64 - 12 * q^65 + 12 * q^66 - 12 * q^67 + 2 * q^68 - q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 - 14 * q^73 - 4 * q^74 + 10 * q^76 + 4 * q^77 - 6 * q^78 + 3 * q^79 + 20 * q^80 + 3 * q^81 + 24 * q^82 + 16 * q^83 - 2 * q^84 - 5 * q^85 + 28 * q^86 - 4 * q^87 - 8 * q^88 - 4 * q^89 - 2 * q^90 + 10 * q^91 + 4 * q^92 + 16 * q^93 + 8 * q^94 - 3 * q^95 - 8 * q^96 - 4 * q^97 + 4 * 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 $

$2$	1.67513	1.18450	0.592248	−	0.805756i	$-0.298240\pi$
$2$	1.67513	1.18450	0.592248	+	0.805756i	$0.298240\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.806063	0.403032
$5$	−3.48119	−1.55684	−0.778419	−	0.627745i	$-0.783978\pi$
$5$	−3.48119	−1.55684	−0.778419	+	0.627745i	$0.783978\pi$
$6$	−1.67513	−0.683869
$7$	1.00000	0.377964	0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000	0.377964	0.188982	+	0.981981i	$0.439481\pi$
$8$	−2.00000	−0.707107
$9$	1.00000	0.333333
$10$	−5.83146	−1.84407
$11$	1.61213	0.486075	0.243037	−	0.970017i	$-0.421856\pi$
$11$	1.61213	0.486075	0.243037	+	0.970017i	$0.421856\pi$
$12$	−0.806063	−0.232690
$13$	3.19394	0.885839	0.442919	−	0.896561i	$-0.353943\pi$
$13$	3.19394	0.885839	0.442919	+	0.896561i	$0.353943\pi$
$14$	1.67513	0.447698
$15$	3.48119	0.898841
$16$	−4.96239	−1.24060
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.67513	0.394832
$19$	−0.193937	−0.0444921	−0.0222460	−	0.999753i	$-0.507082\pi$
$19$	−0.193937	−0.0444921	−0.0222460	+	0.999753i	$0.507082\pi$
$20$	−2.80606	−0.627455
$21$	−1.00000	−0.218218
$22$	2.70052	0.575754
$23$	5.63752	1.17550	0.587752	−	0.809041i	$-0.300013\pi$
$23$	5.63752	1.17550	0.587752	+	0.809041i	$0.300013\pi$
$24$	2.00000	0.408248
$25$	7.11871	1.42374
$26$	5.35026	1.04927
$27$	−1.00000	−0.192450
$28$	0.806063	0.152332
$29$	1.61213	0.299364	0.149682	−	0.988734i	$-0.452175\pi$
$29$	1.61213	0.299364	0.149682	+	0.988734i	$0.452175\pi$
$30$	5.83146	1.06467
$31$	−5.61213	−1.00797	−0.503984	−	0.863713i	$-0.668133\pi$
$31$	−5.61213	−1.00797	−0.503984	+	0.863713i	$0.668133\pi$
$32$	−4.31265	−0.762376
$33$	−1.61213	−0.280635
$34$	1.67513	0.287283
$35$	−3.48119	−0.588429
$36$	0.806063	0.134344
$37$	−9.96239	−1.63781	−0.818903	−	0.573932i	$-0.805418\pi$
$37$	−9.96239	−1.63781	−0.818903	+	0.573932i	$0.805418\pi$
$38$	−0.324869	−0.0527007
$39$	−3.19394	−0.511439
$40$	6.96239	1.10085
$41$	−1.22425	−0.191196	−0.0955982	−	0.995420i	$-0.530476\pi$
$41$	−1.22425	−0.191196	−0.0955982	+	0.995420i	$0.530476\pi$
$42$	−1.67513	−0.258478
$43$	7.73813	1.18005	0.590027	−	0.807383i	$-0.299117\pi$
$43$	7.73813	1.18005	0.590027	+	0.807383i	$0.299117\pi$
$44$	1.29948	0.195903
$45$	−3.48119	−0.518946
$46$	9.44358	1.39238
$47$	4.67513	0.681938	0.340969	−	0.940075i	$-0.389245\pi$
$47$	4.67513	0.681938	0.340969	+	0.940075i	$0.389245\pi$
$48$	4.96239	0.716259
$49$	−6.00000	−0.857143
$50$	11.9248	1.68642
$51$	−1.00000	−0.140028
$52$	2.57452	0.357021
$53$	−10.1065	−1.38823	−0.694117	−	0.719862i	$-0.744205\pi$
$53$	−10.1065	−1.38823	−0.694117	+	0.719862i	$0.744205\pi$
$54$	−1.67513	−0.227956
$55$	−5.61213	−0.756739
$56$	−2.00000	−0.267261
$57$	0.193937	0.0256875
$58$	2.70052	0.354596
$59$	−2.28726	−0.297776	−0.148888	−	0.988854i	$-0.547569\pi$
$59$	−2.28726	−0.297776	−0.148888	+	0.988854i	$0.547569\pi$
$60$	2.80606	0.362261
$61$	1.31265	0.168068	0.0840338	−	0.996463i	$-0.473220\pi$
$61$	1.31265	0.168068	0.0840338	+	0.996463i	$0.473220\pi$
$62$	−9.40105	−1.19393
$63$	1.00000	0.125988
$64$	2.70052	0.337565
$65$	−11.1187	−1.37911
$66$	−2.70052	−0.332411
$67$	−6.93207	−0.846887	−0.423444	−	0.905922i	$-0.639179\pi$
$67$	−6.93207	−0.846887	−0.423444	+	0.905922i	$0.639179\pi$
$68$	0.806063	0.0977495
$69$	−5.63752	−0.678678
$70$	−5.83146	−0.696992
$71$	−0.712742	−0.0845869	−0.0422935	−	0.999105i	$-0.513466\pi$
$71$	−0.712742	−0.0845869	−0.0422935	+	0.999105i	$0.513466\pi$
$72$	−2.00000	−0.235702
$73$	−9.83146	−1.15068	−0.575342	−	0.817913i	$-0.695131\pi$
$73$	−9.83146	−1.15068	−0.575342	+	0.817913i	$0.695131\pi$
$74$	−16.6883	−1.93998
$75$	−7.11871	−0.821998
$76$	−0.156325	−0.0179317
$77$	1.61213	0.183719
$78$	−5.35026	−0.605798
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	17.2750	1.93141
$81$	1.00000	0.111111
$82$	−2.05079	−0.226471
$83$	−0.249646	−0.0274022	−0.0137011	−	0.999906i	$-0.504361\pi$
$83$	−0.249646	−0.0274022	−0.0137011	+	0.999906i	$0.504361\pi$
$84$	−0.806063	−0.0879487
$85$	−3.48119	−0.377589
$86$	12.9624	1.39777
$87$	−1.61213	−0.172838
$88$	−3.22425	−0.343707
$89$	5.08840	0.539369	0.269684	−	0.962949i	$-0.413081\pi$
$89$	5.08840	0.539369	0.269684	+	0.962949i	$0.413081\pi$
$90$	−5.83146	−0.614689
$91$	3.19394	0.334816
$92$	4.54420	0.473765
$93$	5.61213	0.581950
$94$	7.83146	0.807753
$95$	0.675131	0.0692670
$96$	4.31265	0.440158
$97$	−2.86907	−0.291310	−0.145655	−	0.989335i	$-0.546529\pi$
$97$	−2.86907	−0.291310	−0.145655	+	0.989335i	$0.546529\pi$
$98$	−10.0508	−1.01528
$99$	1.61213	0.162025
$100$	5.73813	0.573813
$101$	−0.324869	−0.0323257	−0.0161628	−	0.999869i	$-0.505145\pi$
$101$	−0.324869	−0.0323257	−0.0161628	+	0.999869i	$0.505145\pi$
$102$	−1.67513	−0.165863
$103$	−16.8691	−1.66216	−0.831079	−	0.556154i	$-0.812276\pi$
$103$	−16.8691	−1.66216	−0.831079	+	0.556154i	$0.812276\pi$
$104$	−6.38787	−0.626382
$105$	3.48119	0.339730
$106$	−16.9297	−1.64436
$107$	−14.0630	−1.35952	−0.679761	−	0.733434i	$-0.737916\pi$
$107$	−14.0630	−1.35952	−0.679761	+	0.733434i	$0.737916\pi$
$108$	−0.806063	−0.0775635
$109$	−17.7440	−1.69957	−0.849784	−	0.527131i	$-0.823268\pi$
$109$	−17.7440	−1.69957	−0.849784	+	0.527131i	$0.823268\pi$
$110$	−9.40105	−0.896355
$111$	9.96239	0.945588
$112$	−4.96239	−0.468902
$113$	1.92478	0.181068	0.0905339	−	0.995893i	$-0.471143\pi$
$113$	1.92478	0.181068	0.0905339	+	0.995893i	$0.471143\pi$
$114$	0.324869	0.0304268
$115$	−19.6253	−1.83007
$116$	1.29948	0.120653
$117$	3.19394	0.295280
$118$	−3.83146	−0.352714
$119$	1.00000	0.0916698
$120$	−6.96239	−0.635576
$121$	−8.40105	−0.763732
$122$	2.19886	0.199076
$123$	1.22425	0.110387
$124$	−4.52373	−0.406243
$125$	−7.37565	−0.659699
$126$	1.67513	0.149233
$127$	5.31757	0.471858	0.235929	−	0.971770i	$-0.424187\pi$
$127$	5.31757	0.471858	0.235929	+	0.971770i	$0.424187\pi$
$128$	13.1490	1.16222
$129$	−7.73813	−0.681305
$130$	−18.6253	−1.63355
$131$	−17.4060	−1.52077	−0.760383	−	0.649474i	$-0.774989\pi$
$131$	−17.4060	−1.52077	−0.760383	+	0.649474i	$0.774989\pi$
$132$	−1.29948	−0.113105
$133$	−0.193937	−0.0168164
$134$	−11.6121	−1.00313
$135$	3.48119	0.299614
$136$	−2.00000	−0.171499
$137$	6.21203	0.530730	0.265365	−	0.964148i	$-0.414508\pi$
$137$	6.21203	0.530730	0.265365	+	0.964148i	$0.414508\pi$
$138$	−9.44358	−0.803891
$139$	0.730841	0.0619891	0.0309945	−	0.999520i	$-0.490133\pi$
$139$	0.730841	0.0619891	0.0309945	+	0.999520i	$0.490133\pi$
$140$	−2.80606	−0.237156
$141$	−4.67513	−0.393717
$142$	−1.19394	−0.100193
$143$	5.14903	0.430584
$144$	−4.96239	−0.413532
$145$	−5.61213	−0.466062
$146$	−16.4690	−1.36298
$147$	6.00000	0.494872
$148$	−8.03032	−0.660088
$149$	3.76353	0.308320	0.154160	−	0.988046i	$-0.450733\pi$
$149$	3.76353	0.308320	0.154160	+	0.988046i	$0.450733\pi$
$150$	−11.9248	−0.973654
$151$	11.1114	0.904234	0.452117	−	0.891959i	$-0.350669\pi$
$151$	11.1114	0.904234	0.452117	+	0.891959i	$0.350669\pi$
$152$	0.387873	0.0314607
$153$	1.00000	0.0808452
$154$	2.70052	0.217614
$155$	19.5369	1.56924
$156$	−2.57452	−0.206126
$157$	−6.48119	−0.517256	−0.258628	−	0.965977i	$-0.583270\pi$
$157$	−6.48119	−0.517256	−0.258628	+	0.965977i	$0.583270\pi$
$158$	1.67513	0.133266
$159$	10.1065	0.801497
$160$	15.0132	1.18690
$161$	5.63752	0.444299
$162$	1.67513	0.131611
$163$	−6.29455	−0.493027	−0.246514	−	0.969139i	$-0.579285\pi$
$163$	−6.29455	−0.493027	−0.246514	+	0.969139i	$0.579285\pi$
$164$	−0.986826	−0.0770582
$165$	5.61213	0.436903
$166$	−0.418190	−0.0324579
$167$	−9.71862	−0.752050	−0.376025	−	0.926610i	$-0.622709\pi$
$167$	−9.71862	−0.752050	−0.376025	+	0.926610i	$0.622709\pi$
$168$	2.00000	0.154303
$169$	−2.79877	−0.215290
$170$	−5.83146	−0.447252
$171$	−0.193937	−0.0148307
$172$	6.23743	0.475599
$173$	13.9126	1.05775	0.528876	−	0.848699i	$-0.322614\pi$
$173$	13.9126	1.05775	0.528876	+	0.848699i	$0.322614\pi$
$174$	−2.70052	−0.204726
$175$	7.11871	0.538124
$176$	−8.00000	−0.603023
$177$	2.28726	0.171921
$178$	8.52373	0.638881
$179$	−3.02539	−0.226128	−0.113064	−	0.993588i	$-0.536067\pi$
$179$	−3.02539	−0.226128	−0.113064	+	0.993588i	$0.536067\pi$
$180$	−2.80606	−0.209152
$181$	−12.7431	−0.947184	−0.473592	−	0.880744i	$-0.657043\pi$
$181$	−12.7431	−0.947184	−0.473592	+	0.880744i	$0.657043\pi$
$182$	5.35026	0.396588
$183$	−1.31265	−0.0970339
$184$	−11.2750	−0.831207
$185$	34.6810	2.54980
$186$	9.40105	0.689318
$187$	1.61213	0.117890
$188$	3.76845	0.274843
$189$	−1.00000	−0.0727393
$190$	1.13093	0.0820465
$191$	8.41327	0.608763	0.304381	−	0.952550i	$-0.401550\pi$
$191$	8.41327	0.608763	0.304381	+	0.952550i	$0.401550\pi$
$192$	−2.70052	−0.194893
$193$	16.0943	1.15849	0.579246	−	0.815153i	$-0.303347\pi$
$193$	16.0943	1.15849	0.579246	+	0.815153i	$0.303347\pi$
$194$	−4.80606	−0.345055
$195$	11.1187	0.796228
$196$	−4.83638	−0.345456
$197$	7.41090	0.528004	0.264002	−	0.964522i	$-0.414957\pi$
$197$	7.41090	0.528004	0.264002	+	0.964522i	$0.414957\pi$
$198$	2.70052	0.191918
$199$	−10.5672	−0.749090	−0.374545	−	0.927209i	$-0.622201\pi$
$199$	−10.5672	−0.749090	−0.374545	+	0.927209i	$0.622201\pi$
$200$	−14.2374	−1.00674
$201$	6.93207	0.488951
$202$	−0.544198	−0.0382897
$203$	1.61213	0.113149
$204$	−0.806063	−0.0564357
$205$	4.26187	0.297662
$206$	−28.2579	−1.96882
$207$	5.63752	0.391835
$208$	−15.8496	−1.09897
$209$	−0.312650	−0.0216265
$210$	5.83146	0.402409
$211$	6.95509	0.478808	0.239404	−	0.970920i	$-0.423048\pi$
$211$	6.95509	0.478808	0.239404	+	0.970920i	$0.423048\pi$
$212$	−8.14648	−0.559502
$213$	0.712742	0.0488363
$214$	−23.5574	−1.61035
$215$	−26.9380	−1.83715
$216$	2.00000	0.136083
$217$	−5.61213	−0.380976
$218$	−29.7235	−2.01313
$219$	9.83146	0.664348
$220$	−4.52373	−0.304990
$221$	3.19394	0.214847
$222$	16.6883	1.12005
$223$	−4.61213	−0.308851	−0.154425	−	0.988004i	$-0.549353\pi$
$223$	−4.61213	−0.308851	−0.154425	+	0.988004i	$0.549353\pi$
$224$	−4.31265	−0.288151
$225$	7.11871	0.474581
$226$	3.22425	0.214474
$227$	0.186642	0.0123879	0.00619394	−	0.999981i	$-0.498028\pi$
$227$	0.186642	0.0123879	0.00619394	+	0.999981i	$0.498028\pi$
$228$	0.156325	0.0103529
$229$	−22.7186	−1.50129	−0.750644	−	0.660706i	$-0.770257\pi$
$229$	−22.7186	−1.50129	−0.750644	+	0.660706i	$0.770257\pi$
$230$	−32.8749	−2.16771
$231$	−1.61213	−0.106070
$232$	−3.22425	−0.211683
$233$	−25.7767	−1.68869	−0.844344	−	0.535802i	$-0.820010\pi$
$233$	−25.7767	−1.68869	−0.844344	+	0.535802i	$0.820010\pi$
$234$	5.35026	0.349758
$235$	−16.2750	−1.06167
$236$	−1.84367	−0.120013
$237$	−1.00000	−0.0649570
$238$	1.67513	0.108583
$239$	26.0992	1.68822	0.844108	−	0.536172i	$-0.180130\pi$
$239$	26.0992	1.68822	0.844108	+	0.536172i	$0.180130\pi$
$240$	−17.2750	−1.11510
$241$	−26.2555	−1.69127	−0.845634	−	0.533764i	$-0.820777\pi$
$241$	−26.2555	−1.69127	−0.845634	+	0.533764i	$0.820777\pi$
$242$	−14.0729	−0.904637
$243$	−1.00000	−0.0641500
$244$	1.05808	0.0677366
$245$	20.8872	1.33443
$246$	2.05079	0.130753
$247$	−0.619421	−0.0394128
$248$	11.2243	0.712741
$249$	0.249646	0.0158207
$250$	−12.3552	−0.781411
$251$	2.39280	0.151032	0.0755160	−	0.997145i	$-0.475940\pi$
$251$	2.39280	0.151032	0.0755160	+	0.997145i	$0.475940\pi$
$252$	0.806063	0.0507772
$253$	9.08840	0.571383
$254$	8.90763	0.558915
$255$	3.48119	0.218001
$256$	16.6253	1.03908
$257$	19.3503	1.20704	0.603518	−	0.797349i	$-0.293765\pi$
$257$	19.3503	1.20704	0.603518	+	0.797349i	$0.293765\pi$
$258$	−12.9624	−0.807003
$259$	−9.96239	−0.619033
$260$	−8.96239	−0.555824
$261$	1.61213	0.0997881
$262$	−29.1573	−1.80134
$263$	−15.1612	−0.934883	−0.467441	−	0.884024i	$-0.654824\pi$
$263$	−15.1612	−0.934883	−0.467441	+	0.884024i	$0.654824\pi$
$264$	3.22425	0.198439
$265$	35.1827	2.16125
$266$	−0.324869	−0.0199190
$267$	−5.08840	−0.311405
$268$	−5.58769	−0.341322
$269$	10.7513	0.655519	0.327759	−	0.944761i	$-0.393706\pi$
$269$	10.7513	0.655519	0.327759	+	0.944761i	$0.393706\pi$
$270$	5.83146	0.354891
$271$	30.9053	1.87736	0.938681	−	0.344788i	$-0.112049\pi$
$271$	30.9053	1.87736	0.938681	+	0.344788i	$0.112049\pi$
$272$	−4.96239	−0.300889
$273$	−3.19394	−0.193306
$274$	10.4060	0.628648
$275$	11.4763	0.692045
$276$	−4.54420	−0.273529
$277$	−15.3258	−0.920840	−0.460420	−	0.887701i	$-0.652301\pi$
$277$	−15.3258	−0.920840	−0.460420	+	0.887701i	$0.652301\pi$
$278$	1.22425	0.0734259
$279$	−5.61213	−0.335989
$280$	6.96239	0.416082
$281$	28.6883	1.71140	0.855700	−	0.517472i	$-0.173127\pi$
$281$	28.6883	1.71140	0.855700	+	0.517472i	$0.173127\pi$
$282$	−7.83146	−0.466356
$283$	−18.9380	−1.12574	−0.562872	−	0.826544i	$-0.690304\pi$
$283$	−18.9380	−1.12574	−0.562872	+	0.826544i	$0.690304\pi$
$284$	−0.574515	−0.0340912
$285$	−0.675131	−0.0399913
$286$	8.62530	0.510025
$287$	−1.22425	−0.0722654
$288$	−4.31265	−0.254125
$289$	1.00000	0.0588235
$290$	−9.40105	−0.552048
$291$	2.86907	0.168188
$292$	−7.92478	−0.463763
$293$	−30.1876	−1.76358	−0.881789	−	0.471644i	$-0.843661\pi$
$293$	−30.1876	−1.76358	−0.881789	+	0.471644i	$0.843661\pi$
$294$	10.0508	0.586174
$295$	7.96239	0.463588
$296$	19.9248	1.15810
$297$	−1.61213	−0.0935451
$298$	6.30440	0.365204
$299$	18.0059	1.04131
$300$	−5.73813	−0.331291
$301$	7.73813	0.446019
$302$	18.6131	1.07106
$303$	0.324869	0.0186632
$304$	0.962389	0.0551968
$305$	−4.56959	−0.261654
$306$	1.67513	0.0957609
$307$	6.34534	0.362148	0.181074	−	0.983470i	$-0.442043\pi$
$307$	6.34534	0.362148	0.181074	+	0.983470i	$0.442043\pi$
$308$	1.29948	0.0740445
$309$	16.8691	0.959648
$310$	32.7269	1.85876
$311$	−2.85097	−0.161664	−0.0808318	−	0.996728i	$-0.525758\pi$
$311$	−2.85097	−0.161664	−0.0808318	+	0.996728i	$0.525758\pi$
$312$	6.38787	0.361642
$313$	−12.9380	−0.731296	−0.365648	−	0.930753i	$-0.619153\pi$
$313$	−12.9380	−0.731296	−0.365648	+	0.930753i	$0.619153\pi$
$314$	−10.8568	−0.612687
$315$	−3.48119	−0.196143
$316$	0.806063	0.0453446
$317$	24.0459	1.35055	0.675275	−	0.737566i	$-0.264025\pi$
$317$	24.0459	1.35055	0.675275	+	0.737566i	$0.264025\pi$
$318$	16.9297	0.949371
$319$	2.59895	0.145513
$320$	−9.40105	−0.525535
$321$	14.0630	0.784920
$322$	9.44358	0.526270
$323$	−0.193937	−0.0107909
$324$	0.806063	0.0447813
$325$	22.7367	1.26121
$326$	−10.5442	−0.583989
$327$	17.7440	0.981246
$328$	2.44851	0.135196
$329$	4.67513	0.257748
$330$	9.40105	0.517511
$331$	7.94288	0.436580	0.218290	−	0.975884i	$-0.429952\pi$
$331$	7.94288	0.436580	0.218290	+	0.975884i	$0.429952\pi$
$332$	−0.201231	−0.0110440
$333$	−9.96239	−0.545936
$334$	−16.2800	−0.890800
$335$	24.1319	1.31847
$336$	4.96239	0.270720
$337$	−20.2047	−1.10062	−0.550311	−	0.834960i	$-0.685491\pi$
$337$	−20.2047	−1.10062	−0.550311	+	0.834960i	$0.685491\pi$
$338$	−4.68830	−0.255010
$339$	−1.92478	−0.104540
$340$	−2.80606	−0.152180
$341$	−9.04746	−0.489947
$342$	−0.324869	−0.0175669
$343$	−13.0000	−0.701934
$344$	−15.4763	−0.834425
$345$	19.6253	1.05659
$346$	23.3054	1.25290
$347$	−0.599908	−0.0322048	−0.0161024	−	0.999870i	$-0.505126\pi$
$347$	−0.599908	−0.0322048	−0.0161024	+	0.999870i	$0.505126\pi$
$348$	−1.29948	−0.0696593
$349$	−31.2687	−1.67378	−0.836888	−	0.547375i	$-0.815627\pi$
$349$	−31.2687	−1.67378	−0.836888	+	0.547375i	$0.815627\pi$
$350$	11.9248	0.637406
$351$	−3.19394	−0.170480
$352$	−6.95254	−0.370572
$353$	−27.9951	−1.49003	−0.745014	−	0.667049i	$-0.767557\pi$
$353$	−27.9951	−1.49003	−0.745014	+	0.667049i	$0.767557\pi$
$354$	3.83146	0.203640
$355$	2.48119	0.131688
$356$	4.10157	0.217383
$357$	−1.00000	−0.0529256
$358$	−5.06793	−0.267848
$359$	3.78304	0.199661	0.0998306	−	0.995004i	$-0.468170\pi$
$359$	3.78304	0.199661	0.0998306	+	0.995004i	$0.468170\pi$
$360$	6.96239	0.366950
$361$	−18.9624	−0.998020
$362$	−21.3463	−1.12194
$363$	8.40105	0.440941
$364$	2.57452	0.134941
$365$	34.2252	1.79143
$366$	−2.19886	−0.114936
$367$	20.6942	1.08023	0.540114	−	0.841592i	$-0.318381\pi$
$367$	20.6942	1.08023	0.540114	+	0.841592i	$0.318381\pi$
$368$	−27.9756	−1.45833
$369$	−1.22425	−0.0637321
$370$	58.0952	3.02023
$371$	−10.1065	−0.524703
$372$	4.52373	0.234544
$373$	32.3914	1.67716	0.838581	−	0.544777i	$-0.183386\pi$
$373$	32.3914	1.67716	0.838581	+	0.544777i	$0.183386\pi$
$374$	2.70052	0.139641
$375$	7.37565	0.380877
$376$	−9.35026	−0.482203
$377$	5.14903	0.265189
$378$	−1.67513	−0.0861594
$379$	1.96239	0.100801	0.0504006	−	0.998729i	$-0.483950\pi$
$379$	1.96239	0.100801	0.0504006	+	0.998729i	$0.483950\pi$
$380$	0.544198	0.0279168
$381$	−5.31757	−0.272428
$382$	14.0933	0.721077
$383$	−21.4133	−1.09417	−0.547083	−	0.837078i	$-0.684262\pi$
$383$	−21.4133	−1.09417	−0.547083	+	0.837078i	$0.684262\pi$
$384$	−13.1490	−0.671009
$385$	−5.61213	−0.286020
$386$	26.9600	1.37223
$387$	7.73813	0.393352
$388$	−2.31265	−0.117407
$389$	34.8749	1.76823	0.884115	−	0.467269i	$-0.154762\pi$
$389$	34.8749	1.76823	0.884115	+	0.467269i	$0.154762\pi$
$390$	18.6253	0.943129
$391$	5.63752	0.285102
$392$	12.0000	0.606092
$393$	17.4060	0.878015
$394$	12.4142	0.625419
$395$	−3.48119	−0.175158
$396$	1.29948	0.0653012
$397$	15.1392	0.759814	0.379907	−	0.925025i	$-0.375956\pi$
$397$	15.1392	0.759814	0.379907	+	0.925025i	$0.375956\pi$
$398$	−17.7015	−0.887295
$399$	0.193937	0.00970897
$400$	−35.3258	−1.76629
$401$	8.81431	0.440166	0.220083	−	0.975481i	$-0.429367\pi$
$401$	8.81431	0.440166	0.220083	+	0.975481i	$0.429367\pi$
$402$	11.6121	0.579160
$403$	−17.9248	−0.892897
$404$	−0.261865	−0.0130283
$405$	−3.48119	−0.172982
$406$	2.70052	0.134025
$407$	−16.0606	−0.796096
$408$	2.00000	0.0990148
$409$	13.5515	0.670078	0.335039	−	0.942204i	$-0.391250\pi$
$409$	13.5515	0.670078	0.335039	+	0.942204i	$0.391250\pi$
$410$	7.13918	0.352579
$411$	−6.21203	−0.306417
$412$	−13.5975	−0.669903
$413$	−2.28726	−0.112549
$414$	9.44358	0.464127
$415$	0.869067	0.0426608
$416$	−13.7743	−0.675342
$417$	−0.730841	−0.0357894
$418$	−0.523730	−0.0256165
$419$	−23.4739	−1.14678	−0.573388	−	0.819284i	$-0.694371\pi$
$419$	−23.4739	−1.14678	−0.573388	+	0.819284i	$0.694371\pi$
$420$	2.80606	0.136922
$421$	4.61801	0.225068	0.112534	−	0.993648i	$-0.464103\pi$
$421$	4.61801	0.225068	0.112534	+	0.993648i	$0.464103\pi$
$422$	11.6507	0.567147
$423$	4.67513	0.227313
$424$	20.2130	0.981630
$425$	7.11871	0.345308
$426$	1.19394	0.0578464
$427$	1.31265	0.0635236
$428$	−11.3357	−0.547930
$429$	−5.14903	−0.248598
$430$	−45.1246	−2.17610
$431$	−29.1646	−1.40481	−0.702404	−	0.711778i	$-0.747890\pi$
$431$	−29.1646	−1.40481	−0.702404	+	0.711778i	$0.747890\pi$
$432$	4.96239	0.238753
$433$	−23.1695	−1.11346	−0.556728	−	0.830695i	$-0.687943\pi$
$433$	−23.1695	−1.11346	−0.556728	+	0.830695i	$0.687943\pi$
$434$	−9.40105	−0.451265
$435$	5.61213	0.269081
$436$	−14.3028	−0.684980
$437$	−1.09332	−0.0523006
$438$	16.4690	0.786918
$439$	29.1817	1.39277	0.696384	−	0.717670i	$-0.254791\pi$
$439$	29.1817	1.39277	0.696384	+	0.717670i	$0.254791\pi$
$440$	11.2243	0.535095
$441$	−6.00000	−0.285714
$442$	5.35026	0.254486
$443$	23.4568	1.11446	0.557232	−	0.830357i	$-0.311863\pi$
$443$	23.4568	1.11446	0.557232	+	0.830357i	$0.311863\pi$
$444$	8.03032	0.381102
$445$	−17.7137	−0.839710
$446$	−7.72592	−0.365833
$447$	−3.76353	−0.178009
$448$	2.70052	0.127588
$449$	7.58769	0.358085	0.179043	−	0.983841i	$-0.442700\pi$
$449$	7.58769	0.358085	0.179043	+	0.983841i	$0.442700\pi$
$450$	11.9248	0.562139
$451$	−1.97365	−0.0929357
$452$	1.55149	0.0729761
$453$	−11.1114	−0.522060
$454$	0.312650	0.0146734
$455$	−11.1187	−0.521253
$456$	−0.387873	−0.0181638
$457$	21.3693	0.999614	0.499807	−	0.866137i	$-0.333404\pi$
$457$	21.3693	0.999614	0.499807	+	0.866137i	$0.333404\pi$
$458$	−38.0567	−1.77827
$459$	−1.00000	−0.0466760
$460$	−15.8192	−0.737576
$461$	−24.9829	−1.16357	−0.581784	−	0.813343i	$-0.697645\pi$
$461$	−24.9829	−1.16357	−0.581784	+	0.813343i	$0.697645\pi$
$462$	−2.70052	−0.125640
$463$	4.03269	0.187415	0.0937074	−	0.995600i	$-0.470128\pi$
$463$	4.03269	0.187415	0.0937074	+	0.995600i	$0.470128\pi$
$464$	−8.00000	−0.371391
$465$	−19.5369	−0.906002
$466$	−43.1793	−2.00024
$467$	−20.0362	−0.927165	−0.463582	−	0.886054i	$-0.653436\pi$
$467$	−20.0362	−0.927165	−0.463582	+	0.886054i	$0.653436\pi$
$468$	2.57452	0.119007
$469$	−6.93207	−0.320093
$470$	−27.2628	−1.25754
$471$	6.48119	0.298638
$472$	4.57452	0.210559
$473$	12.4749	0.573594
$474$	−1.67513	−0.0769413
$475$	−1.38058	−0.0633453
$476$	0.806063	0.0369459
$477$	−10.1065	−0.462745
$478$	43.7196	1.99969
$479$	15.9443	0.728513	0.364257	−	0.931299i	$-0.381323\pi$
$479$	15.9443	0.728513	0.364257	+	0.931299i	$0.381323\pi$
$480$	−15.0132	−0.685254
$481$	−31.8192	−1.45083
$482$	−43.9814	−2.00330
$483$	−5.63752	−0.256516
$484$	−6.77178	−0.307808
$485$	9.98778	0.453522
$486$	−1.67513	−0.0759855
$487$	−0.580855	−0.0263210	−0.0131605	−	0.999913i	$-0.504189\pi$
$487$	−0.580855	−0.0263210	−0.0131605	+	0.999913i	$0.504189\pi$
$488$	−2.62530	−0.118842
$489$	6.29455	0.284649
$490$	34.9887	1.58063
$491$	−17.6121	−0.794824	−0.397412	−	0.917640i	$-0.630092\pi$
$491$	−17.6121	−0.794824	−0.397412	+	0.917640i	$0.630092\pi$
$492$	0.986826	0.0444896
$493$	1.61213	0.0726065
$494$	−1.03761	−0.0466843
$495$	−5.61213	−0.252246
$496$	27.8496	1.25048
$497$	−0.712742	−0.0319709
$498$	0.418190	0.0187396
$499$	24.7875	1.10964	0.554821	−	0.831970i	$-0.312787\pi$
$499$	24.7875	1.10964	0.554821	+	0.831970i	$0.312787\pi$
$500$	−5.94525	−0.265879
$501$	9.71862	0.434196
$502$	4.00825	0.178897
$503$	−15.8496	−0.706697	−0.353348	−	0.935492i	$-0.614957\pi$
$503$	−15.8496	−0.706697	−0.353348	+	0.935492i	$0.614957\pi$
$504$	−2.00000	−0.0890871
$505$	1.13093	0.0503258
$506$	15.2243	0.676801
$507$	2.79877	0.124298
$508$	4.28630	0.190174
$509$	−19.0787	−0.845650	−0.422825	−	0.906211i	$-0.638961\pi$
$509$	−19.0787	−0.845650	−0.422825	+	0.906211i	$0.638961\pi$
$510$	5.83146	0.258221
$511$	−9.83146	−0.434918
$512$	1.55149	0.0685669
$513$	0.193937	0.00856251
$514$	32.4142	1.42973
$515$	58.7245	2.58771
$516$	−6.23743	−0.274587
$517$	7.53690	0.331473
$518$	−16.6883	−0.733242
$519$	−13.9126	−0.610694
$520$	22.2374	0.975176
$521$	2.80018	0.122678	0.0613391	−	0.998117i	$-0.480463\pi$
$521$	2.80018	0.122678	0.0613391	+	0.998117i	$0.480463\pi$
$522$	2.70052	0.118199
$523$	13.3806	0.585092	0.292546	−	0.956251i	$-0.405498\pi$
$523$	13.3806	0.585092	0.292546	+	0.956251i	$0.405498\pi$
$524$	−14.0303	−0.612917
$525$	−7.11871	−0.310686
$526$	−25.3971	−1.10737
$527$	−5.61213	−0.244468
$528$	8.00000	0.348155
$529$	8.78163	0.381810
$530$	58.9356	2.56000
$531$	−2.28726	−0.0992585
$532$	−0.156325	−0.00677756
$533$	−3.91019	−0.169369
$534$	−8.52373	−0.368858
$535$	48.9560	2.11655
$536$	13.8641	0.598840
$537$	3.02539	0.130555
$538$	18.0098	0.776460
$539$	−9.67276	−0.416635
$540$	2.80606	0.120754
$541$	−13.3322	−0.573194	−0.286597	−	0.958051i	$-0.592524\pi$
$541$	−13.3322	−0.573194	−0.286597	+	0.958051i	$0.592524\pi$
$542$	51.7704	2.22373
$543$	12.7431	0.546857
$544$	−4.31265	−0.184903
$545$	61.7704	2.64595
$546$	−5.35026	−0.228970
$547$	−29.0821	−1.24346	−0.621729	−	0.783232i	$-0.713570\pi$
$547$	−29.0821	−1.24346	−0.621729	+	0.783232i	$0.713570\pi$
$548$	5.00729	0.213901
$549$	1.31265	0.0560226
$550$	19.2243	0.819725
$551$	−0.312650	−0.0133194
$552$	11.2750	0.479898
$553$	1.00000	0.0425243
$554$	−25.6728	−1.09073
$555$	−34.6810	−1.47213
$556$	0.589104	0.0249836
$557$	−12.9380	−0.548199	−0.274099	−	0.961701i	$-0.588380\pi$
$557$	−12.9380	−0.548199	−0.274099	+	0.961701i	$0.588380\pi$
$558$	−9.40105	−0.397978
$559$	24.7151	1.04534
$560$	17.2750	0.730004
$561$	−1.61213	−0.0680640
$562$	48.0567	2.02715
$563$	15.7113	0.662154	0.331077	−	0.943604i	$-0.392588\pi$
$563$	15.7113	0.662154	0.331077	+	0.943604i	$0.392588\pi$
$564$	−3.76845	−0.158680
$565$	−6.70052	−0.281893
$566$	−31.7235	−1.33344
$567$	1.00000	0.0419961
$568$	1.42548	0.0598120
$569$	−5.91256	−0.247867	−0.123934	−	0.992291i	$-0.539551\pi$
$569$	−5.91256	−0.247867	−0.123934	+	0.992291i	$0.539551\pi$
$570$	−1.13093	−0.0473696
$571$	−10.7005	−0.447803	−0.223901	−	0.974612i	$-0.571879\pi$
$571$	−10.7005	−0.447803	−0.223901	+	0.974612i	$0.571879\pi$
$572$	4.15045	0.173539
$573$	−8.41327	−0.351469
$574$	−2.05079	−0.0855981
$575$	40.1319	1.67362
$576$	2.70052	0.112522
$577$	−9.19157	−0.382650	−0.191325	−	0.981527i	$-0.561278\pi$
$577$	−9.19157	−0.382650	−0.191325	+	0.981527i	$0.561278\pi$
$578$	1.67513	0.0696763
$579$	−16.0943	−0.668855
$580$	−4.52373	−0.187838
$581$	−0.249646	−0.0103571
$582$	4.80606	0.199218
$583$	−16.2930	−0.674785
$584$	19.6629	0.813657
$585$	−11.1187	−0.459702
$586$	−50.5682	−2.08895
$587$	36.3439	1.50007	0.750037	−	0.661396i	$-0.230036\pi$
$587$	36.3439	1.50007	0.750037	+	0.661396i	$0.230036\pi$
$588$	4.83638	0.199449
$589$	1.08840	0.0448466
$590$	13.3380	0.549119
$591$	−7.41090	−0.304844
$592$	49.4372	2.03186
$593$	−27.7621	−1.14005	−0.570027	−	0.821626i	$-0.693067\pi$
$593$	−27.7621	−1.14005	−0.570027	+	0.821626i	$0.693067\pi$
$594$	−2.70052	−0.110804
$595$	−3.48119	−0.142715
$596$	3.03364	0.124263
$597$	10.5672	0.432488
$598$	30.1622	1.23342
$599$	13.4495	0.549530	0.274765	−	0.961511i	$-0.411400\pi$
$599$	13.4495	0.549530	0.274765	+	0.961511i	$0.411400\pi$
$600$	14.2374	0.581241
$601$	20.6531	0.842456	0.421228	−	0.906955i	$-0.361599\pi$
$601$	20.6531	0.842456	0.421228	+	0.906955i	$0.361599\pi$
$602$	12.9624	0.528308
$603$	−6.93207	−0.282296
$604$	8.95651	0.364435
$605$	29.2457	1.18901
$606$	0.544198	0.0221065
$607$	−3.95509	−0.160532	−0.0802662	−	0.996773i	$-0.525577\pi$
$607$	−3.95509	−0.160532	−0.0802662	+	0.996773i	$0.525577\pi$
$608$	0.836381	0.0339197
$609$	−1.61213	−0.0653267
$610$	−7.65466	−0.309928
$611$	14.9321	0.604087
$612$	0.806063	0.0325832
$613$	18.1721	0.733962	0.366981	−	0.930228i	$-0.380391\pi$
$613$	18.1721	0.733962	0.366981	+	0.930228i	$0.380391\pi$
$614$	10.6293	0.428962
$615$	−4.26187	−0.171855
$616$	−3.22425	−0.129909
$617$	−27.7743	−1.11815	−0.559076	−	0.829116i	$-0.688844\pi$
$617$	−27.7743	−1.11815	−0.559076	+	0.829116i	$0.688844\pi$
$618$	28.2579	1.13670
$619$	−43.2823	−1.73966	−0.869832	−	0.493348i	$-0.835773\pi$
$619$	−43.2823	−1.73966	−0.869832	+	0.493348i	$0.835773\pi$
$620$	15.7480	0.632454
$621$	−5.63752	−0.226226
$622$	−4.77575	−0.191490
$623$	5.08840	0.203862
$624$	15.8496	0.634490
$625$	−9.91748	−0.396699
$626$	−21.6728	−0.866218
$627$	0.312650	0.0124861
$628$	−5.22425	−0.208470
$629$	−9.96239	−0.397226
$630$	−5.83146	−0.232331
$631$	27.2243	1.08378	0.541890	−	0.840449i	$-0.317709\pi$
$631$	27.2243	1.08378	0.541890	+	0.840449i	$0.317709\pi$
$632$	−2.00000	−0.0795557
$633$	−6.95509	−0.276440
$634$	40.2800	1.59972
$635$	−18.5115	−0.734607
$636$	8.14648	0.323029
$637$	−19.1636	−0.759290
$638$	4.35359	0.172360
$639$	−0.712742	−0.0281956
$640$	−45.7743	−1.80939
$641$	−10.1573	−0.401188	−0.200594	−	0.979674i	$-0.564287\pi$
$641$	−10.1573	−0.401188	−0.200594	+	0.979674i	$0.564287\pi$
$642$	23.5574	0.929735
$643$	12.7576	0.503113	0.251556	−	0.967843i	$-0.419058\pi$
$643$	12.7576	0.503113	0.251556	+	0.967843i	$0.419058\pi$
$644$	4.54420	0.179066
$645$	26.9380	1.06068
$646$	−0.324869	−0.0127818
$647$	−18.6507	−0.733234	−0.366617	−	0.930372i	$-0.619484\pi$
$647$	−18.6507	−0.733234	−0.366617	+	0.930372i	$0.619484\pi$
$648$	−2.00000	−0.0785674
$649$	−3.68735	−0.144741
$650$	38.0870	1.49389
$651$	5.61213	0.219957
$652$	−5.07381	−0.198706
$653$	−38.7464	−1.51626	−0.758132	−	0.652102i	$-0.773888\pi$
$653$	−38.7464	−1.51626	−0.758132	+	0.652102i	$0.773888\pi$
$654$	29.7235	1.16228
$655$	60.5936	2.36759
$656$	6.07522	0.237198
$657$	−9.83146	−0.383562
$658$	7.83146	0.305302
$659$	16.1974	0.630963	0.315481	−	0.948932i	$-0.397834\pi$
$659$	16.1974	0.630963	0.315481	+	0.948932i	$0.397834\pi$
$660$	4.52373	0.176086
$661$	−14.4812	−0.563253	−0.281627	−	0.959524i	$-0.590874\pi$
$661$	−14.4812	−0.563253	−0.281627	+	0.959524i	$0.590874\pi$
$662$	13.3054	0.517127
$663$	−3.19394	−0.124042
$664$	0.499293	0.0193763
$665$	0.675131	0.0261805
$666$	−16.6883	−0.646659
$667$	9.08840	0.351904
$668$	−7.83383	−0.303100
$669$	4.61213	0.178315
$670$	40.4241	1.56172
$671$	2.11616	0.0816934
$672$	4.31265	0.166364
$673$	15.3199	0.590540	0.295270	−	0.955414i	$-0.404590\pi$
$673$	15.3199	0.590540	0.295270	+	0.955414i	$0.404590\pi$
$674$	−33.8456	−1.30368
$675$	−7.11871	−0.273999
$676$	−2.25599	−0.0867687
$677$	2.89209	0.111152	0.0555760	−	0.998454i	$-0.482300\pi$
$677$	2.89209	0.111152	0.0555760	+	0.998454i	$0.482300\pi$
$678$	−3.22425	−0.123827
$679$	−2.86907	−0.110105
$680$	6.96239	0.266995
$681$	−0.186642	−0.00715215
$682$	−15.1557	−0.580341
$683$	−2.62435	−0.100418	−0.0502089	−	0.998739i	$-0.515989\pi$
$683$	−2.62435	−0.100418	−0.0502089	+	0.998739i	$0.515989\pi$
$684$	−0.156325	−0.00597724
$685$	−21.6253	−0.826260
$686$	−21.7767	−0.831438
$687$	22.7186	0.866769
$688$	−38.3996	−1.46397
$689$	−32.2795	−1.22975
$690$	32.8749	1.25153
$691$	−17.7757	−0.676221	−0.338111	−	0.941106i	$-0.609788\pi$
$691$	−17.7757	−0.676221	−0.338111	+	0.941106i	$0.609788\pi$
$692$	11.2144	0.426308
$693$	1.61213	0.0612396
$694$	−1.00492	−0.0381464
$695$	−2.54420	−0.0965069
$696$	3.22425	0.122215
$697$	−1.22425	−0.0463719
$698$	−52.3792	−1.98258
$699$	25.7767	0.974964
$700$	5.73813	0.216881
$701$	7.39024	0.279126	0.139563	−	0.990213i	$-0.455430\pi$
$701$	7.39024	0.279126	0.139563	+	0.990213i	$0.455430\pi$
$702$	−5.35026	−0.201933
$703$	1.93207	0.0728695
$704$	4.35359	0.164082
$705$	16.2750	0.612953
$706$	−46.8954	−1.76493
$707$	−0.324869	−0.0122180
$708$	1.84367	0.0692895
$709$	−13.5343	−0.508293	−0.254147	−	0.967166i	$-0.581795\pi$
$709$	−13.5343	−0.508293	−0.254147	+	0.967166i	$0.581795\pi$
$710$	4.15633	0.155984
$711$	1.00000	0.0375029
$712$	−10.1768	−0.381391
$713$	−31.6385	−1.18487
$714$	−1.67513	−0.0626902
$715$	−17.9248	−0.670349
$716$	−2.43866	−0.0911369
$717$	−26.0992	−0.974693
$718$	6.33709	0.236498
$719$	−15.5369	−0.579429	−0.289714	−	0.957113i	$-0.593560\pi$
$719$	−15.5369	−0.579429	−0.289714	+	0.957113i	$0.593560\pi$
$720$	17.2750	0.643803
$721$	−16.8691	−0.628237
$722$	−31.7645	−1.18215
$723$	26.2555	0.976454
$724$	−10.2717	−0.381745
$725$	11.4763	0.426218
$726$	14.0729	0.522293
$727$	33.7572	1.25198	0.625992	−	0.779829i	$-0.284694\pi$
$727$	33.7572	1.25198	0.625992	+	0.779829i	$0.284694\pi$
$728$	−6.38787	−0.236750
$729$	1.00000	0.0370370
$730$	57.3317	2.12194
$731$	7.73813	0.286205
$732$	−1.05808	−0.0391077
$733$	41.0263	1.51534	0.757671	−	0.652636i	$-0.226337\pi$
$733$	41.0263	1.51534	0.757671	+	0.652636i	$0.226337\pi$
$734$	34.6655	1.27953
$735$	−20.8872	−0.770435
$736$	−24.3127	−0.896176
$737$	−11.1754	−0.411650
$738$	−2.05079	−0.0754904
$739$	−2.70052	−0.0993404	−0.0496702	−	0.998766i	$-0.515817\pi$
$739$	−2.70052	−0.0993404	−0.0496702	+	0.998766i	$0.515817\pi$
$740$	27.9551	1.02765
$741$	0.619421	0.0227550
$742$	−16.9297	−0.621509
$743$	38.9995	1.43075	0.715377	−	0.698738i	$-0.246255\pi$
$743$	38.9995	1.43075	0.715377	+	0.698738i	$0.246255\pi$
$744$	−11.2243	−0.411501
$745$	−13.1016	−0.480004
$746$	54.2598	1.98659
$747$	−0.249646	−0.00913408
$748$	1.29948	0.0475136
$749$	−14.0630	−0.513851
$750$	12.3552	0.451148
$751$	1.02776	0.0375036	0.0187518	−	0.999824i	$-0.494031\pi$
$751$	1.02776	0.0375036	0.0187518	+	0.999824i	$0.494031\pi$
$752$	−23.1998	−0.846010
$753$	−2.39280	−0.0871984
$754$	8.62530	0.314115
$755$	−38.6810	−1.40775
$756$	−0.806063	−0.0293162
$757$	4.29551	0.156123	0.0780614	−	0.996949i	$-0.475127\pi$
$757$	4.29551	0.156123	0.0780614	+	0.996949i	$0.475127\pi$
$758$	3.28726	0.119399
$759$	−9.08840	−0.329888
$760$	−1.35026	−0.0489791
$761$	−31.2530	−1.13292	−0.566460	−	0.824089i	$-0.691687\pi$
$761$	−31.2530	−1.13292	−0.566460	+	0.824089i	$0.691687\pi$
$762$	−8.90763	−0.322690
$763$	−17.7440	−0.642376
$764$	6.78163	0.245351
$765$	−3.48119	−0.125863
$766$	−35.8700	−1.29604
$767$	−7.30536	−0.263781
$768$	−16.6253	−0.599914
$769$	4.41231	0.159112	0.0795560	−	0.996830i	$-0.474650\pi$
$769$	4.41231	0.159112	0.0795560	+	0.996830i	$0.474650\pi$
$770$	−9.40105	−0.338790
$771$	−19.3503	−0.696883
$772$	12.9730	0.466909
$773$	−17.0884	−0.614627	−0.307313	−	0.951608i	$-0.599430\pi$
$773$	−17.0884	−0.614627	−0.307313	+	0.951608i	$0.599430\pi$
$774$	12.9624	0.465923
$775$	−39.9511	−1.43509
$776$	5.73813	0.205987
$777$	9.96239	0.357399
$778$	58.4201	2.09446
$779$	0.237428	0.00850673
$780$	8.96239	0.320905
$781$	−1.14903	−0.0411156
$782$	9.44358	0.337702
$783$	−1.61213	−0.0576127
$784$	29.7743	1.06337
$785$	22.5623	0.805283
$786$	29.1573	1.04001
$787$	−26.1949	−0.933747	−0.466874	−	0.884324i	$-0.654620\pi$
$787$	−26.1949	−0.933747	−0.466874	+	0.884324i	$0.654620\pi$
$788$	5.97365	0.212803
$789$	15.1612	0.539755
$790$	−5.83146	−0.207474
$791$	1.92478	0.0684372
$792$	−3.22425	−0.114569
$793$	4.19252	0.148881
$794$	25.3601	0.899997
$795$	−35.1827	−1.24780
$796$	−8.51785	−0.301907
$797$	46.5755	1.64979	0.824894	−	0.565288i	$-0.191235\pi$
$797$	46.5755	1.64979	0.824894	+	0.565288i	$0.191235\pi$
$798$	0.324869	0.0115002
$799$	4.67513	0.165394
$800$	−30.7005	−1.08543
$801$	5.08840	0.179790
$802$	14.7651	0.521375
$803$	−15.8496	−0.559319
$804$	5.58769	0.197063
$805$	−19.6253	−0.691701
$806$	−30.0263	−1.05763
$807$	−10.7513	−0.378464
$808$	0.649738	0.0228577
$809$	37.0376	1.30217	0.651087	−	0.759004i	$-0.274313\pi$
$809$	37.0376	1.30217	0.651087	+	0.759004i	$0.274313\pi$
$810$	−5.83146	−0.204896
$811$	3.35660	0.117866	0.0589331	−	0.998262i	$-0.481230\pi$
$811$	3.35660	0.117866	0.0589331	+	0.998262i	$0.481230\pi$
$812$	1.29948	0.0456027
$813$	−30.9053	−1.08389
$814$	−26.9037	−0.942973
$815$	21.9126	0.767563
$816$	4.96239	0.173718
$817$	−1.50071	−0.0525031
$818$	22.7005	0.793705
$819$	3.19394	0.111605
$820$	3.43533	0.119967
$821$	4.67021	0.162991	0.0814957	−	0.996674i	$-0.474030\pi$
$821$	4.67021	0.162991	0.0814957	+	0.996674i	$0.474030\pi$
$822$	−10.4060	−0.362950
$823$	−41.3087	−1.43993	−0.719965	−	0.694010i	$-0.755842\pi$
$823$	−41.3087	−1.43993	−0.719965	+	0.694010i	$0.755842\pi$
$824$	33.7381	1.17532
$825$	−11.4763	−0.399552
$826$	−3.83146	−0.133313
$827$	−43.5364	−1.51391	−0.756955	−	0.653467i	$-0.773314\pi$
$827$	−43.5364	−1.51391	−0.756955	+	0.653467i	$0.773314\pi$
$828$	4.54420	0.157922
$829$	−30.7757	−1.06889	−0.534443	−	0.845205i	$-0.679479\pi$
$829$	−30.7757	−1.06889	−0.534443	+	0.845205i	$0.679479\pi$
$830$	1.45580	0.0505316
$831$	15.3258	0.531647
$832$	8.62530	0.299028
$833$	−6.00000	−0.207888
$834$	−1.22425	−0.0423924
$835$	33.8324	1.17082
$836$	−0.252016	−0.00871616
$837$	5.61213	0.193983
$838$	−39.3219	−1.35835
$839$	−5.03269	−0.173748	−0.0868738	−	0.996219i	$-0.527688\pi$
$839$	−5.03269	−0.173748	−0.0868738	+	0.996219i	$0.527688\pi$
$840$	−6.96239	−0.240225
$841$	−26.4010	−0.910381
$842$	7.73577	0.266592
$843$	−28.6883	−0.988078
$844$	5.60625	0.192975
$845$	9.74306	0.335171
$846$	7.83146	0.269251
$847$	−8.40105	−0.288663
$848$	50.1524	1.72224
$849$	18.9380	0.649949
$850$	11.9248	0.409016
$851$	−56.1632	−1.92525
$852$	0.574515	0.0196826
$853$	−26.2506	−0.898803	−0.449402	−	0.893330i	$-0.648363\pi$
$853$	−26.2506	−0.898803	−0.449402	+	0.893330i	$0.648363\pi$
$854$	2.19886	0.0752435
$855$	0.675131	0.0230890
$856$	28.1260	0.961327
$857$	2.80018	0.0956525	0.0478262	−	0.998856i	$-0.484771\pi$
$857$	2.80018	0.0956525	0.0478262	+	0.998856i	$0.484771\pi$
$858$	−8.62530	−0.294463
$859$	4.66433	0.159145	0.0795724	−	0.996829i	$-0.474645\pi$
$859$	4.66433	0.159145	0.0795724	+	0.996829i	$0.474645\pi$
$860$	−21.7137	−0.740431
$861$	1.22425	0.0417225
$862$	−48.8545	−1.66399
$863$	−12.3733	−0.421192	−0.210596	−	0.977573i	$-0.567540\pi$
$863$	−12.3733	−0.421192	−0.210596	+	0.977573i	$0.567540\pi$
$864$	4.31265	0.146719
$865$	−48.4323	−1.64675
$866$	−38.8119	−1.31888
$867$	−1.00000	−0.0339618
$868$	−4.52373	−0.153545
$869$	1.61213	0.0546877
$870$	9.40105	0.318725
$871$	−22.1406	−0.750205
$872$	35.4880	1.20178
$873$	−2.86907	−0.0971032
$874$	−1.83146	−0.0619499
$875$	−7.37565	−0.249343
$876$	7.92478	0.267753
$877$	5.63023	0.190119	0.0950596	−	0.995472i	$-0.469696\pi$
$877$	5.63023	0.190119	0.0950596	+	0.995472i	$0.469696\pi$
$878$	48.8832	1.64973
$879$	30.1876	1.01820
$880$	27.8496	0.938808
$881$	−6.81194	−0.229500	−0.114750	−	0.993394i	$-0.536607\pi$
$881$	−6.81194	−0.229500	−0.114750	+	0.993394i	$0.536607\pi$
$882$	−10.0508	−0.338428
$883$	−34.8364	−1.17234	−0.586169	−	0.810189i	$-0.699364\pi$
$883$	−34.8364	−1.17234	−0.586169	+	0.810189i	$0.699364\pi$
$884$	2.57452	0.0865903
$885$	−7.96239	−0.267653
$886$	39.2931	1.32008
$887$	30.7523	1.03256	0.516280	−	0.856420i	$-0.327316\pi$
$887$	30.7523	1.03256	0.516280	+	0.856420i	$0.327316\pi$
$888$	−19.9248	−0.668632
$889$	5.31757	0.178346
$890$	−29.6728	−0.994633
$891$	1.61213	0.0540083
$892$	−3.71767	−0.124477
$893$	−0.906679	−0.0303409
$894$	−6.30440	−0.210851
$895$	10.5320	0.352045
$896$	13.1490	0.439278
$897$	−18.0059	−0.601199
$898$	12.7104	0.424151
$899$	−9.04746	−0.301750
$900$	5.73813	0.191271
$901$	−10.1065	−0.336696
$902$	−3.30613	−0.110082
$903$	−7.73813	−0.257509
$904$	−3.84955	−0.128034
$905$	44.3611	1.47461
$906$	−18.6131	−0.618378
$907$	−18.1295	−0.601981	−0.300990	−	0.953627i	$-0.597317\pi$
$907$	−18.1295	−0.601981	−0.300990	+	0.953627i	$0.597317\pi$
$908$	0.150446	0.00499271
$909$	−0.324869	−0.0107752
$910$	−18.6253	−0.617423
$911$	−23.4821	−0.777998	−0.388999	−	0.921238i	$-0.627179\pi$
$911$	−23.4821	−0.777998	−0.388999	+	0.921238i	$0.627179\pi$
$912$	−0.962389	−0.0318679
$913$	−0.402462	−0.0133195
$914$	35.7964	1.18404
$915$	4.56959	0.151066
$916$	−18.3127	−0.605067
$917$	−17.4060	−0.574796
$918$	−1.67513	−0.0552876
$919$	22.6801	0.748146	0.374073	−	0.927399i	$-0.377961\pi$
$919$	22.6801	0.748146	0.374073	+	0.927399i	$0.377961\pi$
$920$	39.2506	1.29405
$921$	−6.34534	−0.209086
$922$	−41.8496	−1.37824
$923$	−2.27645	−0.0749304
$924$	−1.29948	−0.0427496
$925$	−70.9194	−2.33182
$926$	6.75528	0.221992
$927$	−16.8691	−0.554053
$928$	−6.95254	−0.228228
$929$	30.8749	1.01297	0.506487	−	0.862248i	$-0.330944\pi$
$929$	30.8749	1.01297	0.506487	+	0.862248i	$0.330944\pi$
$930$	−32.7269	−1.07316
$931$	1.16362	0.0381361
$932$	−20.7777	−0.680595
$933$	2.85097	0.0933365
$934$	−33.5633	−1.09822
$935$	−5.61213	−0.183536
$936$	−6.38787	−0.208794
$937$	32.5221	1.06245	0.531226	−	0.847230i	$-0.321732\pi$
$937$	32.5221	1.06245	0.531226	+	0.847230i	$0.321732\pi$
$938$	−11.6121	−0.379149
$939$	12.9380	0.422214
$940$	−13.1187	−0.427885
$941$	34.3841	1.12089	0.560445	−	0.828192i	$-0.310630\pi$
$941$	34.3841	1.12089	0.560445	+	0.828192i	$0.310630\pi$
$942$	10.8568	0.353735
$943$	−6.90175	−0.224752
$944$	11.3503	0.369420
$945$	3.48119	0.113243
$946$	20.8970	0.679421
$947$	6.11142	0.198594	0.0992972	−	0.995058i	$-0.468341\pi$
$947$	6.11142	0.198594	0.0992972	+	0.995058i	$0.468341\pi$
$948$	−0.806063	−0.0261797
$949$	−31.4010	−1.01932
$950$	−2.31265	−0.0750323
$951$	−24.0459	−0.779740
$952$	−2.00000	−0.0648204
$953$	41.0757	1.33057	0.665287	−	0.746588i	$-0.268309\pi$
$953$	41.0757	1.33057	0.665287	+	0.746588i	$0.268309\pi$
$954$	−16.9297	−0.548119
$955$	−29.2882	−0.947744
$956$	21.0376	0.680405
$957$	−2.59895	−0.0840122
$958$	26.7088	0.862921
$959$	6.21203	0.200597
$960$	9.40105	0.303417
$961$	0.495968	0.0159990
$962$	−53.3014	−1.71851
$963$	−14.0630	−0.453174
$964$	−21.1636	−0.681634
$965$	−56.0273	−1.80358
$966$	−9.44358	−0.303842
$967$	34.8700	1.12134	0.560672	−	0.828038i	$-0.310543\pi$
$967$	34.8700	1.12134	0.560672	+	0.828038i	$0.310543\pi$
$968$	16.8021	0.540040
$969$	0.193937	0.00623014
$970$	16.7308	0.537195
$971$	19.7283	0.633111	0.316555	−	0.948574i	$-0.397474\pi$
$971$	19.7283	0.633111	0.316555	+	0.948574i	$0.397474\pi$
$972$	−0.806063	−0.0258545
$973$	0.730841	0.0234297
$974$	−0.973008	−0.0311772
$975$	−22.7367	−0.728158
$976$	−6.51388	−0.208504
$977$	48.6712	1.55713	0.778564	−	0.627565i	$-0.215948\pi$
$977$	48.6712	1.55713	0.778564	+	0.627565i	$0.215948\pi$
$978$	10.5442	0.337166
$979$	8.20314	0.262174
$980$	16.8364	0.537818
$981$	−17.7440	−0.566523
$982$	−29.5026	−0.941466
$983$	18.5477	0.591580	0.295790	−	0.955253i	$-0.404417\pi$
$983$	18.5477	0.591580	0.295790	+	0.955253i	$0.404417\pi$
$984$	−2.44851	−0.0780556
$985$	−25.7988	−0.822017
$986$	2.70052	0.0860022
$987$	−4.67513	−0.148811
$988$	−0.499293	−0.0158846
$989$	43.6239	1.38716
$990$	−9.40105	−0.298785
$991$	12.9189	0.410382	0.205191	−	0.978722i	$-0.434218\pi$
$991$	12.9189	0.410382	0.205191	+	0.978722i	$0.434218\pi$
$992$	24.2031	0.768450
$993$	−7.94288	−0.252060
$994$	−1.19394	−0.0378694
$995$	36.7866	1.16621
$996$	0.201231	0.00637624
$997$	−1.99015	−0.0630287	−0.0315144	−	0.999503i	$-0.510033\pi$
$997$	−1.99015	−0.0630287	−0.0315144	+	0.999503i	$0.510033\pi$
$998$	41.5223	1.31437
$999$	9.96239	0.315196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.d.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.d.1.3	✓	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.67513 q^{2} -1.00000 q^{3} +0.806063 q^{4} -3.48119 q^{5} -1.67513 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.67513 q^{2} -1.00000 q^{3} +0.806063 q^{4} -3.48119 q^{5} -1.67513 q^{6} +1.00000 q^{7} -2.00000 q^{8} +1.00000 q^{9} -5.83146 q^{10} +1.61213 q^{11} -0.806063 q^{12} +3.19394 q^{13} +1.67513 q^{14} +3.48119 q^{15} -4.96239 q^{16} +1.00000 q^{17} +1.67513 q^{18} -0.193937 q^{19} -2.80606 q^{20} -1.00000 q^{21} +2.70052 q^{22} +5.63752 q^{23} +2.00000 q^{24} +7.11871 q^{25} +5.35026 q^{26} -1.00000 q^{27} +0.806063 q^{28} +1.61213 q^{29} +5.83146 q^{30} -5.61213 q^{31} -4.31265 q^{32} -1.61213 q^{33} +1.67513 q^{34} -3.48119 q^{35} +0.806063 q^{36} -9.96239 q^{37} -0.324869 q^{38} -3.19394 q^{39} +6.96239 q^{40} -1.22425 q^{41} -1.67513 q^{42} +7.73813 q^{43} +1.29948 q^{44} -3.48119 q^{45} +9.44358 q^{46} +4.67513 q^{47} +4.96239 q^{48} -6.00000 q^{49} +11.9248 q^{50} -1.00000 q^{51} +2.57452 q^{52} -10.1065 q^{53} -1.67513 q^{54} -5.61213 q^{55} -2.00000 q^{56} +0.193937 q^{57} +2.70052 q^{58} -2.28726 q^{59} +2.80606 q^{60} +1.31265 q^{61} -9.40105 q^{62} +1.00000 q^{63} +2.70052 q^{64} -11.1187 q^{65} -2.70052 q^{66} -6.93207 q^{67} +0.806063 q^{68} -5.63752 q^{69} -5.83146 q^{70} -0.712742 q^{71} -2.00000 q^{72} -9.83146 q^{73} -16.6883 q^{74} -7.11871 q^{75} -0.156325 q^{76} +1.61213 q^{77} -5.35026 q^{78} +1.00000 q^{79} +17.2750 q^{80} +1.00000 q^{81} -2.05079 q^{82} -0.249646 q^{83} -0.806063 q^{84} -3.48119 q^{85} +12.9624 q^{86} -1.61213 q^{87} -3.22425 q^{88} +5.08840 q^{89} -5.83146 q^{90} +3.19394 q^{91} +4.54420 q^{92} +5.61213 q^{93} +7.83146 q^{94} +0.675131 q^{95} +4.31265 q^{96} -2.86907 q^{97} -10.0508 q^{98} +1.61213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9	\( 3 q - 3 q^{3} + 2 q^{4} - 5 q^{5} + 3 q^{7} - 6 q^{8} + 3 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 10 q^{13} + 5 q^{15} - 4 q^{16} + 3 q^{17} - q^{19} - 8 q^{20} - 3 q^{21} - 12 q^{22} + q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 2 q^{28} + 4 q^{29} + 2 q^{30} - 16 q^{31} + 8 q^{32} - 4 q^{33} - 5 q^{35} + 2 q^{36} - 19 q^{37} - 6 q^{38} - 10 q^{39} + 10 q^{40} - 2 q^{41} + 14 q^{43} + 24 q^{44} - 5 q^{45} + 12 q^{46} + 9 q^{47} + 4 q^{48} - 18 q^{49} + 14 q^{50} - 3 q^{51} - 4 q^{52} + 17 q^{53} - 16 q^{55} - 6 q^{56} + q^{57} - 12 q^{58} - q^{59} + 8 q^{60} - 17 q^{61} + 12 q^{62} + 3 q^{63} - 12 q^{64} - 12 q^{65} + 12 q^{66} - 12 q^{67} + 2 q^{68} - q^{69} - 2 q^{70} - 8 q^{71} - 6 q^{72} - 14 q^{73} - 4 q^{74} + 10 q^{76} + 4 q^{77} - 6 q^{78} + 3 q^{79} + 20 q^{80} + 3 q^{81} + 24 q^{82} + 16 q^{83} - 2 q^{84} - 5 q^{85} + 28 q^{86} - 4 q^{87} - 8 q^{88} - 4 q^{89} - 2 q^{90} + 10 q^{91} + 4 q^{92} + 16 q^{93} + 8 q^{94} - 3 q^{95} - 8 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 3 * q - 3 * q^3 + 2 * q^4 - 5 * q^5 + 3 * q^7 - 6 * q^8 + 3 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 10 * q^13 + 5 * q^15 - 4 * q^16 + 3 * q^17 - q^19 - 8 * q^20 - 3 * q^21 - 12 * q^22 + q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 2 * q^28 + 4 * q^29 + 2 * q^30 - 16 * q^31 + 8 * q^32 - 4 * q^33 - 5 * q^35 + 2 * q^36 - 19 * q^37 - 6 * q^38 - 10 * q^39 + 10 * q^40 - 2 * q^41 + 14 * q^43 + 24 * q^44 - 5 * q^45 + 12 * q^46 + 9 * q^47 + 4 * q^48 - 18 * q^49 + 14 * q^50 - 3 * q^51 - 4 * q^52 + 17 * q^53 - 16 * q^55 - 6 * q^56 + q^57 - 12 * q^58 - q^59 + 8 * q^60 - 17 * q^61 + 12 * q^62 + 3 * q^63 - 12 * q^64 - 12 * q^65 + 12 * q^66 - 12 * q^67 + 2 * q^68 - q^69 - 2 * q^70 - 8 * q^71 - 6 * q^72 - 14 * q^73 - 4 * q^74 + 10 * q^76 + 4 * q^77 - 6 * q^78 + 3 * q^79 + 20 * q^80 + 3 * q^81 + 24 * q^82 + 16 * q^83 - 2 * q^84 - 5 * q^85 + 28 * q^86 - 4 * q^87 - 8 * q^88 - 4 * q^89 - 2 * q^90 + 10 * q^91 + 4 * q^92 + 16 * q^93 + 8 * q^94 - 3 * q^95 - 8 * q^96 - 4 * q^97 + 4 * q^99

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