LMFDB - Embedded newform 6026.2.a.m.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.27011 q^{3} +1.00000 q^{4} -1.81074 q^{5} -2.27011 q^{6} +2.75406 q^{7} +1.00000 q^{8} +2.15338 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.27011 q^{3} +1.00000 q^{4} -1.81074 q^{5} -2.27011 q^{6} +2.75406 q^{7} +1.00000 q^{8} +2.15338 q^{9} -1.81074 q^{10} -3.69732 q^{11} -2.27011 q^{12} +4.65829 q^{13} +2.75406 q^{14} +4.11056 q^{15} +1.00000 q^{16} +4.00896 q^{17} +2.15338 q^{18} +6.43083 q^{19} -1.81074 q^{20} -6.25202 q^{21} -3.69732 q^{22} +1.00000 q^{23} -2.27011 q^{24} -1.72124 q^{25} +4.65829 q^{26} +1.92191 q^{27} +2.75406 q^{28} -0.101640 q^{29} +4.11056 q^{30} +2.69271 q^{31} +1.00000 q^{32} +8.39332 q^{33} +4.00896 q^{34} -4.98688 q^{35} +2.15338 q^{36} -1.93485 q^{37} +6.43083 q^{38} -10.5748 q^{39} -1.81074 q^{40} -10.3411 q^{41} -6.25202 q^{42} +1.32687 q^{43} -3.69732 q^{44} -3.89921 q^{45} +1.00000 q^{46} -7.72731 q^{47} -2.27011 q^{48} +0.584869 q^{49} -1.72124 q^{50} -9.10078 q^{51} +4.65829 q^{52} -5.32055 q^{53} +1.92191 q^{54} +6.69487 q^{55} +2.75406 q^{56} -14.5987 q^{57} -0.101640 q^{58} -2.92210 q^{59} +4.11056 q^{60} +12.7177 q^{61} +2.69271 q^{62} +5.93056 q^{63} +1.00000 q^{64} -8.43493 q^{65} +8.39332 q^{66} +4.34132 q^{67} +4.00896 q^{68} -2.27011 q^{69} -4.98688 q^{70} -7.06119 q^{71} +2.15338 q^{72} +8.48812 q^{73} -1.93485 q^{74} +3.90739 q^{75} +6.43083 q^{76} -10.1827 q^{77} -10.5748 q^{78} +15.8125 q^{79} -1.81074 q^{80} -10.8231 q^{81} -10.3411 q^{82} +1.11213 q^{83} -6.25202 q^{84} -7.25917 q^{85} +1.32687 q^{86} +0.230735 q^{87} -3.69732 q^{88} -2.13754 q^{89} -3.89921 q^{90} +12.8292 q^{91} +1.00000 q^{92} -6.11274 q^{93} -7.72731 q^{94} -11.6445 q^{95} -2.27011 q^{96} +13.2507 q^{97} +0.584869 q^{98} -7.96175 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * 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
$3$	−2.27011	−1.31065	−0.655323	−	0.755349i	$-0.727468\pi$
$3$	−2.27011	−1.31065	−0.655323	+	0.755349i	$0.727468\pi$
$4$	1.00000	0.500000
$5$	−1.81074	−0.809786	−0.404893	−	0.914364i	$-0.632691\pi$
$5$	−1.81074	−0.809786	−0.404893	+	0.914364i	$0.632691\pi$
$6$	−2.27011	−0.926767
$7$	2.75406	1.04094	0.520469	−	0.853880i	$-0.325757\pi$
$7$	2.75406	1.04094	0.520469	+	0.853880i	$0.325757\pi$
$8$	1.00000	0.353553
$9$	2.15338	0.717795
$10$	−1.81074	−0.572605
$11$	−3.69732	−1.11478	−0.557392	−	0.830249i	$-0.688198\pi$
$11$	−3.69732	−1.11478	−0.557392	+	0.830249i	$0.688198\pi$
$12$	−2.27011	−0.655323
$13$	4.65829	1.29198	0.645989	−	0.763347i	$-0.276445\pi$
$13$	4.65829	1.29198	0.645989	+	0.763347i	$0.276445\pi$
$14$	2.75406	0.736055
$15$	4.11056	1.06134
$16$	1.00000	0.250000
$17$	4.00896	0.972317	0.486158	−	0.873871i	$-0.338398\pi$
$17$	4.00896	0.972317	0.486158	+	0.873871i	$0.338398\pi$
$18$	2.15338	0.507557
$19$	6.43083	1.47533	0.737667	−	0.675165i	$-0.235927\pi$
$19$	6.43083	1.47533	0.737667	+	0.675165i	$0.235927\pi$
$20$	−1.81074	−0.404893
$21$	−6.25202	−1.36430
$22$	−3.69732	−0.788272
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.27011	−0.463384
$25$	−1.72124	−0.344247
$26$	4.65829	0.913566
$27$	1.92191	0.369872
$28$	2.75406	0.520469
$29$	−0.101640	−0.0188742	−0.00943708	−	0.999955i	$-0.503004\pi$
$29$	−0.101640	−0.0188742	−0.00943708	+	0.999955i	$0.503004\pi$
$30$	4.11056	0.750483
$31$	2.69271	0.483625	0.241812	−	0.970323i	$-0.422258\pi$
$31$	2.69271	0.483625	0.241812	+	0.970323i	$0.422258\pi$
$32$	1.00000	0.176777
$33$	8.39332	1.46109
$34$	4.00896	0.687532
$35$	−4.98688	−0.842937
$36$	2.15338	0.358897
$37$	−1.93485	−0.318087	−0.159043	−	0.987272i	$-0.550841\pi$
$37$	−1.93485	−0.318087	−0.159043	+	0.987272i	$0.550841\pi$
$38$	6.43083	1.04322
$39$	−10.5748	−1.69333
$40$	−1.81074	−0.286302
$41$	−10.3411	−1.61501	−0.807506	−	0.589860i	$-0.799183\pi$
$41$	−10.3411	−1.61501	−0.807506	+	0.589860i	$0.799183\pi$
$42$	−6.25202	−0.964707
$43$	1.32687	0.202346	0.101173	−	0.994869i	$-0.467740\pi$
$43$	1.32687	0.202346	0.101173	+	0.994869i	$0.467740\pi$
$44$	−3.69732	−0.557392
$45$	−3.89921	−0.581260
$46$	1.00000	0.147442
$47$	−7.72731	−1.12714	−0.563572	−	0.826067i	$-0.690573\pi$
$47$	−7.72731	−1.12714	−0.563572	+	0.826067i	$0.690573\pi$
$48$	−2.27011	−0.327662
$49$	0.584869	0.0835527
$50$	−1.72124	−0.243420
$51$	−9.10078	−1.27436
$52$	4.65829	0.645989
$53$	−5.32055	−0.730833	−0.365417	−	0.930844i	$-0.619073\pi$
$53$	−5.32055	−0.730833	−0.365417	+	0.930844i	$0.619073\pi$
$54$	1.92191	0.261539
$55$	6.69487	0.902736
$56$	2.75406	0.368027
$57$	−14.5987	−1.93364
$58$	−0.101640	−0.0133460
$59$	−2.92210	−0.380425	−0.190213	−	0.981743i	$-0.560918\pi$
$59$	−2.92210	−0.380425	−0.190213	+	0.981743i	$0.560918\pi$
$60$	4.11056	0.530671
$61$	12.7177	1.62833	0.814165	−	0.580633i	$-0.197195\pi$
$61$	12.7177	1.62833	0.814165	+	0.580633i	$0.197195\pi$
$62$	2.69271	0.341975
$63$	5.93056	0.747180
$64$	1.00000	0.125000
$65$	−8.43493	−1.04622
$66$	8.39332	1.03315
$67$	4.34132	0.530377	0.265188	−	0.964197i	$-0.414566\pi$
$67$	4.34132	0.530377	0.265188	+	0.964197i	$0.414566\pi$
$68$	4.00896	0.486158
$69$	−2.27011	−0.273289
$70$	−4.98688	−0.596046
$71$	−7.06119	−0.838009	−0.419005	−	0.907984i	$-0.637621\pi$
$71$	−7.06119	−0.838009	−0.419005	+	0.907984i	$0.637621\pi$
$72$	2.15338	0.253779
$73$	8.48812	0.993459	0.496730	−	0.867905i	$-0.334534\pi$
$73$	8.48812	0.993459	0.496730	+	0.867905i	$0.334534\pi$
$74$	−1.93485	−0.224921
$75$	3.90739	0.451187
$76$	6.43083	0.737667
$77$	−10.1827	−1.16042
$78$	−10.5748	−1.19736
$79$	15.8125	1.77904	0.889522	−	0.456893i	$-0.151038\pi$
$79$	15.8125	1.77904	0.889522	+	0.456893i	$0.151038\pi$
$80$	−1.81074	−0.202446
$81$	−10.8231	−1.20257
$82$	−10.3411	−1.14199
$83$	1.11213	0.122072	0.0610361	−	0.998136i	$-0.480560\pi$
$83$	1.11213	0.122072	0.0610361	+	0.998136i	$0.480560\pi$
$84$	−6.25202	−0.682151
$85$	−7.25917	−0.787368
$86$	1.32687	0.143080
$87$	0.230735	0.0247373
$88$	−3.69732	−0.394136
$89$	−2.13754	−0.226578	−0.113289	−	0.993562i	$-0.536139\pi$
$89$	−2.13754	−0.226578	−0.113289	+	0.993562i	$0.536139\pi$
$90$	−3.89921	−0.411013
$91$	12.8292	1.34487
$92$	1.00000	0.104257
$93$	−6.11274	−0.633861
$94$	−7.72731	−0.797012
$95$	−11.6445	−1.19470
$96$	−2.27011	−0.231692
$97$	13.2507	1.34541	0.672704	−	0.739911i	$-0.265133\pi$
$97$	13.2507	1.34541	0.672704	+	0.739911i	$0.265133\pi$
$98$	0.584869	0.0590807
$99$	−7.96175	−0.800186
$100$	−1.72124	−0.172124
$101$	4.26314	0.424198	0.212099	−	0.977248i	$-0.431970\pi$
$101$	4.26314	0.424198	0.212099	+	0.977248i	$0.431970\pi$
$102$	−9.10078	−0.901111
$103$	−6.87758	−0.677668	−0.338834	−	0.940846i	$-0.610032\pi$
$103$	−6.87758	−0.677668	−0.338834	+	0.940846i	$0.610032\pi$
$104$	4.65829	0.456783
$105$	11.3208	1.10479
$106$	−5.32055	−0.516777
$107$	−12.5985	−1.21795	−0.608973	−	0.793191i	$-0.708418\pi$
$107$	−12.5985	−1.21795	−0.608973	+	0.793191i	$0.708418\pi$
$108$	1.92191	0.184936
$109$	−14.3119	−1.37083	−0.685417	−	0.728150i	$-0.740380\pi$
$109$	−14.3119	−1.37083	−0.685417	+	0.728150i	$0.740380\pi$
$110$	6.69487	0.638331
$111$	4.39231	0.416899
$112$	2.75406	0.260235
$113$	19.2766	1.81339	0.906694	−	0.421789i	$-0.138598\pi$
$113$	19.2766	1.81339	0.906694	+	0.421789i	$0.138598\pi$
$114$	−14.5987	−1.36729
$115$	−1.81074	−0.168852
$116$	−0.101640	−0.00943708
$117$	10.0311	0.927374
$118$	−2.92210	−0.269001
$119$	11.0409	1.01212
$120$	4.11056	0.375241
$121$	2.67019	0.242745
$122$	12.7177	1.15140
$123$	23.4754	2.11671
$124$	2.69271	0.241812
$125$	12.1704	1.08855
$126$	5.93056	0.528336
$127$	10.9371	0.970514	0.485257	−	0.874371i	$-0.338726\pi$
$127$	10.9371	0.970514	0.485257	+	0.874371i	$0.338726\pi$
$128$	1.00000	0.0883883
$129$	−3.01214	−0.265204
$130$	−8.43493	−0.739792
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	8.39332	0.730544
$133$	17.7109	1.53573
$134$	4.34132	0.375033
$135$	−3.48007	−0.299517
$136$	4.00896	0.343766
$137$	13.8943	1.18707	0.593537	−	0.804807i	$-0.297731\pi$
$137$	13.8943	1.18707	0.593537	+	0.804807i	$0.297731\pi$
$138$	−2.27011	−0.193244
$139$	−11.9258	−1.01153	−0.505766	−	0.862670i	$-0.668790\pi$
$139$	−11.9258	−1.01153	−0.505766	+	0.862670i	$0.668790\pi$
$140$	−4.98688	−0.421468
$141$	17.5418	1.47729
$142$	−7.06119	−0.592562
$143$	−17.2232	−1.44028
$144$	2.15338	0.179449
$145$	0.184044	0.0152840
$146$	8.48812	0.702482
$147$	−1.32771	−0.109508
$148$	−1.93485	−0.159043
$149$	−11.3134	−0.926829	−0.463414	−	0.886142i	$-0.653376\pi$
$149$	−11.3134	−0.926829	−0.463414	+	0.886142i	$0.653376\pi$
$150$	3.90739	0.319037
$151$	24.0616	1.95811	0.979054	−	0.203599i	$-0.0652640\pi$
$151$	24.0616	1.95811	0.979054	+	0.203599i	$0.0652640\pi$
$152$	6.43083	0.521609
$153$	8.63284	0.697924
$154$	−10.1827	−0.820542
$155$	−4.87579	−0.391633
$156$	−10.5748	−0.846663
$157$	21.9569	1.75235	0.876175	−	0.481993i	$-0.160087\pi$
$157$	21.9569	1.75235	0.876175	+	0.481993i	$0.160087\pi$
$158$	15.8125	1.25797
$159$	12.0782	0.957864
$160$	−1.81074	−0.143151
$161$	2.75406	0.217051
$162$	−10.8231	−0.850342
$163$	−12.3485	−0.967206	−0.483603	−	0.875287i	$-0.660672\pi$
$163$	−12.3485	−0.967206	−0.483603	+	0.875287i	$0.660672\pi$
$164$	−10.3411	−0.807506
$165$	−15.1981	−1.18317
$166$	1.11213	0.0863181
$167$	15.6335	1.20976	0.604878	−	0.796318i	$-0.293222\pi$
$167$	15.6335	1.20976	0.604878	+	0.796318i	$0.293222\pi$
$168$	−6.25202	−0.482354
$169$	8.69966	0.669205
$170$	−7.25917	−0.556753
$171$	13.8480	1.05899
$172$	1.32687	0.101173
$173$	−10.9627	−0.833476	−0.416738	−	0.909027i	$-0.636827\pi$
$173$	−10.9627	−0.833476	−0.416738	+	0.909027i	$0.636827\pi$
$174$	0.230735	0.0174919
$175$	−4.74040	−0.358340
$176$	−3.69732	−0.278696
$177$	6.63348	0.498603
$178$	−2.13754	−0.160215
$179$	−7.23995	−0.541139	−0.270570	−	0.962700i	$-0.587212\pi$
$179$	−7.23995	−0.541139	−0.270570	+	0.962700i	$0.587212\pi$
$180$	−3.89921	−0.290630
$181$	7.36721	0.547600	0.273800	−	0.961787i	$-0.411719\pi$
$181$	7.36721	0.547600	0.273800	+	0.961787i	$0.411719\pi$
$182$	12.8292	0.950966
$183$	−28.8705	−2.13417
$184$	1.00000	0.0737210
$185$	3.50350	0.257582
$186$	−6.11274	−0.448208
$187$	−14.8224	−1.08392
$188$	−7.72731	−0.563572
$189$	5.29306	0.385014
$190$	−11.6445	−0.844784
$191$	10.7749	0.779642	0.389821	−	0.920891i	$-0.372537\pi$
$191$	10.7749	0.779642	0.389821	+	0.920891i	$0.372537\pi$
$192$	−2.27011	−0.163831
$193$	17.7801	1.27984	0.639922	−	0.768440i	$-0.278967\pi$
$193$	17.7801	1.27984	0.639922	+	0.768440i	$0.278967\pi$
$194$	13.2507	0.951347
$195$	19.1482	1.37123
$196$	0.584869	0.0417764
$197$	7.90253	0.563032	0.281516	−	0.959557i	$-0.409163\pi$
$197$	7.90253	0.563032	0.281516	+	0.959557i	$0.409163\pi$
$198$	−7.96175	−0.565817
$199$	−21.6123	−1.53206	−0.766028	−	0.642807i	$-0.777770\pi$
$199$	−21.6123	−1.53206	−0.766028	+	0.642807i	$0.777770\pi$
$200$	−1.72124	−0.121710
$201$	−9.85526	−0.695136
$202$	4.26314	0.299953
$203$	−0.279924	−0.0196468
$204$	−9.10078	−0.637182
$205$	18.7250	1.30781
$206$	−6.87758	−0.479184
$207$	2.15338	0.149671
$208$	4.65829	0.322994
$209$	−23.7769	−1.64468
$210$	11.3208	0.781206
$211$	−22.9211	−1.57795	−0.788977	−	0.614423i	$-0.789389\pi$
$211$	−22.9211	−1.57795	−0.788977	+	0.614423i	$0.789389\pi$
$212$	−5.32055	−0.365417
$213$	16.0297	1.09833
$214$	−12.5985	−0.861218
$215$	−2.40261	−0.163857
$216$	1.92191	0.130769
$217$	7.41590	0.503424
$218$	−14.3119	−0.969327
$219$	−19.2689	−1.30207
$220$	6.69487	0.451368
$221$	18.6749	1.25621
$222$	4.39231	0.294792
$223$	−25.4911	−1.70701	−0.853505	−	0.521084i	$-0.825528\pi$
$223$	−25.4911	−1.70701	−0.853505	+	0.521084i	$0.825528\pi$
$224$	2.75406	0.184014
$225$	−3.70648	−0.247099
$226$	19.2766	1.28226
$227$	12.9585	0.860086	0.430043	−	0.902809i	$-0.358498\pi$
$227$	12.9585	0.860086	0.430043	+	0.902809i	$0.358498\pi$
$228$	−14.5987	−0.966821
$229$	−21.0076	−1.38822	−0.694110	−	0.719869i	$-0.744202\pi$
$229$	−21.0076	−1.38822	−0.694110	+	0.719869i	$0.744202\pi$
$230$	−1.81074	−0.119396
$231$	23.1157	1.52090
$232$	−0.101640	−0.00667302
$233$	16.4743	1.07927	0.539635	−	0.841899i	$-0.318562\pi$
$233$	16.4743	1.07927	0.539635	+	0.841899i	$0.318562\pi$
$234$	10.0311	0.655752
$235$	13.9921	0.912745
$236$	−2.92210	−0.190213
$237$	−35.8960	−2.33170
$238$	11.0409	0.715678
$239$	17.6869	1.14407	0.572035	−	0.820229i	$-0.306154\pi$
$239$	17.6869	1.14407	0.572035	+	0.820229i	$0.306154\pi$
$240$	4.11056	0.265336
$241$	17.7352	1.14243	0.571213	−	0.820802i	$-0.306473\pi$
$241$	17.7352	1.14243	0.571213	+	0.820802i	$0.306473\pi$
$242$	2.67019	0.171646
$243$	18.8038	1.20627
$244$	12.7177	0.814165
$245$	−1.05904	−0.0676598
$246$	23.4754	1.49674
$247$	29.9567	1.90610
$248$	2.69271	0.170987
$249$	−2.52465	−0.159993
$250$	12.1704	0.769723
$251$	5.27663	0.333058	0.166529	−	0.986037i	$-0.446744\pi$
$251$	5.27663	0.333058	0.166529	+	0.986037i	$0.446744\pi$
$252$	5.93056	0.373590
$253$	−3.69732	−0.232449
$254$	10.9371	0.686257
$255$	16.4791	1.03196
$256$	1.00000	0.0625000
$257$	12.2124	0.761786	0.380893	−	0.924619i	$-0.375617\pi$
$257$	12.2124	0.761786	0.380893	+	0.924619i	$0.375617\pi$
$258$	−3.01214	−0.187528
$259$	−5.32869	−0.331109
$260$	−8.43493	−0.523112
$261$	−0.218871	−0.0135478
$262$	1.00000	0.0617802
$263$	29.5732	1.82356	0.911781	−	0.410676i	$-0.134707\pi$
$263$	29.5732	1.82356	0.911781	+	0.410676i	$0.134707\pi$
$264$	8.39332	0.516573
$265$	9.63410	0.591818
$266$	17.7109	1.08593
$267$	4.85244	0.296964
$268$	4.34132	0.265188
$269$	21.9667	1.33933	0.669666	−	0.742662i	$-0.266437\pi$
$269$	21.9667	1.33933	0.669666	+	0.742662i	$0.266437\pi$
$270$	−3.48007	−0.211790
$271$	−12.9223	−0.784973	−0.392487	−	0.919758i	$-0.628385\pi$
$271$	−12.9223	−0.784973	−0.392487	+	0.919758i	$0.628385\pi$
$272$	4.00896	0.243079
$273$	−29.1237	−1.76265
$274$	13.8943	0.839388
$275$	6.36397	0.383762
$276$	−2.27011	−0.136644
$277$	−18.2265	−1.09513	−0.547563	−	0.836764i	$-0.684444\pi$
$277$	−18.2265	−1.09513	−0.547563	+	0.836764i	$0.684444\pi$
$278$	−11.9258	−0.715262
$279$	5.79844	0.347143
$280$	−4.98688	−0.298023
$281$	3.48382	0.207827	0.103914	−	0.994586i	$-0.466863\pi$
$281$	3.48382	0.207827	0.103914	+	0.994586i	$0.466863\pi$
$282$	17.5418	1.04460
$283$	7.53303	0.447792	0.223896	−	0.974613i	$-0.428122\pi$
$283$	7.53303	0.447792	0.223896	+	0.974613i	$0.428122\pi$
$284$	−7.06119	−0.419005
$285$	26.4343	1.56584
$286$	−17.2232	−1.01843
$287$	−28.4801	−1.68113
$288$	2.15338	0.126889
$289$	−0.928206	−0.0546003
$290$	0.184044	0.0108074
$291$	−30.0806	−1.76336
$292$	8.48812	0.496730
$293$	17.4488	1.01937	0.509686	−	0.860361i	$-0.329762\pi$
$293$	17.4488	1.01937	0.509686	+	0.860361i	$0.329762\pi$
$294$	−1.32771	−0.0774339
$295$	5.29115	0.308063
$296$	−1.93485	−0.112461
$297$	−7.10592	−0.412327
$298$	−11.3134	−0.655367
$299$	4.65829	0.269396
$300$	3.90739	0.225593
$301$	3.65429	0.210630
$302$	24.0616	1.38459
$303$	−9.67777	−0.555973
$304$	6.43083	0.368834
$305$	−23.0283	−1.31860
$306$	8.63284	0.493506
$307$	18.3659	1.04820	0.524099	−	0.851657i	$-0.324402\pi$
$307$	18.3659	1.04820	0.524099	+	0.851657i	$0.324402\pi$
$308$	−10.1827	−0.580211
$309$	15.6128	0.888183
$310$	−4.87579	−0.276926
$311$	28.2526	1.60206	0.801028	−	0.598627i	$-0.204287\pi$
$311$	28.2526	1.60206	0.801028	+	0.598627i	$0.204287\pi$
$312$	−10.5748	−0.598681
$313$	−8.91799	−0.504074	−0.252037	−	0.967718i	$-0.581101\pi$
$313$	−8.91799	−0.504074	−0.252037	+	0.967718i	$0.581101\pi$
$314$	21.9569	1.23910
$315$	−10.7387	−0.605055
$316$	15.8125	0.889522
$317$	−32.5822	−1.83000	−0.914998	−	0.403458i	$-0.867808\pi$
$317$	−32.5822	−1.83000	−0.914998	+	0.403458i	$0.867808\pi$
$318$	12.0782	0.677312
$319$	0.375797	0.0210406
$320$	−1.81074	−0.101223
$321$	28.6000	1.59630
$322$	2.75406	0.153478
$323$	25.7810	1.43449
$324$	−10.8231	−0.601283
$325$	−8.01802	−0.444760
$326$	−12.3485	−0.683918
$327$	32.4896	1.79668
$328$	−10.3411	−0.570993
$329$	−21.2815	−1.17329
$330$	−15.1981	−0.836626
$331$	24.3121	1.33632	0.668158	−	0.744019i	$-0.267083\pi$
$331$	24.3121	1.33632	0.668158	+	0.744019i	$0.267083\pi$
$332$	1.11213	0.0610361
$333$	−4.16647	−0.228321
$334$	15.6335	0.855426
$335$	−7.86098	−0.429491
$336$	−6.25202	−0.341076
$337$	22.6806	1.23549	0.617746	−	0.786377i	$-0.288046\pi$
$337$	22.6806	1.23549	0.617746	+	0.786377i	$0.288046\pi$
$338$	8.69966	0.473199
$339$	−43.7599	−2.37671
$340$	−7.25917	−0.393684
$341$	−9.95582	−0.539138
$342$	13.8480	0.748817
$343$	−17.6677	−0.953965
$344$	1.32687	0.0715402
$345$	4.11056	0.221305
$346$	−10.9627	−0.589357
$347$	24.6481	1.32318	0.661589	−	0.749867i	$-0.269882\pi$
$347$	24.6481	1.32318	0.661589	+	0.749867i	$0.269882\pi$
$348$	0.230735	0.0123687
$349$	26.4989	1.41846	0.709228	−	0.704979i	$-0.249044\pi$
$349$	26.4989	1.41846	0.709228	+	0.704979i	$0.249044\pi$
$350$	−4.74040	−0.253385
$351$	8.95281	0.477866
$352$	−3.69732	−0.197068
$353$	10.3969	0.553369	0.276684	−	0.960961i	$-0.410764\pi$
$353$	10.3969	0.553369	0.276684	+	0.960961i	$0.410764\pi$
$354$	6.63348	0.352565
$355$	12.7859	0.678608
$356$	−2.13754	−0.113289
$357$	−25.0641	−1.32653
$358$	−7.23995	−0.382643
$359$	−12.5720	−0.663525	−0.331763	−	0.943363i	$-0.607643\pi$
$359$	−12.5720	−0.663525	−0.331763	+	0.943363i	$0.607643\pi$
$360$	−3.89921	−0.205506
$361$	22.3556	1.17661
$362$	7.36721	0.387212
$363$	−6.06162	−0.318153
$364$	12.8292	0.672434
$365$	−15.3697	−0.804489
$366$	−28.8705	−1.50908
$367$	−17.1556	−0.895516	−0.447758	−	0.894155i	$-0.647777\pi$
$367$	−17.1556	−0.895516	−0.447758	+	0.894155i	$0.647777\pi$
$368$	1.00000	0.0521286
$369$	−22.2684	−1.15925
$370$	3.50350	0.182138
$371$	−14.6531	−0.760753
$372$	−6.11274	−0.316931
$373$	18.4286	0.954195	0.477097	−	0.878850i	$-0.341689\pi$
$373$	18.4286	0.954195	0.477097	+	0.878850i	$0.341689\pi$
$374$	−14.8224	−0.766450
$375$	−27.6281	−1.42671
$376$	−7.72731	−0.398506
$377$	−0.473471	−0.0243850
$378$	5.29306	0.272246
$379$	−23.4999	−1.20711	−0.603554	−	0.797322i	$-0.706249\pi$
$379$	−23.4999	−1.20711	−0.603554	+	0.797322i	$0.706249\pi$
$380$	−11.6445	−0.597352
$381$	−24.8285	−1.27200
$382$	10.7749	0.551290
$383$	−0.0335359	−0.00171360	−0.000856801	−	1.00000i	$-0.500273\pi$
$383$	−0.0335359	−0.00171360	−0.000856801		1.00000i	$0.500273\pi$
$384$	−2.27011	−0.115846
$385$	18.4381	0.939693
$386$	17.7801	0.904986
$387$	2.85726	0.145243
$388$	13.2507	0.672704
$389$	−13.5552	−0.687277	−0.343639	−	0.939102i	$-0.611660\pi$
$389$	−13.5552	−0.687277	−0.343639	+	0.939102i	$0.611660\pi$
$390$	19.1482	0.969606
$391$	4.00896	0.202742
$392$	0.584869	0.0295403
$393$	−2.27011	−0.114512
$394$	7.90253	0.398124
$395$	−28.6322	−1.44064
$396$	−7.96175	−0.400093
$397$	9.69121	0.486388	0.243194	−	0.969978i	$-0.421805\pi$
$397$	9.69121	0.486388	0.243194	+	0.969978i	$0.421805\pi$
$398$	−21.6123	−1.08333
$399$	−40.2057	−2.01280
$400$	−1.72124	−0.0860618
$401$	−13.6563	−0.681961	−0.340980	−	0.940070i	$-0.610759\pi$
$401$	−13.6563	−0.681961	−0.340980	+	0.940070i	$0.610759\pi$
$402$	−9.85526	−0.491535
$403$	12.5434	0.624832
$404$	4.26314	0.212099
$405$	19.5978	0.973820
$406$	−0.279924	−0.0138924
$407$	7.15375	0.354598
$408$	−9.10078	−0.450556
$409$	14.9273	0.738109	0.369055	−	0.929408i	$-0.379682\pi$
$409$	14.9273	0.738109	0.369055	+	0.929408i	$0.379682\pi$
$410$	18.7250	0.924763
$411$	−31.5416	−1.55583
$412$	−6.87758	−0.338834
$413$	−8.04765	−0.395999
$414$	2.15338	0.105833
$415$	−2.01377	−0.0988523
$416$	4.65829	0.228391
$417$	27.0728	1.32576
$418$	−23.7769	−1.16296
$419$	−37.9670	−1.85481	−0.927404	−	0.374062i	$-0.877965\pi$
$419$	−37.9670	−1.85481	−0.927404	+	0.374062i	$0.877965\pi$
$420$	11.3208	0.552396
$421$	15.6129	0.760926	0.380463	−	0.924796i	$-0.375765\pi$
$421$	15.6129	0.760926	0.380463	+	0.924796i	$0.375765\pi$
$422$	−22.9211	−1.11578
$423$	−16.6399	−0.809058
$424$	−5.32055	−0.258389
$425$	−6.90038	−0.334717
$426$	16.0297	0.776639
$427$	35.0253	1.69499
$428$	−12.5985	−0.608973
$429$	39.0985	1.88769
$430$	−2.40261	−0.115864
$431$	−4.74475	−0.228547	−0.114273	−	0.993449i	$-0.536454\pi$
$431$	−4.74475	−0.228547	−0.114273	+	0.993449i	$0.536454\pi$
$432$	1.92191	0.0924679
$433$	−3.48483	−0.167470	−0.0837352	−	0.996488i	$-0.526685\pi$
$433$	−3.48483	−0.167470	−0.0837352	+	0.996488i	$0.526685\pi$
$434$	7.41590	0.355974
$435$	−0.417799	−0.0200319
$436$	−14.3119	−0.685417
$437$	6.43083	0.307628
$438$	−19.2689	−0.920706
$439$	−12.8079	−0.611289	−0.305644	−	0.952146i	$-0.598872\pi$
$439$	−12.8079	−0.611289	−0.305644	+	0.952146i	$0.598872\pi$
$440$	6.69487	0.319166
$441$	1.25945	0.0599737
$442$	18.6749	0.888275
$443$	13.8069	0.655986	0.327993	−	0.944680i	$-0.393628\pi$
$443$	13.8069	0.655986	0.327993	+	0.944680i	$0.393628\pi$
$444$	4.39231	0.208450
$445$	3.87051	0.183480
$446$	−25.4911	−1.20704
$447$	25.6826	1.21475
$448$	2.75406	0.130117
$449$	23.4179	1.10516	0.552580	−	0.833460i	$-0.313643\pi$
$449$	23.4179	1.10516	0.552580	+	0.833460i	$0.313643\pi$
$450$	−3.70648	−0.174725
$451$	38.2344	1.80039
$452$	19.2766	0.906694
$453$	−54.6225	−2.56639
$454$	12.9585	0.608172
$455$	−23.2303	−1.08906
$456$	−14.5987	−0.683646
$457$	−22.7518	−1.06428	−0.532142	−	0.846655i	$-0.678613\pi$
$457$	−22.7518	−1.06428	−0.532142	+	0.846655i	$0.678613\pi$
$458$	−21.0076	−0.981620
$459$	7.70487	0.359632
$460$	−1.81074	−0.0844260
$461$	−23.3017	−1.08527	−0.542634	−	0.839969i	$-0.682573\pi$
$461$	−23.3017	−1.08527	−0.542634	+	0.839969i	$0.682573\pi$
$462$	23.1157	1.07544
$463$	30.1375	1.40061	0.700304	−	0.713845i	$-0.253048\pi$
$463$	30.1375	1.40061	0.700304	+	0.713845i	$0.253048\pi$
$464$	−0.101640	−0.00471854
$465$	11.0686	0.513292
$466$	16.4743	0.763159
$467$	−18.2579	−0.844877	−0.422439	−	0.906392i	$-0.638826\pi$
$467$	−18.2579	−0.844877	−0.422439	+	0.906392i	$0.638826\pi$
$468$	10.0311	0.463687
$469$	11.9563	0.552089
$470$	13.9921	0.645408
$471$	−49.8445	−2.29671
$472$	−2.92210	−0.134501
$473$	−4.90587	−0.225572
$474$	−35.8960	−1.64876
$475$	−11.0690	−0.507880
$476$	11.0409	0.506061
$477$	−11.4572	−0.524588
$478$	17.6869	0.808979
$479$	11.4631	0.523763	0.261881	−	0.965100i	$-0.415657\pi$
$479$	11.4631	0.523763	0.261881	+	0.965100i	$0.415657\pi$
$480$	4.11056	0.187621
$481$	−9.01308	−0.410961
$482$	17.7352	0.807817
$483$	−6.25202	−0.284477
$484$	2.67019	0.121372
$485$	−23.9936	−1.08949
$486$	18.8038	0.852959
$487$	19.3792	0.878156	0.439078	−	0.898449i	$-0.355305\pi$
$487$	19.3792	0.878156	0.439078	+	0.898449i	$0.355305\pi$
$488$	12.7177	0.575702
$489$	28.0323	1.26767
$490$	−1.05904	−0.0478427
$491$	8.63766	0.389812	0.194906	−	0.980822i	$-0.437560\pi$
$491$	8.63766	0.389812	0.194906	+	0.980822i	$0.437560\pi$
$492$	23.4754	1.05835
$493$	−0.407473	−0.0183517
$494$	29.9567	1.34781
$495$	14.4166	0.647979
$496$	2.69271	0.120906
$497$	−19.4470	−0.872316
$498$	−2.52465	−0.113132
$499$	−12.5381	−0.561281	−0.280640	−	0.959813i	$-0.590547\pi$
$499$	−12.5381	−0.561281	−0.280640	+	0.959813i	$0.590547\pi$
$500$	12.1704	0.544276
$501$	−35.4897	−1.58556
$502$	5.27663	0.235508
$503$	36.7462	1.63843	0.819216	−	0.573485i	$-0.194409\pi$
$503$	36.7462	1.63843	0.819216	+	0.573485i	$0.194409\pi$
$504$	5.93056	0.264168
$505$	−7.71941	−0.343509
$506$	−3.69732	−0.164366
$507$	−19.7492	−0.877091
$508$	10.9371	0.485257
$509$	−6.54858	−0.290261	−0.145130	−	0.989413i	$-0.546360\pi$
$509$	−6.54858	−0.290261	−0.145130	+	0.989413i	$0.546360\pi$
$510$	16.4791	0.729707
$511$	23.3768	1.03413
$512$	1.00000	0.0441942
$513$	12.3595	0.545684
$514$	12.2124	0.538664
$515$	12.4535	0.548766
$516$	−3.01214	−0.132602
$517$	28.5704	1.25652
$518$	−5.32869	−0.234129
$519$	24.8864	1.09239
$520$	−8.43493	−0.369896
$521$	−14.0049	−0.613564	−0.306782	−	0.951780i	$-0.599252\pi$
$521$	−14.0049	−0.613564	−0.306782	+	0.951780i	$0.599252\pi$
$522$	−0.218871	−0.00957972
$523$	−29.6434	−1.29621	−0.648107	−	0.761549i	$-0.724439\pi$
$523$	−29.6434	−1.29621	−0.648107	+	0.761549i	$0.724439\pi$
$524$	1.00000	0.0436852
$525$	10.7612	0.469658
$526$	29.5732	1.28945
$527$	10.7950	0.470237
$528$	8.39332	0.365272
$529$	1.00000	0.0434783
$530$	9.63410	0.418479
$531$	−6.29240	−0.273067
$532$	17.7109	0.767866
$533$	−48.1719	−2.08656
$534$	4.85244	0.209985
$535$	22.8126	0.986275
$536$	4.34132	0.187516
$537$	16.4355	0.709242
$538$	21.9667	0.947051
$539$	−2.16245	−0.0931433
$540$	−3.48007	−0.149758
$541$	36.3124	1.56119	0.780596	−	0.625035i	$-0.214915\pi$
$541$	36.3124	1.56119	0.780596	+	0.625035i	$0.214915\pi$
$542$	−12.9223	−0.555060
$543$	−16.7244	−0.717711
$544$	4.00896	0.171883
$545$	25.9151	1.11008
$546$	−29.1237	−1.24638
$547$	14.2823	0.610667	0.305333	−	0.952246i	$-0.401232\pi$
$547$	14.2823	0.610667	0.305333	+	0.952246i	$0.401232\pi$
$548$	13.8943	0.593537
$549$	27.3860	1.16881
$550$	6.36397	0.271360
$551$	−0.653633	−0.0278457
$552$	−2.27011	−0.0966221
$553$	43.5486	1.85187
$554$	−18.2265	−0.774371
$555$	−7.95331	−0.337599
$556$	−11.9258	−0.505766
$557$	20.4947	0.868390	0.434195	−	0.900819i	$-0.357033\pi$
$557$	20.4947	0.868390	0.434195	+	0.900819i	$0.357033\pi$
$558$	5.79844	0.245467
$559$	6.18095	0.261427
$560$	−4.98688	−0.210734
$561$	33.6485	1.42064
$562$	3.48382	0.146956
$563$	39.8683	1.68025	0.840124	−	0.542395i	$-0.182482\pi$
$563$	39.8683	1.68025	0.840124	+	0.542395i	$0.182482\pi$
$564$	17.5418	0.738644
$565$	−34.9048	−1.46846
$566$	7.53303	0.316637
$567$	−29.8075	−1.25180
$568$	−7.06119	−0.296281
$569$	34.0073	1.42566	0.712831	−	0.701336i	$-0.247413\pi$
$569$	34.0073	1.42566	0.712831	+	0.701336i	$0.247413\pi$
$570$	26.4343	1.10721
$571$	−34.0898	−1.42661	−0.713307	−	0.700852i	$-0.752803\pi$
$571$	−34.0898	−1.42661	−0.713307	+	0.700852i	$0.752803\pi$
$572$	−17.2232	−0.720138
$573$	−24.4601	−1.02183
$574$	−28.4801	−1.18874
$575$	−1.72124	−0.0717805
$576$	2.15338	0.0897243
$577$	14.6652	0.610519	0.305259	−	0.952269i	$-0.401257\pi$
$577$	14.6652	0.610519	0.305259	+	0.952269i	$0.401257\pi$
$578$	−0.928206	−0.0386083
$579$	−40.3628	−1.67742
$580$	0.184044	0.00764201
$581$	3.06288	0.127070
$582$	−30.0806	−1.24688
$583$	19.6718	0.814722
$584$	8.48812	0.351241
$585$	−18.1636	−0.750974
$586$	17.4488	0.720805
$587$	−28.6183	−1.18120	−0.590601	−	0.806964i	$-0.701109\pi$
$587$	−28.6183	−1.18120	−0.590601	+	0.806964i	$0.701109\pi$
$588$	−1.32771	−0.0547540
$589$	17.3164	0.713508
$590$	5.29115	0.217833
$591$	−17.9396	−0.737936
$592$	−1.93485	−0.0795217
$593$	16.6164	0.682354	0.341177	−	0.939999i	$-0.389174\pi$
$593$	16.6164	0.682354	0.341177	+	0.939999i	$0.389174\pi$
$594$	−7.10592	−0.291559
$595$	−19.9922	−0.819602
$596$	−11.3134	−0.463414
$597$	49.0622	2.00798
$598$	4.65829	0.190492
$599$	−3.64354	−0.148871	−0.0744356	−	0.997226i	$-0.523716\pi$
$599$	−3.64354	−0.148871	−0.0744356	+	0.997226i	$0.523716\pi$
$600$	3.90739	0.159519
$601$	7.47458	0.304894	0.152447	−	0.988312i	$-0.451285\pi$
$601$	7.47458	0.304894	0.152447	+	0.988312i	$0.451285\pi$
$602$	3.65429	0.148938
$603$	9.34852	0.380701
$604$	24.0616	0.979054
$605$	−4.83501	−0.196571
$606$	−9.67777	−0.393133
$607$	−21.8790	−0.888041	−0.444020	−	0.896017i	$-0.646448\pi$
$607$	−21.8790	−0.888041	−0.444020	+	0.896017i	$0.646448\pi$
$608$	6.43083	0.260805
$609$	0.635458	0.0257501
$610$	−23.0283	−0.932390
$611$	−35.9961	−1.45624
$612$	8.63284	0.348962
$613$	−40.9160	−1.65258	−0.826291	−	0.563243i	$-0.809554\pi$
$613$	−40.9160	−1.65258	−0.826291	+	0.563243i	$0.809554\pi$
$614$	18.3659	0.741188
$615$	−42.5078	−1.71408
$616$	−10.1827	−0.410271
$617$	0.932093	0.0375247	0.0187623	−	0.999824i	$-0.494027\pi$
$617$	0.932093	0.0375247	0.0187623	+	0.999824i	$0.494027\pi$
$618$	15.6128	0.628040
$619$	−43.7154	−1.75707	−0.878534	−	0.477679i	$-0.841478\pi$
$619$	−43.7154	−1.75707	−0.878534	+	0.477679i	$0.841478\pi$
$620$	−4.87579	−0.195816
$621$	1.92191	0.0771236
$622$	28.2526	1.13282
$623$	−5.88691	−0.235854
$624$	−10.5748	−0.423331
$625$	−13.4312	−0.537246
$626$	−8.91799	−0.356434
$627$	53.9760	2.15559
$628$	21.9569	0.876175
$629$	−7.75673	−0.309281
$630$	−10.7387	−0.427839
$631$	−12.4796	−0.496806	−0.248403	−	0.968657i	$-0.579906\pi$
$631$	−12.4796	−0.496806	−0.248403	+	0.968657i	$0.579906\pi$
$632$	15.8125	0.628987
$633$	52.0333	2.06814
$634$	−32.5822	−1.29400
$635$	−19.8043	−0.785908
$636$	12.0782	0.478932
$637$	2.72449	0.107948
$638$	0.375797	0.0148780
$639$	−15.2055	−0.601518
$640$	−1.81074	−0.0715756
$641$	19.4722	0.769107	0.384553	−	0.923103i	$-0.374355\pi$
$641$	19.4722	0.769107	0.384553	+	0.923103i	$0.374355\pi$
$642$	28.6000	1.12875
$643$	11.4979	0.453433	0.226716	−	0.973961i	$-0.427201\pi$
$643$	11.4979	0.453433	0.226716	+	0.973961i	$0.427201\pi$
$644$	2.75406	0.108525
$645$	5.45419	0.214759
$646$	25.7810	1.01434
$647$	16.8266	0.661523	0.330761	−	0.943714i	$-0.392694\pi$
$647$	16.8266	0.661523	0.330761	+	0.943714i	$0.392694\pi$
$648$	−10.8231	−0.425171
$649$	10.8039	0.424092
$650$	−8.01802	−0.314493
$651$	−16.8349	−0.659811
$652$	−12.3485	−0.483603
$653$	8.87311	0.347232	0.173616	−	0.984813i	$-0.444455\pi$
$653$	8.87311	0.347232	0.173616	+	0.984813i	$0.444455\pi$
$654$	32.4896	1.27044
$655$	−1.81074	−0.0707513
$656$	−10.3411	−0.403753
$657$	18.2782	0.713100
$658$	−21.2815	−0.829640
$659$	−8.54643	−0.332922	−0.166461	−	0.986048i	$-0.553234\pi$
$659$	−8.54643	−0.332922	−0.166461	+	0.986048i	$0.553234\pi$
$660$	−15.1981	−0.591584
$661$	31.6866	1.23247	0.616233	−	0.787564i	$-0.288658\pi$
$661$	31.6866	1.23247	0.616233	+	0.787564i	$0.288658\pi$
$662$	24.3121	0.944918
$663$	−42.3940	−1.64645
$664$	1.11213	0.0431590
$665$	−32.0698	−1.24361
$666$	−4.16647	−0.161447
$667$	−0.101640	−0.00393553
$668$	15.6335	0.604878
$669$	57.8675	2.23729
$670$	−7.86098	−0.303696
$671$	−47.0213	−1.81524
$672$	−6.25202	−0.241177
$673$	−13.7173	−0.528764	−0.264382	−	0.964418i	$-0.585168\pi$
$673$	−13.7173	−0.528764	−0.264382	+	0.964418i	$0.585168\pi$
$674$	22.6806	0.873625
$675$	−3.30806	−0.127327
$676$	8.69966	0.334602
$677$	6.22810	0.239365	0.119683	−	0.992812i	$-0.461812\pi$
$677$	6.22810	0.239365	0.119683	+	0.992812i	$0.461812\pi$
$678$	−43.7599	−1.68059
$679$	36.4934	1.40049
$680$	−7.25917	−0.278377
$681$	−29.4172	−1.12727
$682$	−9.95582	−0.381228
$683$	8.25264	0.315779	0.157889	−	0.987457i	$-0.449531\pi$
$683$	8.25264	0.315779	0.157889	+	0.987457i	$0.449531\pi$
$684$	13.8480	0.529493
$685$	−25.1590	−0.961275
$686$	−17.6677	−0.674555
$687$	47.6894	1.81947
$688$	1.32687	0.0505865
$689$	−24.7846	−0.944220
$690$	4.11056	0.156486
$691$	−37.9457	−1.44352	−0.721761	−	0.692142i	$-0.756667\pi$
$691$	−37.9457	−1.44352	−0.721761	+	0.692142i	$0.756667\pi$
$692$	−10.9627	−0.416738
$693$	−21.9272	−0.832945
$694$	24.6481	0.935628
$695$	21.5945	0.819125
$696$	0.230735	0.00874597
$697$	−41.4572	−1.57030
$698$	26.4989	1.00300
$699$	−37.3985	−1.41454
$700$	−4.74040	−0.179170
$701$	47.6696	1.80045	0.900227	−	0.435421i	$-0.143400\pi$
$701$	47.6696	1.80045	0.900227	+	0.435421i	$0.143400\pi$
$702$	8.95281	0.337902
$703$	−12.4427	−0.469284
$704$	−3.69732	−0.139348
$705$	−31.7636	−1.19629
$706$	10.3969	0.391291
$707$	11.7409	0.441564
$708$	6.63348	0.249301
$709$	−16.6544	−0.625467	−0.312734	−	0.949841i	$-0.601245\pi$
$709$	−16.6544	−0.625467	−0.312734	+	0.949841i	$0.601245\pi$
$710$	12.7859	0.479848
$711$	34.0503	1.27699
$712$	−2.13754	−0.0801076
$713$	2.69271	0.100843
$714$	−25.0641	−0.938001
$715$	31.1867	1.16631
$716$	−7.23995	−0.270570
$717$	−40.1511	−1.49947
$718$	−12.5720	−0.469183
$719$	−45.3495	−1.69125	−0.845625	−	0.533778i	$-0.820772\pi$
$719$	−45.3495	−1.69125	−0.845625	+	0.533778i	$0.820772\pi$
$720$	−3.89921	−0.145315
$721$	−18.9413	−0.705411
$722$	22.3556	0.831990
$723$	−40.2608	−1.49732
$724$	7.36721	0.273800
$725$	0.174947	0.00649738
$726$	−6.06162	−0.224968
$727$	34.3081	1.27242	0.636209	−	0.771516i	$-0.280501\pi$
$727$	34.3081	1.27242	0.636209	+	0.771516i	$0.280501\pi$
$728$	12.8292	0.475483
$729$	−10.2174	−0.378424
$730$	−15.3697	−0.568860
$731$	5.31938	0.196744
$732$	−28.8705	−1.06708
$733$	−45.7316	−1.68914	−0.844568	−	0.535449i	$-0.820142\pi$
$733$	−45.7316	−1.68914	−0.844568	+	0.535449i	$0.820142\pi$
$734$	−17.1556	−0.633225
$735$	2.40414	0.0886781
$736$	1.00000	0.0368605
$737$	−16.0513	−0.591256
$738$	−22.2684	−0.819711
$739$	47.3456	1.74163	0.870817	−	0.491607i	$-0.163590\pi$
$739$	47.3456	1.74163	0.870817	+	0.491607i	$0.163590\pi$
$740$	3.50350	0.128791
$741$	−68.0049	−2.49822
$742$	−14.6531	−0.537933
$743$	−0.480359	−0.0176227	−0.00881133	−	0.999961i	$-0.502805\pi$
$743$	−0.480359	−0.0176227	−0.00881133	+	0.999961i	$0.502805\pi$
$744$	−6.11274	−0.224104
$745$	20.4856	0.750533
$746$	18.4286	0.674718
$747$	2.39484	0.0876227
$748$	−14.8224	−0.541962
$749$	−34.6972	−1.26781
$750$	−27.6281	−1.00883
$751$	−46.8718	−1.71038	−0.855188	−	0.518318i	$-0.826559\pi$
$751$	−46.8718	−1.71038	−0.855188	+	0.518318i	$0.826559\pi$
$752$	−7.72731	−0.281786
$753$	−11.9785	−0.436521
$754$	−0.473471	−0.0172428
$755$	−43.5693	−1.58565
$756$	5.29306	0.192507
$757$	17.6363	0.641003	0.320502	−	0.947248i	$-0.396149\pi$
$757$	17.6363	0.641003	0.320502	+	0.947248i	$0.396149\pi$
$758$	−23.4999	−0.853554
$759$	8.39332	0.304658
$760$	−11.6445	−0.422392
$761$	15.2743	0.553694	0.276847	−	0.960914i	$-0.410711\pi$
$761$	15.2743	0.553694	0.276847	+	0.960914i	$0.410711\pi$
$762$	−24.8285	−0.899441
$763$	−39.4160	−1.42695
$764$	10.7749	0.389821
$765$	−15.6318	−0.565168
$766$	−0.0335359	−0.00121170
$767$	−13.6120	−0.491500
$768$	−2.27011	−0.0819154
$769$	−4.83977	−0.174527	−0.0872634	−	0.996185i	$-0.527812\pi$
$769$	−4.83977	−0.174527	−0.0872634	+	0.996185i	$0.527812\pi$
$770$	18.4381	0.664463
$771$	−27.7233	−0.998432
$772$	17.7801	0.639922
$773$	−35.7120	−1.28447	−0.642236	−	0.766507i	$-0.721993\pi$
$773$	−35.7120	−1.28447	−0.642236	+	0.766507i	$0.721993\pi$
$774$	2.85726	0.102702
$775$	−4.63479	−0.166487
$776$	13.2507	0.475674
$777$	12.0967	0.433967
$778$	−13.5552	−0.485979
$779$	−66.5020	−2.38268
$780$	19.1482	0.685615
$781$	26.1075	0.934200
$782$	4.00896	0.143360
$783$	−0.195344	−0.00698102
$784$	0.584869	0.0208882
$785$	−39.7581	−1.41903
$786$	−2.27011	−0.0809720
$787$	−20.9918	−0.748276	−0.374138	−	0.927373i	$-0.622061\pi$
$787$	−20.9918	−0.748276	−0.374138	+	0.927373i	$0.622061\pi$
$788$	7.90253	0.281516
$789$	−67.1344	−2.39005
$790$	−28.6322	−1.01869
$791$	53.0889	1.88762
$792$	−7.96175	−0.282909
$793$	59.2426	2.10377
$794$	9.69121	0.343928
$795$	−21.8704	−0.775665
$796$	−21.6123	−0.766028
$797$	−14.1563	−0.501443	−0.250721	−	0.968059i	$-0.580668\pi$
$797$	−14.1563	−0.501443	−0.250721	+	0.968059i	$0.580668\pi$
$798$	−40.2057	−1.42327
$799$	−30.9785	−1.09594
$800$	−1.72124	−0.0608549
$801$	−4.60294	−0.162637
$802$	−13.6563	−0.482219
$803$	−31.3833	−1.10749
$804$	−9.85526	−0.347568
$805$	−4.98688	−0.175764
$806$	12.5434	0.441823
$807$	−49.8667	−1.75539
$808$	4.26314	0.149977
$809$	38.0797	1.33881	0.669405	−	0.742898i	$-0.266549\pi$
$809$	38.0797	1.33881	0.669405	+	0.742898i	$0.266549\pi$
$810$	19.5978	0.688595
$811$	−28.9634	−1.01704	−0.508520	−	0.861050i	$-0.669807\pi$
$811$	−28.9634	−1.01704	−0.508520	+	0.861050i	$0.669807\pi$
$812$	−0.279924	−0.00982342
$813$	29.3350	1.02882
$814$	7.15375	0.250739
$815$	22.3598	0.783229
$816$	−9.10078	−0.318591
$817$	8.53289	0.298528
$818$	14.9273	0.521922
$819$	27.6262	0.965339
$820$	18.7250	0.653906
$821$	44.6184	1.55719	0.778596	−	0.627525i	$-0.215932\pi$
$821$	44.6184	1.55719	0.778596	+	0.627525i	$0.215932\pi$
$822$	−31.5416	−1.10014
$823$	−11.2686	−0.392799	−0.196400	−	0.980524i	$-0.562925\pi$
$823$	−11.2686	−0.392799	−0.196400	+	0.980524i	$0.562925\pi$
$824$	−6.87758	−0.239592
$825$	−14.4469	−0.502976
$826$	−8.04765	−0.280014
$827$	−15.8935	−0.552670	−0.276335	−	0.961061i	$-0.589120\pi$
$827$	−15.8935	−0.552670	−0.276335	+	0.961061i	$0.589120\pi$
$828$	2.15338	0.0748353
$829$	−4.08082	−0.141733	−0.0708664	−	0.997486i	$-0.522576\pi$
$829$	−4.08082	−0.141733	−0.0708664	+	0.997486i	$0.522576\pi$
$830$	−2.01377	−0.0698991
$831$	41.3762	1.43532
$832$	4.65829	0.161497
$833$	2.34472	0.0812397
$834$	27.0728	0.937455
$835$	−28.3081	−0.979643
$836$	−23.7769	−0.822340
$837$	5.17514	0.178879
$838$	−37.9670	−1.31155
$839$	−36.8015	−1.27053	−0.635264	−	0.772295i	$-0.719109\pi$
$839$	−36.8015	−1.27053	−0.635264	+	0.772295i	$0.719109\pi$
$840$	11.3208	0.390603
$841$	−28.9897	−0.999644
$842$	15.6129	0.538056
$843$	−7.90865	−0.272388
$844$	−22.9211	−0.788977
$845$	−15.7528	−0.541912
$846$	−16.6399	−0.572090
$847$	7.35388	0.252682
$848$	−5.32055	−0.182708
$849$	−17.1008	−0.586897
$850$	−6.90038	−0.236681
$851$	−1.93485	−0.0663257
$852$	16.0297	0.549167
$853$	−13.2963	−0.455256	−0.227628	−	0.973748i	$-0.573097\pi$
$853$	−13.2963	−0.455256	−0.227628	+	0.973748i	$0.573097\pi$
$854$	35.0253	1.19854
$855$	−25.0752	−0.857552
$856$	−12.5985	−0.430609
$857$	8.53081	0.291407	0.145703	−	0.989328i	$-0.453455\pi$
$857$	8.53081	0.291407	0.145703	+	0.989328i	$0.453455\pi$
$858$	39.0985	1.33480
$859$	−8.07792	−0.275615	−0.137808	−	0.990459i	$-0.544006\pi$
$859$	−8.07792	−0.275615	−0.137808	+	0.990459i	$0.544006\pi$
$860$	−2.40261	−0.0819285
$861$	64.6529	2.20336
$862$	−4.74475	−0.161607
$863$	−22.2800	−0.758420	−0.379210	−	0.925311i	$-0.623804\pi$
$863$	−22.2800	−0.758420	−0.379210	+	0.925311i	$0.623804\pi$
$864$	1.92191	0.0653847
$865$	19.8505	0.674937
$866$	−3.48483	−0.118419
$867$	2.10713	0.0715617
$868$	7.41590	0.251712
$869$	−58.4639	−1.98325
$870$	−0.417799	−0.0141647
$871$	20.2231	0.685234
$872$	−14.3119	−0.484663
$873$	28.5339	0.965727
$874$	6.43083	0.217526
$875$	33.5180	1.13312
$876$	−19.2689	−0.651037
$877$	−14.1688	−0.478445	−0.239222	−	0.970965i	$-0.576893\pi$
$877$	−14.1688	−0.478445	−0.239222	+	0.970965i	$0.576893\pi$
$878$	−12.8079	−0.432246
$879$	−39.6107	−1.33604
$880$	6.69487	0.225684
$881$	34.4160	1.15950	0.579752	−	0.814793i	$-0.303149\pi$
$881$	34.4160	1.15950	0.579752	+	0.814793i	$0.303149\pi$
$882$	1.25945	0.0424078
$883$	2.77337	0.0933315	0.0466657	−	0.998911i	$-0.485140\pi$
$883$	2.77337	0.0933315	0.0466657	+	0.998911i	$0.485140\pi$
$884$	18.6749	0.628105
$885$	−12.0115	−0.403761
$886$	13.8069	0.463852
$887$	−5.21881	−0.175230	−0.0876152	−	0.996154i	$-0.527925\pi$
$887$	−5.21881	−0.175230	−0.0876152	+	0.996154i	$0.527925\pi$
$888$	4.39231	0.147396
$889$	30.1216	1.01025
$890$	3.87051	0.129740
$891$	40.0165	1.34060
$892$	−25.4911	−0.853505
$893$	−49.6931	−1.66291
$894$	25.6826	0.858955
$895$	13.1096	0.438207
$896$	2.75406	0.0920068
$897$	−10.5748	−0.353083
$898$	23.4179	0.781466
$899$	−0.273688	−0.00912801
$900$	−3.70648	−0.123549
$901$	−21.3299	−0.710601
$902$	38.2344	1.27307
$903$	−8.29563	−0.276061
$904$	19.2766	0.641129
$905$	−13.3401	−0.443439
$906$	−54.6225	−1.81471
$907$	−4.98783	−0.165618	−0.0828091	−	0.996565i	$-0.526389\pi$
$907$	−4.98783	−0.165618	−0.0828091	+	0.996565i	$0.526389\pi$
$908$	12.9585	0.430043
$909$	9.18017	0.304487
$910$	−23.2303	−0.770078
$911$	10.7217	0.355225	0.177612	−	0.984101i	$-0.443163\pi$
$911$	10.7217	0.355225	0.177612	+	0.984101i	$0.443163\pi$
$912$	−14.5987	−0.483410
$913$	−4.11190	−0.136084
$914$	−22.7518	−0.752563
$915$	52.2768	1.72822
$916$	−21.0076	−0.694110
$917$	2.75406	0.0909472
$918$	7.70487	0.254298
$919$	30.5345	1.00724	0.503620	−	0.863926i	$-0.332001\pi$
$919$	30.5345	1.00724	0.503620	+	0.863926i	$0.332001\pi$
$920$	−1.81074	−0.0596982
$921$	−41.6926	−1.37382
$922$	−23.3017	−0.767401
$923$	−32.8931	−1.08269
$924$	23.1157	0.760452
$925$	3.33033	0.109501
$926$	30.1375	0.990379
$927$	−14.8101	−0.486426
$928$	−0.101640	−0.00333651
$929$	15.0845	0.494905	0.247453	−	0.968900i	$-0.420407\pi$
$929$	15.0845	0.494905	0.247453	+	0.968900i	$0.420407\pi$
$930$	11.0686	0.362952
$931$	3.76119	0.123268
$932$	16.4743	0.539635
$933$	−64.1363	−2.09973
$934$	−18.2579	−0.597418
$935$	26.8395	0.877746
$936$	10.0311	0.327876
$937$	−31.2724	−1.02162	−0.510812	−	0.859693i	$-0.670655\pi$
$937$	−31.2724	−1.02162	−0.510812	+	0.859693i	$0.670655\pi$
$938$	11.9563	0.390386
$939$	20.2448	0.660663
$940$	13.9921	0.456373
$941$	4.54397	0.148129	0.0740646	−	0.997253i	$-0.476403\pi$
$941$	4.54397	0.148129	0.0740646	+	0.997253i	$0.476403\pi$
$942$	−49.8445	−1.62402
$943$	−10.3411	−0.336753
$944$	−2.92210	−0.0951063
$945$	−9.58434	−0.311778
$946$	−4.90587	−0.159504
$947$	41.8729	1.36069	0.680344	−	0.732893i	$-0.261831\pi$
$947$	41.8729	1.36069	0.680344	+	0.732893i	$0.261831\pi$
$948$	−35.8960	−1.16585
$949$	39.5401	1.28353
$950$	−11.0690	−0.359125
$951$	73.9650	2.39848
$952$	11.0409	0.357839
$953$	−7.67464	−0.248606	−0.124303	−	0.992244i	$-0.539669\pi$
$953$	−7.67464	−0.248606	−0.124303	+	0.992244i	$0.539669\pi$
$954$	−11.4572	−0.370940
$955$	−19.5104	−0.631343
$956$	17.6869	0.572035
$957$	−0.853100	−0.0275768
$958$	11.4631	0.370356
$959$	38.2659	1.23567
$960$	4.11056	0.132668
$961$	−23.7493	−0.766107
$962$	−9.01308	−0.290593
$963$	−27.1295	−0.874235
$964$	17.7352	0.571213
$965$	−32.1951	−1.03640
$966$	−6.25202	−0.201155
$967$	41.8258	1.34503	0.672514	−	0.740085i	$-0.265215\pi$
$967$	41.8258	1.34503	0.672514	+	0.740085i	$0.265215\pi$
$968$	2.67019	0.0858232
$969$	−58.5256	−1.88011
$970$	−23.9936	−0.770387
$971$	−53.8138	−1.72697	−0.863484	−	0.504377i	$-0.831722\pi$
$971$	−53.8138	−1.72697	−0.863484	+	0.504377i	$0.831722\pi$
$972$	18.8038	0.603133
$973$	−32.8444	−1.05294
$974$	19.3792	0.620950
$975$	18.2018	0.582923
$976$	12.7177	0.407083
$977$	−9.80855	−0.313803	−0.156902	−	0.987614i	$-0.550151\pi$
$977$	−9.80855	−0.313803	−0.156902	+	0.987614i	$0.550151\pi$
$978$	28.0323	0.896375
$979$	7.90316	0.252586
$980$	−1.05904	−0.0338299
$981$	−30.8191	−0.983978
$982$	8.63766	0.275639
$983$	−54.4333	−1.73615	−0.868077	−	0.496430i	$-0.834644\pi$
$983$	−54.4333	−1.73615	−0.868077	+	0.496430i	$0.834644\pi$
$984$	23.4754	0.748370
$985$	−14.3094	−0.455935
$986$	−0.407473	−0.0129766
$987$	48.3113	1.53777
$988$	29.9567	0.953049
$989$	1.32687	0.0421921
$990$	14.4166	0.458191
$991$	37.2744	1.18406	0.592030	−	0.805916i	$-0.298327\pi$
$991$	37.2744	1.18406	0.592030	+	0.805916i	$0.298327\pi$
$992$	2.69271	0.0854936
$993$	−55.1911	−1.75144
$994$	−19.4470	−0.616820
$995$	39.1342	1.24064
$996$	−2.52465	−0.0799967
$997$	−61.2371	−1.93940	−0.969700	−	0.244300i	$-0.921442\pi$
$997$	−61.2371	−1.93940	−0.969700	+	0.244300i	$0.921442\pi$
$998$	−12.5381	−0.396885
$999$	−3.71860	−0.117651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.9	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.9	✓	41	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.27011 q^{3} +1.00000 q^{4} -1.81074 q^{5} -2.27011 q^{6} +2.75406 q^{7} +1.00000 q^{8} +2.15338 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.27011 q^{3} +1.00000 q^{4} -1.81074 q^{5} -2.27011 q^{6} +2.75406 q^{7} +1.00000 q^{8} +2.15338 q^{9} -1.81074 q^{10} -3.69732 q^{11} -2.27011 q^{12} +4.65829 q^{13} +2.75406 q^{14} +4.11056 q^{15} +1.00000 q^{16} +4.00896 q^{17} +2.15338 q^{18} +6.43083 q^{19} -1.81074 q^{20} -6.25202 q^{21} -3.69732 q^{22} +1.00000 q^{23} -2.27011 q^{24} -1.72124 q^{25} +4.65829 q^{26} +1.92191 q^{27} +2.75406 q^{28} -0.101640 q^{29} +4.11056 q^{30} +2.69271 q^{31} +1.00000 q^{32} +8.39332 q^{33} +4.00896 q^{34} -4.98688 q^{35} +2.15338 q^{36} -1.93485 q^{37} +6.43083 q^{38} -10.5748 q^{39} -1.81074 q^{40} -10.3411 q^{41} -6.25202 q^{42} +1.32687 q^{43} -3.69732 q^{44} -3.89921 q^{45} +1.00000 q^{46} -7.72731 q^{47} -2.27011 q^{48} +0.584869 q^{49} -1.72124 q^{50} -9.10078 q^{51} +4.65829 q^{52} -5.32055 q^{53} +1.92191 q^{54} +6.69487 q^{55} +2.75406 q^{56} -14.5987 q^{57} -0.101640 q^{58} -2.92210 q^{59} +4.11056 q^{60} +12.7177 q^{61} +2.69271 q^{62} +5.93056 q^{63} +1.00000 q^{64} -8.43493 q^{65} +8.39332 q^{66} +4.34132 q^{67} +4.00896 q^{68} -2.27011 q^{69} -4.98688 q^{70} -7.06119 q^{71} +2.15338 q^{72} +8.48812 q^{73} -1.93485 q^{74} +3.90739 q^{75} +6.43083 q^{76} -10.1827 q^{77} -10.5748 q^{78} +15.8125 q^{79} -1.81074 q^{80} -10.8231 q^{81} -10.3411 q^{82} +1.11213 q^{83} -6.25202 q^{84} -7.25917 q^{85} +1.32687 q^{86} +0.230735 q^{87} -3.69732 q^{88} -2.13754 q^{89} -3.89921 q^{90} +12.8292 q^{91} +1.00000 q^{92} -6.11274 q^{93} -7.72731 q^{94} -11.6445 q^{95} -2.27011 q^{96} +13.2507 q^{97} +0.584869 q^{98} -7.96175 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

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