LMFDB - Embedded newform 6026.2.a.m.1.15

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			1.15
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.990574 q^{3} +1.00000 q^{4} +4.23904 q^{5} -0.990574 q^{6} -4.18696 q^{7} +1.00000 q^{8} -2.01876 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.990574 q^{3} +1.00000 q^{4} +4.23904 q^{5} -0.990574 q^{6} -4.18696 q^{7} +1.00000 q^{8} -2.01876 q^{9} +4.23904 q^{10} -4.64963 q^{11} -0.990574 q^{12} -2.88609 q^{13} -4.18696 q^{14} -4.19909 q^{15} +1.00000 q^{16} +6.19917 q^{17} -2.01876 q^{18} +4.17285 q^{19} +4.23904 q^{20} +4.14750 q^{21} -4.64963 q^{22} +1.00000 q^{23} -0.990574 q^{24} +12.9695 q^{25} -2.88609 q^{26} +4.97146 q^{27} -4.18696 q^{28} -3.53526 q^{29} -4.19909 q^{30} -6.53898 q^{31} +1.00000 q^{32} +4.60580 q^{33} +6.19917 q^{34} -17.7487 q^{35} -2.01876 q^{36} +8.77913 q^{37} +4.17285 q^{38} +2.85888 q^{39} +4.23904 q^{40} +0.889308 q^{41} +4.14750 q^{42} +9.47962 q^{43} -4.64963 q^{44} -8.55762 q^{45} +1.00000 q^{46} +3.37309 q^{47} -0.990574 q^{48} +10.5307 q^{49} +12.9695 q^{50} -6.14074 q^{51} -2.88609 q^{52} -5.23757 q^{53} +4.97146 q^{54} -19.7100 q^{55} -4.18696 q^{56} -4.13352 q^{57} -3.53526 q^{58} -14.4993 q^{59} -4.19909 q^{60} +5.45134 q^{61} -6.53898 q^{62} +8.45248 q^{63} +1.00000 q^{64} -12.2342 q^{65} +4.60580 q^{66} +12.4749 q^{67} +6.19917 q^{68} -0.990574 q^{69} -17.7487 q^{70} -8.58867 q^{71} -2.01876 q^{72} +5.07471 q^{73} +8.77913 q^{74} -12.8472 q^{75} +4.17285 q^{76} +19.4678 q^{77} +2.85888 q^{78} -7.35263 q^{79} +4.23904 q^{80} +1.13169 q^{81} +0.889308 q^{82} +2.15419 q^{83} +4.14750 q^{84} +26.2785 q^{85} +9.47962 q^{86} +3.50193 q^{87} -4.64963 q^{88} +13.5167 q^{89} -8.55762 q^{90} +12.0839 q^{91} +1.00000 q^{92} +6.47735 q^{93} +3.37309 q^{94} +17.6889 q^{95} -0.990574 q^{96} +11.9593 q^{97} +10.5307 q^{98} +9.38650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.990574	−0.571908	−0.285954	−	0.958243i	$-0.592310\pi$
$3$	−0.990574	−0.571908	−0.285954	+	0.958243i	$0.592310\pi$
$4$	1.00000	0.500000
$5$	4.23904	1.89576	0.947879	−	0.318631i	$-0.103223\pi$
$5$	4.23904	1.89576	0.947879	+	0.318631i	$0.103223\pi$
$6$	−0.990574	−0.404400
$7$	−4.18696	−1.58252	−0.791261	−	0.611478i	$-0.790575\pi$
$7$	−4.18696	−1.58252	−0.791261	+	0.611478i	$0.790575\pi$
$8$	1.00000	0.353553
$9$	−2.01876	−0.672921
$10$	4.23904	1.34050
$11$	−4.64963	−1.40192	−0.700958	−	0.713203i	$-0.747244\pi$
$11$	−4.64963	−1.40192	−0.700958	+	0.713203i	$0.747244\pi$
$12$	−0.990574	−0.285954
$13$	−2.88609	−0.800456	−0.400228	−	0.916416i	$-0.631069\pi$
$13$	−2.88609	−0.800456	−0.400228	+	0.916416i	$0.631069\pi$
$14$	−4.18696	−1.11901
$15$	−4.19909	−1.08420
$16$	1.00000	0.250000
$17$	6.19917	1.50352	0.751760	−	0.659437i	$-0.229205\pi$
$17$	6.19917	1.50352	0.751760	+	0.659437i	$0.229205\pi$
$18$	−2.01876	−0.475827
$19$	4.17285	0.957317	0.478659	−	0.878001i	$-0.341123\pi$
$19$	4.17285	0.957317	0.478659	+	0.878001i	$0.341123\pi$
$20$	4.23904	0.947879
$21$	4.14750	0.905058
$22$	−4.64963	−0.991304
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.990574	−0.202200
$25$	12.9695	2.59390
$26$	−2.88609	−0.566008
$27$	4.97146	0.956757
$28$	−4.18696	−0.791261
$29$	−3.53526	−0.656481	−0.328240	−	0.944594i	$-0.606456\pi$
$29$	−3.53526	−0.656481	−0.328240	+	0.944594i	$0.606456\pi$
$30$	−4.19909	−0.766645
$31$	−6.53898	−1.17444	−0.587218	−	0.809429i	$-0.699777\pi$
$31$	−6.53898	−1.17444	−0.587218	+	0.809429i	$0.699777\pi$
$32$	1.00000	0.176777
$33$	4.60580	0.801767
$34$	6.19917	1.06315
$35$	−17.7487	−3.00008
$36$	−2.01876	−0.336460
$37$	8.77913	1.44328	0.721640	−	0.692268i	$-0.243389\pi$
$37$	8.77913	1.44328	0.721640	+	0.692268i	$0.243389\pi$
$38$	4.17285	0.676925
$39$	2.85888	0.457788
$40$	4.23904	0.670252
$41$	0.889308	0.138887	0.0694433	−	0.997586i	$-0.477878\pi$
$41$	0.889308	0.138887	0.0694433	+	0.997586i	$0.477878\pi$
$42$	4.14750	0.639973
$43$	9.47962	1.44563	0.722814	−	0.691042i	$-0.242848\pi$
$43$	9.47962	1.44563	0.722814	+	0.691042i	$0.242848\pi$
$44$	−4.64963	−0.700958
$45$	−8.55762	−1.27569
$46$	1.00000	0.147442
$47$	3.37309	0.492015	0.246008	−	0.969268i	$-0.420881\pi$
$47$	3.37309	0.492015	0.246008	+	0.969268i	$0.420881\pi$
$48$	−0.990574	−0.142977
$49$	10.5307	1.50438
$50$	12.9695	1.83416
$51$	−6.14074	−0.859875
$52$	−2.88609	−0.400228
$53$	−5.23757	−0.719435	−0.359718	−	0.933061i	$-0.617127\pi$
$53$	−5.23757	−0.719435	−0.359718	+	0.933061i	$0.617127\pi$
$54$	4.97146	0.676530
$55$	−19.7100	−2.65769
$56$	−4.18696	−0.559506
$57$	−4.13352	−0.547498
$58$	−3.53526	−0.464202
$59$	−14.4993	−1.88764	−0.943822	−	0.330453i	$-0.892798\pi$
$59$	−14.4993	−1.88764	−0.943822	+	0.330453i	$0.892798\pi$
$60$	−4.19909	−0.542100
$61$	5.45134	0.697973	0.348986	−	0.937128i	$-0.386526\pi$
$61$	5.45134	0.697973	0.348986	+	0.937128i	$0.386526\pi$
$62$	−6.53898	−0.830452
$63$	8.45248	1.06491
$64$	1.00000	0.125000
$65$	−12.2342	−1.51747
$66$	4.60580	0.566935
$67$	12.4749	1.52405	0.762027	−	0.647545i	$-0.224204\pi$
$67$	12.4749	1.52405	0.762027	+	0.647545i	$0.224204\pi$
$68$	6.19917	0.751760
$69$	−0.990574	−0.119251
$70$	−17.7487	−2.12138
$71$	−8.58867	−1.01929	−0.509644	−	0.860386i	$-0.670223\pi$
$71$	−8.58867	−1.01929	−0.509644	+	0.860386i	$0.670223\pi$
$72$	−2.01876	−0.237913
$73$	5.07471	0.593950	0.296975	−	0.954885i	$-0.404022\pi$
$73$	5.07471	0.593950	0.296975	+	0.954885i	$0.404022\pi$
$74$	8.77913	1.02055
$75$	−12.8472	−1.48347
$76$	4.17285	0.478659
$77$	19.4678	2.21856
$78$	2.85888	0.323705
$79$	−7.35263	−0.827235	−0.413618	−	0.910451i	$-0.635735\pi$
$79$	−7.35263	−0.827235	−0.413618	+	0.910451i	$0.635735\pi$
$80$	4.23904	0.473939
$81$	1.13169	0.125744
$82$	0.889308	0.0982077
$83$	2.15419	0.236453	0.118227	−	0.992987i	$-0.462279\pi$
$83$	2.15419	0.236453	0.118227	+	0.992987i	$0.462279\pi$
$84$	4.14750	0.452529
$85$	26.2785	2.85031
$86$	9.47962	1.02221
$87$	3.50193	0.375447
$88$	−4.64963	−0.495652
$89$	13.5167	1.43276	0.716381	−	0.697709i	$-0.245797\pi$
$89$	13.5167	1.43276	0.716381	+	0.697709i	$0.245797\pi$
$90$	−8.55762	−0.902053
$91$	12.0839	1.26674
$92$	1.00000	0.104257
$93$	6.47735	0.671670
$94$	3.37309	0.347907
$95$	17.6889	1.81484
$96$	−0.990574	−0.101100
$97$	11.9593	1.21428	0.607142	−	0.794594i	$-0.292316\pi$
$97$	11.9593	1.21428	0.607142	+	0.794594i	$0.292316\pi$
$98$	10.5307	1.06376
$99$	9.38650	0.943379
$100$	12.9695	1.29695
$101$	−6.15687	−0.612632	−0.306316	−	0.951930i	$-0.599096\pi$
$101$	−6.15687	−0.612632	−0.306316	+	0.951930i	$0.599096\pi$
$102$	−6.14074	−0.608024
$103$	13.1874	1.29939	0.649695	−	0.760195i	$-0.274897\pi$
$103$	13.1874	1.29939	0.649695	+	0.760195i	$0.274897\pi$
$104$	−2.88609	−0.283004
$105$	17.5814	1.71577
$106$	−5.23757	−0.508717
$107$	6.11832	0.591481	0.295740	−	0.955268i	$-0.404434\pi$
$107$	6.11832	0.591481	0.295740	+	0.955268i	$0.404434\pi$
$108$	4.97146	0.478379
$109$	8.00174	0.766427	0.383214	−	0.923660i	$-0.374817\pi$
$109$	8.00174	0.766427	0.383214	+	0.923660i	$0.374817\pi$
$110$	−19.7100	−1.87927
$111$	−8.69638	−0.825424
$112$	−4.18696	−0.395631
$113$	0.262047	0.0246513	0.0123256	−	0.999924i	$-0.496077\pi$
$113$	0.262047	0.0246513	0.0123256	+	0.999924i	$0.496077\pi$
$114$	−4.13352	−0.387139
$115$	4.23904	0.395293
$116$	−3.53526	−0.328240
$117$	5.82632	0.538644
$118$	−14.4993	−1.33477
$119$	−25.9557	−2.37935
$120$	−4.19909	−0.383322
$121$	10.6191	0.965369
$122$	5.45134	0.493541
$123$	−0.880926	−0.0794304
$124$	−6.53898	−0.587218
$125$	33.7830	3.02164
$126$	8.45248	0.753007
$127$	8.67904	0.770140	0.385070	−	0.922887i	$-0.374177\pi$
$127$	8.67904	0.770140	0.385070	+	0.922887i	$0.374177\pi$
$128$	1.00000	0.0883883
$129$	−9.39027	−0.826767
$130$	−12.2342	−1.07301
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	4.60580	0.400884
$133$	−17.4716	−1.51498
$134$	12.4749	1.07767
$135$	21.0742	1.81378
$136$	6.19917	0.531574
$137$	1.77806	0.151910	0.0759549	−	0.997111i	$-0.475800\pi$
$137$	1.77806	0.151910	0.0759549	+	0.997111i	$0.475800\pi$
$138$	−0.990574	−0.0843233
$139$	2.19802	0.186433	0.0932167	−	0.995646i	$-0.470285\pi$
$139$	2.19802	0.186433	0.0932167	+	0.995646i	$0.470285\pi$
$140$	−17.7487	−1.50004
$141$	−3.34129	−0.281388
$142$	−8.58867	−0.720745
$143$	13.4192	1.12217
$144$	−2.01876	−0.168230
$145$	−14.9861	−1.24453
$146$	5.07471	0.419986
$147$	−10.4314	−0.860367
$148$	8.77913	0.721640
$149$	0.185406	0.0151891	0.00759454	−	0.999971i	$-0.497583\pi$
$149$	0.185406	0.0151891	0.00759454	+	0.999971i	$0.497583\pi$
$150$	−12.8472	−1.04897
$151$	11.8553	0.964771	0.482385	−	0.875959i	$-0.339771\pi$
$151$	11.8553	0.964771	0.482385	+	0.875959i	$0.339771\pi$
$152$	4.17285	0.338463
$153$	−12.5147	−1.01175
$154$	19.4678	1.56876
$155$	−27.7190	−2.22645
$156$	2.85888	0.228894
$157$	−4.19281	−0.334622	−0.167311	−	0.985904i	$-0.553508\pi$
$157$	−4.19281	−0.334622	−0.167311	+	0.985904i	$0.553508\pi$
$158$	−7.35263	−0.584944
$159$	5.18820	0.411451
$160$	4.23904	0.335126
$161$	−4.18696	−0.329979
$162$	1.13169	0.0889141
$163$	7.63248	0.597822	0.298911	−	0.954281i	$-0.403377\pi$
$163$	7.63248	0.597822	0.298911	+	0.954281i	$0.403377\pi$
$164$	0.889308	0.0694433
$165$	19.5242	1.51996
$166$	2.15419	0.167198
$167$	8.43220	0.652503	0.326252	−	0.945283i	$-0.394214\pi$
$167$	8.43220	0.652503	0.326252	+	0.945283i	$0.394214\pi$
$168$	4.14750	0.319986
$169$	−4.67050	−0.359270
$170$	26.2785	2.01547
$171$	−8.42399	−0.644199
$172$	9.47962	0.722814
$173$	−15.3308	−1.16558	−0.582789	−	0.812624i	$-0.698039\pi$
$173$	−15.3308	−1.16558	−0.582789	+	0.812624i	$0.698039\pi$
$174$	3.50193	0.265481
$175$	−54.3027	−4.10490
$176$	−4.64963	−0.350479
$177$	14.3626	1.07956
$178$	13.5167	1.01312
$179$	−3.86562	−0.288930	−0.144465	−	0.989510i	$-0.546146\pi$
$179$	−3.86562	−0.288930	−0.144465	+	0.989510i	$0.546146\pi$
$180$	−8.55762	−0.637847
$181$	22.9661	1.70706	0.853530	−	0.521043i	$-0.174457\pi$
$181$	22.9661	1.70706	0.853530	+	0.521043i	$0.174457\pi$
$182$	12.0839	0.895721
$183$	−5.39996	−0.399176
$184$	1.00000	0.0737210
$185$	37.2151	2.73611
$186$	6.47735	0.474942
$187$	−28.8238	−2.10781
$188$	3.37309	0.246008
$189$	−20.8153	−1.51409
$190$	17.6889	1.28329
$191$	7.94271	0.574714	0.287357	−	0.957824i	$-0.407223\pi$
$191$	7.94271	0.574714	0.287357	+	0.957824i	$0.407223\pi$
$192$	−0.990574	−0.0714885
$193$	−13.3411	−0.960311	−0.480155	−	0.877183i	$-0.659420\pi$
$193$	−13.3411	−0.960311	−0.480155	+	0.877183i	$0.659420\pi$
$194$	11.9593	0.858628
$195$	12.1189	0.867854
$196$	10.5307	0.752189
$197$	11.8119	0.841562	0.420781	−	0.907162i	$-0.361756\pi$
$197$	11.8119	0.841562	0.420781	+	0.907162i	$0.361756\pi$
$198$	9.38650	0.667069
$199$	19.4517	1.37890	0.689449	−	0.724334i	$-0.257853\pi$
$199$	19.4517	1.37890	0.689449	+	0.724334i	$0.257853\pi$
$200$	12.9695	0.917081
$201$	−12.3573	−0.871619
$202$	−6.15687	−0.433196
$203$	14.8020	1.03890
$204$	−6.14074	−0.429938
$205$	3.76982	0.263295
$206$	13.1874	0.918807
$207$	−2.01876	−0.140314
$208$	−2.88609	−0.200114
$209$	−19.4022	−1.34208
$210$	17.5814	1.21323
$211$	−10.1748	−0.700462	−0.350231	−	0.936663i	$-0.613897\pi$
$211$	−10.1748	−0.700462	−0.350231	+	0.936663i	$0.613897\pi$
$212$	−5.23757	−0.359718
$213$	8.50771	0.582939
$214$	6.11832	0.418240
$215$	40.1845	2.74056
$216$	4.97146	0.338265
$217$	27.3785	1.85857
$218$	8.00174	0.541946
$219$	−5.02688	−0.339685
$220$	−19.7100	−1.32885
$221$	−17.8913	−1.20350
$222$	−8.69638	−0.583663
$223$	8.12936	0.544382	0.272191	−	0.962243i	$-0.412252\pi$
$223$	8.12936	0.544382	0.272191	+	0.962243i	$0.412252\pi$
$224$	−4.18696	−0.279753
$225$	−26.1823	−1.74549
$226$	0.262047	0.0174311
$227$	6.67700	0.443168	0.221584	−	0.975141i	$-0.428877\pi$
$227$	6.67700	0.443168	0.221584	+	0.975141i	$0.428877\pi$
$228$	−4.13352	−0.273749
$229$	−21.8855	−1.44623	−0.723116	−	0.690727i	$-0.757291\pi$
$229$	−21.8855	−1.44623	−0.723116	+	0.690727i	$0.757291\pi$
$230$	4.23904	0.279514
$231$	−19.2843	−1.26882
$232$	−3.53526	−0.232101
$233$	−13.8846	−0.909611	−0.454805	−	0.890591i	$-0.650291\pi$
$233$	−13.8846	−0.909611	−0.454805	+	0.890591i	$0.650291\pi$
$234$	5.82632	0.380879
$235$	14.2987	0.932742
$236$	−14.4993	−0.943822
$237$	7.28332	0.473103
$238$	−25.9557	−1.68246
$239$	−17.2121	−1.11336	−0.556679	−	0.830727i	$-0.687925\pi$
$239$	−17.2121	−1.11336	−0.556679	+	0.830727i	$0.687925\pi$
$240$	−4.19909	−0.271050
$241$	24.4972	1.57800	0.789001	−	0.614392i	$-0.210599\pi$
$241$	24.4972	1.57800	0.789001	+	0.614392i	$0.210599\pi$
$242$	10.6191	0.682619
$243$	−16.0354	−1.02867
$244$	5.45134	0.348986
$245$	44.6399	2.85194
$246$	−0.880926	−0.0561658
$247$	−12.0432	−0.766291
$248$	−6.53898	−0.415226
$249$	−2.13389	−0.135230
$250$	33.7830	2.13662
$251$	−22.3581	−1.41123	−0.705616	−	0.708594i	$-0.749330\pi$
$251$	−22.3581	−1.41123	−0.705616	+	0.708594i	$0.749330\pi$
$252$	8.45248	0.532456
$253$	−4.64963	−0.292320
$254$	8.67904	0.544572
$255$	−26.0308	−1.63011
$256$	1.00000	0.0625000
$257$	−0.722583	−0.0450735	−0.0225367	−	0.999746i	$-0.507174\pi$
$257$	−0.722583	−0.0450735	−0.0225367	+	0.999746i	$0.507174\pi$
$258$	−9.39027	−0.584612
$259$	−36.7579	−2.28402
$260$	−12.2342	−0.758736
$261$	7.13685	0.441760
$262$	1.00000	0.0617802
$263$	−9.82028	−0.605544	−0.302772	−	0.953063i	$-0.597912\pi$
$263$	−9.82028	−0.605544	−0.302772	+	0.953063i	$0.597912\pi$
$264$	4.60580	0.283468
$265$	−22.2023	−1.36387
$266$	−17.4716	−1.07125
$267$	−13.3893	−0.819409
$268$	12.4749	0.762027
$269$	2.99155	0.182398	0.0911991	−	0.995833i	$-0.470930\pi$
$269$	2.99155	0.182398	0.0911991	+	0.995833i	$0.470930\pi$
$270$	21.0742	1.28254
$271$	2.70639	0.164401	0.0822007	−	0.996616i	$-0.473805\pi$
$271$	2.70639	0.164401	0.0822007	+	0.996616i	$0.473805\pi$
$272$	6.19917	0.375880
$273$	−11.9700	−0.724459
$274$	1.77806	0.107416
$275$	−60.3033	−3.63643
$276$	−0.990574	−0.0596256
$277$	4.32473	0.259848	0.129924	−	0.991524i	$-0.458527\pi$
$277$	4.32473	0.259848	0.129924	+	0.991524i	$0.458527\pi$
$278$	2.19802	0.131828
$279$	13.2007	0.790302
$280$	−17.7487	−1.06069
$281$	−26.3102	−1.56954	−0.784768	−	0.619790i	$-0.787218\pi$
$281$	−26.3102	−1.56954	−0.784768	+	0.619790i	$0.787218\pi$
$282$	−3.34129	−0.198971
$283$	−18.0689	−1.07409	−0.537043	−	0.843555i	$-0.680459\pi$
$283$	−18.0689	−1.07409	−0.537043	+	0.843555i	$0.680459\pi$
$284$	−8.58867	−0.509644
$285$	−17.5221	−1.03792
$286$	13.4192	0.793496
$287$	−3.72350	−0.219791
$288$	−2.01876	−0.118957
$289$	21.4297	1.26057
$290$	−14.9861	−0.880015
$291$	−11.8466	−0.694459
$292$	5.07471	0.296975
$293$	31.1941	1.82238	0.911191	−	0.411985i	$-0.135164\pi$
$293$	31.1941	1.82238	0.911191	+	0.411985i	$0.135164\pi$
$294$	−10.4314	−0.608371
$295$	−61.4630	−3.57852
$296$	8.77913	0.510277
$297$	−23.1154	−1.34129
$298$	0.185406	0.0107403
$299$	−2.88609	−0.166907
$300$	−12.8472	−0.741735
$301$	−39.6908	−2.28774
$302$	11.8553	0.682196
$303$	6.09884	0.350369
$304$	4.17285	0.239329
$305$	23.1085	1.32319
$306$	−12.5147	−0.715415
$307$	26.0459	1.48652	0.743258	−	0.669005i	$-0.233280\pi$
$307$	26.0459	1.48652	0.743258	+	0.669005i	$0.233280\pi$
$308$	19.4678	1.10928
$309$	−13.0631	−0.743132
$310$	−27.7190	−1.57433
$311$	15.2963	0.867371	0.433685	−	0.901064i	$-0.357213\pi$
$311$	15.2963	0.867371	0.433685	+	0.901064i	$0.357213\pi$
$312$	2.85888	0.161852
$313$	−4.01954	−0.227198	−0.113599	−	0.993527i	$-0.536238\pi$
$313$	−4.01954	−0.227198	−0.113599	+	0.993527i	$0.536238\pi$
$314$	−4.19281	−0.236614
$315$	35.8304	2.01882
$316$	−7.35263	−0.413618
$317$	10.9815	0.616783	0.308392	−	0.951260i	$-0.400209\pi$
$317$	10.9815	0.616783	0.308392	+	0.951260i	$0.400209\pi$
$318$	5.18820	0.290940
$319$	16.4376	0.920331
$320$	4.23904	0.236970
$321$	−6.06065	−0.338273
$322$	−4.18696	−0.233330
$323$	25.8682	1.43934
$324$	1.13169	0.0628718
$325$	−37.4311	−2.07630
$326$	7.63248	0.422724
$327$	−7.92631	−0.438326
$328$	0.889308	0.0491038
$329$	−14.1230	−0.778626
$330$	19.5242	1.07477
$331$	8.54084	0.469447	0.234723	−	0.972062i	$-0.424582\pi$
$331$	8.54084	0.469447	0.234723	+	0.972062i	$0.424582\pi$
$332$	2.15419	0.118227
$333$	−17.7230	−0.971214
$334$	8.43220	0.461389
$335$	52.8817	2.88924
$336$	4.14750	0.226264
$337$	32.5556	1.77342	0.886708	−	0.462329i	$-0.152986\pi$
$337$	32.5556	1.77342	0.886708	+	0.462329i	$0.152986\pi$
$338$	−4.67050	−0.254042
$339$	−0.259577	−0.0140983
$340$	26.2785	1.42515
$341$	30.4038	1.64646
$342$	−8.42399	−0.455517
$343$	−14.7827	−0.798191
$344$	9.47962	0.511107
$345$	−4.19909	−0.226071
$346$	−15.3308	−0.824188
$347$	−19.9106	−1.06886	−0.534428	−	0.845214i	$-0.679473\pi$
$347$	−19.9106	−1.06886	−0.534428	+	0.845214i	$0.679473\pi$
$348$	3.50193	0.187723
$349$	3.41373	0.182733	0.0913663	−	0.995817i	$-0.470877\pi$
$349$	3.41373	0.182733	0.0913663	+	0.995817i	$0.470877\pi$
$350$	−54.3027	−2.90260
$351$	−14.3481	−0.765843
$352$	−4.64963	−0.247826
$353$	−16.9942	−0.904508	−0.452254	−	0.891889i	$-0.649380\pi$
$353$	−16.9942	−0.904508	−0.452254	+	0.891889i	$0.649380\pi$
$354$	14.3626	0.763364
$355$	−36.4077	−1.93232
$356$	13.5167	0.716381
$357$	25.7110	1.36077
$358$	−3.86562	−0.204304
$359$	18.8551	0.995132	0.497566	−	0.867426i	$-0.334227\pi$
$359$	18.8551	0.995132	0.497566	+	0.867426i	$0.334227\pi$
$360$	−8.55762	−0.451026
$361$	−1.58734	−0.0835441
$362$	22.9661	1.20707
$363$	−10.5190	−0.552102
$364$	12.0839	0.633370
$365$	21.5119	1.12599
$366$	−5.39996	−0.282260
$367$	−21.3435	−1.11412	−0.557062	−	0.830471i	$-0.688071\pi$
$367$	−21.3435	−1.11412	−0.557062	+	0.830471i	$0.688071\pi$
$368$	1.00000	0.0521286
$369$	−1.79530	−0.0934597
$370$	37.2151	1.93472
$371$	21.9295	1.13852
$372$	6.47735	0.335835
$373$	−16.3289	−0.845481	−0.422740	−	0.906251i	$-0.638932\pi$
$373$	−16.3289	−0.845481	−0.422740	+	0.906251i	$0.638932\pi$
$374$	−28.8238	−1.49045
$375$	−33.4645	−1.72810
$376$	3.37309	0.173954
$377$	10.2031	0.525484
$378$	−20.8153	−1.07062
$379$	−14.7023	−0.755204	−0.377602	−	0.925968i	$-0.623251\pi$
$379$	−14.7023	−0.755204	−0.377602	+	0.925968i	$0.623251\pi$
$380$	17.6889	0.907420
$381$	−8.59724	−0.440450
$382$	7.94271	0.406384
$383$	7.52661	0.384592	0.192296	−	0.981337i	$-0.438407\pi$
$383$	7.52661	0.384592	0.192296	+	0.981337i	$0.438407\pi$
$384$	−0.990574	−0.0505500
$385$	82.5249	4.20586
$386$	−13.3411	−0.679042
$387$	−19.1371	−0.972794
$388$	11.9593	0.607142
$389$	18.3954	0.932682	0.466341	−	0.884605i	$-0.345572\pi$
$389$	18.3954	0.932682	0.466341	+	0.884605i	$0.345572\pi$
$390$	12.1189	0.613666
$391$	6.19917	0.313505
$392$	10.5307	0.531878
$393$	−0.990574	−0.0499679
$394$	11.8119	0.595074
$395$	−31.1681	−1.56824
$396$	9.38650	0.471689
$397$	−35.9896	−1.80627	−0.903133	−	0.429360i	$-0.858739\pi$
$397$	−35.9896	−1.80627	−0.903133	+	0.429360i	$0.858739\pi$
$398$	19.4517	0.975028
$399$	17.3069	0.866427
$400$	12.9695	0.648474
$401$	−29.8552	−1.49090	−0.745449	−	0.666563i	$-0.767765\pi$
$401$	−29.8552	−1.49090	−0.745449	+	0.666563i	$0.767765\pi$
$402$	−12.3573	−0.616328
$403$	18.8721	0.940085
$404$	−6.15687	−0.306316
$405$	4.79729	0.238379
$406$	14.8020	0.734610
$407$	−40.8197	−2.02336
$408$	−6.14074	−0.304012
$409$	−0.985581	−0.0487338	−0.0243669	−	0.999703i	$-0.507757\pi$
$409$	−0.985581	−0.0487338	−0.0243669	+	0.999703i	$0.507757\pi$
$410$	3.76982	0.186178
$411$	−1.76130	−0.0868785
$412$	13.1874	0.649695
$413$	60.7079	2.98724
$414$	−2.01876	−0.0992168
$415$	9.13171	0.448258
$416$	−2.88609	−0.141502
$417$	−2.17730	−0.106623
$418$	−19.4022	−0.948993
$419$	−3.91510	−0.191265	−0.0956326	−	0.995417i	$-0.530487\pi$
$419$	−3.91510	−0.191265	−0.0956326	+	0.995417i	$0.530487\pi$
$420$	17.5814	0.857885
$421$	12.1728	0.593264	0.296632	−	0.954992i	$-0.404137\pi$
$421$	12.1728	0.593264	0.296632	+	0.954992i	$0.404137\pi$
$422$	−10.1748	−0.495302
$423$	−6.80947	−0.331088
$424$	−5.23757	−0.254359
$425$	80.4000	3.89997
$426$	8.50771	0.412200
$427$	−22.8246	−1.10456
$428$	6.11832	0.295740
$429$	−13.2927	−0.641780
$430$	40.1845	1.93787
$431$	29.0274	1.39820	0.699101	−	0.715023i	$-0.253584\pi$
$431$	29.0274	1.39820	0.699101	+	0.715023i	$0.253584\pi$
$432$	4.97146	0.239189
$433$	−22.4980	−1.08118	−0.540592	−	0.841285i	$-0.681800\pi$
$433$	−22.4980	−1.08118	−0.540592	+	0.841285i	$0.681800\pi$
$434$	27.3785	1.31421
$435$	14.8449	0.711756
$436$	8.00174	0.383214
$437$	4.17285	0.199614
$438$	−5.02688	−0.240194
$439$	36.4289	1.73865	0.869327	−	0.494237i	$-0.164552\pi$
$439$	36.4289	1.73865	0.869327	+	0.494237i	$0.164552\pi$
$440$	−19.7100	−0.939636
$441$	−21.2589	−1.01233
$442$	−17.8913	−0.851004
$443$	7.15995	0.340180	0.170090	−	0.985429i	$-0.445594\pi$
$443$	7.15995	0.340180	0.170090	+	0.985429i	$0.445594\pi$
$444$	−8.69638	−0.412712
$445$	57.2977	2.71617
$446$	8.12936	0.384936
$447$	−0.183659	−0.00868676
$448$	−4.18696	−0.197815
$449$	−25.0404	−1.18173	−0.590866	−	0.806770i	$-0.701214\pi$
$449$	−25.0404	−1.18173	−0.590866	+	0.806770i	$0.701214\pi$
$450$	−26.1823	−1.23425
$451$	−4.13495	−0.194707
$452$	0.262047	0.0123256
$453$	−11.7436	−0.551760
$454$	6.67700	0.313367
$455$	51.2243	2.40143
$456$	−4.13352	−0.193570
$457$	−6.46099	−0.302233	−0.151116	−	0.988516i	$-0.548287\pi$
$457$	−6.46099	−0.302233	−0.151116	+	0.988516i	$0.548287\pi$
$458$	−21.8855	−1.02264
$459$	30.8189	1.43850
$460$	4.23904	0.197646
$461$	8.90625	0.414806	0.207403	−	0.978256i	$-0.433499\pi$
$461$	8.90625	0.414806	0.207403	+	0.978256i	$0.433499\pi$
$462$	−19.2843	−0.897188
$463$	0.254866	0.0118446	0.00592232	−	0.999982i	$-0.498115\pi$
$463$	0.254866	0.0118446	0.00592232	+	0.999982i	$0.498115\pi$
$464$	−3.53526	−0.164120
$465$	27.4577	1.27332
$466$	−13.8846	−0.643192
$467$	1.67439	0.0774815	0.0387407	−	0.999249i	$-0.487665\pi$
$467$	1.67439	0.0774815	0.0387407	+	0.999249i	$0.487665\pi$
$468$	5.82632	0.269322
$469$	−52.2320	−2.41185
$470$	14.2987	0.659548
$471$	4.15328	0.191373
$472$	−14.4993	−0.667383
$473$	−44.0767	−2.02665
$474$	7.28332	0.334534
$475$	54.1197	2.48318
$476$	−25.9557	−1.18968
$477$	10.5734	0.484123
$478$	−17.2121	−0.787264
$479$	16.1791	0.739244	0.369622	−	0.929182i	$-0.379487\pi$
$479$	16.1791	0.739244	0.369622	+	0.929182i	$0.379487\pi$
$480$	−4.19909	−0.191661
$481$	−25.3373	−1.15528
$482$	24.4972	1.11582
$483$	4.14750	0.188718
$484$	10.6191	0.482684
$485$	50.6960	2.30199
$486$	−16.0354	−0.727380
$487$	−36.3583	−1.64755	−0.823775	−	0.566917i	$-0.808136\pi$
$487$	−36.3583	−1.64755	−0.823775	+	0.566917i	$0.808136\pi$
$488$	5.45134	0.246771
$489$	−7.56054	−0.341899
$490$	44.6399	2.01662
$491$	−2.02395	−0.0913395	−0.0456698	−	0.998957i	$-0.514542\pi$
$491$	−2.02395	−0.0913395	−0.0456698	+	0.998957i	$0.514542\pi$
$492$	−0.880926	−0.0397152
$493$	−21.9157	−0.987032
$494$	−12.0432	−0.541849
$495$	39.7898	1.78842
$496$	−6.53898	−0.293609
$497$	35.9604	1.61305
$498$	−2.13389	−0.0956217
$499$	3.92126	0.175540	0.0877699	−	0.996141i	$-0.472026\pi$
$499$	3.92126	0.175540	0.0877699	+	0.996141i	$0.472026\pi$
$500$	33.7830	1.51082
$501$	−8.35272	−0.373172
$502$	−22.3581	−0.997892
$503$	7.59484	0.338637	0.169319	−	0.985561i	$-0.445843\pi$
$503$	7.59484	0.338637	0.169319	+	0.985561i	$0.445843\pi$
$504$	8.45248	0.376504
$505$	−26.0992	−1.16140
$506$	−4.64963	−0.206701
$507$	4.62648	0.205469
$508$	8.67904	0.385070
$509$	−38.3098	−1.69805	−0.849026	−	0.528350i	$-0.822811\pi$
$509$	−38.3098	−1.69805	−0.849026	+	0.528350i	$0.822811\pi$
$510$	−26.0308	−1.15267
$511$	−21.2476	−0.939940
$512$	1.00000	0.0441942
$513$	20.7451	0.915920
$514$	−0.722583	−0.0318717
$515$	55.9018	2.46333
$516$	−9.39027	−0.413383
$517$	−15.6836	−0.689764
$518$	−36.7579	−1.61505
$519$	15.1863	0.666604
$520$	−12.2342	−0.536507
$521$	8.63269	0.378205	0.189102	−	0.981957i	$-0.439442\pi$
$521$	8.63269	0.378205	0.189102	+	0.981957i	$0.439442\pi$
$522$	7.13685	0.312371
$523$	−7.44523	−0.325557	−0.162779	−	0.986663i	$-0.552046\pi$
$523$	−7.44523	−0.325557	−0.162779	+	0.986663i	$0.552046\pi$
$524$	1.00000	0.0436852
$525$	53.7909	2.34763
$526$	−9.82028	−0.428184
$527$	−40.5363	−1.76579
$528$	4.60580	0.200442
$529$	1.00000	0.0434783
$530$	−22.2023	−0.964405
$531$	29.2706	1.27024
$532$	−17.4716	−0.757488
$533$	−2.56662	−0.111173
$534$	−13.3893	−0.579410
$535$	25.9358	1.12130
$536$	12.4749	0.538834
$537$	3.82918	0.165241
$538$	2.99155	0.128975
$539$	−48.9636	−2.10901
$540$	21.0742	0.906890
$541$	−12.2464	−0.526515	−0.263257	−	0.964726i	$-0.584797\pi$
$541$	−12.2464	−0.526515	−0.263257	+	0.964726i	$0.584797\pi$
$542$	2.70639	0.116249
$543$	−22.7497	−0.976282
$544$	6.19917	0.265787
$545$	33.9197	1.45296
$546$	−11.9700	−0.512270
$547$	−23.8729	−1.02073	−0.510366	−	0.859957i	$-0.670490\pi$
$547$	−23.8729	−1.02073	−0.510366	+	0.859957i	$0.670490\pi$
$548$	1.77806	0.0759549
$549$	−11.0050	−0.469680
$550$	−60.3033	−2.57134
$551$	−14.7521	−0.628460
$552$	−0.990574	−0.0421616
$553$	30.7852	1.30912
$554$	4.32473	0.183740
$555$	−36.8643	−1.56480
$556$	2.19802	0.0932167
$557$	−13.8877	−0.588441	−0.294220	−	0.955738i	$-0.595060\pi$
$557$	−13.8877	−0.588441	−0.294220	+	0.955738i	$0.595060\pi$
$558$	13.2007	0.558828
$559$	−27.3590	−1.15716
$560$	−17.7487	−0.750020
$561$	28.5521	1.20547
$562$	−26.3102	−1.10983
$563$	−0.309278	−0.0130345	−0.00651726	−	0.999979i	$-0.502075\pi$
$563$	−0.309278	−0.0130345	−0.00651726	+	0.999979i	$0.502075\pi$
$564$	−3.34129	−0.140694
$565$	1.11083	0.0467328
$566$	−18.0689	−0.759494
$567$	−4.73835	−0.198992
$568$	−8.58867	−0.360372
$569$	−22.8905	−0.959621	−0.479811	−	0.877372i	$-0.659295\pi$
$569$	−22.8905	−0.959621	−0.479811	+	0.877372i	$0.659295\pi$
$570$	−17.5221	−0.733922
$571$	10.2796	0.430187	0.215094	−	0.976593i	$-0.430994\pi$
$571$	10.2796	0.430187	0.215094	+	0.976593i	$0.430994\pi$
$572$	13.4192	0.561086
$573$	−7.86784	−0.328684
$574$	−3.72350	−0.155416
$575$	12.9695	0.540865
$576$	−2.01876	−0.0841151
$577$	27.5574	1.14723	0.573614	−	0.819126i	$-0.305541\pi$
$577$	27.5574	1.14723	0.573614	+	0.819126i	$0.305541\pi$
$578$	21.4297	0.891358
$579$	13.2153	0.549210
$580$	−14.9861	−0.622264
$581$	−9.01952	−0.374193
$582$	−11.8466	−0.491056
$583$	24.3527	1.00859
$584$	5.07471	0.209993
$585$	24.6980	1.02114
$586$	31.1941	1.28862
$587$	−26.2100	−1.08180	−0.540901	−	0.841086i	$-0.681917\pi$
$587$	−26.2100	−1.08180	−0.540901	+	0.841086i	$0.681917\pi$
$588$	−10.4314	−0.430183
$589$	−27.2862	−1.12431
$590$	−61.4630	−2.53039
$591$	−11.7005	−0.481296
$592$	8.77913	0.360820
$593$	−18.2345	−0.748803	−0.374401	−	0.927267i	$-0.622152\pi$
$593$	−18.2345	−0.748803	−0.374401	+	0.927267i	$0.622152\pi$
$594$	−23.1154	−0.948438
$595$	−110.027	−4.51068
$596$	0.185406	0.00759454
$597$	−19.2684	−0.788603
$598$	−2.88609	−0.118021
$599$	21.6096	0.882946	0.441473	−	0.897275i	$-0.354456\pi$
$599$	21.6096	0.882946	0.441473	+	0.897275i	$0.354456\pi$
$600$	−12.8472	−0.524486
$601$	32.0050	1.30551	0.652756	−	0.757568i	$-0.273613\pi$
$601$	32.0050	1.30551	0.652756	+	0.757568i	$0.273613\pi$
$602$	−39.6908	−1.61768
$603$	−25.1839	−1.02557
$604$	11.8553	0.482385
$605$	45.0146	1.83010
$606$	6.09884	0.247748
$607$	−0.0175697	−0.000713133 0	−0.000356567	−	1.00000i	$-0.500113\pi$
$607$	−0.0175697	−0.000713133 0	−0.000356567		1.00000i	$0.500113\pi$
$608$	4.17285	0.169231
$609$	−14.6625	−0.594153
$610$	23.1085	0.935634
$611$	−9.73503	−0.393837
$612$	−12.5147	−0.505875
$613$	44.0824	1.78047	0.890236	−	0.455499i	$-0.150539\pi$
$613$	44.0824	1.78047	0.890236	+	0.455499i	$0.150539\pi$
$614$	26.0459	1.05113
$615$	−3.73428	−0.150581
$616$	19.4678	0.784381
$617$	−34.7123	−1.39746	−0.698731	−	0.715384i	$-0.746252\pi$
$617$	−34.7123	−1.39746	−0.698731	+	0.715384i	$0.746252\pi$
$618$	−13.0631	−0.525474
$619$	46.2712	1.85980	0.929898	−	0.367818i	$-0.119895\pi$
$619$	46.2712	1.85980	0.929898	+	0.367818i	$0.119895\pi$
$620$	−27.7190	−1.11322
$621$	4.97146	0.199498
$622$	15.2963	0.613324
$623$	−56.5937	−2.26738
$624$	2.85888	0.114447
$625$	78.3601	3.13440
$626$	−4.01954	−0.160653
$627$	19.2193	0.767546
$628$	−4.19281	−0.167311
$629$	54.4233	2.17000
$630$	35.8304	1.42752
$631$	31.5763	1.25703	0.628517	−	0.777796i	$-0.283662\pi$
$631$	31.5763	1.25703	0.628517	+	0.777796i	$0.283662\pi$
$632$	−7.35263	−0.292472
$633$	10.0789	0.400600
$634$	10.9815	0.436131
$635$	36.7908	1.46000
$636$	5.18820	0.205725
$637$	−30.3924	−1.20419
$638$	16.4376	0.650772
$639$	17.3385	0.685900
$640$	4.23904	0.167563
$641$	−31.0538	−1.22655	−0.613276	−	0.789869i	$-0.710149\pi$
$641$	−31.0538	−1.22655	−0.613276	+	0.789869i	$0.710149\pi$
$642$	−6.06065	−0.239195
$643$	−42.4715	−1.67491	−0.837457	−	0.546504i	$-0.815958\pi$
$643$	−42.4715	−1.67491	−0.837457	+	0.546504i	$0.815958\pi$
$644$	−4.18696	−0.164989
$645$	−39.8057	−1.56735
$646$	25.8682	1.01777
$647$	34.9220	1.37292	0.686462	−	0.727165i	$-0.259163\pi$
$647$	34.9220	1.37292	0.686462	+	0.727165i	$0.259163\pi$
$648$	1.13169	0.0444571
$649$	67.4163	2.64632
$650$	−37.4311	−1.46817
$651$	−27.1204	−1.06293
$652$	7.63248	0.298911
$653$	45.4001	1.77664	0.888322	−	0.459222i	$-0.151872\pi$
$653$	45.4001	1.77664	0.888322	+	0.459222i	$0.151872\pi$
$654$	−7.92631	−0.309943
$655$	4.23904	0.165633
$656$	0.889308	0.0347217
$657$	−10.2446	−0.399682
$658$	−14.1230	−0.550572
$659$	−17.5372	−0.683153	−0.341577	−	0.939854i	$-0.610961\pi$
$659$	−17.5372	−0.683153	−0.341577	+	0.939854i	$0.610961\pi$
$660$	19.5242	0.759978
$661$	18.6886	0.726902	0.363451	−	0.931613i	$-0.381598\pi$
$661$	18.6886	0.726902	0.363451	+	0.931613i	$0.381598\pi$
$662$	8.54084	0.331949
$663$	17.7227	0.688293
$664$	2.15419	0.0835988
$665$	−74.0627	−2.87203
$666$	−17.7230	−0.686752
$667$	−3.53526	−0.136886
$668$	8.43220	0.326252
$669$	−8.05273	−0.311337
$670$	52.8817	2.04300
$671$	−25.3467	−0.978499
$672$	4.14750	0.159993
$673$	−43.4269	−1.67398	−0.836992	−	0.547215i	$-0.815688\pi$
$673$	−43.4269	−1.67398	−0.836992	+	0.547215i	$0.815688\pi$
$674$	32.5556	1.25400
$675$	64.4772	2.48173
$676$	−4.67050	−0.179635
$677$	47.7304	1.83443	0.917214	−	0.398395i	$-0.130433\pi$
$677$	47.7304	1.83443	0.917214	+	0.398395i	$0.130433\pi$
$678$	−0.259577	−0.00996898
$679$	−50.0731	−1.92163
$680$	26.2785	1.00774
$681$	−6.61406	−0.253451
$682$	30.4038	1.16422
$683$	−39.4114	−1.50804	−0.754018	−	0.656854i	$-0.771887\pi$
$683$	−39.4114	−1.50804	−0.754018	+	0.656854i	$0.771887\pi$
$684$	−8.42399	−0.322099
$685$	7.53726	0.287984
$686$	−14.7827	−0.564406
$687$	21.6792	0.827112
$688$	9.47962	0.361407
$689$	15.1161	0.575876
$690$	−4.19909	−0.159856
$691$	−10.5570	−0.401606	−0.200803	−	0.979632i	$-0.564355\pi$
$691$	−10.5570	−0.401606	−0.200803	+	0.979632i	$0.564355\pi$
$692$	−15.3308	−0.582789
$693$	−39.3009	−1.49292
$694$	−19.9106	−0.755795
$695$	9.31749	0.353433
$696$	3.50193	0.132740
$697$	5.51297	0.208819
$698$	3.41373	0.129211
$699$	13.7537	0.520214
$700$	−54.3027	−2.05245
$701$	−21.6842	−0.818999	−0.409500	−	0.912310i	$-0.634297\pi$
$701$	−21.6842	−0.818999	−0.409500	+	0.912310i	$0.634297\pi$
$702$	−14.3481	−0.541532
$703$	36.6340	1.38168
$704$	−4.64963	−0.175240
$705$	−14.1639	−0.533443
$706$	−16.9942	−0.639584
$707$	25.7786	0.969504
$708$	14.3626	0.539780
$709$	25.4200	0.954669	0.477335	−	0.878722i	$-0.341603\pi$
$709$	25.4200	0.954669	0.477335	+	0.878722i	$0.341603\pi$
$710$	−36.4077	−1.36636
$711$	14.8432	0.556664
$712$	13.5167	0.506558
$713$	−6.53898	−0.244887
$714$	25.7110	0.962211
$715$	56.8847	2.12737
$716$	−3.86562	−0.144465
$717$	17.0499	0.636739
$718$	18.8551	0.703664
$719$	−24.5047	−0.913871	−0.456936	−	0.889500i	$-0.651053\pi$
$719$	−24.5047	−0.913871	−0.456936	+	0.889500i	$0.651053\pi$
$720$	−8.55762	−0.318924
$721$	−55.2150	−2.05631
$722$	−1.58734	−0.0590746
$723$	−24.2663	−0.902472
$724$	22.9661	0.853530
$725$	−45.8505	−1.70284
$726$	−10.5190	−0.390395
$727$	10.8062	0.400781	0.200391	−	0.979716i	$-0.435779\pi$
$727$	10.8062	0.400781	0.200391	+	0.979716i	$0.435779\pi$
$728$	12.0839	0.447860
$729$	12.4892	0.462562
$730$	21.5119	0.796192
$731$	58.7658	2.17353
$732$	−5.39996	−0.199588
$733$	9.98461	0.368790	0.184395	−	0.982852i	$-0.440967\pi$
$733$	9.98461	0.368790	0.184395	+	0.982852i	$0.440967\pi$
$734$	−21.3435	−0.787804
$735$	−44.2191	−1.63105
$736$	1.00000	0.0368605
$737$	−58.0037	−2.13660
$738$	−1.79530	−0.0660860
$739$	−5.77419	−0.212407	−0.106204	−	0.994344i	$-0.533870\pi$
$739$	−5.77419	−0.212407	−0.106204	+	0.994344i	$0.533870\pi$
$740$	37.2151	1.36805
$741$	11.9297	0.438248
$742$	21.9295	0.805057
$743$	−39.5518	−1.45102	−0.725508	−	0.688214i	$-0.758395\pi$
$743$	−39.5518	−1.45102	−0.725508	+	0.688214i	$0.758395\pi$
$744$	6.47735	0.237471
$745$	0.785946	0.0287948
$746$	−16.3289	−0.597845
$747$	−4.34880	−0.159114
$748$	−28.8238	−1.05390
$749$	−25.6172	−0.936032
$750$	−33.4645	−1.22195
$751$	−44.8947	−1.63823	−0.819116	−	0.573628i	$-0.805536\pi$
$751$	−44.8947	−1.63823	−0.819116	+	0.573628i	$0.805536\pi$
$752$	3.37309	0.123004
$753$	22.1474	0.807095
$754$	10.2031	0.371574
$755$	50.2551	1.82897
$756$	−20.8153	−0.757045
$757$	−4.44653	−0.161612	−0.0808059	−	0.996730i	$-0.525749\pi$
$757$	−4.44653	−0.161612	−0.0808059	+	0.996730i	$0.525749\pi$
$758$	−14.7023	−0.534010
$759$	4.60580	0.167180
$760$	17.6889	0.641643
$761$	15.4999	0.561870	0.280935	−	0.959727i	$-0.409356\pi$
$761$	15.4999	0.561870	0.280935	+	0.959727i	$0.409356\pi$
$762$	−8.59724	−0.311445
$763$	−33.5030	−1.21289
$764$	7.94271	0.287357
$765$	−53.0501	−1.91803
$766$	7.52661	0.271947
$767$	41.8462	1.51098
$768$	−0.990574	−0.0357443
$769$	−43.8962	−1.58294	−0.791470	−	0.611209i	$-0.790684\pi$
$769$	−43.8962	−1.58294	−0.791470	+	0.611209i	$0.790684\pi$
$770$	82.5249	2.97399
$771$	0.715772	0.0257779
$772$	−13.3411	−0.480155
$773$	31.7418	1.14167	0.570837	−	0.821063i	$-0.306619\pi$
$773$	31.7418	1.14167	0.570837	+	0.821063i	$0.306619\pi$
$774$	−19.1371	−0.687869
$775$	−84.8072	−3.04637
$776$	11.9593	0.429314
$777$	36.4114	1.30625
$778$	18.3954	0.659506
$779$	3.71095	0.132959
$780$	12.1189	0.433927
$781$	39.9341	1.42896
$782$	6.19917	0.221682
$783$	−17.5754	−0.628093
$784$	10.5307	0.376095
$785$	−17.7735	−0.634363
$786$	−0.990574	−0.0353326
$787$	−54.7862	−1.95292	−0.976458	−	0.215708i	$-0.930794\pi$
$787$	−54.7862	−1.95292	−0.976458	+	0.215708i	$0.930794\pi$
$788$	11.8119	0.420781
$789$	9.72771	0.346316
$790$	−31.1681	−1.10891
$791$	−1.09718	−0.0390112
$792$	9.38650	0.333535
$793$	−15.7330	−0.558697
$794$	−35.9896	−1.27722
$795$	21.9930	0.780011
$796$	19.4517	0.689449
$797$	7.67887	0.272000	0.136000	−	0.990709i	$-0.456575\pi$
$797$	7.67887	0.272000	0.136000	+	0.990709i	$0.456575\pi$
$798$	17.3069	0.612657
$799$	20.9103	0.739755
$800$	12.9695	0.458540
$801$	−27.2869	−0.964136
$802$	−29.8552	−1.05422
$803$	−23.5955	−0.832668
$804$	−12.3573	−0.435809
$805$	−17.7487	−0.625560
$806$	18.8721	0.664740
$807$	−2.96335	−0.104315
$808$	−6.15687	−0.216598
$809$	11.5713	0.406825	0.203413	−	0.979093i	$-0.434797\pi$
$809$	11.5713	0.406825	0.203413	+	0.979093i	$0.434797\pi$
$810$	4.79729	0.168560
$811$	48.2486	1.69424	0.847118	−	0.531404i	$-0.178336\pi$
$811$	48.2486	1.69424	0.847118	+	0.531404i	$0.178336\pi$
$812$	14.8020	0.519448
$813$	−2.68088	−0.0940225
$814$	−40.8197	−1.43073
$815$	32.3544	1.13333
$816$	−6.14074	−0.214969
$817$	39.5570	1.38392
$818$	−0.985581	−0.0344600
$819$	−24.3946	−0.852416
$820$	3.76982	0.131648
$821$	25.0746	0.875108	0.437554	−	0.899192i	$-0.355845\pi$
$821$	25.0746	0.875108	0.437554	+	0.899192i	$0.355845\pi$
$822$	−1.76130	−0.0614323
$823$	44.0536	1.53561	0.767807	−	0.640682i	$-0.221348\pi$
$823$	44.0536	1.53561	0.767807	+	0.640682i	$0.221348\pi$
$824$	13.1874	0.459404
$825$	59.7349	2.07970
$826$	60.7079	2.11230
$827$	−41.3204	−1.43685	−0.718426	−	0.695603i	$-0.755137\pi$
$827$	−41.3204	−1.43685	−0.718426	+	0.695603i	$0.755137\pi$
$828$	−2.01876	−0.0701569
$829$	31.5601	1.09613	0.548064	−	0.836437i	$-0.315365\pi$
$829$	31.5601	1.09613	0.548064	+	0.836437i	$0.315365\pi$
$830$	9.13171	0.316966
$831$	−4.28397	−0.148609
$832$	−2.88609	−0.100057
$833$	65.2813	2.26186
$834$	−2.17730	−0.0753937
$835$	35.7445	1.23699
$836$	−19.4022	−0.671039
$837$	−32.5083	−1.12365
$838$	−3.91510	−0.135245
$839$	−36.8533	−1.27232	−0.636159	−	0.771558i	$-0.719478\pi$
$839$	−36.8533	−1.27232	−0.636159	+	0.771558i	$0.719478\pi$
$840$	17.5814	0.606616
$841$	−16.5020	−0.569033
$842$	12.1728	0.419501
$843$	26.0622	0.897630
$844$	−10.1748	−0.350231
$845$	−19.7985	−0.681088
$846$	−6.80947	−0.234114
$847$	−44.4616	−1.52772
$848$	−5.23757	−0.179859
$849$	17.8986	0.614279
$850$	80.4000	2.75770
$851$	8.77913	0.300945
$852$	8.50771	0.291469
$853$	32.4495	1.11105	0.555525	−	0.831500i	$-0.312517\pi$
$853$	32.4495	1.11105	0.555525	+	0.831500i	$0.312517\pi$
$854$	−22.8246	−0.781040
$855$	−35.7097	−1.22124
$856$	6.11832	0.209120
$857$	14.7119	0.502549	0.251274	−	0.967916i	$-0.419150\pi$
$857$	14.7119	0.502549	0.251274	+	0.967916i	$0.419150\pi$
$858$	−13.2927	−0.453807
$859$	−53.6414	−1.83022	−0.915111	−	0.403202i	$-0.867897\pi$
$859$	−53.6414	−1.83022	−0.915111	+	0.403202i	$0.867897\pi$
$860$	40.1845	1.37028
$861$	3.68840	0.125700
$862$	29.0274	0.988678
$863$	−19.0429	−0.648228	−0.324114	−	0.946018i	$-0.605066\pi$
$863$	−19.0429	−0.648228	−0.324114	+	0.946018i	$0.605066\pi$
$864$	4.97146	0.169132
$865$	−64.9878	−2.20965
$866$	−22.4980	−0.764512
$867$	−21.2277	−0.720931
$868$	27.3785	0.929286
$869$	34.1870	1.15971
$870$	14.8449	0.503288
$871$	−36.0037	−1.21994
$872$	8.00174	0.270973
$873$	−24.1430	−0.817117
$874$	4.17285	0.141149
$875$	−141.448	−4.78182
$876$	−5.02688	−0.169843
$877$	−32.1103	−1.08429	−0.542144	−	0.840286i	$-0.682387\pi$
$877$	−32.1103	−1.08429	−0.542144	+	0.840286i	$0.682387\pi$
$878$	36.4289	1.22941
$879$	−30.9001	−1.04223
$880$	−19.7100	−0.664423
$881$	38.3259	1.29123	0.645617	−	0.763662i	$-0.276600\pi$
$881$	38.3259	1.29123	0.645617	+	0.763662i	$0.276600\pi$
$882$	−21.2589	−0.715824
$883$	−46.9520	−1.58006	−0.790030	−	0.613068i	$-0.789935\pi$
$883$	−46.9520	−1.58006	−0.790030	+	0.613068i	$0.789935\pi$
$884$	−17.8913	−0.601751
$885$	60.8837	2.04658
$886$	7.15995	0.240543
$887$	−20.8413	−0.699784	−0.349892	−	0.936790i	$-0.613782\pi$
$887$	−20.8413	−0.699784	−0.349892	+	0.936790i	$0.613782\pi$
$888$	−8.69638	−0.291831
$889$	−36.3388	−1.21876
$890$	57.2977	1.92062
$891$	−5.26195	−0.176282
$892$	8.12936	0.272191
$893$	14.0754	0.471015
$894$	−0.183659	−0.00614247
$895$	−16.3865	−0.547741
$896$	−4.18696	−0.139877
$897$	2.85888	0.0954553
$898$	−25.0404	−0.835610
$899$	23.1170	0.770995
$900$	−26.1823	−0.872744
$901$	−32.4686	−1.08168
$902$	−4.13495	−0.137679
$903$	39.3167	1.30838
$904$	0.262047	0.00871554
$905$	97.3545	3.23617
$906$	−11.7436	−0.390153
$907$	−17.7743	−0.590185	−0.295092	−	0.955469i	$-0.595350\pi$
$907$	−17.7743	−0.590185	−0.295092	+	0.955469i	$0.595350\pi$
$908$	6.67700	0.221584
$909$	12.4293	0.412253
$910$	51.2243	1.69807
$911$	−42.0898	−1.39450	−0.697248	−	0.716830i	$-0.745592\pi$
$911$	−42.0898	−1.39450	−0.697248	+	0.716830i	$0.745592\pi$
$912$	−4.13352	−0.136874
$913$	−10.0162	−0.331488
$914$	−6.46099	−0.213711
$915$	−22.8906	−0.756742
$916$	−21.8855	−0.723116
$917$	−4.18696	−0.138266
$918$	30.8189	1.01718
$919$	57.6152	1.90055	0.950274	−	0.311414i	$-0.100803\pi$
$919$	57.6152	1.90055	0.950274	+	0.311414i	$0.100803\pi$
$920$	4.23904	0.139757
$921$	−25.8004	−0.850151
$922$	8.90625	0.293312
$923$	24.7876	0.815895
$924$	−19.2843	−0.634408
$925$	113.861	3.74372
$926$	0.254866	0.00837543
$927$	−26.6222	−0.874387
$928$	−3.53526	−0.116051
$929$	2.85572	0.0936932	0.0468466	−	0.998902i	$-0.485083\pi$
$929$	2.85572	0.0936932	0.0468466	+	0.998902i	$0.485083\pi$
$930$	27.4577	0.900375
$931$	43.9428	1.44017
$932$	−13.8846	−0.454805
$933$	−15.1521	−0.496057
$934$	1.67439	0.0547877
$935$	−122.185	−3.99589
$936$	5.82632	0.190439
$937$	−1.60737	−0.0525105	−0.0262553	−	0.999655i	$-0.508358\pi$
$937$	−1.60737	−0.0525105	−0.0262553	+	0.999655i	$0.508358\pi$
$938$	−52.2320	−1.70544
$939$	3.98165	0.129936
$940$	14.2987	0.466371
$941$	8.19586	0.267177	0.133589	−	0.991037i	$-0.457350\pi$
$941$	8.19586	0.267177	0.133589	+	0.991037i	$0.457350\pi$
$942$	4.15328	0.135321
$943$	0.889308	0.0289599
$944$	−14.4993	−0.471911
$945$	−88.2370	−2.87035
$946$	−44.0767	−1.43306
$947$	−0.322617	−0.0104836	−0.00524182	−	0.999986i	$-0.501669\pi$
$947$	−0.322617	−0.0104836	−0.00524182	+	0.999986i	$0.501669\pi$
$948$	7.28332	0.236551
$949$	−14.6461	−0.475431
$950$	54.1197	1.75587
$951$	−10.8780	−0.352743
$952$	−25.9557	−0.841229
$953$	43.3459	1.40411	0.702056	−	0.712122i	$-0.252266\pi$
$953$	43.3459	1.40411	0.702056	+	0.712122i	$0.252266\pi$
$954$	10.5734	0.342327
$955$	33.6695	1.08952
$956$	−17.2121	−0.556679
$957$	−16.2827	−0.526345
$958$	16.1791	0.522724
$959$	−7.44466	−0.240401
$960$	−4.19909	−0.135525
$961$	11.7583	0.379299
$962$	−25.3373	−0.816908
$963$	−12.3514	−0.398020
$964$	24.4972	0.789001
$965$	−56.5533	−1.82052
$966$	4.14750	0.133444
$967$	51.0793	1.64260	0.821299	−	0.570498i	$-0.193250\pi$
$967$	51.0793	1.64260	0.821299	+	0.570498i	$0.193250\pi$
$968$	10.6191	0.341309
$969$	−25.6244	−0.823173
$970$	50.6960	1.62775
$971$	31.3491	1.00604	0.503021	−	0.864274i	$-0.332222\pi$
$971$	31.3491	1.00604	0.503021	+	0.864274i	$0.332222\pi$
$972$	−16.0354	−0.514336
$973$	−9.20302	−0.295035
$974$	−36.3583	−1.16499
$975$	37.0782	1.18745
$976$	5.45134	0.174493
$977$	50.6186	1.61943	0.809717	−	0.586821i	$-0.199621\pi$
$977$	50.6186	1.61943	0.809717	+	0.586821i	$0.199621\pi$
$978$	−7.56054	−0.241759
$979$	−62.8475	−2.00861
$980$	44.6399	1.42597
$981$	−16.1536	−0.515745
$982$	−2.02395	−0.0645868
$983$	39.5002	1.25986	0.629930	−	0.776652i	$-0.283083\pi$
$983$	39.5002	1.25986	0.629930	+	0.776652i	$0.283083\pi$
$984$	−0.880926	−0.0280829
$985$	50.0711	1.59540
$986$	−21.9157	−0.697937
$987$	13.9899	0.445303
$988$	−12.0432	−0.383145
$989$	9.47962	0.301434
$990$	39.7898	1.26460
$991$	−43.8891	−1.39418	−0.697092	−	0.716982i	$-0.745523\pi$
$991$	−43.8891	−1.39418	−0.697092	+	0.716982i	$0.745523\pi$
$992$	−6.53898	−0.207613
$993$	−8.46033	−0.268481
$994$	35.9604	1.14060
$995$	82.4568	2.61406
$996$	−2.13389	−0.0676148
$997$	−1.28493	−0.0406942	−0.0203471	−	0.999793i	$-0.506477\pi$
$997$	−1.28493	−0.0406942	−0.0203471	+	0.999793i	$0.506477\pi$
$998$	3.92126	0.124125
$999$	43.6451	1.38087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.15	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.990574 q^{3} +1.00000 q^{4} +4.23904 q^{5} -0.990574 q^{6} -4.18696 q^{7} +1.00000 q^{8} -2.01876 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.990574 q^{3} +1.00000 q^{4} +4.23904 q^{5} -0.990574 q^{6} -4.18696 q^{7} +1.00000 q^{8} -2.01876 q^{9} +4.23904 q^{10} -4.64963 q^{11} -0.990574 q^{12} -2.88609 q^{13} -4.18696 q^{14} -4.19909 q^{15} +1.00000 q^{16} +6.19917 q^{17} -2.01876 q^{18} +4.17285 q^{19} +4.23904 q^{20} +4.14750 q^{21} -4.64963 q^{22} +1.00000 q^{23} -0.990574 q^{24} +12.9695 q^{25} -2.88609 q^{26} +4.97146 q^{27} -4.18696 q^{28} -3.53526 q^{29} -4.19909 q^{30} -6.53898 q^{31} +1.00000 q^{32} +4.60580 q^{33} +6.19917 q^{34} -17.7487 q^{35} -2.01876 q^{36} +8.77913 q^{37} +4.17285 q^{38} +2.85888 q^{39} +4.23904 q^{40} +0.889308 q^{41} +4.14750 q^{42} +9.47962 q^{43} -4.64963 q^{44} -8.55762 q^{45} +1.00000 q^{46} +3.37309 q^{47} -0.990574 q^{48} +10.5307 q^{49} +12.9695 q^{50} -6.14074 q^{51} -2.88609 q^{52} -5.23757 q^{53} +4.97146 q^{54} -19.7100 q^{55} -4.18696 q^{56} -4.13352 q^{57} -3.53526 q^{58} -14.4993 q^{59} -4.19909 q^{60} +5.45134 q^{61} -6.53898 q^{62} +8.45248 q^{63} +1.00000 q^{64} -12.2342 q^{65} +4.60580 q^{66} +12.4749 q^{67} +6.19917 q^{68} -0.990574 q^{69} -17.7487 q^{70} -8.58867 q^{71} -2.01876 q^{72} +5.07471 q^{73} +8.77913 q^{74} -12.8472 q^{75} +4.17285 q^{76} +19.4678 q^{77} +2.85888 q^{78} -7.35263 q^{79} +4.23904 q^{80} +1.13169 q^{81} +0.889308 q^{82} +2.15419 q^{83} +4.14750 q^{84} +26.2785 q^{85} +9.47962 q^{86} +3.50193 q^{87} -4.64963 q^{88} +13.5167 q^{89} -8.55762 q^{90} +12.0839 q^{91} +1.00000 q^{92} +6.47735 q^{93} +3.37309 q^{94} +17.6889 q^{95} -0.990574 q^{96} +11.9593 q^{97} +10.5307 q^{98} +9.38650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 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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