LMFDB - Embedded newform 6026.2.a.i.1.21

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.17821 q^{3} +1.00000 q^{4} +2.64147 q^{5} -2.17821 q^{6} +0.866712 q^{7} -1.00000 q^{8} +1.74461 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.17821 q^{3} +1.00000 q^{4} +2.64147 q^{5} -2.17821 q^{6} +0.866712 q^{7} -1.00000 q^{8} +1.74461 q^{9} -2.64147 q^{10} -2.06584 q^{11} +2.17821 q^{12} -5.30632 q^{13} -0.866712 q^{14} +5.75368 q^{15} +1.00000 q^{16} -4.65436 q^{17} -1.74461 q^{18} -1.86097 q^{19} +2.64147 q^{20} +1.88788 q^{21} +2.06584 q^{22} +1.00000 q^{23} -2.17821 q^{24} +1.97736 q^{25} +5.30632 q^{26} -2.73451 q^{27} +0.866712 q^{28} -5.76377 q^{29} -5.75368 q^{30} -1.84099 q^{31} -1.00000 q^{32} -4.49984 q^{33} +4.65436 q^{34} +2.28939 q^{35} +1.74461 q^{36} -9.12218 q^{37} +1.86097 q^{38} -11.5583 q^{39} -2.64147 q^{40} -3.84150 q^{41} -1.88788 q^{42} +8.82296 q^{43} -2.06584 q^{44} +4.60833 q^{45} -1.00000 q^{46} +7.58108 q^{47} +2.17821 q^{48} -6.24881 q^{49} -1.97736 q^{50} -10.1382 q^{51} -5.30632 q^{52} -7.00945 q^{53} +2.73451 q^{54} -5.45686 q^{55} -0.866712 q^{56} -4.05358 q^{57} +5.76377 q^{58} +4.34771 q^{59} +5.75368 q^{60} +0.363810 q^{61} +1.84099 q^{62} +1.51207 q^{63} +1.00000 q^{64} -14.0165 q^{65} +4.49984 q^{66} +0.0197830 q^{67} -4.65436 q^{68} +2.17821 q^{69} -2.28939 q^{70} +11.5417 q^{71} -1.74461 q^{72} -0.613159 q^{73} +9.12218 q^{74} +4.30712 q^{75} -1.86097 q^{76} -1.79049 q^{77} +11.5583 q^{78} +12.1792 q^{79} +2.64147 q^{80} -11.1902 q^{81} +3.84150 q^{82} -16.2914 q^{83} +1.88788 q^{84} -12.2943 q^{85} -8.82296 q^{86} -12.5547 q^{87} +2.06584 q^{88} -2.82211 q^{89} -4.60833 q^{90} -4.59905 q^{91} +1.00000 q^{92} -4.01006 q^{93} -7.58108 q^{94} -4.91569 q^{95} -2.17821 q^{96} +15.3689 q^{97} +6.24881 q^{98} -3.60408 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * 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
$3$	2.17821	1.25759	0.628796	−	0.777571i	$-0.283548\pi$
$3$	2.17821	1.25759	0.628796	+	0.777571i	$0.283548\pi$
$4$	1.00000	0.500000
$5$	2.64147	1.18130	0.590651	−	0.806927i	$-0.298871\pi$
$5$	2.64147	1.18130	0.590651	+	0.806927i	$0.298871\pi$
$6$	−2.17821	−0.889251
$7$	0.866712	0.327586	0.163793	−	0.986495i	$-0.447627\pi$
$7$	0.866712	0.327586	0.163793	+	0.986495i	$0.447627\pi$
$8$	−1.00000	−0.353553
$9$	1.74461	0.581536
$10$	−2.64147	−0.835306
$11$	−2.06584	−0.622875	−0.311437	−	0.950267i	$-0.600810\pi$
$11$	−2.06584	−0.622875	−0.311437	+	0.950267i	$0.600810\pi$
$12$	2.17821	0.628796
$13$	−5.30632	−1.47171	−0.735854	−	0.677140i	$-0.763219\pi$
$13$	−5.30632	−1.47171	−0.735854	+	0.677140i	$0.763219\pi$
$14$	−0.866712	−0.231639
$15$	5.75368	1.48559
$16$	1.00000	0.250000
$17$	−4.65436	−1.12885	−0.564424	−	0.825485i	$-0.690902\pi$
$17$	−4.65436	−1.12885	−0.564424	+	0.825485i	$0.690902\pi$
$18$	−1.74461	−0.411208
$19$	−1.86097	−0.426935	−0.213468	−	0.976950i	$-0.568476\pi$
$19$	−1.86097	−0.426935	−0.213468	+	0.976950i	$0.568476\pi$
$20$	2.64147	0.590651
$21$	1.88788	0.411970
$22$	2.06584	0.440439
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.17821	−0.444626
$25$	1.97736	0.395473
$26$	5.30632	1.04066
$27$	−2.73451	−0.526257
$28$	0.866712	0.163793
$29$	−5.76377	−1.07030	−0.535152	−	0.844756i	$-0.679746\pi$
$29$	−5.76377	−1.07030	−0.535152	+	0.844756i	$0.679746\pi$
$30$	−5.75368	−1.05047
$31$	−1.84099	−0.330651	−0.165326	−	0.986239i	$-0.552868\pi$
$31$	−1.84099	−0.330651	−0.165326	+	0.986239i	$0.552868\pi$
$32$	−1.00000	−0.176777
$33$	−4.49984	−0.783322
$34$	4.65436	0.798216
$35$	2.28939	0.386978
$36$	1.74461	0.290768
$37$	−9.12218	−1.49968	−0.749839	−	0.661620i	$-0.769869\pi$
$37$	−9.12218	−1.49968	−0.749839	+	0.661620i	$0.769869\pi$
$38$	1.86097	0.301889
$39$	−11.5583	−1.85081
$40$	−2.64147	−0.417653
$41$	−3.84150	−0.599941	−0.299970	−	0.953949i	$-0.596977\pi$
$41$	−3.84150	−0.599941	−0.299970	+	0.953949i	$0.596977\pi$
$42$	−1.88788	−0.291307
$43$	8.82296	1.34549	0.672744	−	0.739875i	$-0.265115\pi$
$43$	8.82296	1.34549	0.672744	+	0.739875i	$0.265115\pi$
$44$	−2.06584	−0.311437
$45$	4.60833	0.686969
$46$	−1.00000	−0.147442
$47$	7.58108	1.10581	0.552907	−	0.833243i	$-0.313518\pi$
$47$	7.58108	1.10581	0.552907	+	0.833243i	$0.313518\pi$
$48$	2.17821	0.314398
$49$	−6.24881	−0.892687
$50$	−1.97736	−0.279642
$51$	−10.1382	−1.41963
$52$	−5.30632	−0.735854
$53$	−7.00945	−0.962823	−0.481411	−	0.876495i	$-0.659876\pi$
$53$	−7.00945	−0.962823	−0.481411	+	0.876495i	$0.659876\pi$
$54$	2.73451	0.372120
$55$	−5.45686	−0.735803
$56$	−0.866712	−0.115819
$57$	−4.05358	−0.536910
$58$	5.76377	0.756820
$59$	4.34771	0.566024	0.283012	−	0.959116i	$-0.408666\pi$
$59$	4.34771	0.566024	0.283012	+	0.959116i	$0.408666\pi$
$60$	5.75368	0.742797
$61$	0.363810	0.0465810	0.0232905	−	0.999729i	$-0.492586\pi$
$61$	0.363810	0.0465810	0.0232905	+	0.999729i	$0.492586\pi$
$62$	1.84099	0.233806
$63$	1.51207	0.190503
$64$	1.00000	0.125000
$65$	−14.0165	−1.73853
$66$	4.49984	0.553892
$67$	0.0197830	0.00241687	0.00120844	−	0.999999i	$-0.499615\pi$
$67$	0.0197830	0.00241687	0.00120844	+	0.999999i	$0.499615\pi$
$68$	−4.65436	−0.564424
$69$	2.17821	0.262226
$70$	−2.28939	−0.273635
$71$	11.5417	1.36975	0.684873	−	0.728662i	$-0.259858\pi$
$71$	11.5417	1.36975	0.684873	+	0.728662i	$0.259858\pi$
$72$	−1.74461	−0.205604
$73$	−0.613159	−0.0717649	−0.0358824	−	0.999356i	$-0.511424\pi$
$73$	−0.613159	−0.0717649	−0.0358824	+	0.999356i	$0.511424\pi$
$74$	9.12218	1.06043
$75$	4.30712	0.497343
$76$	−1.86097	−0.213468
$77$	−1.79049	−0.204045
$78$	11.5583	1.30872
$79$	12.1792	1.37026	0.685131	−	0.728420i	$-0.259745\pi$
$79$	12.1792	1.37026	0.685131	+	0.728420i	$0.259745\pi$
$80$	2.64147	0.295325
$81$	−11.1902	−1.24335
$82$	3.84150	0.424222
$83$	−16.2914	−1.78822	−0.894108	−	0.447851i	$-0.852189\pi$
$83$	−16.2914	−1.78822	−0.894108	+	0.447851i	$0.852189\pi$
$84$	1.88788	0.205985
$85$	−12.2943	−1.33351
$86$	−8.82296	−0.951404
$87$	−12.5547	−1.34601
$88$	2.06584	0.220219
$89$	−2.82211	−0.299143	−0.149571	−	0.988751i	$-0.547789\pi$
$89$	−2.82211	−0.299143	−0.149571	+	0.988751i	$0.547789\pi$
$90$	−4.60833	−0.485760
$91$	−4.59905	−0.482112
$92$	1.00000	0.104257
$93$	−4.01006	−0.415824
$94$	−7.58108	−0.781929
$95$	−4.91569	−0.504339
$96$	−2.17821	−0.222313
$97$	15.3689	1.56048	0.780240	−	0.625481i	$-0.215097\pi$
$97$	15.3689	1.56048	0.780240	+	0.625481i	$0.215097\pi$
$98$	6.24881	0.631225
$99$	−3.60408	−0.362224
$100$	1.97736	0.197736
$101$	−0.797736	−0.0793777	−0.0396888	−	0.999212i	$-0.512637\pi$
$101$	−0.797736	−0.0793777	−0.0396888	+	0.999212i	$0.512637\pi$
$102$	10.1382	1.00383
$103$	1.91684	0.188872	0.0944360	−	0.995531i	$-0.469895\pi$
$103$	1.91684	0.188872	0.0944360	+	0.995531i	$0.469895\pi$
$104$	5.30632	0.520328
$105$	4.98678	0.486660
$106$	7.00945	0.680818
$107$	6.75639	0.653165	0.326582	−	0.945169i	$-0.394103\pi$
$107$	6.75639	0.653165	0.326582	+	0.945169i	$0.394103\pi$
$108$	−2.73451	−0.263129
$109$	−13.4229	−1.28568	−0.642838	−	0.766002i	$-0.722243\pi$
$109$	−13.4229	−1.28568	−0.642838	+	0.766002i	$0.722243\pi$
$110$	5.45686	0.520291
$111$	−19.8700	−1.88598
$112$	0.866712	0.0818966
$113$	−4.82181	−0.453598	−0.226799	−	0.973942i	$-0.572826\pi$
$113$	−4.82181	−0.453598	−0.226799	+	0.973942i	$0.572826\pi$
$114$	4.05358	0.379653
$115$	2.64147	0.246318
$116$	−5.76377	−0.535152
$117$	−9.25744	−0.855851
$118$	−4.34771	−0.400239
$119$	−4.03399	−0.369795
$120$	−5.75368	−0.525237
$121$	−6.73230	−0.612027
$122$	−0.363810	−0.0329378
$123$	−8.36759	−0.754480
$124$	−1.84099	−0.165326
$125$	−7.98420	−0.714129
$126$	−1.51207	−0.134706
$127$	−17.6369	−1.56502	−0.782512	−	0.622635i	$-0.786062\pi$
$127$	−17.6369	−1.56502	−0.782512	+	0.622635i	$0.786062\pi$
$128$	−1.00000	−0.0883883
$129$	19.2183	1.69207
$130$	14.0165	1.22933
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−4.49984	−0.391661
$133$	−1.61292	−0.139858
$134$	−0.0197830	−0.00170899
$135$	−7.22313	−0.621668
$136$	4.65436	0.399108
$137$	4.78508	0.408817	0.204408	−	0.978886i	$-0.434473\pi$
$137$	4.78508	0.408817	0.204408	+	0.978886i	$0.434473\pi$
$138$	−2.17821	−0.185422
$139$	−4.79909	−0.407053	−0.203527	−	0.979069i	$-0.565240\pi$
$139$	−4.79909	−0.407053	−0.203527	+	0.979069i	$0.565240\pi$
$140$	2.28939	0.193489
$141$	16.5132	1.39066
$142$	−11.5417	−0.968557
$143$	10.9620	0.916690
$144$	1.74461	0.145384
$145$	−15.2248	−1.26435
$146$	0.613159	0.0507454
$147$	−13.6112	−1.12264
$148$	−9.12218	−0.749839
$149$	−12.7382	−1.04356	−0.521778	−	0.853081i	$-0.674731\pi$
$149$	−12.7382	−1.04356	−0.521778	+	0.853081i	$0.674731\pi$
$150$	−4.30712	−0.351675
$151$	7.42133	0.603939	0.301970	−	0.953318i	$-0.402356\pi$
$151$	7.42133	0.603939	0.301970	+	0.953318i	$0.402356\pi$
$152$	1.86097	0.150944
$153$	−8.12002	−0.656465
$154$	1.79049	0.144282
$155$	−4.86292	−0.390599
$156$	−11.5583	−0.925404
$157$	−5.34909	−0.426904	−0.213452	−	0.976954i	$-0.568471\pi$
$157$	−5.34909	−0.426904	−0.213452	+	0.976954i	$0.568471\pi$
$158$	−12.1792	−0.968921
$159$	−15.2681	−1.21084
$160$	−2.64147	−0.208827
$161$	0.866712	0.0683065
$162$	11.1902	0.879183
$163$	7.27586	0.569889	0.284945	−	0.958544i	$-0.408025\pi$
$163$	7.27586	0.569889	0.284945	+	0.958544i	$0.408025\pi$
$164$	−3.84150	−0.299970
$165$	−11.8862	−0.925339
$166$	16.2914	1.26446
$167$	−10.7614	−0.832743	−0.416372	−	0.909194i	$-0.636699\pi$
$167$	−10.7614	−0.832743	−0.416372	+	0.909194i	$0.636699\pi$
$168$	−1.88788	−0.145653
$169$	15.1570	1.16593
$170$	12.2943	0.942933
$171$	−3.24666	−0.248278
$172$	8.82296	0.672744
$173$	1.23106	0.0935957	0.0467979	−	0.998904i	$-0.485098\pi$
$173$	1.23106	0.0935957	0.0467979	+	0.998904i	$0.485098\pi$
$174$	12.5547	0.951770
$175$	1.71381	0.129552
$176$	−2.06584	−0.155719
$177$	9.47023	0.711826
$178$	2.82211	0.211526
$179$	16.0508	1.19969	0.599846	−	0.800116i	$-0.295229\pi$
$179$	16.0508	1.19969	0.599846	+	0.800116i	$0.295229\pi$
$180$	4.60833	0.343484
$181$	−5.48651	−0.407809	−0.203905	−	0.978991i	$-0.565363\pi$
$181$	−5.48651	−0.407809	−0.203905	+	0.978991i	$0.565363\pi$
$182$	4.59905	0.340904
$183$	0.792454	0.0585799
$184$	−1.00000	−0.0737210
$185$	−24.0960	−1.77157
$186$	4.01006	0.294032
$187$	9.61517	0.703131
$188$	7.58108	0.552907
$189$	−2.37003	−0.172395
$190$	4.91569	0.356622
$191$	−13.6216	−0.985623	−0.492812	−	0.870136i	$-0.664031\pi$
$191$	−13.6216	−0.985623	−0.492812	+	0.870136i	$0.664031\pi$
$192$	2.17821	0.157199
$193$	−4.17318	−0.300392	−0.150196	−	0.988656i	$-0.547990\pi$
$193$	−4.17318	−0.300392	−0.150196	+	0.988656i	$0.547990\pi$
$194$	−15.3689	−1.10343
$195$	−30.5309	−2.18636
$196$	−6.24881	−0.446344
$197$	18.9986	1.35359	0.676797	−	0.736170i	$-0.263367\pi$
$197$	18.9986	1.35359	0.676797	+	0.736170i	$0.263367\pi$
$198$	3.60408	0.256131
$199$	17.8991	1.26884	0.634418	−	0.772990i	$-0.281240\pi$
$199$	17.8991	1.26884	0.634418	+	0.772990i	$0.281240\pi$
$200$	−1.97736	−0.139821
$201$	0.0430915	0.00303944
$202$	0.797736	0.0561285
$203$	−4.99553	−0.350617
$204$	−10.1382	−0.709814
$205$	−10.1472	−0.708711
$206$	−1.91684	−0.133553
$207$	1.74461	0.121259
$208$	−5.30632	−0.367927
$209$	3.84446	0.265927
$210$	−4.98678	−0.344121
$211$	−17.5627	−1.20907	−0.604533	−	0.796580i	$-0.706640\pi$
$211$	−17.5627	−1.20907	−0.604533	+	0.796580i	$0.706640\pi$
$212$	−7.00945	−0.481411
$213$	25.1402	1.72258
$214$	−6.75639	−0.461857
$215$	23.3056	1.58943
$216$	2.73451	0.186060
$217$	−1.59561	−0.108317
$218$	13.4229	0.909110
$219$	−1.33559	−0.0902509
$220$	−5.45686	−0.367901
$221$	24.6975	1.66133
$222$	19.8700	1.33359
$223$	−9.12896	−0.611321	−0.305660	−	0.952141i	$-0.598877\pi$
$223$	−9.12896	−0.611321	−0.305660	+	0.952141i	$0.598877\pi$
$224$	−0.866712	−0.0579096
$225$	3.44972	0.229982
$226$	4.82181	0.320742
$227$	−0.890828	−0.0591263	−0.0295632	−	0.999563i	$-0.509412\pi$
$227$	−0.890828	−0.0591263	−0.0295632	+	0.999563i	$0.509412\pi$
$228$	−4.05358	−0.268455
$229$	7.75649	0.512564	0.256282	−	0.966602i	$-0.417503\pi$
$229$	7.75649	0.512564	0.256282	+	0.966602i	$0.417503\pi$
$230$	−2.64147	−0.174173
$231$	−3.90007	−0.256606
$232$	5.76377	0.378410
$233$	2.12735	0.139367	0.0696835	−	0.997569i	$-0.477801\pi$
$233$	2.12735	0.139367	0.0696835	+	0.997569i	$0.477801\pi$
$234$	9.25744	0.605178
$235$	20.0252	1.30630
$236$	4.34771	0.283012
$237$	26.5288	1.72323
$238$	4.03399	0.261485
$239$	10.6055	0.686012	0.343006	−	0.939333i	$-0.388555\pi$
$239$	10.6055	0.686012	0.343006	+	0.939333i	$0.388555\pi$
$240$	5.75368	0.371399
$241$	0.865529	0.0557537	0.0278768	−	0.999611i	$-0.491125\pi$
$241$	0.865529	0.0557537	0.0278768	+	0.999611i	$0.491125\pi$
$242$	6.73230	0.432768
$243$	−16.1710	−1.03737
$244$	0.363810	0.0232905
$245$	−16.5060	−1.05453
$246$	8.36759	0.533498
$247$	9.87489	0.628324
$248$	1.84099	0.116903
$249$	−35.4862	−2.24884
$250$	7.98420	0.504965
$251$	−8.31005	−0.524526	−0.262263	−	0.964996i	$-0.584469\pi$
$251$	−8.31005	−0.524526	−0.262263	+	0.964996i	$0.584469\pi$
$252$	1.51207	0.0952515
$253$	−2.06584	−0.129878
$254$	17.6369	1.10664
$255$	−26.7797	−1.67701
$256$	1.00000	0.0625000
$257$	15.7897	0.984932	0.492466	−	0.870332i	$-0.336096\pi$
$257$	15.7897	0.984932	0.492466	+	0.870332i	$0.336096\pi$
$258$	−19.2183	−1.19648
$259$	−7.90631	−0.491274
$260$	−14.0165	−0.869266
$261$	−10.0555	−0.622420
$262$	−1.00000	−0.0617802
$263$	14.6166	0.901296	0.450648	−	0.892702i	$-0.351193\pi$
$263$	14.6166	0.901296	0.450648	+	0.892702i	$0.351193\pi$
$264$	4.49984	0.276946
$265$	−18.5153	−1.13738
$266$	1.61292	0.0988946
$267$	−6.14715	−0.376199
$268$	0.0197830	0.00120844
$269$	5.30093	0.323204	0.161602	−	0.986856i	$-0.448334\pi$
$269$	5.30093	0.323204	0.161602	+	0.986856i	$0.448334\pi$
$270$	7.22313	0.439586
$271$	−1.55389	−0.0943919	−0.0471959	−	0.998886i	$-0.515029\pi$
$271$	−1.55389	−0.0943919	−0.0471959	+	0.998886i	$0.515029\pi$
$272$	−4.65436	−0.282212
$273$	−10.0177	−0.606299
$274$	−4.78508	−0.289077
$275$	−4.08492	−0.246330
$276$	2.17821	0.131113
$277$	−5.00152	−0.300512	−0.150256	−	0.988647i	$-0.548010\pi$
$277$	−5.00152	−0.300512	−0.150256	+	0.988647i	$0.548010\pi$
$278$	4.79909	0.287830
$279$	−3.21180	−0.192286
$280$	−2.28939	−0.136817
$281$	2.46356	0.146963	0.0734817	−	0.997297i	$-0.476589\pi$
$281$	2.46356	0.146963	0.0734817	+	0.997297i	$0.476589\pi$
$282$	−16.5132	−0.983347
$283$	−18.7890	−1.11689	−0.558444	−	0.829542i	$-0.688602\pi$
$283$	−18.7890	−1.11689	−0.558444	+	0.829542i	$0.688602\pi$
$284$	11.5417	0.684873
$285$	−10.7074	−0.634252
$286$	−10.9620	−0.648198
$287$	−3.32947	−0.196532
$288$	−1.74461	−0.102802
$289$	4.66305	0.274297
$290$	15.2248	0.894032
$291$	33.4768	1.96244
$292$	−0.613159	−0.0358824
$293$	5.88653	0.343894	0.171947	−	0.985106i	$-0.444994\pi$
$293$	5.88653	0.343894	0.171947	+	0.985106i	$0.444994\pi$
$294$	13.6112	0.793823
$295$	11.4843	0.668644
$296$	9.12218	0.530216
$297$	5.64907	0.327792
$298$	12.7382	0.737906
$299$	−5.30632	−0.306872
$300$	4.30712	0.248672
$301$	7.64696	0.440764
$302$	−7.42133	−0.427050
$303$	−1.73764	−0.0998247
$304$	−1.86097	−0.106734
$305$	0.960992	0.0550262
$306$	8.12002	0.464191
$307$	16.2516	0.927530	0.463765	−	0.885958i	$-0.346498\pi$
$307$	16.2516	0.927530	0.463765	+	0.885958i	$0.346498\pi$
$308$	−1.79049	−0.102023
$309$	4.17529	0.237524
$310$	4.86292	0.276195
$311$	2.83222	0.160601	0.0803003	−	0.996771i	$-0.474412\pi$
$311$	2.83222	0.160601	0.0803003	+	0.996771i	$0.474412\pi$
$312$	11.5583	0.654359
$313$	23.6581	1.33723	0.668616	−	0.743608i	$-0.266887\pi$
$313$	23.6581	1.33723	0.668616	+	0.743608i	$0.266887\pi$
$314$	5.34909	0.301867
$315$	3.99409	0.225042
$316$	12.1792	0.685131
$317$	−0.751806	−0.0422256	−0.0211128	−	0.999777i	$-0.506721\pi$
$317$	−0.751806	−0.0422256	−0.0211128	+	0.999777i	$0.506721\pi$
$318$	15.2681	0.856191
$319$	11.9070	0.666666
$320$	2.64147	0.147663
$321$	14.7169	0.821415
$322$	−0.866712	−0.0483000
$323$	8.66161	0.481945
$324$	−11.1902	−0.621676
$325$	−10.4925	−0.582021
$326$	−7.27586	−0.402973
$327$	−29.2378	−1.61685
$328$	3.84150	0.212111
$329$	6.57062	0.362250
$330$	11.8862	0.654314
$331$	17.8894	0.983291	0.491646	−	0.870795i	$-0.336396\pi$
$331$	17.8894	0.983291	0.491646	+	0.870795i	$0.336396\pi$
$332$	−16.2914	−0.894108
$333$	−15.9146	−0.872116
$334$	10.7614	0.588839
$335$	0.0522561	0.00285505
$336$	1.88788	0.102992
$337$	10.4393	0.568667	0.284334	−	0.958725i	$-0.408228\pi$
$337$	10.4393	0.568667	0.284334	+	0.958725i	$0.408228\pi$
$338$	−15.1570	−0.824434
$339$	−10.5029	−0.570441
$340$	−12.2943	−0.666755
$341$	3.80319	0.205954
$342$	3.24666	0.175559
$343$	−11.4829	−0.620018
$344$	−8.82296	−0.475702
$345$	5.75368	0.309768
$346$	−1.23106	−0.0661822
$347$	−15.5704	−0.835861	−0.417930	−	0.908479i	$-0.637244\pi$
$347$	−15.5704	−0.835861	−0.417930	+	0.908479i	$0.637244\pi$
$348$	−12.5547	−0.673003
$349$	−3.68100	−0.197040	−0.0985198	−	0.995135i	$-0.531411\pi$
$349$	−3.68100	−0.197040	−0.0985198	+	0.995135i	$0.531411\pi$
$350$	−1.71381	−0.0916067
$351$	14.5102	0.774497
$352$	2.06584	0.110110
$353$	13.8193	0.735526	0.367763	−	0.929920i	$-0.380124\pi$
$353$	13.8193	0.735526	0.367763	+	0.929920i	$0.380124\pi$
$354$	−9.47023	−0.503337
$355$	30.4870	1.61808
$356$	−2.82211	−0.149571
$357$	−8.78688	−0.465051
$358$	−16.0508	−0.848310
$359$	−1.97381	−0.104174	−0.0520869	−	0.998643i	$-0.516587\pi$
$359$	−1.97381	−0.104174	−0.0520869	+	0.998643i	$0.516587\pi$
$360$	−4.60833	−0.242880
$361$	−15.5368	−0.817726
$362$	5.48651	0.288365
$363$	−14.6644	−0.769680
$364$	−4.59905	−0.241056
$365$	−1.61964	−0.0847759
$366$	−0.792454	−0.0414222
$367$	24.8160	1.29539	0.647693	−	0.761902i	$-0.275734\pi$
$367$	24.8160	1.29539	0.647693	+	0.761902i	$0.275734\pi$
$368$	1.00000	0.0521286
$369$	−6.70190	−0.348887
$370$	24.0960	1.25269
$371$	−6.07518	−0.315408
$372$	−4.01006	−0.207912
$373$	13.2927	0.688270	0.344135	−	0.938920i	$-0.388172\pi$
$373$	13.2927	0.688270	0.344135	+	0.938920i	$0.388172\pi$
$374$	−9.61517	−0.497188
$375$	−17.3913	−0.898082
$376$	−7.58108	−0.390965
$377$	30.5844	1.57518
$378$	2.37003	0.121901
$379$	−23.7799	−1.22149	−0.610747	−	0.791826i	$-0.709131\pi$
$379$	−23.7799	−1.22149	−0.610747	+	0.791826i	$0.709131\pi$
$380$	−4.91569	−0.252170
$381$	−38.4170	−1.96816
$382$	13.6216	0.696941
$383$	−9.52675	−0.486794	−0.243397	−	0.969927i	$-0.578262\pi$
$383$	−9.52675	−0.486794	−0.243397	+	0.969927i	$0.578262\pi$
$384$	−2.17821	−0.111156
$385$	−4.72953	−0.241039
$386$	4.17318	0.212409
$387$	15.3926	0.782449
$388$	15.3689	0.780240
$389$	−3.34394	−0.169544	−0.0847722	−	0.996400i	$-0.527016\pi$
$389$	−3.34394	−0.169544	−0.0847722	+	0.996400i	$0.527016\pi$
$390$	30.5309	1.54599
$391$	−4.65436	−0.235381
$392$	6.24881	0.315613
$393$	2.17821	0.109876
$394$	−18.9986	−0.957136
$395$	32.1709	1.61869
$396$	−3.60408	−0.181112
$397$	−23.8867	−1.19884	−0.599421	−	0.800434i	$-0.704602\pi$
$397$	−23.8867	−1.19884	−0.599421	+	0.800434i	$0.704602\pi$
$398$	−17.8991	−0.897202
$399$	−3.51329	−0.175884
$400$	1.97736	0.0988682
$401$	4.08624	0.204057	0.102029	−	0.994781i	$-0.467467\pi$
$401$	4.08624	0.204057	0.102029	+	0.994781i	$0.467467\pi$
$402$	−0.0430915	−0.00214921
$403$	9.76888	0.486622
$404$	−0.797736	−0.0396888
$405$	−29.5585	−1.46877
$406$	4.99553	0.247924
$407$	18.8450	0.934111
$408$	10.1382	0.501915
$409$	8.37428	0.414082	0.207041	−	0.978332i	$-0.433617\pi$
$409$	8.37428	0.414082	0.207041	+	0.978332i	$0.433617\pi$
$410$	10.1472	0.501134
$411$	10.4229	0.514124
$412$	1.91684	0.0944360
$413$	3.76821	0.185422
$414$	−1.74461	−0.0857427
$415$	−43.0333	−2.11242
$416$	5.30632	0.260164
$417$	−10.4534	−0.511907
$418$	−3.84446	−0.188039
$419$	−1.65940	−0.0810669	−0.0405335	−	0.999178i	$-0.512906\pi$
$419$	−1.65940	−0.0810669	−0.0405335	+	0.999178i	$0.512906\pi$
$420$	4.98678	0.243330
$421$	−4.89053	−0.238350	−0.119175	−	0.992873i	$-0.538025\pi$
$421$	−4.89053	−0.238350	−0.119175	+	0.992873i	$0.538025\pi$
$422$	17.5627	0.854938
$423$	13.2260	0.643071
$424$	7.00945	0.340409
$425$	−9.20336	−0.446429
$426$	−25.1402	−1.21805
$427$	0.315318	0.0152593
$428$	6.75639	0.326582
$429$	23.8776	1.15282
$430$	−23.3056	−1.12389
$431$	10.7303	0.516860	0.258430	−	0.966030i	$-0.416795\pi$
$431$	10.7303	0.516860	0.258430	+	0.966030i	$0.416795\pi$
$432$	−2.73451	−0.131564
$433$	−27.1757	−1.30598	−0.652990	−	0.757366i	$-0.726486\pi$
$433$	−27.1757	−1.30598	−0.652990	+	0.757366i	$0.726486\pi$
$434$	1.59561	0.0765916
$435$	−33.1629	−1.59004
$436$	−13.4229	−0.642838
$437$	−1.86097	−0.0890221
$438$	1.33559	0.0638170
$439$	−6.79328	−0.324225	−0.162113	−	0.986772i	$-0.551831\pi$
$439$	−6.79328	−0.324225	−0.162113	+	0.986772i	$0.551831\pi$
$440$	5.45686	0.260146
$441$	−10.9017	−0.519129
$442$	−24.6975	−1.17474
$443$	21.0256	0.998955	0.499478	−	0.866327i	$-0.333525\pi$
$443$	21.0256	0.998955	0.499478	+	0.866327i	$0.333525\pi$
$444$	−19.8700	−0.942991
$445$	−7.45451	−0.353378
$446$	9.12896	0.432269
$447$	−27.7466	−1.31237
$448$	0.866712	0.0409483
$449$	39.4207	1.86038	0.930190	−	0.367079i	$-0.119642\pi$
$449$	39.4207	1.86038	0.930190	+	0.367079i	$0.119642\pi$
$450$	−3.44972	−0.162621
$451$	7.93592	0.373688
$452$	−4.82181	−0.226799
$453$	16.1652	0.759509
$454$	0.890828	0.0418086
$455$	−12.1483	−0.569519
$456$	4.05358	0.189826
$457$	−19.4473	−0.909704	−0.454852	−	0.890567i	$-0.650308\pi$
$457$	−19.4473	−0.909704	−0.454852	+	0.890567i	$0.650308\pi$
$458$	−7.75649	−0.362437
$459$	12.7274	0.594064
$460$	2.64147	0.123159
$461$	−37.9498	−1.76750	−0.883750	−	0.467960i	$-0.844989\pi$
$461$	−37.9498	−1.76750	−0.883750	+	0.467960i	$0.844989\pi$
$462$	3.90007	0.181447
$463$	−22.9027	−1.06438	−0.532190	−	0.846625i	$-0.678631\pi$
$463$	−22.9027	−1.06438	−0.532190	+	0.846625i	$0.678631\pi$
$464$	−5.76377	−0.267576
$465$	−10.5925	−0.491214
$466$	−2.12735	−0.0985474
$467$	−27.0638	−1.25236	−0.626182	−	0.779677i	$-0.715383\pi$
$467$	−27.0638	−1.25236	−0.626182	+	0.779677i	$0.715383\pi$
$468$	−9.25744	−0.427925
$469$	0.0171461	0.000791734 0
$470$	−20.0252	−0.923694
$471$	−11.6515	−0.536870
$472$	−4.34771	−0.200120
$473$	−18.2268	−0.838071
$474$	−26.5288	−1.21851
$475$	−3.67981	−0.168841
$476$	−4.03399	−0.184898
$477$	−12.2287	−0.559916
$478$	−10.6055	−0.485084
$479$	−14.1721	−0.647538	−0.323769	−	0.946136i	$-0.604950\pi$
$479$	−14.1721	−0.647538	−0.323769	+	0.946136i	$0.604950\pi$
$480$	−5.75368	−0.262618
$481$	48.4052	2.20709
$482$	−0.865529	−0.0394238
$483$	1.88788	0.0859016
$484$	−6.73230	−0.306014
$485$	40.5966	1.84340
$486$	16.1710	0.733532
$487$	36.2013	1.64044	0.820219	−	0.572049i	$-0.193851\pi$
$487$	36.2013	1.64044	0.820219	+	0.572049i	$0.193851\pi$
$488$	−0.363810	−0.0164689
$489$	15.8484	0.716688
$490$	16.5060	0.745667
$491$	4.71715	0.212882	0.106441	−	0.994319i	$-0.466054\pi$
$491$	4.71715	0.212882	0.106441	+	0.994319i	$0.466054\pi$
$492$	−8.36759	−0.377240
$493$	26.8266	1.20821
$494$	−9.87489	−0.444292
$495$	−9.52007	−0.427895
$496$	−1.84099	−0.0826628
$497$	10.0033	0.448710
$498$	35.4862	1.59017
$499$	27.5118	1.23160	0.615799	−	0.787903i	$-0.288833\pi$
$499$	27.5118	1.23160	0.615799	+	0.787903i	$0.288833\pi$
$500$	−7.98420	−0.357064
$501$	−23.4406	−1.04725
$502$	8.31005	0.370896
$503$	15.0353	0.670391	0.335195	−	0.942149i	$-0.391198\pi$
$503$	15.0353	0.670391	0.335195	+	0.942149i	$0.391198\pi$
$504$	−1.51207	−0.0673530
$505$	−2.10720	−0.0937690
$506$	2.06584	0.0918379
$507$	33.0152	1.46626
$508$	−17.6369	−0.782512
$509$	−4.00475	−0.177507	−0.0887536	−	0.996054i	$-0.528288\pi$
$509$	−4.00475	−0.177507	−0.0887536	+	0.996054i	$0.528288\pi$
$510$	26.7797	1.18582
$511$	−0.531433	−0.0235092
$512$	−1.00000	−0.0441942
$513$	5.08884	0.224678
$514$	−15.7897	−0.696452
$515$	5.06328	0.223115
$516$	19.2183	0.846037
$517$	−15.6613	−0.688784
$518$	7.90631	0.347383
$519$	2.68151	0.117705
$520$	14.0165	0.614664
$521$	20.0596	0.878829	0.439415	−	0.898284i	$-0.355186\pi$
$521$	20.0596	0.878829	0.439415	+	0.898284i	$0.355186\pi$
$522$	10.0555	0.440118
$523$	14.3097	0.625719	0.312860	−	0.949799i	$-0.398713\pi$
$523$	14.3097	0.625719	0.312860	+	0.949799i	$0.398713\pi$
$524$	1.00000	0.0436852
$525$	3.73303	0.162923
$526$	−14.6166	−0.637312
$527$	8.56862	0.373255
$528$	−4.49984	−0.195830
$529$	1.00000	0.0434783
$530$	18.5153	0.804252
$531$	7.58504	0.329163
$532$	−1.61292	−0.0699291
$533$	20.3842	0.882938
$534$	6.14715	0.266013
$535$	17.8468	0.771585
$536$	−0.0197830	−0.000854493 0
$537$	34.9620	1.50872
$538$	−5.30093	−0.228539
$539$	12.9091	0.556032
$540$	−7.22313	−0.310834
$541$	6.59870	0.283700	0.141850	−	0.989888i	$-0.454695\pi$
$541$	6.59870	0.283700	0.141850	+	0.989888i	$0.454695\pi$
$542$	1.55389	0.0667451
$543$	−11.9508	−0.512858
$544$	4.65436	0.199554
$545$	−35.4561	−1.51877
$546$	10.0177	0.428718
$547$	−5.93402	−0.253720	−0.126860	−	0.991921i	$-0.540490\pi$
$547$	−5.93402	−0.253720	−0.126860	+	0.991921i	$0.540490\pi$
$548$	4.78508	0.204408
$549$	0.634705	0.0270885
$550$	4.08492	0.174182
$551$	10.7262	0.456951
$552$	−2.17821	−0.0927109
$553$	10.5558	0.448879
$554$	5.00152	0.212494
$555$	−52.4861	−2.22791
$556$	−4.79909	−0.203527
$557$	21.7384	0.921087	0.460544	−	0.887637i	$-0.347654\pi$
$557$	21.7384	0.921087	0.460544	+	0.887637i	$0.347654\pi$
$558$	3.21180	0.135966
$559$	−46.8174	−1.98017
$560$	2.28939	0.0967445
$561$	20.9439	0.884251
$562$	−2.46356	−0.103919
$563$	30.0102	1.26478	0.632389	−	0.774651i	$-0.282074\pi$
$563$	30.0102	1.26478	0.632389	+	0.774651i	$0.282074\pi$
$564$	16.5132	0.695331
$565$	−12.7367	−0.535836
$566$	18.7890	0.789760
$567$	−9.69865	−0.407305
$568$	−11.5417	−0.484278
$569$	9.38049	0.393250	0.196625	−	0.980479i	$-0.437002\pi$
$569$	9.38049	0.393250	0.196625	+	0.980479i	$0.437002\pi$
$570$	10.7074	0.448484
$571$	2.69778	0.112899	0.0564493	−	0.998405i	$-0.482022\pi$
$571$	2.69778	0.112899	0.0564493	+	0.998405i	$0.482022\pi$
$572$	10.9620	0.458345
$573$	−29.6707	−1.23951
$574$	3.32947	0.138969
$575$	1.97736	0.0824618
$576$	1.74461	0.0726919
$577$	29.1631	1.21408	0.607038	−	0.794673i	$-0.292358\pi$
$577$	29.1631	1.21408	0.607038	+	0.794673i	$0.292358\pi$
$578$	−4.66305	−0.193957
$579$	−9.09006	−0.377770
$580$	−15.2248	−0.632176
$581$	−14.1200	−0.585795
$582$	−33.4768	−1.38766
$583$	14.4804	0.599718
$584$	0.613159	0.0253727
$585$	−24.4533	−1.01102
$586$	−5.88653	−0.243170
$587$	−28.2011	−1.16398	−0.581992	−	0.813194i	$-0.697727\pi$
$587$	−28.2011	−1.16398	−0.581992	+	0.813194i	$0.697727\pi$
$588$	−13.6112	−0.561318
$589$	3.42602	0.141167
$590$	−11.4843	−0.472803
$591$	41.3830	1.70227
$592$	−9.12218	−0.374919
$593$	−16.5721	−0.680535	−0.340267	−	0.940329i	$-0.610518\pi$
$593$	−16.5721	−0.680535	−0.340267	+	0.940329i	$0.610518\pi$
$594$	−5.64907	−0.231784
$595$	−10.6557	−0.436839
$596$	−12.7382	−0.521778
$597$	38.9881	1.59568
$598$	5.30632	0.216992
$599$	4.34026	0.177338	0.0886691	−	0.996061i	$-0.471739\pi$
$599$	4.34026	0.177338	0.0886691	+	0.996061i	$0.471739\pi$
$600$	−4.30712	−0.175837
$601$	−6.65966	−0.271653	−0.135827	−	0.990733i	$-0.543369\pi$
$601$	−6.65966	−0.271653	−0.135827	+	0.990733i	$0.543369\pi$
$602$	−7.64696	−0.311667
$603$	0.0345135	0.00140550
$604$	7.42133	0.301970
$605$	−17.7832	−0.722988
$606$	1.73764	0.0705867
$607$	−38.4622	−1.56113	−0.780567	−	0.625073i	$-0.785069\pi$
$607$	−38.4622	−1.56113	−0.780567	+	0.625073i	$0.785069\pi$
$608$	1.86097	0.0754722
$609$	−10.8813	−0.440933
$610$	−0.960992	−0.0389094
$611$	−40.2277	−1.62744
$612$	−8.12002	−0.328233
$613$	6.89485	0.278480	0.139240	−	0.990259i	$-0.455534\pi$
$613$	6.89485	0.278480	0.139240	+	0.990259i	$0.455534\pi$
$614$	−16.2516	−0.655863
$615$	−22.1027	−0.891268
$616$	1.79049	0.0721409
$617$	−20.0279	−0.806294	−0.403147	−	0.915135i	$-0.632084\pi$
$617$	−20.0279	−0.806294	−0.403147	+	0.915135i	$0.632084\pi$
$618$	−4.17529	−0.167955
$619$	−32.0797	−1.28939	−0.644696	−	0.764439i	$-0.723016\pi$
$619$	−32.0797	−1.28939	−0.644696	+	0.764439i	$0.723016\pi$
$620$	−4.86292	−0.195299
$621$	−2.73451	−0.109732
$622$	−2.83222	−0.113562
$623$	−2.44595	−0.0979951
$624$	−11.5583	−0.462702
$625$	−30.9769	−1.23907
$626$	−23.6581	−0.945566
$627$	8.37406	0.334428
$628$	−5.34909	−0.213452
$629$	42.4579	1.69291
$630$	−3.99409	−0.159128
$631$	−21.5652	−0.858497	−0.429249	−	0.903186i	$-0.641222\pi$
$631$	−21.5652	−0.858497	−0.429249	+	0.903186i	$0.641222\pi$
$632$	−12.1792	−0.484461
$633$	−38.2553	−1.52051
$634$	0.751806	0.0298580
$635$	−46.5874	−1.84877
$636$	−15.2681	−0.605419
$637$	33.1582	1.31378
$638$	−11.9070	−0.471404
$639$	20.1357	0.796556
$640$	−2.64147	−0.104413
$641$	−4.93492	−0.194918	−0.0974589	−	0.995240i	$-0.531071\pi$
$641$	−4.93492	−0.194918	−0.0974589	+	0.995240i	$0.531071\pi$
$642$	−14.7169	−0.580828
$643$	1.32496	0.0522512	0.0261256	−	0.999659i	$-0.491683\pi$
$643$	1.32496	0.0522512	0.0261256	+	0.999659i	$0.491683\pi$
$644$	0.866712	0.0341532
$645$	50.7645	1.99885
$646$	−8.66161	−0.340786
$647$	16.0838	0.632321	0.316161	−	0.948706i	$-0.397606\pi$
$647$	16.0838	0.632321	0.316161	+	0.948706i	$0.397606\pi$
$648$	11.1902	0.439591
$649$	−8.98168	−0.352562
$650$	10.4925	0.411551
$651$	−3.47557	−0.136218
$652$	7.27586	0.284945
$653$	−20.7975	−0.813868	−0.406934	−	0.913458i	$-0.633402\pi$
$653$	−20.7975	−0.813868	−0.406934	+	0.913458i	$0.633402\pi$
$654$	29.2378	1.14329
$655$	2.64147	0.103211
$656$	−3.84150	−0.149985
$657$	−1.06972	−0.0417338
$658$	−6.57062	−0.256149
$659$	−43.7328	−1.70359	−0.851794	−	0.523877i	$-0.824485\pi$
$659$	−43.7328	−1.70359	−0.851794	+	0.523877i	$0.824485\pi$
$660$	−11.8862	−0.462670
$661$	−5.52964	−0.215078	−0.107539	−	0.994201i	$-0.534297\pi$
$661$	−5.52964	−0.215078	−0.107539	+	0.994201i	$0.534297\pi$
$662$	−17.8894	−0.695292
$663$	53.7964	2.08928
$664$	16.2914	0.632230
$665$	−4.26049	−0.165215
$666$	15.9146	0.616679
$667$	−5.76377	−0.223174
$668$	−10.7614	−0.416372
$669$	−19.8848	−0.768791
$670$	−0.0522561	−0.00201883
$671$	−0.751573	−0.0290142
$672$	−1.88788	−0.0728266
$673$	47.8998	1.84640	0.923201	−	0.384318i	$-0.125564\pi$
$673$	47.8998	1.84640	0.923201	+	0.384318i	$0.125564\pi$
$674$	−10.4393	−0.402109
$675$	−5.40713	−0.208120
$676$	15.1570	0.582963
$677$	9.08489	0.349161	0.174580	−	0.984643i	$-0.444143\pi$
$677$	9.08489	0.349161	0.174580	+	0.984643i	$0.444143\pi$
$678$	10.5029	0.403363
$679$	13.3204	0.511192
$680$	12.2943	0.471467
$681$	−1.94041	−0.0743568
$682$	−3.80319	−0.145632
$683$	−23.1214	−0.884717	−0.442358	−	0.896838i	$-0.645858\pi$
$683$	−23.1214	−0.884717	−0.442358	+	0.896838i	$0.645858\pi$
$684$	−3.24666	−0.124139
$685$	12.6396	0.482936
$686$	11.4829	0.438419
$687$	16.8953	0.644595
$688$	8.82296	0.336372
$689$	37.1944	1.41699
$690$	−5.75368	−0.219039
$691$	−14.9972	−0.570519	−0.285259	−	0.958450i	$-0.592080\pi$
$691$	−14.9972	−0.570519	−0.285259	+	0.958450i	$0.592080\pi$
$692$	1.23106	0.0467979
$693$	−3.12370	−0.118660
$694$	15.5704	0.591043
$695$	−12.6766	−0.480853
$696$	12.5547	0.475885
$697$	17.8797	0.677242
$698$	3.68100	0.139328
$699$	4.63381	0.175267
$700$	1.71381	0.0647758
$701$	−46.4227	−1.75336	−0.876680	−	0.481074i	$-0.840247\pi$
$701$	−46.4227	−1.75336	−0.876680	+	0.481074i	$0.840247\pi$
$702$	−14.5102	−0.547652
$703$	16.9761	0.640265
$704$	−2.06584	−0.0778593
$705$	43.6191	1.64279
$706$	−13.8193	−0.520095
$707$	−0.691407	−0.0260030
$708$	9.47023	0.355913
$709$	7.47661	0.280790	0.140395	−	0.990096i	$-0.455163\pi$
$709$	7.47661	0.280790	0.140395	+	0.990096i	$0.455163\pi$
$710$	−30.4870	−1.14416
$711$	21.2478	0.796856
$712$	2.82211	0.105763
$713$	−1.84099	−0.0689456
$714$	8.78688	0.328841
$715$	28.9558	1.08289
$716$	16.0508	0.599846
$717$	23.1010	0.862723
$718$	1.97381	0.0736620
$719$	−2.76750	−0.103210	−0.0516052	−	0.998668i	$-0.516434\pi$
$719$	−2.76750	−0.103210	−0.0516052	+	0.998668i	$0.516434\pi$
$720$	4.60833	0.171742
$721$	1.66135	0.0618719
$722$	15.5368	0.578220
$723$	1.88531	0.0701153
$724$	−5.48651	−0.203905
$725$	−11.3971	−0.423276
$726$	14.6644	0.544246
$727$	−29.7034	−1.10164	−0.550819	−	0.834625i	$-0.685685\pi$
$727$	−29.7034	−1.10164	−0.550819	+	0.834625i	$0.685685\pi$
$728$	4.59905	0.170452
$729$	−1.65340	−0.0612369
$730$	1.61964	0.0599456
$731$	−41.0652	−1.51885
$732$	0.792454	0.0292900
$733$	16.5183	0.610119	0.305059	−	0.952333i	$-0.401324\pi$
$733$	16.5183	0.610119	0.305059	+	0.952333i	$0.401324\pi$
$734$	−24.8160	−0.915976
$735$	−35.9537	−1.32617
$736$	−1.00000	−0.0368605
$737$	−0.0408684	−0.00150541
$738$	6.70190	0.246700
$739$	−15.9267	−0.585873	−0.292937	−	0.956132i	$-0.594632\pi$
$739$	−15.9267	−0.585873	−0.292937	+	0.956132i	$0.594632\pi$
$740$	−24.0960	−0.885786
$741$	21.5096	0.790175
$742$	6.07518	0.223027
$743$	42.8847	1.57329	0.786644	−	0.617407i	$-0.211817\pi$
$743$	42.8847	1.57329	0.786644	+	0.617407i	$0.211817\pi$
$744$	4.01006	0.147016
$745$	−33.6477	−1.23275
$746$	−13.2927	−0.486680
$747$	−28.4221	−1.03991
$748$	9.61517	0.351565
$749$	5.85585	0.213968
$750$	17.3913	0.635040
$751$	−33.3295	−1.21621	−0.608105	−	0.793857i	$-0.708070\pi$
$751$	−33.3295	−1.21621	−0.608105	+	0.793857i	$0.708070\pi$
$752$	7.58108	0.276454
$753$	−18.1011	−0.659639
$754$	−30.5844	−1.11382
$755$	19.6032	0.713434
$756$	−2.37003	−0.0861973
$757$	−14.5184	−0.527682	−0.263841	−	0.964566i	$-0.584989\pi$
$757$	−14.5184	−0.527682	−0.263841	+	0.964566i	$0.584989\pi$
$758$	23.7799	0.863726
$759$	−4.49984	−0.163334
$760$	4.91569	0.178311
$761$	38.0674	1.37994	0.689970	−	0.723838i	$-0.257624\pi$
$761$	38.0674	1.37994	0.689970	+	0.723838i	$0.257624\pi$
$762$	38.4170	1.39170
$763$	−11.6337	−0.421170
$764$	−13.6216	−0.492812
$765$	−21.4488	−0.775483
$766$	9.52675	0.344216
$767$	−23.0703	−0.833022
$768$	2.17821	0.0785994
$769$	−53.1271	−1.91581	−0.957907	−	0.287079i	$-0.907316\pi$
$769$	−53.1271	−1.91581	−0.957907	+	0.287079i	$0.907316\pi$
$770$	4.72953	0.170440
$771$	34.3932	1.23864
$772$	−4.17318	−0.150196
$773$	−15.6876	−0.564245	−0.282123	−	0.959378i	$-0.591039\pi$
$773$	−15.6876	−0.564245	−0.282123	+	0.959378i	$0.591039\pi$
$774$	−15.3926	−0.553275
$775$	−3.64031	−0.130764
$776$	−15.3689	−0.551713
$777$	−17.2216	−0.617822
$778$	3.34394	0.119886
$779$	7.14890	0.256136
$780$	−30.5309	−1.09318
$781$	−23.8433	−0.853180
$782$	4.65436	0.166440
$783$	15.7611	0.563256
$784$	−6.24881	−0.223172
$785$	−14.1295	−0.504302
$786$	−2.17821	−0.0776942
$787$	−47.9116	−1.70786	−0.853932	−	0.520385i	$-0.825789\pi$
$787$	−47.9116	−1.70786	−0.853932	+	0.520385i	$0.825789\pi$
$788$	18.9986	0.676797
$789$	31.8380	1.13346
$790$	−32.1709	−1.14459
$791$	−4.17912	−0.148593
$792$	3.60408	0.128065
$793$	−1.93049	−0.0685537
$794$	23.8867	0.847709
$795$	−40.3302	−1.43036
$796$	17.8991	0.634418
$797$	25.2797	0.895453	0.447727	−	0.894170i	$-0.352234\pi$
$797$	25.2797	0.895453	0.447727	+	0.894170i	$0.352234\pi$
$798$	3.51329	0.124369
$799$	−35.2851	−1.24830
$800$	−1.97736	−0.0699104
$801$	−4.92347	−0.173962
$802$	−4.08624	−0.144290
$803$	1.26669	0.0447005
$804$	0.0430915	0.00151972
$805$	2.28939	0.0806905
$806$	−9.76888	−0.344094
$807$	11.5466	0.406458
$808$	0.797736	0.0280642
$809$	−37.7614	−1.32762	−0.663811	−	0.747901i	$-0.731062\pi$
$809$	−37.7614	−1.32762	−0.663811	+	0.747901i	$0.731062\pi$
$810$	29.5585	1.03858
$811$	11.3070	0.397042	0.198521	−	0.980097i	$-0.436386\pi$
$811$	11.3070	0.397042	0.198521	+	0.980097i	$0.436386\pi$
$812$	−4.99553	−0.175309
$813$	−3.38469	−0.118706
$814$	−18.8450	−0.660517
$815$	19.2190	0.673211
$816$	−10.1382	−0.354907
$817$	−16.4192	−0.574436
$818$	−8.37428	−0.292800
$819$	−8.02354	−0.280365
$820$	−10.1472	−0.354355
$821$	−5.61984	−0.196134	−0.0980669	−	0.995180i	$-0.531266\pi$
$821$	−5.61984	−0.196134	−0.0980669	+	0.995180i	$0.531266\pi$
$822$	−10.4229	−0.363541
$823$	−16.1323	−0.562338	−0.281169	−	0.959658i	$-0.590722\pi$
$823$	−16.1323	−0.562338	−0.281169	+	0.959658i	$0.590722\pi$
$824$	−1.91684	−0.0667763
$825$	−8.89782	−0.309783
$826$	−3.76821	−0.131113
$827$	−41.2032	−1.43278	−0.716388	−	0.697702i	$-0.754206\pi$
$827$	−41.2032	−1.43278	−0.716388	+	0.697702i	$0.754206\pi$
$828$	1.74461	0.0606293
$829$	−39.1064	−1.35822	−0.679111	−	0.734035i	$-0.737635\pi$
$829$	−39.1064	−1.35822	−0.679111	+	0.734035i	$0.737635\pi$
$830$	43.0333	1.49371
$831$	−10.8944	−0.377921
$832$	−5.30632	−0.183964
$833$	29.0842	1.00771
$834$	10.4534	0.361973
$835$	−28.4260	−0.983721
$836$	3.84446	0.132964
$837$	5.03421	0.174008
$838$	1.65940	0.0573230
$839$	52.0860	1.79821	0.899105	−	0.437733i	$-0.144219\pi$
$839$	52.0860	1.79821	0.899105	+	0.437733i	$0.144219\pi$
$840$	−4.98678	−0.172060
$841$	4.22101	0.145552
$842$	4.89053	0.168539
$843$	5.36615	0.184820
$844$	−17.5627	−0.604533
$845$	40.0369	1.37731
$846$	−13.2260	−0.454720
$847$	−5.83496	−0.200492
$848$	−7.00945	−0.240706
$849$	−40.9264	−1.40459
$850$	9.20336	0.315673
$851$	−9.12218	−0.312704
$852$	25.1402	0.861290
$853$	10.5409	0.360914	0.180457	−	0.983583i	$-0.442242\pi$
$853$	10.5409	0.360914	0.180457	+	0.983583i	$0.442242\pi$
$854$	−0.315318	−0.0107900
$855$	−8.57595	−0.293291
$856$	−6.75639	−0.230929
$857$	44.3168	1.51383	0.756916	−	0.653512i	$-0.226705\pi$
$857$	44.3168	1.51383	0.756916	+	0.653512i	$0.226705\pi$
$858$	−23.8776	−0.815168
$859$	23.5763	0.804413	0.402207	−	0.915549i	$-0.368243\pi$
$859$	23.5763	0.804413	0.402207	+	0.915549i	$0.368243\pi$
$860$	23.3056	0.794714
$861$	−7.25229	−0.247157
$862$	−10.7303	−0.365475
$863$	44.1748	1.50373	0.751863	−	0.659319i	$-0.229155\pi$
$863$	44.1748	1.50373	0.751863	+	0.659319i	$0.229155\pi$
$864$	2.73451	0.0930300
$865$	3.25181	0.110565
$866$	27.1757	0.923468
$867$	10.1571	0.344953
$868$	−1.59561	−0.0541584
$869$	−25.1602	−0.853501
$870$	33.1629	1.12433
$871$	−0.104975	−0.00355693
$872$	13.4229	0.454555
$873$	26.8128	0.907474
$874$	1.86097	0.0629482
$875$	−6.92000	−0.233939
$876$	−1.33559	−0.0451254
$877$	−58.9841	−1.99175	−0.995877	−	0.0907182i	$-0.971084\pi$
$877$	−58.9841	−1.99175	−0.995877	+	0.0907182i	$0.971084\pi$
$878$	6.79328	0.229262
$879$	12.8221	0.432479
$880$	−5.45686	−0.183951
$881$	−29.5235	−0.994673	−0.497336	−	0.867558i	$-0.665689\pi$
$881$	−29.5235	−0.994673	−0.497336	+	0.867558i	$0.665689\pi$
$882$	10.9017	0.367080
$883$	−22.7955	−0.767130	−0.383565	−	0.923514i	$-0.625304\pi$
$883$	−22.7955	−0.767130	−0.383565	+	0.923514i	$0.625304\pi$
$884$	24.6975	0.830667
$885$	25.0153	0.840881
$886$	−21.0256	−0.706368
$887$	−57.2916	−1.92366	−0.961832	−	0.273642i	$-0.911772\pi$
$887$	−57.2916	−1.92366	−0.961832	+	0.273642i	$0.911772\pi$
$888$	19.8700	0.666795
$889$	−15.2861	−0.512681
$890$	7.45451	0.249876
$891$	23.1171	0.774453
$892$	−9.12896	−0.305660
$893$	−14.1082	−0.472111
$894$	27.7466	0.927984
$895$	42.3977	1.41720
$896$	−0.866712	−0.0289548
$897$	−11.5583	−0.385920
$898$	−39.4207	−1.31549
$899$	10.6110	0.353898
$900$	3.44972	0.114991
$901$	32.6245	1.08688
$902$	−7.93592	−0.264237
$903$	16.6567	0.554300
$904$	4.82181	0.160371
$905$	−14.4925	−0.481746
$906$	−16.1652	−0.537054
$907$	−24.2786	−0.806157	−0.403078	−	0.915165i	$-0.632060\pi$
$907$	−24.2786	−0.806157	−0.403078	+	0.915165i	$0.632060\pi$
$908$	−0.890828	−0.0295632
$909$	−1.39174	−0.0461609
$910$	12.1483	0.402711
$911$	29.3691	0.973041	0.486521	−	0.873669i	$-0.338266\pi$
$911$	29.3691	0.973041	0.486521	+	0.873669i	$0.338266\pi$
$912$	−4.05358	−0.134227
$913$	33.6555	1.11383
$914$	19.4473	0.643258
$915$	2.09324	0.0692005
$916$	7.75649	0.256282
$917$	0.866712	0.0286214
$918$	−12.7274	−0.420067
$919$	27.2543	0.899035	0.449518	−	0.893272i	$-0.351596\pi$
$919$	27.2543	0.899035	0.449518	+	0.893272i	$0.351596\pi$
$920$	−2.64147	−0.0870867
$921$	35.3995	1.16645
$922$	37.9498	1.24981
$923$	−61.2439	−2.01587
$924$	−3.90007	−0.128303
$925$	−18.0379	−0.593082
$926$	22.9027	0.752631
$927$	3.34413	0.109836
$928$	5.76377	0.189205
$929$	−9.68647	−0.317803	−0.158901	−	0.987294i	$-0.550795\pi$
$929$	−9.68647	−0.317803	−0.158901	+	0.987294i	$0.550795\pi$
$930$	10.5925	0.347341
$931$	11.6288	0.381120
$932$	2.12735	0.0696835
$933$	6.16918	0.201970
$934$	27.0638	0.885554
$935$	25.3982	0.830609
$936$	9.25744	0.302589
$937$	−20.2019	−0.659969	−0.329984	−	0.943986i	$-0.607043\pi$
$937$	−20.2019	−0.659969	−0.329984	+	0.943986i	$0.607043\pi$
$938$	−0.0171461	−0.000559841 0
$939$	51.5322	1.68169
$940$	20.0252	0.653150
$941$	−58.0931	−1.89378	−0.946890	−	0.321558i	$-0.895794\pi$
$941$	−58.0931	−1.89378	−0.946890	+	0.321558i	$0.895794\pi$
$942$	11.6515	0.379625
$943$	−3.84150	−0.125096
$944$	4.34771	0.141506
$945$	−6.26038	−0.203650
$946$	18.2268	0.592605
$947$	9.07212	0.294804	0.147402	−	0.989077i	$-0.452909\pi$
$947$	9.07212	0.294804	0.147402	+	0.989077i	$0.452909\pi$
$948$	26.5288	0.861614
$949$	3.25362	0.105617
$950$	3.67981	0.119389
$951$	−1.63759	−0.0531026
$952$	4.03399	0.130742
$953$	−12.1339	−0.393057	−0.196528	−	0.980498i	$-0.562967\pi$
$953$	−12.1339	−0.393057	−0.196528	+	0.980498i	$0.562967\pi$
$954$	12.2287	0.395920
$955$	−35.9810	−1.16432
$956$	10.6055	0.343006
$957$	25.9360	0.838393
$958$	14.1721	0.457878
$959$	4.14728	0.133923
$960$	5.75368	0.185699
$961$	−27.6108	−0.890670
$962$	−48.4052	−1.56065
$963$	11.7872	0.379839
$964$	0.865529	0.0278768
$965$	−11.0233	−0.354853
$966$	−1.88788	−0.0607416
$967$	−8.80732	−0.283224	−0.141612	−	0.989922i	$-0.545229\pi$
$967$	−8.80732	−0.283224	−0.141612	+	0.989922i	$0.545229\pi$
$968$	6.73230	0.216384
$969$	18.8668	0.606090
$970$	−40.5966	−1.30348
$971$	−7.98077	−0.256115	−0.128058	−	0.991767i	$-0.540874\pi$
$971$	−7.98077	−0.256115	−0.128058	+	0.991767i	$0.540874\pi$
$972$	−16.1710	−0.518686
$973$	−4.15943	−0.133345
$974$	−36.2013	−1.15997
$975$	−22.8549	−0.731944
$976$	0.363810	0.0116453
$977$	17.9472	0.574182	0.287091	−	0.957903i	$-0.407312\pi$
$977$	17.9472	0.574182	0.287091	+	0.957903i	$0.407312\pi$
$978$	−15.8484	−0.506775
$979$	5.83003	0.186328
$980$	−16.5060	−0.527266
$981$	−23.4176	−0.747666
$982$	−4.71715	−0.150530
$983$	8.36313	0.266742	0.133371	−	0.991066i	$-0.457420\pi$
$983$	8.36313	0.266742	0.133371	+	0.991066i	$0.457420\pi$
$984$	8.36759	0.266749
$985$	50.1842	1.59900
$986$	−26.8266	−0.854334
$987$	14.3122	0.455562
$988$	9.87489	0.314162
$989$	8.82296	0.280554
$990$	9.52007	0.302568
$991$	−3.41683	−0.108539	−0.0542697	−	0.998526i	$-0.517283\pi$
$991$	−3.41683	−0.108539	−0.0542697	+	0.998526i	$0.517283\pi$
$992$	1.84099	0.0584515
$993$	38.9669	1.23658
$994$	−10.0033	−0.317286
$995$	47.2800	1.49888
$996$	−35.4862	−1.12442
$997$	−36.5455	−1.15741	−0.578703	−	0.815538i	$-0.696441\pi$
$997$	−36.5455	−1.15741	−0.578703	+	0.815538i	$0.696441\pi$
$998$	−27.5118	−0.870871
$999$	24.9447	0.789216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.21	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.21	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.17821 q^{3} +1.00000 q^{4} +2.64147 q^{5} -2.17821 q^{6} +0.866712 q^{7} -1.00000 q^{8} +1.74461 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.17821 q^{3} +1.00000 q^{4} +2.64147 q^{5} -2.17821 q^{6} +0.866712 q^{7} -1.00000 q^{8} +1.74461 q^{9} -2.64147 q^{10} -2.06584 q^{11} +2.17821 q^{12} -5.30632 q^{13} -0.866712 q^{14} +5.75368 q^{15} +1.00000 q^{16} -4.65436 q^{17} -1.74461 q^{18} -1.86097 q^{19} +2.64147 q^{20} +1.88788 q^{21} +2.06584 q^{22} +1.00000 q^{23} -2.17821 q^{24} +1.97736 q^{25} +5.30632 q^{26} -2.73451 q^{27} +0.866712 q^{28} -5.76377 q^{29} -5.75368 q^{30} -1.84099 q^{31} -1.00000 q^{32} -4.49984 q^{33} +4.65436 q^{34} +2.28939 q^{35} +1.74461 q^{36} -9.12218 q^{37} +1.86097 q^{38} -11.5583 q^{39} -2.64147 q^{40} -3.84150 q^{41} -1.88788 q^{42} +8.82296 q^{43} -2.06584 q^{44} +4.60833 q^{45} -1.00000 q^{46} +7.58108 q^{47} +2.17821 q^{48} -6.24881 q^{49} -1.97736 q^{50} -10.1382 q^{51} -5.30632 q^{52} -7.00945 q^{53} +2.73451 q^{54} -5.45686 q^{55} -0.866712 q^{56} -4.05358 q^{57} +5.76377 q^{58} +4.34771 q^{59} +5.75368 q^{60} +0.363810 q^{61} +1.84099 q^{62} +1.51207 q^{63} +1.00000 q^{64} -14.0165 q^{65} +4.49984 q^{66} +0.0197830 q^{67} -4.65436 q^{68} +2.17821 q^{69} -2.28939 q^{70} +11.5417 q^{71} -1.74461 q^{72} -0.613159 q^{73} +9.12218 q^{74} +4.30712 q^{75} -1.86097 q^{76} -1.79049 q^{77} +11.5583 q^{78} +12.1792 q^{79} +2.64147 q^{80} -11.1902 q^{81} +3.84150 q^{82} -16.2914 q^{83} +1.88788 q^{84} -12.2943 q^{85} -8.82296 q^{86} -12.5547 q^{87} +2.06584 q^{88} -2.82211 q^{89} -4.60833 q^{90} -4.59905 q^{91} +1.00000 q^{92} -4.01006 q^{93} -7.58108 q^{94} -4.91569 q^{95} -2.17821 q^{96} +15.3689 q^{97} +6.24881 q^{98} -3.60408 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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