LMFDB - Embedded newform 6026.2.a.i.1.10

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			1.10
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.936776 q^{3} +1.00000 q^{4} +1.38125 q^{5} +0.936776 q^{6} +2.49293 q^{7} -1.00000 q^{8} -2.12245 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.936776 q^{3} +1.00000 q^{4} +1.38125 q^{5} +0.936776 q^{6} +2.49293 q^{7} -1.00000 q^{8} -2.12245 q^{9} -1.38125 q^{10} -1.29654 q^{11} -0.936776 q^{12} -0.532498 q^{13} -2.49293 q^{14} -1.29392 q^{15} +1.00000 q^{16} -4.49376 q^{17} +2.12245 q^{18} -6.56345 q^{19} +1.38125 q^{20} -2.33531 q^{21} +1.29654 q^{22} +1.00000 q^{23} +0.936776 q^{24} -3.09214 q^{25} +0.532498 q^{26} +4.79859 q^{27} +2.49293 q^{28} +9.38832 q^{29} +1.29392 q^{30} +8.74238 q^{31} -1.00000 q^{32} +1.21457 q^{33} +4.49376 q^{34} +3.44336 q^{35} -2.12245 q^{36} +5.61854 q^{37} +6.56345 q^{38} +0.498831 q^{39} -1.38125 q^{40} -6.09722 q^{41} +2.33531 q^{42} +7.17129 q^{43} -1.29654 q^{44} -2.93164 q^{45} -1.00000 q^{46} +6.97895 q^{47} -0.936776 q^{48} -0.785322 q^{49} +3.09214 q^{50} +4.20964 q^{51} -0.532498 q^{52} +0.607361 q^{53} -4.79859 q^{54} -1.79085 q^{55} -2.49293 q^{56} +6.14849 q^{57} -9.38832 q^{58} -0.436665 q^{59} -1.29392 q^{60} -2.24866 q^{61} -8.74238 q^{62} -5.29111 q^{63} +1.00000 q^{64} -0.735514 q^{65} -1.21457 q^{66} -8.74609 q^{67} -4.49376 q^{68} -0.936776 q^{69} -3.44336 q^{70} +3.67124 q^{71} +2.12245 q^{72} -13.3102 q^{73} -5.61854 q^{74} +2.89664 q^{75} -6.56345 q^{76} -3.23218 q^{77} -0.498831 q^{78} -9.05511 q^{79} +1.38125 q^{80} +1.87215 q^{81} +6.09722 q^{82} -7.36070 q^{83} -2.33531 q^{84} -6.20701 q^{85} -7.17129 q^{86} -8.79476 q^{87} +1.29654 q^{88} -7.67148 q^{89} +2.93164 q^{90} -1.32748 q^{91} +1.00000 q^{92} -8.18965 q^{93} -6.97895 q^{94} -9.06579 q^{95} +0.936776 q^{96} -5.31188 q^{97} +0.785322 q^{98} +2.75184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.936776	−0.540848	−0.270424	−	0.962741i	$-0.587164\pi$
$3$	−0.936776	−0.540848	−0.270424	+	0.962741i	$0.587164\pi$
$4$	1.00000	0.500000
$5$	1.38125	0.617715	0.308857	−	0.951108i	$-0.400053\pi$
$5$	1.38125	0.617715	0.308857	+	0.951108i	$0.400053\pi$
$6$	0.936776	0.382437
$7$	2.49293	0.942237	0.471119	−	0.882070i	$-0.343850\pi$
$7$	2.49293	0.942237	0.471119	+	0.882070i	$0.343850\pi$
$8$	−1.00000	−0.353553
$9$	−2.12245	−0.707483
$10$	−1.38125	−0.436790
$11$	−1.29654	−0.390922	−0.195461	−	0.980712i	$-0.562620\pi$
$11$	−1.29654	−0.390922	−0.195461	+	0.980712i	$0.562620\pi$
$12$	−0.936776	−0.270424
$13$	−0.532498	−0.147688	−0.0738441	−	0.997270i	$-0.523527\pi$
$13$	−0.532498	−0.147688	−0.0738441	+	0.997270i	$0.523527\pi$
$14$	−2.49293	−0.666262
$15$	−1.29392	−0.334090
$16$	1.00000	0.250000
$17$	−4.49376	−1.08990	−0.544948	−	0.838470i	$-0.683451\pi$
$17$	−4.49376	−1.08990	−0.544948	+	0.838470i	$0.683451\pi$
$18$	2.12245	0.500266
$19$	−6.56345	−1.50576	−0.752880	−	0.658158i	$-0.771336\pi$
$19$	−6.56345	−1.50576	−0.752880	+	0.658158i	$0.771336\pi$
$20$	1.38125	0.308857
$21$	−2.33531	−0.509607
$22$	1.29654	0.276423
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	0.936776	0.191219
$25$	−3.09214	−0.618428
$26$	0.532498	0.104431
$27$	4.79859	0.923489
$28$	2.49293	0.471119
$29$	9.38832	1.74337	0.871684	−	0.490069i	$-0.163028\pi$
$29$	9.38832	1.74337	0.871684	+	0.490069i	$0.163028\pi$
$30$	1.29392	0.236237
$31$	8.74238	1.57018	0.785089	−	0.619383i	$-0.212617\pi$
$31$	8.74238	1.57018	0.785089	+	0.619383i	$0.212617\pi$
$32$	−1.00000	−0.176777
$33$	1.21457	0.211429
$34$	4.49376	0.770673
$35$	3.44336	0.582034
$36$	−2.12245	−0.353742
$37$	5.61854	0.923683	0.461841	−	0.886963i	$-0.347189\pi$
$37$	5.61854	0.923683	0.461841	+	0.886963i	$0.347189\pi$
$38$	6.56345	1.06473
$39$	0.498831	0.0798769
$40$	−1.38125	−0.218395
$41$	−6.09722	−0.952226	−0.476113	−	0.879384i	$-0.657955\pi$
$41$	−6.09722	−0.952226	−0.476113	+	0.879384i	$0.657955\pi$
$42$	2.33531	0.360347
$43$	7.17129	1.09361	0.546806	−	0.837260i	$-0.315844\pi$
$43$	7.17129	1.09361	0.546806	+	0.837260i	$0.315844\pi$
$44$	−1.29654	−0.195461
$45$	−2.93164	−0.437023
$46$	−1.00000	−0.147442
$47$	6.97895	1.01798	0.508992	−	0.860771i	$-0.330018\pi$
$47$	6.97895	1.01798	0.508992	+	0.860771i	$0.330018\pi$
$48$	−0.936776	−0.135212
$49$	−0.785322	−0.112189
$50$	3.09214	0.437295
$51$	4.20964	0.589468
$52$	−0.532498	−0.0738441
$53$	0.607361	0.0834274	0.0417137	−	0.999130i	$-0.486718\pi$
$53$	0.607361	0.0834274	0.0417137	+	0.999130i	$0.486718\pi$
$54$	−4.79859	−0.653005
$55$	−1.79085	−0.241478
$56$	−2.49293	−0.333131
$57$	6.14849	0.814387
$58$	−9.38832	−1.23275
$59$	−0.436665	−0.0568490	−0.0284245	−	0.999596i	$-0.509049\pi$
$59$	−0.436665	−0.0568490	−0.0284245	+	0.999596i	$0.509049\pi$
$60$	−1.29392	−0.167045
$61$	−2.24866	−0.287911	−0.143955	−	0.989584i	$-0.545982\pi$
$61$	−2.24866	−0.287911	−0.143955	+	0.989584i	$0.545982\pi$
$62$	−8.74238	−1.11028
$63$	−5.29111	−0.666617
$64$	1.00000	0.125000
$65$	−0.735514	−0.0912293
$66$	−1.21457	−0.149503
$67$	−8.74609	−1.06851	−0.534253	−	0.845325i	$-0.679407\pi$
$67$	−8.74609	−1.06851	−0.534253	+	0.845325i	$0.679407\pi$
$68$	−4.49376	−0.544948
$69$	−0.936776	−0.112775
$70$	−3.44336	−0.411560
$71$	3.67124	0.435696	0.217848	−	0.975983i	$-0.430096\pi$
$71$	3.67124	0.435696	0.217848	+	0.975983i	$0.430096\pi$
$72$	2.12245	0.250133
$73$	−13.3102	−1.55784	−0.778918	−	0.627125i	$-0.784231\pi$
$73$	−13.3102	−1.55784	−0.778918	+	0.627125i	$0.784231\pi$
$74$	−5.61854	−0.653142
$75$	2.89664	0.334476
$76$	−6.56345	−0.752880
$77$	−3.23218	−0.368341
$78$	−0.498831	−0.0564815
$79$	−9.05511	−1.01878	−0.509390	−	0.860536i	$-0.670129\pi$
$79$	−9.05511	−1.01878	−0.509390	+	0.860536i	$0.670129\pi$
$80$	1.38125	0.154429
$81$	1.87215	0.208016
$82$	6.09722	0.673325
$83$	−7.36070	−0.807942	−0.403971	−	0.914772i	$-0.632370\pi$
$83$	−7.36070	−0.807942	−0.403971	+	0.914772i	$0.632370\pi$
$84$	−2.33531	−0.254804
$85$	−6.20701	−0.673245
$86$	−7.17129	−0.773300
$87$	−8.79476	−0.942897
$88$	1.29654	0.138212
$89$	−7.67148	−0.813175	−0.406588	−	0.913612i	$-0.633281\pi$
$89$	−7.67148	−0.813175	−0.406588	+	0.913612i	$0.633281\pi$
$90$	2.93164	0.309022
$91$	−1.32748	−0.139157
$92$	1.00000	0.104257
$93$	−8.18965	−0.849228
$94$	−6.97895	−0.719823
$95$	−9.06579	−0.930130
$96$	0.936776	0.0956093
$97$	−5.31188	−0.539340	−0.269670	−	0.962953i	$-0.586915\pi$
$97$	−5.31188	−0.539340	−0.269670	+	0.962953i	$0.586915\pi$
$98$	0.785322	0.0793295
$99$	2.75184	0.276571
$100$	−3.09214	−0.309214
$101$	17.5882	1.75009	0.875046	−	0.484040i	$-0.160831\pi$
$101$	17.5882	1.75009	0.875046	+	0.484040i	$0.160831\pi$
$102$	−4.20964	−0.416817
$103$	−5.88185	−0.579556	−0.289778	−	0.957094i	$-0.593581\pi$
$103$	−5.88185	−0.579556	−0.289778	+	0.957094i	$0.593581\pi$
$104$	0.532498	0.0522157
$105$	−3.22566	−0.314792
$106$	−0.607361	−0.0589921
$107$	−2.12314	−0.205252	−0.102626	−	0.994720i	$-0.532724\pi$
$107$	−2.12314	−0.205252	−0.102626	+	0.994720i	$0.532724\pi$
$108$	4.79859	0.461745
$109$	9.69916	0.929011	0.464506	−	0.885570i	$-0.346232\pi$
$109$	9.69916	0.929011	0.464506	+	0.885570i	$0.346232\pi$
$110$	1.79085	0.170751
$111$	−5.26332	−0.499572
$112$	2.49293	0.235559
$113$	0.192906	0.0181470	0.00907352	−	0.999959i	$-0.497112\pi$
$113$	0.192906	0.0181470	0.00907352	+	0.999959i	$0.497112\pi$
$114$	−6.14849	−0.575858
$115$	1.38125	0.128802
$116$	9.38832	0.871684
$117$	1.13020	0.104487
$118$	0.436665	0.0401983
$119$	−11.2026	−1.02694
$120$	1.29392	0.118119
$121$	−9.31898	−0.847180
$122$	2.24866	0.203584
$123$	5.71173	0.515009
$124$	8.74238	0.785089
$125$	−11.1773	−0.999727
$126$	5.29111	0.471370
$127$	−11.7953	−1.04666	−0.523330	−	0.852130i	$-0.675310\pi$
$127$	−11.7953	−1.04666	−0.523330	+	0.852130i	$0.675310\pi$
$128$	−1.00000	−0.0883883
$129$	−6.71789	−0.591477
$130$	0.735514	0.0645088
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.21457	0.105715
$133$	−16.3622	−1.41878
$134$	8.74609	0.755547
$135$	6.62806	0.570453
$136$	4.49376	0.385336
$137$	3.16549	0.270446	0.135223	−	0.990815i	$-0.456825\pi$
$137$	3.16549	0.270446	0.135223	+	0.990815i	$0.456825\pi$
$138$	0.936776	0.0797437
$139$	20.6429	1.75090	0.875452	−	0.483305i	$-0.160564\pi$
$139$	20.6429	1.75090	0.875452	+	0.483305i	$0.160564\pi$
$140$	3.44336	0.291017
$141$	−6.53771	−0.550575
$142$	−3.67124	−0.308084
$143$	0.690405	0.0577345
$144$	−2.12245	−0.176871
$145$	12.9676	1.07690
$146$	13.3102	1.10156
$147$	0.735671	0.0606771
$148$	5.61854	0.461841
$149$	−11.5985	−0.950184	−0.475092	−	0.879936i	$-0.657585\pi$
$149$	−11.5985	−0.950184	−0.475092	+	0.879936i	$0.657585\pi$
$150$	−2.89664	−0.236510
$151$	−3.10142	−0.252390	−0.126195	−	0.992005i	$-0.540277\pi$
$151$	−3.10142	−0.252390	−0.126195	+	0.992005i	$0.540277\pi$
$152$	6.56345	0.532366
$153$	9.53778	0.771083
$154$	3.23218	0.260456
$155$	12.0754	0.969922
$156$	0.498831	0.0399385
$157$	3.16050	0.252235	0.126118	−	0.992015i	$-0.459748\pi$
$157$	3.16050	0.252235	0.126118	+	0.992015i	$0.459748\pi$
$158$	9.05511	0.720386
$159$	−0.568961	−0.0451216
$160$	−1.38125	−0.109198
$161$	2.49293	0.196470
$162$	−1.87215	−0.147090
$163$	−11.5854	−0.907441	−0.453721	−	0.891144i	$-0.649904\pi$
$163$	−11.5854	−0.907441	−0.453721	+	0.891144i	$0.649904\pi$
$164$	−6.09722	−0.476113
$165$	1.67763	0.130603
$166$	7.36070	0.571301
$167$	−9.73825	−0.753569	−0.376784	−	0.926301i	$-0.622970\pi$
$167$	−9.73825	−0.753569	−0.376784	+	0.926301i	$0.622970\pi$
$168$	2.33531	0.180173
$169$	−12.7164	−0.978188
$170$	6.20701	0.476056
$171$	13.9306	1.06530
$172$	7.17129	0.546806
$173$	−9.97288	−0.758224	−0.379112	−	0.925351i	$-0.623770\pi$
$173$	−9.97288	−0.758224	−0.379112	+	0.925351i	$0.623770\pi$
$174$	8.79476	0.666729
$175$	−7.70848	−0.582706
$176$	−1.29654	−0.0977304
$177$	0.409058	0.0307467
$178$	7.67148	0.575002
$179$	−11.7814	−0.880584	−0.440292	−	0.897855i	$-0.645125\pi$
$179$	−11.7814	−0.880584	−0.440292	+	0.897855i	$0.645125\pi$
$180$	−2.93164	−0.218512
$181$	1.37301	0.102055	0.0510274	−	0.998697i	$-0.483750\pi$
$181$	1.37301	0.102055	0.0510274	+	0.998697i	$0.483750\pi$
$182$	1.32748	0.0983992
$183$	2.10649	0.155716
$184$	−1.00000	−0.0737210
$185$	7.76062	0.570572
$186$	8.18965	0.600495
$187$	5.82634	0.426064
$188$	6.97895	0.508992
$189$	11.9625	0.870146
$190$	9.06579	0.657701
$191$	0.683085	0.0494263	0.0247131	−	0.999695i	$-0.492133\pi$
$191$	0.683085	0.0494263	0.0247131	+	0.999695i	$0.492133\pi$
$192$	−0.936776	−0.0676060
$193$	−0.407793	−0.0293536	−0.0146768	−	0.999892i	$-0.504672\pi$
$193$	−0.407793	−0.0293536	−0.0146768	+	0.999892i	$0.504672\pi$
$194$	5.31188	0.381371
$195$	0.689012	0.0493412
$196$	−0.785322	−0.0560944
$197$	−7.19013	−0.512275	−0.256138	−	0.966640i	$-0.582450\pi$
$197$	−7.19013	−0.512275	−0.256138	+	0.966640i	$0.582450\pi$
$198$	−2.75184	−0.195565
$199$	3.59473	0.254824	0.127412	−	0.991850i	$-0.459333\pi$
$199$	3.59473	0.254824	0.127412	+	0.991850i	$0.459333\pi$
$200$	3.09214	0.218647
$201$	8.19313	0.577899
$202$	−17.5882	−1.23750
$203$	23.4044	1.64267
$204$	4.20964	0.294734
$205$	−8.42180	−0.588204
$206$	5.88185	0.409808
$207$	−2.12245	−0.147520
$208$	−0.532498	−0.0369221
$209$	8.50978	0.588634
$210$	3.22566	0.222592
$211$	−25.4830	−1.75432	−0.877160	−	0.480198i	$-0.840565\pi$
$211$	−25.4830	−1.75432	−0.877160	+	0.480198i	$0.840565\pi$
$212$	0.607361	0.0417137
$213$	−3.43913	−0.235645
$214$	2.12314	0.145135
$215$	9.90536	0.675540
$216$	−4.79859	−0.326503
$217$	21.7941	1.47948
$218$	−9.69916	−0.656910
$219$	12.4686	0.842553
$220$	−1.79085	−0.120739
$221$	2.39292	0.160965
$222$	5.26332	0.353251
$223$	−25.4651	−1.70527	−0.852635	−	0.522507i	$-0.824997\pi$
$223$	−25.4651	−1.70527	−0.852635	+	0.522507i	$0.824997\pi$
$224$	−2.49293	−0.166566
$225$	6.56292	0.437528
$226$	−0.192906	−0.0128319
$227$	11.8102	0.783871	0.391936	−	0.919993i	$-0.371806\pi$
$227$	11.8102	0.783871	0.391936	+	0.919993i	$0.371806\pi$
$228$	6.14849	0.407193
$229$	−20.8857	−1.38017	−0.690083	−	0.723731i	$-0.742426\pi$
$229$	−20.8857	−1.38017	−0.690083	+	0.723731i	$0.742426\pi$
$230$	−1.38125	−0.0910771
$231$	3.02783	0.199216
$232$	−9.38832	−0.616374
$233$	14.9353	0.978442	0.489221	−	0.872160i	$-0.337281\pi$
$233$	14.9353	0.978442	0.489221	+	0.872160i	$0.337281\pi$
$234$	−1.13020	−0.0738835
$235$	9.63969	0.628824
$236$	−0.436665	−0.0284245
$237$	8.48262	0.551005
$238$	11.2026	0.726157
$239$	−11.7803	−0.762006	−0.381003	−	0.924574i	$-0.624421\pi$
$239$	−11.7803	−0.762006	−0.381003	+	0.924574i	$0.624421\pi$
$240$	−1.29392	−0.0835225
$241$	0.115681	0.00745169	0.00372585	−	0.999993i	$-0.498814\pi$
$241$	0.115681	0.00745169	0.00372585	+	0.999993i	$0.498814\pi$
$242$	9.31898	0.599047
$243$	−16.1496	−1.03599
$244$	−2.24866	−0.143955
$245$	−1.08473	−0.0693007
$246$	−5.71173	−0.364167
$247$	3.49502	0.222383
$248$	−8.74238	−0.555142
$249$	6.89533	0.436974
$250$	11.1773	0.706914
$251$	−30.5995	−1.93143	−0.965713	−	0.259613i	$-0.916405\pi$
$251$	−30.5995	−1.93143	−0.965713	+	0.259613i	$0.916405\pi$
$252$	−5.29111	−0.333309
$253$	−1.29654	−0.0815128
$254$	11.7953	0.740100
$255$	5.81458	0.364123
$256$	1.00000	0.0625000
$257$	6.16866	0.384790	0.192395	−	0.981318i	$-0.438374\pi$
$257$	6.16866	0.384790	0.192395	+	0.981318i	$0.438374\pi$
$258$	6.71789	0.418238
$259$	14.0066	0.870328
$260$	−0.735514	−0.0456146
$261$	−19.9262	−1.23340
$262$	−1.00000	−0.0617802
$263$	5.69520	0.351181	0.175591	−	0.984463i	$-0.443817\pi$
$263$	5.69520	0.351181	0.175591	+	0.984463i	$0.443817\pi$
$264$	−1.21457	−0.0747515
$265$	0.838919	0.0515344
$266$	16.3622	1.00323
$267$	7.18646	0.439804
$268$	−8.74609	−0.534253
$269$	27.1772	1.65702	0.828510	−	0.559974i	$-0.189189\pi$
$269$	27.1772	1.65702	0.828510	+	0.559974i	$0.189189\pi$
$270$	−6.62806	−0.403371
$271$	−19.6099	−1.19122	−0.595609	−	0.803275i	$-0.703089\pi$
$271$	−19.6099	−1.19122	−0.595609	+	0.803275i	$0.703089\pi$
$272$	−4.49376	−0.272474
$273$	1.24355	0.0752630
$274$	−3.16549	−0.191234
$275$	4.00909	0.241757
$276$	−0.936776	−0.0563873
$277$	11.5177	0.692032	0.346016	−	0.938229i	$-0.387534\pi$
$277$	11.5177	0.692032	0.346016	+	0.938229i	$0.387534\pi$
$278$	−20.6429	−1.23808
$279$	−18.5553	−1.11087
$280$	−3.44336	−0.205780
$281$	3.50568	0.209131	0.104566	−	0.994518i	$-0.466655\pi$
$281$	3.50568	0.209131	0.104566	+	0.994518i	$0.466655\pi$
$282$	6.53771	0.389315
$283$	−16.2648	−0.966844	−0.483422	−	0.875388i	$-0.660606\pi$
$283$	−16.2648	−0.966844	−0.483422	+	0.875388i	$0.660606\pi$
$284$	3.67124	0.217848
$285$	8.49261	0.503059
$286$	−0.690405	−0.0408245
$287$	−15.1999	−0.897223
$288$	2.12245	0.125067
$289$	3.19385	0.187873
$290$	−12.9676	−0.761486
$291$	4.97605	0.291701
$292$	−13.3102	−0.778918
$293$	−2.83217	−0.165457	−0.0827286	−	0.996572i	$-0.526363\pi$
$293$	−2.83217	−0.165457	−0.0827286	+	0.996572i	$0.526363\pi$
$294$	−0.735671	−0.0429052
$295$	−0.603145	−0.0351165
$296$	−5.61854	−0.326571
$297$	−6.22156	−0.361012
$298$	11.5985	0.671882
$299$	−0.532498	−0.0307951
$300$	2.89664	0.167238
$301$	17.8775	1.03044
$302$	3.10142	0.178467
$303$	−16.4762	−0.946533
$304$	−6.56345	−0.376440
$305$	−3.10596	−0.177847
$306$	−9.53778	−0.545238
$307$	−23.5112	−1.34185	−0.670927	−	0.741523i	$-0.734104\pi$
$307$	−23.5112	−1.34185	−0.670927	+	0.741523i	$0.734104\pi$
$308$	−3.23218	−0.184170
$309$	5.50998	0.313452
$310$	−12.0754	−0.685839
$311$	10.8460	0.615022	0.307511	−	0.951545i	$-0.400504\pi$
$311$	10.8460	0.615022	0.307511	+	0.951545i	$0.400504\pi$
$312$	−0.498831	−0.0282408
$313$	19.7921	1.11872	0.559359	−	0.828926i	$-0.311047\pi$
$313$	19.7921	1.11872	0.559359	+	0.828926i	$0.311047\pi$
$314$	−3.16050	−0.178357
$315$	−7.30836	−0.411779
$316$	−9.05511	−0.509390
$317$	−31.5696	−1.77313	−0.886564	−	0.462607i	$-0.846914\pi$
$317$	−31.5696	−1.77313	−0.886564	+	0.462607i	$0.846914\pi$
$318$	0.568961	0.0319058
$319$	−12.1723	−0.681520
$320$	1.38125	0.0772144
$321$	1.98891	0.111010
$322$	−2.49293	−0.138925
$323$	29.4946	1.64112
$324$	1.87215	0.104008
$325$	1.64656	0.0913346
$326$	11.5854	0.641658
$327$	−9.08595	−0.502454
$328$	6.09722	0.336663
$329$	17.3980	0.959183
$330$	−1.67763	−0.0923502
$331$	15.7971	0.868289	0.434144	−	0.900843i	$-0.357051\pi$
$331$	15.7971	0.868289	0.434144	+	0.900843i	$0.357051\pi$
$332$	−7.36070	−0.403971
$333$	−11.9251	−0.653490
$334$	9.73825	0.532854
$335$	−12.0806	−0.660032
$336$	−2.33531	−0.127402
$337$	−14.6876	−0.800087	−0.400043	−	0.916496i	$-0.631005\pi$
$337$	−14.6876	−0.800087	−0.400043	+	0.916496i	$0.631005\pi$
$338$	12.7164	0.691683
$339$	−0.180709	−0.00981479
$340$	−6.20701	−0.336623
$341$	−11.3348	−0.613816
$342$	−13.9306	−0.753281
$343$	−19.4082	−1.04795
$344$	−7.17129	−0.386650
$345$	−1.29392	−0.0696626
$346$	9.97288	0.536145
$347$	−7.46473	−0.400728	−0.200364	−	0.979722i	$-0.564212\pi$
$347$	−7.46473	−0.400728	−0.200364	+	0.979722i	$0.564212\pi$
$348$	−8.79476	−0.471448
$349$	−11.9085	−0.637450	−0.318725	−	0.947847i	$-0.603255\pi$
$349$	−11.9085	−0.637450	−0.318725	+	0.947847i	$0.603255\pi$
$350$	7.70848	0.412036
$351$	−2.55524	−0.136389
$352$	1.29654	0.0691058
$353$	−0.279427	−0.0148724	−0.00743621	−	0.999972i	$-0.502367\pi$
$353$	−0.279427	−0.0148724	−0.00743621	+	0.999972i	$0.502367\pi$
$354$	−0.409058	−0.0217412
$355$	5.07091	0.269136
$356$	−7.67148	−0.406588
$357$	10.4943	0.555419
$358$	11.7814	0.622667
$359$	9.12238	0.481461	0.240730	−	0.970592i	$-0.422613\pi$
$359$	9.12238	0.481461	0.240730	+	0.970592i	$0.422613\pi$
$360$	2.93164	0.154511
$361$	24.0789	1.26731
$362$	−1.37301	−0.0721636
$363$	8.72980	0.458196
$364$	−1.32748	−0.0695787
$365$	−18.3847	−0.962299
$366$	−2.10649	−0.110108
$367$	22.4485	1.17180	0.585900	−	0.810383i	$-0.300741\pi$
$367$	22.4485	1.17180	0.585900	+	0.810383i	$0.300741\pi$
$368$	1.00000	0.0521286
$369$	12.9410	0.673684
$370$	−7.76062	−0.403456
$371$	1.51411	0.0786084
$372$	−8.18965	−0.424614
$373$	−3.66142	−0.189581	−0.0947905	−	0.995497i	$-0.530218\pi$
$373$	−3.66142	−0.189581	−0.0947905	+	0.995497i	$0.530218\pi$
$374$	−5.82634	−0.301273
$375$	10.4706	0.540701
$376$	−6.97895	−0.359912
$377$	−4.99926	−0.257475
$378$	−11.9625	−0.615286
$379$	18.5474	0.952714	0.476357	−	0.879252i	$-0.341957\pi$
$379$	18.5474	0.952714	0.476357	+	0.879252i	$0.341957\pi$
$380$	−9.06579	−0.465065
$381$	11.0495	0.566084
$382$	−0.683085	−0.0349496
$383$	−3.65393	−0.186707	−0.0933536	−	0.995633i	$-0.529759\pi$
$383$	−3.65393	−0.186707	−0.0933536	+	0.995633i	$0.529759\pi$
$384$	0.936776	0.0478047
$385$	−4.46445	−0.227530
$386$	0.407793	0.0207561
$387$	−15.2207	−0.773712
$388$	−5.31188	−0.269670
$389$	−2.41585	−0.122489	−0.0612443	−	0.998123i	$-0.519507\pi$
$389$	−2.41585	−0.122489	−0.0612443	+	0.998123i	$0.519507\pi$
$390$	−0.689012	−0.0348895
$391$	−4.49376	−0.227259
$392$	0.785322	0.0396647
$393$	−0.936776	−0.0472541
$394$	7.19013	0.362233
$395$	−12.5074	−0.629316
$396$	2.75184	0.138285
$397$	15.8509	0.795536	0.397768	−	0.917486i	$-0.369785\pi$
$397$	15.8509	0.795536	0.397768	+	0.917486i	$0.369785\pi$
$398$	−3.59473	−0.180187
$399$	15.3277	0.767346
$400$	−3.09214	−0.154607
$401$	−4.53493	−0.226464	−0.113232	−	0.993569i	$-0.536120\pi$
$401$	−4.53493	−0.226464	−0.113232	+	0.993569i	$0.536120\pi$
$402$	−8.19313	−0.408636
$403$	−4.65530	−0.231897
$404$	17.5882	0.875046
$405$	2.58591	0.128495
$406$	−23.4044	−1.16154
$407$	−7.28466	−0.361087
$408$	−4.20964	−0.208408
$409$	−17.2859	−0.854733	−0.427366	−	0.904078i	$-0.640559\pi$
$409$	−17.2859	−0.854733	−0.427366	+	0.904078i	$0.640559\pi$
$410$	8.42180	0.415923
$411$	−2.96536	−0.146270
$412$	−5.88185	−0.289778
$413$	−1.08857	−0.0535652
$414$	2.12245	0.104313
$415$	−10.1670	−0.499078
$416$	0.532498	0.0261078
$417$	−19.3377	−0.946973
$418$	−8.50978	−0.416227
$419$	1.27685	0.0623781	0.0311890	−	0.999514i	$-0.490071\pi$
$419$	1.27685	0.0623781	0.0311890	+	0.999514i	$0.490071\pi$
$420$	−3.22566	−0.157396
$421$	−28.2406	−1.37636	−0.688181	−	0.725539i	$-0.741591\pi$
$421$	−28.2406	−1.37636	−0.688181	+	0.725539i	$0.741591\pi$
$422$	25.4830	1.24049
$423$	−14.8125	−0.720207
$424$	−0.607361	−0.0294961
$425$	13.8953	0.674023
$426$	3.43913	0.166626
$427$	−5.60573	−0.271280
$428$	−2.12314	−0.102626
$429$	−0.646755	−0.0312256
$430$	−9.90536	−0.477679
$431$	4.07729	0.196396	0.0981982	−	0.995167i	$-0.468692\pi$
$431$	4.07729	0.196396	0.0981982	+	0.995167i	$0.468692\pi$
$432$	4.79859	0.230872
$433$	40.1696	1.93043	0.965214	−	0.261460i	$-0.0842039\pi$
$433$	40.1696	1.93043	0.965214	+	0.261460i	$0.0842039\pi$
$434$	−21.7941	−1.04615
$435$	−12.1478	−0.582441
$436$	9.69916	0.464506
$437$	−6.56345	−0.313973
$438$	−12.4686	−0.595775
$439$	0.902219	0.0430606	0.0215303	−	0.999768i	$-0.493146\pi$
$439$	0.902219	0.0430606	0.0215303	+	0.999768i	$0.493146\pi$
$440$	1.79085	0.0853754
$441$	1.66681	0.0793717
$442$	−2.39292	−0.113819
$443$	−18.8332	−0.894791	−0.447395	−	0.894336i	$-0.647648\pi$
$443$	−18.8332	−0.894791	−0.447395	+	0.894336i	$0.647648\pi$
$444$	−5.26332	−0.249786
$445$	−10.5963	−0.502310
$446$	25.4651	1.20581
$447$	10.8652	0.513905
$448$	2.49293	0.117780
$449$	−28.7296	−1.35583	−0.677917	−	0.735139i	$-0.737117\pi$
$449$	−28.7296	−1.35583	−0.677917	+	0.735139i	$0.737117\pi$
$450$	−6.56292	−0.309379
$451$	7.90529	0.372246
$452$	0.192906	0.00907352
$453$	2.90534	0.136505
$454$	−11.8102	−0.554281
$455$	−1.83358	−0.0859596
$456$	−6.14849	−0.287929
$457$	18.8061	0.879712	0.439856	−	0.898068i	$-0.355029\pi$
$457$	18.8061	0.879712	0.439856	+	0.898068i	$0.355029\pi$
$458$	20.8857	0.975924
$459$	−21.5637	−1.00651
$460$	1.38125	0.0644012
$461$	36.4941	1.69970	0.849850	−	0.527025i	$-0.176693\pi$
$461$	36.4941	1.69970	0.849850	+	0.527025i	$0.176693\pi$
$462$	−3.02783	−0.140867
$463$	−22.2870	−1.03577	−0.517883	−	0.855452i	$-0.673280\pi$
$463$	−22.2870	−1.03577	−0.517883	+	0.855452i	$0.673280\pi$
$464$	9.38832	0.435842
$465$	−11.3120	−0.524581
$466$	−14.9353	−0.691863
$467$	36.9088	1.70794	0.853969	−	0.520324i	$-0.174189\pi$
$467$	36.9088	1.70794	0.853969	+	0.520324i	$0.174189\pi$
$468$	1.13020	0.0522435
$469$	−21.8034	−1.00679
$470$	−9.63969	−0.444646
$471$	−2.96068	−0.136421
$472$	0.436665	0.0200992
$473$	−9.29786	−0.427516
$474$	−8.48262	−0.389619
$475$	20.2951	0.931204
$476$	−11.2026	−0.513470
$477$	−1.28909	−0.0590235
$478$	11.7803	0.538819
$479$	37.6259	1.71917	0.859587	−	0.510990i	$-0.170721\pi$
$479$	37.6259	1.71917	0.859587	+	0.510990i	$0.170721\pi$
$480$	1.29392	0.0590593
$481$	−2.99186	−0.136417
$482$	−0.115681	−0.00526914
$483$	−2.33531	−0.106260
$484$	−9.31898	−0.423590
$485$	−7.33705	−0.333158
$486$	16.1496	0.732559
$487$	38.7739	1.75701	0.878506	−	0.477731i	$-0.158541\pi$
$487$	38.7739	1.75701	0.878506	+	0.477731i	$0.158541\pi$
$488$	2.24866	0.101792
$489$	10.8530	0.490788
$490$	1.08473	0.0490030
$491$	−8.16329	−0.368404	−0.184202	−	0.982888i	$-0.558970\pi$
$491$	−8.16329	−0.368404	−0.184202	+	0.982888i	$0.558970\pi$
$492$	5.71173	0.257505
$493$	−42.1888	−1.90009
$494$	−3.49502	−0.157249
$495$	3.80099	0.170842
$496$	8.74238	0.392544
$497$	9.15213	0.410529
$498$	−6.89533	−0.308987
$499$	−32.2183	−1.44229	−0.721145	−	0.692784i	$-0.756384\pi$
$499$	−32.2183	−1.44229	−0.721145	+	0.692784i	$0.756384\pi$
$500$	−11.1773	−0.499864
$501$	9.12257	0.407566
$502$	30.5995	1.36572
$503$	23.9695	1.06875	0.534373	−	0.845249i	$-0.320548\pi$
$503$	23.9695	1.06875	0.534373	+	0.845249i	$0.320548\pi$
$504$	5.29111	0.235685
$505$	24.2937	1.08106
$506$	1.29654	0.0576382
$507$	11.9125	0.529051
$508$	−11.7953	−0.523330
$509$	−4.33842	−0.192297	−0.0961485	−	0.995367i	$-0.530652\pi$
$509$	−4.33842	−0.192297	−0.0961485	+	0.995367i	$0.530652\pi$
$510$	−5.81458	−0.257474
$511$	−33.1813	−1.46785
$512$	−1.00000	−0.0441942
$513$	−31.4953	−1.39055
$514$	−6.16866	−0.272088
$515$	−8.12432	−0.358000
$516$	−6.71789	−0.295739
$517$	−9.04848	−0.397952
$518$	−14.0066	−0.615415
$519$	9.34236	0.410084
$520$	0.735514	0.0322544
$521$	12.2003	0.534503	0.267252	−	0.963627i	$-0.413885\pi$
$521$	12.2003	0.534503	0.267252	+	0.963627i	$0.413885\pi$
$522$	19.9262	0.872148
$523$	−11.3549	−0.496517	−0.248258	−	0.968694i	$-0.579858\pi$
$523$	−11.3549	−0.496517	−0.248258	+	0.968694i	$0.579858\pi$
$524$	1.00000	0.0436852
$525$	7.22112	0.315155
$526$	−5.69520	−0.248323
$527$	−39.2861	−1.71133
$528$	1.21457	0.0528573
$529$	1.00000	0.0434783
$530$	−0.838919	−0.0364403
$531$	0.926801	0.0402197
$532$	−16.3622	−0.709391
$533$	3.24676	0.140633
$534$	−7.18646	−0.310989
$535$	−2.93259	−0.126787
$536$	8.74609	0.377774
$537$	11.0366	0.476262
$538$	−27.1772	−1.17169
$539$	1.01820	0.0438570
$540$	6.62806	0.285226
$541$	−9.31967	−0.400684	−0.200342	−	0.979726i	$-0.564205\pi$
$541$	−9.31967	−0.400684	−0.200342	+	0.979726i	$0.564205\pi$
$542$	19.6099	0.842318
$543$	−1.28620	−0.0551961
$544$	4.49376	0.192668
$545$	13.3970	0.573864
$546$	−1.24355	−0.0532190
$547$	−31.0071	−1.32577	−0.662883	−	0.748723i	$-0.730668\pi$
$547$	−31.0071	−1.32577	−0.662883	+	0.748723i	$0.730668\pi$
$548$	3.16549	0.135223
$549$	4.77266	0.203692
$550$	−4.00909	−0.170948
$551$	−61.6198	−2.62509
$552$	0.936776	0.0398718
$553$	−22.5737	−0.959932
$554$	−11.5177	−0.489340
$555$	−7.26997	−0.308593
$556$	20.6429	0.875452
$557$	−32.2904	−1.36819	−0.684094	−	0.729393i	$-0.739802\pi$
$557$	−32.2904	−1.36819	−0.684094	+	0.729393i	$0.739802\pi$
$558$	18.5553	0.785507
$559$	−3.81869	−0.161514
$560$	3.44336	0.145509
$561$	−5.45797	−0.230436
$562$	−3.50568	−0.147878
$563$	−21.8210	−0.919646	−0.459823	−	0.888011i	$-0.652087\pi$
$563$	−21.8210	−0.919646	−0.459823	+	0.888011i	$0.652087\pi$
$564$	−6.53771	−0.275287
$565$	0.266451	0.0112097
$566$	16.2648	0.683662
$567$	4.66712	0.196001
$568$	−3.67124	−0.154042
$569$	−21.6536	−0.907767	−0.453883	−	0.891061i	$-0.649962\pi$
$569$	−21.6536	−0.907767	−0.453883	+	0.891061i	$0.649962\pi$
$570$	−8.49261	−0.355716
$571$	−23.4711	−0.982237	−0.491118	−	0.871093i	$-0.663412\pi$
$571$	−23.4711	−0.982237	−0.491118	+	0.871093i	$0.663412\pi$
$572$	0.690405	0.0288673
$573$	−0.639897	−0.0267321
$574$	15.1999	0.634432
$575$	−3.09214	−0.128951
$576$	−2.12245	−0.0884354
$577$	−13.2931	−0.553398	−0.276699	−	0.960957i	$-0.589240\pi$
$577$	−13.2931	−0.553398	−0.276699	+	0.960957i	$0.589240\pi$
$578$	−3.19385	−0.132847
$579$	0.382011	0.0158758
$580$	12.9676	0.538452
$581$	−18.3497	−0.761273
$582$	−4.97605	−0.206264
$583$	−0.787468	−0.0326136
$584$	13.3102	0.550779
$585$	1.56109	0.0645432
$586$	2.83217	0.116996
$587$	4.88252	0.201523	0.100762	−	0.994911i	$-0.467872\pi$
$587$	4.88252	0.201523	0.100762	+	0.994911i	$0.467872\pi$
$588$	0.735671	0.0303386
$589$	−57.3802	−2.36431
$590$	0.603145	0.0248311
$591$	6.73554	0.277063
$592$	5.61854	0.230921
$593$	−14.9675	−0.614642	−0.307321	−	0.951606i	$-0.599432\pi$
$593$	−14.9675	−0.614642	−0.307321	+	0.951606i	$0.599432\pi$
$594$	6.22156	0.255274
$595$	−15.4736	−0.634357
$596$	−11.5985	−0.475092
$597$	−3.36746	−0.137821
$598$	0.532498	0.0217755
$599$	−27.8084	−1.13622	−0.568109	−	0.822953i	$-0.692325\pi$
$599$	−27.8084	−1.13622	−0.568109	+	0.822953i	$0.692325\pi$
$600$	−2.89664	−0.118255
$601$	−36.3320	−1.48201	−0.741007	−	0.671498i	$-0.765651\pi$
$601$	−36.3320	−1.48201	−0.741007	+	0.671498i	$0.765651\pi$
$602$	−17.8775	−0.728632
$603$	18.5632	0.755950
$604$	−3.10142	−0.126195
$605$	−12.8719	−0.523316
$606$	16.4762	0.669300
$607$	−45.0589	−1.82889	−0.914443	−	0.404716i	$-0.867370\pi$
$607$	−45.0589	−1.82889	−0.914443	+	0.404716i	$0.867370\pi$
$608$	6.56345	0.266183
$609$	−21.9247	−0.888433
$610$	3.10596	0.125757
$611$	−3.71627	−0.150344
$612$	9.53778	0.385542
$613$	−14.2772	−0.576650	−0.288325	−	0.957533i	$-0.593098\pi$
$613$	−14.2772	−0.576650	−0.288325	+	0.957533i	$0.593098\pi$
$614$	23.5112	0.948835
$615$	7.88934	0.318129
$616$	3.23218	0.130228
$617$	29.5515	1.18970	0.594849	−	0.803837i	$-0.297212\pi$
$617$	29.5515	1.18970	0.594849	+	0.803837i	$0.297212\pi$
$618$	−5.50998	−0.221644
$619$	8.68462	0.349064	0.174532	−	0.984651i	$-0.444159\pi$
$619$	8.68462	0.349064	0.174532	+	0.984651i	$0.444159\pi$
$620$	12.0754	0.484961
$621$	4.79859	0.192561
$622$	−10.8460	−0.434886
$623$	−19.1244	−0.766204
$624$	0.498831	0.0199692
$625$	0.0220452	0.000881808 0
$626$	−19.7921	−0.791053
$627$	−7.97176	−0.318361
$628$	3.16050	0.126118
$629$	−25.2484	−1.00672
$630$	7.30836	0.291172
$631$	2.13449	0.0849726	0.0424863	−	0.999097i	$-0.486472\pi$
$631$	2.13449	0.0849726	0.0424863	+	0.999097i	$0.486472\pi$
$632$	9.05511	0.360193
$633$	23.8718	0.948820
$634$	31.5696	1.25379
$635$	−16.2922	−0.646537
$636$	−0.568961	−0.0225608
$637$	0.418182	0.0165690
$638$	12.1723	0.481907
$639$	−7.79202	−0.308248
$640$	−1.38125	−0.0545988
$641$	7.84892	0.310014	0.155007	−	0.987913i	$-0.450460\pi$
$641$	7.84892	0.310014	0.155007	+	0.987913i	$0.450460\pi$
$642$	−1.98891	−0.0784959
$643$	31.3502	1.23633	0.618165	−	0.786049i	$-0.287876\pi$
$643$	31.3502	1.23633	0.618165	+	0.786049i	$0.287876\pi$
$644$	2.49293	0.0982350
$645$	−9.27911	−0.365364
$646$	−29.4946	−1.16045
$647$	19.8691	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$647$	19.8691	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$648$	−1.87215	−0.0735448
$649$	0.566154	0.0222235
$650$	−1.64656	−0.0645833
$651$	−20.4162	−0.800174
$652$	−11.5854	−0.453721
$653$	3.89288	0.152340	0.0761702	−	0.997095i	$-0.475731\pi$
$653$	3.89288	0.152340	0.0761702	+	0.997095i	$0.475731\pi$
$654$	9.08595	0.355289
$655$	1.38125	0.0539700
$656$	−6.09722	−0.238056
$657$	28.2502	1.10214
$658$	−17.3980	−0.678245
$659$	−19.7748	−0.770317	−0.385159	−	0.922850i	$-0.625853\pi$
$659$	−19.7748	−0.770317	−0.385159	+	0.922850i	$0.625853\pi$
$660$	1.67763	0.0653015
$661$	−21.7597	−0.846354	−0.423177	−	0.906047i	$-0.639085\pi$
$661$	−21.7597	−0.846354	−0.423177	+	0.906047i	$0.639085\pi$
$662$	−15.7971	−0.613973
$663$	−2.24163	−0.0870575
$664$	7.36070	0.285651
$665$	−22.6003	−0.876403
$666$	11.9251	0.462087
$667$	9.38832	0.363517
$668$	−9.73825	−0.376784
$669$	23.8551	0.922292
$670$	12.0806	0.466713
$671$	2.91547	0.112551
$672$	2.33531	0.0900867
$673$	−6.64428	−0.256118	−0.128059	−	0.991767i	$-0.540875\pi$
$673$	−6.64428	−0.256118	−0.128059	+	0.991767i	$0.540875\pi$
$674$	14.6876	0.565747
$675$	−14.8379	−0.571112
$676$	−12.7164	−0.489094
$677$	29.4872	1.13328	0.566642	−	0.823964i	$-0.308242\pi$
$677$	29.4872	1.13328	0.566642	+	0.823964i	$0.308242\pi$
$678$	0.180709	0.00694010
$679$	−13.2421	−0.508186
$680$	6.20701	0.238028
$681$	−11.0635	−0.423955
$682$	11.3348	0.434034
$683$	24.3576	0.932016	0.466008	−	0.884780i	$-0.345692\pi$
$683$	24.3576	0.932016	0.466008	+	0.884780i	$0.345692\pi$
$684$	13.9306	0.532650
$685$	4.37234	0.167059
$686$	19.4082	0.741010
$687$	19.5652	0.746460
$688$	7.17129	0.273403
$689$	−0.323418	−0.0123213
$690$	1.29392	0.0492589
$691$	−47.7353	−1.81594	−0.907969	−	0.419038i	$-0.862367\pi$
$691$	−47.7353	−1.81594	−0.907969	+	0.419038i	$0.862367\pi$
$692$	−9.97288	−0.379112
$693$	6.86014	0.260595
$694$	7.46473	0.283357
$695$	28.5130	1.08156
$696$	8.79476	0.333364
$697$	27.3994	1.03783
$698$	11.9085	0.450745
$699$	−13.9910	−0.529188
$700$	−7.70848	−0.291353
$701$	44.1090	1.66598	0.832988	−	0.553292i	$-0.186629\pi$
$701$	44.1090	1.66598	0.832988	+	0.553292i	$0.186629\pi$
$702$	2.55524	0.0964412
$703$	−36.8770	−1.39084
$704$	−1.29654	−0.0488652
$705$	−9.03023	−0.340098
$706$	0.279427	0.0105164
$707$	43.8461	1.64900
$708$	0.409058	0.0153733
$709$	2.29225	0.0860872	0.0430436	−	0.999073i	$-0.486295\pi$
$709$	2.29225	0.0860872	0.0430436	+	0.999073i	$0.486295\pi$
$710$	−5.07091	−0.190308
$711$	19.2190	0.720770
$712$	7.67148	0.287501
$713$	8.74238	0.327405
$714$	−10.4943	−0.392740
$715$	0.953623	0.0356635
$716$	−11.7814	−0.440292
$717$	11.0355	0.412129
$718$	−9.12238	−0.340444
$719$	−21.5034	−0.801942	−0.400971	−	0.916091i	$-0.631327\pi$
$719$	−21.5034	−0.801942	−0.400971	+	0.916091i	$0.631327\pi$
$720$	−2.93164	−0.109256
$721$	−14.6630	−0.546079
$722$	−24.0789	−0.896124
$723$	−0.108368	−0.00403023
$724$	1.37301	0.0510274
$725$	−29.0300	−1.07815
$726$	−8.72980	−0.323993
$727$	34.2339	1.26967	0.634833	−	0.772650i	$-0.281069\pi$
$727$	34.2339	1.26967	0.634833	+	0.772650i	$0.281069\pi$
$728$	1.32748	0.0491996
$729$	9.51208	0.352299
$730$	18.3847	0.680448
$731$	−32.2260	−1.19192
$732$	2.10649	0.0778580
$733$	−37.9137	−1.40037	−0.700187	−	0.713960i	$-0.746900\pi$
$733$	−37.9137	−1.40037	−0.700187	+	0.713960i	$0.746900\pi$
$734$	−22.4485	−0.828588
$735$	1.01615	0.0374812
$736$	−1.00000	−0.0368605
$737$	11.3397	0.417702
$738$	−12.9410	−0.476367
$739$	−40.8369	−1.50221	−0.751105	−	0.660182i	$-0.770479\pi$
$739$	−40.8369	−1.50221	−0.751105	+	0.660182i	$0.770479\pi$
$740$	7.76062	0.285286
$741$	−3.27405	−0.120275
$742$	−1.51411	−0.0555846
$743$	−42.0599	−1.54303	−0.771513	−	0.636213i	$-0.780500\pi$
$743$	−42.0599	−1.54303	−0.771513	+	0.636213i	$0.780500\pi$
$744$	8.18965	0.300247
$745$	−16.0204	−0.586943
$746$	3.66142	0.134054
$747$	15.6227	0.571605
$748$	5.82634	0.213032
$749$	−5.29283	−0.193396
$750$	−10.4706	−0.382333
$751$	20.4074	0.744678	0.372339	−	0.928097i	$-0.378556\pi$
$751$	20.4074	0.744678	0.372339	+	0.928097i	$0.378556\pi$
$752$	6.97895	0.254496
$753$	28.6649	1.04461
$754$	4.99926	0.182062
$755$	−4.28385	−0.155905
$756$	11.9625	0.435073
$757$	16.8969	0.614129	0.307065	−	0.951689i	$-0.400653\pi$
$757$	16.8969	0.614129	0.307065	+	0.951689i	$0.400653\pi$
$758$	−18.5474	−0.673671
$759$	1.21457	0.0440860
$760$	9.06579	0.328851
$761$	21.7485	0.788383	0.394192	−	0.919028i	$-0.371025\pi$
$761$	21.7485	0.788383	0.394192	+	0.919028i	$0.371025\pi$
$762$	−11.0495	−0.400282
$763$	24.1793	0.875349
$764$	0.683085	0.0247131
$765$	13.1741	0.476310
$766$	3.65393	0.132022
$767$	0.232523	0.00839593
$768$	−0.936776	−0.0338030
$769$	−8.84077	−0.318806	−0.159403	−	0.987214i	$-0.550957\pi$
$769$	−8.84077	−0.318806	−0.159403	+	0.987214i	$0.550957\pi$
$770$	4.46445	0.160888
$771$	−5.77865	−0.208113
$772$	−0.407793	−0.0146768
$773$	38.0472	1.36846	0.684232	−	0.729264i	$-0.260138\pi$
$773$	38.0472	1.36846	0.684232	+	0.729264i	$0.260138\pi$
$774$	15.2207	0.547097
$775$	−27.0327	−0.971042
$776$	5.31188	0.190686
$777$	−13.1211	−0.470715
$778$	2.41585	0.0866125
$779$	40.0188	1.43382
$780$	0.689012	0.0246706
$781$	−4.75991	−0.170323
$782$	4.49376	0.160696
$783$	45.0507	1.60998
$784$	−0.785322	−0.0280472
$785$	4.36545	0.155810
$786$	0.936776	0.0334137
$787$	47.6748	1.69942	0.849711	−	0.527249i	$-0.176776\pi$
$787$	47.6748	1.69942	0.849711	+	0.527249i	$0.176776\pi$
$788$	−7.19013	−0.256138
$789$	−5.33513	−0.189936
$790$	12.5074	0.444993
$791$	0.480899	0.0170988
$792$	−2.75184	−0.0977824
$793$	1.19740	0.0425211
$794$	−15.8509	−0.562529
$795$	−0.785879	−0.0278723
$796$	3.59473	0.127412
$797$	2.00493	0.0710183	0.0355091	−	0.999369i	$-0.488695\pi$
$797$	2.00493	0.0710183	0.0355091	+	0.999369i	$0.488695\pi$
$798$	−15.3277	−0.542595
$799$	−31.3617	−1.10950
$800$	3.09214	0.109324
$801$	16.2823	0.575308
$802$	4.53493	0.160134
$803$	17.2572	0.608992
$804$	8.19313	0.288950
$805$	3.44336	0.121362
$806$	4.65530	0.163976
$807$	−25.4589	−0.896196
$808$	−17.5882	−0.618751
$809$	4.24063	0.149093	0.0745464	−	0.997218i	$-0.476249\pi$
$809$	4.24063	0.149093	0.0745464	+	0.997218i	$0.476249\pi$
$810$	−2.58591	−0.0908595
$811$	−9.37816	−0.329312	−0.164656	−	0.986351i	$-0.552651\pi$
$811$	−9.37816	−0.329312	−0.164656	+	0.986351i	$0.552651\pi$
$812$	23.4044	0.821333
$813$	18.3701	0.644268
$814$	7.28466	0.255327
$815$	−16.0024	−0.560540
$816$	4.20964	0.147367
$817$	−47.0684	−1.64672
$818$	17.2859	0.604387
$819$	2.81750	0.0984516
$820$	−8.42180	−0.294102
$821$	−3.94270	−0.137601	−0.0688005	−	0.997630i	$-0.521917\pi$
$821$	−3.94270	−0.137601	−0.0688005	+	0.997630i	$0.521917\pi$
$822$	2.96536	0.103429
$823$	7.82578	0.272789	0.136395	−	0.990655i	$-0.456448\pi$
$823$	7.82578	0.272789	0.136395	+	0.990655i	$0.456448\pi$
$824$	5.88185	0.204904
$825$	−3.75562	−0.130754
$826$	1.08857	0.0378763
$827$	−27.3167	−0.949895	−0.474947	−	0.880014i	$-0.657533\pi$
$827$	−27.3167	−0.949895	−0.474947	+	0.880014i	$0.657533\pi$
$828$	−2.12245	−0.0737602
$829$	31.7497	1.10271	0.551356	−	0.834270i	$-0.314111\pi$
$829$	31.7497	1.10271	0.551356	+	0.834270i	$0.314111\pi$
$830$	10.1670	0.352901
$831$	−10.7895	−0.374284
$832$	−0.532498	−0.0184610
$833$	3.52905	0.122274
$834$	19.3377	0.669611
$835$	−13.4510	−0.465491
$836$	8.50978	0.294317
$837$	41.9511	1.45004
$838$	−1.27685	−0.0441080
$839$	−51.7729	−1.78740	−0.893699	−	0.448667i	$-0.851899\pi$
$839$	−51.7729	−1.78740	−0.893699	+	0.448667i	$0.851899\pi$
$840$	3.22566	0.111296
$841$	59.1406	2.03933
$842$	28.2406	0.973235
$843$	−3.28404	−0.113108
$844$	−25.4830	−0.877160
$845$	−17.5646	−0.604241
$846$	14.8125	0.509263
$847$	−23.2315	−0.798245
$848$	0.607361	0.0208569
$849$	15.2365	0.522915
$850$	−13.8953	−0.476606
$851$	5.61854	0.192601
$852$	−3.43913	−0.117823
$853$	14.3979	0.492976	0.246488	−	0.969146i	$-0.420723\pi$
$853$	14.3979	0.492976	0.246488	+	0.969146i	$0.420723\pi$
$854$	5.60573	0.191824
$855$	19.2417	0.658052
$856$	2.12314	0.0725674
$857$	11.9525	0.408290	0.204145	−	0.978941i	$-0.434559\pi$
$857$	11.9525	0.408290	0.204145	+	0.978941i	$0.434559\pi$
$858$	0.646755	0.0220798
$859$	−14.4561	−0.493236	−0.246618	−	0.969113i	$-0.579319\pi$
$859$	−14.4561	−0.493236	−0.246618	+	0.969113i	$0.579319\pi$
$860$	9.90536	0.337770
$861$	14.2389	0.485261
$862$	−4.07729	−0.138873
$863$	5.33211	0.181507	0.0907535	−	0.995873i	$-0.471072\pi$
$863$	5.33211	0.181507	0.0907535	+	0.995873i	$0.471072\pi$
$864$	−4.79859	−0.163251
$865$	−13.7751	−0.468366
$866$	−40.1696	−1.36502
$867$	−2.99192	−0.101611
$868$	21.7941	0.739740
$869$	11.7403	0.398263
$870$	12.1478	0.411848
$871$	4.65728	0.157806
$872$	−9.69916	−0.328455
$873$	11.2742	0.381574
$874$	6.56345	0.222012
$875$	−27.8642	−0.941980
$876$	12.4686	0.421277
$877$	42.8468	1.44683	0.723417	−	0.690411i	$-0.242570\pi$
$877$	42.8468	1.44683	0.723417	+	0.690411i	$0.242570\pi$
$878$	−0.902219	−0.0304484
$879$	2.65311	0.0894872
$880$	−1.79085	−0.0603695
$881$	−13.9353	−0.469493	−0.234747	−	0.972057i	$-0.575426\pi$
$881$	−13.9353	−0.469493	−0.234747	+	0.972057i	$0.575426\pi$
$882$	−1.66681	−0.0561243
$883$	18.3696	0.618185	0.309092	−	0.951032i	$-0.399975\pi$
$883$	18.3696	0.618185	0.309092	+	0.951032i	$0.399975\pi$
$884$	2.39292	0.0804824
$885$	0.565012	0.0189927
$886$	18.8332	0.632713
$887$	−7.62969	−0.256180	−0.128090	−	0.991763i	$-0.540885\pi$
$887$	−7.62969	−0.256180	−0.128090	+	0.991763i	$0.540885\pi$
$888$	5.26332	0.176625
$889$	−29.4047	−0.986202
$890$	10.5963	0.355187
$891$	−2.42731	−0.0813180
$892$	−25.4651	−0.852635
$893$	−45.8060	−1.53284
$894$	−10.8652	−0.363386
$895$	−16.2731	−0.543950
$896$	−2.49293	−0.0832828
$897$	0.498831	0.0166555
$898$	28.7296	0.958719
$899$	82.0763	2.73740
$900$	6.56292	0.218764
$901$	−2.72933	−0.0909272
$902$	−7.90529	−0.263217
$903$	−16.7472	−0.557312
$904$	−0.192906	−0.00641595
$905$	1.89647	0.0630407
$906$	−2.90534	−0.0965234
$907$	−18.3669	−0.609862	−0.304931	−	0.952374i	$-0.598633\pi$
$907$	−18.3669	−0.609862	−0.304931	+	0.952374i	$0.598633\pi$
$908$	11.8102	0.391936
$909$	−37.3301	−1.23816
$910$	1.83358	0.0607826
$911$	23.7045	0.785366	0.392683	−	0.919674i	$-0.371547\pi$
$911$	23.7045	0.785366	0.392683	+	0.919674i	$0.371547\pi$
$912$	6.14849	0.203597
$913$	9.54344	0.315842
$914$	−18.8061	−0.622050
$915$	2.90959	0.0961881
$916$	−20.8857	−0.690083
$917$	2.49293	0.0823237
$918$	21.5637	0.711708
$919$	26.8920	0.887086	0.443543	−	0.896253i	$-0.353721\pi$
$919$	26.8920	0.887086	0.443543	+	0.896253i	$0.353721\pi$
$920$	−1.38125	−0.0455385
$921$	22.0247	0.725739
$922$	−36.4941	−1.20187
$923$	−1.95493	−0.0643472
$924$	3.02783	0.0996082
$925$	−17.3733	−0.571231
$926$	22.2870	0.732397
$927$	12.4839	0.410026
$928$	−9.38832	−0.308187
$929$	17.1007	0.561056	0.280528	−	0.959846i	$-0.409490\pi$
$929$	17.1007	0.561056	0.280528	+	0.959846i	$0.409490\pi$
$930$	11.3120	0.370934
$931$	5.15442	0.168929
$932$	14.9353	0.489221
$933$	−10.1603	−0.332633
$934$	−36.9088	−1.20769
$935$	8.04764	0.263186
$936$	−1.13020	−0.0369417
$937$	54.5264	1.78130	0.890650	−	0.454690i	$-0.150250\pi$
$937$	54.5264	1.78130	0.890650	+	0.454690i	$0.150250\pi$
$938$	21.8034	0.711905
$939$	−18.5408	−0.605056
$940$	9.63969	0.314412
$941$	21.9661	0.716074	0.358037	−	0.933707i	$-0.383446\pi$
$941$	21.9661	0.716074	0.358037	+	0.933707i	$0.383446\pi$
$942$	2.96068	0.0964642
$943$	−6.09722	−0.198553
$944$	−0.436665	−0.0142122
$945$	16.5233	0.537502
$946$	9.29786	0.302300
$947$	13.7835	0.447904	0.223952	−	0.974600i	$-0.428104\pi$
$947$	13.7835	0.447904	0.223952	+	0.974600i	$0.428104\pi$
$948$	8.48262	0.275503
$949$	7.08763	0.230074
$950$	−20.2951	−0.658461
$951$	29.5737	0.958992
$952$	11.2026	0.363078
$953$	17.3360	0.561568	0.280784	−	0.959771i	$-0.409406\pi$
$953$	17.3360	0.561568	0.280784	+	0.959771i	$0.409406\pi$
$954$	1.28909	0.0417359
$955$	0.943512	0.0305313
$956$	−11.7803	−0.381003
$957$	11.4028	0.368599
$958$	−37.6259	−1.21564
$959$	7.89134	0.254825
$960$	−1.29392	−0.0417612
$961$	45.4292	1.46546
$962$	2.99186	0.0964615
$963$	4.50626	0.145212
$964$	0.115681	0.00372585
$965$	−0.563265	−0.0181322
$966$	2.33531	0.0751375
$967$	−41.0432	−1.31986	−0.659930	−	0.751327i	$-0.729414\pi$
$967$	−41.0432	−1.31986	−0.659930	+	0.751327i	$0.729414\pi$
$968$	9.31898	0.299523
$969$	−27.6298	−0.887597
$970$	7.33705	0.235579
$971$	−21.5678	−0.692144	−0.346072	−	0.938208i	$-0.612485\pi$
$971$	−21.5678	−0.692144	−0.346072	+	0.938208i	$0.612485\pi$
$972$	−16.1496	−0.517997
$973$	51.4611	1.64977
$974$	−38.7739	−1.24240
$975$	−1.54246	−0.0493981
$976$	−2.24866	−0.0719777
$977$	15.2171	0.486837	0.243419	−	0.969921i	$-0.421731\pi$
$977$	15.2171	0.486837	0.243419	+	0.969921i	$0.421731\pi$
$978$	−10.8530	−0.347039
$979$	9.94638	0.317888
$980$	−1.08473	−0.0346504
$981$	−20.5860	−0.657260
$982$	8.16329	0.260501
$983$	4.11398	0.131215	0.0656077	−	0.997845i	$-0.479101\pi$
$983$	4.11398	0.131215	0.0656077	+	0.997845i	$0.479101\pi$
$984$	−5.71173	−0.182083
$985$	−9.93138	−0.316440
$986$	42.1888	1.34357
$987$	−16.2980	−0.518772
$988$	3.49502	0.111192
$989$	7.17129	0.228034
$990$	−3.80099	−0.120803
$991$	8.21859	0.261072	0.130536	−	0.991444i	$-0.458330\pi$
$991$	8.21859	0.261072	0.130536	+	0.991444i	$0.458330\pi$
$992$	−8.74238	−0.277571
$993$	−14.7984	−0.469612
$994$	−9.15213	−0.290288
$995$	4.96523	0.157408
$996$	6.89533	0.218487
$997$	−1.29169	−0.0409083	−0.0204541	−	0.999791i	$-0.506511\pi$
$997$	−1.29169	−0.0409083	−0.0204541	+	0.999791i	$0.506511\pi$
$998$	32.2183	1.01985
$999$	26.9611	0.853011

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.10	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.10	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.936776 q^{3} +1.00000 q^{4} +1.38125 q^{5} +0.936776 q^{6} +2.49293 q^{7} -1.00000 q^{8} -2.12245 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.936776 q^{3} +1.00000 q^{4} +1.38125 q^{5} +0.936776 q^{6} +2.49293 q^{7} -1.00000 q^{8} -2.12245 q^{9} -1.38125 q^{10} -1.29654 q^{11} -0.936776 q^{12} -0.532498 q^{13} -2.49293 q^{14} -1.29392 q^{15} +1.00000 q^{16} -4.49376 q^{17} +2.12245 q^{18} -6.56345 q^{19} +1.38125 q^{20} -2.33531 q^{21} +1.29654 q^{22} +1.00000 q^{23} +0.936776 q^{24} -3.09214 q^{25} +0.532498 q^{26} +4.79859 q^{27} +2.49293 q^{28} +9.38832 q^{29} +1.29392 q^{30} +8.74238 q^{31} -1.00000 q^{32} +1.21457 q^{33} +4.49376 q^{34} +3.44336 q^{35} -2.12245 q^{36} +5.61854 q^{37} +6.56345 q^{38} +0.498831 q^{39} -1.38125 q^{40} -6.09722 q^{41} +2.33531 q^{42} +7.17129 q^{43} -1.29654 q^{44} -2.93164 q^{45} -1.00000 q^{46} +6.97895 q^{47} -0.936776 q^{48} -0.785322 q^{49} +3.09214 q^{50} +4.20964 q^{51} -0.532498 q^{52} +0.607361 q^{53} -4.79859 q^{54} -1.79085 q^{55} -2.49293 q^{56} +6.14849 q^{57} -9.38832 q^{58} -0.436665 q^{59} -1.29392 q^{60} -2.24866 q^{61} -8.74238 q^{62} -5.29111 q^{63} +1.00000 q^{64} -0.735514 q^{65} -1.21457 q^{66} -8.74609 q^{67} -4.49376 q^{68} -0.936776 q^{69} -3.44336 q^{70} +3.67124 q^{71} +2.12245 q^{72} -13.3102 q^{73} -5.61854 q^{74} +2.89664 q^{75} -6.56345 q^{76} -3.23218 q^{77} -0.498831 q^{78} -9.05511 q^{79} +1.38125 q^{80} +1.87215 q^{81} +6.09722 q^{82} -7.36070 q^{83} -2.33531 q^{84} -6.20701 q^{85} -7.17129 q^{86} -8.79476 q^{87} +1.29654 q^{88} -7.67148 q^{89} +2.93164 q^{90} -1.32748 q^{91} +1.00000 q^{92} -8.18965 q^{93} -6.97895 q^{94} -9.06579 q^{95} +0.936776 q^{96} -5.31188 q^{97} +0.785322 q^{98} +2.75184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 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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