LMFDB - Embedded newform 6026.2.a.i.1.3

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			1.3
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.94225 q^{3} +1.00000 q^{4} +2.28313 q^{5} +2.94225 q^{6} -4.71427 q^{7} -1.00000 q^{8} +5.65684 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.94225 q^{3} +1.00000 q^{4} +2.28313 q^{5} +2.94225 q^{6} -4.71427 q^{7} -1.00000 q^{8} +5.65684 q^{9} -2.28313 q^{10} +1.43615 q^{11} -2.94225 q^{12} +1.73070 q^{13} +4.71427 q^{14} -6.71755 q^{15} +1.00000 q^{16} +7.47107 q^{17} -5.65684 q^{18} -7.14393 q^{19} +2.28313 q^{20} +13.8706 q^{21} -1.43615 q^{22} +1.00000 q^{23} +2.94225 q^{24} +0.212702 q^{25} -1.73070 q^{26} -7.81709 q^{27} -4.71427 q^{28} -5.24580 q^{29} +6.71755 q^{30} +3.25473 q^{31} -1.00000 q^{32} -4.22552 q^{33} -7.47107 q^{34} -10.7633 q^{35} +5.65684 q^{36} -6.14760 q^{37} +7.14393 q^{38} -5.09215 q^{39} -2.28313 q^{40} -9.37564 q^{41} -13.8706 q^{42} +7.90519 q^{43} +1.43615 q^{44} +12.9153 q^{45} -1.00000 q^{46} -0.303773 q^{47} -2.94225 q^{48} +15.2244 q^{49} -0.212702 q^{50} -21.9818 q^{51} +1.73070 q^{52} +9.05835 q^{53} +7.81709 q^{54} +3.27893 q^{55} +4.71427 q^{56} +21.0192 q^{57} +5.24580 q^{58} -1.29960 q^{59} -6.71755 q^{60} -5.05350 q^{61} -3.25473 q^{62} -26.6679 q^{63} +1.00000 q^{64} +3.95141 q^{65} +4.22552 q^{66} -5.76921 q^{67} +7.47107 q^{68} -2.94225 q^{69} +10.7633 q^{70} -5.45129 q^{71} -5.65684 q^{72} +5.77775 q^{73} +6.14760 q^{74} -0.625821 q^{75} -7.14393 q^{76} -6.77042 q^{77} +5.09215 q^{78} +10.7178 q^{79} +2.28313 q^{80} +6.02932 q^{81} +9.37564 q^{82} -10.2866 q^{83} +13.8706 q^{84} +17.0575 q^{85} -7.90519 q^{86} +15.4344 q^{87} -1.43615 q^{88} +2.27214 q^{89} -12.9153 q^{90} -8.15898 q^{91} +1.00000 q^{92} -9.57622 q^{93} +0.303773 q^{94} -16.3105 q^{95} +2.94225 q^{96} +18.1969 q^{97} -15.2244 q^{98} +8.12409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.94225	−1.69871	−0.849355	−	0.527823i	$-0.823009\pi$
$3$	−2.94225	−1.69871	−0.849355	+	0.527823i	$0.823009\pi$
$4$	1.00000	0.500000
$5$	2.28313	1.02105	0.510524	−	0.859863i	$-0.329451\pi$
$5$	2.28313	1.02105	0.510524	+	0.859863i	$0.329451\pi$
$6$	2.94225	1.20117
$7$	−4.71427	−1.78183	−0.890914	−	0.454172i	$-0.849935\pi$
$7$	−4.71427	−1.78183	−0.890914	+	0.454172i	$0.849935\pi$
$8$	−1.00000	−0.353553
$9$	5.65684	1.88561
$10$	−2.28313	−0.721990
$11$	1.43615	0.433017	0.216508	−	0.976281i	$-0.430533\pi$
$11$	1.43615	0.433017	0.216508	+	0.976281i	$0.430533\pi$
$12$	−2.94225	−0.849355
$13$	1.73070	0.480009	0.240005	−	0.970772i	$-0.422851\pi$
$13$	1.73070	0.480009	0.240005	+	0.970772i	$0.422851\pi$
$14$	4.71427	1.25994
$15$	−6.71755	−1.73446
$16$	1.00000	0.250000
$17$	7.47107	1.81200	0.906001	−	0.423276i	$-0.139120\pi$
$17$	7.47107	1.81200	0.906001	+	0.423276i	$0.139120\pi$
$18$	−5.65684	−1.33333
$19$	−7.14393	−1.63893	−0.819465	−	0.573129i	$-0.805729\pi$
$19$	−7.14393	−1.63893	−0.819465	+	0.573129i	$0.805729\pi$
$20$	2.28313	0.510524
$21$	13.8706	3.02681
$22$	−1.43615	−0.306189
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.94225	0.600584
$25$	0.212702	0.0425403
$26$	−1.73070	−0.339418
$27$	−7.81709	−1.50440
$28$	−4.71427	−0.890914
$29$	−5.24580	−0.974120	−0.487060	−	0.873369i	$-0.661931\pi$
$29$	−5.24580	−0.974120	−0.487060	+	0.873369i	$0.661931\pi$
$30$	6.71755	1.22645
$31$	3.25473	0.584566	0.292283	−	0.956332i	$-0.405585\pi$
$31$	3.25473	0.584566	0.292283	+	0.956332i	$0.405585\pi$
$32$	−1.00000	−0.176777
$33$	−4.22552	−0.735569
$34$	−7.47107	−1.28128
$35$	−10.7633	−1.81933
$36$	5.65684	0.942807
$37$	−6.14760	−1.01066	−0.505330	−	0.862926i	$-0.668629\pi$
$37$	−6.14760	−1.01066	−0.505330	+	0.862926i	$0.668629\pi$
$38$	7.14393	1.15890
$39$	−5.09215	−0.815396
$40$	−2.28313	−0.360995
$41$	−9.37564	−1.46423	−0.732114	−	0.681182i	$-0.761466\pi$
$41$	−9.37564	−1.46423	−0.732114	+	0.681182i	$0.761466\pi$
$42$	−13.8706	−2.14028
$43$	7.90519	1.20553	0.602765	−	0.797919i	$-0.294066\pi$
$43$	7.90519	1.20553	0.602765	+	0.797919i	$0.294066\pi$
$44$	1.43615	0.216508
$45$	12.9153	1.92530
$46$	−1.00000	−0.147442
$47$	−0.303773	−0.0443099	−0.0221550	−	0.999755i	$-0.507053\pi$
$47$	−0.303773	−0.0443099	−0.0221550	+	0.999755i	$0.507053\pi$
$48$	−2.94225	−0.424677
$49$	15.2244	2.17491
$50$	−0.212702	−0.0300805
$51$	−21.9818	−3.07806
$52$	1.73070	0.240005
$53$	9.05835	1.24426	0.622130	−	0.782914i	$-0.286268\pi$
$53$	9.05835	1.24426	0.622130	+	0.782914i	$0.286268\pi$
$54$	7.81709	1.06377
$55$	3.27893	0.442131
$56$	4.71427	0.629971
$57$	21.0192	2.78407
$58$	5.24580	0.688807
$59$	−1.29960	−0.169194	−0.0845968	−	0.996415i	$-0.526960\pi$
$59$	−1.29960	−0.169194	−0.0845968	+	0.996415i	$0.526960\pi$
$60$	−6.71755	−0.867232
$61$	−5.05350	−0.647035	−0.323517	−	0.946222i	$-0.604865\pi$
$61$	−5.05350	−0.647035	−0.323517	+	0.946222i	$0.604865\pi$
$62$	−3.25473	−0.413351
$63$	−26.6679	−3.35984
$64$	1.00000	0.125000
$65$	3.95141	0.490113
$66$	4.22552	0.520126
$67$	−5.76921	−0.704821	−0.352411	−	0.935846i	$-0.614638\pi$
$67$	−5.76921	−0.704821	−0.352411	+	0.935846i	$0.614638\pi$
$68$	7.47107	0.906001
$69$	−2.94225	−0.354205
$70$	10.7633	1.28646
$71$	−5.45129	−0.646950	−0.323475	−	0.946237i	$-0.604851\pi$
$71$	−5.45129	−0.646950	−0.323475	+	0.946237i	$0.604851\pi$
$72$	−5.65684	−0.666665
$73$	5.77775	0.676235	0.338118	−	0.941104i	$-0.390210\pi$
$73$	5.77775	0.676235	0.338118	+	0.941104i	$0.390210\pi$
$74$	6.14760	0.714644
$75$	−0.625821	−0.0722636
$76$	−7.14393	−0.819465
$77$	−6.77042	−0.771561
$78$	5.09215	0.576572
$79$	10.7178	1.20584	0.602921	−	0.797801i	$-0.294003\pi$
$79$	10.7178	1.20584	0.602921	+	0.797801i	$0.294003\pi$
$80$	2.28313	0.255262
$81$	6.02932	0.669924
$82$	9.37564	1.03537
$83$	−10.2866	−1.12910	−0.564549	−	0.825399i	$-0.690950\pi$
$83$	−10.2866	−1.12910	−0.564549	+	0.825399i	$0.690950\pi$
$84$	13.8706	1.51340
$85$	17.0575	1.85014
$86$	−7.90519	−0.852439
$87$	15.4344	1.65475
$88$	−1.43615	−0.153095
$89$	2.27214	0.240847	0.120423	−	0.992723i	$-0.461575\pi$
$89$	2.27214	0.240847	0.120423	+	0.992723i	$0.461575\pi$
$90$	−12.9153	−1.36139
$91$	−8.15898	−0.855294
$92$	1.00000	0.104257
$93$	−9.57622	−0.993008
$94$	0.303773	0.0313318
$95$	−16.3105	−1.67343
$96$	2.94225	0.300292
$97$	18.1969	1.84761	0.923807	−	0.382858i	$-0.125060\pi$
$97$	18.1969	1.84761	0.923807	+	0.382858i	$0.125060\pi$
$98$	−15.2244	−1.53789
$99$	8.12409	0.816502
$100$	0.212702	0.0212702
$101$	−6.53995	−0.650749	−0.325375	−	0.945585i	$-0.605490\pi$
$101$	−6.53995	−0.650749	−0.325375	+	0.945585i	$0.605490\pi$
$102$	21.9818	2.17652
$103$	6.89029	0.678921	0.339460	−	0.940620i	$-0.389756\pi$
$103$	6.89029	0.678921	0.339460	+	0.940620i	$0.389756\pi$
$104$	−1.73070	−0.169709
$105$	31.6684	3.09052
$106$	−9.05835	−0.879825
$107$	−2.55452	−0.246954	−0.123477	−	0.992347i	$-0.539405\pi$
$107$	−2.55452	−0.246954	−0.123477	+	0.992347i	$0.539405\pi$
$108$	−7.81709	−0.752200
$109$	−5.12564	−0.490947	−0.245473	−	0.969403i	$-0.578943\pi$
$109$	−5.12564	−0.490947	−0.245473	+	0.969403i	$0.578943\pi$
$110$	−3.27893	−0.312634
$111$	18.0878	1.71682
$112$	−4.71427	−0.445457
$113$	8.61364	0.810303	0.405151	−	0.914250i	$-0.367219\pi$
$113$	8.61364	0.810303	0.405151	+	0.914250i	$0.367219\pi$
$114$	−21.0192	−1.96863
$115$	2.28313	0.212903
$116$	−5.24580	−0.487060
$117$	9.79028	0.905112
$118$	1.29960	0.119638
$119$	−35.2207	−3.22868
$120$	6.71755	0.613226
$121$	−8.93746	−0.812497
$122$	5.05350	0.457523
$123$	27.5855	2.48730
$124$	3.25473	0.292283
$125$	−10.9300	−0.977613
$126$	26.6679	2.37576
$127$	19.3539	1.71738	0.858692	−	0.512491i	$-0.171277\pi$
$127$	19.3539	1.71738	0.858692	+	0.512491i	$0.171277\pi$
$128$	−1.00000	−0.0883883
$129$	−23.2591	−2.04785
$130$	−3.95141	−0.346562
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−4.22552	−0.367785
$133$	33.6784	2.92029
$134$	5.76921	0.498384
$135$	−17.8475	−1.53607
$136$	−7.47107	−0.640639
$137$	−11.4988	−0.982411	−0.491205	−	0.871044i	$-0.663444\pi$
$137$	−11.4988	−0.982411	−0.491205	+	0.871044i	$0.663444\pi$
$138$	2.94225	0.250461
$139$	−3.08554	−0.261712	−0.130856	−	0.991401i	$-0.541773\pi$
$139$	−3.08554	−0.261712	−0.130856	+	0.991401i	$0.541773\pi$
$140$	−10.7633	−0.909667
$141$	0.893778	0.0752697
$142$	5.45129	0.457462
$143$	2.48555	0.207852
$144$	5.65684	0.471403
$145$	−11.9769	−0.994624
$146$	−5.77775	−0.478170
$147$	−44.7940	−3.69454
$148$	−6.14760	−0.505330
$149$	1.21139	0.0992412	0.0496206	−	0.998768i	$-0.484199\pi$
$149$	1.21139	0.0992412	0.0496206	+	0.998768i	$0.484199\pi$
$150$	0.625821	0.0510981
$151$	9.36316	0.761963	0.380982	−	0.924583i	$-0.375586\pi$
$151$	9.36316	0.761963	0.380982	+	0.924583i	$0.375586\pi$
$152$	7.14393	0.579449
$153$	42.2627	3.41673
$154$	6.77042	0.545576
$155$	7.43098	0.596870
$156$	−5.09215	−0.407698
$157$	10.8119	0.862884	0.431442	−	0.902141i	$-0.358005\pi$
$157$	10.8119	0.862884	0.431442	+	0.902141i	$0.358005\pi$
$158$	−10.7178	−0.852659
$159$	−26.6519	−2.11364
$160$	−2.28313	−0.180498
$161$	−4.71427	−0.371537
$162$	−6.02932	−0.473708
$163$	−6.25972	−0.490299	−0.245150	−	0.969485i	$-0.578837\pi$
$163$	−6.25972	−0.490299	−0.245150	+	0.969485i	$0.578837\pi$
$164$	−9.37564	−0.732114
$165$	−9.64744	−0.751052
$166$	10.2866	0.798393
$167$	4.64774	0.359653	0.179827	−	0.983698i	$-0.442446\pi$
$167$	4.64774	0.359653	0.179827	+	0.983698i	$0.442446\pi$
$168$	−13.8706	−1.07014
$169$	−10.0047	−0.769591
$170$	−17.0575	−1.30825
$171$	−40.4121	−3.09039
$172$	7.90519	0.602765
$173$	−10.1928	−0.774942	−0.387471	−	0.921882i	$-0.626651\pi$
$173$	−10.1928	−0.774942	−0.387471	+	0.921882i	$0.626651\pi$
$174$	−15.4344	−1.17008
$175$	−1.00273	−0.0757995
$176$	1.43615	0.108254
$177$	3.82375	0.287411
$178$	−2.27214	−0.170304
$179$	8.23191	0.615282	0.307641	−	0.951502i	$-0.400460\pi$
$179$	8.23191	0.615282	0.307641	+	0.951502i	$0.400460\pi$
$180$	12.9153	0.962651
$181$	26.6264	1.97913	0.989564	−	0.144095i	$-0.0460269\pi$
$181$	26.6264	1.97913	0.989564	+	0.144095i	$0.0460269\pi$
$182$	8.15898	0.604784
$183$	14.8687	1.09912
$184$	−1.00000	−0.0737210
$185$	−14.0358	−1.03193
$186$	9.57622	0.702163
$187$	10.7296	0.784627
$188$	−0.303773	−0.0221550
$189$	36.8519	2.68058
$190$	16.3105	1.18329
$191$	−12.0127	−0.869211	−0.434606	−	0.900621i	$-0.643112\pi$
$191$	−12.0127	−0.869211	−0.434606	+	0.900621i	$0.643112\pi$
$192$	−2.94225	−0.212339
$193$	−3.64531	−0.262395	−0.131198	−	0.991356i	$-0.541882\pi$
$193$	−3.64531	−0.262395	−0.131198	+	0.991356i	$0.541882\pi$
$194$	−18.1969	−1.30646
$195$	−11.6261	−0.832559
$196$	15.2244	1.08746
$197$	5.05009	0.359804	0.179902	−	0.983685i	$-0.442422\pi$
$197$	5.05009	0.359804	0.179902	+	0.983685i	$0.442422\pi$
$198$	−8.12409	−0.577354
$199$	−7.59628	−0.538486	−0.269243	−	0.963072i	$-0.586773\pi$
$199$	−7.59628	−0.538486	−0.269243	+	0.963072i	$0.586773\pi$
$200$	−0.212702	−0.0150403
$201$	16.9745	1.19729
$202$	6.53995	0.460149
$203$	24.7301	1.73571
$204$	−21.9818	−1.53903
$205$	−21.4058	−1.49505
$206$	−6.89029	−0.480070
$207$	5.65684	0.393178
$208$	1.73070	0.120002
$209$	−10.2598	−0.709684
$210$	−31.6684	−2.18533
$211$	−20.3582	−1.40152	−0.700760	−	0.713397i	$-0.747156\pi$
$211$	−20.3582	−1.40152	−0.700760	+	0.713397i	$0.747156\pi$
$212$	9.05835	0.622130
$213$	16.0391	1.09898
$214$	2.55452	0.174623
$215$	18.0486	1.23091
$216$	7.81709	0.531886
$217$	−15.3437	−1.04160
$218$	5.12564	0.347152
$219$	−16.9996	−1.14873
$220$	3.27893	0.221066
$221$	12.9302	0.869777
$222$	−18.0878	−1.21397
$223$	−23.8002	−1.59378	−0.796890	−	0.604125i	$-0.793523\pi$
$223$	−23.8002	−1.59378	−0.796890	+	0.604125i	$0.793523\pi$
$224$	4.71427	0.314986
$225$	1.20322	0.0802146
$226$	−8.61364	−0.572971
$227$	24.2069	1.60667	0.803334	−	0.595529i	$-0.203057\pi$
$227$	24.2069	1.60667	0.803334	+	0.595529i	$0.203057\pi$
$228$	21.0192	1.39203
$229$	−18.0713	−1.19418	−0.597091	−	0.802174i	$-0.703677\pi$
$229$	−18.0713	−1.19418	−0.597091	+	0.802174i	$0.703677\pi$
$230$	−2.28313	−0.150545
$231$	19.9203	1.31066
$232$	5.24580	0.344403
$233$	22.3843	1.46645	0.733224	−	0.679987i	$-0.238015\pi$
$233$	22.3843	1.46645	0.733224	+	0.679987i	$0.238015\pi$
$234$	−9.79028	−0.640011
$235$	−0.693556	−0.0452426
$236$	−1.29960	−0.0845968
$237$	−31.5343	−2.04837
$238$	35.2207	2.28302
$239$	21.1116	1.36560	0.682799	−	0.730606i	$-0.260762\pi$
$239$	21.1116	1.36560	0.682799	+	0.730606i	$0.260762\pi$
$240$	−6.71755	−0.433616
$241$	−19.4969	−1.25591	−0.627954	−	0.778251i	$-0.716107\pi$
$241$	−19.4969	−1.25591	−0.627954	+	0.778251i	$0.716107\pi$
$242$	8.93746	0.574522
$243$	5.71150	0.366393
$244$	−5.05350	−0.323517
$245$	34.7593	2.22069
$246$	−27.5855	−1.75879
$247$	−12.3640	−0.786701
$248$	−3.25473	−0.206675
$249$	30.2657	1.91801
$250$	10.9300	0.691277
$251$	7.90434	0.498917	0.249459	−	0.968385i	$-0.419747\pi$
$251$	7.90434	0.498917	0.249459	+	0.968385i	$0.419747\pi$
$252$	−26.6679	−1.67992
$253$	1.43615	0.0902902
$254$	−19.3539	−1.21437
$255$	−50.1873	−3.14285
$256$	1.00000	0.0625000
$257$	31.1940	1.94583	0.972913	−	0.231172i	$-0.0742559\pi$
$257$	31.1940	1.94583	0.972913	+	0.231172i	$0.0742559\pi$
$258$	23.2591	1.44805
$259$	28.9815	1.80082
$260$	3.95141	0.245056
$261$	−29.6746	−1.83681
$262$	−1.00000	−0.0617802
$263$	−14.9055	−0.919114	−0.459557	−	0.888148i	$-0.651992\pi$
$263$	−14.9055	−0.919114	−0.459557	+	0.888148i	$0.651992\pi$
$264$	4.22552	0.260063
$265$	20.6814	1.27045
$266$	−33.6784	−2.06496
$267$	−6.68522	−0.409129
$268$	−5.76921	−0.352411
$269$	19.5124	1.18969	0.594847	−	0.803839i	$-0.297212\pi$
$269$	19.5124	1.18969	0.594847	+	0.803839i	$0.297212\pi$
$270$	17.8475	1.08616
$271$	6.79759	0.412924	0.206462	−	0.978455i	$-0.433805\pi$
$271$	6.79759	0.412924	0.206462	+	0.978455i	$0.433805\pi$
$272$	7.47107	0.453000
$273$	24.0058	1.45290
$274$	11.4988	0.694669
$275$	0.305472	0.0184207
$276$	−2.94225	−0.177103
$277$	7.31058	0.439250	0.219625	−	0.975584i	$-0.429517\pi$
$277$	7.31058	0.439250	0.219625	+	0.975584i	$0.429517\pi$
$278$	3.08554	0.185058
$279$	18.4115	1.10227
$280$	10.7633	0.643231
$281$	−6.80311	−0.405839	−0.202920	−	0.979195i	$-0.565043\pi$
$281$	−6.80311	−0.405839	−0.202920	+	0.979195i	$0.565043\pi$
$282$	−0.893778	−0.0532237
$283$	3.07532	0.182809	0.0914044	−	0.995814i	$-0.470864\pi$
$283$	3.07532	0.182809	0.0914044	+	0.995814i	$0.470864\pi$
$284$	−5.45129	−0.323475
$285$	47.9897	2.84267
$286$	−2.48555	−0.146974
$287$	44.1993	2.60900
$288$	−5.65684	−0.333332
$289$	38.8170	2.28335
$290$	11.9769	0.703305
$291$	−53.5398	−3.13856
$292$	5.77775	0.338118
$293$	−27.0749	−1.58173	−0.790867	−	0.611988i	$-0.790370\pi$
$293$	−27.0749	−1.58173	−0.790867	+	0.611988i	$0.790370\pi$
$294$	44.7940	2.61244
$295$	−2.96716	−0.172755
$296$	6.14760	0.357322
$297$	−11.2265	−0.651430
$298$	−1.21139	−0.0701741
$299$	1.73070	0.100089
$300$	−0.625821	−0.0361318
$301$	−37.2672	−2.14805
$302$	−9.36316	−0.538789
$303$	19.2422	1.10543
$304$	−7.14393	−0.409732
$305$	−11.5378	−0.660654
$306$	−42.2627	−2.41600
$307$	19.7213	1.12555	0.562776	−	0.826609i	$-0.309733\pi$
$307$	19.7213	1.12555	0.562776	+	0.826609i	$0.309733\pi$
$308$	−6.77042	−0.385781
$309$	−20.2730	−1.15329
$310$	−7.43098	−0.422051
$311$	−14.3327	−0.812733	−0.406367	−	0.913710i	$-0.633204\pi$
$311$	−14.3327	−0.812733	−0.406367	+	0.913710i	$0.633204\pi$
$312$	5.09215	0.288286
$313$	−21.3038	−1.20416	−0.602082	−	0.798434i	$-0.705662\pi$
$313$	−21.3038	−1.20416	−0.602082	+	0.798434i	$0.705662\pi$
$314$	−10.8119	−0.610151
$315$	−60.8864	−3.43056
$316$	10.7178	0.602921
$317$	−8.14817	−0.457647	−0.228823	−	0.973468i	$-0.573488\pi$
$317$	−8.14817	−0.457647	−0.228823	+	0.973468i	$0.573488\pi$
$318$	26.6519	1.49457
$319$	−7.53377	−0.421810
$320$	2.28313	0.127631
$321$	7.51603	0.419504
$322$	4.71427	0.262716
$323$	−53.3728	−2.96974
$324$	6.02932	0.334962
$325$	0.368122	0.0204197
$326$	6.25972	0.346694
$327$	15.0809	0.833976
$328$	9.37564	0.517683
$329$	1.43207	0.0789526
$330$	9.64744	0.531074
$331$	−13.9827	−0.768557	−0.384278	−	0.923217i	$-0.625550\pi$
$331$	−13.9827	−0.768557	−0.384278	+	0.923217i	$0.625550\pi$
$332$	−10.2866	−0.564549
$333$	−34.7760	−1.90571
$334$	−4.64774	−0.254313
$335$	−13.1719	−0.719657
$336$	13.8706	0.756702
$337$	22.2988	1.21469	0.607347	−	0.794437i	$-0.292234\pi$
$337$	22.2988	1.21469	0.607347	+	0.794437i	$0.292234\pi$
$338$	10.0047	0.544183
$339$	−25.3435	−1.37647
$340$	17.0575	0.925071
$341$	4.67429	0.253127
$342$	40.4121	2.18523
$343$	−38.7720	−2.09349
$344$	−7.90519	−0.426219
$345$	−6.71755	−0.361661
$346$	10.1928	0.547967
$347$	−29.8703	−1.60352	−0.801761	−	0.597645i	$-0.796103\pi$
$347$	−29.8703	−1.60352	−0.801761	+	0.597645i	$0.796103\pi$
$348$	15.4344	0.827373
$349$	−21.8531	−1.16977	−0.584884	−	0.811117i	$-0.698860\pi$
$349$	−21.8531	−1.16977	−0.584884	+	0.811117i	$0.698860\pi$
$350$	1.00273	0.0535984
$351$	−13.5290	−0.722125
$352$	−1.43615	−0.0765473
$353$	−9.64790	−0.513506	−0.256753	−	0.966477i	$-0.582653\pi$
$353$	−9.64790	−0.513506	−0.256753	+	0.966477i	$0.582653\pi$
$354$	−3.82375	−0.203230
$355$	−12.4460	−0.660567
$356$	2.27214	0.120423
$357$	103.628	5.48458
$358$	−8.23191	−0.435070
$359$	1.63180	0.0861233	0.0430617	−	0.999072i	$-0.486289\pi$
$359$	1.63180	0.0861233	0.0430617	+	0.999072i	$0.486289\pi$
$360$	−12.9153	−0.680697
$361$	32.0357	1.68609
$362$	−26.6264	−1.39945
$363$	26.2963	1.38020
$364$	−8.15898	−0.427647
$365$	13.1914	0.690469
$366$	−14.8687	−0.777198
$367$	−32.5145	−1.69725	−0.848623	−	0.528998i	$-0.822568\pi$
$367$	−32.5145	−1.69725	−0.848623	+	0.528998i	$0.822568\pi$
$368$	1.00000	0.0521286
$369$	−53.0365	−2.76097
$370$	14.0358	0.729686
$371$	−42.7035	−2.21706
$372$	−9.57622	−0.496504
$373$	−21.2621	−1.10091	−0.550455	−	0.834865i	$-0.685546\pi$
$373$	−21.2621	−1.10091	−0.550455	+	0.834865i	$0.685546\pi$
$374$	−10.7296	−0.554815
$375$	32.1589	1.66068
$376$	0.303773	0.0156659
$377$	−9.07888	−0.467586
$378$	−36.8519	−1.89546
$379$	−24.8326	−1.27556	−0.637781	−	0.770218i	$-0.720148\pi$
$379$	−24.8326	−1.27556	−0.637781	+	0.770218i	$0.720148\pi$
$380$	−16.3105	−0.836713
$381$	−56.9442	−2.91734
$382$	12.0127	0.614625
$383$	−8.38736	−0.428574	−0.214287	−	0.976771i	$-0.568743\pi$
$383$	−8.38736	−0.428574	−0.214287	+	0.976771i	$0.568743\pi$
$384$	2.94225	0.150146
$385$	−15.4578	−0.787802
$386$	3.64531	0.185542
$387$	44.7184	2.27316
$388$	18.1969	0.923807
$389$	−33.0039	−1.67336	−0.836682	−	0.547688i	$-0.815508\pi$
$389$	−33.0039	−1.67336	−0.836682	+	0.547688i	$0.815508\pi$
$390$	11.6261	0.588708
$391$	7.47107	0.377828
$392$	−15.2244	−0.768947
$393$	−2.94225	−0.148417
$394$	−5.05009	−0.254420
$395$	24.4701	1.23122
$396$	8.12409	0.408251
$397$	31.0067	1.55618	0.778092	−	0.628151i	$-0.216188\pi$
$397$	31.0067	1.55618	0.778092	+	0.628151i	$0.216188\pi$
$398$	7.59628	0.380767
$399$	−99.0904	−4.96073
$400$	0.212702	0.0106351
$401$	−9.59094	−0.478949	−0.239474	−	0.970903i	$-0.576975\pi$
$401$	−9.59094	−0.478949	−0.239474	+	0.970903i	$0.576975\pi$
$402$	−16.9745	−0.846609
$403$	5.63295	0.280597
$404$	−6.53995	−0.325375
$405$	13.7657	0.684025
$406$	−24.7301	−1.22734
$407$	−8.82890	−0.437632
$408$	21.9818	1.08826
$409$	−9.47826	−0.468670	−0.234335	−	0.972156i	$-0.575291\pi$
$409$	−9.47826	−0.468670	−0.234335	+	0.972156i	$0.575291\pi$
$410$	21.4058	1.05716
$411$	33.8324	1.66883
$412$	6.89029	0.339460
$413$	6.12667	0.301474
$414$	−5.65684	−0.278019
$415$	−23.4856	−1.15286
$416$	−1.73070	−0.0848544
$417$	9.07842	0.444572
$418$	10.2598	0.501822
$419$	6.38892	0.312119	0.156060	−	0.987748i	$-0.450121\pi$
$419$	6.38892	0.312119	0.156060	+	0.987748i	$0.450121\pi$
$420$	31.6684	1.54526
$421$	1.58840	0.0774139	0.0387069	−	0.999251i	$-0.487676\pi$
$421$	1.58840	0.0774139	0.0387069	+	0.999251i	$0.487676\pi$
$422$	20.3582	0.991024
$423$	−1.71840	−0.0835514
$424$	−9.05835	−0.439912
$425$	1.58911	0.0770831
$426$	−16.0391	−0.777096
$427$	23.8236	1.15290
$428$	−2.55452	−0.123477
$429$	−7.31311	−0.353080
$430$	−18.0486	−0.870381
$431$	−1.09420	−0.0527057	−0.0263528	−	0.999653i	$-0.508389\pi$
$431$	−1.09420	−0.0527057	−0.0263528	+	0.999653i	$0.508389\pi$
$432$	−7.81709	−0.376100
$433$	−14.6104	−0.702132	−0.351066	−	0.936351i	$-0.614181\pi$
$433$	−14.6104	−0.702132	−0.351066	+	0.936351i	$0.614181\pi$
$434$	15.3437	0.736520
$435$	35.2389	1.68958
$436$	−5.12564	−0.245473
$437$	−7.14393	−0.341740
$438$	16.9996	0.812272
$439$	−15.3855	−0.734311	−0.367155	−	0.930160i	$-0.619668\pi$
$439$	−15.3855	−0.734311	−0.367155	+	0.930160i	$0.619668\pi$
$440$	−3.27893	−0.156317
$441$	86.1219	4.10104
$442$	−12.9302	−0.615026
$443$	−26.9669	−1.28124	−0.640618	−	0.767860i	$-0.721322\pi$
$443$	−26.9669	−1.28124	−0.640618	+	0.767860i	$0.721322\pi$
$444$	18.0878	0.858408
$445$	5.18761	0.245916
$446$	23.8002	1.12697
$447$	−3.56422	−0.168582
$448$	−4.71427	−0.222729
$449$	9.18812	0.433614	0.216807	−	0.976214i	$-0.430436\pi$
$449$	9.18812	0.433614	0.216807	+	0.976214i	$0.430436\pi$
$450$	−1.20322	−0.0567203
$451$	−13.4649	−0.634035
$452$	8.61364	0.405151
$453$	−27.5488	−1.29435
$454$	−24.2069	−1.13609
$455$	−18.6281	−0.873297
$456$	−21.0192	−0.984316
$457$	7.14228	0.334102	0.167051	−	0.985948i	$-0.446576\pi$
$457$	7.14228	0.334102	0.167051	+	0.985948i	$0.446576\pi$
$458$	18.0713	0.844414
$459$	−58.4021	−2.72597
$460$	2.28313	0.106452
$461$	−17.9737	−0.837118	−0.418559	−	0.908190i	$-0.637465\pi$
$461$	−17.9737	−0.837118	−0.418559	+	0.908190i	$0.637465\pi$
$462$	−19.9203	−0.926775
$463$	−24.6083	−1.14365	−0.571823	−	0.820377i	$-0.693764\pi$
$463$	−24.6083	−1.14365	−0.571823	+	0.820377i	$0.693764\pi$
$464$	−5.24580	−0.243530
$465$	−21.8638	−1.01391
$466$	−22.3843	−1.03693
$467$	−37.8524	−1.75160	−0.875801	−	0.482673i	$-0.839666\pi$
$467$	−37.8524	−1.75160	−0.875801	+	0.482673i	$0.839666\pi$
$468$	9.79028	0.452556
$469$	27.1976	1.25587
$470$	0.693556	0.0319913
$471$	−31.8113	−1.46579
$472$	1.29960	0.0598190
$473$	11.3531	0.522015
$474$	31.5343	1.44842
$475$	−1.51952	−0.0697206
$476$	−35.2207	−1.61434
$477$	51.2416	2.34619
$478$	−21.1116	−0.965624
$479$	−19.1001	−0.872707	−0.436354	−	0.899775i	$-0.643730\pi$
$479$	−19.1001	−0.872707	−0.436354	+	0.899775i	$0.643730\pi$
$480$	6.71755	0.306613
$481$	−10.6396	−0.485126
$482$	19.4969	0.888061
$483$	13.8706	0.631133
$484$	−8.93746	−0.406248
$485$	41.5460	1.88650
$486$	−5.71150	−0.259079
$487$	−0.962350	−0.0436082	−0.0218041	−	0.999762i	$-0.506941\pi$
$487$	−0.962350	−0.0436082	−0.0218041	+	0.999762i	$0.506941\pi$
$488$	5.05350	0.228761
$489$	18.4177	0.832876
$490$	−34.7593	−1.57027
$491$	17.2832	0.779979	0.389990	−	0.920819i	$-0.372479\pi$
$491$	17.2832	0.779979	0.389990	+	0.920819i	$0.372479\pi$
$492$	27.5855	1.24365
$493$	−39.1917	−1.76511
$494$	12.3640	0.556282
$495$	18.5484	0.833688
$496$	3.25473	0.146142
$497$	25.6989	1.15275
$498$	−30.2657	−1.35624
$499$	−11.8894	−0.532242	−0.266121	−	0.963940i	$-0.585742\pi$
$499$	−11.8894	−0.532242	−0.266121	+	0.963940i	$0.585742\pi$
$500$	−10.9300	−0.488806
$501$	−13.6748	−0.610946
$502$	−7.90434	−0.352788
$503$	−1.02453	−0.0456816	−0.0228408	−	0.999739i	$-0.507271\pi$
$503$	−1.02453	−0.0456816	−0.0228408	+	0.999739i	$0.507271\pi$
$504$	26.6679	1.18788
$505$	−14.9316	−0.664447
$506$	−1.43615	−0.0638448
$507$	29.4363	1.30731
$508$	19.3539	0.858692
$509$	37.5337	1.66365	0.831827	−	0.555036i	$-0.187295\pi$
$509$	37.5337	1.66365	0.831827	+	0.555036i	$0.187295\pi$
$510$	50.1873	2.22233
$511$	−27.2379	−1.20493
$512$	−1.00000	−0.0441942
$513$	55.8447	2.46560
$514$	−31.1940	−1.37591
$515$	15.7315	0.693211
$516$	−23.2591	−1.02392
$517$	−0.436265	−0.0191869
$518$	−28.9815	−1.27337
$519$	29.9897	1.31640
$520$	−3.95141	−0.173281
$521$	−5.49704	−0.240830	−0.120415	−	0.992724i	$-0.538423\pi$
$521$	−5.49704	−0.240830	−0.120415	+	0.992724i	$0.538423\pi$
$522$	29.6746	1.29882
$523$	7.64410	0.334253	0.167126	−	0.985935i	$-0.446551\pi$
$523$	7.64410	0.334253	0.167126	+	0.985935i	$0.446551\pi$
$524$	1.00000	0.0436852
$525$	2.95029	0.128761
$526$	14.9055	0.649912
$527$	24.3163	1.05923
$528$	−4.22552	−0.183892
$529$	1.00000	0.0434783
$530$	−20.6814	−0.898344
$531$	−7.35163	−0.319034
$532$	33.6784	1.46015
$533$	−16.2264	−0.702843
$534$	6.68522	0.289298
$535$	−5.83230	−0.252152
$536$	5.76921	0.249192
$537$	−24.2204	−1.04519
$538$	−19.5124	−0.841241
$539$	21.8646	0.941773
$540$	−17.8475	−0.768033
$541$	3.03620	0.130536	0.0652682	−	0.997868i	$-0.479210\pi$
$541$	3.03620	0.130536	0.0652682	+	0.997868i	$0.479210\pi$
$542$	−6.79759	−0.291981
$543$	−78.3417	−3.36196
$544$	−7.47107	−0.320320
$545$	−11.7025	−0.501281
$546$	−24.0058	−1.02735
$547$	−3.59299	−0.153625	−0.0768126	−	0.997046i	$-0.524474\pi$
$547$	−3.59299	−0.153625	−0.0768126	+	0.997046i	$0.524474\pi$
$548$	−11.4988	−0.491205
$549$	−28.5869	−1.22006
$550$	−0.305472	−0.0130254
$551$	37.4756	1.59651
$552$	2.94225	0.125231
$553$	−50.5264	−2.14860
$554$	−7.31058	−0.310597
$555$	41.2968	1.75295
$556$	−3.08554	−0.130856
$557$	−39.0331	−1.65389	−0.826943	−	0.562286i	$-0.809922\pi$
$557$	−39.0331	−1.65389	−0.826943	+	0.562286i	$0.809922\pi$
$558$	−18.4115	−0.779419
$559$	13.6815	0.578666
$560$	−10.7633	−0.454833
$561$	−31.5692	−1.33285
$562$	6.80311	0.286972
$563$	−43.6217	−1.83844	−0.919218	−	0.393750i	$-0.871178\pi$
$563$	−43.6217	−1.83844	−0.919218	+	0.393750i	$0.871178\pi$
$564$	0.893778	0.0376348
$565$	19.6661	0.827359
$566$	−3.07532	−0.129265
$567$	−28.4239	−1.19369
$568$	5.45129	0.228731
$569$	−41.4391	−1.73722	−0.868609	−	0.495498i	$-0.834986\pi$
$569$	−41.4391	−1.73722	−0.868609	+	0.495498i	$0.834986\pi$
$570$	−47.9897	−2.01007
$571$	24.1265	1.00966	0.504832	−	0.863218i	$-0.331554\pi$
$571$	24.1265	1.00966	0.504832	+	0.863218i	$0.331554\pi$
$572$	2.48555	0.103926
$573$	35.3445	1.47654
$574$	−44.1993	−1.84484
$575$	0.212702	0.00887027
$576$	5.65684	0.235702
$577$	−47.2119	−1.96546	−0.982729	−	0.185049i	$-0.940756\pi$
$577$	−47.2119	−1.96546	−0.982729	+	0.185049i	$0.940756\pi$
$578$	−38.8170	−1.61457
$579$	10.7254	0.445734
$580$	−11.9769	−0.497312
$581$	48.4938	2.01186
$582$	53.5398	2.21930
$583$	13.0092	0.538785
$584$	−5.77775	−0.239085
$585$	22.3525	0.924163
$586$	27.0749	1.11846
$587$	−3.10269	−0.128062	−0.0640308	−	0.997948i	$-0.520396\pi$
$587$	−3.10269	−0.128062	−0.0640308	+	0.997948i	$0.520396\pi$
$588$	−44.7940	−1.84727
$589$	−23.2515	−0.958063
$590$	2.96716	0.122156
$591$	−14.8586	−0.611202
$592$	−6.14760	−0.252665
$593$	−40.1515	−1.64883	−0.824413	−	0.565988i	$-0.808495\pi$
$593$	−40.1515	−1.64883	−0.824413	+	0.565988i	$0.808495\pi$
$594$	11.2265	0.460631
$595$	−80.4136	−3.29664
$596$	1.21139	0.0496206
$597$	22.3501	0.914731
$598$	−1.73070	−0.0707735
$599$	46.8814	1.91552	0.957760	−	0.287568i	$-0.0928468\pi$
$599$	46.8814	1.91552	0.957760	+	0.287568i	$0.0928468\pi$
$600$	0.625821	0.0255490
$601$	35.0919	1.43143	0.715714	−	0.698394i	$-0.246102\pi$
$601$	35.0919	1.43143	0.715714	+	0.698394i	$0.246102\pi$
$602$	37.2672	1.51890
$603$	−32.6355	−1.32902
$604$	9.36316	0.380982
$605$	−20.4054	−0.829599
$606$	−19.2422	−0.781660
$607$	−24.8390	−1.00818	−0.504092	−	0.863650i	$-0.668173\pi$
$607$	−24.8390	−1.00818	−0.504092	+	0.863650i	$0.668173\pi$
$608$	7.14393	0.289725
$609$	−72.7622	−2.94847
$610$	11.5378	0.467153
$611$	−0.525740	−0.0212692
$612$	42.2627	1.70837
$613$	−39.3082	−1.58764	−0.793822	−	0.608150i	$-0.791912\pi$
$613$	−39.3082	−1.58764	−0.793822	+	0.608150i	$0.791912\pi$
$614$	−19.7213	−0.795886
$615$	62.9813	2.53965
$616$	6.77042	0.272788
$617$	−14.9204	−0.600673	−0.300337	−	0.953833i	$-0.597099\pi$
$617$	−14.9204	−0.600673	−0.300337	+	0.953833i	$0.597099\pi$
$618$	20.2730	0.815499
$619$	17.1311	0.688557	0.344278	−	0.938868i	$-0.388124\pi$
$619$	17.1311	0.688557	0.344278	+	0.938868i	$0.388124\pi$
$620$	7.43098	0.298435
$621$	−7.81709	−0.313689
$622$	14.3327	0.574689
$623$	−10.7115	−0.429148
$624$	−5.09215	−0.203849
$625$	−26.0183	−1.04073
$626$	21.3038	0.851472
$627$	30.1868	1.20555
$628$	10.8119	0.431442
$629$	−45.9292	−1.83132
$630$	60.8864	2.42577
$631$	−4.52986	−0.180331	−0.0901655	−	0.995927i	$-0.528740\pi$
$631$	−4.52986	−0.180331	−0.0901655	+	0.995927i	$0.528740\pi$
$632$	−10.7178	−0.426329
$633$	59.8991	2.38077
$634$	8.14817	0.323605
$635$	44.1877	1.75353
$636$	−26.6519	−1.05682
$637$	26.3488	1.04398
$638$	7.53377	0.298265
$639$	−30.8371	−1.21990
$640$	−2.28313	−0.0902488
$641$	0.237243	0.00937052	0.00468526	−	0.999989i	$-0.498509\pi$
$641$	0.237243	0.00937052	0.00468526	+	0.999989i	$0.498509\pi$
$642$	−7.51603	−0.296634
$643$	45.6389	1.79982	0.899912	−	0.436072i	$-0.143631\pi$
$643$	45.6389	1.79982	0.899912	+	0.436072i	$0.143631\pi$
$644$	−4.71427	−0.185768
$645$	−53.1035	−2.09095
$646$	53.3728	2.09993
$647$	13.8304	0.543729	0.271864	−	0.962336i	$-0.412360\pi$
$647$	13.8304	0.543729	0.271864	+	0.962336i	$0.412360\pi$
$648$	−6.02932	−0.236854
$649$	−1.86643	−0.0732636
$650$	−0.368122	−0.0144389
$651$	45.1449	1.76937
$652$	−6.25972	−0.245150
$653$	−22.4062	−0.876824	−0.438412	−	0.898774i	$-0.644459\pi$
$653$	−22.4062	−0.876824	−0.438412	+	0.898774i	$0.644459\pi$
$654$	−15.0809	−0.589710
$655$	2.28313	0.0892094
$656$	−9.37564	−0.366057
$657$	32.6838	1.27512
$658$	−1.43207	−0.0558280
$659$	−5.32384	−0.207387	−0.103694	−	0.994609i	$-0.533066\pi$
$659$	−5.32384	−0.207387	−0.103694	+	0.994609i	$0.533066\pi$
$660$	−9.64744	−0.375526
$661$	−7.92351	−0.308189	−0.154094	−	0.988056i	$-0.549246\pi$
$661$	−7.92351	−0.308189	−0.154094	+	0.988056i	$0.549246\pi$
$662$	13.9827	0.543452
$663$	−38.0438	−1.47750
$664$	10.2866	0.399197
$665$	76.8924	2.98176
$666$	34.7760	1.34754
$667$	−5.24580	−0.203118
$668$	4.64774	0.179827
$669$	70.0262	2.70737
$670$	13.1719	0.508874
$671$	−7.25761	−0.280177
$672$	−13.8706	−0.535069
$673$	−3.73612	−0.144017	−0.0720084	−	0.997404i	$-0.522941\pi$
$673$	−3.73612	−0.144017	−0.0720084	+	0.997404i	$0.522941\pi$
$674$	−22.2988	−0.858918
$675$	−1.66271	−0.0639976
$676$	−10.0047	−0.384796
$677$	−4.77921	−0.183680	−0.0918401	−	0.995774i	$-0.529275\pi$
$677$	−4.77921	−0.183680	−0.0918401	+	0.995774i	$0.529275\pi$
$678$	25.3435	0.973311
$679$	−85.7852	−3.29213
$680$	−17.0575	−0.654124
$681$	−71.2228	−2.72926
$682$	−4.67429	−0.178988
$683$	11.4538	0.438267	0.219133	−	0.975695i	$-0.429677\pi$
$683$	11.4538	0.438267	0.219133	+	0.975695i	$0.429677\pi$
$684$	−40.4121	−1.54519
$685$	−26.2533	−1.00309
$686$	38.7720	1.48032
$687$	53.1702	2.02857
$688$	7.90519	0.301383
$689$	15.6773	0.597256
$690$	6.71755	0.255733
$691$	−11.0261	−0.419454	−0.209727	−	0.977760i	$-0.567257\pi$
$691$	−11.0261	−0.419454	−0.209727	+	0.977760i	$0.567257\pi$
$692$	−10.1928	−0.387471
$693$	−38.2992	−1.45487
$694$	29.8703	1.13386
$695$	−7.04469	−0.267220
$696$	−15.4344	−0.585041
$697$	−70.0461	−2.65318
$698$	21.8531	0.827151
$699$	−65.8604	−2.49107
$700$	−1.00273	−0.0378998
$701$	−0.324924	−0.0122722	−0.00613610	−	0.999981i	$-0.501953\pi$
$701$	−0.324924	−0.0122722	−0.00613610	+	0.999981i	$0.501953\pi$
$702$	13.5290	0.510620
$703$	43.9180	1.65640
$704$	1.43615	0.0541271
$705$	2.04061	0.0768540
$706$	9.64790	0.363103
$707$	30.8311	1.15952
$708$	3.82375	0.143705
$709$	4.73783	0.177933	0.0889664	−	0.996035i	$-0.471644\pi$
$709$	4.73783	0.177933	0.0889664	+	0.996035i	$0.471644\pi$
$710$	12.4460	0.467091
$711$	60.6286	2.27375
$712$	−2.27214	−0.0851522
$713$	3.25473	0.121890
$714$	−103.628	−3.87819
$715$	5.67484	0.212227
$716$	8.23191	0.307641
$717$	−62.1158	−2.31976
$718$	−1.63180	−0.0608984
$719$	−29.0124	−1.08198	−0.540990	−	0.841029i	$-0.681951\pi$
$719$	−29.0124	−1.08198	−0.540990	+	0.841029i	$0.681951\pi$
$720$	12.9153	0.481326
$721$	−32.4827	−1.20972
$722$	−32.0357	−1.19225
$723$	57.3648	2.13342
$724$	26.6264	0.989564
$725$	−1.11579	−0.0414394
$726$	−26.2963	−0.975946
$727$	−5.24302	−0.194453	−0.0972263	−	0.995262i	$-0.530997\pi$
$727$	−5.24302	−0.194453	−0.0972263	+	0.995262i	$0.530997\pi$
$728$	8.15898	0.302392
$729$	−34.8926	−1.29232
$730$	−13.1914	−0.488235
$731$	59.0603	2.18442
$732$	14.8687	0.549562
$733$	−17.9141	−0.661672	−0.330836	−	0.943688i	$-0.607331\pi$
$733$	−17.9141	−0.661672	−0.330836	+	0.943688i	$0.607331\pi$
$734$	32.5145	1.20013
$735$	−102.271	−3.77231
$736$	−1.00000	−0.0368605
$737$	−8.28547	−0.305199
$738$	53.0365	1.95230
$739$	−34.1168	−1.25501	−0.627504	−	0.778614i	$-0.715923\pi$
$739$	−34.1168	−1.25501	−0.627504	+	0.778614i	$0.715923\pi$
$740$	−14.0358	−0.515966
$741$	36.3779	1.33638
$742$	42.7035	1.56770
$743$	−4.69768	−0.172341	−0.0861706	−	0.996280i	$-0.527463\pi$
$743$	−4.69768	−0.172341	−0.0861706	+	0.996280i	$0.527463\pi$
$744$	9.57622	0.351081
$745$	2.76577	0.101330
$746$	21.2621	0.778461
$747$	−58.1895	−2.12904
$748$	10.7296	0.392313
$749$	12.0427	0.440030
$750$	−32.1589	−1.17428
$751$	10.4145	0.380029	0.190014	−	0.981781i	$-0.439147\pi$
$751$	10.4145	0.380029	0.190014	+	0.981781i	$0.439147\pi$
$752$	−0.303773	−0.0110775
$753$	−23.2565	−0.847515
$754$	9.07888	0.330633
$755$	21.3774	0.778001
$756$	36.8519	1.34029
$757$	20.0173	0.727541	0.363770	−	0.931489i	$-0.381489\pi$
$757$	20.0173	0.727541	0.363770	+	0.931489i	$0.381489\pi$
$758$	24.8326	0.901959
$759$	−4.22552	−0.153377
$760$	16.3105	0.591646
$761$	−28.4692	−1.03201	−0.516004	−	0.856586i	$-0.672581\pi$
$761$	−28.4692	−1.03201	−0.516004	+	0.856586i	$0.672581\pi$
$762$	56.9442	2.06287
$763$	24.1637	0.874783
$764$	−12.0127	−0.434606
$765$	96.4914	3.48865
$766$	8.38736	0.303048
$767$	−2.24922	−0.0812144
$768$	−2.94225	−0.106169
$769$	−29.7125	−1.07146	−0.535731	−	0.844389i	$-0.679964\pi$
$769$	−29.7125	−1.07146	−0.535731	+	0.844389i	$0.679964\pi$
$770$	15.4578	0.557060
$771$	−91.7805	−3.30539
$772$	−3.64531	−0.131198
$773$	9.17020	0.329829	0.164915	−	0.986308i	$-0.447265\pi$
$773$	9.17020	0.329829	0.164915	+	0.986308i	$0.447265\pi$
$774$	−44.7184	−1.60737
$775$	0.692285	0.0248676
$776$	−18.1969	−0.653230
$777$	−85.2708	−3.05907
$778$	33.0039	1.18325
$779$	66.9789	2.39977
$780$	−11.6261	−0.416279
$781$	−7.82890	−0.280140
$782$	−7.47107	−0.267165
$783$	41.0068	1.46547
$784$	15.2244	0.543728
$785$	24.6850	0.881046
$786$	2.94225	0.104947
$787$	2.60447	0.0928393	0.0464197	−	0.998922i	$-0.485219\pi$
$787$	2.60447	0.0928393	0.0464197	+	0.998922i	$0.485219\pi$
$788$	5.05009	0.179902
$789$	43.8558	1.56131
$790$	−24.4701	−0.870606
$791$	−40.6071	−1.44382
$792$	−8.12409	−0.288677
$793$	−8.74608	−0.310583
$794$	−31.0067	−1.10039
$795$	−60.8499	−2.15813
$796$	−7.59628	−0.269243
$797$	−3.91991	−0.138850	−0.0694251	−	0.997587i	$-0.522116\pi$
$797$	−3.91991	−0.138850	−0.0694251	+	0.997587i	$0.522116\pi$
$798$	99.0904	3.50776
$799$	−2.26951	−0.0802896
$800$	−0.212702	−0.00752014
$801$	12.8532	0.454144
$802$	9.59094	0.338668
$803$	8.29774	0.292821
$804$	16.9745	0.598643
$805$	−10.7633	−0.379357
$806$	−5.63295	−0.198412
$807$	−57.4105	−2.02095
$808$	6.53995	0.230075
$809$	−27.7065	−0.974110	−0.487055	−	0.873371i	$-0.661929\pi$
$809$	−27.7065	−0.974110	−0.487055	+	0.873371i	$0.661929\pi$
$810$	−13.7657	−0.483679
$811$	7.00465	0.245967	0.122983	−	0.992409i	$-0.460754\pi$
$811$	7.00465	0.245967	0.122983	+	0.992409i	$0.460754\pi$
$812$	24.7301	0.867857
$813$	−20.0002	−0.701438
$814$	8.82890	0.309453
$815$	−14.2918	−0.500619
$816$	−21.9818	−0.769516
$817$	−56.4741	−1.97578
$818$	9.47826	0.331400
$819$	−46.1541	−1.61275
$820$	−21.4058	−0.747524
$821$	−34.7576	−1.21305	−0.606524	−	0.795065i	$-0.707437\pi$
$821$	−34.7576	−1.21305	−0.606524	+	0.795065i	$0.707437\pi$
$822$	−33.8324	−1.18004
$823$	−20.7040	−0.721695	−0.360847	−	0.932625i	$-0.617512\pi$
$823$	−20.7040	−0.721695	−0.360847	+	0.932625i	$0.617512\pi$
$824$	−6.89029	−0.240035
$825$	−0.898776	−0.0312914
$826$	−6.12667	−0.213174
$827$	10.7536	0.373939	0.186969	−	0.982366i	$-0.440134\pi$
$827$	10.7536	0.373939	0.186969	+	0.982366i	$0.440134\pi$
$828$	5.65684	0.196589
$829$	19.0991	0.663338	0.331669	−	0.943396i	$-0.392388\pi$
$829$	19.0991	0.663338	0.331669	+	0.943396i	$0.392388\pi$
$830$	23.4856	0.815199
$831$	−21.5096	−0.746158
$832$	1.73070	0.0600011
$833$	113.743	3.94094
$834$	−9.07842	−0.314360
$835$	10.6114	0.367223
$836$	−10.2598	−0.354842
$837$	−25.4425	−0.879421
$838$	−6.38892	−0.220702
$839$	37.9412	1.30987	0.654937	−	0.755683i	$-0.272695\pi$
$839$	37.9412	1.30987	0.654937	+	0.755683i	$0.272695\pi$
$840$	−31.6684	−1.09266
$841$	−1.48163	−0.0510907
$842$	−1.58840	−0.0547399
$843$	20.0165	0.689403
$844$	−20.3582	−0.700760
$845$	−22.8420	−0.785790
$846$	1.71840	0.0590797
$847$	42.1336	1.44773
$848$	9.05835	0.311065
$849$	−9.04836	−0.310539
$850$	−1.58911	−0.0545060
$851$	−6.14760	−0.210737
$852$	16.0391	0.549490
$853$	−6.26064	−0.214360	−0.107180	−	0.994240i	$-0.534182\pi$
$853$	−6.26064	−0.214360	−0.107180	+	0.994240i	$0.534182\pi$
$854$	−23.8236	−0.815227
$855$	−92.2662	−3.15544
$856$	2.55452	0.0873115
$857$	25.7589	0.879908	0.439954	−	0.898020i	$-0.354995\pi$
$857$	25.7589	0.879908	0.439954	+	0.898020i	$0.354995\pi$
$858$	7.31311	0.249665
$859$	11.6471	0.397394	0.198697	−	0.980061i	$-0.436329\pi$
$859$	11.6471	0.397394	0.198697	+	0.980061i	$0.436329\pi$
$860$	18.0486	0.615453
$861$	−130.045	−4.43194
$862$	1.09420	0.0372685
$863$	32.1383	1.09400	0.547000	−	0.837133i	$-0.315770\pi$
$863$	32.1383	1.09400	0.547000	+	0.837133i	$0.315770\pi$
$864$	7.81709	0.265943
$865$	−23.2715	−0.791253
$866$	14.6104	0.496482
$867$	−114.209	−3.87875
$868$	−15.3437	−0.520798
$869$	15.3923	0.522150
$870$	−35.2389	−1.19471
$871$	−9.98476	−0.338321
$872$	5.12564	0.173576
$873$	102.937	3.48389
$874$	7.14393	0.241647
$875$	51.5272	1.74194
$876$	−16.9996	−0.574363
$877$	26.6486	0.899860	0.449930	−	0.893064i	$-0.351449\pi$
$877$	26.6486	0.899860	0.449930	+	0.893064i	$0.351449\pi$
$878$	15.3855	0.519236
$879$	79.6612	2.68691
$880$	3.27893	0.110533
$881$	−12.8234	−0.432031	−0.216016	−	0.976390i	$-0.569306\pi$
$881$	−12.8234	−0.432031	−0.216016	+	0.976390i	$0.569306\pi$
$882$	−86.1219	−2.89988
$883$	26.2115	0.882087	0.441043	−	0.897486i	$-0.354609\pi$
$883$	26.2115	0.882087	0.441043	+	0.897486i	$0.354609\pi$
$884$	12.9302	0.434889
$885$	8.73013	0.293460
$886$	26.9669	0.905970
$887$	−16.2097	−0.544268	−0.272134	−	0.962259i	$-0.587729\pi$
$887$	−16.2097	−0.544268	−0.272134	+	0.962259i	$0.587729\pi$
$888$	−18.0878	−0.606986
$889$	−91.2398	−3.06008
$890$	−5.18761	−0.173889
$891$	8.65903	0.290088
$892$	−23.8002	−0.796890
$893$	2.17014	0.0726208
$894$	3.56422	0.119205
$895$	18.7946	0.628233
$896$	4.71427	0.157493
$897$	−5.09215	−0.170022
$898$	−9.18812	−0.306611
$899$	−17.0736	−0.569437
$900$	1.20322	0.0401073
$901$	67.6756	2.25460
$902$	13.4649	0.448331
$903$	109.650	3.64891
$904$	−8.61364	−0.286485
$905$	60.7917	2.02079
$906$	27.5488	0.915246
$907$	−33.3600	−1.10770	−0.553851	−	0.832616i	$-0.686842\pi$
$907$	−33.3600	−1.10770	−0.553851	+	0.832616i	$0.686842\pi$
$908$	24.2069	0.803334
$909$	−36.9955	−1.22706
$910$	18.6281	0.617514
$911$	−8.18479	−0.271174	−0.135587	−	0.990765i	$-0.543292\pi$
$911$	−8.18479	−0.271174	−0.135587	+	0.990765i	$0.543292\pi$
$912$	21.0192	0.696016
$913$	−14.7731	−0.488919
$914$	−7.14228	−0.236245
$915$	33.9472	1.12226
$916$	−18.0713	−0.597091
$917$	−4.71427	−0.155679
$918$	58.4021	1.92756
$919$	−2.69643	−0.0889470	−0.0444735	−	0.999011i	$-0.514161\pi$
$919$	−2.69643	−0.0889470	−0.0444735	+	0.999011i	$0.514161\pi$
$920$	−2.28313	−0.0752727
$921$	−58.0249	−1.91199
$922$	17.9737	0.591932
$923$	−9.43454	−0.310542
$924$	19.9203	0.655329
$925$	−1.30760	−0.0429938
$926$	24.6083	0.808680
$927$	38.9773	1.28018
$928$	5.24580	0.172202
$929$	−22.2282	−0.729282	−0.364641	−	0.931148i	$-0.618808\pi$
$929$	−22.2282	−0.729282	−0.364641	+	0.931148i	$0.618808\pi$
$930$	21.8638	0.716942
$931$	−108.762	−3.56453
$932$	22.3843	0.733224
$933$	42.1704	1.38060
$934$	37.8524	1.23857
$935$	24.4971	0.801142
$936$	−9.79028	−0.320005
$937$	−44.4880	−1.45336	−0.726681	−	0.686976i	$-0.758938\pi$
$937$	−44.4880	−1.45336	−0.726681	+	0.686976i	$0.758938\pi$
$938$	−27.1976	−0.888034
$939$	62.6812	2.04552
$940$	−0.693556	−0.0226213
$941$	24.8054	0.808634	0.404317	−	0.914619i	$-0.367509\pi$
$941$	24.8054	0.808634	0.404317	+	0.914619i	$0.367509\pi$
$942$	31.8113	1.03647
$943$	−9.37564	−0.305313
$944$	−1.29960	−0.0422984
$945$	84.1378	2.73700
$946$	−11.3531	−0.369120
$947$	40.9263	1.32993	0.664963	−	0.746877i	$-0.268447\pi$
$947$	40.9263	1.32993	0.664963	+	0.746877i	$0.268447\pi$
$948$	−31.5343	−1.02419
$949$	9.99955	0.324599
$950$	1.51952	0.0492999
$951$	23.9740	0.777409
$952$	35.2207	1.14151
$953$	0.541449	0.0175393	0.00876963	−	0.999962i	$-0.497209\pi$
$953$	0.541449	0.0175393	0.00876963	+	0.999962i	$0.497209\pi$
$954$	−51.2416	−1.65901
$955$	−27.4267	−0.887507
$956$	21.1116	0.682799
$957$	22.1662	0.716533
$958$	19.1001	0.617097
$959$	54.2086	1.75049
$960$	−6.71755	−0.216808
$961$	−20.4068	−0.658282
$962$	10.6396	0.343036
$963$	−14.4505	−0.465660
$964$	−19.4969	−0.627954
$965$	−8.32274	−0.267918
$966$	−13.8706	−0.446279
$967$	−6.52760	−0.209913	−0.104957	−	0.994477i	$-0.533470\pi$
$967$	−6.52760	−0.209913	−0.104957	+	0.994477i	$0.533470\pi$
$968$	8.93746	0.287261
$969$	157.036	5.04473
$970$	−41.5460	−1.33396
$971$	46.8342	1.50298	0.751491	−	0.659743i	$-0.229335\pi$
$971$	46.8342	1.50298	0.751491	+	0.659743i	$0.229335\pi$
$972$	5.71150	0.183197
$973$	14.5461	0.466325
$974$	0.962350	0.0308357
$975$	−1.08311	−0.0346872
$976$	−5.05350	−0.161759
$977$	15.5997	0.499079	0.249540	−	0.968365i	$-0.419721\pi$
$977$	15.5997	0.499079	0.249540	+	0.968365i	$0.419721\pi$
$978$	−18.4177	−0.588932
$979$	3.26315	0.104291
$980$	34.7593	1.11035
$981$	−28.9949	−0.925736
$982$	−17.2832	−0.551529
$983$	40.5147	1.29222	0.646109	−	0.763245i	$-0.276395\pi$
$983$	40.5147	1.29222	0.646109	+	0.763245i	$0.276395\pi$
$984$	−27.5855	−0.879393
$985$	11.5300	0.367377
$986$	39.1917	1.24812
$987$	−4.21351	−0.134118
$988$	−12.3640	−0.393351
$989$	7.90519	0.251370
$990$	−18.5484	−0.589507
$991$	51.3373	1.63078	0.815392	−	0.578910i	$-0.196522\pi$
$991$	51.3373	1.63078	0.815392	+	0.578910i	$0.196522\pi$
$992$	−3.25473	−0.103338
$993$	41.1405	1.30555
$994$	−25.6989	−0.815119
$995$	−17.3433	−0.549820
$996$	30.2657	0.959005
$997$	−5.30366	−0.167969	−0.0839844	−	0.996467i	$-0.526765\pi$
$997$	−5.30366	−0.167969	−0.0839844	+	0.996467i	$0.526765\pi$
$998$	11.8894	0.376352
$999$	48.0563	1.52044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.3	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.94225 q^{3} +1.00000 q^{4} +2.28313 q^{5} +2.94225 q^{6} -4.71427 q^{7} -1.00000 q^{8} +5.65684 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.94225 q^{3} +1.00000 q^{4} +2.28313 q^{5} +2.94225 q^{6} -4.71427 q^{7} -1.00000 q^{8} +5.65684 q^{9} -2.28313 q^{10} +1.43615 q^{11} -2.94225 q^{12} +1.73070 q^{13} +4.71427 q^{14} -6.71755 q^{15} +1.00000 q^{16} +7.47107 q^{17} -5.65684 q^{18} -7.14393 q^{19} +2.28313 q^{20} +13.8706 q^{21} -1.43615 q^{22} +1.00000 q^{23} +2.94225 q^{24} +0.212702 q^{25} -1.73070 q^{26} -7.81709 q^{27} -4.71427 q^{28} -5.24580 q^{29} +6.71755 q^{30} +3.25473 q^{31} -1.00000 q^{32} -4.22552 q^{33} -7.47107 q^{34} -10.7633 q^{35} +5.65684 q^{36} -6.14760 q^{37} +7.14393 q^{38} -5.09215 q^{39} -2.28313 q^{40} -9.37564 q^{41} -13.8706 q^{42} +7.90519 q^{43} +1.43615 q^{44} +12.9153 q^{45} -1.00000 q^{46} -0.303773 q^{47} -2.94225 q^{48} +15.2244 q^{49} -0.212702 q^{50} -21.9818 q^{51} +1.73070 q^{52} +9.05835 q^{53} +7.81709 q^{54} +3.27893 q^{55} +4.71427 q^{56} +21.0192 q^{57} +5.24580 q^{58} -1.29960 q^{59} -6.71755 q^{60} -5.05350 q^{61} -3.25473 q^{62} -26.6679 q^{63} +1.00000 q^{64} +3.95141 q^{65} +4.22552 q^{66} -5.76921 q^{67} +7.47107 q^{68} -2.94225 q^{69} +10.7633 q^{70} -5.45129 q^{71} -5.65684 q^{72} +5.77775 q^{73} +6.14760 q^{74} -0.625821 q^{75} -7.14393 q^{76} -6.77042 q^{77} +5.09215 q^{78} +10.7178 q^{79} +2.28313 q^{80} +6.02932 q^{81} +9.37564 q^{82} -10.2866 q^{83} +13.8706 q^{84} +17.0575 q^{85} -7.90519 q^{86} +15.4344 q^{87} -1.43615 q^{88} +2.27214 q^{89} -12.9153 q^{90} -8.15898 q^{91} +1.00000 q^{92} -9.57622 q^{93} +0.303773 q^{94} -16.3105 q^{95} +2.94225 q^{96} +18.1969 q^{97} -15.2244 q^{98} +8.12409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 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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