LMFDB - Embedded newform 6026.2.a.i.1.5

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			1.5
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.37203 q^{3} +1.00000 q^{4} +3.53118 q^{5} +2.37203 q^{6} -2.86520 q^{7} -1.00000 q^{8} +2.62654 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.37203 q^{3} +1.00000 q^{4} +3.53118 q^{5} +2.37203 q^{6} -2.86520 q^{7} -1.00000 q^{8} +2.62654 q^{9} -3.53118 q^{10} -4.60247 q^{11} -2.37203 q^{12} +2.65812 q^{13} +2.86520 q^{14} -8.37608 q^{15} +1.00000 q^{16} -6.58468 q^{17} -2.62654 q^{18} +1.84283 q^{19} +3.53118 q^{20} +6.79636 q^{21} +4.60247 q^{22} +1.00000 q^{23} +2.37203 q^{24} +7.46926 q^{25} -2.65812 q^{26} +0.885865 q^{27} -2.86520 q^{28} +2.39794 q^{29} +8.37608 q^{30} -6.52436 q^{31} -1.00000 q^{32} +10.9172 q^{33} +6.58468 q^{34} -10.1176 q^{35} +2.62654 q^{36} +3.71765 q^{37} -1.84283 q^{38} -6.30514 q^{39} -3.53118 q^{40} +0.349877 q^{41} -6.79636 q^{42} +5.24396 q^{43} -4.60247 q^{44} +9.27479 q^{45} -1.00000 q^{46} +13.5458 q^{47} -2.37203 q^{48} +1.20940 q^{49} -7.46926 q^{50} +15.6191 q^{51} +2.65812 q^{52} +12.3827 q^{53} -0.885865 q^{54} -16.2522 q^{55} +2.86520 q^{56} -4.37125 q^{57} -2.39794 q^{58} -2.43257 q^{59} -8.37608 q^{60} +8.63341 q^{61} +6.52436 q^{62} -7.52557 q^{63} +1.00000 q^{64} +9.38629 q^{65} -10.9172 q^{66} -7.42685 q^{67} -6.58468 q^{68} -2.37203 q^{69} +10.1176 q^{70} -1.64634 q^{71} -2.62654 q^{72} -4.60406 q^{73} -3.71765 q^{74} -17.7173 q^{75} +1.84283 q^{76} +13.1870 q^{77} +6.30514 q^{78} +7.32188 q^{79} +3.53118 q^{80} -9.98091 q^{81} -0.349877 q^{82} -7.98777 q^{83} +6.79636 q^{84} -23.2517 q^{85} -5.24396 q^{86} -5.68799 q^{87} +4.60247 q^{88} +5.19792 q^{89} -9.27479 q^{90} -7.61604 q^{91} +1.00000 q^{92} +15.4760 q^{93} -13.5458 q^{94} +6.50736 q^{95} +2.37203 q^{96} -4.38352 q^{97} -1.20940 q^{98} -12.0886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.37203	−1.36949	−0.684747	−	0.728781i	$-0.740087\pi$
$3$	−2.37203	−1.36949	−0.684747	+	0.728781i	$0.740087\pi$
$4$	1.00000	0.500000
$5$	3.53118	1.57919	0.789597	−	0.613626i	$-0.210290\pi$
$5$	3.53118	1.57919	0.789597	+	0.613626i	$0.210290\pi$
$6$	2.37203	0.968378
$7$	−2.86520	−1.08295	−0.541473	−	0.840718i	$-0.682133\pi$
$7$	−2.86520	−1.08295	−0.541473	+	0.840718i	$0.682133\pi$
$8$	−1.00000	−0.353553
$9$	2.62654	0.875513
$10$	−3.53118	−1.11666
$11$	−4.60247	−1.38770	−0.693849	−	0.720121i	$-0.744086\pi$
$11$	−4.60247	−1.38770	−0.693849	+	0.720121i	$0.744086\pi$
$12$	−2.37203	−0.684747
$13$	2.65812	0.737229	0.368614	−	0.929582i	$-0.379832\pi$
$13$	2.65812	0.737229	0.368614	+	0.929582i	$0.379832\pi$
$14$	2.86520	0.765758
$15$	−8.37608	−2.16269
$16$	1.00000	0.250000
$17$	−6.58468	−1.59702	−0.798510	−	0.601982i	$-0.794378\pi$
$17$	−6.58468	−1.59702	−0.798510	+	0.601982i	$0.794378\pi$
$18$	−2.62654	−0.619081
$19$	1.84283	0.422774	0.211387	−	0.977402i	$-0.432202\pi$
$19$	1.84283	0.422774	0.211387	+	0.977402i	$0.432202\pi$
$20$	3.53118	0.789597
$21$	6.79636	1.48309
$22$	4.60247	0.981250
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.37203	0.484189
$25$	7.46926	1.49385
$26$	−2.65812	−0.521299
$27$	0.885865	0.170485
$28$	−2.86520	−0.541473
$29$	2.39794	0.445286	0.222643	−	0.974900i	$-0.428532\pi$
$29$	2.39794	0.445286	0.222643	+	0.974900i	$0.428532\pi$
$30$	8.37608	1.52926
$31$	−6.52436	−1.17181	−0.585905	−	0.810380i	$-0.699261\pi$
$31$	−6.52436	−1.17181	−0.585905	+	0.810380i	$0.699261\pi$
$32$	−1.00000	−0.176777
$33$	10.9172	1.90044
$34$	6.58468	1.12926
$35$	−10.1176	−1.71018
$36$	2.62654	0.437756
$37$	3.71765	0.611179	0.305589	−	0.952163i	$-0.401147\pi$
$37$	3.71765	0.611179	0.305589	+	0.952163i	$0.401147\pi$
$38$	−1.84283	−0.298946
$39$	−6.30514	−1.00963
$40$	−3.53118	−0.558329
$41$	0.349877	0.0546416	0.0273208	−	0.999627i	$-0.491302\pi$
$41$	0.349877	0.0546416	0.0273208	+	0.999627i	$0.491302\pi$
$42$	−6.79636	−1.04870
$43$	5.24396	0.799697	0.399848	−	0.916581i	$-0.369063\pi$
$43$	5.24396	0.799697	0.399848	+	0.916581i	$0.369063\pi$
$44$	−4.60247	−0.693849
$45$	9.27479	1.38260
$46$	−1.00000	−0.147442
$47$	13.5458	1.97586	0.987929	−	0.154906i	$-0.0495075\pi$
$47$	13.5458	1.97586	0.987929	+	0.154906i	$0.0495075\pi$
$48$	−2.37203	−0.342373
$49$	1.20940	0.172771
$50$	−7.46926	−1.05631
$51$	15.6191	2.18711
$52$	2.65812	0.368614
$53$	12.3827	1.70089	0.850446	−	0.526063i	$-0.176332\pi$
$53$	12.3827	1.70089	0.850446	+	0.526063i	$0.176332\pi$
$54$	−0.885865	−0.120551
$55$	−16.2522	−2.19144
$56$	2.86520	0.382879
$57$	−4.37125	−0.578986
$58$	−2.39794	−0.314865
$59$	−2.43257	−0.316693	−0.158347	−	0.987384i	$-0.550616\pi$
$59$	−2.43257	−0.316693	−0.158347	+	0.987384i	$0.550616\pi$
$60$	−8.37608	−1.08135
$61$	8.63341	1.10540	0.552698	−	0.833382i	$-0.313598\pi$
$61$	8.63341	1.10540	0.552698	+	0.833382i	$0.313598\pi$
$62$	6.52436	0.828594
$63$	−7.52557	−0.948132
$64$	1.00000	0.125000
$65$	9.38629	1.16423
$66$	−10.9172	−1.34382
$67$	−7.42685	−0.907334	−0.453667	−	0.891171i	$-0.649884\pi$
$67$	−7.42685	−0.907334	−0.453667	+	0.891171i	$0.649884\pi$
$68$	−6.58468	−0.798510
$69$	−2.37203	−0.285559
$70$	10.1176	1.20928
$71$	−1.64634	−0.195384	−0.0976921	−	0.995217i	$-0.531146\pi$
$71$	−1.64634	−0.195384	−0.0976921	+	0.995217i	$0.531146\pi$
$72$	−2.62654	−0.309540
$73$	−4.60406	−0.538865	−0.269432	−	0.963019i	$-0.586836\pi$
$73$	−4.60406	−0.538865	−0.269432	+	0.963019i	$0.586836\pi$
$74$	−3.71765	−0.432169
$75$	−17.7173	−2.04582
$76$	1.84283	0.211387
$77$	13.1870	1.50280
$78$	6.30514	0.713916
$79$	7.32188	0.823776	0.411888	−	0.911235i	$-0.364870\pi$
$79$	7.32188	0.823776	0.411888	+	0.911235i	$0.364870\pi$
$80$	3.53118	0.394798
$81$	−9.98091	−1.10899
$82$	−0.349877	−0.0386375
$83$	−7.98777	−0.876772	−0.438386	−	0.898787i	$-0.644450\pi$
$83$	−7.98777	−0.876772	−0.438386	+	0.898787i	$0.644450\pi$
$84$	6.79636	0.741543
$85$	−23.2517	−2.52200
$86$	−5.24396	−0.565471
$87$	−5.68799	−0.609816
$88$	4.60247	0.490625
$89$	5.19792	0.550978	0.275489	−	0.961304i	$-0.411160\pi$
$89$	5.19792	0.550978	0.275489	+	0.961304i	$0.411160\pi$
$90$	−9.27479	−0.977648
$91$	−7.61604	−0.798378
$92$	1.00000	0.104257
$93$	15.4760	1.60479
$94$	−13.5458	−1.39714
$95$	6.50736	0.667641
$96$	2.37203	0.242095
$97$	−4.38352	−0.445079	−0.222539	−	0.974924i	$-0.571435\pi$
$97$	−4.38352	−0.445079	−0.222539	+	0.974924i	$0.571435\pi$
$98$	−1.20940	−0.122168
$99$	−12.0886	−1.21495
$100$	7.46926	0.746926
$101$	−6.86910	−0.683501	−0.341750	−	0.939791i	$-0.611020\pi$
$101$	−6.86910	−0.683501	−0.341750	+	0.939791i	$0.611020\pi$
$102$	−15.6191	−1.54652
$103$	−9.31126	−0.917466	−0.458733	−	0.888574i	$-0.651697\pi$
$103$	−9.31126	−0.917466	−0.458733	+	0.888574i	$0.651697\pi$
$104$	−2.65812	−0.260650
$105$	23.9992	2.34208
$106$	−12.3827	−1.20271
$107$	0.856111	0.0827634	0.0413817	−	0.999143i	$-0.486824\pi$
$107$	0.856111	0.0827634	0.0413817	+	0.999143i	$0.486824\pi$
$108$	0.885865	0.0852424
$109$	−10.8634	−1.04052	−0.520262	−	0.854006i	$-0.674166\pi$
$109$	−10.8634	−1.04052	−0.520262	+	0.854006i	$0.674166\pi$
$110$	16.2522	1.54958
$111$	−8.81840	−0.837005
$112$	−2.86520	−0.270736
$113$	1.39476	0.131208	0.0656039	−	0.997846i	$-0.479103\pi$
$113$	1.39476	0.131208	0.0656039	+	0.997846i	$0.479103\pi$
$114$	4.37125	0.409405
$115$	3.53118	0.329285
$116$	2.39794	0.222643
$117$	6.98164	0.645453
$118$	2.43257	0.223936
$119$	18.8665	1.72948
$120$	8.37608	0.764628
$121$	10.1828	0.925705
$122$	−8.63341	−0.781633
$123$	−0.829920	−0.0748314
$124$	−6.52436	−0.585905
$125$	8.71940	0.779887
$126$	7.52557	0.670431
$127$	−19.2048	−1.70415	−0.852074	−	0.523421i	$-0.824656\pi$
$127$	−19.2048	−1.70415	−0.852074	+	0.523421i	$0.824656\pi$
$128$	−1.00000	−0.0883883
$129$	−12.4389	−1.09518
$130$	−9.38629	−0.823232
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	10.9172	0.950221
$133$	−5.28008	−0.457841
$134$	7.42685	0.641582
$135$	3.12815	0.269228
$136$	6.58468	0.564632
$137$	−13.4176	−1.14634	−0.573171	−	0.819435i	$-0.694287\pi$
$137$	−13.4176	−1.14634	−0.573171	+	0.819435i	$0.694287\pi$
$138$	2.37203	0.201921
$139$	−0.128035	−0.0108598	−0.00542988	−	0.999985i	$-0.501728\pi$
$139$	−0.128035	−0.0108598	−0.00542988	+	0.999985i	$0.501728\pi$
$140$	−10.1176	−0.855090
$141$	−32.1311	−2.70593
$142$	1.64634	0.138157
$143$	−12.2339	−1.02305
$144$	2.62654	0.218878
$145$	8.46756	0.703193
$146$	4.60406	0.381035
$147$	−2.86873	−0.236609
$148$	3.71765	0.305589
$149$	10.8685	0.890385	0.445192	−	0.895435i	$-0.353135\pi$
$149$	10.8685	0.890385	0.445192	+	0.895435i	$0.353135\pi$
$150$	17.7173	1.44661
$151$	−20.2227	−1.64570	−0.822850	−	0.568258i	$-0.807618\pi$
$151$	−20.2227	−1.64570	−0.822850	+	0.568258i	$0.807618\pi$
$152$	−1.84283	−0.149473
$153$	−17.2949	−1.39821
$154$	−13.1870	−1.06264
$155$	−23.0387	−1.85051
$156$	−6.30514	−0.504815
$157$	10.8903	0.869138	0.434569	−	0.900639i	$-0.356901\pi$
$157$	10.8903	0.869138	0.434569	+	0.900639i	$0.356901\pi$
$158$	−7.32188	−0.582497
$159$	−29.3721	−2.32936
$160$	−3.53118	−0.279165
$161$	−2.86520	−0.225810
$162$	9.98091	0.784175
$163$	−1.48802	−0.116550	−0.0582752	−	0.998301i	$-0.518560\pi$
$163$	−1.48802	−0.116550	−0.0582752	+	0.998301i	$0.518560\pi$
$164$	0.349877	0.0273208
$165$	38.5507	3.00117
$166$	7.98777	0.619971
$167$	−1.28328	−0.0993032	−0.0496516	−	0.998767i	$-0.515811\pi$
$167$	−1.28328	−0.0993032	−0.0496516	+	0.998767i	$0.515811\pi$
$168$	−6.79636	−0.524350
$169$	−5.93442	−0.456494
$170$	23.2517	1.78332
$171$	4.84026	0.370144
$172$	5.24396	0.399848
$173$	15.6009	1.18612	0.593058	−	0.805160i	$-0.297920\pi$
$173$	15.6009	1.18612	0.593058	+	0.805160i	$0.297920\pi$
$174$	5.68799	0.431205
$175$	−21.4009	−1.61776
$176$	−4.60247	−0.346924
$177$	5.77013	0.433710
$178$	−5.19792	−0.389601
$179$	2.30979	0.172642	0.0863208	−	0.996267i	$-0.472489\pi$
$179$	2.30979	0.172642	0.0863208	+	0.996267i	$0.472489\pi$
$180$	9.27479	0.691302
$181$	−1.65690	−0.123156	−0.0615782	−	0.998102i	$-0.519613\pi$
$181$	−1.65690	−0.123156	−0.0615782	+	0.998102i	$0.519613\pi$
$182$	7.61604	0.564539
$183$	−20.4787	−1.51383
$184$	−1.00000	−0.0737210
$185$	13.1277	0.965169
$186$	−15.4760	−1.13475
$187$	30.3058	2.21618
$188$	13.5458	0.987929
$189$	−2.53818	−0.184626
$190$	−6.50736	−0.472094
$191$	−15.3327	−1.10943	−0.554717	−	0.832039i	$-0.687173\pi$
$191$	−15.3327	−1.10943	−0.554717	+	0.832039i	$0.687173\pi$
$192$	−2.37203	−0.171187
$193$	18.0487	1.29917	0.649587	−	0.760287i	$-0.274942\pi$
$193$	18.0487	1.29917	0.649587	+	0.760287i	$0.274942\pi$
$194$	4.38352	0.314718
$195$	−22.2646	−1.59440
$196$	1.20940	0.0863855
$197$	12.4726	0.888636	0.444318	−	0.895869i	$-0.353446\pi$
$197$	12.4726	0.888636	0.444318	+	0.895869i	$0.353446\pi$
$198$	12.0886	0.859097
$199$	14.9259	1.05807	0.529035	−	0.848600i	$-0.322554\pi$
$199$	14.9259	1.05807	0.529035	+	0.848600i	$0.322554\pi$
$200$	−7.46926	−0.528156
$201$	17.6167	1.24259
$202$	6.86910	0.483308
$203$	−6.87058	−0.482221
$204$	15.6191	1.09355
$205$	1.23548	0.0862897
$206$	9.31126	0.648746
$207$	2.62654	0.182557
$208$	2.65812	0.184307
$209$	−8.48156	−0.586682
$210$	−23.9992	−1.65610
$211$	17.6352	1.21405	0.607027	−	0.794681i	$-0.292362\pi$
$211$	17.6352	1.21405	0.607027	+	0.794681i	$0.292362\pi$
$212$	12.3827	0.850446
$213$	3.90516	0.267577
$214$	−0.856111	−0.0585225
$215$	18.5174	1.26288
$216$	−0.885865	−0.0602755
$217$	18.6936	1.26901
$218$	10.8634	0.735762
$219$	10.9210	0.737972
$220$	−16.2522	−1.09572
$221$	−17.5028	−1.17737
$222$	8.81840	0.591852
$223$	15.1656	1.01557	0.507783	−	0.861485i	$-0.330465\pi$
$223$	15.1656	1.01557	0.507783	+	0.861485i	$0.330465\pi$
$224$	2.86520	0.191440
$225$	19.6183	1.30789
$226$	−1.39476	−0.0927780
$227$	1.68550	0.111870	0.0559352	−	0.998434i	$-0.482186\pi$
$227$	1.68550	0.111870	0.0559352	+	0.998434i	$0.482186\pi$
$228$	−4.37125	−0.289493
$229$	0.649134	0.0428960	0.0214480	−	0.999770i	$-0.493172\pi$
$229$	0.649134	0.0428960	0.0214480	+	0.999770i	$0.493172\pi$
$230$	−3.53118	−0.232839
$231$	−31.2800	−2.05808
$232$	−2.39794	−0.157432
$233$	2.37661	0.155697	0.0778484	−	0.996965i	$-0.475195\pi$
$233$	2.37661	0.155697	0.0778484	+	0.996965i	$0.475195\pi$
$234$	−6.98164	−0.456404
$235$	47.8327	3.12026
$236$	−2.43257	−0.158347
$237$	−17.3677	−1.12816
$238$	−18.8665	−1.22293
$239$	−17.5990	−1.13838	−0.569192	−	0.822204i	$-0.692744\pi$
$239$	−17.5990	−1.13838	−0.569192	+	0.822204i	$0.692744\pi$
$240$	−8.37608	−0.540674
$241$	−22.2621	−1.43403	−0.717013	−	0.697060i	$-0.754491\pi$
$241$	−22.2621	−1.43403	−0.717013	+	0.697060i	$0.754491\pi$
$242$	−10.1828	−0.654572
$243$	21.0175	1.34827
$244$	8.63341	0.552698
$245$	4.27060	0.272839
$246$	0.829920	0.0529138
$247$	4.89845	0.311681
$248$	6.52436	0.414297
$249$	18.9472	1.20073
$250$	−8.71940	−0.551463
$251$	25.2953	1.59662	0.798311	−	0.602245i	$-0.205727\pi$
$251$	25.2953	1.59662	0.798311	+	0.602245i	$0.205727\pi$
$252$	−7.52557	−0.474066
$253$	−4.60247	−0.289355
$254$	19.2048	1.20502
$255$	55.1538	3.45387
$256$	1.00000	0.0625000
$257$	−21.9256	−1.36768	−0.683839	−	0.729633i	$-0.739691\pi$
$257$	−21.9256	−1.36768	−0.683839	+	0.729633i	$0.739691\pi$
$258$	12.4389	0.774409
$259$	−10.6518	−0.661873
$260$	9.38629	0.582113
$261$	6.29828	0.389854
$262$	−1.00000	−0.0617802
$263$	−5.77093	−0.355851	−0.177925	−	0.984044i	$-0.556939\pi$
$263$	−5.77093	−0.355851	−0.177925	+	0.984044i	$0.556939\pi$
$264$	−10.9172	−0.671908
$265$	43.7255	2.68604
$266$	5.28008	0.323742
$267$	−12.3296	−0.754561
$268$	−7.42685	−0.453667
$269$	−5.91183	−0.360450	−0.180225	−	0.983625i	$-0.557683\pi$
$269$	−5.91183	−0.360450	−0.180225	+	0.983625i	$0.557683\pi$
$270$	−3.12815	−0.190373
$271$	−25.4696	−1.54717	−0.773584	−	0.633693i	$-0.781538\pi$
$271$	−25.4696	−1.54717	−0.773584	+	0.633693i	$0.781538\pi$
$272$	−6.58468	−0.399255
$273$	18.0655	1.09337
$274$	13.4176	0.810587
$275$	−34.3770	−2.07301
$276$	−2.37203	−0.142780
$277$	12.3341	0.741086	0.370543	−	0.928815i	$-0.379172\pi$
$277$	12.3341	0.741086	0.370543	+	0.928815i	$0.379172\pi$
$278$	0.128035	0.00767900
$279$	−17.1365	−1.02593
$280$	10.1176	0.604640
$281$	−27.6165	−1.64746	−0.823732	−	0.566979i	$-0.808112\pi$
$281$	−27.6165	−1.64746	−0.823732	+	0.566979i	$0.808112\pi$
$282$	32.1311	1.91338
$283$	−8.49092	−0.504733	−0.252366	−	0.967632i	$-0.581209\pi$
$283$	−8.49092	−0.504733	−0.252366	+	0.967632i	$0.581209\pi$
$284$	−1.64634	−0.0976921
$285$	−15.4357	−0.914330
$286$	12.2339	0.723406
$287$	−1.00247	−0.0591739
$288$	−2.62654	−0.154770
$289$	26.3580	1.55047
$290$	−8.46756	−0.497232
$291$	10.3978	0.609532
$292$	−4.60406	−0.269432
$293$	−9.55457	−0.558184	−0.279092	−	0.960264i	$-0.590033\pi$
$293$	−9.55457	−0.558184	−0.279092	+	0.960264i	$0.590033\pi$
$294$	2.86873	0.167308
$295$	−8.58985	−0.500120
$296$	−3.71765	−0.216084
$297$	−4.07717	−0.236581
$298$	−10.8685	−0.629597
$299$	2.65812	0.153723
$300$	−17.7173	−1.02291
$301$	−15.0250	−0.866028
$302$	20.2227	1.16369
$303$	16.2937	0.936050
$304$	1.84283	0.105693
$305$	30.4862	1.74563
$306$	17.2949	0.988684
$307$	18.8150	1.07383	0.536913	−	0.843637i	$-0.319590\pi$
$307$	18.8150	1.07383	0.536913	+	0.843637i	$0.319590\pi$
$308$	13.1870	0.751400
$309$	22.0866	1.25646
$310$	23.0387	1.30851
$311$	1.17689	0.0667352	0.0333676	−	0.999443i	$-0.489377\pi$
$311$	1.17689	0.0667352	0.0333676	+	0.999443i	$0.489377\pi$
$312$	6.30514	0.356958
$313$	−13.7512	−0.777265	−0.388633	−	0.921393i	$-0.627052\pi$
$313$	−13.7512	−0.777265	−0.388633	+	0.921393i	$0.627052\pi$
$314$	−10.8903	−0.614573
$315$	−26.5742	−1.49728
$316$	7.32188	0.411888
$317$	4.27224	0.239953	0.119976	−	0.992777i	$-0.461718\pi$
$317$	4.27224	0.239953	0.119976	+	0.992777i	$0.461718\pi$
$318$	29.3721	1.64711
$319$	−11.0364	−0.617922
$320$	3.53118	0.197399
$321$	−2.03072	−0.113344
$322$	2.86520	0.159672
$323$	−12.1344	−0.675178
$324$	−9.98091	−0.554495
$325$	19.8541	1.10131
$326$	1.48802	0.0824136
$327$	25.7683	1.42499
$328$	−0.349877	−0.0193187
$329$	−38.8115	−2.13975
$330$	−38.5507	−2.12215
$331$	−31.3277	−1.72193	−0.860963	−	0.508668i	$-0.830138\pi$
$331$	−31.3277	−1.72193	−0.860963	+	0.508668i	$0.830138\pi$
$332$	−7.98777	−0.438386
$333$	9.76456	0.535095
$334$	1.28328	0.0702180
$335$	−26.2256	−1.43286
$336$	6.79636	0.370772
$337$	−32.6826	−1.78033	−0.890167	−	0.455634i	$-0.849412\pi$
$337$	−32.6826	−1.78033	−0.890167	+	0.455634i	$0.849412\pi$
$338$	5.93442	0.322790
$339$	−3.30841	−0.179688
$340$	−23.2517	−1.26100
$341$	30.0282	1.62612
$342$	−4.84026	−0.261731
$343$	16.5913	0.895844
$344$	−5.24396	−0.282736
$345$	−8.37608	−0.450953
$346$	−15.6009	−0.838711
$347$	−19.5655	−1.05033	−0.525165	−	0.851000i	$-0.675997\pi$
$347$	−19.5655	−1.05033	−0.525165	+	0.851000i	$0.675997\pi$
$348$	−5.68799	−0.304908
$349$	−13.9082	−0.744489	−0.372244	−	0.928135i	$-0.621412\pi$
$349$	−13.9082	−0.744489	−0.372244	+	0.928135i	$0.621412\pi$
$350$	21.4009	1.14393
$351$	2.35473	0.125686
$352$	4.60247	0.245313
$353$	−21.3628	−1.13703	−0.568514	−	0.822673i	$-0.692482\pi$
$353$	−21.3628	−1.13703	−0.568514	+	0.822673i	$0.692482\pi$
$354$	−5.77013	−0.306679
$355$	−5.81351	−0.308549
$356$	5.19792	0.275489
$357$	−44.7518	−2.36852
$358$	−2.30979	−0.122076
$359$	−6.05902	−0.319783	−0.159891	−	0.987135i	$-0.551114\pi$
$359$	−6.05902	−0.319783	−0.159891	+	0.987135i	$0.551114\pi$
$360$	−9.27479	−0.488824
$361$	−15.6040	−0.821262
$362$	1.65690	0.0870848
$363$	−24.1538	−1.26775
$364$	−7.61604	−0.399189
$365$	−16.2578	−0.850971
$366$	20.4787	1.07044
$367$	−26.9114	−1.40477	−0.702383	−	0.711799i	$-0.747881\pi$
$367$	−26.9114	−1.40477	−0.702383	+	0.711799i	$0.747881\pi$
$368$	1.00000	0.0521286
$369$	0.918966	0.0478394
$370$	−13.1277	−0.682478
$371$	−35.4789	−1.84197
$372$	15.4760	0.802393
$373$	18.0155	0.932806	0.466403	−	0.884572i	$-0.345550\pi$
$373$	18.0155	0.932806	0.466403	+	0.884572i	$0.345550\pi$
$374$	−30.3058	−1.56708
$375$	−20.6827	−1.06805
$376$	−13.5458	−0.698571
$377$	6.37400	0.328278
$378$	2.53818	0.130550
$379$	−12.2255	−0.627981	−0.313991	−	0.949426i	$-0.601666\pi$
$379$	−12.2255	−0.627981	−0.313991	+	0.949426i	$0.601666\pi$
$380$	6.50736	0.333821
$381$	45.5544	2.33382
$382$	15.3327	0.784488
$383$	−10.9076	−0.557354	−0.278677	−	0.960385i	$-0.589896\pi$
$383$	−10.9076	−0.557354	−0.278677	+	0.960385i	$0.589896\pi$
$384$	2.37203	0.121047
$385$	46.5658	2.37321
$386$	−18.0487	−0.918655
$387$	13.7735	0.700145
$388$	−4.38352	−0.222539
$389$	19.6342	0.995494	0.497747	−	0.867322i	$-0.334161\pi$
$389$	19.6342	0.995494	0.497747	+	0.867322i	$0.334161\pi$
$390$	22.2646	1.12741
$391$	−6.58468	−0.333002
$392$	−1.20940	−0.0610838
$393$	−2.37203	−0.119653
$394$	−12.4726	−0.628361
$395$	25.8549	1.30090
$396$	−12.0886	−0.607473
$397$	−22.9879	−1.15373	−0.576864	−	0.816840i	$-0.695724\pi$
$397$	−22.9879	−1.15373	−0.576864	+	0.816840i	$0.695724\pi$
$398$	−14.9259	−0.748168
$399$	12.5245	0.627010
$400$	7.46926	0.373463
$401$	−36.6215	−1.82879	−0.914396	−	0.404820i	$-0.867334\pi$
$401$	−36.6215	−1.82879	−0.914396	+	0.404820i	$0.867334\pi$
$402$	−17.6167	−0.878642
$403$	−17.3425	−0.863891
$404$	−6.86910	−0.341750
$405$	−35.2444	−1.75131
$406$	6.87058	0.340981
$407$	−17.1104	−0.848131
$408$	−15.6191	−0.773259
$409$	−2.15209	−0.106414	−0.0532069	−	0.998584i	$-0.516944\pi$
$409$	−2.15209	−0.106414	−0.0532069	+	0.998584i	$0.516944\pi$
$410$	−1.23548	−0.0610160
$411$	31.8270	1.56991
$412$	−9.31126	−0.458733
$413$	6.96981	0.342962
$414$	−2.62654	−0.129087
$415$	−28.2063	−1.38459
$416$	−2.65812	−0.130325
$417$	0.303702	0.0148724
$418$	8.48156	0.414847
$419$	−17.0774	−0.834284	−0.417142	−	0.908841i	$-0.636968\pi$
$419$	−17.0774	−0.834284	−0.417142	+	0.908841i	$0.636968\pi$
$420$	23.9992	1.17104
$421$	0.0841046	0.00409901	0.00204950	−	0.999998i	$-0.499348\pi$
$421$	0.0841046	0.00409901	0.00204950	+	0.999998i	$0.499348\pi$
$422$	−17.6352	−0.858466
$423$	35.5786	1.72989
$424$	−12.3827	−0.601356
$425$	−49.1827	−2.38571
$426$	−3.90516	−0.189206
$427$	−24.7365	−1.19708
$428$	0.856111	0.0413817
$429$	29.0192	1.40106
$430$	−18.5174	−0.892988
$431$	−12.7222	−0.612809	−0.306404	−	0.951901i	$-0.599126\pi$
$431$	−12.7222	−0.612809	−0.306404	+	0.951901i	$0.599126\pi$
$432$	0.885865	0.0426212
$433$	38.6024	1.85511	0.927557	−	0.373681i	$-0.121905\pi$
$433$	38.6024	1.85511	0.927557	+	0.373681i	$0.121905\pi$
$434$	−18.6936	−0.897322
$435$	−20.0853	−0.963018
$436$	−10.8634	−0.520262
$437$	1.84283	0.0881544
$438$	−10.9210	−0.521825
$439$	−25.2085	−1.20314	−0.601569	−	0.798821i	$-0.705457\pi$
$439$	−25.2085	−1.20314	−0.601569	+	0.798821i	$0.705457\pi$
$440$	16.2522	0.774792
$441$	3.17653	0.151263
$442$	17.5028	0.832525
$443$	37.5340	1.78330	0.891648	−	0.452730i	$-0.149550\pi$
$443$	37.5340	1.78330	0.891648	+	0.452730i	$0.149550\pi$
$444$	−8.81840	−0.418503
$445$	18.3548	0.870101
$446$	−15.1656	−0.718113
$447$	−25.7805	−1.21938
$448$	−2.86520	−0.135368
$449$	33.5043	1.58117	0.790584	−	0.612354i	$-0.209777\pi$
$449$	33.5043	1.58117	0.790584	+	0.612354i	$0.209777\pi$
$450$	−19.6183	−0.924815
$451$	−1.61030	−0.0758261
$452$	1.39476	0.0656039
$453$	47.9689	2.25378
$454$	−1.68550	−0.0791043
$455$	−26.8936	−1.26079
$456$	4.37125	0.204702
$457$	−24.4964	−1.14589	−0.572947	−	0.819592i	$-0.694200\pi$
$457$	−24.4964	−1.14589	−0.572947	+	0.819592i	$0.694200\pi$
$458$	−0.649134	−0.0303320
$459$	−5.83314	−0.272267
$460$	3.53118	0.164642
$461$	1.63657	0.0762225	0.0381112	−	0.999274i	$-0.487866\pi$
$461$	1.63657	0.0762225	0.0381112	+	0.999274i	$0.487866\pi$
$462$	31.2800	1.45528
$463$	35.5683	1.65300	0.826499	−	0.562938i	$-0.190329\pi$
$463$	35.5683	1.65300	0.826499	+	0.562938i	$0.190329\pi$
$464$	2.39794	0.111322
$465$	54.6486	2.53427
$466$	−2.37661	−0.110094
$467$	1.65707	0.0766801	0.0383401	−	0.999265i	$-0.487793\pi$
$467$	1.65707	0.0766801	0.0383401	+	0.999265i	$0.487793\pi$
$468$	6.98164	0.322726
$469$	21.2794	0.982593
$470$	−47.8327	−2.20636
$471$	−25.8321	−1.19028
$472$	2.43257	0.111968
$473$	−24.1352	−1.10974
$474$	17.3677	0.797727
$475$	13.7646	0.631561
$476$	18.8665	0.864742
$477$	32.5236	1.48915
$478$	17.5990	0.804960
$479$	15.7331	0.718866	0.359433	−	0.933171i	$-0.382970\pi$
$479$	15.7331	0.718866	0.359433	+	0.933171i	$0.382970\pi$
$480$	8.37608	0.382314
$481$	9.88195	0.450578
$482$	22.2621	1.01401
$483$	6.79636	0.309245
$484$	10.1828	0.462852
$485$	−15.4790	−0.702865
$486$	−21.0175	−0.953371
$487$	−8.28468	−0.375415	−0.187707	−	0.982225i	$-0.560106\pi$
$487$	−8.28468	−0.375415	−0.187707	+	0.982225i	$0.560106\pi$
$488$	−8.63341	−0.390816
$489$	3.52962	0.159615
$490$	−4.27060	−0.192926
$491$	−39.5767	−1.78607	−0.893037	−	0.449984i	$-0.851430\pi$
$491$	−39.5767	−1.78607	−0.893037	+	0.449984i	$0.851430\pi$
$492$	−0.829920	−0.0374157
$493$	−15.7897	−0.711130
$494$	−4.89845	−0.220392
$495$	−42.6869	−1.91864
$496$	−6.52436	−0.292952
$497$	4.71709	0.211590
$498$	−18.9472	−0.849046
$499$	9.09192	0.407010	0.203505	−	0.979074i	$-0.434767\pi$
$499$	9.09192	0.407010	0.203505	+	0.979074i	$0.434767\pi$
$500$	8.71940	0.389943
$501$	3.04398	0.135995
$502$	−25.2953	−1.12898
$503$	8.35263	0.372425	0.186213	−	0.982509i	$-0.440379\pi$
$503$	8.35263	0.372425	0.186213	+	0.982509i	$0.440379\pi$
$504$	7.52557	0.335215
$505$	−24.2560	−1.07938
$506$	4.60247	0.204605
$507$	14.0766	0.625166
$508$	−19.2048	−0.852074
$509$	−16.9820	−0.752714	−0.376357	−	0.926475i	$-0.622823\pi$
$509$	−16.9820	−0.752714	−0.376357	+	0.926475i	$0.622823\pi$
$510$	−55.1538	−2.44225
$511$	13.1916	0.583561
$512$	−1.00000	−0.0441942
$513$	1.63250	0.0720765
$514$	21.9256	0.967095
$515$	−32.8798	−1.44886
$516$	−12.4389	−0.547590
$517$	−62.3442	−2.74189
$518$	10.6518	0.468015
$519$	−37.0059	−1.62438
$520$	−9.38629	−0.411616
$521$	−22.3861	−0.980751	−0.490376	−	0.871511i	$-0.663140\pi$
$521$	−22.3861	−0.980751	−0.490376	+	0.871511i	$0.663140\pi$
$522$	−6.29828	−0.275668
$523$	−4.29538	−0.187824	−0.0939119	−	0.995581i	$-0.529937\pi$
$523$	−4.29538	−0.187824	−0.0939119	+	0.995581i	$0.529937\pi$
$524$	1.00000	0.0436852
$525$	50.7637	2.21551
$526$	5.77093	0.251624
$527$	42.9608	1.87140
$528$	10.9172	0.475111
$529$	1.00000	0.0434783
$530$	−43.7255	−1.89931
$531$	−6.38923	−0.277269
$532$	−5.28008	−0.228920
$533$	0.930014	0.0402834
$534$	12.3296	0.533555
$535$	3.02308	0.130699
$536$	7.42685	0.320791
$537$	−5.47889	−0.236431
$538$	5.91183	0.254877
$539$	−5.56622	−0.239754
$540$	3.12815	0.134614
$541$	−30.6922	−1.31956	−0.659780	−	0.751459i	$-0.729351\pi$
$541$	−30.6922	−1.31956	−0.659780	+	0.751459i	$0.729351\pi$
$542$	25.4696	1.09401
$543$	3.93022	0.168662
$544$	6.58468	0.282316
$545$	−38.3607	−1.64319
$546$	−18.0655	−0.773132
$547$	19.1282	0.817864	0.408932	−	0.912565i	$-0.365901\pi$
$547$	19.1282	0.817864	0.408932	+	0.912565i	$0.365901\pi$
$548$	−13.4176	−0.573171
$549$	22.6760	0.967788
$550$	34.3770	1.46584
$551$	4.41899	0.188255
$552$	2.37203	0.100960
$553$	−20.9787	−0.892104
$554$	−12.3341	−0.524027
$555$	−31.1394	−1.32179
$556$	−0.128035	−0.00542988
$557$	40.4673	1.71465	0.857327	−	0.514772i	$-0.172123\pi$
$557$	40.4673	1.71465	0.857327	+	0.514772i	$0.172123\pi$
$558$	17.1365	0.725445
$559$	13.9391	0.589559
$560$	−10.1176	−0.427545
$561$	−71.8863	−3.03504
$562$	27.6165	1.16493
$563$	23.7118	0.999334	0.499667	−	0.866218i	$-0.333456\pi$
$563$	23.7118	0.999334	0.499667	+	0.866218i	$0.333456\pi$
$564$	−32.1311	−1.35296
$565$	4.92515	0.207203
$566$	8.49092	0.356900
$567$	28.5974	1.20098
$568$	1.64634	0.0690787
$569$	−0.740963	−0.0310628	−0.0155314	−	0.999879i	$-0.504944\pi$
$569$	−0.740963	−0.0310628	−0.0155314	+	0.999879i	$0.504944\pi$
$570$	15.4357	0.646529
$571$	−7.78316	−0.325715	−0.162858	−	0.986650i	$-0.552071\pi$
$571$	−7.78316	−0.325715	−0.162858	+	0.986650i	$0.552071\pi$
$572$	−12.2339	−0.511525
$573$	36.3696	1.51936
$574$	1.00247	0.0418423
$575$	7.46926	0.311490
$576$	2.62654	0.109439
$577$	−15.1287	−0.629818	−0.314909	−	0.949122i	$-0.601974\pi$
$577$	−15.1287	−0.629818	−0.314909	+	0.949122i	$0.601974\pi$
$578$	−26.3580	−1.09635
$579$	−42.8121	−1.77921
$580$	8.46756	0.351596
$581$	22.8866	0.949496
$582$	−10.3978	−0.431004
$583$	−56.9909	−2.36032
$584$	4.60406	0.190517
$585$	24.6535	1.01929
$586$	9.55457	0.394696
$587$	4.55083	0.187833	0.0939163	−	0.995580i	$-0.470061\pi$
$587$	4.55083	0.187833	0.0939163	+	0.995580i	$0.470061\pi$
$588$	−2.86873	−0.118304
$589$	−12.0233	−0.495410
$590$	8.58985	0.353638
$591$	−29.5854	−1.21698
$592$	3.71765	0.152795
$593$	3.57161	0.146668	0.0733341	−	0.997307i	$-0.476636\pi$
$593$	3.57161	0.146668	0.0733341	+	0.997307i	$0.476636\pi$
$594$	4.07717	0.167288
$595$	66.6209	2.73119
$596$	10.8685	0.445192
$597$	−35.4047	−1.44902
$598$	−2.65812	−0.108698
$599$	−19.7144	−0.805507	−0.402753	−	0.915309i	$-0.631947\pi$
$599$	−19.7144	−0.805507	−0.402753	+	0.915309i	$0.631947\pi$
$600$	17.7173	0.723307
$601$	−33.0536	−1.34828	−0.674142	−	0.738602i	$-0.735487\pi$
$601$	−33.0536	−1.34828	−0.674142	+	0.738602i	$0.735487\pi$
$602$	15.0250	0.612374
$603$	−19.5069	−0.794382
$604$	−20.2227	−0.822850
$605$	35.9572	1.46187
$606$	−16.2937	−0.661887
$607$	43.9075	1.78215	0.891075	−	0.453856i	$-0.149952\pi$
$607$	43.9075	1.78215	0.891075	+	0.453856i	$0.149952\pi$
$608$	−1.84283	−0.0747365
$609$	16.2972	0.660398
$610$	−30.4862	−1.23435
$611$	36.0063	1.45666
$612$	−17.2949	−0.699105
$613$	−29.5240	−1.19246	−0.596232	−	0.802812i	$-0.703336\pi$
$613$	−29.5240	−1.19246	−0.596232	+	0.802812i	$0.703336\pi$
$614$	−18.8150	−0.759310
$615$	−2.93060	−0.118173
$616$	−13.1870	−0.531320
$617$	29.9401	1.20534	0.602672	−	0.797989i	$-0.294103\pi$
$617$	29.9401	1.20534	0.602672	+	0.797989i	$0.294103\pi$
$618$	−22.0866	−0.888454
$619$	4.22964	0.170004	0.0850018	−	0.996381i	$-0.472910\pi$
$619$	4.22964	0.170004	0.0850018	+	0.996381i	$0.472910\pi$
$620$	−23.0387	−0.925257
$621$	0.885865	0.0355485
$622$	−1.17689	−0.0471889
$623$	−14.8931	−0.596680
$624$	−6.30514	−0.252407
$625$	−6.55649	−0.262259
$626$	13.7512	0.549610
$627$	20.1185	0.803457
$628$	10.8903	0.434569
$629$	−24.4796	−0.976064
$630$	26.5742	1.05874
$631$	−46.6851	−1.85850	−0.929252	−	0.369446i	$-0.879548\pi$
$631$	−46.6851	−1.85850	−0.929252	+	0.369446i	$0.879548\pi$
$632$	−7.32188	−0.291249
$633$	−41.8312	−1.66264
$634$	−4.27224	−0.169672
$635$	−67.8156	−2.69118
$636$	−29.3721	−1.16468
$637$	3.21472	0.127372
$638$	11.0364	0.436937
$639$	−4.32416	−0.171061
$640$	−3.53118	−0.139582
$641$	39.5775	1.56322	0.781609	−	0.623768i	$-0.214399\pi$
$641$	39.5775	1.56322	0.781609	+	0.623768i	$0.214399\pi$
$642$	2.03072	0.0801462
$643$	17.9126	0.706404	0.353202	−	0.935547i	$-0.385093\pi$
$643$	17.9126	0.706404	0.353202	+	0.935547i	$0.385093\pi$
$644$	−2.86520	−0.112905
$645$	−43.9239	−1.72950
$646$	12.1344	0.477423
$647$	−23.0255	−0.905224	−0.452612	−	0.891707i	$-0.649508\pi$
$647$	−23.0255	−0.905224	−0.452612	+	0.891707i	$0.649508\pi$
$648$	9.98091	0.392087
$649$	11.1958	0.439475
$650$	−19.8541	−0.778744
$651$	−44.3419	−1.73789
$652$	−1.48802	−0.0582752
$653$	20.5208	0.803040	0.401520	−	0.915850i	$-0.368482\pi$
$653$	20.5208	0.803040	0.401520	+	0.915850i	$0.368482\pi$
$654$	−25.7683	−1.00762
$655$	3.53118	0.137975
$656$	0.349877	0.0136604
$657$	−12.0927	−0.471783
$658$	38.8115	1.51303
$659$	12.3967	0.482908	0.241454	−	0.970412i	$-0.422376\pi$
$659$	12.3967	0.482908	0.241454	+	0.970412i	$0.422376\pi$
$660$	38.5507	1.50058
$661$	−5.06913	−0.197166	−0.0985831	−	0.995129i	$-0.531431\pi$
$661$	−5.06913	−0.197166	−0.0985831	+	0.995129i	$0.531431\pi$
$662$	31.3277	1.21759
$663$	41.5173	1.61240
$664$	7.98777	0.309986
$665$	−18.6449	−0.723019
$666$	−9.76456	−0.378369
$667$	2.39794	0.0928486
$668$	−1.28328	−0.0496516
$669$	−35.9734	−1.39081
$670$	26.2256	1.01318
$671$	−39.7351	−1.53395
$672$	−6.79636	−0.262175
$673$	6.79725	0.262015	0.131007	−	0.991381i	$-0.458179\pi$
$673$	6.79725	0.262015	0.131007	+	0.991381i	$0.458179\pi$
$674$	32.6826	1.25889
$675$	6.61675	0.254679
$676$	−5.93442	−0.228247
$677$	−36.2236	−1.39218	−0.696092	−	0.717952i	$-0.745080\pi$
$677$	−36.2236	−1.39218	−0.696092	+	0.717952i	$0.745080\pi$
$678$	3.30841	0.127059
$679$	12.5597	0.481996
$680$	23.2517	0.891662
$681$	−3.99805	−0.153206
$682$	−30.0282	−1.14984
$683$	−13.3243	−0.509842	−0.254921	−	0.966962i	$-0.582049\pi$
$683$	−13.3243	−0.509842	−0.254921	+	0.966962i	$0.582049\pi$
$684$	4.84026	0.185072
$685$	−47.3800	−1.81030
$686$	−16.5913	−0.633457
$687$	−1.53977	−0.0587458
$688$	5.24396	0.199924
$689$	32.9146	1.25395
$690$	8.37608	0.318872
$691$	20.6876	0.786993	0.393497	−	0.919326i	$-0.371265\pi$
$691$	20.6876	0.786993	0.393497	+	0.919326i	$0.371265\pi$
$692$	15.6009	0.593058
$693$	34.6362	1.31572
$694$	19.5655	0.742696
$695$	−0.452114	−0.0171496
$696$	5.68799	0.215603
$697$	−2.30383	−0.0872638
$698$	13.9082	0.526433
$699$	−5.63739	−0.213226
$700$	−21.4009	−0.808880
$701$	14.8534	0.561004	0.280502	−	0.959853i	$-0.409499\pi$
$701$	14.8534	0.561004	0.280502	+	0.959853i	$0.409499\pi$
$702$	−2.35473	−0.0888736
$703$	6.85100	0.258390
$704$	−4.60247	−0.173462
$705$	−113.461	−4.27318
$706$	21.3628	0.804001
$707$	19.6814	0.740194
$708$	5.77013	0.216855
$709$	−3.73424	−0.140242	−0.0701211	−	0.997538i	$-0.522339\pi$
$709$	−3.73424	−0.140242	−0.0701211	+	0.997538i	$0.522339\pi$
$710$	5.81351	0.218177
$711$	19.2312	0.721226
$712$	−5.19792	−0.194800
$713$	−6.52436	−0.244339
$714$	44.7518	1.67480
$715$	−43.2002	−1.61559
$716$	2.30979	0.0863208
$717$	41.7454	1.55901
$718$	6.05902	0.226120
$719$	−48.2345	−1.79884	−0.899422	−	0.437082i	$-0.856012\pi$
$719$	−48.2345	−1.79884	−0.899422	+	0.437082i	$0.856012\pi$
$720$	9.27479	0.345651
$721$	26.6787	0.993565
$722$	15.6040	0.580720
$723$	52.8063	1.96389
$724$	−1.65690	−0.0615782
$725$	17.9108	0.665191
$726$	24.1538	0.896432
$727$	27.0226	1.00221	0.501107	−	0.865385i	$-0.332926\pi$
$727$	27.0226	1.00221	0.501107	+	0.865385i	$0.332926\pi$
$728$	7.61604	0.282269
$729$	−19.9113	−0.737457
$730$	16.2578	0.601728
$731$	−34.5298	−1.27713
$732$	−20.4787	−0.756916
$733$	−15.2136	−0.561928	−0.280964	−	0.959718i	$-0.590654\pi$
$733$	−15.2136	−0.561928	−0.280964	+	0.959718i	$0.590654\pi$
$734$	26.9114	0.993319
$735$	−10.1300	−0.373651
$736$	−1.00000	−0.0368605
$737$	34.1819	1.25910
$738$	−0.918966	−0.0338276
$739$	1.87499	0.0689727	0.0344863	−	0.999405i	$-0.489020\pi$
$739$	1.87499	0.0689727	0.0344863	+	0.999405i	$0.489020\pi$
$740$	13.1277	0.482585
$741$	−11.6193	−0.426845
$742$	35.4789	1.30247
$743$	−49.8667	−1.82943	−0.914717	−	0.404096i	$-0.867586\pi$
$743$	−49.8667	−1.82943	−0.914717	+	0.404096i	$0.867586\pi$
$744$	−15.4760	−0.567377
$745$	38.3788	1.40609
$746$	−18.0155	−0.659594
$747$	−20.9802	−0.767625
$748$	30.3058	1.10809
$749$	−2.45293	−0.0896282
$750$	20.6827	0.755225
$751$	−19.9923	−0.729530	−0.364765	−	0.931100i	$-0.618851\pi$
$751$	−19.9923	−0.729530	−0.364765	+	0.931100i	$0.618851\pi$
$752$	13.5458	0.493965
$753$	−60.0012	−2.18656
$754$	−6.37400	−0.232127
$755$	−71.4101	−2.59888
$756$	−2.53818	−0.0923129
$757$	22.8026	0.828776	0.414388	−	0.910100i	$-0.363996\pi$
$757$	22.8026	0.828776	0.414388	+	0.910100i	$0.363996\pi$
$758$	12.2255	0.444050
$759$	10.9172	0.396270
$760$	−6.50736	−0.236047
$761$	−22.5876	−0.818799	−0.409399	−	0.912355i	$-0.634262\pi$
$761$	−22.5876	−0.818799	−0.409399	+	0.912355i	$0.634262\pi$
$762$	−45.5544	−1.65026
$763$	31.1259	1.12683
$764$	−15.3327	−0.554717
$765$	−61.0715	−2.20804
$766$	10.9076	0.394109
$767$	−6.46605	−0.233475
$768$	−2.37203	−0.0855933
$769$	−7.91301	−0.285350	−0.142675	−	0.989770i	$-0.545570\pi$
$769$	−7.91301	−0.285350	−0.142675	+	0.989770i	$0.545570\pi$
$770$	−46.5658	−1.67812
$771$	52.0081	1.87303
$772$	18.0487	0.649587
$773$	19.8640	0.714460	0.357230	−	0.934016i	$-0.383721\pi$
$773$	19.8640	0.714460	0.357230	+	0.934016i	$0.383721\pi$
$774$	−13.7735	−0.495077
$775$	−48.7321	−1.75051
$776$	4.38352	0.157359
$777$	25.2665	0.906431
$778$	−19.6342	−0.703920
$779$	0.644763	0.0231010
$780$	−22.2646	−0.797200
$781$	7.57721	0.271134
$782$	6.58468	0.235468
$783$	2.12425	0.0759145
$784$	1.20940	0.0431927
$785$	38.4555	1.37254
$786$	2.37203	0.0846076
$787$	−44.3764	−1.58185	−0.790924	−	0.611914i	$-0.790400\pi$
$787$	−44.3764	−1.58185	−0.790924	+	0.611914i	$0.790400\pi$
$788$	12.4726	0.444318
$789$	13.6888	0.487335
$790$	−25.8549	−0.919876
$791$	−3.99627	−0.142091
$792$	12.0886	0.429548
$793$	22.9486	0.814929
$794$	22.9879	0.815809
$795$	−103.718	−3.67851
$796$	14.9259	0.529035
$797$	46.7683	1.65662	0.828309	−	0.560272i	$-0.189303\pi$
$797$	46.7683	1.65662	0.828309	+	0.560272i	$0.189303\pi$
$798$	−12.5245	−0.443363
$799$	−89.1948	−3.15548
$800$	−7.46926	−0.264078
$801$	13.6525	0.482388
$802$	36.6215	1.29315
$803$	21.1901	0.747781
$804$	17.6167	0.621294
$805$	−10.1176	−0.356597
$806$	17.3425	0.610863
$807$	14.0230	0.493635
$808$	6.86910	0.241654
$809$	37.5122	1.31886	0.659430	−	0.751766i	$-0.270798\pi$
$809$	37.5122	1.31886	0.659430	+	0.751766i	$0.270798\pi$
$810$	35.2444	1.23836
$811$	−31.7522	−1.11497	−0.557484	−	0.830187i	$-0.688233\pi$
$811$	−31.7522	−1.11497	−0.557484	+	0.830187i	$0.688233\pi$
$812$	−6.87058	−0.241110
$813$	60.4147	2.11884
$814$	17.1104	0.599719
$815$	−5.25446	−0.184056
$816$	15.6191	0.546777
$817$	9.66372	0.338091
$818$	2.15209	0.0752459
$819$	−20.0038	−0.698990
$820$	1.23548	0.0431449
$821$	−8.28674	−0.289209	−0.144605	−	0.989490i	$-0.546191\pi$
$821$	−8.28674	−0.289209	−0.144605	+	0.989490i	$0.546191\pi$
$822$	−31.8270	−1.11009
$823$	−25.8356	−0.900574	−0.450287	−	0.892884i	$-0.648678\pi$
$823$	−25.8356	−0.900574	−0.450287	+	0.892884i	$0.648678\pi$
$824$	9.31126	0.324373
$825$	81.5435	2.83898
$826$	−6.96981	−0.242511
$827$	39.0464	1.35778	0.678888	−	0.734242i	$-0.262462\pi$
$827$	39.0464	1.35778	0.678888	+	0.734242i	$0.262462\pi$
$828$	2.62654	0.0912785
$829$	−32.1720	−1.11738	−0.558691	−	0.829376i	$-0.688696\pi$
$829$	−32.1720	−1.11738	−0.558691	+	0.829376i	$0.688696\pi$
$830$	28.2063	0.979054
$831$	−29.2570	−1.01491
$832$	2.65812	0.0921536
$833$	−7.96349	−0.275919
$834$	−0.303702	−0.0105163
$835$	−4.53150	−0.156819
$836$	−8.48156	−0.293341
$837$	−5.77970	−0.199776
$838$	17.0774	0.589928
$839$	−39.8153	−1.37458	−0.687289	−	0.726385i	$-0.741199\pi$
$839$	−39.8153	−1.37458	−0.687289	+	0.726385i	$0.741199\pi$
$840$	−23.9992	−0.828051
$841$	−23.2499	−0.801720
$842$	−0.0841046	−0.00289843
$843$	65.5073	2.25619
$844$	17.6352	0.607027
$845$	−20.9555	−0.720892
$846$	−35.5786	−1.22322
$847$	−29.1757	−1.00249
$848$	12.3827	0.425223
$849$	20.1407	0.691228
$850$	49.1827	1.68695
$851$	3.71765	0.127440
$852$	3.90516	0.133789
$853$	−12.6996	−0.434826	−0.217413	−	0.976080i	$-0.569762\pi$
$853$	−12.6996	−0.434826	−0.217413	+	0.976080i	$0.569762\pi$
$854$	24.7365	0.846466
$855$	17.0918	0.584528
$856$	−0.856111	−0.0292613
$857$	−36.0254	−1.23061	−0.615303	−	0.788291i	$-0.710966\pi$
$857$	−36.0254	−1.23061	−0.615303	+	0.788291i	$0.710966\pi$
$858$	−29.0192	−0.990700
$859$	40.0603	1.36684	0.683420	−	0.730026i	$-0.260492\pi$
$859$	40.0603	1.36684	0.683420	+	0.730026i	$0.260492\pi$
$860$	18.5174	0.631438
$861$	2.37789	0.0810383
$862$	12.7222	0.433321
$863$	19.4249	0.661232	0.330616	−	0.943765i	$-0.392744\pi$
$863$	19.4249	0.661232	0.330616	+	0.943765i	$0.392744\pi$
$864$	−0.885865	−0.0301377
$865$	55.0897	1.87311
$866$	−38.6024	−1.31176
$867$	−62.5220	−2.12336
$868$	18.6936	0.634503
$869$	−33.6987	−1.14315
$870$	20.0853	0.680956
$871$	−19.7414	−0.668912
$872$	10.8634	0.367881
$873$	−11.5135	−0.389672
$874$	−1.84283	−0.0623346
$875$	−24.9829	−0.844575
$876$	10.9210	0.368986
$877$	−40.3489	−1.36248	−0.681242	−	0.732058i	$-0.738560\pi$
$877$	−40.3489	−1.36248	−0.681242	+	0.732058i	$0.738560\pi$
$878$	25.2085	0.850747
$879$	22.6637	0.764429
$880$	−16.2522	−0.547861
$881$	21.7726	0.733539	0.366769	−	0.930312i	$-0.380464\pi$
$881$	21.7726	0.733539	0.366769	+	0.930312i	$0.380464\pi$
$882$	−3.17653	−0.106959
$883$	−26.7765	−0.901102	−0.450551	−	0.892751i	$-0.648772\pi$
$883$	−26.7765	−0.901102	−0.450551	+	0.892751i	$0.648772\pi$
$884$	−17.5028	−0.588684
$885$	20.3754	0.684911
$886$	−37.5340	−1.26098
$887$	−25.4827	−0.855626	−0.427813	−	0.903867i	$-0.640716\pi$
$887$	−25.4827	−0.855626	−0.427813	+	0.903867i	$0.640716\pi$
$888$	8.81840	0.295926
$889$	55.0256	1.84550
$890$	−18.3548	−0.615255
$891$	45.9369	1.53894
$892$	15.1656	0.507783
$893$	24.9626	0.835341
$894$	25.7805	0.862229
$895$	8.15628	0.272634
$896$	2.86520	0.0957198
$897$	−6.30514	−0.210522
$898$	−33.5043	−1.11805
$899$	−15.6450	−0.521790
$900$	19.6183	0.653943
$901$	−81.5360	−2.71636
$902$	1.61030	0.0536171
$903$	35.6399	1.18602
$904$	−1.39476	−0.0463890
$905$	−5.85082	−0.194488
$906$	−47.9689	−1.59366
$907$	−28.5005	−0.946342	−0.473171	−	0.880971i	$-0.656891\pi$
$907$	−28.5005	−0.946342	−0.473171	+	0.880971i	$0.656891\pi$
$908$	1.68550	0.0559352
$909$	−18.0419	−0.598413
$910$	26.8936	0.891516
$911$	60.1730	1.99362	0.996810	−	0.0798139i	$-0.0254326\pi$
$911$	60.1730	1.99362	0.996810	+	0.0798139i	$0.0254326\pi$
$912$	−4.37125	−0.144746
$913$	36.7635	1.21669
$914$	24.4964	0.810269
$915$	−72.3142	−2.39063
$916$	0.649134	0.0214480
$917$	−2.86520	−0.0946174
$918$	5.83314	0.192522
$919$	23.7586	0.783725	0.391862	−	0.920024i	$-0.371831\pi$
$919$	23.7586	0.783725	0.391862	+	0.920024i	$0.371831\pi$
$920$	−3.53118	−0.116420
$921$	−44.6297	−1.47060
$922$	−1.63657	−0.0538974
$923$	−4.37615	−0.144043
$924$	−31.2800	−1.02904
$925$	27.7681	0.913010
$926$	−35.5683	−1.16885
$927$	−24.4564	−0.803253
$928$	−2.39794	−0.0787162
$929$	8.42074	0.276276	0.138138	−	0.990413i	$-0.455888\pi$
$929$	8.42074	0.276276	0.138138	+	0.990413i	$0.455888\pi$
$930$	−54.6486	−1.79200
$931$	2.22871	0.0730430
$932$	2.37661	0.0778484
$933$	−2.79162	−0.0913934
$934$	−1.65707	−0.0542210
$935$	107.015	3.49978
$936$	−6.98164	−0.228202
$937$	9.88632	0.322972	0.161486	−	0.986875i	$-0.448371\pi$
$937$	9.88632	0.322972	0.161486	+	0.986875i	$0.448371\pi$
$938$	−21.2794	−0.694798
$939$	32.6184	1.06446
$940$	47.8327	1.56013
$941$	−32.6253	−1.06355	−0.531777	−	0.846885i	$-0.678475\pi$
$941$	−32.6253	−1.06355	−0.531777	+	0.846885i	$0.678475\pi$
$942$	25.8321	0.841654
$943$	0.349877	0.0113936
$944$	−2.43257	−0.0791734
$945$	−8.96279	−0.291560
$946$	24.1352	0.784703
$947$	24.1008	0.783172	0.391586	−	0.920141i	$-0.371926\pi$
$947$	24.1008	0.783172	0.391586	+	0.920141i	$0.371926\pi$
$948$	−17.3677	−0.564078
$949$	−12.2381	−0.397266
$950$	−13.7646	−0.446581
$951$	−10.1339	−0.328614
$952$	−18.8665	−0.611465
$953$	−0.345883	−0.0112043	−0.00560213	−	0.999984i	$-0.501783\pi$
$953$	−0.345883	−0.0112043	−0.00560213	+	0.999984i	$0.501783\pi$
$954$	−32.5236	−1.05299
$955$	−54.1425	−1.75201
$956$	−17.5990	−0.569192
$957$	26.1788	0.846241
$958$	−15.7331	−0.508315
$959$	38.4442	1.24143
$960$	−8.37608	−0.270337
$961$	11.5672	0.373137
$962$	−9.88195	−0.318607
$963$	2.24861	0.0724604
$964$	−22.2621	−0.717013
$965$	63.7333	2.05165
$966$	−6.79636	−0.218669
$967$	21.8543	0.702787	0.351393	−	0.936228i	$-0.385708\pi$
$967$	21.8543	0.702787	0.351393	+	0.936228i	$0.385708\pi$
$968$	−10.1828	−0.327286
$969$	28.7833	0.924651
$970$	15.4790	0.497001
$971$	−15.1720	−0.486892	−0.243446	−	0.969914i	$-0.578278\pi$
$971$	−15.1720	−0.486892	−0.243446	+	0.969914i	$0.578278\pi$
$972$	21.0175	0.674135
$973$	0.366845	0.0117605
$974$	8.28468	0.265458
$975$	−47.0947	−1.50824
$976$	8.63341	0.276349
$977$	−44.0516	−1.40934	−0.704668	−	0.709537i	$-0.748904\pi$
$977$	−44.0516	−1.40934	−0.704668	+	0.709537i	$0.748904\pi$
$978$	−3.52962	−0.112865
$979$	−23.9233	−0.764591
$980$	4.27060	0.136419
$981$	−28.5331	−0.910993
$982$	39.5767	1.26294
$983$	37.5443	1.19748	0.598739	−	0.800944i	$-0.295669\pi$
$983$	37.5443	1.19748	0.598739	+	0.800944i	$0.295669\pi$
$984$	0.829920	0.0264569
$985$	44.0431	1.40333
$986$	15.7897	0.502845
$987$	92.0621	2.93037
$988$	4.89845	0.155840
$989$	5.24396	0.166748
$990$	42.6869	1.35668
$991$	−18.8640	−0.599233	−0.299617	−	0.954060i	$-0.596859\pi$
$991$	−18.8640	−0.599233	−0.299617	+	0.954060i	$0.596859\pi$
$992$	6.52436	0.207149
$993$	74.3103	2.35817
$994$	−4.71709	−0.149617
$995$	52.7061	1.67090
$996$	18.9472	0.600367
$997$	−20.6152	−0.652889	−0.326445	−	0.945216i	$-0.605851\pi$
$997$	−20.6152	−0.652889	−0.326445	+	0.945216i	$0.605851\pi$
$998$	−9.09192	−0.287800
$999$	3.29334	0.104197

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.5	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.37203 q^{3} +1.00000 q^{4} +3.53118 q^{5} +2.37203 q^{6} -2.86520 q^{7} -1.00000 q^{8} +2.62654 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.37203 q^{3} +1.00000 q^{4} +3.53118 q^{5} +2.37203 q^{6} -2.86520 q^{7} -1.00000 q^{8} +2.62654 q^{9} -3.53118 q^{10} -4.60247 q^{11} -2.37203 q^{12} +2.65812 q^{13} +2.86520 q^{14} -8.37608 q^{15} +1.00000 q^{16} -6.58468 q^{17} -2.62654 q^{18} +1.84283 q^{19} +3.53118 q^{20} +6.79636 q^{21} +4.60247 q^{22} +1.00000 q^{23} +2.37203 q^{24} +7.46926 q^{25} -2.65812 q^{26} +0.885865 q^{27} -2.86520 q^{28} +2.39794 q^{29} +8.37608 q^{30} -6.52436 q^{31} -1.00000 q^{32} +10.9172 q^{33} +6.58468 q^{34} -10.1176 q^{35} +2.62654 q^{36} +3.71765 q^{37} -1.84283 q^{38} -6.30514 q^{39} -3.53118 q^{40} +0.349877 q^{41} -6.79636 q^{42} +5.24396 q^{43} -4.60247 q^{44} +9.27479 q^{45} -1.00000 q^{46} +13.5458 q^{47} -2.37203 q^{48} +1.20940 q^{49} -7.46926 q^{50} +15.6191 q^{51} +2.65812 q^{52} +12.3827 q^{53} -0.885865 q^{54} -16.2522 q^{55} +2.86520 q^{56} -4.37125 q^{57} -2.39794 q^{58} -2.43257 q^{59} -8.37608 q^{60} +8.63341 q^{61} +6.52436 q^{62} -7.52557 q^{63} +1.00000 q^{64} +9.38629 q^{65} -10.9172 q^{66} -7.42685 q^{67} -6.58468 q^{68} -2.37203 q^{69} +10.1176 q^{70} -1.64634 q^{71} -2.62654 q^{72} -4.60406 q^{73} -3.71765 q^{74} -17.7173 q^{75} +1.84283 q^{76} +13.1870 q^{77} +6.30514 q^{78} +7.32188 q^{79} +3.53118 q^{80} -9.98091 q^{81} -0.349877 q^{82} -7.98777 q^{83} +6.79636 q^{84} -23.2517 q^{85} -5.24396 q^{86} -5.68799 q^{87} +4.60247 q^{88} +5.19792 q^{89} -9.27479 q^{90} -7.61604 q^{91} +1.00000 q^{92} +15.4760 q^{93} -13.5458 q^{94} +6.50736 q^{95} +2.37203 q^{96} -4.38352 q^{97} -1.20940 q^{98} -12.0886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 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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