LMFDB - Embedded newform 6026.2.a.i.1.4

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			1.4
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.39972 q^{3} +1.00000 q^{4} +1.46275 q^{5} +2.39972 q^{6} +0.813594 q^{7} -1.00000 q^{8} +2.75865 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.39972 q^{3} +1.00000 q^{4} +1.46275 q^{5} +2.39972 q^{6} +0.813594 q^{7} -1.00000 q^{8} +2.75865 q^{9} -1.46275 q^{10} +3.06412 q^{11} -2.39972 q^{12} +2.86180 q^{13} -0.813594 q^{14} -3.51019 q^{15} +1.00000 q^{16} +0.904748 q^{17} -2.75865 q^{18} -1.54618 q^{19} +1.46275 q^{20} -1.95240 q^{21} -3.06412 q^{22} +1.00000 q^{23} +2.39972 q^{24} -2.86036 q^{25} -2.86180 q^{26} +0.579184 q^{27} +0.813594 q^{28} +1.89799 q^{29} +3.51019 q^{30} -4.44494 q^{31} -1.00000 q^{32} -7.35302 q^{33} -0.904748 q^{34} +1.19009 q^{35} +2.75865 q^{36} -3.09637 q^{37} +1.54618 q^{38} -6.86752 q^{39} -1.46275 q^{40} -3.00239 q^{41} +1.95240 q^{42} -1.65231 q^{43} +3.06412 q^{44} +4.03521 q^{45} -1.00000 q^{46} -7.73379 q^{47} -2.39972 q^{48} -6.33806 q^{49} +2.86036 q^{50} -2.17114 q^{51} +2.86180 q^{52} -4.92913 q^{53} -0.579184 q^{54} +4.48205 q^{55} -0.813594 q^{56} +3.71040 q^{57} -1.89799 q^{58} -9.37352 q^{59} -3.51019 q^{60} +9.96319 q^{61} +4.44494 q^{62} +2.24442 q^{63} +1.00000 q^{64} +4.18611 q^{65} +7.35302 q^{66} +3.71486 q^{67} +0.904748 q^{68} -2.39972 q^{69} -1.19009 q^{70} -12.1090 q^{71} -2.75865 q^{72} +1.67829 q^{73} +3.09637 q^{74} +6.86405 q^{75} -1.54618 q^{76} +2.49295 q^{77} +6.86752 q^{78} -11.4921 q^{79} +1.46275 q^{80} -9.66581 q^{81} +3.00239 q^{82} -4.73564 q^{83} -1.95240 q^{84} +1.32342 q^{85} +1.65231 q^{86} -4.55463 q^{87} -3.06412 q^{88} +6.25332 q^{89} -4.03521 q^{90} +2.32835 q^{91} +1.00000 q^{92} +10.6666 q^{93} +7.73379 q^{94} -2.26168 q^{95} +2.39972 q^{96} +4.11638 q^{97} +6.33806 q^{98} +8.45282 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.39972	−1.38548	−0.692739	−	0.721189i	$-0.743596\pi$
$3$	−2.39972	−1.38548	−0.692739	+	0.721189i	$0.743596\pi$
$4$	1.00000	0.500000
$5$	1.46275	0.654163	0.327081	−	0.944996i	$-0.393935\pi$
$5$	1.46275	0.654163	0.327081	+	0.944996i	$0.393935\pi$
$6$	2.39972	0.979681
$7$	0.813594	0.307510	0.153755	−	0.988109i	$-0.450863\pi$
$7$	0.813594	0.307510	0.153755	+	0.988109i	$0.450863\pi$
$8$	−1.00000	−0.353553
$9$	2.75865	0.919548
$10$	−1.46275	−0.462563
$11$	3.06412	0.923867	0.461933	−	0.886915i	$-0.347156\pi$
$11$	3.06412	0.923867	0.461933	+	0.886915i	$0.347156\pi$
$12$	−2.39972	−0.692739
$13$	2.86180	0.793721	0.396861	−	0.917879i	$-0.370100\pi$
$13$	2.86180	0.793721	0.396861	+	0.917879i	$0.370100\pi$
$14$	−0.813594	−0.217442
$15$	−3.51019	−0.906328
$16$	1.00000	0.250000
$17$	0.904748	0.219434	0.109717	−	0.993963i	$-0.465006\pi$
$17$	0.904748	0.219434	0.109717	+	0.993963i	$0.465006\pi$
$18$	−2.75865	−0.650219
$19$	−1.54618	−0.354719	−0.177359	−	0.984146i	$-0.556755\pi$
$19$	−1.54618	−0.354719	−0.177359	+	0.984146i	$0.556755\pi$
$20$	1.46275	0.327081
$21$	−1.95240	−0.426048
$22$	−3.06412	−0.653272
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.39972	0.489840
$25$	−2.86036	−0.572071
$26$	−2.86180	−0.561246
$27$	0.579184	0.111464
$28$	0.813594	0.153755
$29$	1.89799	0.352447	0.176224	−	0.984350i	$-0.443612\pi$
$29$	1.89799	0.352447	0.176224	+	0.984350i	$0.443612\pi$
$30$	3.51019	0.640870
$31$	−4.44494	−0.798335	−0.399167	−	0.916878i	$-0.630701\pi$
$31$	−4.44494	−0.798335	−0.399167	+	0.916878i	$0.630701\pi$
$32$	−1.00000	−0.176777
$33$	−7.35302	−1.28000
$34$	−0.904748	−0.155163
$35$	1.19009	0.201161
$36$	2.75865	0.459774
$37$	−3.09637	−0.509040	−0.254520	−	0.967068i	$-0.581917\pi$
$37$	−3.09637	−0.509040	−0.254520	+	0.967068i	$0.581917\pi$
$38$	1.54618	0.250824
$39$	−6.86752	−1.09968
$40$	−1.46275	−0.231281
$41$	−3.00239	−0.468895	−0.234447	−	0.972129i	$-0.575328\pi$
$41$	−3.00239	−0.468895	−0.234447	+	0.972129i	$0.575328\pi$
$42$	1.95240	0.301261
$43$	−1.65231	−0.251976	−0.125988	−	0.992032i	$-0.540210\pi$
$43$	−1.65231	−0.251976	−0.125988	+	0.992032i	$0.540210\pi$
$44$	3.06412	0.461933
$45$	4.03521	0.601534
$46$	−1.00000	−0.147442
$47$	−7.73379	−1.12809	−0.564045	−	0.825744i	$-0.690756\pi$
$47$	−7.73379	−1.12809	−0.564045	+	0.825744i	$0.690756\pi$
$48$	−2.39972	−0.346369
$49$	−6.33806	−0.905438
$50$	2.86036	0.404515
$51$	−2.17114	−0.304021
$52$	2.86180	0.396861
$53$	−4.92913	−0.677068	−0.338534	−	0.940954i	$-0.609931\pi$
$53$	−4.92913	−0.677068	−0.338534	+	0.940954i	$0.609931\pi$
$54$	−0.579184	−0.0788169
$55$	4.48205	0.604359
$56$	−0.813594	−0.108721
$57$	3.71040	0.491455
$58$	−1.89799	−0.249218
$59$	−9.37352	−1.22033	−0.610164	−	0.792275i	$-0.708897\pi$
$59$	−9.37352	−1.22033	−0.610164	+	0.792275i	$0.708897\pi$
$60$	−3.51019	−0.453164
$61$	9.96319	1.27566	0.637828	−	0.770179i	$-0.279833\pi$
$61$	9.96319	1.27566	0.637828	+	0.770179i	$0.279833\pi$
$62$	4.44494	0.564508
$63$	2.24442	0.282770
$64$	1.00000	0.125000
$65$	4.18611	0.519223
$66$	7.35302	0.905094
$67$	3.71486	0.453843	0.226921	−	0.973913i	$-0.427134\pi$
$67$	3.71486	0.453843	0.226921	+	0.973913i	$0.427134\pi$
$68$	0.904748	0.109717
$69$	−2.39972	−0.288892
$70$	−1.19009	−0.142243
$71$	−12.1090	−1.43708	−0.718538	−	0.695488i	$-0.755188\pi$
$71$	−12.1090	−1.43708	−0.718538	+	0.695488i	$0.755188\pi$
$72$	−2.75865	−0.325109
$73$	1.67829	0.196429	0.0982145	−	0.995165i	$-0.468687\pi$
$73$	1.67829	0.196429	0.0982145	+	0.995165i	$0.468687\pi$
$74$	3.09637	0.359946
$75$	6.86405	0.792592
$76$	−1.54618	−0.177359
$77$	2.49295	0.284098
$78$	6.86752	0.777593
$79$	−11.4921	−1.29296	−0.646480	−	0.762931i	$-0.723760\pi$
$79$	−11.4921	−1.29296	−0.646480	+	0.762931i	$0.723760\pi$
$80$	1.46275	0.163541
$81$	−9.66581	−1.07398
$82$	3.00239	0.331559
$83$	−4.73564	−0.519804	−0.259902	−	0.965635i	$-0.583690\pi$
$83$	−4.73564	−0.519804	−0.259902	+	0.965635i	$0.583690\pi$
$84$	−1.95240	−0.213024
$85$	1.32342	0.143545
$86$	1.65231	0.178174
$87$	−4.55463	−0.488308
$88$	−3.06412	−0.326636
$89$	6.25332	0.662851	0.331425	−	0.943481i	$-0.392470\pi$
$89$	6.25332	0.662851	0.331425	+	0.943481i	$0.392470\pi$
$90$	−4.03521	−0.425349
$91$	2.32835	0.244077
$92$	1.00000	0.104257
$93$	10.6666	1.10608
$94$	7.73379	0.797680
$95$	−2.26168	−0.232044
$96$	2.39972	0.244920
$97$	4.11638	0.417955	0.208977	−	0.977920i	$-0.432987\pi$
$97$	4.11638	0.417955	0.208977	+	0.977920i	$0.432987\pi$
$98$	6.33806	0.640241
$99$	8.45282	0.849540
$100$	−2.86036	−0.286036
$101$	−0.635708	−0.0632554	−0.0316277	−	0.999500i	$-0.510069\pi$
$101$	−0.635708	−0.0632554	−0.0316277	+	0.999500i	$0.510069\pi$
$102$	2.17114	0.214975
$103$	−3.18439	−0.313767	−0.156883	−	0.987617i	$-0.550145\pi$
$103$	−3.18439	−0.313767	−0.156883	+	0.987617i	$0.550145\pi$
$104$	−2.86180	−0.280623
$105$	−2.85587	−0.278705
$106$	4.92913	0.478759
$107$	−7.80643	−0.754676	−0.377338	−	0.926076i	$-0.623161\pi$
$107$	−7.80643	−0.754676	−0.377338	+	0.926076i	$0.623161\pi$
$108$	0.579184	0.0557320
$109$	9.57356	0.916981	0.458490	−	0.888699i	$-0.348390\pi$
$109$	9.57356	0.916981	0.458490	+	0.888699i	$0.348390\pi$
$110$	−4.48205	−0.427346
$111$	7.43041	0.705263
$112$	0.813594	0.0768774
$113$	−14.3790	−1.35266	−0.676332	−	0.736597i	$-0.736432\pi$
$113$	−14.3790	−1.35266	−0.676332	+	0.736597i	$0.736432\pi$
$114$	−3.71040	−0.347511
$115$	1.46275	0.136402
$116$	1.89799	0.176224
$117$	7.89470	0.729865
$118$	9.37352	0.862902
$119$	0.736098	0.0674780
$120$	3.51019	0.320435
$121$	−1.61118	−0.146471
$122$	−9.96319	−0.902025
$123$	7.20489	0.649643
$124$	−4.44494	−0.399167
$125$	−11.4978	−1.02839
$126$	−2.24442	−0.199949
$127$	−1.50464	−0.133515	−0.0667575	−	0.997769i	$-0.521265\pi$
$127$	−1.50464	−0.133515	−0.0667575	+	0.997769i	$0.521265\pi$
$128$	−1.00000	−0.0883883
$129$	3.96509	0.349107
$130$	−4.18611	−0.367146
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−7.35302	−0.639998
$133$	−1.25797	−0.109079
$134$	−3.71486	−0.320915
$135$	0.847202	0.0729155
$136$	−0.904748	−0.0775815
$137$	0.999989	0.0854349	0.0427174	−	0.999087i	$-0.486398\pi$
$137$	0.999989	0.0854349	0.0427174	+	0.999087i	$0.486398\pi$
$138$	2.39972	0.204278
$139$	−11.6809	−0.990764	−0.495382	−	0.868675i	$-0.664972\pi$
$139$	−11.6809	−0.990764	−0.495382	+	0.868675i	$0.664972\pi$
$140$	1.19009	0.100581
$141$	18.5589	1.56294
$142$	12.1090	1.01617
$143$	8.76890	0.733292
$144$	2.75865	0.229887
$145$	2.77628	0.230558
$146$	−1.67829	−0.138896
$147$	15.2096	1.25446
$148$	−3.09637	−0.254520
$149$	0.487928	0.0399726	0.0199863	−	0.999800i	$-0.493638\pi$
$149$	0.487928	0.0399726	0.0199863	+	0.999800i	$0.493638\pi$
$150$	−6.86405	−0.560447
$151$	10.9684	0.892592	0.446296	−	0.894885i	$-0.352743\pi$
$151$	10.9684	0.892592	0.446296	+	0.894885i	$0.352743\pi$
$152$	1.54618	0.125412
$153$	2.49588	0.201780
$154$	−2.49295	−0.200888
$155$	−6.50185	−0.522241
$156$	−6.86752	−0.549841
$157$	−11.1294	−0.888224	−0.444112	−	0.895971i	$-0.646481\pi$
$157$	−11.1294	−0.888224	−0.444112	+	0.895971i	$0.646481\pi$
$158$	11.4921	0.914261
$159$	11.8285	0.938062
$160$	−1.46275	−0.115641
$161$	0.813594	0.0641202
$162$	9.66581	0.759418
$163$	1.59275	0.124754	0.0623768	−	0.998053i	$-0.480132\pi$
$163$	1.59275	0.124754	0.0623768	+	0.998053i	$0.480132\pi$
$164$	−3.00239	−0.234447
$165$	−10.7556	−0.837326
$166$	4.73564	0.367557
$167$	2.58158	0.199769	0.0998843	−	0.994999i	$-0.468153\pi$
$167$	2.58158	0.199769	0.0998843	+	0.994999i	$0.468153\pi$
$168$	1.95240	0.150631
$169$	−4.81009	−0.370007
$170$	−1.32342	−0.101502
$171$	−4.26537	−0.326181
$172$	−1.65231	−0.125988
$173$	4.05919	0.308615	0.154307	−	0.988023i	$-0.450685\pi$
$173$	4.05919	0.308615	0.154307	+	0.988023i	$0.450685\pi$
$174$	4.55463	0.345286
$175$	−2.32717	−0.175917
$176$	3.06412	0.230967
$177$	22.4938	1.69074
$178$	−6.25332	−0.468706
$179$	23.3718	1.74689	0.873447	−	0.486919i	$-0.161879\pi$
$179$	23.3718	1.74689	0.873447	+	0.486919i	$0.161879\pi$
$180$	4.03521	0.300767
$181$	−19.1396	−1.42263	−0.711317	−	0.702871i	$-0.751901\pi$
$181$	−19.1396	−1.42263	−0.711317	+	0.702871i	$0.751901\pi$
$182$	−2.32835	−0.172588
$183$	−23.9089	−1.76739
$184$	−1.00000	−0.0737210
$185$	−4.52922	−0.332995
$186$	−10.6666	−0.782113
$187$	2.77226	0.202727
$188$	−7.73379	−0.564045
$189$	0.471220	0.0342762
$190$	2.26168	0.164080
$191$	10.6728	0.772255	0.386127	−	0.922445i	$-0.373813\pi$
$191$	10.6728	0.772255	0.386127	+	0.922445i	$0.373813\pi$
$192$	−2.39972	−0.173185
$193$	22.2628	1.60251	0.801255	−	0.598323i	$-0.204166\pi$
$193$	22.2628	1.60251	0.801255	+	0.598323i	$0.204166\pi$
$194$	−4.11638	−0.295539
$195$	−10.0455	−0.719371
$196$	−6.33806	−0.452719
$197$	26.9338	1.91895	0.959477	−	0.281786i	$-0.0909268\pi$
$197$	26.9338	1.91895	0.959477	+	0.281786i	$0.0909268\pi$
$198$	−8.45282	−0.600715
$199$	−7.31007	−0.518197	−0.259099	−	0.965851i	$-0.583425\pi$
$199$	−7.31007	−0.518197	−0.259099	+	0.965851i	$0.583425\pi$
$200$	2.86036	0.202258
$201$	−8.91462	−0.628789
$202$	0.635708	0.0447283
$203$	1.54419	0.108381
$204$	−2.17114	−0.152010
$205$	−4.39175	−0.306733
$206$	3.18439	0.221867
$207$	2.75865	0.191739
$208$	2.86180	0.198430
$209$	−4.73769	−0.327713
$210$	2.85587	0.197074
$211$	4.26394	0.293542	0.146771	−	0.989171i	$-0.453112\pi$
$211$	4.26394	0.293542	0.146771	+	0.989171i	$0.453112\pi$
$212$	−4.92913	−0.338534
$213$	29.0582	1.99104
$214$	7.80643	0.533637
$215$	−2.41693	−0.164833
$216$	−0.579184	−0.0394084
$217$	−3.61638	−0.245496
$218$	−9.57356	−0.648403
$219$	−4.02742	−0.272148
$220$	4.48205	0.302179
$221$	2.58921	0.174169
$222$	−7.43041	−0.498697
$223$	24.7642	1.65834	0.829168	−	0.558999i	$-0.188814\pi$
$223$	24.7642	1.65834	0.829168	+	0.558999i	$0.188814\pi$
$224$	−0.813594	−0.0543605
$225$	−7.89071	−0.526047
$226$	14.3790	0.956478
$227$	17.4784	1.16008	0.580042	−	0.814587i	$-0.303036\pi$
$227$	17.4784	1.16008	0.580042	+	0.814587i	$0.303036\pi$
$228$	3.71040	0.245727
$229$	−5.44225	−0.359634	−0.179817	−	0.983700i	$-0.557551\pi$
$229$	−5.44225	−0.359634	−0.179817	+	0.983700i	$0.557551\pi$
$230$	−1.46275	−0.0964510
$231$	−5.98237	−0.393611
$232$	−1.89799	−0.124609
$233$	−10.4212	−0.682717	−0.341358	−	0.939933i	$-0.610887\pi$
$233$	−10.4212	−0.682717	−0.341358	+	0.939933i	$0.610887\pi$
$234$	−7.89470	−0.516092
$235$	−11.3126	−0.737954
$236$	−9.37352	−0.610164
$237$	27.5778	1.79137
$238$	−0.736098	−0.0477141
$239$	−21.2310	−1.37332	−0.686660	−	0.726978i	$-0.740924\pi$
$239$	−21.2310	−1.37332	−0.686660	+	0.726978i	$0.740924\pi$
$240$	−3.51019	−0.226582
$241$	24.5765	1.58311	0.791557	−	0.611095i	$-0.209271\pi$
$241$	24.5765	1.58311	0.791557	+	0.611095i	$0.209271\pi$
$242$	1.61118	0.103570
$243$	21.4577	1.37651
$244$	9.96319	0.637828
$245$	−9.27102	−0.592304
$246$	−7.20489	−0.459367
$247$	−4.42487	−0.281548
$248$	4.44494	0.282254
$249$	11.3642	0.720177
$250$	11.4978	0.727182
$251$	−10.9984	−0.694213	−0.347107	−	0.937826i	$-0.612836\pi$
$251$	−10.9984	−0.694213	−0.347107	+	0.937826i	$0.612836\pi$
$252$	2.24442	0.141385
$253$	3.06412	0.192639
$254$	1.50464	0.0944093
$255$	−3.17584	−0.198879
$256$	1.00000	0.0625000
$257$	5.98703	0.373460	0.186730	−	0.982411i	$-0.440211\pi$
$257$	5.98703	0.373460	0.186730	+	0.982411i	$0.440211\pi$
$258$	−3.96509	−0.246856
$259$	−2.51919	−0.156535
$260$	4.18611	0.259611
$261$	5.23587	0.324092
$262$	−1.00000	−0.0617802
$263$	−6.34520	−0.391262	−0.195631	−	0.980678i	$-0.562675\pi$
$263$	−6.34520	−0.391262	−0.195631	+	0.980678i	$0.562675\pi$
$264$	7.35302	0.452547
$265$	−7.21009	−0.442912
$266$	1.25797	0.0771308
$267$	−15.0062	−0.918365
$268$	3.71486	0.226921
$269$	−14.4617	−0.881745	−0.440873	−	0.897570i	$-0.645331\pi$
$269$	−14.4617	−0.881745	−0.440873	+	0.897570i	$0.645331\pi$
$270$	−0.847202	−0.0515591
$271$	−29.1109	−1.76836	−0.884180	−	0.467147i	$-0.845282\pi$
$271$	−29.1109	−1.76836	−0.884180	+	0.467147i	$0.845282\pi$
$272$	0.904748	0.0548584
$273$	−5.58737	−0.338163
$274$	−0.999989	−0.0604116
$275$	−8.76447	−0.528518
$276$	−2.39972	−0.144446
$277$	−8.96632	−0.538734	−0.269367	−	0.963038i	$-0.586814\pi$
$277$	−8.96632	−0.538734	−0.269367	+	0.963038i	$0.586814\pi$
$278$	11.6809	0.700576
$279$	−12.2620	−0.734107
$280$	−1.19009	−0.0711213
$281$	18.2968	1.09149	0.545746	−	0.837950i	$-0.316246\pi$
$281$	18.2968	1.09149	0.545746	+	0.837950i	$0.316246\pi$
$282$	−18.5589	−1.10517
$283$	−22.0620	−1.31145	−0.655725	−	0.754999i	$-0.727637\pi$
$283$	−22.0620	−1.31145	−0.655725	+	0.754999i	$0.727637\pi$
$284$	−12.1090	−0.718538
$285$	5.42740	0.321491
$286$	−8.76890	−0.518516
$287$	−2.44273	−0.144190
$288$	−2.75865	−0.162555
$289$	−16.1814	−0.951849
$290$	−2.77628	−0.163029
$291$	−9.87814	−0.579067
$292$	1.67829	0.0982145
$293$	19.7031	1.15107	0.575534	−	0.817778i	$-0.304794\pi$
$293$	19.7031	1.15107	0.575534	+	0.817778i	$0.304794\pi$
$294$	−15.2096	−0.887040
$295$	−13.7111	−0.798293
$296$	3.09637	0.179973
$297$	1.77469	0.102978
$298$	−0.487928	−0.0282649
$299$	2.86180	0.165502
$300$	6.86405	0.396296
$301$	−1.34431	−0.0774849
$302$	−10.9684	−0.631158
$303$	1.52552	0.0876389
$304$	−1.54618	−0.0886797
$305$	14.5737	0.834487
$306$	−2.49588	−0.142680
$307$	−11.3388	−0.647138	−0.323569	−	0.946205i	$-0.604883\pi$
$307$	−11.3388	−0.647138	−0.323569	+	0.946205i	$0.604883\pi$
$308$	2.49295	0.142049
$309$	7.64163	0.434717
$310$	6.50185	0.369280
$311$	3.59044	0.203595	0.101798	−	0.994805i	$-0.467541\pi$
$311$	3.59044	0.203595	0.101798	+	0.994805i	$0.467541\pi$
$312$	6.86752	0.388797
$313$	−27.1652	−1.53547	−0.767735	−	0.640767i	$-0.778616\pi$
$313$	−27.1652	−1.53547	−0.767735	+	0.640767i	$0.778616\pi$
$314$	11.1294	0.628069
$315$	3.28303	0.184978
$316$	−11.4921	−0.646480
$317$	7.90363	0.443912	0.221956	−	0.975057i	$-0.428756\pi$
$317$	7.90363	0.443912	0.221956	+	0.975057i	$0.428756\pi$
$318$	−11.8285	−0.663310
$319$	5.81565	0.325614
$320$	1.46275	0.0817703
$321$	18.7332	1.04559
$322$	−0.813594	−0.0453398
$323$	−1.39891	−0.0778372
$324$	−9.66581	−0.536990
$325$	−8.18577	−0.454065
$326$	−1.59275	−0.0882141
$327$	−22.9738	−1.27046
$328$	3.00239	0.165779
$329$	−6.29217	−0.346899
$330$	10.7556	0.592079
$331$	−27.3514	−1.50337	−0.751684	−	0.659523i	$-0.770758\pi$
$331$	−27.3514	−1.50337	−0.751684	+	0.659523i	$0.770758\pi$
$332$	−4.73564	−0.259902
$333$	−8.54178	−0.468087
$334$	−2.58158	−0.141258
$335$	5.43392	0.296887
$336$	−1.95240	−0.106512
$337$	−11.1571	−0.607766	−0.303883	−	0.952709i	$-0.598283\pi$
$337$	−11.1571	−0.607766	−0.303883	+	0.952709i	$0.598283\pi$
$338$	4.81009	0.261634
$339$	34.5056	1.87409
$340$	1.32342	0.0717727
$341$	−13.6198	−0.737555
$342$	4.26537	0.230645
$343$	−10.8518	−0.585941
$344$	1.65231	0.0890868
$345$	−3.51019	−0.188982
$346$	−4.05919	−0.218223
$347$	4.08794	0.219452	0.109726	−	0.993962i	$-0.465003\pi$
$347$	4.08794	0.219452	0.109726	+	0.993962i	$0.465003\pi$
$348$	−4.55463	−0.244154
$349$	27.7722	1.48661	0.743305	−	0.668953i	$-0.233257\pi$
$349$	27.7722	1.48661	0.743305	+	0.668953i	$0.233257\pi$
$350$	2.32717	0.124392
$351$	1.65751	0.0884713
$352$	−3.06412	−0.163318
$353$	−3.21943	−0.171353	−0.0856764	−	0.996323i	$-0.527305\pi$
$353$	−3.21943	−0.171353	−0.0856764	+	0.996323i	$0.527305\pi$
$354$	−22.4938	−1.19553
$355$	−17.7125	−0.940081
$356$	6.25332	0.331425
$357$	−1.76643	−0.0934892
$358$	−23.3718	−1.23524
$359$	−7.93004	−0.418531	−0.209266	−	0.977859i	$-0.567107\pi$
$359$	−7.93004	−0.418531	−0.209266	+	0.977859i	$0.567107\pi$
$360$	−4.03521	−0.212674
$361$	−16.6093	−0.874175
$362$	19.1396	1.00595
$363$	3.86637	0.202932
$364$	2.32835	0.122038
$365$	2.45492	0.128496
$366$	23.9089	1.24974
$367$	−35.5396	−1.85515	−0.927575	−	0.373637i	$-0.878111\pi$
$367$	−35.5396	−1.85515	−0.927575	+	0.373637i	$0.878111\pi$
$368$	1.00000	0.0521286
$369$	−8.28253	−0.431171
$370$	4.52922	0.235463
$371$	−4.01031	−0.208205
$372$	10.6666	0.553038
$373$	27.2806	1.41253	0.706267	−	0.707945i	$-0.250378\pi$
$373$	27.2806	1.41253	0.706267	+	0.707945i	$0.250378\pi$
$374$	−2.77226	−0.143350
$375$	27.5914	1.42481
$376$	7.73379	0.398840
$377$	5.43166	0.279745
$378$	−0.471220	−0.0242370
$379$	−1.29574	−0.0665575	−0.0332788	−	0.999446i	$-0.510595\pi$
$379$	−1.29574	−0.0665575	−0.0332788	+	0.999446i	$0.510595\pi$
$380$	−2.26168	−0.116022
$381$	3.61070	0.184982
$382$	−10.6728	−0.546067
$383$	−0.0745281	−0.00380821	−0.00190410	−	0.999998i	$-0.500606\pi$
$383$	−0.0745281	−0.00380821	−0.00190410	+	0.999998i	$0.500606\pi$
$384$	2.39972	0.122460
$385$	3.64657	0.185846
$386$	−22.2628	−1.13315
$387$	−4.55815	−0.231704
$388$	4.11638	0.208977
$389$	25.9727	1.31687	0.658434	−	0.752639i	$-0.271219\pi$
$389$	25.9727	1.31687	0.658434	+	0.752639i	$0.271219\pi$
$390$	10.0455	0.508672
$391$	0.904748	0.0457551
$392$	6.33806	0.320121
$393$	−2.39972	−0.121050
$394$	−26.9338	−1.35691
$395$	−16.8101	−0.845806
$396$	8.45282	0.424770
$397$	4.73923	0.237855	0.118928	−	0.992903i	$-0.462054\pi$
$397$	4.73923	0.237855	0.118928	+	0.992903i	$0.462054\pi$
$398$	7.31007	0.366421
$399$	3.01876	0.151127
$400$	−2.86036	−0.143018
$401$	32.2131	1.60864	0.804322	−	0.594194i	$-0.202529\pi$
$401$	32.2131	1.60864	0.804322	+	0.594194i	$0.202529\pi$
$402$	8.91462	0.444621
$403$	−12.7205	−0.633655
$404$	−0.635708	−0.0316277
$405$	−14.1387	−0.702557
$406$	−1.54419	−0.0766369
$407$	−9.48764	−0.470285
$408$	2.17114	0.107487
$409$	−28.0134	−1.38517	−0.692586	−	0.721335i	$-0.743529\pi$
$409$	−28.0134	−1.38517	−0.692586	+	0.721335i	$0.743529\pi$
$410$	4.39175	0.216893
$411$	−2.39969	−0.118368
$412$	−3.18439	−0.156883
$413$	−7.62624	−0.375263
$414$	−2.75865	−0.135580
$415$	−6.92706	−0.340036
$416$	−2.86180	−0.140311
$417$	28.0309	1.37268
$418$	4.73769	0.231728
$419$	−39.3205	−1.92093	−0.960467	−	0.278394i	$-0.910198\pi$
$419$	−39.3205	−1.92093	−0.960467	+	0.278394i	$0.910198\pi$
$420$	−2.85587	−0.139352
$421$	−29.7676	−1.45078	−0.725391	−	0.688337i	$-0.758341\pi$
$421$	−29.7676	−1.45078	−0.725391	+	0.688337i	$0.758341\pi$
$422$	−4.26394	−0.207565
$423$	−21.3348	−1.03733
$424$	4.92913	0.239380
$425$	−2.58790	−0.125532
$426$	−29.0582	−1.40788
$427$	8.10600	0.392277
$428$	−7.80643	−0.377338
$429$	−21.0429	−1.01596
$430$	2.41693	0.116555
$431$	−31.8325	−1.53332	−0.766658	−	0.642056i	$-0.778082\pi$
$431$	−31.8325	−1.53332	−0.766658	+	0.642056i	$0.778082\pi$
$432$	0.579184	0.0278660
$433$	17.8782	0.859174	0.429587	−	0.903026i	$-0.358659\pi$
$433$	17.8782	0.859174	0.429587	+	0.903026i	$0.358659\pi$
$434$	3.61638	0.173592
$435$	−6.66229	−0.319433
$436$	9.57356	0.458490
$437$	−1.54618	−0.0739639
$438$	4.02742	0.192438
$439$	−5.09555	−0.243197	−0.121599	−	0.992579i	$-0.538802\pi$
$439$	−5.09555	−0.243197	−0.121599	+	0.992579i	$0.538802\pi$
$440$	−4.48205	−0.213673
$441$	−17.4845	−0.832594
$442$	−2.58921	−0.123156
$443$	16.2288	0.771054	0.385527	−	0.922697i	$-0.374020\pi$
$443$	16.2288	0.771054	0.385527	+	0.922697i	$0.374020\pi$
$444$	7.43041	0.352632
$445$	9.14706	0.433612
$446$	−24.7642	−1.17262
$447$	−1.17089	−0.0553811
$448$	0.813594	0.0384387
$449$	−25.0366	−1.18155	−0.590775	−	0.806836i	$-0.701178\pi$
$449$	−25.0366	−1.18155	−0.590775	+	0.806836i	$0.701178\pi$
$450$	7.89071	0.371972
$451$	−9.19968	−0.433196
$452$	−14.3790	−0.676332
$453$	−26.3210	−1.23667
$454$	−17.4784	−0.820303
$455$	3.40579	0.159666
$456$	−3.71040	−0.173755
$457$	12.8166	0.599534	0.299767	−	0.954012i	$-0.403091\pi$
$457$	12.8166	0.599534	0.299767	+	0.954012i	$0.403091\pi$
$458$	5.44225	0.254300
$459$	0.524015	0.0244589
$460$	1.46275	0.0682012
$461$	3.21953	0.149948	0.0749742	−	0.997185i	$-0.476113\pi$
$461$	3.21953	0.149948	0.0749742	+	0.997185i	$0.476113\pi$
$462$	5.98237	0.278325
$463$	−31.5623	−1.46682	−0.733412	−	0.679784i	$-0.762073\pi$
$463$	−31.5623	−1.46682	−0.733412	+	0.679784i	$0.762073\pi$
$464$	1.89799	0.0881118
$465$	15.6026	0.723553
$466$	10.4212	0.482754
$467$	17.8579	0.826367	0.413184	−	0.910648i	$-0.364417\pi$
$467$	17.8579	0.826367	0.413184	+	0.910648i	$0.364417\pi$
$468$	7.89470	0.364933
$469$	3.02239	0.139561
$470$	11.3126	0.521812
$471$	26.7075	1.23061
$472$	9.37352	0.431451
$473$	−5.06289	−0.232792
$474$	−27.5778	−1.26669
$475$	4.42263	0.202924
$476$	0.736098	0.0337390
$477$	−13.5977	−0.622596
$478$	21.2310	0.971084
$479$	14.6987	0.671601	0.335800	−	0.941933i	$-0.390993\pi$
$479$	14.6987	0.671601	0.335800	+	0.941933i	$0.390993\pi$
$480$	3.51019	0.160218
$481$	−8.86120	−0.404036
$482$	−24.5765	−1.11943
$483$	−1.95240	−0.0888371
$484$	−1.61118	−0.0732353
$485$	6.02124	0.273410
$486$	−21.4577	−0.973340
$487$	26.7250	1.21103	0.605513	−	0.795836i	$-0.292968\pi$
$487$	26.7250	1.21103	0.605513	+	0.795836i	$0.292968\pi$
$488$	−9.96319	−0.451013
$489$	−3.82214	−0.172843
$490$	9.27102	0.418822
$491$	−24.3950	−1.10093	−0.550465	−	0.834858i	$-0.685549\pi$
$491$	−24.3950	−1.10093	−0.550465	+	0.834858i	$0.685549\pi$
$492$	7.20489	0.324822
$493$	1.71720	0.0773388
$494$	4.42487	0.199084
$495$	12.3644	0.555737
$496$	−4.44494	−0.199584
$497$	−9.85183	−0.441915
$498$	−11.3642	−0.509242
$499$	−33.1929	−1.48592	−0.742959	−	0.669337i	$-0.766578\pi$
$499$	−33.1929	−1.48592	−0.742959	+	0.669337i	$0.766578\pi$
$500$	−11.4978	−0.514195
$501$	−6.19506	−0.276775
$502$	10.9984	0.490883
$503$	−8.45644	−0.377054	−0.188527	−	0.982068i	$-0.560371\pi$
$503$	−8.45644	−0.377054	−0.188527	+	0.982068i	$0.560371\pi$
$504$	−2.24442	−0.0999743
$505$	−0.929884	−0.0413793
$506$	−3.06412	−0.136217
$507$	11.5429	0.512636
$508$	−1.50464	−0.0667575
$509$	−20.0036	−0.886645	−0.443323	−	0.896362i	$-0.646200\pi$
$509$	−20.0036	−0.886645	−0.443323	+	0.896362i	$0.646200\pi$
$510$	3.17584	0.140629
$511$	1.36545	0.0604038
$512$	−1.00000	−0.0441942
$513$	−0.895524	−0.0395383
$514$	−5.98703	−0.264076
$515$	−4.65797	−0.205255
$516$	3.96509	0.174553
$517$	−23.6973	−1.04220
$518$	2.51919	0.110687
$519$	−9.74091	−0.427579
$520$	−4.18611	−0.183573
$521$	32.2500	1.41290	0.706450	−	0.707763i	$-0.250296\pi$
$521$	32.2500	1.41290	0.706450	+	0.707763i	$0.250296\pi$
$522$	−5.23587	−0.229168
$523$	−1.40551	−0.0614587	−0.0307294	−	0.999528i	$-0.509783\pi$
$523$	−1.40551	−0.0614587	−0.0307294	+	0.999528i	$0.509783\pi$
$524$	1.00000	0.0436852
$525$	5.58455	0.243730
$526$	6.34520	0.276664
$527$	−4.02155	−0.175182
$528$	−7.35302	−0.319999
$529$	1.00000	0.0434783
$530$	7.21009	0.313186
$531$	−25.8582	−1.12215
$532$	−1.25797	−0.0545397
$533$	−8.59225	−0.372172
$534$	15.0062	0.649382
$535$	−11.4189	−0.493681
$536$	−3.71486	−0.160458
$537$	−56.0858	−2.42028
$538$	14.4617	0.623488
$539$	−19.4206	−0.836504
$540$	0.847202	0.0364578
$541$	32.8351	1.41169	0.705845	−	0.708367i	$-0.250568\pi$
$541$	32.8351	1.41169	0.705845	+	0.708367i	$0.250568\pi$
$542$	29.1109	1.25042
$543$	45.9296	1.97103
$544$	−0.904748	−0.0387908
$545$	14.0037	0.599854
$546$	5.58737	0.239117
$547$	−25.5926	−1.09426	−0.547131	−	0.837047i	$-0.684280\pi$
$547$	−25.5926	−1.09426	−0.547131	+	0.837047i	$0.684280\pi$
$548$	0.999989	0.0427174
$549$	27.4849	1.17303
$550$	8.76447	0.373718
$551$	−2.93463	−0.125020
$552$	2.39972	0.102139
$553$	−9.34989	−0.397598
$554$	8.96632	0.380943
$555$	10.8688	0.461357
$556$	−11.6809	−0.495382
$557$	−26.3568	−1.11677	−0.558386	−	0.829581i	$-0.688579\pi$
$557$	−26.3568	−1.11677	−0.558386	+	0.829581i	$0.688579\pi$
$558$	12.2620	0.519092
$559$	−4.72860	−0.199998
$560$	1.19009	0.0502903
$561$	−6.65263	−0.280874
$562$	−18.2968	−0.771802
$563$	2.49675	0.105225	0.0526127	−	0.998615i	$-0.483245\pi$
$563$	2.49675	0.105225	0.0526127	+	0.998615i	$0.483245\pi$
$564$	18.5589	0.781472
$565$	−21.0329	−0.884863
$566$	22.0620	0.927336
$567$	−7.86405	−0.330259
$568$	12.1090	0.508083
$569$	5.96413	0.250029	0.125015	−	0.992155i	$-0.460102\pi$
$569$	5.96413	0.250029	0.125015	+	0.992155i	$0.460102\pi$
$570$	−5.42740	−0.227329
$571$	8.39480	0.351311	0.175656	−	0.984452i	$-0.443795\pi$
$571$	8.39480	0.351311	0.175656	+	0.984452i	$0.443795\pi$
$572$	8.76890	0.366646
$573$	−25.6116	−1.06994
$574$	2.44273	0.101957
$575$	−2.86036	−0.119285
$576$	2.75865	0.114944
$577$	−3.29637	−0.137230	−0.0686149	−	0.997643i	$-0.521858\pi$
$577$	−3.29637	−0.137230	−0.0686149	+	0.997643i	$0.521858\pi$
$578$	16.1814	0.673059
$579$	−53.4244	−2.22024
$580$	2.77628	0.115279
$581$	−3.85289	−0.159845
$582$	9.87814	0.409462
$583$	−15.1034	−0.625520
$584$	−1.67829	−0.0694481
$585$	11.5480	0.477450
$586$	−19.7031	−0.813928
$587$	−13.1105	−0.541130	−0.270565	−	0.962702i	$-0.587210\pi$
$587$	−13.1105	−0.541130	−0.270565	+	0.962702i	$0.587210\pi$
$588$	15.2096	0.627232
$589$	6.87269	0.283184
$590$	13.7111	0.564479
$591$	−64.6335	−2.65867
$592$	−3.09637	−0.127260
$593$	27.6631	1.13599	0.567994	−	0.823033i	$-0.307720\pi$
$593$	27.6631	1.13599	0.567994	+	0.823033i	$0.307720\pi$
$594$	−1.77469	−0.0728163
$595$	1.07673	0.0441416
$596$	0.487928	0.0199863
$597$	17.5421	0.717950
$598$	−2.86180	−0.117028
$599$	8.01598	0.327524	0.163762	−	0.986500i	$-0.447637\pi$
$599$	8.01598	0.327524	0.163762	+	0.986500i	$0.447637\pi$
$600$	−6.86405	−0.280224
$601$	2.38505	0.0972882	0.0486441	−	0.998816i	$-0.484510\pi$
$601$	2.38505	0.0972882	0.0486441	+	0.998816i	$0.484510\pi$
$602$	1.34431	0.0547901
$603$	10.2480	0.417330
$604$	10.9684	0.446296
$605$	−2.35675	−0.0958156
$606$	−1.52552	−0.0619701
$607$	1.14297	0.0463918	0.0231959	−	0.999731i	$-0.492616\pi$
$607$	1.14297	0.0463918	0.0231959	+	0.999731i	$0.492616\pi$
$608$	1.54618	0.0627060
$609$	−3.70562	−0.150159
$610$	−14.5737	−0.590071
$611$	−22.1326	−0.895389
$612$	2.49588	0.100890
$613$	10.0729	0.406839	0.203419	−	0.979092i	$-0.434795\pi$
$613$	10.0729	0.406839	0.203419	+	0.979092i	$0.434795\pi$
$614$	11.3388	0.457595
$615$	10.5390	0.424972
$616$	−2.49295	−0.100444
$617$	40.3538	1.62458	0.812292	−	0.583251i	$-0.198220\pi$
$617$	40.3538	1.62458	0.812292	+	0.583251i	$0.198220\pi$
$618$	−7.64163	−0.307391
$619$	−11.2636	−0.452721	−0.226361	−	0.974044i	$-0.572683\pi$
$619$	−11.2636	−0.452721	−0.226361	+	0.974044i	$0.572683\pi$
$620$	−6.50185	−0.261120
$621$	0.579184	0.0232418
$622$	−3.59044	−0.143964
$623$	5.08767	0.203833
$624$	−6.86752	−0.274921
$625$	−2.51658	−0.100663
$626$	27.1652	1.08574
$627$	11.3691	0.454039
$628$	−11.1294	−0.444112
$629$	−2.80143	−0.111701
$630$	−3.28303	−0.130799
$631$	−38.7095	−1.54100	−0.770500	−	0.637440i	$-0.779993\pi$
$631$	−38.7095	−1.54100	−0.770500	+	0.637440i	$0.779993\pi$
$632$	11.4921	0.457130
$633$	−10.2322	−0.406695
$634$	−7.90363	−0.313893
$635$	−2.20091	−0.0873405
$636$	11.8285	0.469031
$637$	−18.1383	−0.718665
$638$	−5.81565	−0.230244
$639$	−33.4045	−1.32146
$640$	−1.46275	−0.0578204
$641$	−27.4830	−1.08551	−0.542757	−	0.839890i	$-0.682620\pi$
$641$	−27.4830	−1.08551	−0.542757	+	0.839890i	$0.682620\pi$
$642$	−18.7332	−0.739342
$643$	−15.8256	−0.624100	−0.312050	−	0.950066i	$-0.601016\pi$
$643$	−15.8256	−0.624100	−0.312050	+	0.950066i	$0.601016\pi$
$644$	0.813594	0.0320601
$645$	5.79994	0.228372
$646$	1.39891	0.0550392
$647$	25.4030	0.998696	0.499348	−	0.866402i	$-0.333573\pi$
$647$	25.4030	0.998696	0.499348	+	0.866402i	$0.333573\pi$
$648$	9.66581	0.379709
$649$	−28.7216	−1.12742
$650$	8.18577	0.321073
$651$	8.67828	0.340129
$652$	1.59275	0.0623768
$653$	−33.5484	−1.31285	−0.656424	−	0.754392i	$-0.727932\pi$
$653$	−33.5484	−1.31285	−0.656424	+	0.754392i	$0.727932\pi$
$654$	22.9738	0.898348
$655$	1.46275	0.0571545
$656$	−3.00239	−0.117224
$657$	4.62980	0.180626
$658$	6.29217	0.245294
$659$	−31.3720	−1.22208	−0.611039	−	0.791600i	$-0.709248\pi$
$659$	−31.3720	−1.22208	−0.611039	+	0.791600i	$0.709248\pi$
$660$	−10.7556	−0.418663
$661$	−25.8043	−1.00367	−0.501836	−	0.864963i	$-0.667342\pi$
$661$	−25.8043	−1.00367	−0.501836	+	0.864963i	$0.667342\pi$
$662$	27.3514	1.06304
$663$	−6.21338	−0.241308
$664$	4.73564	0.183778
$665$	−1.84009	−0.0713557
$666$	8.54178	0.330987
$667$	1.89799	0.0734903
$668$	2.58158	0.0998843
$669$	−59.4272	−2.29759
$670$	−5.43392	−0.209931
$671$	30.5284	1.17854
$672$	1.95240	0.0753153
$673$	34.0308	1.31179	0.655895	−	0.754852i	$-0.272292\pi$
$673$	34.0308	1.31179	0.655895	+	0.754852i	$0.272292\pi$
$674$	11.1571	0.429755
$675$	−1.65667	−0.0637653
$676$	−4.81009	−0.185003
$677$	24.5707	0.944330	0.472165	−	0.881510i	$-0.343473\pi$
$677$	24.5707	0.944330	0.472165	+	0.881510i	$0.343473\pi$
$678$	−34.5056	−1.32518
$679$	3.34906	0.128525
$680$	−1.32342	−0.0507509
$681$	−41.9433	−1.60727
$682$	13.6198	0.521530
$683$	22.0909	0.845286	0.422643	−	0.906296i	$-0.361102\pi$
$683$	22.0909	0.845286	0.422643	+	0.906296i	$0.361102\pi$
$684$	−4.26537	−0.163090
$685$	1.46274	0.0558883
$686$	10.8518	0.414323
$687$	13.0599	0.498265
$688$	−1.65231	−0.0629939
$689$	−14.1062	−0.537403
$690$	3.51019	0.133631
$691$	−39.4704	−1.50152	−0.750762	−	0.660572i	$-0.770314\pi$
$691$	−39.4704	−1.50152	−0.750762	+	0.660572i	$0.770314\pi$
$692$	4.05919	0.154307
$693$	6.87716	0.261242
$694$	−4.08794	−0.155176
$695$	−17.0863	−0.648120
$696$	4.55463	0.172643
$697$	−2.71641	−0.102891
$698$	−27.7722	−1.05119
$699$	25.0080	0.945889
$700$	−2.32717	−0.0879587
$701$	−28.1663	−1.06383	−0.531913	−	0.846799i	$-0.678527\pi$
$701$	−28.1663	−1.06383	−0.531913	+	0.846799i	$0.678527\pi$
$702$	−1.65751	−0.0625586
$703$	4.78755	0.180566
$704$	3.06412	0.115483
$705$	27.1471	1.02242
$706$	3.21943	0.121165
$707$	−0.517209	−0.0194516
$708$	22.4938	0.845369
$709$	−31.5986	−1.18671	−0.593355	−	0.804941i	$-0.702197\pi$
$709$	−31.5986	−1.18671	−0.593355	+	0.804941i	$0.702197\pi$
$710$	17.7125	0.664738
$711$	−31.7026	−1.18894
$712$	−6.25332	−0.234353
$713$	−4.44494	−0.166464
$714$	1.76643	0.0661069
$715$	12.8267	0.479692
$716$	23.3718	0.873447
$717$	50.9485	1.90270
$718$	7.93004	0.295946
$719$	5.90943	0.220385	0.110192	−	0.993910i	$-0.464853\pi$
$719$	5.90943	0.220385	0.110192	+	0.993910i	$0.464853\pi$
$720$	4.03521	0.150384
$721$	−2.59080	−0.0964864
$722$	16.6093	0.618135
$723$	−58.9768	−2.19337
$724$	−19.1396	−0.711317
$725$	−5.42892	−0.201625
$726$	−3.86637	−0.143494
$727$	−2.00384	−0.0743185	−0.0371592	−	0.999309i	$-0.511831\pi$
$727$	−2.00384	−0.0743185	−0.0371592	+	0.999309i	$0.511831\pi$
$728$	−2.32835	−0.0862942
$729$	−22.4949	−0.833145
$730$	−2.45492	−0.0908607
$731$	−1.49493	−0.0552919
$732$	−23.9089	−0.883697
$733$	15.6155	0.576772	0.288386	−	0.957514i	$-0.406881\pi$
$733$	15.6155	0.576772	0.288386	+	0.957514i	$0.406881\pi$
$734$	35.5396	1.31179
$735$	22.2478	0.820623
$736$	−1.00000	−0.0368605
$737$	11.3828	0.419290
$738$	8.28253	0.304884
$739$	21.6004	0.794584	0.397292	−	0.917692i	$-0.369950\pi$
$739$	21.6004	0.794584	0.397292	+	0.917692i	$0.369950\pi$
$740$	−4.52922	−0.166497
$741$	10.6184	0.390078
$742$	4.01031	0.147223
$743$	44.6605	1.63843	0.819217	−	0.573483i	$-0.194408\pi$
$743$	44.6605	1.63843	0.819217	+	0.573483i	$0.194408\pi$
$744$	−10.6666	−0.391057
$745$	0.713717	0.0261486
$746$	−27.2806	−0.998813
$747$	−13.0639	−0.477985
$748$	2.77226	0.101364
$749$	−6.35127	−0.232070
$750$	−27.5914	−1.00749
$751$	−22.4340	−0.818630	−0.409315	−	0.912393i	$-0.634232\pi$
$751$	−22.4340	−0.818630	−0.409315	+	0.912393i	$0.634232\pi$
$752$	−7.73379	−0.282022
$753$	26.3931	0.961817
$754$	−5.43166	−0.197809
$755$	16.0440	0.583901
$756$	0.471220	0.0171381
$757$	−23.7009	−0.861425	−0.430712	−	0.902489i	$-0.641738\pi$
$757$	−23.7009	−0.861425	−0.430712	+	0.902489i	$0.641738\pi$
$758$	1.29574	0.0470633
$759$	−7.35302	−0.266898
$760$	2.26168	0.0820398
$761$	−22.7413	−0.824372	−0.412186	−	0.911100i	$-0.635235\pi$
$761$	−22.7413	−0.824372	−0.412186	+	0.911100i	$0.635235\pi$
$762$	−3.61070	−0.130802
$763$	7.78899	0.281980
$764$	10.6728	0.386127
$765$	3.65085	0.131997
$766$	0.0745281	0.00269281
$767$	−26.8252	−0.968600
$768$	−2.39972	−0.0865924
$769$	9.26088	0.333956	0.166978	−	0.985961i	$-0.446599\pi$
$769$	9.26088	0.333956	0.166978	+	0.985961i	$0.446599\pi$
$770$	−3.64657	−0.131413
$771$	−14.3672	−0.517421
$772$	22.2628	0.801255
$773$	−11.1153	−0.399790	−0.199895	−	0.979817i	$-0.564060\pi$
$773$	−11.1153	−0.399790	−0.199895	+	0.979817i	$0.564060\pi$
$774$	4.55815	0.163839
$775$	12.7141	0.456704
$776$	−4.11638	−0.147769
$777$	6.04534	0.216875
$778$	−25.9727	−0.931166
$779$	4.64224	0.166326
$780$	−10.0455	−0.359686
$781$	−37.1035	−1.32767
$782$	−0.904748	−0.0323537
$783$	1.09928	0.0392851
$784$	−6.33806	−0.226359
$785$	−16.2796	−0.581043
$786$	2.39972	0.0855951
$787$	13.2209	0.471274	0.235637	−	0.971841i	$-0.424282\pi$
$787$	13.2209	0.471274	0.235637	+	0.971841i	$0.424282\pi$
$788$	26.9338	0.959477
$789$	15.2267	0.542084
$790$	16.8101	0.598075
$791$	−11.6987	−0.415957
$792$	−8.45282	−0.300358
$793$	28.5127	1.01252
$794$	−4.73923	−0.168189
$795$	17.3022	0.613645
$796$	−7.31007	−0.259099
$797$	28.4079	1.00626	0.503129	−	0.864211i	$-0.332182\pi$
$797$	28.4079	1.00626	0.503129	+	0.864211i	$0.332182\pi$
$798$	−3.01876	−0.106863
$799$	−6.99714	−0.247541
$800$	2.86036	0.101129
$801$	17.2507	0.609523
$802$	−32.2131	−1.13748
$803$	5.14248	0.181474
$804$	−8.91462	−0.314395
$805$	1.19009	0.0419450
$806$	12.7205	0.448062
$807$	34.7040	1.22164
$808$	0.635708	0.0223641
$809$	−3.29101	−0.115706	−0.0578529	−	0.998325i	$-0.518425\pi$
$809$	−3.29101	−0.115706	−0.0578529	+	0.998325i	$0.518425\pi$
$810$	14.1387	0.496783
$811$	30.5075	1.07126	0.535632	−	0.844451i	$-0.320073\pi$
$811$	30.5075	1.07126	0.535632	+	0.844451i	$0.320073\pi$
$812$	1.54419	0.0541904
$813$	69.8579	2.45002
$814$	9.48764	0.332542
$815$	2.32979	0.0816092
$816$	−2.17114	−0.0760051
$817$	2.55478	0.0893805
$818$	28.0134	0.979465
$819$	6.42308	0.224441
$820$	−4.39175	−0.153367
$821$	6.94957	0.242542	0.121271	−	0.992619i	$-0.461303\pi$
$821$	6.94957	0.242542	0.121271	+	0.992619i	$0.461303\pi$
$822$	2.39969	0.0836989
$823$	−30.9266	−1.07803	−0.539017	−	0.842295i	$-0.681204\pi$
$823$	−30.9266	−1.07803	−0.539017	+	0.842295i	$0.681204\pi$
$824$	3.18439	0.110933
$825$	21.0323	0.732249
$826$	7.62624	0.265351
$827$	−25.4075	−0.883506	−0.441753	−	0.897137i	$-0.645643\pi$
$827$	−25.4075	−0.883506	−0.441753	+	0.897137i	$0.645643\pi$
$828$	2.75865	0.0958695
$829$	11.1445	0.387066	0.193533	−	0.981094i	$-0.438005\pi$
$829$	11.1445	0.387066	0.193533	+	0.981094i	$0.438005\pi$
$830$	6.92706	0.240442
$831$	21.5166	0.746404
$832$	2.86180	0.0992151
$833$	−5.73435	−0.198684
$834$	−28.0309	−0.970632
$835$	3.77621	0.130681
$836$	−4.73769	−0.163856
$837$	−2.57444	−0.0889855
$838$	39.3205	1.35831
$839$	−29.8408	−1.03022	−0.515110	−	0.857124i	$-0.672249\pi$
$839$	−29.8408	−1.03022	−0.515110	+	0.857124i	$0.672249\pi$
$840$	2.85587	0.0985369
$841$	−25.3977	−0.875781
$842$	29.7676	1.02586
$843$	−43.9070	−1.51224
$844$	4.26394	0.146771
$845$	−7.03596	−0.242045
$846$	21.3348	0.733505
$847$	−1.31084	−0.0450411
$848$	−4.92913	−0.169267
$849$	52.9426	1.81699
$850$	2.58790	0.0887643
$851$	−3.09637	−0.106142
$852$	29.0582	0.995518
$853$	−44.3501	−1.51852	−0.759259	−	0.650789i	$-0.774438\pi$
$853$	−44.3501	−1.51852	−0.759259	+	0.650789i	$0.774438\pi$
$854$	−8.10600	−0.277381
$855$	−6.23918	−0.213375
$856$	7.80643	0.266818
$857$	1.22977	0.0420083	0.0210041	−	0.999779i	$-0.493314\pi$
$857$	1.22977	0.0420083	0.0210041	+	0.999779i	$0.493314\pi$
$858$	21.0429	0.718392
$859$	44.6251	1.52259	0.761294	−	0.648407i	$-0.224565\pi$
$859$	44.6251	1.52259	0.761294	+	0.648407i	$0.224565\pi$
$860$	−2.41693	−0.0824165
$861$	5.86186	0.199772
$862$	31.8325	1.08422
$863$	−36.8766	−1.25529	−0.627647	−	0.778498i	$-0.715982\pi$
$863$	−36.8766	−1.25529	−0.627647	+	0.778498i	$0.715982\pi$
$864$	−0.579184	−0.0197042
$865$	5.93759	0.201884
$866$	−17.8782	−0.607528
$867$	38.8309	1.31877
$868$	−3.61638	−0.122748
$869$	−35.2131	−1.19452
$870$	6.66229	0.225873
$871$	10.6312	0.360225
$872$	−9.57356	−0.324202
$873$	11.3556	0.384330
$874$	1.54618	0.0523004
$875$	−9.35450	−0.316240
$876$	−4.02742	−0.136074
$877$	36.0441	1.21712	0.608561	−	0.793507i	$-0.291747\pi$
$877$	36.0441	1.21712	0.608561	+	0.793507i	$0.291747\pi$
$878$	5.09555	0.171967
$879$	−47.2819	−1.59478
$880$	4.48205	0.151090
$881$	49.4966	1.66758	0.833791	−	0.552081i	$-0.186166\pi$
$881$	49.4966	1.66758	0.833791	+	0.552081i	$0.186166\pi$
$882$	17.4845	0.588733
$883$	−42.8645	−1.44251	−0.721253	−	0.692672i	$-0.756433\pi$
$883$	−42.8645	−1.44251	−0.721253	+	0.692672i	$0.756433\pi$
$884$	2.58921	0.0870846
$885$	32.9029	1.10602
$886$	−16.2288	−0.545218
$887$	36.4516	1.22393	0.611963	−	0.790887i	$-0.290380\pi$
$887$	36.4516	1.22393	0.611963	+	0.790887i	$0.290380\pi$
$888$	−7.43041	−0.249348
$889$	−1.22416	−0.0410571
$890$	−9.14706	−0.306610
$891$	−29.6172	−0.992213
$892$	24.7642	0.829168
$893$	11.9579	0.400154
$894$	1.17089	0.0391604
$895$	34.1872	1.14275
$896$	−0.813594	−0.0271803
$897$	−6.86752	−0.229300
$898$	25.0366	0.835482
$899$	−8.43643	−0.281371
$900$	−7.89071	−0.263024
$901$	−4.45962	−0.148571
$902$	9.19968	0.306316
$903$	3.22597	0.107354
$904$	14.3790	0.478239
$905$	−27.9965	−0.930634
$906$	26.3210	0.874456
$907$	−35.9212	−1.19274	−0.596372	−	0.802708i	$-0.703392\pi$
$907$	−35.9212	−1.19274	−0.596372	+	0.802708i	$0.703392\pi$
$908$	17.4784	0.580042
$909$	−1.75369	−0.0581664
$910$	−3.40579	−0.112901
$911$	−24.6376	−0.816278	−0.408139	−	0.912920i	$-0.633822\pi$
$911$	−24.6376	−0.816278	−0.408139	+	0.912920i	$0.633822\pi$
$912$	3.71040	0.122864
$913$	−14.5106	−0.480229
$914$	−12.8166	−0.423935
$915$	−34.9727	−1.15616
$916$	−5.44225	−0.179817
$917$	0.813594	0.0268672
$918$	−0.524015	−0.0172951
$919$	40.7959	1.34573	0.672866	−	0.739764i	$-0.265063\pi$
$919$	40.7959	1.34573	0.672866	+	0.739764i	$0.265063\pi$
$920$	−1.46275	−0.0482255
$921$	27.2098	0.896595
$922$	−3.21953	−0.106029
$923$	−34.6536	−1.14064
$924$	−5.98237	−0.196806
$925$	8.85672	0.291207
$926$	31.5623	1.03720
$927$	−8.78459	−0.288524
$928$	−1.89799	−0.0623044
$929$	−14.1678	−0.464831	−0.232416	−	0.972617i	$-0.574663\pi$
$929$	−14.1678	−0.464831	−0.232416	+	0.972617i	$0.574663\pi$
$930$	−15.6026	−0.511629
$931$	9.79981	0.321176
$932$	−10.4212	−0.341358
$933$	−8.61605	−0.282077
$934$	−17.8579	−0.584330
$935$	4.05512	0.132617
$936$	−7.89470	−0.258046
$937$	8.00799	0.261610	0.130805	−	0.991408i	$-0.458244\pi$
$937$	8.00799	0.261610	0.130805	+	0.991408i	$0.458244\pi$
$938$	−3.02239	−0.0986846
$939$	65.1889	2.12736
$940$	−11.3126	−0.368977
$941$	−30.2572	−0.986356	−0.493178	−	0.869928i	$-0.664165\pi$
$941$	−30.2572	−0.986356	−0.493178	+	0.869928i	$0.664165\pi$
$942$	−26.7075	−0.870176
$943$	−3.00239	−0.0977713
$944$	−9.37352	−0.305082
$945$	0.689278	0.0224222
$946$	5.06289	0.164609
$947$	−17.0199	−0.553073	−0.276537	−	0.961003i	$-0.589187\pi$
$947$	−17.0199	−0.553073	−0.276537	+	0.961003i	$0.589187\pi$
$948$	27.5778	0.895684
$949$	4.80293	0.155910
$950$	−4.42263	−0.143489
$951$	−18.9665	−0.615030
$952$	−0.736098	−0.0238571
$953$	−18.4305	−0.597022	−0.298511	−	0.954406i	$-0.596490\pi$
$953$	−18.4305	−0.597022	−0.298511	+	0.954406i	$0.596490\pi$
$954$	13.5977	0.440242
$955$	15.6116	0.505180
$956$	−21.2310	−0.686660
$957$	−13.9559	−0.451131
$958$	−14.6987	−0.474894
$959$	0.813585	0.0262720
$960$	−3.51019	−0.113291
$961$	−11.2425	−0.362662
$962$	8.86120	0.285696
$963$	−21.5352	−0.693961
$964$	24.5765	0.791557
$965$	32.5649	1.04830
$966$	1.95240	0.0628173
$967$	39.9945	1.28614	0.643069	−	0.765808i	$-0.277661\pi$
$967$	39.9945	1.28614	0.643069	+	0.765808i	$0.277661\pi$
$968$	1.61118	0.0517852
$969$	3.35698	0.107842
$970$	−6.02124	−0.193330
$971$	56.3989	1.80993	0.904963	−	0.425490i	$-0.139898\pi$
$971$	56.3989	1.80993	0.904963	+	0.425490i	$0.139898\pi$
$972$	21.4577	0.688255
$973$	−9.50354	−0.304669
$974$	−26.7250	−0.856324
$975$	19.6435	0.629097
$976$	9.96319	0.318914
$977$	16.0810	0.514478	0.257239	−	0.966348i	$-0.417187\pi$
$977$	16.0810	0.514478	0.257239	+	0.966348i	$0.417187\pi$
$978$	3.82214	0.122219
$979$	19.1609	0.612386
$980$	−9.27102	−0.296152
$981$	26.4101	0.843208
$982$	24.3950	0.778475
$983$	7.09242	0.226213	0.113107	−	0.993583i	$-0.463920\pi$
$983$	7.09242	0.226213	0.113107	+	0.993583i	$0.463920\pi$
$984$	−7.20489	−0.229684
$985$	39.3975	1.25531
$986$	−1.71720	−0.0546868
$987$	15.0994	0.480620
$988$	−4.42487	−0.140774
$989$	−1.65231	−0.0525406
$990$	−12.3644	−0.392966
$991$	−30.5461	−0.970329	−0.485165	−	0.874423i	$-0.661240\pi$
$991$	−30.5461	−0.970329	−0.485165	+	0.874423i	$0.661240\pi$
$992$	4.44494	0.141127
$993$	65.6356	2.08288
$994$	9.85183	0.312481
$995$	−10.6928	−0.338985
$996$	11.3642	0.360088
$997$	27.9063	0.883802	0.441901	−	0.897064i	$-0.354304\pi$
$997$	27.9063	0.883802	0.441901	+	0.897064i	$0.354304\pi$
$998$	33.1929	1.05070
$999$	−1.79337	−0.0567396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.4	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.39972 q^{3} +1.00000 q^{4} +1.46275 q^{5} +2.39972 q^{6} +0.813594 q^{7} -1.00000 q^{8} +2.75865 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.39972 q^{3} +1.00000 q^{4} +1.46275 q^{5} +2.39972 q^{6} +0.813594 q^{7} -1.00000 q^{8} +2.75865 q^{9} -1.46275 q^{10} +3.06412 q^{11} -2.39972 q^{12} +2.86180 q^{13} -0.813594 q^{14} -3.51019 q^{15} +1.00000 q^{16} +0.904748 q^{17} -2.75865 q^{18} -1.54618 q^{19} +1.46275 q^{20} -1.95240 q^{21} -3.06412 q^{22} +1.00000 q^{23} +2.39972 q^{24} -2.86036 q^{25} -2.86180 q^{26} +0.579184 q^{27} +0.813594 q^{28} +1.89799 q^{29} +3.51019 q^{30} -4.44494 q^{31} -1.00000 q^{32} -7.35302 q^{33} -0.904748 q^{34} +1.19009 q^{35} +2.75865 q^{36} -3.09637 q^{37} +1.54618 q^{38} -6.86752 q^{39} -1.46275 q^{40} -3.00239 q^{41} +1.95240 q^{42} -1.65231 q^{43} +3.06412 q^{44} +4.03521 q^{45} -1.00000 q^{46} -7.73379 q^{47} -2.39972 q^{48} -6.33806 q^{49} +2.86036 q^{50} -2.17114 q^{51} +2.86180 q^{52} -4.92913 q^{53} -0.579184 q^{54} +4.48205 q^{55} -0.813594 q^{56} +3.71040 q^{57} -1.89799 q^{58} -9.37352 q^{59} -3.51019 q^{60} +9.96319 q^{61} +4.44494 q^{62} +2.24442 q^{63} +1.00000 q^{64} +4.18611 q^{65} +7.35302 q^{66} +3.71486 q^{67} +0.904748 q^{68} -2.39972 q^{69} -1.19009 q^{70} -12.1090 q^{71} -2.75865 q^{72} +1.67829 q^{73} +3.09637 q^{74} +6.86405 q^{75} -1.54618 q^{76} +2.49295 q^{77} +6.86752 q^{78} -11.4921 q^{79} +1.46275 q^{80} -9.66581 q^{81} +3.00239 q^{82} -4.73564 q^{83} -1.95240 q^{84} +1.32342 q^{85} +1.65231 q^{86} -4.55463 q^{87} -3.06412 q^{88} +6.25332 q^{89} -4.03521 q^{90} +2.32835 q^{91} +1.00000 q^{92} +10.6666 q^{93} +7.73379 q^{94} -2.26168 q^{95} +2.39972 q^{96} +4.11638 q^{97} +6.33806 q^{98} +8.45282 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 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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