LMFDB - Embedded newform 2230.2.a.p.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2230,2,Mod(1,2230)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2230, 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("2230.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2230 = 2 \cdot 5 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2230.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:	$17.8066396507$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.67955408.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 30x^{2} + 24x + 4 $ x^6 - x^5 - 11x^4 + 30x^2 + 24*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.13450$ of defining polynomial
Character	$\chi$	$=$	2230.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.13450 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.13450 q^{6} +2.94362 q^{7} -1.00000 q^{8} +1.55608 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.13450 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.13450 q^{6} +2.94362 q^{7} -1.00000 q^{8} +1.55608 q^{9} +1.00000 q^{10} +4.88769 q^{11} +2.13450 q^{12} +1.18156 q^{13} -2.94362 q^{14} -2.13450 q^{15} +1.00000 q^{16} +1.72348 q^{17} -1.55608 q^{18} +3.50901 q^{19} -1.00000 q^{20} +6.28315 q^{21} -4.88769 q^{22} -1.51609 q^{23} -2.13450 q^{24} +1.00000 q^{25} -1.18156 q^{26} -3.08205 q^{27} +2.94362 q^{28} +5.12726 q^{29} +2.13450 q^{30} -1.83007 q^{31} -1.00000 q^{32} +10.4327 q^{33} -1.72348 q^{34} -2.94362 q^{35} +1.55608 q^{36} -9.24316 q^{37} -3.50901 q^{38} +2.52204 q^{39} +1.00000 q^{40} +0.682260 q^{41} -6.28315 q^{42} -6.76997 q^{43} +4.88769 q^{44} -1.55608 q^{45} +1.51609 q^{46} +9.01802 q^{47} +2.13450 q^{48} +1.66490 q^{49} -1.00000 q^{50} +3.67877 q^{51} +1.18156 q^{52} +9.35047 q^{53} +3.08205 q^{54} -4.88769 q^{55} -2.94362 q^{56} +7.48997 q^{57} -5.12726 q^{58} -9.94967 q^{59} -2.13450 q^{60} -13.9563 q^{61} +1.83007 q^{62} +4.58049 q^{63} +1.00000 q^{64} -1.18156 q^{65} -10.4327 q^{66} +6.03189 q^{67} +1.72348 q^{68} -3.23608 q^{69} +2.94362 q^{70} +10.6224 q^{71} -1.55608 q^{72} -5.91560 q^{73} +9.24316 q^{74} +2.13450 q^{75} +3.50901 q^{76} +14.3875 q^{77} -2.52204 q^{78} +0.792340 q^{79} -1.00000 q^{80} -11.2469 q^{81} -0.682260 q^{82} +13.7940 q^{83} +6.28315 q^{84} -1.72348 q^{85} +6.76997 q^{86} +10.9441 q^{87} -4.88769 q^{88} -4.20666 q^{89} +1.55608 q^{90} +3.47807 q^{91} -1.51609 q^{92} -3.90628 q^{93} -9.01802 q^{94} -3.50901 q^{95} -2.13450 q^{96} -11.0914 q^{97} -1.66490 q^{98} +7.60561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9} + 6 q^{10} + 14 q^{11} - q^{12} + 9 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 4 q^{17} - 5 q^{18} + q^{19} - 6 q^{20} + 14 q^{21} - 14 q^{22} + 9 q^{23} + q^{24} + 6 q^{25} - 9 q^{26} - 28 q^{27} - 6 q^{28} - 9 q^{29} - q^{30} + q^{31} - 6 q^{32} - 6 q^{33} - 4 q^{34} + 6 q^{35} + 5 q^{36} - 18 q^{37} - q^{38} - 18 q^{39} + 6 q^{40} + 11 q^{41} - 14 q^{42} - 26 q^{43} + 14 q^{44} - 5 q^{45} - 9 q^{46} + 14 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} + 14 q^{51} + 9 q^{52} + 14 q^{53} + 28 q^{54} - 14 q^{55} + 6 q^{56} + 9 q^{57} + 9 q^{58} + 18 q^{59} + q^{60} + 24 q^{61} - q^{62} + 6 q^{64} - 9 q^{65} + 6 q^{66} - 8 q^{67} + 4 q^{68} + 20 q^{69} - 6 q^{70} + 32 q^{71} - 5 q^{72} - 12 q^{73} + 18 q^{74} - q^{75} + q^{76} + 12 q^{77} + 18 q^{78} + 8 q^{79} - 6 q^{80} + 14 q^{81} - 11 q^{82} + 36 q^{83} + 14 q^{84} - 4 q^{85} + 26 q^{86} - 9 q^{87} - 14 q^{88} + 11 q^{89} + 5 q^{90} + 10 q^{91} + 9 q^{92} + 8 q^{93} - 14 q^{94} - q^{95} + q^{96} - q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9 + 6 * q^10 + 14 * q^11 - q^12 + 9 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 4 * q^17 - 5 * q^18 + q^19 - 6 * q^20 + 14 * q^21 - 14 * q^22 + 9 * q^23 + q^24 + 6 * q^25 - 9 * q^26 - 28 * q^27 - 6 * q^28 - 9 * q^29 - q^30 + q^31 - 6 * q^32 - 6 * q^33 - 4 * q^34 + 6 * q^35 + 5 * q^36 - 18 * q^37 - q^38 - 18 * q^39 + 6 * q^40 + 11 * q^41 - 14 * q^42 - 26 * q^43 + 14 * q^44 - 5 * q^45 - 9 * q^46 + 14 * q^47 - q^48 + 6 * q^49 - 6 * q^50 + 14 * q^51 + 9 * q^52 + 14 * q^53 + 28 * q^54 - 14 * q^55 + 6 * q^56 + 9 * q^57 + 9 * q^58 + 18 * q^59 + q^60 + 24 * q^61 - q^62 + 6 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 + 4 * q^68 + 20 * q^69 - 6 * q^70 + 32 * q^71 - 5 * q^72 - 12 * q^73 + 18 * q^74 - q^75 + q^76 + 12 * q^77 + 18 * q^78 + 8 * q^79 - 6 * q^80 + 14 * q^81 - 11 * q^82 + 36 * q^83 + 14 * q^84 - 4 * q^85 + 26 * q^86 - 9 * q^87 - 14 * q^88 + 11 * q^89 + 5 * q^90 + 10 * q^91 + 9 * q^92 + 8 * q^93 - 14 * q^94 - q^95 + q^96 - q^97 - 6 * q^98 + 16 * 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
$3$	2.13450	1.23235	0.616176	−	0.787608i	$-0.288681\pi$
$3$	2.13450	1.23235	0.616176	+	0.787608i	$0.288681\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.13450	−0.871405
$7$	2.94362	1.11258	0.556292	−	0.830987i	$-0.312224\pi$
$7$	2.94362	1.11258	0.556292	+	0.830987i	$0.312224\pi$
$8$	−1.00000	−0.353553
$9$	1.55608	0.518692
$10$	1.00000	0.316228
$11$	4.88769	1.47369	0.736846	−	0.676060i	$-0.236314\pi$
$11$	4.88769	1.47369	0.736846	+	0.676060i	$0.236314\pi$
$12$	2.13450	0.616176
$13$	1.18156	0.327707	0.163853	−	0.986485i	$-0.447608\pi$
$13$	1.18156	0.327707	0.163853	+	0.986485i	$0.447608\pi$
$14$	−2.94362	−0.786716
$15$	−2.13450	−0.551125
$16$	1.00000	0.250000
$17$	1.72348	0.418006	0.209003	−	0.977915i	$-0.432978\pi$
$17$	1.72348	0.418006	0.209003	+	0.977915i	$0.432978\pi$
$18$	−1.55608	−0.366770
$19$	3.50901	0.805022	0.402511	−	0.915415i	$-0.368138\pi$
$19$	3.50901	0.805022	0.402511	+	0.915415i	$0.368138\pi$
$20$	−1.00000	−0.223607
$21$	6.28315	1.37110
$22$	−4.88769	−1.04206
$23$	−1.51609	−0.316126	−0.158063	−	0.987429i	$-0.550525\pi$
$23$	−1.51609	−0.316126	−0.158063	+	0.987429i	$0.550525\pi$
$24$	−2.13450	−0.435702
$25$	1.00000	0.200000
$26$	−1.18156	−0.231723
$27$	−3.08205	−0.593141
$28$	2.94362	0.556292
$29$	5.12726	0.952108	0.476054	−	0.879416i	$-0.342067\pi$
$29$	5.12726	0.952108	0.476054	+	0.879416i	$0.342067\pi$
$30$	2.13450	0.389704
$31$	−1.83007	−0.328691	−0.164345	−	0.986403i	$-0.552551\pi$
$31$	−1.83007	−0.328691	−0.164345	+	0.986403i	$0.552551\pi$
$32$	−1.00000	−0.176777
$33$	10.4327	1.81611
$34$	−1.72348	−0.295575
$35$	−2.94362	−0.497563
$36$	1.55608	0.259346
$37$	−9.24316	−1.51957	−0.759783	−	0.650177i	$-0.774695\pi$
$37$	−9.24316	−1.51957	−0.759783	+	0.650177i	$0.774695\pi$
$38$	−3.50901	−0.569236
$39$	2.52204	0.403850
$40$	1.00000	0.158114
$41$	0.682260	0.106551	0.0532756	−	0.998580i	$-0.483034\pi$
$41$	0.682260	0.106551	0.0532756	+	0.998580i	$0.483034\pi$
$42$	−6.28315	−0.969511
$43$	−6.76997	−1.03241	−0.516206	−	0.856465i	$-0.672656\pi$
$43$	−6.76997	−1.03241	−0.516206	+	0.856465i	$0.672656\pi$
$44$	4.88769	0.736846
$45$	−1.55608	−0.231966
$46$	1.51609	0.223535
$47$	9.01802	1.31541	0.657707	−	0.753274i	$-0.271527\pi$
$47$	9.01802	1.31541	0.657707	+	0.753274i	$0.271527\pi$
$48$	2.13450	0.308088
$49$	1.66490	0.237843
$50$	−1.00000	−0.141421
$51$	3.67877	0.515131
$52$	1.18156	0.163853
$53$	9.35047	1.28439	0.642193	−	0.766543i	$-0.278025\pi$
$53$	9.35047	1.28439	0.642193	+	0.766543i	$0.278025\pi$
$54$	3.08205	0.419414
$55$	−4.88769	−0.659055
$56$	−2.94362	−0.393358
$57$	7.48997	0.992071
$58$	−5.12726	−0.673242
$59$	−9.94967	−1.29534	−0.647669	−	0.761922i	$-0.724256\pi$
$59$	−9.94967	−1.29534	−0.647669	+	0.761922i	$0.724256\pi$
$60$	−2.13450	−0.275562
$61$	−13.9563	−1.78692	−0.893461	−	0.449141i	$-0.851730\pi$
$61$	−13.9563	−1.78692	−0.893461	+	0.449141i	$0.851730\pi$
$62$	1.83007	0.232419
$63$	4.58049	0.577088
$64$	1.00000	0.125000
$65$	−1.18156	−0.146555
$66$	−10.4327	−1.28418
$67$	6.03189	0.736913	0.368456	−	0.929645i	$-0.379886\pi$
$67$	6.03189	0.736913	0.368456	+	0.929645i	$0.379886\pi$
$68$	1.72348	0.209003
$69$	−3.23608	−0.389578
$70$	2.94362	0.351830
$71$	10.6224	1.26065	0.630323	−	0.776333i	$-0.282922\pi$
$71$	10.6224	1.26065	0.630323	+	0.776333i	$0.282922\pi$
$72$	−1.55608	−0.183385
$73$	−5.91560	−0.692368	−0.346184	−	0.938167i	$-0.612523\pi$
$73$	−5.91560	−0.692368	−0.346184	+	0.938167i	$0.612523\pi$
$74$	9.24316	1.07450
$75$	2.13450	0.246470
$76$	3.50901	0.402511
$77$	14.3875	1.63961
$78$	−2.52204	−0.285565
$79$	0.792340	0.0891452	0.0445726	−	0.999006i	$-0.485807\pi$
$79$	0.792340	0.0891452	0.0445726	+	0.999006i	$0.485807\pi$
$80$	−1.00000	−0.111803
$81$	−11.2469	−1.24965
$82$	−0.682260	−0.0753430
$83$	13.7940	1.51408	0.757042	−	0.653366i	$-0.226644\pi$
$83$	13.7940	1.51408	0.757042	+	0.653366i	$0.226644\pi$
$84$	6.28315	0.685548
$85$	−1.72348	−0.186938
$86$	6.76997	0.730025
$87$	10.9441	1.17333
$88$	−4.88769	−0.521029
$89$	−4.20666	−0.445905	−0.222952	−	0.974829i	$-0.571569\pi$
$89$	−4.20666	−0.445905	−0.222952	+	0.974829i	$0.571569\pi$
$90$	1.55608	0.164025
$91$	3.47807	0.364601
$92$	−1.51609	−0.158063
$93$	−3.90628	−0.405063
$94$	−9.01802	−0.930138
$95$	−3.50901	−0.360017
$96$	−2.13450	−0.217851
$97$	−11.0914	−1.12616	−0.563081	−	0.826402i	$-0.690384\pi$
$97$	−11.0914	−1.12616	−0.563081	+	0.826402i	$0.690384\pi$
$98$	−1.66490	−0.168180
$99$	7.60561	0.764392
$100$	1.00000	0.100000
$101$	18.5689	1.84768	0.923838	−	0.382783i	$-0.125034\pi$
$101$	18.5689	1.84768	0.923838	+	0.382783i	$0.125034\pi$
$102$	−3.67877	−0.364253
$103$	14.5857	1.43717	0.718586	−	0.695438i	$-0.244789\pi$
$103$	14.5857	1.43717	0.718586	+	0.695438i	$0.244789\pi$
$104$	−1.18156	−0.115862
$105$	−6.28315	−0.613172
$106$	−9.35047	−0.908198
$107$	7.12063	0.688377	0.344188	−	0.938901i	$-0.388154\pi$
$107$	7.12063	0.688377	0.344188	+	0.938901i	$0.388154\pi$
$108$	−3.08205	−0.296571
$109$	5.01471	0.480322	0.240161	−	0.970733i	$-0.422800\pi$
$109$	5.01471	0.480322	0.240161	+	0.970733i	$0.422800\pi$
$110$	4.88769	0.466023
$111$	−19.7295	−1.87264
$112$	2.94362	0.278146
$113$	−9.11501	−0.857468	−0.428734	−	0.903431i	$-0.641040\pi$
$113$	−9.11501	−0.857468	−0.428734	+	0.903431i	$0.641040\pi$
$114$	−7.48997	−0.701500
$115$	1.51609	0.141376
$116$	5.12726	0.476054
$117$	1.83860	0.169979
$118$	9.94967	0.915942
$119$	5.07328	0.465067
$120$	2.13450	0.194852
$121$	12.8895	1.17177
$122$	13.9563	1.26354
$123$	1.45628	0.131309
$124$	−1.83007	−0.164345
$125$	−1.00000	−0.0894427
$126$	−4.58049	−0.408063
$127$	0.747627	0.0663411	0.0331706	−	0.999450i	$-0.489440\pi$
$127$	0.747627	0.0663411	0.0331706	+	0.999450i	$0.489440\pi$
$128$	−1.00000	−0.0883883
$129$	−14.4505	−1.27229
$130$	1.18156	0.103630
$131$	14.1204	1.23371	0.616853	−	0.787078i	$-0.288407\pi$
$131$	14.1204	1.23371	0.616853	+	0.787078i	$0.288407\pi$
$132$	10.4327	0.908054
$133$	10.3292	0.895654
$134$	−6.03189	−0.521076
$135$	3.08205	0.265261
$136$	−1.72348	−0.147788
$137$	−12.0399	−1.02864	−0.514321	−	0.857598i	$-0.671956\pi$
$137$	−12.0399	−1.02864	−0.514321	+	0.857598i	$0.671956\pi$
$138$	3.23608	0.275474
$139$	9.71606	0.824106	0.412053	−	0.911160i	$-0.364812\pi$
$139$	9.71606	0.824106	0.412053	+	0.911160i	$0.364812\pi$
$140$	−2.94362	−0.248781
$141$	19.2489	1.62105
$142$	−10.6224	−0.891411
$143$	5.77511	0.482939
$144$	1.55608	0.129673
$145$	−5.12726	−0.425795
$146$	5.91560	0.489578
$147$	3.55372	0.293106
$148$	−9.24316	−0.759783
$149$	−18.1445	−1.48646	−0.743229	−	0.669037i	$-0.766707\pi$
$149$	−18.1445	−1.48646	−0.743229	+	0.669037i	$0.766707\pi$
$150$	−2.13450	−0.174281
$151$	17.8080	1.44920	0.724599	−	0.689171i	$-0.242025\pi$
$151$	17.8080	1.44920	0.724599	+	0.689171i	$0.242025\pi$
$152$	−3.50901	−0.284618
$153$	2.68187	0.216816
$154$	−14.3875	−1.15938
$155$	1.83007	0.146995
$156$	2.52204	0.201925
$157$	−8.54108	−0.681653	−0.340826	−	0.940126i	$-0.610707\pi$
$157$	−8.54108	−0.681653	−0.340826	+	0.940126i	$0.610707\pi$
$158$	−0.792340	−0.0630352
$159$	19.9585	1.58282
$160$	1.00000	0.0790569
$161$	−4.46278	−0.351717
$162$	11.2469	0.883636
$163$	−15.6136	−1.22295	−0.611475	−	0.791264i	$-0.709423\pi$
$163$	−15.6136	−1.22295	−0.611475	+	0.791264i	$0.709423\pi$
$164$	0.682260	0.0532756
$165$	−10.4327	−0.812188
$166$	−13.7940	−1.07062
$167$	−16.9665	−1.31290	−0.656452	−	0.754368i	$-0.727944\pi$
$167$	−16.9665	−1.31290	−0.656452	+	0.754368i	$0.727944\pi$
$168$	−6.28315	−0.484755
$169$	−11.6039	−0.892608
$170$	1.72348	0.132185
$171$	5.46028	0.417558
$172$	−6.76997	−0.516206
$173$	8.86101	0.673690	0.336845	−	0.941560i	$-0.390640\pi$
$173$	8.86101	0.673690	0.336845	+	0.941560i	$0.390640\pi$
$174$	−10.9441	−0.829671
$175$	2.94362	0.222517
$176$	4.88769	0.368423
$177$	−21.2375	−1.59631
$178$	4.20666	0.315302
$179$	−20.7403	−1.55020	−0.775102	−	0.631836i	$-0.782302\pi$
$179$	−20.7403	−1.55020	−0.775102	+	0.631836i	$0.782302\pi$
$180$	−1.55608	−0.115983
$181$	10.9538	0.814188	0.407094	−	0.913386i	$-0.366542\pi$
$181$	10.9538	0.814188	0.407094	+	0.913386i	$0.366542\pi$
$182$	−3.47807	−0.257812
$183$	−29.7897	−2.20212
$184$	1.51609	0.111767
$185$	9.24316	0.679570
$186$	3.90628	0.286422
$187$	8.42385	0.616013
$188$	9.01802	0.657707
$189$	−9.07239	−0.659919
$190$	3.50901	0.254570
$191$	20.0091	1.44781	0.723904	−	0.689901i	$-0.242346\pi$
$191$	20.0091	1.44781	0.723904	+	0.689901i	$0.242346\pi$
$192$	2.13450	0.154044
$193$	−4.39641	−0.316461	−0.158230	−	0.987402i	$-0.550579\pi$
$193$	−4.39641	−0.316461	−0.158230	+	0.987402i	$0.550579\pi$
$194$	11.0914	0.796317
$195$	−2.52204	−0.180607
$196$	1.66490	0.118921
$197$	−21.8553	−1.55713	−0.778565	−	0.627565i	$-0.784052\pi$
$197$	−21.8553	−1.55713	−0.778565	+	0.627565i	$0.784052\pi$
$198$	−7.60561	−0.540507
$199$	−11.1500	−0.790402	−0.395201	−	0.918595i	$-0.629325\pi$
$199$	−11.1500	−0.790402	−0.395201	+	0.918595i	$0.629325\pi$
$200$	−1.00000	−0.0707107
$201$	12.8750	0.908136
$202$	−18.5689	−1.30650
$203$	15.0927	1.05930
$204$	3.67877	0.257565
$205$	−0.682260	−0.0476511
$206$	−14.5857	−1.01623
$207$	−2.35914	−0.163972
$208$	1.18156	0.0819266
$209$	17.1509	1.18636
$210$	6.28315	0.433578
$211$	6.35671	0.437614	0.218807	−	0.975768i	$-0.429784\pi$
$211$	6.35671	0.437614	0.218807	+	0.975768i	$0.429784\pi$
$212$	9.35047	0.642193
$213$	22.6735	1.55356
$214$	−7.12063	−0.486756
$215$	6.76997	0.461708
$216$	3.08205	0.209707
$217$	−5.38704	−0.365696
$218$	−5.01471	−0.339639
$219$	−12.6268	−0.853241
$220$	−4.88769	−0.329528
$221$	2.03640	0.136983
$222$	19.7295	1.32416
$223$	1.00000	0.0669650
$223$	1.00000	0.0669650
$224$	−2.94362	−0.196679
$225$	1.55608	0.103738
$226$	9.11501	0.606321
$227$	−4.24805	−0.281953	−0.140976	−	0.990013i	$-0.545024\pi$
$227$	−4.24805	−0.281953	−0.140976	+	0.990013i	$0.545024\pi$
$228$	7.48997	0.496035
$229$	7.33025	0.484397	0.242198	−	0.970227i	$-0.422132\pi$
$229$	7.33025	0.484397	0.242198	+	0.970227i	$0.422132\pi$
$230$	−1.51609	−0.0999678
$231$	30.7101	2.02057
$232$	−5.12726	−0.336621
$233$	13.9826	0.916030	0.458015	−	0.888945i	$-0.348561\pi$
$233$	13.9826	0.916030	0.458015	+	0.888945i	$0.348561\pi$
$234$	−1.83860	−0.120193
$235$	−9.01802	−0.588271
$236$	−9.94967	−0.647669
$237$	1.69125	0.109858
$238$	−5.07328	−0.328852
$239$	7.57521	0.490000	0.245000	−	0.969523i	$-0.421212\pi$
$239$	7.57521	0.490000	0.245000	+	0.969523i	$0.421212\pi$
$240$	−2.13450	−0.137781
$241$	−23.0746	−1.48637	−0.743183	−	0.669089i	$-0.766685\pi$
$241$	−23.0746	−1.48637	−0.743183	+	0.669089i	$0.766685\pi$
$242$	−12.8895	−0.828567
$243$	−14.7602	−0.946868
$244$	−13.9563	−0.893461
$245$	−1.66490	−0.106367
$246$	−1.45628	−0.0928491
$247$	4.14611	0.263811
$248$	1.83007	0.116210
$249$	29.4432	1.86589
$250$	1.00000	0.0632456
$251$	−14.1193	−0.891201	−0.445600	−	0.895232i	$-0.647010\pi$
$251$	−14.1193	−0.891201	−0.445600	+	0.895232i	$0.647010\pi$
$252$	4.58049	0.288544
$253$	−7.41015	−0.465872
$254$	−0.747627	−0.0469103
$255$	−3.67877	−0.230374
$256$	1.00000	0.0625000
$257$	4.62239	0.288337	0.144168	−	0.989553i	$-0.453949\pi$
$257$	4.62239	0.288337	0.144168	+	0.989553i	$0.453949\pi$
$258$	14.4505	0.899648
$259$	−27.2083	−1.69064
$260$	−1.18156	−0.0732774
$261$	7.97840	0.493850
$262$	−14.1204	−0.872362
$263$	0.970610	0.0598503	0.0299252	−	0.999552i	$-0.490473\pi$
$263$	0.970610	0.0598503	0.0299252	+	0.999552i	$0.490473\pi$
$264$	−10.4327	−0.642091
$265$	−9.35047	−0.574395
$266$	−10.3292	−0.633323
$267$	−8.97910	−0.549512
$268$	6.03189	0.368456
$269$	−14.2768	−0.870474	−0.435237	−	0.900316i	$-0.643335\pi$
$269$	−14.2768	−0.870474	−0.435237	+	0.900316i	$0.643335\pi$
$270$	−3.08205	−0.187568
$271$	14.8530	0.902257	0.451128	−	0.892459i	$-0.351022\pi$
$271$	14.8530	0.902257	0.451128	+	0.892459i	$0.351022\pi$
$272$	1.72348	0.104502
$273$	7.42393	0.449317
$274$	12.0399	0.727359
$275$	4.88769	0.294739
$276$	−3.23608	−0.194789
$277$	11.1006	0.666972	0.333486	−	0.942755i	$-0.391775\pi$
$277$	11.1006	0.666972	0.333486	+	0.942755i	$0.391775\pi$
$278$	−9.71606	−0.582731
$279$	−2.84773	−0.170489
$280$	2.94362	0.175915
$281$	26.8121	1.59948	0.799738	−	0.600349i	$-0.204972\pi$
$281$	26.8121	1.59948	0.799738	+	0.600349i	$0.204972\pi$
$282$	−19.2489	−1.14626
$283$	3.27664	0.194776	0.0973879	−	0.995247i	$-0.468951\pi$
$283$	3.27664	0.194776	0.0973879	+	0.995247i	$0.468951\pi$
$284$	10.6224	0.630323
$285$	−7.48997	−0.443667
$286$	−5.77511	−0.341489
$287$	2.00831	0.118547
$288$	−1.55608	−0.0916926
$289$	−14.0296	−0.825271
$290$	5.12726	0.301083
$291$	−23.6746	−1.38783
$292$	−5.91560	−0.346184
$293$	−23.5985	−1.37864	−0.689320	−	0.724457i	$-0.742091\pi$
$293$	−23.5985	−1.37864	−0.689320	+	0.724457i	$0.742091\pi$
$294$	−3.55372	−0.207257
$295$	9.94967	0.579292
$296$	9.24316	0.537248
$297$	−15.0641	−0.874108
$298$	18.1445	1.05108
$299$	−1.79135	−0.103596
$300$	2.13450	0.123235
$301$	−19.9282	−1.14864
$302$	−17.8080	−1.02474
$303$	39.6353	2.27699
$304$	3.50901	0.201255
$305$	13.9563	0.799136
$306$	−2.68187	−0.153312
$307$	0.150742	0.00860331	0.00430165	−	0.999991i	$-0.498631\pi$
$307$	0.150742	0.00860331	0.00430165	+	0.999991i	$0.498631\pi$
$308$	14.3875	0.819803
$309$	31.1331	1.77110
$310$	−1.83007	−0.103941
$311$	4.60390	0.261063	0.130532	−	0.991444i	$-0.458332\pi$
$311$	4.60390	0.261063	0.130532	+	0.991444i	$0.458332\pi$
$312$	−2.52204	−0.142782
$313$	17.7806	1.00502	0.502508	−	0.864573i	$-0.332411\pi$
$313$	17.7806	1.00502	0.502508	+	0.864573i	$0.332411\pi$
$314$	8.54108	0.482001
$315$	−4.58049	−0.258082
$316$	0.792340	0.0445726
$317$	23.8147	1.33757	0.668784	−	0.743457i	$-0.266815\pi$
$317$	23.8147	1.33757	0.668784	+	0.743457i	$0.266815\pi$
$318$	−19.9585	−1.11922
$319$	25.0604	1.40311
$320$	−1.00000	−0.0559017
$321$	15.1990	0.848323
$322$	4.46278	0.248701
$323$	6.04772	0.336504
$324$	−11.2469	−0.624825
$325$	1.18156	0.0655413
$326$	15.6136	0.864756
$327$	10.7039	0.591926
$328$	−0.682260	−0.0376715
$329$	26.5456	1.46351
$330$	10.4327	0.574304
$331$	36.1186	1.98526	0.992629	−	0.121193i	$-0.0386719\pi$
$331$	36.1186	1.98526	0.992629	+	0.121193i	$0.0386719\pi$
$332$	13.7940	0.757042
$333$	−14.3831	−0.788186
$334$	16.9665	0.928363
$335$	−6.03189	−0.329557
$336$	6.28315	0.342774
$337$	−11.2380	−0.612172	−0.306086	−	0.952004i	$-0.599020\pi$
$337$	−11.2380	−0.612172	−0.306086	+	0.952004i	$0.599020\pi$
$338$	11.6039	0.631169
$339$	−19.4560	−1.05670
$340$	−1.72348	−0.0934690
$341$	−8.94482	−0.484389
$342$	−5.46028	−0.295258
$343$	−15.7045	−0.847964
$344$	6.76997	0.365013
$345$	3.23608	0.174225
$346$	−8.86101	−0.476371
$347$	−30.6989	−1.64800	−0.824001	−	0.566588i	$-0.808263\pi$
$347$	−30.6989	−1.64800	−0.824001	+	0.566588i	$0.808263\pi$
$348$	10.9441	0.586666
$349$	17.5626	0.940105	0.470052	−	0.882639i	$-0.344235\pi$
$349$	17.5626	0.940105	0.470052	+	0.882639i	$0.344235\pi$
$350$	−2.94362	−0.157343
$351$	−3.64164	−0.194376
$352$	−4.88769	−0.260515
$353$	−10.6920	−0.569079	−0.284539	−	0.958664i	$-0.591841\pi$
$353$	−10.6920	−0.569079	−0.284539	+	0.958664i	$0.591841\pi$
$354$	21.2375	1.12876
$355$	−10.6224	−0.563778
$356$	−4.20666	−0.222952
$357$	10.8289	0.573126
$358$	20.7403	1.09616
$359$	23.0313	1.21554	0.607772	−	0.794111i	$-0.292063\pi$
$359$	23.0313	1.21554	0.607772	+	0.794111i	$0.292063\pi$
$360$	1.55608	0.0820124
$361$	−6.68685	−0.351940
$362$	−10.9538	−0.575718
$363$	27.5125	1.44403
$364$	3.47807	0.182300
$365$	5.91560	0.309636
$366$	29.7897	1.55713
$367$	−27.3778	−1.42911	−0.714554	−	0.699580i	$-0.753370\pi$
$367$	−27.3778	−1.42911	−0.714554	+	0.699580i	$0.753370\pi$
$368$	−1.51609	−0.0790315
$369$	1.06165	0.0552672
$370$	−9.24316	−0.480529
$371$	27.5242	1.42899
$372$	−3.90628	−0.202531
$373$	0.673310	0.0348627	0.0174313	−	0.999848i	$-0.494451\pi$
$373$	0.673310	0.0348627	0.0174313	+	0.999848i	$0.494451\pi$
$374$	−8.42385	−0.435587
$375$	−2.13450	−0.110225
$376$	−9.01802	−0.465069
$377$	6.05817	0.312012
$378$	9.07239	0.466633
$379$	2.85212	0.146503	0.0732517	−	0.997313i	$-0.476662\pi$
$379$	2.85212	0.146503	0.0732517	+	0.997313i	$0.476662\pi$
$380$	−3.50901	−0.180008
$381$	1.59581	0.0817556
$382$	−20.0091	−1.02375
$383$	−17.1127	−0.874419	−0.437209	−	0.899360i	$-0.644033\pi$
$383$	−17.1127	−0.874419	−0.437209	+	0.899360i	$0.644033\pi$
$384$	−2.13450	−0.108926
$385$	−14.3875	−0.733254
$386$	4.39641	0.223772
$387$	−10.5346	−0.535503
$388$	−11.0914	−0.563081
$389$	−35.3435	−1.79199	−0.895994	−	0.444065i	$-0.853536\pi$
$389$	−35.3435	−1.79199	−0.895994	+	0.444065i	$0.853536\pi$
$390$	2.52204	0.127709
$391$	−2.61295	−0.132143
$392$	−1.66490	−0.0840901
$393$	30.1400	1.52036
$394$	21.8553	1.10106
$395$	−0.792340	−0.0398669
$396$	7.60561	0.382196
$397$	−9.06350	−0.454884	−0.227442	−	0.973792i	$-0.573036\pi$
$397$	−9.06350	−0.454884	−0.227442	+	0.973792i	$0.573036\pi$
$398$	11.1500	0.558899
$399$	22.0476	1.10376
$400$	1.00000	0.0500000
$401$	3.16303	0.157954	0.0789772	−	0.996876i	$-0.474835\pi$
$401$	3.16303	0.157954	0.0789772	+	0.996876i	$0.474835\pi$
$402$	−12.8750	−0.642149
$403$	−2.16234	−0.107714
$404$	18.5689	0.923838
$405$	11.2469	0.558861
$406$	−15.0927	−0.749038
$407$	−45.1777	−2.23937
$408$	−3.67877	−0.182126
$409$	6.37643	0.315294	0.157647	−	0.987496i	$-0.449609\pi$
$409$	6.37643	0.315294	0.157647	+	0.987496i	$0.449609\pi$
$410$	0.682260	0.0336944
$411$	−25.6992	−1.26765
$412$	14.5857	0.718586
$413$	−29.2881	−1.44117
$414$	2.35914	0.115946
$415$	−13.7940	−0.677119
$416$	−1.18156	−0.0579309
$417$	20.7389	1.01559
$418$	−17.1509	−0.838880
$419$	3.85214	0.188189	0.0940946	−	0.995563i	$-0.470004\pi$
$419$	3.85214	0.188189	0.0940946	+	0.995563i	$0.470004\pi$
$420$	−6.28315	−0.306586
$421$	−15.1353	−0.737650	−0.368825	−	0.929499i	$-0.620240\pi$
$421$	−15.1353	−0.737650	−0.368825	+	0.929499i	$0.620240\pi$
$422$	−6.35671	−0.309440
$423$	14.0327	0.682294
$424$	−9.35047	−0.454099
$425$	1.72348	0.0836013
$426$	−22.6735	−1.09853
$427$	−41.0821	−1.98810
$428$	7.12063	0.344188
$429$	12.3269	0.595151
$430$	−6.76997	−0.326477
$431$	26.3547	1.26946	0.634731	−	0.772733i	$-0.281111\pi$
$431$	26.3547	1.26946	0.634731	+	0.772733i	$0.281111\pi$
$432$	−3.08205	−0.148285
$433$	−4.88170	−0.234599	−0.117300	−	0.993097i	$-0.537424\pi$
$433$	−4.88170	−0.234599	−0.117300	+	0.993097i	$0.537424\pi$
$434$	5.38704	0.258586
$435$	−10.9441	−0.524730
$436$	5.01471	0.240161
$437$	−5.31996	−0.254488
$438$	12.6268	0.603333
$439$	−27.4018	−1.30782	−0.653909	−	0.756573i	$-0.726872\pi$
$439$	−27.4018	−1.30782	−0.653909	+	0.756573i	$0.726872\pi$
$440$	4.88769	0.233011
$441$	2.59071	0.123367
$442$	−2.03640	−0.0968619
$443$	−21.0022	−0.997842	−0.498921	−	0.866647i	$-0.666270\pi$
$443$	−21.0022	−0.997842	−0.498921	+	0.866647i	$0.666270\pi$
$444$	−19.7295	−0.936320
$445$	4.20666	0.199415
$446$	−1.00000	−0.0473514
$447$	−38.7294	−1.83184
$448$	2.94362	0.139073
$449$	−2.13623	−0.100815	−0.0504076	−	0.998729i	$-0.516052\pi$
$449$	−2.13623	−0.100815	−0.0504076	+	0.998729i	$0.516052\pi$
$450$	−1.55608	−0.0733541
$451$	3.33467	0.157024
$452$	−9.11501	−0.428734
$453$	38.0112	1.78592
$454$	4.24805	0.199371
$455$	−3.47807	−0.163055
$456$	−7.48997	−0.350750
$457$	3.99174	0.186726	0.0933628	−	0.995632i	$-0.470238\pi$
$457$	3.99174	0.186726	0.0933628	+	0.995632i	$0.470238\pi$
$458$	−7.33025	−0.342520
$459$	−5.31187	−0.247937
$460$	1.51609	0.0706879
$461$	−9.81448	−0.457106	−0.228553	−	0.973531i	$-0.573399\pi$
$461$	−9.81448	−0.457106	−0.228553	+	0.973531i	$0.573399\pi$
$462$	−30.7101	−1.42876
$463$	−5.92453	−0.275336	−0.137668	−	0.990478i	$-0.543961\pi$
$463$	−5.92453	−0.275336	−0.137668	+	0.990478i	$0.543961\pi$
$464$	5.12726	0.238027
$465$	3.90628	0.181149
$466$	−13.9826	−0.647731
$467$	12.6924	0.587335	0.293667	−	0.955908i	$-0.405124\pi$
$467$	12.6924	0.587335	0.293667	+	0.955908i	$0.405124\pi$
$468$	1.83860	0.0849893
$469$	17.7556	0.819877
$470$	9.01802	0.415970
$471$	−18.2309	−0.840036
$472$	9.94967	0.457971
$473$	−33.0895	−1.52146
$474$	−1.69125	−0.0776815
$475$	3.50901	0.161004
$476$	5.07328	0.232534
$477$	14.5500	0.666200
$478$	−7.57521	−0.346482
$479$	33.2614	1.51975	0.759876	−	0.650068i	$-0.225260\pi$
$479$	33.2614	1.51975	0.759876	+	0.650068i	$0.225260\pi$
$480$	2.13450	0.0974260
$481$	−10.9214	−0.497972
$482$	23.0746	1.05102
$483$	−9.52579	−0.433439
$484$	12.8895	0.585885
$485$	11.0914	0.503635
$486$	14.7602	0.669537
$487$	−34.5446	−1.56537	−0.782683	−	0.622421i	$-0.786149\pi$
$487$	−34.5446	−1.56537	−0.782683	+	0.622421i	$0.786149\pi$
$488$	13.9563	0.631772
$489$	−33.3271	−1.50710
$490$	1.66490	0.0752125
$491$	−5.39981	−0.243690	−0.121845	−	0.992549i	$-0.538881\pi$
$491$	−5.39981	−0.243690	−0.121845	+	0.992549i	$0.538881\pi$
$492$	1.45628	0.0656543
$493$	8.83674	0.397987
$494$	−4.14611	−0.186542
$495$	−7.60561	−0.341847
$496$	−1.83007	−0.0821726
$497$	31.2683	1.40257
$498$	−29.4432	−1.31938
$499$	−30.0164	−1.34372	−0.671859	−	0.740679i	$-0.734504\pi$
$499$	−30.0164	−1.34372	−0.671859	+	0.740679i	$0.734504\pi$
$500$	−1.00000	−0.0447214
$501$	−36.2148	−1.61796
$502$	14.1193	0.630174
$503$	−14.1772	−0.632131	−0.316066	−	0.948737i	$-0.602362\pi$
$503$	−14.1772	−0.632131	−0.316066	+	0.948737i	$0.602362\pi$
$504$	−4.58049	−0.204031
$505$	−18.5689	−0.826306
$506$	7.41015	0.329422
$507$	−24.7685	−1.10001
$508$	0.747627	0.0331706
$509$	−38.7002	−1.71536	−0.857678	−	0.514187i	$-0.828094\pi$
$509$	−38.7002	−1.71536	−0.857678	+	0.514187i	$0.828094\pi$
$510$	3.67877	0.162899
$511$	−17.4133	−0.770318
$512$	−1.00000	−0.0441942
$513$	−10.8149	−0.477492
$514$	−4.62239	−0.203885
$515$	−14.5857	−0.642723
$516$	−14.4505	−0.636147
$517$	44.0772	1.93852
$518$	27.2083	1.19547
$519$	18.9138	0.830224
$520$	1.18156	0.0518149
$521$	32.9341	1.44287	0.721434	−	0.692484i	$-0.243484\pi$
$521$	32.9341	1.44287	0.721434	+	0.692484i	$0.243484\pi$
$522$	−7.97840	−0.349205
$523$	−0.100231	−0.00438279	−0.00219139	−	0.999998i	$-0.500698\pi$
$523$	−0.100231	−0.00438279	−0.00219139	+	0.999998i	$0.500698\pi$
$524$	14.1204	0.616853
$525$	6.28315	0.274219
$526$	−0.970610	−0.0423206
$527$	−3.15410	−0.137395
$528$	10.4327	0.454027
$529$	−20.7015	−0.900064
$530$	9.35047	0.406158
$531$	−15.4824	−0.671881
$532$	10.3292	0.447827
$533$	0.806133	0.0349175
$534$	8.97910	0.388564
$535$	−7.12063	−0.307851
$536$	−6.03189	−0.260538
$537$	−44.2701	−1.91040
$538$	14.2768	0.615518
$539$	8.13751	0.350507
$540$	3.08205	0.132630
$541$	21.7799	0.936389	0.468195	−	0.883625i	$-0.344905\pi$
$541$	21.7799	0.936389	0.468195	+	0.883625i	$0.344905\pi$
$542$	−14.8530	−0.637992
$543$	23.3808	1.00337
$544$	−1.72348	−0.0738938
$545$	−5.01471	−0.214807
$546$	−7.42393	−0.317715
$547$	−31.5835	−1.35041	−0.675205	−	0.737630i	$-0.735945\pi$
$547$	−31.5835	−1.35041	−0.675205	+	0.737630i	$0.735945\pi$
$548$	−12.0399	−0.514321
$549$	−21.7171	−0.926862
$550$	−4.88769	−0.208412
$551$	17.9916	0.766468
$552$	3.23608	0.137737
$553$	2.33235	0.0991815
$554$	−11.1006	−0.471620
$555$	19.7295	0.837470
$556$	9.71606	0.412053
$557$	−17.5855	−0.745121	−0.372560	−	0.928008i	$-0.621520\pi$
$557$	−17.5855	−0.745121	−0.372560	+	0.928008i	$0.621520\pi$
$558$	2.84773	0.120554
$559$	−7.99915	−0.338328
$560$	−2.94362	−0.124391
$561$	17.9807	0.759145
$562$	−26.8121	−1.13100
$563$	−26.0481	−1.09779	−0.548897	−	0.835890i	$-0.684952\pi$
$563$	−26.0481	−1.09779	−0.548897	+	0.835890i	$0.684952\pi$
$564$	19.2489	0.810526
$565$	9.11501	0.383471
$566$	−3.27664	−0.137727
$567$	−33.1065	−1.39034
$568$	−10.6224	−0.445706
$569$	−21.3159	−0.893607	−0.446804	−	0.894632i	$-0.647438\pi$
$569$	−21.3159	−0.893607	−0.446804	+	0.894632i	$0.647438\pi$
$570$	7.48997	0.313720
$571$	−35.3663	−1.48003	−0.740017	−	0.672589i	$-0.765182\pi$
$571$	−35.3663	−1.48003	−0.740017	+	0.672589i	$0.765182\pi$
$572$	5.77511	0.241469
$573$	42.7094	1.78421
$574$	−2.00831	−0.0838254
$575$	−1.51609	−0.0632252
$576$	1.55608	0.0648365
$577$	−1.38457	−0.0576402	−0.0288201	−	0.999585i	$-0.509175\pi$
$577$	−1.38457	−0.0576402	−0.0288201	+	0.999585i	$0.509175\pi$
$578$	14.0296	0.583555
$579$	−9.38413	−0.389991
$580$	−5.12726	−0.212898
$581$	40.6042	1.68455
$582$	23.6746	0.981343
$583$	45.7022	1.89279
$584$	5.91560	0.244789
$585$	−1.83860	−0.0760168
$586$	23.5985	0.974846
$587$	25.7020	1.06084	0.530418	−	0.847736i	$-0.322035\pi$
$587$	25.7020	1.06084	0.530418	+	0.847736i	$0.322035\pi$
$588$	3.55372	0.146553
$589$	−6.42174	−0.264603
$590$	−9.94967	−0.409622
$591$	−46.6502	−1.91893
$592$	−9.24316	−0.379891
$593$	−20.8407	−0.855823	−0.427911	−	0.903821i	$-0.640751\pi$
$593$	−20.8407	−0.855823	−0.427911	+	0.903821i	$0.640751\pi$
$594$	15.0641	0.618088
$595$	−5.07328	−0.207984
$596$	−18.1445	−0.743229
$597$	−23.7996	−0.974054
$598$	1.79135	0.0732538
$599$	38.4242	1.56997	0.784985	−	0.619514i	$-0.212670\pi$
$599$	38.4242	1.56997	0.784985	+	0.619514i	$0.212670\pi$
$600$	−2.13450	−0.0871405
$601$	−12.0623	−0.492033	−0.246016	−	0.969266i	$-0.579122\pi$
$601$	−12.0623	−0.492033	−0.246016	+	0.969266i	$0.579122\pi$
$602$	19.9282	0.812214
$603$	9.38608	0.382231
$604$	17.8080	0.724599
$605$	−12.8895	−0.524032
$606$	−39.6353	−1.61007
$607$	24.8747	1.00963	0.504816	−	0.863227i	$-0.331560\pi$
$607$	24.8747	1.00963	0.504816	+	0.863227i	$0.331560\pi$
$608$	−3.50901	−0.142309
$609$	32.2153	1.30543
$610$	−13.9563	−0.565074
$611$	10.6554	0.431069
$612$	2.68187	0.108408
$613$	−31.5893	−1.27588	−0.637941	−	0.770085i	$-0.720214\pi$
$613$	−31.5893	−1.27588	−0.637941	+	0.770085i	$0.720214\pi$
$614$	−0.150742	−0.00608346
$615$	−1.45628	−0.0587230
$616$	−14.3875	−0.579689
$617$	−26.5252	−1.06786	−0.533932	−	0.845527i	$-0.679286\pi$
$617$	−26.5252	−1.06786	−0.533932	+	0.845527i	$0.679286\pi$
$618$	−31.1331	−1.25236
$619$	40.7097	1.63626	0.818130	−	0.575033i	$-0.195011\pi$
$619$	40.7097	1.63626	0.818130	+	0.575033i	$0.195011\pi$
$620$	1.83007	0.0734974
$621$	4.67266	0.187507
$622$	−4.60390	−0.184599
$623$	−12.3828	−0.496107
$624$	2.52204	0.100962
$625$	1.00000	0.0400000
$626$	−17.7806	−0.710654
$627$	36.6086	1.46201
$628$	−8.54108	−0.340826
$629$	−15.9304	−0.635188
$630$	4.58049	0.182491
$631$	7.72316	0.307454	0.153727	−	0.988113i	$-0.450872\pi$
$631$	7.72316	0.307454	0.153727	+	0.988113i	$0.450872\pi$
$632$	−0.792340	−0.0315176
$633$	13.5684	0.539294
$634$	−23.8147	−0.945803
$635$	−0.747627	−0.0296687
$636$	19.9585	0.791408
$637$	1.96718	0.0779426
$638$	−25.0604	−0.992152
$639$	16.5292	0.653887
$640$	1.00000	0.0395285
$641$	−28.5017	−1.12575	−0.562876	−	0.826542i	$-0.690305\pi$
$641$	−28.5017	−1.12575	−0.562876	+	0.826542i	$0.690305\pi$
$642$	−15.1990	−0.599855
$643$	4.76526	0.187923	0.0939617	−	0.995576i	$-0.470047\pi$
$643$	4.76526	0.187923	0.0939617	+	0.995576i	$0.470047\pi$
$644$	−4.46278	−0.175858
$645$	14.4505	0.568987
$646$	−6.04772	−0.237944
$647$	−37.4316	−1.47159	−0.735794	−	0.677206i	$-0.763191\pi$
$647$	−37.4316	−1.47159	−0.735794	+	0.677206i	$0.763191\pi$
$648$	11.2469	0.441818
$649$	−48.6309	−1.90893
$650$	−1.18156	−0.0463447
$651$	−11.4986	−0.450666
$652$	−15.6136	−0.611475
$653$	34.8685	1.36451	0.682254	−	0.731115i	$-0.261000\pi$
$653$	34.8685	1.36451	0.682254	+	0.731115i	$0.261000\pi$
$654$	−10.7039	−0.418555
$655$	−14.1204	−0.551730
$656$	0.682260	0.0266378
$657$	−9.20511	−0.359126
$658$	−26.5456	−1.03486
$659$	13.7645	0.536190	0.268095	−	0.963392i	$-0.413606\pi$
$659$	13.7645	0.536190	0.268095	+	0.963392i	$0.413606\pi$
$660$	−10.4327	−0.406094
$661$	6.88583	0.267828	0.133914	−	0.990993i	$-0.457245\pi$
$661$	6.88583	0.267828	0.133914	+	0.990993i	$0.457245\pi$
$662$	−36.1186	−1.40379
$663$	4.34670	0.168812
$664$	−13.7940	−0.535310
$665$	−10.3292	−0.400549
$666$	14.3831	0.557332
$667$	−7.77336	−0.300986
$668$	−16.9665	−0.656452
$669$	2.13450	0.0825244
$670$	6.03189	0.233032
$671$	−68.2140	−2.63337
$672$	−6.28315	−0.242378
$673$	−19.6393	−0.757038	−0.378519	−	0.925593i	$-0.623567\pi$
$673$	−19.6393	−0.757038	−0.378519	+	0.925593i	$0.623567\pi$
$674$	11.2380	0.432871
$675$	−3.08205	−0.118628
$676$	−11.6039	−0.446304
$677$	−25.3687	−0.974999	−0.487499	−	0.873123i	$-0.662091\pi$
$677$	−25.3687	−0.974999	−0.487499	+	0.873123i	$0.662091\pi$
$678$	19.4560	0.747201
$679$	−32.6489	−1.25295
$680$	1.72348	0.0660926
$681$	−9.06744	−0.347465
$682$	8.94482	0.342515
$683$	−23.6002	−0.903038	−0.451519	−	0.892262i	$-0.649118\pi$
$683$	−23.6002	−0.903038	−0.451519	+	0.892262i	$0.649118\pi$
$684$	5.46028	0.208779
$685$	12.0399	0.460022
$686$	15.7045	0.599601
$687$	15.6464	0.596947
$688$	−6.76997	−0.258103
$689$	11.0482	0.420902
$690$	−3.23608	−0.123195
$691$	11.0977	0.422178	0.211089	−	0.977467i	$-0.432299\pi$
$691$	11.0977	0.422178	0.211089	+	0.977467i	$0.432299\pi$
$692$	8.86101	0.336845
$693$	22.3880	0.850451
$694$	30.6989	1.16531
$695$	−9.71606	−0.368551
$696$	−10.9441	−0.414835
$697$	1.17586	0.0445390
$698$	−17.5626	−0.664754
$699$	29.8458	1.12887
$700$	2.94362	0.111258
$701$	−36.4476	−1.37661	−0.688303	−	0.725423i	$-0.741644\pi$
$701$	−36.4476	−1.37661	−0.688303	+	0.725423i	$0.741644\pi$
$702$	3.64164	0.137445
$703$	−32.4343	−1.22328
$704$	4.88769	0.184212
$705$	−19.2489	−0.724957
$706$	10.6920	0.402399
$707$	54.6599	2.05570
$708$	−21.2375	−0.798156
$709$	39.9645	1.50090	0.750449	−	0.660928i	$-0.229837\pi$
$709$	39.9645	1.50090	0.750449	+	0.660928i	$0.229837\pi$
$710$	10.6224	0.398651
$711$	1.23294	0.0462389
$712$	4.20666	0.157651
$713$	2.77455	0.103908
$714$	−10.8289	−0.405262
$715$	−5.77511	−0.215977
$716$	−20.7403	−0.775102
$717$	16.1693	0.603852
$718$	−23.0313	−0.859520
$719$	31.5864	1.17798	0.588988	−	0.808142i	$-0.299527\pi$
$719$	31.5864	1.17798	0.588988	+	0.808142i	$0.299527\pi$
$720$	−1.55608	−0.0579915
$721$	42.9348	1.59898
$722$	6.68685	0.248859
$723$	−49.2526	−1.83173
$724$	10.9538	0.407094
$725$	5.12726	0.190422
$726$	−27.5125	−1.02109
$727$	−10.7517	−0.398758	−0.199379	−	0.979922i	$-0.563892\pi$
$727$	−10.7517	−0.398758	−0.199379	+	0.979922i	$0.563892\pi$
$728$	−3.47807	−0.128906
$729$	2.23493	0.0827753
$730$	−5.91560	−0.218946
$731$	−11.6679	−0.431554
$732$	−29.7897	−1.10106
$733$	7.10675	0.262494	0.131247	−	0.991350i	$-0.458102\pi$
$733$	7.10675	0.262494	0.131247	+	0.991350i	$0.458102\pi$
$734$	27.3778	1.01053
$735$	−3.55372	−0.131081
$736$	1.51609	0.0558837
$737$	29.4820	1.08598
$738$	−1.06165	−0.0390798
$739$	−18.2706	−0.672094	−0.336047	−	0.941845i	$-0.609090\pi$
$739$	−18.2706	−0.672094	−0.336047	+	0.941845i	$0.609090\pi$
$740$	9.24316	0.339785
$741$	8.84987	0.325108
$742$	−27.5242	−1.01045
$743$	−27.6208	−1.01331	−0.506655	−	0.862149i	$-0.669118\pi$
$743$	−27.6208	−1.01331	−0.506655	+	0.862149i	$0.669118\pi$
$744$	3.90628	0.143211
$745$	18.1445	0.664764
$746$	−0.673310	−0.0246516
$747$	21.4645	0.785343
$748$	8.42385	0.308006
$749$	20.9604	0.765877
$750$	2.13450	0.0779408
$751$	−19.3759	−0.707038	−0.353519	−	0.935427i	$-0.615015\pi$
$751$	−19.3759	−0.707038	−0.353519	+	0.935427i	$0.615015\pi$
$752$	9.01802	0.328853
$753$	−30.1375	−1.09827
$754$	−6.05817	−0.220626
$755$	−17.8080	−0.648101
$756$	−9.07239	−0.329960
$757$	−0.517273	−0.0188006	−0.00940030	−	0.999956i	$-0.502992\pi$
$757$	−0.517273	−0.0188006	−0.00940030	+	0.999956i	$0.502992\pi$
$758$	−2.85212	−0.103594
$759$	−15.8169	−0.574119
$760$	3.50901	0.127285
$761$	−16.6258	−0.602685	−0.301343	−	0.953516i	$-0.597435\pi$
$761$	−16.6258	−0.602685	−0.301343	+	0.953516i	$0.597435\pi$
$762$	−1.59581	−0.0578100
$763$	14.7614	0.534399
$764$	20.0091	0.723904
$765$	−2.68187	−0.0969633
$766$	17.1127	0.618307
$767$	−11.7562	−0.424490
$768$	2.13450	0.0770220
$769$	−10.4927	−0.378377	−0.189188	−	0.981941i	$-0.560586\pi$
$769$	−10.4927	−0.378377	−0.189188	+	0.981941i	$0.560586\pi$
$770$	14.3875	0.518489
$771$	9.86648	0.355332
$772$	−4.39641	−0.158230
$773$	−47.7679	−1.71809	−0.859045	−	0.511899i	$-0.828942\pi$
$773$	−47.7679	−1.71809	−0.859045	+	0.511899i	$0.828942\pi$
$774$	10.5346	0.378658
$775$	−1.83007	−0.0657381
$776$	11.0914	0.398158
$777$	−58.0761	−2.08347
$778$	35.3435	1.26713
$779$	2.39406	0.0857760
$780$	−2.52204	−0.0903036
$781$	51.9189	1.85780
$782$	2.61295	0.0934389
$783$	−15.8025	−0.564734
$784$	1.66490	0.0594607
$785$	8.54108	0.304844
$786$	−30.1400	−1.07506
$787$	−40.7277	−1.45179	−0.725893	−	0.687808i	$-0.758573\pi$
$787$	−40.7277	−1.45179	−0.725893	+	0.687808i	$0.758573\pi$
$788$	−21.8553	−0.778565
$789$	2.07176	0.0737567
$790$	0.792340	0.0281902
$791$	−26.8311	−0.954005
$792$	−7.60561	−0.270254
$793$	−16.4902	−0.585586
$794$	9.06350	0.321652
$795$	−19.9585	−0.707857
$796$	−11.1500	−0.395201
$797$	31.2035	1.10528	0.552642	−	0.833419i	$-0.313620\pi$
$797$	31.2035	1.10528	0.552642	+	0.833419i	$0.313620\pi$
$798$	−22.0476	−0.780477
$799$	15.5424	0.549851
$800$	−1.00000	−0.0353553
$801$	−6.54588	−0.231287
$802$	−3.16303	−0.111691
$803$	−28.9136	−1.02034
$804$	12.8750	0.454068
$805$	4.46278	0.157292
$806$	2.16234	0.0761653
$807$	−30.4739	−1.07273
$808$	−18.5689	−0.653252
$809$	33.5685	1.18021	0.590103	−	0.807328i	$-0.299087\pi$
$809$	33.5685	1.18021	0.590103	+	0.807328i	$0.299087\pi$
$810$	−11.2469	−0.395174
$811$	19.2935	0.677485	0.338742	−	0.940879i	$-0.389998\pi$
$811$	19.2935	0.677485	0.338742	+	0.940879i	$0.389998\pi$
$812$	15.0927	0.529650
$813$	31.7037	1.11190
$814$	45.1777	1.58348
$815$	15.6136	0.546920
$816$	3.67877	0.128783
$817$	−23.7559	−0.831114
$818$	−6.37643	−0.222947
$819$	5.41214	0.189116
$820$	−0.682260	−0.0238256
$821$	14.7134	0.513502	0.256751	−	0.966478i	$-0.417348\pi$
$821$	14.7134	0.513502	0.256751	+	0.966478i	$0.417348\pi$
$822$	25.6992	0.896363
$823$	21.4458	0.747553	0.373777	−	0.927519i	$-0.378063\pi$
$823$	21.4458	0.747553	0.373777	+	0.927519i	$0.378063\pi$
$824$	−14.5857	−0.508117
$825$	10.4327	0.363222
$826$	29.2881	1.01906
$827$	5.18881	0.180432	0.0902162	−	0.995922i	$-0.471244\pi$
$827$	5.18881	0.180432	0.0902162	+	0.995922i	$0.471244\pi$
$828$	−2.35914	−0.0819859
$829$	−26.4094	−0.917237	−0.458618	−	0.888633i	$-0.651655\pi$
$829$	−26.4094	−0.917237	−0.458618	+	0.888633i	$0.651655\pi$
$830$	13.7940	0.478796
$831$	23.6942	0.821944
$832$	1.18156	0.0409633
$833$	2.86943	0.0994198
$834$	−20.7389	−0.718129
$835$	16.9665	0.587149
$836$	17.1509	0.593178
$837$	5.64038	0.194960
$838$	−3.85214	−0.133070
$839$	23.1884	0.800553	0.400277	−	0.916394i	$-0.368914\pi$
$839$	23.1884	0.800553	0.400277	+	0.916394i	$0.368914\pi$
$840$	6.28315	0.216789
$841$	−2.71124	−0.0934910
$842$	15.1353	0.521597
$843$	57.2304	1.97112
$844$	6.35671	0.218807
$845$	11.6039	0.399187
$846$	−14.0327	−0.482455
$847$	37.9417	1.30369
$848$	9.35047	0.321096
$849$	6.99397	0.240032
$850$	−1.72348	−0.0591150
$851$	14.0134	0.480374
$852$	22.6735	0.776780
$853$	0.587610	0.0201194	0.0100597	−	0.999949i	$-0.496798\pi$
$853$	0.587610	0.0201194	0.0100597	+	0.999949i	$0.496798\pi$
$854$	41.0821	1.40580
$855$	−5.46028	−0.186738
$856$	−7.12063	−0.243378
$857$	20.8324	0.711623	0.355811	−	0.934558i	$-0.384205\pi$
$857$	20.8324	0.711623	0.355811	+	0.934558i	$0.384205\pi$
$858$	−12.3269	−0.420835
$859$	−8.67562	−0.296008	−0.148004	−	0.988987i	$-0.547285\pi$
$859$	−8.67562	−0.296008	−0.148004	+	0.988987i	$0.547285\pi$
$860$	6.76997	0.230854
$861$	4.28674	0.146092
$862$	−26.3547	−0.897645
$863$	−0.612338	−0.0208442	−0.0104221	−	0.999946i	$-0.503318\pi$
$863$	−0.612338	−0.0208442	−0.0104221	+	0.999946i	$0.503318\pi$
$864$	3.08205	0.104854
$865$	−8.86101	−0.301283
$866$	4.88170	0.165887
$867$	−29.9461	−1.01702
$868$	−5.38704	−0.182848
$869$	3.87271	0.131373
$870$	10.9441	0.371040
$871$	7.12706	0.241491
$872$	−5.01471	−0.169820
$873$	−17.2591	−0.584131
$874$	5.31996	0.179950
$875$	−2.94362	−0.0995125
$876$	−12.6268	−0.426621
$877$	16.5942	0.560345	0.280172	−	0.959950i	$-0.409608\pi$
$877$	16.5942	0.560345	0.280172	+	0.959950i	$0.409608\pi$
$878$	27.4018	0.924768
$879$	−50.3710	−1.69897
$880$	−4.88769	−0.164764
$881$	−25.2628	−0.851124	−0.425562	−	0.904929i	$-0.639924\pi$
$881$	−25.2628	−0.851124	−0.425562	+	0.904929i	$0.639924\pi$
$882$	−2.59071	−0.0872337
$883$	−15.8970	−0.534976	−0.267488	−	0.963561i	$-0.586194\pi$
$883$	−15.8970	−0.534976	−0.267488	+	0.963561i	$0.586194\pi$
$884$	2.03640	0.0684917
$885$	21.2375	0.713892
$886$	21.0022	0.705581
$887$	−33.8814	−1.13762	−0.568812	−	0.822467i	$-0.692597\pi$
$887$	−33.8814	−1.13762	−0.568812	+	0.822467i	$0.692597\pi$
$888$	19.7295	0.662078
$889$	2.20073	0.0738101
$890$	−4.20666	−0.141008
$891$	−54.9711	−1.84160
$892$	1.00000	0.0334825
$893$	31.6443	1.05894
$894$	38.7294	1.29531
$895$	20.7403	0.693272
$896$	−2.94362	−0.0983394
$897$	−3.82363	−0.127667
$898$	2.13623	0.0712871
$899$	−9.38325	−0.312949
$900$	1.55608	0.0518692
$901$	16.1154	0.536881
$902$	−3.33467	−0.111032
$903$	−42.5367	−1.41553
$904$	9.11501	0.303161
$905$	−10.9538	−0.364116
$906$	−38.0112	−1.26284
$907$	22.2997	0.740450	0.370225	−	0.928942i	$-0.379281\pi$
$907$	22.2997	0.740450	0.370225	+	0.928942i	$0.379281\pi$
$908$	−4.24805	−0.140976
$909$	28.8946	0.958375
$910$	3.47807	0.115297
$911$	−7.50040	−0.248499	−0.124250	−	0.992251i	$-0.539652\pi$
$911$	−7.50040	−0.248499	−0.124250	+	0.992251i	$0.539652\pi$
$912$	7.48997	0.248018
$913$	67.4206	2.23130
$914$	−3.99174	−0.132035
$915$	29.7897	0.984817
$916$	7.33025	0.242198
$917$	41.5651	1.37260
$918$	5.31187	0.175318
$919$	−3.96890	−0.130922	−0.0654610	−	0.997855i	$-0.520852\pi$
$919$	−3.96890	−0.130922	−0.0654610	+	0.997855i	$0.520852\pi$
$920$	−1.51609	−0.0499839
$921$	0.321759	0.0106023
$922$	9.81448	0.323223
$923$	12.5510	0.413122
$924$	30.7101	1.01029
$925$	−9.24316	−0.303913
$926$	5.92453	0.194692
$927$	22.6965	0.745450
$928$	−5.12726	−0.168310
$929$	3.10767	0.101959	0.0509797	−	0.998700i	$-0.483766\pi$
$929$	3.10767	0.101959	0.0509797	+	0.998700i	$0.483766\pi$
$930$	−3.90628	−0.128092
$931$	5.84215	0.191469
$932$	13.9826	0.458015
$933$	9.82700	0.321722
$934$	−12.6924	−0.415309
$935$	−8.42385	−0.275489
$936$	−1.83860	−0.0600965
$937$	0.216264	0.00706505	0.00353252	−	0.999994i	$-0.498876\pi$
$937$	0.216264	0.00706505	0.00353252	+	0.999994i	$0.498876\pi$
$938$	−17.7556	−0.579741
$939$	37.9525	1.23853
$940$	−9.01802	−0.294135
$941$	−45.0298	−1.46793	−0.733964	−	0.679188i	$-0.762332\pi$
$941$	−45.0298	−1.46793	−0.733964	+	0.679188i	$0.762332\pi$
$942$	18.2309	0.593995
$943$	−1.03437	−0.0336836
$944$	−9.94967	−0.323834
$945$	9.07239	0.295125
$946$	33.0895	1.07583
$947$	37.6716	1.22416	0.612081	−	0.790795i	$-0.290333\pi$
$947$	37.6716	1.22416	0.612081	+	0.790795i	$0.290333\pi$
$948$	1.69125	0.0549291
$949$	−6.98965	−0.226894
$950$	−3.50901	−0.113847
$951$	50.8324	1.64835
$952$	−5.07328	−0.164426
$953$	−4.50584	−0.145958	−0.0729792	−	0.997333i	$-0.523251\pi$
$953$	−4.50584	−0.145958	−0.0729792	+	0.997333i	$0.523251\pi$
$954$	−14.5500	−0.471075
$955$	−20.0091	−0.647479
$956$	7.57521	0.245000
$957$	53.4914	1.72913
$958$	−33.2614	−1.07463
$959$	−35.4410	−1.14445
$960$	−2.13450	−0.0688906
$961$	−27.6508	−0.891963
$962$	10.9214	0.352119
$963$	11.0802	0.357055
$964$	−23.0746	−0.743183
$965$	4.39641	0.141526
$966$	9.52579	0.306487
$967$	30.3005	0.974397	0.487199	−	0.873291i	$-0.338019\pi$
$967$	30.3005	0.974397	0.487199	+	0.873291i	$0.338019\pi$
$968$	−12.8895	−0.414283
$969$	12.9088	0.414692
$970$	−11.0914	−0.356124
$971$	4.64548	0.149081	0.0745403	−	0.997218i	$-0.476251\pi$
$971$	4.64548	0.149081	0.0745403	+	0.997218i	$0.476251\pi$
$972$	−14.7602	−0.473434
$973$	28.6004	0.916886
$974$	34.5446	1.10688
$975$	2.52204	0.0807700
$976$	−13.9563	−0.446730
$977$	37.7279	1.20702	0.603511	−	0.797355i	$-0.293768\pi$
$977$	37.7279	1.20702	0.603511	+	0.797355i	$0.293768\pi$
$978$	33.3271	1.06568
$979$	−20.5608	−0.657127
$980$	−1.66490	−0.0531833
$981$	7.80327	0.249139
$982$	5.39981	0.172315
$983$	31.7295	1.01201	0.506007	−	0.862530i	$-0.331121\pi$
$983$	31.7295	1.01201	0.506007	+	0.862530i	$0.331121\pi$
$984$	−1.45628	−0.0464246
$985$	21.8553	0.696369
$986$	−8.83674	−0.281419
$987$	56.6615	1.80356
$988$	4.14611	0.131905
$989$	10.2639	0.326372
$990$	7.60561	0.241722
$991$	−43.2187	−1.37289	−0.686444	−	0.727182i	$-0.740829\pi$
$991$	−43.2187	−1.37289	−0.686444	+	0.727182i	$0.740829\pi$
$992$	1.83007	0.0581048
$993$	77.0950	2.44654
$994$	−31.2683	−0.991770
$995$	11.1500	0.353479
$996$	29.4432	0.932943
$997$	47.3007	1.49803	0.749015	−	0.662553i	$-0.230527\pi$
$997$	47.3007	1.49803	0.749015	+	0.662553i	$0.230527\pi$
$998$	30.0164	0.950152
$999$	28.4879	0.901317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2230.2.a.p.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2230.2.a.p.1.6	✓	6	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:	\( N \)	\(=\)	\( 2230 = 2 \cdot 5 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2230.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.13450 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.13450 q^{6} +2.94362 q^{7} -1.00000 q^{8} +1.55608 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.13450 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.13450 q^{6} +2.94362 q^{7} -1.00000 q^{8} +1.55608 q^{9} +1.00000 q^{10} +4.88769 q^{11} +2.13450 q^{12} +1.18156 q^{13} -2.94362 q^{14} -2.13450 q^{15} +1.00000 q^{16} +1.72348 q^{17} -1.55608 q^{18} +3.50901 q^{19} -1.00000 q^{20} +6.28315 q^{21} -4.88769 q^{22} -1.51609 q^{23} -2.13450 q^{24} +1.00000 q^{25} -1.18156 q^{26} -3.08205 q^{27} +2.94362 q^{28} +5.12726 q^{29} +2.13450 q^{30} -1.83007 q^{31} -1.00000 q^{32} +10.4327 q^{33} -1.72348 q^{34} -2.94362 q^{35} +1.55608 q^{36} -9.24316 q^{37} -3.50901 q^{38} +2.52204 q^{39} +1.00000 q^{40} +0.682260 q^{41} -6.28315 q^{42} -6.76997 q^{43} +4.88769 q^{44} -1.55608 q^{45} +1.51609 q^{46} +9.01802 q^{47} +2.13450 q^{48} +1.66490 q^{49} -1.00000 q^{50} +3.67877 q^{51} +1.18156 q^{52} +9.35047 q^{53} +3.08205 q^{54} -4.88769 q^{55} -2.94362 q^{56} +7.48997 q^{57} -5.12726 q^{58} -9.94967 q^{59} -2.13450 q^{60} -13.9563 q^{61} +1.83007 q^{62} +4.58049 q^{63} +1.00000 q^{64} -1.18156 q^{65} -10.4327 q^{66} +6.03189 q^{67} +1.72348 q^{68} -3.23608 q^{69} +2.94362 q^{70} +10.6224 q^{71} -1.55608 q^{72} -5.91560 q^{73} +9.24316 q^{74} +2.13450 q^{75} +3.50901 q^{76} +14.3875 q^{77} -2.52204 q^{78} +0.792340 q^{79} -1.00000 q^{80} -11.2469 q^{81} -0.682260 q^{82} +13.7940 q^{83} +6.28315 q^{84} -1.72348 q^{85} +6.76997 q^{86} +10.9441 q^{87} -4.88769 q^{88} -4.20666 q^{89} +1.55608 q^{90} +3.47807 q^{91} -1.51609 q^{92} -3.90628 q^{93} -9.01802 q^{94} -3.50901 q^{95} -2.13450 q^{96} -11.0914 q^{97} -1.66490 q^{98} +7.60561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9	\( 6 q - 6 q^{2} - q^{3} + 6 q^{4} - 6 q^{5} + q^{6} - 6 q^{7} - 6 q^{8} + 5 q^{9} + 6 q^{10} + 14 q^{11} - q^{12} + 9 q^{13} + 6 q^{14} + q^{15} + 6 q^{16} + 4 q^{17} - 5 q^{18} + q^{19} - 6 q^{20} + 14 q^{21} - 14 q^{22} + 9 q^{23} + q^{24} + 6 q^{25} - 9 q^{26} - 28 q^{27} - 6 q^{28} - 9 q^{29} - q^{30} + q^{31} - 6 q^{32} - 6 q^{33} - 4 q^{34} + 6 q^{35} + 5 q^{36} - 18 q^{37} - q^{38} - 18 q^{39} + 6 q^{40} + 11 q^{41} - 14 q^{42} - 26 q^{43} + 14 q^{44} - 5 q^{45} - 9 q^{46} + 14 q^{47} - q^{48} + 6 q^{49} - 6 q^{50} + 14 q^{51} + 9 q^{52} + 14 q^{53} + 28 q^{54} - 14 q^{55} + 6 q^{56} + 9 q^{57} + 9 q^{58} + 18 q^{59} + q^{60} + 24 q^{61} - q^{62} + 6 q^{64} - 9 q^{65} + 6 q^{66} - 8 q^{67} + 4 q^{68} + 20 q^{69} - 6 q^{70} + 32 q^{71} - 5 q^{72} - 12 q^{73} + 18 q^{74} - q^{75} + q^{76} + 12 q^{77} + 18 q^{78} + 8 q^{79} - 6 q^{80} + 14 q^{81} - 11 q^{82} + 36 q^{83} + 14 q^{84} - 4 q^{85} + 26 q^{86} - 9 q^{87} - 14 q^{88} + 11 q^{89} + 5 q^{90} + 10 q^{91} + 9 q^{92} + 8 q^{93} - 14 q^{94} - q^{95} + q^{96} - q^{97} - 6 q^{98} + 16 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - q^3 + 6 * q^4 - 6 * q^5 + q^6 - 6 * q^7 - 6 * q^8 + 5 * q^9 + 6 * q^10 + 14 * q^11 - q^12 + 9 * q^13 + 6 * q^14 + q^15 + 6 * q^16 + 4 * q^17 - 5 * q^18 + q^19 - 6 * q^20 + 14 * q^21 - 14 * q^22 + 9 * q^23 + q^24 + 6 * q^25 - 9 * q^26 - 28 * q^27 - 6 * q^28 - 9 * q^29 - q^30 + q^31 - 6 * q^32 - 6 * q^33 - 4 * q^34 + 6 * q^35 + 5 * q^36 - 18 * q^37 - q^38 - 18 * q^39 + 6 * q^40 + 11 * q^41 - 14 * q^42 - 26 * q^43 + 14 * q^44 - 5 * q^45 - 9 * q^46 + 14 * q^47 - q^48 + 6 * q^49 - 6 * q^50 + 14 * q^51 + 9 * q^52 + 14 * q^53 + 28 * q^54 - 14 * q^55 + 6 * q^56 + 9 * q^57 + 9 * q^58 + 18 * q^59 + q^60 + 24 * q^61 - q^62 + 6 * q^64 - 9 * q^65 + 6 * q^66 - 8 * q^67 + 4 * q^68 + 20 * q^69 - 6 * q^70 + 32 * q^71 - 5 * q^72 - 12 * q^73 + 18 * q^74 - q^75 + q^76 + 12 * q^77 + 18 * q^78 + 8 * q^79 - 6 * q^80 + 14 * q^81 - 11 * q^82 + 36 * q^83 + 14 * q^84 - 4 * q^85 + 26 * q^86 - 9 * q^87 - 14 * q^88 + 11 * q^89 + 5 * q^90 + 10 * q^91 + 9 * q^92 + 8 * q^93 - 14 * q^94 - q^95 + q^96 - q^97 - 6 * q^98 + 16 * q^99

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