LMFDB - Embedded newform 2645.2.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, 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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.732051 q^{2} -0.732051 q^{3} -1.46410 q^{4} +1.00000 q^{5} -0.535898 q^{6} -2.00000 q^{7} -2.53590 q^{8} -2.46410 q^{9} +O(q^{10})$	\(q+0.732051 q^{2} -0.732051 q^{3} -1.46410 q^{4} +1.00000 q^{5} -0.535898 q^{6} -2.00000 q^{7} -2.53590 q^{8} -2.46410 q^{9} +0.732051 q^{10} +3.73205 q^{11} +1.07180 q^{12} +3.46410 q^{13} -1.46410 q^{14} -0.732051 q^{15} +1.07180 q^{16} +3.46410 q^{17} -1.80385 q^{18} -2.26795 q^{19} -1.46410 q^{20} +1.46410 q^{21} +2.73205 q^{22} +1.85641 q^{24} +1.00000 q^{25} +2.53590 q^{26} +4.00000 q^{27} +2.92820 q^{28} -9.46410 q^{29} -0.535898 q^{30} -4.46410 q^{31} +5.85641 q^{32} -2.73205 q^{33} +2.53590 q^{34} -2.00000 q^{35} +3.60770 q^{36} +4.19615 q^{37} -1.66025 q^{38} -2.53590 q^{39} -2.53590 q^{40} +9.00000 q^{41} +1.07180 q^{42} -4.00000 q^{43} -5.46410 q^{44} -2.46410 q^{45} -1.26795 q^{47} -0.784610 q^{48} -3.00000 q^{49} +0.732051 q^{50} -2.53590 q^{51} -5.07180 q^{52} -8.39230 q^{53} +2.92820 q^{54} +3.73205 q^{55} +5.07180 q^{56} +1.66025 q^{57} -6.92820 q^{58} -3.46410 q^{59} +1.07180 q^{60} -12.6603 q^{61} -3.26795 q^{62} +4.92820 q^{63} +2.14359 q^{64} +3.46410 q^{65} -2.00000 q^{66} -14.1962 q^{67} -5.07180 q^{68} -1.46410 q^{70} -7.00000 q^{71} +6.24871 q^{72} +12.1962 q^{73} +3.07180 q^{74} -0.732051 q^{75} +3.32051 q^{76} -7.46410 q^{77} -1.85641 q^{78} +6.66025 q^{79} +1.07180 q^{80} +4.46410 q^{81} +6.58846 q^{82} -16.0000 q^{83} -2.14359 q^{84} +3.46410 q^{85} -2.92820 q^{86} +6.92820 q^{87} -9.46410 q^{88} -8.53590 q^{89} -1.80385 q^{90} -6.92820 q^{91} +3.26795 q^{93} -0.928203 q^{94} -2.26795 q^{95} -4.28719 q^{96} -16.0000 q^{97} -2.19615 q^{98} -9.19615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} + 16 q^{12} + 4 q^{14} + 2 q^{15} + 16 q^{16} - 14 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 2 q^{22} - 24 q^{24} + 2 q^{25} + 12 q^{26} + 8 q^{27} - 8 q^{28} - 12 q^{29} - 8 q^{30} - 2 q^{31} - 16 q^{32} - 2 q^{33} + 12 q^{34} - 4 q^{35} + 28 q^{36} - 2 q^{37} + 14 q^{38} - 12 q^{39} - 12 q^{40} + 18 q^{41} + 16 q^{42} - 8 q^{43} - 4 q^{44} + 2 q^{45} - 6 q^{47} + 40 q^{48} - 6 q^{49} - 2 q^{50} - 12 q^{51} - 24 q^{52} + 4 q^{53} - 8 q^{54} + 4 q^{55} + 24 q^{56} - 14 q^{57} + 16 q^{60} - 8 q^{61} - 10 q^{62} - 4 q^{63} + 32 q^{64} - 4 q^{66} - 18 q^{67} - 24 q^{68} + 4 q^{70} - 14 q^{71} - 36 q^{72} + 14 q^{73} + 20 q^{74} + 2 q^{75} - 28 q^{76} - 8 q^{77} + 24 q^{78} - 4 q^{79} + 16 q^{80} + 2 q^{81} - 18 q^{82} - 32 q^{83} - 32 q^{84} + 8 q^{86} - 12 q^{88} - 24 q^{89} - 14 q^{90} + 10 q^{93} + 12 q^{94} - 8 q^{95} - 64 q^{96} - 32 q^{97} + 6 q^{98} - 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 + 16 * q^12 + 4 * q^14 + 2 * q^15 + 16 * q^16 - 14 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 2 * q^22 - 24 * q^24 + 2 * q^25 + 12 * q^26 + 8 * q^27 - 8 * q^28 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 16 * q^32 - 2 * q^33 + 12 * q^34 - 4 * q^35 + 28 * q^36 - 2 * q^37 + 14 * q^38 - 12 * q^39 - 12 * q^40 + 18 * q^41 + 16 * q^42 - 8 * q^43 - 4 * q^44 + 2 * q^45 - 6 * q^47 + 40 * q^48 - 6 * q^49 - 2 * q^50 - 12 * q^51 - 24 * q^52 + 4 * q^53 - 8 * q^54 + 4 * q^55 + 24 * q^56 - 14 * q^57 + 16 * q^60 - 8 * q^61 - 10 * q^62 - 4 * q^63 + 32 * q^64 - 4 * q^66 - 18 * q^67 - 24 * q^68 + 4 * q^70 - 14 * q^71 - 36 * q^72 + 14 * q^73 + 20 * q^74 + 2 * q^75 - 28 * q^76 - 8 * q^77 + 24 * q^78 - 4 * q^79 + 16 * q^80 + 2 * q^81 - 18 * q^82 - 32 * q^83 - 32 * q^84 + 8 * q^86 - 12 * q^88 - 24 * q^89 - 14 * q^90 + 10 * q^93 + 12 * q^94 - 8 * q^95 - 64 * q^96 - 32 * q^97 + 6 * q^98 - 8 * 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 $

$2$	0.732051	0.517638	0.258819	−	0.965926i	$-0.416667\pi$
$2$	0.732051	0.517638	0.258819	+	0.965926i	$0.416667\pi$
$3$	−0.732051	−0.422650	−0.211325	−	0.977416i	$-0.567778\pi$
$3$	−0.732051	−0.422650	−0.211325	+	0.977416i	$0.567778\pi$
$4$	−1.46410	−0.732051
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.535898	−0.218780
$7$	−2.00000	−0.755929	−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000	−0.755929	−0.377964	+	0.925820i	$0.623376\pi$
$8$	−2.53590	−0.896575
$9$	−2.46410	−0.821367
$10$	0.732051	0.231495
$11$	3.73205	1.12526	0.562628	−	0.826710i	$-0.309790\pi$
$11$	3.73205	1.12526	0.562628	+	0.826710i	$0.309790\pi$
$12$	1.07180	0.309401
$13$	3.46410	0.960769	0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410	0.960769	0.480384	+	0.877058i	$0.340497\pi$
$14$	−1.46410	−0.391298
$15$	−0.732051	−0.189015
$16$	1.07180	0.267949
$17$	3.46410	0.840168	0.420084	−	0.907485i	$-0.362001\pi$
$17$	3.46410	0.840168	0.420084	+	0.907485i	$0.362001\pi$
$18$	−1.80385	−0.425171
$19$	−2.26795	−0.520303	−0.260152	−	0.965568i	$-0.583773\pi$
$19$	−2.26795	−0.520303	−0.260152	+	0.965568i	$0.583773\pi$
$20$	−1.46410	−0.327383
$21$	1.46410	0.319493
$22$	2.73205	0.582475
$23$	0	0
$23$	0	0
$24$	1.85641	0.378937
$25$	1.00000	0.200000
$26$	2.53590	0.497331
$27$	4.00000	0.769800
$28$	2.92820	0.553378
$29$	−9.46410	−1.75744	−0.878720	−	0.477338i	$-0.841602\pi$
$29$	−9.46410	−1.75744	−0.878720	+	0.477338i	$0.841602\pi$
$30$	−0.535898	−0.0978412
$31$	−4.46410	−0.801776	−0.400888	−	0.916127i	$-0.631298\pi$
$31$	−4.46410	−0.801776	−0.400888	+	0.916127i	$0.631298\pi$
$32$	5.85641	1.03528
$33$	−2.73205	−0.475589
$34$	2.53590	0.434903
$35$	−2.00000	−0.338062
$36$	3.60770	0.601283
$37$	4.19615	0.689843	0.344922	−	0.938631i	$-0.387905\pi$
$37$	4.19615	0.689843	0.344922	+	0.938631i	$0.387905\pi$
$38$	−1.66025	−0.269329
$39$	−2.53590	−0.406069
$40$	−2.53590	−0.400961
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	1.07180	0.165382
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	−5.46410	−0.823744
$45$	−2.46410	−0.367327
$46$	0	0
$47$	−1.26795	−0.184949	−0.0924747	−	0.995715i	$-0.529478\pi$
$47$	−1.26795	−0.184949	−0.0924747	+	0.995715i	$0.529478\pi$
$48$	−0.784610	−0.113249
$49$	−3.00000	−0.428571
$50$	0.732051	0.103528
$51$	−2.53590	−0.355097
$52$	−5.07180	−0.703332
$53$	−8.39230	−1.15277	−0.576386	−	0.817178i	$-0.695537\pi$
$53$	−8.39230	−1.15277	−0.576386	+	0.817178i	$0.695537\pi$
$54$	2.92820	0.398478
$55$	3.73205	0.503230
$56$	5.07180	0.677747
$57$	1.66025	0.219906
$58$	−6.92820	−0.909718
$59$	−3.46410	−0.450988	−0.225494	−	0.974245i	$-0.572400\pi$
$59$	−3.46410	−0.450988	−0.225494	+	0.974245i	$0.572400\pi$
$60$	1.07180	0.138368
$61$	−12.6603	−1.62098	−0.810490	−	0.585753i	$-0.800799\pi$
$61$	−12.6603	−1.62098	−0.810490	+	0.585753i	$0.800799\pi$
$62$	−3.26795	−0.415030
$63$	4.92820	0.620895
$64$	2.14359	0.267949
$65$	3.46410	0.429669
$66$	−2.00000	−0.246183
$67$	−14.1962	−1.73434	−0.867168	−	0.498016i	$-0.834062\pi$
$67$	−14.1962	−1.73434	−0.867168	+	0.498016i	$0.834062\pi$
$68$	−5.07180	−0.615046
$69$	0	0
$70$	−1.46410	−0.174994
$71$	−7.00000	−0.830747	−0.415374	−	0.909651i	$-0.636349\pi$
$71$	−7.00000	−0.830747	−0.415374	+	0.909651i	$0.636349\pi$
$72$	6.24871	0.736418
$73$	12.1962	1.42745	0.713726	−	0.700425i	$-0.247006\pi$
$73$	12.1962	1.42745	0.713726	+	0.700425i	$0.247006\pi$
$74$	3.07180	0.357089
$75$	−0.732051	−0.0845299
$76$	3.32051	0.380888
$77$	−7.46410	−0.850613
$78$	−1.85641	−0.210197
$79$	6.66025	0.749337	0.374669	−	0.927159i	$-0.377757\pi$
$79$	6.66025	0.749337	0.374669	+	0.927159i	$0.377757\pi$
$80$	1.07180	0.119831
$81$	4.46410	0.496011
$82$	6.58846	0.727573
$83$	−16.0000	−1.75623	−0.878114	−	0.478451i	$-0.841198\pi$
$83$	−16.0000	−1.75623	−0.878114	+	0.478451i	$0.841198\pi$
$84$	−2.14359	−0.233885
$85$	3.46410	0.375735
$86$	−2.92820	−0.315756
$87$	6.92820	0.742781
$88$	−9.46410	−1.00888
$89$	−8.53590	−0.904803	−0.452402	−	0.891814i	$-0.649433\pi$
$89$	−8.53590	−0.904803	−0.452402	+	0.891814i	$0.649433\pi$
$90$	−1.80385	−0.190142
$91$	−6.92820	−0.726273
$92$	0	0
$93$	3.26795	0.338871
$94$	−0.928203	−0.0957369
$95$	−2.26795	−0.232687
$96$	−4.28719	−0.437559
$97$	−16.0000	−1.62455	−0.812277	−	0.583272i	$-0.801772\pi$
$97$	−16.0000	−1.62455	−0.812277	+	0.583272i	$0.801772\pi$
$98$	−2.19615	−0.221845
$99$	−9.19615	−0.924248
$100$	−1.46410	−0.146410
$101$	−2.46410	−0.245187	−0.122594	−	0.992457i	$-0.539121\pi$
$101$	−2.46410	−0.245187	−0.122594	+	0.992457i	$0.539121\pi$
$102$	−1.85641	−0.183812
$103$	−6.19615	−0.610525	−0.305263	−	0.952268i	$-0.598744\pi$
$103$	−6.19615	−0.610525	−0.305263	+	0.952268i	$0.598744\pi$
$104$	−8.78461	−0.861402
$105$	1.46410	0.142882
$106$	−6.14359	−0.596719
$107$	6.73205	0.650812	0.325406	−	0.945574i	$-0.394499\pi$
$107$	6.73205	0.650812	0.325406	+	0.945574i	$0.394499\pi$
$108$	−5.85641	−0.563533
$109$	8.12436	0.778172	0.389086	−	0.921201i	$-0.372791\pi$
$109$	8.12436	0.778172	0.389086	+	0.921201i	$0.372791\pi$
$110$	2.73205	0.260491
$111$	−3.07180	−0.291562
$112$	−2.14359	−0.202551
$113$	1.46410	0.137731	0.0688655	−	0.997626i	$-0.478062\pi$
$113$	1.46410	0.137731	0.0688655	+	0.997626i	$0.478062\pi$
$114$	1.21539	0.113832
$115$	0	0
$116$	13.8564	1.28654
$117$	−8.53590	−0.789144
$118$	−2.53590	−0.233448
$119$	−6.92820	−0.635107
$120$	1.85641	0.169466
$121$	2.92820	0.266200
$122$	−9.26795	−0.839081
$123$	−6.58846	−0.594061
$124$	6.53590	0.586941
$125$	1.00000	0.0894427
$126$	3.60770	0.321399
$127$	−5.07180	−0.450049	−0.225025	−	0.974353i	$-0.572246\pi$
$127$	−5.07180	−0.450049	−0.225025	+	0.974353i	$0.572246\pi$
$128$	−10.1436	−0.896575
$129$	2.92820	0.257814
$130$	2.53590	0.222413
$131$	−3.39230	−0.296387	−0.148194	−	0.988958i	$-0.547346\pi$
$131$	−3.39230	−0.296387	−0.148194	+	0.988958i	$0.547346\pi$
$132$	4.00000	0.348155
$133$	4.53590	0.393312
$134$	−10.3923	−0.897758
$135$	4.00000	0.344265
$136$	−8.78461	−0.753274
$137$	−9.12436	−0.779546	−0.389773	−	0.920911i	$-0.627447\pi$
$137$	−9.12436	−0.779546	−0.389773	+	0.920911i	$0.627447\pi$
$138$	0	0
$139$	13.0000	1.10265	0.551323	−	0.834292i	$-0.314123\pi$
$139$	13.0000	1.10265	0.551323	+	0.834292i	$0.314123\pi$
$140$	2.92820	0.247478
$141$	0.928203	0.0781688
$142$	−5.12436	−0.430026
$143$	12.9282	1.08111
$144$	−2.64102	−0.220085
$145$	−9.46410	−0.785951
$146$	8.92820	0.738903
$147$	2.19615	0.181136
$148$	−6.14359	−0.505000
$149$	15.7321	1.28882	0.644410	−	0.764680i	$-0.277103\pi$
$149$	15.7321	1.28882	0.644410	+	0.764680i	$0.277103\pi$
$150$	−0.535898	−0.0437559
$151$	16.4641	1.33983	0.669915	−	0.742438i	$-0.266331\pi$
$151$	16.4641	1.33983	0.669915	+	0.742438i	$0.266331\pi$
$152$	5.75129	0.466491
$153$	−8.53590	−0.690086
$154$	−5.46410	−0.440310
$155$	−4.46410	−0.358565
$156$	3.71281	0.297263
$157$	−11.1244	−0.887820	−0.443910	−	0.896071i	$-0.646409\pi$
$157$	−11.1244	−0.887820	−0.443910	+	0.896071i	$0.646409\pi$
$158$	4.87564	0.387885
$159$	6.14359	0.487219
$160$	5.85641	0.462990
$161$	0	0
$162$	3.26795	0.256754
$163$	−24.9282	−1.95253	−0.976264	−	0.216585i	$-0.930508\pi$
$163$	−24.9282	−1.95253	−0.976264	+	0.216585i	$0.930508\pi$
$164$	−13.1769	−1.02894
$165$	−2.73205	−0.212690
$166$	−11.7128	−0.909091
$167$	14.1962	1.09853	0.549266	−	0.835648i	$-0.314908\pi$
$167$	14.1962	1.09853	0.549266	+	0.835648i	$0.314908\pi$
$168$	−3.71281	−0.286450
$169$	−1.00000	−0.0769231
$170$	2.53590	0.194495
$171$	5.58846	0.427360
$172$	5.85641	0.446547
$173$	−13.8564	−1.05348	−0.526742	−	0.850026i	$-0.676586\pi$
$173$	−13.8564	−1.05348	−0.526742	+	0.850026i	$0.676586\pi$
$174$	5.07180	0.384492
$175$	−2.00000	−0.151186
$176$	4.00000	0.301511
$177$	2.53590	0.190610
$178$	−6.24871	−0.468361
$179$	−11.5359	−0.862234	−0.431117	−	0.902296i	$-0.641880\pi$
$179$	−11.5359	−0.862234	−0.431117	+	0.902296i	$0.641880\pi$
$180$	3.60770	0.268902
$181$	1.73205	0.128742	0.0643712	−	0.997926i	$-0.479496\pi$
$181$	1.73205	0.128742	0.0643712	+	0.997926i	$0.479496\pi$
$182$	−5.07180	−0.375947
$183$	9.26795	0.685107
$184$	0	0
$185$	4.19615	0.308507
$186$	2.39230	0.175412
$187$	12.9282	0.945404
$188$	1.85641	0.135392
$189$	−8.00000	−0.581914
$190$	−1.66025	−0.120447
$191$	−7.46410	−0.540083	−0.270042	−	0.962849i	$-0.587037\pi$
$191$	−7.46410	−0.540083	−0.270042	+	0.962849i	$0.587037\pi$
$192$	−1.56922	−0.113249
$193$	25.6603	1.84707	0.923533	−	0.383520i	$-0.125288\pi$
$193$	25.6603	1.84707	0.923533	+	0.383520i	$0.125288\pi$
$194$	−11.7128	−0.840931
$195$	−2.53590	−0.181599
$196$	4.39230	0.313736
$197$	3.66025	0.260782	0.130391	−	0.991463i	$-0.458377\pi$
$197$	3.66025	0.260782	0.130391	+	0.991463i	$0.458377\pi$
$198$	−6.73205	−0.478426
$199$	−11.1962	−0.793674	−0.396837	−	0.917889i	$-0.629892\pi$
$199$	−11.1962	−0.793674	−0.396837	+	0.917889i	$0.629892\pi$
$200$	−2.53590	−0.179315
$201$	10.3923	0.733017
$202$	−1.80385	−0.126918
$203$	18.9282	1.32850
$204$	3.71281	0.259949
$205$	9.00000	0.628587
$206$	−4.53590	−0.316031
$207$	0	0
$208$	3.71281	0.257437
$209$	−8.46410	−0.585474
$210$	1.07180	0.0739610
$211$	28.8564	1.98656	0.993278	−	0.115749i	$-0.0369269\pi$
$211$	28.8564	1.98656	0.993278	+	0.115749i	$0.0369269\pi$
$212$	12.2872	0.843887
$213$	5.12436	0.351115
$214$	4.92820	0.336885
$215$	−4.00000	−0.272798
$216$	−10.1436	−0.690184
$217$	8.92820	0.606086
$218$	5.94744	0.402812
$219$	−8.92820	−0.603312
$220$	−5.46410	−0.368390
$221$	12.0000	0.807207
$222$	−2.24871	−0.150924
$223$	−2.00000	−0.133930	−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000	−0.133930	−0.0669650	+	0.997755i	$0.521332\pi$
$224$	−11.7128	−0.782595
$225$	−2.46410	−0.164273
$226$	1.07180	0.0712949
$227$	−15.8564	−1.05243	−0.526213	−	0.850353i	$-0.676389\pi$
$227$	−15.8564	−1.05243	−0.526213	+	0.850353i	$0.676389\pi$
$228$	−2.43078	−0.160982
$229$	7.58846	0.501459	0.250730	−	0.968057i	$-0.419329\pi$
$229$	7.58846	0.501459	0.250730	+	0.968057i	$0.419329\pi$
$230$	0	0
$231$	5.46410	0.359511
$232$	24.0000	1.57568
$233$	10.7321	0.703080	0.351540	−	0.936173i	$-0.385658\pi$
$233$	10.7321	0.703080	0.351540	+	0.936173i	$0.385658\pi$
$234$	−6.24871	−0.408491
$235$	−1.26795	−0.0827119
$236$	5.07180	0.330146
$237$	−4.87564	−0.316707
$238$	−5.07180	−0.328756
$239$	−20.8564	−1.34909	−0.674544	−	0.738234i	$-0.735660\pi$
$239$	−20.8564	−1.34909	−0.674544	+	0.738234i	$0.735660\pi$
$240$	−0.784610	−0.0506463
$241$	7.19615	0.463545	0.231772	−	0.972770i	$-0.425548\pi$
$241$	7.19615	0.463545	0.231772	+	0.972770i	$0.425548\pi$
$242$	2.14359	0.137795
$243$	−15.2679	−0.979439
$244$	18.5359	1.18664
$245$	−3.00000	−0.191663
$246$	−4.82309	−0.307509
$247$	−7.85641	−0.499891
$248$	11.3205	0.718853
$249$	11.7128	0.742269
$250$	0.732051	0.0462990
$251$	−22.6603	−1.43030	−0.715151	−	0.698970i	$-0.753642\pi$
$251$	−22.6603	−1.43030	−0.715151	+	0.698970i	$0.753642\pi$
$252$	−7.21539	−0.454527
$253$	0	0
$254$	−3.71281	−0.232963
$255$	−2.53590	−0.158804
$256$	−11.7128	−0.732051
$257$	−14.5359	−0.906724	−0.453362	−	0.891326i	$-0.649776\pi$
$257$	−14.5359	−0.906724	−0.453362	+	0.891326i	$0.649776\pi$
$258$	2.14359	0.133454
$259$	−8.39230	−0.521472
$260$	−5.07180	−0.314539
$261$	23.3205	1.44350
$262$	−2.48334	−0.153421
$263$	−11.6603	−0.719002	−0.359501	−	0.933145i	$-0.617053\pi$
$263$	−11.6603	−0.719002	−0.359501	+	0.933145i	$0.617053\pi$
$264$	6.92820	0.426401
$265$	−8.39230	−0.515535
$266$	3.32051	0.203593
$267$	6.24871	0.382415
$268$	20.7846	1.26962
$269$	19.5359	1.19112	0.595562	−	0.803309i	$-0.296929\pi$
$269$	19.5359	1.19112	0.595562	+	0.803309i	$0.296929\pi$
$270$	2.92820	0.178205
$271$	−11.8564	−0.720225	−0.360113	−	0.932909i	$-0.617262\pi$
$271$	−11.8564	−0.720225	−0.360113	+	0.932909i	$0.617262\pi$
$272$	3.71281	0.225122
$273$	5.07180	0.306959
$274$	−6.67949	−0.403523
$275$	3.73205	0.225051
$276$	0	0
$277$	1.07180	0.0643980	0.0321990	−	0.999481i	$-0.489749\pi$
$277$	1.07180	0.0643980	0.0321990	+	0.999481i	$0.489749\pi$
$278$	9.51666	0.570771
$279$	11.0000	0.658553
$280$	5.07180	0.303098
$281$	−15.5885	−0.929929	−0.464965	−	0.885329i	$-0.653933\pi$
$281$	−15.5885	−0.929929	−0.464965	+	0.885329i	$0.653933\pi$
$282$	0.679492	0.0404632
$283$	19.1244	1.13682	0.568412	−	0.822744i	$-0.307558\pi$
$283$	19.1244	1.13682	0.568412	+	0.822744i	$0.307558\pi$
$284$	10.2487	0.608149
$285$	1.66025	0.0983450
$286$	9.46410	0.559624
$287$	−18.0000	−1.06251
$288$	−14.4308	−0.850342
$289$	−5.00000	−0.294118
$290$	−6.92820	−0.406838
$291$	11.7128	0.686617
$292$	−17.8564	−1.04497
$293$	−9.07180	−0.529980	−0.264990	−	0.964251i	$-0.585369\pi$
$293$	−9.07180	−0.529980	−0.264990	+	0.964251i	$0.585369\pi$
$294$	1.60770	0.0937627
$295$	−3.46410	−0.201688
$296$	−10.6410	−0.618497
$297$	14.9282	0.866222
$298$	11.5167	0.667142
$299$	0	0
$300$	1.07180	0.0618802
$301$	8.00000	0.461112
$302$	12.0526	0.693547
$303$	1.80385	0.103628
$304$	−2.43078	−0.139415
$305$	−12.6603	−0.724924
$306$	−6.24871	−0.357215
$307$	−0.143594	−0.00819532	−0.00409766	−	0.999992i	$-0.501304\pi$
$307$	−0.143594	−0.00819532	−0.00409766	+	0.999992i	$0.501304\pi$
$308$	10.9282	0.622692
$309$	4.53590	0.258038
$310$	−3.26795	−0.185607
$311$	29.8564	1.69300	0.846501	−	0.532388i	$-0.178705\pi$
$311$	29.8564	1.69300	0.846501	+	0.532388i	$0.178705\pi$
$312$	6.43078	0.364071
$313$	−26.5885	−1.50287	−0.751434	−	0.659808i	$-0.770638\pi$
$313$	−26.5885	−1.50287	−0.751434	+	0.659808i	$0.770638\pi$
$314$	−8.14359	−0.459570
$315$	4.92820	0.277673
$316$	−9.75129	−0.548553
$317$	−8.58846	−0.482376	−0.241188	−	0.970478i	$-0.577537\pi$
$317$	−8.58846	−0.482376	−0.241188	+	0.970478i	$0.577537\pi$
$318$	4.49742	0.252203
$319$	−35.3205	−1.97757
$320$	2.14359	0.119831
$321$	−4.92820	−0.275065
$322$	0	0
$323$	−7.85641	−0.437142
$324$	−6.53590	−0.363105
$325$	3.46410	0.192154
$326$	−18.2487	−1.01070
$327$	−5.94744	−0.328894
$328$	−22.8231	−1.26019
$329$	2.53590	0.139809
$330$	−2.00000	−0.110096
$331$	−24.3205	−1.33678	−0.668388	−	0.743813i	$-0.733015\pi$
$331$	−24.3205	−1.33678	−0.668388	+	0.743813i	$0.733015\pi$
$332$	23.4256	1.28565
$333$	−10.3397	−0.566615
$334$	10.3923	0.568642
$335$	−14.1962	−0.775619
$336$	1.56922	0.0856079
$337$	3.80385	0.207209	0.103604	−	0.994619i	$-0.466962\pi$
$337$	3.80385	0.207209	0.103604	+	0.994619i	$0.466962\pi$
$338$	−0.732051	−0.0398183
$339$	−1.07180	−0.0582120
$340$	−5.07180	−0.275057
$341$	−16.6603	−0.902203
$342$	4.09103	0.221218
$343$	20.0000	1.07990
$344$	10.1436	0.546906
$345$	0	0
$346$	−10.1436	−0.545323
$347$	−27.6603	−1.48488	−0.742440	−	0.669912i	$-0.766332\pi$
$347$	−27.6603	−1.48488	−0.742440	+	0.669912i	$0.766332\pi$
$348$	−10.1436	−0.543754
$349$	21.8564	1.16995	0.584973	−	0.811053i	$-0.301105\pi$
$349$	21.8564	1.16995	0.584973	+	0.811053i	$0.301105\pi$
$350$	−1.46410	−0.0782595
$351$	13.8564	0.739600
$352$	21.8564	1.16495
$353$	−21.6603	−1.15286	−0.576429	−	0.817147i	$-0.695554\pi$
$353$	−21.6603	−1.15286	−0.576429	+	0.817147i	$0.695554\pi$
$354$	1.85641	0.0986669
$355$	−7.00000	−0.371521
$356$	12.4974	0.662362
$357$	5.07180	0.268428
$358$	−8.44486	−0.446325
$359$	−2.92820	−0.154545	−0.0772723	−	0.997010i	$-0.524621\pi$
$359$	−2.92820	−0.154545	−0.0772723	+	0.997010i	$0.524621\pi$
$360$	6.24871	0.329336
$361$	−13.8564	−0.729285
$362$	1.26795	0.0666419
$363$	−2.14359	−0.112509
$364$	10.1436	0.531669
$365$	12.1962	0.638376
$366$	6.78461	0.354637
$367$	−2.19615	−0.114638	−0.0573191	−	0.998356i	$-0.518255\pi$
$367$	−2.19615	−0.114638	−0.0573191	+	0.998356i	$0.518255\pi$
$368$	0	0
$369$	−22.1769	−1.15448
$370$	3.07180	0.159695
$371$	16.7846	0.871414
$372$	−4.78461	−0.248070
$373$	30.7321	1.59125	0.795623	−	0.605793i	$-0.207144\pi$
$373$	30.7321	1.59125	0.795623	+	0.605793i	$0.207144\pi$
$374$	9.46410	0.489377
$375$	−0.732051	−0.0378029
$376$	3.21539	0.165821
$377$	−32.7846	−1.68849
$378$	−5.85641	−0.301221
$379$	−27.1769	−1.39598	−0.697992	−	0.716105i	$-0.745923\pi$
$379$	−27.1769	−1.39598	−0.697992	+	0.716105i	$0.745923\pi$
$380$	3.32051	0.170338
$381$	3.71281	0.190213
$382$	−5.46410	−0.279568
$383$	16.0526	0.820247	0.410124	−	0.912030i	$-0.365486\pi$
$383$	16.0526	0.820247	0.410124	+	0.912030i	$0.365486\pi$
$384$	7.42563	0.378937
$385$	−7.46410	−0.380406
$386$	18.7846	0.956111
$387$	9.85641	0.501029
$388$	23.4256	1.18926
$389$	17.1962	0.871880	0.435940	−	0.899976i	$-0.356416\pi$
$389$	17.1962	0.871880	0.435940	+	0.899976i	$0.356416\pi$
$390$	−1.85641	−0.0940028
$391$	0	0
$392$	7.60770	0.384247
$393$	2.48334	0.125268
$394$	2.67949	0.134991
$395$	6.66025	0.335114
$396$	13.4641	0.676597
$397$	−9.85641	−0.494679	−0.247339	−	0.968929i	$-0.579556\pi$
$397$	−9.85641	−0.494679	−0.247339	+	0.968929i	$0.579556\pi$
$398$	−8.19615	−0.410836
$399$	−3.32051	−0.166233
$400$	1.07180	0.0535898
$401$	8.66025	0.432472	0.216236	−	0.976341i	$-0.430622\pi$
$401$	8.66025	0.432472	0.216236	+	0.976341i	$0.430622\pi$
$402$	7.60770	0.379437
$403$	−15.4641	−0.770322
$404$	3.60770	0.179490
$405$	4.46410	0.221823
$406$	13.8564	0.687682
$407$	15.6603	0.776250
$408$	6.43078	0.318371
$409$	−23.7846	−1.17607	−0.588037	−	0.808834i	$-0.700099\pi$
$409$	−23.7846	−1.17607	−0.588037	+	0.808834i	$0.700099\pi$
$410$	6.58846	0.325381
$411$	6.67949	0.329475
$412$	9.07180	0.446935
$413$	6.92820	0.340915
$414$	0	0
$415$	−16.0000	−0.785409
$416$	20.2872	0.994661
$417$	−9.51666	−0.466033
$418$	−6.19615	−0.303064
$419$	−24.8038	−1.21175	−0.605874	−	0.795561i	$-0.707176\pi$
$419$	−24.8038	−1.21175	−0.605874	+	0.795561i	$0.707176\pi$
$420$	−2.14359	−0.104597
$421$	36.5167	1.77971	0.889857	−	0.456240i	$-0.150804\pi$
$421$	36.5167	1.77971	0.889857	+	0.456240i	$0.150804\pi$
$422$	21.1244	1.02832
$423$	3.12436	0.151911
$424$	21.2820	1.03355
$425$	3.46410	0.168034
$426$	3.75129	0.181751
$427$	25.3205	1.22535
$428$	−9.85641	−0.476427
$429$	−9.46410	−0.456931
$430$	−2.92820	−0.141210
$431$	33.5885	1.61790	0.808950	−	0.587878i	$-0.200037\pi$
$431$	33.5885	1.61790	0.808950	+	0.587878i	$0.200037\pi$
$432$	4.28719	0.206267
$433$	16.5885	0.797190	0.398595	−	0.917127i	$-0.369498\pi$
$433$	16.5885	0.797190	0.398595	+	0.917127i	$0.369498\pi$
$434$	6.53590	0.313733
$435$	6.92820	0.332182
$436$	−11.8949	−0.569662
$437$	0	0
$438$	−6.53590	−0.312297
$439$	30.3923	1.45055	0.725273	−	0.688462i	$-0.241714\pi$
$439$	30.3923	1.45055	0.725273	+	0.688462i	$0.241714\pi$
$440$	−9.46410	−0.451183
$441$	7.39230	0.352015
$442$	8.78461	0.417841
$443$	22.3923	1.06389	0.531945	−	0.846779i	$-0.321461\pi$
$443$	22.3923	1.06389	0.531945	+	0.846779i	$0.321461\pi$
$444$	4.49742	0.213438
$445$	−8.53590	−0.404640
$446$	−1.46410	−0.0693272
$447$	−11.5167	−0.544719
$448$	−4.28719	−0.202551
$449$	13.0718	0.616896	0.308448	−	0.951241i	$-0.400190\pi$
$449$	13.0718	0.616896	0.308448	+	0.951241i	$0.400190\pi$
$450$	−1.80385	−0.0850342
$451$	33.5885	1.58162
$452$	−2.14359	−0.100826
$453$	−12.0526	−0.566279
$454$	−11.6077	−0.544776
$455$	−6.92820	−0.324799
$456$	−4.21024	−0.197162
$457$	23.3205	1.09089	0.545444	−	0.838147i	$-0.316361\pi$
$457$	23.3205	1.09089	0.545444	+	0.838147i	$0.316361\pi$
$458$	5.55514	0.259574
$459$	13.8564	0.646762
$460$	0	0
$461$	−7.39230	−0.344294	−0.172147	−	0.985071i	$-0.555070\pi$
$461$	−7.39230	−0.344294	−0.172147	+	0.985071i	$0.555070\pi$
$462$	4.00000	0.186097
$463$	−28.9282	−1.34441	−0.672204	−	0.740366i	$-0.734652\pi$
$463$	−28.9282	−1.34441	−0.672204	+	0.740366i	$0.734652\pi$
$464$	−10.1436	−0.470905
$465$	3.26795	0.151548
$466$	7.85641	0.363941
$467$	27.4641	1.27089	0.635444	−	0.772147i	$-0.280817\pi$
$467$	27.4641	1.27089	0.635444	+	0.772147i	$0.280817\pi$
$468$	12.4974	0.577694
$469$	28.3923	1.31103
$470$	−0.928203	−0.0428148
$471$	8.14359	0.375237
$472$	8.78461	0.404344
$473$	−14.9282	−0.686400
$474$	−3.56922	−0.163940
$475$	−2.26795	−0.104061
$476$	10.1436	0.464931
$477$	20.6795	0.946849
$478$	−15.2679	−0.698340
$479$	−9.05256	−0.413622	−0.206811	−	0.978381i	$-0.566309\pi$
$479$	−9.05256	−0.413622	−0.206811	+	0.978381i	$0.566309\pi$
$480$	−4.28719	−0.195682
$481$	14.5359	0.662780
$482$	5.26795	0.239949
$483$	0	0
$484$	−4.28719	−0.194872
$485$	−16.0000	−0.726523
$486$	−11.1769	−0.506995
$487$	−6.33975	−0.287281	−0.143641	−	0.989630i	$-0.545881\pi$
$487$	−6.33975	−0.287281	−0.143641	+	0.989630i	$0.545881\pi$
$488$	32.1051	1.45333
$489$	18.2487	0.825235
$490$	−2.19615	−0.0992121
$491$	−1.32051	−0.0595937	−0.0297968	−	0.999556i	$-0.509486\pi$
$491$	−1.32051	−0.0595937	−0.0297968	+	0.999556i	$0.509486\pi$
$492$	9.64617	0.434883
$493$	−32.7846	−1.47654
$494$	−5.75129	−0.258763
$495$	−9.19615	−0.413336
$496$	−4.78461	−0.214835
$497$	14.0000	0.627986
$498$	8.57437	0.384227
$499$	13.7846	0.617084	0.308542	−	0.951211i	$-0.400159\pi$
$499$	13.7846	0.617084	0.308542	+	0.951211i	$0.400159\pi$
$500$	−1.46410	−0.0654766
$501$	−10.3923	−0.464294
$502$	−16.5885	−0.740379
$503$	18.3923	0.820072	0.410036	−	0.912069i	$-0.365516\pi$
$503$	18.3923	0.820072	0.410036	+	0.912069i	$0.365516\pi$
$504$	−12.4974	−0.556679
$505$	−2.46410	−0.109651
$506$	0	0
$507$	0.732051	0.0325115
$508$	7.42563	0.329459
$509$	13.7128	0.607810	0.303905	−	0.952702i	$-0.401709\pi$
$509$	13.7128	0.607810	0.303905	+	0.952702i	$0.401709\pi$
$510$	−1.85641	−0.0822031
$511$	−24.3923	−1.07905
$512$	11.7128	0.517638
$513$	−9.07180	−0.400530
$514$	−10.6410	−0.469355
$515$	−6.19615	−0.273035
$516$	−4.28719	−0.188733
$517$	−4.73205	−0.208115
$518$	−6.14359	−0.269934
$519$	10.1436	0.445254
$520$	−8.78461	−0.385231
$521$	−13.7321	−0.601612	−0.300806	−	0.953685i	$-0.597256\pi$
$521$	−13.7321	−0.601612	−0.300806	+	0.953685i	$0.597256\pi$
$522$	17.0718	0.747212
$523$	−26.3923	−1.15405	−0.577027	−	0.816725i	$-0.695787\pi$
$523$	−26.3923	−1.15405	−0.577027	+	0.816725i	$0.695787\pi$
$524$	4.96668	0.216970
$525$	1.46410	0.0638986
$526$	−8.53590	−0.372183
$527$	−15.4641	−0.673627
$528$	−2.92820	−0.127434
$529$	0	0
$530$	−6.14359	−0.266861
$531$	8.53590	0.370426
$532$	−6.64102	−0.287925
$533$	31.1769	1.35042
$534$	4.57437	0.197953
$535$	6.73205	0.291052
$536$	36.0000	1.55496
$537$	8.44486	0.364423
$538$	14.3013	0.616572
$539$	−11.1962	−0.482252
$540$	−5.85641	−0.252020
$541$	45.6410	1.96226	0.981130	−	0.193348i	$-0.0619346\pi$
$541$	45.6410	1.96226	0.981130	+	0.193348i	$0.0619346\pi$
$542$	−8.67949	−0.372816
$543$	−1.26795	−0.0544129
$544$	20.2872	0.869806
$545$	8.12436	0.348009
$546$	3.71281	0.158894
$547$	5.51666	0.235875	0.117938	−	0.993021i	$-0.462372\pi$
$547$	5.51666	0.235875	0.117938	+	0.993021i	$0.462372\pi$
$548$	13.3590	0.570668
$549$	31.1962	1.33142
$550$	2.73205	0.116495
$551$	21.4641	0.914401
$552$	0	0
$553$	−13.3205	−0.566446
$554$	0.784610	0.0333349
$555$	−3.07180	−0.130391
$556$	−19.0333	−0.807193
$557$	−20.7321	−0.878445	−0.439223	−	0.898378i	$-0.644746\pi$
$557$	−20.7321	−0.878445	−0.439223	+	0.898378i	$0.644746\pi$
$558$	8.05256	0.340892
$559$	−13.8564	−0.586064
$560$	−2.14359	−0.0905834
$561$	−9.46410	−0.399575
$562$	−11.4115	−0.481367
$563$	−42.5885	−1.79489	−0.897445	−	0.441127i	$-0.854579\pi$
$563$	−42.5885	−1.79489	−0.897445	+	0.441127i	$0.854579\pi$
$564$	−1.35898	−0.0572235
$565$	1.46410	0.0615952
$566$	14.0000	0.588464
$567$	−8.92820	−0.374949
$568$	17.7513	0.744828
$569$	23.7321	0.994899	0.497450	−	0.867493i	$-0.334270\pi$
$569$	23.7321	0.994899	0.497450	+	0.867493i	$0.334270\pi$
$570$	1.21539	0.0509071
$571$	−31.1962	−1.30552	−0.652759	−	0.757565i	$-0.726389\pi$
$571$	−31.1962	−1.30552	−0.652759	+	0.757565i	$0.726389\pi$
$572$	−18.9282	−0.791428
$573$	5.46410	0.228266
$574$	−13.1769	−0.549994
$575$	0	0
$576$	−5.28203	−0.220085
$577$	22.5885	0.940370	0.470185	−	0.882568i	$-0.344187\pi$
$577$	22.5885	0.940370	0.470185	+	0.882568i	$0.344187\pi$
$578$	−3.66025	−0.152246
$579$	−18.7846	−0.780662
$580$	13.8564	0.575356
$581$	32.0000	1.32758
$582$	8.57437	0.355419
$583$	−31.3205	−1.29716
$584$	−30.9282	−1.27982
$585$	−8.53590	−0.352916
$586$	−6.64102	−0.274338
$587$	43.7128	1.80422	0.902110	−	0.431505i	$-0.142017\pi$
$587$	43.7128	1.80422	0.902110	+	0.431505i	$0.142017\pi$
$588$	−3.21539	−0.132600
$589$	10.1244	0.417167
$590$	−2.53590	−0.104401
$591$	−2.67949	−0.110220
$592$	4.49742	0.184843
$593$	4.58846	0.188425	0.0942127	−	0.995552i	$-0.469967\pi$
$593$	4.58846	0.188425	0.0942127	+	0.995552i	$0.469967\pi$
$594$	10.9282	0.448390
$595$	−6.92820	−0.284029
$596$	−23.0333	−0.943482
$597$	8.19615	0.335446
$598$	0	0
$599$	−18.4641	−0.754423	−0.377211	−	0.926127i	$-0.623117\pi$
$599$	−18.4641	−0.754423	−0.377211	+	0.926127i	$0.623117\pi$
$600$	1.85641	0.0757875
$601$	23.2487	0.948335	0.474167	−	0.880435i	$-0.342749\pi$
$601$	23.2487	0.948335	0.474167	+	0.880435i	$0.342749\pi$
$602$	5.85641	0.238689
$603$	34.9808	1.42453
$604$	−24.1051	−0.980823
$605$	2.92820	0.119048
$606$	1.32051	0.0536420
$607$	−2.00000	−0.0811775	−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000	−0.0811775	−0.0405887	+	0.999176i	$0.512923\pi$
$608$	−13.2820	−0.538658
$609$	−13.8564	−0.561490
$610$	−9.26795	−0.375248
$611$	−4.39230	−0.177694
$612$	12.4974	0.505178
$613$	−5.26795	−0.212770	−0.106385	−	0.994325i	$-0.533928\pi$
$613$	−5.26795	−0.212770	−0.106385	+	0.994325i	$0.533928\pi$
$614$	−0.105118	−0.00424221
$615$	−6.58846	−0.265672
$616$	18.9282	0.762639
$617$	2.33975	0.0941946	0.0470973	−	0.998890i	$-0.485003\pi$
$617$	2.33975	0.0941946	0.0470973	+	0.998890i	$0.485003\pi$
$618$	3.32051	0.133570
$619$	40.9090	1.64427	0.822135	−	0.569292i	$-0.192783\pi$
$619$	40.9090	1.64427	0.822135	+	0.569292i	$0.192783\pi$
$620$	6.53590	0.262488
$621$	0	0
$622$	21.8564	0.876362
$623$	17.0718	0.683967
$624$	−2.71797	−0.108806
$625$	1.00000	0.0400000
$626$	−19.4641	−0.777942
$627$	6.19615	0.247450
$628$	16.2872	0.649930
$629$	14.5359	0.579584
$630$	3.60770	0.143734
$631$	8.41154	0.334858	0.167429	−	0.985884i	$-0.446453\pi$
$631$	8.41154	0.334858	0.167429	+	0.985884i	$0.446453\pi$
$632$	−16.8897	−0.671837
$633$	−21.1244	−0.839618
$634$	−6.28719	−0.249696
$635$	−5.07180	−0.201268
$636$	−8.99485	−0.356669
$637$	−10.3923	−0.411758
$638$	−25.8564	−1.02366
$639$	17.2487	0.682348
$640$	−10.1436	−0.400961
$641$	13.1962	0.521217	0.260608	−	0.965445i	$-0.416077\pi$
$641$	13.1962	0.521217	0.260608	+	0.965445i	$0.416077\pi$
$642$	−3.60770	−0.142384
$643$	−25.3731	−1.00062	−0.500308	−	0.865847i	$-0.666780\pi$
$643$	−25.3731	−1.00062	−0.500308	+	0.865847i	$0.666780\pi$
$644$	0	0
$645$	2.92820	0.115298
$646$	−5.75129	−0.226281
$647$	−37.4641	−1.47287	−0.736433	−	0.676511i	$-0.763491\pi$
$647$	−37.4641	−1.47287	−0.736433	+	0.676511i	$0.763491\pi$
$648$	−11.3205	−0.444712
$649$	−12.9282	−0.507476
$650$	2.53590	0.0994661
$651$	−6.53590	−0.256162
$652$	36.4974	1.42935
$653$	8.33975	0.326359	0.163180	−	0.986596i	$-0.447825\pi$
$653$	8.33975	0.326359	0.163180	+	0.986596i	$0.447825\pi$
$654$	−4.35383	−0.170248
$655$	−3.39230	−0.132548
$656$	9.64617	0.376620
$657$	−30.0526	−1.17246
$658$	1.85641	0.0723703
$659$	9.58846	0.373513	0.186757	−	0.982406i	$-0.440202\pi$
$659$	9.58846	0.373513	0.186757	+	0.982406i	$0.440202\pi$
$660$	4.00000	0.155700
$661$	−35.5885	−1.38423	−0.692115	−	0.721787i	$-0.743321\pi$
$661$	−35.5885	−1.38423	−0.692115	+	0.721787i	$0.743321\pi$
$662$	−17.8038	−0.691966
$663$	−8.78461	−0.341166
$664$	40.5744	1.57459
$665$	4.53590	0.175895
$666$	−7.56922	−0.293301
$667$	0	0
$668$	−20.7846	−0.804181
$669$	1.46410	0.0566054
$670$	−10.3923	−0.401490
$671$	−47.2487	−1.82402
$672$	8.57437	0.330764
$673$	−33.3205	−1.28441	−0.642206	−	0.766532i	$-0.721980\pi$
$673$	−33.3205	−1.28441	−0.642206	+	0.766532i	$0.721980\pi$
$674$	2.78461	0.107259
$675$	4.00000	0.153960
$676$	1.46410	0.0563116
$677$	−11.3205	−0.435082	−0.217541	−	0.976051i	$-0.569804\pi$
$677$	−11.3205	−0.435082	−0.217541	+	0.976051i	$0.569804\pi$
$678$	−0.784610	−0.0301328
$679$	32.0000	1.22805
$680$	−8.78461	−0.336874
$681$	11.6077	0.444808
$682$	−12.1962	−0.467015
$683$	48.9282	1.87219	0.936093	−	0.351753i	$-0.114414\pi$
$683$	48.9282	1.87219	0.936093	+	0.351753i	$0.114414\pi$
$684$	−8.18207	−0.312849
$685$	−9.12436	−0.348624
$686$	14.6410	0.558997
$687$	−5.55514	−0.211942
$688$	−4.28719	−0.163447
$689$	−29.0718	−1.10755
$690$	0	0
$691$	19.7846	0.752642	0.376321	−	0.926489i	$-0.377189\pi$
$691$	19.7846	0.752642	0.376321	+	0.926489i	$0.377189\pi$
$692$	20.2872	0.771203
$693$	18.3923	0.698666
$694$	−20.2487	−0.768631
$695$	13.0000	0.493118
$696$	−17.5692	−0.665960
$697$	31.1769	1.18091
$698$	16.0000	0.605609
$699$	−7.85641	−0.297157
$700$	2.92820	0.110676
$701$	−18.0000	−0.679851	−0.339925	−	0.940452i	$-0.610402\pi$
$701$	−18.0000	−0.679851	−0.339925	+	0.940452i	$0.610402\pi$
$702$	10.1436	0.382845
$703$	−9.51666	−0.358928
$704$	8.00000	0.301511
$705$	0.928203	0.0349582
$706$	−15.8564	−0.596764
$707$	4.92820	0.185344
$708$	−3.71281	−0.139536
$709$	−20.6410	−0.775190	−0.387595	−	0.921830i	$-0.626694\pi$
$709$	−20.6410	−0.775190	−0.387595	+	0.921830i	$0.626694\pi$
$710$	−5.12436	−0.192314
$711$	−16.4115	−0.615481
$712$	21.6462	0.811225
$713$	0	0
$714$	3.71281	0.138949
$715$	12.9282	0.483487
$716$	16.8897	0.631199
$717$	15.2679	0.570192
$718$	−2.14359	−0.0799982
$719$	4.92820	0.183791	0.0918955	−	0.995769i	$-0.470707\pi$
$719$	4.92820	0.183791	0.0918955	+	0.995769i	$0.470707\pi$
$720$	−2.64102	−0.0984249
$721$	12.3923	0.461514
$722$	−10.1436	−0.377505
$723$	−5.26795	−0.195917
$724$	−2.53590	−0.0942459
$725$	−9.46410	−0.351488
$726$	−1.56922	−0.0582392
$727$	−45.2679	−1.67890	−0.839448	−	0.543441i	$-0.817121\pi$
$727$	−45.2679	−1.67890	−0.839448	+	0.543441i	$0.817121\pi$
$728$	17.5692	0.651159
$729$	−2.21539	−0.0820515
$730$	8.92820	0.330448
$731$	−13.8564	−0.512498
$732$	−13.5692	−0.501533
$733$	21.3731	0.789432	0.394716	−	0.918803i	$-0.370843\pi$
$733$	21.3731	0.789432	0.394716	+	0.918803i	$0.370843\pi$
$734$	−1.60770	−0.0593411
$735$	2.19615	0.0810063
$736$	0	0
$737$	−52.9808	−1.95157
$738$	−16.2346	−0.597605
$739$	−27.0000	−0.993211	−0.496606	−	0.867976i	$-0.665420\pi$
$739$	−27.0000	−0.993211	−0.496606	+	0.867976i	$0.665420\pi$
$740$	−6.14359	−0.225843
$741$	5.75129	0.211279
$742$	12.2872	0.451077
$743$	−50.7846	−1.86311	−0.931553	−	0.363605i	$-0.881546\pi$
$743$	−50.7846	−1.86311	−0.931553	+	0.363605i	$0.881546\pi$
$744$	−8.28719	−0.303823
$745$	15.7321	0.576378
$746$	22.4974	0.823689
$747$	39.4256	1.44251
$748$	−18.9282	−0.692084
$749$	−13.4641	−0.491968
$750$	−0.535898	−0.0195682
$751$	−28.1051	−1.02557	−0.512785	−	0.858517i	$-0.671386\pi$
$751$	−28.1051	−1.02557	−0.512785	+	0.858517i	$0.671386\pi$
$752$	−1.35898	−0.0495570
$753$	16.5885	0.604517
$754$	−24.0000	−0.874028
$755$	16.4641	0.599190
$756$	11.7128	0.425991
$757$	13.8038	0.501709	0.250855	−	0.968025i	$-0.419288\pi$
$757$	13.8038	0.501709	0.250855	+	0.968025i	$0.419288\pi$
$758$	−19.8949	−0.722615
$759$	0	0
$760$	5.75129	0.208621
$761$	−14.3205	−0.519118	−0.259559	−	0.965727i	$-0.583577\pi$
$761$	−14.3205	−0.519118	−0.259559	+	0.965727i	$0.583577\pi$
$762$	2.71797	0.0984616
$763$	−16.2487	−0.588243
$764$	10.9282	0.395369
$765$	−8.53590	−0.308616
$766$	11.7513	0.424591
$767$	−12.0000	−0.433295
$768$	8.57437	0.309401
$769$	17.1962	0.620109	0.310055	−	0.950719i	$-0.399653\pi$
$769$	17.1962	0.620109	0.310055	+	0.950719i	$0.399653\pi$
$770$	−5.46410	−0.196913
$771$	10.6410	0.383227
$772$	−37.5692	−1.35215
$773$	−40.4449	−1.45470	−0.727350	−	0.686266i	$-0.759248\pi$
$773$	−40.4449	−1.45470	−0.727350	+	0.686266i	$0.759248\pi$
$774$	7.21539	0.259352
$775$	−4.46410	−0.160355
$776$	40.5744	1.45654
$777$	6.14359	0.220400
$778$	12.5885	0.451318
$779$	−20.4115	−0.731319
$780$	3.71281	0.132940
$781$	−26.1244	−0.934803
$782$	0	0
$783$	−37.8564	−1.35288
$784$	−3.21539	−0.114835
$785$	−11.1244	−0.397045
$786$	1.81793	0.0648434
$787$	−41.0333	−1.46268	−0.731340	−	0.682013i	$-0.761105\pi$
$787$	−41.0333	−1.46268	−0.731340	+	0.682013i	$0.761105\pi$
$788$	−5.35898	−0.190906
$789$	8.53590	0.303886
$790$	4.87564	0.173468
$791$	−2.92820	−0.104115
$792$	23.3205	0.828658
$793$	−43.8564	−1.55739
$794$	−7.21539	−0.256065
$795$	6.14359	0.217891
$796$	16.3923	0.581010
$797$	−22.1962	−0.786228	−0.393114	−	0.919490i	$-0.628602\pi$
$797$	−22.1962	−0.786228	−0.393114	+	0.919490i	$0.628602\pi$
$798$	−2.43078	−0.0860487
$799$	−4.39230	−0.155389
$800$	5.85641	0.207055
$801$	21.0333	0.743176
$802$	6.33975	0.223864
$803$	45.5167	1.60625
$804$	−15.2154	−0.536605
$805$	0	0
$806$	−11.3205	−0.398748
$807$	−14.3013	−0.503429
$808$	6.24871	0.219829
$809$	12.8564	0.452007	0.226004	−	0.974126i	$-0.427434\pi$
$809$	12.8564	0.452007	0.226004	+	0.974126i	$0.427434\pi$
$810$	3.26795	0.114824
$811$	2.71281	0.0952597	0.0476299	−	0.998865i	$-0.484833\pi$
$811$	2.71281	0.0952597	0.0476299	+	0.998865i	$0.484833\pi$
$812$	−27.7128	−0.972529
$813$	8.67949	0.304403
$814$	11.4641	0.401817
$815$	−24.9282	−0.873197
$816$	−2.71797	−0.0951479
$817$	9.07180	0.317382
$818$	−17.4115	−0.608780
$819$	17.0718	0.596537
$820$	−13.1769	−0.460158
$821$	25.6410	0.894878	0.447439	−	0.894315i	$-0.352336\pi$
$821$	25.6410	0.894878	0.447439	+	0.894315i	$0.352336\pi$
$822$	4.88973	0.170549
$823$	−56.6936	−1.97621	−0.988107	−	0.153769i	$-0.950859\pi$
$823$	−56.6936	−1.97621	−0.988107	+	0.153769i	$0.950859\pi$
$824$	15.7128	0.547382
$825$	−2.73205	−0.0951178
$826$	5.07180	0.176470
$827$	−10.7846	−0.375018	−0.187509	−	0.982263i	$-0.560041\pi$
$827$	−10.7846	−0.375018	−0.187509	+	0.982263i	$0.560041\pi$
$828$	0	0
$829$	19.6795	0.683497	0.341749	−	0.939791i	$-0.388981\pi$
$829$	19.6795	0.683497	0.341749	+	0.939791i	$0.388981\pi$
$830$	−11.7128	−0.406558
$831$	−0.784610	−0.0272178
$832$	7.42563	0.257437
$833$	−10.3923	−0.360072
$834$	−6.96668	−0.241236
$835$	14.1962	0.491278
$836$	12.3923	0.428597
$837$	−17.8564	−0.617208
$838$	−18.1577	−0.627247
$839$	13.7321	0.474083	0.237042	−	0.971500i	$-0.423822\pi$
$839$	13.7321	0.474083	0.237042	+	0.971500i	$0.423822\pi$
$840$	−3.71281	−0.128104
$841$	60.5692	2.08859
$842$	26.7321	0.921247
$843$	11.4115	0.393034
$844$	−42.2487	−1.45426
$845$	−1.00000	−0.0344010
$846$	2.28719	0.0786351
$847$	−5.85641	−0.201229
$848$	−8.99485	−0.308884
$849$	−14.0000	−0.480479
$850$	2.53590	0.0869806
$851$	0	0
$852$	−7.50258	−0.257034
$853$	−14.5885	−0.499499	−0.249750	−	0.968310i	$-0.580348\pi$
$853$	−14.5885	−0.499499	−0.249750	+	0.968310i	$0.580348\pi$
$854$	18.5359	0.634285
$855$	5.58846	0.191121
$856$	−17.0718	−0.583502
$857$	−8.19615	−0.279975	−0.139988	−	0.990153i	$-0.544706\pi$
$857$	−8.19615	−0.279975	−0.139988	+	0.990153i	$0.544706\pi$
$858$	−6.92820	−0.236525
$859$	0.535898	0.0182846	0.00914231	−	0.999958i	$-0.497090\pi$
$859$	0.535898	0.0182846	0.00914231	+	0.999958i	$0.497090\pi$
$860$	5.85641	0.199702
$861$	13.1769	0.449068
$862$	24.5885	0.837486
$863$	20.4449	0.695951	0.347976	−	0.937504i	$-0.386869\pi$
$863$	20.4449	0.695951	0.347976	+	0.937504i	$0.386869\pi$
$864$	23.4256	0.796956
$865$	−13.8564	−0.471132
$866$	12.1436	0.412656
$867$	3.66025	0.124309
$868$	−13.0718	−0.443686
$869$	24.8564	0.843196
$870$	5.07180	0.171950
$871$	−49.1769	−1.66630
$872$	−20.6025	−0.697690
$873$	39.4256	1.33436
$874$	0	0
$875$	−2.00000	−0.0676123
$876$	13.0718	0.441655
$877$	−3.51666	−0.118749	−0.0593746	−	0.998236i	$-0.518911\pi$
$877$	−3.51666	−0.118749	−0.0593746	+	0.998236i	$0.518911\pi$
$878$	22.2487	0.750858
$879$	6.64102	0.223996
$880$	4.00000	0.134840
$881$	24.2487	0.816960	0.408480	−	0.912767i	$-0.366059\pi$
$881$	24.2487	0.816960	0.408480	+	0.912767i	$0.366059\pi$
$882$	5.41154	0.182216
$883$	18.1436	0.610581	0.305290	−	0.952259i	$-0.401247\pi$
$883$	18.1436	0.610581	0.305290	+	0.952259i	$0.401247\pi$
$884$	−17.5692	−0.590917
$885$	2.53590	0.0852433
$886$	16.3923	0.550710
$887$	40.9282	1.37423	0.687117	−	0.726547i	$-0.258876\pi$
$887$	40.9282	1.37423	0.687117	+	0.726547i	$0.258876\pi$
$888$	7.78976	0.261407
$889$	10.1436	0.340205
$890$	−6.24871	−0.209457
$891$	16.6603	0.558140
$892$	2.92820	0.0980435
$893$	2.87564	0.0962298
$894$	−8.43078	−0.281967
$895$	−11.5359	−0.385603
$896$	20.2872	0.677747
$897$	0	0
$898$	9.56922	0.319329
$899$	42.2487	1.40907
$900$	3.60770	0.120257
$901$	−29.0718	−0.968522
$902$	24.5885	0.818706
$903$	−5.85641	−0.194889
$904$	−3.71281	−0.123486
$905$	1.73205	0.0575753
$906$	−8.82309	−0.293127
$907$	−23.1244	−0.767832	−0.383916	−	0.923368i	$-0.625425\pi$
$907$	−23.1244	−0.767832	−0.383916	+	0.923368i	$0.625425\pi$
$908$	23.2154	0.770430
$909$	6.07180	0.201389
$910$	−5.07180	−0.168128
$911$	−31.4449	−1.04181	−0.520907	−	0.853613i	$-0.674406\pi$
$911$	−31.4449	−1.04181	−0.520907	+	0.853613i	$0.674406\pi$
$912$	1.77945	0.0589236
$913$	−59.7128	−1.97621
$914$	17.0718	0.564685
$915$	9.26795	0.306389
$916$	−11.1103	−0.367094
$917$	6.78461	0.224048
$918$	10.1436	0.334788
$919$	6.66025	0.219702	0.109851	−	0.993948i	$-0.464963\pi$
$919$	6.66025	0.219702	0.109851	+	0.993948i	$0.464963\pi$
$920$	0	0
$921$	0.105118	0.00346375
$922$	−5.41154	−0.178220
$923$	−24.2487	−0.798156
$924$	−8.00000	−0.263181
$925$	4.19615	0.137969
$926$	−21.1769	−0.695917
$927$	15.2679	0.501465
$928$	−55.4256	−1.81944
$929$	27.2487	0.894001	0.447001	−	0.894534i	$-0.352492\pi$
$929$	27.2487	0.894001	0.447001	+	0.894534i	$0.352492\pi$
$930$	2.39230	0.0784468
$931$	6.80385	0.222987
$932$	−15.7128	−0.514690
$933$	−21.8564	−0.715547
$934$	20.1051	0.657860
$935$	12.9282	0.422797
$936$	21.6462	0.707527
$937$	−40.4974	−1.32299	−0.661497	−	0.749948i	$-0.730078\pi$
$937$	−40.4974	−1.32299	−0.661497	+	0.749948i	$0.730078\pi$
$938$	20.7846	0.678642
$939$	19.4641	0.635187
$940$	1.85641	0.0605493
$941$	31.0526	1.01228	0.506142	−	0.862450i	$-0.331071\pi$
$941$	31.0526	1.01228	0.506142	+	0.862450i	$0.331071\pi$
$942$	5.96152	0.194237
$943$	0	0
$944$	−3.71281	−0.120842
$945$	−8.00000	−0.260240
$946$	−10.9282	−0.355307
$947$	−1.66025	−0.0539510	−0.0269755	−	0.999636i	$-0.508588\pi$
$947$	−1.66025	−0.0539510	−0.0269755	+	0.999636i	$0.508588\pi$
$948$	7.13844	0.231846
$949$	42.2487	1.37145
$950$	−1.66025	−0.0538658
$951$	6.28719	0.203876
$952$	17.5692	0.569422
$953$	34.3013	1.11113	0.555564	−	0.831474i	$-0.312503\pi$
$953$	34.3013	1.11113	0.555564	+	0.831474i	$0.312503\pi$
$954$	15.1384	0.490125
$955$	−7.46410	−0.241533
$956$	30.5359	0.987602
$957$	25.8564	0.835819
$958$	−6.62693	−0.214106
$959$	18.2487	0.589282
$960$	−1.56922	−0.0506463
$961$	−11.0718	−0.357155
$962$	10.6410	0.343080
$963$	−16.5885	−0.534556
$964$	−10.5359	−0.339338
$965$	25.6603	0.826033
$966$	0	0
$967$	−5.60770	−0.180331	−0.0901657	−	0.995927i	$-0.528740\pi$
$967$	−5.60770	−0.180331	−0.0901657	+	0.995927i	$0.528740\pi$
$968$	−7.42563	−0.238669
$969$	5.75129	0.184758
$970$	−11.7128	−0.376076
$971$	−21.4641	−0.688816	−0.344408	−	0.938820i	$-0.611920\pi$
$971$	−21.4641	−0.688816	−0.344408	+	0.938820i	$0.611920\pi$
$972$	22.3538	0.716999
$973$	−26.0000	−0.833522
$974$	−4.64102	−0.148708
$975$	−2.53590	−0.0812137
$976$	−13.5692	−0.434340
$977$	46.1051	1.47503	0.737517	−	0.675329i	$-0.235998\pi$
$977$	46.1051	1.47503	0.737517	+	0.675329i	$0.235998\pi$
$978$	13.3590	0.427173
$979$	−31.8564	−1.01814
$980$	4.39230	0.140307
$981$	−20.0192	−0.639165
$982$	−0.966679	−0.0308480
$983$	−3.26795	−0.104231	−0.0521157	−	0.998641i	$-0.516596\pi$
$983$	−3.26795	−0.104231	−0.0521157	+	0.998641i	$0.516596\pi$
$984$	16.7077	0.532621
$985$	3.66025	0.116625
$986$	−24.0000	−0.764316
$987$	−1.85641	−0.0590901
$988$	11.5026	0.365946
$989$	0	0
$990$	−6.73205	−0.213959
$991$	3.85641	0.122503	0.0612514	−	0.998122i	$-0.480491\pi$
$991$	3.85641	0.122503	0.0612514	+	0.998122i	$0.480491\pi$
$992$	−26.1436	−0.830060
$993$	17.8038	0.564988
$994$	10.2487	0.325069
$995$	−11.1962	−0.354942
$996$	−17.1487	−0.543379
$997$	16.1436	0.511273	0.255636	−	0.966773i	$-0.417715\pi$
$997$	16.1436	0.511273	0.255636	+	0.966773i	$0.417715\pi$
$998$	10.0910	0.319426
$999$	16.7846	0.531042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.f.1.2	yes	2
23.22	odd	2		2645.2.a.e.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2645.2.a.e.1.2	✓	2	23.22	odd	2
2645.2.a.f.1.2	yes	2	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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q+0.732051 q^{2} -0.732051 q^{3} -1.46410 q^{4} +1.00000 q^{5} -0.535898 q^{6} -2.00000 q^{7} -2.53590 q^{8} -2.46410 q^{9} +O(q^{10})\)	\(q+0.732051 q^{2} -0.732051 q^{3} -1.46410 q^{4} +1.00000 q^{5} -0.535898 q^{6} -2.00000 q^{7} -2.53590 q^{8} -2.46410 q^{9} +0.732051 q^{10} +3.73205 q^{11} +1.07180 q^{12} +3.46410 q^{13} -1.46410 q^{14} -0.732051 q^{15} +1.07180 q^{16} +3.46410 q^{17} -1.80385 q^{18} -2.26795 q^{19} -1.46410 q^{20} +1.46410 q^{21} +2.73205 q^{22} +1.85641 q^{24} +1.00000 q^{25} +2.53590 q^{26} +4.00000 q^{27} +2.92820 q^{28} -9.46410 q^{29} -0.535898 q^{30} -4.46410 q^{31} +5.85641 q^{32} -2.73205 q^{33} +2.53590 q^{34} -2.00000 q^{35} +3.60770 q^{36} +4.19615 q^{37} -1.66025 q^{38} -2.53590 q^{39} -2.53590 q^{40} +9.00000 q^{41} +1.07180 q^{42} -4.00000 q^{43} -5.46410 q^{44} -2.46410 q^{45} -1.26795 q^{47} -0.784610 q^{48} -3.00000 q^{49} +0.732051 q^{50} -2.53590 q^{51} -5.07180 q^{52} -8.39230 q^{53} +2.92820 q^{54} +3.73205 q^{55} +5.07180 q^{56} +1.66025 q^{57} -6.92820 q^{58} -3.46410 q^{59} +1.07180 q^{60} -12.6603 q^{61} -3.26795 q^{62} +4.92820 q^{63} +2.14359 q^{64} +3.46410 q^{65} -2.00000 q^{66} -14.1962 q^{67} -5.07180 q^{68} -1.46410 q^{70} -7.00000 q^{71} +6.24871 q^{72} +12.1962 q^{73} +3.07180 q^{74} -0.732051 q^{75} +3.32051 q^{76} -7.46410 q^{77} -1.85641 q^{78} +6.66025 q^{79} +1.07180 q^{80} +4.46410 q^{81} +6.58846 q^{82} -16.0000 q^{83} -2.14359 q^{84} +3.46410 q^{85} -2.92820 q^{86} +6.92820 q^{87} -9.46410 q^{88} -8.53590 q^{89} -1.80385 q^{90} -6.92820 q^{91} +3.26795 q^{93} -0.928203 q^{94} -2.26795 q^{95} -4.28719 q^{96} -16.0000 q^{97} -2.19615 q^{98} -9.19615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} - 8 q^{6} - 4 q^{7} - 12 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} + 16 q^{12} + 4 q^{14} + 2 q^{15} + 16 q^{16} - 14 q^{18} - 8 q^{19} + 4 q^{20} - 4 q^{21} + 2 q^{22} - 24 q^{24} + 2 q^{25} + 12 q^{26} + 8 q^{27} - 8 q^{28} - 12 q^{29} - 8 q^{30} - 2 q^{31} - 16 q^{32} - 2 q^{33} + 12 q^{34} - 4 q^{35} + 28 q^{36} - 2 q^{37} + 14 q^{38} - 12 q^{39} - 12 q^{40} + 18 q^{41} + 16 q^{42} - 8 q^{43} - 4 q^{44} + 2 q^{45} - 6 q^{47} + 40 q^{48} - 6 q^{49} - 2 q^{50} - 12 q^{51} - 24 q^{52} + 4 q^{53} - 8 q^{54} + 4 q^{55} + 24 q^{56} - 14 q^{57} + 16 q^{60} - 8 q^{61} - 10 q^{62} - 4 q^{63} + 32 q^{64} - 4 q^{66} - 18 q^{67} - 24 q^{68} + 4 q^{70} - 14 q^{71} - 36 q^{72} + 14 q^{73} + 20 q^{74} + 2 q^{75} - 28 q^{76} - 8 q^{77} + 24 q^{78} - 4 q^{79} + 16 q^{80} + 2 q^{81} - 18 q^{82} - 32 q^{83} - 32 q^{84} + 8 q^{86} - 12 q^{88} - 24 q^{89} - 14 q^{90} + 10 q^{93} + 12 q^{94} - 8 q^{95} - 64 q^{96} - 32 q^{97} + 6 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^7 - 12 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 + 16 * q^12 + 4 * q^14 + 2 * q^15 + 16 * q^16 - 14 * q^18 - 8 * q^19 + 4 * q^20 - 4 * q^21 + 2 * q^22 - 24 * q^24 + 2 * q^25 + 12 * q^26 + 8 * q^27 - 8 * q^28 - 12 * q^29 - 8 * q^30 - 2 * q^31 - 16 * q^32 - 2 * q^33 + 12 * q^34 - 4 * q^35 + 28 * q^36 - 2 * q^37 + 14 * q^38 - 12 * q^39 - 12 * q^40 + 18 * q^41 + 16 * q^42 - 8 * q^43 - 4 * q^44 + 2 * q^45 - 6 * q^47 + 40 * q^48 - 6 * q^49 - 2 * q^50 - 12 * q^51 - 24 * q^52 + 4 * q^53 - 8 * q^54 + 4 * q^55 + 24 * q^56 - 14 * q^57 + 16 * q^60 - 8 * q^61 - 10 * q^62 - 4 * q^63 + 32 * q^64 - 4 * q^66 - 18 * q^67 - 24 * q^68 + 4 * q^70 - 14 * q^71 - 36 * q^72 + 14 * q^73 + 20 * q^74 + 2 * q^75 - 28 * q^76 - 8 * q^77 + 24 * q^78 - 4 * q^79 + 16 * q^80 + 2 * q^81 - 18 * q^82 - 32 * q^83 - 32 * q^84 + 8 * q^86 - 12 * q^88 - 24 * q^89 - 14 * q^90 + 10 * q^93 + 12 * q^94 - 8 * q^95 - 64 * q^96 - 32 * q^97 + 6 * q^98 - 8 * q^99

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