LMFDB - Embedded newform 4010.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4010,2,Mod(1,4010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4010, 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("4010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4010 = 2 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4010.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:	$32.0200112105$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 12x^{8} + 34x^{7} + 46x^{6} - 104x^{5} - 90x^{4} + 89x^{3} + 82x^{2} + 12x - 1 $ x^10 - 3x^9 - 12x^8 + 34x^7 + 46x^6 - 104x^5 - 90x^4 + 89x^3 + 82x^2 + 12*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.96171$ of defining polynomial
Character	$\chi$	$=$	4010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.223737 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.223737 q^{6} -0.465545 q^{7} -1.00000 q^{8} -2.94994 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.223737 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.223737 q^{6} -0.465545 q^{7} -1.00000 q^{8} -2.94994 q^{9} -1.00000 q^{10} +6.17044 q^{11} +0.223737 q^{12} -4.22120 q^{13} +0.465545 q^{14} +0.223737 q^{15} +1.00000 q^{16} +1.20014 q^{17} +2.94994 q^{18} -2.12314 q^{19} +1.00000 q^{20} -0.104160 q^{21} -6.17044 q^{22} -0.690450 q^{23} -0.223737 q^{24} +1.00000 q^{25} +4.22120 q^{26} -1.33122 q^{27} -0.465545 q^{28} -9.84937 q^{29} -0.223737 q^{30} +1.38297 q^{31} -1.00000 q^{32} +1.38056 q^{33} -1.20014 q^{34} -0.465545 q^{35} -2.94994 q^{36} +6.67643 q^{37} +2.12314 q^{38} -0.944440 q^{39} -1.00000 q^{40} -7.06932 q^{41} +0.104160 q^{42} +4.32772 q^{43} +6.17044 q^{44} -2.94994 q^{45} +0.690450 q^{46} +2.50929 q^{47} +0.223737 q^{48} -6.78327 q^{49} -1.00000 q^{50} +0.268517 q^{51} -4.22120 q^{52} -3.84117 q^{53} +1.33122 q^{54} +6.17044 q^{55} +0.465545 q^{56} -0.475026 q^{57} +9.84937 q^{58} -9.21300 q^{59} +0.223737 q^{60} -6.81367 q^{61} -1.38297 q^{62} +1.37333 q^{63} +1.00000 q^{64} -4.22120 q^{65} -1.38056 q^{66} +5.63972 q^{67} +1.20014 q^{68} -0.154479 q^{69} +0.465545 q^{70} -3.71289 q^{71} +2.94994 q^{72} +2.89694 q^{73} -6.67643 q^{74} +0.223737 q^{75} -2.12314 q^{76} -2.87261 q^{77} +0.944440 q^{78} -0.949571 q^{79} +1.00000 q^{80} +8.55198 q^{81} +7.06932 q^{82} +14.2879 q^{83} -0.104160 q^{84} +1.20014 q^{85} -4.32772 q^{86} -2.20367 q^{87} -6.17044 q^{88} -13.0690 q^{89} +2.94994 q^{90} +1.96516 q^{91} -0.690450 q^{92} +0.309423 q^{93} -2.50929 q^{94} -2.12314 q^{95} -0.223737 q^{96} -7.25226 q^{97} +6.78327 q^{98} -18.2024 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * 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
$3$	0.223737	0.129175	0.0645874	−	0.997912i	$-0.479427\pi$
$3$	0.223737	0.129175	0.0645874	+	0.997912i	$0.479427\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.223737	−0.0913404
$7$	−0.465545	−0.175959	−0.0879797	−	0.996122i	$-0.528041\pi$
$7$	−0.465545	−0.175959	−0.0879797	+	0.996122i	$0.528041\pi$
$8$	−1.00000	−0.353553
$9$	−2.94994	−0.983314
$10$	−1.00000	−0.316228
$11$	6.17044	1.86046	0.930228	−	0.366982i	$-0.119609\pi$
$11$	6.17044	1.86046	0.930228	+	0.366982i	$0.119609\pi$
$12$	0.223737	0.0645874
$13$	−4.22120	−1.17075	−0.585375	−	0.810763i	$-0.699053\pi$
$13$	−4.22120	−1.17075	−0.585375	+	0.810763i	$0.699053\pi$
$14$	0.465545	0.124422
$15$	0.223737	0.0577687
$16$	1.00000	0.250000
$17$	1.20014	0.291078	0.145539	−	0.989353i	$-0.453508\pi$
$17$	1.20014	0.291078	0.145539	+	0.989353i	$0.453508\pi$
$18$	2.94994	0.695308
$19$	−2.12314	−0.487082	−0.243541	−	0.969891i	$-0.578309\pi$
$19$	−2.12314	−0.487082	−0.243541	+	0.969891i	$0.578309\pi$
$20$	1.00000	0.223607
$21$	−0.104160	−0.0227295
$22$	−6.17044	−1.31554
$23$	−0.690450	−0.143969	−0.0719844	−	0.997406i	$-0.522933\pi$
$23$	−0.690450	−0.143969	−0.0719844	+	0.997406i	$0.522933\pi$
$24$	−0.223737	−0.0456702
$25$	1.00000	0.200000
$26$	4.22120	0.827846
$27$	−1.33122	−0.256194
$28$	−0.465545	−0.0879797
$29$	−9.84937	−1.82898	−0.914491	−	0.404607i	$-0.867408\pi$
$29$	−9.84937	−1.82898	−0.914491	+	0.404607i	$0.867408\pi$
$30$	−0.223737	−0.0408487
$31$	1.38297	0.248389	0.124195	−	0.992258i	$-0.460365\pi$
$31$	1.38297	0.248389	0.124195	+	0.992258i	$0.460365\pi$
$32$	−1.00000	−0.176777
$33$	1.38056	0.240324
$34$	−1.20014	−0.205823
$35$	−0.465545	−0.0786914
$36$	−2.94994	−0.491657
$37$	6.67643	1.09760	0.548799	−	0.835954i	$-0.315085\pi$
$37$	6.67643	1.09760	0.548799	+	0.835954i	$0.315085\pi$
$38$	2.12314	0.344419
$39$	−0.944440	−0.151231
$40$	−1.00000	−0.158114
$41$	−7.06932	−1.10404	−0.552021	−	0.833830i	$-0.686143\pi$
$41$	−7.06932	−1.10404	−0.552021	+	0.833830i	$0.686143\pi$
$42$	0.104160	0.0160722
$43$	4.32772	0.659971	0.329985	−	0.943986i	$-0.392956\pi$
$43$	4.32772	0.659971	0.329985	+	0.943986i	$0.392956\pi$
$44$	6.17044	0.930228
$45$	−2.94994	−0.439751
$46$	0.690450	0.101801
$47$	2.50929	0.366017	0.183008	−	0.983111i	$-0.441416\pi$
$47$	2.50929	0.366017	0.183008	+	0.983111i	$0.441416\pi$
$48$	0.223737	0.0322937
$49$	−6.78327	−0.969038
$50$	−1.00000	−0.141421
$51$	0.268517	0.0375999
$52$	−4.22120	−0.585375
$53$	−3.84117	−0.527625	−0.263812	−	0.964574i	$-0.584980\pi$
$53$	−3.84117	−0.527625	−0.263812	+	0.964574i	$0.584980\pi$
$54$	1.33122	0.181157
$55$	6.17044	0.832021
$56$	0.465545	0.0622110
$57$	−0.475026	−0.0629188
$58$	9.84937	1.29329
$59$	−9.21300	−1.19943	−0.599715	−	0.800214i	$-0.704719\pi$
$59$	−9.21300	−1.19943	−0.599715	+	0.800214i	$0.704719\pi$
$60$	0.223737	0.0288844
$61$	−6.81367	−0.872401	−0.436200	−	0.899850i	$-0.643676\pi$
$61$	−6.81367	−0.872401	−0.436200	+	0.899850i	$0.643676\pi$
$62$	−1.38297	−0.175638
$63$	1.37333	0.173023
$64$	1.00000	0.125000
$65$	−4.22120	−0.523575
$66$	−1.38056	−0.169935
$67$	5.63972	0.689001	0.344501	−	0.938786i	$-0.388048\pi$
$67$	5.63972	0.689001	0.344501	+	0.938786i	$0.388048\pi$
$68$	1.20014	0.145539
$69$	−0.154479	−0.0185971
$70$	0.465545	0.0556432
$71$	−3.71289	−0.440638	−0.220319	−	0.975428i	$-0.570710\pi$
$71$	−3.71289	−0.440638	−0.220319	+	0.975428i	$0.570710\pi$
$72$	2.94994	0.347654
$73$	2.89694	0.339061	0.169531	−	0.985525i	$-0.445775\pi$
$73$	2.89694	0.339061	0.169531	+	0.985525i	$0.445775\pi$
$74$	−6.67643	−0.776119
$75$	0.223737	0.0258350
$76$	−2.12314	−0.243541
$77$	−2.87261	−0.327365
$78$	0.944440	0.106937
$79$	−0.949571	−0.106835	−0.0534175	−	0.998572i	$-0.517011\pi$
$79$	−0.949571	−0.106835	−0.0534175	+	0.998572i	$0.517011\pi$
$80$	1.00000	0.111803
$81$	8.55198	0.950220
$82$	7.06932	0.780676
$83$	14.2879	1.56830	0.784151	−	0.620570i	$-0.213099\pi$
$83$	14.2879	1.56830	0.784151	+	0.620570i	$0.213099\pi$
$84$	−0.104160	−0.0113648
$85$	1.20014	0.130174
$86$	−4.32772	−0.466670
$87$	−2.20367	−0.236258
$88$	−6.17044	−0.657771
$89$	−13.0690	−1.38531	−0.692656	−	0.721268i	$-0.743559\pi$
$89$	−13.0690	−1.38531	−0.692656	+	0.721268i	$0.743559\pi$
$90$	2.94994	0.310951
$91$	1.96516	0.206004
$92$	−0.690450	−0.0719844
$93$	0.309423	0.0320856
$94$	−2.50929	−0.258813
$95$	−2.12314	−0.217830
$96$	−0.223737	−0.0228351
$97$	−7.25226	−0.736355	−0.368178	−	0.929756i	$-0.620018\pi$
$97$	−7.25226	−0.736355	−0.368178	+	0.929756i	$0.620018\pi$
$98$	6.78327	0.685214
$99$	−18.2024	−1.82941
$100$	1.00000	0.100000
$101$	3.41556	0.339861	0.169930	−	0.985456i	$-0.445646\pi$
$101$	3.41556	0.339861	0.169930	+	0.985456i	$0.445646\pi$
$102$	−0.268517	−0.0265872
$103$	4.07066	0.401094	0.200547	−	0.979684i	$-0.435728\pi$
$103$	4.07066	0.401094	0.200547	+	0.979684i	$0.435728\pi$
$104$	4.22120	0.413923
$105$	−0.104160	−0.0101650
$106$	3.84117	0.373087
$107$	−12.7930	−1.23675	−0.618374	−	0.785884i	$-0.712208\pi$
$107$	−12.7930	−1.23675	−0.618374	+	0.785884i	$0.712208\pi$
$108$	−1.33122	−0.128097
$109$	−15.7644	−1.50995	−0.754977	−	0.655751i	$-0.772352\pi$
$109$	−15.7644	−1.50995	−0.754977	+	0.655751i	$0.772352\pi$
$110$	−6.17044	−0.588328
$111$	1.49377	0.141782
$112$	−0.465545	−0.0439898
$113$	−4.94582	−0.465264	−0.232632	−	0.972565i	$-0.574734\pi$
$113$	−4.94582	−0.465264	−0.232632	+	0.972565i	$0.574734\pi$
$114$	0.475026	0.0444903
$115$	−0.690450	−0.0643848
$116$	−9.84937	−0.914491
$117$	12.4523	1.15122
$118$	9.21300	0.848125
$119$	−0.558721	−0.0512178
$120$	−0.223737	−0.0204243
$121$	27.0743	2.46130
$122$	6.81367	0.616881
$123$	−1.58167	−0.142615
$124$	1.38297	0.124195
$125$	1.00000	0.0894427
$126$	−1.37333	−0.122346
$127$	7.48068	0.663803	0.331902	−	0.943314i	$-0.392310\pi$
$127$	7.48068	0.663803	0.331902	+	0.943314i	$0.392310\pi$
$128$	−1.00000	−0.0883883
$129$	0.968273	0.0852516
$130$	4.22120	0.370224
$131$	−12.8152	−1.11967	−0.559836	−	0.828603i	$-0.689136\pi$
$131$	−12.8152	−1.11967	−0.559836	+	0.828603i	$0.689136\pi$
$132$	1.38056	0.120162
$133$	0.988418	0.0857067
$134$	−5.63972	−0.487197
$135$	−1.33122	−0.114574
$136$	−1.20014	−0.102912
$137$	−15.4820	−1.32272	−0.661358	−	0.750070i	$-0.730020\pi$
$137$	−15.4820	−1.32272	−0.661358	+	0.750070i	$0.730020\pi$
$138$	0.154479	0.0131502
$139$	7.12322	0.604184	0.302092	−	0.953279i	$-0.402315\pi$
$139$	7.12322	0.604184	0.302092	+	0.953279i	$0.402315\pi$
$140$	−0.465545	−0.0393457
$141$	0.561421	0.0472802
$142$	3.71289	0.311578
$143$	−26.0466	−2.17813
$144$	−2.94994	−0.245828
$145$	−9.84937	−0.817945
$146$	−2.89694	−0.239753
$147$	−1.51767	−0.125175
$148$	6.67643	0.548799
$149$	12.8092	1.04937	0.524687	−	0.851295i	$-0.324182\pi$
$149$	12.8092	1.04937	0.524687	+	0.851295i	$0.324182\pi$
$150$	−0.223737	−0.0182681
$151$	−18.7986	−1.52981	−0.764905	−	0.644143i	$-0.777214\pi$
$151$	−18.7986	−1.52981	−0.764905	+	0.644143i	$0.777214\pi$
$152$	2.12314	0.172210
$153$	−3.54035	−0.286221
$154$	2.87261	0.231482
$155$	1.38297	0.111083
$156$	−0.944440	−0.0756157
$157$	−17.4414	−1.39198	−0.695988	−	0.718054i	$-0.745033\pi$
$157$	−17.4414	−1.39198	−0.695988	+	0.718054i	$0.745033\pi$
$158$	0.949571	0.0755438
$159$	−0.859413	−0.0681559
$160$	−1.00000	−0.0790569
$161$	0.321435	0.0253327
$162$	−8.55198	−0.671907
$163$	−20.5938	−1.61303	−0.806514	−	0.591215i	$-0.798649\pi$
$163$	−20.5938	−1.61303	−0.806514	+	0.591215i	$0.798649\pi$
$164$	−7.06932	−0.552021
$165$	1.38056	0.107476
$166$	−14.2879	−1.10896
$167$	24.2024	1.87284	0.936419	−	0.350883i	$-0.114118\pi$
$167$	24.2024	1.87284	0.936419	+	0.350883i	$0.114118\pi$
$168$	0.104160	0.00803610
$169$	4.81853	0.370656
$170$	−1.20014	−0.0920468
$171$	6.26315	0.478955
$172$	4.32772	0.329985
$173$	5.58475	0.424601	0.212300	−	0.977204i	$-0.431904\pi$
$173$	5.58475	0.424601	0.212300	+	0.977204i	$0.431904\pi$
$174$	2.20367	0.167060
$175$	−0.465545	−0.0351919
$176$	6.17044	0.465114
$177$	−2.06129	−0.154936
$178$	13.0690	0.979563
$179$	−12.7410	−0.952306	−0.476153	−	0.879362i	$-0.657969\pi$
$179$	−12.7410	−0.952306	−0.476153	+	0.879362i	$0.657969\pi$
$180$	−2.94994	−0.219876
$181$	−4.11942	−0.306194	−0.153097	−	0.988211i	$-0.548925\pi$
$181$	−4.11942	−0.306194	−0.153097	+	0.988211i	$0.548925\pi$
$182$	−1.96516	−0.145667
$183$	−1.52447	−0.112692
$184$	0.690450	0.0509007
$185$	6.67643	0.490861
$186$	−0.309423	−0.0226880
$187$	7.40541	0.541537
$188$	2.50929	0.183008
$189$	0.619744	0.0450798
$190$	2.12314	0.154029
$191$	9.89876	0.716249	0.358125	−	0.933674i	$-0.383416\pi$
$191$	9.89876	0.716249	0.358125	+	0.933674i	$0.383416\pi$
$192$	0.223737	0.0161469
$193$	−8.42443	−0.606404	−0.303202	−	0.952926i	$-0.598056\pi$
$193$	−8.42443	−0.606404	−0.303202	+	0.952926i	$0.598056\pi$
$194$	7.25226	0.520682
$195$	−0.944440	−0.0676328
$196$	−6.78327	−0.484519
$197$	13.6917	0.975493	0.487747	−	0.872985i	$-0.337819\pi$
$197$	13.6917	0.975493	0.487747	+	0.872985i	$0.337819\pi$
$198$	18.2024	1.29359
$199$	24.5276	1.73871	0.869357	−	0.494184i	$-0.164533\pi$
$199$	24.5276	1.73871	0.869357	+	0.494184i	$0.164533\pi$
$200$	−1.00000	−0.0707107
$201$	1.26182	0.0890016
$202$	−3.41556	−0.240318
$203$	4.58532	0.321826
$204$	0.268517	0.0188000
$205$	−7.06932	−0.493743
$206$	−4.07066	−0.283616
$207$	2.03679	0.141567
$208$	−4.22120	−0.292688
$209$	−13.1007	−0.906195
$210$	0.104160	0.00718771
$211$	−12.7980	−0.881053	−0.440527	−	0.897739i	$-0.645208\pi$
$211$	−12.7980	−0.881053	−0.440527	+	0.897739i	$0.645208\pi$
$212$	−3.84117	−0.263812
$213$	−0.830711	−0.0569194
$214$	12.7930	0.874513
$215$	4.32772	0.295148
$216$	1.33122	0.0905783
$217$	−0.643836	−0.0437064
$218$	15.7644	1.06770
$219$	0.648154	0.0437982
$220$	6.17044	0.416011
$221$	−5.06605	−0.340779
$222$	−1.49377	−0.100255
$223$	−15.4771	−1.03642	−0.518212	−	0.855252i	$-0.673402\pi$
$223$	−15.4771	−1.03642	−0.518212	+	0.855252i	$0.673402\pi$
$224$	0.465545	0.0311055
$225$	−2.94994	−0.196663
$226$	4.94582	0.328991
$227$	22.3520	1.48355	0.741776	−	0.670648i	$-0.233984\pi$
$227$	22.3520	1.48355	0.741776	+	0.670648i	$0.233984\pi$
$228$	−0.475026	−0.0314594
$229$	−5.95136	−0.393277	−0.196639	−	0.980476i	$-0.563003\pi$
$229$	−5.95136	−0.393277	−0.196639	+	0.980476i	$0.563003\pi$
$230$	0.690450	0.0455269
$231$	−0.642711	−0.0422873
$232$	9.84937	0.646643
$233$	5.81744	0.381113	0.190557	−	0.981676i	$-0.438971\pi$
$233$	5.81744	0.381113	0.190557	+	0.981676i	$0.438971\pi$
$234$	−12.4523	−0.814032
$235$	2.50929	0.163688
$236$	−9.21300	−0.599715
$237$	−0.212454	−0.0138004
$238$	0.558721	0.0362165
$239$	23.3866	1.51275	0.756376	−	0.654137i	$-0.226968\pi$
$239$	23.3866	1.51275	0.756376	+	0.654137i	$0.226968\pi$
$240$	0.223737	0.0144422
$241$	−21.2691	−1.37007	−0.685033	−	0.728512i	$-0.740212\pi$
$241$	−21.2691	−1.37007	−0.685033	+	0.728512i	$0.740212\pi$
$242$	−27.0743	−1.74040
$243$	5.90707	0.378939
$244$	−6.81367	−0.436200
$245$	−6.78327	−0.433367
$246$	1.58167	0.100844
$247$	8.96221	0.570252
$248$	−1.38297	−0.0878189
$249$	3.19674	0.202585
$250$	−1.00000	−0.0632456
$251$	−13.8455	−0.873922	−0.436961	−	0.899481i	$-0.643945\pi$
$251$	−13.8455	−0.873922	−0.436961	+	0.899481i	$0.643945\pi$
$252$	1.37333	0.0865116
$253$	−4.26038	−0.267848
$254$	−7.48068	−0.469380
$255$	0.268517	0.0168152
$256$	1.00000	0.0625000
$257$	−29.3052	−1.82801	−0.914005	−	0.405702i	$-0.867027\pi$
$257$	−29.3052	−1.82801	−0.914005	+	0.405702i	$0.867027\pi$
$258$	−0.968273	−0.0602820
$259$	−3.10818	−0.193133
$260$	−4.22120	−0.261788
$261$	29.0551	1.79846
$262$	12.8152	0.791728
$263$	−19.1480	−1.18072	−0.590358	−	0.807141i	$-0.701013\pi$
$263$	−19.1480	−1.18072	−0.590358	+	0.807141i	$0.701013\pi$
$264$	−1.38056	−0.0849674
$265$	−3.84117	−0.235961
$266$	−0.988418	−0.0606038
$267$	−2.92402	−0.178947
$268$	5.63972	0.344501
$269$	−0.785668	−0.0479030	−0.0239515	−	0.999713i	$-0.507625\pi$
$269$	−0.785668	−0.0479030	−0.0239515	+	0.999713i	$0.507625\pi$
$270$	1.33122	0.0810157
$271$	3.61875	0.219823	0.109912	−	0.993941i	$-0.464943\pi$
$271$	3.61875	0.219823	0.109912	+	0.993941i	$0.464943\pi$
$272$	1.20014	0.0727694
$273$	0.439679	0.0266106
$274$	15.4820	0.935302
$275$	6.17044	0.372091
$276$	−0.154479	−0.00929857
$277$	27.3303	1.64212	0.821059	−	0.570844i	$-0.193384\pi$
$277$	27.3303	1.64212	0.821059	+	0.570844i	$0.193384\pi$
$278$	−7.12322	−0.427222
$279$	−4.07969	−0.244245
$280$	0.465545	0.0278216
$281$	29.1906	1.74136	0.870682	−	0.491847i	$-0.163678\pi$
$281$	29.1906	1.74136	0.870682	+	0.491847i	$0.163678\pi$
$282$	−0.561421	−0.0334321
$283$	−5.48019	−0.325764	−0.162882	−	0.986646i	$-0.552079\pi$
$283$	−5.48019	−0.325764	−0.162882	+	0.986646i	$0.552079\pi$
$284$	−3.71289	−0.220319
$285$	−0.475026	−0.0281381
$286$	26.0466	1.54017
$287$	3.29108	0.194267
$288$	2.94994	0.173827
$289$	−15.5597	−0.915274
$290$	9.84937	0.578375
$291$	−1.62260	−0.0951185
$292$	2.89694	0.169531
$293$	−15.3116	−0.894515	−0.447258	−	0.894405i	$-0.647599\pi$
$293$	−15.3116	−0.894515	−0.447258	+	0.894405i	$0.647599\pi$
$294$	1.51767	0.0885124
$295$	−9.21300	−0.536401
$296$	−6.67643	−0.388060
$297$	−8.21423	−0.476638
$298$	−12.8092	−0.742020
$299$	2.91453	0.168552
$300$	0.223737	0.0129175
$301$	−2.01475	−0.116128
$302$	18.7986	1.08174
$303$	0.764188	0.0439014
$304$	−2.12314	−0.121771
$305$	−6.81367	−0.390150
$306$	3.54035	0.202389
$307$	15.2082	0.867975	0.433988	−	0.900919i	$-0.357106\pi$
$307$	15.2082	0.867975	0.433988	+	0.900919i	$0.357106\pi$
$308$	−2.87261	−0.163682
$309$	0.910759	0.0518113
$310$	−1.38297	−0.0785476
$311$	−26.2950	−1.49105	−0.745527	−	0.666475i	$-0.767802\pi$
$311$	−26.2950	−1.49105	−0.745527	+	0.666475i	$0.767802\pi$
$312$	0.944440	0.0534684
$313$	5.62420	0.317898	0.158949	−	0.987287i	$-0.449189\pi$
$313$	5.62420	0.317898	0.158949	+	0.987287i	$0.449189\pi$
$314$	17.4414	0.984275
$315$	1.37333	0.0773784
$316$	−0.949571	−0.0534175
$317$	−5.47504	−0.307509	−0.153754	−	0.988109i	$-0.549136\pi$
$317$	−5.47504	−0.307509	−0.153754	+	0.988109i	$0.549136\pi$
$318$	0.859413	0.0481935
$319$	−60.7749	−3.40274
$320$	1.00000	0.0559017
$321$	−2.86228	−0.159757
$322$	−0.321435	−0.0179129
$323$	−2.54808	−0.141779
$324$	8.55198	0.475110
$325$	−4.22120	−0.234150
$326$	20.5938	1.14058
$327$	−3.52708	−0.195048
$328$	7.06932	0.390338
$329$	−1.16818	−0.0644041
$330$	−1.38056	−0.0759972
$331$	5.77869	0.317626	0.158813	−	0.987309i	$-0.449233\pi$
$331$	5.77869	0.317626	0.158813	+	0.987309i	$0.449233\pi$
$332$	14.2879	0.784151
$333$	−19.6951	−1.07928
$334$	−24.2024	−1.32430
$335$	5.63972	0.308131
$336$	−0.104160	−0.00568238
$337$	−29.5860	−1.61165	−0.805826	−	0.592153i	$-0.798278\pi$
$337$	−29.5860	−1.61165	−0.805826	+	0.592153i	$0.798278\pi$
$338$	−4.81853	−0.262094
$339$	−1.10656	−0.0601004
$340$	1.20014	0.0650870
$341$	8.53355	0.462117
$342$	−6.26315	−0.338672
$343$	6.41673	0.346471
$344$	−4.32772	−0.233335
$345$	−0.154479	−0.00831690
$346$	−5.58475	−0.300238
$347$	−23.8256	−1.27902	−0.639511	−	0.768782i	$-0.720863\pi$
$347$	−23.8256	−1.27902	−0.639511	+	0.768782i	$0.720863\pi$
$348$	−2.20367	−0.118129
$349$	27.2318	1.45769	0.728843	−	0.684681i	$-0.240058\pi$
$349$	27.2318	1.45769	0.728843	+	0.684681i	$0.240058\pi$
$350$	0.465545	0.0248844
$351$	5.61936	0.299940
$352$	−6.17044	−0.328885
$353$	16.6058	0.883837	0.441919	−	0.897055i	$-0.354298\pi$
$353$	16.6058	0.883837	0.441919	+	0.897055i	$0.354298\pi$
$354$	2.06129	0.109556
$355$	−3.71289	−0.197059
$356$	−13.0690	−0.692656
$357$	−0.125007	−0.00661606
$358$	12.7410	0.673382
$359$	−10.1818	−0.537375	−0.268687	−	0.963227i	$-0.586590\pi$
$359$	−10.1818	−0.537375	−0.268687	+	0.963227i	$0.586590\pi$
$360$	2.94994	0.155476
$361$	−14.4923	−0.762751
$362$	4.11942	0.216512
$363$	6.05753	0.317938
$364$	1.96516	0.103002
$365$	2.89694	0.151633
$366$	1.52447	0.0796855
$367$	−14.6483	−0.764635	−0.382318	−	0.924031i	$-0.624874\pi$
$367$	−14.6483	−0.764635	−0.382318	+	0.924031i	$0.624874\pi$
$368$	−0.690450	−0.0359922
$369$	20.8541	1.08562
$370$	−6.67643	−0.347091
$371$	1.78823	0.0928405
$372$	0.309423	0.0160428
$373$	−34.3658	−1.77939	−0.889697	−	0.456551i	$-0.849085\pi$
$373$	−34.3658	−1.77939	−0.889697	+	0.456551i	$0.849085\pi$
$374$	−7.40541	−0.382925
$375$	0.223737	0.0115537
$376$	−2.50929	−0.129407
$377$	41.5761	2.14128
$378$	−0.619744	−0.0318762
$379$	−24.3264	−1.24956	−0.624782	−	0.780800i	$-0.714812\pi$
$379$	−24.3264	−1.24956	−0.624782	+	0.780800i	$0.714812\pi$
$380$	−2.12314	−0.108915
$381$	1.67371	0.0857467
$382$	−9.89876	−0.506465
$383$	18.2216	0.931080	0.465540	−	0.885027i	$-0.345860\pi$
$383$	18.2216	0.931080	0.465540	+	0.885027i	$0.345860\pi$
$384$	−0.223737	−0.0114176
$385$	−2.87261	−0.146402
$386$	8.42443	0.428792
$387$	−12.7665	−0.648959
$388$	−7.25226	−0.368178
$389$	−14.8767	−0.754281	−0.377140	−	0.926156i	$-0.623093\pi$
$389$	−14.8767	−0.754281	−0.377140	+	0.926156i	$0.623093\pi$
$390$	0.944440	0.0478236
$391$	−0.828640	−0.0419061
$392$	6.78327	0.342607
$393$	−2.86725	−0.144634
$394$	−13.6917	−0.689778
$395$	−0.949571	−0.0477781
$396$	−18.2024	−0.914706
$397$	15.8903	0.797510	0.398755	−	0.917057i	$-0.369442\pi$
$397$	15.8903	0.797510	0.398755	+	0.917057i	$0.369442\pi$
$398$	−24.5276	−1.22946
$399$	0.221146	0.0110711
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−1.26182	−0.0629336
$403$	−5.83781	−0.290802
$404$	3.41556	0.169930
$405$	8.55198	0.424951
$406$	−4.58532	−0.227566
$407$	41.1965	2.04203
$408$	−0.268517	−0.0132936
$409$	2.81572	0.139229	0.0696143	−	0.997574i	$-0.477823\pi$
$409$	2.81572	0.139229	0.0696143	+	0.997574i	$0.477823\pi$
$410$	7.06932	0.349129
$411$	−3.46390	−0.170862
$412$	4.07066	0.200547
$413$	4.28906	0.211051
$414$	−2.03679	−0.100103
$415$	14.2879	0.701366
$416$	4.22120	0.206961
$417$	1.59373	0.0780453
$418$	13.1007	0.640777
$419$	−7.95481	−0.388618	−0.194309	−	0.980940i	$-0.562246\pi$
$419$	−7.95481	−0.388618	−0.194309	+	0.980940i	$0.562246\pi$
$420$	−0.104160	−0.00508248
$421$	−20.6725	−1.00752	−0.503758	−	0.863845i	$-0.668050\pi$
$421$	−20.6725	−1.00752	−0.503758	+	0.863845i	$0.668050\pi$
$422$	12.7980	0.622999
$423$	−7.40225	−0.359910
$424$	3.84117	0.186544
$425$	1.20014	0.0582155
$426$	0.830711	0.0402481
$427$	3.17207	0.153507
$428$	−12.7930	−0.618374
$429$	−5.82761	−0.281360
$430$	−4.32772	−0.208701
$431$	8.65440	0.416868	0.208434	−	0.978036i	$-0.433163\pi$
$431$	8.65440	0.416868	0.208434	+	0.978036i	$0.433163\pi$
$432$	−1.33122	−0.0640486
$433$	−26.3018	−1.26398	−0.631992	−	0.774975i	$-0.717763\pi$
$433$	−26.3018	−1.26398	−0.631992	+	0.774975i	$0.717763\pi$
$434$	0.643836	0.0309051
$435$	−2.20367	−0.105658
$436$	−15.7644	−0.754977
$437$	1.46592	0.0701246
$438$	−0.648154	−0.0309700
$439$	7.91844	0.377926	0.188963	−	0.981984i	$-0.439487\pi$
$439$	7.91844	0.377926	0.188963	+	0.981984i	$0.439487\pi$
$440$	−6.17044	−0.294164
$441$	20.0102	0.952869
$442$	5.06605	0.240967
$443$	−2.52617	−0.120022	−0.0600109	−	0.998198i	$-0.519114\pi$
$443$	−2.52617	−0.120022	−0.0600109	+	0.998198i	$0.519114\pi$
$444$	1.49377	0.0708911
$445$	−13.0690	−0.619530
$446$	15.4771	0.732863
$447$	2.86591	0.135553
$448$	−0.465545	−0.0219949
$449$	18.4140	0.869008	0.434504	−	0.900670i	$-0.356924\pi$
$449$	18.4140	0.869008	0.434504	+	0.900670i	$0.356924\pi$
$450$	2.94994	0.139062
$451$	−43.6208	−2.05402
$452$	−4.94582	−0.232632
$453$	−4.20595	−0.197613
$454$	−22.3520	−1.04903
$455$	1.96516	0.0921280
$456$	0.475026	0.0222451
$457$	−31.4150	−1.46953	−0.734765	−	0.678322i	$-0.762708\pi$
$457$	−31.4150	−1.46953	−0.734765	+	0.678322i	$0.762708\pi$
$458$	5.95136	0.278089
$459$	−1.59766	−0.0745724
$460$	−0.690450	−0.0321924
$461$	39.3309	1.83182	0.915912	−	0.401378i	$-0.131469\pi$
$461$	39.3309	1.83182	0.915912	+	0.401378i	$0.131469\pi$
$462$	0.642711	0.0299016
$463$	−23.1919	−1.07782	−0.538909	−	0.842364i	$-0.681163\pi$
$463$	−23.1919	−1.07782	−0.538909	+	0.842364i	$0.681163\pi$
$464$	−9.84937	−0.457245
$465$	0.309423	0.0143491
$466$	−5.81744	−0.269488
$467$	−14.8344	−0.686452	−0.343226	−	0.939253i	$-0.611520\pi$
$467$	−14.8344	−0.686452	−0.343226	+	0.939253i	$0.611520\pi$
$468$	12.4523	0.575608
$469$	−2.62554	−0.121236
$470$	−2.50929	−0.115745
$471$	−3.90229	−0.179808
$472$	9.21300	0.424063
$473$	26.7039	1.22785
$474$	0.212454	0.00975836
$475$	−2.12314	−0.0974165
$476$	−0.558721	−0.0256089
$477$	11.3312	0.518821
$478$	−23.3866	−1.06968
$479$	−25.2619	−1.15425	−0.577123	−	0.816657i	$-0.695825\pi$
$479$	−25.2619	−1.15425	−0.577123	+	0.816657i	$0.695825\pi$
$480$	−0.223737	−0.0102122
$481$	−28.1826	−1.28501
$482$	21.2691	0.968782
$483$	0.0719171	0.00327234
$484$	27.0743	1.23065
$485$	−7.25226	−0.329308
$486$	−5.90707	−0.267950
$487$	−26.5813	−1.20452	−0.602258	−	0.798302i	$-0.705732\pi$
$487$	−26.5813	−1.20452	−0.602258	+	0.798302i	$0.705732\pi$
$488$	6.81367	0.308440
$489$	−4.60760	−0.208363
$490$	6.78327	0.306437
$491$	−14.8140	−0.668547	−0.334273	−	0.942476i	$-0.608491\pi$
$491$	−14.8140	−0.668547	−0.334273	+	0.942476i	$0.608491\pi$
$492$	−1.58167	−0.0713073
$493$	−11.8207	−0.532376
$494$	−8.96221	−0.403229
$495$	−18.2024	−0.818138
$496$	1.38297	0.0620973
$497$	1.72851	0.0775344
$498$	−3.19674	−0.143249
$499$	−16.0747	−0.719603	−0.359801	−	0.933029i	$-0.617156\pi$
$499$	−16.0747	−0.719603	−0.359801	+	0.933029i	$0.617156\pi$
$500$	1.00000	0.0447214
$501$	5.41498	0.241924
$502$	13.8455	0.617956
$503$	17.4153	0.776512	0.388256	−	0.921552i	$-0.373078\pi$
$503$	17.4153	0.776512	0.388256	+	0.921552i	$0.373078\pi$
$504$	−1.37333	−0.0611730
$505$	3.41556	0.151990
$506$	4.26038	0.189397
$507$	1.07809	0.0478795
$508$	7.48068	0.331902
$509$	−22.7315	−1.00756	−0.503778	−	0.863833i	$-0.668057\pi$
$509$	−22.7315	−1.00756	−0.503778	+	0.863833i	$0.668057\pi$
$510$	−0.268517	−0.0118901
$511$	−1.34866	−0.0596610
$512$	−1.00000	−0.0441942
$513$	2.82638	0.124788
$514$	29.3052	1.29260
$515$	4.07066	0.179375
$516$	0.968273	0.0426258
$517$	15.4834	0.680959
$518$	3.10818	0.136565
$519$	1.24952	0.0548478
$520$	4.22120	0.185112
$521$	4.37519	0.191680	0.0958402	−	0.995397i	$-0.469446\pi$
$521$	4.37519	0.191680	0.0958402	+	0.995397i	$0.469446\pi$
$522$	−29.0551	−1.27171
$523$	5.79741	0.253503	0.126752	−	0.991934i	$-0.459545\pi$
$523$	5.79741	0.253503	0.126752	+	0.991934i	$0.459545\pi$
$524$	−12.8152	−0.559836
$525$	−0.104160	−0.00454590
$526$	19.1480	0.834892
$527$	1.65977	0.0723006
$528$	1.38056	0.0600810
$529$	−22.5233	−0.979273
$530$	3.84117	0.166850
$531$	27.1778	1.17942
$532$	0.988418	0.0428533
$533$	29.8410	1.29256
$534$	2.92402	0.126535
$535$	−12.7930	−0.553091
$536$	−5.63972	−0.243599
$537$	−2.85063	−0.123014
$538$	0.785668	0.0338725
$539$	−41.8557	−1.80285
$540$	−1.33122	−0.0572868
$541$	−3.62022	−0.155646	−0.0778228	−	0.996967i	$-0.524797\pi$
$541$	−3.62022	−0.155646	−0.0778228	+	0.996967i	$0.524797\pi$
$542$	−3.61875	−0.155439
$543$	−0.921668	−0.0395526
$544$	−1.20014	−0.0514558
$545$	−15.7644	−0.675272
$546$	−0.439679	−0.0188165
$547$	38.7497	1.65682	0.828408	−	0.560125i	$-0.189247\pi$
$547$	38.7497	1.65682	0.828408	+	0.560125i	$0.189247\pi$
$548$	−15.4820	−0.661358
$549$	20.0999	0.857844
$550$	−6.17044	−0.263108
$551$	20.9116	0.890864
$552$	0.154479	0.00657508
$553$	0.442068	0.0187986
$554$	−27.3303	−1.16115
$555$	1.49377	0.0634069
$556$	7.12322	0.302092
$557$	32.7860	1.38919	0.694594	−	0.719402i	$-0.255584\pi$
$557$	32.7860	1.38919	0.694594	+	0.719402i	$0.255584\pi$
$558$	4.07969	0.172707
$559$	−18.2682	−0.772661
$560$	−0.465545	−0.0196729
$561$	1.65687	0.0699530
$562$	−29.1906	−1.23133
$563$	−11.7215	−0.494003	−0.247001	−	0.969015i	$-0.579445\pi$
$563$	−11.7215	−0.494003	−0.247001	+	0.969015i	$0.579445\pi$
$564$	0.561421	0.0236401
$565$	−4.94582	−0.208072
$566$	5.48019	0.230350
$567$	−3.98133	−0.167200
$568$	3.71289	0.155789
$569$	17.1213	0.717760	0.358880	−	0.933384i	$-0.383159\pi$
$569$	17.1213	0.717760	0.358880	+	0.933384i	$0.383159\pi$
$570$	0.475026	0.0198967
$571$	−40.2838	−1.68582	−0.842912	−	0.538051i	$-0.819161\pi$
$571$	−40.2838	−1.68582	−0.842912	+	0.538051i	$0.819161\pi$
$572$	−26.0466	−1.08907
$573$	2.21472	0.0925214
$574$	−3.29108	−0.137367
$575$	−0.690450	−0.0287938
$576$	−2.94994	−0.122914
$577$	15.8660	0.660510	0.330255	−	0.943892i	$-0.392865\pi$
$577$	15.8660	0.660510	0.330255	+	0.943892i	$0.392865\pi$
$578$	15.5597	0.647196
$579$	−1.88486	−0.0783321
$580$	−9.84937	−0.408973
$581$	−6.65166	−0.275958
$582$	1.62260	0.0672590
$583$	−23.7017	−0.981623
$584$	−2.89694	−0.119876
$585$	12.4523	0.514839
$586$	15.3116	0.632518
$587$	−2.62424	−0.108314	−0.0541569	−	0.998532i	$-0.517247\pi$
$587$	−2.62424	−0.108314	−0.0541569	+	0.998532i	$0.517247\pi$
$588$	−1.51767	−0.0625877
$589$	−2.93625	−0.120986
$590$	9.21300	0.379293
$591$	3.06334	0.126009
$592$	6.67643	0.274400
$593$	−12.7863	−0.525072	−0.262536	−	0.964922i	$-0.584559\pi$
$593$	−12.7863	−0.525072	−0.262536	+	0.964922i	$0.584559\pi$
$594$	8.21423	0.337034
$595$	−0.558721	−0.0229053
$596$	12.8092	0.524687
$597$	5.48774	0.224598
$598$	−2.91453	−0.119184
$599$	−22.3214	−0.912028	−0.456014	−	0.889973i	$-0.650723\pi$
$599$	−22.3214	−0.912028	−0.456014	+	0.889973i	$0.650723\pi$
$600$	−0.223737	−0.00913404
$601$	8.57834	0.349918	0.174959	−	0.984576i	$-0.444021\pi$
$601$	8.57834	0.349918	0.174959	+	0.984576i	$0.444021\pi$
$602$	2.01475	0.0821149
$603$	−16.6368	−0.677504
$604$	−18.7986	−0.764905
$605$	27.0743	1.10073
$606$	−0.764188	−0.0310430
$607$	36.3319	1.47467	0.737333	−	0.675530i	$-0.236085\pi$
$607$	36.3319	1.47467	0.737333	+	0.675530i	$0.236085\pi$
$608$	2.12314	0.0861048
$609$	1.02591	0.0415719
$610$	6.81367	0.275877
$611$	−10.5922	−0.428514
$612$	−3.54035	−0.143110
$613$	10.0621	0.406405	0.203203	−	0.979137i	$-0.434865\pi$
$613$	10.0621	0.406405	0.203203	+	0.979137i	$0.434865\pi$
$614$	−15.2082	−0.613751
$615$	−1.58167	−0.0637791
$616$	2.87261	0.115741
$617$	44.2627	1.78195	0.890974	−	0.454054i	$-0.150023\pi$
$617$	44.2627	1.78195	0.890974	+	0.454054i	$0.150023\pi$
$618$	−0.910759	−0.0366361
$619$	36.4444	1.46482	0.732412	−	0.680862i	$-0.238395\pi$
$619$	36.4444	1.46482	0.732412	+	0.680862i	$0.238395\pi$
$620$	1.38297	0.0555415
$621$	0.919144	0.0368840
$622$	26.2950	1.05433
$623$	6.08420	0.243758
$624$	−0.944440	−0.0378079
$625$	1.00000	0.0400000
$626$	−5.62420	−0.224788
$627$	−2.93112	−0.117058
$628$	−17.4414	−0.695988
$629$	8.01268	0.319486
$630$	−1.37333	−0.0547148
$631$	−15.5830	−0.620350	−0.310175	−	0.950679i	$-0.600388\pi$
$631$	−15.5830	−0.620350	−0.310175	+	0.950679i	$0.600388\pi$
$632$	0.949571	0.0377719
$633$	−2.86340	−0.113810
$634$	5.47504	0.217442
$635$	7.48068	0.296862
$636$	−0.859413	−0.0340779
$637$	28.6335	1.13450
$638$	60.7749	2.40610
$639$	10.9528	0.433286
$640$	−1.00000	−0.0395285
$641$	−8.89075	−0.351164	−0.175582	−	0.984465i	$-0.556181\pi$
$641$	−8.89075	−0.351164	−0.175582	+	0.984465i	$0.556181\pi$
$642$	2.86228	0.112965
$643$	−5.39515	−0.212764	−0.106382	−	0.994325i	$-0.533927\pi$
$643$	−5.39515	−0.212764	−0.106382	+	0.994325i	$0.533927\pi$
$644$	0.321435	0.0126663
$645$	0.968273	0.0381257
$646$	2.54808	0.100253
$647$	−9.98088	−0.392389	−0.196195	−	0.980565i	$-0.562858\pi$
$647$	−9.98088	−0.392389	−0.196195	+	0.980565i	$0.562858\pi$
$648$	−8.55198	−0.335954
$649$	−56.8482	−2.23149
$650$	4.22120	0.165569
$651$	−0.144050	−0.00564577
$652$	−20.5938	−0.806514
$653$	41.7998	1.63575	0.817877	−	0.575393i	$-0.195151\pi$
$653$	41.7998	1.63575	0.817877	+	0.575393i	$0.195151\pi$
$654$	3.52708	0.137920
$655$	−12.8152	−0.500733
$656$	−7.06932	−0.276011
$657$	−8.54581	−0.333404
$658$	1.16818	0.0455406
$659$	2.65148	0.103287	0.0516434	−	0.998666i	$-0.483554\pi$
$659$	2.65148	0.103287	0.0516434	+	0.998666i	$0.483554\pi$
$660$	1.38056	0.0537381
$661$	9.20619	0.358079	0.179040	−	0.983842i	$-0.442701\pi$
$661$	9.20619	0.358079	0.179040	+	0.983842i	$0.442701\pi$
$662$	−5.77869	−0.224595
$663$	−1.13346	−0.0440201
$664$	−14.2879	−0.554479
$665$	0.988418	0.0383292
$666$	19.6951	0.763169
$667$	6.80050	0.263316
$668$	24.2024	0.936419
$669$	−3.46281	−0.133880
$670$	−5.63972	−0.217881
$671$	−42.0433	−1.62306
$672$	0.104160	0.00401805
$673$	2.53826	0.0978428	0.0489214	−	0.998803i	$-0.484422\pi$
$673$	2.53826	0.0978428	0.0489214	+	0.998803i	$0.484422\pi$
$674$	29.5860	1.13961
$675$	−1.33122	−0.0512388
$676$	4.81853	0.185328
$677$	−19.8646	−0.763458	−0.381729	−	0.924274i	$-0.624671\pi$
$677$	−19.8646	−0.763458	−0.381729	+	0.924274i	$0.624671\pi$
$678$	1.10656	0.0424974
$679$	3.37625	0.129569
$680$	−1.20014	−0.0460234
$681$	5.00097	0.191637
$682$	−8.53355	−0.326766
$683$	0.359755	0.0137656	0.00688282	−	0.999976i	$-0.497809\pi$
$683$	0.359755	0.0137656	0.00688282	+	0.999976i	$0.497809\pi$
$684$	6.26315	0.239477
$685$	−15.4820	−0.591537
$686$	−6.41673	−0.244992
$687$	−1.33154	−0.0508015
$688$	4.32772	0.164993
$689$	16.2143	0.617717
$690$	0.154479	0.00588093
$691$	25.4382	0.967714	0.483857	−	0.875147i	$-0.339235\pi$
$691$	25.4382	0.967714	0.483857	+	0.875147i	$0.339235\pi$
$692$	5.58475	0.212300
$693$	8.47404	0.321902
$694$	23.8256	0.904406
$695$	7.12322	0.270199
$696$	2.20367	0.0835300
$697$	−8.48420	−0.321362
$698$	−27.2318	−1.03074
$699$	1.30158	0.0492303
$700$	−0.465545	−0.0175959
$701$	39.4988	1.49185	0.745924	−	0.666031i	$-0.232008\pi$
$701$	39.4988	1.49185	0.745924	+	0.666031i	$0.232008\pi$
$702$	−5.61936	−0.212089
$703$	−14.1750	−0.534621
$704$	6.17044	0.232557
$705$	0.561421	0.0211443
$706$	−16.6058	−0.624967
$707$	−1.59009	−0.0598017
$708$	−2.06129	−0.0774681
$709$	38.0028	1.42723	0.713613	−	0.700540i	$-0.247058\pi$
$709$	38.0028	1.42723	0.713613	+	0.700540i	$0.247058\pi$
$710$	3.71289	0.139342
$711$	2.80118	0.105052
$712$	13.0690	0.489782
$713$	−0.954874	−0.0357603
$714$	0.125007	0.00467826
$715$	−26.0466	−0.974089
$716$	−12.7410	−0.476153
$717$	5.23245	0.195410
$718$	10.1818	0.379981
$719$	28.8205	1.07482	0.537412	−	0.843320i	$-0.319402\pi$
$719$	28.8205	1.07482	0.537412	+	0.843320i	$0.319402\pi$
$720$	−2.94994	−0.109938
$721$	−1.89507	−0.0705762
$722$	14.4923	0.539346
$723$	−4.75870	−0.176978
$724$	−4.11942	−0.153097
$725$	−9.84937	−0.365796
$726$	−6.05753	−0.224816
$727$	−49.4658	−1.83458	−0.917292	−	0.398216i	$-0.869630\pi$
$727$	−49.4658	−1.83458	−0.917292	+	0.398216i	$0.869630\pi$
$728$	−1.96516	−0.0728336
$729$	−24.3343	−0.901271
$730$	−2.89694	−0.107221
$731$	5.19389	0.192103
$732$	−1.52447	−0.0563461
$733$	43.1912	1.59530	0.797652	−	0.603118i	$-0.206075\pi$
$733$	43.1912	1.59530	0.797652	+	0.603118i	$0.206075\pi$
$734$	14.6483	0.540679
$735$	−1.51767	−0.0559801
$736$	0.690450	0.0254503
$737$	34.7995	1.28186
$738$	−20.8541	−0.767649
$739$	−14.6073	−0.537339	−0.268670	−	0.963232i	$-0.586584\pi$
$739$	−14.6073	−0.537339	−0.268670	+	0.963232i	$0.586584\pi$
$740$	6.67643	0.245430
$741$	2.00518	0.0736622
$742$	−1.78823	−0.0656482
$743$	41.4080	1.51911	0.759556	−	0.650442i	$-0.225416\pi$
$743$	41.4080	1.51911	0.759556	+	0.650442i	$0.225416\pi$
$744$	−0.309423	−0.0113440
$745$	12.8092	0.469294
$746$	34.3658	1.25822
$747$	−42.1485	−1.54213
$748$	7.40541	0.270769
$749$	5.95573	0.217617
$750$	−0.223737	−0.00816973
$751$	−31.3070	−1.14241	−0.571205	−	0.820807i	$-0.693524\pi$
$751$	−31.3070	−1.14241	−0.571205	+	0.820807i	$0.693524\pi$
$752$	2.50929	0.0915042
$753$	−3.09776	−0.112889
$754$	−41.5761	−1.51411
$755$	−18.7986	−0.684152
$756$	0.619744	0.0225399
$757$	13.2452	0.481406	0.240703	−	0.970599i	$-0.422622\pi$
$757$	13.2452	0.481406	0.240703	+	0.970599i	$0.422622\pi$
$758$	24.3264	0.883574
$759$	−0.953206	−0.0345992
$760$	2.12314	0.0770145
$761$	−27.7894	−1.00737	−0.503683	−	0.863889i	$-0.668022\pi$
$761$	−27.7894	−1.00737	−0.503683	+	0.863889i	$0.668022\pi$
$762$	−1.67371	−0.0606320
$763$	7.33902	0.265691
$764$	9.89876	0.358125
$765$	−3.54035	−0.128002
$766$	−18.2216	−0.658373
$767$	38.8899	1.40423
$768$	0.223737	0.00807343
$769$	−1.50117	−0.0541335	−0.0270668	−	0.999634i	$-0.508617\pi$
$769$	−1.50117	−0.0541335	−0.0270668	+	0.999634i	$0.508617\pi$
$770$	2.87261	0.103522
$771$	−6.55668	−0.236133
$772$	−8.42443	−0.303202
$773$	39.0725	1.40534	0.702670	−	0.711516i	$-0.251991\pi$
$773$	39.0725	1.40534	0.702670	+	0.711516i	$0.251991\pi$
$774$	12.7665	0.458883
$775$	1.38297	0.0496779
$776$	7.25226	0.260341
$777$	−0.695415	−0.0249479
$778$	14.8767	0.533357
$779$	15.0092	0.537760
$780$	−0.944440	−0.0338164
$781$	−22.9101	−0.819789
$782$	0.828640	0.0296321
$783$	13.1117	0.468575
$784$	−6.78327	−0.242260
$785$	−17.4414	−0.622510
$786$	2.86725	0.102271
$787$	40.2946	1.43635	0.718174	−	0.695864i	$-0.244978\pi$
$787$	40.2946	1.43635	0.718174	+	0.695864i	$0.244978\pi$
$788$	13.6917	0.487747
$789$	−4.28412	−0.152519
$790$	0.949571	0.0337842
$791$	2.30250	0.0818675
$792$	18.2024	0.646795
$793$	28.7619	1.02136
$794$	−15.8903	−0.563925
$795$	−0.859413	−0.0304802
$796$	24.5276	0.869357
$797$	18.1418	0.642614	0.321307	−	0.946975i	$-0.395878\pi$
$797$	18.1418	0.642614	0.321307	+	0.946975i	$0.395878\pi$
$798$	−0.221146	−0.00782848
$799$	3.01150	0.106539
$800$	−1.00000	−0.0353553
$801$	38.5528	1.36220
$802$	−1.00000	−0.0353112
$803$	17.8754	0.630809
$804$	1.26182	0.0445008
$805$	0.321435	0.0113291
$806$	5.83781	0.205628
$807$	−0.175783	−0.00618786
$808$	−3.41556	−0.120159
$809$	45.7120	1.60715	0.803574	−	0.595205i	$-0.202929\pi$
$809$	45.7120	1.60715	0.803574	+	0.595205i	$0.202929\pi$
$810$	−8.55198	−0.300486
$811$	46.4323	1.63046	0.815230	−	0.579137i	$-0.196611\pi$
$811$	46.4323	1.63046	0.815230	+	0.579137i	$0.196611\pi$
$812$	4.58532	0.160913
$813$	0.809650	0.0283957
$814$	−41.1965	−1.44394
$815$	−20.5938	−0.721368
$816$	0.268517	0.00939998
$817$	−9.18836	−0.321460
$818$	−2.81572	−0.0984494
$819$	−5.79710	−0.202567
$820$	−7.06932	−0.246871
$821$	40.5631	1.41566	0.707831	−	0.706382i	$-0.249674\pi$
$821$	40.5631	1.41566	0.707831	+	0.706382i	$0.249674\pi$
$822$	3.46390	0.120817
$823$	17.9067	0.624189	0.312094	−	0.950051i	$-0.398969\pi$
$823$	17.9067	0.624189	0.312094	+	0.950051i	$0.398969\pi$
$824$	−4.07066	−0.141808
$825$	1.38056	0.0480648
$826$	−4.28906	−0.149236
$827$	−37.7630	−1.31315	−0.656574	−	0.754262i	$-0.727995\pi$
$827$	−37.7630	−1.31315	−0.656574	+	0.754262i	$0.727995\pi$
$828$	2.03679	0.0707833
$829$	−3.76049	−0.130607	−0.0653036	−	0.997865i	$-0.520802\pi$
$829$	−3.76049	−0.130607	−0.0653036	+	0.997865i	$0.520802\pi$
$830$	−14.2879	−0.495941
$831$	6.11481	0.212120
$832$	−4.22120	−0.146344
$833$	−8.14090	−0.282065
$834$	−1.59373	−0.0551864
$835$	24.2024	0.837559
$836$	−13.1007	−0.453098
$837$	−1.84105	−0.0636359
$838$	7.95481	0.274794
$839$	54.0314	1.86537	0.932686	−	0.360689i	$-0.117458\pi$
$839$	54.0314	1.86537	0.932686	+	0.360689i	$0.117458\pi$
$840$	0.104160	0.00359385
$841$	68.0100	2.34517
$842$	20.6725	0.712422
$843$	6.53102	0.224940
$844$	−12.7980	−0.440527
$845$	4.81853	0.165763
$846$	7.40225	0.254494
$847$	−12.6043	−0.433088
$848$	−3.84117	−0.131906
$849$	−1.22612	−0.0420805
$850$	−1.20014	−0.0411646
$851$	−4.60974	−0.158020
$852$	−0.830711	−0.0284597
$853$	6.08028	0.208185	0.104092	−	0.994568i	$-0.466806\pi$
$853$	6.08028	0.208185	0.104092	+	0.994568i	$0.466806\pi$
$854$	−3.17207	−0.108546
$855$	6.26315	0.214195
$856$	12.7930	0.437257
$857$	18.9392	0.646950	0.323475	−	0.946237i	$-0.395149\pi$
$857$	18.9392	0.646950	0.323475	+	0.946237i	$0.395149\pi$
$858$	5.82761	0.198951
$859$	20.8115	0.710078	0.355039	−	0.934852i	$-0.384468\pi$
$859$	20.8115	0.710078	0.355039	+	0.934852i	$0.384468\pi$
$860$	4.32772	0.147574
$861$	0.736339	0.0250944
$862$	−8.65440	−0.294770
$863$	−9.26376	−0.315342	−0.157671	−	0.987492i	$-0.550399\pi$
$863$	−9.26376	−0.315342	−0.157671	+	0.987492i	$0.550399\pi$
$864$	1.33122	0.0452892
$865$	5.58475	0.189887
$866$	26.3018	0.893772
$867$	−3.48128	−0.118230
$868$	−0.643836	−0.0218532
$869$	−5.85926	−0.198762
$870$	2.20367	0.0747115
$871$	−23.8064	−0.806648
$872$	15.7644	0.533849
$873$	21.3937	0.724068
$874$	−1.46592	−0.0495856
$875$	−0.465545	−0.0157383
$876$	0.648154	0.0218991
$877$	−44.2706	−1.49491	−0.747456	−	0.664312i	$-0.768725\pi$
$877$	−44.2706	−1.49491	−0.747456	+	0.664312i	$0.768725\pi$
$878$	−7.91844	−0.267234
$879$	−3.42578	−0.115549
$880$	6.17044	0.208005
$881$	−29.7098	−1.00095	−0.500474	−	0.865752i	$-0.666841\pi$
$881$	−29.7098	−1.00095	−0.500474	+	0.865752i	$0.666841\pi$
$882$	−20.0102	−0.673780
$883$	−7.15526	−0.240794	−0.120397	−	0.992726i	$-0.538417\pi$
$883$	−7.15526	−0.240794	−0.120397	+	0.992726i	$0.538417\pi$
$884$	−5.06605	−0.170390
$885$	−2.06129	−0.0692896
$886$	2.52617	0.0848683
$887$	−34.3751	−1.15420	−0.577101	−	0.816673i	$-0.695816\pi$
$887$	−34.3751	−1.15420	−0.577101	+	0.816673i	$0.695816\pi$
$888$	−1.49377	−0.0501275
$889$	−3.48259	−0.116802
$890$	13.0690	0.438074
$891$	52.7694	1.76784
$892$	−15.4771	−0.518212
$893$	−5.32757	−0.178280
$894$	−2.86591	−0.0958503
$895$	−12.7410	−0.425884
$896$	0.465545	0.0155528
$897$	0.652089	0.0217726
$898$	−18.4140	−0.614482
$899$	−13.6214	−0.454299
$900$	−2.94994	−0.0983314
$901$	−4.60995	−0.153580
$902$	43.6208	1.45241
$903$	−0.450774	−0.0150008
$904$	4.94582	0.164496
$905$	−4.11942	−0.136934
$906$	4.20595	0.139733
$907$	−46.9550	−1.55911	−0.779557	−	0.626331i	$-0.784556\pi$
$907$	−46.9550	−1.55911	−0.779557	+	0.626331i	$0.784556\pi$
$908$	22.3520	0.741776
$909$	−10.0757	−0.334190
$910$	−1.96516	−0.0651443
$911$	−31.4013	−1.04037	−0.520185	−	0.854054i	$-0.674137\pi$
$911$	−31.4013	−1.04037	−0.520185	+	0.854054i	$0.674137\pi$
$912$	−0.475026	−0.0157297
$913$	88.1627	2.91776
$914$	31.4150	1.03911
$915$	−1.52447	−0.0503975
$916$	−5.95136	−0.196639
$917$	5.96607	0.197017
$918$	1.59766	0.0527307
$919$	2.25524	0.0743934	0.0371967	−	0.999308i	$-0.488157\pi$
$919$	2.25524	0.0743934	0.0371967	+	0.999308i	$0.488157\pi$
$920$	0.690450	0.0227635
$921$	3.40263	0.112121
$922$	−39.3309	−1.29530
$923$	15.6728	0.515878
$924$	−0.642711	−0.0211436
$925$	6.67643	0.219520
$926$	23.1919	0.762132
$927$	−12.0082	−0.394401
$928$	9.84937	0.323321
$929$	−4.19376	−0.137593	−0.0687965	−	0.997631i	$-0.521916\pi$
$929$	−4.19376	−0.137593	−0.0687965	+	0.997631i	$0.521916\pi$
$930$	−0.309423	−0.0101464
$931$	14.4018	0.472001
$932$	5.81744	0.190557
$933$	−5.88318	−0.192607
$934$	14.8344	0.485395
$935$	7.40541	0.242183
$936$	−12.4523	−0.407016
$937$	−17.2328	−0.562970	−0.281485	−	0.959566i	$-0.590827\pi$
$937$	−17.2328	−0.562970	−0.281485	+	0.959566i	$0.590827\pi$
$938$	2.62554	0.0857269
$939$	1.25834	0.0410645
$940$	2.50929	0.0818439
$941$	39.4974	1.28758	0.643789	−	0.765203i	$-0.277361\pi$
$941$	39.4974	1.28758	0.643789	+	0.765203i	$0.277361\pi$
$942$	3.90229	0.127144
$943$	4.88101	0.158948
$944$	−9.21300	−0.299858
$945$	0.619744	0.0201603
$946$	−26.7039	−0.868219
$947$	5.95315	0.193451	0.0967257	−	0.995311i	$-0.469163\pi$
$947$	5.95315	0.193451	0.0967257	+	0.995311i	$0.469163\pi$
$948$	−0.212454	−0.00690020
$949$	−12.2286	−0.396956
$950$	2.12314	0.0688838
$951$	−1.22497	−0.0397224
$952$	0.558721	0.0181082
$953$	16.5723	0.536830	0.268415	−	0.963303i	$-0.413500\pi$
$953$	16.5723	0.536830	0.268415	+	0.963303i	$0.413500\pi$
$954$	−11.3312	−0.366862
$955$	9.89876	0.320316
$956$	23.3866	0.756376
$957$	−13.5976	−0.439548
$958$	25.2619	0.816176
$959$	7.20756	0.232744
$960$	0.223737	0.00722109
$961$	−29.0874	−0.938303
$962$	28.1826	0.908642
$963$	37.7387	1.21611
$964$	−21.2691	−0.685033
$965$	−8.42443	−0.271192
$966$	−0.0719171	−0.00231389
$967$	56.4282	1.81461	0.907304	−	0.420475i	$-0.138137\pi$
$967$	56.4282	1.81461	0.907304	+	0.420475i	$0.138137\pi$
$968$	−27.0743	−0.870200
$969$	−0.570100	−0.0183143
$970$	7.25226	0.232856
$971$	58.0871	1.86410	0.932052	−	0.362324i	$-0.118017\pi$
$971$	58.0871	1.86410	0.932052	+	0.362324i	$0.118017\pi$
$972$	5.90707	0.189469
$973$	−3.31618	−0.106312
$974$	26.5813	0.851721
$975$	−0.944440	−0.0302463
$976$	−6.81367	−0.218100
$977$	30.6485	0.980531	0.490266	−	0.871573i	$-0.336900\pi$
$977$	30.6485	0.980531	0.490266	+	0.871573i	$0.336900\pi$
$978$	4.60760	0.147335
$979$	−80.6414	−2.57731
$980$	−6.78327	−0.216684
$981$	46.5040	1.48476
$982$	14.8140	0.472734
$983$	36.9101	1.17725	0.588624	−	0.808407i	$-0.299670\pi$
$983$	36.9101	1.17725	0.588624	+	0.808407i	$0.299670\pi$
$984$	1.58167	0.0504218
$985$	13.6917	0.436254
$986$	11.8207	0.376446
$987$	−0.261367	−0.00831939
$988$	8.96221	0.285126
$989$	−2.98807	−0.0950152
$990$	18.2024	0.578511
$991$	2.49442	0.0792380	0.0396190	−	0.999215i	$-0.487386\pi$
$991$	2.49442	0.0792380	0.0396190	+	0.999215i	$0.487386\pi$
$992$	−1.38297	−0.0439094
$993$	1.29291	0.0410292
$994$	−1.72851	−0.0548251
$995$	24.5276	0.777577
$996$	3.19674	0.101293
$997$	40.2257	1.27396	0.636980	−	0.770881i	$-0.280184\pi$
$997$	40.2257	1.27396	0.636980	+	0.770881i	$0.280184\pi$
$998$	16.0747	0.508836
$999$	−8.88783	−0.281198

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.6	✓	10	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:	\( N \)	\(=\)	\( 4010 = 2 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.223737 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.223737 q^{6} -0.465545 q^{7} -1.00000 q^{8} -2.94994 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.223737 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.223737 q^{6} -0.465545 q^{7} -1.00000 q^{8} -2.94994 q^{9} -1.00000 q^{10} +6.17044 q^{11} +0.223737 q^{12} -4.22120 q^{13} +0.465545 q^{14} +0.223737 q^{15} +1.00000 q^{16} +1.20014 q^{17} +2.94994 q^{18} -2.12314 q^{19} +1.00000 q^{20} -0.104160 q^{21} -6.17044 q^{22} -0.690450 q^{23} -0.223737 q^{24} +1.00000 q^{25} +4.22120 q^{26} -1.33122 q^{27} -0.465545 q^{28} -9.84937 q^{29} -0.223737 q^{30} +1.38297 q^{31} -1.00000 q^{32} +1.38056 q^{33} -1.20014 q^{34} -0.465545 q^{35} -2.94994 q^{36} +6.67643 q^{37} +2.12314 q^{38} -0.944440 q^{39} -1.00000 q^{40} -7.06932 q^{41} +0.104160 q^{42} +4.32772 q^{43} +6.17044 q^{44} -2.94994 q^{45} +0.690450 q^{46} +2.50929 q^{47} +0.223737 q^{48} -6.78327 q^{49} -1.00000 q^{50} +0.268517 q^{51} -4.22120 q^{52} -3.84117 q^{53} +1.33122 q^{54} +6.17044 q^{55} +0.465545 q^{56} -0.475026 q^{57} +9.84937 q^{58} -9.21300 q^{59} +0.223737 q^{60} -6.81367 q^{61} -1.38297 q^{62} +1.37333 q^{63} +1.00000 q^{64} -4.22120 q^{65} -1.38056 q^{66} +5.63972 q^{67} +1.20014 q^{68} -0.154479 q^{69} +0.465545 q^{70} -3.71289 q^{71} +2.94994 q^{72} +2.89694 q^{73} -6.67643 q^{74} +0.223737 q^{75} -2.12314 q^{76} -2.87261 q^{77} +0.944440 q^{78} -0.949571 q^{79} +1.00000 q^{80} +8.55198 q^{81} +7.06932 q^{82} +14.2879 q^{83} -0.104160 q^{84} +1.20014 q^{85} -4.32772 q^{86} -2.20367 q^{87} -6.17044 q^{88} -13.0690 q^{89} +2.94994 q^{90} +1.96516 q^{91} -0.690450 q^{92} +0.309423 q^{93} -2.50929 q^{94} -2.12314 q^{95} -0.223737 q^{96} -7.25226 q^{97} +6.78327 q^{98} -18.2024 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9} - 10 q^{10} - 11 q^{11} - 4 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 10 q^{16} + 9 q^{17} - 6 q^{18} - 13 q^{19} + 10 q^{20} - 24 q^{21} + 11 q^{22} - 3 q^{23} + 4 q^{24} + 10 q^{25} - 6 q^{26} - 10 q^{27} - 3 q^{28} - 4 q^{29} + 4 q^{30} - 17 q^{31} - 10 q^{32} - 2 q^{33} - 9 q^{34} - 3 q^{35} + 6 q^{36} - 15 q^{37} + 13 q^{38} - 6 q^{39} - 10 q^{40} - 11 q^{41} + 24 q^{42} - 11 q^{43} - 11 q^{44} + 6 q^{45} + 3 q^{46} + 3 q^{47} - 4 q^{48} - 5 q^{49} - 10 q^{50} - 21 q^{51} + 6 q^{52} + 25 q^{53} + 10 q^{54} - 11 q^{55} + 3 q^{56} + 31 q^{57} + 4 q^{58} - 46 q^{59} - 4 q^{60} - 54 q^{61} + 17 q^{62} - 6 q^{63} + 10 q^{64} + 6 q^{65} + 2 q^{66} - 26 q^{67} + 9 q^{68} - 9 q^{69} + 3 q^{70} - 16 q^{71} - 6 q^{72} + 4 q^{73} + 15 q^{74} - 4 q^{75} - 13 q^{76} + 11 q^{77} + 6 q^{78} - 19 q^{79} + 10 q^{80} - 6 q^{81} + 11 q^{82} + 19 q^{83} - 24 q^{84} + 9 q^{85} + 11 q^{86} + 28 q^{87} + 11 q^{88} - 30 q^{89} - 6 q^{90} - 38 q^{91} - 3 q^{92} - 18 q^{93} - 3 q^{94} - 13 q^{95} + 4 q^{96} - 16 q^{97} + 5 q^{98} - 59 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 4 * q^3 + 10 * q^4 + 10 * q^5 + 4 * q^6 - 3 * q^7 - 10 * q^8 + 6 * q^9 - 10 * q^10 - 11 * q^11 - 4 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 10 * q^16 + 9 * q^17 - 6 * q^18 - 13 * q^19 + 10 * q^20 - 24 * q^21 + 11 * q^22 - 3 * q^23 + 4 * q^24 + 10 * q^25 - 6 * q^26 - 10 * q^27 - 3 * q^28 - 4 * q^29 + 4 * q^30 - 17 * q^31 - 10 * q^32 - 2 * q^33 - 9 * q^34 - 3 * q^35 + 6 * q^36 - 15 * q^37 + 13 * q^38 - 6 * q^39 - 10 * q^40 - 11 * q^41 + 24 * q^42 - 11 * q^43 - 11 * q^44 + 6 * q^45 + 3 * q^46 + 3 * q^47 - 4 * q^48 - 5 * q^49 - 10 * q^50 - 21 * q^51 + 6 * q^52 + 25 * q^53 + 10 * q^54 - 11 * q^55 + 3 * q^56 + 31 * q^57 + 4 * q^58 - 46 * q^59 - 4 * q^60 - 54 * q^61 + 17 * q^62 - 6 * q^63 + 10 * q^64 + 6 * q^65 + 2 * q^66 - 26 * q^67 + 9 * q^68 - 9 * q^69 + 3 * q^70 - 16 * q^71 - 6 * q^72 + 4 * q^73 + 15 * q^74 - 4 * q^75 - 13 * q^76 + 11 * q^77 + 6 * q^78 - 19 * q^79 + 10 * q^80 - 6 * q^81 + 11 * q^82 + 19 * q^83 - 24 * q^84 + 9 * q^85 + 11 * q^86 + 28 * q^87 + 11 * q^88 - 30 * q^89 - 6 * q^90 - 38 * q^91 - 3 * q^92 - 18 * q^93 - 3 * q^94 - 13 * q^95 + 4 * q^96 - 16 * q^97 + 5 * q^98 - 59 * q^99

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