LMFDB - Embedded newform 4010.2.a.i.1.9

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			1.9
Root			$-0.309245$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.30797 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.30797 q^{6} -5.12569 q^{7} -1.00000 q^{8} +2.32671 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.30797 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.30797 q^{6} -5.12569 q^{7} -1.00000 q^{8} +2.32671 q^{9} -1.00000 q^{10} -1.82595 q^{11} +2.30797 q^{12} +2.86793 q^{13} +5.12569 q^{14} +2.30797 q^{15} +1.00000 q^{16} +5.18022 q^{17} -2.32671 q^{18} -1.72311 q^{19} +1.00000 q^{20} -11.8299 q^{21} +1.82595 q^{22} -0.231977 q^{23} -2.30797 q^{24} +1.00000 q^{25} -2.86793 q^{26} -1.55393 q^{27} -5.12569 q^{28} +0.413275 q^{29} -2.30797 q^{30} -5.80270 q^{31} -1.00000 q^{32} -4.21423 q^{33} -5.18022 q^{34} -5.12569 q^{35} +2.32671 q^{36} -0.773298 q^{37} +1.72311 q^{38} +6.61910 q^{39} -1.00000 q^{40} -8.47555 q^{41} +11.8299 q^{42} -10.9517 q^{43} -1.82595 q^{44} +2.32671 q^{45} +0.231977 q^{46} -13.3750 q^{47} +2.30797 q^{48} +19.2727 q^{49} -1.00000 q^{50} +11.9558 q^{51} +2.86793 q^{52} +3.57653 q^{53} +1.55393 q^{54} -1.82595 q^{55} +5.12569 q^{56} -3.97687 q^{57} -0.413275 q^{58} -8.35966 q^{59} +2.30797 q^{60} +7.09267 q^{61} +5.80270 q^{62} -11.9260 q^{63} +1.00000 q^{64} +2.86793 q^{65} +4.21423 q^{66} +10.1853 q^{67} +5.18022 q^{68} -0.535395 q^{69} +5.12569 q^{70} -7.02748 q^{71} -2.32671 q^{72} -7.84968 q^{73} +0.773298 q^{74} +2.30797 q^{75} -1.72311 q^{76} +9.35925 q^{77} -6.61910 q^{78} +8.27089 q^{79} +1.00000 q^{80} -10.5665 q^{81} +8.47555 q^{82} +2.73735 q^{83} -11.8299 q^{84} +5.18022 q^{85} +10.9517 q^{86} +0.953824 q^{87} +1.82595 q^{88} +1.59254 q^{89} -2.32671 q^{90} -14.7001 q^{91} -0.231977 q^{92} -13.3924 q^{93} +13.3750 q^{94} -1.72311 q^{95} -2.30797 q^{96} -11.7123 q^{97} -19.2727 q^{98} -4.24846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.30797	1.33251	0.666253	−	0.745726i	$-0.267897\pi$
$3$	2.30797	1.33251	0.666253	+	0.745726i	$0.267897\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.30797	−0.942224
$7$	−5.12569	−1.93733	−0.968664	−	0.248375i	$-0.920104\pi$
$7$	−5.12569	−1.93733	−0.968664	+	0.248375i	$0.920104\pi$
$8$	−1.00000	−0.353553
$9$	2.32671	0.775571
$10$	−1.00000	−0.316228
$11$	−1.82595	−0.550545	−0.275272	−	0.961366i	$-0.588768\pi$
$11$	−1.82595	−0.550545	−0.275272	+	0.961366i	$0.588768\pi$
$12$	2.30797	0.666253
$13$	2.86793	0.795422	0.397711	−	0.917511i	$-0.369805\pi$
$13$	2.86793	0.795422	0.397711	+	0.917511i	$0.369805\pi$
$14$	5.12569	1.36990
$15$	2.30797	0.595915
$16$	1.00000	0.250000
$17$	5.18022	1.25639	0.628193	−	0.778057i	$-0.283795\pi$
$17$	5.18022	1.25639	0.628193	+	0.778057i	$0.283795\pi$
$18$	−2.32671	−0.548411
$19$	−1.72311	−0.395307	−0.197654	−	0.980272i	$-0.563332\pi$
$19$	−1.72311	−0.395307	−0.197654	+	0.980272i	$0.563332\pi$
$20$	1.00000	0.223607
$21$	−11.8299	−2.58150
$22$	1.82595	0.389294
$23$	−0.231977	−0.0483705	−0.0241853	−	0.999707i	$-0.507699\pi$
$23$	−0.231977	−0.0483705	−0.0241853	+	0.999707i	$0.507699\pi$
$24$	−2.30797	−0.471112
$25$	1.00000	0.200000
$26$	−2.86793	−0.562448
$27$	−1.55393	−0.299053
$28$	−5.12569	−0.968664
$29$	0.413275	0.0767432	0.0383716	−	0.999264i	$-0.487783\pi$
$29$	0.413275	0.0767432	0.0383716	+	0.999264i	$0.487783\pi$
$30$	−2.30797	−0.421375
$31$	−5.80270	−1.04219	−0.521097	−	0.853497i	$-0.674477\pi$
$31$	−5.80270	−1.04219	−0.521097	+	0.853497i	$0.674477\pi$
$32$	−1.00000	−0.176777
$33$	−4.21423	−0.733604
$34$	−5.18022	−0.888400
$35$	−5.12569	−0.866399
$36$	2.32671	0.387785
$37$	−0.773298	−0.127129	−0.0635647	−	0.997978i	$-0.520247\pi$
$37$	−0.773298	−0.127129	−0.0635647	+	0.997978i	$0.520247\pi$
$38$	1.72311	0.279525
$39$	6.61910	1.05990
$40$	−1.00000	−0.158114
$41$	−8.47555	−1.32366	−0.661829	−	0.749655i	$-0.730220\pi$
$41$	−8.47555	−1.32366	−0.661829	+	0.749655i	$0.730220\pi$
$42$	11.8299	1.82540
$43$	−10.9517	−1.67012	−0.835058	−	0.550161i	$-0.814566\pi$
$43$	−10.9517	−1.67012	−0.835058	+	0.550161i	$0.814566\pi$
$44$	−1.82595	−0.275272
$45$	2.32671	0.346846
$46$	0.231977	0.0342031
$47$	−13.3750	−1.95095	−0.975475	−	0.220111i	$-0.929358\pi$
$47$	−13.3750	−1.95095	−0.975475	+	0.220111i	$0.929358\pi$
$48$	2.30797	0.333126
$49$	19.2727	2.75324
$50$	−1.00000	−0.141421
$51$	11.9558	1.67414
$52$	2.86793	0.397711
$53$	3.57653	0.491274	0.245637	−	0.969362i	$-0.421003\pi$
$53$	3.57653	0.491274	0.245637	+	0.969362i	$0.421003\pi$
$54$	1.55393	0.211463
$55$	−1.82595	−0.246211
$56$	5.12569	0.684949
$57$	−3.97687	−0.526749
$58$	−0.413275	−0.0542656
$59$	−8.35966	−1.08833	−0.544167	−	0.838977i	$-0.683154\pi$
$59$	−8.35966	−1.08833	−0.544167	+	0.838977i	$0.683154\pi$
$60$	2.30797	0.297957
$61$	7.09267	0.908123	0.454061	−	0.890970i	$-0.349975\pi$
$61$	7.09267	0.908123	0.454061	+	0.890970i	$0.349975\pi$
$62$	5.80270	0.736943
$63$	−11.9260	−1.50253
$64$	1.00000	0.125000
$65$	2.86793	0.355723
$66$	4.21423	0.518736
$67$	10.1853	1.24433	0.622163	−	0.782888i	$-0.286254\pi$
$67$	10.1853	1.24433	0.622163	+	0.782888i	$0.286254\pi$
$68$	5.18022	0.628193
$69$	−0.535395	−0.0644540
$70$	5.12569	0.612637
$71$	−7.02748	−0.834008	−0.417004	−	0.908905i	$-0.636920\pi$
$71$	−7.02748	−0.834008	−0.417004	+	0.908905i	$0.636920\pi$
$72$	−2.32671	−0.274206
$73$	−7.84968	−0.918735	−0.459368	−	0.888246i	$-0.651924\pi$
$73$	−7.84968	−0.918735	−0.459368	+	0.888246i	$0.651924\pi$
$74$	0.773298	0.0898940
$75$	2.30797	0.266501
$76$	−1.72311	−0.197654
$77$	9.35925	1.06659
$78$	−6.61910	−0.749465
$79$	8.27089	0.930548	0.465274	−	0.885167i	$-0.345956\pi$
$79$	8.27089	0.930548	0.465274	+	0.885167i	$0.345956\pi$
$80$	1.00000	0.111803
$81$	−10.5665	−1.17406
$82$	8.47555	0.935968
$83$	2.73735	0.300464	0.150232	−	0.988651i	$-0.451998\pi$
$83$	2.73735	0.300464	0.150232	+	0.988651i	$0.451998\pi$
$84$	−11.8299	−1.29075
$85$	5.18022	0.561873
$86$	10.9517	1.18095
$87$	0.953824	0.102261
$88$	1.82595	0.194647
$89$	1.59254	0.168809	0.0844043	−	0.996432i	$-0.473101\pi$
$89$	1.59254	0.168809	0.0844043	+	0.996432i	$0.473101\pi$
$90$	−2.32671	−0.245257
$91$	−14.7001	−1.54099
$92$	−0.231977	−0.0241853
$93$	−13.3924	−1.38873
$94$	13.3750	1.37953
$95$	−1.72311	−0.176787
$96$	−2.30797	−0.235556
$97$	−11.7123	−1.18920	−0.594602	−	0.804021i	$-0.702690\pi$
$97$	−11.7123	−1.18920	−0.594602	+	0.804021i	$0.702690\pi$
$98$	−19.2727	−1.94683
$99$	−4.24846	−0.426986
$100$	1.00000	0.100000
$101$	6.71868	0.668533	0.334267	−	0.942479i	$-0.391511\pi$
$101$	6.71868	0.668533	0.334267	+	0.942479i	$0.391511\pi$
$102$	−11.9558	−1.18380
$103$	−4.23187	−0.416978	−0.208489	−	0.978025i	$-0.566855\pi$
$103$	−4.23187	−0.416978	−0.208489	+	0.978025i	$0.566855\pi$
$104$	−2.86793	−0.281224
$105$	−11.8299	−1.15448
$106$	−3.57653	−0.347383
$107$	1.56139	0.150945	0.0754727	−	0.997148i	$-0.475953\pi$
$107$	1.56139	0.150945	0.0754727	+	0.997148i	$0.475953\pi$
$108$	−1.55393	−0.149527
$109$	7.83377	0.750340	0.375170	−	0.926956i	$-0.377584\pi$
$109$	7.83377	0.750340	0.375170	+	0.926956i	$0.377584\pi$
$110$	1.82595	0.174098
$111$	−1.78475	−0.169401
$112$	−5.12569	−0.484332
$113$	1.88823	0.177630	0.0888150	−	0.996048i	$-0.471692\pi$
$113$	1.88823	0.177630	0.0888150	+	0.996048i	$0.471692\pi$
$114$	3.97687	0.372468
$115$	−0.231977	−0.0216319
$116$	0.413275	0.0383716
$117$	6.67285	0.616906
$118$	8.35966	0.769569
$119$	−26.5522	−2.43403
$120$	−2.30797	−0.210688
$121$	−7.66590	−0.696900
$122$	−7.09267	−0.642140
$123$	−19.5613	−1.76378
$124$	−5.80270	−0.521097
$125$	1.00000	0.0894427
$126$	11.9260	1.06245
$127$	20.4205	1.81203	0.906014	−	0.423248i	$-0.139110\pi$
$127$	20.4205	1.81203	0.906014	+	0.423248i	$0.139110\pi$
$128$	−1.00000	−0.0883883
$129$	−25.2761	−2.22544
$130$	−2.86793	−0.251534
$131$	−9.20972	−0.804657	−0.402329	−	0.915495i	$-0.631799\pi$
$131$	−9.20972	−0.804657	−0.402329	+	0.915495i	$0.631799\pi$
$132$	−4.21423	−0.366802
$133$	8.83210	0.765840
$134$	−10.1853	−0.879872
$135$	−1.55393	−0.133741
$136$	−5.18022	−0.444200
$137$	−11.2959	−0.965073	−0.482537	−	0.875876i	$-0.660284\pi$
$137$	−11.2959	−0.965073	−0.482537	+	0.875876i	$0.660284\pi$
$138$	0.535395	0.0455758
$139$	−9.18054	−0.778683	−0.389342	−	0.921093i	$-0.627297\pi$
$139$	−9.18054	−0.778683	−0.389342	+	0.921093i	$0.627297\pi$
$140$	−5.12569	−0.433200
$141$	−30.8691	−2.59965
$142$	7.02748	0.589733
$143$	−5.23670	−0.437915
$144$	2.32671	0.193893
$145$	0.413275	0.0343206
$146$	7.84968	0.649644
$147$	44.4807	3.66871
$148$	−0.773298	−0.0635647
$149$	−12.1799	−0.997813	−0.498907	−	0.866656i	$-0.666265\pi$
$149$	−12.1799	−0.997813	−0.498907	+	0.866656i	$0.666265\pi$
$150$	−2.30797	−0.188445
$151$	−19.0556	−1.55072	−0.775360	−	0.631520i	$-0.782431\pi$
$151$	−19.0556	−1.55072	−0.775360	+	0.631520i	$0.782431\pi$
$152$	1.72311	0.139762
$153$	12.0529	0.974417
$154$	−9.35925	−0.754190
$155$	−5.80270	−0.466084
$156$	6.61910	0.529952
$157$	−11.3912	−0.909118	−0.454559	−	0.890717i	$-0.650203\pi$
$157$	−11.3912	−0.909118	−0.454559	+	0.890717i	$0.650203\pi$
$158$	−8.27089	−0.657997
$159$	8.25451	0.654625
$160$	−1.00000	−0.0790569
$161$	1.18904	0.0937095
$162$	10.5665	0.830186
$163$	−19.6319	−1.53769	−0.768845	−	0.639435i	$-0.779168\pi$
$163$	−19.6319	−1.53769	−0.768845	+	0.639435i	$0.779168\pi$
$164$	−8.47555	−0.661829
$165$	−4.21423	−0.328078
$166$	−2.73735	−0.212460
$167$	19.5853	1.51556	0.757778	−	0.652513i	$-0.226285\pi$
$167$	19.5853	1.51556	0.757778	+	0.652513i	$0.226285\pi$
$168$	11.8299	0.912698
$169$	−4.77496	−0.367304
$170$	−5.18022	−0.397304
$171$	−4.00917	−0.306589
$172$	−10.9517	−0.835058
$173$	−2.69712	−0.205058	−0.102529	−	0.994730i	$-0.532693\pi$
$173$	−2.69712	−0.205058	−0.102529	+	0.994730i	$0.532693\pi$
$174$	−0.953824	−0.0723092
$175$	−5.12569	−0.387466
$176$	−1.82595	−0.137636
$177$	−19.2938	−1.45021
$178$	−1.59254	−0.119366
$179$	−20.0859	−1.50129	−0.750644	−	0.660707i	$-0.770256\pi$
$179$	−20.0859	−1.50129	−0.750644	+	0.660707i	$0.770256\pi$
$180$	2.32671	0.173423
$181$	21.3607	1.58773	0.793866	−	0.608093i	$-0.208065\pi$
$181$	21.3607	1.58773	0.793866	+	0.608093i	$0.208065\pi$
$182$	14.7001	1.08965
$183$	16.3696	1.21008
$184$	0.231977	0.0171016
$185$	−0.773298	−0.0568540
$186$	13.3924	0.981981
$187$	−9.45882	−0.691697
$188$	−13.3750	−0.975475
$189$	7.96495	0.579365
$190$	1.72311	0.125007
$191$	−11.3414	−0.820633	−0.410316	−	0.911943i	$-0.634582\pi$
$191$	−11.3414	−0.820633	−0.410316	+	0.911943i	$0.634582\pi$
$192$	2.30797	0.166563
$193$	8.85428	0.637345	0.318672	−	0.947865i	$-0.396763\pi$
$193$	8.85428	0.637345	0.318672	+	0.947865i	$0.396763\pi$
$194$	11.7123	0.840894
$195$	6.61910	0.474003
$196$	19.2727	1.37662
$197$	17.6270	1.25587	0.627937	−	0.778264i	$-0.283899\pi$
$197$	17.6270	1.25587	0.627937	+	0.778264i	$0.283899\pi$
$198$	4.24846	0.301925
$199$	−12.1913	−0.864220	−0.432110	−	0.901821i	$-0.642231\pi$
$199$	−12.1913	−0.864220	−0.432110	+	0.901821i	$0.642231\pi$
$200$	−1.00000	−0.0707107
$201$	23.5072	1.65807
$202$	−6.71868	−0.472725
$203$	−2.11832	−0.148677
$204$	11.9558	0.837071
$205$	−8.47555	−0.591958
$206$	4.23187	0.294848
$207$	−0.539743	−0.0375147
$208$	2.86793	0.198855
$209$	3.14630	0.217634
$210$	11.8299	0.816342
$211$	−14.3087	−0.985052	−0.492526	−	0.870298i	$-0.663926\pi$
$211$	−14.3087	−0.985052	−0.492526	+	0.870298i	$0.663926\pi$
$212$	3.57653	0.245637
$213$	−16.2192	−1.11132
$214$	−1.56139	−0.106735
$215$	−10.9517	−0.746899
$216$	1.55393	0.105731
$217$	29.7428	2.01907
$218$	−7.83377	−0.530570
$219$	−18.1168	−1.22422
$220$	−1.82595	−0.123106
$221$	14.8565	0.999357
$222$	1.78475	0.119784
$223$	−5.89664	−0.394868	−0.197434	−	0.980316i	$-0.563261\pi$
$223$	−5.89664	−0.394868	−0.197434	+	0.980316i	$0.563261\pi$
$224$	5.12569	0.342474
$225$	2.32671	0.155114
$226$	−1.88823	−0.125603
$227$	−1.03025	−0.0683801	−0.0341900	−	0.999415i	$-0.510885\pi$
$227$	−1.03025	−0.0683801	−0.0341900	+	0.999415i	$0.510885\pi$
$228$	−3.97687	−0.263375
$229$	−24.4978	−1.61886	−0.809431	−	0.587215i	$-0.800224\pi$
$229$	−24.4978	−1.61886	−0.809431	+	0.587215i	$0.800224\pi$
$230$	0.231977	0.0152961
$231$	21.6008	1.42123
$232$	−0.413275	−0.0271328
$233$	−0.0260579	−0.00170711	−0.000853556	−	1.00000i	$-0.500272\pi$
$233$	−0.0260579	−0.00170711	−0.000853556		1.00000i	$0.500272\pi$
$234$	−6.67285	−0.436218
$235$	−13.3750	−0.872491
$236$	−8.35966	−0.544167
$237$	19.0889	1.23996
$238$	26.5522	1.72112
$239$	23.2032	1.50089	0.750446	−	0.660931i	$-0.229839\pi$
$239$	23.2032	1.50089	0.750446	+	0.660931i	$0.229839\pi$
$240$	2.30797	0.148979
$241$	10.5016	0.676465	0.338232	−	0.941063i	$-0.390171\pi$
$241$	10.5016	0.676465	0.338232	+	0.941063i	$0.390171\pi$
$242$	7.66590	0.492783
$243$	−19.7255	−1.26539
$244$	7.09267	0.454061
$245$	19.2727	1.23129
$246$	19.5613	1.24718
$247$	−4.94175	−0.314436
$248$	5.80270	0.368472
$249$	6.31772	0.400369
$250$	−1.00000	−0.0632456
$251$	−14.3549	−0.906074	−0.453037	−	0.891492i	$-0.649659\pi$
$251$	−14.3549	−0.906074	−0.453037	+	0.891492i	$0.649659\pi$
$252$	−11.9260	−0.751267
$253$	0.423578	0.0266301
$254$	−20.4205	−1.28130
$255$	11.9558	0.748699
$256$	1.00000	0.0625000
$257$	24.1714	1.50777	0.753885	−	0.657007i	$-0.228178\pi$
$257$	24.1714	1.50777	0.753885	+	0.657007i	$0.228178\pi$
$258$	25.2761	1.57362
$259$	3.96368	0.246291
$260$	2.86793	0.177862
$261$	0.961571	0.0595197
$262$	9.20972	0.568979
$263$	−1.26365	−0.0779200	−0.0389600	−	0.999241i	$-0.512404\pi$
$263$	−1.26365	−0.0779200	−0.0389600	+	0.999241i	$0.512404\pi$
$264$	4.21423	0.259368
$265$	3.57653	0.219704
$266$	−8.83210	−0.541531
$267$	3.67552	0.224938
$268$	10.1853	0.622163
$269$	−19.8337	−1.20928	−0.604640	−	0.796499i	$-0.706683\pi$
$269$	−19.8337	−1.20928	−0.604640	+	0.796499i	$0.706683\pi$
$270$	1.55393	0.0945690
$271$	11.2534	0.683594	0.341797	−	0.939774i	$-0.388965\pi$
$271$	11.2534	0.683594	0.341797	+	0.939774i	$0.388965\pi$
$272$	5.18022	0.314097
$273$	−33.9274	−2.05338
$274$	11.2959	0.682410
$275$	−1.82595	−0.110109
$276$	−0.535395	−0.0322270
$277$	−13.8413	−0.831643	−0.415822	−	0.909446i	$-0.636506\pi$
$277$	−13.8413	−0.831643	−0.415822	+	0.909446i	$0.636506\pi$
$278$	9.18054	0.550612
$279$	−13.5012	−0.808296
$280$	5.12569	0.306318
$281$	−29.1862	−1.74110	−0.870552	−	0.492076i	$-0.836238\pi$
$281$	−29.1862	−1.74110	−0.870552	+	0.492076i	$0.836238\pi$
$282$	30.8691	1.83823
$283$	5.31391	0.315879	0.157940	−	0.987449i	$-0.449515\pi$
$283$	5.31391	0.315879	0.157940	+	0.987449i	$0.449515\pi$
$284$	−7.02748	−0.417004
$285$	−3.97687	−0.235569
$286$	5.23670	0.309653
$287$	43.4430	2.56436
$288$	−2.32671	−0.137103
$289$	9.83464	0.578508
$290$	−0.413275	−0.0242683
$291$	−27.0316	−1.58462
$292$	−7.84968	−0.459368
$293$	24.4177	1.42650	0.713248	−	0.700911i	$-0.247223\pi$
$293$	24.4177	1.42650	0.713248	+	0.700911i	$0.247223\pi$
$294$	−44.4807	−2.59417
$295$	−8.35966	−0.486718
$296$	0.773298	0.0449470
$297$	2.83739	0.164642
$298$	12.1799	0.705561
$299$	−0.665294	−0.0384749
$300$	2.30797	0.133251
$301$	56.1349	3.23556
$302$	19.0556	1.09652
$303$	15.5065	0.890824
$304$	−1.72311	−0.0988269
$305$	7.09267	0.406125
$306$	−12.0529	−0.689017
$307$	29.2291	1.66819	0.834096	−	0.551619i	$-0.185990\pi$
$307$	29.2291	1.66819	0.834096	+	0.551619i	$0.185990\pi$
$308$	9.35925	0.533293
$309$	−9.76702	−0.555626
$310$	5.80270	0.329571
$311$	−8.05463	−0.456736	−0.228368	−	0.973575i	$-0.573339\pi$
$311$	−8.05463	−0.456736	−0.228368	+	0.973575i	$0.573339\pi$
$312$	−6.61910	−0.374732
$313$	15.8471	0.895728	0.447864	−	0.894102i	$-0.352185\pi$
$313$	15.8471	0.895728	0.447864	+	0.894102i	$0.352185\pi$
$314$	11.3912	0.642844
$315$	−11.9260	−0.671954
$316$	8.27089	0.465274
$317$	2.72043	0.152795	0.0763973	−	0.997077i	$-0.475658\pi$
$317$	2.72043	0.152795	0.0763973	+	0.997077i	$0.475658\pi$
$318$	−8.25451	−0.462890
$319$	−0.754619	−0.0422506
$320$	1.00000	0.0559017
$321$	3.60364	0.201136
$322$	−1.18904	−0.0662627
$323$	−8.92606	−0.496659
$324$	−10.5665	−0.587030
$325$	2.86793	0.159084
$326$	19.6319	1.08731
$327$	18.0801	0.999831
$328$	8.47555	0.467984
$329$	68.5563	3.77963
$330$	4.21423	0.231986
$331$	15.5224	0.853187	0.426593	−	0.904444i	$-0.359714\pi$
$331$	15.5224	0.853187	0.426593	+	0.904444i	$0.359714\pi$
$332$	2.73735	0.150232
$333$	−1.79924	−0.0985978
$334$	−19.5853	−1.07166
$335$	10.1853	0.556480
$336$	−11.8299	−0.645375
$337$	−34.2266	−1.86444	−0.932222	−	0.361886i	$-0.882133\pi$
$337$	−34.2266	−1.86444	−0.932222	+	0.361886i	$0.882133\pi$
$338$	4.77496	0.259724
$339$	4.35798	0.236693
$340$	5.18022	0.280937
$341$	10.5954	0.573775
$342$	4.00917	0.216791
$343$	−62.9059	−3.39660
$344$	10.9517	0.590475
$345$	−0.535395	−0.0288247
$346$	2.69712	0.144998
$347$	−3.94198	−0.211616	−0.105808	−	0.994387i	$-0.533743\pi$
$347$	−3.94198	−0.211616	−0.105808	+	0.994387i	$0.533743\pi$
$348$	0.953824	0.0511303
$349$	−24.9824	−1.33728	−0.668640	−	0.743587i	$-0.733123\pi$
$349$	−24.9824	−1.33728	−0.668640	+	0.743587i	$0.733123\pi$
$350$	5.12569	0.273980
$351$	−4.45656	−0.237874
$352$	1.82595	0.0973235
$353$	−21.7570	−1.15801	−0.579003	−	0.815325i	$-0.696558\pi$
$353$	−21.7570	−1.15801	−0.579003	+	0.815325i	$0.696558\pi$
$354$	19.2938	1.02545
$355$	−7.02748	−0.372980
$356$	1.59254	0.0844043
$357$	−61.2815	−3.24336
$358$	20.0859	1.06157
$359$	25.8043	1.36190	0.680949	−	0.732331i	$-0.261568\pi$
$359$	25.8043	1.36190	0.680949	+	0.732331i	$0.261568\pi$
$360$	−2.32671	−0.122628
$361$	−16.0309	−0.843732
$362$	−21.3607	−1.12270
$363$	−17.6927	−0.928624
$364$	−14.7001	−0.770496
$365$	−7.84968	−0.410871
$366$	−16.3696	−0.855655
$367$	8.98516	0.469022	0.234511	−	0.972114i	$-0.424651\pi$
$367$	8.98516	0.469022	0.234511	+	0.972114i	$0.424651\pi$
$368$	−0.231977	−0.0120926
$369$	−19.7202	−1.02659
$370$	0.773298	0.0402018
$371$	−18.3322	−0.951758
$372$	−13.3924	−0.694365
$373$	−18.0327	−0.933700	−0.466850	−	0.884336i	$-0.654611\pi$
$373$	−18.0327	−0.933700	−0.466850	+	0.884336i	$0.654611\pi$
$374$	9.45882	0.489104
$375$	2.30797	0.119183
$376$	13.3750	0.689765
$377$	1.18524	0.0610432
$378$	−7.96495	−0.409673
$379$	−12.1860	−0.625955	−0.312977	−	0.949761i	$-0.601326\pi$
$379$	−12.1860	−0.625955	−0.312977	+	0.949761i	$0.601326\pi$
$380$	−1.72311	−0.0883934
$381$	47.1299	2.41454
$382$	11.3414	0.580275
$383$	28.3229	1.44723	0.723616	−	0.690202i	$-0.242479\pi$
$383$	28.3229	1.44723	0.723616	+	0.690202i	$0.242479\pi$
$384$	−2.30797	−0.117778
$385$	9.35925	0.476992
$386$	−8.85428	−0.450671
$387$	−25.4814	−1.29529
$388$	−11.7123	−0.594602
$389$	14.5586	0.738152	0.369076	−	0.929399i	$-0.379674\pi$
$389$	14.5586	0.738152	0.369076	+	0.929399i	$0.379674\pi$
$390$	−6.61910	−0.335171
$391$	−1.20169	−0.0607721
$392$	−19.2727	−0.973417
$393$	−21.2557	−1.07221
$394$	−17.6270	−0.888037
$395$	8.27089	0.416154
$396$	−4.24846	−0.213493
$397$	33.7418	1.69345	0.846727	−	0.532027i	$-0.178570\pi$
$397$	33.7418	1.69345	0.846727	+	0.532027i	$0.178570\pi$
$398$	12.1913	0.611096
$399$	20.3842	1.02049
$400$	1.00000	0.0500000
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−23.5072	−1.17243
$403$	−16.6417	−0.828984
$404$	6.71868	0.334267
$405$	−10.5665	−0.525056
$406$	2.11832	0.105130
$407$	1.41200	0.0699904
$408$	−11.9558	−0.591899
$409$	8.73493	0.431915	0.215957	−	0.976403i	$-0.430713\pi$
$409$	8.73493	0.431915	0.215957	+	0.976403i	$0.430713\pi$
$410$	8.47555	0.418578
$411$	−26.0705	−1.28597
$412$	−4.23187	−0.208489
$413$	42.8490	2.10846
$414$	0.539743	0.0265269
$415$	2.73735	0.134371
$416$	−2.86793	−0.140612
$417$	−21.1884	−1.03760
$418$	−3.14630	−0.153891
$419$	−4.49937	−0.219808	−0.109904	−	0.993942i	$-0.535054\pi$
$419$	−4.49937	−0.219808	−0.109904	+	0.993942i	$0.535054\pi$
$420$	−11.8299	−0.577241
$421$	−12.0532	−0.587439	−0.293720	−	0.955892i	$-0.594893\pi$
$421$	−12.0532	−0.587439	−0.293720	+	0.955892i	$0.594893\pi$
$422$	14.3087	0.696537
$423$	−31.1199	−1.51310
$424$	−3.57653	−0.173692
$425$	5.18022	0.251277
$426$	16.2192	0.785822
$427$	−36.3548	−1.75933
$428$	1.56139	0.0754727
$429$	−12.0861	−0.583524
$430$	10.9517	0.528137
$431$	16.8432	0.811309	0.405655	−	0.914026i	$-0.367044\pi$
$431$	16.8432	0.811309	0.405655	+	0.914026i	$0.367044\pi$
$432$	−1.55393	−0.0747634
$433$	7.54922	0.362792	0.181396	−	0.983410i	$-0.441938\pi$
$433$	7.54922	0.362792	0.181396	+	0.983410i	$0.441938\pi$
$434$	−29.7428	−1.42770
$435$	0.953824	0.0457324
$436$	7.83377	0.375170
$437$	0.399720	0.0191212
$438$	18.1168	0.865654
$439$	23.5893	1.12586	0.562928	−	0.826506i	$-0.309675\pi$
$439$	23.5893	1.12586	0.562928	+	0.826506i	$0.309675\pi$
$440$	1.82595	0.0870488
$441$	44.8420	2.13533
$442$	−14.8565	−0.706652
$443$	6.87149	0.326474	0.163237	−	0.986587i	$-0.447806\pi$
$443$	6.87149	0.326474	0.163237	+	0.986587i	$0.447806\pi$
$444$	−1.78475	−0.0847003
$445$	1.59254	0.0754935
$446$	5.89664	0.279214
$447$	−28.1107	−1.32959
$448$	−5.12569	−0.242166
$449$	7.37577	0.348084	0.174042	−	0.984738i	$-0.444317\pi$
$449$	7.37577	0.348084	0.174042	+	0.984738i	$0.444317\pi$
$450$	−2.32671	−0.109682
$451$	15.4759	0.728733
$452$	1.88823	0.0888150
$453$	−43.9796	−2.06634
$454$	1.03025	0.0483520
$455$	−14.7001	−0.689153
$456$	3.97687	0.186234
$457$	−37.2443	−1.74221	−0.871107	−	0.491093i	$-0.836598\pi$
$457$	−37.2443	−1.74221	−0.871107	+	0.491093i	$0.836598\pi$
$458$	24.4978	1.14471
$459$	−8.04968	−0.375727
$460$	−0.231977	−0.0108160
$461$	−17.2287	−0.802420	−0.401210	−	0.915986i	$-0.631410\pi$
$461$	−17.2287	−0.802420	−0.401210	+	0.915986i	$0.631410\pi$
$462$	−21.6008	−1.00496
$463$	−9.75535	−0.453370	−0.226685	−	0.973968i	$-0.572789\pi$
$463$	−9.75535	−0.453370	−0.226685	+	0.973968i	$0.572789\pi$
$464$	0.413275	0.0191858
$465$	−13.3924	−0.621059
$466$	0.0260579	0.00120711
$467$	−2.98148	−0.137966	−0.0689831	−	0.997618i	$-0.521975\pi$
$467$	−2.98148	−0.137966	−0.0689831	+	0.997618i	$0.521975\pi$
$468$	6.67285	0.308453
$469$	−52.2064	−2.41067
$470$	13.3750	0.616945
$471$	−26.2906	−1.21140
$472$	8.35966	0.384784
$473$	19.9972	0.919474
$474$	−19.0889	−0.876784
$475$	−1.72311	−0.0790615
$476$	−26.5522	−1.21702
$477$	8.32155	0.381017
$478$	−23.2032	−1.06129
$479$	0.647726	0.0295954	0.0147977	−	0.999891i	$-0.495290\pi$
$479$	0.647726	0.0295954	0.0147977	+	0.999891i	$0.495290\pi$
$480$	−2.30797	−0.105344
$481$	−2.21777	−0.101121
$482$	−10.5016	−0.478333
$483$	2.74427	0.124868
$484$	−7.66590	−0.348450
$485$	−11.7123	−0.531828
$486$	19.7255	0.894765
$487$	−5.61871	−0.254608	−0.127304	−	0.991864i	$-0.540632\pi$
$487$	−5.61871	−0.254608	−0.127304	+	0.991864i	$0.540632\pi$
$488$	−7.09267	−0.321070
$489$	−45.3098	−2.04898
$490$	−19.2727	−0.870651
$491$	31.2742	1.41138	0.705692	−	0.708519i	$-0.250636\pi$
$491$	31.2742	1.41138	0.705692	+	0.708519i	$0.250636\pi$
$492$	−19.5613	−0.881891
$493$	2.14085	0.0964191
$494$	4.94175	0.222340
$495$	−4.24846	−0.190954
$496$	−5.80270	−0.260549
$497$	36.0207	1.61575
$498$	−6.31772	−0.283104
$499$	12.9780	0.580976	0.290488	−	0.956879i	$-0.406182\pi$
$499$	12.9780	0.580976	0.290488	+	0.956879i	$0.406182\pi$
$500$	1.00000	0.0447214
$501$	45.2022	2.01949
$502$	14.3549	0.640691
$503$	−34.2674	−1.52791	−0.763954	−	0.645270i	$-0.776745\pi$
$503$	−34.2674	−1.52791	−0.763954	+	0.645270i	$0.776745\pi$
$504$	11.9260	0.531226
$505$	6.71868	0.298977
$506$	−0.423578	−0.0188303
$507$	−11.0204	−0.489435
$508$	20.4205	0.906014
$509$	35.4963	1.57334	0.786672	−	0.617371i	$-0.211802\pi$
$509$	35.4963	1.57334	0.786672	+	0.617371i	$0.211802\pi$
$510$	−11.9558	−0.529410
$511$	40.2350	1.77989
$512$	−1.00000	−0.0441942
$513$	2.67758	0.118218
$514$	−24.1714	−1.06615
$515$	−4.23187	−0.186478
$516$	−25.2761	−1.11272
$517$	24.4222	1.07409
$518$	−3.96368	−0.174154
$519$	−6.22486	−0.273241
$520$	−2.86793	−0.125767
$521$	10.3684	0.454250	0.227125	−	0.973866i	$-0.427067\pi$
$521$	10.3684	0.454250	0.227125	+	0.973866i	$0.427067\pi$
$522$	−0.961571	−0.0420868
$523$	18.8843	0.825754	0.412877	−	0.910787i	$-0.364524\pi$
$523$	18.8843	0.825754	0.412877	+	0.910787i	$0.364524\pi$
$524$	−9.20972	−0.402329
$525$	−11.8299	−0.516300
$526$	1.26365	0.0550977
$527$	−30.0592	−1.30940
$528$	−4.21423	−0.183401
$529$	−22.9462	−0.997660
$530$	−3.57653	−0.155354
$531$	−19.4505	−0.844080
$532$	8.83210	0.382920
$533$	−24.3073	−1.05287
$534$	−3.67552	−0.159055
$535$	1.56139	0.0675048
$536$	−10.1853	−0.439936
$537$	−46.3575	−2.00047
$538$	19.8337	0.855090
$539$	−35.1910	−1.51578
$540$	−1.55393	−0.0668704
$541$	−2.77574	−0.119339	−0.0596693	−	0.998218i	$-0.519005\pi$
$541$	−2.77574	−0.119339	−0.0596693	+	0.998218i	$0.519005\pi$
$542$	−11.2534	−0.483374
$543$	49.2999	2.11566
$544$	−5.18022	−0.222100
$545$	7.83377	0.335562
$546$	33.9274	1.45196
$547$	38.9675	1.66613	0.833064	−	0.553176i	$-0.186584\pi$
$547$	38.9675	1.66613	0.833064	+	0.553176i	$0.186584\pi$
$548$	−11.2959	−0.482537
$549$	16.5026	0.704313
$550$	1.82595	0.0778588
$551$	−0.712116	−0.0303371
$552$	0.535395	0.0227879
$553$	−42.3940	−1.80278
$554$	13.8413	0.588061
$555$	−1.78475	−0.0757582
$556$	−9.18054	−0.389342
$557$	−5.49865	−0.232985	−0.116493	−	0.993192i	$-0.537165\pi$
$557$	−5.49865	−0.232985	−0.116493	+	0.993192i	$0.537165\pi$
$558$	13.5012	0.571551
$559$	−31.4087	−1.32845
$560$	−5.12569	−0.216600
$561$	−21.8306	−0.921690
$562$	29.1862	1.23115
$563$	36.2516	1.52782	0.763912	−	0.645320i	$-0.223276\pi$
$563$	36.2516	1.52782	0.763912	+	0.645320i	$0.223276\pi$
$564$	−30.8691	−1.29983
$565$	1.88823	0.0794386
$566$	−5.31391	−0.223360
$567$	54.1608	2.27454
$568$	7.02748	0.294866
$569$	9.19206	0.385351	0.192676	−	0.981262i	$-0.438283\pi$
$569$	9.19206	0.385351	0.192676	+	0.981262i	$0.438283\pi$
$570$	3.97687	0.166573
$571$	19.6825	0.823688	0.411844	−	0.911254i	$-0.364885\pi$
$571$	19.6825	0.823688	0.411844	+	0.911254i	$0.364885\pi$
$572$	−5.23670	−0.218958
$573$	−26.1755	−1.09350
$574$	−43.4430	−1.81328
$575$	−0.231977	−0.00967410
$576$	2.32671	0.0969463
$577$	−3.53813	−0.147294	−0.0736471	−	0.997284i	$-0.523464\pi$
$577$	−3.53813	−0.147294	−0.0736471	+	0.997284i	$0.523464\pi$
$578$	−9.83464	−0.409067
$579$	20.4354	0.849265
$580$	0.413275	0.0171603
$581$	−14.0308	−0.582097
$582$	27.0316	1.12050
$583$	−6.53056	−0.270468
$584$	7.84968	0.324822
$585$	6.67285	0.275889
$586$	−24.4177	−1.00869
$587$	47.1302	1.94527	0.972636	−	0.232336i	$-0.0746370\pi$
$587$	47.1302	1.94527	0.972636	+	0.232336i	$0.0746370\pi$
$588$	44.4807	1.83435
$589$	9.99865	0.411987
$590$	8.35966	0.344162
$591$	40.6826	1.67346
$592$	−0.773298	−0.0317823
$593$	−3.98467	−0.163631	−0.0818154	−	0.996647i	$-0.526072\pi$
$593$	−3.98467	−0.163631	−0.0818154	+	0.996647i	$0.526072\pi$
$594$	−2.83739	−0.116420
$595$	−26.5522	−1.08853
$596$	−12.1799	−0.498907
$597$	−28.1372	−1.15158
$598$	0.665294	0.0272059
$599$	33.0504	1.35040	0.675201	−	0.737633i	$-0.264057\pi$
$599$	33.0504	1.35040	0.675201	+	0.737633i	$0.264057\pi$
$600$	−2.30797	−0.0942224
$601$	−36.8508	−1.50318	−0.751588	−	0.659633i	$-0.770712\pi$
$601$	−36.8508	−1.50318	−0.751588	+	0.659633i	$0.770712\pi$
$602$	−56.1349	−2.28789
$603$	23.6981	0.965063
$604$	−19.0556	−0.775360
$605$	−7.66590	−0.311663
$606$	−15.5065	−0.629908
$607$	27.5452	1.11802	0.559012	−	0.829160i	$-0.311181\pi$
$607$	27.5452	1.11802	0.559012	+	0.829160i	$0.311181\pi$
$608$	1.72311	0.0698811
$609$	−4.88901	−0.198113
$610$	−7.09267	−0.287174
$611$	−38.3587	−1.55183
$612$	12.0529	0.487208
$613$	26.4420	1.06798	0.533992	−	0.845490i	$-0.320691\pi$
$613$	26.4420	1.06798	0.533992	+	0.845490i	$0.320691\pi$
$614$	−29.2291	−1.17959
$615$	−19.5613	−0.788787
$616$	−9.35925	−0.377095
$617$	4.83808	0.194774	0.0973868	−	0.995247i	$-0.468952\pi$
$617$	4.83808	0.194774	0.0973868	+	0.995247i	$0.468952\pi$
$618$	9.76702	0.392887
$619$	14.2988	0.574717	0.287358	−	0.957823i	$-0.407223\pi$
$619$	14.2988	0.574717	0.287358	+	0.957823i	$0.407223\pi$
$620$	−5.80270	−0.233042
$621$	0.360475	0.0144654
$622$	8.05463	0.322961
$623$	−8.16285	−0.327038
$624$	6.61910	0.264976
$625$	1.00000	0.0400000
$626$	−15.8471	−0.633376
$627$	7.26157	0.289999
$628$	−11.3912	−0.454559
$629$	−4.00585	−0.159724
$630$	11.9260	0.475143
$631$	17.0071	0.677043	0.338522	−	0.940959i	$-0.390073\pi$
$631$	17.0071	0.677043	0.338522	+	0.940959i	$0.390073\pi$
$632$	−8.27089	−0.328998
$633$	−33.0240	−1.31259
$634$	−2.72043	−0.108042
$635$	20.4205	0.810364
$636$	8.25451	0.327312
$637$	55.2728	2.18999
$638$	0.754619	0.0298757
$639$	−16.3509	−0.646832
$640$	−1.00000	−0.0395285
$641$	5.83510	0.230472	0.115236	−	0.993338i	$-0.463237\pi$
$641$	5.83510	0.230472	0.115236	+	0.993338i	$0.463237\pi$
$642$	−3.60364	−0.142224
$643$	34.7747	1.37138	0.685690	−	0.727894i	$-0.259501\pi$
$643$	34.7747	1.37138	0.685690	+	0.727894i	$0.259501\pi$
$644$	1.18904	0.0468548
$645$	−25.2761	−0.995247
$646$	8.92606	0.351191
$647$	8.47425	0.333157	0.166579	−	0.986028i	$-0.446728\pi$
$647$	8.47425	0.333157	0.166579	+	0.986028i	$0.446728\pi$
$648$	10.5665	0.415093
$649$	15.2643	0.599177
$650$	−2.86793	−0.112490
$651$	68.6454	2.69043
$652$	−19.6319	−0.768845
$653$	0.0423644	0.00165785	0.000828923	−	1.00000i	$-0.499736\pi$
$653$	0.0423644	0.00165785	0.000828923		1.00000i	$0.499736\pi$
$654$	−18.0801	−0.706988
$655$	−9.20972	−0.359854
$656$	−8.47555	−0.330915
$657$	−18.2639	−0.712544
$658$	−68.5563	−2.67260
$659$	26.3834	1.02775	0.513876	−	0.857864i	$-0.328209\pi$
$659$	26.3834	1.02775	0.513876	+	0.857864i	$0.328209\pi$
$660$	−4.21423	−0.164039
$661$	−49.0691	−1.90857	−0.954283	−	0.298906i	$-0.903378\pi$
$661$	−49.0691	−1.90857	−0.954283	+	0.298906i	$0.903378\pi$
$662$	−15.5224	−0.603294
$663$	34.2883	1.33165
$664$	−2.73735	−0.106230
$665$	8.83210	0.342494
$666$	1.79924	0.0697192
$667$	−0.0958701	−0.00371211
$668$	19.5853	0.757778
$669$	−13.6093	−0.526164
$670$	−10.1853	−0.393491
$671$	−12.9509	−0.499962
$672$	11.8299	0.456349
$673$	48.2721	1.86075	0.930377	−	0.366605i	$-0.119480\pi$
$673$	48.2721	1.86075	0.930377	+	0.366605i	$0.119480\pi$
$674$	34.2266	1.31836
$675$	−1.55393	−0.0598107
$676$	−4.77496	−0.183652
$677$	26.8038	1.03016	0.515078	−	0.857143i	$-0.327763\pi$
$677$	26.8038	1.03016	0.515078	+	0.857143i	$0.327763\pi$
$678$	−4.35798	−0.167367
$679$	60.0336	2.30388
$680$	−5.18022	−0.198652
$681$	−2.37778	−0.0911168
$682$	−10.5954	−0.405720
$683$	−2.71524	−0.103896	−0.0519478	−	0.998650i	$-0.516543\pi$
$683$	−2.71524	−0.103896	−0.0519478	+	0.998650i	$0.516543\pi$
$684$	−4.00917	−0.153294
$685$	−11.2959	−0.431594
$686$	62.9059	2.40176
$687$	−56.5402	−2.15714
$688$	−10.9517	−0.417529
$689$	10.2572	0.390770
$690$	0.535395	0.0203821
$691$	−20.7474	−0.789268	−0.394634	−	0.918838i	$-0.629129\pi$
$691$	−20.7474	−0.789268	−0.394634	+	0.918838i	$0.629129\pi$
$692$	−2.69712	−0.102529
$693$	21.7763	0.827213
$694$	3.94198	0.149635
$695$	−9.18054	−0.348238
$696$	−0.953824	−0.0361546
$697$	−43.9052	−1.66303
$698$	24.9824	0.945599
$699$	−0.0601408	−0.00227474
$700$	−5.12569	−0.193733
$701$	0.0465657	0.00175876	0.000879382	−	1.00000i	$-0.499720\pi$
$701$	0.0465657	0.00175876	0.000879382		1.00000i	$0.499720\pi$
$702$	4.45656	0.168202
$703$	1.33247	0.0502552
$704$	−1.82595	−0.0688181
$705$	−30.8691	−1.16260
$706$	21.7570	0.818834
$707$	−34.4379	−1.29517
$708$	−19.2938	−0.725106
$709$	−12.0686	−0.453248	−0.226624	−	0.973982i	$-0.572769\pi$
$709$	−12.0686	−0.453248	−0.226624	+	0.973982i	$0.572769\pi$
$710$	7.02748	0.263737
$711$	19.2440	0.721706
$712$	−1.59254	−0.0596829
$713$	1.34609	0.0504115
$714$	61.2815	2.29340
$715$	−5.23670	−0.195842
$716$	−20.0859	−0.750644
$717$	53.5523	1.99995
$718$	−25.8043	−0.963007
$719$	−24.4646	−0.912377	−0.456188	−	0.889883i	$-0.650786\pi$
$719$	−24.4646	−0.912377	−0.456188	+	0.889883i	$0.650786\pi$
$720$	2.32671	0.0867114
$721$	21.6912	0.807824
$722$	16.0309	0.596609
$723$	24.2373	0.901393
$724$	21.3607	0.793866
$725$	0.413275	0.0153486
$726$	17.6927	0.656636
$727$	−32.2257	−1.19519	−0.597593	−	0.801799i	$-0.703876\pi$
$727$	−32.2257	−1.19519	−0.597593	+	0.801799i	$0.703876\pi$
$728$	14.7001	0.544823
$729$	−13.8261	−0.512077
$730$	7.84968	0.290530
$731$	−56.7321	−2.09831
$732$	16.3696	0.605039
$733$	35.2482	1.30192	0.650960	−	0.759112i	$-0.274366\pi$
$733$	35.2482	1.30192	0.650960	+	0.759112i	$0.274366\pi$
$734$	−8.98516	−0.331648
$735$	44.4807	1.64070
$736$	0.231977	0.00855078
$737$	−18.5978	−0.685057
$738$	19.7202	0.725909
$739$	41.8010	1.53768	0.768838	−	0.639444i	$-0.220835\pi$
$739$	41.8010	1.53768	0.768838	+	0.639444i	$0.220835\pi$
$740$	−0.773298	−0.0284270
$741$	−11.4054	−0.418988
$742$	18.3322	0.672995
$743$	1.82320	0.0668865	0.0334433	−	0.999441i	$-0.489353\pi$
$743$	1.82320	0.0668865	0.0334433	+	0.999441i	$0.489353\pi$
$744$	13.3924	0.490990
$745$	−12.1799	−0.446236
$746$	18.0327	0.660226
$747$	6.36903	0.233031
$748$	−9.45882	−0.345849
$749$	−8.00321	−0.292431
$750$	−2.30797	−0.0842750
$751$	18.9084	0.689977	0.344989	−	0.938607i	$-0.387883\pi$
$751$	18.9084	0.689977	0.344989	+	0.938607i	$0.387883\pi$
$752$	−13.3750	−0.487737
$753$	−33.1307	−1.20735
$754$	−1.18524	−0.0431640
$755$	−19.0556	−0.693503
$756$	7.96495	0.289682
$757$	−25.6931	−0.933830	−0.466915	−	0.884302i	$-0.654635\pi$
$757$	−25.6931	−0.933830	−0.466915	+	0.884302i	$0.654635\pi$
$758$	12.1860	0.442617
$759$	0.977604	0.0354848
$760$	1.72311	0.0625036
$761$	−12.6870	−0.459905	−0.229952	−	0.973202i	$-0.573857\pi$
$761$	−12.6870	−0.459905	−0.229952	+	0.973202i	$0.573857\pi$
$762$	−47.1299	−1.70734
$763$	−40.1535	−1.45365
$764$	−11.3414	−0.410316
$765$	12.0529	0.435772
$766$	−28.3229	−1.02335
$767$	−23.9749	−0.865685
$768$	2.30797	0.0832816
$769$	−29.7039	−1.07115	−0.535575	−	0.844488i	$-0.679905\pi$
$769$	−29.7039	−1.07115	−0.535575	+	0.844488i	$0.679905\pi$
$770$	−9.35925	−0.337284
$771$	55.7868	2.00911
$772$	8.85428	0.318672
$773$	−18.8053	−0.676380	−0.338190	−	0.941078i	$-0.609815\pi$
$773$	−18.8053	−0.676380	−0.338190	+	0.941078i	$0.609815\pi$
$774$	25.4814	0.915911
$775$	−5.80270	−0.208439
$776$	11.7123	0.420447
$777$	9.14805	0.328184
$778$	−14.5586	−0.521952
$779$	14.6043	0.523252
$780$	6.61910	0.237002
$781$	12.8318	0.459159
$782$	1.20169	0.0429723
$783$	−0.642199	−0.0229503
$784$	19.2727	0.688310
$785$	−11.3912	−0.406570
$786$	21.2557	0.758167
$787$	1.57307	0.0560741	0.0280370	−	0.999607i	$-0.491074\pi$
$787$	1.57307	0.0560741	0.0280370	+	0.999607i	$0.491074\pi$
$788$	17.6270	0.627937
$789$	−2.91646	−0.103829
$790$	−8.27089	−0.294265
$791$	−9.67849	−0.344128
$792$	4.24846	0.150962
$793$	20.3413	0.722341
$794$	−33.7418	−1.19745
$795$	8.25451	0.292757
$796$	−12.1913	−0.432110
$797$	8.26168	0.292644	0.146322	−	0.989237i	$-0.453256\pi$
$797$	8.26168	0.292644	0.146322	+	0.989237i	$0.453256\pi$
$798$	−20.3842	−0.721593
$799$	−69.2856	−2.45115
$800$	−1.00000	−0.0353553
$801$	3.70537	0.130923
$802$	−1.00000	−0.0353112
$803$	14.3331	0.505805
$804$	23.5072	0.829036
$805$	1.18904	0.0419082
$806$	16.6417	0.586180
$807$	−45.7754	−1.61137
$808$	−6.71868	−0.236362
$809$	−10.7860	−0.379217	−0.189609	−	0.981860i	$-0.560722\pi$
$809$	−10.7860	−0.379217	−0.189609	+	0.981860i	$0.560722\pi$
$810$	10.5665	0.371271
$811$	−14.1210	−0.495854	−0.247927	−	0.968779i	$-0.579749\pi$
$811$	−14.1210	−0.495854	−0.247927	+	0.968779i	$0.579749\pi$
$812$	−2.11832	−0.0743384
$813$	25.9724	0.910892
$814$	−1.41200	−0.0494907
$815$	−19.6319	−0.687676
$816$	11.9558	0.418536
$817$	18.8709	0.660210
$818$	−8.73493	−0.305410
$819$	−34.2030	−1.19515
$820$	−8.47555	−0.295979
$821$	−34.9677	−1.22038	−0.610190	−	0.792255i	$-0.708907\pi$
$821$	−34.9677	−1.22038	−0.610190	+	0.792255i	$0.708907\pi$
$822$	26.0705	0.909315
$823$	−28.7138	−1.00090	−0.500451	−	0.865765i	$-0.666832\pi$
$823$	−28.7138	−1.00090	−0.500451	+	0.865765i	$0.666832\pi$
$824$	4.23187	0.147424
$825$	−4.21423	−0.146721
$826$	−42.8490	−1.49091
$827$	15.4099	0.535855	0.267928	−	0.963439i	$-0.413661\pi$
$827$	15.4099	0.535855	0.267928	+	0.963439i	$0.413661\pi$
$828$	−0.539743	−0.0187574
$829$	−43.5715	−1.51330	−0.756651	−	0.653819i	$-0.773166\pi$
$829$	−43.5715	−1.51330	−0.756651	+	0.653819i	$0.773166\pi$
$830$	−2.73735	−0.0950150
$831$	−31.9453	−1.10817
$832$	2.86793	0.0994277
$833$	99.8367	3.45913
$834$	21.1884	0.733694
$835$	19.5853	0.677777
$836$	3.14630	0.108817
$837$	9.01697	0.311672
$838$	4.49937	0.155428
$839$	−40.4824	−1.39761	−0.698803	−	0.715314i	$-0.746284\pi$
$839$	−40.4824	−1.39761	−0.698803	+	0.715314i	$0.746284\pi$
$840$	11.8299	0.408171
$841$	−28.8292	−0.994110
$842$	12.0532	0.415382
$843$	−67.3609	−2.32003
$844$	−14.3087	−0.492526
$845$	−4.77496	−0.164264
$846$	31.1199	1.06992
$847$	39.2930	1.35012
$848$	3.57653	0.122818
$849$	12.2643	0.420910
$850$	−5.18022	−0.177680
$851$	0.179387	0.00614931
$852$	−16.2192	−0.555660
$853$	54.6849	1.87237	0.936187	−	0.351501i	$-0.114329\pi$
$853$	54.6849	1.87237	0.936187	+	0.351501i	$0.114329\pi$
$854$	36.3548	1.24404
$855$	−4.00917	−0.137111
$856$	−1.56139	−0.0533673
$857$	−7.45735	−0.254738	−0.127369	−	0.991855i	$-0.540653\pi$
$857$	−7.45735	−0.254738	−0.127369	+	0.991855i	$0.540653\pi$
$858$	12.0861	0.412614
$859$	−27.1284	−0.925610	−0.462805	−	0.886460i	$-0.653157\pi$
$859$	−27.1284	−0.925610	−0.462805	+	0.886460i	$0.653157\pi$
$860$	−10.9517	−0.373449
$861$	100.265	3.41702
$862$	−16.8432	−0.573682
$863$	38.9673	1.32646	0.663232	−	0.748414i	$-0.269184\pi$
$863$	38.9673	1.32646	0.663232	+	0.748414i	$0.269184\pi$
$864$	1.55393	0.0528657
$865$	−2.69712	−0.0917048
$866$	−7.54922	−0.256533
$867$	22.6980	0.770865
$868$	29.7428	1.00954
$869$	−15.1022	−0.512308
$870$	−0.953824	−0.0323377
$871$	29.2106	0.989764
$872$	−7.83377	−0.265285
$873$	−27.2511	−0.922311
$874$	−0.399720	−0.0135207
$875$	−5.12569	−0.173280
$876$	−18.1168	−0.612110
$877$	43.9381	1.48368	0.741842	−	0.670574i	$-0.233952\pi$
$877$	43.9381	1.48368	0.741842	+	0.670574i	$0.233952\pi$
$878$	−23.5893	−0.796100
$879$	56.3552	1.90081
$880$	−1.82595	−0.0615528
$881$	−2.74025	−0.0923215	−0.0461608	−	0.998934i	$-0.514699\pi$
$881$	−2.74025	−0.0923215	−0.0461608	+	0.998934i	$0.514699\pi$
$882$	−44.8420	−1.50991
$883$	18.4545	0.621045	0.310523	−	0.950566i	$-0.399496\pi$
$883$	18.4545	0.621045	0.310523	+	0.950566i	$0.399496\pi$
$884$	14.8565	0.499679
$885$	−19.2938	−0.648554
$886$	−6.87149	−0.230852
$887$	4.12679	0.138564	0.0692820	−	0.997597i	$-0.477929\pi$
$887$	4.12679	0.138564	0.0692820	+	0.997597i	$0.477929\pi$
$888$	1.78475	0.0598921
$889$	−104.669	−3.51049
$890$	−1.59254	−0.0533820
$891$	19.2940	0.646373
$892$	−5.89664	−0.197434
$893$	23.0466	0.771225
$894$	28.1107	0.940163
$895$	−20.0859	−0.671396
$896$	5.12569	0.171237
$897$	−1.53548	−0.0512681
$898$	−7.37577	−0.246133
$899$	−2.39811	−0.0799813
$900$	2.32671	0.0775571
$901$	18.5272	0.617230
$902$	−15.4759	−0.515292
$903$	129.558	4.31141
$904$	−1.88823	−0.0628017
$905$	21.3607	0.710055
$906$	43.9796	1.46112
$907$	−1.81472	−0.0602568	−0.0301284	−	0.999546i	$-0.509592\pi$
$907$	−1.81472	−0.0602568	−0.0301284	+	0.999546i	$0.509592\pi$
$908$	−1.03025	−0.0341900
$909$	15.6324	0.518495
$910$	14.7001	0.487305
$911$	47.8218	1.58441	0.792204	−	0.610256i	$-0.208934\pi$
$911$	47.8218	1.58441	0.792204	+	0.610256i	$0.208934\pi$
$912$	−3.97687	−0.131687
$913$	−4.99827	−0.165419
$914$	37.2443	1.23193
$915$	16.3696	0.541164
$916$	−24.4978	−0.809431
$917$	47.2062	1.55889
$918$	8.04968	0.265679
$919$	−10.0624	−0.331928	−0.165964	−	0.986132i	$-0.553074\pi$
$919$	−10.0624	−0.331928	−0.165964	+	0.986132i	$0.553074\pi$
$920$	0.231977	0.00764805
$921$	67.4598	2.22288
$922$	17.2287	0.567397
$923$	−20.1543	−0.663388
$924$	21.6008	0.710616
$925$	−0.773298	−0.0254259
$926$	9.75535	0.320581
$927$	−9.84634	−0.323396
$928$	−0.413275	−0.0135664
$929$	38.7262	1.27056	0.635282	−	0.772280i	$-0.280884\pi$
$929$	38.7262	1.27056	0.635282	+	0.772280i	$0.280884\pi$
$930$	13.3924	0.439155
$931$	−33.2089	−1.08838
$932$	−0.0260579	−0.000853556 0
$933$	−18.5898	−0.608603
$934$	2.98148	0.0975568
$935$	−9.45882	−0.309336
$936$	−6.67285	−0.218109
$937$	−28.7252	−0.938410	−0.469205	−	0.883089i	$-0.655459\pi$
$937$	−28.7252	−0.938410	−0.469205	+	0.883089i	$0.655459\pi$
$938$	52.2064	1.70460
$939$	36.5745	1.19356
$940$	−13.3750	−0.436246
$941$	3.52295	0.114845	0.0574225	−	0.998350i	$-0.481712\pi$
$941$	3.52295	0.114845	0.0574225	+	0.998350i	$0.481712\pi$
$942$	26.2906	0.856593
$943$	1.96613	0.0640260
$944$	−8.35966	−0.272084
$945$	7.96495	0.259100
$946$	−19.9972	−0.650166
$947$	52.5309	1.70702	0.853512	−	0.521073i	$-0.174468\pi$
$947$	52.5309	1.70702	0.853512	+	0.521073i	$0.174468\pi$
$948$	19.0889	0.619980
$949$	−22.5123	−0.730782
$950$	1.72311	0.0559049
$951$	6.27867	0.203600
$952$	26.5522	0.860561
$953$	21.0748	0.682680	0.341340	−	0.939940i	$-0.389119\pi$
$953$	21.0748	0.682680	0.341340	+	0.939940i	$0.389119\pi$
$954$	−8.32155	−0.269420
$955$	−11.3414	−0.366998
$956$	23.2032	0.750446
$957$	−1.74164	−0.0562991
$958$	−0.647726	−0.0209271
$959$	57.8992	1.86966
$960$	2.30797	0.0744893
$961$	2.67127	0.0861700
$962$	2.21777	0.0715037
$963$	3.63291	0.117069
$964$	10.5016	0.338232
$965$	8.85428	0.285029
$966$	−2.74427	−0.0882953
$967$	16.9212	0.544150	0.272075	−	0.962276i	$-0.412290\pi$
$967$	16.9212	0.544150	0.272075	+	0.962276i	$0.412290\pi$
$968$	7.66590	0.246392
$969$	−20.6010	−0.661801
$970$	11.7123	0.376059
$971$	8.87437	0.284792	0.142396	−	0.989810i	$-0.454519\pi$
$971$	8.87437	0.284792	0.142396	+	0.989810i	$0.454519\pi$
$972$	−19.7255	−0.632694
$973$	47.0566	1.50857
$974$	5.61871	0.180035
$975$	6.61910	0.211981
$976$	7.09267	0.227031
$977$	−26.8400	−0.858689	−0.429345	−	0.903141i	$-0.641255\pi$
$977$	−26.8400	−0.858689	−0.429345	+	0.903141i	$0.641255\pi$
$978$	45.3098	1.44885
$979$	−2.90789	−0.0929367
$980$	19.2727	0.615643
$981$	18.2269	0.581941
$982$	−31.2742	−0.997999
$983$	17.7900	0.567412	0.283706	−	0.958911i	$-0.408436\pi$
$983$	17.7900	0.567412	0.283706	+	0.958911i	$0.408436\pi$
$984$	19.5613	0.623591
$985$	17.6270	0.561644
$986$	−2.14085	−0.0681786
$987$	158.226	5.03638
$988$	−4.94175	−0.157218
$989$	2.54054	0.0807844
$990$	4.24846	0.135025
$991$	13.5584	0.430698	0.215349	−	0.976537i	$-0.430911\pi$
$991$	13.5584	0.430698	0.215349	+	0.976537i	$0.430911\pi$
$992$	5.80270	0.184236
$993$	35.8251	1.13688
$994$	−36.0207	−1.14251
$995$	−12.1913	−0.386491
$996$	6.31772	0.200185
$997$	−7.95242	−0.251856	−0.125928	−	0.992039i	$-0.540191\pi$
$997$	−7.95242	−0.251856	−0.125928	+	0.992039i	$0.540191\pi$
$998$	−12.9780	−0.410812
$999$	1.20165	0.0380185

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.i.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.i.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.30797 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.30797 q^{6} -5.12569 q^{7} -1.00000 q^{8} +2.32671 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.30797 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.30797 q^{6} -5.12569 q^{7} -1.00000 q^{8} +2.32671 q^{9} -1.00000 q^{10} -1.82595 q^{11} +2.30797 q^{12} +2.86793 q^{13} +5.12569 q^{14} +2.30797 q^{15} +1.00000 q^{16} +5.18022 q^{17} -2.32671 q^{18} -1.72311 q^{19} +1.00000 q^{20} -11.8299 q^{21} +1.82595 q^{22} -0.231977 q^{23} -2.30797 q^{24} +1.00000 q^{25} -2.86793 q^{26} -1.55393 q^{27} -5.12569 q^{28} +0.413275 q^{29} -2.30797 q^{30} -5.80270 q^{31} -1.00000 q^{32} -4.21423 q^{33} -5.18022 q^{34} -5.12569 q^{35} +2.32671 q^{36} -0.773298 q^{37} +1.72311 q^{38} +6.61910 q^{39} -1.00000 q^{40} -8.47555 q^{41} +11.8299 q^{42} -10.9517 q^{43} -1.82595 q^{44} +2.32671 q^{45} +0.231977 q^{46} -13.3750 q^{47} +2.30797 q^{48} +19.2727 q^{49} -1.00000 q^{50} +11.9558 q^{51} +2.86793 q^{52} +3.57653 q^{53} +1.55393 q^{54} -1.82595 q^{55} +5.12569 q^{56} -3.97687 q^{57} -0.413275 q^{58} -8.35966 q^{59} +2.30797 q^{60} +7.09267 q^{61} +5.80270 q^{62} -11.9260 q^{63} +1.00000 q^{64} +2.86793 q^{65} +4.21423 q^{66} +10.1853 q^{67} +5.18022 q^{68} -0.535395 q^{69} +5.12569 q^{70} -7.02748 q^{71} -2.32671 q^{72} -7.84968 q^{73} +0.773298 q^{74} +2.30797 q^{75} -1.72311 q^{76} +9.35925 q^{77} -6.61910 q^{78} +8.27089 q^{79} +1.00000 q^{80} -10.5665 q^{81} +8.47555 q^{82} +2.73735 q^{83} -11.8299 q^{84} +5.18022 q^{85} +10.9517 q^{86} +0.953824 q^{87} +1.82595 q^{88} +1.59254 q^{89} -2.32671 q^{90} -14.7001 q^{91} -0.231977 q^{92} -13.3924 q^{93} +13.3750 q^{94} -1.72311 q^{95} -2.30797 q^{96} -11.7123 q^{97} -19.2727 q^{98} -4.24846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 4 q^{3} + 10 q^{4} + 10 q^{5} + 4 q^{6} - 3 q^{7} - 10 q^{8} + 6 q^{9}+O(q^{10}) \) 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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