LMFDB - Embedded newform 4010.2.a.h.1.5

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 2x^{8} - 8x^{7} + 16x^{6} + 17x^{5} - 36x^{4} - 4x^{3} + 17x^{2} - 2 $ x^9 - 2x^8 - 8x^7 + 16x^6 + 17x^5 - 36x^4 - 4x^3 + 17*x^2 - 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.23442$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.375168 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.375168 q^{6} +3.43840 q^{7} +1.00000 q^{8} -2.85925 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.375168 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.375168 q^{6} +3.43840 q^{7} +1.00000 q^{8} -2.85925 q^{9} +1.00000 q^{10} -3.38583 q^{11} -0.375168 q^{12} -5.75656 q^{13} +3.43840 q^{14} -0.375168 q^{15} +1.00000 q^{16} -0.0635395 q^{17} -2.85925 q^{18} -1.00803 q^{19} +1.00000 q^{20} -1.28998 q^{21} -3.38583 q^{22} -3.87690 q^{23} -0.375168 q^{24} +1.00000 q^{25} -5.75656 q^{26} +2.19820 q^{27} +3.43840 q^{28} +2.35153 q^{29} -0.375168 q^{30} -6.49127 q^{31} +1.00000 q^{32} +1.27026 q^{33} -0.0635395 q^{34} +3.43840 q^{35} -2.85925 q^{36} -5.12976 q^{37} -1.00803 q^{38} +2.15968 q^{39} +1.00000 q^{40} -10.6118 q^{41} -1.28998 q^{42} +1.98346 q^{43} -3.38583 q^{44} -2.85925 q^{45} -3.87690 q^{46} -11.7625 q^{47} -0.375168 q^{48} +4.82258 q^{49} +1.00000 q^{50} +0.0238380 q^{51} -5.75656 q^{52} +0.644829 q^{53} +2.19820 q^{54} -3.38583 q^{55} +3.43840 q^{56} +0.378181 q^{57} +2.35153 q^{58} +7.31355 q^{59} -0.375168 q^{60} -3.20714 q^{61} -6.49127 q^{62} -9.83123 q^{63} +1.00000 q^{64} -5.75656 q^{65} +1.27026 q^{66} -2.21850 q^{67} -0.0635395 q^{68} +1.45449 q^{69} +3.43840 q^{70} +5.30701 q^{71} -2.85925 q^{72} +9.80955 q^{73} -5.12976 q^{74} -0.375168 q^{75} -1.00803 q^{76} -11.6418 q^{77} +2.15968 q^{78} -14.8113 q^{79} +1.00000 q^{80} +7.75305 q^{81} -10.6118 q^{82} +0.940494 q^{83} -1.28998 q^{84} -0.0635395 q^{85} +1.98346 q^{86} -0.882219 q^{87} -3.38583 q^{88} +14.4035 q^{89} -2.85925 q^{90} -19.7933 q^{91} -3.87690 q^{92} +2.43532 q^{93} -11.7625 q^{94} -1.00803 q^{95} -0.375168 q^{96} -2.27297 q^{97} +4.82258 q^{98} +9.68093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9} + 9 q^{10} - 11 q^{11} - 4 q^{12} - 14 q^{13} - 7 q^{14} - 4 q^{15} + 9 q^{16} - 13 q^{17} - 7 q^{18} - 11 q^{19} + 9 q^{20} - 8 q^{21} - 11 q^{22} - 9 q^{23} - 4 q^{24} + 9 q^{25} - 14 q^{26} - 4 q^{27} - 7 q^{28} - 20 q^{29} - 4 q^{30} - 11 q^{31} + 9 q^{32} + 4 q^{33} - 13 q^{34} - 7 q^{35} - 7 q^{36} - 25 q^{37} - 11 q^{38} - 8 q^{39} + 9 q^{40} - 29 q^{41} - 8 q^{42} - 11 q^{43} - 11 q^{44} - 7 q^{45} - 9 q^{46} - 3 q^{47} - 4 q^{48} - 18 q^{49} + 9 q^{50} + q^{51} - 14 q^{52} - 9 q^{53} - 4 q^{54} - 11 q^{55} - 7 q^{56} - 17 q^{57} - 20 q^{58} - 10 q^{59} - 4 q^{60} - 10 q^{61} - 11 q^{62} + 16 q^{63} + 9 q^{64} - 14 q^{65} + 4 q^{66} - 16 q^{67} - 13 q^{68} + 5 q^{69} - 7 q^{70} - 8 q^{71} - 7 q^{72} - 22 q^{73} - 25 q^{74} - 4 q^{75} - 11 q^{76} - 15 q^{77} - 8 q^{78} - 9 q^{79} + 9 q^{80} - 15 q^{81} - 29 q^{82} + 11 q^{83} - 8 q^{84} - 13 q^{85} - 11 q^{86} + 12 q^{87} - 11 q^{88} - 28 q^{89} - 7 q^{90} - 6 q^{91} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 4 q^{96} - 28 q^{97} - 18 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9 + 9 * q^10 - 11 * q^11 - 4 * q^12 - 14 * q^13 - 7 * q^14 - 4 * q^15 + 9 * q^16 - 13 * q^17 - 7 * q^18 - 11 * q^19 + 9 * q^20 - 8 * q^21 - 11 * q^22 - 9 * q^23 - 4 * q^24 + 9 * q^25 - 14 * q^26 - 4 * q^27 - 7 * q^28 - 20 * q^29 - 4 * q^30 - 11 * q^31 + 9 * q^32 + 4 * q^33 - 13 * q^34 - 7 * q^35 - 7 * q^36 - 25 * q^37 - 11 * q^38 - 8 * q^39 + 9 * q^40 - 29 * q^41 - 8 * q^42 - 11 * q^43 - 11 * q^44 - 7 * q^45 - 9 * q^46 - 3 * q^47 - 4 * q^48 - 18 * q^49 + 9 * q^50 + q^51 - 14 * q^52 - 9 * q^53 - 4 * q^54 - 11 * q^55 - 7 * q^56 - 17 * q^57 - 20 * q^58 - 10 * q^59 - 4 * q^60 - 10 * q^61 - 11 * q^62 + 16 * q^63 + 9 * q^64 - 14 * q^65 + 4 * q^66 - 16 * q^67 - 13 * q^68 + 5 * q^69 - 7 * q^70 - 8 * q^71 - 7 * q^72 - 22 * q^73 - 25 * q^74 - 4 * q^75 - 11 * q^76 - 15 * q^77 - 8 * q^78 - 9 * q^79 + 9 * q^80 - 15 * q^81 - 29 * q^82 + 11 * q^83 - 8 * q^84 - 13 * q^85 - 11 * q^86 + 12 * q^87 - 11 * q^88 - 28 * q^89 - 7 * q^90 - 6 * q^91 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 4 * q^96 - 28 * q^97 - 18 * q^98 + 9 * 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
$3$	−0.375168	−0.216604	−0.108302	−	0.994118i	$-0.534541\pi$
$3$	−0.375168	−0.216604	−0.108302	+	0.994118i	$0.534541\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.375168	−0.153162
$7$	3.43840	1.29959	0.649796	−	0.760109i	$-0.274854\pi$
$7$	3.43840	1.29959	0.649796	+	0.760109i	$0.274854\pi$
$8$	1.00000	0.353553
$9$	−2.85925	−0.953083
$10$	1.00000	0.316228
$11$	−3.38583	−1.02087	−0.510433	−	0.859917i	$-0.670515\pi$
$11$	−3.38583	−1.02087	−0.510433	+	0.859917i	$0.670515\pi$
$12$	−0.375168	−0.108302
$13$	−5.75656	−1.59658	−0.798291	−	0.602272i	$-0.794262\pi$
$13$	−5.75656	−1.59658	−0.798291	+	0.602272i	$0.794262\pi$
$14$	3.43840	0.918950
$15$	−0.375168	−0.0968680
$16$	1.00000	0.250000
$17$	−0.0635395	−0.0154106	−0.00770530	−	0.999970i	$-0.502453\pi$
$17$	−0.0635395	−0.0154106	−0.00770530	+	0.999970i	$0.502453\pi$
$18$	−2.85925	−0.673931
$19$	−1.00803	−0.231258	−0.115629	−	0.993292i	$-0.536888\pi$
$19$	−1.00803	−0.231258	−0.115629	+	0.993292i	$0.536888\pi$
$20$	1.00000	0.223607
$21$	−1.28998	−0.281496
$22$	−3.38583	−0.721861
$23$	−3.87690	−0.808390	−0.404195	−	0.914673i	$-0.632448\pi$
$23$	−3.87690	−0.808390	−0.404195	+	0.914673i	$0.632448\pi$
$24$	−0.375168	−0.0765809
$25$	1.00000	0.200000
$26$	−5.75656	−1.12895
$27$	2.19820	0.423045
$28$	3.43840	0.649796
$29$	2.35153	0.436668	0.218334	−	0.975874i	$-0.429938\pi$
$29$	2.35153	0.436668	0.218334	+	0.975874i	$0.429938\pi$
$30$	−0.375168	−0.0684961
$31$	−6.49127	−1.16587	−0.582933	−	0.812520i	$-0.698095\pi$
$31$	−6.49127	−1.16587	−0.582933	+	0.812520i	$0.698095\pi$
$32$	1.00000	0.176777
$33$	1.27026	0.221123
$34$	−0.0635395	−0.0108969
$35$	3.43840	0.581195
$36$	−2.85925	−0.476541
$37$	−5.12976	−0.843327	−0.421663	−	0.906752i	$-0.638554\pi$
$37$	−5.12976	−0.843327	−0.421663	+	0.906752i	$0.638554\pi$
$38$	−1.00803	−0.163524
$39$	2.15968	0.345825
$40$	1.00000	0.158114
$41$	−10.6118	−1.65729	−0.828644	−	0.559776i	$-0.810887\pi$
$41$	−10.6118	−1.65729	−0.828644	+	0.559776i	$0.810887\pi$
$42$	−1.28998	−0.199048
$43$	1.98346	0.302474	0.151237	−	0.988498i	$-0.451674\pi$
$43$	1.98346	0.302474	0.151237	+	0.988498i	$0.451674\pi$
$44$	−3.38583	−0.510433
$45$	−2.85925	−0.426232
$46$	−3.87690	−0.571618
$47$	−11.7625	−1.71573	−0.857866	−	0.513873i	$-0.828210\pi$
$47$	−11.7625	−1.71573	−0.857866	+	0.513873i	$0.828210\pi$
$48$	−0.375168	−0.0541509
$49$	4.82258	0.688940
$50$	1.00000	0.141421
$51$	0.0238380	0.00333799
$52$	−5.75656	−0.798291
$53$	0.644829	0.0885740	0.0442870	−	0.999019i	$-0.485898\pi$
$53$	0.644829	0.0885740	0.0442870	+	0.999019i	$0.485898\pi$
$54$	2.19820	0.299138
$55$	−3.38583	−0.456545
$56$	3.43840	0.459475
$57$	0.378181	0.0500912
$58$	2.35153	0.308771
$59$	7.31355	0.952143	0.476071	−	0.879407i	$-0.342060\pi$
$59$	7.31355	0.952143	0.476071	+	0.879407i	$0.342060\pi$
$60$	−0.375168	−0.0484340
$61$	−3.20714	−0.410632	−0.205316	−	0.978696i	$-0.565822\pi$
$61$	−3.20714	−0.410632	−0.205316	+	0.978696i	$0.565822\pi$
$62$	−6.49127	−0.824392
$63$	−9.83123	−1.23862
$64$	1.00000	0.125000
$65$	−5.75656	−0.714013
$66$	1.27026	0.156358
$67$	−2.21850	−0.271033	−0.135517	−	0.990775i	$-0.543269\pi$
$67$	−2.21850	−0.271033	−0.135517	+	0.990775i	$0.543269\pi$
$68$	−0.0635395	−0.00770530
$69$	1.45449	0.175100
$70$	3.43840	0.410967
$71$	5.30701	0.629827	0.314913	−	0.949120i	$-0.398025\pi$
$71$	5.30701	0.629827	0.314913	+	0.949120i	$0.398025\pi$
$72$	−2.85925	−0.336966
$73$	9.80955	1.14812	0.574060	−	0.818813i	$-0.305367\pi$
$73$	9.80955	1.14812	0.574060	+	0.818813i	$0.305367\pi$
$74$	−5.12976	−0.596322
$75$	−0.375168	−0.0433207
$76$	−1.00803	−0.115629
$77$	−11.6418	−1.32671
$78$	2.15968	0.244535
$79$	−14.8113	−1.66641	−0.833203	−	0.552967i	$-0.813496\pi$
$79$	−14.8113	−1.66641	−0.833203	+	0.552967i	$0.813496\pi$
$80$	1.00000	0.111803
$81$	7.75305	0.861450
$82$	−10.6118	−1.17188
$83$	0.940494	0.103233	0.0516163	−	0.998667i	$-0.483563\pi$
$83$	0.940494	0.103233	0.0516163	+	0.998667i	$0.483563\pi$
$84$	−1.28998	−0.140748
$85$	−0.0635395	−0.00689183
$86$	1.98346	0.213882
$87$	−0.882219	−0.0945838
$88$	−3.38583	−0.360931
$89$	14.4035	1.52677	0.763383	−	0.645946i	$-0.223537\pi$
$89$	14.4035	1.52677	0.763383	+	0.645946i	$0.223537\pi$
$90$	−2.85925	−0.301391
$91$	−19.7933	−2.07491
$92$	−3.87690	−0.404195
$93$	2.43532	0.252531
$94$	−11.7625	−1.21321
$95$	−1.00803	−0.103422
$96$	−0.375168	−0.0382905
$97$	−2.27297	−0.230785	−0.115392	−	0.993320i	$-0.536813\pi$
$97$	−2.27297	−0.230785	−0.115392	+	0.993320i	$0.536813\pi$
$98$	4.82258	0.487154
$99$	9.68093	0.972970
$100$	1.00000	0.100000
$101$	6.39639	0.636465	0.318232	−	0.948013i	$-0.396911\pi$
$101$	6.39639	0.636465	0.318232	+	0.948013i	$0.396911\pi$
$102$	0.0238380	0.00236031
$103$	3.49942	0.344809	0.172404	−	0.985026i	$-0.444846\pi$
$103$	3.49942	0.344809	0.172404	+	0.985026i	$0.444846\pi$
$104$	−5.75656	−0.564477
$105$	−1.28998	−0.125889
$106$	0.644829	0.0626313
$107$	−11.4300	−1.10498	−0.552491	−	0.833519i	$-0.686323\pi$
$107$	−11.4300	−1.10498	−0.552491	+	0.833519i	$0.686323\pi$
$108$	2.19820	0.211522
$109$	−0.0536094	−0.00513485	−0.00256742	−	0.999997i	$-0.500817\pi$
$109$	−0.0536094	−0.00513485	−0.00256742	+	0.999997i	$0.500817\pi$
$110$	−3.38583	−0.322826
$111$	1.92452	0.182668
$112$	3.43840	0.324898
$113$	0.155014	0.0145825	0.00729123	−	0.999973i	$-0.497679\pi$
$113$	0.155014	0.0145825	0.00729123	+	0.999973i	$0.497679\pi$
$114$	0.378181	0.0354199
$115$	−3.87690	−0.361523
$116$	2.35153	0.218334
$117$	16.4594	1.52168
$118$	7.31355	0.673267
$119$	−0.218474	−0.0200275
$120$	−0.375168	−0.0342480
$121$	0.463848	0.0421680
$122$	−3.20714	−0.290361
$123$	3.98122	0.358974
$124$	−6.49127	−0.582933
$125$	1.00000	0.0894427
$126$	−9.83123	−0.875836
$127$	−10.9726	−0.973661	−0.486831	−	0.873496i	$-0.661847\pi$
$127$	−10.9726	−0.973661	−0.486831	+	0.873496i	$0.661847\pi$
$128$	1.00000	0.0883883
$129$	−0.744130	−0.0655170
$130$	−5.75656	−0.504884
$131$	6.27064	0.547869	0.273934	−	0.961748i	$-0.411675\pi$
$131$	6.27064	0.547869	0.273934	+	0.961748i	$0.411675\pi$
$132$	1.27026	0.110562
$133$	−3.46600	−0.300541
$134$	−2.21850	−0.191650
$135$	2.19820	0.189191
$136$	−0.0635395	−0.00544847
$137$	10.3249	0.882119	0.441059	−	0.897478i	$-0.354603\pi$
$137$	10.3249	0.882119	0.441059	+	0.897478i	$0.354603\pi$
$138$	1.45449	0.123815
$139$	14.1235	1.19794	0.598968	−	0.800773i	$-0.295578\pi$
$139$	14.1235	1.19794	0.598968	+	0.800773i	$0.295578\pi$
$140$	3.43840	0.290598
$141$	4.41291	0.371634
$142$	5.30701	0.445355
$143$	19.4907	1.62990
$144$	−2.85925	−0.238271
$145$	2.35153	0.195284
$146$	9.80955	0.811844
$147$	−1.80928	−0.149227
$148$	−5.12976	−0.421663
$149$	−16.6057	−1.36039	−0.680196	−	0.733030i	$-0.738105\pi$
$149$	−16.6057	−1.36039	−0.680196	+	0.733030i	$0.738105\pi$
$150$	−0.375168	−0.0306324
$151$	12.8359	1.04457	0.522287	−	0.852770i	$-0.325079\pi$
$151$	12.8359	1.04457	0.522287	+	0.852770i	$0.325079\pi$
$152$	−1.00803	−0.0817619
$153$	0.181675	0.0146876
$154$	−11.6418	−0.938126
$155$	−6.49127	−0.521391
$156$	2.15968	0.172913
$157$	−9.13431	−0.728997	−0.364498	−	0.931204i	$-0.618760\pi$
$157$	−9.13431	−0.728997	−0.364498	+	0.931204i	$0.618760\pi$
$158$	−14.8113	−1.17833
$159$	−0.241919	−0.0191854
$160$	1.00000	0.0790569
$161$	−13.3303	−1.05058
$162$	7.75305	0.609137
$163$	10.6788	0.836426	0.418213	−	0.908349i	$-0.362657\pi$
$163$	10.6788	0.836426	0.418213	+	0.908349i	$0.362657\pi$
$164$	−10.6118	−0.828644
$165$	1.27026	0.0988893
$166$	0.940494	0.0729965
$167$	12.0958	0.936000	0.468000	−	0.883728i	$-0.344975\pi$
$167$	12.0958	0.936000	0.468000	+	0.883728i	$0.344975\pi$
$168$	−1.28998	−0.0995240
$169$	20.1380	1.54907
$170$	−0.0635395	−0.00487326
$171$	2.88221	0.220408
$172$	1.98346	0.151237
$173$	−8.51243	−0.647188	−0.323594	−	0.946196i	$-0.604891\pi$
$173$	−8.51243	−0.647188	−0.323594	+	0.946196i	$0.604891\pi$
$174$	−0.882219	−0.0668808
$175$	3.43840	0.259918
$176$	−3.38583	−0.255217
$177$	−2.74381	−0.206237
$178$	14.4035	1.07959
$179$	−3.19678	−0.238939	−0.119469	−	0.992838i	$-0.538119\pi$
$179$	−3.19678	−0.238939	−0.119469	+	0.992838i	$0.538119\pi$
$180$	−2.85925	−0.213116
$181$	−2.60419	−0.193568	−0.0967838	−	0.995305i	$-0.530856\pi$
$181$	−2.60419	−0.193568	−0.0967838	+	0.995305i	$0.530856\pi$
$182$	−19.7933	−1.46718
$183$	1.20322	0.0889444
$184$	−3.87690	−0.285809
$185$	−5.12976	−0.377147
$186$	2.43532	0.178566
$187$	0.215134	0.0157322
$188$	−11.7625	−0.857866
$189$	7.55830	0.549786
$190$	−1.00803	−0.0731301
$191$	−19.1936	−1.38880	−0.694400	−	0.719589i	$-0.744330\pi$
$191$	−19.1936	−1.38880	−0.694400	+	0.719589i	$0.744330\pi$
$192$	−0.375168	−0.0270754
$193$	6.67776	0.480676	0.240338	−	0.970689i	$-0.422742\pi$
$193$	6.67776	0.480676	0.240338	+	0.970689i	$0.422742\pi$
$194$	−2.27297	−0.163189
$195$	2.15968	0.154658
$196$	4.82258	0.344470
$197$	−22.4189	−1.59728	−0.798640	−	0.601809i	$-0.794447\pi$
$197$	−22.4189	−1.59728	−0.798640	+	0.601809i	$0.794447\pi$
$198$	9.68093	0.687994
$199$	−1.94284	−0.137724	−0.0688622	−	0.997626i	$-0.521937\pi$
$199$	−1.94284	−0.137724	−0.0688622	+	0.997626i	$0.521937\pi$
$200$	1.00000	0.0707107
$201$	0.832312	0.0587068
$202$	6.39639	0.450049
$203$	8.08549	0.567490
$204$	0.0238380	0.00166899
$205$	−10.6118	−0.741162
$206$	3.49942	0.243816
$207$	11.0850	0.770463
$208$	−5.75656	−0.399146
$209$	3.41301	0.236083
$210$	−1.28998	−0.0890169
$211$	1.91780	0.132027	0.0660134	−	0.997819i	$-0.478972\pi$
$211$	1.91780	0.132027	0.0660134	+	0.997819i	$0.478972\pi$
$212$	0.644829	0.0442870
$213$	−1.99102	−0.136423
$214$	−11.4300	−0.781340
$215$	1.98346	0.135271
$216$	2.19820	0.149569
$217$	−22.3196	−1.51515
$218$	−0.0536094	−0.00363089
$219$	−3.68023	−0.248687
$220$	−3.38583	−0.228273
$221$	0.365769	0.0246043
$222$	1.92452	0.129165
$223$	−22.9937	−1.53977	−0.769887	−	0.638180i	$-0.779688\pi$
$223$	−22.9937	−1.53977	−0.769887	+	0.638180i	$0.779688\pi$
$224$	3.43840	0.229738
$225$	−2.85925	−0.190617
$226$	0.155014	0.0103114
$227$	20.1913	1.34014	0.670071	−	0.742297i	$-0.266264\pi$
$227$	20.1913	1.34014	0.670071	+	0.742297i	$0.266264\pi$
$228$	0.378181	0.0250456
$229$	−4.15083	−0.274294	−0.137147	−	0.990551i	$-0.543793\pi$
$229$	−4.15083	−0.274294	−0.137147	+	0.990551i	$0.543793\pi$
$230$	−3.87690	−0.255635
$231$	4.36765	0.287370
$232$	2.35153	0.154385
$233$	16.8766	1.10562	0.552811	−	0.833307i	$-0.313555\pi$
$233$	16.8766	1.10562	0.552811	+	0.833307i	$0.313555\pi$
$234$	16.4594	1.07599
$235$	−11.7625	−0.767299
$236$	7.31355	0.476071
$237$	5.55675	0.360950
$238$	−0.218474	−0.0141616
$239$	21.9324	1.41869	0.709344	−	0.704862i	$-0.248991\pi$
$239$	21.9324	1.41869	0.709344	+	0.704862i	$0.248991\pi$
$240$	−0.375168	−0.0242170
$241$	7.80572	0.502811	0.251405	−	0.967882i	$-0.419107\pi$
$241$	7.80572	0.502811	0.251405	+	0.967882i	$0.419107\pi$
$242$	0.463848	0.0298173
$243$	−9.50331	−0.609638
$244$	−3.20714	−0.205316
$245$	4.82258	0.308103
$246$	3.98122	0.253833
$247$	5.80278	0.369222
$248$	−6.49127	−0.412196
$249$	−0.352844	−0.0223606
$250$	1.00000	0.0632456
$251$	−21.8497	−1.37914	−0.689571	−	0.724218i	$-0.742201\pi$
$251$	−21.8497	−1.37914	−0.689571	+	0.724218i	$0.742201\pi$
$252$	−9.83123	−0.619310
$253$	13.1265	0.825258
$254$	−10.9726	−0.688482
$255$	0.0238380	0.00149279
$256$	1.00000	0.0625000
$257$	−3.65757	−0.228153	−0.114076	−	0.993472i	$-0.536391\pi$
$257$	−3.65757	−0.228153	−0.114076	+	0.993472i	$0.536391\pi$
$258$	−0.744130	−0.0463275
$259$	−17.6381	−1.09598
$260$	−5.75656	−0.357007
$261$	−6.72360	−0.416181
$262$	6.27064	0.387402
$263$	−14.3614	−0.885564	−0.442782	−	0.896629i	$-0.646008\pi$
$263$	−14.3614	−0.885564	−0.442782	+	0.896629i	$0.646008\pi$
$264$	1.27026	0.0781789
$265$	0.644829	0.0396115
$266$	−3.46600	−0.212514
$267$	−5.40373	−0.330703
$268$	−2.21850	−0.135517
$269$	23.6498	1.44196	0.720978	−	0.692958i	$-0.243693\pi$
$269$	23.6498	1.44196	0.720978	+	0.692958i	$0.243693\pi$
$270$	2.19820	0.133778
$271$	15.0994	0.917221	0.458610	−	0.888637i	$-0.348347\pi$
$271$	15.0994	0.917221	0.458610	+	0.888637i	$0.348347\pi$
$272$	−0.0635395	−0.00385265
$273$	7.42583	0.449432
$274$	10.3249	0.623752
$275$	−3.38583	−0.204173
$276$	1.45449	0.0875501
$277$	−4.04147	−0.242828	−0.121414	−	0.992602i	$-0.538743\pi$
$277$	−4.04147	−0.242828	−0.121414	+	0.992602i	$0.538743\pi$
$278$	14.1235	0.847069
$279$	18.5602	1.11117
$280$	3.43840	0.205484
$281$	3.00447	0.179231	0.0896157	−	0.995976i	$-0.471436\pi$
$281$	3.00447	0.179231	0.0896157	+	0.995976i	$0.471436\pi$
$282$	4.41291	0.262785
$283$	−13.6809	−0.813244	−0.406622	−	0.913597i	$-0.633293\pi$
$283$	−13.6809	−0.813244	−0.406622	+	0.913597i	$0.633293\pi$
$284$	5.30701	0.314913
$285$	0.378181	0.0224015
$286$	19.4907	1.15251
$287$	−36.4877	−2.15380
$288$	−2.85925	−0.168483
$289$	−16.9960	−0.999763
$290$	2.35153	0.138086
$291$	0.852745	0.0499888
$292$	9.80955	0.574060
$293$	−19.9103	−1.16317	−0.581586	−	0.813485i	$-0.697568\pi$
$293$	−19.9103	−1.16317	−0.581586	+	0.813485i	$0.697568\pi$
$294$	−1.80928	−0.105519
$295$	7.31355	0.425811
$296$	−5.12976	−0.298161
$297$	−7.44275	−0.431872
$298$	−16.6057	−0.961942
$299$	22.3176	1.29066
$300$	−0.375168	−0.0216604
$301$	6.81991	0.393093
$302$	12.8359	0.738625
$303$	−2.39972	−0.137861
$304$	−1.00803	−0.0578144
$305$	−3.20714	−0.183640
$306$	0.181675	0.0103857
$307$	−6.49029	−0.370421	−0.185210	−	0.982699i	$-0.559297\pi$
$307$	−6.49029	−0.370421	−0.185210	+	0.982699i	$0.559297\pi$
$308$	−11.6418	−0.663355
$309$	−1.31287	−0.0746868
$310$	−6.49127	−0.368679
$311$	−23.6581	−1.34153	−0.670763	−	0.741672i	$-0.734033\pi$
$311$	−23.6581	−1.34153	−0.670763	+	0.741672i	$0.734033\pi$
$312$	2.15968	0.122268
$313$	−2.94904	−0.166690	−0.0833449	−	0.996521i	$-0.526560\pi$
$313$	−2.94904	−0.166690	−0.0833449	+	0.996521i	$0.526560\pi$
$314$	−9.13431	−0.515479
$315$	−9.83123	−0.553927
$316$	−14.8113	−0.833203
$317$	30.6656	1.72235	0.861176	−	0.508307i	$-0.169728\pi$
$317$	30.6656	1.72235	0.861176	+	0.508307i	$0.169728\pi$
$318$	−0.241919	−0.0135662
$319$	−7.96188	−0.445779
$320$	1.00000	0.0559017
$321$	4.28818	0.239343
$322$	−13.3303	−0.742871
$323$	0.0640497	0.00356382
$324$	7.75305	0.430725
$325$	−5.75656	−0.319316
$326$	10.6788	0.591443
$327$	0.0201125	0.00111223
$328$	−10.6118	−0.585940
$329$	−40.4441	−2.22975
$330$	1.27026	0.0699253
$331$	−4.18326	−0.229933	−0.114967	−	0.993369i	$-0.536676\pi$
$331$	−4.18326	−0.229933	−0.114967	+	0.993369i	$0.536676\pi$
$332$	0.940494	0.0516163
$333$	14.6673	0.803760
$334$	12.0958	0.661852
$335$	−2.21850	−0.121210
$336$	−1.28998	−0.0703741
$337$	−32.9064	−1.79253	−0.896263	−	0.443523i	$-0.853729\pi$
$337$	−32.9064	−1.79253	−0.896263	+	0.443523i	$0.853729\pi$
$338$	20.1380	1.09536
$339$	−0.0581562	−0.00315861
$340$	−0.0635395	−0.00344591
$341$	21.9783	1.19019
$342$	2.88221	0.155852
$343$	−7.48684	−0.404251
$344$	1.98346	0.106941
$345$	1.45449	0.0783072
$346$	−8.51243	−0.457631
$347$	35.5757	1.90980	0.954901	−	0.296925i	$-0.0959610\pi$
$347$	35.5757	1.90980	0.954901	+	0.296925i	$0.0959610\pi$
$348$	−0.882219	−0.0472919
$349$	5.99265	0.320779	0.160390	−	0.987054i	$-0.448725\pi$
$349$	5.99265	0.320779	0.160390	+	0.987054i	$0.448725\pi$
$350$	3.43840	0.183790
$351$	−12.6541	−0.675426
$352$	−3.38583	−0.180465
$353$	7.20337	0.383396	0.191698	−	0.981454i	$-0.438601\pi$
$353$	7.20337	0.383396	0.191698	+	0.981454i	$0.438601\pi$
$354$	−2.74381	−0.145832
$355$	5.30701	0.281667
$356$	14.4035	0.763383
$357$	0.0819646	0.00433802
$358$	−3.19678	−0.168955
$359$	−10.7730	−0.568576	−0.284288	−	0.958739i	$-0.591757\pi$
$359$	−10.7730	−0.568576	−0.284288	+	0.958739i	$0.591757\pi$
$360$	−2.85925	−0.150696
$361$	−17.9839	−0.946520
$362$	−2.60419	−0.136873
$363$	−0.174021	−0.00913374
$364$	−19.7933	−1.03745
$365$	9.80955	0.513455
$366$	1.20322	0.0628932
$367$	−12.7249	−0.664236	−0.332118	−	0.943238i	$-0.607763\pi$
$367$	−12.7249	−0.664236	−0.332118	+	0.943238i	$0.607763\pi$
$368$	−3.87690	−0.202098
$369$	30.3418	1.57953
$370$	−5.12976	−0.266683
$371$	2.21718	0.115110
$372$	2.43532	0.126265
$373$	−30.2304	−1.56527	−0.782635	−	0.622481i	$-0.786125\pi$
$373$	−30.2304	−1.56527	−0.782635	+	0.622481i	$0.786125\pi$
$374$	0.215134	0.0111243
$375$	−0.375168	−0.0193736
$376$	−11.7625	−0.606603
$377$	−13.5367	−0.697176
$378$	7.55830	0.388757
$379$	−21.8385	−1.12177	−0.560883	−	0.827895i	$-0.689538\pi$
$379$	−21.8385	−1.12177	−0.560883	+	0.827895i	$0.689538\pi$
$380$	−1.00803	−0.0517108
$381$	4.11657	0.210898
$382$	−19.1936	−0.982030
$383$	−21.4566	−1.09638	−0.548190	−	0.836354i	$-0.684683\pi$
$383$	−21.4566	−1.09638	−0.548190	+	0.836354i	$0.684683\pi$
$384$	−0.375168	−0.0191452
$385$	−11.6418	−0.593323
$386$	6.67776	0.339889
$387$	−5.67119	−0.288283
$388$	−2.27297	−0.115392
$389$	−18.7628	−0.951313	−0.475657	−	0.879631i	$-0.657790\pi$
$389$	−18.7628	−0.951313	−0.475657	+	0.879631i	$0.657790\pi$
$390$	2.15968	0.109360
$391$	0.246337	0.0124578
$392$	4.82258	0.243577
$393$	−2.35255	−0.118670
$394$	−22.4189	−1.12945
$395$	−14.8113	−0.745240
$396$	9.68093	0.486485
$397$	−19.6195	−0.984676	−0.492338	−	0.870404i	$-0.663858\pi$
$397$	−19.6195	−0.984676	−0.492338	+	0.870404i	$0.663858\pi$
$398$	−1.94284	−0.0973858
$399$	1.30034	0.0650982
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	0.832312	0.0415120
$403$	37.3674	1.86140
$404$	6.39639	0.318232
$405$	7.75305	0.385252
$406$	8.08549	0.401276
$407$	17.3685	0.860924
$408$	0.0238380	0.00118016
$409$	−17.5079	−0.865708	−0.432854	−	0.901464i	$-0.642493\pi$
$409$	−17.5079	−0.865708	−0.432854	+	0.901464i	$0.642493\pi$
$410$	−10.6118	−0.524080
$411$	−3.87359	−0.191070
$412$	3.49942	0.172404
$413$	25.1469	1.23740
$414$	11.0850	0.544800
$415$	0.940494	0.0461671
$416$	−5.75656	−0.282239
$417$	−5.29867	−0.259477
$418$	3.41301	0.166936
$419$	−5.74889	−0.280852	−0.140426	−	0.990091i	$-0.544847\pi$
$419$	−5.74889	−0.280852	−0.140426	+	0.990091i	$0.544847\pi$
$420$	−1.28998	−0.0629445
$421$	17.1179	0.834276	0.417138	−	0.908843i	$-0.363033\pi$
$421$	17.1179	0.834276	0.417138	+	0.908843i	$0.363033\pi$
$422$	1.91780	0.0933570
$423$	33.6318	1.63524
$424$	0.644829	0.0313156
$425$	−0.0635395	−0.00308212
$426$	−1.99102	−0.0964654
$427$	−11.0274	−0.533654
$428$	−11.4300	−0.552491
$429$	−7.31231	−0.353041
$430$	1.98346	0.0956507
$431$	5.30470	0.255518	0.127759	−	0.991805i	$-0.459222\pi$
$431$	5.30470	0.255518	0.127759	+	0.991805i	$0.459222\pi$
$432$	2.19820	0.105761
$433$	19.8622	0.954519	0.477259	−	0.878762i	$-0.341630\pi$
$433$	19.8622	0.954519	0.477259	+	0.878762i	$0.341630\pi$
$434$	−22.3196	−1.07137
$435$	−0.882219	−0.0422992
$436$	−0.0536094	−0.00256742
$437$	3.90803	0.186946
$438$	−3.68023	−0.175848
$439$	−0.474222	−0.0226334	−0.0113167	−	0.999936i	$-0.503602\pi$
$439$	−0.474222	−0.0226334	−0.0113167	+	0.999936i	$0.503602\pi$
$440$	−3.38583	−0.161413
$441$	−13.7889	−0.656617
$442$	0.365769	0.0173979
$443$	33.8254	1.60709	0.803547	−	0.595242i	$-0.202944\pi$
$443$	33.8254	1.60709	0.803547	+	0.595242i	$0.202944\pi$
$444$	1.92452	0.0913338
$445$	14.4035	0.682791
$446$	−22.9937	−1.08878
$447$	6.22993	0.294666
$448$	3.43840	0.162449
$449$	19.6041	0.925176	0.462588	−	0.886573i	$-0.346921\pi$
$449$	19.6041	0.925176	0.462588	+	0.886573i	$0.346921\pi$
$450$	−2.85925	−0.134786
$451$	35.9298	1.69187
$452$	0.155014	0.00729123
$453$	−4.81564	−0.226258
$454$	20.1913	0.947624
$455$	−19.7933	−0.927926
$456$	0.378181	0.0177099
$457$	−35.5672	−1.66376	−0.831881	−	0.554954i	$-0.812736\pi$
$457$	−35.5672	−1.66376	−0.831881	+	0.554954i	$0.812736\pi$
$458$	−4.15083	−0.193955
$459$	−0.139673	−0.00651937
$460$	−3.87690	−0.180762
$461$	5.81131	0.270660	0.135330	−	0.990801i	$-0.456791\pi$
$461$	5.81131	0.270660	0.135330	+	0.990801i	$0.456791\pi$
$462$	4.36765	0.203201
$463$	18.3243	0.851602	0.425801	−	0.904817i	$-0.359992\pi$
$463$	18.3243	0.851602	0.425801	+	0.904817i	$0.359992\pi$
$464$	2.35153	0.109167
$465$	2.43532	0.112935
$466$	16.8766	0.781793
$467$	38.5130	1.78217	0.891086	−	0.453835i	$-0.149945\pi$
$467$	38.5130	1.78217	0.891086	+	0.453835i	$0.149945\pi$
$468$	16.4594	0.760838
$469$	−7.62810	−0.352233
$470$	−11.7625	−0.542562
$471$	3.42690	0.157903
$472$	7.31355	0.336633
$473$	−6.71565	−0.308786
$474$	5.55675	0.255230
$475$	−1.00803	−0.0462515
$476$	−0.218474	−0.0100137
$477$	−1.84373	−0.0844184
$478$	21.9324	1.00316
$479$	−10.0936	−0.461190	−0.230595	−	0.973050i	$-0.574067\pi$
$479$	−10.0936	−0.461190	−0.230595	+	0.973050i	$0.574067\pi$
$480$	−0.375168	−0.0171240
$481$	29.5297	1.34644
$482$	7.80572	0.355541
$483$	5.00112	0.227559
$484$	0.463848	0.0210840
$485$	−2.27297	−0.103210
$486$	−9.50331	−0.431079
$487$	41.1635	1.86530	0.932648	−	0.360787i	$-0.117492\pi$
$487$	41.1635	1.86530	0.932648	+	0.360787i	$0.117492\pi$
$488$	−3.20714	−0.145180
$489$	−4.00634	−0.181173
$490$	4.82258	0.217862
$491$	−26.6005	−1.20047	−0.600233	−	0.799825i	$-0.704925\pi$
$491$	−26.6005	−1.20047	−0.600233	+	0.799825i	$0.704925\pi$
$492$	3.98122	0.179487
$493$	−0.149415	−0.00672931
$494$	5.80278	0.261079
$495$	9.68093	0.435126
$496$	−6.49127	−0.291467
$497$	18.2476	0.818518
$498$	−0.352844	−0.0158113
$499$	1.47382	0.0659773	0.0329887	−	0.999456i	$-0.489497\pi$
$499$	1.47382	0.0659773	0.0329887	+	0.999456i	$0.489497\pi$
$500$	1.00000	0.0447214
$501$	−4.53796	−0.202741
$502$	−21.8497	−0.975201
$503$	22.5992	1.00765	0.503823	−	0.863807i	$-0.331926\pi$
$503$	22.5992	1.00765	0.503823	+	0.863807i	$0.331926\pi$
$504$	−9.83123	−0.437918
$505$	6.39639	0.284636
$506$	13.1265	0.583546
$507$	−7.55513	−0.335535
$508$	−10.9726	−0.486831
$509$	−18.1009	−0.802307	−0.401154	−	0.916011i	$-0.631391\pi$
$509$	−18.1009	−0.802307	−0.401154	+	0.916011i	$0.631391\pi$
$510$	0.0238380	0.00105556
$511$	33.7291	1.49209
$512$	1.00000	0.0441942
$513$	−2.21585	−0.0978323
$514$	−3.65757	−0.161328
$515$	3.49942	0.154203
$516$	−0.744130	−0.0327585
$517$	39.8257	1.75153
$518$	−17.6381	−0.774976
$519$	3.19359	0.140183
$520$	−5.75656	−0.252442
$521$	−36.5763	−1.60244	−0.801219	−	0.598371i	$-0.795815\pi$
$521$	−36.5763	−1.60244	−0.801219	+	0.598371i	$0.795815\pi$
$522$	−6.72360	−0.294284
$523$	36.9566	1.61600	0.808000	−	0.589182i	$-0.200550\pi$
$523$	36.9566	1.61600	0.808000	+	0.589182i	$0.200550\pi$
$524$	6.27064	0.273934
$525$	−1.28998	−0.0562993
$526$	−14.3614	−0.626188
$527$	0.412452	0.0179667
$528$	1.27026	0.0552808
$529$	−7.96961	−0.346505
$530$	0.644829	0.0280096
$531$	−20.9112	−0.907471
$532$	−3.46600	−0.150270
$533$	61.0876	2.64600
$534$	−5.40373	−0.233842
$535$	−11.4300	−0.494163
$536$	−2.21850	−0.0958248
$537$	1.19933	0.0517549
$538$	23.6498	1.01962
$539$	−16.3284	−0.703315
$540$	2.19820	0.0945957
$541$	−6.18227	−0.265796	−0.132898	−	0.991130i	$-0.542428\pi$
$541$	−6.18227	−0.265796	−0.132898	+	0.991130i	$0.542428\pi$
$542$	15.0994	0.648573
$543$	0.977008	0.0419274
$544$	−0.0635395	−0.00272423
$545$	−0.0536094	−0.00229637
$546$	7.42583	0.317796
$547$	3.75968	0.160752	0.0803762	−	0.996765i	$-0.474388\pi$
$547$	3.75968	0.160752	0.0803762	+	0.996765i	$0.474388\pi$
$548$	10.3249	0.441059
$549$	9.17001	0.391366
$550$	−3.38583	−0.144372
$551$	−2.37041	−0.100983
$552$	1.45449	0.0619073
$553$	−50.9273	−2.16565
$554$	−4.04147	−0.171706
$555$	1.92452	0.0816914
$556$	14.1235	0.598968
$557$	1.55530	0.0659001	0.0329500	−	0.999457i	$-0.489510\pi$
$557$	1.55530	0.0659001	0.0329500	+	0.999457i	$0.489510\pi$
$558$	18.5602	0.785714
$559$	−11.4179	−0.482925
$560$	3.43840	0.145299
$561$	−0.0807115	−0.00340764
$562$	3.00447	0.126736
$563$	9.38213	0.395410	0.197705	−	0.980262i	$-0.436651\pi$
$563$	9.38213	0.395410	0.197705	+	0.980262i	$0.436651\pi$
$564$	4.41291	0.185817
$565$	0.155014	0.00652147
$566$	−13.6809	−0.575050
$567$	26.6581	1.11953
$568$	5.30701	0.222677
$569$	43.2932	1.81494	0.907472	−	0.420113i	$-0.138009\pi$
$569$	43.2932	1.81494	0.907472	+	0.420113i	$0.138009\pi$
$570$	0.378181	0.0158402
$571$	19.2853	0.807064	0.403532	−	0.914966i	$-0.367782\pi$
$571$	19.2853	0.807064	0.403532	+	0.914966i	$0.367782\pi$
$572$	19.4907	0.814948
$573$	7.20083	0.300819
$574$	−36.4877	−1.52297
$575$	−3.87690	−0.161678
$576$	−2.85925	−0.119135
$577$	−8.53859	−0.355466	−0.177733	−	0.984079i	$-0.556876\pi$
$577$	−8.53859	−0.355466	−0.177733	+	0.984079i	$0.556876\pi$
$578$	−16.9960	−0.706939
$579$	−2.50528	−0.104116
$580$	2.35153	0.0976419
$581$	3.23379	0.134160
$582$	0.852745	0.0353474
$583$	−2.18328	−0.0904222
$584$	9.80955	0.405922
$585$	16.4594	0.680514
$586$	−19.9103	−0.822487
$587$	22.0299	0.909272	0.454636	−	0.890677i	$-0.349769\pi$
$587$	22.0299	0.909272	0.454636	+	0.890677i	$0.349769\pi$
$588$	−1.80928	−0.0746134
$589$	6.54339	0.269616
$590$	7.31355	0.301094
$591$	8.41086	0.345977
$592$	−5.12976	−0.210832
$593$	23.8247	0.978363	0.489182	−	0.872182i	$-0.337296\pi$
$593$	23.8247	0.978363	0.489182	+	0.872182i	$0.337296\pi$
$594$	−7.44275	−0.305380
$595$	−0.218474	−0.00895657
$596$	−16.6057	−0.680196
$597$	0.728892	0.0298316
$598$	22.3176	0.912636
$599$	11.8168	0.482821	0.241411	−	0.970423i	$-0.422390\pi$
$599$	11.8168	0.482821	0.241411	+	0.970423i	$0.422390\pi$
$600$	−0.375168	−0.0153162
$601$	−34.0177	−1.38761	−0.693806	−	0.720161i	$-0.744068\pi$
$601$	−34.0177	−1.38761	−0.693806	+	0.720161i	$0.744068\pi$
$602$	6.81991	0.277959
$603$	6.34325	0.258317
$604$	12.8359	0.522287
$605$	0.463848	0.0188581
$606$	−2.39972	−0.0974821
$607$	36.8268	1.49476	0.747378	−	0.664399i	$-0.231313\pi$
$607$	36.8268	1.49476	0.747378	+	0.664399i	$0.231313\pi$
$608$	−1.00803	−0.0408810
$609$	−3.03342	−0.122920
$610$	−3.20714	−0.129853
$611$	67.7114	2.73931
$612$	0.181675	0.00734379
$613$	9.65476	0.389952	0.194976	−	0.980808i	$-0.437537\pi$
$613$	9.65476	0.389952	0.194976	+	0.980808i	$0.437537\pi$
$614$	−6.49029	−0.261927
$615$	3.98122	0.160538
$616$	−11.6418	−0.469063
$617$	−16.6425	−0.670002	−0.335001	−	0.942218i	$-0.608737\pi$
$617$	−16.6425	−0.670002	−0.335001	+	0.942218i	$0.608737\pi$
$618$	−1.31287	−0.0528115
$619$	−12.8270	−0.515562	−0.257781	−	0.966203i	$-0.582991\pi$
$619$	−12.8270	−0.515562	−0.257781	+	0.966203i	$0.582991\pi$
$620$	−6.49127	−0.260696
$621$	−8.52223	−0.341985
$622$	−23.6581	−0.948602
$623$	49.5249	1.98417
$624$	2.15968	0.0864563
$625$	1.00000	0.0400000
$626$	−2.94904	−0.117868
$627$	−1.28046	−0.0511365
$628$	−9.13431	−0.364498
$629$	0.325942	0.0129962
$630$	−9.83123	−0.391686
$631$	3.16050	0.125818	0.0629088	−	0.998019i	$-0.479962\pi$
$631$	3.16050	0.125818	0.0629088	+	0.998019i	$0.479962\pi$
$632$	−14.8113	−0.589164
$633$	−0.719498	−0.0285975
$634$	30.6656	1.21789
$635$	−10.9726	−0.435434
$636$	−0.241919	−0.00959272
$637$	−27.7615	−1.09995
$638$	−7.96188	−0.315214
$639$	−15.1741	−0.600277
$640$	1.00000	0.0395285
$641$	−24.8882	−0.983025	−0.491512	−	0.870871i	$-0.663556\pi$
$641$	−24.8882	−0.983025	−0.491512	+	0.870871i	$0.663556\pi$
$642$	4.28818	0.169241
$643$	9.34765	0.368635	0.184318	−	0.982867i	$-0.440992\pi$
$643$	9.34765	0.368635	0.184318	+	0.982867i	$0.440992\pi$
$644$	−13.3303	−0.525289
$645$	−0.744130	−0.0293001
$646$	0.0640497	0.00252000
$647$	40.2718	1.58325	0.791624	−	0.611009i	$-0.209236\pi$
$647$	40.2718	1.58325	0.791624	+	0.611009i	$0.209236\pi$
$648$	7.75305	0.304569
$649$	−24.7624	−0.972010
$650$	−5.75656	−0.225791
$651$	8.37360	0.328187
$652$	10.6788	0.418213
$653$	6.28548	0.245970	0.122985	−	0.992409i	$-0.460753\pi$
$653$	6.28548	0.245970	0.122985	+	0.992409i	$0.460753\pi$
$654$	0.0201125	0.000786463 0
$655$	6.27064	0.245014
$656$	−10.6118	−0.414322
$657$	−28.0479	−1.09425
$658$	−40.4441	−1.57667
$659$	−31.7554	−1.23701	−0.618507	−	0.785780i	$-0.712262\pi$
$659$	−31.7554	−1.23701	−0.618507	+	0.785780i	$0.712262\pi$
$660$	1.27026	0.0494447
$661$	26.4761	1.02980	0.514901	−	0.857249i	$-0.327829\pi$
$661$	26.4761	1.02980	0.514901	+	0.857249i	$0.327829\pi$
$662$	−4.18326	−0.162587
$663$	−0.137225	−0.00532937
$664$	0.940494	0.0364983
$665$	−3.46600	−0.134406
$666$	14.6673	0.568344
$667$	−9.11665	−0.352998
$668$	12.0958	0.468000
$669$	8.62652	0.333521
$670$	−2.21850	−0.0857083
$671$	10.8588	0.419200
$672$	−1.28998	−0.0497620
$673$	−19.0590	−0.734670	−0.367335	−	0.930089i	$-0.619730\pi$
$673$	−19.0590	−0.734670	−0.367335	+	0.930089i	$0.619730\pi$
$674$	−32.9064	−1.26751
$675$	2.19820	0.0846089
$676$	20.1380	0.774537
$677$	37.1768	1.42882	0.714410	−	0.699728i	$-0.246695\pi$
$677$	37.1768	1.42882	0.714410	+	0.699728i	$0.246695\pi$
$678$	−0.0581562	−0.00223348
$679$	−7.81536	−0.299926
$680$	−0.0635395	−0.00243663
$681$	−7.57513	−0.290280
$682$	21.9783	0.841594
$683$	34.1574	1.30700	0.653498	−	0.756929i	$-0.273301\pi$
$683$	34.1574	1.30700	0.653498	+	0.756929i	$0.273301\pi$
$684$	2.88221	0.110204
$685$	10.3249	0.394495
$686$	−7.48684	−0.285849
$687$	1.55726	0.0594131
$688$	1.98346	0.0756186
$689$	−3.71199	−0.141416
$690$	1.45449	0.0553716
$691$	−43.7664	−1.66495	−0.832476	−	0.554060i	$-0.813078\pi$
$691$	−43.7664	−1.66495	−0.832476	+	0.554060i	$0.813078\pi$
$692$	−8.51243	−0.323594
$693$	33.2869	1.26446
$694$	35.5757	1.35043
$695$	14.1235	0.535733
$696$	−0.882219	−0.0334404
$697$	0.674270	0.0255398
$698$	5.99265	0.226825
$699$	−6.33156	−0.239482
$700$	3.43840	0.129959
$701$	24.4992	0.925322	0.462661	−	0.886535i	$-0.346895\pi$
$701$	24.4992	0.925322	0.462661	+	0.886535i	$0.346895\pi$
$702$	−12.6541	−0.477598
$703$	5.17094	0.195026
$704$	−3.38583	−0.127608
$705$	4.41291	0.166200
$706$	7.20337	0.271102
$707$	21.9933	0.827145
$708$	−2.74381	−0.103119
$709$	44.1359	1.65756	0.828779	−	0.559575i	$-0.189036\pi$
$709$	44.1359	1.65756	0.828779	+	0.559575i	$0.189036\pi$
$710$	5.30701	0.199169
$711$	42.3493	1.58822
$712$	14.4035	0.539793
$713$	25.1660	0.942475
$714$	0.0819646	0.00306745
$715$	19.4907	0.728912
$716$	−3.19678	−0.119469
$717$	−8.22834	−0.307293
$718$	−10.7730	−0.402044
$719$	−26.1583	−0.975540	−0.487770	−	0.872972i	$-0.662190\pi$
$719$	−26.1583	−0.975540	−0.487770	+	0.872972i	$0.662190\pi$
$720$	−2.85925	−0.106558
$721$	12.0324	0.448110
$722$	−17.9839	−0.669291
$723$	−2.92846	−0.108911
$724$	−2.60419	−0.0967838
$725$	2.35153	0.0873336
$726$	−0.174021	−0.00645853
$727$	11.0692	0.410534	0.205267	−	0.978706i	$-0.434194\pi$
$727$	11.0692	0.410534	0.205267	+	0.978706i	$0.434194\pi$
$728$	−19.7933	−0.733590
$729$	−19.6938	−0.729400
$730$	9.80955	0.363068
$731$	−0.126028	−0.00466131
$732$	1.20322	0.0444722
$733$	2.78550	0.102885	0.0514425	−	0.998676i	$-0.483618\pi$
$733$	2.78550	0.102885	0.0514425	+	0.998676i	$0.483618\pi$
$734$	−12.7249	−0.469686
$735$	−1.80928	−0.0667362
$736$	−3.87690	−0.142905
$737$	7.51148	0.276689
$738$	30.3418	1.11690
$739$	−23.4701	−0.863360	−0.431680	−	0.902027i	$-0.642079\pi$
$739$	−23.4701	−0.863360	−0.431680	+	0.902027i	$0.642079\pi$
$740$	−5.12976	−0.188574
$741$	−2.17702	−0.0799748
$742$	2.21718	0.0813951
$743$	−26.9638	−0.989206	−0.494603	−	0.869119i	$-0.664687\pi$
$743$	−26.9638	−0.989206	−0.494603	+	0.869119i	$0.664687\pi$
$744$	2.43532	0.0892831
$745$	−16.6057	−0.608386
$746$	−30.2304	−1.10681
$747$	−2.68911	−0.0983893
$748$	0.215134	0.00786608
$749$	−39.3009	−1.43603
$750$	−0.375168	−0.0136992
$751$	−8.03591	−0.293235	−0.146617	−	0.989193i	$-0.546839\pi$
$751$	−8.03591	−0.293235	−0.146617	+	0.989193i	$0.546839\pi$
$752$	−11.7625	−0.428933
$753$	8.19733	0.298727
$754$	−13.5367	−0.492978
$755$	12.8359	0.467147
$756$	7.55830	0.274893
$757$	−22.9266	−0.833280	−0.416640	−	0.909072i	$-0.636792\pi$
$757$	−22.9266	−0.833280	−0.416640	+	0.909072i	$0.636792\pi$
$758$	−21.8385	−0.793209
$759$	−4.92466	−0.178754
$760$	−1.00803	−0.0365651
$761$	−31.3576	−1.13671	−0.568355	−	0.822783i	$-0.692420\pi$
$761$	−31.3576	−1.13671	−0.568355	+	0.822783i	$0.692420\pi$
$762$	4.11657	0.149128
$763$	−0.184330	−0.00667321
$764$	−19.1936	−0.694400
$765$	0.181675	0.00656848
$766$	−21.4566	−0.775258
$767$	−42.1009	−1.52017
$768$	−0.375168	−0.0135377
$769$	−29.5581	−1.06589	−0.532946	−	0.846150i	$-0.678915\pi$
$769$	−29.5581	−1.06589	−0.532946	+	0.846150i	$0.678915\pi$
$770$	−11.6418	−0.419542
$771$	1.37220	0.0494187
$772$	6.67776	0.240338
$773$	−17.1939	−0.618423	−0.309211	−	0.950993i	$-0.600065\pi$
$773$	−17.1939	−0.618423	−0.309211	+	0.950993i	$0.600065\pi$
$774$	−5.67119	−0.203847
$775$	−6.49127	−0.233173
$776$	−2.27297	−0.0815947
$777$	6.61727	0.237393
$778$	−18.7628	−0.672680
$779$	10.6970	0.383261
$780$	2.15968	0.0773289
$781$	−17.9686	−0.642969
$782$	0.246337	0.00880898
$783$	5.16914	0.184730
$784$	4.82258	0.172235
$785$	−9.13431	−0.326017
$786$	−2.35255	−0.0839126
$787$	45.1992	1.61118	0.805588	−	0.592476i	$-0.201849\pi$
$787$	45.1992	1.61118	0.805588	+	0.592476i	$0.201849\pi$
$788$	−22.4189	−0.798640
$789$	5.38796	0.191816
$790$	−14.8113	−0.526964
$791$	0.532999	0.0189512
$792$	9.68093	0.343997
$793$	18.4621	0.655608
$794$	−19.6195	−0.696271
$795$	−0.241919	−0.00857999
$796$	−1.94284	−0.0688622
$797$	−20.1842	−0.714959	−0.357480	−	0.933921i	$-0.616364\pi$
$797$	−20.1842	−0.714959	−0.357480	+	0.933921i	$0.616364\pi$
$798$	1.30034	0.0460314
$799$	0.747382	0.0264405
$800$	1.00000	0.0353553
$801$	−41.1831	−1.45513
$802$	−1.00000	−0.0353112
$803$	−33.2135	−1.17208
$804$	0.832312	0.0293534
$805$	−13.3303	−0.469833
$806$	37.3674	1.31621
$807$	−8.87267	−0.312333
$808$	6.39639	0.225024
$809$	−5.07432	−0.178403	−0.0892017	−	0.996014i	$-0.528432\pi$
$809$	−5.07432	−0.178403	−0.0892017	+	0.996014i	$0.528432\pi$
$810$	7.75305	0.272414
$811$	44.6919	1.56935	0.784673	−	0.619910i	$-0.212831\pi$
$811$	44.6919	1.56935	0.784673	+	0.619910i	$0.212831\pi$
$812$	8.08549	0.283745
$813$	−5.66480	−0.198673
$814$	17.3685	0.608765
$815$	10.6788	0.374061
$816$	0.0238380	0.000834497 0
$817$	−1.99938	−0.0699495
$818$	−17.5079	−0.612148
$819$	56.5941	1.97756
$820$	−10.6118	−0.370581
$821$	30.9469	1.08005	0.540026	−	0.841648i	$-0.318414\pi$
$821$	30.9469	1.08005	0.540026	+	0.841648i	$0.318414\pi$
$822$	−3.87359	−0.135107
$823$	37.8406	1.31904	0.659519	−	0.751687i	$-0.270760\pi$
$823$	37.8406	1.31904	0.659519	+	0.751687i	$0.270760\pi$
$824$	3.49942	0.121908
$825$	1.27026	0.0442247
$826$	25.1469	0.874972
$827$	31.1265	1.08237	0.541187	−	0.840902i	$-0.317975\pi$
$827$	31.1265	1.08237	0.541187	+	0.840902i	$0.317975\pi$
$828$	11.0850	0.385232
$829$	34.7307	1.20625	0.603124	−	0.797648i	$-0.293923\pi$
$829$	34.7307	1.20625	0.603124	+	0.797648i	$0.293923\pi$
$830$	0.940494	0.0326450
$831$	1.51623	0.0525975
$832$	−5.75656	−0.199573
$833$	−0.306424	−0.0106170
$834$	−5.29867	−0.183478
$835$	12.0958	0.418592
$836$	3.41301	0.118042
$837$	−14.2691	−0.493214
$838$	−5.74889	−0.198592
$839$	−14.7909	−0.510640	−0.255320	−	0.966857i	$-0.582181\pi$
$839$	−14.7909	−0.510640	−0.255320	+	0.966857i	$0.582181\pi$
$840$	−1.28998	−0.0445085
$841$	−23.4703	−0.809321
$842$	17.1179	0.589923
$843$	−1.12718	−0.0388222
$844$	1.91780	0.0660134
$845$	20.1380	0.692767
$846$	33.6318	1.15629
$847$	1.59489	0.0548012
$848$	0.644829	0.0221435
$849$	5.13263	0.176152
$850$	−0.0635395	−0.00217939
$851$	19.8876	0.681737
$852$	−1.99102	−0.0682113
$853$	5.95491	0.203892	0.101946	−	0.994790i	$-0.467493\pi$
$853$	5.95491	0.203892	0.101946	+	0.994790i	$0.467493\pi$
$854$	−11.0274	−0.377351
$855$	2.88221	0.0985693
$856$	−11.4300	−0.390670
$857$	−18.6322	−0.636465	−0.318232	−	0.948013i	$-0.603089\pi$
$857$	−18.6322	−0.636465	−0.318232	+	0.948013i	$0.603089\pi$
$858$	−7.31231	−0.249638
$859$	9.75143	0.332715	0.166357	−	0.986066i	$-0.446799\pi$
$859$	9.75143	0.332715	0.166357	+	0.986066i	$0.446799\pi$
$860$	1.98346	0.0676353
$861$	13.6890	0.466520
$862$	5.30470	0.180679
$863$	−5.03323	−0.171333	−0.0856665	−	0.996324i	$-0.527302\pi$
$863$	−5.03323	−0.171333	−0.0856665	+	0.996324i	$0.527302\pi$
$864$	2.19820	0.0747844
$865$	−8.51243	−0.289431
$866$	19.8622	0.674947
$867$	6.37635	0.216552
$868$	−22.3196	−0.757576
$869$	50.1487	1.70118
$870$	−0.882219	−0.0299100
$871$	12.7709	0.432727
$872$	−0.0536094	−0.00181544
$873$	6.49898	0.219957
$874$	3.90803	0.132191
$875$	3.43840	0.116239
$876$	−3.68023	−0.124344
$877$	−44.1525	−1.49093	−0.745463	−	0.666548i	$-0.767771\pi$
$877$	−44.1525	−1.49093	−0.745463	+	0.666548i	$0.767771\pi$
$878$	−0.474222	−0.0160042
$879$	7.46972	0.251947
$880$	−3.38583	−0.114136
$881$	−9.52816	−0.321012	−0.160506	−	0.987035i	$-0.551313\pi$
$881$	−9.52816	−0.321012	−0.160506	+	0.987035i	$0.551313\pi$
$882$	−13.7889	−0.464298
$883$	51.3873	1.72932	0.864660	−	0.502357i	$-0.167534\pi$
$883$	51.3873	1.72932	0.864660	+	0.502357i	$0.167534\pi$
$884$	0.365769	0.0123021
$885$	−2.74381	−0.0922322
$886$	33.8254	1.13639
$887$	−27.9208	−0.937489	−0.468745	−	0.883334i	$-0.655294\pi$
$887$	−27.9208	−0.937489	−0.468745	+	0.883334i	$0.655294\pi$
$888$	1.92452	0.0645827
$889$	−37.7282	−1.26536
$890$	14.4035	0.482806
$891$	−26.2505	−0.879425
$892$	−22.9937	−0.769887
$893$	11.8569	0.396776
$894$	6.22993	0.208360
$895$	−3.19678	−0.106857
$896$	3.43840	0.114869
$897$	−8.37287	−0.279562
$898$	19.6041	0.654198
$899$	−15.2644	−0.509097
$900$	−2.85925	−0.0953083
$901$	−0.0409721	−0.00136498
$902$	35.9298	1.19633
$903$	−2.55861	−0.0851454
$904$	0.155014	0.00515568
$905$	−2.60419	−0.0865661
$906$	−4.81564	−0.159989
$907$	−22.1386	−0.735100	−0.367550	−	0.930004i	$-0.619803\pi$
$907$	−22.1386	−0.735100	−0.367550	+	0.930004i	$0.619803\pi$
$908$	20.1913	0.670071
$909$	−18.2889	−0.606604
$910$	−19.7933	−0.656143
$911$	−18.5885	−0.615863	−0.307932	−	0.951409i	$-0.599637\pi$
$911$	−18.5885	−0.615863	−0.307932	+	0.951409i	$0.599637\pi$
$912$	0.378181	0.0125228
$913$	−3.18435	−0.105387
$914$	−35.5672	−1.17646
$915$	1.20322	0.0397771
$916$	−4.15083	−0.137147
$917$	21.5610	0.712006
$918$	−0.139673	−0.00460989
$919$	19.2906	0.636337	0.318169	−	0.948034i	$-0.396932\pi$
$919$	19.2906	0.636337	0.318169	+	0.948034i	$0.396932\pi$
$920$	−3.87690	−0.127818
$921$	2.43495	0.0802344
$922$	5.81131	0.191385
$923$	−30.5501	−1.00557
$924$	4.36765	0.143685
$925$	−5.12976	−0.168665
$926$	18.3243	0.602174
$927$	−10.0057	−0.328631
$928$	2.35153	0.0771927
$929$	29.4070	0.964813	0.482407	−	0.875947i	$-0.339763\pi$
$929$	29.4070	0.964813	0.482407	+	0.875947i	$0.339763\pi$
$930$	2.43532	0.0798573
$931$	−4.86130	−0.159323
$932$	16.8766	0.552811
$933$	8.87576	0.290579
$934$	38.5130	1.26019
$935$	0.215134	0.00703563
$936$	16.4594	0.537993
$937$	−43.4801	−1.42043	−0.710217	−	0.703983i	$-0.751403\pi$
$937$	−43.4801	−1.42043	−0.710217	+	0.703983i	$0.751403\pi$
$938$	−7.62810	−0.249066
$939$	1.10639	0.0361056
$940$	−11.7625	−0.383650
$941$	−59.6417	−1.94426	−0.972132	−	0.234436i	$-0.924676\pi$
$941$	−59.6417	−1.94426	−0.972132	+	0.234436i	$0.924676\pi$
$942$	3.42690	0.111655
$943$	41.1410	1.33974
$944$	7.31355	0.238036
$945$	7.55830	0.245872
$946$	−6.71565	−0.218344
$947$	49.3935	1.60507	0.802537	−	0.596602i	$-0.203483\pi$
$947$	49.3935	1.60507	0.802537	+	0.596602i	$0.203483\pi$
$948$	5.55675	0.180475
$949$	−56.4692	−1.83307
$950$	−1.00803	−0.0327048
$951$	−11.5048	−0.373068
$952$	−0.218474	−0.00708079
$953$	56.6504	1.83509	0.917543	−	0.397637i	$-0.130170\pi$
$953$	56.6504	1.83509	0.917543	+	0.397637i	$0.130170\pi$
$954$	−1.84373	−0.0596928
$955$	−19.1936	−0.621091
$956$	21.9324	0.709344
$957$	2.98704	0.0965574
$958$	−10.0936	−0.326111
$959$	35.5012	1.14639
$960$	−0.375168	−0.0121085
$961$	11.1366	0.359245
$962$	29.5297	0.952077
$963$	32.6813	1.05314
$964$	7.80572	0.251405
$965$	6.67776	0.214965
$966$	5.00112	0.160908
$967$	−9.63750	−0.309921	−0.154961	−	0.987921i	$-0.549525\pi$
$967$	−9.63750	−0.309921	−0.154961	+	0.987921i	$0.549525\pi$
$968$	0.463848	0.0149086
$969$	−0.0240294	−0.000771936 0
$970$	−2.27297	−0.0729806
$971$	−20.9998	−0.673914	−0.336957	−	0.941520i	$-0.609398\pi$
$971$	−20.9998	−0.673914	−0.336957	+	0.941520i	$0.609398\pi$
$972$	−9.50331	−0.304819
$973$	48.5621	1.55683
$974$	41.1635	1.31896
$975$	2.15968	0.0691651
$976$	−3.20714	−0.102658
$977$	−60.3870	−1.93195	−0.965975	−	0.258634i	$-0.916728\pi$
$977$	−60.3870	−1.93195	−0.965975	+	0.258634i	$0.916728\pi$
$978$	−4.00634	−0.128109
$979$	−48.7678	−1.55862
$980$	4.82258	0.154052
$981$	0.153283	0.00489393
$982$	−26.6005	−0.848857
$983$	−23.5187	−0.750129	−0.375065	−	0.926999i	$-0.622379\pi$
$983$	−23.5187	−0.750129	−0.375065	+	0.926999i	$0.622379\pi$
$984$	3.98122	0.126917
$985$	−22.4189	−0.714326
$986$	−0.149415	−0.00475834
$987$	15.1733	0.482972
$988$	5.80278	0.184611
$989$	−7.68967	−0.244517
$990$	9.68093	0.307680
$991$	−10.8645	−0.345123	−0.172561	−	0.984999i	$-0.555204\pi$
$991$	−10.8645	−0.345123	−0.172561	+	0.984999i	$0.555204\pi$
$992$	−6.49127	−0.206098
$993$	1.56943	0.0498043
$994$	18.2476	0.578779
$995$	−1.94284	−0.0615922
$996$	−0.352844	−0.0111803
$997$	−32.9452	−1.04338	−0.521692	−	0.853134i	$-0.674699\pi$
$997$	−32.9452	−1.04338	−0.521692	+	0.853134i	$0.674699\pi$
$998$	1.47382	0.0466530
$999$	−11.2763	−0.356765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.h.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.h.1.5	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.375168 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.375168 q^{6} +3.43840 q^{7} +1.00000 q^{8} -2.85925 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.375168 q^{3} +1.00000 q^{4} +1.00000 q^{5} -0.375168 q^{6} +3.43840 q^{7} +1.00000 q^{8} -2.85925 q^{9} +1.00000 q^{10} -3.38583 q^{11} -0.375168 q^{12} -5.75656 q^{13} +3.43840 q^{14} -0.375168 q^{15} +1.00000 q^{16} -0.0635395 q^{17} -2.85925 q^{18} -1.00803 q^{19} +1.00000 q^{20} -1.28998 q^{21} -3.38583 q^{22} -3.87690 q^{23} -0.375168 q^{24} +1.00000 q^{25} -5.75656 q^{26} +2.19820 q^{27} +3.43840 q^{28} +2.35153 q^{29} -0.375168 q^{30} -6.49127 q^{31} +1.00000 q^{32} +1.27026 q^{33} -0.0635395 q^{34} +3.43840 q^{35} -2.85925 q^{36} -5.12976 q^{37} -1.00803 q^{38} +2.15968 q^{39} +1.00000 q^{40} -10.6118 q^{41} -1.28998 q^{42} +1.98346 q^{43} -3.38583 q^{44} -2.85925 q^{45} -3.87690 q^{46} -11.7625 q^{47} -0.375168 q^{48} +4.82258 q^{49} +1.00000 q^{50} +0.0238380 q^{51} -5.75656 q^{52} +0.644829 q^{53} +2.19820 q^{54} -3.38583 q^{55} +3.43840 q^{56} +0.378181 q^{57} +2.35153 q^{58} +7.31355 q^{59} -0.375168 q^{60} -3.20714 q^{61} -6.49127 q^{62} -9.83123 q^{63} +1.00000 q^{64} -5.75656 q^{65} +1.27026 q^{66} -2.21850 q^{67} -0.0635395 q^{68} +1.45449 q^{69} +3.43840 q^{70} +5.30701 q^{71} -2.85925 q^{72} +9.80955 q^{73} -5.12976 q^{74} -0.375168 q^{75} -1.00803 q^{76} -11.6418 q^{77} +2.15968 q^{78} -14.8113 q^{79} +1.00000 q^{80} +7.75305 q^{81} -10.6118 q^{82} +0.940494 q^{83} -1.28998 q^{84} -0.0635395 q^{85} +1.98346 q^{86} -0.882219 q^{87} -3.38583 q^{88} +14.4035 q^{89} -2.85925 q^{90} -19.7933 q^{91} -3.87690 q^{92} +2.43532 q^{93} -11.7625 q^{94} -1.00803 q^{95} -0.375168 q^{96} -2.27297 q^{97} +4.82258 q^{98} +9.68093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9} + 9 q^{10} - 11 q^{11} - 4 q^{12} - 14 q^{13} - 7 q^{14} - 4 q^{15} + 9 q^{16} - 13 q^{17} - 7 q^{18} - 11 q^{19} + 9 q^{20} - 8 q^{21} - 11 q^{22} - 9 q^{23} - 4 q^{24} + 9 q^{25} - 14 q^{26} - 4 q^{27} - 7 q^{28} - 20 q^{29} - 4 q^{30} - 11 q^{31} + 9 q^{32} + 4 q^{33} - 13 q^{34} - 7 q^{35} - 7 q^{36} - 25 q^{37} - 11 q^{38} - 8 q^{39} + 9 q^{40} - 29 q^{41} - 8 q^{42} - 11 q^{43} - 11 q^{44} - 7 q^{45} - 9 q^{46} - 3 q^{47} - 4 q^{48} - 18 q^{49} + 9 q^{50} + q^{51} - 14 q^{52} - 9 q^{53} - 4 q^{54} - 11 q^{55} - 7 q^{56} - 17 q^{57} - 20 q^{58} - 10 q^{59} - 4 q^{60} - 10 q^{61} - 11 q^{62} + 16 q^{63} + 9 q^{64} - 14 q^{65} + 4 q^{66} - 16 q^{67} - 13 q^{68} + 5 q^{69} - 7 q^{70} - 8 q^{71} - 7 q^{72} - 22 q^{73} - 25 q^{74} - 4 q^{75} - 11 q^{76} - 15 q^{77} - 8 q^{78} - 9 q^{79} + 9 q^{80} - 15 q^{81} - 29 q^{82} + 11 q^{83} - 8 q^{84} - 13 q^{85} - 11 q^{86} + 12 q^{87} - 11 q^{88} - 28 q^{89} - 7 q^{90} - 6 q^{91} - 9 q^{92} + 16 q^{93} - 3 q^{94} - 11 q^{95} - 4 q^{96} - 28 q^{97} - 18 q^{98} + 9 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 4 * q^3 + 9 * q^4 + 9 * q^5 - 4 * q^6 - 7 * q^7 + 9 * q^8 - 7 * q^9 + 9 * q^10 - 11 * q^11 - 4 * q^12 - 14 * q^13 - 7 * q^14 - 4 * q^15 + 9 * q^16 - 13 * q^17 - 7 * q^18 - 11 * q^19 + 9 * q^20 - 8 * q^21 - 11 * q^22 - 9 * q^23 - 4 * q^24 + 9 * q^25 - 14 * q^26 - 4 * q^27 - 7 * q^28 - 20 * q^29 - 4 * q^30 - 11 * q^31 + 9 * q^32 + 4 * q^33 - 13 * q^34 - 7 * q^35 - 7 * q^36 - 25 * q^37 - 11 * q^38 - 8 * q^39 + 9 * q^40 - 29 * q^41 - 8 * q^42 - 11 * q^43 - 11 * q^44 - 7 * q^45 - 9 * q^46 - 3 * q^47 - 4 * q^48 - 18 * q^49 + 9 * q^50 + q^51 - 14 * q^52 - 9 * q^53 - 4 * q^54 - 11 * q^55 - 7 * q^56 - 17 * q^57 - 20 * q^58 - 10 * q^59 - 4 * q^60 - 10 * q^61 - 11 * q^62 + 16 * q^63 + 9 * q^64 - 14 * q^65 + 4 * q^66 - 16 * q^67 - 13 * q^68 + 5 * q^69 - 7 * q^70 - 8 * q^71 - 7 * q^72 - 22 * q^73 - 25 * q^74 - 4 * q^75 - 11 * q^76 - 15 * q^77 - 8 * q^78 - 9 * q^79 + 9 * q^80 - 15 * q^81 - 29 * q^82 + 11 * q^83 - 8 * q^84 - 13 * q^85 - 11 * q^86 + 12 * q^87 - 11 * q^88 - 28 * q^89 - 7 * q^90 - 6 * q^91 - 9 * q^92 + 16 * q^93 - 3 * q^94 - 11 * q^95 - 4 * q^96 - 28 * q^97 - 18 * q^98 + 9 * q^99

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