LMFDB - Embedded newform 4010.2.a.h.1.1

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			1.1
Root			$-1.87174$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.53021 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53021 q^{6} +1.34700 q^{7} +1.00000 q^{8} +3.40195 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.53021 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53021 q^{6} +1.34700 q^{7} +1.00000 q^{8} +3.40195 q^{9} +1.00000 q^{10} -0.577693 q^{11} -2.53021 q^{12} -1.36751 q^{13} +1.34700 q^{14} -2.53021 q^{15} +1.00000 q^{16} +0.712207 q^{17} +3.40195 q^{18} -4.53294 q^{19} +1.00000 q^{20} -3.40818 q^{21} -0.577693 q^{22} -2.32266 q^{23} -2.53021 q^{24} +1.00000 q^{25} -1.36751 q^{26} -1.01701 q^{27} +1.34700 q^{28} -5.17745 q^{29} -2.53021 q^{30} +3.76472 q^{31} +1.00000 q^{32} +1.46168 q^{33} +0.712207 q^{34} +1.34700 q^{35} +3.40195 q^{36} -10.4271 q^{37} -4.53294 q^{38} +3.46007 q^{39} +1.00000 q^{40} -5.67548 q^{41} -3.40818 q^{42} -2.95319 q^{43} -0.577693 q^{44} +3.40195 q^{45} -2.32266 q^{46} -1.51744 q^{47} -2.53021 q^{48} -5.18560 q^{49} +1.00000 q^{50} -1.80203 q^{51} -1.36751 q^{52} +7.64079 q^{53} -1.01701 q^{54} -0.577693 q^{55} +1.34700 q^{56} +11.4693 q^{57} -5.17745 q^{58} +8.28272 q^{59} -2.53021 q^{60} +2.71207 q^{61} +3.76472 q^{62} +4.58241 q^{63} +1.00000 q^{64} -1.36751 q^{65} +1.46168 q^{66} +7.91417 q^{67} +0.712207 q^{68} +5.87682 q^{69} +1.34700 q^{70} -11.6362 q^{71} +3.40195 q^{72} -4.57773 q^{73} -10.4271 q^{74} -2.53021 q^{75} -4.53294 q^{76} -0.778150 q^{77} +3.46007 q^{78} +14.3600 q^{79} +1.00000 q^{80} -7.63260 q^{81} -5.67548 q^{82} +9.43838 q^{83} -3.40818 q^{84} +0.712207 q^{85} -2.95319 q^{86} +13.1000 q^{87} -0.577693 q^{88} -13.5779 q^{89} +3.40195 q^{90} -1.84202 q^{91} -2.32266 q^{92} -9.52553 q^{93} -1.51744 q^{94} -4.53294 q^{95} -2.53021 q^{96} -10.3604 q^{97} -5.18560 q^{98} -1.96528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.53021	−1.46082	−0.730408	−	0.683011i	$-0.760670\pi$
$3$	−2.53021	−1.46082	−0.730408	+	0.683011i	$0.760670\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.53021	−1.03295
$7$	1.34700	0.509117	0.254558	−	0.967057i	$-0.418070\pi$
$7$	1.34700	0.509117	0.254558	+	0.967057i	$0.418070\pi$
$8$	1.00000	0.353553
$9$	3.40195	1.13398
$10$	1.00000	0.316228
$11$	−0.577693	−0.174181	−0.0870905	−	0.996200i	$-0.527757\pi$
$11$	−0.577693	−0.174181	−0.0870905	+	0.996200i	$0.527757\pi$
$12$	−2.53021	−0.730408
$13$	−1.36751	−0.379278	−0.189639	−	0.981854i	$-0.560732\pi$
$13$	−1.36751	−0.379278	−0.189639	+	0.981854i	$0.560732\pi$
$14$	1.34700	0.360000
$15$	−2.53021	−0.653297
$16$	1.00000	0.250000
$17$	0.712207	0.172736	0.0863678	−	0.996263i	$-0.472474\pi$
$17$	0.712207	0.172736	0.0863678	+	0.996263i	$0.472474\pi$
$18$	3.40195	0.801847
$19$	−4.53294	−1.03993	−0.519964	−	0.854188i	$-0.674054\pi$
$19$	−4.53294	−1.03993	−0.519964	+	0.854188i	$0.674054\pi$
$20$	1.00000	0.223607
$21$	−3.40818	−0.743725
$22$	−0.577693	−0.123165
$23$	−2.32266	−0.484309	−0.242154	−	0.970238i	$-0.577854\pi$
$23$	−2.32266	−0.484309	−0.242154	+	0.970238i	$0.577854\pi$
$24$	−2.53021	−0.516476
$25$	1.00000	0.200000
$26$	−1.36751	−0.268190
$27$	−1.01701	−0.195723
$28$	1.34700	0.254558
$29$	−5.17745	−0.961429	−0.480714	−	0.876877i	$-0.659623\pi$
$29$	−5.17745	−0.961429	−0.480714	+	0.876877i	$0.659623\pi$
$30$	−2.53021	−0.461950
$31$	3.76472	0.676164	0.338082	−	0.941117i	$-0.390222\pi$
$31$	3.76472	0.676164	0.338082	+	0.941117i	$0.390222\pi$
$32$	1.00000	0.176777
$33$	1.46168	0.254446
$34$	0.712207	0.122143
$35$	1.34700	0.227684
$36$	3.40195	0.566991
$37$	−10.4271	−1.71421	−0.857105	−	0.515142i	$-0.827739\pi$
$37$	−10.4271	−1.71421	−0.857105	+	0.515142i	$0.827739\pi$
$38$	−4.53294	−0.735339
$39$	3.46007	0.554055
$40$	1.00000	0.158114
$41$	−5.67548	−0.886362	−0.443181	−	0.896432i	$-0.646150\pi$
$41$	−5.67548	−0.886362	−0.443181	+	0.896432i	$0.646150\pi$
$42$	−3.40818	−0.525893
$43$	−2.95319	−0.450358	−0.225179	−	0.974317i	$-0.572297\pi$
$43$	−2.95319	−0.450358	−0.225179	+	0.974317i	$0.572297\pi$
$44$	−0.577693	−0.0870905
$45$	3.40195	0.507132
$46$	−2.32266	−0.342458
$47$	−1.51744	−0.221341	−0.110671	−	0.993857i	$-0.535300\pi$
$47$	−1.51744	−0.221341	−0.110671	+	0.993857i	$0.535300\pi$
$48$	−2.53021	−0.365204
$49$	−5.18560	−0.740800
$50$	1.00000	0.141421
$51$	−1.80203	−0.252335
$52$	−1.36751	−0.189639
$53$	7.64079	1.04954	0.524772	−	0.851243i	$-0.324151\pi$
$53$	7.64079	1.04954	0.524772	+	0.851243i	$0.324151\pi$
$54$	−1.01701	−0.138397
$55$	−0.577693	−0.0778961
$56$	1.34700	0.180000
$57$	11.4693	1.51914
$58$	−5.17745	−0.679833
$59$	8.28272	1.07832	0.539159	−	0.842204i	$-0.318742\pi$
$59$	8.28272	1.07832	0.539159	+	0.842204i	$0.318742\pi$
$60$	−2.53021	−0.326648
$61$	2.71207	0.347245	0.173622	−	0.984812i	$-0.444453\pi$
$61$	2.71207	0.347245	0.173622	+	0.984812i	$0.444453\pi$
$62$	3.76472	0.478120
$63$	4.58241	0.577329
$64$	1.00000	0.125000
$65$	−1.36751	−0.169618
$66$	1.46168	0.179921
$67$	7.91417	0.966869	0.483435	−	0.875380i	$-0.339389\pi$
$67$	7.91417	0.966869	0.483435	+	0.875380i	$0.339389\pi$
$68$	0.712207	0.0863678
$69$	5.87682	0.707486
$70$	1.34700	0.160997
$71$	−11.6362	−1.38096	−0.690480	−	0.723351i	$-0.742601\pi$
$71$	−11.6362	−1.38096	−0.690480	+	0.723351i	$0.742601\pi$
$72$	3.40195	0.400923
$73$	−4.57773	−0.535782	−0.267891	−	0.963449i	$-0.586327\pi$
$73$	−4.57773	−0.535782	−0.267891	+	0.963449i	$0.586327\pi$
$74$	−10.4271	−1.21213
$75$	−2.53021	−0.292163
$76$	−4.53294	−0.519964
$77$	−0.778150	−0.0886784
$78$	3.46007	0.391776
$79$	14.3600	1.61563	0.807814	−	0.589438i	$-0.200651\pi$
$79$	14.3600	1.61563	0.807814	+	0.589438i	$0.200651\pi$
$80$	1.00000	0.111803
$81$	−7.63260	−0.848067
$82$	−5.67548	−0.626752
$83$	9.43838	1.03600	0.517998	−	0.855382i	$-0.326677\pi$
$83$	9.43838	1.03600	0.517998	+	0.855382i	$0.326677\pi$
$84$	−3.40818	−0.371863
$85$	0.712207	0.0772497
$86$	−2.95319	−0.318451
$87$	13.1000	1.40447
$88$	−0.577693	−0.0615823
$89$	−13.5779	−1.43925	−0.719626	−	0.694362i	$-0.755687\pi$
$89$	−13.5779	−1.43925	−0.719626	+	0.694362i	$0.755687\pi$
$90$	3.40195	0.358597
$91$	−1.84202	−0.193097
$92$	−2.32266	−0.242154
$93$	−9.52553	−0.987751
$94$	−1.51744	−0.156512
$95$	−4.53294	−0.465069
$96$	−2.53021	−0.258238
$97$	−10.3604	−1.05194	−0.525971	−	0.850502i	$-0.676298\pi$
$97$	−10.3604	−1.05194	−0.525971	+	0.850502i	$0.676298\pi$
$98$	−5.18560	−0.523825
$99$	−1.96528	−0.197518
$100$	1.00000	0.100000
$101$	−11.1309	−1.10756	−0.553781	−	0.832662i	$-0.686815\pi$
$101$	−11.1309	−1.10756	−0.553781	+	0.832662i	$0.686815\pi$
$102$	−1.80203	−0.178428
$103$	2.07849	0.204800	0.102400	−	0.994743i	$-0.467348\pi$
$103$	2.07849	0.204800	0.102400	+	0.994743i	$0.467348\pi$
$104$	−1.36751	−0.134095
$105$	−3.40818	−0.332604
$106$	7.64079	0.742139
$107$	−3.44015	−0.332572	−0.166286	−	0.986078i	$-0.553177\pi$
$107$	−3.44015	−0.332572	−0.166286	+	0.986078i	$0.553177\pi$
$108$	−1.01701	−0.0978617
$109$	3.39952	0.325615	0.162808	−	0.986658i	$-0.447945\pi$
$109$	3.39952	0.325615	0.162808	+	0.986658i	$0.447945\pi$
$110$	−0.577693	−0.0550808
$111$	26.3828	2.50414
$112$	1.34700	0.127279
$113$	0.290887	0.0273643	0.0136822	−	0.999906i	$-0.495645\pi$
$113$	0.290887	0.0273643	0.0136822	+	0.999906i	$0.495645\pi$
$114$	11.4693	1.07420
$115$	−2.32266	−0.216589
$116$	−5.17745	−0.480714
$117$	−4.65218	−0.430094
$118$	8.28272	0.762486
$119$	0.959340	0.0879426
$120$	−2.53021	−0.230975
$121$	−10.6663	−0.969661
$122$	2.71207	0.245539
$123$	14.3602	1.29481
$124$	3.76472	0.338082
$125$	1.00000	0.0894427
$126$	4.58241	0.408233
$127$	−18.9143	−1.67837	−0.839185	−	0.543846i	$-0.816968\pi$
$127$	−18.9143	−1.67837	−0.839185	+	0.543846i	$0.816968\pi$
$128$	1.00000	0.0883883
$129$	7.47219	0.657890
$130$	−1.36751	−0.119938
$131$	−17.9107	−1.56486	−0.782432	−	0.622736i	$-0.786021\pi$
$131$	−17.9107	−1.56486	−0.782432	+	0.622736i	$0.786021\pi$
$132$	1.46168	0.127223
$133$	−6.10585	−0.529444
$134$	7.91417	0.683680
$135$	−1.01701	−0.0875302
$136$	0.712207	0.0610713
$137$	−6.36326	−0.543650	−0.271825	−	0.962347i	$-0.587627\pi$
$137$	−6.36326	−0.543650	−0.271825	+	0.962347i	$0.587627\pi$
$138$	5.87682	0.500268
$139$	16.3348	1.38550	0.692750	−	0.721177i	$-0.256399\pi$
$139$	16.3348	1.38550	0.692750	+	0.721177i	$0.256399\pi$
$140$	1.34700	0.113842
$141$	3.83943	0.323339
$142$	−11.6362	−0.976487
$143$	0.789998	0.0660629
$144$	3.40195	0.283496
$145$	−5.17745	−0.429964
$146$	−4.57773	−0.378855
$147$	13.1206	1.08217
$148$	−10.4271	−0.857105
$149$	14.9990	1.22877	0.614384	−	0.789007i	$-0.289405\pi$
$149$	14.9990	1.22877	0.614384	+	0.789007i	$0.289405\pi$
$150$	−2.53021	−0.206591
$151$	−23.2183	−1.88948	−0.944739	−	0.327825i	$-0.893684\pi$
$151$	−23.2183	−1.88948	−0.944739	+	0.327825i	$0.893684\pi$
$152$	−4.53294	−0.367670
$153$	2.42289	0.195879
$154$	−0.778150	−0.0627051
$155$	3.76472	0.302390
$156$	3.46007	0.277027
$157$	9.50463	0.758552	0.379276	−	0.925284i	$-0.376173\pi$
$157$	9.50463	0.758552	0.379276	+	0.925284i	$0.376173\pi$
$158$	14.3600	1.14242
$159$	−19.3328	−1.53319
$160$	1.00000	0.0790569
$161$	−3.12862	−0.246569
$162$	−7.63260	−0.599674
$163$	10.0142	0.784369	0.392185	−	0.919887i	$-0.371719\pi$
$163$	10.0142	0.784369	0.392185	+	0.919887i	$0.371719\pi$
$164$	−5.67548	−0.443181
$165$	1.46168	0.113792
$166$	9.43838	0.732560
$167$	−3.33553	−0.258111	−0.129056	−	0.991637i	$-0.541195\pi$
$167$	−3.33553	−0.258111	−0.129056	+	0.991637i	$0.541195\pi$
$168$	−3.40818	−0.262947
$169$	−11.1299	−0.856148
$170$	0.712207	0.0546238
$171$	−15.4208	−1.17926
$172$	−2.95319	−0.225179
$173$	6.32321	0.480745	0.240372	−	0.970681i	$-0.422730\pi$
$173$	6.32321	0.480745	0.240372	+	0.970681i	$0.422730\pi$
$174$	13.1000	0.993111
$175$	1.34700	0.101823
$176$	−0.577693	−0.0435452
$177$	−20.9570	−1.57522
$178$	−13.5779	−1.01770
$179$	11.2160	0.838323	0.419161	−	0.907912i	$-0.362324\pi$
$179$	11.2160	0.838323	0.419161	+	0.907912i	$0.362324\pi$
$180$	3.40195	0.253566
$181$	−14.8885	−1.10666	−0.553328	−	0.832964i	$-0.686642\pi$
$181$	−14.8885	−1.10666	−0.553328	+	0.832964i	$0.686642\pi$
$182$	−1.84202	−0.136540
$183$	−6.86209	−0.507260
$184$	−2.32266	−0.171229
$185$	−10.4271	−0.766618
$186$	−9.52553	−0.698445
$187$	−0.411437	−0.0300873
$188$	−1.51744	−0.110671
$189$	−1.36991	−0.0996460
$190$	−4.53294	−0.328854
$191$	−24.1693	−1.74883	−0.874415	−	0.485179i	$-0.838754\pi$
$191$	−24.1693	−1.74883	−0.874415	+	0.485179i	$0.838754\pi$
$192$	−2.53021	−0.182602
$193$	−3.81992	−0.274964	−0.137482	−	0.990504i	$-0.543901\pi$
$193$	−3.81992	−0.274964	−0.137482	+	0.990504i	$0.543901\pi$
$194$	−10.3604	−0.743835
$195$	3.46007	0.247781
$196$	−5.18560	−0.370400
$197$	16.8215	1.19848	0.599242	−	0.800568i	$-0.295469\pi$
$197$	16.8215	1.19848	0.599242	+	0.800568i	$0.295469\pi$
$198$	−1.96528	−0.139666
$199$	5.35270	0.379443	0.189721	−	0.981838i	$-0.439242\pi$
$199$	5.35270	0.379443	0.189721	+	0.981838i	$0.439242\pi$
$200$	1.00000	0.0707107
$201$	−20.0245	−1.41242
$202$	−11.1309	−0.783164
$203$	−6.97401	−0.489479
$204$	−1.80203	−0.126167
$205$	−5.67548	−0.396393
$206$	2.07849	0.144815
$207$	−7.90157	−0.549197
$208$	−1.36751	−0.0948194
$209$	2.61864	0.181135
$210$	−3.40818	−0.235187
$211$	5.87544	0.404482	0.202241	−	0.979336i	$-0.435178\pi$
$211$	5.87544	0.404482	0.202241	+	0.979336i	$0.435178\pi$
$212$	7.64079	0.524772
$213$	29.4420	2.01733
$214$	−3.44015	−0.235164
$215$	−2.95319	−0.201406
$216$	−1.01701	−0.0691987
$217$	5.07106	0.344246
$218$	3.39952	0.230245
$219$	11.5826	0.782679
$220$	−0.577693	−0.0389480
$221$	−0.973947	−0.0655148
$222$	26.3828	1.77070
$223$	−14.0073	−0.937999	−0.469000	−	0.883198i	$-0.655385\pi$
$223$	−14.0073	−0.937999	−0.469000	+	0.883198i	$0.655385\pi$
$224$	1.34700	0.0899999
$225$	3.40195	0.226796
$226$	0.290887	0.0193495
$227$	0.104371	0.00692736	0.00346368	−	0.999994i	$-0.498897\pi$
$227$	0.104371	0.00692736	0.00346368	+	0.999994i	$0.498897\pi$
$228$	11.4693	0.759571
$229$	−23.1599	−1.53045	−0.765226	−	0.643762i	$-0.777373\pi$
$229$	−23.1599	−1.53045	−0.765226	+	0.643762i	$0.777373\pi$
$230$	−2.32266	−0.153152
$231$	1.96888	0.129543
$232$	−5.17745	−0.339916
$233$	−12.7567	−0.835718	−0.417859	−	0.908512i	$-0.637219\pi$
$233$	−12.7567	−0.835718	−0.417859	+	0.908512i	$0.637219\pi$
$234$	−4.65218	−0.304122
$235$	−1.51744	−0.0989868
$236$	8.28272	0.539159
$237$	−36.3338	−2.36013
$238$	0.959340	0.0621848
$239$	6.63612	0.429255	0.214627	−	0.976696i	$-0.431146\pi$
$239$	6.63612	0.429255	0.214627	+	0.976696i	$0.431146\pi$
$240$	−2.53021	−0.163324
$241$	−13.5244	−0.871182	−0.435591	−	0.900145i	$-0.643461\pi$
$241$	−13.5244	−0.871182	−0.435591	+	0.900145i	$0.643461\pi$
$242$	−10.6663	−0.685654
$243$	22.3631	1.43459
$244$	2.71207	0.173622
$245$	−5.18560	−0.331296
$246$	14.3602	0.915570
$247$	6.19881	0.394421
$248$	3.76472	0.239060
$249$	−23.8811	−1.51340
$250$	1.00000	0.0632456
$251$	8.04276	0.507654	0.253827	−	0.967250i	$-0.418311\pi$
$251$	8.04276	0.507654	0.253827	+	0.967250i	$0.418311\pi$
$252$	4.58241	0.288665
$253$	1.34179	0.0843573
$254$	−18.9143	−1.18679
$255$	−1.80203	−0.112848
$256$	1.00000	0.0625000
$257$	13.7741	0.859205	0.429602	−	0.903018i	$-0.358654\pi$
$257$	13.7741	0.859205	0.429602	+	0.903018i	$0.358654\pi$
$258$	7.47219	0.465198
$259$	−14.0453	−0.872732
$260$	−1.36751	−0.0848091
$261$	−17.6134	−1.09024
$262$	−17.9107	−1.10653
$263$	−18.5973	−1.14676	−0.573379	−	0.819291i	$-0.694368\pi$
$263$	−18.5973	−1.14676	−0.573379	+	0.819291i	$0.694368\pi$
$264$	1.46168	0.0899603
$265$	7.64079	0.469370
$266$	−6.10585	−0.374373
$267$	34.3548	2.10248
$268$	7.91417	0.483435
$269$	−16.4379	−1.00224	−0.501120	−	0.865378i	$-0.667078\pi$
$269$	−16.4379	−1.00224	−0.501120	+	0.865378i	$0.667078\pi$
$270$	−1.01701	−0.0618932
$271$	−15.7107	−0.954355	−0.477177	−	0.878807i	$-0.658340\pi$
$271$	−15.7107	−0.954355	−0.477177	+	0.878807i	$0.658340\pi$
$272$	0.712207	0.0431839
$273$	4.66070	0.282078
$274$	−6.36326	−0.384419
$275$	−0.577693	−0.0348362
$276$	5.87682	0.353743
$277$	7.68405	0.461690	0.230845	−	0.972991i	$-0.425851\pi$
$277$	7.68405	0.461690	0.230845	+	0.972991i	$0.425851\pi$
$278$	16.3348	0.979697
$279$	12.8074	0.766758
$280$	1.34700	0.0804984
$281$	−21.2116	−1.26538	−0.632689	−	0.774406i	$-0.718049\pi$
$281$	−21.2116	−1.26538	−0.632689	+	0.774406i	$0.718049\pi$
$282$	3.83943	0.228635
$283$	16.7144	0.993567	0.496783	−	0.867875i	$-0.334514\pi$
$283$	16.7144	0.993567	0.496783	+	0.867875i	$0.334514\pi$
$284$	−11.6362	−0.690480
$285$	11.4693	0.679381
$286$	0.789998	0.0467136
$287$	−7.64485	−0.451261
$288$	3.40195	0.200462
$289$	−16.4928	−0.970162
$290$	−5.17745	−0.304031
$291$	26.2140	1.53669
$292$	−4.57773	−0.267891
$293$	−12.0250	−0.702510	−0.351255	−	0.936280i	$-0.614245\pi$
$293$	−12.0250	−0.702510	−0.351255	+	0.936280i	$0.614245\pi$
$294$	13.1206	0.765212
$295$	8.28272	0.482239
$296$	−10.4271	−0.606065
$297$	0.587518	0.0340913
$298$	14.9990	0.868870
$299$	3.17625	0.183687
$300$	−2.53021	−0.146082
$301$	−3.97794	−0.229285
$302$	−23.2183	−1.33606
$303$	28.1634	1.61794
$304$	−4.53294	−0.259982
$305$	2.71207	0.155292
$306$	2.42289	0.138507
$307$	−5.42432	−0.309582	−0.154791	−	0.987947i	$-0.549470\pi$
$307$	−5.42432	−0.309582	−0.154791	+	0.987947i	$0.549470\pi$
$308$	−0.778150	−0.0443392
$309$	−5.25901	−0.299175
$310$	3.76472	0.213822
$311$	−21.0957	−1.19623	−0.598114	−	0.801411i	$-0.704083\pi$
$311$	−21.0957	−1.19623	−0.598114	+	0.801411i	$0.704083\pi$
$312$	3.46007	0.195888
$313$	26.7483	1.51191	0.755953	−	0.654626i	$-0.227174\pi$
$313$	26.7483	1.51191	0.755953	+	0.654626i	$0.227174\pi$
$314$	9.50463	0.536377
$315$	4.58241	0.258189
$316$	14.3600	0.807814
$317$	−23.2271	−1.30456	−0.652282	−	0.757977i	$-0.726188\pi$
$317$	−23.2271	−1.30456	−0.652282	+	0.757977i	$0.726188\pi$
$318$	−19.3328	−1.08413
$319$	2.99098	0.167463
$320$	1.00000	0.0559017
$321$	8.70429	0.485826
$322$	−3.12862	−0.174351
$323$	−3.22839	−0.179632
$324$	−7.63260	−0.424033
$325$	−1.36751	−0.0758555
$326$	10.0142	0.554633
$327$	−8.60150	−0.475664
$328$	−5.67548	−0.313376
$329$	−2.04398	−0.112688
$330$	1.46168	0.0804630
$331$	−10.1808	−0.559589	−0.279795	−	0.960060i	$-0.590266\pi$
$331$	−10.1808	−0.559589	−0.279795	+	0.960060i	$0.590266\pi$
$332$	9.43838	0.517998
$333$	−35.4725	−1.94388
$334$	−3.33553	−0.182512
$335$	7.91417	0.432397
$336$	−3.40818	−0.185931
$337$	−7.95932	−0.433572	−0.216786	−	0.976219i	$-0.569557\pi$
$337$	−7.95932	−0.433572	−0.216786	+	0.976219i	$0.569557\pi$
$338$	−11.1299	−0.605388
$339$	−0.736004	−0.0399742
$340$	0.712207	0.0386249
$341$	−2.17485	−0.117775
$342$	−15.4208	−0.833862
$343$	−16.4140	−0.886270
$344$	−2.95319	−0.159225
$345$	5.87682	0.316397
$346$	6.32321	0.339938
$347$	−18.5026	−0.993273	−0.496637	−	0.867959i	$-0.665432\pi$
$347$	−18.5026	−0.993273	−0.496637	+	0.867959i	$0.665432\pi$
$348$	13.1000	0.702235
$349$	−8.78113	−0.470043	−0.235021	−	0.971990i	$-0.575516\pi$
$349$	−8.78113	−0.470043	−0.235021	+	0.971990i	$0.575516\pi$
$350$	1.34700	0.0719999
$351$	1.39076	0.0742335
$352$	−0.577693	−0.0307911
$353$	−3.47737	−0.185082	−0.0925408	−	0.995709i	$-0.529499\pi$
$353$	−3.47737	−0.185082	−0.0925408	+	0.995709i	$0.529499\pi$
$354$	−20.9570	−1.11385
$355$	−11.6362	−0.617584
$356$	−13.5779	−0.719626
$357$	−2.42733	−0.128468
$358$	11.2160	0.592784
$359$	35.5011	1.87368	0.936838	−	0.349764i	$-0.113738\pi$
$359$	35.5011	1.87368	0.936838	+	0.349764i	$0.113738\pi$
$360$	3.40195	0.179298
$361$	1.54752	0.0814482
$362$	−14.8885	−0.782524
$363$	26.9879	1.41650
$364$	−1.84202	−0.0965483
$365$	−4.57773	−0.239609
$366$	−6.86209	−0.358687
$367$	22.9485	1.19790	0.598952	−	0.800785i	$-0.295584\pi$
$367$	22.9485	1.19790	0.598952	+	0.800785i	$0.295584\pi$
$368$	−2.32266	−0.121077
$369$	−19.3077	−1.00512
$370$	−10.4271	−0.542081
$371$	10.2921	0.534340
$372$	−9.52553	−0.493876
$373$	−29.0007	−1.50160	−0.750799	−	0.660531i	$-0.770331\pi$
$373$	−29.0007	−1.50160	−0.750799	+	0.660531i	$0.770331\pi$
$374$	−0.411437	−0.0212749
$375$	−2.53021	−0.130659
$376$	−1.51744	−0.0782559
$377$	7.08019	0.364649
$378$	−1.36991	−0.0704604
$379$	−23.6493	−1.21478	−0.607392	−	0.794402i	$-0.707784\pi$
$379$	−23.6493	−1.21478	−0.607392	+	0.794402i	$0.707784\pi$
$380$	−4.53294	−0.232535
$381$	47.8570	2.45179
$382$	−24.1693	−1.23661
$383$	21.2622	1.08645	0.543223	−	0.839589i	$-0.317204\pi$
$383$	21.2622	1.08645	0.543223	+	0.839589i	$0.317204\pi$
$384$	−2.53021	−0.129119
$385$	−0.778150	−0.0396582
$386$	−3.81992	−0.194429
$387$	−10.0466	−0.510698
$388$	−10.3604	−0.525971
$389$	−2.09950	−0.106449	−0.0532244	−	0.998583i	$-0.516950\pi$
$389$	−2.09950	−0.106449	−0.0532244	+	0.998583i	$0.516950\pi$
$390$	3.46007	0.175207
$391$	−1.65422	−0.0836574
$392$	−5.18560	−0.261912
$393$	45.3178	2.28598
$394$	16.8215	0.847456
$395$	14.3600	0.722530
$396$	−1.96528	−0.0987590
$397$	25.7179	1.29075	0.645373	−	0.763868i	$-0.276702\pi$
$397$	25.7179	1.29075	0.645373	+	0.763868i	$0.276702\pi$
$398$	5.35270	0.268306
$399$	15.4491	0.773420
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−20.0245	−0.998730
$403$	−5.14828	−0.256454
$404$	−11.1309	−0.553781
$405$	−7.63260	−0.379267
$406$	−6.97401	−0.346114
$407$	6.02368	0.298583
$408$	−1.80203	−0.0892139
$409$	16.4639	0.814090	0.407045	−	0.913408i	$-0.366559\pi$
$409$	16.4639	0.814090	0.407045	+	0.913408i	$0.366559\pi$
$410$	−5.67548	−0.280292
$411$	16.1004	0.794173
$412$	2.07849	0.102400
$413$	11.1568	0.548990
$414$	−7.90157	−0.388341
$415$	9.43838	0.463312
$416$	−1.36751	−0.0670475
$417$	−41.3305	−2.02396
$418$	2.61864	0.128082
$419$	12.2354	0.597739	0.298869	−	0.954294i	$-0.403390\pi$
$419$	12.2354	0.597739	0.298869	+	0.954294i	$0.403390\pi$
$420$	−3.40818	−0.166302
$421$	31.9850	1.55885	0.779427	−	0.626494i	$-0.215511\pi$
$421$	31.9850	1.55885	0.779427	+	0.626494i	$0.215511\pi$
$422$	5.87544	0.286012
$423$	−5.16225	−0.250997
$424$	7.64079	0.371070
$425$	0.712207	0.0345471
$426$	29.4420	1.42647
$427$	3.65314	0.176788
$428$	−3.44015	−0.166286
$429$	−1.99886	−0.0965058
$430$	−2.95319	−0.142416
$431$	−1.31348	−0.0632679	−0.0316339	−	0.999500i	$-0.510071\pi$
$431$	−1.31348	−0.0632679	−0.0316339	+	0.999500i	$0.510071\pi$
$432$	−1.01701	−0.0489308
$433$	15.3615	0.738225	0.369112	−	0.929385i	$-0.379662\pi$
$433$	15.3615	0.738225	0.369112	+	0.929385i	$0.379662\pi$
$434$	5.07106	0.243419
$435$	13.1000	0.628098
$436$	3.39952	0.162808
$437$	10.5285	0.503646
$438$	11.5826	0.553438
$439$	8.35739	0.398877	0.199438	−	0.979910i	$-0.436088\pi$
$439$	8.35739	0.398877	0.199438	+	0.979910i	$0.436088\pi$
$440$	−0.577693	−0.0275404
$441$	−17.6411	−0.840054
$442$	−0.973947	−0.0463259
$443$	4.13484	0.196452	0.0982260	−	0.995164i	$-0.468683\pi$
$443$	4.13484	0.196452	0.0982260	+	0.995164i	$0.468683\pi$
$444$	26.3828	1.25207
$445$	−13.5779	−0.643653
$446$	−14.0073	−0.663266
$447$	−37.9506	−1.79500
$448$	1.34700	0.0636396
$449$	30.7710	1.45217	0.726086	−	0.687604i	$-0.241337\pi$
$449$	30.7710	1.45217	0.726086	+	0.687604i	$0.241337\pi$
$450$	3.40195	0.160369
$451$	3.27869	0.154387
$452$	0.290887	0.0136822
$453$	58.7471	2.76018
$454$	0.104371	0.00489838
$455$	−1.84202	−0.0863554
$456$	11.4693	0.537098
$457$	36.3195	1.69896	0.849478	−	0.527625i	$-0.176917\pi$
$457$	36.3195	1.69896	0.849478	+	0.527625i	$0.176917\pi$
$458$	−23.1599	−1.08219
$459$	−0.724321	−0.0338084
$460$	−2.32266	−0.108295
$461$	23.5395	1.09634	0.548172	−	0.836365i	$-0.315324\pi$
$461$	23.5395	1.09634	0.548172	+	0.836365i	$0.315324\pi$
$462$	1.96888	0.0916006
$463$	27.1789	1.26311	0.631556	−	0.775330i	$-0.282416\pi$
$463$	27.1789	1.26311	0.631556	+	0.775330i	$0.282416\pi$
$464$	−5.17745	−0.240357
$465$	−9.52553	−0.441736
$466$	−12.7567	−0.590942
$467$	7.71061	0.356805	0.178402	−	0.983958i	$-0.442907\pi$
$467$	7.71061	0.356805	0.178402	+	0.983958i	$0.442907\pi$
$468$	−4.65218	−0.215047
$469$	10.6603	0.492249
$470$	−1.51744	−0.0699942
$471$	−24.0487	−1.10810
$472$	8.28272	0.381243
$473$	1.70604	0.0784437
$474$	−36.3338	−1.66887
$475$	−4.53294	−0.207985
$476$	0.959340	0.0439713
$477$	25.9936	1.19016
$478$	6.63612	0.303529
$479$	0.598714	0.0273559	0.0136780	−	0.999906i	$-0.495646\pi$
$479$	0.598714	0.0273559	0.0136780	+	0.999906i	$0.495646\pi$
$480$	−2.53021	−0.115488
$481$	14.2592	0.650161
$482$	−13.5244	−0.616019
$483$	7.91605	0.360193
$484$	−10.6663	−0.484831
$485$	−10.3604	−0.470443
$486$	22.3631	1.01441
$487$	−6.84020	−0.309959	−0.154980	−	0.987918i	$-0.549531\pi$
$487$	−6.84020	−0.309959	−0.154980	+	0.987918i	$0.549531\pi$
$488$	2.71207	0.122769
$489$	−25.3379	−1.14582
$490$	−5.18560	−0.234262
$491$	−31.9131	−1.44022	−0.720109	−	0.693861i	$-0.755908\pi$
$491$	−31.9131	−1.44022	−0.720109	+	0.693861i	$0.755908\pi$
$492$	14.3602	0.647406
$493$	−3.68742	−0.166073
$494$	6.19881	0.278898
$495$	−1.96528	−0.0883328
$496$	3.76472	0.169041
$497$	−15.6739	−0.703070
$498$	−23.8811	−1.07014
$499$	−7.28819	−0.326264	−0.163132	−	0.986604i	$-0.552160\pi$
$499$	−7.28819	−0.326264	−0.163132	+	0.986604i	$0.552160\pi$
$500$	1.00000	0.0447214
$501$	8.43959	0.377053
$502$	8.04276	0.358966
$503$	37.2400	1.66045	0.830225	−	0.557428i	$-0.188212\pi$
$503$	37.2400	1.66045	0.830225	+	0.557428i	$0.188212\pi$
$504$	4.58241	0.204117
$505$	−11.1309	−0.495317
$506$	1.34179	0.0596496
$507$	28.1610	1.25068
$508$	−18.9143	−0.839185
$509$	16.5745	0.734651	0.367326	−	0.930092i	$-0.380274\pi$
$509$	16.5745	0.734651	0.367326	+	0.930092i	$0.380274\pi$
$510$	−1.80203	−0.0797953
$511$	−6.16618	−0.272776
$512$	1.00000	0.0441942
$513$	4.61003	0.203538
$514$	13.7741	0.607549
$515$	2.07849	0.0915893
$516$	7.47219	0.328945
$517$	0.876613	0.0385534
$518$	−14.0453	−0.617115
$519$	−15.9990	−0.702280
$520$	−1.36751	−0.0599691
$521$	20.3506	0.891577	0.445789	−	0.895138i	$-0.352923\pi$
$521$	20.3506	0.891577	0.445789	+	0.895138i	$0.352923\pi$
$522$	−17.6134	−0.770918
$523$	0.0678669	0.00296761	0.00148381	−	0.999999i	$-0.499528\pi$
$523$	0.0678669	0.00296761	0.00148381	+	0.999999i	$0.499528\pi$
$524$	−17.9107	−0.782432
$525$	−3.40818	−0.148745
$526$	−18.5973	−0.810880
$527$	2.68126	0.116798
$528$	1.46168	0.0636116
$529$	−17.6052	−0.765445
$530$	7.64079	0.331895
$531$	28.1774	1.22279
$532$	−6.10585	−0.264722
$533$	7.76125	0.336177
$534$	34.3548	1.48668
$535$	−3.44015	−0.148731
$536$	7.91417	0.341840
$537$	−28.3788	−1.22463
$538$	−16.4379	−0.708690
$539$	2.99569	0.129033
$540$	−1.01701	−0.0437651
$541$	−7.41750	−0.318903	−0.159452	−	0.987206i	$-0.550973\pi$
$541$	−7.41750	−0.318903	−0.159452	+	0.987206i	$0.550973\pi$
$542$	−15.7107	−0.674831
$543$	37.6711	1.61662
$544$	0.712207	0.0305356
$545$	3.39952	0.145620
$546$	4.66070	0.199460
$547$	−29.6797	−1.26901	−0.634506	−	0.772918i	$-0.718796\pi$
$547$	−29.6797	−1.26901	−0.634506	+	0.772918i	$0.718796\pi$
$548$	−6.36326	−0.271825
$549$	9.22631	0.393769
$550$	−0.577693	−0.0246329
$551$	23.4691	0.999816
$552$	5.87682	0.250134
$553$	19.3429	0.822542
$554$	7.68405	0.326464
$555$	26.3828	1.11989
$556$	16.3348	0.692750
$557$	32.8144	1.39039	0.695196	−	0.718821i	$-0.255318\pi$
$557$	32.8144	1.39039	0.695196	+	0.718821i	$0.255318\pi$
$558$	12.8074	0.542180
$559$	4.03851	0.170811
$560$	1.34700	0.0569210
$561$	1.04102	0.0439519
$562$	−21.2116	−0.894757
$563$	38.0850	1.60509	0.802546	−	0.596591i	$-0.203478\pi$
$563$	38.0850	1.60509	0.802546	+	0.596591i	$0.203478\pi$
$564$	3.83943	0.161669
$565$	0.290887	0.0122377
$566$	16.7144	0.702558
$567$	−10.2811	−0.431765
$568$	−11.6362	−0.488243
$569$	−6.07163	−0.254536	−0.127268	−	0.991868i	$-0.540621\pi$
$569$	−6.07163	−0.254536	−0.127268	+	0.991868i	$0.540621\pi$
$570$	11.4693	0.480395
$571$	32.1672	1.34615	0.673077	−	0.739573i	$-0.264972\pi$
$571$	32.1672	1.34615	0.673077	+	0.739573i	$0.264972\pi$
$572$	0.789998	0.0330315
$573$	61.1533	2.55472
$574$	−7.64485	−0.319090
$575$	−2.32266	−0.0968617
$576$	3.40195	0.141748
$577$	−31.3404	−1.30472	−0.652359	−	0.757910i	$-0.726221\pi$
$577$	−31.3404	−1.30472	−0.652359	+	0.757910i	$0.726221\pi$
$578$	−16.4928	−0.686008
$579$	9.66518	0.401671
$580$	−5.17745	−0.214982
$581$	12.7135	0.527443
$582$	26.2140	1.08661
$583$	−4.41403	−0.182810
$584$	−4.57773	−0.189428
$585$	−4.65218	−0.192344
$586$	−12.0250	−0.496749
$587$	19.6618	0.811531	0.405766	−	0.913977i	$-0.367005\pi$
$587$	19.6618	0.811531	0.405766	+	0.913977i	$0.367005\pi$
$588$	13.1206	0.541086
$589$	−17.0652	−0.703161
$590$	8.28272	0.340994
$591$	−42.5619	−1.75076
$592$	−10.4271	−0.428552
$593$	−5.59485	−0.229753	−0.114876	−	0.993380i	$-0.536647\pi$
$593$	−5.59485	−0.229753	−0.114876	+	0.993380i	$0.536647\pi$
$594$	0.587518	0.0241062
$595$	0.959340	0.0393291
$596$	14.9990	0.614384
$597$	−13.5434	−0.554296
$598$	3.17625	0.129887
$599$	−46.6427	−1.90577	−0.952884	−	0.303335i	$-0.901900\pi$
$599$	−46.6427	−1.90577	−0.952884	+	0.303335i	$0.901900\pi$
$600$	−2.53021	−0.103295
$601$	22.3050	0.909839	0.454920	−	0.890532i	$-0.349668\pi$
$601$	22.3050	0.909839	0.454920	+	0.890532i	$0.349668\pi$
$602$	−3.97794	−0.162129
$603$	26.9236	1.09641
$604$	−23.2183	−0.944739
$605$	−10.6663	−0.433646
$606$	28.1634	1.14406
$607$	−12.4202	−0.504120	−0.252060	−	0.967712i	$-0.581108\pi$
$607$	−12.4202	−0.504120	−0.252060	+	0.967712i	$0.581108\pi$
$608$	−4.53294	−0.183835
$609$	17.6457	0.715039
$610$	2.71207	0.109808
$611$	2.07511	0.0839498
$612$	2.42289	0.0979396
$613$	−20.1283	−0.812974	−0.406487	−	0.913657i	$-0.633246\pi$
$613$	−20.1283	−0.812974	−0.406487	+	0.913657i	$0.633246\pi$
$614$	−5.42432	−0.218908
$615$	14.3602	0.579057
$616$	−0.778150	−0.0313525
$617$	20.3777	0.820375	0.410187	−	0.912001i	$-0.365463\pi$
$617$	20.3777	0.820375	0.410187	+	0.912001i	$0.365463\pi$
$618$	−5.25901	−0.211549
$619$	−31.3515	−1.26012	−0.630061	−	0.776546i	$-0.716970\pi$
$619$	−31.3515	−1.26012	−0.630061	+	0.776546i	$0.716970\pi$
$620$	3.76472	0.151195
$621$	2.36217	0.0947905
$622$	−21.0957	−0.845860
$623$	−18.2893	−0.732747
$624$	3.46007	0.138514
$625$	1.00000	0.0400000
$626$	26.7483	1.06908
$627$	−6.62571	−0.264606
$628$	9.50463	0.379276
$629$	−7.42628	−0.296105
$630$	4.58241	0.182567
$631$	−18.4437	−0.734234	−0.367117	−	0.930175i	$-0.619655\pi$
$631$	−18.4437	−0.734234	−0.367117	+	0.930175i	$0.619655\pi$
$632$	14.3600	0.571210
$633$	−14.8661	−0.590873
$634$	−23.2271	−0.922466
$635$	−18.9143	−0.750590
$636$	−19.3328	−0.766594
$637$	7.09134	0.280969
$638$	2.99098	0.118414
$639$	−39.5857	−1.56599
$640$	1.00000	0.0395285
$641$	25.6953	1.01490	0.507452	−	0.861680i	$-0.330587\pi$
$641$	25.6953	1.01490	0.507452	+	0.861680i	$0.330587\pi$
$642$	8.70429	0.343531
$643$	38.0151	1.49917	0.749584	−	0.661910i	$-0.230254\pi$
$643$	38.0151	1.49917	0.749584	+	0.661910i	$0.230254\pi$
$644$	−3.12862	−0.123285
$645$	7.47219	0.294217
$646$	−3.22839	−0.127019
$647$	−5.62827	−0.221270	−0.110635	−	0.993861i	$-0.535288\pi$
$647$	−5.62827	−0.221270	−0.110635	+	0.993861i	$0.535288\pi$
$648$	−7.63260	−0.299837
$649$	−4.78487	−0.187823
$650$	−1.36751	−0.0536380
$651$	−12.8308	−0.502880
$652$	10.0142	0.392185
$653$	14.4818	0.566718	0.283359	−	0.959014i	$-0.408551\pi$
$653$	14.4818	0.566718	0.283359	+	0.959014i	$0.408551\pi$
$654$	−8.60150	−0.336345
$655$	−17.9107	−0.699829
$656$	−5.67548	−0.221590
$657$	−15.5732	−0.607568
$658$	−2.04398	−0.0796828
$659$	5.23053	0.203753	0.101876	−	0.994797i	$-0.467515\pi$
$659$	5.23053	0.203753	0.101876	+	0.994797i	$0.467515\pi$
$660$	1.46168	0.0568959
$661$	−11.1750	−0.434659	−0.217329	−	0.976098i	$-0.569735\pi$
$661$	−11.1750	−0.434659	−0.217329	+	0.976098i	$0.569735\pi$
$662$	−10.1808	−0.395689
$663$	2.46429	0.0957050
$664$	9.43838	0.366280
$665$	−6.10585	−0.236775
$666$	−35.4725	−1.37453
$667$	12.0255	0.465628
$668$	−3.33553	−0.129056
$669$	35.4414	1.37024
$670$	7.91417	0.305751
$671$	−1.56674	−0.0604834
$672$	−3.40818	−0.131473
$673$	−51.1516	−1.97175	−0.985875	−	0.167481i	$-0.946437\pi$
$673$	−51.1516	−1.97175	−0.985875	+	0.167481i	$0.946437\pi$
$674$	−7.95932	−0.306581
$675$	−1.01701	−0.0391447
$676$	−11.1299	−0.428074
$677$	21.5740	0.829157	0.414578	−	0.910014i	$-0.363929\pi$
$677$	21.5740	0.829157	0.414578	+	0.910014i	$0.363929\pi$
$678$	−0.736004	−0.0282661
$679$	−13.9555	−0.535561
$680$	0.712207	0.0273119
$681$	−0.264081	−0.0101196
$682$	−2.17485	−0.0832794
$683$	19.1083	0.731158	0.365579	−	0.930780i	$-0.380871\pi$
$683$	19.1083	0.731158	0.365579	+	0.930780i	$0.380871\pi$
$684$	−15.4208	−0.589629
$685$	−6.36326	−0.243128
$686$	−16.4140	−0.626688
$687$	58.5995	2.23571
$688$	−2.95319	−0.112589
$689$	−10.4488	−0.398068
$690$	5.87682	0.223727
$691$	2.40075	0.0913288	0.0456644	−	0.998957i	$-0.485460\pi$
$691$	2.40075	0.0913288	0.0456644	+	0.998957i	$0.485460\pi$
$692$	6.32321	0.240372
$693$	−2.64722	−0.100560
$694$	−18.5026	−0.702350
$695$	16.3348	0.619615
$696$	13.1000	0.496555
$697$	−4.04212	−0.153106
$698$	−8.78113	−0.332371
$699$	32.2770	1.22083
$700$	1.34700	0.0509117
$701$	−34.7838	−1.31377	−0.656883	−	0.753993i	$-0.728125\pi$
$701$	−34.7838	−1.31377	−0.656883	+	0.753993i	$0.728125\pi$
$702$	1.39076	0.0524910
$703$	47.2655	1.78265
$704$	−0.577693	−0.0217726
$705$	3.83943	0.144601
$706$	−3.47737	−0.130872
$707$	−14.9932	−0.563878
$708$	−20.9570	−0.787612
$709$	−15.2011	−0.570888	−0.285444	−	0.958395i	$-0.592141\pi$
$709$	−15.2011	−0.570888	−0.285444	+	0.958395i	$0.592141\pi$
$710$	−11.6362	−0.436698
$711$	48.8520	1.83209
$712$	−13.5779	−0.508852
$713$	−8.74418	−0.327472
$714$	−2.42733	−0.0908405
$715$	0.789998	0.0295442
$716$	11.2160	0.419161
$717$	−16.7907	−0.627062
$718$	35.5011	1.32489
$719$	45.0323	1.67942	0.839711	−	0.543034i	$-0.182725\pi$
$719$	45.0323	1.67942	0.839711	+	0.543034i	$0.182725\pi$
$720$	3.40195	0.126783
$721$	2.79972	0.104267
$722$	1.54752	0.0575926
$723$	34.2195	1.27264
$724$	−14.8885	−0.553328
$725$	−5.17745	−0.192286
$726$	26.9879	1.00161
$727$	33.6268	1.24715	0.623575	−	0.781764i	$-0.285680\pi$
$727$	33.6268	1.24715	0.623575	+	0.781764i	$0.285680\pi$
$728$	−1.84202	−0.0682699
$729$	−33.6854	−1.24761
$730$	−4.57773	−0.169429
$731$	−2.10329	−0.0777928
$732$	−6.86209	−0.253630
$733$	−18.3351	−0.677222	−0.338611	−	0.940926i	$-0.609957\pi$
$733$	−18.3351	−0.677222	−0.338611	+	0.940926i	$0.609957\pi$
$734$	22.9485	0.847046
$735$	13.1206	0.483962
$736$	−2.32266	−0.0856145
$737$	−4.57196	−0.168410
$738$	−19.3077	−0.710726
$739$	36.8137	1.35421	0.677107	−	0.735885i	$-0.263233\pi$
$739$	36.8137	1.35421	0.677107	+	0.735885i	$0.263233\pi$
$740$	−10.4271	−0.383309
$741$	−15.6843	−0.576176
$742$	10.2921	0.377835
$743$	11.4104	0.418606	0.209303	−	0.977851i	$-0.432880\pi$
$743$	11.4104	0.418606	0.209303	+	0.977851i	$0.432880\pi$
$744$	−9.52553	−0.349223
$745$	14.9990	0.549522
$746$	−29.0007	−1.06179
$747$	32.1089	1.17480
$748$	−0.411437	−0.0150436
$749$	−4.63387	−0.169318
$750$	−2.53021	−0.0923901
$751$	44.7034	1.63125	0.815625	−	0.578580i	$-0.196393\pi$
$751$	44.7034	1.63125	0.815625	+	0.578580i	$0.196393\pi$
$752$	−1.51744	−0.0553353
$753$	−20.3498	−0.741590
$754$	7.08019	0.257845
$755$	−23.2183	−0.845000
$756$	−1.36991	−0.0498230
$757$	−35.3738	−1.28568	−0.642841	−	0.766000i	$-0.722244\pi$
$757$	−35.3738	−1.28568	−0.642841	+	0.766000i	$0.722244\pi$
$758$	−23.6493	−0.858983
$759$	−3.39499	−0.123230
$760$	−4.53294	−0.164427
$761$	3.72876	0.135167	0.0675837	−	0.997714i	$-0.478471\pi$
$761$	3.72876	0.135167	0.0675837	+	0.997714i	$0.478471\pi$
$762$	47.8570	1.73368
$763$	4.57914	0.165776
$764$	−24.1693	−0.874415
$765$	2.42289	0.0875998
$766$	21.2622	0.768233
$767$	−11.3267	−0.408982
$768$	−2.53021	−0.0913010
$769$	32.4765	1.17113	0.585566	−	0.810625i	$-0.300872\pi$
$769$	32.4765	1.17113	0.585566	+	0.810625i	$0.300872\pi$
$770$	−0.778150	−0.0280426
$771$	−34.8513	−1.25514
$772$	−3.81992	−0.137482
$773$	13.2688	0.477244	0.238622	−	0.971113i	$-0.423304\pi$
$773$	13.2688	0.477244	0.238622	+	0.971113i	$0.423304\pi$
$774$	−10.0466	−0.361118
$775$	3.76472	0.135233
$776$	−10.3604	−0.371918
$777$	35.5375	1.27490
$778$	−2.09950	−0.0752707
$779$	25.7266	0.921752
$780$	3.46007	0.123890
$781$	6.72214	0.240537
$782$	−1.65422	−0.0591547
$783$	5.26551	0.188174
$784$	−5.18560	−0.185200
$785$	9.50463	0.339235
$786$	45.3178	1.61643
$787$	−7.36400	−0.262498	−0.131249	−	0.991349i	$-0.541899\pi$
$787$	−7.36400	−0.262498	−0.131249	+	0.991349i	$0.541899\pi$
$788$	16.8215	0.599242
$789$	47.0550	1.67520
$790$	14.3600	0.510906
$791$	0.391823	0.0139316
$792$	−1.96528	−0.0698332
$793$	−3.70877	−0.131702
$794$	25.7179	0.912695
$795$	−19.3328	−0.685663
$796$	5.35270	0.189721
$797$	21.2271	0.751902	0.375951	−	0.926640i	$-0.377316\pi$
$797$	21.2271	0.751902	0.375951	+	0.926640i	$0.377316\pi$
$798$	15.4491	0.546891
$799$	−1.08073	−0.0382335
$800$	1.00000	0.0353553
$801$	−46.1912	−1.63209
$802$	−1.00000	−0.0353112
$803$	2.64452	0.0933231
$804$	−20.0245	−0.706209
$805$	−3.12862	−0.110269
$806$	−5.14828	−0.181340
$807$	41.5914	1.46409
$808$	−11.1309	−0.391582
$809$	−46.3842	−1.63078	−0.815391	−	0.578910i	$-0.803478\pi$
$809$	−46.3842	−1.63078	−0.815391	+	0.578910i	$0.803478\pi$
$810$	−7.63260	−0.268182
$811$	−34.2938	−1.20422	−0.602110	−	0.798413i	$-0.705673\pi$
$811$	−34.2938	−1.20422	−0.602110	+	0.798413i	$0.705673\pi$
$812$	−6.97401	−0.244740
$813$	39.7512	1.39414
$814$	6.02368	0.211130
$815$	10.0142	0.350781
$816$	−1.80203	−0.0630837
$817$	13.3866	0.468339
$818$	16.4639	0.575648
$819$	−6.26647	−0.218968
$820$	−5.67548	−0.198197
$821$	−15.0798	−0.526289	−0.263145	−	0.964756i	$-0.584760\pi$
$821$	−15.0798	−0.526289	−0.263145	+	0.964756i	$0.584760\pi$
$822$	16.1004	0.561565
$823$	−46.3503	−1.61567	−0.807835	−	0.589409i	$-0.799361\pi$
$823$	−46.3503	−1.61567	−0.807835	+	0.589409i	$0.799361\pi$
$824$	2.07849	0.0724077
$825$	1.46168	0.0508892
$826$	11.1568	0.388194
$827$	3.66928	0.127593	0.0637966	−	0.997963i	$-0.479679\pi$
$827$	3.66928	0.127593	0.0637966	+	0.997963i	$0.479679\pi$
$828$	−7.90157	−0.274599
$829$	10.8391	0.376459	0.188229	−	0.982125i	$-0.439725\pi$
$829$	10.8391	0.376459	0.188229	+	0.982125i	$0.439725\pi$
$830$	9.43838	0.327611
$831$	−19.4422	−0.674444
$832$	−1.36751	−0.0474097
$833$	−3.69322	−0.127963
$834$	−41.3305	−1.43116
$835$	−3.33553	−0.115431
$836$	2.61864	0.0905677
$837$	−3.82875	−0.132341
$838$	12.2354	0.422665
$839$	−32.7307	−1.12999	−0.564995	−	0.825095i	$-0.691122\pi$
$839$	−32.7307	−1.12999	−0.564995	+	0.825095i	$0.691122\pi$
$840$	−3.40818	−0.117593
$841$	−2.19398	−0.0756544
$842$	31.9850	1.10228
$843$	53.6697	1.84848
$844$	5.87544	0.202241
$845$	−11.1299	−0.382881
$846$	−5.16225	−0.177482
$847$	−14.3674	−0.493670
$848$	7.64079	0.262386
$849$	−42.2908	−1.45142
$850$	0.712207	0.0244285
$851$	24.2187	0.830206
$852$	29.4420	1.00866
$853$	−26.5876	−0.910342	−0.455171	−	0.890404i	$-0.650422\pi$
$853$	−26.5876	−0.910342	−0.455171	+	0.890404i	$0.650422\pi$
$854$	3.65314	0.125008
$855$	−15.4208	−0.527381
$856$	−3.44015	−0.117582
$857$	25.2839	0.863681	0.431840	−	0.901950i	$-0.357864\pi$
$857$	25.2839	0.863681	0.431840	+	0.901950i	$0.357864\pi$
$858$	−1.99886	−0.0682399
$859$	−43.4137	−1.48126	−0.740628	−	0.671916i	$-0.765472\pi$
$859$	−43.4137	−1.48126	−0.740628	+	0.671916i	$0.765472\pi$
$860$	−2.95319	−0.100703
$861$	19.3431	0.659210
$862$	−1.31348	−0.0447372
$863$	30.9138	1.05232	0.526158	−	0.850387i	$-0.323632\pi$
$863$	30.9138	1.05232	0.526158	+	0.850387i	$0.323632\pi$
$864$	−1.01701	−0.0345993
$865$	6.32321	0.214996
$866$	15.3615	0.522004
$867$	41.7301	1.41723
$868$	5.07106	0.172123
$869$	−8.29567	−0.281411
$870$	13.1000	0.444133
$871$	−10.8227	−0.366712
$872$	3.39952	0.115122
$873$	−35.2456	−1.19288
$874$	10.5285	0.356131
$875$	1.34700	0.0455368
$876$	11.5826	0.391340
$877$	6.41905	0.216756	0.108378	−	0.994110i	$-0.465434\pi$
$877$	6.41905	0.216756	0.108378	+	0.994110i	$0.465434\pi$
$878$	8.35739	0.282048
$879$	30.4258	1.02624
$880$	−0.577693	−0.0194740
$881$	10.4366	0.351617	0.175808	−	0.984424i	$-0.443746\pi$
$881$	10.4366	0.351617	0.175808	+	0.984424i	$0.443746\pi$
$882$	−17.6411	−0.594008
$883$	55.0443	1.85239	0.926194	−	0.377047i	$-0.123060\pi$
$883$	55.0443	1.85239	0.926194	+	0.377047i	$0.123060\pi$
$884$	−0.973947	−0.0327574
$885$	−20.9570	−0.704462
$886$	4.13484	0.138913
$887$	12.9884	0.436108	0.218054	−	0.975937i	$-0.430029\pi$
$887$	12.9884	0.436108	0.218054	+	0.975937i	$0.430029\pi$
$888$	26.3828	0.885349
$889$	−25.4774	−0.854486
$890$	−13.5779	−0.455131
$891$	4.40930	0.147717
$892$	−14.0073	−0.469000
$893$	6.87845	0.230179
$894$	−37.9506	−1.26926
$895$	11.2160	0.374909
$896$	1.34700	0.0450000
$897$	−8.03658	−0.268333
$898$	30.7710	1.02684
$899$	−19.4917	−0.650084
$900$	3.40195	0.113398
$901$	5.44183	0.181294
$902$	3.27869	0.109168
$903$	10.0650	0.334942
$904$	0.290887	0.00967475
$905$	−14.8885	−0.494911
$906$	58.7471	1.95174
$907$	46.7580	1.55257	0.776287	−	0.630379i	$-0.217101\pi$
$907$	46.7580	1.55257	0.776287	+	0.630379i	$0.217101\pi$
$908$	0.104371	0.00346368
$909$	−37.8666	−1.25596
$910$	−1.84202	−0.0610625
$911$	17.1715	0.568916	0.284458	−	0.958689i	$-0.408186\pi$
$911$	17.1715	0.568916	0.284458	+	0.958689i	$0.408186\pi$
$912$	11.4693	0.379785
$913$	−5.45248	−0.180451
$914$	36.3195	1.20134
$915$	−6.86209	−0.226854
$916$	−23.1599	−0.765226
$917$	−24.1256	−0.796698
$918$	−0.724321	−0.0239062
$919$	44.6786	1.47381	0.736906	−	0.675996i	$-0.236286\pi$
$919$	44.6786	1.47381	0.736906	+	0.675996i	$0.236286\pi$
$920$	−2.32266	−0.0765759
$921$	13.7247	0.452243
$922$	23.5395	0.775233
$923$	15.9125	0.523768
$924$	1.96888	0.0647714
$925$	−10.4271	−0.342842
$926$	27.1789	0.893155
$927$	7.07092	0.232239
$928$	−5.17745	−0.169958
$929$	2.43373	0.0798482	0.0399241	−	0.999203i	$-0.487288\pi$
$929$	2.43373	0.0798482	0.0399241	+	0.999203i	$0.487288\pi$
$930$	−9.52553	−0.312354
$931$	23.5060	0.770378
$932$	−12.7567	−0.417859
$933$	53.3765	1.74747
$934$	7.71061	0.252299
$935$	−0.411437	−0.0134554
$936$	−4.65218	−0.152061
$937$	11.8038	0.385612	0.192806	−	0.981237i	$-0.438241\pi$
$937$	11.8038	0.385612	0.192806	+	0.981237i	$0.438241\pi$
$938$	10.6603	0.348073
$939$	−67.6788	−2.20862
$940$	−1.51744	−0.0494934
$941$	29.0878	0.948236	0.474118	−	0.880461i	$-0.342767\pi$
$941$	29.0878	0.948236	0.474118	+	0.880461i	$0.342767\pi$
$942$	−24.0487	−0.783548
$943$	13.1822	0.429273
$944$	8.28272	0.269580
$945$	−1.36991	−0.0445630
$946$	1.70604	0.0554681
$947$	−52.2523	−1.69797	−0.848985	−	0.528416i	$-0.822786\pi$
$947$	−52.2523	−1.69797	−0.848985	+	0.528416i	$0.822786\pi$
$948$	−36.3338	−1.18007
$949$	6.26007	0.203210
$950$	−4.53294	−0.147068
$951$	58.7694	1.90573
$952$	0.959340	0.0310924
$953$	−17.7740	−0.575757	−0.287879	−	0.957667i	$-0.592950\pi$
$953$	−17.7740	−0.575757	−0.287879	+	0.957667i	$0.592950\pi$
$954$	25.9936	0.841573
$955$	−24.1693	−0.782100
$956$	6.63612	0.214627
$957$	−7.56779	−0.244632
$958$	0.598714	0.0193436
$959$	−8.57129	−0.276781
$960$	−2.53021	−0.0816621
$961$	−16.8269	−0.542802
$962$	14.2592	0.459734
$963$	−11.7032	−0.377131
$964$	−13.5244	−0.435591
$965$	−3.81992	−0.122967
$966$	7.91605	0.254695
$967$	32.2832	1.03816	0.519079	−	0.854726i	$-0.326275\pi$
$967$	32.2832	1.03816	0.519079	+	0.854726i	$0.326275\pi$
$968$	−10.6663	−0.342827
$969$	8.16850	0.262410
$970$	−10.3604	−0.332653
$971$	−35.5361	−1.14041	−0.570204	−	0.821503i	$-0.693136\pi$
$971$	−35.5361	−1.14041	−0.570204	+	0.821503i	$0.693136\pi$
$972$	22.3631	0.717296
$973$	22.0029	0.705381
$974$	−6.84020	−0.219174
$975$	3.46007	0.110811
$976$	2.71207	0.0868111
$977$	7.13941	0.228410	0.114205	−	0.993457i	$-0.463568\pi$
$977$	7.13941	0.228410	0.114205	+	0.993457i	$0.463568\pi$
$978$	−25.3379	−0.810216
$979$	7.84384	0.250690
$980$	−5.18560	−0.165648
$981$	11.5650	0.369242
$982$	−31.9131	−1.01839
$983$	−14.6521	−0.467329	−0.233664	−	0.972317i	$-0.575072\pi$
$983$	−14.6521	−0.467329	−0.233664	+	0.972317i	$0.575072\pi$
$984$	14.3602	0.457785
$985$	16.8215	0.535978
$986$	−3.68742	−0.117431
$987$	5.17170	0.164617
$988$	6.19881	0.197211
$989$	6.85927	0.218112
$990$	−1.96528	−0.0624607
$991$	−17.1998	−0.546371	−0.273185	−	0.961961i	$-0.588077\pi$
$991$	−17.1998	−0.546371	−0.273185	+	0.961961i	$0.588077\pi$
$992$	3.76472	0.119530
$993$	25.7596	0.817457
$994$	−15.6739	−0.497146
$995$	5.35270	0.169692
$996$	−23.8811	−0.756700
$997$	32.3971	1.02603	0.513014	−	0.858380i	$-0.328529\pi$
$997$	32.3971	1.02603	0.513014	+	0.858380i	$0.328529\pi$
$998$	−7.28819	−0.230704
$999$	10.6045	0.335511

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.h.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.53021 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53021 q^{6} +1.34700 q^{7} +1.00000 q^{8} +3.40195 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.53021 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53021 q^{6} +1.34700 q^{7} +1.00000 q^{8} +3.40195 q^{9} +1.00000 q^{10} -0.577693 q^{11} -2.53021 q^{12} -1.36751 q^{13} +1.34700 q^{14} -2.53021 q^{15} +1.00000 q^{16} +0.712207 q^{17} +3.40195 q^{18} -4.53294 q^{19} +1.00000 q^{20} -3.40818 q^{21} -0.577693 q^{22} -2.32266 q^{23} -2.53021 q^{24} +1.00000 q^{25} -1.36751 q^{26} -1.01701 q^{27} +1.34700 q^{28} -5.17745 q^{29} -2.53021 q^{30} +3.76472 q^{31} +1.00000 q^{32} +1.46168 q^{33} +0.712207 q^{34} +1.34700 q^{35} +3.40195 q^{36} -10.4271 q^{37} -4.53294 q^{38} +3.46007 q^{39} +1.00000 q^{40} -5.67548 q^{41} -3.40818 q^{42} -2.95319 q^{43} -0.577693 q^{44} +3.40195 q^{45} -2.32266 q^{46} -1.51744 q^{47} -2.53021 q^{48} -5.18560 q^{49} +1.00000 q^{50} -1.80203 q^{51} -1.36751 q^{52} +7.64079 q^{53} -1.01701 q^{54} -0.577693 q^{55} +1.34700 q^{56} +11.4693 q^{57} -5.17745 q^{58} +8.28272 q^{59} -2.53021 q^{60} +2.71207 q^{61} +3.76472 q^{62} +4.58241 q^{63} +1.00000 q^{64} -1.36751 q^{65} +1.46168 q^{66} +7.91417 q^{67} +0.712207 q^{68} +5.87682 q^{69} +1.34700 q^{70} -11.6362 q^{71} +3.40195 q^{72} -4.57773 q^{73} -10.4271 q^{74} -2.53021 q^{75} -4.53294 q^{76} -0.778150 q^{77} +3.46007 q^{78} +14.3600 q^{79} +1.00000 q^{80} -7.63260 q^{81} -5.67548 q^{82} +9.43838 q^{83} -3.40818 q^{84} +0.712207 q^{85} -2.95319 q^{86} +13.1000 q^{87} -0.577693 q^{88} -13.5779 q^{89} +3.40195 q^{90} -1.84202 q^{91} -2.32266 q^{92} -9.52553 q^{93} -1.51744 q^{94} -4.53294 q^{95} -2.53021 q^{96} -10.3604 q^{97} -5.18560 q^{98} -1.96528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) \) 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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