LMFDB - Embedded newform 4010.2.a.h.1.8

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			1.8
Root			$-0.408238$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.13041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.13041 q^{6} -0.772637 q^{7} +1.00000 q^{8} -1.72217 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.13041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.13041 q^{6} -0.772637 q^{7} +1.00000 q^{8} -1.72217 q^{9} +1.00000 q^{10} -5.33391 q^{11} +1.13041 q^{12} -2.27234 q^{13} -0.772637 q^{14} +1.13041 q^{15} +1.00000 q^{16} -1.51384 q^{17} -1.72217 q^{18} -4.75817 q^{19} +1.00000 q^{20} -0.873397 q^{21} -5.33391 q^{22} +3.57439 q^{23} +1.13041 q^{24} +1.00000 q^{25} -2.27234 q^{26} -5.33799 q^{27} -0.772637 q^{28} +0.625927 q^{29} +1.13041 q^{30} +4.86323 q^{31} +1.00000 q^{32} -6.02951 q^{33} -1.51384 q^{34} -0.772637 q^{35} -1.72217 q^{36} -4.40381 q^{37} -4.75817 q^{38} -2.56868 q^{39} +1.00000 q^{40} +0.597190 q^{41} -0.873397 q^{42} -3.51285 q^{43} -5.33391 q^{44} -1.72217 q^{45} +3.57439 q^{46} +1.44660 q^{47} +1.13041 q^{48} -6.40303 q^{49} +1.00000 q^{50} -1.71127 q^{51} -2.27234 q^{52} -1.59288 q^{53} -5.33799 q^{54} -5.33391 q^{55} -0.772637 q^{56} -5.37869 q^{57} +0.625927 q^{58} -9.14211 q^{59} +1.13041 q^{60} +3.55913 q^{61} +4.86323 q^{62} +1.33061 q^{63} +1.00000 q^{64} -2.27234 q^{65} -6.02951 q^{66} +9.65100 q^{67} -1.51384 q^{68} +4.04053 q^{69} -0.772637 q^{70} -10.1869 q^{71} -1.72217 q^{72} -13.4010 q^{73} -4.40381 q^{74} +1.13041 q^{75} -4.75817 q^{76} +4.12118 q^{77} -2.56868 q^{78} -0.0209108 q^{79} +1.00000 q^{80} -0.867606 q^{81} +0.597190 q^{82} -15.8258 q^{83} -0.873397 q^{84} -1.51384 q^{85} -3.51285 q^{86} +0.707555 q^{87} -5.33391 q^{88} +10.7396 q^{89} -1.72217 q^{90} +1.75570 q^{91} +3.57439 q^{92} +5.49745 q^{93} +1.44660 q^{94} -4.75817 q^{95} +1.13041 q^{96} -14.7898 q^{97} -6.40303 q^{98} +9.18592 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	1.13041	0.652643	0.326321	−	0.945259i	$-0.394191\pi$
$3$	1.13041	0.652643	0.326321	+	0.945259i	$0.394191\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.13041	0.461488
$7$	−0.772637	−0.292029	−0.146015	−	0.989282i	$-0.546645\pi$
$7$	−0.772637	−0.292029	−0.146015	+	0.989282i	$0.546645\pi$
$8$	1.00000	0.353553
$9$	−1.72217	−0.574057
$10$	1.00000	0.316228
$11$	−5.33391	−1.60824	−0.804118	−	0.594470i	$-0.797362\pi$
$11$	−5.33391	−1.60824	−0.804118	+	0.594470i	$0.797362\pi$
$12$	1.13041	0.326321
$13$	−2.27234	−0.630235	−0.315117	−	0.949053i	$-0.602044\pi$
$13$	−2.27234	−0.630235	−0.315117	+	0.949053i	$0.602044\pi$
$14$	−0.772637	−0.206496
$15$	1.13041	0.291871
$16$	1.00000	0.250000
$17$	−1.51384	−0.367161	−0.183581	−	0.983005i	$-0.558769\pi$
$17$	−1.51384	−0.367161	−0.183581	+	0.983005i	$0.558769\pi$
$18$	−1.72217	−0.405920
$19$	−4.75817	−1.09160	−0.545800	−	0.837916i	$-0.683774\pi$
$19$	−4.75817	−1.09160	−0.545800	+	0.837916i	$0.683774\pi$
$20$	1.00000	0.223607
$21$	−0.873397	−0.190591
$22$	−5.33391	−1.13719
$23$	3.57439	0.745312	0.372656	−	0.927970i	$-0.378447\pi$
$23$	3.57439	0.745312	0.372656	+	0.927970i	$0.378447\pi$
$24$	1.13041	0.230744
$25$	1.00000	0.200000
$26$	−2.27234	−0.445643
$27$	−5.33799	−1.02730
$28$	−0.772637	−0.146015
$29$	0.625927	0.116232	0.0581159	−	0.998310i	$-0.481491\pi$
$29$	0.625927	0.116232	0.0581159	+	0.998310i	$0.481491\pi$
$30$	1.13041	0.206384
$31$	4.86323	0.873462	0.436731	−	0.899592i	$-0.356136\pi$
$31$	4.86323	0.873462	0.436731	+	0.899592i	$0.356136\pi$
$32$	1.00000	0.176777
$33$	−6.02951	−1.04960
$34$	−1.51384	−0.259622
$35$	−0.772637	−0.130600
$36$	−1.72217	−0.287029
$37$	−4.40381	−0.723982	−0.361991	−	0.932182i	$-0.617903\pi$
$37$	−4.40381	−0.723982	−0.361991	+	0.932182i	$0.617903\pi$
$38$	−4.75817	−0.771877
$39$	−2.56868	−0.411318
$40$	1.00000	0.158114
$41$	0.597190	0.0932653	0.0466327	−	0.998912i	$-0.485151\pi$
$41$	0.597190	0.0932653	0.0466327	+	0.998912i	$0.485151\pi$
$42$	−0.873397	−0.134768
$43$	−3.51285	−0.535705	−0.267852	−	0.963460i	$-0.586314\pi$
$43$	−3.51285	−0.535705	−0.267852	+	0.963460i	$0.586314\pi$
$44$	−5.33391	−0.804118
$45$	−1.72217	−0.256726
$46$	3.57439	0.527015
$47$	1.44660	0.211008	0.105504	−	0.994419i	$-0.466354\pi$
$47$	1.44660	0.211008	0.105504	+	0.994419i	$0.466354\pi$
$48$	1.13041	0.163161
$49$	−6.40303	−0.914719
$50$	1.00000	0.141421
$51$	−1.71127	−0.239625
$52$	−2.27234	−0.315117
$53$	−1.59288	−0.218799	−0.109399	−	0.993998i	$-0.534893\pi$
$53$	−1.59288	−0.218799	−0.109399	+	0.993998i	$0.534893\pi$
$54$	−5.33799	−0.726409
$55$	−5.33391	−0.719225
$56$	−0.772637	−0.103248
$57$	−5.37869	−0.712424
$58$	0.625927	0.0821883
$59$	−9.14211	−1.19020	−0.595100	−	0.803651i	$-0.702888\pi$
$59$	−9.14211	−1.19020	−0.595100	+	0.803651i	$0.702888\pi$
$60$	1.13041	0.145935
$61$	3.55913	0.455700	0.227850	−	0.973696i	$-0.426830\pi$
$61$	3.55913	0.455700	0.227850	+	0.973696i	$0.426830\pi$
$62$	4.86323	0.617631
$63$	1.33061	0.167642
$64$	1.00000	0.125000
$65$	−2.27234	−0.281850
$66$	−6.02951	−0.742182
$67$	9.65100	1.17906	0.589529	−	0.807747i	$-0.299313\pi$
$67$	9.65100	1.17906	0.589529	+	0.807747i	$0.299313\pi$
$68$	−1.51384	−0.183581
$69$	4.04053	0.486422
$70$	−0.772637	−0.0923478
$71$	−10.1869	−1.20896	−0.604481	−	0.796620i	$-0.706619\pi$
$71$	−10.1869	−1.20896	−0.604481	+	0.796620i	$0.706619\pi$
$72$	−1.72217	−0.202960
$73$	−13.4010	−1.56847	−0.784234	−	0.620465i	$-0.786944\pi$
$73$	−13.4010	−1.56847	−0.784234	+	0.620465i	$0.786944\pi$
$74$	−4.40381	−0.511932
$75$	1.13041	0.130529
$76$	−4.75817	−0.545800
$77$	4.12118	0.469652
$78$	−2.56868	−0.290846
$79$	−0.0209108	−0.00235265	−0.00117633	−	0.999999i	$-0.500374\pi$
$79$	−0.0209108	−0.00235265	−0.00117633	+	0.999999i	$0.500374\pi$
$80$	1.00000	0.111803
$81$	−0.867606	−0.0964006
$82$	0.597190	0.0659486
$83$	−15.8258	−1.73711	−0.868553	−	0.495596i	$-0.834950\pi$
$83$	−15.8258	−1.73711	−0.868553	+	0.495596i	$0.834950\pi$
$84$	−0.873397	−0.0952954
$85$	−1.51384	−0.164199
$86$	−3.51285	−0.378800
$87$	0.707555	0.0758578
$88$	−5.33391	−0.568597
$89$	10.7396	1.13840	0.569198	−	0.822200i	$-0.307254\pi$
$89$	10.7396	1.13840	0.569198	+	0.822200i	$0.307254\pi$
$90$	−1.72217	−0.181533
$91$	1.75570	0.184047
$92$	3.57439	0.372656
$93$	5.49745	0.570059
$94$	1.44660	0.149205
$95$	−4.75817	−0.488178
$96$	1.13041	0.115372
$97$	−14.7898	−1.50168	−0.750839	−	0.660486i	$-0.770350\pi$
$97$	−14.7898	−1.50168	−0.750839	+	0.660486i	$0.770350\pi$
$98$	−6.40303	−0.646804
$99$	9.18592	0.923220
$100$	1.00000	0.100000
$101$	−10.6246	−1.05719	−0.528595	−	0.848874i	$-0.677281\pi$
$101$	−10.6246	−1.05719	−0.528595	+	0.848874i	$0.677281\pi$
$102$	−1.71127	−0.169441
$103$	15.2717	1.50476	0.752381	−	0.658728i	$-0.228905\pi$
$103$	15.2717	1.50476	0.752381	+	0.658728i	$0.228905\pi$
$104$	−2.27234	−0.222822
$105$	−0.873397	−0.0852348
$106$	−1.59288	−0.154714
$107$	−2.37112	−0.229225	−0.114612	−	0.993410i	$-0.536563\pi$
$107$	−2.37112	−0.229225	−0.114612	+	0.993410i	$0.536563\pi$
$108$	−5.33799	−0.513649
$109$	−7.60216	−0.728155	−0.364078	−	0.931369i	$-0.618616\pi$
$109$	−7.60216	−0.728155	−0.364078	+	0.931369i	$0.618616\pi$
$110$	−5.33391	−0.508569
$111$	−4.97811	−0.472501
$112$	−0.772637	−0.0730074
$113$	4.71641	0.443683	0.221841	−	0.975083i	$-0.428793\pi$
$113$	4.71641	0.443683	0.221841	+	0.975083i	$0.428793\pi$
$114$	−5.37869	−0.503760
$115$	3.57439	0.333314
$116$	0.625927	0.0581159
$117$	3.91337	0.361791
$118$	−9.14211	−0.841599
$119$	1.16965	0.107222
$120$	1.13041	0.103192
$121$	17.4506	1.58642
$122$	3.55913	0.322228
$123$	0.675069	0.0608689
$124$	4.86323	0.436731
$125$	1.00000	0.0894427
$126$	1.33061	0.118541
$127$	−3.72312	−0.330373	−0.165187	−	0.986262i	$-0.552823\pi$
$127$	−3.72312	−0.330373	−0.165187	+	0.986262i	$0.552823\pi$
$128$	1.00000	0.0883883
$129$	−3.97096	−0.349624
$130$	−2.27234	−0.199298
$131$	9.39051	0.820453	0.410226	−	0.911984i	$-0.365450\pi$
$131$	9.39051	0.820453	0.410226	+	0.911984i	$0.365450\pi$
$132$	−6.02951	−0.524802
$133$	3.67634	0.318779
$134$	9.65100	0.833720
$135$	−5.33799	−0.459421
$136$	−1.51384	−0.129811
$137$	−19.9288	−1.70264	−0.851318	−	0.524650i	$-0.824196\pi$
$137$	−19.9288	−1.70264	−0.851318	+	0.524650i	$0.824196\pi$
$138$	4.04053	0.343953
$139$	13.7233	1.16399	0.581996	−	0.813192i	$-0.302272\pi$
$139$	13.7233	1.16399	0.581996	+	0.813192i	$0.302272\pi$
$140$	−0.772637	−0.0652998
$141$	1.63525	0.137713
$142$	−10.1869	−0.854865
$143$	12.1205	1.01357
$144$	−1.72217	−0.143514
$145$	0.625927	0.0519804
$146$	−13.4010	−1.10907
$147$	−7.23805	−0.596985
$148$	−4.40381	−0.361991
$149$	17.5266	1.43583	0.717917	−	0.696128i	$-0.245096\pi$
$149$	17.5266	1.43583	0.717917	+	0.696128i	$0.245096\pi$
$150$	1.13041	0.0922976
$151$	7.19502	0.585522	0.292761	−	0.956186i	$-0.405426\pi$
$151$	7.19502	0.585522	0.292761	+	0.956186i	$0.405426\pi$
$152$	−4.75817	−0.385939
$153$	2.60710	0.210772
$154$	4.12118	0.332094
$155$	4.86323	0.390624
$156$	−2.56868	−0.205659
$157$	11.8163	0.943042	0.471521	−	0.881855i	$-0.343705\pi$
$157$	11.8163	0.943042	0.471521	+	0.881855i	$0.343705\pi$
$158$	−0.0209108	−0.00166358
$159$	−1.80061	−0.142797
$160$	1.00000	0.0790569
$161$	−2.76171	−0.217653
$162$	−0.867606	−0.0681655
$163$	−14.3102	−1.12086	−0.560432	−	0.828200i	$-0.689365\pi$
$163$	−14.3102	−1.12086	−0.560432	+	0.828200i	$0.689365\pi$
$164$	0.597190	0.0466327
$165$	−6.02951	−0.469397
$166$	−15.8258	−1.22832
$167$	19.1563	1.48236	0.741178	−	0.671309i	$-0.234268\pi$
$167$	19.1563	1.48236	0.741178	+	0.671309i	$0.234268\pi$
$168$	−0.873397	−0.0673841
$169$	−7.83645	−0.602804
$170$	−1.51384	−0.116107
$171$	8.19439	0.626641
$172$	−3.51285	−0.267852
$173$	14.1639	1.07686	0.538430	−	0.842670i	$-0.319018\pi$
$173$	14.1639	1.07686	0.538430	+	0.842670i	$0.319018\pi$
$174$	0.707555	0.0536396
$175$	−0.772637	−0.0584059
$176$	−5.33391	−0.402059
$177$	−10.3343	−0.776776
$178$	10.7396	0.804968
$179$	−7.48379	−0.559365	−0.279682	−	0.960093i	$-0.590229\pi$
$179$	−7.48379	−0.559365	−0.279682	+	0.960093i	$0.590229\pi$
$180$	−1.72217	−0.128363
$181$	16.3626	1.21622	0.608112	−	0.793851i	$-0.291927\pi$
$181$	16.3626	1.21622	0.608112	+	0.793851i	$0.291927\pi$
$182$	1.75570	0.130141
$183$	4.02328	0.297409
$184$	3.57439	0.263508
$185$	−4.40381	−0.323774
$186$	5.49745	0.403092
$187$	8.07472	0.590482
$188$	1.44660	0.105504
$189$	4.12433	0.300001
$190$	−4.75817	−0.345194
$191$	−1.05971	−0.0766778	−0.0383389	−	0.999265i	$-0.512207\pi$
$191$	−1.05971	−0.0766778	−0.0383389	+	0.999265i	$0.512207\pi$
$192$	1.13041	0.0815803
$193$	−15.1080	−1.08750	−0.543750	−	0.839247i	$-0.682996\pi$
$193$	−15.1080	−1.08750	−0.543750	+	0.839247i	$0.682996\pi$
$194$	−14.7898	−1.06185
$195$	−2.56868	−0.183947
$196$	−6.40303	−0.457359
$197$	−1.77050	−0.126143	−0.0630716	−	0.998009i	$-0.520090\pi$
$197$	−1.77050	−0.126143	−0.0630716	+	0.998009i	$0.520090\pi$
$198$	9.18592	0.652815
$199$	−8.71461	−0.617762	−0.308881	−	0.951101i	$-0.599955\pi$
$199$	−8.71461	−0.617762	−0.308881	+	0.951101i	$0.599955\pi$
$200$	1.00000	0.0707107
$201$	10.9096	0.769504
$202$	−10.6246	−0.747546
$203$	−0.483615	−0.0339431
$204$	−1.71127	−0.119813
$205$	0.597190	0.0417095
$206$	15.2717	1.06403
$207$	−6.15572	−0.427852
$208$	−2.27234	−0.157559
$209$	25.3797	1.75555
$210$	−0.873397	−0.0602701
$211$	25.1490	1.73133	0.865663	−	0.500628i	$-0.166897\pi$
$211$	25.1490	1.73133	0.865663	+	0.500628i	$0.166897\pi$
$212$	−1.59288	−0.109399
$213$	−11.5154	−0.789020
$214$	−2.37112	−0.162086
$215$	−3.51285	−0.239574
$216$	−5.33799	−0.363204
$217$	−3.75751	−0.255077
$218$	−7.60216	−0.514884
$219$	−15.1486	−1.02365
$220$	−5.33391	−0.359612
$221$	3.43997	0.231398
$222$	−4.97811	−0.334109
$223$	6.44595	0.431653	0.215826	−	0.976432i	$-0.430755\pi$
$223$	6.44595	0.431653	0.215826	+	0.976432i	$0.430755\pi$
$224$	−0.772637	−0.0516240
$225$	−1.72217	−0.114811
$226$	4.71641	0.313731
$227$	−6.70110	−0.444768	−0.222384	−	0.974959i	$-0.571384\pi$
$227$	−6.70110	−0.444768	−0.222384	+	0.974959i	$0.571384\pi$
$228$	−5.37869	−0.356212
$229$	1.65727	0.109515	0.0547577	−	0.998500i	$-0.482561\pi$
$229$	1.65727	0.109515	0.0547577	+	0.998500i	$0.482561\pi$
$230$	3.57439	0.235688
$231$	4.65863	0.306515
$232$	0.625927	0.0410941
$233$	4.45698	0.291986	0.145993	−	0.989286i	$-0.453362\pi$
$233$	4.45698	0.291986	0.145993	+	0.989286i	$0.453362\pi$
$234$	3.91337	0.255825
$235$	1.44660	0.0943656
$236$	−9.14211	−0.595100
$237$	−0.0236378	−0.00153544
$238$	1.16965	0.0758173
$239$	−1.54755	−0.100103	−0.0500515	−	0.998747i	$-0.515939\pi$
$239$	−1.54755	−0.100103	−0.0500515	+	0.998747i	$0.515939\pi$
$240$	1.13041	0.0729677
$241$	−12.8777	−0.829526	−0.414763	−	0.909929i	$-0.636136\pi$
$241$	−12.8777	−0.829526	−0.414763	+	0.909929i	$0.636136\pi$
$242$	17.4506	1.12177
$243$	15.0332	0.964382
$244$	3.55913	0.227850
$245$	−6.40303	−0.409075
$246$	0.675069	0.0430408
$247$	10.8122	0.687964
$248$	4.86323	0.308816
$249$	−17.8896	−1.13371
$250$	1.00000	0.0632456
$251$	10.4752	0.661192	0.330596	−	0.943772i	$-0.392750\pi$
$251$	10.4752	0.661192	0.330596	+	0.943772i	$0.392750\pi$
$252$	1.33061	0.0838208
$253$	−19.0655	−1.19864
$254$	−3.72312	−0.233609
$255$	−1.71127	−0.107164
$256$	1.00000	0.0625000
$257$	−1.75520	−0.109487	−0.0547433	−	0.998500i	$-0.517434\pi$
$257$	−1.75520	−0.109487	−0.0547433	+	0.998500i	$0.517434\pi$
$258$	−3.97096	−0.247221
$259$	3.40255	0.211424
$260$	−2.27234	−0.140925
$261$	−1.07795	−0.0667237
$262$	9.39051	0.580148
$263$	24.0003	1.47992	0.739962	−	0.672648i	$-0.234843\pi$
$263$	24.0003	1.47992	0.739962	+	0.672648i	$0.234843\pi$
$264$	−6.02951	−0.371091
$265$	−1.59288	−0.0978498
$266$	3.67634	0.225411
$267$	12.1402	0.742966
$268$	9.65100	0.589529
$269$	−3.19623	−0.194877	−0.0974387	−	0.995242i	$-0.531065\pi$
$269$	−3.19623	−0.194877	−0.0974387	+	0.995242i	$0.531065\pi$
$270$	−5.33799	−0.324860
$271$	8.92985	0.542450	0.271225	−	0.962516i	$-0.412571\pi$
$271$	8.92985	0.542450	0.271225	+	0.962516i	$0.412571\pi$
$272$	−1.51384	−0.0917903
$273$	1.98466	0.120117
$274$	−19.9288	−1.20395
$275$	−5.33391	−0.321647
$276$	4.04053	0.243211
$277$	14.7064	0.883623	0.441812	−	0.897108i	$-0.354336\pi$
$277$	14.7064	0.883623	0.441812	+	0.897108i	$0.354336\pi$
$278$	13.7233	0.823067
$279$	−8.37532	−0.501417
$280$	−0.772637	−0.0461739
$281$	−6.97397	−0.416032	−0.208016	−	0.978125i	$-0.566701\pi$
$281$	−6.97397	−0.416032	−0.208016	+	0.978125i	$0.566701\pi$
$282$	1.63525	0.0973776
$283$	16.1996	0.962967	0.481484	−	0.876455i	$-0.340098\pi$
$283$	16.1996	0.962967	0.481484	+	0.876455i	$0.340098\pi$
$284$	−10.1869	−0.604481
$285$	−5.37869	−0.318606
$286$	12.1205	0.716699
$287$	−0.461411	−0.0272362
$288$	−1.72217	−0.101480
$289$	−14.7083	−0.865193
$290$	0.625927	0.0367557
$291$	−16.7186	−0.980059
$292$	−13.4010	−0.784234
$293$	11.0979	0.648348	0.324174	−	0.945998i	$-0.394914\pi$
$293$	11.0979	0.648348	0.324174	+	0.945998i	$0.394914\pi$
$294$	−7.23805	−0.422132
$295$	−9.14211	−0.532274
$296$	−4.40381	−0.255966
$297$	28.4724	1.65214
$298$	17.5266	1.01529
$299$	−8.12224	−0.469721
$300$	1.13041	0.0652643
$301$	2.71416	0.156442
$302$	7.19502	0.414027
$303$	−12.0102	−0.689967
$304$	−4.75817	−0.272900
$305$	3.55913	0.203795
$306$	2.60710	0.149038
$307$	−11.6033	−0.662235	−0.331117	−	0.943590i	$-0.607426\pi$
$307$	−11.6033	−0.662235	−0.331117	+	0.943590i	$0.607426\pi$
$308$	4.12118	0.234826
$309$	17.2632	0.982072
$310$	4.86323	0.276213
$311$	−2.29029	−0.129871	−0.0649353	−	0.997889i	$-0.520684\pi$
$311$	−2.29029	−0.129871	−0.0649353	+	0.997889i	$0.520684\pi$
$312$	−2.56868	−0.145423
$313$	−31.5774	−1.78486	−0.892429	−	0.451188i	$-0.851000\pi$
$313$	−31.5774	−1.78486	−0.892429	+	0.451188i	$0.851000\pi$
$314$	11.8163	0.666831
$315$	1.33061	0.0749716
$316$	−0.0209108	−0.00117633
$317$	17.1946	0.965746	0.482873	−	0.875690i	$-0.339593\pi$
$317$	17.1946	0.965746	0.482873	+	0.875690i	$0.339593\pi$
$318$	−1.80061	−0.100973
$319$	−3.33864	−0.186928
$320$	1.00000	0.0559017
$321$	−2.68034	−0.149602
$322$	−2.76171	−0.153904
$323$	7.20313	0.400793
$324$	−0.867606	−0.0482003
$325$	−2.27234	−0.126047
$326$	−14.3102	−0.792571
$327$	−8.59357	−0.475225
$328$	0.597190	0.0329743
$329$	−1.11769	−0.0616205
$330$	−6.02951	−0.331914
$331$	−10.2884	−0.565502	−0.282751	−	0.959193i	$-0.591247\pi$
$331$	−10.2884	−0.565502	−0.282751	+	0.959193i	$0.591247\pi$
$332$	−15.8258	−0.868553
$333$	7.58412	0.415607
$334$	19.1563	1.04818
$335$	9.65100	0.527291
$336$	−0.873397	−0.0476477
$337$	−23.9321	−1.30366	−0.651832	−	0.758363i	$-0.725999\pi$
$337$	−23.9321	−1.30366	−0.651832	+	0.758363i	$0.725999\pi$
$338$	−7.83645	−0.426247
$339$	5.33148	0.289566
$340$	−1.51384	−0.0820997
$341$	−25.9401	−1.40473
$342$	8.19439	0.443102
$343$	10.3557	0.559154
$344$	−3.51285	−0.189400
$345$	4.04053	0.217535
$346$	14.1639	0.761455
$347$	15.4134	0.827436	0.413718	−	0.910405i	$-0.364230\pi$
$347$	15.4134	0.827436	0.413718	+	0.910405i	$0.364230\pi$
$348$	0.707555	0.0379289
$349$	21.7096	1.16209	0.581045	−	0.813872i	$-0.302644\pi$
$349$	21.7096	1.16209	0.581045	+	0.813872i	$0.302644\pi$
$350$	−0.772637	−0.0412992
$351$	12.1298	0.647438
$352$	−5.33391	−0.284299
$353$	−18.7957	−1.00039	−0.500196	−	0.865912i	$-0.666739\pi$
$353$	−18.7957	−1.00039	−0.500196	+	0.865912i	$0.666739\pi$
$354$	−10.3343	−0.549264
$355$	−10.1869	−0.540664
$356$	10.7396	0.569198
$357$	1.32219	0.0699776
$358$	−7.48379	−0.395531
$359$	−25.4699	−1.34425	−0.672126	−	0.740437i	$-0.734619\pi$
$359$	−25.4699	−1.34425	−0.672126	+	0.740437i	$0.734619\pi$
$360$	−1.72217	−0.0907664
$361$	3.64019	0.191589
$362$	16.3626	0.860000
$363$	19.7264	1.03537
$364$	1.75570	0.0920235
$365$	−13.4010	−0.701440
$366$	4.02328	0.210300
$367$	−26.9266	−1.40556	−0.702779	−	0.711408i	$-0.748058\pi$
$367$	−26.9266	−1.40556	−0.702779	+	0.711408i	$0.748058\pi$
$368$	3.57439	0.186328
$369$	−1.02846	−0.0535397
$370$	−4.40381	−0.228943
$371$	1.23072	0.0638957
$372$	5.49745	0.285029
$373$	34.8862	1.80634	0.903169	−	0.429285i	$-0.141235\pi$
$373$	34.8862	1.80634	0.903169	+	0.429285i	$0.141235\pi$
$374$	8.07472	0.417534
$375$	1.13041	0.0583741
$376$	1.44660	0.0746025
$377$	−1.42232	−0.0732533
$378$	4.12433	0.212133
$379$	12.9783	0.666651	0.333325	−	0.942812i	$-0.391829\pi$
$379$	12.9783	0.666651	0.333325	+	0.942812i	$0.391829\pi$
$380$	−4.75817	−0.244089
$381$	−4.20865	−0.215616
$382$	−1.05971	−0.0542194
$383$	−7.47775	−0.382095	−0.191048	−	0.981581i	$-0.561189\pi$
$383$	−7.47775	−0.382095	−0.191048	+	0.981581i	$0.561189\pi$
$384$	1.13041	0.0576860
$385$	4.12118	0.210035
$386$	−15.1080	−0.768979
$387$	6.04973	0.307525
$388$	−14.7898	−0.750839
$389$	29.2231	1.48167	0.740835	−	0.671687i	$-0.234430\pi$
$389$	29.2231	1.48167	0.740835	+	0.671687i	$0.234430\pi$
$390$	−2.56868	−0.130070
$391$	−5.41107	−0.273650
$392$	−6.40303	−0.323402
$393$	10.6151	0.535463
$394$	−1.77050	−0.0891967
$395$	−0.0209108	−0.00105214
$396$	9.18592	0.461610
$397$	−11.8660	−0.595539	−0.297770	−	0.954638i	$-0.596243\pi$
$397$	−11.8660	−0.595539	−0.297770	+	0.954638i	$0.596243\pi$
$398$	−8.71461	−0.436824
$399$	4.15577	0.208049
$400$	1.00000	0.0500000
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	10.9096	0.544121
$403$	−11.0509	−0.550486
$404$	−10.6246	−0.528595
$405$	−0.867606	−0.0431117
$406$	−0.483615	−0.0240014
$407$	23.4895	1.16433
$408$	−1.71127	−0.0847203
$409$	−2.89470	−0.143134	−0.0715669	−	0.997436i	$-0.522800\pi$
$409$	−2.89470	−0.143134	−0.0715669	+	0.997436i	$0.522800\pi$
$410$	0.597190	0.0294931
$411$	−22.5278	−1.11121
$412$	15.2717	0.752381
$413$	7.06353	0.347574
$414$	−6.15572	−0.302537
$415$	−15.8258	−0.776858
$416$	−2.27234	−0.111411
$417$	15.5129	0.759671
$418$	25.3797	1.24136
$419$	−12.6123	−0.616152	−0.308076	−	0.951362i	$-0.599685\pi$
$419$	−12.6123	−0.616152	−0.308076	+	0.951362i	$0.599685\pi$
$420$	−0.873397	−0.0426174
$421$	−25.9563	−1.26503	−0.632517	−	0.774547i	$-0.717978\pi$
$421$	−25.9563	−1.26503	−0.632517	+	0.774547i	$0.717978\pi$
$422$	25.1490	1.22423
$423$	−2.49129	−0.121131
$424$	−1.59288	−0.0773571
$425$	−1.51384	−0.0734322
$426$	−11.5154	−0.557922
$427$	−2.74992	−0.133078
$428$	−2.37112	−0.114612
$429$	13.7011	0.661496
$430$	−3.51285	−0.169405
$431$	6.11679	0.294635	0.147318	−	0.989089i	$-0.452936\pi$
$431$	6.11679	0.294635	0.147318	+	0.989089i	$0.452936\pi$
$432$	−5.33799	−0.256824
$433$	−16.4695	−0.791473	−0.395737	−	0.918364i	$-0.629511\pi$
$433$	−16.4695	−0.791473	−0.395737	+	0.918364i	$0.629511\pi$
$434$	−3.75751	−0.180366
$435$	0.707555	0.0339247
$436$	−7.60216	−0.364078
$437$	−17.0076	−0.813582
$438$	−15.1486	−0.723829
$439$	−36.6548	−1.74944	−0.874719	−	0.484630i	$-0.838954\pi$
$439$	−36.6548	−1.74944	−0.874719	+	0.484630i	$0.838954\pi$
$440$	−5.33391	−0.254284
$441$	11.0271	0.525101
$442$	3.43997	0.163623
$443$	−7.65080	−0.363500	−0.181750	−	0.983345i	$-0.558176\pi$
$443$	−7.65080	−0.363500	−0.181750	+	0.983345i	$0.558176\pi$
$444$	−4.97811	−0.236251
$445$	10.7396	0.509106
$446$	6.44595	0.305225
$447$	19.8122	0.937087
$448$	−0.772637	−0.0365037
$449$	−20.0643	−0.946892	−0.473446	−	0.880823i	$-0.656990\pi$
$449$	−20.0643	−0.946892	−0.473446	+	0.880823i	$0.656990\pi$
$450$	−1.72217	−0.0811840
$451$	−3.18536	−0.149993
$452$	4.71641	0.221841
$453$	8.13332	0.382137
$454$	−6.70110	−0.314498
$455$	1.75570	0.0823084
$456$	−5.37869	−0.251880
$457$	−17.6954	−0.827757	−0.413879	−	0.910332i	$-0.635826\pi$
$457$	−17.6954	−0.827757	−0.413879	+	0.910332i	$0.635826\pi$
$458$	1.65727	0.0774391
$459$	8.08089	0.377184
$460$	3.57439	0.166657
$461$	−10.5350	−0.490665	−0.245333	−	0.969439i	$-0.578897\pi$
$461$	−10.5350	−0.490665	−0.245333	+	0.969439i	$0.578897\pi$
$462$	4.65863	0.216739
$463$	4.94235	0.229690	0.114845	−	0.993383i	$-0.463363\pi$
$463$	4.94235	0.229690	0.114845	+	0.993383i	$0.463363\pi$
$464$	0.625927	0.0290579
$465$	5.49745	0.254938
$466$	4.45698	0.206465
$467$	−26.9161	−1.24553	−0.622765	−	0.782409i	$-0.713991\pi$
$467$	−26.9161	−1.24553	−0.622765	+	0.782409i	$0.713991\pi$
$468$	3.91337	0.180895
$469$	−7.45673	−0.344320
$470$	1.44660	0.0667265
$471$	13.3572	0.615469
$472$	−9.14211	−0.420800
$473$	18.7372	0.861539
$474$	−0.0236378	−0.00108572
$475$	−4.75817	−0.218320
$476$	1.16965	0.0536109
$477$	2.74321	0.125603
$478$	−1.54755	−0.0707835
$479$	−23.1792	−1.05908	−0.529542	−	0.848284i	$-0.677636\pi$
$479$	−23.1792	−1.05908	−0.529542	+	0.848284i	$0.677636\pi$
$480$	1.13041	0.0515959
$481$	10.0070	0.456278
$482$	−12.8777	−0.586564
$483$	−3.12186	−0.142050
$484$	17.4506	0.793211
$485$	−14.7898	−0.671571
$486$	15.0332	0.681921
$487$	18.6233	0.843902	0.421951	−	0.906619i	$-0.361345\pi$
$487$	18.6233	0.843902	0.421951	+	0.906619i	$0.361345\pi$
$488$	3.55913	0.161114
$489$	−16.1764	−0.731524
$490$	−6.40303	−0.289259
$491$	28.7028	1.29534	0.647669	−	0.761922i	$-0.275744\pi$
$491$	28.7028	1.29534	0.647669	+	0.761922i	$0.275744\pi$
$492$	0.675069	0.0304345
$493$	−0.947557	−0.0426758
$494$	10.8122	0.486464
$495$	9.18592	0.412876
$496$	4.86323	0.218366
$497$	7.87077	0.353052
$498$	−17.8896	−0.801654
$499$	−23.7016	−1.06103	−0.530515	−	0.847675i	$-0.678002\pi$
$499$	−23.7016	−1.06103	−0.530515	+	0.847675i	$0.678002\pi$
$500$	1.00000	0.0447214
$501$	21.6544	0.967449
$502$	10.4752	0.467533
$503$	7.95821	0.354839	0.177419	−	0.984135i	$-0.443225\pi$
$503$	7.95821	0.354839	0.177419	+	0.984135i	$0.443225\pi$
$504$	1.33061	0.0592703
$505$	−10.6246	−0.472790
$506$	−19.0655	−0.847564
$507$	−8.85841	−0.393416
$508$	−3.72312	−0.165187
$509$	−7.28460	−0.322884	−0.161442	−	0.986882i	$-0.551614\pi$
$509$	−7.28460	−0.322884	−0.161442	+	0.986882i	$0.551614\pi$
$510$	−1.71127	−0.0757761
$511$	10.3541	0.458039
$512$	1.00000	0.0441942
$513$	25.3991	1.12140
$514$	−1.75520	−0.0774188
$515$	15.2717	0.672950
$516$	−3.97096	−0.174812
$517$	−7.71602	−0.339350
$518$	3.40255	0.149499
$519$	16.0110	0.702805
$520$	−2.27234	−0.0996489
$521$	22.3145	0.977618	0.488809	−	0.872391i	$-0.337432\pi$
$521$	22.3145	0.977618	0.488809	+	0.872391i	$0.337432\pi$
$522$	−1.07795	−0.0471808
$523$	32.9463	1.44064	0.720320	−	0.693642i	$-0.243995\pi$
$523$	32.9463	1.44064	0.720320	+	0.693642i	$0.243995\pi$
$524$	9.39051	0.410226
$525$	−0.873397	−0.0381182
$526$	24.0003	1.04646
$527$	−7.36218	−0.320701
$528$	−6.02951	−0.262401
$529$	−10.2237	−0.444510
$530$	−1.59288	−0.0691903
$531$	15.7443	0.683244
$532$	3.67634	0.159390
$533$	−1.35702	−0.0587791
$534$	12.1402	0.525356
$535$	−2.37112	−0.102512
$536$	9.65100	0.416860
$537$	−8.45976	−0.365065
$538$	−3.19623	−0.137799
$539$	34.1532	1.47108
$540$	−5.33799	−0.229711
$541$	43.5131	1.87077	0.935387	−	0.353625i	$-0.115051\pi$
$541$	43.5131	1.87077	0.935387	+	0.353625i	$0.115051\pi$
$542$	8.92985	0.383570
$543$	18.4965	0.793760
$544$	−1.51384	−0.0649055
$545$	−7.60216	−0.325641
$546$	1.98466	0.0849356
$547$	−2.28300	−0.0976138	−0.0488069	−	0.998808i	$-0.515542\pi$
$547$	−2.28300	−0.0976138	−0.0488069	+	0.998808i	$0.515542\pi$
$548$	−19.9288	−0.851318
$549$	−6.12943	−0.261598
$550$	−5.33391	−0.227439
$551$	−2.97827	−0.126879
$552$	4.04053	0.171976
$553$	0.0161565	0.000687043 0
$554$	14.7064	0.624816
$555$	−4.97811	−0.211309
$556$	13.7233	0.581996
$557$	12.0625	0.511103	0.255552	−	0.966795i	$-0.417743\pi$
$557$	12.0625	0.511103	0.255552	+	0.966795i	$0.417743\pi$
$558$	−8.37532	−0.354556
$559$	7.98240	0.337620
$560$	−0.772637	−0.0326499
$561$	9.12774	0.385374
$562$	−6.97397	−0.294179
$563$	−2.84539	−0.119919	−0.0599594	−	0.998201i	$-0.519097\pi$
$563$	−2.84539	−0.119919	−0.0599594	+	0.998201i	$0.519097\pi$
$564$	1.63525	0.0688564
$565$	4.71641	0.198421
$566$	16.1996	0.680921
$567$	0.670345	0.0281518
$568$	−10.1869	−0.427433
$569$	−3.03083	−0.127059	−0.0635296	−	0.997980i	$-0.520236\pi$
$569$	−3.03083	−0.127059	−0.0635296	+	0.997980i	$0.520236\pi$
$570$	−5.37869	−0.225288
$571$	32.5638	1.36275	0.681377	−	0.731933i	$-0.261381\pi$
$571$	32.5638	1.36275	0.681377	+	0.731933i	$0.261381\pi$
$572$	12.1205	0.506783
$573$	−1.19791	−0.0500432
$574$	−0.461411	−0.0192589
$575$	3.57439	0.149062
$576$	−1.72217	−0.0717572
$577$	−18.5436	−0.771979	−0.385989	−	0.922503i	$-0.626140\pi$
$577$	−18.5436	−0.771979	−0.385989	+	0.922503i	$0.626140\pi$
$578$	−14.7083	−0.611784
$579$	−17.0783	−0.709749
$580$	0.625927	0.0259902
$581$	12.2276	0.507286
$582$	−16.7186	−0.693006
$583$	8.49628	0.351880
$584$	−13.4010	−0.554537
$585$	3.91337	0.161798
$586$	11.0979	0.458451
$587$	17.4255	0.719229	0.359615	−	0.933101i	$-0.382908\pi$
$587$	17.4255	0.719229	0.359615	+	0.933101i	$0.382908\pi$
$588$	−7.23805	−0.298492
$589$	−23.1401	−0.953471
$590$	−9.14211	−0.376375
$591$	−2.00140	−0.0823265
$592$	−4.40381	−0.180995
$593$	8.88782	0.364979	0.182489	−	0.983208i	$-0.441584\pi$
$593$	8.88782	0.364979	0.182489	+	0.983208i	$0.441584\pi$
$594$	28.4724	1.16824
$595$	1.16965	0.0479511
$596$	17.5266	0.717917
$597$	−9.85109	−0.403178
$598$	−8.12224	−0.332143
$599$	−13.9922	−0.571705	−0.285853	−	0.958274i	$-0.592277\pi$
$599$	−13.9922	−0.571705	−0.285853	+	0.958274i	$0.592277\pi$
$600$	1.13041	0.0461488
$601$	−1.30483	−0.0532250	−0.0266125	−	0.999646i	$-0.508472\pi$
$601$	−1.30483	−0.0532250	−0.0266125	+	0.999646i	$0.508472\pi$
$602$	2.71416	0.110621
$603$	−16.6207	−0.676847
$604$	7.19502	0.292761
$605$	17.4506	0.709469
$606$	−12.0102	−0.487881
$607$	−26.5667	−1.07831	−0.539155	−	0.842207i	$-0.681256\pi$
$607$	−26.5667	−1.07831	−0.539155	+	0.842207i	$0.681256\pi$
$608$	−4.75817	−0.192969
$609$	−0.546683	−0.0221527
$610$	3.55913	0.144105
$611$	−3.28717	−0.132984
$612$	2.60710	0.105386
$613$	26.4797	1.06950	0.534752	−	0.845009i	$-0.320405\pi$
$613$	26.4797	1.06950	0.534752	+	0.845009i	$0.320405\pi$
$614$	−11.6033	−0.468271
$615$	0.675069	0.0272214
$616$	4.12118	0.166047
$617$	−22.7479	−0.915795	−0.457897	−	0.889005i	$-0.651397\pi$
$617$	−22.7479	−0.915795	−0.457897	+	0.889005i	$0.651397\pi$
$618$	17.2632	0.694430
$619$	−15.1435	−0.608668	−0.304334	−	0.952565i	$-0.598434\pi$
$619$	−15.1435	−0.608668	−0.304334	+	0.952565i	$0.598434\pi$
$620$	4.86323	0.195312
$621$	−19.0801	−0.765657
$622$	−2.29029	−0.0918324
$623$	−8.29782	−0.332445
$624$	−2.56868	−0.102830
$625$	1.00000	0.0400000
$626$	−31.5774	−1.26209
$627$	28.6894	1.14575
$628$	11.8163	0.471521
$629$	6.66668	0.265818
$630$	1.33061	0.0530129
$631$	−25.8869	−1.03054	−0.515270	−	0.857028i	$-0.672308\pi$
$631$	−25.8869	−1.03054	−0.515270	+	0.857028i	$0.672308\pi$
$632$	−0.0209108	−0.000831788 0
$633$	28.4286	1.12994
$634$	17.1946	0.682886
$635$	−3.72312	−0.147747
$636$	−1.80061	−0.0713987
$637$	14.5499	0.576488
$638$	−3.33864	−0.132178
$639$	17.5436	0.694014
$640$	1.00000	0.0395285
$641$	−7.32391	−0.289277	−0.144639	−	0.989485i	$-0.546202\pi$
$641$	−7.32391	−0.289277	−0.144639	+	0.989485i	$0.546202\pi$
$642$	−2.68034	−0.105785
$643$	1.09646	0.0432402	0.0216201	−	0.999766i	$-0.493118\pi$
$643$	1.09646	0.0432402	0.0216201	+	0.999766i	$0.493118\pi$
$644$	−2.76171	−0.108826
$645$	−3.97096	−0.156356
$646$	7.20313	0.283403
$647$	−10.0051	−0.393341	−0.196671	−	0.980470i	$-0.563013\pi$
$647$	−10.0051	−0.393341	−0.196671	+	0.980470i	$0.563013\pi$
$648$	−0.867606	−0.0340828
$649$	48.7632	1.91412
$650$	−2.27234	−0.0891287
$651$	−4.24753	−0.166474
$652$	−14.3102	−0.560432
$653$	−31.9170	−1.24901	−0.624504	−	0.781022i	$-0.714699\pi$
$653$	−31.9170	−1.24901	−0.624504	+	0.781022i	$0.714699\pi$
$654$	−8.59357	−0.336035
$655$	9.39051	0.366918
$656$	0.597190	0.0233163
$657$	23.0788	0.900390
$658$	−1.11769	−0.0435723
$659$	−17.0475	−0.664078	−0.332039	−	0.943266i	$-0.607736\pi$
$659$	−17.0475	−0.664078	−0.332039	+	0.943266i	$0.607736\pi$
$660$	−6.02951	−0.234698
$661$	−38.0184	−1.47875	−0.739373	−	0.673296i	$-0.764878\pi$
$661$	−38.0184	−1.47875	−0.739373	+	0.673296i	$0.764878\pi$
$662$	−10.2884	−0.399870
$663$	3.88858	0.151020
$664$	−15.8258	−0.614160
$665$	3.67634	0.142562
$666$	7.58412	0.293879
$667$	2.23731	0.0866289
$668$	19.1563	0.741178
$669$	7.28657	0.281715
$670$	9.65100	0.372851
$671$	−18.9841	−0.732872
$672$	−0.873397	−0.0336920
$673$	42.8993	1.65365	0.826824	−	0.562460i	$-0.190145\pi$
$673$	42.8993	1.65365	0.826824	+	0.562460i	$0.190145\pi$
$674$	−23.9321	−0.921830
$675$	−5.33799	−0.205459
$676$	−7.83645	−0.301402
$677$	16.8315	0.646888	0.323444	−	0.946247i	$-0.395159\pi$
$677$	16.8315	0.646888	0.323444	+	0.946247i	$0.395159\pi$
$678$	5.33148	0.204754
$679$	11.4272	0.438534
$680$	−1.51384	−0.0580533
$681$	−7.57500	−0.290275
$682$	−25.9401	−0.993296
$683$	9.41040	0.360079	0.180039	−	0.983659i	$-0.442377\pi$
$683$	9.41040	0.360079	0.180039	+	0.983659i	$0.442377\pi$
$684$	8.19439	0.313320
$685$	−19.9288	−0.761442
$686$	10.3557	0.395382
$687$	1.87339	0.0714745
$688$	−3.51285	−0.133926
$689$	3.61957	0.137895
$690$	4.04053	0.153820
$691$	29.9484	1.13929	0.569646	−	0.821890i	$-0.307080\pi$
$691$	29.9484	1.13929	0.569646	+	0.821890i	$0.307080\pi$
$692$	14.1639	0.538430
$693$	−7.09738	−0.269607
$694$	15.4134	0.585085
$695$	13.7233	0.520553
$696$	0.707555	0.0268198
$697$	−0.904052	−0.0342434
$698$	21.7096	0.821721
$699$	5.03821	0.190563
$700$	−0.772637	−0.0292029
$701$	−24.7828	−0.936033	−0.468017	−	0.883720i	$-0.655031\pi$
$701$	−24.7828	−0.936033	−0.468017	+	0.883720i	$0.655031\pi$
$702$	12.1298	0.457808
$703$	20.9541	0.790298
$704$	−5.33391	−0.201029
$705$	1.63525	0.0615870
$706$	−18.7957	−0.707384
$707$	8.20898	0.308731
$708$	−10.3343	−0.388388
$709$	−40.7049	−1.52871	−0.764353	−	0.644798i	$-0.776941\pi$
$709$	−40.7049	−1.52871	−0.764353	+	0.644798i	$0.776941\pi$
$710$	−10.1869	−0.382307
$711$	0.0360120	0.00135056
$712$	10.7396	0.402484
$713$	17.3831	0.651002
$714$	1.32219	0.0494816
$715$	12.1205	0.453280
$716$	−7.48379	−0.279682
$717$	−1.74937	−0.0653315
$718$	−25.4699	−0.950529
$719$	−0.436536	−0.0162800	−0.00814002	−	0.999967i	$-0.502591\pi$
$719$	−0.436536	−0.0162800	−0.00814002	+	0.999967i	$0.502591\pi$
$720$	−1.72217	−0.0641816
$721$	−11.7995	−0.439435
$722$	3.64019	0.135474
$723$	−14.5571	−0.541384
$724$	16.3626	0.608112
$725$	0.625927	0.0232464
$726$	19.7264	0.732115
$727$	−12.7637	−0.473380	−0.236690	−	0.971585i	$-0.576063\pi$
$727$	−12.7637	−0.473380	−0.236690	+	0.971585i	$0.576063\pi$
$728$	1.75570	0.0650705
$729$	19.5965	0.725798
$730$	−13.4010	−0.495993
$731$	5.31791	0.196690
$732$	4.02328	0.148705
$733$	0.111292	0.00411066	0.00205533	−	0.999998i	$-0.499346\pi$
$733$	0.111292	0.00411066	0.00205533	+	0.999998i	$0.499346\pi$
$734$	−26.9266	−0.993880
$735$	−7.23805	−0.266980
$736$	3.57439	0.131754
$737$	−51.4776	−1.89620
$738$	−1.02846	−0.0378583
$739$	−26.4580	−0.973273	−0.486636	−	0.873605i	$-0.661776\pi$
$739$	−26.4580	−0.973273	−0.486636	+	0.873605i	$0.661776\pi$
$740$	−4.40381	−0.161887
$741$	12.2222	0.448995
$742$	1.23072	0.0451811
$743$	31.8720	1.16927	0.584635	−	0.811296i	$-0.301238\pi$
$743$	31.8720	1.16927	0.584635	+	0.811296i	$0.301238\pi$
$744$	5.49745	0.201546
$745$	17.5266	0.642125
$746$	34.8862	1.27727
$747$	27.2547	0.997199
$748$	8.07472	0.295241
$749$	1.83202	0.0669404
$750$	1.13041	0.0412768
$751$	18.6747	0.681448	0.340724	−	0.940163i	$-0.389328\pi$
$751$	18.6747	0.681448	0.340724	+	0.940163i	$0.389328\pi$
$752$	1.44660	0.0527520
$753$	11.8413	0.431522
$754$	−1.42232	−0.0517979
$755$	7.19502	0.261853
$756$	4.12433	0.150001
$757$	−29.9263	−1.08769	−0.543845	−	0.839186i	$-0.683032\pi$
$757$	−29.9263	−1.08769	−0.543845	+	0.839186i	$0.683032\pi$
$758$	12.9783	0.471393
$759$	−21.5518	−0.782282
$760$	−4.75817	−0.172597
$761$	−54.0990	−1.96109	−0.980544	−	0.196298i	$-0.937108\pi$
$761$	−54.0990	−1.96109	−0.980544	+	0.196298i	$0.937108\pi$
$762$	−4.20865	−0.152463
$763$	5.87372	0.212643
$764$	−1.05971	−0.0383389
$765$	2.60710	0.0942599
$766$	−7.47775	−0.270182
$767$	20.7740	0.750106
$768$	1.13041	0.0407902
$769$	−30.9532	−1.11620	−0.558100	−	0.829773i	$-0.688470\pi$
$769$	−30.9532	−1.11620	−0.558100	+	0.829773i	$0.688470\pi$
$770$	4.12118	0.148517
$771$	−1.98410	−0.0714557
$772$	−15.1080	−0.543750
$773$	52.8611	1.90128	0.950641	−	0.310292i	$-0.100427\pi$
$773$	52.8611	1.90128	0.950641	+	0.310292i	$0.100427\pi$
$774$	6.04973	0.217453
$775$	4.86323	0.174692
$776$	−14.7898	−0.530923
$777$	3.84627	0.137984
$778$	29.2231	1.04770
$779$	−2.84153	−0.101808
$780$	−2.56868	−0.0919735
$781$	54.3360	1.94430
$782$	−5.41107	−0.193499
$783$	−3.34120	−0.119405
$784$	−6.40303	−0.228680
$785$	11.8163	0.421741
$786$	10.6151	0.378629
$787$	−26.8965	−0.958757	−0.479378	−	0.877608i	$-0.659138\pi$
$787$	−26.8965	−0.958757	−0.479378	+	0.877608i	$0.659138\pi$
$788$	−1.77050	−0.0630716
$789$	27.1302	0.965862
$790$	−0.0209108	−0.000743974 0
$791$	−3.64407	−0.129568
$792$	9.18592	0.326407
$793$	−8.08756	−0.287198
$794$	−11.8660	−0.421110
$795$	−1.80061	−0.0638610
$796$	−8.71461	−0.308881
$797$	−44.4420	−1.57422	−0.787108	−	0.616816i	$-0.788422\pi$
$797$	−44.4420	−1.57422	−0.787108	+	0.616816i	$0.788422\pi$
$798$	4.15577	0.147113
$799$	−2.18992	−0.0774739
$800$	1.00000	0.0353553
$801$	−18.4955	−0.653505
$802$	−1.00000	−0.0353112
$803$	71.4797	2.52247
$804$	10.9096	0.384752
$805$	−2.76171	−0.0973374
$806$	−11.0509	−0.389253
$807$	−3.61305	−0.127185
$808$	−10.6246	−0.373773
$809$	18.2437	0.641416	0.320708	−	0.947178i	$-0.396079\pi$
$809$	18.2437	0.641416	0.320708	+	0.947178i	$0.396079\pi$
$810$	−0.867606	−0.0304846
$811$	32.2953	1.13404	0.567020	−	0.823704i	$-0.308096\pi$
$811$	32.2953	1.13404	0.567020	+	0.823704i	$0.308096\pi$
$812$	−0.483615	−0.0169715
$813$	10.0944	0.354026
$814$	23.4895	0.823308
$815$	−14.3102	−0.501266
$816$	−1.71127	−0.0599063
$817$	16.7147	0.584775
$818$	−2.89470	−0.101211
$819$	−3.02361	−0.105654
$820$	0.597190	0.0208548
$821$	−9.64636	−0.336660	−0.168330	−	0.985731i	$-0.553837\pi$
$821$	−9.64636	−0.336660	−0.168330	+	0.985731i	$0.553837\pi$
$822$	−22.5278	−0.785746
$823$	6.20736	0.216375	0.108188	−	0.994131i	$-0.465495\pi$
$823$	6.20736	0.216375	0.108188	+	0.994131i	$0.465495\pi$
$824$	15.2717	0.532014
$825$	−6.02951	−0.209921
$826$	7.06353	0.245772
$827$	9.24115	0.321346	0.160673	−	0.987008i	$-0.448633\pi$
$827$	9.24115	0.321346	0.160673	+	0.987008i	$0.448633\pi$
$828$	−6.15572	−0.213926
$829$	2.36900	0.0822789	0.0411394	−	0.999153i	$-0.486901\pi$
$829$	2.36900	0.0822789	0.0411394	+	0.999153i	$0.486901\pi$
$830$	−15.8258	−0.549321
$831$	16.6243	0.576690
$832$	−2.27234	−0.0787793
$833$	9.69319	0.335849
$834$	15.5129	0.537168
$835$	19.1563	0.662930
$836$	25.3797	0.877774
$837$	−25.9599	−0.897305
$838$	−12.6123	−0.435685
$839$	10.2793	0.354882	0.177441	−	0.984131i	$-0.443218\pi$
$839$	10.2793	0.354882	0.177441	+	0.984131i	$0.443218\pi$
$840$	−0.873397	−0.0301351
$841$	−28.6082	−0.986490
$842$	−25.9563	−0.894514
$843$	−7.88345	−0.271520
$844$	25.1490	0.865663
$845$	−7.83645	−0.269582
$846$	−2.49129	−0.0856523
$847$	−13.4830	−0.463282
$848$	−1.59288	−0.0546997
$849$	18.3122	0.628474
$850$	−1.51384	−0.0519244
$851$	−15.7409	−0.539592
$852$	−11.5154	−0.394510
$853$	−27.8692	−0.954224	−0.477112	−	0.878843i	$-0.658316\pi$
$853$	−27.8692	−0.954224	−0.477112	+	0.878843i	$0.658316\pi$
$854$	−2.74992	−0.0941002
$855$	8.19439	0.280242
$856$	−2.37112	−0.0810432
$857$	−31.2489	−1.06744	−0.533720	−	0.845661i	$-0.679207\pi$
$857$	−31.2489	−1.06744	−0.533720	+	0.845661i	$0.679207\pi$
$858$	13.7011	0.467749
$859$	6.73196	0.229691	0.114846	−	0.993383i	$-0.463363\pi$
$859$	6.73196	0.229691	0.114846	+	0.993383i	$0.463363\pi$
$860$	−3.51285	−0.119787
$861$	−0.521584	−0.0177755
$862$	6.11679	0.208339
$863$	0.426889	0.0145315	0.00726574	−	0.999974i	$-0.497687\pi$
$863$	0.426889	0.0145315	0.00726574	+	0.999974i	$0.497687\pi$
$864$	−5.33799	−0.181602
$865$	14.1639	0.481587
$866$	−16.4695	−0.559656
$867$	−16.6264	−0.564662
$868$	−3.75751	−0.127538
$869$	0.111536	0.00378362
$870$	0.707555	0.0239884
$871$	−21.9304	−0.743083
$872$	−7.60216	−0.257442
$873$	25.4706	0.862049
$874$	−17.0076	−0.575289
$875$	−0.772637	−0.0261199
$876$	−15.1486	−0.511825
$877$	−5.58174	−0.188482	−0.0942410	−	0.995549i	$-0.530042\pi$
$877$	−5.58174	−0.188482	−0.0942410	+	0.995549i	$0.530042\pi$
$878$	−36.6548	−1.23704
$879$	12.5452	0.423139
$880$	−5.33391	−0.179806
$881$	−29.9571	−1.00928	−0.504640	−	0.863330i	$-0.668375\pi$
$881$	−29.9571	−1.00928	−0.504640	+	0.863330i	$0.668375\pi$
$882$	11.0271	0.371303
$883$	−39.1216	−1.31655	−0.658273	−	0.752780i	$-0.728713\pi$
$883$	−39.1216	−1.31655	−0.658273	+	0.752780i	$0.728713\pi$
$884$	3.43997	0.115699
$885$	−10.3343	−0.347385
$886$	−7.65080	−0.257034
$887$	−39.0313	−1.31054	−0.655271	−	0.755394i	$-0.727446\pi$
$887$	−39.0313	−1.31054	−0.655271	+	0.755394i	$0.727446\pi$
$888$	−4.97811	−0.167054
$889$	2.87662	0.0964787
$890$	10.7396	0.359993
$891$	4.62773	0.155035
$892$	6.44595	0.215826
$893$	−6.88316	−0.230336
$894$	19.8122	0.662621
$895$	−7.48379	−0.250156
$896$	−0.772637	−0.0258120
$897$	−9.18147	−0.306560
$898$	−20.0643	−0.669554
$899$	3.04403	0.101524
$900$	−1.72217	−0.0574057
$901$	2.41137	0.0803345
$902$	−3.18536	−0.106061
$903$	3.06811	0.102100
$904$	4.71641	0.156865
$905$	16.3626	0.543912
$906$	8.13332	0.270212
$907$	−1.76370	−0.0585628	−0.0292814	−	0.999571i	$-0.509322\pi$
$907$	−1.76370	−0.0585628	−0.0292814	+	0.999571i	$0.509322\pi$
$908$	−6.70110	−0.222384
$909$	18.2974	0.606888
$910$	1.75570	0.0582008
$911$	−22.7208	−0.752774	−0.376387	−	0.926463i	$-0.622834\pi$
$911$	−22.7208	−0.752774	−0.376387	+	0.926463i	$0.622834\pi$
$912$	−5.37869	−0.178106
$913$	84.4134	2.79368
$914$	−17.6954	−0.585313
$915$	4.02328	0.133005
$916$	1.65727	0.0547577
$917$	−7.25546	−0.239596
$918$	8.08089	0.266709
$919$	10.6919	0.352692	0.176346	−	0.984328i	$-0.443572\pi$
$919$	10.6919	0.352692	0.176346	+	0.984328i	$0.443572\pi$
$920$	3.57439	0.117844
$921$	−13.1165	−0.432203
$922$	−10.5350	−0.346953
$923$	23.1481	0.761930
$924$	4.65863	0.153258
$925$	−4.40381	−0.144796
$926$	4.94235	0.162416
$927$	−26.3004	−0.863820
$928$	0.625927	0.0205471
$929$	34.3869	1.12820	0.564098	−	0.825708i	$-0.309224\pi$
$929$	34.3869	1.12820	0.564098	+	0.825708i	$0.309224\pi$
$930$	5.49745	0.180268
$931$	30.4667	0.998506
$932$	4.45698	0.145993
$933$	−2.58897	−0.0847591
$934$	−26.9161	−0.880722
$935$	8.07472	0.264071
$936$	3.91337	0.127912
$937$	16.8747	0.551273	0.275637	−	0.961262i	$-0.411111\pi$
$937$	16.8747	0.551273	0.275637	+	0.961262i	$0.411111\pi$
$938$	−7.45673	−0.243471
$939$	−35.6954	−1.16487
$940$	1.44660	0.0471828
$941$	−0.895905	−0.0292057	−0.0146028	−	0.999893i	$-0.504648\pi$
$941$	−0.895905	−0.0292057	−0.0146028	+	0.999893i	$0.504648\pi$
$942$	13.3572	0.435203
$943$	2.13459	0.0695118
$944$	−9.14211	−0.297550
$945$	4.12433	0.134165
$946$	18.7372	0.609200
$947$	24.7523	0.804343	0.402172	−	0.915564i	$-0.368256\pi$
$947$	24.7523	0.804343	0.402172	+	0.915564i	$0.368256\pi$
$948$	−0.0236378	−0.000767720 0
$949$	30.4517	0.988503
$950$	−4.75817	−0.154375
$951$	19.4370	0.630287
$952$	1.16965	0.0379087
$953$	13.2321	0.428630	0.214315	−	0.976765i	$-0.431248\pi$
$953$	13.2321	0.428630	0.214315	+	0.976765i	$0.431248\pi$
$954$	2.74321	0.0888148
$955$	−1.05971	−0.0342914
$956$	−1.54755	−0.0500515
$957$	−3.77404	−0.121997
$958$	−23.1792	−0.748886
$959$	15.3978	0.497220
$960$	1.13041	0.0364838
$961$	−7.34898	−0.237064
$962$	10.0070	0.322638
$963$	4.08348	0.131588
$964$	−12.8777	−0.414763
$965$	−15.1080	−0.486345
$966$	−3.12186	−0.100444
$967$	29.5290	0.949587	0.474794	−	0.880097i	$-0.342523\pi$
$967$	29.5290	0.949587	0.474794	+	0.880097i	$0.342523\pi$
$968$	17.4506	0.560885
$969$	8.14249	0.261575
$970$	−14.7898	−0.474872
$971$	53.8577	1.72838	0.864188	−	0.503169i	$-0.167833\pi$
$971$	53.8577	1.72838	0.864188	+	0.503169i	$0.167833\pi$
$972$	15.0332	0.482191
$973$	−10.6031	−0.339920
$974$	18.6233	0.596729
$975$	−2.56868	−0.0822636
$976$	3.55913	0.113925
$977$	56.7100	1.81432	0.907158	−	0.420791i	$-0.138247\pi$
$977$	56.7100	1.81432	0.907158	+	0.420791i	$0.138247\pi$
$978$	−16.1764	−0.517266
$979$	−57.2842	−1.83081
$980$	−6.40303	−0.204537
$981$	13.0922	0.418003
$982$	28.7028	0.915943
$983$	−8.41180	−0.268295	−0.134147	−	0.990961i	$-0.542830\pi$
$983$	−8.41180	−0.268295	−0.134147	+	0.990961i	$0.542830\pi$
$984$	0.675069	0.0215204
$985$	−1.77050	−0.0564130
$986$	−0.947557	−0.0301763
$987$	−1.26345	−0.0402162
$988$	10.8122	0.343982
$989$	−12.5563	−0.399267
$990$	9.18592	0.291948
$991$	−15.7119	−0.499106	−0.249553	−	0.968361i	$-0.580284\pi$
$991$	−15.7119	−0.499106	−0.249553	+	0.968361i	$0.580284\pi$
$992$	4.86323	0.154408
$993$	−11.6301	−0.369070
$994$	7.87077	0.249646
$995$	−8.71461	−0.276272
$996$	−17.8896	−0.566855
$997$	−37.2216	−1.17882	−0.589411	−	0.807834i	$-0.700640\pi$
$997$	−37.2216	−1.17882	−0.589411	+	0.807834i	$0.700640\pi$
$998$	−23.7016	−0.750262
$999$	23.5075	0.743744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4010.2.a.h.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4010.2.a.h.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.13041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.13041 q^{6} -0.772637 q^{7} +1.00000 q^{8} -1.72217 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.13041 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.13041 q^{6} -0.772637 q^{7} +1.00000 q^{8} -1.72217 q^{9} +1.00000 q^{10} -5.33391 q^{11} +1.13041 q^{12} -2.27234 q^{13} -0.772637 q^{14} +1.13041 q^{15} +1.00000 q^{16} -1.51384 q^{17} -1.72217 q^{18} -4.75817 q^{19} +1.00000 q^{20} -0.873397 q^{21} -5.33391 q^{22} +3.57439 q^{23} +1.13041 q^{24} +1.00000 q^{25} -2.27234 q^{26} -5.33799 q^{27} -0.772637 q^{28} +0.625927 q^{29} +1.13041 q^{30} +4.86323 q^{31} +1.00000 q^{32} -6.02951 q^{33} -1.51384 q^{34} -0.772637 q^{35} -1.72217 q^{36} -4.40381 q^{37} -4.75817 q^{38} -2.56868 q^{39} +1.00000 q^{40} +0.597190 q^{41} -0.873397 q^{42} -3.51285 q^{43} -5.33391 q^{44} -1.72217 q^{45} +3.57439 q^{46} +1.44660 q^{47} +1.13041 q^{48} -6.40303 q^{49} +1.00000 q^{50} -1.71127 q^{51} -2.27234 q^{52} -1.59288 q^{53} -5.33799 q^{54} -5.33391 q^{55} -0.772637 q^{56} -5.37869 q^{57} +0.625927 q^{58} -9.14211 q^{59} +1.13041 q^{60} +3.55913 q^{61} +4.86323 q^{62} +1.33061 q^{63} +1.00000 q^{64} -2.27234 q^{65} -6.02951 q^{66} +9.65100 q^{67} -1.51384 q^{68} +4.04053 q^{69} -0.772637 q^{70} -10.1869 q^{71} -1.72217 q^{72} -13.4010 q^{73} -4.40381 q^{74} +1.13041 q^{75} -4.75817 q^{76} +4.12118 q^{77} -2.56868 q^{78} -0.0209108 q^{79} +1.00000 q^{80} -0.867606 q^{81} +0.597190 q^{82} -15.8258 q^{83} -0.873397 q^{84} -1.51384 q^{85} -3.51285 q^{86} +0.707555 q^{87} -5.33391 q^{88} +10.7396 q^{89} -1.72217 q^{90} +1.75570 q^{91} +3.57439 q^{92} +5.49745 q^{93} +1.44660 q^{94} -4.75817 q^{95} +1.13041 q^{96} -14.7898 q^{97} -6.40303 q^{98} +9.18592 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 4 q^{3} + 9 q^{4} + 9 q^{5} - 4 q^{6} - 7 q^{7} + 9 q^{8} - 7 q^{9}+O(q^{10}) \) 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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