LMFDB - Embedded newform 4006.2.a.g.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4006,2,Mod(1,4006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4006 = 2 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4006.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:	$31.9880710497$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.956879 q^{3} +1.00000 q^{4} -0.0953014 q^{5} +0.956879 q^{6} -4.20577 q^{7} -1.00000 q^{8} -2.08438 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.956879 q^{3} +1.00000 q^{4} -0.0953014 q^{5} +0.956879 q^{6} -4.20577 q^{7} -1.00000 q^{8} -2.08438 q^{9} +0.0953014 q^{10} -0.121483 q^{11} -0.956879 q^{12} -1.63495 q^{13} +4.20577 q^{14} +0.0911919 q^{15} +1.00000 q^{16} +3.22305 q^{17} +2.08438 q^{18} -1.33888 q^{19} -0.0953014 q^{20} +4.02442 q^{21} +0.121483 q^{22} +7.51615 q^{23} +0.956879 q^{24} -4.99092 q^{25} +1.63495 q^{26} +4.86514 q^{27} -4.20577 q^{28} +9.09309 q^{29} -0.0911919 q^{30} +1.34519 q^{31} -1.00000 q^{32} +0.116245 q^{33} -3.22305 q^{34} +0.400816 q^{35} -2.08438 q^{36} -0.847194 q^{37} +1.33888 q^{38} +1.56445 q^{39} +0.0953014 q^{40} -2.51290 q^{41} -4.02442 q^{42} +6.69337 q^{43} -0.121483 q^{44} +0.198645 q^{45} -7.51615 q^{46} +11.4944 q^{47} -0.956879 q^{48} +10.6885 q^{49} +4.99092 q^{50} -3.08407 q^{51} -1.63495 q^{52} +6.97986 q^{53} -4.86514 q^{54} +0.0115775 q^{55} +4.20577 q^{56} +1.28114 q^{57} -9.09309 q^{58} -3.92557 q^{59} +0.0911919 q^{60} -10.4678 q^{61} -1.34519 q^{62} +8.76644 q^{63} +1.00000 q^{64} +0.155813 q^{65} -0.116245 q^{66} -14.1662 q^{67} +3.22305 q^{68} -7.19205 q^{69} -0.400816 q^{70} +5.68177 q^{71} +2.08438 q^{72} +0.786531 q^{73} +0.847194 q^{74} +4.77571 q^{75} -1.33888 q^{76} +0.510931 q^{77} -1.56445 q^{78} -1.19208 q^{79} -0.0953014 q^{80} +1.59779 q^{81} +2.51290 q^{82} -11.7356 q^{83} +4.02442 q^{84} -0.307161 q^{85} -6.69337 q^{86} -8.70099 q^{87} +0.121483 q^{88} -5.77411 q^{89} -0.198645 q^{90} +6.87624 q^{91} +7.51615 q^{92} -1.28719 q^{93} -11.4944 q^{94} +0.127597 q^{95} +0.956879 q^{96} +4.53164 q^{97} -10.6885 q^{98} +0.253217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) $ 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.956879	−0.552454	−0.276227	−	0.961092i	$-0.589084\pi$
$3$	−0.956879	−0.552454	−0.276227	+	0.961092i	$0.589084\pi$
$4$	1.00000	0.500000
$5$	−0.0953014	−0.0426201	−0.0213100	−	0.999773i	$-0.506784\pi$
$5$	−0.0953014	−0.0426201	−0.0213100	+	0.999773i	$0.506784\pi$
$6$	0.956879	0.390644
$7$	−4.20577	−1.58963	−0.794817	−	0.606850i	$-0.792433\pi$
$7$	−4.20577	−1.58963	−0.794817	+	0.606850i	$0.792433\pi$
$8$	−1.00000	−0.353553
$9$	−2.08438	−0.694794
$10$	0.0953014	0.0301369
$11$	−0.121483	−0.0366286	−0.0183143	−	0.999832i	$-0.505830\pi$
$11$	−0.121483	−0.0366286	−0.0183143	+	0.999832i	$0.505830\pi$
$12$	−0.956879	−0.276227
$13$	−1.63495	−0.453454	−0.226727	−	0.973958i	$-0.572802\pi$
$13$	−1.63495	−0.453454	−0.226727	+	0.973958i	$0.572802\pi$
$14$	4.20577	1.12404
$15$	0.0911919	0.0235457
$16$	1.00000	0.250000
$17$	3.22305	0.781703	0.390852	−	0.920454i	$-0.372181\pi$
$17$	3.22305	0.781703	0.390852	+	0.920454i	$0.372181\pi$
$18$	2.08438	0.491294
$19$	−1.33888	−0.307159	−0.153580	−	0.988136i	$-0.549080\pi$
$19$	−1.33888	−0.307159	−0.153580	+	0.988136i	$0.549080\pi$
$20$	−0.0953014	−0.0213100
$21$	4.02442	0.878200
$22$	0.121483	0.0259003
$23$	7.51615	1.56723	0.783613	−	0.621249i	$-0.213374\pi$
$23$	7.51615	1.56723	0.783613	+	0.621249i	$0.213374\pi$
$24$	0.956879	0.195322
$25$	−4.99092	−0.998184
$26$	1.63495	0.320640
$27$	4.86514	0.936297
$28$	−4.20577	−0.794817
$29$	9.09309	1.68854	0.844272	−	0.535914i	$-0.180033\pi$
$29$	9.09309	1.68854	0.844272	+	0.535914i	$0.180033\pi$
$30$	−0.0911919	−0.0166493
$31$	1.34519	0.241604	0.120802	−	0.992677i	$-0.461453\pi$
$31$	1.34519	0.241604	0.120802	+	0.992677i	$0.461453\pi$
$32$	−1.00000	−0.176777
$33$	0.116245	0.0202356
$34$	−3.22305	−0.552748
$35$	0.400816	0.0677503
$36$	−2.08438	−0.347397
$37$	−0.847194	−0.139278	−0.0696389	−	0.997572i	$-0.522185\pi$
$37$	−0.847194	−0.139278	−0.0696389	+	0.997572i	$0.522185\pi$
$38$	1.33888	0.217194
$39$	1.56445	0.250513
$40$	0.0953014	0.0150685
$41$	−2.51290	−0.392449	−0.196225	−	0.980559i	$-0.562868\pi$
$41$	−2.51290	−0.392449	−0.196225	+	0.980559i	$0.562868\pi$
$42$	−4.02442	−0.620981
$43$	6.69337	1.02073	0.510365	−	0.859958i	$-0.329510\pi$
$43$	6.69337	1.02073	0.510365	+	0.859958i	$0.329510\pi$
$44$	−0.121483	−0.0183143
$45$	0.198645	0.0296122
$46$	−7.51615	−1.10820
$47$	11.4944	1.67664	0.838319	−	0.545181i	$-0.183539\pi$
$47$	11.4944	1.67664	0.838319	+	0.545181i	$0.183539\pi$
$48$	−0.956879	−0.138114
$49$	10.6885	1.52693
$50$	4.99092	0.705822
$51$	−3.08407	−0.431856
$52$	−1.63495	−0.226727
$53$	6.97986	0.958757	0.479379	−	0.877608i	$-0.340862\pi$
$53$	6.97986	0.958757	0.479379	+	0.877608i	$0.340862\pi$
$54$	−4.86514	−0.662062
$55$	0.0115775	0.00156111
$56$	4.20577	0.562020
$57$	1.28114	0.169692
$58$	−9.09309	−1.19398
$59$	−3.92557	−0.511066	−0.255533	−	0.966800i	$-0.582251\pi$
$59$	−3.92557	−0.511066	−0.255533	+	0.966800i	$0.582251\pi$
$60$	0.0911919	0.0117728
$61$	−10.4678	−1.34026	−0.670130	−	0.742243i	$-0.733762\pi$
$61$	−10.4678	−1.34026	−0.670130	+	0.742243i	$0.733762\pi$
$62$	−1.34519	−0.170840
$63$	8.76644	1.10447
$64$	1.00000	0.125000
$65$	0.155813	0.0193262
$66$	−0.116245	−0.0143087
$67$	−14.1662	−1.73068	−0.865339	−	0.501187i	$-0.832897\pi$
$67$	−14.1662	−1.73068	−0.865339	+	0.501187i	$0.832897\pi$
$68$	3.22305	0.390852
$69$	−7.19205	−0.865821
$70$	−0.400816	−0.0479067
$71$	5.68177	0.674302	0.337151	−	0.941451i	$-0.390537\pi$
$71$	5.68177	0.674302	0.337151	+	0.941451i	$0.390537\pi$
$72$	2.08438	0.245647
$73$	0.786531	0.0920565	0.0460283	−	0.998940i	$-0.485344\pi$
$73$	0.786531	0.0920565	0.0460283	+	0.998940i	$0.485344\pi$
$74$	0.847194	0.0984843
$75$	4.77571	0.551451
$76$	−1.33888	−0.153580
$77$	0.510931	0.0582260
$78$	−1.56445	−0.177139
$79$	−1.19208	−0.134119	−0.0670595	−	0.997749i	$-0.521362\pi$
$79$	−1.19208	−0.134119	−0.0670595	+	0.997749i	$0.521362\pi$
$80$	−0.0953014	−0.0106550
$81$	1.59779	0.177533
$82$	2.51290	0.277504
$83$	−11.7356	−1.28815	−0.644075	−	0.764963i	$-0.722757\pi$
$83$	−11.7356	−1.28815	−0.644075	+	0.764963i	$0.722757\pi$
$84$	4.02442	0.439100
$85$	−0.307161	−0.0333163
$86$	−6.69337	−0.721765
$87$	−8.70099	−0.932844
$88$	0.121483	0.0129502
$89$	−5.77411	−0.612055	−0.306027	−	0.952023i	$-0.599000\pi$
$89$	−5.77411	−0.612055	−0.306027	+	0.952023i	$0.599000\pi$
$90$	−0.198645	−0.0209390
$91$	6.87624	0.720825
$92$	7.51615	0.783613
$93$	−1.28719	−0.133475
$94$	−11.4944	−1.18556
$95$	0.127597	0.0130912
$96$	0.956879	0.0976611
$97$	4.53164	0.460119	0.230059	−	0.973177i	$-0.426108\pi$
$97$	4.53164	0.460119	0.230059	+	0.973177i	$0.426108\pi$
$98$	−10.6885	−1.07971
$99$	0.253217	0.0254493
$100$	−4.99092	−0.499092
$101$	−18.8485	−1.87549	−0.937746	−	0.347322i	$-0.887091\pi$
$101$	−18.8485	−1.87549	−0.937746	+	0.347322i	$0.887091\pi$
$102$	3.08407	0.305368
$103$	−16.0310	−1.57958	−0.789792	−	0.613374i	$-0.789812\pi$
$103$	−16.0310	−1.57958	−0.789792	+	0.613374i	$0.789812\pi$
$104$	1.63495	0.160320
$105$	−0.383533	−0.0374290
$106$	−6.97986	−0.677944
$107$	−7.85447	−0.759321	−0.379660	−	0.925126i	$-0.623959\pi$
$107$	−7.85447	−0.759321	−0.379660	+	0.925126i	$0.623959\pi$
$108$	4.86514	0.468148
$109$	12.9103	1.23659	0.618293	−	0.785947i	$-0.287824\pi$
$109$	12.9103	1.23659	0.618293	+	0.785947i	$0.287824\pi$
$110$	−0.0115775	−0.00110387
$111$	0.810662	0.0769446
$112$	−4.20577	−0.397408
$113$	−5.40353	−0.508321	−0.254160	−	0.967162i	$-0.581799\pi$
$113$	−5.40353	−0.508321	−0.254160	+	0.967162i	$0.581799\pi$
$114$	−1.28114	−0.119990
$115$	−0.716300	−0.0667953
$116$	9.09309	0.844272
$117$	3.40786	0.315057
$118$	3.92557	0.361378
$119$	−13.5554	−1.24262
$120$	−0.0911919	−0.00832465
$121$	−10.9852	−0.998658
$122$	10.4678	0.947708
$123$	2.40454	0.216810
$124$	1.34519	0.120802
$125$	0.952148	0.0851627
$126$	−8.76644	−0.780977
$127$	−11.4199	−1.01335	−0.506675	−	0.862137i	$-0.669126\pi$
$127$	−11.4199	−1.01335	−0.506675	+	0.862137i	$0.669126\pi$
$128$	−1.00000	−0.0883883
$129$	−6.40475	−0.563907
$130$	−0.155813	−0.0136657
$131$	2.73835	0.239251	0.119625	−	0.992819i	$-0.461831\pi$
$131$	2.73835	0.239251	0.119625	+	0.992819i	$0.461831\pi$
$132$	0.116245	0.0101178
$133$	5.63101	0.488271
$134$	14.1662	1.22377
$135$	−0.463655	−0.0399050
$136$	−3.22305	−0.276374
$137$	−12.1095	−1.03458	−0.517292	−	0.855809i	$-0.673060\pi$
$137$	−12.1095	−1.03458	−0.517292	+	0.855809i	$0.673060\pi$
$138$	7.19205	0.612228
$139$	16.1577	1.37048	0.685241	−	0.728316i	$-0.259697\pi$
$139$	16.1577	1.37048	0.685241	+	0.728316i	$0.259697\pi$
$140$	0.400816	0.0338752
$141$	−10.9988	−0.926266
$142$	−5.68177	−0.476803
$143$	0.198619	0.0166094
$144$	−2.08438	−0.173699
$145$	−0.866584	−0.0719659
$146$	−0.786531	−0.0650938
$147$	−10.2276	−0.843562
$148$	−0.847194	−0.0696389
$149$	−4.96833	−0.407021	−0.203511	−	0.979073i	$-0.565235\pi$
$149$	−4.96833	−0.407021	−0.203511	+	0.979073i	$0.565235\pi$
$150$	−4.77571	−0.389935
$151$	14.1500	1.15151	0.575754	−	0.817623i	$-0.304709\pi$
$151$	14.1500	1.15151	0.575754	+	0.817623i	$0.304709\pi$
$152$	1.33888	0.108597
$153$	−6.71806	−0.543123
$154$	−0.510931	−0.0411720
$155$	−0.128199	−0.0102972
$156$	1.56445	0.125256
$157$	−3.45379	−0.275642	−0.137821	−	0.990457i	$-0.544010\pi$
$157$	−3.45379	−0.275642	−0.137821	+	0.990457i	$0.544010\pi$
$158$	1.19208	0.0948365
$159$	−6.67888	−0.529670
$160$	0.0953014	0.00753424
$161$	−31.6113	−2.49132
$162$	−1.59779	−0.125535
$163$	7.63173	0.597764	0.298882	−	0.954290i	$-0.403386\pi$
$163$	7.63173	0.597764	0.298882	+	0.954290i	$0.403386\pi$
$164$	−2.51290	−0.196225
$165$	−0.0110783	−0.000862444 0
$166$	11.7356	0.910859
$167$	13.2615	1.02621	0.513103	−	0.858327i	$-0.328496\pi$
$167$	13.2615	1.02621	0.513103	+	0.858327i	$0.328496\pi$
$168$	−4.02442	−0.310491
$169$	−10.3269	−0.794380
$170$	0.307161	0.0235582
$171$	2.79073	0.213412
$172$	6.69337	0.510365
$173$	23.1657	1.76126	0.880628	−	0.473809i	$-0.157121\pi$
$173$	23.1657	1.76126	0.880628	+	0.473809i	$0.157121\pi$
$174$	8.70099	0.659620
$175$	20.9907	1.58675
$176$	−0.121483	−0.00915714
$177$	3.75630	0.282341
$178$	5.77411	0.432788
$179$	0.199393	0.0149033	0.00745165	−	0.999972i	$-0.497628\pi$
$179$	0.199393	0.0149033	0.00745165	+	0.999972i	$0.497628\pi$
$180$	0.198645	0.0148061
$181$	−23.4780	−1.74511	−0.872554	−	0.488518i	$-0.837538\pi$
$181$	−23.4780	−1.74511	−0.872554	+	0.488518i	$0.837538\pi$
$182$	−6.87624	−0.509701
$183$	10.0164	0.740433
$184$	−7.51615	−0.554098
$185$	0.0807387	0.00593603
$186$	1.28719	0.0943812
$187$	−0.391546	−0.0286327
$188$	11.4944	0.838319
$189$	−20.4617	−1.48837
$190$	−0.127597	−0.00925684
$191$	19.7628	1.42999	0.714994	−	0.699130i	$-0.246429\pi$
$191$	19.7628	1.42999	0.714994	+	0.699130i	$0.246429\pi$
$192$	−0.956879	−0.0690568
$193$	9.71439	0.699257	0.349628	−	0.936888i	$-0.386308\pi$
$193$	9.71439	0.699257	0.349628	+	0.936888i	$0.386308\pi$
$194$	−4.53164	−0.325353
$195$	−0.149094	−0.0106769
$196$	10.6885	0.763467
$197$	−1.91169	−0.136202	−0.0681011	−	0.997678i	$-0.521694\pi$
$197$	−1.91169	−0.136202	−0.0681011	+	0.997678i	$0.521694\pi$
$198$	−0.253217	−0.0179954
$199$	10.3431	0.733205	0.366602	−	0.930378i	$-0.380521\pi$
$199$	10.3431	0.733205	0.366602	+	0.930378i	$0.380521\pi$
$200$	4.99092	0.352911
$201$	13.5554	0.956121
$202$	18.8485	1.32617
$203$	−38.2435	−2.68417
$204$	−3.08407	−0.215928
$205$	0.239483	0.0167262
$206$	16.0310	1.11693
$207$	−15.6665	−1.08890
$208$	−1.63495	−0.113363
$209$	0.162651	0.0112508
$210$	0.383533	0.0264663
$211$	26.4053	1.81782	0.908909	−	0.416995i	$-0.136917\pi$
$211$	26.4053	1.81782	0.908909	+	0.416995i	$0.136917\pi$
$212$	6.97986	0.479379
$213$	−5.43676	−0.372521
$214$	7.85447	0.536921
$215$	−0.637888	−0.0435036
$216$	−4.86514	−0.331031
$217$	−5.65758	−0.384062
$218$	−12.9103	−0.874399
$219$	−0.752615	−0.0508570
$220$	0.0115775	0.000780556 0
$221$	−5.26952	−0.354466
$222$	−0.810662	−0.0544081
$223$	−2.87973	−0.192841	−0.0964204	−	0.995341i	$-0.530739\pi$
$223$	−2.87973	−0.192841	−0.0964204	+	0.995341i	$0.530739\pi$
$224$	4.20577	0.281010
$225$	10.4030	0.693532
$226$	5.40353	0.359437
$227$	−17.7575	−1.17861	−0.589305	−	0.807911i	$-0.700598\pi$
$227$	−17.7575	−1.17861	−0.589305	+	0.807911i	$0.700598\pi$
$228$	1.28114	0.0848458
$229$	−7.68778	−0.508023	−0.254011	−	0.967201i	$-0.581750\pi$
$229$	−7.68778	−0.508023	−0.254011	+	0.967201i	$0.581750\pi$
$230$	0.716300	0.0472314
$231$	−0.488899	−0.0321672
$232$	−9.09309	−0.596991
$233$	−8.84240	−0.579285	−0.289643	−	0.957135i	$-0.593536\pi$
$233$	−8.84240	−0.579285	−0.289643	+	0.957135i	$0.593536\pi$
$234$	−3.40786	−0.222779
$235$	−1.09544	−0.0714584
$236$	−3.92557	−0.255533
$237$	1.14067	0.0740947
$238$	13.5554	0.878666
$239$	−20.4693	−1.32405	−0.662025	−	0.749481i	$-0.730303\pi$
$239$	−20.4693	−1.32405	−0.662025	+	0.749481i	$0.730303\pi$
$240$	0.0911919	0.00588641
$241$	−30.2979	−1.95166	−0.975828	−	0.218538i	$-0.929871\pi$
$241$	−30.2979	−1.95166	−0.975828	+	0.218538i	$0.929871\pi$
$242$	10.9852	0.706158
$243$	−16.1243	−1.03438
$244$	−10.4678	−0.670130
$245$	−1.01863	−0.0650781
$246$	−2.40454	−0.153308
$247$	2.18900	0.139283
$248$	−1.34519	−0.0854199
$249$	11.2296	0.711644
$250$	−0.952148	−0.0602192
$251$	12.1789	0.768727	0.384363	−	0.923182i	$-0.374421\pi$
$251$	12.1789	0.768727	0.384363	+	0.923182i	$0.374421\pi$
$252$	8.76644	0.552234
$253$	−0.913087	−0.0574053
$254$	11.4199	0.716547
$255$	0.293916	0.0184057
$256$	1.00000	0.0625000
$257$	12.0370	0.750845	0.375423	−	0.926854i	$-0.377498\pi$
$257$	12.0370	0.750845	0.375423	+	0.926854i	$0.377498\pi$
$258$	6.40475	0.398742
$259$	3.56311	0.221401
$260$	0.155813	0.00966312
$261$	−18.9535	−1.17319
$262$	−2.73835	−0.169176
$263$	0.138602	0.00854655	0.00427328	−	0.999991i	$-0.498640\pi$
$263$	0.138602	0.00854655	0.00427328	+	0.999991i	$0.498640\pi$
$264$	−0.116245	−0.00715437
$265$	−0.665190	−0.0408623
$266$	−5.63101	−0.345260
$267$	5.52513	0.338132
$268$	−14.1662	−0.865339
$269$	−19.3871	−1.18205	−0.591027	−	0.806652i	$-0.701277\pi$
$269$	−19.3871	−1.18205	−0.591027	+	0.806652i	$0.701277\pi$
$270$	0.463655	0.0282171
$271$	−8.81160	−0.535267	−0.267633	−	0.963521i	$-0.586242\pi$
$271$	−8.81160	−0.535267	−0.267633	+	0.963521i	$0.586242\pi$
$272$	3.22305	0.195426
$273$	−6.57973	−0.398223
$274$	12.1095	0.731561
$275$	0.606313	0.0365620
$276$	−7.19205	−0.432911
$277$	25.6127	1.53892	0.769458	−	0.638698i	$-0.220527\pi$
$277$	25.6127	1.53892	0.769458	+	0.638698i	$0.220527\pi$
$278$	−16.1577	−0.969077
$279$	−2.80390	−0.167865
$280$	−0.400816	−0.0239534
$281$	−13.4325	−0.801316	−0.400658	−	0.916228i	$-0.631219\pi$
$281$	−13.4325	−0.801316	−0.400658	+	0.916228i	$0.631219\pi$
$282$	10.9988	0.654969
$283$	9.19969	0.546865	0.273432	−	0.961891i	$-0.411841\pi$
$283$	9.19969	0.546865	0.273432	+	0.961891i	$0.411841\pi$
$284$	5.68177	0.337151
$285$	−0.122095	−0.00723227
$286$	−0.198619	−0.0117446
$287$	10.5687	0.623850
$288$	2.08438	0.122823
$289$	−6.61198	−0.388940
$290$	0.866584	0.0508876
$291$	−4.33624	−0.254195
$292$	0.786531	0.0460283
$293$	−6.94996	−0.406021	−0.203010	−	0.979177i	$-0.565073\pi$
$293$	−6.94996	−0.406021	−0.203010	+	0.979177i	$0.565073\pi$
$294$	10.2276	0.596488
$295$	0.374112	0.0217817
$296$	0.847194	0.0492421
$297$	−0.591033	−0.0342952
$298$	4.96833	0.287808
$299$	−12.2885	−0.710665
$300$	4.77571	0.275725
$301$	−28.1508	−1.62259
$302$	−14.1500	−0.814239
$303$	18.0357	1.03612
$304$	−1.33888	−0.0767898
$305$	0.997593	0.0571220
$306$	6.71806	0.384046
$307$	26.4614	1.51023	0.755116	−	0.655591i	$-0.227581\pi$
$307$	26.4614	1.51023	0.755116	+	0.655591i	$0.227581\pi$
$308$	0.510931	0.0291130
$309$	15.3398	0.872649
$310$	0.128199	0.00728121
$311$	−5.51240	−0.312580	−0.156290	−	0.987711i	$-0.549953\pi$
$311$	−5.51240	−0.312580	−0.156290	+	0.987711i	$0.549953\pi$
$312$	−1.56445	−0.0885696
$313$	6.03203	0.340950	0.170475	−	0.985362i	$-0.445470\pi$
$313$	6.03203	0.340950	0.170475	+	0.985362i	$0.445470\pi$
$314$	3.45379	0.194908
$315$	−0.835454	−0.0470725
$316$	−1.19208	−0.0670595
$317$	26.5260	1.48985	0.744923	−	0.667150i	$-0.232486\pi$
$317$	26.5260	1.48985	0.744923	+	0.667150i	$0.232486\pi$
$318$	6.67888	0.374533
$319$	−1.10466	−0.0618490
$320$	−0.0953014	−0.00532751
$321$	7.51578	0.419490
$322$	31.6113	1.76163
$323$	−4.31526	−0.240107
$324$	1.59779	0.0887664
$325$	8.15991	0.452630
$326$	−7.63173	−0.422683
$327$	−12.3536	−0.683158
$328$	2.51290	0.138752
$329$	−48.3430	−2.66524
$330$	0.0110783	0.000609840 0
$331$	−31.7469	−1.74497	−0.872483	−	0.488645i	$-0.837491\pi$
$331$	−31.7469	−1.74497	−0.872483	+	0.488645i	$0.837491\pi$
$332$	−11.7356	−0.644075
$333$	1.76588	0.0967694
$334$	−13.2615	−0.725638
$335$	1.35006	0.0737616
$336$	4.02442	0.219550
$337$	31.0606	1.69198	0.845989	−	0.533200i	$-0.179011\pi$
$337$	31.0606	1.69198	0.845989	+	0.533200i	$0.179011\pi$
$338$	10.3269	0.561711
$339$	5.17052	0.280824
$340$	−0.307161	−0.0166581
$341$	−0.163419	−0.00884961
$342$	−2.79073	−0.150905
$343$	−15.5132	−0.837633
$344$	−6.69337	−0.360882
$345$	0.685413	0.0369014
$346$	−23.1657	−1.24540
$347$	6.01579	0.322945	0.161472	−	0.986877i	$-0.448376\pi$
$347$	6.01579	0.322945	0.161472	+	0.986877i	$0.448376\pi$
$348$	−8.70099	−0.466422
$349$	18.7258	1.00237	0.501184	−	0.865341i	$-0.332898\pi$
$349$	18.7258	1.00237	0.501184	+	0.865341i	$0.332898\pi$
$350$	−20.9907	−1.12200
$351$	−7.95427	−0.424567
$352$	0.121483	0.00647508
$353$	17.2725	0.919324	0.459662	−	0.888094i	$-0.347971\pi$
$353$	17.2725	0.919324	0.459662	+	0.888094i	$0.347971\pi$
$354$	−3.75630	−0.199645
$355$	−0.541480	−0.0287388
$356$	−5.77411	−0.306027
$357$	12.9709	0.686492
$358$	−0.199393	−0.0105382
$359$	1.11572	0.0588852	0.0294426	−	0.999566i	$-0.490627\pi$
$359$	1.11572	0.0588852	0.0294426	+	0.999566i	$0.490627\pi$
$360$	−0.198645	−0.0104695
$361$	−17.2074	−0.905653
$362$	23.4780	1.23398
$363$	10.5116	0.551713
$364$	6.87624	0.360413
$365$	−0.0749575	−0.00392346
$366$	−10.0164	−0.523565
$367$	−9.30017	−0.485465	−0.242733	−	0.970093i	$-0.578044\pi$
$367$	−9.30017	−0.485465	−0.242733	+	0.970093i	$0.578044\pi$
$368$	7.51615	0.391807
$369$	5.23785	0.272671
$370$	−0.0807387	−0.00419741
$371$	−29.3557	−1.52407
$372$	−1.28719	−0.0667376
$373$	−34.6933	−1.79635	−0.898176	−	0.439635i	$-0.855108\pi$
$373$	−34.6933	−1.79635	−0.898176	+	0.439635i	$0.855108\pi$
$374$	0.391546	0.0202464
$375$	−0.911091	−0.0470485
$376$	−11.4944	−0.592781
$377$	−14.8668	−0.765677
$378$	20.4617	1.05244
$379$	23.6958	1.21717	0.608587	−	0.793487i	$-0.291737\pi$
$379$	23.6958	1.21717	0.608587	+	0.793487i	$0.291737\pi$
$380$	0.127597	0.00654558
$381$	10.9274	0.559830
$382$	−19.7628	−1.01115
$383$	1.12378	0.0574225	0.0287112	−	0.999588i	$-0.490860\pi$
$383$	1.12378	0.0574225	0.0287112	+	0.999588i	$0.490860\pi$
$384$	0.956879	0.0488305
$385$	−0.0486924	−0.00248160
$386$	−9.71439	−0.494449
$387$	−13.9515	−0.709197
$388$	4.53164	0.230059
$389$	−28.5254	−1.44629	−0.723147	−	0.690694i	$-0.757305\pi$
$389$	−28.5254	−1.44629	−0.723147	+	0.690694i	$0.757305\pi$
$390$	0.149094	0.00754969
$391$	24.2249	1.22511
$392$	−10.6885	−0.539853
$393$	−2.62027	−0.132175
$394$	1.91169	0.0963095
$395$	0.113607	0.00571616
$396$	0.253217	0.0127247
$397$	−14.8873	−0.747171	−0.373586	−	0.927596i	$-0.621872\pi$
$397$	−14.8873	−0.747171	−0.373586	+	0.927596i	$0.621872\pi$
$398$	−10.3431	−0.518454
$399$	−5.38820	−0.269747
$400$	−4.99092	−0.249546
$401$	2.77313	0.138484	0.0692419	−	0.997600i	$-0.477942\pi$
$401$	2.77313	0.138484	0.0692419	+	0.997600i	$0.477942\pi$
$402$	−13.5554	−0.676080
$403$	−2.19933	−0.109556
$404$	−18.8485	−0.937746
$405$	−0.152272	−0.00756646
$406$	38.2435	1.89799
$407$	0.102920	0.00510155
$408$	3.08407	0.152684
$409$	−37.2648	−1.84263	−0.921314	−	0.388820i	$-0.872883\pi$
$409$	−37.2648	−1.84263	−0.921314	+	0.388820i	$0.872883\pi$
$410$	−0.239483	−0.0118272
$411$	11.5873	0.571560
$412$	−16.0310	−0.789792
$413$	16.5101	0.812407
$414$	15.6665	0.769968
$415$	1.11842	0.0549010
$416$	1.63495	0.0801601
$417$	−15.4610	−0.757129
$418$	−0.162651	−0.00795552
$419$	−29.5915	−1.44564	−0.722821	−	0.691036i	$-0.757155\pi$
$419$	−29.5915	−1.44564	−0.722821	+	0.691036i	$0.757155\pi$
$420$	−0.383533	−0.0187145
$421$	−24.0854	−1.17385	−0.586925	−	0.809641i	$-0.699662\pi$
$421$	−24.0854	−1.17385	−0.586925	+	0.809641i	$0.699662\pi$
$422$	−26.4053	−1.28539
$423$	−23.9588	−1.16492
$424$	−6.97986	−0.338972
$425$	−16.0860	−0.780283
$426$	5.43676	0.263412
$427$	44.0251	2.13052
$428$	−7.85447	−0.379660
$429$	−0.190055	−0.00917592
$430$	0.637888	0.0307617
$431$	34.2509	1.64981	0.824904	−	0.565274i	$-0.191229\pi$
$431$	34.2509	1.64981	0.824904	+	0.565274i	$0.191229\pi$
$432$	4.86514	0.234074
$433$	−40.1135	−1.92773	−0.963865	−	0.266390i	$-0.914169\pi$
$433$	−40.1135	−1.92773	−0.963865	+	0.266390i	$0.914169\pi$
$434$	5.65758	0.271573
$435$	0.829217	0.0397579
$436$	12.9103	0.618293
$437$	−10.0632	−0.481388
$438$	0.752615	0.0359613
$439$	−30.1300	−1.43803	−0.719014	−	0.694995i	$-0.755406\pi$
$439$	−30.1300	−1.43803	−0.719014	+	0.694995i	$0.755406\pi$
$440$	−0.0115775	−0.000551937 0
$441$	−22.2790	−1.06090
$442$	5.26952	0.250646
$443$	11.0205	0.523599	0.261800	−	0.965122i	$-0.415684\pi$
$443$	11.0205	0.523599	0.261800	+	0.965122i	$0.415684\pi$
$444$	0.810662	0.0384723
$445$	0.550281	0.0260858
$446$	2.87973	0.136359
$447$	4.75409	0.224861
$448$	−4.20577	−0.198704
$449$	−6.50049	−0.306777	−0.153389	−	0.988166i	$-0.549019\pi$
$449$	−6.50049	−0.306777	−0.153389	+	0.988166i	$0.549019\pi$
$450$	−10.4030	−0.490401
$451$	0.305275	0.0143749
$452$	−5.40353	−0.254160
$453$	−13.5398	−0.636156
$454$	17.7575	0.833403
$455$	−0.655315	−0.0307216
$456$	−1.28114	−0.0599950
$457$	8.73969	0.408826	0.204413	−	0.978885i	$-0.434472\pi$
$457$	8.73969	0.408826	0.204413	+	0.978885i	$0.434472\pi$
$458$	7.68778	0.359226
$459$	15.6806	0.731906
$460$	−0.716300	−0.0333977
$461$	−25.5346	−1.18927	−0.594633	−	0.803997i	$-0.702703\pi$
$461$	−25.5346	−1.18927	−0.594633	+	0.803997i	$0.702703\pi$
$462$	0.488899	0.0227457
$463$	−14.6280	−0.679820	−0.339910	−	0.940458i	$-0.610397\pi$
$463$	−14.6280	−0.679820	−0.339910	+	0.940458i	$0.610397\pi$
$464$	9.09309	0.422136
$465$	0.122671	0.00568873
$466$	8.84240	0.409616
$467$	1.24904	0.0577987	0.0288993	−	0.999582i	$-0.490800\pi$
$467$	1.24904	0.0577987	0.0288993	+	0.999582i	$0.490800\pi$
$468$	3.40786	0.157529
$469$	59.5799	2.75114
$470$	1.09544	0.0505287
$471$	3.30486	0.152280
$472$	3.92557	0.180689
$473$	−0.813132	−0.0373879
$474$	−1.14067	−0.0523928
$475$	6.68222	0.306601
$476$	−13.5554	−0.621311
$477$	−14.5487	−0.666139
$478$	20.4693	0.936245
$479$	11.4826	0.524655	0.262327	−	0.964979i	$-0.415510\pi$
$479$	11.4826	0.524655	0.262327	+	0.964979i	$0.415510\pi$
$480$	−0.0911919	−0.00416232
$481$	1.38512	0.0631560
$482$	30.2979	1.38003
$483$	30.2482	1.37634
$484$	−10.9852	−0.499329
$485$	−0.431872	−0.0196103
$486$	16.1243	0.731414
$487$	−21.9886	−0.996400	−0.498200	−	0.867062i	$-0.666005\pi$
$487$	−21.9886	−0.996400	−0.498200	+	0.867062i	$0.666005\pi$
$488$	10.4678	0.473854
$489$	−7.30265	−0.330237
$490$	1.01863	0.0460171
$491$	−23.7027	−1.06969	−0.534845	−	0.844950i	$-0.679630\pi$
$491$	−23.7027	−1.06969	−0.534845	+	0.844950i	$0.679630\pi$
$492$	2.40454	0.108405
$493$	29.3074	1.31994
$494$	−2.18900	−0.0984876
$495$	−0.0241320	−0.00108465
$496$	1.34519	0.0604010
$497$	−23.8962	−1.07189
$498$	−11.2296	−0.503208
$499$	−14.8704	−0.665692	−0.332846	−	0.942981i	$-0.608009\pi$
$499$	−14.8704	−0.665692	−0.332846	+	0.942981i	$0.608009\pi$
$500$	0.952148	0.0425814
$501$	−12.6897	−0.566933
$502$	−12.1789	−0.543572
$503$	−24.9490	−1.11242	−0.556210	−	0.831042i	$-0.687745\pi$
$503$	−24.9490	−1.11242	−0.556210	+	0.831042i	$0.687745\pi$
$504$	−8.76644	−0.390488
$505$	1.79628	0.0799336
$506$	0.913087	0.0405917
$507$	9.88163	0.438859
$508$	−11.4199	−0.506675
$509$	−10.6418	−0.471689	−0.235845	−	0.971791i	$-0.575786\pi$
$509$	−10.6418	−0.471689	−0.235845	+	0.971791i	$0.575786\pi$
$510$	−0.293916	−0.0130148
$511$	−3.30797	−0.146336
$512$	−1.00000	−0.0441942
$513$	−6.51382	−0.287592
$514$	−12.0370	−0.530928
$515$	1.52778	0.0673220
$516$	−6.40475	−0.281953
$517$	−1.39638	−0.0614128
$518$	−3.56311	−0.156554
$519$	−22.1668	−0.973013
$520$	−0.155813	−0.00683286
$521$	−28.6167	−1.25372	−0.626861	−	0.779131i	$-0.715661\pi$
$521$	−28.6167	−1.25372	−0.626861	+	0.779131i	$0.715661\pi$
$522$	18.9535	0.829571
$523$	32.4165	1.41747	0.708737	−	0.705473i	$-0.249265\pi$
$523$	32.4165	1.41747	0.708737	+	0.705473i	$0.249265\pi$
$524$	2.73835	0.119625
$525$	−20.0855	−0.876605
$526$	−0.138602	−0.00604333
$527$	4.33562	0.188863
$528$	0.116245	0.00505890
$529$	33.4926	1.45620
$530$	0.665190	0.0288940
$531$	8.18239	0.355085
$532$	5.63101	0.244135
$533$	4.10847	0.177958
$534$	−5.52513	−0.239096
$535$	0.748542	0.0323623
$536$	14.1662	0.611887
$537$	−0.190795	−0.00823340
$538$	19.3871	0.835838
$539$	−1.29848	−0.0559294
$540$	−0.463655	−0.0199525
$541$	41.3176	1.77638	0.888190	−	0.459476i	$-0.151963\pi$
$541$	41.3176	1.77638	0.888190	+	0.459476i	$0.151963\pi$
$542$	8.81160	0.378491
$543$	22.4656	0.964092
$544$	−3.22305	−0.138187
$545$	−1.23037	−0.0527034
$546$	6.57973	0.281586
$547$	1.57191	0.0672100	0.0336050	−	0.999435i	$-0.489301\pi$
$547$	1.57191	0.0672100	0.0336050	+	0.999435i	$0.489301\pi$
$548$	−12.1095	−0.517292
$549$	21.8188	0.931205
$550$	−0.606313	−0.0258533
$551$	−12.1745	−0.518652
$552$	7.19205	0.306114
$553$	5.01360	0.213200
$554$	−25.6127	−1.08818
$555$	−0.0772572	−0.00327939
$556$	16.1577	0.685241
$557$	−11.5447	−0.489165	−0.244583	−	0.969628i	$-0.578651\pi$
$557$	−11.5447	−0.489165	−0.244583	+	0.969628i	$0.578651\pi$
$558$	2.80390	0.118699
$559$	−10.9433	−0.462854
$560$	0.400816	0.0169376
$561$	0.374662	0.0158183
$562$	13.4325	0.566616
$563$	13.1451	0.553999	0.276999	−	0.960870i	$-0.410660\pi$
$563$	13.1451	0.553999	0.276999	+	0.960870i	$0.410660\pi$
$564$	−10.9988	−0.463133
$565$	0.514964	0.0216647
$566$	−9.19969	−0.386692
$567$	−6.71997	−0.282212
$568$	−5.68177	−0.238402
$569$	−9.75665	−0.409020	−0.204510	−	0.978864i	$-0.565560\pi$
$569$	−9.75665	−0.409020	−0.204510	+	0.978864i	$0.565560\pi$
$570$	0.122095	0.00511399
$571$	−15.2353	−0.637578	−0.318789	−	0.947826i	$-0.603276\pi$
$571$	−15.2353	−0.637578	−0.318789	+	0.947826i	$0.603276\pi$
$572$	0.198619	0.00830468
$573$	−18.9107	−0.790004
$574$	−10.5687	−0.441129
$575$	−37.5125	−1.56438
$576$	−2.08438	−0.0868493
$577$	37.1399	1.54616	0.773078	−	0.634311i	$-0.218716\pi$
$577$	37.1399	1.54616	0.773078	+	0.634311i	$0.218716\pi$
$578$	6.61198	0.275022
$579$	−9.29549	−0.386308
$580$	−0.866584	−0.0359830
$581$	49.3573	2.04769
$582$	4.33624	0.179743
$583$	−0.847936	−0.0351179
$584$	−0.786531	−0.0325469
$585$	−0.324774	−0.0134278
$586$	6.94996	0.287100
$587$	−9.51896	−0.392890	−0.196445	−	0.980515i	$-0.562940\pi$
$587$	−9.51896	−0.392890	−0.196445	+	0.980515i	$0.562940\pi$
$588$	−10.2276	−0.421781
$589$	−1.80105	−0.0742109
$590$	−0.374112	−0.0154020
$591$	1.82926	0.0752455
$592$	−0.847194	−0.0348194
$593$	39.9184	1.63925	0.819625	−	0.572900i	$-0.194182\pi$
$593$	39.9184	1.63925	0.819625	+	0.572900i	$0.194182\pi$
$594$	0.591033	0.0242504
$595$	1.29185	0.0529606
$596$	−4.96833	−0.203511
$597$	−9.89712	−0.405062
$598$	12.2885	0.502516
$599$	−33.5087	−1.36913	−0.684564	−	0.728952i	$-0.740008\pi$
$599$	−33.5087	−1.36913	−0.684564	+	0.728952i	$0.740008\pi$
$600$	−4.77571	−0.194967
$601$	−6.98904	−0.285089	−0.142545	−	0.989788i	$-0.545528\pi$
$601$	−6.98904	−0.285089	−0.142545	+	0.989788i	$0.545528\pi$
$602$	28.1508	1.14734
$603$	29.5278	1.20246
$604$	14.1500	0.575754
$605$	1.04691	0.0425629
$606$	−18.0357	−0.732650
$607$	34.3477	1.39413	0.697066	−	0.717007i	$-0.254489\pi$
$607$	34.3477	1.39413	0.697066	+	0.717007i	$0.254489\pi$
$608$	1.33888	0.0542986
$609$	36.5944	1.48288
$610$	−0.997593	−0.0403914
$611$	−18.7929	−0.760278
$612$	−6.71806	−0.271561
$613$	−38.4326	−1.55228	−0.776139	−	0.630561i	$-0.782825\pi$
$613$	−38.4326	−1.55228	−0.776139	+	0.630561i	$0.782825\pi$
$614$	−26.4614	−1.06790
$615$	−0.229156	−0.00924047
$616$	−0.510931	−0.0205860
$617$	−26.4663	−1.06549	−0.532747	−	0.846275i	$-0.678840\pi$
$617$	−26.4663	−1.06549	−0.532747	+	0.846275i	$0.678840\pi$
$618$	−15.3398	−0.617056
$619$	−0.365349	−0.0146846	−0.00734231	−	0.999973i	$-0.502337\pi$
$619$	−0.365349	−0.0146846	−0.00734231	+	0.999973i	$0.502337\pi$
$620$	−0.128199	−0.00514859
$621$	36.5671	1.46739
$622$	5.51240	0.221027
$623$	24.2846	0.972943
$624$	1.56445	0.0626282
$625$	24.8638	0.994554
$626$	−6.03203	−0.241088
$627$	−0.155637	−0.00621556
$628$	−3.45379	−0.137821
$629$	−2.73054	−0.108874
$630$	0.835454	0.0332853
$631$	−15.5463	−0.618890	−0.309445	−	0.950917i	$-0.600143\pi$
$631$	−15.5463	−0.618890	−0.309445	+	0.950917i	$0.600143\pi$
$632$	1.19208	0.0474182
$633$	−25.2667	−1.00426
$634$	−26.5260	−1.05348
$635$	1.08833	0.0431891
$636$	−6.67888	−0.264835
$637$	−17.4752	−0.692394
$638$	1.10466	0.0437338
$639$	−11.8430	−0.468501
$640$	0.0953014	0.00376712
$641$	−23.9183	−0.944717	−0.472359	−	0.881406i	$-0.656597\pi$
$641$	−23.9183	−0.944717	−0.472359	+	0.881406i	$0.656597\pi$
$642$	−7.51578	−0.296624
$643$	−6.78173	−0.267445	−0.133723	−	0.991019i	$-0.542693\pi$
$643$	−6.78173	−0.267445	−0.133723	+	0.991019i	$0.542693\pi$
$644$	−31.6113	−1.24566
$645$	0.610381	0.0240337
$646$	4.31526	0.169782
$647$	8.83427	0.347311	0.173655	−	0.984806i	$-0.444442\pi$
$647$	8.83427	0.347311	0.173655	+	0.984806i	$0.444442\pi$
$648$	−1.59779	−0.0627673
$649$	0.476891	0.0187196
$650$	−8.15991	−0.320058
$651$	5.41363	0.212177
$652$	7.63173	0.298882
$653$	16.4307	0.642984	0.321492	−	0.946912i	$-0.395816\pi$
$653$	16.4307	0.642984	0.321492	+	0.946912i	$0.395816\pi$
$654$	12.3536	0.483066
$655$	−0.260969	−0.0101969
$656$	−2.51290	−0.0981123
$657$	−1.63943	−0.0639603
$658$	48.3430	1.88461
$659$	34.4579	1.34229	0.671145	−	0.741326i	$-0.265803\pi$
$659$	34.4579	1.34229	0.671145	+	0.741326i	$0.265803\pi$
$660$	−0.0110783	−0.000431222 0
$661$	−5.72848	−0.222812	−0.111406	−	0.993775i	$-0.535535\pi$
$661$	−5.72848	−0.222812	−0.111406	+	0.993775i	$0.535535\pi$
$662$	31.7469	1.23388
$663$	5.04230	0.195827
$664$	11.7356	0.455430
$665$	−0.536643	−0.0208101
$666$	−1.76588	−0.0684263
$667$	68.3451	2.64633
$668$	13.2615	0.513103
$669$	2.75555	0.106536
$670$	−1.35006	−0.0521574
$671$	1.27166	0.0490918
$672$	−4.02442	−0.155245
$673$	23.4230	0.902891	0.451445	−	0.892299i	$-0.350909\pi$
$673$	23.4230	0.902891	0.451445	+	0.892299i	$0.350909\pi$
$674$	−31.0606	−1.19641
$675$	−24.2815	−0.934596
$676$	−10.3269	−0.397190
$677$	34.8354	1.33883	0.669416	−	0.742887i	$-0.266544\pi$
$677$	34.8354	1.33883	0.669416	+	0.742887i	$0.266544\pi$
$678$	−5.17052	−0.198573
$679$	−19.0591	−0.731420
$680$	0.307161	0.0117791
$681$	16.9918	0.651128
$682$	0.163419	0.00625762
$683$	4.47021	0.171048	0.0855239	−	0.996336i	$-0.472744\pi$
$683$	4.47021	0.171048	0.0855239	+	0.996336i	$0.472744\pi$
$684$	2.79073	0.106706
$685$	1.15405	0.0440940
$686$	15.5132	0.592296
$687$	7.35628	0.280660
$688$	6.69337	0.255182
$689$	−11.4117	−0.434752
$690$	−0.685413	−0.0260932
$691$	25.7956	0.981311	0.490656	−	0.871354i	$-0.336757\pi$
$691$	25.7956	0.981311	0.490656	+	0.871354i	$0.336757\pi$
$692$	23.1657	0.880628
$693$	−1.06498	−0.0404551
$694$	−6.01579	−0.228356
$695$	−1.53986	−0.0584101
$696$	8.70099	0.329810
$697$	−8.09919	−0.306779
$698$	−18.7258	−0.708781
$699$	8.46111	0.320029
$700$	20.9907	0.793373
$701$	−26.4901	−1.00052	−0.500259	−	0.865876i	$-0.666762\pi$
$701$	−26.4901	−1.00052	−0.500259	+	0.865876i	$0.666762\pi$
$702$	7.95427	0.300214
$703$	1.13429	0.0427805
$704$	−0.121483	−0.00457857
$705$	1.04820	0.0394775
$706$	−17.2725	−0.650060
$707$	79.2724	2.98134
$708$	3.75630	0.141170
$709$	−34.3646	−1.29059	−0.645295	−	0.763933i	$-0.723266\pi$
$709$	−34.3646	−1.29059	−0.645295	+	0.763933i	$0.723266\pi$
$710$	0.541480	0.0203214
$711$	2.48474	0.0931851
$712$	5.77411	0.216394
$713$	10.1107	0.378648
$714$	−12.9709	−0.485423
$715$	−0.0189287	−0.000707893 0
$716$	0.199393	0.00745165
$717$	19.5867	0.731478
$718$	−1.11572	−0.0416381
$719$	6.24457	0.232883	0.116442	−	0.993198i	$-0.462851\pi$
$719$	6.24457	0.232883	0.116442	+	0.993198i	$0.462851\pi$
$720$	0.198645	0.00740304
$721$	67.4229	2.51096
$722$	17.2074	0.640393
$723$	28.9914	1.07820
$724$	−23.4780	−0.872554
$725$	−45.3829	−1.68548
$726$	−10.5116	−0.390120
$727$	36.3330	1.34752	0.673758	−	0.738952i	$-0.264679\pi$
$727$	36.3330	1.34752	0.673758	+	0.738952i	$0.264679\pi$
$728$	−6.87624	−0.254850
$729$	10.6356	0.393913
$730$	0.0749575	0.00277430
$731$	21.5730	0.797908
$732$	10.0164	0.370217
$733$	−30.4147	−1.12339	−0.561696	−	0.827344i	$-0.689851\pi$
$733$	−30.4147	−1.12339	−0.561696	+	0.827344i	$0.689851\pi$
$734$	9.30017	0.343276
$735$	0.974709	0.0359527
$736$	−7.51615	−0.277049
$737$	1.72096	0.0633923
$738$	−5.23785	−0.192808
$739$	3.06910	0.112899	0.0564493	−	0.998405i	$-0.482022\pi$
$739$	3.06910	0.112899	0.0564493	+	0.998405i	$0.482022\pi$
$740$	0.0807387	0.00296801
$741$	−2.09461	−0.0769473
$742$	29.3557	1.07768
$743$	−16.1309	−0.591787	−0.295893	−	0.955221i	$-0.595617\pi$
$743$	−16.1309	−0.591787	−0.295893	+	0.955221i	$0.595617\pi$
$744$	1.28719	0.0471906
$745$	0.473489	0.0173473
$746$	34.6933	1.27021
$747$	24.4615	0.894999
$748$	−0.391546	−0.0143163
$749$	33.0341	1.20704
$750$	0.911091	0.0332683
$751$	−34.5642	−1.26127	−0.630634	−	0.776081i	$-0.717205\pi$
$751$	−34.5642	−1.26127	−0.630634	+	0.776081i	$0.717205\pi$
$752$	11.4944	0.419159
$753$	−11.6538	−0.424686
$754$	14.8668	0.541415
$755$	−1.34851	−0.0490774
$756$	−20.4617	−0.744184
$757$	30.4546	1.10689	0.553446	−	0.832885i	$-0.313312\pi$
$757$	30.4546	1.10689	0.553446	+	0.832885i	$0.313312\pi$
$758$	−23.6958	−0.860672
$759$	0.873714	0.0317138
$760$	−0.127597	−0.00462842
$761$	−32.9139	−1.19313	−0.596564	−	0.802565i	$-0.703468\pi$
$761$	−32.9139	−1.19313	−0.596564	+	0.802565i	$0.703468\pi$
$762$	−10.9274	−0.395859
$763$	−54.2980	−1.96572
$764$	19.7628	0.714994
$765$	0.640240	0.0231479
$766$	−1.12378	−0.0406038
$767$	6.41812	0.231745
$768$	−0.956879	−0.0345284
$769$	−31.4149	−1.13285	−0.566426	−	0.824113i	$-0.691674\pi$
$769$	−31.4149	−1.13285	−0.566426	+	0.824113i	$0.691674\pi$
$770$	0.0486924	0.00175475
$771$	−11.5179	−0.414808
$772$	9.71439	0.349628
$773$	−53.2187	−1.91414	−0.957072	−	0.289850i	$-0.906395\pi$
$773$	−53.2187	−1.91414	−0.957072	+	0.289850i	$0.906395\pi$
$774$	13.9515	0.501478
$775$	−6.71375	−0.241165
$776$	−4.53164	−0.162676
$777$	−3.40946	−0.122314
$778$	28.5254	1.02268
$779$	3.36446	0.120544
$780$	−0.149094	−0.00533843
$781$	−0.690239	−0.0246987
$782$	−24.2249	−0.866281
$783$	44.2392	1.58098
$784$	10.6885	0.381734
$785$	0.329151	0.0117479
$786$	2.62027	0.0934620
$787$	−28.9785	−1.03297	−0.516486	−	0.856296i	$-0.672760\pi$
$787$	−28.9785	−1.03297	−0.516486	+	0.856296i	$0.672760\pi$
$788$	−1.91169	−0.0681011
$789$	−0.132625	−0.00472158
$790$	−0.113607	−0.00404194
$791$	22.7260	0.808044
$792$	−0.253217	−0.00899769
$793$	17.1143	0.607746
$794$	14.8873	0.528330
$795$	0.636507	0.0225746
$796$	10.3431	0.366602
$797$	4.76493	0.168782	0.0843912	−	0.996433i	$-0.473105\pi$
$797$	4.76493	0.168782	0.0843912	+	0.996433i	$0.473105\pi$
$798$	5.38820	0.190740
$799$	37.0471	1.31063
$800$	4.99092	0.176456
$801$	12.0355	0.425252
$802$	−2.77313	−0.0979228
$803$	−0.0955503	−0.00337190
$804$	13.5554	0.478060
$805$	3.01260	0.106180
$806$	2.19933	0.0774680
$807$	18.5511	0.653031
$808$	18.8485	0.663086
$809$	40.1670	1.41220	0.706098	−	0.708114i	$-0.250454\pi$
$809$	40.1670	1.41220	0.706098	+	0.708114i	$0.250454\pi$
$810$	0.152272	0.00535030
$811$	−31.8495	−1.11839	−0.559193	−	0.829038i	$-0.688889\pi$
$811$	−31.8495	−1.11839	−0.559193	+	0.829038i	$0.688889\pi$
$812$	−38.2435	−1.34208
$813$	8.43164	0.295711
$814$	−0.102920	−0.00360734
$815$	−0.727315	−0.0254767
$816$	−3.08407	−0.107964
$817$	−8.96160	−0.313527
$818$	37.2648	1.30293
$819$	−14.3327	−0.500825
$820$	0.239483	0.00836311
$821$	−23.3451	−0.814750	−0.407375	−	0.913261i	$-0.633556\pi$
$821$	−23.3451	−0.814750	−0.407375	+	0.913261i	$0.633556\pi$
$822$	−11.5873	−0.404154
$823$	−42.1552	−1.46944	−0.734718	−	0.678372i	$-0.762686\pi$
$823$	−42.1552	−1.46944	−0.734718	+	0.678372i	$0.762686\pi$
$824$	16.0310	0.558467
$825$	−0.580168	−0.0201989
$826$	−16.5101	−0.574459
$827$	37.8380	1.31576	0.657878	−	0.753125i	$-0.271454\pi$
$827$	37.8380	1.31576	0.657878	+	0.753125i	$0.271454\pi$
$828$	−15.6665	−0.544450
$829$	−21.8002	−0.757154	−0.378577	−	0.925570i	$-0.623586\pi$
$829$	−21.8002	−0.757154	−0.378577	+	0.925570i	$0.623586\pi$
$830$	−1.11842	−0.0388209
$831$	−24.5082	−0.850181
$832$	−1.63495	−0.0566817
$833$	34.4497	1.19361
$834$	15.4610	0.535371
$835$	−1.26384	−0.0437370
$836$	0.162651	0.00562540
$837$	6.54456	0.226213
$838$	29.5915	1.02222
$839$	−2.66289	−0.0919330	−0.0459665	−	0.998943i	$-0.514637\pi$
$839$	−2.66289	−0.0919330	−0.0459665	+	0.998943i	$0.514637\pi$
$840$	0.383533	0.0132331
$841$	53.6843	1.85118
$842$	24.0854	0.830037
$843$	12.8533	0.442691
$844$	26.4053	0.908909
$845$	0.984171	0.0338565
$846$	23.9588	0.823721
$847$	46.2015	1.58750
$848$	6.97986	0.239689
$849$	−8.80299	−0.302118
$850$	16.0860	0.551744
$851$	−6.36764	−0.218280
$852$	−5.43676	−0.186260
$853$	−53.5322	−1.83291	−0.916454	−	0.400139i	$-0.868962\pi$
$853$	−53.5322	−1.83291	−0.916454	+	0.400139i	$0.868962\pi$
$854$	−44.0251	−1.50651
$855$	−0.265960	−0.00909566
$856$	7.85447	0.268460
$857$	36.5661	1.24907	0.624537	−	0.780995i	$-0.285288\pi$
$857$	36.5661	1.24907	0.624537	+	0.780995i	$0.285288\pi$
$858$	0.190055	0.00648835
$859$	8.17959	0.279084	0.139542	−	0.990216i	$-0.455437\pi$
$859$	8.17959	0.279084	0.139542	+	0.990216i	$0.455437\pi$
$860$	−0.637888	−0.0217518
$861$	−10.1130	−0.344649
$862$	−34.2509	−1.16659
$863$	−8.52967	−0.290353	−0.145177	−	0.989406i	$-0.546375\pi$
$863$	−8.52967	−0.290353	−0.145177	+	0.989406i	$0.546375\pi$
$864$	−4.86514	−0.165515
$865$	−2.20772	−0.0750648
$866$	40.1135	1.36311
$867$	6.32686	0.214872
$868$	−5.65758	−0.192031
$869$	0.144817	0.00491259
$870$	−0.829217	−0.0281131
$871$	23.1611	0.784783
$872$	−12.9103	−0.437199
$873$	−9.44568	−0.319688
$874$	10.0632	0.340393
$875$	−4.00452	−0.135378
$876$	−0.752615	−0.0254285
$877$	−20.2942	−0.685287	−0.342643	−	0.939466i	$-0.611322\pi$
$877$	−20.2942	−0.685287	−0.342643	+	0.939466i	$0.611322\pi$
$878$	30.1300	1.01684
$879$	6.65027	0.224308
$880$	0.0115775	0.000390278 0
$881$	10.6036	0.357243	0.178621	−	0.983918i	$-0.442836\pi$
$881$	10.6036	0.357243	0.178621	+	0.983918i	$0.442836\pi$
$882$	22.2790	0.750173
$883$	32.7047	1.10060	0.550301	−	0.834966i	$-0.314513\pi$
$883$	32.7047	1.10060	0.550301	+	0.834966i	$0.314513\pi$
$884$	−5.26952	−0.177233
$885$	−0.357980	−0.0120334
$886$	−11.0205	−0.370241
$887$	−12.5042	−0.419850	−0.209925	−	0.977717i	$-0.567322\pi$
$887$	−12.5042	−0.419850	−0.209925	+	0.977717i	$0.567322\pi$
$888$	−0.810662	−0.0272040
$889$	48.0294	1.61086
$890$	−0.550281	−0.0184455
$891$	−0.194105	−0.00650277
$892$	−2.87973	−0.0964204
$893$	−15.3896	−0.514995
$894$	−4.75409	−0.159001
$895$	−0.0190024	−0.000635180 0
$896$	4.20577	0.140505
$897$	11.7587	0.392610
$898$	6.50049	0.216924
$899$	12.2320	0.407959
$900$	10.4030	0.346766
$901$	22.4964	0.749464
$902$	−0.305275	−0.0101646
$903$	26.9369	0.896405
$904$	5.40353	0.179719
$905$	2.23749	0.0743766
$906$	13.5398	0.449830
$907$	−26.3180	−0.873876	−0.436938	−	0.899492i	$-0.643937\pi$
$907$	−26.3180	−0.873876	−0.436938	+	0.899492i	$0.643937\pi$
$908$	−17.7575	−0.589305
$909$	39.2874	1.30308
$910$	0.655315	0.0217235
$911$	−9.48305	−0.314187	−0.157094	−	0.987584i	$-0.550212\pi$
$911$	−9.48305	−0.314187	−0.157094	+	0.987584i	$0.550212\pi$
$912$	1.28114	0.0424229
$913$	1.42568	0.0471831
$914$	−8.73969	−0.289083
$915$	−0.954576	−0.0315573
$916$	−7.68778	−0.254011
$917$	−11.5169	−0.380321
$918$	−15.6806	−0.517536
$919$	33.0466	1.09011	0.545054	−	0.838401i	$-0.316509\pi$
$919$	33.0466	1.09011	0.545054	+	0.838401i	$0.316509\pi$
$920$	0.716300	0.0236157
$921$	−25.3204	−0.834334
$922$	25.5346	0.840938
$923$	−9.28941	−0.305765
$924$	−0.488899	−0.0160836
$925$	4.22827	0.139025
$926$	14.6280	0.480705
$927$	33.4148	1.09749
$928$	−9.09309	−0.298495
$929$	41.3770	1.35754	0.678768	−	0.734353i	$-0.262514\pi$
$929$	41.3770	1.35754	0.678768	+	0.734353i	$0.262514\pi$
$930$	−0.122671	−0.00402254
$931$	−14.3106	−0.469012
$932$	−8.84240	−0.289643
$933$	5.27470	0.172686
$934$	−1.24904	−0.0408698
$935$	0.0373149	0.00122033
$936$	−3.40786	−0.111389
$937$	9.40734	0.307324	0.153662	−	0.988123i	$-0.450893\pi$
$937$	9.40734	0.307324	0.153662	+	0.988123i	$0.450893\pi$
$938$	−59.5799	−1.94535
$939$	−5.77192	−0.188360
$940$	−1.09544	−0.0357292
$941$	−30.9469	−1.00884	−0.504420	−	0.863459i	$-0.668293\pi$
$941$	−30.9469	−1.00884	−0.504420	+	0.863459i	$0.668293\pi$
$942$	−3.30486	−0.107678
$943$	−18.8874	−0.615057
$944$	−3.92557	−0.127766
$945$	1.95003	0.0634344
$946$	0.813132	0.0264372
$947$	−3.65377	−0.118732	−0.0593658	−	0.998236i	$-0.518908\pi$
$947$	−3.65377	−0.118732	−0.0593658	+	0.998236i	$0.518908\pi$
$948$	1.14067	0.0370473
$949$	−1.28594	−0.0417434
$950$	−6.68222	−0.216800
$951$	−25.3821	−0.823072
$952$	13.5554	0.439333
$953$	28.6327	0.927504	0.463752	−	0.885965i	$-0.346503\pi$
$953$	28.6327	0.927504	0.463752	+	0.885965i	$0.346503\pi$
$954$	14.5487	0.471031
$955$	−1.88343	−0.0609462
$956$	−20.4693	−0.662025
$957$	1.05702	0.0341687
$958$	−11.4826	−0.370987
$959$	50.9298	1.64461
$960$	0.0911919	0.00294321
$961$	−29.1905	−0.941627
$962$	−1.38512	−0.0446581
$963$	16.3717	0.527571
$964$	−30.2979	−0.975828
$965$	−0.925795	−0.0298024
$966$	−30.2482	−0.973218
$967$	2.85719	0.0918811	0.0459406	−	0.998944i	$-0.485372\pi$
$967$	2.85719	0.0918811	0.0459406	+	0.998944i	$0.485372\pi$
$968$	10.9852	0.353079
$969$	4.12918	0.132648
$970$	0.431872	0.0138666
$971$	37.8413	1.21439	0.607193	−	0.794555i	$-0.292296\pi$
$971$	37.8413	1.21439	0.607193	+	0.794555i	$0.292296\pi$
$972$	−16.1243	−0.517188
$973$	−67.9558	−2.17856
$974$	21.9886	0.704561
$975$	−7.80804	−0.250058
$976$	−10.4678	−0.335065
$977$	−53.8163	−1.72174	−0.860868	−	0.508828i	$-0.830079\pi$
$977$	−53.8163	−1.72174	−0.860868	+	0.508828i	$0.830079\pi$
$978$	7.30265	0.233513
$979$	0.701458	0.0224187
$980$	−1.01863	−0.0325390
$981$	−26.9101	−0.859173
$982$	23.7027	0.756384
$983$	42.2353	1.34710	0.673548	−	0.739143i	$-0.264769\pi$
$983$	42.2353	1.34710	0.673548	+	0.739143i	$0.264769\pi$
$984$	−2.40454	−0.0766540
$985$	0.182187	0.00580495
$986$	−29.3074	−0.933339
$987$	46.2585	1.47242
$988$	2.18900	0.0696413
$989$	50.3084	1.59971
$990$	0.0241320	0.000766965 0
$991$	59.5820	1.89269	0.946343	−	0.323165i	$-0.104747\pi$
$991$	59.5820	1.89269	0.946343	+	0.323165i	$0.104747\pi$
$992$	−1.34519	−0.0427100
$993$	30.3779	0.964014
$994$	23.8962	0.757942
$995$	−0.985715	−0.0312493
$996$	11.2296	0.355822
$997$	−29.0071	−0.918665	−0.459333	−	0.888264i	$-0.651911\pi$
$997$	−29.0071	−0.918665	−0.459333	+	0.888264i	$0.651911\pi$
$998$	14.8704	0.470715
$999$	−4.12172	−0.130405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4006.2.a.g.1.14	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4006.2.a.g.1.14	✓	40	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:	\( N \)	\(=\)	\( 4006 = 2 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.956879 q^{3} +1.00000 q^{4} -0.0953014 q^{5} +0.956879 q^{6} -4.20577 q^{7} -1.00000 q^{8} -2.08438 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.956879 q^{3} +1.00000 q^{4} -0.0953014 q^{5} +0.956879 q^{6} -4.20577 q^{7} -1.00000 q^{8} -2.08438 q^{9} +0.0953014 q^{10} -0.121483 q^{11} -0.956879 q^{12} -1.63495 q^{13} +4.20577 q^{14} +0.0911919 q^{15} +1.00000 q^{16} +3.22305 q^{17} +2.08438 q^{18} -1.33888 q^{19} -0.0953014 q^{20} +4.02442 q^{21} +0.121483 q^{22} +7.51615 q^{23} +0.956879 q^{24} -4.99092 q^{25} +1.63495 q^{26} +4.86514 q^{27} -4.20577 q^{28} +9.09309 q^{29} -0.0911919 q^{30} +1.34519 q^{31} -1.00000 q^{32} +0.116245 q^{33} -3.22305 q^{34} +0.400816 q^{35} -2.08438 q^{36} -0.847194 q^{37} +1.33888 q^{38} +1.56445 q^{39} +0.0953014 q^{40} -2.51290 q^{41} -4.02442 q^{42} +6.69337 q^{43} -0.121483 q^{44} +0.198645 q^{45} -7.51615 q^{46} +11.4944 q^{47} -0.956879 q^{48} +10.6885 q^{49} +4.99092 q^{50} -3.08407 q^{51} -1.63495 q^{52} +6.97986 q^{53} -4.86514 q^{54} +0.0115775 q^{55} +4.20577 q^{56} +1.28114 q^{57} -9.09309 q^{58} -3.92557 q^{59} +0.0911919 q^{60} -10.4678 q^{61} -1.34519 q^{62} +8.76644 q^{63} +1.00000 q^{64} +0.155813 q^{65} -0.116245 q^{66} -14.1662 q^{67} +3.22305 q^{68} -7.19205 q^{69} -0.400816 q^{70} +5.68177 q^{71} +2.08438 q^{72} +0.786531 q^{73} +0.847194 q^{74} +4.77571 q^{75} -1.33888 q^{76} +0.510931 q^{77} -1.56445 q^{78} -1.19208 q^{79} -0.0953014 q^{80} +1.59779 q^{81} +2.51290 q^{82} -11.7356 q^{83} +4.02442 q^{84} -0.307161 q^{85} -6.69337 q^{86} -8.70099 q^{87} +0.121483 q^{88} -5.77411 q^{89} -0.198645 q^{90} +6.87624 q^{91} +7.51615 q^{92} -1.28719 q^{93} -11.4944 q^{94} +0.127597 q^{95} +0.956879 q^{96} +4.53164 q^{97} -10.6885 q^{98} +0.253217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9}+O(q^{10}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9	\( 40 q - 40 q^{2} - q^{3} + 40 q^{4} - 23 q^{5} + q^{6} + 12 q^{7} - 40 q^{8} + 29 q^{9} + 23 q^{10} - 28 q^{11} - q^{12} - 12 q^{13} - 12 q^{14} - 14 q^{15} + 40 q^{16} - 10 q^{17} - 29 q^{18} + 3 q^{19} - 23 q^{20} - 40 q^{21} + 28 q^{22} - 10 q^{23} + q^{24} + 43 q^{25} + 12 q^{26} - 7 q^{27} + 12 q^{28} - 37 q^{29} + 14 q^{30} - 16 q^{31} - 40 q^{32} - 11 q^{33} + 10 q^{34} - 24 q^{35} + 29 q^{36} - 17 q^{37} - 3 q^{38} - 10 q^{39} + 23 q^{40} - 58 q^{41} + 40 q^{42} + 37 q^{43} - 28 q^{44} - 66 q^{45} + 10 q^{46} - 34 q^{47} - q^{48} + 28 q^{49} - 43 q^{50} - 7 q^{51} - 12 q^{52} - 43 q^{53} + 7 q^{54} + 28 q^{55} - 12 q^{56} - 25 q^{57} + 37 q^{58} - 92 q^{59} - 14 q^{60} - 37 q^{61} + 16 q^{62} + 14 q^{63} + 40 q^{64} - 54 q^{65} + 11 q^{66} - 10 q^{67} - 10 q^{68} - 49 q^{69} + 24 q^{70} - 87 q^{71} - 29 q^{72} + 12 q^{73} + 17 q^{74} - 31 q^{75} + 3 q^{76} - 53 q^{77} + 10 q^{78} + 14 q^{79} - 23 q^{80} - 4 q^{81} + 58 q^{82} - 42 q^{83} - 40 q^{84} - 24 q^{85} - 37 q^{86} + 24 q^{87} + 28 q^{88} - 118 q^{89} + 66 q^{90} - 35 q^{91} - 10 q^{92} - 22 q^{93} + 34 q^{94} - 18 q^{95} + q^{96} + 2 q^{97} - 28 q^{98} - 48 q^{99}+O(q^{100}) \) 40 * q - 40 * q^2 - q^3 + 40 * q^4 - 23 * q^5 + q^6 + 12 * q^7 - 40 * q^8 + 29 * q^9 + 23 * q^10 - 28 * q^11 - q^12 - 12 * q^13 - 12 * q^14 - 14 * q^15 + 40 * q^16 - 10 * q^17 - 29 * q^18 + 3 * q^19 - 23 * q^20 - 40 * q^21 + 28 * q^22 - 10 * q^23 + q^24 + 43 * q^25 + 12 * q^26 - 7 * q^27 + 12 * q^28 - 37 * q^29 + 14 * q^30 - 16 * q^31 - 40 * q^32 - 11 * q^33 + 10 * q^34 - 24 * q^35 + 29 * q^36 - 17 * q^37 - 3 * q^38 - 10 * q^39 + 23 * q^40 - 58 * q^41 + 40 * q^42 + 37 * q^43 - 28 * q^44 - 66 * q^45 + 10 * q^46 - 34 * q^47 - q^48 + 28 * q^49 - 43 * q^50 - 7 * q^51 - 12 * q^52 - 43 * q^53 + 7 * q^54 + 28 * q^55 - 12 * q^56 - 25 * q^57 + 37 * q^58 - 92 * q^59 - 14 * q^60 - 37 * q^61 + 16 * q^62 + 14 * q^63 + 40 * q^64 - 54 * q^65 + 11 * q^66 - 10 * q^67 - 10 * q^68 - 49 * q^69 + 24 * q^70 - 87 * q^71 - 29 * q^72 + 12 * q^73 + 17 * q^74 - 31 * q^75 + 3 * q^76 - 53 * q^77 + 10 * q^78 + 14 * q^79 - 23 * q^80 - 4 * q^81 + 58 * q^82 - 42 * q^83 - 40 * q^84 - 24 * q^85 - 37 * q^86 + 24 * q^87 + 28 * q^88 - 118 * q^89 + 66 * q^90 - 35 * q^91 - 10 * q^92 - 22 * q^93 + 34 * q^94 - 18 * q^95 + q^96 + 2 * q^97 - 28 * q^98 - 48 * q^99

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