LMFDB - Embedded newform 6034.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.88014$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.88014 q^{3} +1.00000 q^{4} -1.11289 q^{5} -2.88014 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.29519 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.88014 q^{3} +1.00000 q^{4} -1.11289 q^{5} -2.88014 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.29519 q^{9} -1.11289 q^{10} +1.58420 q^{11} -2.88014 q^{12} +1.03563 q^{13} -1.00000 q^{14} +3.20526 q^{15} +1.00000 q^{16} -3.95723 q^{17} +5.29519 q^{18} +3.63947 q^{19} -1.11289 q^{20} +2.88014 q^{21} +1.58420 q^{22} -2.60922 q^{23} -2.88014 q^{24} -3.76149 q^{25} +1.03563 q^{26} -6.61047 q^{27} -1.00000 q^{28} +0.755529 q^{29} +3.20526 q^{30} -7.11128 q^{31} +1.00000 q^{32} -4.56272 q^{33} -3.95723 q^{34} +1.11289 q^{35} +5.29519 q^{36} +5.29489 q^{37} +3.63947 q^{38} -2.98277 q^{39} -1.11289 q^{40} -3.82781 q^{41} +2.88014 q^{42} +2.27822 q^{43} +1.58420 q^{44} -5.89294 q^{45} -2.60922 q^{46} +6.15371 q^{47} -2.88014 q^{48} +1.00000 q^{49} -3.76149 q^{50} +11.3974 q^{51} +1.03563 q^{52} +3.71469 q^{53} -6.61047 q^{54} -1.76304 q^{55} -1.00000 q^{56} -10.4822 q^{57} +0.755529 q^{58} -11.3573 q^{59} +3.20526 q^{60} +7.20253 q^{61} -7.11128 q^{62} -5.29519 q^{63} +1.00000 q^{64} -1.15254 q^{65} -4.56272 q^{66} +10.8935 q^{67} -3.95723 q^{68} +7.51493 q^{69} +1.11289 q^{70} +3.27820 q^{71} +5.29519 q^{72} +11.7995 q^{73} +5.29489 q^{74} +10.8336 q^{75} +3.63947 q^{76} -1.58420 q^{77} -2.98277 q^{78} +14.0389 q^{79} -1.11289 q^{80} +3.15348 q^{81} -3.82781 q^{82} +2.97419 q^{83} +2.88014 q^{84} +4.40395 q^{85} +2.27822 q^{86} -2.17603 q^{87} +1.58420 q^{88} -13.1209 q^{89} -5.89294 q^{90} -1.03563 q^{91} -2.60922 q^{92} +20.4815 q^{93} +6.15371 q^{94} -4.05031 q^{95} -2.88014 q^{96} -11.5367 q^{97} +1.00000 q^{98} +8.38866 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.88014	−1.66285	−0.831424	−	0.555638i	$-0.812474\pi$
$3$	−2.88014	−1.66285	−0.831424	+	0.555638i	$0.812474\pi$
$4$	1.00000	0.500000
$5$	−1.11289	−0.497698	−0.248849	−	0.968542i	$-0.580052\pi$
$5$	−1.11289	−0.497698	−0.248849	+	0.968542i	$0.580052\pi$
$6$	−2.88014	−1.17581
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	5.29519	1.76506
$10$	−1.11289	−0.351925
$11$	1.58420	0.477655	0.238828	−	0.971062i	$-0.423237\pi$
$11$	1.58420	0.477655	0.238828	+	0.971062i	$0.423237\pi$
$12$	−2.88014	−0.831424
$13$	1.03563	0.287233	0.143616	−	0.989633i	$-0.454127\pi$
$13$	1.03563	0.287233	0.143616	+	0.989633i	$0.454127\pi$
$14$	−1.00000	−0.267261
$15$	3.20526	0.827595
$16$	1.00000	0.250000
$17$	−3.95723	−0.959770	−0.479885	−	0.877331i	$-0.659322\pi$
$17$	−3.95723	−0.959770	−0.479885	+	0.877331i	$0.659322\pi$
$18$	5.29519	1.24809
$19$	3.63947	0.834951	0.417476	−	0.908688i	$-0.362915\pi$
$19$	3.63947	0.834951	0.417476	+	0.908688i	$0.362915\pi$
$20$	−1.11289	−0.248849
$21$	2.88014	0.628498
$22$	1.58420	0.337753
$23$	−2.60922	−0.544061	−0.272030	−	0.962289i	$-0.587695\pi$
$23$	−2.60922	−0.544061	−0.272030	+	0.962289i	$0.587695\pi$
$24$	−2.88014	−0.587906
$25$	−3.76149	−0.752297
$26$	1.03563	0.203104
$27$	−6.61047	−1.27218
$28$	−1.00000	−0.188982
$29$	0.755529	0.140298	0.0701491	−	0.997537i	$-0.477652\pi$
$29$	0.755529	0.140298	0.0701491	+	0.997537i	$0.477652\pi$
$30$	3.20526	0.585198
$31$	−7.11128	−1.27722	−0.638612	−	0.769529i	$-0.720491\pi$
$31$	−7.11128	−1.27722	−0.638612	+	0.769529i	$0.720491\pi$
$32$	1.00000	0.176777
$33$	−4.56272	−0.794268
$34$	−3.95723	−0.678660
$35$	1.11289	0.188112
$36$	5.29519	0.882532
$37$	5.29489	0.870474	0.435237	−	0.900316i	$-0.356665\pi$
$37$	5.29489	0.870474	0.435237	+	0.900316i	$0.356665\pi$
$38$	3.63947	0.590400
$39$	−2.98277	−0.477625
$40$	−1.11289	−0.175963
$41$	−3.82781	−0.597803	−0.298902	−	0.954284i	$-0.596620\pi$
$41$	−3.82781	−0.597803	−0.298902	+	0.954284i	$0.596620\pi$
$42$	2.88014	0.444415
$43$	2.27822	0.347425	0.173713	−	0.984796i	$-0.444424\pi$
$43$	2.27822	0.347425	0.173713	+	0.984796i	$0.444424\pi$
$44$	1.58420	0.238828
$45$	−5.89294	−0.878468
$46$	−2.60922	−0.384709
$47$	6.15371	0.897611	0.448805	−	0.893630i	$-0.351850\pi$
$47$	6.15371	0.897611	0.448805	+	0.893630i	$0.351850\pi$
$48$	−2.88014	−0.415712
$49$	1.00000	0.142857
$50$	−3.76149	−0.531954
$51$	11.3974	1.59595
$52$	1.03563	0.143616
$53$	3.71469	0.510252	0.255126	−	0.966908i	$-0.417883\pi$
$53$	3.71469	0.510252	0.255126	+	0.966908i	$0.417883\pi$
$54$	−6.61047	−0.899571
$55$	−1.76304	−0.237728
$56$	−1.00000	−0.133631
$57$	−10.4822	−1.38840
$58$	0.755529	0.0992058
$59$	−11.3573	−1.47860	−0.739299	−	0.673378i	$-0.764843\pi$
$59$	−11.3573	−1.47860	−0.739299	+	0.673378i	$0.764843\pi$
$60$	3.20526	0.413798
$61$	7.20253	0.922190	0.461095	−	0.887351i	$-0.347457\pi$
$61$	7.20253	0.922190	0.461095	+	0.887351i	$0.347457\pi$
$62$	−7.11128	−0.903134
$63$	−5.29519	−0.667131
$64$	1.00000	0.125000
$65$	−1.15254	−0.142955
$66$	−4.56272	−0.561632
$67$	10.8935	1.33085	0.665425	−	0.746465i	$-0.268251\pi$
$67$	10.8935	1.33085	0.665425	+	0.746465i	$0.268251\pi$
$68$	−3.95723	−0.479885
$69$	7.51493	0.904691
$70$	1.11289	0.133015
$71$	3.27820	0.389051	0.194525	−	0.980897i	$-0.437683\pi$
$71$	3.27820	0.389051	0.194525	+	0.980897i	$0.437683\pi$
$72$	5.29519	0.624044
$73$	11.7995	1.38103	0.690513	−	0.723320i	$-0.257385\pi$
$73$	11.7995	1.38103	0.690513	+	0.723320i	$0.257385\pi$
$74$	5.29489	0.615518
$75$	10.8336	1.25096
$76$	3.63947	0.417476
$77$	−1.58420	−0.180537
$78$	−2.98277	−0.337732
$79$	14.0389	1.57950	0.789750	−	0.613429i	$-0.210210\pi$
$79$	14.0389	1.57950	0.789750	+	0.613429i	$0.210210\pi$
$80$	−1.11289	−0.124424
$81$	3.15348	0.350387
$82$	−3.82781	−0.422711
$83$	2.97419	0.326460	0.163230	−	0.986588i	$-0.447809\pi$
$83$	2.97419	0.326460	0.163230	+	0.986588i	$0.447809\pi$
$84$	2.88014	0.314249
$85$	4.40395	0.477675
$86$	2.27822	0.245667
$87$	−2.17603	−0.233295
$88$	1.58420	0.168877
$89$	−13.1209	−1.39081	−0.695406	−	0.718617i	$-0.744775\pi$
$89$	−13.1209	−1.39081	−0.695406	+	0.718617i	$0.744775\pi$
$90$	−5.89294	−0.621171
$91$	−1.03563	−0.108564
$92$	−2.60922	−0.272030
$93$	20.4815	2.12383
$94$	6.15371	0.634707
$95$	−4.05031	−0.415553
$96$	−2.88014	−0.293953
$97$	−11.5367	−1.17138	−0.585688	−	0.810537i	$-0.699175\pi$
$97$	−11.5367	−1.17138	−0.585688	+	0.810537i	$0.699175\pi$
$98$	1.00000	0.101015
$99$	8.38866	0.843092
$100$	−3.76149	−0.376149
$101$	−9.14108	−0.909571	−0.454786	−	0.890601i	$-0.650284\pi$
$101$	−9.14108	−0.909571	−0.454786	+	0.890601i	$0.650284\pi$
$102$	11.3974	1.12851
$103$	−4.01456	−0.395567	−0.197783	−	0.980246i	$-0.563374\pi$
$103$	−4.01456	−0.395567	−0.197783	+	0.980246i	$0.563374\pi$
$104$	1.03563	0.101552
$105$	−3.20526	−0.312802
$106$	3.71469	0.360803
$107$	3.90689	0.377694	0.188847	−	0.982007i	$-0.439525\pi$
$107$	3.90689	0.377694	0.188847	+	0.982007i	$0.439525\pi$
$108$	−6.61047	−0.636092
$109$	−5.14546	−0.492845	−0.246423	−	0.969162i	$-0.579255\pi$
$109$	−5.14546	−0.492845	−0.246423	+	0.969162i	$0.579255\pi$
$110$	−1.76304	−0.168099
$111$	−15.2500	−1.44747
$112$	−1.00000	−0.0944911
$113$	−8.66104	−0.814762	−0.407381	−	0.913258i	$-0.633558\pi$
$113$	−8.66104	−0.814762	−0.407381	+	0.913258i	$0.633558\pi$
$114$	−10.4822	−0.981745
$115$	2.90377	0.270778
$116$	0.755529	0.0701491
$117$	5.48388	0.506984
$118$	−11.3573	−1.04553
$119$	3.95723	0.362759
$120$	3.20526	0.292599
$121$	−8.49030	−0.771846
$122$	7.20253	0.652087
$123$	11.0246	0.994056
$124$	−7.11128	−0.638612
$125$	9.75053	0.872114
$126$	−5.29519	−0.471733
$127$	2.56885	0.227949	0.113974	−	0.993484i	$-0.463642\pi$
$127$	2.56885	0.227949	0.113974	+	0.993484i	$0.463642\pi$
$128$	1.00000	0.0883883
$129$	−6.56158	−0.577715
$130$	−1.15254	−0.101085
$131$	2.55347	0.223097	0.111549	−	0.993759i	$-0.464419\pi$
$131$	2.55347	0.223097	0.111549	+	0.993759i	$0.464419\pi$
$132$	−4.56272	−0.397134
$133$	−3.63947	−0.315582
$134$	10.8935	0.941052
$135$	7.35669	0.633163
$136$	−3.95723	−0.339330
$137$	13.2744	1.13411	0.567056	−	0.823679i	$-0.308082\pi$
$137$	13.2744	1.13411	0.567056	+	0.823679i	$0.308082\pi$
$138$	7.51493	0.639713
$139$	12.0708	1.02383	0.511916	−	0.859036i	$-0.328936\pi$
$139$	12.0708	1.02383	0.511916	+	0.859036i	$0.328936\pi$
$140$	1.11289	0.0940560
$141$	−17.7235	−1.49259
$142$	3.27820	0.275100
$143$	1.64065	0.137198
$144$	5.29519	0.441266
$145$	−0.840817	−0.0698261
$146$	11.7995	0.976533
$147$	−2.88014	−0.237550
$148$	5.29489	0.435237
$149$	−23.6895	−1.94072	−0.970360	−	0.241663i	$-0.922307\pi$
$149$	−23.6895	−1.94072	−0.970360	+	0.241663i	$0.922307\pi$
$150$	10.8336	0.884559
$151$	−14.5714	−1.18581	−0.592903	−	0.805274i	$-0.702018\pi$
$151$	−14.5714	−1.18581	−0.592903	+	0.805274i	$0.702018\pi$
$152$	3.63947	0.295200
$153$	−20.9543	−1.69406
$154$	−1.58420	−0.127659
$155$	7.91404	0.635671
$156$	−2.98277	−0.238812
$157$	−20.0390	−1.59929	−0.799644	−	0.600475i	$-0.794978\pi$
$157$	−20.0390	−1.59929	−0.799644	+	0.600475i	$0.794978\pi$
$158$	14.0389	1.11687
$159$	−10.6988	−0.848472
$160$	−1.11289	−0.0879813
$161$	2.60922	0.205636
$162$	3.15348	0.247761
$163$	−19.2354	−1.50663	−0.753315	−	0.657660i	$-0.771546\pi$
$163$	−19.2354	−1.50663	−0.753315	+	0.657660i	$0.771546\pi$
$164$	−3.82781	−0.298902
$165$	5.07779	0.395305
$166$	2.97419	0.230842
$167$	−8.08055	−0.625292	−0.312646	−	0.949870i	$-0.601215\pi$
$167$	−8.08055	−0.625292	−0.312646	+	0.949870i	$0.601215\pi$
$168$	2.88014	0.222207
$169$	−11.9275	−0.917497
$170$	4.40395	0.337768
$171$	19.2717	1.47374
$172$	2.27822	0.173713
$173$	0.918935	0.0698653	0.0349327	−	0.999390i	$-0.488878\pi$
$173$	0.918935	0.0698653	0.0349327	+	0.999390i	$0.488878\pi$
$174$	−2.17603	−0.164964
$175$	3.76149	0.284342
$176$	1.58420	0.119414
$177$	32.7106	2.45868
$178$	−13.1209	−0.983452
$179$	−11.5750	−0.865157	−0.432578	−	0.901596i	$-0.642396\pi$
$179$	−11.5750	−0.865157	−0.432578	+	0.901596i	$0.642396\pi$
$180$	−5.89294	−0.439234
$181$	10.0703	0.748519	0.374259	−	0.927324i	$-0.377897\pi$
$181$	10.0703	0.748519	0.374259	+	0.927324i	$0.377897\pi$
$182$	−1.03563	−0.0767662
$183$	−20.7443	−1.53346
$184$	−2.60922	−0.192355
$185$	−5.89260	−0.433233
$186$	20.4815	1.50177
$187$	−6.26906	−0.458439
$188$	6.15371	0.448805
$189$	6.61047	0.480841
$190$	−4.05031	−0.293840
$191$	−3.17137	−0.229472	−0.114736	−	0.993396i	$-0.536602\pi$
$191$	−3.17137	−0.229472	−0.114736	+	0.993396i	$0.536602\pi$
$192$	−2.88014	−0.207856
$193$	−2.97922	−0.214449	−0.107225	−	0.994235i	$-0.534196\pi$
$193$	−2.97922	−0.214449	−0.107225	+	0.994235i	$0.534196\pi$
$194$	−11.5367	−0.828287
$195$	3.31948	0.237713
$196$	1.00000	0.0714286
$197$	−3.03942	−0.216550	−0.108275	−	0.994121i	$-0.534533\pi$
$197$	−3.03942	−0.216550	−0.108275	+	0.994121i	$0.534533\pi$
$198$	8.38866	0.596156
$199$	2.39477	0.169760	0.0848802	−	0.996391i	$-0.472949\pi$
$199$	2.39477	0.169760	0.0848802	+	0.996391i	$0.472949\pi$
$200$	−3.76149	−0.265977
$201$	−31.3747	−2.21300
$202$	−9.14108	−0.643164
$203$	−0.755529	−0.0530277
$204$	11.3974	0.797976
$205$	4.25991	0.297525
$206$	−4.01456	−0.279708
$207$	−13.8163	−0.960302
$208$	1.03563	0.0718082
$209$	5.76565	0.398819
$210$	−3.20526	−0.221184
$211$	13.9263	0.958729	0.479364	−	0.877616i	$-0.340867\pi$
$211$	13.9263	0.958729	0.479364	+	0.877616i	$0.340867\pi$
$212$	3.71469	0.255126
$213$	−9.44167	−0.646932
$214$	3.90689	0.267070
$215$	−2.53540	−0.172913
$216$	−6.61047	−0.449785
$217$	7.11128	0.482745
$218$	−5.14546	−0.348494
$219$	−33.9842	−2.29644
$220$	−1.76304	−0.118864
$221$	−4.09824	−0.275678
$222$	−15.2500	−1.02351
$223$	−22.8118	−1.52759	−0.763797	−	0.645457i	$-0.776667\pi$
$223$	−22.8118	−1.52759	−0.763797	+	0.645457i	$0.776667\pi$
$224$	−1.00000	−0.0668153
$225$	−19.9178	−1.32785
$226$	−8.66104	−0.576124
$227$	−26.3374	−1.74807	−0.874036	−	0.485862i	$-0.838506\pi$
$227$	−26.3374	−1.74807	−0.874036	+	0.485862i	$0.838506\pi$
$228$	−10.4822	−0.694198
$229$	−29.1051	−1.92332	−0.961660	−	0.274244i	$-0.911572\pi$
$229$	−29.1051	−1.92332	−0.961660	+	0.274244i	$0.911572\pi$
$230$	2.90377	0.191469
$231$	4.56272	0.300205
$232$	0.755529	0.0496029
$233$	21.6222	1.41652	0.708258	−	0.705953i	$-0.249481\pi$
$233$	21.6222	1.41652	0.708258	+	0.705953i	$0.249481\pi$
$234$	5.48388	0.358492
$235$	−6.84837	−0.446739
$236$	−11.3573	−0.739299
$237$	−40.4339	−2.62647
$238$	3.95723	0.256509
$239$	−15.8980	−1.02836	−0.514179	−	0.857683i	$-0.671903\pi$
$239$	−15.8980	−1.02836	−0.514179	+	0.857683i	$0.671903\pi$
$240$	3.20526	0.206899
$241$	−28.1730	−1.81478	−0.907392	−	0.420285i	$-0.861930\pi$
$241$	−28.1730	−1.81478	−0.907392	+	0.420285i	$0.861930\pi$
$242$	−8.49030	−0.545777
$243$	10.7489	0.689545
$244$	7.20253	0.461095
$245$	−1.11289	−0.0710997
$246$	11.0246	0.702904
$247$	3.76915	0.239825
$248$	−7.11128	−0.451567
$249$	−8.56609	−0.542854
$250$	9.75053	0.616678
$251$	−2.95895	−0.186767	−0.0933837	−	0.995630i	$-0.529768\pi$
$251$	−2.95895	−0.186767	−0.0933837	+	0.995630i	$0.529768\pi$
$252$	−5.29519	−0.333566
$253$	−4.13354	−0.259874
$254$	2.56885	0.161184
$255$	−12.6840	−0.794302
$256$	1.00000	0.0625000
$257$	16.7393	1.04417	0.522086	−	0.852893i	$-0.325154\pi$
$257$	16.7393	1.04417	0.522086	+	0.852893i	$0.325154\pi$
$258$	−6.56158	−0.408506
$259$	−5.29489	−0.329008
$260$	−1.15254	−0.0714776
$261$	4.00067	0.247635
$262$	2.55347	0.157754
$263$	26.1309	1.61130	0.805649	−	0.592394i	$-0.201817\pi$
$263$	26.1309	1.61130	0.805649	+	0.592394i	$0.201817\pi$
$264$	−4.56272	−0.280816
$265$	−4.13403	−0.253951
$266$	−3.63947	−0.223150
$267$	37.7900	2.31271
$268$	10.8935	0.665425
$269$	−4.63186	−0.282410	−0.141205	−	0.989980i	$-0.545098\pi$
$269$	−4.63186	−0.282410	−0.141205	+	0.989980i	$0.545098\pi$
$270$	7.35669	0.447714
$271$	3.39988	0.206528	0.103264	−	0.994654i	$-0.467071\pi$
$271$	3.39988	0.206528	0.103264	+	0.994654i	$0.467071\pi$
$272$	−3.95723	−0.239943
$273$	2.98277	0.180525
$274$	13.2744	0.801938
$275$	−5.95896	−0.359339
$276$	7.51493	0.452345
$277$	5.23329	0.314438	0.157219	−	0.987564i	$-0.449747\pi$
$277$	5.23329	0.314438	0.157219	+	0.987564i	$0.449747\pi$
$278$	12.0708	0.723959
$279$	−37.6556	−2.25438
$280$	1.11289	0.0665076
$281$	10.7961	0.644043	0.322021	−	0.946732i	$-0.395638\pi$
$281$	10.7961	0.644043	0.322021	+	0.946732i	$0.395638\pi$
$282$	−17.7235	−1.05542
$283$	−0.562606	−0.0334434	−0.0167217	−	0.999860i	$-0.505323\pi$
$283$	−0.562606	−0.0334434	−0.0167217	+	0.999860i	$0.505323\pi$
$284$	3.27820	0.194525
$285$	11.6655	0.691002
$286$	1.64065	0.0970138
$287$	3.82781	0.225948
$288$	5.29519	0.312022
$289$	−1.34029	−0.0788409
$290$	−0.840817	−0.0493745
$291$	33.2273	1.94782
$292$	11.7995	0.690513
$293$	−20.5147	−1.19848	−0.599241	−	0.800568i	$-0.704531\pi$
$293$	−20.5147	−1.19848	−0.599241	+	0.800568i	$0.704531\pi$
$294$	−2.88014	−0.167973
$295$	12.6394	0.735894
$296$	5.29489	0.307759
$297$	−10.4723	−0.607666
$298$	−23.6895	−1.37230
$299$	−2.70220	−0.156272
$300$	10.8336	0.625478
$301$	−2.27822	−0.131314
$302$	−14.5714	−0.838491
$303$	26.3276	1.51248
$304$	3.63947	0.208738
$305$	−8.01560	−0.458972
$306$	−20.9543	−1.19788
$307$	1.83680	0.104832	0.0524158	−	0.998625i	$-0.483308\pi$
$307$	1.83680	0.104832	0.0524158	+	0.998625i	$0.483308\pi$
$308$	−1.58420	−0.0902683
$309$	11.5625	0.657767
$310$	7.91404	0.449487
$311$	7.48365	0.424359	0.212180	−	0.977231i	$-0.431944\pi$
$311$	7.48365	0.424359	0.212180	+	0.977231i	$0.431944\pi$
$312$	−2.98277	−0.168866
$313$	34.8664	1.97077	0.985383	−	0.170352i	$-0.0544906\pi$
$313$	34.8664	1.97077	0.985383	+	0.170352i	$0.0544906\pi$
$314$	−20.0390	−1.13087
$315$	5.89294	0.332030
$316$	14.0389	0.789750
$317$	−33.1022	−1.85921	−0.929603	−	0.368563i	$-0.879850\pi$
$317$	−33.1022	−1.85921	−0.929603	+	0.368563i	$0.879850\pi$
$318$	−10.6988	−0.599960
$319$	1.19691	0.0670142
$320$	−1.11289	−0.0622122
$321$	−11.2524	−0.628047
$322$	2.60922	0.145406
$323$	−14.4022	−0.801361
$324$	3.15348	0.175193
$325$	−3.89552	−0.216085
$326$	−19.2354	−1.06535
$327$	14.8196	0.819527
$328$	−3.82781	−0.211355
$329$	−6.15371	−0.339265
$330$	5.07779	0.279523
$331$	−10.2454	−0.563140	−0.281570	−	0.959541i	$-0.590855\pi$
$331$	−10.2454	−0.563140	−0.281570	+	0.959541i	$0.590855\pi$
$332$	2.97419	0.163230
$333$	28.0374	1.53644
$334$	−8.08055	−0.442148
$335$	−12.1232	−0.662360
$336$	2.88014	0.157124
$337$	4.85692	0.264573	0.132287	−	0.991211i	$-0.457768\pi$
$337$	4.85692	0.264573	0.132287	+	0.991211i	$0.457768\pi$
$338$	−11.9275	−0.648769
$339$	24.9450	1.35483
$340$	4.40395	0.238838
$341$	−11.2657	−0.610073
$342$	19.2717	1.04209
$343$	−1.00000	−0.0539949
$344$	2.27822	0.122833
$345$	−8.36325	−0.450262
$346$	0.918935	0.0494022
$347$	−32.8932	−1.76580	−0.882901	−	0.469559i	$-0.844413\pi$
$347$	−32.8932	−1.76580	−0.882901	+	0.469559i	$0.844413\pi$
$348$	−2.17603	−0.116647
$349$	−22.7417	−1.21734	−0.608668	−	0.793425i	$-0.708296\pi$
$349$	−22.7417	−1.21734	−0.608668	+	0.793425i	$0.708296\pi$
$350$	3.76149	0.201060
$351$	−6.84602	−0.365413
$352$	1.58420	0.0844383
$353$	4.33045	0.230486	0.115243	−	0.993337i	$-0.463235\pi$
$353$	4.33045	0.230486	0.115243	+	0.993337i	$0.463235\pi$
$354$	32.7106	1.73855
$355$	−3.64826	−0.193630
$356$	−13.1209	−0.695406
$357$	−11.3974	−0.603213
$358$	−11.5750	−0.611758
$359$	−12.1500	−0.641251	−0.320626	−	0.947206i	$-0.603893\pi$
$359$	−12.1500	−0.641251	−0.320626	+	0.947206i	$0.603893\pi$
$360$	−5.89294	−0.310585
$361$	−5.75428	−0.302857
$362$	10.0703	0.529283
$363$	24.4532	1.28346
$364$	−1.03563	−0.0542819
$365$	−13.1315	−0.687333
$366$	−20.7443	−1.08432
$367$	22.6966	1.18475	0.592375	−	0.805662i	$-0.298190\pi$
$367$	22.6966	1.18475	0.592375	+	0.805662i	$0.298190\pi$
$368$	−2.60922	−0.136015
$369$	−20.2690	−1.05516
$370$	−5.89260	−0.306342
$371$	−3.71469	−0.192857
$372$	20.4815	1.06191
$373$	19.9513	1.03304	0.516520	−	0.856275i	$-0.327227\pi$
$373$	19.9513	1.03304	0.516520	+	0.856275i	$0.327227\pi$
$374$	−6.26906	−0.324166
$375$	−28.0829	−1.45019
$376$	6.15371	0.317353
$377$	0.782451	0.0402983
$378$	6.61047	0.340006
$379$	18.3532	0.942743	0.471371	−	0.881935i	$-0.343759\pi$
$379$	18.3532	0.942743	0.471371	+	0.881935i	$0.343759\pi$
$380$	−4.05031	−0.207777
$381$	−7.39865	−0.379044
$382$	−3.17137	−0.162261
$383$	11.4961	0.587423	0.293711	−	0.955894i	$-0.405110\pi$
$383$	11.4961	0.587423	0.293711	+	0.955894i	$0.405110\pi$
$384$	−2.88014	−0.146976
$385$	1.76304	0.0898527
$386$	−2.97922	−0.151639
$387$	12.0636	0.613227
$388$	−11.5367	−0.585688
$389$	7.87777	0.399419	0.199709	−	0.979855i	$-0.436000\pi$
$389$	7.87777	0.399419	0.199709	+	0.979855i	$0.436000\pi$
$390$	3.31948	0.168088
$391$	10.3253	0.522174
$392$	1.00000	0.0505076
$393$	−7.35433	−0.370977
$394$	−3.03942	−0.153124
$395$	−15.6237	−0.786113
$396$	8.38866	0.421546
$397$	−9.78157	−0.490923	−0.245462	−	0.969406i	$-0.578939\pi$
$397$	−9.78157	−0.490923	−0.245462	+	0.969406i	$0.578939\pi$
$398$	2.39477	0.120039
$399$	10.4822	0.524765
$400$	−3.76149	−0.188074
$401$	−3.99052	−0.199277	−0.0996385	−	0.995024i	$-0.531769\pi$
$401$	−3.99052	−0.199277	−0.0996385	+	0.995024i	$0.531769\pi$
$402$	−31.3747	−1.56483
$403$	−7.36468	−0.366861
$404$	−9.14108	−0.454786
$405$	−3.50946	−0.174387
$406$	−0.755529	−0.0374963
$407$	8.38817	0.415786
$408$	11.3974	0.564254
$409$	−34.7964	−1.72057	−0.860287	−	0.509811i	$-0.829715\pi$
$409$	−34.7964	−1.72057	−0.860287	+	0.509811i	$0.829715\pi$
$410$	4.25991	0.210382
$411$	−38.2322	−1.88586
$412$	−4.01456	−0.197783
$413$	11.3573	0.558857
$414$	−13.8163	−0.679036
$415$	−3.30994	−0.162478
$416$	1.03563	0.0507761
$417$	−34.7656	−1.70248
$418$	5.76565	0.282007
$419$	−6.76977	−0.330725	−0.165363	−	0.986233i	$-0.552879\pi$
$419$	−6.76977	−0.330725	−0.165363	+	0.986233i	$0.552879\pi$
$420$	−3.20526	−0.156401
$421$	−21.3986	−1.04291	−0.521453	−	0.853280i	$-0.674610\pi$
$421$	−21.3986	−1.04291	−0.521453	+	0.853280i	$0.674610\pi$
$422$	13.9263	0.677924
$423$	32.5851	1.58434
$424$	3.71469	0.180401
$425$	14.8851	0.722032
$426$	−9.44167	−0.457450
$427$	−7.20253	−0.348555
$428$	3.90689	0.188847
$429$	−4.72531	−0.228140
$430$	−2.53540	−0.122268
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−6.61047	−0.318046
$433$	−7.81523	−0.375576	−0.187788	−	0.982210i	$-0.560132\pi$
$433$	−7.81523	−0.375576	−0.187788	+	0.982210i	$0.560132\pi$
$434$	7.11128	0.341352
$435$	2.42167	0.116110
$436$	−5.14546	−0.246423
$437$	−9.49619	−0.454264
$438$	−33.9842	−1.62383
$439$	38.7958	1.85162	0.925812	−	0.377984i	$-0.123382\pi$
$439$	38.7958	1.85162	0.925812	+	0.377984i	$0.123382\pi$
$440$	−1.76304	−0.0840495
$441$	5.29519	0.252152
$442$	−4.09824	−0.194934
$443$	−24.7290	−1.17491	−0.587455	−	0.809257i	$-0.699870\pi$
$443$	−24.7290	−1.17491	−0.587455	+	0.809257i	$0.699870\pi$
$444$	−15.2500	−0.723733
$445$	14.6021	0.692204
$446$	−22.8118	−1.08017
$447$	68.2291	3.22712
$448$	−1.00000	−0.0472456
$449$	−0.365550	−0.0172514	−0.00862569	−	0.999963i	$-0.502746\pi$
$449$	−0.365550	−0.0172514	−0.00862569	+	0.999963i	$0.502746\pi$
$450$	−19.9178	−0.938933
$451$	−6.06402	−0.285544
$452$	−8.66104	−0.407381
$453$	41.9677	1.97181
$454$	−26.3374	−1.23607
$455$	1.15254	0.0540320
$456$	−10.4822	−0.490872
$457$	27.4402	1.28360	0.641800	−	0.766872i	$-0.278188\pi$
$457$	27.4402	1.28360	0.641800	+	0.766872i	$0.278188\pi$
$458$	−29.1051	−1.35999
$459$	26.1592	1.22101
$460$	2.90377	0.135389
$461$	−26.6862	−1.24290	−0.621450	−	0.783454i	$-0.713456\pi$
$461$	−26.6862	−1.24290	−0.621450	+	0.783454i	$0.713456\pi$
$462$	4.56272	0.212277
$463$	−40.7272	−1.89275	−0.946377	−	0.323063i	$-0.895287\pi$
$463$	−40.7272	−1.89275	−0.946377	+	0.323063i	$0.895287\pi$
$464$	0.755529	0.0350746
$465$	−22.7935	−1.05702
$466$	21.6222	1.00163
$467$	−4.54278	−0.210215	−0.105108	−	0.994461i	$-0.533519\pi$
$467$	−4.54278	−0.210215	−0.105108	+	0.994461i	$0.533519\pi$
$468$	5.48388	0.253492
$469$	−10.8935	−0.503014
$470$	−6.84837	−0.315892
$471$	57.7151	2.65937
$472$	−11.3573	−0.522763
$473$	3.60916	0.165949
$474$	−40.4339	−1.85719
$475$	−13.6898	−0.628131
$476$	3.95723	0.181380
$477$	19.6700	0.900627
$478$	−15.8980	−0.727159
$479$	−22.0242	−1.00631	−0.503156	−	0.864196i	$-0.667828\pi$
$479$	−22.0242	−1.00631	−0.503156	+	0.864196i	$0.667828\pi$
$480$	3.20526	0.146300
$481$	5.48356	0.250029
$482$	−28.1730	−1.28325
$483$	−7.51493	−0.341941
$484$	−8.49030	−0.385923
$485$	12.8390	0.582991
$486$	10.7489	0.487582
$487$	33.2152	1.50512	0.752562	−	0.658521i	$-0.228818\pi$
$487$	33.2152	1.50512	0.752562	+	0.658521i	$0.228818\pi$
$488$	7.20253	0.326043
$489$	55.4005	2.50530
$490$	−1.11289	−0.0502750
$491$	−20.8315	−0.940114	−0.470057	−	0.882636i	$-0.655767\pi$
$491$	−20.8315	−0.940114	−0.470057	+	0.882636i	$0.655767\pi$
$492$	11.0246	0.497028
$493$	−2.98981	−0.134654
$494$	3.76915	0.169582
$495$	−9.33562	−0.419605
$496$	−7.11128	−0.319306
$497$	−3.27820	−0.147047
$498$	−8.56609	−0.383856
$499$	29.2893	1.31117	0.655585	−	0.755121i	$-0.272422\pi$
$499$	29.2893	1.31117	0.655585	+	0.755121i	$0.272422\pi$
$500$	9.75053	0.436057
$501$	23.2731	1.03977
$502$	−2.95895	−0.132064
$503$	−10.8544	−0.483976	−0.241988	−	0.970279i	$-0.577799\pi$
$503$	−10.8544	−0.483976	−0.241988	+	0.970279i	$0.577799\pi$
$504$	−5.29519	−0.235867
$505$	10.1730	0.452691
$506$	−4.13354	−0.183758
$507$	34.3527	1.52566
$508$	2.56885	0.113974
$509$	−32.6715	−1.44814	−0.724068	−	0.689728i	$-0.757730\pi$
$509$	−32.6715	−1.44814	−0.724068	+	0.689728i	$0.757730\pi$
$510$	−12.6840	−0.561656
$511$	−11.7995	−0.521979
$512$	1.00000	0.0441942
$513$	−24.0586	−1.06221
$514$	16.7393	0.738341
$515$	4.46775	0.196873
$516$	−6.56158	−0.288858
$517$	9.74872	0.428748
$518$	−5.29489	−0.232644
$519$	−2.64666	−0.116175
$520$	−1.15254	−0.0505423
$521$	10.5276	0.461221	0.230610	−	0.973046i	$-0.425928\pi$
$521$	10.5276	0.461221	0.230610	+	0.973046i	$0.425928\pi$
$522$	4.00067	0.175105
$523$	22.9127	1.00190	0.500952	−	0.865475i	$-0.332983\pi$
$523$	22.9127	1.00190	0.500952	+	0.865475i	$0.332983\pi$
$524$	2.55347	0.111549
$525$	−10.8336	−0.472817
$526$	26.1309	1.13936
$527$	28.1410	1.22584
$528$	−4.56272	−0.198567
$529$	−16.1919	−0.703998
$530$	−4.13403	−0.179571
$531$	−60.1392	−2.60982
$532$	−3.63947	−0.157791
$533$	−3.96420	−0.171709
$534$	37.7900	1.63533
$535$	−4.34793	−0.187977
$536$	10.8935	0.470526
$537$	33.3376	1.43862
$538$	−4.63186	−0.199694
$539$	1.58420	0.0682365
$540$	7.35669	0.316582
$541$	−10.5110	−0.451903	−0.225951	−	0.974139i	$-0.572549\pi$
$541$	−10.5110	−0.451903	−0.225951	+	0.974139i	$0.572549\pi$
$542$	3.39988	0.146037
$543$	−29.0038	−1.24467
$544$	−3.95723	−0.169665
$545$	5.72630	0.245288
$546$	2.98277	0.127651
$547$	−17.6411	−0.754279	−0.377139	−	0.926157i	$-0.623092\pi$
$547$	−17.6411	−0.754279	−0.377139	+	0.926157i	$0.623092\pi$
$548$	13.2744	0.567056
$549$	38.1388	1.62772
$550$	−5.95896	−0.254091
$551$	2.74972	0.117142
$552$	7.51493	0.319856
$553$	−14.0389	−0.596995
$554$	5.23329	0.222341
$555$	16.9715	0.720400
$556$	12.0708	0.511916
$557$	15.4260	0.653622	0.326811	−	0.945090i	$-0.394026\pi$
$557$	15.4260	0.653622	0.326811	+	0.945090i	$0.394026\pi$
$558$	−37.6556	−1.59409
$559$	2.35940	0.0997919
$560$	1.11289	0.0470280
$561$	18.0558	0.762315
$562$	10.7961	0.455407
$563$	7.27851	0.306753	0.153376	−	0.988168i	$-0.450985\pi$
$563$	7.27851	0.306753	0.153376	+	0.988168i	$0.450985\pi$
$564$	−17.7235	−0.746295
$565$	9.63875	0.405505
$566$	−0.562606	−0.0236481
$567$	−3.15348	−0.132434
$568$	3.27820	0.137550
$569$	−1.97827	−0.0829334	−0.0414667	−	0.999140i	$-0.513203\pi$
$569$	−1.97827	−0.0829334	−0.0414667	+	0.999140i	$0.513203\pi$
$570$	11.6655	0.488612
$571$	20.0995	0.841140	0.420570	−	0.907260i	$-0.361830\pi$
$571$	20.0995	0.841140	0.420570	+	0.907260i	$0.361830\pi$
$572$	1.64065	0.0685991
$573$	9.13397	0.381577
$574$	3.82781	0.159770
$575$	9.81456	0.409295
$576$	5.29519	0.220633
$577$	3.48484	0.145076	0.0725378	−	0.997366i	$-0.476890\pi$
$577$	3.48484	0.145076	0.0725378	+	0.997366i	$0.476890\pi$
$578$	−1.34029	−0.0557489
$579$	8.58058	0.356597
$580$	−0.840817	−0.0349130
$581$	−2.97419	−0.123390
$582$	33.2273	1.37732
$583$	5.88482	0.243725
$584$	11.7995	0.488266
$585$	−6.10293	−0.252325
$586$	−20.5147	−0.847455
$587$	9.42283	0.388922	0.194461	−	0.980910i	$-0.437704\pi$
$587$	9.42283	0.388922	0.194461	+	0.980910i	$0.437704\pi$
$588$	−2.88014	−0.118775
$589$	−25.8813	−1.06642
$590$	12.6394	0.520356
$591$	8.75396	0.360090
$592$	5.29489	0.217618
$593$	11.0055	0.451941	0.225970	−	0.974134i	$-0.427445\pi$
$593$	11.0055	0.451941	0.225970	+	0.974134i	$0.427445\pi$
$594$	−10.4723	−0.429685
$595$	−4.40395	−0.180544
$596$	−23.6895	−0.970360
$597$	−6.89726	−0.282286
$598$	−2.70220	−0.110501
$599$	−22.8975	−0.935565	−0.467782	−	0.883844i	$-0.654947\pi$
$599$	−22.8975	−0.935565	−0.467782	+	0.883844i	$0.654947\pi$
$600$	10.8336	0.442280
$601$	−15.7343	−0.641815	−0.320907	−	0.947111i	$-0.603988\pi$
$601$	−15.7343	−0.641815	−0.320907	+	0.947111i	$0.603988\pi$
$602$	−2.27822	−0.0928533
$603$	57.6830	2.34903
$604$	−14.5714	−0.592903
$605$	9.44873	0.384146
$606$	26.3276	1.06948
$607$	−46.8774	−1.90270	−0.951348	−	0.308118i	$-0.900301\pi$
$607$	−46.8774	−1.90270	−0.951348	+	0.308118i	$0.900301\pi$
$608$	3.63947	0.147600
$609$	2.17603	0.0881771
$610$	−8.01560	−0.324542
$611$	6.37298	0.257823
$612$	−20.9543	−0.847028
$613$	−31.6731	−1.27926	−0.639632	−	0.768681i	$-0.720913\pi$
$613$	−31.6731	−1.27926	−0.639632	+	0.768681i	$0.720913\pi$
$614$	1.83680	0.0741271
$615$	−12.2691	−0.494739
$616$	−1.58420	−0.0638294
$617$	−44.1014	−1.77546	−0.887728	−	0.460368i	$-0.847718\pi$
$617$	−44.1014	−1.77546	−0.887728	+	0.460368i	$0.847718\pi$
$618$	11.5625	0.465112
$619$	−26.7008	−1.07320	−0.536598	−	0.843838i	$-0.680291\pi$
$619$	−26.7008	−1.07320	−0.536598	+	0.843838i	$0.680291\pi$
$620$	7.91404	0.317836
$621$	17.2482	0.692146
$622$	7.48365	0.300067
$623$	13.1209	0.525677
$624$	−2.98277	−0.119406
$625$	7.95620	0.318248
$626$	34.8664	1.39354
$627$	−16.6059	−0.663175
$628$	−20.0390	−0.799644
$629$	−20.9531	−0.835455
$630$	5.89294	0.234780
$631$	33.8816	1.34880	0.674402	−	0.738365i	$-0.264402\pi$
$631$	33.8816	1.34880	0.674402	+	0.738365i	$0.264402\pi$
$632$	14.0389	0.558437
$633$	−40.1098	−1.59422
$634$	−33.1022	−1.31466
$635$	−2.85884	−0.113450
$636$	−10.6988	−0.424236
$637$	1.03563	0.0410333
$638$	1.19691	0.0473862
$639$	17.3587	0.686700
$640$	−1.11289	−0.0439907
$641$	43.7781	1.72913	0.864566	−	0.502519i	$-0.167593\pi$
$641$	43.7781	1.72913	0.864566	+	0.502519i	$0.167593\pi$
$642$	−11.2524	−0.444096
$643$	−36.1792	−1.42677	−0.713384	−	0.700774i	$-0.752838\pi$
$643$	−36.1792	−1.42677	−0.713384	+	0.700774i	$0.752838\pi$
$644$	2.60922	0.102818
$645$	7.30229	0.287527
$646$	−14.4022	−0.566648
$647$	41.4457	1.62940	0.814700	−	0.579883i	$-0.196902\pi$
$647$	41.4457	1.62940	0.814700	+	0.579883i	$0.196902\pi$
$648$	3.15348	0.123880
$649$	−17.9923	−0.706260
$650$	−3.89552	−0.152795
$651$	−20.4815	−0.802732
$652$	−19.2354	−0.753315
$653$	0.813204	0.0318231	0.0159116	−	0.999873i	$-0.494935\pi$
$653$	0.813204	0.0318231	0.0159116	+	0.999873i	$0.494935\pi$
$654$	14.8196	0.579493
$655$	−2.84171	−0.111035
$656$	−3.82781	−0.149451
$657$	62.4806	2.43760
$658$	−6.15371	−0.239897
$659$	48.3914	1.88506	0.942530	−	0.334121i	$-0.108439\pi$
$659$	48.3914	1.88506	0.942530	+	0.334121i	$0.108439\pi$
$660$	5.07779	0.197653
$661$	−29.3253	−1.14062	−0.570311	−	0.821429i	$-0.693177\pi$
$661$	−29.3253	−1.14062	−0.570311	+	0.821429i	$0.693177\pi$
$662$	−10.2454	−0.398200
$663$	11.8035	0.458410
$664$	2.97419	0.115421
$665$	4.05031	0.157064
$666$	28.0374	1.08643
$667$	−1.97134	−0.0763308
$668$	−8.08055	−0.312646
$669$	65.7012	2.54016
$670$	−12.1232	−0.468360
$671$	11.4103	0.440489
$672$	2.88014	0.111104
$673$	−27.3963	−1.05605	−0.528024	−	0.849230i	$-0.677067\pi$
$673$	−27.3963	−1.05605	−0.528024	+	0.849230i	$0.677067\pi$
$674$	4.85692	0.187082
$675$	24.8652	0.957061
$676$	−11.9275	−0.458749
$677$	−20.0929	−0.772234	−0.386117	−	0.922450i	$-0.626184\pi$
$677$	−20.0929	−0.772234	−0.386117	+	0.922450i	$0.626184\pi$
$678$	24.9450	0.958007
$679$	11.5367	0.442738
$680$	4.40395	0.168884
$681$	75.8552	2.90678
$682$	−11.2657	−0.431387
$683$	19.8790	0.760647	0.380324	−	0.924853i	$-0.375813\pi$
$683$	19.8790	0.760647	0.380324	+	0.924853i	$0.375813\pi$
$684$	19.2717	0.736871
$685$	−14.7729	−0.564445
$686$	−1.00000	−0.0381802
$687$	83.8267	3.19819
$688$	2.27822	0.0868563
$689$	3.84706	0.146561
$690$	−8.36325	−0.318384
$691$	50.1412	1.90746	0.953730	−	0.300665i	$-0.0972085\pi$
$691$	50.1412	1.90746	0.953730	+	0.300665i	$0.0972085\pi$
$692$	0.918935	0.0349327
$693$	−8.38866	−0.318659
$694$	−32.8932	−1.24861
$695$	−13.4334	−0.509559
$696$	−2.17603	−0.0824821
$697$	15.1475	0.573754
$698$	−22.7417	−0.860786
$699$	−62.2749	−2.35545
$700$	3.76149	0.142171
$701$	−34.0395	−1.28565	−0.642827	−	0.766012i	$-0.722238\pi$
$701$	−34.0395	−1.28565	−0.642827	+	0.766012i	$0.722238\pi$
$702$	−6.84602	−0.258386
$703$	19.2706	0.726803
$704$	1.58420	0.0597069
$705$	19.7243	0.742858
$706$	4.33045	0.162979
$707$	9.14108	0.343786
$708$	32.7106	1.22934
$709$	−22.8725	−0.858995	−0.429498	−	0.903068i	$-0.641309\pi$
$709$	−22.8725	−0.858995	−0.429498	+	0.903068i	$0.641309\pi$
$710$	−3.64826	−0.136917
$711$	74.3386	2.78792
$712$	−13.1209	−0.491726
$713$	18.5549	0.694888
$714$	−11.3974	−0.426536
$715$	−1.82586	−0.0682833
$716$	−11.5750	−0.432578
$717$	45.7885	1.71000
$718$	−12.1500	−0.453433
$719$	31.1085	1.16015	0.580076	−	0.814562i	$-0.303023\pi$
$719$	31.1085	1.16015	0.580076	+	0.814562i	$0.303023\pi$
$720$	−5.89294	−0.219617
$721$	4.01456	0.149510
$722$	−5.75428	−0.214152
$723$	81.1422	3.01771
$724$	10.0703	0.374259
$725$	−2.84191	−0.105546
$726$	24.4532	0.907545
$727$	16.1405	0.598619	0.299310	−	0.954156i	$-0.403244\pi$
$727$	16.1405	0.598619	0.299310	+	0.954156i	$0.403244\pi$
$728$	−1.03563	−0.0383831
$729$	−40.4189	−1.49700
$730$	−13.1315	−0.486018
$731$	−9.01544	−0.333448
$732$	−20.7443	−0.766731
$733$	14.8689	0.549195	0.274597	−	0.961559i	$-0.411455\pi$
$733$	14.8689	0.549195	0.274597	+	0.961559i	$0.411455\pi$
$734$	22.6966	0.837745
$735$	3.20526	0.118228
$736$	−2.60922	−0.0961773
$737$	17.2575	0.635687
$738$	−20.2690	−0.746111
$739$	10.5669	0.388710	0.194355	−	0.980931i	$-0.437739\pi$
$739$	10.5669	0.388710	0.194355	+	0.980931i	$0.437739\pi$
$740$	−5.89260	−0.216616
$741$	−10.8557	−0.398793
$742$	−3.71469	−0.136371
$743$	1.14477	0.0419977	0.0209988	−	0.999779i	$-0.493315\pi$
$743$	1.14477	0.0419977	0.0209988	+	0.999779i	$0.493315\pi$
$744$	20.4815	0.750887
$745$	26.3637	0.965892
$746$	19.9513	0.730469
$747$	15.7489	0.576223
$748$	−6.26906	−0.229220
$749$	−3.90689	−0.142755
$750$	−28.0829	−1.02544
$751$	−1.44288	−0.0526513	−0.0263257	−	0.999653i	$-0.508381\pi$
$751$	−1.44288	−0.0526513	−0.0263257	+	0.999653i	$0.508381\pi$
$752$	6.15371	0.224403
$753$	8.52219	0.310566
$754$	0.782451	0.0284952
$755$	16.2163	0.590173
$756$	6.61047	0.240420
$757$	8.40672	0.305547	0.152774	−	0.988261i	$-0.451179\pi$
$757$	8.40672	0.305547	0.152774	+	0.988261i	$0.451179\pi$
$758$	18.3532	0.666620
$759$	11.9052	0.432130
$760$	−4.05031	−0.146920
$761$	−38.4985	−1.39557	−0.697785	−	0.716307i	$-0.745831\pi$
$761$	−38.4985	−1.39557	−0.697785	+	0.716307i	$0.745831\pi$
$762$	−7.39865	−0.268025
$763$	5.14546	0.186278
$764$	−3.17137	−0.114736
$765$	23.3198	0.843128
$766$	11.4961	0.415371
$767$	−11.7620	−0.424702
$768$	−2.88014	−0.103928
$769$	−4.90539	−0.176893	−0.0884464	−	0.996081i	$-0.528190\pi$
$769$	−4.90539	−0.176893	−0.0884464	+	0.996081i	$0.528190\pi$
$770$	1.76304	0.0635354
$771$	−48.2116	−1.73630
$772$	−2.97922	−0.107225
$773$	−22.1591	−0.797006	−0.398503	−	0.917167i	$-0.630470\pi$
$773$	−22.1591	−0.797006	−0.398503	+	0.917167i	$0.630470\pi$
$774$	12.0636	0.433617
$775$	26.7490	0.960852
$776$	−11.5367	−0.414144
$777$	15.2500	0.547091
$778$	7.87777	0.282432
$779$	−13.9312	−0.499136
$780$	3.31948	0.118856
$781$	5.19333	0.185832
$782$	10.3253	0.369232
$783$	−4.99440	−0.178485
$784$	1.00000	0.0357143
$785$	22.3011	0.795962
$786$	−7.35433	−0.262320
$787$	27.5287	0.981293	0.490647	−	0.871359i	$-0.336761\pi$
$787$	27.5287	0.981293	0.490647	+	0.871359i	$0.336761\pi$
$788$	−3.03942	−0.108275
$789$	−75.2604	−2.67934
$790$	−15.6237	−0.555866
$791$	8.66104	0.307951
$792$	8.38866	0.298078
$793$	7.45918	0.264883
$794$	−9.78157	−0.347135
$795$	11.9066	0.422282
$796$	2.39477	0.0848802
$797$	40.1780	1.42318	0.711590	−	0.702595i	$-0.247975\pi$
$797$	40.1780	1.42318	0.711590	+	0.702595i	$0.247975\pi$
$798$	10.4822	0.371065
$799$	−24.3517	−0.861500
$800$	−3.76149	−0.132989
$801$	−69.4776	−2.45487
$802$	−3.99052	−0.140910
$803$	18.6928	0.659654
$804$	−31.3747	−1.10650
$805$	−2.90377	−0.102344
$806$	−7.36468	−0.259410
$807$	13.3404	0.469604
$808$	−9.14108	−0.321582
$809$	−47.7309	−1.67813	−0.839065	−	0.544032i	$-0.816897\pi$
$809$	−47.7309	−1.67813	−0.839065	+	0.544032i	$0.816897\pi$
$810$	−3.50946	−0.123310
$811$	15.6480	0.549475	0.274737	−	0.961519i	$-0.411409\pi$
$811$	15.6480	0.549475	0.274737	+	0.961519i	$0.411409\pi$
$812$	−0.755529	−0.0265139
$813$	−9.79211	−0.343424
$814$	8.38817	0.294005
$815$	21.4067	0.749846
$816$	11.3974	0.398988
$817$	8.29150	0.290083
$818$	−34.7964	−1.21663
$819$	−5.48388	−0.191622
$820$	4.25991	0.148763
$821$	−27.8761	−0.972882	−0.486441	−	0.873713i	$-0.661705\pi$
$821$	−27.8761	−0.972882	−0.486441	+	0.873713i	$0.661705\pi$
$822$	−38.2322	−1.33350
$823$	4.72435	0.164681	0.0823403	−	0.996604i	$-0.473761\pi$
$823$	4.72435	0.164681	0.0823403	+	0.996604i	$0.473761\pi$
$824$	−4.01456	−0.139854
$825$	17.1626	0.597526
$826$	11.3573	0.395172
$827$	26.3557	0.916479	0.458239	−	0.888829i	$-0.348480\pi$
$827$	26.3557	0.916479	0.458239	+	0.888829i	$0.348480\pi$
$828$	−13.8163	−0.480151
$829$	−6.00676	−0.208623	−0.104312	−	0.994545i	$-0.533264\pi$
$829$	−6.00676	−0.208623	−0.104312	+	0.994545i	$0.533264\pi$
$830$	−3.30994	−0.114890
$831$	−15.0726	−0.522862
$832$	1.03563	0.0359041
$833$	−3.95723	−0.137110
$834$	−34.7656	−1.20383
$835$	8.99273	0.311206
$836$	5.76565	0.199409
$837$	47.0089	1.62487
$838$	−6.76977	−0.233858
$839$	−17.2315	−0.594896	−0.297448	−	0.954738i	$-0.596135\pi$
$839$	−17.2315	−0.594896	−0.297448	+	0.954738i	$0.596135\pi$
$840$	−3.20526	−0.110592
$841$	−28.4292	−0.980316
$842$	−21.3986	−0.737446
$843$	−31.0943	−1.07095
$844$	13.9263	0.479364
$845$	13.2739	0.456636
$846$	32.5851	1.12030
$847$	8.49030	0.291730
$848$	3.71469	0.127563
$849$	1.62038	0.0556114
$850$	14.8851	0.510554
$851$	−13.8155	−0.473591
$852$	−9.44167	−0.323466
$853$	52.0356	1.78166	0.890832	−	0.454332i	$-0.150122\pi$
$853$	52.0356	1.78166	0.890832	+	0.454332i	$0.150122\pi$
$854$	−7.20253	−0.246466
$855$	−21.4472	−0.733478
$856$	3.90689	0.133535
$857$	7.80497	0.266613	0.133306	−	0.991075i	$-0.457441\pi$
$857$	7.80497	0.266613	0.133306	+	0.991075i	$0.457441\pi$
$858$	−4.72531	−0.161319
$859$	27.7484	0.946763	0.473381	−	0.880858i	$-0.343033\pi$
$859$	27.7484	0.946763	0.473381	+	0.880858i	$0.343033\pi$
$860$	−2.53540	−0.0864563
$861$	−11.0246	−0.375718
$862$	1.00000	0.0340601
$863$	−42.3914	−1.44302	−0.721510	−	0.692404i	$-0.756552\pi$
$863$	−42.3914	−1.44302	−0.721510	+	0.692404i	$0.756552\pi$
$864$	−6.61047	−0.224893
$865$	−1.02267	−0.0347718
$866$	−7.81523	−0.265572
$867$	3.86023	0.131100
$868$	7.11128	0.241373
$869$	22.2405	0.754456
$870$	2.42167	0.0821023
$871$	11.2816	0.382264
$872$	−5.14546	−0.174247
$873$	−61.0891	−2.06755
$874$	−9.49619	−0.321213
$875$	−9.75053	−0.329628
$876$	−33.9842	−1.14822
$877$	−7.62081	−0.257337	−0.128668	−	0.991688i	$-0.541070\pi$
$877$	−7.62081	−0.257337	−0.128668	+	0.991688i	$0.541070\pi$
$878$	38.7958	1.30930
$879$	59.0852	1.99289
$880$	−1.76304	−0.0594320
$881$	54.5148	1.83665	0.918324	−	0.395829i	$-0.129543\pi$
$881$	54.5148	1.83665	0.918324	+	0.395829i	$0.129543\pi$
$882$	5.29519	0.178298
$883$	−18.6788	−0.628593	−0.314297	−	0.949325i	$-0.601769\pi$
$883$	−18.6788	−0.628593	−0.314297	+	0.949325i	$0.601769\pi$
$884$	−4.09824	−0.137839
$885$	−36.4032	−1.22368
$886$	−24.7290	−0.830787
$887$	−6.13165	−0.205881	−0.102940	−	0.994688i	$-0.532825\pi$
$887$	−6.13165	−0.205881	−0.102940	+	0.994688i	$0.532825\pi$
$888$	−15.2500	−0.511756
$889$	−2.56885	−0.0861565
$890$	14.6021	0.489462
$891$	4.99575	0.167364
$892$	−22.8118	−0.763797
$893$	22.3962	0.749461
$894$	68.2291	2.28192
$895$	12.8817	0.430587
$896$	−1.00000	−0.0334077
$897$	7.78270	0.259857
$898$	−0.365550	−0.0121986
$899$	−5.37278	−0.179192
$900$	−19.9178	−0.663926
$901$	−14.6999	−0.489725
$902$	−6.06402	−0.201910
$903$	6.56158	0.218356
$904$	−8.66104	−0.288062
$905$	−11.2071	−0.372536
$906$	41.9677	1.39428
$907$	−0.383483	−0.0127334	−0.00636668	−	0.999980i	$-0.502027\pi$
$907$	−0.383483	−0.0127334	−0.00636668	+	0.999980i	$0.502027\pi$
$908$	−26.3374	−0.874036
$909$	−48.4038	−1.60545
$910$	1.15254	0.0382064
$911$	−14.6946	−0.486854	−0.243427	−	0.969919i	$-0.578272\pi$
$911$	−14.6946	−0.486854	−0.243427	+	0.969919i	$0.578272\pi$
$912$	−10.4822	−0.347099
$913$	4.71173	0.155935
$914$	27.4402	0.907642
$915$	23.0860	0.763200
$916$	−29.1051	−0.961660
$917$	−2.55347	−0.0843228
$918$	26.1592	0.863381
$919$	7.27138	0.239861	0.119930	−	0.992782i	$-0.461733\pi$
$919$	7.27138	0.239861	0.119930	+	0.992782i	$0.461733\pi$
$920$	2.90377	0.0957344
$921$	−5.29023	−0.174319
$922$	−26.6862	−0.878863
$923$	3.39501	0.111748
$924$	4.56272	0.150103
$925$	−19.9166	−0.654855
$926$	−40.7272	−1.33838
$927$	−21.2579	−0.698201
$928$	0.755529	0.0248015
$929$	31.1008	1.02038	0.510192	−	0.860060i	$-0.329574\pi$
$929$	31.1008	1.02038	0.510192	+	0.860060i	$0.329574\pi$
$930$	−22.7935	−0.747429
$931$	3.63947	0.119279
$932$	21.6222	0.708258
$933$	−21.5540	−0.705645
$934$	−4.54278	−0.148644
$935$	6.97675	0.228164
$936$	5.48388	0.179246
$937$	−5.73245	−0.187271	−0.0936355	−	0.995607i	$-0.529849\pi$
$937$	−5.73245	−0.187271	−0.0936355	+	0.995607i	$0.529849\pi$
$938$	−10.8935	−0.355684
$939$	−100.420	−3.27709
$940$	−6.84837	−0.223369
$941$	−18.9877	−0.618983	−0.309491	−	0.950902i	$-0.600159\pi$
$941$	−18.9877	−0.618983	−0.309491	+	0.950902i	$0.600159\pi$
$942$	57.7151	1.88046
$943$	9.98761	0.325241
$944$	−11.3573	−0.369649
$945$	−7.35669	−0.239313
$946$	3.60916	0.117344
$947$	−32.3946	−1.05268	−0.526342	−	0.850273i	$-0.676437\pi$
$947$	−32.3946	−1.05268	−0.526342	+	0.850273i	$0.676437\pi$
$948$	−40.4339	−1.31323
$949$	12.2199	0.396676
$950$	−13.6898	−0.444156
$951$	95.3389	3.09158
$952$	3.95723	0.128255
$953$	−53.0660	−1.71898	−0.859488	−	0.511155i	$-0.829218\pi$
$953$	−53.0660	−1.71898	−0.859488	+	0.511155i	$0.829218\pi$
$954$	19.6700	0.636840
$955$	3.52937	0.114208
$956$	−15.8980	−0.514179
$957$	−3.44727	−0.111434
$958$	−22.0242	−0.711570
$959$	−13.2744	−0.428654
$960$	3.20526	0.103449
$961$	19.5703	0.631301
$962$	5.48356	0.176797
$963$	20.6877	0.666653
$964$	−28.1730	−0.907392
$965$	3.31554	0.106731
$966$	−7.51493	−0.241789
$967$	23.1527	0.744541	0.372271	−	0.928124i	$-0.378579\pi$
$967$	23.1527	0.744541	0.372271	+	0.928124i	$0.378579\pi$
$968$	−8.49030	−0.272889
$969$	41.4804	1.33254
$970$	12.8390	0.412237
$971$	42.5615	1.36586	0.682931	−	0.730482i	$-0.260705\pi$
$971$	42.5615	1.36586	0.682931	+	0.730482i	$0.260705\pi$
$972$	10.7489	0.344773
$973$	−12.0708	−0.386972
$974$	33.2152	1.06428
$975$	11.2196	0.359316
$976$	7.20253	0.230547
$977$	−0.721707	−0.0230895	−0.0115447	−	0.999933i	$-0.503675\pi$
$977$	−0.721707	−0.0230895	−0.0115447	+	0.999933i	$0.503675\pi$
$978$	55.4005	1.77151
$979$	−20.7862	−0.664328
$980$	−1.11289	−0.0355498
$981$	−27.2462	−0.869904
$982$	−20.8315	−0.664761
$983$	−16.3222	−0.520597	−0.260298	−	0.965528i	$-0.583821\pi$
$983$	−16.3222	−0.520597	−0.260298	+	0.965528i	$0.583821\pi$
$984$	11.0246	0.351452
$985$	3.38253	0.107776
$986$	−2.98981	−0.0952148
$987$	17.7235	0.564146
$988$	3.76915	0.119913
$989$	−5.94438	−0.189020
$990$	−9.33562	−0.296705
$991$	−6.95338	−0.220881	−0.110441	−	0.993883i	$-0.535226\pi$
$991$	−6.95338	−0.220881	−0.110441	+	0.993883i	$0.535226\pi$
$992$	−7.11128	−0.225783
$993$	29.5083	0.936416
$994$	−3.27820	−0.103978
$995$	−2.66510	−0.0844894
$996$	−8.56609	−0.271427
$997$	38.8528	1.23048	0.615240	−	0.788340i	$-0.289059\pi$
$997$	38.8528	1.23048	0.615240	+	0.788340i	$0.289059\pi$
$998$	29.2893	0.927138
$999$	−35.0017	−1.10740

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.2	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.88014 q^{3} +1.00000 q^{4} -1.11289 q^{5} -2.88014 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.29519 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.88014 q^{3} +1.00000 q^{4} -1.11289 q^{5} -2.88014 q^{6} -1.00000 q^{7} +1.00000 q^{8} +5.29519 q^{9} -1.11289 q^{10} +1.58420 q^{11} -2.88014 q^{12} +1.03563 q^{13} -1.00000 q^{14} +3.20526 q^{15} +1.00000 q^{16} -3.95723 q^{17} +5.29519 q^{18} +3.63947 q^{19} -1.11289 q^{20} +2.88014 q^{21} +1.58420 q^{22} -2.60922 q^{23} -2.88014 q^{24} -3.76149 q^{25} +1.03563 q^{26} -6.61047 q^{27} -1.00000 q^{28} +0.755529 q^{29} +3.20526 q^{30} -7.11128 q^{31} +1.00000 q^{32} -4.56272 q^{33} -3.95723 q^{34} +1.11289 q^{35} +5.29519 q^{36} +5.29489 q^{37} +3.63947 q^{38} -2.98277 q^{39} -1.11289 q^{40} -3.82781 q^{41} +2.88014 q^{42} +2.27822 q^{43} +1.58420 q^{44} -5.89294 q^{45} -2.60922 q^{46} +6.15371 q^{47} -2.88014 q^{48} +1.00000 q^{49} -3.76149 q^{50} +11.3974 q^{51} +1.03563 q^{52} +3.71469 q^{53} -6.61047 q^{54} -1.76304 q^{55} -1.00000 q^{56} -10.4822 q^{57} +0.755529 q^{58} -11.3573 q^{59} +3.20526 q^{60} +7.20253 q^{61} -7.11128 q^{62} -5.29519 q^{63} +1.00000 q^{64} -1.15254 q^{65} -4.56272 q^{66} +10.8935 q^{67} -3.95723 q^{68} +7.51493 q^{69} +1.11289 q^{70} +3.27820 q^{71} +5.29519 q^{72} +11.7995 q^{73} +5.29489 q^{74} +10.8336 q^{75} +3.63947 q^{76} -1.58420 q^{77} -2.98277 q^{78} +14.0389 q^{79} -1.11289 q^{80} +3.15348 q^{81} -3.82781 q^{82} +2.97419 q^{83} +2.88014 q^{84} +4.40395 q^{85} +2.27822 q^{86} -2.17603 q^{87} +1.58420 q^{88} -13.1209 q^{89} -5.89294 q^{90} -1.03563 q^{91} -2.60922 q^{92} +20.4815 q^{93} +6.15371 q^{94} -4.05031 q^{95} -2.88014 q^{96} -11.5367 q^{97} +1.00000 q^{98} +8.38866 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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