LMFDB - Embedded newform 8034.2.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 $ x^12 - 6x^11 - 8x^10 + 94x^9 - 7x^8 - 580x^7 + 180x^6 + 1787x^5 - 308x^4 - 2790x^3 - 352x^2 + 1768*x + 768
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$3.23048$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.42840 q^{5} -1.00000 q^{6} -2.28162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.42840 q^{5} -1.00000 q^{6} -2.28162 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.42840 q^{10} -0.378203 q^{11} +1.00000 q^{12} +1.00000 q^{13} +2.28162 q^{14} +1.42840 q^{15} +1.00000 q^{16} -1.07828 q^{17} -1.00000 q^{18} -6.85408 q^{19} +1.42840 q^{20} -2.28162 q^{21} +0.378203 q^{22} -1.64807 q^{23} -1.00000 q^{24} -2.95968 q^{25} -1.00000 q^{26} +1.00000 q^{27} -2.28162 q^{28} -5.09337 q^{29} -1.42840 q^{30} +10.3699 q^{31} -1.00000 q^{32} -0.378203 q^{33} +1.07828 q^{34} -3.25906 q^{35} +1.00000 q^{36} +9.76199 q^{37} +6.85408 q^{38} +1.00000 q^{39} -1.42840 q^{40} +0.952622 q^{41} +2.28162 q^{42} +2.65892 q^{43} -0.378203 q^{44} +1.42840 q^{45} +1.64807 q^{46} +7.38329 q^{47} +1.00000 q^{48} -1.79420 q^{49} +2.95968 q^{50} -1.07828 q^{51} +1.00000 q^{52} +7.79122 q^{53} -1.00000 q^{54} -0.540224 q^{55} +2.28162 q^{56} -6.85408 q^{57} +5.09337 q^{58} -0.731526 q^{59} +1.42840 q^{60} -4.05568 q^{61} -10.3699 q^{62} -2.28162 q^{63} +1.00000 q^{64} +1.42840 q^{65} +0.378203 q^{66} -9.03946 q^{67} -1.07828 q^{68} -1.64807 q^{69} +3.25906 q^{70} +3.02171 q^{71} -1.00000 q^{72} -11.2549 q^{73} -9.76199 q^{74} -2.95968 q^{75} -6.85408 q^{76} +0.862916 q^{77} -1.00000 q^{78} +5.25463 q^{79} +1.42840 q^{80} +1.00000 q^{81} -0.952622 q^{82} -11.2812 q^{83} -2.28162 q^{84} -1.54021 q^{85} -2.65892 q^{86} -5.09337 q^{87} +0.378203 q^{88} -5.26838 q^{89} -1.42840 q^{90} -2.28162 q^{91} -1.64807 q^{92} +10.3699 q^{93} -7.38329 q^{94} -9.79035 q^{95} -1.00000 q^{96} -10.0419 q^{97} +1.79420 q^{98} -0.378203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.42840	0.638798	0.319399	−	0.947620i	$-0.396519\pi$
$5$	1.42840	0.638798	0.319399	+	0.947620i	$0.396519\pi$
$6$	−1.00000	−0.408248
$7$	−2.28162	−0.862372	−0.431186	−	0.902263i	$-0.641905\pi$
$7$	−2.28162	−0.862372	−0.431186	+	0.902263i	$0.641905\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.42840	−0.451698
$11$	−0.378203	−0.114033	−0.0570163	−	0.998373i	$-0.518159\pi$
$11$	−0.378203	−0.114033	−0.0570163	+	0.998373i	$0.518159\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.28162	0.609789
$15$	1.42840	0.368810
$16$	1.00000	0.250000
$17$	−1.07828	−0.261521	−0.130761	−	0.991414i	$-0.541742\pi$
$17$	−1.07828	−0.261521	−0.130761	+	0.991414i	$0.541742\pi$
$18$	−1.00000	−0.235702
$19$	−6.85408	−1.57243	−0.786217	−	0.617950i	$-0.787963\pi$
$19$	−6.85408	−1.57243	−0.786217	+	0.617950i	$0.787963\pi$
$20$	1.42840	0.319399
$21$	−2.28162	−0.497891
$22$	0.378203	0.0806332
$23$	−1.64807	−0.343647	−0.171824	−	0.985128i	$-0.554966\pi$
$23$	−1.64807	−0.343647	−0.171824	+	0.985128i	$0.554966\pi$
$24$	−1.00000	−0.204124
$25$	−2.95968	−0.591937
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−2.28162	−0.431186
$29$	−5.09337	−0.945816	−0.472908	−	0.881112i	$-0.656796\pi$
$29$	−5.09337	−0.945816	−0.472908	+	0.881112i	$0.656796\pi$
$30$	−1.42840	−0.260788
$31$	10.3699	1.86248	0.931240	−	0.364406i	$-0.118728\pi$
$31$	10.3699	1.86248	0.931240	+	0.364406i	$0.118728\pi$
$32$	−1.00000	−0.176777
$33$	−0.378203	−0.0658367
$34$	1.07828	0.184923
$35$	−3.25906	−0.550881
$36$	1.00000	0.166667
$37$	9.76199	1.60486	0.802430	−	0.596746i	$-0.203540\pi$
$37$	9.76199	1.60486	0.802430	+	0.596746i	$0.203540\pi$
$38$	6.85408	1.11188
$39$	1.00000	0.160128
$40$	−1.42840	−0.225849
$41$	0.952622	0.148775	0.0743873	−	0.997229i	$-0.476300\pi$
$41$	0.952622	0.148775	0.0743873	+	0.997229i	$0.476300\pi$
$42$	2.28162	0.352062
$43$	2.65892	0.405482	0.202741	−	0.979232i	$-0.435015\pi$
$43$	2.65892	0.405482	0.202741	+	0.979232i	$0.435015\pi$
$44$	−0.378203	−0.0570163
$45$	1.42840	0.212933
$46$	1.64807	0.242995
$47$	7.38329	1.07696	0.538482	−	0.842637i	$-0.318998\pi$
$47$	7.38329	1.07696	0.538482	+	0.842637i	$0.318998\pi$
$48$	1.00000	0.144338
$49$	−1.79420	−0.256315
$50$	2.95968	0.418563
$51$	−1.07828	−0.150989
$52$	1.00000	0.138675
$53$	7.79122	1.07021	0.535103	−	0.844787i	$-0.320273\pi$
$53$	7.79122	1.07021	0.535103	+	0.844787i	$0.320273\pi$
$54$	−1.00000	−0.136083
$55$	−0.540224	−0.0728438
$56$	2.28162	0.304894
$57$	−6.85408	−0.907846
$58$	5.09337	0.668793
$59$	−0.731526	−0.0952366	−0.0476183	−	0.998866i	$-0.515163\pi$
$59$	−0.731526	−0.0952366	−0.0476183	+	0.998866i	$0.515163\pi$
$60$	1.42840	0.184405
$61$	−4.05568	−0.519277	−0.259638	−	0.965706i	$-0.583603\pi$
$61$	−4.05568	−0.519277	−0.259638	+	0.965706i	$0.583603\pi$
$62$	−10.3699	−1.31697
$63$	−2.28162	−0.287457
$64$	1.00000	0.125000
$65$	1.42840	0.177171
$66$	0.378203	0.0465536
$67$	−9.03946	−1.10435	−0.552173	−	0.833730i	$-0.686201\pi$
$67$	−9.03946	−1.10435	−0.552173	+	0.833730i	$0.686201\pi$
$68$	−1.07828	−0.130761
$69$	−1.64807	−0.198405
$70$	3.25906	0.389532
$71$	3.02171	0.358611	0.179306	−	0.983793i	$-0.442615\pi$
$71$	3.02171	0.358611	0.179306	+	0.983793i	$0.442615\pi$
$72$	−1.00000	−0.117851
$73$	−11.2549	−1.31728	−0.658641	−	0.752457i	$-0.728868\pi$
$73$	−11.2549	−1.31728	−0.658641	+	0.752457i	$0.728868\pi$
$74$	−9.76199	−1.13481
$75$	−2.95968	−0.341755
$76$	−6.85408	−0.786217
$77$	0.862916	0.0983384
$78$	−1.00000	−0.113228
$79$	5.25463	0.591193	0.295596	−	0.955313i	$-0.404482\pi$
$79$	5.25463	0.591193	0.295596	+	0.955313i	$0.404482\pi$
$80$	1.42840	0.159700
$81$	1.00000	0.111111
$82$	−0.952622	−0.105200
$83$	−11.2812	−1.23827	−0.619136	−	0.785284i	$-0.712517\pi$
$83$	−11.2812	−1.23827	−0.619136	+	0.785284i	$0.712517\pi$
$84$	−2.28162	−0.248945
$85$	−1.54021	−0.167059
$86$	−2.65892	−0.286719
$87$	−5.09337	−0.546067
$88$	0.378203	0.0403166
$89$	−5.26838	−0.558447	−0.279223	−	0.960226i	$-0.590077\pi$
$89$	−5.26838	−0.558447	−0.279223	+	0.960226i	$0.590077\pi$
$90$	−1.42840	−0.150566
$91$	−2.28162	−0.239179
$92$	−1.64807	−0.171824
$93$	10.3699	1.07530
$94$	−7.38329	−0.761528
$95$	−9.79035	−1.00447
$96$	−1.00000	−0.102062
$97$	−10.0419	−1.01960	−0.509802	−	0.860292i	$-0.670281\pi$
$97$	−10.0419	−1.01960	−0.509802	+	0.860292i	$0.670281\pi$
$98$	1.79420	0.181242
$99$	−0.378203	−0.0380108
$100$	−2.95968	−0.295968
$101$	6.99307	0.695836	0.347918	−	0.937525i	$-0.386889\pi$
$101$	6.99307	0.695836	0.347918	+	0.937525i	$0.386889\pi$
$102$	1.07828	0.106766
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−3.25906	−0.318052
$106$	−7.79122	−0.756751
$107$	−10.4990	−1.01497	−0.507487	−	0.861660i	$-0.669425\pi$
$107$	−10.4990	−1.01497	−0.507487	+	0.861660i	$0.669425\pi$
$108$	1.00000	0.0962250
$109$	0.860752	0.0824450	0.0412225	−	0.999150i	$-0.486875\pi$
$109$	0.860752	0.0824450	0.0412225	+	0.999150i	$0.486875\pi$
$110$	0.540224	0.0515083
$111$	9.76199	0.926567
$112$	−2.28162	−0.215593
$113$	−2.84635	−0.267762	−0.133881	−	0.990997i	$-0.542744\pi$
$113$	−2.84635	−0.267762	−0.133881	+	0.990997i	$0.542744\pi$
$114$	6.85408	0.641944
$115$	−2.35410	−0.219521
$116$	−5.09337	−0.472908
$117$	1.00000	0.0924500
$118$	0.731526	0.0673424
$119$	2.46023	0.225528
$120$	−1.42840	−0.130394
$121$	−10.8570	−0.986997
$122$	4.05568	0.367184
$123$	0.952622	0.0858951
$124$	10.3699	0.931240
$125$	−11.3696	−1.01693
$126$	2.28162	0.203263
$127$	−1.00129	−0.0888504	−0.0444252	−	0.999013i	$-0.514146\pi$
$127$	−1.00129	−0.0888504	−0.0444252	+	0.999013i	$0.514146\pi$
$128$	−1.00000	−0.0883883
$129$	2.65892	0.234105
$130$	−1.42840	−0.125279
$131$	−7.05133	−0.616078	−0.308039	−	0.951374i	$-0.599673\pi$
$131$	−7.05133	−0.616078	−0.308039	+	0.951374i	$0.599673\pi$
$132$	−0.378203	−0.0329183
$133$	15.6384	1.35602
$134$	9.03946	0.780890
$135$	1.42840	0.122937
$136$	1.07828	0.0924617
$137$	−6.33167	−0.540951	−0.270476	−	0.962727i	$-0.587181\pi$
$137$	−6.33167	−0.540951	−0.270476	+	0.962727i	$0.587181\pi$
$138$	1.64807	0.140293
$139$	−15.7204	−1.33339	−0.666693	−	0.745332i	$-0.732291\pi$
$139$	−15.7204	−1.33339	−0.666693	+	0.745332i	$0.732291\pi$
$140$	−3.25906	−0.275441
$141$	7.38329	0.621785
$142$	−3.02171	−0.253577
$143$	−0.378203	−0.0316269
$144$	1.00000	0.0833333
$145$	−7.27536	−0.604185
$146$	11.2549	0.931459
$147$	−1.79420	−0.147984
$148$	9.76199	0.802430
$149$	−10.5290	−0.862570	−0.431285	−	0.902216i	$-0.641940\pi$
$149$	−10.5290	−0.862570	−0.431285	+	0.902216i	$0.641940\pi$
$150$	2.95968	0.241657
$151$	−5.65260	−0.460002	−0.230001	−	0.973190i	$-0.573873\pi$
$151$	−5.65260	−0.460002	−0.230001	+	0.973190i	$0.573873\pi$
$152$	6.85408	0.555940
$153$	−1.07828	−0.0871737
$154$	−0.862916	−0.0695358
$155$	14.8123	1.18975
$156$	1.00000	0.0800641
$157$	13.3002	1.06147	0.530736	−	0.847537i	$-0.321916\pi$
$157$	13.3002	1.06147	0.530736	+	0.847537i	$0.321916\pi$
$158$	−5.25463	−0.418036
$159$	7.79122	0.617884
$160$	−1.42840	−0.112925
$161$	3.76028	0.296352
$162$	−1.00000	−0.0785674
$163$	−6.40325	−0.501542	−0.250771	−	0.968046i	$-0.580684\pi$
$163$	−6.40325	−0.501542	−0.250771	+	0.968046i	$0.580684\pi$
$164$	0.952622	0.0743873
$165$	−0.540224	−0.0420564
$166$	11.2812	0.875591
$167$	4.33757	0.335651	0.167826	−	0.985817i	$-0.446325\pi$
$167$	4.33757	0.335651	0.167826	+	0.985817i	$0.446325\pi$
$168$	2.28162	0.176031
$169$	1.00000	0.0769231
$170$	1.54021	0.118129
$171$	−6.85408	−0.524145
$172$	2.65892	0.202741
$173$	−9.30906	−0.707755	−0.353878	−	0.935292i	$-0.615137\pi$
$173$	−9.30906	−0.707755	−0.353878	+	0.935292i	$0.615137\pi$
$174$	5.09337	0.386128
$175$	6.75288	0.510470
$176$	−0.378203	−0.0285081
$177$	−0.731526	−0.0549849
$178$	5.26838	0.394882
$179$	6.22986	0.465642	0.232821	−	0.972520i	$-0.425204\pi$
$179$	6.22986	0.465642	0.232821	+	0.972520i	$0.425204\pi$
$180$	1.42840	0.106466
$181$	−5.27430	−0.392035	−0.196018	−	0.980600i	$-0.562801\pi$
$181$	−5.27430	−0.392035	−0.196018	+	0.980600i	$0.562801\pi$
$182$	2.28162	0.169125
$183$	−4.05568	−0.299805
$184$	1.64807	0.121498
$185$	13.9440	1.02518
$186$	−10.3699	−0.760354
$187$	0.407809	0.0298219
$188$	7.38329	0.538482
$189$	−2.28162	−0.165964
$190$	9.79035	0.710266
$191$	−2.75574	−0.199399	−0.0996993	−	0.995018i	$-0.531788\pi$
$191$	−2.75574	−0.199399	−0.0996993	+	0.995018i	$0.531788\pi$
$192$	1.00000	0.0721688
$193$	−6.08283	−0.437852	−0.218926	−	0.975742i	$-0.570255\pi$
$193$	−6.08283	−0.437852	−0.218926	+	0.975742i	$0.570255\pi$
$194$	10.0419	0.720969
$195$	1.42840	0.102290
$196$	−1.79420	−0.128157
$197$	−10.1965	−0.726468	−0.363234	−	0.931698i	$-0.618328\pi$
$197$	−10.1965	−0.726468	−0.363234	+	0.931698i	$0.618328\pi$
$198$	0.378203	0.0268777
$199$	1.25424	0.0889107	0.0444554	−	0.999011i	$-0.485845\pi$
$199$	1.25424	0.0889107	0.0444554	+	0.999011i	$0.485845\pi$
$200$	2.95968	0.209281
$201$	−9.03946	−0.637594
$202$	−6.99307	−0.492030
$203$	11.6211	0.815645
$204$	−1.07828	−0.0754947
$205$	1.36072	0.0950369
$206$	1.00000	0.0696733
$207$	−1.64807	−0.114549
$208$	1.00000	0.0693375
$209$	2.59224	0.179309
$210$	3.25906	0.224896
$211$	−16.2651	−1.11973	−0.559867	−	0.828582i	$-0.689148\pi$
$211$	−16.2651	−1.11973	−0.559867	+	0.828582i	$0.689148\pi$
$212$	7.79122	0.535103
$213$	3.02171	0.207044
$214$	10.4990	0.717695
$215$	3.79799	0.259021
$216$	−1.00000	−0.0680414
$217$	−23.6601	−1.60615
$218$	−0.860752	−0.0582974
$219$	−11.2549	−0.760533
$220$	−0.540224	−0.0364219
$221$	−1.07828	−0.0725329
$222$	−9.76199	−0.655182
$223$	−21.2527	−1.42319	−0.711593	−	0.702592i	$-0.752026\pi$
$223$	−21.2527	−1.42319	−0.711593	+	0.702592i	$0.752026\pi$
$224$	2.28162	0.152447
$225$	−2.95968	−0.197312
$226$	2.84635	0.189336
$227$	−25.4900	−1.69183	−0.845914	−	0.533319i	$-0.820945\pi$
$227$	−25.4900	−1.69183	−0.845914	+	0.533319i	$0.820945\pi$
$228$	−6.85408	−0.453923
$229$	25.8974	1.71135	0.855674	−	0.517515i	$-0.173143\pi$
$229$	25.8974	1.71135	0.855674	+	0.517515i	$0.173143\pi$
$230$	2.35410	0.155225
$231$	0.862916	0.0567757
$232$	5.09337	0.334396
$233$	−0.935399	−0.0612800	−0.0306400	−	0.999530i	$-0.509755\pi$
$233$	−0.935399	−0.0612800	−0.0306400	+	0.999530i	$0.509755\pi$
$234$	−1.00000	−0.0653720
$235$	10.5463	0.687962
$236$	−0.731526	−0.0476183
$237$	5.25463	0.341325
$238$	−2.46023	−0.159473
$239$	−7.83371	−0.506720	−0.253360	−	0.967372i	$-0.581536\pi$
$239$	−7.83371	−0.506720	−0.253360	+	0.967372i	$0.581536\pi$
$240$	1.42840	0.0922026
$241$	23.8091	1.53368	0.766841	−	0.641837i	$-0.221827\pi$
$241$	23.8091	1.53368	0.766841	+	0.641837i	$0.221827\pi$
$242$	10.8570	0.697912
$243$	1.00000	0.0641500
$244$	−4.05568	−0.259638
$245$	−2.56284	−0.163734
$246$	−0.952622	−0.0607370
$247$	−6.85408	−0.436115
$248$	−10.3699	−0.658486
$249$	−11.2812	−0.714917
$250$	11.3696	0.719076
$251$	−7.47104	−0.471568	−0.235784	−	0.971805i	$-0.575766\pi$
$251$	−7.47104	−0.471568	−0.235784	+	0.971805i	$0.575766\pi$
$252$	−2.28162	−0.143729
$253$	0.623307	0.0391870
$254$	1.00129	0.0628267
$255$	−1.54021	−0.0964517
$256$	1.00000	0.0625000
$257$	−29.3198	−1.82892	−0.914459	−	0.404679i	$-0.867383\pi$
$257$	−29.3198	−1.82892	−0.914459	+	0.404679i	$0.867383\pi$
$258$	−2.65892	−0.165537
$259$	−22.2732	−1.38399
$260$	1.42840	0.0885854
$261$	−5.09337	−0.315272
$262$	7.05133	0.435633
$263$	−25.4645	−1.57021	−0.785106	−	0.619362i	$-0.787391\pi$
$263$	−25.4645	−1.57021	−0.785106	+	0.619362i	$0.787391\pi$
$264$	0.378203	0.0232768
$265$	11.1290	0.683646
$266$	−15.6384	−0.958853
$267$	−5.26838	−0.322420
$268$	−9.03946	−0.552173
$269$	−23.3373	−1.42290	−0.711451	−	0.702736i	$-0.751961\pi$
$269$	−23.3373	−1.42290	−0.711451	+	0.702736i	$0.751961\pi$
$270$	−1.42840	−0.0869294
$271$	−6.22070	−0.377881	−0.188940	−	0.981989i	$-0.560505\pi$
$271$	−6.22070	−0.377881	−0.188940	+	0.981989i	$0.560505\pi$
$272$	−1.07828	−0.0653803
$273$	−2.28162	−0.138090
$274$	6.33167	0.382510
$275$	1.11936	0.0675001
$276$	−1.64807	−0.0992024
$277$	10.9355	0.657053	0.328526	−	0.944495i	$-0.393448\pi$
$277$	10.9355	0.657053	0.328526	+	0.944495i	$0.393448\pi$
$278$	15.7204	0.942846
$279$	10.3699	0.620827
$280$	3.25906	0.194766
$281$	16.4408	0.980778	0.490389	−	0.871504i	$-0.336855\pi$
$281$	16.4408	0.980778	0.490389	+	0.871504i	$0.336855\pi$
$282$	−7.38329	−0.439668
$283$	17.3544	1.03161	0.515805	−	0.856706i	$-0.327493\pi$
$283$	17.3544	1.03161	0.515805	+	0.856706i	$0.327493\pi$
$284$	3.02171	0.179306
$285$	−9.79035	−0.579930
$286$	0.378203	0.0223636
$287$	−2.17352	−0.128299
$288$	−1.00000	−0.0589256
$289$	−15.8373	−0.931607
$290$	7.27536	0.427224
$291$	−10.0419	−0.588669
$292$	−11.2549	−0.658641
$293$	9.58413	0.559911	0.279956	−	0.960013i	$-0.409680\pi$
$293$	9.58413	0.559911	0.279956	+	0.960013i	$0.409680\pi$
$294$	1.79420	0.104640
$295$	−1.04491	−0.0608369
$296$	−9.76199	−0.567404
$297$	−0.378203	−0.0219456
$298$	10.5290	0.609929
$299$	−1.64807	−0.0953106
$300$	−2.95968	−0.170877
$301$	−6.06665	−0.349676
$302$	5.65260	0.325271
$303$	6.99307	0.401741
$304$	−6.85408	−0.393109
$305$	−5.79312	−0.331713
$306$	1.07828	0.0616411
$307$	−12.5014	−0.713495	−0.356747	−	0.934201i	$-0.616114\pi$
$307$	−12.5014	−0.713495	−0.356747	+	0.934201i	$0.616114\pi$
$308$	0.862916	0.0491692
$309$	−1.00000	−0.0568880
$310$	−14.8123	−0.841279
$311$	−26.1921	−1.48522	−0.742609	−	0.669725i	$-0.766412\pi$
$311$	−26.1921	−1.48522	−0.742609	+	0.669725i	$0.766412\pi$
$312$	−1.00000	−0.0566139
$313$	7.61225	0.430270	0.215135	−	0.976584i	$-0.430981\pi$
$313$	7.61225	0.430270	0.215135	+	0.976584i	$0.430981\pi$
$314$	−13.3002	−0.750574
$315$	−3.25906	−0.183627
$316$	5.25463	0.295596
$317$	7.73483	0.434431	0.217216	−	0.976124i	$-0.430303\pi$
$317$	7.73483	0.434431	0.217216	+	0.976124i	$0.430303\pi$
$318$	−7.79122	−0.436910
$319$	1.92633	0.107854
$320$	1.42840	0.0798498
$321$	−10.4990	−0.585995
$322$	−3.76028	−0.209552
$323$	7.39062	0.411225
$324$	1.00000	0.0555556
$325$	−2.95968	−0.164174
$326$	6.40325	0.354643
$327$	0.860752	0.0475997
$328$	−0.952622	−0.0525998
$329$	−16.8459	−0.928743
$330$	0.540224	0.0297383
$331$	25.0994	1.37959	0.689794	−	0.724006i	$-0.257701\pi$
$331$	25.0994	1.37959	0.689794	+	0.724006i	$0.257701\pi$
$332$	−11.2812	−0.619136
$333$	9.76199	0.534954
$334$	−4.33757	−0.237341
$335$	−12.9119	−0.705454
$336$	−2.28162	−0.124473
$337$	−13.9072	−0.757576	−0.378788	−	0.925483i	$-0.623659\pi$
$337$	−13.9072	−0.757576	−0.378788	+	0.925483i	$0.623659\pi$
$338$	−1.00000	−0.0543928
$339$	−2.84635	−0.154592
$340$	−1.54021	−0.0835296
$341$	−3.92191	−0.212383
$342$	6.85408	0.370626
$343$	20.0650	1.08341
$344$	−2.65892	−0.143359
$345$	−2.35410	−0.126741
$346$	9.30906	0.500458
$347$	−29.0558	−1.55980	−0.779898	−	0.625907i	$-0.784729\pi$
$347$	−29.0558	−1.55980	−0.779898	+	0.625907i	$0.784729\pi$
$348$	−5.09337	−0.273033
$349$	23.8454	1.27642	0.638209	−	0.769864i	$-0.279676\pi$
$349$	23.8454	1.27642	0.638209	+	0.769864i	$0.279676\pi$
$350$	−6.75288	−0.360957
$351$	1.00000	0.0533761
$352$	0.378203	0.0201583
$353$	25.2391	1.34334	0.671671	−	0.740850i	$-0.265577\pi$
$353$	25.2391	1.34334	0.671671	+	0.740850i	$0.265577\pi$
$354$	0.731526	0.0388802
$355$	4.31620	0.229080
$356$	−5.26838	−0.279223
$357$	2.46023	0.130209
$358$	−6.22986	−0.329259
$359$	−10.1016	−0.533144	−0.266572	−	0.963815i	$-0.585891\pi$
$359$	−10.1016	−0.533144	−0.266572	+	0.963815i	$0.585891\pi$
$360$	−1.42840	−0.0752831
$361$	27.9785	1.47255
$362$	5.27430	0.277211
$363$	−10.8570	−0.569843
$364$	−2.28162	−0.119589
$365$	−16.0764	−0.841477
$366$	4.05568	0.211994
$367$	7.36016	0.384197	0.192099	−	0.981376i	$-0.438471\pi$
$367$	7.36016	0.384197	0.192099	+	0.981376i	$0.438471\pi$
$368$	−1.64807	−0.0859118
$369$	0.952622	0.0495915
$370$	−13.9440	−0.724913
$371$	−17.7766	−0.922916
$372$	10.3699	0.537652
$373$	−11.0954	−0.574496	−0.287248	−	0.957856i	$-0.592740\pi$
$373$	−11.0954	−0.574496	−0.287248	+	0.957856i	$0.592740\pi$
$374$	−0.407809	−0.0210873
$375$	−11.3696	−0.587123
$376$	−7.38329	−0.380764
$377$	−5.09337	−0.262322
$378$	2.28162	0.117354
$379$	2.69689	0.138530	0.0692649	−	0.997598i	$-0.477935\pi$
$379$	2.69689	0.138530	0.0692649	+	0.997598i	$0.477935\pi$
$380$	−9.79035	−0.502234
$381$	−1.00129	−0.0512978
$382$	2.75574	0.140996
$383$	−3.30815	−0.169038	−0.0845192	−	0.996422i	$-0.526935\pi$
$383$	−3.30815	−0.169038	−0.0845192	+	0.996422i	$0.526935\pi$
$384$	−1.00000	−0.0510310
$385$	1.23259	0.0628184
$386$	6.08283	0.309608
$387$	2.65892	0.135161
$388$	−10.0419	−0.509802
$389$	23.1855	1.17555	0.587776	−	0.809024i	$-0.300004\pi$
$389$	23.1855	1.17555	0.587776	+	0.809024i	$0.300004\pi$
$390$	−1.42840	−0.0723296
$391$	1.77708	0.0898711
$392$	1.79420	0.0906210
$393$	−7.05133	−0.355693
$394$	10.1965	0.513691
$395$	7.50570	0.377653
$396$	−0.378203	−0.0190054
$397$	32.2041	1.61628	0.808138	−	0.588994i	$-0.200476\pi$
$397$	32.2041	1.61628	0.808138	+	0.588994i	$0.200476\pi$
$398$	−1.25424	−0.0628694
$399$	15.6384	0.782900
$400$	−2.95968	−0.147984
$401$	−0.522173	−0.0260761	−0.0130380	−	0.999915i	$-0.504150\pi$
$401$	−0.522173	−0.0260761	−0.0130380	+	0.999915i	$0.504150\pi$
$402$	9.03946	0.450847
$403$	10.3699	0.516559
$404$	6.99307	0.347918
$405$	1.42840	0.0709776
$406$	−11.6211	−0.576748
$407$	−3.69201	−0.183006
$408$	1.07828	0.0533828
$409$	28.7704	1.42260	0.711302	−	0.702887i	$-0.248106\pi$
$409$	28.7704	1.42260	0.711302	+	0.702887i	$0.248106\pi$
$410$	−1.36072	−0.0672013
$411$	−6.33167	−0.312318
$412$	−1.00000	−0.0492665
$413$	1.66907	0.0821293
$414$	1.64807	0.0809984
$415$	−16.1140	−0.791006
$416$	−1.00000	−0.0490290
$417$	−15.7204	−0.769831
$418$	−2.59224	−0.126790
$419$	−37.5198	−1.83296	−0.916482	−	0.400075i	$-0.868984\pi$
$419$	−37.5198	−1.83296	−0.916482	+	0.400075i	$0.868984\pi$
$420$	−3.25906	−0.159026
$421$	2.98562	0.145510	0.0727552	−	0.997350i	$-0.476821\pi$
$421$	2.98562	0.145510	0.0727552	+	0.997350i	$0.476821\pi$
$422$	16.2651	0.791772
$423$	7.38329	0.358988
$424$	−7.79122	−0.378375
$425$	3.19137	0.154804
$426$	−3.02171	−0.146403
$427$	9.25353	0.447810
$428$	−10.4990	−0.507487
$429$	−0.378203	−0.0182598
$430$	−3.79799	−0.183156
$431$	−11.3097	−0.544770	−0.272385	−	0.962188i	$-0.587812\pi$
$431$	−11.3097	−0.544770	−0.272385	+	0.962188i	$0.587812\pi$
$432$	1.00000	0.0481125
$433$	−2.35879	−0.113356	−0.0566781	−	0.998393i	$-0.518051\pi$
$433$	−2.35879	−0.113356	−0.0566781	+	0.998393i	$0.518051\pi$
$434$	23.6601	1.13572
$435$	−7.27536	−0.348827
$436$	0.860752	0.0412225
$437$	11.2960	0.540363
$438$	11.2549	0.537778
$439$	26.2481	1.25275	0.626376	−	0.779521i	$-0.284538\pi$
$439$	26.2481	1.25275	0.626376	+	0.779521i	$0.284538\pi$
$440$	0.540224	0.0257542
$441$	−1.79420	−0.0854383
$442$	1.07828	0.0512885
$443$	6.78372	0.322304	0.161152	−	0.986930i	$-0.448479\pi$
$443$	6.78372	0.322304	0.161152	+	0.986930i	$0.448479\pi$
$444$	9.76199	0.463283
$445$	−7.52533	−0.356735
$446$	21.2527	1.00634
$447$	−10.5290	−0.498005
$448$	−2.28162	−0.107796
$449$	37.5659	1.77284	0.886422	−	0.462879i	$-0.153183\pi$
$449$	37.5659	1.77284	0.886422	+	0.462879i	$0.153183\pi$
$450$	2.95968	0.139521
$451$	−0.360285	−0.0169651
$452$	−2.84635	−0.133881
$453$	−5.65260	−0.265582
$454$	25.4900	1.19630
$455$	−3.25906	−0.152787
$456$	6.85408	0.320972
$457$	−7.90872	−0.369954	−0.184977	−	0.982743i	$-0.559221\pi$
$457$	−7.90872	−0.369954	−0.184977	+	0.982743i	$0.559221\pi$
$458$	−25.8974	−1.21011
$459$	−1.07828	−0.0503298
$460$	−2.35410	−0.109761
$461$	0.520571	0.0242454	0.0121227	−	0.999927i	$-0.496141\pi$
$461$	0.520571	0.0242454	0.0121227	+	0.999927i	$0.496141\pi$
$462$	−0.862916	−0.0401465
$463$	−9.28449	−0.431487	−0.215744	−	0.976450i	$-0.569218\pi$
$463$	−9.28449	−0.431487	−0.215744	+	0.976450i	$0.569218\pi$
$464$	−5.09337	−0.236454
$465$	14.8123	0.686902
$466$	0.935399	0.0433315
$467$	−0.410904	−0.0190144	−0.00950719	−	0.999955i	$-0.503026\pi$
$467$	−0.410904	−0.0190144	−0.00950719	+	0.999955i	$0.503026\pi$
$468$	1.00000	0.0462250
$469$	20.6246	0.952357
$470$	−10.5463	−0.486463
$471$	13.3002	0.612841
$472$	0.731526	0.0336712
$473$	−1.00561	−0.0462381
$474$	−5.25463	−0.241353
$475$	20.2859	0.930782
$476$	2.46023	0.112764
$477$	7.79122	0.356736
$478$	7.83371	0.358305
$479$	−35.7133	−1.63178	−0.815890	−	0.578207i	$-0.803753\pi$
$479$	−35.7133	−1.63178	−0.815890	+	0.578207i	$0.803753\pi$
$480$	−1.42840	−0.0651971
$481$	9.76199	0.445108
$482$	−23.8091	−1.08448
$483$	3.76028	0.171099
$484$	−10.8570	−0.493498
$485$	−14.3439	−0.651322
$486$	−1.00000	−0.0453609
$487$	9.35930	0.424110	0.212055	−	0.977258i	$-0.431984\pi$
$487$	9.35930	0.424110	0.212055	+	0.977258i	$0.431984\pi$
$488$	4.05568	0.183592
$489$	−6.40325	−0.289565
$490$	2.56284	0.115777
$491$	−24.5502	−1.10793	−0.553967	−	0.832539i	$-0.686887\pi$
$491$	−24.5502	−1.10793	−0.553967	+	0.832539i	$0.686887\pi$
$492$	0.952622	0.0429475
$493$	5.49208	0.247351
$494$	6.85408	0.308380
$495$	−0.540224	−0.0242813
$496$	10.3699	0.465620
$497$	−6.89441	−0.309256
$498$	11.2812	0.505523
$499$	0.932509	0.0417448	0.0208724	−	0.999782i	$-0.493356\pi$
$499$	0.932509	0.0417448	0.0208724	+	0.999782i	$0.493356\pi$
$500$	−11.3696	−0.508463
$501$	4.33757	0.193788
$502$	7.47104	0.333449
$503$	−34.4919	−1.53792	−0.768958	−	0.639299i	$-0.779225\pi$
$503$	−34.4919	−1.53792	−0.768958	+	0.639299i	$0.779225\pi$
$504$	2.28162	0.101631
$505$	9.98887	0.444499
$506$	−0.623307	−0.0277094
$507$	1.00000	0.0444116
$508$	−1.00129	−0.0444252
$509$	−24.9502	−1.10590	−0.552948	−	0.833215i	$-0.686497\pi$
$509$	−24.9502	−1.10590	−0.552948	+	0.833215i	$0.686497\pi$
$510$	1.54021	0.0682017
$511$	25.6793	1.13599
$512$	−1.00000	−0.0441942
$513$	−6.85408	−0.302615
$514$	29.3198	1.29324
$515$	−1.42840	−0.0629426
$516$	2.65892	0.117053
$517$	−2.79238	−0.122809
$518$	22.2732	0.978626
$519$	−9.30906	−0.408623
$520$	−1.42840	−0.0626393
$521$	0.944534	0.0413808	0.0206904	−	0.999786i	$-0.493414\pi$
$521$	0.944534	0.0413808	0.0206904	+	0.999786i	$0.493414\pi$
$522$	5.09337	0.222931
$523$	37.5492	1.64191	0.820955	−	0.570993i	$-0.193442\pi$
$523$	37.5492	1.64191	0.820955	+	0.570993i	$0.193442\pi$
$524$	−7.05133	−0.308039
$525$	6.75288	0.294720
$526$	25.4645	1.11031
$527$	−11.1816	−0.487078
$528$	−0.378203	−0.0164592
$529$	−20.2839	−0.881907
$530$	−11.1290	−0.483411
$531$	−0.731526	−0.0317455
$532$	15.6384	0.678012
$533$	0.952622	0.0412626
$534$	5.26838	0.227985
$535$	−14.9967	−0.648363
$536$	9.03946	0.390445
$537$	6.22986	0.268839
$538$	23.3373	1.00614
$539$	0.678574	0.0292282
$540$	1.42840	0.0614684
$541$	−8.92867	−0.383874	−0.191937	−	0.981407i	$-0.561477\pi$
$541$	−8.92867	−0.383874	−0.191937	+	0.981407i	$0.561477\pi$
$542$	6.22070	0.267202
$543$	−5.27430	−0.226342
$544$	1.07828	0.0462309
$545$	1.22949	0.0526657
$546$	2.28162	0.0976444
$547$	1.16295	0.0497243	0.0248622	−	0.999691i	$-0.492085\pi$
$547$	1.16295	0.0497243	0.0248622	+	0.999691i	$0.492085\pi$
$548$	−6.33167	−0.270476
$549$	−4.05568	−0.173092
$550$	−1.11936	−0.0477297
$551$	34.9104	1.48723
$552$	1.64807	0.0701467
$553$	−11.9891	−0.509828
$554$	−10.9355	−0.464606
$555$	13.9440	0.591889
$556$	−15.7204	−0.666693
$557$	39.8724	1.68945	0.844723	−	0.535203i	$-0.179765\pi$
$557$	39.8724	1.68945	0.844723	+	0.535203i	$0.179765\pi$
$558$	−10.3699	−0.438991
$559$	2.65892	0.112460
$560$	−3.25906	−0.137720
$561$	0.407809	0.0172177
$562$	−16.4408	−0.693515
$563$	20.4700	0.862707	0.431353	−	0.902183i	$-0.358036\pi$
$563$	20.4700	0.862707	0.431353	+	0.902183i	$0.358036\pi$
$564$	7.38329	0.310893
$565$	−4.06571	−0.171046
$566$	−17.3544	−0.729458
$567$	−2.28162	−0.0958191
$568$	−3.02171	−0.126788
$569$	44.0758	1.84775	0.923876	−	0.382692i	$-0.125003\pi$
$569$	44.0758	1.84775	0.923876	+	0.382692i	$0.125003\pi$
$570$	9.79035	0.410072
$571$	−21.6029	−0.904053	−0.452026	−	0.892005i	$-0.649299\pi$
$571$	−21.6029	−0.904053	−0.452026	+	0.892005i	$0.649299\pi$
$572$	−0.378203	−0.0158135
$573$	−2.75574	−0.115123
$574$	2.17352	0.0907211
$575$	4.87778	0.203418
$576$	1.00000	0.0416667
$577$	−15.4529	−0.643314	−0.321657	−	0.946856i	$-0.604240\pi$
$577$	−15.4529	−0.643314	−0.321657	+	0.946856i	$0.604240\pi$
$578$	15.8373	0.658745
$579$	−6.08283	−0.252794
$580$	−7.27536	−0.302093
$581$	25.7394	1.06785
$582$	10.0419	0.416252
$583$	−2.94666	−0.122038
$584$	11.2549	0.465730
$585$	1.42840	0.0590569
$586$	−9.58413	−0.395917
$587$	36.1032	1.49014	0.745068	−	0.666988i	$-0.232417\pi$
$587$	36.1032	1.49014	0.745068	+	0.666988i	$0.232417\pi$
$588$	−1.79420	−0.0739918
$589$	−71.0758	−2.92863
$590$	1.04491	0.0430182
$591$	−10.1965	−0.419427
$592$	9.76199	0.401215
$593$	−1.69894	−0.0697669	−0.0348835	−	0.999391i	$-0.511106\pi$
$593$	−1.69894	−0.0697669	−0.0348835	+	0.999391i	$0.511106\pi$
$594$	0.378203	0.0155179
$595$	3.51418	0.144067
$596$	−10.5290	−0.431285
$597$	1.25424	0.0513326
$598$	1.64807	0.0673948
$599$	−20.6681	−0.844477	−0.422238	−	0.906485i	$-0.638755\pi$
$599$	−20.6681	−0.844477	−0.422238	+	0.906485i	$0.638755\pi$
$600$	2.95968	0.120829
$601$	2.38180	0.0971556	0.0485778	−	0.998819i	$-0.484531\pi$
$601$	2.38180	0.0971556	0.0485778	+	0.998819i	$0.484531\pi$
$602$	6.06665	0.247258
$603$	−9.03946	−0.368115
$604$	−5.65260	−0.230001
$605$	−15.5080	−0.630492
$606$	−6.99307	−0.284074
$607$	1.91188	0.0776006	0.0388003	−	0.999247i	$-0.487646\pi$
$607$	1.91188	0.0776006	0.0388003	+	0.999247i	$0.487646\pi$
$608$	6.85408	0.277970
$609$	11.6211	0.470913
$610$	5.79312	0.234557
$611$	7.38329	0.298696
$612$	−1.07828	−0.0435869
$613$	3.62282	0.146324	0.0731621	−	0.997320i	$-0.476691\pi$
$613$	3.62282	0.146324	0.0731621	+	0.997320i	$0.476691\pi$
$614$	12.5014	0.504517
$615$	1.36072	0.0548696
$616$	−0.862916	−0.0347679
$617$	15.5713	0.626876	0.313438	−	0.949609i	$-0.398519\pi$
$617$	15.5713	0.626876	0.313438	+	0.949609i	$0.398519\pi$
$618$	1.00000	0.0402259
$619$	3.00732	0.120874	0.0604371	−	0.998172i	$-0.480751\pi$
$619$	3.00732	0.120874	0.0604371	+	0.998172i	$0.480751\pi$
$620$	14.8123	0.594874
$621$	−1.64807	−0.0661350
$622$	26.1921	1.05021
$623$	12.0204	0.481589
$624$	1.00000	0.0400320
$625$	−1.44184	−0.0576737
$626$	−7.61225	−0.304247
$627$	2.59224	0.103524
$628$	13.3002	0.530736
$629$	−10.5262	−0.419705
$630$	3.25906	0.129844
$631$	−7.36563	−0.293221	−0.146610	−	0.989194i	$-0.546836\pi$
$631$	−7.36563	−0.293221	−0.146610	+	0.989194i	$0.546836\pi$
$632$	−5.25463	−0.209018
$633$	−16.2651	−0.646479
$634$	−7.73483	−0.307189
$635$	−1.43024	−0.0567575
$636$	7.79122	0.308942
$637$	−1.79420	−0.0710890
$638$	−1.92633	−0.0762641
$639$	3.02171	0.119537
$640$	−1.42840	−0.0564623
$641$	−38.7570	−1.53081	−0.765405	−	0.643549i	$-0.777461\pi$
$641$	−38.7570	−1.53081	−0.765405	+	0.643549i	$0.777461\pi$
$642$	10.4990	0.414361
$643$	8.06468	0.318040	0.159020	−	0.987275i	$-0.449167\pi$
$643$	8.06468	0.318040	0.159020	+	0.987275i	$0.449167\pi$
$644$	3.76028	0.148176
$645$	3.79799	0.149546
$646$	−7.39062	−0.290780
$647$	−19.2342	−0.756176	−0.378088	−	0.925770i	$-0.623418\pi$
$647$	−19.2342	−0.756176	−0.378088	+	0.925770i	$0.623418\pi$
$648$	−1.00000	−0.0392837
$649$	0.276665	0.0108601
$650$	2.95968	0.116088
$651$	−23.6601	−0.927311
$652$	−6.40325	−0.250771
$653$	−44.8678	−1.75581	−0.877906	−	0.478834i	$-0.841060\pi$
$653$	−44.8678	−1.75581	−0.877906	+	0.478834i	$0.841060\pi$
$654$	−0.860752	−0.0336580
$655$	−10.0721	−0.393549
$656$	0.952622	0.0371936
$657$	−11.2549	−0.439094
$658$	16.8459	0.656720
$659$	−7.62830	−0.297156	−0.148578	−	0.988901i	$-0.547470\pi$
$659$	−7.62830	−0.297156	−0.148578	+	0.988901i	$0.547470\pi$
$660$	−0.540224	−0.0210282
$661$	35.8892	1.39593	0.697963	−	0.716133i	$-0.254090\pi$
$661$	35.8892	1.39593	0.697963	+	0.716133i	$0.254090\pi$
$662$	−25.0994	−0.975516
$663$	−1.07828	−0.0418769
$664$	11.2812	0.437795
$665$	22.3379	0.866225
$666$	−9.76199	−0.378269
$667$	8.39426	0.325027
$668$	4.33757	0.167826
$669$	−21.2527	−0.821677
$670$	12.9119	0.498831
$671$	1.53387	0.0592144
$672$	2.28162	0.0880154
$673$	43.3613	1.67145	0.835727	−	0.549145i	$-0.185047\pi$
$673$	43.3613	1.67145	0.835727	+	0.549145i	$0.185047\pi$
$674$	13.9072	0.535687
$675$	−2.95968	−0.113918
$676$	1.00000	0.0384615
$677$	31.0734	1.19425	0.597125	−	0.802148i	$-0.296310\pi$
$677$	31.0734	1.19425	0.597125	+	0.802148i	$0.296310\pi$
$678$	2.84635	0.109313
$679$	22.9119	0.879278
$680$	1.54021	0.0590644
$681$	−25.4900	−0.976778
$682$	3.92191	0.150178
$683$	15.9518	0.610379	0.305190	−	0.952292i	$-0.401280\pi$
$683$	15.9518	0.610379	0.305190	+	0.952292i	$0.401280\pi$
$684$	−6.85408	−0.262072
$685$	−9.04413	−0.345559
$686$	−20.0650	−0.766087
$687$	25.8974	0.988047
$688$	2.65892	0.101370
$689$	7.79122	0.296822
$690$	2.35410	0.0896192
$691$	−21.3599	−0.812568	−0.406284	−	0.913747i	$-0.633176\pi$
$691$	−21.3599	−0.812568	−0.406284	+	0.913747i	$0.633176\pi$
$692$	−9.30906	−0.353878
$693$	0.862916	0.0327795
$694$	29.0558	1.10294
$695$	−22.4549	−0.851765
$696$	5.09337	0.193064
$697$	−1.02719	−0.0389077
$698$	−23.8454	−0.902563
$699$	−0.935399	−0.0353801
$700$	6.75288	0.255235
$701$	23.2980	0.879954	0.439977	−	0.898009i	$-0.354987\pi$
$701$	23.2980	0.879954	0.439977	+	0.898009i	$0.354987\pi$
$702$	−1.00000	−0.0377426
$703$	−66.9095	−2.52354
$704$	−0.378203	−0.0142541
$705$	10.5463	0.397195
$706$	−25.2391	−0.949886
$707$	−15.9555	−0.600069
$708$	−0.731526	−0.0274924
$709$	−18.2292	−0.684612	−0.342306	−	0.939589i	$-0.611208\pi$
$709$	−18.2292	−0.684612	−0.342306	+	0.939589i	$0.611208\pi$
$710$	−4.31620	−0.161984
$711$	5.25463	0.197064
$712$	5.26838	0.197441
$713$	−17.0903	−0.640036
$714$	−2.46023	−0.0920716
$715$	−0.540224	−0.0202032
$716$	6.22986	0.232821
$717$	−7.83371	−0.292555
$718$	10.1016	0.376989
$719$	−17.6809	−0.659388	−0.329694	−	0.944088i	$-0.606946\pi$
$719$	−17.6809	−0.659388	−0.329694	+	0.944088i	$0.606946\pi$
$720$	1.42840	0.0532332
$721$	2.28162	0.0849720
$722$	−27.9785	−1.04125
$723$	23.8091	0.885472
$724$	−5.27430	−0.196018
$725$	15.0748	0.559863
$726$	10.8570	0.402940
$727$	21.3312	0.791129	0.395564	−	0.918438i	$-0.370549\pi$
$727$	21.3312	0.791129	0.395564	+	0.918438i	$0.370549\pi$
$728$	2.28162	0.0845625
$729$	1.00000	0.0370370
$730$	16.0764	0.595014
$731$	−2.86706	−0.106042
$732$	−4.05568	−0.149902
$733$	−24.7459	−0.914010	−0.457005	−	0.889464i	$-0.651078\pi$
$733$	−24.7459	−0.914010	−0.457005	+	0.889464i	$0.651078\pi$
$734$	−7.36016	−0.271669
$735$	−2.56284	−0.0945316
$736$	1.64807	0.0607488
$737$	3.41875	0.125931
$738$	−0.952622	−0.0350665
$739$	−41.3679	−1.52174	−0.760871	−	0.648903i	$-0.775228\pi$
$739$	−41.3679	−1.52174	−0.760871	+	0.648903i	$0.775228\pi$
$740$	13.9440	0.512591
$741$	−6.85408	−0.251791
$742$	17.7766	0.652600
$743$	−11.8013	−0.432949	−0.216475	−	0.976288i	$-0.569456\pi$
$743$	−11.8013	−0.432949	−0.216475	+	0.976288i	$0.569456\pi$
$744$	−10.3699	−0.380177
$745$	−15.0396	−0.551008
$746$	11.0954	0.406230
$747$	−11.2812	−0.412757
$748$	0.407809	0.0149110
$749$	23.9547	0.875284
$750$	11.3696	0.415158
$751$	−40.1233	−1.46412	−0.732060	−	0.681240i	$-0.761441\pi$
$751$	−40.1233	−1.46412	−0.732060	+	0.681240i	$0.761441\pi$
$752$	7.38329	0.269241
$753$	−7.47104	−0.272260
$754$	5.09337	0.185490
$755$	−8.07415	−0.293848
$756$	−2.28162	−0.0829818
$757$	−6.41345	−0.233101	−0.116550	−	0.993185i	$-0.537184\pi$
$757$	−6.41345	−0.233101	−0.116550	+	0.993185i	$0.537184\pi$
$758$	−2.69689	−0.0979553
$759$	0.623307	0.0226246
$760$	9.79035	0.355133
$761$	−1.13877	−0.0412802	−0.0206401	−	0.999787i	$-0.506570\pi$
$761$	−1.13877	−0.0412802	−0.0206401	+	0.999787i	$0.506570\pi$
$762$	1.00129	0.0362730
$763$	−1.96391	−0.0710983
$764$	−2.75574	−0.0996993
$765$	−1.54021	−0.0556864
$766$	3.30815	0.119528
$767$	−0.731526	−0.0264139
$768$	1.00000	0.0360844
$769$	20.4055	0.735842	0.367921	−	0.929857i	$-0.380070\pi$
$769$	20.4055	0.735842	0.367921	+	0.929857i	$0.380070\pi$
$770$	−1.23259	−0.0444193
$771$	−29.3198	−1.05593
$772$	−6.08283	−0.218926
$773$	−18.8481	−0.677921	−0.338960	−	0.940801i	$-0.610075\pi$
$773$	−18.8481	−0.677921	−0.338960	+	0.940801i	$0.610075\pi$
$774$	−2.65892	−0.0955730
$775$	−30.6915	−1.10247
$776$	10.0419	0.360485
$777$	−22.2732	−0.799045
$778$	−23.1855	−0.831240
$779$	−6.52935	−0.233938
$780$	1.42840	0.0511448
$781$	−1.14282	−0.0408934
$782$	−1.77708	−0.0635484
$783$	−5.09337	−0.182022
$784$	−1.79420	−0.0640787
$785$	18.9980	0.678066
$786$	7.05133	0.251513
$787$	17.2663	0.615476	0.307738	−	0.951471i	$-0.400428\pi$
$787$	17.2663	0.615476	0.307738	+	0.951471i	$0.400428\pi$
$788$	−10.1965	−0.363234
$789$	−25.4645	−0.906562
$790$	−7.50570	−0.267041
$791$	6.49428	0.230910
$792$	0.378203	0.0134389
$793$	−4.05568	−0.144021
$794$	−32.2041	−1.14288
$795$	11.1290	0.394703
$796$	1.25424	0.0444554
$797$	−20.5117	−0.726561	−0.363280	−	0.931680i	$-0.618343\pi$
$797$	−20.5117	−0.726561	−0.363280	+	0.931680i	$0.618343\pi$
$798$	−15.6384	−0.553594
$799$	−7.96125	−0.281649
$800$	2.95968	0.104641
$801$	−5.26838	−0.186149
$802$	0.522173	0.0184386
$803$	4.25662	0.150213
$804$	−9.03946	−0.318797
$805$	5.37117	0.189309
$806$	−10.3699	−0.365262
$807$	−23.3373	−0.821512
$808$	−6.99307	−0.246015
$809$	1.44475	0.0507948	0.0253974	−	0.999677i	$-0.491915\pi$
$809$	1.44475	0.0507948	0.0253974	+	0.999677i	$0.491915\pi$
$810$	−1.42840	−0.0501887
$811$	21.9751	0.771651	0.385825	−	0.922572i	$-0.373917\pi$
$811$	21.9751	0.771651	0.385825	+	0.922572i	$0.373917\pi$
$812$	11.6211	0.407822
$813$	−6.22070	−0.218170
$814$	3.69201	0.129405
$815$	−9.14638	−0.320384
$816$	−1.07828	−0.0377473
$817$	−18.2245	−0.637594
$818$	−28.7704	−1.00593
$819$	−2.28162	−0.0797263
$820$	1.36072	0.0475185
$821$	36.6375	1.27866	0.639329	−	0.768934i	$-0.279212\pi$
$821$	36.6375	1.27866	0.639329	+	0.768934i	$0.279212\pi$
$822$	6.33167	0.220842
$823$	45.4973	1.58594	0.792969	−	0.609262i	$-0.208534\pi$
$823$	45.4973	1.58594	0.792969	+	0.609262i	$0.208534\pi$
$824$	1.00000	0.0348367
$825$	1.11936	0.0389712
$826$	−1.66907	−0.0580742
$827$	26.1671	0.909921	0.454960	−	0.890512i	$-0.349653\pi$
$827$	26.1671	0.909921	0.454960	+	0.890512i	$0.349653\pi$
$828$	−1.64807	−0.0572746
$829$	−44.0402	−1.52958	−0.764790	−	0.644279i	$-0.777158\pi$
$829$	−44.0402	−1.52958	−0.764790	+	0.644279i	$0.777158\pi$
$830$	16.1140	0.559326
$831$	10.9355	0.379350
$832$	1.00000	0.0346688
$833$	1.93465	0.0670318
$834$	15.7204	0.544353
$835$	6.19576	0.214413
$836$	2.59224	0.0896543
$837$	10.3699	0.358434
$838$	37.5198	1.29610
$839$	−3.26703	−0.112790	−0.0563952	−	0.998409i	$-0.517961\pi$
$839$	−3.26703	−0.112790	−0.0563952	+	0.998409i	$0.517961\pi$
$840$	3.25906	0.112448
$841$	−3.05754	−0.105433
$842$	−2.98562	−0.102891
$843$	16.4408	0.566252
$844$	−16.2651	−0.559867
$845$	1.42840	0.0491383
$846$	−7.38329	−0.253843
$847$	24.7715	0.851158
$848$	7.79122	0.267552
$849$	17.3544	0.595600
$850$	−3.19137	−0.109463
$851$	−16.0885	−0.551506
$852$	3.02171	0.103522
$853$	53.1514	1.81987	0.909935	−	0.414751i	$-0.136131\pi$
$853$	53.1514	1.81987	0.909935	+	0.414751i	$0.136131\pi$
$854$	−9.25353	−0.316649
$855$	−9.79035	−0.334823
$856$	10.4990	0.358847
$857$	25.3084	0.864519	0.432259	−	0.901749i	$-0.357717\pi$
$857$	25.3084	0.864519	0.432259	+	0.901749i	$0.357717\pi$
$858$	0.378203	0.0129116
$859$	−29.3493	−1.00138	−0.500692	−	0.865625i	$-0.666921\pi$
$859$	−29.3493	−1.00138	−0.500692	+	0.865625i	$0.666921\pi$
$860$	3.79799	0.129511
$861$	−2.17352	−0.0740735
$862$	11.3097	0.385210
$863$	−41.2065	−1.40268	−0.701342	−	0.712825i	$-0.747415\pi$
$863$	−41.2065	−1.40268	−0.701342	+	0.712825i	$0.747415\pi$
$864$	−1.00000	−0.0340207
$865$	−13.2970	−0.452113
$866$	2.35879	0.0801549
$867$	−15.8373	−0.537863
$868$	−23.6601	−0.803075
$869$	−1.98732	−0.0674152
$870$	7.27536	0.246658
$871$	−9.03946	−0.306290
$872$	−0.860752	−0.0291487
$873$	−10.0419	−0.339868
$874$	−11.2960	−0.382094
$875$	25.9411	0.876969
$876$	−11.2549	−0.380267
$877$	23.5574	0.795477	0.397738	−	0.917499i	$-0.369795\pi$
$877$	23.5574	0.795477	0.397738	+	0.917499i	$0.369795\pi$
$878$	−26.2481	−0.885829
$879$	9.58413	0.323265
$880$	−0.540224	−0.0182109
$881$	−13.5194	−0.455481	−0.227741	−	0.973722i	$-0.573134\pi$
$881$	−13.5194	−0.455481	−0.227741	+	0.973722i	$0.573134\pi$
$882$	1.79420	0.0604140
$883$	51.2268	1.72392	0.861959	−	0.506978i	$-0.169237\pi$
$883$	51.2268	1.72392	0.861959	+	0.506978i	$0.169237\pi$
$884$	−1.07828	−0.0362665
$885$	−1.04491	−0.0351242
$886$	−6.78372	−0.227903
$887$	7.59434	0.254993	0.127496	−	0.991839i	$-0.459306\pi$
$887$	7.59434	0.254993	0.127496	+	0.991839i	$0.459306\pi$
$888$	−9.76199	−0.327591
$889$	2.28457	0.0766221
$890$	7.52533	0.252250
$891$	−0.378203	−0.0126703
$892$	−21.2527	−0.711593
$893$	−50.6057	−1.69345
$894$	10.5290	0.352143
$895$	8.89871	0.297451
$896$	2.28162	0.0762236
$897$	−1.64807	−0.0550276
$898$	−37.5659	−1.25359
$899$	−52.8175	−1.76156
$900$	−2.95968	−0.0986562
$901$	−8.40112	−0.279882
$902$	0.360285	0.0119962
$903$	−6.06665	−0.201886
$904$	2.84635	0.0946681
$905$	−7.53379	−0.250432
$906$	5.65260	0.187795
$907$	−50.9773	−1.69267	−0.846336	−	0.532649i	$-0.821196\pi$
$907$	−50.9773	−1.69267	−0.846336	+	0.532649i	$0.821196\pi$
$908$	−25.4900	−0.845914
$909$	6.99307	0.231945
$910$	3.25906	0.108037
$911$	−19.8064	−0.656216	−0.328108	−	0.944640i	$-0.606411\pi$
$911$	−19.8064	−0.656216	−0.328108	+	0.944640i	$0.606411\pi$
$912$	−6.85408	−0.226961
$913$	4.26658	0.141203
$914$	7.90872	0.261597
$915$	−5.79312	−0.191515
$916$	25.8974	0.855674
$917$	16.0885	0.531288
$918$	1.07828	0.0355885
$919$	−54.6613	−1.80311	−0.901555	−	0.432666i	$-0.857573\pi$
$919$	−54.6613	−1.80311	−0.901555	+	0.432666i	$0.857573\pi$
$920$	2.35410	0.0776125
$921$	−12.5014	−0.411936
$922$	−0.520571	−0.0171441
$923$	3.02171	0.0994609
$924$	0.862916	0.0283879
$925$	−28.8924	−0.949976
$926$	9.28449	0.305107
$927$	−1.00000	−0.0328443
$928$	5.09337	0.167198
$929$	−33.8676	−1.11116	−0.555580	−	0.831463i	$-0.687504\pi$
$929$	−33.8676	−1.11116	−0.555580	+	0.831463i	$0.687504\pi$
$930$	−14.8123	−0.485713
$931$	12.2976	0.403039
$932$	−0.935399	−0.0306400
$933$	−26.1921	−0.857491
$934$	0.410904	0.0134452
$935$	0.582512	0.0190502
$936$	−1.00000	−0.0326860
$937$	−26.9085	−0.879062	−0.439531	−	0.898227i	$-0.644855\pi$
$937$	−26.9085	−0.879062	−0.439531	+	0.898227i	$0.644855\pi$
$938$	−20.6246	−0.673418
$939$	7.61225	0.248416
$940$	10.5463	0.343981
$941$	7.77064	0.253316	0.126658	−	0.991946i	$-0.459575\pi$
$941$	7.77064	0.253316	0.126658	+	0.991946i	$0.459575\pi$
$942$	−13.3002	−0.433344
$943$	−1.56999	−0.0511260
$944$	−0.731526	−0.0238091
$945$	−3.25906	−0.106017
$946$	1.00561	0.0326953
$947$	−0.0677911	−0.00220291	−0.00110146	−	0.999999i	$-0.500351\pi$
$947$	−0.0677911	−0.00220291	−0.00110146	+	0.999999i	$0.500351\pi$
$948$	5.25463	0.170663
$949$	−11.2549	−0.365348
$950$	−20.2859	−0.658162
$951$	7.73483	0.250819
$952$	−2.46023	−0.0797364
$953$	1.00211	0.0324615	0.0162308	−	0.999868i	$-0.494833\pi$
$953$	1.00211	0.0324615	0.0162308	+	0.999868i	$0.494833\pi$
$954$	−7.79122	−0.252250
$955$	−3.93629	−0.127375
$956$	−7.83371	−0.253360
$957$	1.92633	0.0622694
$958$	35.7133	1.15384
$959$	14.4465	0.466501
$960$	1.42840	0.0461013
$961$	76.5338	2.46883
$962$	−9.76199	−0.314739
$963$	−10.4990	−0.338324
$964$	23.8091	0.766841
$965$	−8.68869	−0.279699
$966$	−3.76028	−0.120985
$967$	−17.9495	−0.577218	−0.288609	−	0.957447i	$-0.593193\pi$
$967$	−17.9495	−0.577218	−0.288609	+	0.957447i	$0.593193\pi$
$968$	10.8570	0.348956
$969$	7.39062	0.237421
$970$	14.3439	0.460554
$971$	−12.1550	−0.390072	−0.195036	−	0.980796i	$-0.562482\pi$
$971$	−12.1550	−0.390072	−0.195036	+	0.980796i	$0.562482\pi$
$972$	1.00000	0.0320750
$973$	35.8680	1.14987
$974$	−9.35930	−0.299891
$975$	−2.95968	−0.0947858
$976$	−4.05568	−0.129819
$977$	−9.80531	−0.313700	−0.156850	−	0.987622i	$-0.550134\pi$
$977$	−9.80531	−0.313700	−0.156850	+	0.987622i	$0.550134\pi$
$978$	6.40325	0.204753
$979$	1.99252	0.0636811
$980$	−2.56284	−0.0818668
$981$	0.860752	0.0274817
$982$	24.5502	0.783427
$983$	27.1478	0.865880	0.432940	−	0.901423i	$-0.357476\pi$
$983$	27.1478	0.865880	0.432940	+	0.901423i	$0.357476\pi$
$984$	−0.952622	−0.0303685
$985$	−14.5646	−0.464067
$986$	−5.49208	−0.174903
$987$	−16.8459	−0.536210
$988$	−6.85408	−0.218057
$989$	−4.38210	−0.139343
$990$	0.540224	0.0171694
$991$	53.6231	1.70339	0.851697	−	0.524035i	$-0.175574\pi$
$991$	53.6231	1.70339	0.851697	+	0.524035i	$0.175574\pi$
$992$	−10.3699	−0.329243
$993$	25.0994	0.796505
$994$	6.89441	0.218677
$995$	1.79155	0.0567960
$996$	−11.2812	−0.357458
$997$	−32.0001	−1.01345	−0.506727	−	0.862106i	$-0.669145\pi$
$997$	−32.0001	−1.01345	−0.506727	+	0.862106i	$0.669145\pi$
$998$	−0.932509	−0.0295181
$999$	9.76199	0.308856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.w.1.9	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.w.1.9	✓	12	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.42840 q^{5} -1.00000 q^{6} -2.28162 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.42840 q^{5} -1.00000 q^{6} -2.28162 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.42840 q^{10} -0.378203 q^{11} +1.00000 q^{12} +1.00000 q^{13} +2.28162 q^{14} +1.42840 q^{15} +1.00000 q^{16} -1.07828 q^{17} -1.00000 q^{18} -6.85408 q^{19} +1.42840 q^{20} -2.28162 q^{21} +0.378203 q^{22} -1.64807 q^{23} -1.00000 q^{24} -2.95968 q^{25} -1.00000 q^{26} +1.00000 q^{27} -2.28162 q^{28} -5.09337 q^{29} -1.42840 q^{30} +10.3699 q^{31} -1.00000 q^{32} -0.378203 q^{33} +1.07828 q^{34} -3.25906 q^{35} +1.00000 q^{36} +9.76199 q^{37} +6.85408 q^{38} +1.00000 q^{39} -1.42840 q^{40} +0.952622 q^{41} +2.28162 q^{42} +2.65892 q^{43} -0.378203 q^{44} +1.42840 q^{45} +1.64807 q^{46} +7.38329 q^{47} +1.00000 q^{48} -1.79420 q^{49} +2.95968 q^{50} -1.07828 q^{51} +1.00000 q^{52} +7.79122 q^{53} -1.00000 q^{54} -0.540224 q^{55} +2.28162 q^{56} -6.85408 q^{57} +5.09337 q^{58} -0.731526 q^{59} +1.42840 q^{60} -4.05568 q^{61} -10.3699 q^{62} -2.28162 q^{63} +1.00000 q^{64} +1.42840 q^{65} +0.378203 q^{66} -9.03946 q^{67} -1.07828 q^{68} -1.64807 q^{69} +3.25906 q^{70} +3.02171 q^{71} -1.00000 q^{72} -11.2549 q^{73} -9.76199 q^{74} -2.95968 q^{75} -6.85408 q^{76} +0.862916 q^{77} -1.00000 q^{78} +5.25463 q^{79} +1.42840 q^{80} +1.00000 q^{81} -0.952622 q^{82} -11.2812 q^{83} -2.28162 q^{84} -1.54021 q^{85} -2.65892 q^{86} -5.09337 q^{87} +0.378203 q^{88} -5.26838 q^{89} -1.42840 q^{90} -2.28162 q^{91} -1.64807 q^{92} +10.3699 q^{93} -7.38329 q^{94} -9.79035 q^{95} -1.00000 q^{96} -10.0419 q^{97} +1.79420 q^{98} -0.378203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * q^99

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