LMFDB - Embedded newform 8034.2.a.bc.1.15

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:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 48 x^{13} + 44 x^{12} + 872 x^{11} - 707 x^{10} - 7580 x^{9} + 5112 x^{8} + \cdots + 2048 $ x^15 - x^14 - 48x^13 + 44x^12 + 872x^11 - 707x^10 - 7580x^9 + 5112x^8 + 33191x^7 - 16428x^6 - 71361x^5 + 21747x^4 + 65434x^3 - 11840x^2 - 17600*x + 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-4.10857$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.10857 q^{5} -1.00000 q^{6} +1.08136 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.10857 q^{5} -1.00000 q^{6} +1.08136 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.10857 q^{10} +1.94311 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.08136 q^{14} -4.10857 q^{15} +1.00000 q^{16} +3.29001 q^{17} +1.00000 q^{18} +5.56641 q^{19} +4.10857 q^{20} -1.08136 q^{21} +1.94311 q^{22} +4.23927 q^{23} -1.00000 q^{24} +11.8804 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.08136 q^{28} +5.73866 q^{29} -4.10857 q^{30} -9.76349 q^{31} +1.00000 q^{32} -1.94311 q^{33} +3.29001 q^{34} +4.44286 q^{35} +1.00000 q^{36} -0.721621 q^{37} +5.56641 q^{38} +1.00000 q^{39} +4.10857 q^{40} +2.73623 q^{41} -1.08136 q^{42} -1.00708 q^{43} +1.94311 q^{44} +4.10857 q^{45} +4.23927 q^{46} -7.53102 q^{47} -1.00000 q^{48} -5.83065 q^{49} +11.8804 q^{50} -3.29001 q^{51} -1.00000 q^{52} +6.31473 q^{53} -1.00000 q^{54} +7.98340 q^{55} +1.08136 q^{56} -5.56641 q^{57} +5.73866 q^{58} +5.34007 q^{59} -4.10857 q^{60} -9.12177 q^{61} -9.76349 q^{62} +1.08136 q^{63} +1.00000 q^{64} -4.10857 q^{65} -1.94311 q^{66} -3.91535 q^{67} +3.29001 q^{68} -4.23927 q^{69} +4.44286 q^{70} -3.70178 q^{71} +1.00000 q^{72} -12.7190 q^{73} -0.721621 q^{74} -11.8804 q^{75} +5.56641 q^{76} +2.10121 q^{77} +1.00000 q^{78} +7.86754 q^{79} +4.10857 q^{80} +1.00000 q^{81} +2.73623 q^{82} -11.0081 q^{83} -1.08136 q^{84} +13.5172 q^{85} -1.00708 q^{86} -5.73866 q^{87} +1.94311 q^{88} +3.37812 q^{89} +4.10857 q^{90} -1.08136 q^{91} +4.23927 q^{92} +9.76349 q^{93} -7.53102 q^{94} +22.8700 q^{95} -1.00000 q^{96} -3.56041 q^{97} -5.83065 q^{98} +1.94311 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * 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
$5$	4.10857	1.83741	0.918704	−	0.394946i	$-0.129237\pi$
$5$	4.10857	1.83741	0.918704	+	0.394946i	$0.129237\pi$
$6$	−1.00000	−0.408248
$7$	1.08136	0.408717	0.204359	−	0.978896i	$-0.434489\pi$
$7$	1.08136	0.408717	0.204359	+	0.978896i	$0.434489\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	4.10857	1.29924
$11$	1.94311	0.585870	0.292935	−	0.956132i	$-0.405368\pi$
$11$	1.94311	0.585870	0.292935	+	0.956132i	$0.405368\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.08136	0.289007
$15$	−4.10857	−1.06083
$16$	1.00000	0.250000
$17$	3.29001	0.797944	0.398972	−	0.916963i	$-0.369367\pi$
$17$	3.29001	0.797944	0.398972	+	0.916963i	$0.369367\pi$
$18$	1.00000	0.235702
$19$	5.56641	1.27702	0.638511	−	0.769613i	$-0.279551\pi$
$19$	5.56641	1.27702	0.638511	+	0.769613i	$0.279551\pi$
$20$	4.10857	0.918704
$21$	−1.08136	−0.235973
$22$	1.94311	0.414272
$23$	4.23927	0.883949	0.441974	−	0.897028i	$-0.354278\pi$
$23$	4.23927	0.883949	0.441974	+	0.897028i	$0.354278\pi$
$24$	−1.00000	−0.204124
$25$	11.8804	2.37607
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.08136	0.204359
$29$	5.73866	1.06564	0.532821	−	0.846228i	$-0.321132\pi$
$29$	5.73866	1.06564	0.532821	+	0.846228i	$0.321132\pi$
$30$	−4.10857	−0.750119
$31$	−9.76349	−1.75358	−0.876788	−	0.480878i	$-0.840318\pi$
$31$	−9.76349	−1.75358	−0.876788	+	0.480878i	$0.840318\pi$
$32$	1.00000	0.176777
$33$	−1.94311	−0.338252
$34$	3.29001	0.564231
$35$	4.44286	0.750980
$36$	1.00000	0.166667
$37$	−0.721621	−0.118634	−0.0593168	−	0.998239i	$-0.518892\pi$
$37$	−0.721621	−0.118634	−0.0593168	+	0.998239i	$0.518892\pi$
$38$	5.56641	0.902990
$39$	1.00000	0.160128
$40$	4.10857	0.649622
$41$	2.73623	0.427327	0.213663	−	0.976907i	$-0.431460\pi$
$41$	2.73623	0.427327	0.213663	+	0.976907i	$0.431460\pi$
$42$	−1.08136	−0.166858
$43$	−1.00708	−0.153579	−0.0767895	−	0.997047i	$-0.524467\pi$
$43$	−1.00708	−0.153579	−0.0767895	+	0.997047i	$0.524467\pi$
$44$	1.94311	0.292935
$45$	4.10857	0.612470
$46$	4.23927	0.625046
$47$	−7.53102	−1.09851	−0.549256	−	0.835654i	$-0.685089\pi$
$47$	−7.53102	−1.09851	−0.549256	+	0.835654i	$0.685089\pi$
$48$	−1.00000	−0.144338
$49$	−5.83065	−0.832950
$50$	11.8804	1.68014
$51$	−3.29001	−0.460693
$52$	−1.00000	−0.138675
$53$	6.31473	0.867395	0.433697	−	0.901059i	$-0.357209\pi$
$53$	6.31473	0.867395	0.433697	+	0.901059i	$0.357209\pi$
$54$	−1.00000	−0.136083
$55$	7.98340	1.07648
$56$	1.08136	0.144503
$57$	−5.56641	−0.737289
$58$	5.73866	0.753523
$59$	5.34007	0.695218	0.347609	−	0.937640i	$-0.386994\pi$
$59$	5.34007	0.695218	0.347609	+	0.937640i	$0.386994\pi$
$60$	−4.10857	−0.530414
$61$	−9.12177	−1.16792	−0.583962	−	0.811781i	$-0.698498\pi$
$61$	−9.12177	−1.16792	−0.583962	+	0.811781i	$0.698498\pi$
$62$	−9.76349	−1.23996
$63$	1.08136	0.136239
$64$	1.00000	0.125000
$65$	−4.10857	−0.509605
$66$	−1.94311	−0.239180
$67$	−3.91535	−0.478336	−0.239168	−	0.970978i	$-0.576875\pi$
$67$	−3.91535	−0.478336	−0.239168	+	0.970978i	$0.576875\pi$
$68$	3.29001	0.398972
$69$	−4.23927	−0.510348
$70$	4.44286	0.531023
$71$	−3.70178	−0.439320	−0.219660	−	0.975576i	$-0.570495\pi$
$71$	−3.70178	−0.439320	−0.219660	+	0.975576i	$0.570495\pi$
$72$	1.00000	0.117851
$73$	−12.7190	−1.48864	−0.744320	−	0.667823i	$-0.767226\pi$
$73$	−12.7190	−1.48864	−0.744320	+	0.667823i	$0.767226\pi$
$74$	−0.721621	−0.0838867
$75$	−11.8804	−1.37182
$76$	5.56641	0.638511
$77$	2.10121	0.239455
$78$	1.00000	0.113228
$79$	7.86754	0.885168	0.442584	−	0.896727i	$-0.354062\pi$
$79$	7.86754	0.885168	0.442584	+	0.896727i	$0.354062\pi$
$80$	4.10857	0.459352
$81$	1.00000	0.111111
$82$	2.73623	0.302166
$83$	−11.0081	−1.20830	−0.604148	−	0.796872i	$-0.706487\pi$
$83$	−11.0081	−1.20830	−0.604148	+	0.796872i	$0.706487\pi$
$84$	−1.08136	−0.117986
$85$	13.5172	1.46615
$86$	−1.00708	−0.108597
$87$	−5.73866	−0.615249
$88$	1.94311	0.207136
$89$	3.37812	0.358080	0.179040	−	0.983842i	$-0.442701\pi$
$89$	3.37812	0.358080	0.179040	+	0.983842i	$0.442701\pi$
$90$	4.10857	0.433081
$91$	−1.08136	−0.113358
$92$	4.23927	0.441974
$93$	9.76349	1.01243
$94$	−7.53102	−0.776766
$95$	22.8700	2.34641
$96$	−1.00000	−0.102062
$97$	−3.56041	−0.361505	−0.180753	−	0.983529i	$-0.557853\pi$
$97$	−3.56041	−0.361505	−0.180753	+	0.983529i	$0.557853\pi$
$98$	−5.83065	−0.588985
$99$	1.94311	0.195290
$100$	11.8804	1.18804
$101$	−6.29949	−0.626822	−0.313411	−	0.949618i	$-0.601472\pi$
$101$	−6.29949	−0.626822	−0.313411	+	0.949618i	$0.601472\pi$
$102$	−3.29001	−0.325759
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−4.44286	−0.433579
$106$	6.31473	0.613341
$107$	0.737374	0.0712846	0.0356423	−	0.999365i	$-0.488652\pi$
$107$	0.737374	0.0712846	0.0356423	+	0.999365i	$0.488652\pi$
$108$	−1.00000	−0.0962250
$109$	7.22763	0.692282	0.346141	−	0.938183i	$-0.387492\pi$
$109$	7.22763	0.692282	0.346141	+	0.938183i	$0.387492\pi$
$110$	7.98340	0.761188
$111$	0.721621	0.0684932
$112$	1.08136	0.102179
$113$	−0.412595	−0.0388137	−0.0194068	−	0.999812i	$-0.506178\pi$
$113$	−0.412595	−0.0388137	−0.0194068	+	0.999812i	$0.506178\pi$
$114$	−5.56641	−0.521342
$115$	17.4173	1.62418
$116$	5.73866	0.532821
$117$	−1.00000	−0.0924500
$118$	5.34007	0.491593
$119$	3.55769	0.326133
$120$	−4.10857	−0.375059
$121$	−7.22432	−0.656757
$122$	−9.12177	−0.825847
$123$	−2.73623	−0.246717
$124$	−9.76349	−0.876788
$125$	28.2684	2.52840
$126$	1.08136	0.0963356
$127$	8.14381	0.722646	0.361323	−	0.932441i	$-0.382325\pi$
$127$	8.14381	0.722646	0.361323	+	0.932441i	$0.382325\pi$
$128$	1.00000	0.0883883
$129$	1.00708	0.0886689
$130$	−4.10857	−0.360345
$131$	−1.82445	−0.159403	−0.0797014	−	0.996819i	$-0.525397\pi$
$131$	−1.82445	−0.159403	−0.0797014	+	0.996819i	$0.525397\pi$
$132$	−1.94311	−0.169126
$133$	6.01931	0.521941
$134$	−3.91535	−0.338235
$135$	−4.10857	−0.353609
$136$	3.29001	0.282116
$137$	16.2132	1.38518	0.692592	−	0.721330i	$-0.256469\pi$
$137$	16.2132	1.38518	0.692592	+	0.721330i	$0.256469\pi$
$138$	−4.23927	−0.360871
$139$	−15.7184	−1.33321	−0.666607	−	0.745410i	$-0.732254\pi$
$139$	−15.7184	−1.33321	−0.666607	+	0.745410i	$0.732254\pi$
$140$	4.44286	0.375490
$141$	7.53102	0.634227
$142$	−3.70178	−0.310646
$143$	−1.94311	−0.162491
$144$	1.00000	0.0833333
$145$	23.5777	1.95802
$146$	−12.7190	−1.05263
$147$	5.83065	0.480904
$148$	−0.721621	−0.0593168
$149$	3.39227	0.277906	0.138953	−	0.990299i	$-0.455626\pi$
$149$	3.39227	0.277906	0.138953	+	0.990299i	$0.455626\pi$
$150$	−11.8804	−0.970027
$151$	−1.86945	−0.152134	−0.0760670	−	0.997103i	$-0.524236\pi$
$151$	−1.86945	−0.152134	−0.0760670	+	0.997103i	$0.524236\pi$
$152$	5.56641	0.451495
$153$	3.29001	0.265981
$154$	2.10121	0.169320
$155$	−40.1140	−3.22203
$156$	1.00000	0.0800641
$157$	2.95582	0.235900	0.117950	−	0.993020i	$-0.462368\pi$
$157$	2.95582	0.235900	0.117950	+	0.993020i	$0.462368\pi$
$158$	7.86754	0.625908
$159$	−6.31473	−0.500791
$160$	4.10857	0.324811
$161$	4.58419	0.361285
$162$	1.00000	0.0785674
$163$	−6.68930	−0.523946	−0.261973	−	0.965075i	$-0.584373\pi$
$163$	−6.68930	−0.523946	−0.261973	+	0.965075i	$0.584373\pi$
$164$	2.73623	0.213663
$165$	−7.98340	−0.621507
$166$	−11.0081	−0.854395
$167$	−5.25050	−0.406296	−0.203148	−	0.979148i	$-0.565117\pi$
$167$	−5.25050	−0.406296	−0.203148	+	0.979148i	$0.565117\pi$
$168$	−1.08136	−0.0834290
$169$	1.00000	0.0769231
$170$	13.5172	1.03672
$171$	5.56641	0.425674
$172$	−1.00708	−0.0767895
$173$	−8.82486	−0.670941	−0.335471	−	0.942051i	$-0.608895\pi$
$173$	−8.82486	−0.670941	−0.335471	+	0.942051i	$0.608895\pi$
$174$	−5.73866	−0.435047
$175$	12.8470	0.971141
$176$	1.94311	0.146467
$177$	−5.34007	−0.401384
$178$	3.37812	0.253201
$179$	1.87031	0.139793	0.0698966	−	0.997554i	$-0.477733\pi$
$179$	1.87031	0.139793	0.0698966	+	0.997554i	$0.477733\pi$
$180$	4.10857	0.306235
$181$	−21.6013	−1.60561	−0.802806	−	0.596241i	$-0.796660\pi$
$181$	−21.6013	−1.60561	−0.802806	+	0.596241i	$0.796660\pi$
$182$	−1.08136	−0.0801560
$183$	9.12177	0.674301
$184$	4.23927	0.312523
$185$	−2.96483	−0.217979
$186$	9.76349	0.715894
$187$	6.39284	0.467491
$188$	−7.53102	−0.549256
$189$	−1.08136	−0.0786577
$190$	22.8700	1.65916
$191$	−17.5991	−1.27342	−0.636712	−	0.771102i	$-0.719706\pi$
$191$	−17.5991	−1.27342	−0.636712	+	0.771102i	$0.719706\pi$
$192$	−1.00000	−0.0721688
$193$	−7.66750	−0.551919	−0.275959	−	0.961169i	$-0.588996\pi$
$193$	−7.66750	−0.551919	−0.275959	+	0.961169i	$0.588996\pi$
$194$	−3.56041	−0.255623
$195$	4.10857	0.294221
$196$	−5.83065	−0.416475
$197$	12.4756	0.888849	0.444424	−	0.895816i	$-0.353408\pi$
$197$	12.4756	0.888849	0.444424	+	0.895816i	$0.353408\pi$
$198$	1.94311	0.138091
$199$	3.77199	0.267389	0.133695	−	0.991023i	$-0.457316\pi$
$199$	3.77199	0.267389	0.133695	+	0.991023i	$0.457316\pi$
$200$	11.8804	0.840068
$201$	3.91535	0.276167
$202$	−6.29949	−0.443230
$203$	6.20558	0.435546
$204$	−3.29001	−0.230346
$205$	11.2420	0.785174
$206$	−1.00000	−0.0696733
$207$	4.23927	0.294650
$208$	−1.00000	−0.0693375
$209$	10.8161	0.748168
$210$	−4.44286	−0.306586
$211$	−11.0391	−0.759966	−0.379983	−	0.924993i	$-0.624070\pi$
$211$	−11.0391	−0.759966	−0.379983	+	0.924993i	$0.624070\pi$
$212$	6.31473	0.433697
$213$	3.70178	0.253642
$214$	0.737374	0.0504058
$215$	−4.13768	−0.282187
$216$	−1.00000	−0.0680414
$217$	−10.5579	−0.716716
$218$	7.22763	0.489517
$219$	12.7190	0.859467
$220$	7.98340	0.538241
$221$	−3.29001	−0.221310
$222$	0.721621	0.0484320
$223$	−19.7509	−1.32262	−0.661308	−	0.750115i	$-0.729998\pi$
$223$	−19.7509	−1.32262	−0.661308	+	0.750115i	$0.729998\pi$
$224$	1.08136	0.0722517
$225$	11.8804	0.792023
$226$	−0.412595	−0.0274454
$227$	−15.9220	−1.05678	−0.528389	−	0.849003i	$-0.677204\pi$
$227$	−15.9220	−1.05678	−0.528389	+	0.849003i	$0.677204\pi$
$228$	−5.56641	−0.368644
$229$	14.3924	0.951074	0.475537	−	0.879696i	$-0.342254\pi$
$229$	14.3924	0.951074	0.475537	+	0.879696i	$0.342254\pi$
$230$	17.4173	1.14847
$231$	−2.10121	−0.138249
$232$	5.73866	0.376762
$233$	21.0680	1.38021	0.690105	−	0.723709i	$-0.257564\pi$
$233$	21.0680	1.38021	0.690105	+	0.723709i	$0.257564\pi$
$234$	−1.00000	−0.0653720
$235$	−30.9417	−2.01842
$236$	5.34007	0.347609
$237$	−7.86754	−0.511052
$238$	3.55769	0.230611
$239$	24.6679	1.59563	0.797816	−	0.602900i	$-0.205988\pi$
$239$	24.6679	1.59563	0.797816	+	0.602900i	$0.205988\pi$
$240$	−4.10857	−0.265207
$241$	12.8439	0.827350	0.413675	−	0.910425i	$-0.364245\pi$
$241$	12.8439	0.827350	0.413675	+	0.910425i	$0.364245\pi$
$242$	−7.22432	−0.464397
$243$	−1.00000	−0.0641500
$244$	−9.12177	−0.583962
$245$	−23.9556	−1.53047
$246$	−2.73623	−0.174455
$247$	−5.56641	−0.354182
$248$	−9.76349	−0.619982
$249$	11.0081	0.697610
$250$	28.2684	1.78785
$251$	−24.4841	−1.54543	−0.772713	−	0.634756i	$-0.781101\pi$
$251$	−24.4841	−1.54543	−0.772713	+	0.634756i	$0.781101\pi$
$252$	1.08136	0.0681195
$253$	8.23737	0.517879
$254$	8.14381	0.510988
$255$	−13.5172	−0.846481
$256$	1.00000	0.0625000
$257$	3.27567	0.204330	0.102165	−	0.994767i	$-0.467423\pi$
$257$	3.27567	0.204330	0.102165	+	0.994767i	$0.467423\pi$
$258$	1.00708	0.0626984
$259$	−0.780335	−0.0484876
$260$	−4.10857	−0.254803
$261$	5.73866	0.355214
$262$	−1.82445	−0.112715
$263$	8.28156	0.510663	0.255331	−	0.966854i	$-0.417815\pi$
$263$	8.28156	0.510663	0.255331	+	0.966854i	$0.417815\pi$
$264$	−1.94311	−0.119590
$265$	25.9445	1.59376
$266$	6.01931	0.369068
$267$	−3.37812	−0.206738
$268$	−3.91535	−0.239168
$269$	20.5589	1.25350	0.626749	−	0.779221i	$-0.284385\pi$
$269$	20.5589	1.25350	0.626749	+	0.779221i	$0.284385\pi$
$270$	−4.10857	−0.250040
$271$	−11.0715	−0.672544	−0.336272	−	0.941765i	$-0.609166\pi$
$271$	−11.0715	−0.672544	−0.336272	+	0.941765i	$0.609166\pi$
$272$	3.29001	0.199486
$273$	1.08136	0.0654471
$274$	16.2132	0.979473
$275$	23.0848	1.39207
$276$	−4.23927	−0.255174
$277$	−28.3155	−1.70131	−0.850656	−	0.525723i	$-0.823795\pi$
$277$	−28.3155	−1.70131	−0.850656	+	0.525723i	$0.823795\pi$
$278$	−15.7184	−0.942724
$279$	−9.76349	−0.584525
$280$	4.44286	0.265512
$281$	24.4791	1.46030	0.730152	−	0.683285i	$-0.239449\pi$
$281$	24.4791	1.46030	0.730152	+	0.683285i	$0.239449\pi$
$282$	7.53102	0.448466
$283$	1.81030	0.107611	0.0538055	−	0.998551i	$-0.482865\pi$
$283$	1.81030	0.107611	0.0538055	+	0.998551i	$0.482865\pi$
$284$	−3.70178	−0.219660
$285$	−22.8700	−1.35470
$286$	−1.94311	−0.114898
$287$	2.95886	0.174656
$288$	1.00000	0.0589256
$289$	−6.17586	−0.363286
$290$	23.5777	1.38453
$291$	3.56041	0.208715
$292$	−12.7190	−0.744320
$293$	−19.4393	−1.13566	−0.567829	−	0.823146i	$-0.692217\pi$
$293$	−19.4393	−1.13566	−0.567829	+	0.823146i	$0.692217\pi$
$294$	5.83065	0.340051
$295$	21.9401	1.27740
$296$	−0.721621	−0.0419433
$297$	−1.94311	−0.112751
$298$	3.39227	0.196509
$299$	−4.23927	−0.245163
$300$	−11.8804	−0.685912
$301$	−1.08903	−0.0627704
$302$	−1.86945	−0.107575
$303$	6.29949	0.361896
$304$	5.56641	0.319255
$305$	−37.4774	−2.14595
$306$	3.29001	0.188077
$307$	−22.9394	−1.30922	−0.654611	−	0.755966i	$-0.727168\pi$
$307$	−22.9394	−1.30922	−0.654611	+	0.755966i	$0.727168\pi$
$308$	2.10121	0.119727
$309$	1.00000	0.0568880
$310$	−40.1140	−2.27832
$311$	30.3781	1.72258	0.861291	−	0.508112i	$-0.169656\pi$
$311$	30.3781	1.72258	0.861291	+	0.508112i	$0.169656\pi$
$312$	1.00000	0.0566139
$313$	9.29840	0.525577	0.262788	−	0.964853i	$-0.415358\pi$
$313$	9.29840	0.525577	0.262788	+	0.964853i	$0.415358\pi$
$314$	2.95582	0.166807
$315$	4.44286	0.250327
$316$	7.86754	0.442584
$317$	27.1474	1.52475	0.762374	−	0.647137i	$-0.224034\pi$
$317$	27.1474	1.52475	0.762374	+	0.647137i	$0.224034\pi$
$318$	−6.31473	−0.354112
$319$	11.1508	0.624328
$320$	4.10857	0.229676
$321$	−0.737374	−0.0411562
$322$	4.58419	0.255467
$323$	18.3135	1.01899
$324$	1.00000	0.0555556
$325$	−11.8804	−0.659003
$326$	−6.68930	−0.370486
$327$	−7.22763	−0.399689
$328$	2.73623	0.151083
$329$	−8.14378	−0.448981
$330$	−7.98340	−0.439472
$331$	−18.1767	−0.999081	−0.499541	−	0.866290i	$-0.666498\pi$
$331$	−18.1767	−0.999081	−0.499541	+	0.866290i	$0.666498\pi$
$332$	−11.0081	−0.604148
$333$	−0.721621	−0.0395446
$334$	−5.25050	−0.287295
$335$	−16.0865	−0.878899
$336$	−1.08136	−0.0589932
$337$	−5.52986	−0.301230	−0.150615	−	0.988592i	$-0.548125\pi$
$337$	−5.52986	−0.301230	−0.150615	+	0.988592i	$0.548125\pi$
$338$	1.00000	0.0543928
$339$	0.412595	0.0224091
$340$	13.5172	0.733074
$341$	−18.9715	−1.02737
$342$	5.56641	0.300997
$343$	−13.8746	−0.749158
$344$	−1.00708	−0.0542984
$345$	−17.4173	−0.937718
$346$	−8.82486	−0.474427
$347$	28.9834	1.55591	0.777955	−	0.628320i	$-0.216257\pi$
$347$	28.9834	1.55591	0.777955	+	0.628320i	$0.216257\pi$
$348$	−5.73866	−0.307625
$349$	3.47838	0.186193	0.0930967	−	0.995657i	$-0.470323\pi$
$349$	3.47838	0.186193	0.0930967	+	0.995657i	$0.470323\pi$
$350$	12.8470	0.686700
$351$	1.00000	0.0533761
$352$	1.94311	0.103568
$353$	8.39501	0.446822	0.223411	−	0.974724i	$-0.428281\pi$
$353$	8.39501	0.446822	0.223411	+	0.974724i	$0.428281\pi$
$354$	−5.34007	−0.283822
$355$	−15.2090	−0.807211
$356$	3.37812	0.179040
$357$	−3.55769	−0.188293
$358$	1.87031	0.0988487
$359$	−20.5902	−1.08671	−0.543355	−	0.839503i	$-0.682846\pi$
$359$	−20.5902	−1.08671	−0.543355	+	0.839503i	$0.682846\pi$
$360$	4.10857	0.216541
$361$	11.9849	0.630783
$362$	−21.6013	−1.13534
$363$	7.22432	0.379179
$364$	−1.08136	−0.0566789
$365$	−52.2567	−2.73524
$366$	9.12177	0.476803
$367$	−20.1506	−1.05185	−0.525927	−	0.850530i	$-0.676281\pi$
$367$	−20.1506	−1.05185	−0.525927	+	0.850530i	$0.676281\pi$
$368$	4.23927	0.220987
$369$	2.73623	0.142442
$370$	−2.96483	−0.154134
$371$	6.82852	0.354519
$372$	9.76349	0.506214
$373$	7.45519	0.386015	0.193008	−	0.981197i	$-0.438176\pi$
$373$	7.45519	0.386015	0.193008	+	0.981197i	$0.438176\pi$
$374$	6.39284	0.330566
$375$	−28.2684	−1.45977
$376$	−7.53102	−0.388383
$377$	−5.73866	−0.295556
$378$	−1.08136	−0.0556194
$379$	6.30499	0.323866	0.161933	−	0.986802i	$-0.448227\pi$
$379$	6.30499	0.323866	0.161933	+	0.986802i	$0.448227\pi$
$380$	22.8700	1.17320
$381$	−8.14381	−0.417220
$382$	−17.5991	−0.900447
$383$	−3.64218	−0.186107	−0.0930534	−	0.995661i	$-0.529663\pi$
$383$	−3.64218	−0.186107	−0.0930534	+	0.995661i	$0.529663\pi$
$384$	−1.00000	−0.0510310
$385$	8.63297	0.439977
$386$	−7.66750	−0.390265
$387$	−1.00708	−0.0511930
$388$	−3.56041	−0.180753
$389$	−24.6613	−1.25038	−0.625189	−	0.780473i	$-0.714978\pi$
$389$	−24.6613	−1.25038	−0.625189	+	0.780473i	$0.714978\pi$
$390$	4.10857	0.208046
$391$	13.9472	0.705341
$392$	−5.83065	−0.294492
$393$	1.82445	0.0920313
$394$	12.4756	0.628511
$395$	32.3244	1.62642
$396$	1.94311	0.0976449
$397$	−18.1777	−0.912314	−0.456157	−	0.889899i	$-0.650775\pi$
$397$	−18.1777	−0.912314	−0.456157	+	0.889899i	$0.650775\pi$
$398$	3.77199	0.189073
$399$	−6.01931	−0.301342
$400$	11.8804	0.594018
$401$	−19.3316	−0.965372	−0.482686	−	0.875793i	$-0.660339\pi$
$401$	−19.3316	−0.965372	−0.482686	+	0.875793i	$0.660339\pi$
$402$	3.91535	0.195280
$403$	9.76349	0.486354
$404$	−6.29949	−0.313411
$405$	4.10857	0.204157
$406$	6.20558	0.307978
$407$	−1.40219	−0.0695039
$408$	−3.29001	−0.162880
$409$	30.9524	1.53050	0.765250	−	0.643734i	$-0.222616\pi$
$409$	30.9524	1.53050	0.765250	+	0.643734i	$0.222616\pi$
$410$	11.2420	0.555202
$411$	−16.2132	−0.799736
$412$	−1.00000	−0.0492665
$413$	5.77456	0.284148
$414$	4.23927	0.208349
$415$	−45.2276	−2.22013
$416$	−1.00000	−0.0490290
$417$	15.7184	0.769731
$418$	10.8161	0.529035
$419$	19.3432	0.944977	0.472489	−	0.881337i	$-0.343356\pi$
$419$	19.3432	0.944977	0.472489	+	0.881337i	$0.343356\pi$
$420$	−4.44286	−0.216789
$421$	38.1559	1.85960	0.929801	−	0.368062i	$-0.119979\pi$
$421$	38.1559	1.85960	0.929801	+	0.368062i	$0.119979\pi$
$422$	−11.0391	−0.537377
$423$	−7.53102	−0.366171
$424$	6.31473	0.306670
$425$	39.0864	1.89597
$426$	3.70178	0.179352
$427$	−9.86396	−0.477350
$428$	0.737374	0.0356423
$429$	1.94311	0.0938142
$430$	−4.13768	−0.199537
$431$	−9.67949	−0.466245	−0.233122	−	0.972447i	$-0.574894\pi$
$431$	−9.67949	−0.466245	−0.233122	+	0.972447i	$0.574894\pi$
$432$	−1.00000	−0.0481125
$433$	−19.9384	−0.958180	−0.479090	−	0.877766i	$-0.659033\pi$
$433$	−19.9384	−0.958180	−0.479090	+	0.877766i	$0.659033\pi$
$434$	−10.5579	−0.506795
$435$	−23.5777	−1.13046
$436$	7.22763	0.346141
$437$	23.5975	1.12882
$438$	12.7190	0.607735
$439$	28.0392	1.33824	0.669119	−	0.743155i	$-0.266672\pi$
$439$	28.0392	1.33824	0.669119	+	0.743155i	$0.266672\pi$
$440$	7.98340	0.380594
$441$	−5.83065	−0.277650
$442$	−3.29001	−0.156490
$443$	−22.6671	−1.07695	−0.538474	−	0.842642i	$-0.680999\pi$
$443$	−22.6671	−1.07695	−0.538474	+	0.842642i	$0.680999\pi$
$444$	0.721621	0.0342466
$445$	13.8793	0.657940
$446$	−19.7509	−0.935230
$447$	−3.39227	−0.160449
$448$	1.08136	0.0510896
$449$	19.7650	0.932770	0.466385	−	0.884582i	$-0.345556\pi$
$449$	19.7650	0.932770	0.466385	+	0.884582i	$0.345556\pi$
$450$	11.8804	0.560045
$451$	5.31679	0.250358
$452$	−0.412595	−0.0194068
$453$	1.86945	0.0878346
$454$	−15.9220	−0.747254
$455$	−4.44286	−0.208284
$456$	−5.56641	−0.260671
$457$	−29.8725	−1.39738	−0.698688	−	0.715427i	$-0.746232\pi$
$457$	−29.8725	−1.39738	−0.698688	+	0.715427i	$0.746232\pi$
$458$	14.3924	0.672511
$459$	−3.29001	−0.153564
$460$	17.4173	0.812088
$461$	8.02794	0.373899	0.186949	−	0.982370i	$-0.440140\pi$
$461$	8.02794	0.373899	0.186949	+	0.982370i	$0.440140\pi$
$462$	−2.10121	−0.0977571
$463$	16.1898	0.752404	0.376202	−	0.926538i	$-0.377230\pi$
$463$	16.1898	0.752404	0.376202	+	0.926538i	$0.377230\pi$
$464$	5.73866	0.266411
$465$	40.1140	1.86024
$466$	21.0680	0.975956
$467$	15.1940	0.703095	0.351548	−	0.936170i	$-0.385656\pi$
$467$	15.1940	0.703095	0.351548	+	0.936170i	$0.385656\pi$
$468$	−1.00000	−0.0462250
$469$	−4.23392	−0.195504
$470$	−30.9417	−1.42724
$471$	−2.95582	−0.136197
$472$	5.34007	0.245797
$473$	−1.95688	−0.0899773
$474$	−7.86754	−0.361368
$475$	66.1309	3.03429
$476$	3.55769	0.163067
$477$	6.31473	0.289132
$478$	24.6679	1.12828
$479$	−8.06166	−0.368347	−0.184173	−	0.982894i	$-0.558961\pi$
$479$	−8.06166	−0.368347	−0.184173	+	0.982894i	$0.558961\pi$
$480$	−4.10857	−0.187530
$481$	0.721621	0.0329031
$482$	12.8439	0.585025
$483$	−4.58419	−0.208588
$484$	−7.22432	−0.328378
$485$	−14.6282	−0.664233
$486$	−1.00000	−0.0453609
$487$	33.4341	1.51504	0.757521	−	0.652810i	$-0.226410\pi$
$487$	33.4341	1.51504	0.757521	+	0.652810i	$0.226410\pi$
$488$	−9.12177	−0.412923
$489$	6.68930	0.302501
$490$	−23.9556	−1.08221
$491$	−8.29680	−0.374429	−0.187215	−	0.982319i	$-0.559946\pi$
$491$	−8.29680	−0.374429	−0.187215	+	0.982319i	$0.559946\pi$
$492$	−2.73623	−0.123359
$493$	18.8802	0.850323
$494$	−5.56641	−0.250444
$495$	7.98340	0.358827
$496$	−9.76349	−0.438394
$497$	−4.00297	−0.179558
$498$	11.0081	0.493285
$499$	26.0825	1.16761	0.583807	−	0.811892i	$-0.301562\pi$
$499$	26.0825	1.16761	0.583807	+	0.811892i	$0.301562\pi$
$500$	28.2684	1.26420
$501$	5.25050	0.234575
$502$	−24.4841	−1.09278
$503$	−34.7353	−1.54877	−0.774385	−	0.632715i	$-0.781941\pi$
$503$	−34.7353	−1.54877	−0.774385	+	0.632715i	$0.781941\pi$
$504$	1.08136	0.0481678
$505$	−25.8819	−1.15173
$506$	8.23737	0.366196
$507$	−1.00000	−0.0444116
$508$	8.14381	0.361323
$509$	24.7532	1.09717	0.548584	−	0.836096i	$-0.315167\pi$
$509$	24.7532	1.09717	0.548584	+	0.836096i	$0.315167\pi$
$510$	−13.5172	−0.598553
$511$	−13.7538	−0.608433
$512$	1.00000	0.0441942
$513$	−5.56641	−0.245763
$514$	3.27567	0.144483
$515$	−4.10857	−0.181045
$516$	1.00708	0.0443344
$517$	−14.6336	−0.643585
$518$	−0.780335	−0.0342859
$519$	8.82486	0.387368
$520$	−4.10857	−0.180173
$521$	35.0415	1.53519	0.767597	−	0.640933i	$-0.221452\pi$
$521$	35.0415	1.53519	0.767597	+	0.640933i	$0.221452\pi$
$522$	5.73866	0.251174
$523$	11.4032	0.498627	0.249314	−	0.968423i	$-0.419795\pi$
$523$	11.4032	0.498627	0.249314	+	0.968423i	$0.419795\pi$
$524$	−1.82445	−0.0797014
$525$	−12.8470	−0.560688
$526$	8.28156	0.361093
$527$	−32.1219	−1.39925
$528$	−1.94311	−0.0845630
$529$	−5.02859	−0.218634
$530$	25.9445	1.12696
$531$	5.34007	0.231739
$532$	6.01931	0.260970
$533$	−2.73623	−0.118519
$534$	−3.37812	−0.146186
$535$	3.02955	0.130979
$536$	−3.91535	−0.169117
$537$	−1.87031	−0.0807096
$538$	20.5589	0.886357
$539$	−11.3296	−0.488000
$540$	−4.10857	−0.176805
$541$	−28.2165	−1.21312	−0.606562	−	0.795036i	$-0.707452\pi$
$541$	−28.2165	−1.21312	−0.606562	+	0.795036i	$0.707452\pi$
$542$	−11.0715	−0.475561
$543$	21.6013	0.927000
$544$	3.29001	0.141058
$545$	29.6952	1.27200
$546$	1.08136	0.0462781
$547$	37.0522	1.58424	0.792118	−	0.610368i	$-0.208978\pi$
$547$	37.0522	1.58424	0.792118	+	0.610368i	$0.208978\pi$
$548$	16.2132	0.692592
$549$	−9.12177	−0.389308
$550$	23.0848	0.984340
$551$	31.9437	1.36085
$552$	−4.23927	−0.180435
$553$	8.50768	0.361783
$554$	−28.3155	−1.20301
$555$	2.96483	0.125850
$556$	−15.7184	−0.666607
$557$	1.47666	0.0625682	0.0312841	−	0.999511i	$-0.490040\pi$
$557$	1.47666	0.0625682	0.0312841	+	0.999511i	$0.490040\pi$
$558$	−9.76349	−0.413322
$559$	1.00708	0.0425951
$560$	4.44286	0.187745
$561$	−6.39284	−0.269906
$562$	24.4791	1.03259
$563$	34.5977	1.45812	0.729059	−	0.684451i	$-0.239958\pi$
$563$	34.5977	1.45812	0.729059	+	0.684451i	$0.239958\pi$
$564$	7.53102	0.317113
$565$	−1.69518	−0.0713166
$566$	1.81030	0.0760924
$567$	1.08136	0.0454130
$568$	−3.70178	−0.155323
$569$	−5.04434	−0.211470	−0.105735	−	0.994394i	$-0.533719\pi$
$569$	−5.04434	−0.211470	−0.105735	+	0.994394i	$0.533719\pi$
$570$	−22.8700	−0.957918
$571$	−8.80528	−0.368489	−0.184245	−	0.982880i	$-0.558984\pi$
$571$	−8.80528	−0.368489	−0.184245	+	0.982880i	$0.558984\pi$
$572$	−1.94311	−0.0812455
$573$	17.5991	0.735212
$574$	2.95886	0.123500
$575$	50.3640	2.10032
$576$	1.00000	0.0416667
$577$	29.0192	1.20809	0.604044	−	0.796951i	$-0.293555\pi$
$577$	29.0192	1.20809	0.604044	+	0.796951i	$0.293555\pi$
$578$	−6.17586	−0.256882
$579$	7.66750	0.318650
$580$	23.5777	0.979010
$581$	−11.9038	−0.493852
$582$	3.56041	0.147584
$583$	12.2702	0.508180
$584$	−12.7190	−0.526314
$585$	−4.10857	−0.169868
$586$	−19.4393	−0.803032
$587$	12.3121	0.508174	0.254087	−	0.967181i	$-0.418225\pi$
$587$	12.3121	0.508174	0.254087	+	0.967181i	$0.418225\pi$
$588$	5.83065	0.240452
$589$	−54.3476	−2.23935
$590$	21.9401	0.903258
$591$	−12.4756	−0.513177
$592$	−0.721621	−0.0296584
$593$	11.5334	0.473621	0.236811	−	0.971556i	$-0.423898\pi$
$593$	11.5334	0.473621	0.236811	+	0.971556i	$0.423898\pi$
$594$	−1.94311	−0.0797268
$595$	14.6170	0.599240
$596$	3.39227	0.138953
$597$	−3.77199	−0.154377
$598$	−4.23927	−0.173357
$599$	−16.5041	−0.674341	−0.337170	−	0.941444i	$-0.609470\pi$
$599$	−16.5041	−0.674341	−0.337170	+	0.941444i	$0.609470\pi$
$600$	−11.8804	−0.485013
$601$	−29.2661	−1.19379	−0.596894	−	0.802320i	$-0.703599\pi$
$601$	−29.2661	−1.19379	−0.596894	+	0.802320i	$0.703599\pi$
$602$	−1.08903	−0.0443854
$603$	−3.91535	−0.159445
$604$	−1.86945	−0.0760670
$605$	−29.6816	−1.20673
$606$	6.29949	0.255899
$607$	−26.7272	−1.08482	−0.542412	−	0.840112i	$-0.682489\pi$
$607$	−26.7272	−1.08482	−0.542412	+	0.840112i	$0.682489\pi$
$608$	5.56641	0.225748
$609$	−6.20558	−0.251463
$610$	−37.4774	−1.51742
$611$	7.53102	0.304673
$612$	3.29001	0.132991
$613$	8.94000	0.361083	0.180542	−	0.983567i	$-0.442215\pi$
$613$	8.94000	0.361083	0.180542	+	0.983567i	$0.442215\pi$
$614$	−22.9394	−0.925760
$615$	−11.2420	−0.453320
$616$	2.10121	0.0846601
$617$	−16.2807	−0.655435	−0.327718	−	0.944776i	$-0.606279\pi$
$617$	−16.2807	−0.655435	−0.327718	+	0.944776i	$0.606279\pi$
$618$	1.00000	0.0402259
$619$	−11.9378	−0.479819	−0.239910	−	0.970795i	$-0.577118\pi$
$619$	−11.9378	−0.479819	−0.239910	+	0.970795i	$0.577118\pi$
$620$	−40.1140	−1.61102
$621$	−4.23927	−0.170116
$622$	30.3781	1.21805
$623$	3.65298	0.146354
$624$	1.00000	0.0400320
$625$	56.7410	2.26964
$626$	9.29840	0.371639
$627$	−10.8161	−0.431955
$628$	2.95582	0.117950
$629$	−2.37414	−0.0946630
$630$	4.44286	0.177008
$631$	34.0937	1.35725	0.678624	−	0.734486i	$-0.262577\pi$
$631$	34.0937	1.35725	0.678624	+	0.734486i	$0.262577\pi$
$632$	7.86754	0.312954
$633$	11.0391	0.438767
$634$	27.1474	1.07816
$635$	33.4594	1.32780
$636$	−6.31473	−0.250395
$637$	5.83065	0.231019
$638$	11.1508	0.441466
$639$	−3.70178	−0.146440
$640$	4.10857	0.162406
$641$	48.1232	1.90075	0.950377	−	0.311102i	$-0.100698\pi$
$641$	48.1232	1.90075	0.950377	+	0.311102i	$0.100698\pi$
$642$	−0.737374	−0.0291018
$643$	2.07504	0.0818315	0.0409157	−	0.999163i	$-0.486972\pi$
$643$	2.07504	0.0818315	0.0409157	+	0.999163i	$0.486972\pi$
$644$	4.58419	0.180643
$645$	4.13768	0.162921
$646$	18.3135	0.720535
$647$	−17.5737	−0.690894	−0.345447	−	0.938438i	$-0.612273\pi$
$647$	−17.5737	−0.690894	−0.345447	+	0.938438i	$0.612273\pi$
$648$	1.00000	0.0392837
$649$	10.3763	0.407307
$650$	−11.8804	−0.465986
$651$	10.5579	0.413796
$652$	−6.68930	−0.261973
$653$	41.4486	1.62201	0.811006	−	0.585039i	$-0.198921\pi$
$653$	41.4486	1.62201	0.811006	+	0.585039i	$0.198921\pi$
$654$	−7.22763	−0.282623
$655$	−7.49588	−0.292888
$656$	2.73623	0.106832
$657$	−12.7190	−0.496214
$658$	−8.14378	−0.317478
$659$	−15.7497	−0.613520	−0.306760	−	0.951787i	$-0.599245\pi$
$659$	−15.7497	−0.613520	−0.306760	+	0.951787i	$0.599245\pi$
$660$	−7.98340	−0.310754
$661$	17.7941	0.692109	0.346054	−	0.938214i	$-0.387521\pi$
$661$	17.7941	0.692109	0.346054	+	0.938214i	$0.387521\pi$
$662$	−18.1767	−0.706457
$663$	3.29001	0.127773
$664$	−11.0081	−0.427197
$665$	24.7308	0.959018
$666$	−0.721621	−0.0279622
$667$	24.3277	0.941974
$668$	−5.25050	−0.203148
$669$	19.7509	0.763612
$670$	−16.0865	−0.621475
$671$	−17.7246	−0.684251
$672$	−1.08136	−0.0417145
$673$	−4.75654	−0.183351	−0.0916757	−	0.995789i	$-0.529222\pi$
$673$	−4.75654	−0.183351	−0.0916757	+	0.995789i	$0.529222\pi$
$674$	−5.52986	−0.213002
$675$	−11.8804	−0.457275
$676$	1.00000	0.0384615
$677$	7.37777	0.283551	0.141775	−	0.989899i	$-0.454719\pi$
$677$	7.37777	0.283551	0.141775	+	0.989899i	$0.454719\pi$
$678$	0.412595	0.0158456
$679$	−3.85010	−0.147753
$680$	13.5172	0.518362
$681$	15.9220	0.610131
$682$	−18.9715	−0.726458
$683$	−13.5732	−0.519365	−0.259683	−	0.965694i	$-0.583618\pi$
$683$	−13.5732	−0.519365	−0.259683	+	0.965694i	$0.583618\pi$
$684$	5.56641	0.212837
$685$	66.6129	2.54515
$686$	−13.8746	−0.529735
$687$	−14.3924	−0.549103
$688$	−1.00708	−0.0383947
$689$	−6.31473	−0.240572
$690$	−17.4173	−0.663067
$691$	−9.36218	−0.356154	−0.178077	−	0.984017i	$-0.556988\pi$
$691$	−9.36218	−0.356154	−0.178077	+	0.984017i	$0.556988\pi$
$692$	−8.82486	−0.335471
$693$	2.10121	0.0798183
$694$	28.9834	1.10019
$695$	−64.5800	−2.44966
$696$	−5.73866	−0.217523
$697$	9.00220	0.340983
$698$	3.47838	0.131659
$699$	−21.0680	−0.796865
$700$	12.8470	0.485570
$701$	−19.9820	−0.754711	−0.377356	−	0.926068i	$-0.623167\pi$
$701$	−19.9820	−0.754711	−0.377356	+	0.926068i	$0.623167\pi$
$702$	1.00000	0.0377426
$703$	−4.01683	−0.151498
$704$	1.94311	0.0732337
$705$	30.9417	1.16533
$706$	8.39501	0.315951
$707$	−6.81204	−0.256193
$708$	−5.34007	−0.200692
$709$	−17.8979	−0.672171	−0.336086	−	0.941831i	$-0.609103\pi$
$709$	−17.8979	−0.672171	−0.336086	+	0.941831i	$0.609103\pi$
$710$	−15.2090	−0.570784
$711$	7.86754	0.295056
$712$	3.37812	0.126601
$713$	−41.3901	−1.55007
$714$	−3.55769	−0.133143
$715$	−7.98340	−0.298562
$716$	1.87031	0.0698966
$717$	−24.6679	−0.921239
$718$	−20.5902	−0.768420
$719$	4.97052	0.185369	0.0926845	−	0.995696i	$-0.470455\pi$
$719$	4.97052	0.185369	0.0926845	+	0.995696i	$0.470455\pi$
$720$	4.10857	0.153117
$721$	−1.08136	−0.0402721
$722$	11.9849	0.446031
$723$	−12.8439	−0.477671
$724$	−21.6013	−0.802806
$725$	68.1773	2.53204
$726$	7.22432	0.268120
$727$	−19.5779	−0.726103	−0.363052	−	0.931769i	$-0.618265\pi$
$727$	−19.5779	−0.726103	−0.363052	+	0.931769i	$0.618265\pi$
$728$	−1.08136	−0.0400780
$729$	1.00000	0.0370370
$730$	−52.2567	−1.93411
$731$	−3.31331	−0.122547
$732$	9.12177	0.337150
$733$	43.6858	1.61357	0.806786	−	0.590843i	$-0.201205\pi$
$733$	43.6858	1.61357	0.806786	+	0.590843i	$0.201205\pi$
$734$	−20.1506	−0.743773
$735$	23.9556	0.883617
$736$	4.23927	0.156262
$737$	−7.60795	−0.280243
$738$	2.73623	0.100722
$739$	18.0459	0.663829	0.331914	−	0.943309i	$-0.392305\pi$
$739$	18.0459	0.663829	0.331914	+	0.943309i	$0.392305\pi$
$740$	−2.96483	−0.108989
$741$	5.56641	0.204487
$742$	6.82852	0.250683
$743$	1.11335	0.0408449	0.0204224	−	0.999791i	$-0.493499\pi$
$743$	1.11335	0.0408449	0.0204224	+	0.999791i	$0.493499\pi$
$744$	9.76349	0.357947
$745$	13.9374	0.510626
$746$	7.45519	0.272954
$747$	−11.0081	−0.402765
$748$	6.39284	0.233745
$749$	0.797369	0.0291352
$750$	−28.2684	−1.03222
$751$	14.9853	0.546820	0.273410	−	0.961898i	$-0.411848\pi$
$751$	14.9853	0.546820	0.273410	+	0.961898i	$0.411848\pi$
$752$	−7.53102	−0.274628
$753$	24.4841	0.892252
$754$	−5.73866	−0.208990
$755$	−7.68078	−0.279532
$756$	−1.08136	−0.0393288
$757$	33.5533	1.21952	0.609758	−	0.792587i	$-0.291266\pi$
$757$	33.5533	1.21952	0.609758	+	0.792587i	$0.291266\pi$
$758$	6.30499	0.229008
$759$	−8.23737	−0.298997
$760$	22.8700	0.829581
$761$	8.51222	0.308568	0.154284	−	0.988027i	$-0.450693\pi$
$761$	8.51222	0.308568	0.154284	+	0.988027i	$0.450693\pi$
$762$	−8.14381	−0.295019
$763$	7.81570	0.282947
$764$	−17.5991	−0.636712
$765$	13.5172	0.488716
$766$	−3.64218	−0.131597
$767$	−5.34007	−0.192819
$768$	−1.00000	−0.0360844
$769$	−33.8906	−1.22213	−0.611063	−	0.791582i	$-0.709258\pi$
$769$	−33.8906	−1.22213	−0.611063	+	0.791582i	$0.709258\pi$
$770$	8.63297	0.311110
$771$	−3.27567	−0.117970
$772$	−7.66750	−0.275959
$773$	−54.3237	−1.95389	−0.976943	−	0.213499i	$-0.931514\pi$
$773$	−54.3237	−1.95389	−0.976943	+	0.213499i	$0.931514\pi$
$774$	−1.00708	−0.0361989
$775$	−115.994	−4.16662
$776$	−3.56041	−0.127811
$777$	0.780335	0.0279943
$778$	−24.6613	−0.884151
$779$	15.2309	0.545705
$780$	4.10857	0.147110
$781$	−7.19296	−0.257384
$782$	13.9472	0.498752
$783$	−5.73866	−0.205083
$784$	−5.83065	−0.208238
$785$	12.1442	0.433445
$786$	1.82445	0.0650760
$787$	46.3832	1.65338	0.826691	−	0.562656i	$-0.190220\pi$
$787$	46.3832	1.65338	0.826691	+	0.562656i	$0.190220\pi$
$788$	12.4756	0.444424
$789$	−8.28156	−0.294831
$790$	32.3244	1.15005
$791$	−0.446166	−0.0158638
$792$	1.94311	0.0690454
$793$	9.12177	0.323924
$794$	−18.1777	−0.645104
$795$	−25.9445	−0.920157
$796$	3.77199	0.133695
$797$	−34.1125	−1.20833	−0.604163	−	0.796861i	$-0.706492\pi$
$797$	−34.1125	−1.20833	−0.604163	+	0.796861i	$0.706492\pi$
$798$	−6.01931	−0.213081
$799$	−24.7771	−0.876551
$800$	11.8804	0.420034
$801$	3.37812	0.119360
$802$	−19.3316	−0.682621
$803$	−24.7143	−0.872149
$804$	3.91535	0.138084
$805$	18.8345	0.663828
$806$	9.76349	0.343904
$807$	−20.5589	−0.723708
$808$	−6.29949	−0.221615
$809$	22.7610	0.800235	0.400118	−	0.916464i	$-0.368969\pi$
$809$	22.7610	0.800235	0.400118	+	0.916464i	$0.368969\pi$
$810$	4.10857	0.144360
$811$	10.7541	0.377626	0.188813	−	0.982013i	$-0.439536\pi$
$811$	10.7541	0.377626	0.188813	+	0.982013i	$0.439536\pi$
$812$	6.20558	0.217773
$813$	11.0715	0.388294
$814$	−1.40219	−0.0491467
$815$	−27.4835	−0.962704
$816$	−3.29001	−0.115173
$817$	−5.60584	−0.196124
$818$	30.9524	1.08223
$819$	−1.08136	−0.0377859
$820$	11.2420	0.392587
$821$	−2.79374	−0.0975023	−0.0487511	−	0.998811i	$-0.515524\pi$
$821$	−2.79374	−0.0975023	−0.0487511	+	0.998811i	$0.515524\pi$
$822$	−16.2132	−0.565499
$823$	−27.1977	−0.948053	−0.474026	−	0.880511i	$-0.657200\pi$
$823$	−27.1977	−0.948053	−0.474026	+	0.880511i	$0.657200\pi$
$824$	−1.00000	−0.0348367
$825$	−23.0848	−0.803710
$826$	5.77456	0.200923
$827$	8.39731	0.292003	0.146002	−	0.989284i	$-0.453360\pi$
$827$	8.39731	0.292003	0.146002	+	0.989284i	$0.453360\pi$
$828$	4.23927	0.147325
$829$	−39.2512	−1.36325	−0.681626	−	0.731701i	$-0.738727\pi$
$829$	−39.2512	−1.36325	−0.681626	+	0.731701i	$0.738727\pi$
$830$	−45.2276	−1.56987
$831$	28.3155	0.982253
$832$	−1.00000	−0.0346688
$833$	−19.1829	−0.664647
$834$	15.7184	0.544282
$835$	−21.5720	−0.746531
$836$	10.8161	0.374084
$837$	9.76349	0.337476
$838$	19.3432	0.668200
$839$	−28.4064	−0.980697	−0.490348	−	0.871526i	$-0.663130\pi$
$839$	−28.4064	−0.980697	−0.490348	+	0.871526i	$0.663130\pi$
$840$	−4.44286	−0.153293
$841$	3.93223	0.135594
$842$	38.1559	1.31494
$843$	−24.4791	−0.843106
$844$	−11.0391	−0.379983
$845$	4.10857	0.141339
$846$	−7.53102	−0.258922
$847$	−7.81212	−0.268428
$848$	6.31473	0.216849
$849$	−1.81030	−0.0621292
$850$	39.0864	1.34065
$851$	−3.05914	−0.104866
$852$	3.70178	0.126821
$853$	−9.60722	−0.328945	−0.164472	−	0.986382i	$-0.552592\pi$
$853$	−9.60722	−0.328945	−0.164472	+	0.986382i	$0.552592\pi$
$854$	−9.86396	−0.337538
$855$	22.8700	0.782137
$856$	0.737374	0.0252029
$857$	27.9151	0.953562	0.476781	−	0.879022i	$-0.341803\pi$
$857$	27.9151	0.953562	0.476781	+	0.879022i	$0.341803\pi$
$858$	1.94311	0.0663367
$859$	−27.7473	−0.946727	−0.473363	−	0.880867i	$-0.656960\pi$
$859$	−27.7473	−0.946727	−0.473363	+	0.880867i	$0.656960\pi$
$860$	−4.13768	−0.141094
$861$	−2.95886	−0.100838
$862$	−9.67949	−0.329685
$863$	−32.8331	−1.11765	−0.558825	−	0.829285i	$-0.688748\pi$
$863$	−32.8331	−1.11765	−0.558825	+	0.829285i	$0.688748\pi$
$864$	−1.00000	−0.0340207
$865$	−36.2575	−1.23279
$866$	−19.9384	−0.677536
$867$	6.17586	0.209743
$868$	−10.5579	−0.358358
$869$	15.2875	0.518593
$870$	−23.5777	−0.799359
$871$	3.91535	0.132667
$872$	7.22763	0.244759
$873$	−3.56041	−0.120502
$874$	23.5975	0.798197
$875$	30.5684	1.03340
$876$	12.7190	0.429734
$877$	−9.31727	−0.314622	−0.157311	−	0.987549i	$-0.550283\pi$
$877$	−9.31727	−0.314622	−0.157311	+	0.987549i	$0.550283\pi$
$878$	28.0392	0.946277
$879$	19.4393	0.655673
$880$	7.98340	0.269120
$881$	8.29518	0.279472	0.139736	−	0.990189i	$-0.455375\pi$
$881$	8.29518	0.279472	0.139736	+	0.990189i	$0.455375\pi$
$882$	−5.83065	−0.196328
$883$	−16.6831	−0.561432	−0.280716	−	0.959791i	$-0.590572\pi$
$883$	−16.6831	−0.561432	−0.280716	+	0.959791i	$0.590572\pi$
$884$	−3.29001	−0.110655
$885$	−21.9401	−0.737507
$886$	−22.6671	−0.761517
$887$	−37.9842	−1.27539	−0.637693	−	0.770291i	$-0.720111\pi$
$887$	−37.9842	−1.27539	−0.637693	+	0.770291i	$0.720111\pi$
$888$	0.721621	0.0242160
$889$	8.80643	0.295358
$890$	13.8793	0.465234
$891$	1.94311	0.0650966
$892$	−19.7509	−0.661308
$893$	−41.9207	−1.40282
$894$	−3.39227	−0.113454
$895$	7.68428	0.256857
$896$	1.08136	0.0361258
$897$	4.23927	0.141545
$898$	19.7650	0.659568
$899$	−56.0294	−1.86868
$900$	11.8804	0.396012
$901$	20.7755	0.692132
$902$	5.31679	0.177030
$903$	1.08903	0.0362405
$904$	−0.412595	−0.0137227
$905$	−88.7504	−2.95016
$906$	1.86945	0.0621084
$907$	11.2104	0.372235	0.186117	−	0.982527i	$-0.440409\pi$
$907$	11.2104	0.372235	0.186117	+	0.982527i	$0.440409\pi$
$908$	−15.9220	−0.528389
$909$	−6.29949	−0.208941
$910$	−4.44286	−0.147279
$911$	−10.5819	−0.350595	−0.175297	−	0.984516i	$-0.556089\pi$
$911$	−10.5819	−0.350595	−0.175297	+	0.984516i	$0.556089\pi$
$912$	−5.56641	−0.184322
$913$	−21.3900	−0.707904
$914$	−29.8725	−0.988094
$915$	37.4774	1.23897
$916$	14.3924	0.475537
$917$	−1.97289	−0.0651507
$918$	−3.29001	−0.108586
$919$	0.249990	0.00824640	0.00412320	−	0.999991i	$-0.498688\pi$
$919$	0.249990	0.00824640	0.00412320	+	0.999991i	$0.498688\pi$
$920$	17.4173	0.574233
$921$	22.9394	0.755880
$922$	8.02794	0.264386
$923$	3.70178	0.121846
$924$	−2.10121	−0.0691247
$925$	−8.57311	−0.281882
$926$	16.1898	0.532030
$927$	−1.00000	−0.0328443
$928$	5.73866	0.188381
$929$	−8.91055	−0.292346	−0.146173	−	0.989259i	$-0.546696\pi$
$929$	−8.91055	−0.292346	−0.146173	+	0.989259i	$0.546696\pi$
$930$	40.1140	1.31539
$931$	−32.4558	−1.06370
$932$	21.0680	0.690105
$933$	−30.3781	−0.994533
$934$	15.1940	0.497163
$935$	26.2654	0.858972
$936$	−1.00000	−0.0326860
$937$	50.1970	1.63986	0.819932	−	0.572462i	$-0.194011\pi$
$937$	50.1970	1.63986	0.819932	+	0.572462i	$0.194011\pi$
$938$	−4.23392	−0.138242
$939$	−9.29840	−0.303442
$940$	−30.9417	−1.00921
$941$	−21.3817	−0.697025	−0.348512	−	0.937304i	$-0.613313\pi$
$941$	−21.3817	−0.697025	−0.348512	+	0.937304i	$0.613313\pi$
$942$	−2.95582	−0.0963059
$943$	11.5996	0.377735
$944$	5.34007	0.173805
$945$	−4.44286	−0.144526
$946$	−1.95688	−0.0636235
$947$	−13.4273	−0.436328	−0.218164	−	0.975912i	$-0.570007\pi$
$947$	−13.4273	−0.436328	−0.218164	+	0.975912i	$0.570007\pi$
$948$	−7.86754	−0.255526
$949$	12.7190	0.412875
$950$	66.1309	2.14557
$951$	−27.1474	−0.880313
$952$	3.55769	0.115306
$953$	25.9491	0.840574	0.420287	−	0.907391i	$-0.361929\pi$
$953$	25.9491	0.840574	0.420287	+	0.907391i	$0.361929\pi$
$954$	6.31473	0.204447
$955$	−72.3070	−2.33980
$956$	24.6679	0.797816
$957$	−11.1508	−0.360456
$958$	−8.06166	−0.260460
$959$	17.5323	0.566148
$960$	−4.10857	−0.132604
$961$	64.3258	2.07503
$962$	0.721621	0.0232660
$963$	0.737374	0.0237615
$964$	12.8439	0.413675
$965$	−31.5025	−1.01410
$966$	−4.58419	−0.147494
$967$	51.5075	1.65637	0.828184	−	0.560456i	$-0.189374\pi$
$967$	51.5075	1.65637	0.828184	+	0.560456i	$0.189374\pi$
$968$	−7.22432	−0.232199
$969$	−18.3135	−0.588315
$970$	−14.6282	−0.469683
$971$	5.76955	0.185154	0.0925769	−	0.995706i	$-0.470490\pi$
$971$	5.76955	0.185154	0.0925769	+	0.995706i	$0.470490\pi$
$972$	−1.00000	−0.0320750
$973$	−16.9973	−0.544907
$974$	33.4341	1.07130
$975$	11.8804	0.380476
$976$	−9.12177	−0.291981
$977$	−30.2599	−0.968099	−0.484050	−	0.875040i	$-0.660835\pi$
$977$	−30.2599	−0.968099	−0.484050	+	0.875040i	$0.660835\pi$
$978$	6.68930	0.213900
$979$	6.56407	0.209788
$980$	−23.9556	−0.765235
$981$	7.22763	0.230761
$982$	−8.29680	−0.264762
$983$	−6.72633	−0.214537	−0.107268	−	0.994230i	$-0.534210\pi$
$983$	−6.72633	−0.214537	−0.107268	+	0.994230i	$0.534210\pi$
$984$	−2.73623	−0.0872277
$985$	51.2568	1.63318
$986$	18.8802	0.601269
$987$	8.14378	0.259219
$988$	−5.56641	−0.177091
$989$	−4.26930	−0.135756
$990$	7.98340	0.253729
$991$	−15.4282	−0.490094	−0.245047	−	0.969511i	$-0.578803\pi$
$991$	−15.4282	−0.490094	−0.245047	+	0.969511i	$0.578803\pi$
$992$	−9.76349	−0.309991
$993$	18.1767	0.576820
$994$	−4.00297	−0.126967
$995$	15.4975	0.491303
$996$	11.0081	0.348805
$997$	−22.4185	−0.710002	−0.355001	−	0.934866i	$-0.615520\pi$
$997$	−22.4185	−0.710002	−0.355001	+	0.934866i	$0.615520\pi$
$998$	26.0825	0.825628
$999$	0.721621	0.0228311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bc.1.15	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bc.1.15	✓	15	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.10857 q^{5} -1.00000 q^{6} +1.08136 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.10857 q^{5} -1.00000 q^{6} +1.08136 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.10857 q^{10} +1.94311 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.08136 q^{14} -4.10857 q^{15} +1.00000 q^{16} +3.29001 q^{17} +1.00000 q^{18} +5.56641 q^{19} +4.10857 q^{20} -1.08136 q^{21} +1.94311 q^{22} +4.23927 q^{23} -1.00000 q^{24} +11.8804 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.08136 q^{28} +5.73866 q^{29} -4.10857 q^{30} -9.76349 q^{31} +1.00000 q^{32} -1.94311 q^{33} +3.29001 q^{34} +4.44286 q^{35} +1.00000 q^{36} -0.721621 q^{37} +5.56641 q^{38} +1.00000 q^{39} +4.10857 q^{40} +2.73623 q^{41} -1.08136 q^{42} -1.00708 q^{43} +1.94311 q^{44} +4.10857 q^{45} +4.23927 q^{46} -7.53102 q^{47} -1.00000 q^{48} -5.83065 q^{49} +11.8804 q^{50} -3.29001 q^{51} -1.00000 q^{52} +6.31473 q^{53} -1.00000 q^{54} +7.98340 q^{55} +1.08136 q^{56} -5.56641 q^{57} +5.73866 q^{58} +5.34007 q^{59} -4.10857 q^{60} -9.12177 q^{61} -9.76349 q^{62} +1.08136 q^{63} +1.00000 q^{64} -4.10857 q^{65} -1.94311 q^{66} -3.91535 q^{67} +3.29001 q^{68} -4.23927 q^{69} +4.44286 q^{70} -3.70178 q^{71} +1.00000 q^{72} -12.7190 q^{73} -0.721621 q^{74} -11.8804 q^{75} +5.56641 q^{76} +2.10121 q^{77} +1.00000 q^{78} +7.86754 q^{79} +4.10857 q^{80} +1.00000 q^{81} +2.73623 q^{82} -11.0081 q^{83} -1.08136 q^{84} +13.5172 q^{85} -1.00708 q^{86} -5.73866 q^{87} +1.94311 q^{88} +3.37812 q^{89} +4.10857 q^{90} -1.08136 q^{91} +4.23927 q^{92} +9.76349 q^{93} -7.53102 q^{94} +22.8700 q^{95} -1.00000 q^{96} -3.56041 q^{97} -5.83065 q^{98} +1.94311 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9	\( 15 q + 15 q^{2} - 15 q^{3} + 15 q^{4} - q^{5} - 15 q^{6} + 5 q^{7} + 15 q^{8} + 15 q^{9} - q^{10} + 3 q^{11} - 15 q^{12} - 15 q^{13} + 5 q^{14} + q^{15} + 15 q^{16} - 2 q^{17} + 15 q^{18} + 8 q^{19} - q^{20} - 5 q^{21} + 3 q^{22} + 3 q^{23} - 15 q^{24} + 22 q^{25} - 15 q^{26} - 15 q^{27} + 5 q^{28} + 26 q^{29} + q^{30} + 15 q^{32} - 3 q^{33} - 2 q^{34} - 8 q^{35} + 15 q^{36} + 25 q^{37} + 8 q^{38} + 15 q^{39} - q^{40} - q^{41} - 5 q^{42} + 10 q^{43} + 3 q^{44} - q^{45} + 3 q^{46} - 3 q^{47} - 15 q^{48} + 32 q^{49} + 22 q^{50} + 2 q^{51} - 15 q^{52} + 13 q^{53} - 15 q^{54} - 2 q^{55} + 5 q^{56} - 8 q^{57} + 26 q^{58} + 28 q^{59} + q^{60} + 22 q^{61} + 5 q^{63} + 15 q^{64} + q^{65} - 3 q^{66} + 29 q^{67} - 2 q^{68} - 3 q^{69} - 8 q^{70} + 18 q^{71} + 15 q^{72} + 23 q^{73} + 25 q^{74} - 22 q^{75} + 8 q^{76} + 17 q^{77} + 15 q^{78} + 27 q^{79} - q^{80} + 15 q^{81} - q^{82} + 7 q^{83} - 5 q^{84} + 43 q^{85} + 10 q^{86} - 26 q^{87} + 3 q^{88} + 35 q^{89} - q^{90} - 5 q^{91} + 3 q^{92} - 3 q^{94} + 6 q^{95} - 15 q^{96} + 19 q^{97} + 32 q^{98} + 3 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 - 15 * q^3 + 15 * q^4 - q^5 - 15 * q^6 + 5 * q^7 + 15 * q^8 + 15 * q^9 - q^10 + 3 * q^11 - 15 * q^12 - 15 * q^13 + 5 * q^14 + q^15 + 15 * q^16 - 2 * q^17 + 15 * q^18 + 8 * q^19 - q^20 - 5 * q^21 + 3 * q^22 + 3 * q^23 - 15 * q^24 + 22 * q^25 - 15 * q^26 - 15 * q^27 + 5 * q^28 + 26 * q^29 + q^30 + 15 * q^32 - 3 * q^33 - 2 * q^34 - 8 * q^35 + 15 * q^36 + 25 * q^37 + 8 * q^38 + 15 * q^39 - q^40 - q^41 - 5 * q^42 + 10 * q^43 + 3 * q^44 - q^45 + 3 * q^46 - 3 * q^47 - 15 * q^48 + 32 * q^49 + 22 * q^50 + 2 * q^51 - 15 * q^52 + 13 * q^53 - 15 * q^54 - 2 * q^55 + 5 * q^56 - 8 * q^57 + 26 * q^58 + 28 * q^59 + q^60 + 22 * q^61 + 5 * q^63 + 15 * q^64 + q^65 - 3 * q^66 + 29 * q^67 - 2 * q^68 - 3 * q^69 - 8 * q^70 + 18 * q^71 + 15 * q^72 + 23 * q^73 + 25 * q^74 - 22 * q^75 + 8 * q^76 + 17 * q^77 + 15 * q^78 + 27 * q^79 - q^80 + 15 * q^81 - q^82 + 7 * q^83 - 5 * q^84 + 43 * q^85 + 10 * q^86 - 26 * q^87 + 3 * q^88 + 35 * q^89 - q^90 - 5 * q^91 + 3 * q^92 - 3 * q^94 + 6 * q^95 - 15 * q^96 + 19 * q^97 + 32 * q^98 + 3 * q^99

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