LMFDB - Embedded newform 8034.2.a.w.1.4

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			1.4
Root			$-2.08335$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.71945 q^{5} -1.00000 q^{6} +2.07930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.71945 q^{5} -1.00000 q^{6} +2.07930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.71945 q^{10} -4.17067 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.07930 q^{14} -1.71945 q^{15} +1.00000 q^{16} -3.34293 q^{17} -1.00000 q^{18} +3.21672 q^{19} -1.71945 q^{20} +2.07930 q^{21} +4.17067 q^{22} -3.16834 q^{23} -1.00000 q^{24} -2.04350 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.07930 q^{28} +7.68812 q^{29} +1.71945 q^{30} -4.89876 q^{31} -1.00000 q^{32} -4.17067 q^{33} +3.34293 q^{34} -3.57525 q^{35} +1.00000 q^{36} +6.91253 q^{37} -3.21672 q^{38} +1.00000 q^{39} +1.71945 q^{40} +2.12821 q^{41} -2.07930 q^{42} +0.0584673 q^{43} -4.17067 q^{44} -1.71945 q^{45} +3.16834 q^{46} +8.24152 q^{47} +1.00000 q^{48} -2.67649 q^{49} +2.04350 q^{50} -3.34293 q^{51} +1.00000 q^{52} -4.72692 q^{53} -1.00000 q^{54} +7.17124 q^{55} -2.07930 q^{56} +3.21672 q^{57} -7.68812 q^{58} +3.20023 q^{59} -1.71945 q^{60} +1.94455 q^{61} +4.89876 q^{62} +2.07930 q^{63} +1.00000 q^{64} -1.71945 q^{65} +4.17067 q^{66} -8.47636 q^{67} -3.34293 q^{68} -3.16834 q^{69} +3.57525 q^{70} -1.76140 q^{71} -1.00000 q^{72} +10.0154 q^{73} -6.91253 q^{74} -2.04350 q^{75} +3.21672 q^{76} -8.67209 q^{77} -1.00000 q^{78} +5.26682 q^{79} -1.71945 q^{80} +1.00000 q^{81} -2.12821 q^{82} -16.0174 q^{83} +2.07930 q^{84} +5.74799 q^{85} -0.0584673 q^{86} +7.68812 q^{87} +4.17067 q^{88} -7.65296 q^{89} +1.71945 q^{90} +2.07930 q^{91} -3.16834 q^{92} -4.89876 q^{93} -8.24152 q^{94} -5.53097 q^{95} -1.00000 q^{96} -2.20578 q^{97} +2.67649 q^{98} -4.17067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.71945	−0.768960	−0.384480	−	0.923133i	$-0.625619\pi$
$5$	−1.71945	−0.768960	−0.384480	+	0.923133i	$0.625619\pi$
$6$	−1.00000	−0.408248
$7$	2.07930	0.785903	0.392952	−	0.919559i	$-0.371454\pi$
$7$	2.07930	0.785903	0.392952	+	0.919559i	$0.371454\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.71945	0.543737
$11$	−4.17067	−1.25750	−0.628752	−	0.777606i	$-0.716434\pi$
$11$	−4.17067	−1.25750	−0.628752	+	0.777606i	$0.716434\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.07930	−0.555718
$15$	−1.71945	−0.443959
$16$	1.00000	0.250000
$17$	−3.34293	−0.810779	−0.405390	−	0.914144i	$-0.632864\pi$
$17$	−3.34293	−0.810779	−0.405390	+	0.914144i	$0.632864\pi$
$18$	−1.00000	−0.235702
$19$	3.21672	0.737966	0.368983	−	0.929436i	$-0.379706\pi$
$19$	3.21672	0.737966	0.368983	+	0.929436i	$0.379706\pi$
$20$	−1.71945	−0.384480
$21$	2.07930	0.453741
$22$	4.17067	0.889189
$23$	−3.16834	−0.660645	−0.330322	−	0.943868i	$-0.607157\pi$
$23$	−3.16834	−0.660645	−0.330322	+	0.943868i	$0.607157\pi$
$24$	−1.00000	−0.204124
$25$	−2.04350	−0.408701
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	2.07930	0.392952
$29$	7.68812	1.42765	0.713824	−	0.700325i	$-0.246962\pi$
$29$	7.68812	1.42765	0.713824	+	0.700325i	$0.246962\pi$
$30$	1.71945	0.313927
$31$	−4.89876	−0.879843	−0.439922	−	0.898036i	$-0.644994\pi$
$31$	−4.89876	−0.879843	−0.439922	+	0.898036i	$0.644994\pi$
$32$	−1.00000	−0.176777
$33$	−4.17067	−0.726020
$34$	3.34293	0.573308
$35$	−3.57525	−0.604328
$36$	1.00000	0.166667
$37$	6.91253	1.13641	0.568207	−	0.822886i	$-0.307637\pi$
$37$	6.91253	1.13641	0.568207	+	0.822886i	$0.307637\pi$
$38$	−3.21672	−0.521821
$39$	1.00000	0.160128
$40$	1.71945	0.271868
$41$	2.12821	0.332371	0.166186	−	0.986095i	$-0.446855\pi$
$41$	2.12821	0.332371	0.166186	+	0.986095i	$0.446855\pi$
$42$	−2.07930	−0.320844
$43$	0.0584673	0.00891618	0.00445809	−	0.999990i	$-0.498581\pi$
$43$	0.0584673	0.00891618	0.00445809	+	0.999990i	$0.498581\pi$
$44$	−4.17067	−0.628752
$45$	−1.71945	−0.256320
$46$	3.16834	0.467146
$47$	8.24152	1.20215	0.601075	−	0.799193i	$-0.294739\pi$
$47$	8.24152	1.20215	0.601075	+	0.799193i	$0.294739\pi$
$48$	1.00000	0.144338
$49$	−2.67649	−0.382356
$50$	2.04350	0.288995
$51$	−3.34293	−0.468104
$52$	1.00000	0.138675
$53$	−4.72692	−0.649293	−0.324646	−	0.945835i	$-0.605245\pi$
$53$	−4.72692	−0.649293	−0.324646	+	0.945835i	$0.605245\pi$
$54$	−1.00000	−0.136083
$55$	7.17124	0.966970
$56$	−2.07930	−0.277859
$57$	3.21672	0.426065
$58$	−7.68812	−1.00950
$59$	3.20023	0.416635	0.208317	−	0.978061i	$-0.433201\pi$
$59$	3.20023	0.416635	0.208317	+	0.978061i	$0.433201\pi$
$60$	−1.71945	−0.221980
$61$	1.94455	0.248974	0.124487	−	0.992221i	$-0.460271\pi$
$61$	1.94455	0.248974	0.124487	+	0.992221i	$0.460271\pi$
$62$	4.89876	0.622143
$63$	2.07930	0.261968
$64$	1.00000	0.125000
$65$	−1.71945	−0.213271
$66$	4.17067	0.513374
$67$	−8.47636	−1.03555	−0.517776	−	0.855516i	$-0.673240\pi$
$67$	−8.47636	−1.03555	−0.517776	+	0.855516i	$0.673240\pi$
$68$	−3.34293	−0.405390
$69$	−3.16834	−0.381423
$70$	3.57525	0.427324
$71$	−1.76140	−0.209040	−0.104520	−	0.994523i	$-0.533331\pi$
$71$	−1.76140	−0.209040	−0.104520	+	0.994523i	$0.533331\pi$
$72$	−1.00000	−0.117851
$73$	10.0154	1.17221	0.586105	−	0.810235i	$-0.300660\pi$
$73$	10.0154	1.17221	0.586105	+	0.810235i	$0.300660\pi$
$74$	−6.91253	−0.803566
$75$	−2.04350	−0.235964
$76$	3.21672	0.368983
$77$	−8.67209	−0.988276
$78$	−1.00000	−0.113228
$79$	5.26682	0.592564	0.296282	−	0.955101i	$-0.404253\pi$
$79$	5.26682	0.592564	0.296282	+	0.955101i	$0.404253\pi$
$80$	−1.71945	−0.192240
$81$	1.00000	0.111111
$82$	−2.12821	−0.235022
$83$	−16.0174	−1.75814	−0.879070	−	0.476694i	$-0.841835\pi$
$83$	−16.0174	−1.75814	−0.879070	+	0.476694i	$0.841835\pi$
$84$	2.07930	0.226871
$85$	5.74799	0.623457
$86$	−0.0584673	−0.00630469
$87$	7.68812	0.824253
$88$	4.17067	0.444595
$89$	−7.65296	−0.811212	−0.405606	−	0.914048i	$-0.632939\pi$
$89$	−7.65296	−0.811212	−0.405606	+	0.914048i	$0.632939\pi$
$90$	1.71945	0.181246
$91$	2.07930	0.217970
$92$	−3.16834	−0.330322
$93$	−4.89876	−0.507978
$94$	−8.24152	−0.850048
$95$	−5.53097	−0.567466
$96$	−1.00000	−0.102062
$97$	−2.20578	−0.223964	−0.111982	−	0.993710i	$-0.535720\pi$
$97$	−2.20578	−0.223964	−0.111982	+	0.993710i	$0.535720\pi$
$98$	2.67649	0.270367
$99$	−4.17067	−0.419168
$100$	−2.04350	−0.204350
$101$	−18.0449	−1.79553	−0.897765	−	0.440474i	$-0.854810\pi$
$101$	−18.0449	−1.79553	−0.897765	+	0.440474i	$0.854810\pi$
$102$	3.34293	0.330999
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−3.57525	−0.348909
$106$	4.72692	0.459119
$107$	−12.7003	−1.22778	−0.613890	−	0.789391i	$-0.710396\pi$
$107$	−12.7003	−1.22778	−0.613890	+	0.789391i	$0.710396\pi$
$108$	1.00000	0.0962250
$109$	6.46568	0.619300	0.309650	−	0.950851i	$-0.399788\pi$
$109$	6.46568	0.619300	0.309650	+	0.950851i	$0.399788\pi$
$110$	−7.17124	−0.683751
$111$	6.91253	0.656109
$112$	2.07930	0.196476
$113$	12.2618	1.15350	0.576748	−	0.816922i	$-0.304321\pi$
$113$	12.2618	1.15350	0.576748	+	0.816922i	$0.304321\pi$
$114$	−3.21672	−0.301273
$115$	5.44779	0.508009
$116$	7.68812	0.713824
$117$	1.00000	0.0924500
$118$	−3.20023	−0.294605
$119$	−6.95097	−0.637194
$120$	1.71945	0.156963
$121$	6.39447	0.581315
$122$	−1.94455	−0.176051
$123$	2.12821	0.191895
$124$	−4.89876	−0.439922
$125$	12.1109	1.08323
$126$	−2.07930	−0.185239
$127$	2.84286	0.252263	0.126132	−	0.992014i	$-0.459744\pi$
$127$	2.84286	0.252263	0.126132	+	0.992014i	$0.459744\pi$
$128$	−1.00000	−0.0883883
$129$	0.0584673	0.00514776
$130$	1.71945	0.150805
$131$	−19.9421	−1.74235	−0.871176	−	0.490971i	$-0.836642\pi$
$131$	−19.9421	−1.74235	−0.871176	+	0.490971i	$0.836642\pi$
$132$	−4.17067	−0.363010
$133$	6.68854	0.579970
$134$	8.47636	0.732246
$135$	−1.71945	−0.147986
$136$	3.34293	0.286654
$137$	−13.6536	−1.16650	−0.583252	−	0.812291i	$-0.698220\pi$
$137$	−13.6536	−1.16650	−0.583252	+	0.812291i	$0.698220\pi$
$138$	3.16834	0.269707
$139$	15.7883	1.33915	0.669574	−	0.742745i	$-0.266477\pi$
$139$	15.7883	1.33915	0.669574	+	0.742745i	$0.266477\pi$
$140$	−3.57525	−0.302164
$141$	8.24152	0.694061
$142$	1.76140	0.147814
$143$	−4.17067	−0.348769
$144$	1.00000	0.0833333
$145$	−13.2193	−1.09780
$146$	−10.0154	−0.828878
$147$	−2.67649	−0.220753
$148$	6.91253	0.568207
$149$	5.60769	0.459400	0.229700	−	0.973262i	$-0.426226\pi$
$149$	5.60769	0.459400	0.229700	+	0.973262i	$0.426226\pi$
$150$	2.04350	0.166851
$151$	−21.8696	−1.77972	−0.889862	−	0.456229i	$-0.849200\pi$
$151$	−21.8696	−1.77972	−0.889862	+	0.456229i	$0.849200\pi$
$152$	−3.21672	−0.260910
$153$	−3.34293	−0.270260
$154$	8.67209	0.698817
$155$	8.42315	0.676564
$156$	1.00000	0.0800641
$157$	−6.73068	−0.537167	−0.268583	−	0.963256i	$-0.586555\pi$
$157$	−6.73068	−0.537167	−0.268583	+	0.963256i	$0.586555\pi$
$158$	−5.26682	−0.419006
$159$	−4.72692	−0.374869
$160$	1.71945	0.135934
$161$	−6.58795	−0.519203
$162$	−1.00000	−0.0785674
$163$	−5.72060	−0.448072	−0.224036	−	0.974581i	$-0.571923\pi$
$163$	−5.72060	−0.448072	−0.224036	+	0.974581i	$0.571923\pi$
$164$	2.12821	0.166186
$165$	7.17124	0.558280
$166$	16.0174	1.24319
$167$	14.9623	1.15782	0.578910	−	0.815391i	$-0.303478\pi$
$167$	14.9623	1.15782	0.578910	+	0.815391i	$0.303478\pi$
$168$	−2.07930	−0.160422
$169$	1.00000	0.0769231
$170$	−5.74799	−0.440850
$171$	3.21672	0.245989
$172$	0.0584673	0.00445809
$173$	−20.0856	−1.52708	−0.763539	−	0.645762i	$-0.776540\pi$
$173$	−20.0856	−1.52708	−0.763539	+	0.645762i	$0.776540\pi$
$174$	−7.68812	−0.582835
$175$	−4.24907	−0.321199
$176$	−4.17067	−0.314376
$177$	3.20023	0.240544
$178$	7.65296	0.573613
$179$	−19.1234	−1.42935	−0.714675	−	0.699457i	$-0.753425\pi$
$179$	−19.1234	−1.42935	−0.714675	+	0.699457i	$0.753425\pi$
$180$	−1.71945	−0.128160
$181$	−6.63039	−0.492833	−0.246417	−	0.969164i	$-0.579253\pi$
$181$	−6.63039	−0.492833	−0.246417	+	0.969164i	$0.579253\pi$
$182$	−2.07930	−0.154128
$183$	1.94455	0.143745
$184$	3.16834	0.233573
$185$	−11.8857	−0.873856
$186$	4.89876	0.359194
$187$	13.9422	1.01956
$188$	8.24152	0.601075
$189$	2.07930	0.151247
$190$	5.53097	0.401259
$191$	−9.22135	−0.667233	−0.333617	−	0.942709i	$-0.608269\pi$
$191$	−9.22135	−0.667233	−0.333617	+	0.942709i	$0.608269\pi$
$192$	1.00000	0.0721688
$193$	−4.66229	−0.335599	−0.167800	−	0.985821i	$-0.553666\pi$
$193$	−4.66229	−0.335599	−0.167800	+	0.985821i	$0.553666\pi$
$194$	2.20578	0.158366
$195$	−1.71945	−0.123132
$196$	−2.67649	−0.191178
$197$	8.89204	0.633532	0.316766	−	0.948504i	$-0.397403\pi$
$197$	8.89204	0.633532	0.316766	+	0.948504i	$0.397403\pi$
$198$	4.17067	0.296396
$199$	−13.4916	−0.956391	−0.478195	−	0.878254i	$-0.658709\pi$
$199$	−13.4916	−0.956391	−0.478195	+	0.878254i	$0.658709\pi$
$200$	2.04350	0.144498
$201$	−8.47636	−0.597876
$202$	18.0449	1.26963
$203$	15.9859	1.12199
$204$	−3.34293	−0.234052
$205$	−3.65935	−0.255580
$206$	1.00000	0.0696733
$207$	−3.16834	−0.220215
$208$	1.00000	0.0693375
$209$	−13.4159	−0.927995
$210$	3.57525	0.246716
$211$	−7.92962	−0.545898	−0.272949	−	0.962029i	$-0.587999\pi$
$211$	−7.92962	−0.545898	−0.272949	+	0.962029i	$0.587999\pi$
$212$	−4.72692	−0.324646
$213$	−1.76140	−0.120689
$214$	12.7003	0.868172
$215$	−0.100531	−0.00685619
$216$	−1.00000	−0.0680414
$217$	−10.1860	−0.691472
$218$	−6.46568	−0.437911
$219$	10.0154	0.676776
$220$	7.17124	0.483485
$221$	−3.34293	−0.224870
$222$	−6.91253	−0.463939
$223$	−3.35526	−0.224685	−0.112342	−	0.993670i	$-0.535835\pi$
$223$	−3.35526	−0.224685	−0.112342	+	0.993670i	$0.535835\pi$
$224$	−2.07930	−0.138929
$225$	−2.04350	−0.136234
$226$	−12.2618	−0.815645
$227$	−1.28365	−0.0851986	−0.0425993	−	0.999092i	$-0.513564\pi$
$227$	−1.28365	−0.0851986	−0.0425993	+	0.999092i	$0.513564\pi$
$228$	3.21672	0.213032
$229$	−6.54398	−0.432438	−0.216219	−	0.976345i	$-0.569373\pi$
$229$	−6.54398	−0.432438	−0.216219	+	0.976345i	$0.569373\pi$
$230$	−5.44779	−0.359217
$231$	−8.67209	−0.570582
$232$	−7.68812	−0.504750
$233$	−1.47551	−0.0966637	−0.0483318	−	0.998831i	$-0.515390\pi$
$233$	−1.47551	−0.0966637	−0.0483318	+	0.998831i	$0.515390\pi$
$234$	−1.00000	−0.0653720
$235$	−14.1708	−0.924404
$236$	3.20023	0.208317
$237$	5.26682	0.342117
$238$	6.95097	0.450564
$239$	18.4065	1.19062	0.595309	−	0.803497i	$-0.297030\pi$
$239$	18.4065	1.19062	0.595309	+	0.803497i	$0.297030\pi$
$240$	−1.71945	−0.110990
$241$	−7.89644	−0.508654	−0.254327	−	0.967118i	$-0.581854\pi$
$241$	−7.89644	−0.508654	−0.254327	+	0.967118i	$0.581854\pi$
$242$	−6.39447	−0.411052
$243$	1.00000	0.0641500
$244$	1.94455	0.124487
$245$	4.60208	0.294016
$246$	−2.12821	−0.135690
$247$	3.21672	0.204675
$248$	4.89876	0.311072
$249$	−16.0174	−1.01506
$250$	−12.1109	−0.765962
$251$	13.4455	0.848674	0.424337	−	0.905504i	$-0.360507\pi$
$251$	13.4455	0.848674	0.424337	+	0.905504i	$0.360507\pi$
$252$	2.07930	0.130984
$253$	13.2141	0.830763
$254$	−2.84286	−0.178377
$255$	5.74799	0.359953
$256$	1.00000	0.0625000
$257$	25.5686	1.59492	0.797462	−	0.603369i	$-0.206175\pi$
$257$	25.5686	1.59492	0.797462	+	0.603369i	$0.206175\pi$
$258$	−0.0584673	−0.00364002
$259$	14.3733	0.893111
$260$	−1.71945	−0.106636
$261$	7.68812	0.475882
$262$	19.9421	1.23203
$263$	−9.78932	−0.603635	−0.301818	−	0.953366i	$-0.597593\pi$
$263$	−9.78932	−0.603635	−0.301818	+	0.953366i	$0.597593\pi$
$264$	4.17067	0.256687
$265$	8.12769	0.499280
$266$	−6.68854	−0.410101
$267$	−7.65296	−0.468353
$268$	−8.47636	−0.517776
$269$	28.9797	1.76692	0.883462	−	0.468503i	$-0.155207\pi$
$269$	28.9797	1.76692	0.883462	+	0.468503i	$0.155207\pi$
$270$	1.71945	0.104642
$271$	−1.76169	−0.107015	−0.0535074	−	0.998567i	$-0.517040\pi$
$271$	−1.76169	−0.107015	−0.0535074	+	0.998567i	$0.517040\pi$
$272$	−3.34293	−0.202695
$273$	2.07930	0.125845
$274$	13.6536	0.824843
$275$	8.52278	0.513943
$276$	−3.16834	−0.190712
$277$	20.3481	1.22260	0.611300	−	0.791399i	$-0.290647\pi$
$277$	20.3481	1.22260	0.611300	+	0.791399i	$0.290647\pi$
$278$	−15.7883	−0.946921
$279$	−4.89876	−0.293281
$280$	3.57525	0.213662
$281$	−2.83942	−0.169385	−0.0846927	−	0.996407i	$-0.526991\pi$
$281$	−2.83942	−0.169385	−0.0846927	+	0.996407i	$0.526991\pi$
$282$	−8.24152	−0.490775
$283$	−12.5214	−0.744322	−0.372161	−	0.928168i	$-0.621383\pi$
$283$	−12.5214	−0.744322	−0.372161	+	0.928168i	$0.621383\pi$
$284$	−1.76140	−0.104520
$285$	−5.53097	−0.327627
$286$	4.17067	0.246617
$287$	4.42520	0.261211
$288$	−1.00000	−0.0589256
$289$	−5.82483	−0.342637
$290$	13.2193	0.776264
$291$	−2.20578	−0.129305
$292$	10.0154	0.586105
$293$	−0.436085	−0.0254764	−0.0127382	−	0.999919i	$-0.504055\pi$
$293$	−0.436085	−0.0254764	−0.0127382	+	0.999919i	$0.504055\pi$
$294$	2.67649	0.156096
$295$	−5.50263	−0.320375
$296$	−6.91253	−0.401783
$297$	−4.17067	−0.242007
$298$	−5.60769	−0.324845
$299$	−3.16834	−0.183230
$300$	−2.04350	−0.117982
$301$	0.121571	0.00700726
$302$	21.8696	1.25846
$303$	−18.0449	−1.03665
$304$	3.21672	0.184491
$305$	−3.34355	−0.191451
$306$	3.34293	0.191103
$307$	−14.4308	−0.823607	−0.411804	−	0.911273i	$-0.635101\pi$
$307$	−14.4308	−0.823607	−0.411804	+	0.911273i	$0.635101\pi$
$308$	−8.67209	−0.494138
$309$	−1.00000	−0.0568880
$310$	−8.42315	−0.478403
$311$	−29.3998	−1.66711	−0.833556	−	0.552435i	$-0.813699\pi$
$311$	−29.3998	−1.66711	−0.833556	+	0.552435i	$0.813699\pi$
$312$	−1.00000	−0.0566139
$313$	−19.8482	−1.12188	−0.560942	−	0.827855i	$-0.689561\pi$
$313$	−19.8482	−1.12188	−0.560942	+	0.827855i	$0.689561\pi$
$314$	6.73068	0.379834
$315$	−3.57525	−0.201443
$316$	5.26682	0.296282
$317$	−15.1910	−0.853212	−0.426606	−	0.904438i	$-0.640291\pi$
$317$	−15.1910	−0.853212	−0.426606	+	0.904438i	$0.640291\pi$
$318$	4.72692	0.265073
$319$	−32.0646	−1.79527
$320$	−1.71945	−0.0961200
$321$	−12.7003	−0.708859
$322$	6.58795	0.367132
$323$	−10.7533	−0.598327
$324$	1.00000	0.0555556
$325$	−2.04350	−0.113353
$326$	5.72060	0.316835
$327$	6.46568	0.357553
$328$	−2.12821	−0.117511
$329$	17.1366	0.944773
$330$	−7.17124	−0.394764
$331$	6.93505	0.381185	0.190592	−	0.981669i	$-0.438959\pi$
$331$	6.93505	0.381185	0.190592	+	0.981669i	$0.438959\pi$
$332$	−16.0174	−0.879070
$333$	6.91253	0.378804
$334$	−14.9623	−0.818702
$335$	14.5746	0.796298
$336$	2.07930	0.113435
$337$	−8.13952	−0.443388	−0.221694	−	0.975116i	$-0.571159\pi$
$337$	−8.13952	−0.443388	−0.221694	+	0.975116i	$0.571159\pi$
$338$	−1.00000	−0.0543928
$339$	12.2618	0.665972
$340$	5.74799	0.311728
$341$	20.4311	1.10641
$342$	−3.21672	−0.173940
$343$	−20.1204	−1.08640
$344$	−0.0584673	−0.00315235
$345$	5.44779	0.293299
$346$	20.0856	1.07981
$347$	−1.37702	−0.0739221	−0.0369611	−	0.999317i	$-0.511768\pi$
$347$	−1.37702	−0.0739221	−0.0369611	+	0.999317i	$0.511768\pi$
$348$	7.68812	0.412126
$349$	26.4328	1.41491	0.707457	−	0.706756i	$-0.249842\pi$
$349$	26.4328	1.41491	0.707457	+	0.706756i	$0.249842\pi$
$350$	4.24907	0.227122
$351$	1.00000	0.0533761
$352$	4.17067	0.222297
$353$	−16.4525	−0.875680	−0.437840	−	0.899053i	$-0.644256\pi$
$353$	−16.4525	−0.875680	−0.437840	+	0.899053i	$0.644256\pi$
$354$	−3.20023	−0.170090
$355$	3.02864	0.160744
$356$	−7.65296	−0.405606
$357$	−6.95097	−0.367884
$358$	19.1234	1.01070
$359$	10.5179	0.555112	0.277556	−	0.960709i	$-0.410476\pi$
$359$	10.5179	0.555112	0.277556	+	0.960709i	$0.410476\pi$
$360$	1.71945	0.0906228
$361$	−8.65272	−0.455407
$362$	6.63039	0.348486
$363$	6.39447	0.335623
$364$	2.07930	0.108985
$365$	−17.2209	−0.901383
$366$	−1.94455	−0.101643
$367$	5.07178	0.264745	0.132372	−	0.991200i	$-0.457741\pi$
$367$	5.07178	0.264745	0.132372	+	0.991200i	$0.457741\pi$
$368$	−3.16834	−0.165161
$369$	2.12821	0.110790
$370$	11.8857	0.617910
$371$	−9.82871	−0.510281
$372$	−4.89876	−0.253989
$373$	−17.1209	−0.886485	−0.443242	−	0.896402i	$-0.646172\pi$
$373$	−17.1209	−0.886485	−0.443242	+	0.896402i	$0.646172\pi$
$374$	−13.9422	−0.720936
$375$	12.1109	0.625406
$376$	−8.24152	−0.425024
$377$	7.68812	0.395958
$378$	−2.07930	−0.106948
$379$	15.0132	0.771175	0.385587	−	0.922671i	$-0.373999\pi$
$379$	15.0132	0.771175	0.385587	+	0.922671i	$0.373999\pi$
$380$	−5.53097	−0.283733
$381$	2.84286	0.145644
$382$	9.22135	0.471805
$383$	23.8022	1.21623	0.608117	−	0.793848i	$-0.291925\pi$
$383$	23.8022	1.21623	0.608117	+	0.793848i	$0.291925\pi$
$384$	−1.00000	−0.0510310
$385$	14.9112	0.759945
$386$	4.66229	0.237304
$387$	0.0584673	0.00297206
$388$	−2.20578	−0.111982
$389$	−28.7020	−1.45525	−0.727623	−	0.685977i	$-0.759375\pi$
$389$	−28.7020	−1.45525	−0.727623	+	0.685977i	$0.759375\pi$
$390$	1.71945	0.0870675
$391$	10.5915	0.535637
$392$	2.67649	0.135183
$393$	−19.9421	−1.00595
$394$	−8.89204	−0.447975
$395$	−9.05601	−0.455658
$396$	−4.17067	−0.209584
$397$	1.63976	0.0822974	0.0411487	−	0.999153i	$-0.486898\pi$
$397$	1.63976	0.0822974	0.0411487	+	0.999153i	$0.486898\pi$
$398$	13.4916	0.676270
$399$	6.68854	0.334846
$400$	−2.04350	−0.102175
$401$	−1.73416	−0.0865996	−0.0432998	−	0.999062i	$-0.513787\pi$
$401$	−1.73416	−0.0865996	−0.0432998	+	0.999062i	$0.513787\pi$
$402$	8.47636	0.422762
$403$	−4.89876	−0.244025
$404$	−18.0449	−0.897765
$405$	−1.71945	−0.0854400
$406$	−15.9859	−0.793369
$407$	−28.8299	−1.42904
$408$	3.34293	0.165500
$409$	−16.4451	−0.813160	−0.406580	−	0.913615i	$-0.633279\pi$
$409$	−16.4451	−0.813160	−0.406580	+	0.913615i	$0.633279\pi$
$410$	3.65935	0.180722
$411$	−13.6536	−0.673481
$412$	−1.00000	−0.0492665
$413$	6.65426	0.327435
$414$	3.16834	0.155715
$415$	27.5411	1.35194
$416$	−1.00000	−0.0490290
$417$	15.7883	0.773158
$418$	13.4159	0.656191
$419$	−4.04844	−0.197779	−0.0988897	−	0.995098i	$-0.531529\pi$
$419$	−4.04844	−0.197779	−0.0988897	+	0.995098i	$0.531529\pi$
$420$	−3.57525	−0.174454
$421$	−25.1134	−1.22395	−0.611975	−	0.790877i	$-0.709625\pi$
$421$	−25.1134	−1.22395	−0.611975	+	0.790877i	$0.709625\pi$
$422$	7.92962	0.386008
$423$	8.24152	0.400716
$424$	4.72692	0.229560
$425$	6.83129	0.331366
$426$	1.76140	0.0853403
$427$	4.04331	0.195670
$428$	−12.7003	−0.613890
$429$	−4.17067	−0.201362
$430$	0.100531	0.00484806
$431$	13.7857	0.664035	0.332018	−	0.943273i	$-0.392271\pi$
$431$	13.7857	0.664035	0.332018	+	0.943273i	$0.392271\pi$
$432$	1.00000	0.0481125
$433$	−27.8209	−1.33699	−0.668493	−	0.743718i	$-0.733060\pi$
$433$	−27.8209	−1.33699	−0.668493	+	0.743718i	$0.733060\pi$
$434$	10.1860	0.488944
$435$	−13.2193	−0.633817
$436$	6.46568	0.309650
$437$	−10.1917	−0.487533
$438$	−10.0154	−0.478553
$439$	−0.721623	−0.0344412	−0.0172206	−	0.999852i	$-0.505482\pi$
$439$	−0.721623	−0.0344412	−0.0172206	+	0.999852i	$0.505482\pi$
$440$	−7.17124	−0.341875
$441$	−2.67649	−0.127452
$442$	3.34293	0.159007
$443$	−28.5213	−1.35509	−0.677543	−	0.735483i	$-0.736955\pi$
$443$	−28.5213	−1.35509	−0.677543	+	0.735483i	$0.736955\pi$
$444$	6.91253	0.328054
$445$	13.1588	0.623789
$446$	3.35526	0.158876
$447$	5.60769	0.265235
$448$	2.07930	0.0982379
$449$	−21.0796	−0.994808	−0.497404	−	0.867519i	$-0.665713\pi$
$449$	−21.0796	−0.994808	−0.497404	+	0.867519i	$0.665713\pi$
$450$	2.04350	0.0963317
$451$	−8.87607	−0.417958
$452$	12.2618	0.576748
$453$	−21.8696	−1.02752
$454$	1.28365	0.0602445
$455$	−3.57525	−0.167610
$456$	−3.21672	−0.150637
$457$	37.2739	1.74360	0.871799	−	0.489863i	$-0.162953\pi$
$457$	37.2739	1.74360	0.871799	+	0.489863i	$0.162953\pi$
$458$	6.54398	0.305780
$459$	−3.34293	−0.156035
$460$	5.44779	0.254005
$461$	−27.0955	−1.26197	−0.630983	−	0.775797i	$-0.717348\pi$
$461$	−27.0955	−1.26197	−0.630983	+	0.775797i	$0.717348\pi$
$462$	8.67209	0.403462
$463$	4.26509	0.198215	0.0991077	−	0.995077i	$-0.468401\pi$
$463$	4.26509	0.198215	0.0991077	+	0.995077i	$0.468401\pi$
$464$	7.68812	0.356912
$465$	8.42315	0.390614
$466$	1.47551	0.0683515
$467$	−10.4283	−0.482563	−0.241282	−	0.970455i	$-0.577568\pi$
$467$	−10.4283	−0.482563	−0.241282	+	0.970455i	$0.577568\pi$
$468$	1.00000	0.0462250
$469$	−17.6249	−0.813844
$470$	14.1708	0.653653
$471$	−6.73068	−0.310133
$472$	−3.20023	−0.147303
$473$	−0.243848	−0.0112121
$474$	−5.26682	−0.241913
$475$	−6.57338	−0.301607
$476$	−6.95097	−0.318597
$477$	−4.72692	−0.216431
$478$	−18.4065	−0.841894
$479$	28.8986	1.32041	0.660206	−	0.751084i	$-0.270469\pi$
$479$	28.8986	1.32041	0.660206	+	0.751084i	$0.270469\pi$
$480$	1.71945	0.0784816
$481$	6.91253	0.315184
$482$	7.89644	0.359673
$483$	−6.58795	−0.299762
$484$	6.39447	0.290658
$485$	3.79273	0.172219
$486$	−1.00000	−0.0453609
$487$	12.2855	0.556709	0.278354	−	0.960478i	$-0.410211\pi$
$487$	12.2855	0.556709	0.278354	+	0.960478i	$0.410211\pi$
$488$	−1.94455	−0.0880257
$489$	−5.72060	−0.258695
$490$	−4.60208	−0.207901
$491$	−12.1091	−0.546478	−0.273239	−	0.961946i	$-0.588095\pi$
$491$	−12.1091	−0.546478	−0.273239	+	0.961946i	$0.588095\pi$
$492$	2.12821	0.0959473
$493$	−25.7008	−1.15751
$494$	−3.21672	−0.144727
$495$	7.17124	0.322323
$496$	−4.89876	−0.219961
$497$	−3.66250	−0.164285
$498$	16.0174	0.717757
$499$	22.1382	0.991043	0.495522	−	0.868596i	$-0.334977\pi$
$499$	22.1382	0.991043	0.495522	+	0.868596i	$0.334977\pi$
$500$	12.1109	0.541617
$501$	14.9623	0.668468
$502$	−13.4455	−0.600103
$503$	8.26073	0.368328	0.184164	−	0.982896i	$-0.441042\pi$
$503$	8.26073	0.368328	0.184164	+	0.982896i	$0.441042\pi$
$504$	−2.07930	−0.0926196
$505$	31.0272	1.38069
$506$	−13.2141	−0.587438
$507$	1.00000	0.0444116
$508$	2.84286	0.126132
$509$	−25.7853	−1.14291	−0.571456	−	0.820632i	$-0.693621\pi$
$509$	−25.7853	−1.14291	−0.571456	+	0.820632i	$0.693621\pi$
$510$	−5.74799	−0.254525
$511$	20.8250	0.921244
$512$	−1.00000	−0.0441942
$513$	3.21672	0.142022
$514$	−25.5686	−1.12778
$515$	1.71945	0.0757679
$516$	0.0584673	0.00257388
$517$	−34.3726	−1.51171
$518$	−14.3733	−0.631525
$519$	−20.0856	−0.881659
$520$	1.71945	0.0754027
$521$	−14.2152	−0.622778	−0.311389	−	0.950283i	$-0.600794\pi$
$521$	−14.2152	−0.622778	−0.311389	+	0.950283i	$0.600794\pi$
$522$	−7.68812	−0.336500
$523$	−33.4547	−1.46287	−0.731435	−	0.681911i	$-0.761149\pi$
$523$	−33.4547	−1.46287	−0.731435	+	0.681911i	$0.761149\pi$
$524$	−19.9421	−0.871176
$525$	−4.24907	−0.185445
$526$	9.78932	0.426835
$527$	16.3762	0.713359
$528$	−4.17067	−0.181505
$529$	−12.9616	−0.563548
$530$	−8.12769	−0.353044
$531$	3.20023	0.138878
$532$	6.68854	0.289985
$533$	2.12821	0.0921831
$534$	7.65296	0.331176
$535$	21.8374	0.944114
$536$	8.47636	0.366123
$537$	−19.1234	−0.825235
$538$	−28.9797	−1.24940
$539$	11.1628	0.480814
$540$	−1.71945	−0.0739932
$541$	−10.5204	−0.452307	−0.226154	−	0.974092i	$-0.572615\pi$
$541$	−10.5204	−0.452307	−0.226154	+	0.974092i	$0.572615\pi$
$542$	1.76169	0.0756709
$543$	−6.63039	−0.284537
$544$	3.34293	0.143327
$545$	−11.1174	−0.476217
$546$	−2.07930	−0.0889860
$547$	−30.4223	−1.30076	−0.650381	−	0.759608i	$-0.725391\pi$
$547$	−30.4223	−1.30076	−0.650381	+	0.759608i	$0.725391\pi$
$548$	−13.6536	−0.583252
$549$	1.94455	0.0829914
$550$	−8.52278	−0.363412
$551$	24.7305	1.05355
$552$	3.16834	0.134854
$553$	10.9513	0.465698
$554$	−20.3481	−0.864509
$555$	−11.8857	−0.504521
$556$	15.7883	0.669574
$557$	10.0678	0.426586	0.213293	−	0.976988i	$-0.431581\pi$
$557$	10.0678	0.426586	0.213293	+	0.976988i	$0.431581\pi$
$558$	4.89876	0.207381
$559$	0.0584673	0.00247290
$560$	−3.57525	−0.151082
$561$	13.9422	0.588642
$562$	2.83942	0.119774
$563$	12.6046	0.531222	0.265611	−	0.964080i	$-0.414426\pi$
$563$	12.6046	0.531222	0.265611	+	0.964080i	$0.414426\pi$
$564$	8.24152	0.347031
$565$	−21.0836	−0.886993
$566$	12.5214	0.526315
$567$	2.07930	0.0873226
$568$	1.76140	0.0739069
$569$	34.6331	1.45190	0.725948	−	0.687750i	$-0.241401\pi$
$569$	34.6331	1.45190	0.725948	+	0.687750i	$0.241401\pi$
$570$	5.53097	0.231667
$571$	16.8351	0.704527	0.352263	−	0.935901i	$-0.385412\pi$
$571$	16.8351	0.704527	0.352263	+	0.935901i	$0.385412\pi$
$572$	−4.17067	−0.174384
$573$	−9.22135	−0.385227
$574$	−4.42520	−0.184704
$575$	6.47452	0.270006
$576$	1.00000	0.0416667
$577$	11.1484	0.464112	0.232056	−	0.972702i	$-0.425455\pi$
$577$	11.1484	0.464112	0.232056	+	0.972702i	$0.425455\pi$
$578$	5.82483	0.242281
$579$	−4.66229	−0.193758
$580$	−13.2193	−0.548902
$581$	−33.3051	−1.38173
$582$	2.20578	0.0914327
$583$	19.7144	0.816488
$584$	−10.0154	−0.414439
$585$	−1.71945	−0.0710904
$586$	0.436085	0.0180145
$587$	18.7838	0.775289	0.387644	−	0.921809i	$-0.373289\pi$
$587$	18.7838	0.775289	0.387644	+	0.921809i	$0.373289\pi$
$588$	−2.67649	−0.110377
$589$	−15.7579	−0.649294
$590$	5.50263	0.226540
$591$	8.89204	0.365770
$592$	6.91253	0.284103
$593$	3.38313	0.138928	0.0694642	−	0.997584i	$-0.477871\pi$
$593$	3.38313	0.138928	0.0694642	+	0.997584i	$0.477871\pi$
$594$	4.17067	0.171125
$595$	11.9518	0.489977
$596$	5.60769	0.229700
$597$	−13.4916	−0.552172
$598$	3.16834	0.129563
$599$	4.98938	0.203861	0.101930	−	0.994792i	$-0.467498\pi$
$599$	4.98938	0.203861	0.101930	+	0.994792i	$0.467498\pi$
$600$	2.04350	0.0834257
$601$	15.8393	0.646100	0.323050	−	0.946382i	$-0.395292\pi$
$601$	15.8393	0.646100	0.323050	+	0.946382i	$0.395292\pi$
$602$	−0.121571	−0.00495488
$603$	−8.47636	−0.345184
$604$	−21.8696	−0.889862
$605$	−10.9949	−0.447008
$606$	18.0449	0.733022
$607$	−16.6413	−0.675449	−0.337725	−	0.941245i	$-0.609657\pi$
$607$	−16.6413	−0.675449	−0.337725	+	0.941245i	$0.609657\pi$
$608$	−3.21672	−0.130455
$609$	15.9859	0.647783
$610$	3.34355	0.135376
$611$	8.24152	0.333416
$612$	−3.34293	−0.135130
$613$	34.6382	1.39902	0.699512	−	0.714621i	$-0.253401\pi$
$613$	34.6382	1.39902	0.699512	+	0.714621i	$0.253401\pi$
$614$	14.4308	0.582378
$615$	−3.65935	−0.147559
$616$	8.67209	0.349408
$617$	−10.2630	−0.413172	−0.206586	−	0.978428i	$-0.566235\pi$
$617$	−10.2630	−0.413172	−0.206586	+	0.978428i	$0.566235\pi$
$618$	1.00000	0.0402259
$619$	2.78018	0.111745	0.0558725	−	0.998438i	$-0.482206\pi$
$619$	2.78018	0.111745	0.0558725	+	0.998438i	$0.482206\pi$
$620$	8.42315	0.338282
$621$	−3.16834	−0.127141
$622$	29.3998	1.17883
$623$	−15.9128	−0.637534
$624$	1.00000	0.0400320
$625$	−10.6066	−0.424263
$626$	19.8482	0.793292
$627$	−13.4159	−0.535778
$628$	−6.73068	−0.268583
$629$	−23.1081	−0.921380
$630$	3.57525	0.142441
$631$	−30.4086	−1.21055	−0.605273	−	0.796018i	$-0.706936\pi$
$631$	−30.4086	−1.21055	−0.605273	+	0.796018i	$0.706936\pi$
$632$	−5.26682	−0.209503
$633$	−7.92962	−0.315174
$634$	15.1910	0.603312
$635$	−4.88815	−0.193980
$636$	−4.72692	−0.187435
$637$	−2.67649	−0.106046
$638$	32.0646	1.26945
$639$	−1.76140	−0.0696801
$640$	1.71945	0.0679671
$641$	−3.64584	−0.144002	−0.0720009	−	0.997405i	$-0.522938\pi$
$641$	−3.64584	−0.144002	−0.0720009	+	0.997405i	$0.522938\pi$
$642$	12.7003	0.501239
$643$	−14.2838	−0.563299	−0.281649	−	0.959517i	$-0.590882\pi$
$643$	−14.2838	−0.563299	−0.281649	+	0.959517i	$0.590882\pi$
$644$	−6.58795	−0.259601
$645$	−0.100531	−0.00395842
$646$	10.7533	0.423081
$647$	−29.0889	−1.14360	−0.571801	−	0.820392i	$-0.693755\pi$
$647$	−29.0889	−1.14360	−0.571801	+	0.820392i	$0.693755\pi$
$648$	−1.00000	−0.0392837
$649$	−13.3471	−0.523920
$650$	2.04350	0.0801528
$651$	−10.1860	−0.399221
$652$	−5.72060	−0.224036
$653$	−43.4883	−1.70183	−0.850915	−	0.525304i	$-0.823952\pi$
$653$	−43.4883	−1.70183	−0.850915	+	0.525304i	$0.823952\pi$
$654$	−6.46568	−0.252828
$655$	34.2894	1.33980
$656$	2.12821	0.0830928
$657$	10.0154	0.390737
$658$	−17.1366	−0.668055
$659$	35.2543	1.37331	0.686657	−	0.726982i	$-0.259077\pi$
$659$	35.2543	1.37331	0.686657	+	0.726982i	$0.259077\pi$
$660$	7.17124	0.279140
$661$	18.7162	0.727975	0.363987	−	0.931404i	$-0.381415\pi$
$661$	18.7162	0.727975	0.363987	+	0.931404i	$0.381415\pi$
$662$	−6.93505	−0.269538
$663$	−3.34293	−0.129829
$664$	16.0174	0.621596
$665$	−11.5006	−0.445973
$666$	−6.91253	−0.267855
$667$	−24.3586	−0.943168
$668$	14.9623	0.578910
$669$	−3.35526	−0.129722
$670$	−14.5746	−0.563068
$671$	−8.11008	−0.313086
$672$	−2.07930	−0.0802109
$673$	38.1951	1.47231	0.736156	−	0.676812i	$-0.236639\pi$
$673$	38.1951	1.47231	0.736156	+	0.676812i	$0.236639\pi$
$674$	8.13952	0.313523
$675$	−2.04350	−0.0786545
$676$	1.00000	0.0384615
$677$	48.1041	1.84879	0.924395	−	0.381437i	$-0.124571\pi$
$677$	48.1041	1.84879	0.924395	+	0.381437i	$0.124571\pi$
$678$	−12.2618	−0.470913
$679$	−4.58650	−0.176014
$680$	−5.74799	−0.220425
$681$	−1.28365	−0.0491894
$682$	−20.4311	−0.782347
$683$	−17.2269	−0.659170	−0.329585	−	0.944126i	$-0.606909\pi$
$683$	−17.2269	−0.659170	−0.329585	+	0.944126i	$0.606909\pi$
$684$	3.21672	0.122994
$685$	23.4766	0.896994
$686$	20.1204	0.768199
$687$	−6.54398	−0.249668
$688$	0.0584673	0.00222905
$689$	−4.72692	−0.180081
$690$	−5.44779	−0.207394
$691$	−9.00548	−0.342585	−0.171292	−	0.985220i	$-0.554794\pi$
$691$	−9.00548	−0.342585	−0.171292	+	0.985220i	$0.554794\pi$
$692$	−20.0856	−0.763539
$693$	−8.67209	−0.329425
$694$	1.37702	0.0522708
$695$	−27.1472	−1.02975
$696$	−7.68812	−0.291417
$697$	−7.11446	−0.269480
$698$	−26.4328	−1.00050
$699$	−1.47551	−0.0558088
$700$	−4.24907	−0.160600
$701$	32.0734	1.21140	0.605698	−	0.795695i	$-0.292894\pi$
$701$	32.0734	1.21140	0.605698	+	0.795695i	$0.292894\pi$
$702$	−1.00000	−0.0377426
$703$	22.2357	0.838634
$704$	−4.17067	−0.157188
$705$	−14.1708	−0.533705
$706$	16.4525	0.619199
$707$	−37.5208	−1.41111
$708$	3.20023	0.120272
$709$	27.1827	1.02087	0.510433	−	0.859917i	$-0.329485\pi$
$709$	27.1827	1.02087	0.510433	+	0.859917i	$0.329485\pi$
$710$	−3.02864	−0.113663
$711$	5.26682	0.197521
$712$	7.65296	0.286807
$713$	15.5209	0.581264
$714$	6.95097	0.260133
$715$	7.17124	0.268189
$716$	−19.1234	−0.714675
$717$	18.4065	0.687404
$718$	−10.5179	−0.392523
$719$	2.28008	0.0850325	0.0425163	−	0.999096i	$-0.486463\pi$
$719$	2.28008	0.0850325	0.0425163	+	0.999096i	$0.486463\pi$
$720$	−1.71945	−0.0640800
$721$	−2.07930	−0.0774374
$722$	8.65272	0.322021
$723$	−7.89644	−0.293672
$724$	−6.63039	−0.246417
$725$	−15.7107	−0.583481
$726$	−6.39447	−0.237321
$727$	−40.2051	−1.49113	−0.745563	−	0.666435i	$-0.767819\pi$
$727$	−40.2051	−1.49113	−0.745563	+	0.666435i	$0.767819\pi$
$728$	−2.07930	−0.0770642
$729$	1.00000	0.0370370
$730$	17.2209	0.637374
$731$	−0.195452	−0.00722906
$732$	1.94455	0.0718727
$733$	−33.7731	−1.24744	−0.623718	−	0.781649i	$-0.714379\pi$
$733$	−33.7731	−1.24744	−0.623718	+	0.781649i	$0.714379\pi$
$734$	−5.07178	−0.187203
$735$	4.60208	0.169750
$736$	3.16834	0.116787
$737$	35.3521	1.30221
$738$	−2.12821	−0.0783406
$739$	−8.14184	−0.299503	−0.149751	−	0.988724i	$-0.547847\pi$
$739$	−8.14184	−0.299503	−0.149751	+	0.988724i	$0.547847\pi$
$740$	−11.8857	−0.436928
$741$	3.21672	0.118169
$742$	9.82871	0.360823
$743$	13.1760	0.483380	0.241690	−	0.970354i	$-0.422298\pi$
$743$	13.1760	0.483380	0.241690	+	0.970354i	$0.422298\pi$
$744$	4.89876	0.179597
$745$	−9.64212	−0.353260
$746$	17.1209	0.626839
$747$	−16.0174	−0.586046
$748$	13.9422	0.509779
$749$	−26.4077	−0.964917
$750$	−12.1109	−0.442229
$751$	−32.4857	−1.18542	−0.592709	−	0.805416i	$-0.701942\pi$
$751$	−32.4857	−1.18542	−0.592709	+	0.805416i	$0.701942\pi$
$752$	8.24152	0.300537
$753$	13.4455	0.489982
$754$	−7.68812	−0.279985
$755$	37.6036	1.36854
$756$	2.07930	0.0756236
$757$	28.5693	1.03837	0.519184	−	0.854662i	$-0.326236\pi$
$757$	28.5693	1.03837	0.519184	+	0.854662i	$0.326236\pi$
$758$	−15.0132	−0.545303
$759$	13.2141	0.479641
$760$	5.53097	0.200630
$761$	−16.9883	−0.615826	−0.307913	−	0.951414i	$-0.599631\pi$
$761$	−16.9883	−0.615826	−0.307913	+	0.951414i	$0.599631\pi$
$762$	−2.84286	−0.102986
$763$	13.4441	0.486710
$764$	−9.22135	−0.333617
$765$	5.74799	0.207819
$766$	−23.8022	−0.860007
$767$	3.20023	0.115554
$768$	1.00000	0.0360844
$769$	−27.7040	−0.999031	−0.499515	−	0.866305i	$-0.666489\pi$
$769$	−27.7040	−0.999031	−0.499515	+	0.866305i	$0.666489\pi$
$770$	−14.9112	−0.537362
$771$	25.5686	0.920830
$772$	−4.66229	−0.167800
$773$	−19.0774	−0.686167	−0.343084	−	0.939305i	$-0.611471\pi$
$773$	−19.0774	−0.686167	−0.343084	+	0.939305i	$0.611471\pi$
$774$	−0.0584673	−0.00210156
$775$	10.0106	0.359593
$776$	2.20578	0.0791831
$777$	14.3733	0.515638
$778$	28.7020	1.02901
$779$	6.84586	0.245278
$780$	−1.71945	−0.0615661
$781$	7.34623	0.262869
$782$	−10.5915	−0.378753
$783$	7.68812	0.274751
$784$	−2.67649	−0.0955890
$785$	11.5730	0.413059
$786$	19.9421	0.711312
$787$	23.7380	0.846168	0.423084	−	0.906090i	$-0.360947\pi$
$787$	23.7380	0.846168	0.423084	+	0.906090i	$0.360947\pi$
$788$	8.89204	0.316766
$789$	−9.78932	−0.348509
$790$	9.05601	0.322199
$791$	25.4961	0.906537
$792$	4.17067	0.148198
$793$	1.94455	0.0690530
$794$	−1.63976	−0.0581930
$795$	8.12769	0.288259
$796$	−13.4916	−0.478195
$797$	11.4045	0.403969	0.201984	−	0.979389i	$-0.435261\pi$
$797$	11.4045	0.403969	0.201984	+	0.979389i	$0.435261\pi$
$798$	−6.68854	−0.236772
$799$	−27.5508	−0.974678
$800$	2.04350	0.0722488
$801$	−7.65296	−0.270404
$802$	1.73416	0.0612352
$803$	−41.7708	−1.47406
$804$	−8.47636	−0.298938
$805$	11.3276	0.399246
$806$	4.89876	0.172551
$807$	28.9797	1.02013
$808$	18.0449	0.634816
$809$	−30.3731	−1.06786	−0.533931	−	0.845528i	$-0.679286\pi$
$809$	−30.3731	−1.06786	−0.533931	+	0.845528i	$0.679286\pi$
$810$	1.71945	0.0604152
$811$	39.4757	1.38618	0.693090	−	0.720851i	$-0.256249\pi$
$811$	39.4757	1.38618	0.693090	+	0.720851i	$0.256249\pi$
$812$	15.9859	0.560996
$813$	−1.76169	−0.0617851
$814$	28.8299	1.01049
$815$	9.83627	0.344549
$816$	−3.34293	−0.117026
$817$	0.188073	0.00657984
$818$	16.4451	0.574991
$819$	2.07930	0.0726568
$820$	−3.65935	−0.127790
$821$	−17.0232	−0.594114	−0.297057	−	0.954860i	$-0.596005\pi$
$821$	−17.0232	−0.594114	−0.297057	+	0.954860i	$0.596005\pi$
$822$	13.6536	0.476223
$823$	−8.37425	−0.291908	−0.145954	−	0.989291i	$-0.546625\pi$
$823$	−8.37425	−0.291908	−0.145954	+	0.989291i	$0.546625\pi$
$824$	1.00000	0.0348367
$825$	8.52278	0.296725
$826$	−6.65426	−0.231531
$827$	40.5432	1.40982	0.704912	−	0.709295i	$-0.250987\pi$
$827$	40.5432	1.40982	0.704912	+	0.709295i	$0.250987\pi$
$828$	−3.16834	−0.110107
$829$	17.5392	0.609161	0.304580	−	0.952487i	$-0.401484\pi$
$829$	17.5392	0.609161	0.304580	+	0.952487i	$0.401484\pi$
$830$	−27.5411	−0.955965
$831$	20.3481	0.705869
$832$	1.00000	0.0346688
$833$	8.94732	0.310006
$834$	−15.7883	−0.546705
$835$	−25.7269	−0.890317
$836$	−13.4159	−0.463997
$837$	−4.89876	−0.169326
$838$	4.04844	0.139851
$839$	34.2631	1.18289	0.591446	−	0.806344i	$-0.298557\pi$
$839$	34.2631	1.18289	0.591446	+	0.806344i	$0.298557\pi$
$840$	3.57525	0.123358
$841$	30.1071	1.03818
$842$	25.1134	0.865464
$843$	−2.83942	−0.0977948
$844$	−7.92962	−0.272949
$845$	−1.71945	−0.0591508
$846$	−8.24152	−0.283349
$847$	13.2960	0.456858
$848$	−4.72692	−0.162323
$849$	−12.5214	−0.429735
$850$	−6.83129	−0.234311
$851$	−21.9013	−0.750766
$852$	−1.76140	−0.0603447
$853$	−30.3174	−1.03805	−0.519025	−	0.854759i	$-0.673705\pi$
$853$	−30.3174	−1.03805	−0.519025	+	0.854759i	$0.673705\pi$
$854$	−4.04331	−0.138359
$855$	−5.53097	−0.189155
$856$	12.7003	0.434086
$857$	−52.1434	−1.78118	−0.890592	−	0.454804i	$-0.849709\pi$
$857$	−52.1434	−1.78118	−0.890592	+	0.454804i	$0.849709\pi$
$858$	4.17067	0.142384
$859$	3.83046	0.130694	0.0653468	−	0.997863i	$-0.479185\pi$
$859$	3.83046	0.130694	0.0653468	+	0.997863i	$0.479185\pi$
$860$	−0.100531	−0.00342809
$861$	4.42520	0.150811
$862$	−13.7857	−0.469544
$863$	−24.5175	−0.834585	−0.417293	−	0.908772i	$-0.637021\pi$
$863$	−24.5175	−0.834585	−0.417293	+	0.908772i	$0.637021\pi$
$864$	−1.00000	−0.0340207
$865$	34.5361	1.17426
$866$	27.8209	0.945392
$867$	−5.82483	−0.197821
$868$	−10.1860	−0.345736
$869$	−21.9662	−0.745151
$870$	13.2193	0.448176
$871$	−8.47636	−0.287210
$872$	−6.46568	−0.218956
$873$	−2.20578	−0.0746545
$874$	10.1917	0.344738
$875$	25.1823	0.851317
$876$	10.0154	0.338388
$877$	−34.2882	−1.15783	−0.578916	−	0.815387i	$-0.696524\pi$
$877$	−34.2882	−1.15783	−0.578916	+	0.815387i	$0.696524\pi$
$878$	0.721623	0.0243536
$879$	−0.436085	−0.0147088
$880$	7.17124	0.241742
$881$	−42.2080	−1.42202	−0.711011	−	0.703181i	$-0.751763\pi$
$881$	−42.2080	−1.42202	−0.711011	+	0.703181i	$0.751763\pi$
$882$	2.67649	0.0901222
$883$	35.5092	1.19498	0.597490	−	0.801876i	$-0.296165\pi$
$883$	35.5092	1.19498	0.597490	+	0.801876i	$0.296165\pi$
$884$	−3.34293	−0.112435
$885$	−5.50263	−0.184969
$886$	28.5213	0.958190
$887$	−13.6487	−0.458280	−0.229140	−	0.973394i	$-0.573591\pi$
$887$	−13.6487	−0.458280	−0.229140	+	0.973394i	$0.573591\pi$
$888$	−6.91253	−0.231969
$889$	5.91118	0.198254
$890$	−13.1588	−0.441086
$891$	−4.17067	−0.139723
$892$	−3.35526	−0.112342
$893$	26.5106	0.887145
$894$	−5.60769	−0.187549
$895$	32.8816	1.09911
$896$	−2.07930	−0.0694647
$897$	−3.16834	−0.105788
$898$	21.0796	0.703435
$899$	−37.6622	−1.25611
$900$	−2.04350	−0.0681168
$901$	15.8018	0.526433
$902$	8.87607	0.295541
$903$	0.121571	0.00404564
$904$	−12.2618	−0.407823
$905$	11.4006	0.378969
$906$	21.8696	0.726570
$907$	−18.7493	−0.622561	−0.311280	−	0.950318i	$-0.600758\pi$
$907$	−18.7493	−0.622561	−0.311280	+	0.950318i	$0.600758\pi$
$908$	−1.28365	−0.0425993
$909$	−18.0449	−0.598510
$910$	3.57525	0.118518
$911$	−27.0544	−0.896351	−0.448176	−	0.893946i	$-0.647926\pi$
$911$	−27.0544	−0.896351	−0.448176	+	0.893946i	$0.647926\pi$
$912$	3.21672	0.106516
$913$	66.8033	2.21087
$914$	−37.2739	−1.23291
$915$	−3.34355	−0.110534
$916$	−6.54398	−0.216219
$917$	−41.4658	−1.36932
$918$	3.34293	0.110333
$919$	29.4764	0.972337	0.486169	−	0.873865i	$-0.338394\pi$
$919$	29.4764	0.972337	0.486169	+	0.873865i	$0.338394\pi$
$920$	−5.44779	−0.179608
$921$	−14.4308	−0.475510
$922$	27.0955	0.892344
$923$	−1.76140	−0.0579773
$924$	−8.67209	−0.285291
$925$	−14.1258	−0.464453
$926$	−4.26509	−0.140160
$927$	−1.00000	−0.0328443
$928$	−7.68812	−0.252375
$929$	−11.3610	−0.372742	−0.186371	−	0.982479i	$-0.559673\pi$
$929$	−11.3610	−0.372742	−0.186371	+	0.982479i	$0.559673\pi$
$930$	−8.42315	−0.276206
$931$	−8.60952	−0.282166
$932$	−1.47551	−0.0483318
$933$	−29.3998	−0.962507
$934$	10.4283	0.341224
$935$	−23.9729	−0.783999
$936$	−1.00000	−0.0326860
$937$	14.4433	0.471842	0.235921	−	0.971772i	$-0.424189\pi$
$937$	14.4433	0.471842	0.235921	+	0.971772i	$0.424189\pi$
$938$	17.6249	0.575474
$939$	−19.8482	−0.647721
$940$	−14.1708	−0.462202
$941$	53.6009	1.74734	0.873671	−	0.486518i	$-0.161733\pi$
$941$	53.6009	1.74734	0.873671	+	0.486518i	$0.161733\pi$
$942$	6.73068	0.219297
$943$	−6.74291	−0.219579
$944$	3.20023	0.104159
$945$	−3.57525	−0.116303
$946$	0.243848	0.00792817
$947$	−12.5622	−0.408218	−0.204109	−	0.978948i	$-0.565430\pi$
$947$	−12.5622	−0.408218	−0.204109	+	0.978948i	$0.565430\pi$
$948$	5.26682	0.171058
$949$	10.0154	0.325113
$950$	6.57338	0.213269
$951$	−15.1910	−0.492602
$952$	6.95097	0.225282
$953$	38.6404	1.25169	0.625843	−	0.779949i	$-0.284755\pi$
$953$	38.6404	1.25169	0.625843	+	0.779949i	$0.284755\pi$
$954$	4.72692	0.153040
$955$	15.8556	0.513076
$956$	18.4065	0.595309
$957$	−32.0646	−1.03650
$958$	−28.8986	−0.933673
$959$	−28.3899	−0.916759
$960$	−1.71945	−0.0554949
$961$	−7.00216	−0.225876
$962$	−6.91253	−0.222869
$963$	−12.7003	−0.409260
$964$	−7.89644	−0.254327
$965$	8.01656	0.258062
$966$	6.58795	0.211964
$967$	−11.8396	−0.380735	−0.190367	−	0.981713i	$-0.560968\pi$
$967$	−11.8396	−0.380735	−0.190367	+	0.981713i	$0.560968\pi$
$968$	−6.39447	−0.205526
$969$	−10.7533	−0.345444
$970$	−3.79273	−0.121777
$971$	−7.00827	−0.224906	−0.112453	−	0.993657i	$-0.535871\pi$
$971$	−7.00827	−0.224906	−0.112453	+	0.993657i	$0.535871\pi$
$972$	1.00000	0.0320750
$973$	32.8288	1.05244
$974$	−12.2855	−0.393653
$975$	−2.04350	−0.0654445
$976$	1.94455	0.0622436
$977$	21.2603	0.680178	0.340089	−	0.940393i	$-0.389543\pi$
$977$	21.2603	0.680178	0.340089	+	0.940393i	$0.389543\pi$
$978$	5.72060	0.182925
$979$	31.9179	1.02010
$980$	4.60208	0.147008
$981$	6.46568	0.206433
$982$	12.1091	0.386418
$983$	3.68168	0.117427	0.0587136	−	0.998275i	$-0.481300\pi$
$983$	3.68168	0.117427	0.0587136	+	0.998275i	$0.481300\pi$
$984$	−2.12821	−0.0678450
$985$	−15.2894	−0.487161
$986$	25.7008	0.818481
$987$	17.1366	0.545465
$988$	3.21672	0.102337
$989$	−0.185244	−0.00589043
$990$	−7.17124	−0.227917
$991$	−25.9361	−0.823886	−0.411943	−	0.911210i	$-0.635150\pi$
$991$	−25.9361	−0.823886	−0.411943	+	0.911210i	$0.635150\pi$
$992$	4.89876	0.155536
$993$	6.93505	0.220077
$994$	3.66250	0.116167
$995$	23.1980	0.735426
$996$	−16.0174	−0.507531
$997$	10.1865	0.322609	0.161305	−	0.986905i	$-0.448430\pi$
$997$	10.1865	0.322609	0.161305	+	0.986905i	$0.448430\pi$
$998$	−22.1382	−0.700774
$999$	6.91253	0.218703

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.w.1.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.w.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.71945 q^{5} -1.00000 q^{6} +2.07930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.71945 q^{5} -1.00000 q^{6} +2.07930 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.71945 q^{10} -4.17067 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.07930 q^{14} -1.71945 q^{15} +1.00000 q^{16} -3.34293 q^{17} -1.00000 q^{18} +3.21672 q^{19} -1.71945 q^{20} +2.07930 q^{21} +4.17067 q^{22} -3.16834 q^{23} -1.00000 q^{24} -2.04350 q^{25} -1.00000 q^{26} +1.00000 q^{27} +2.07930 q^{28} +7.68812 q^{29} +1.71945 q^{30} -4.89876 q^{31} -1.00000 q^{32} -4.17067 q^{33} +3.34293 q^{34} -3.57525 q^{35} +1.00000 q^{36} +6.91253 q^{37} -3.21672 q^{38} +1.00000 q^{39} +1.71945 q^{40} +2.12821 q^{41} -2.07930 q^{42} +0.0584673 q^{43} -4.17067 q^{44} -1.71945 q^{45} +3.16834 q^{46} +8.24152 q^{47} +1.00000 q^{48} -2.67649 q^{49} +2.04350 q^{50} -3.34293 q^{51} +1.00000 q^{52} -4.72692 q^{53} -1.00000 q^{54} +7.17124 q^{55} -2.07930 q^{56} +3.21672 q^{57} -7.68812 q^{58} +3.20023 q^{59} -1.71945 q^{60} +1.94455 q^{61} +4.89876 q^{62} +2.07930 q^{63} +1.00000 q^{64} -1.71945 q^{65} +4.17067 q^{66} -8.47636 q^{67} -3.34293 q^{68} -3.16834 q^{69} +3.57525 q^{70} -1.76140 q^{71} -1.00000 q^{72} +10.0154 q^{73} -6.91253 q^{74} -2.04350 q^{75} +3.21672 q^{76} -8.67209 q^{77} -1.00000 q^{78} +5.26682 q^{79} -1.71945 q^{80} +1.00000 q^{81} -2.12821 q^{82} -16.0174 q^{83} +2.07930 q^{84} +5.74799 q^{85} -0.0584673 q^{86} +7.68812 q^{87} +4.17067 q^{88} -7.65296 q^{89} +1.71945 q^{90} +2.07930 q^{91} -3.16834 q^{92} -4.89876 q^{93} -8.24152 q^{94} -5.53097 q^{95} -1.00000 q^{96} -2.20578 q^{97} +2.67649 q^{98} -4.17067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 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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