LMFDB - Embedded newform 8034.2.a.q.1.1

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:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 $ x^8 - 2x^7 - 11x^6 + 21x^5 + 23x^4 - 29x^3 - 27x^2 + x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.96271$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.96271 q^{5} +1.00000 q^{6} +0.133176 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.96271 q^{5} +1.00000 q^{6} +0.133176 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.96271 q^{10} +0.829532 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.133176 q^{14} -3.96271 q^{15} +1.00000 q^{16} -7.00392 q^{17} +1.00000 q^{18} +2.69311 q^{19} -3.96271 q^{20} +0.133176 q^{21} +0.829532 q^{22} +2.07146 q^{23} +1.00000 q^{24} +10.7031 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.133176 q^{28} +0.727357 q^{29} -3.96271 q^{30} +7.57160 q^{31} +1.00000 q^{32} +0.829532 q^{33} -7.00392 q^{34} -0.527737 q^{35} +1.00000 q^{36} -6.98878 q^{37} +2.69311 q^{38} -1.00000 q^{39} -3.96271 q^{40} -0.446893 q^{41} +0.133176 q^{42} +10.3946 q^{43} +0.829532 q^{44} -3.96271 q^{45} +2.07146 q^{46} +5.80531 q^{47} +1.00000 q^{48} -6.98226 q^{49} +10.7031 q^{50} -7.00392 q^{51} -1.00000 q^{52} -8.83345 q^{53} +1.00000 q^{54} -3.28719 q^{55} +0.133176 q^{56} +2.69311 q^{57} +0.727357 q^{58} -10.1232 q^{59} -3.96271 q^{60} +5.99269 q^{61} +7.57160 q^{62} +0.133176 q^{63} +1.00000 q^{64} +3.96271 q^{65} +0.829532 q^{66} -13.4078 q^{67} -7.00392 q^{68} +2.07146 q^{69} -0.527737 q^{70} -10.6971 q^{71} +1.00000 q^{72} -8.51639 q^{73} -6.98878 q^{74} +10.7031 q^{75} +2.69311 q^{76} +0.110474 q^{77} -1.00000 q^{78} -7.01281 q^{79} -3.96271 q^{80} +1.00000 q^{81} -0.446893 q^{82} -1.00352 q^{83} +0.133176 q^{84} +27.7545 q^{85} +10.3946 q^{86} +0.727357 q^{87} +0.829532 q^{88} +4.77140 q^{89} -3.96271 q^{90} -0.133176 q^{91} +2.07146 q^{92} +7.57160 q^{93} +5.80531 q^{94} -10.6720 q^{95} +1.00000 q^{96} +14.5759 q^{97} -6.98226 q^{98} +0.829532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * 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
$5$	−3.96271	−1.77218	−0.886088	−	0.463516i	$-0.846588\pi$
$5$	−3.96271	−1.77218	−0.886088	+	0.463516i	$0.846588\pi$
$6$	1.00000	0.408248
$7$	0.133176	0.0503358	0.0251679	−	0.999683i	$-0.491988\pi$
$7$	0.133176	0.0503358	0.0251679	+	0.999683i	$0.491988\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.96271	−1.25312
$11$	0.829532	0.250113	0.125057	−	0.992150i	$-0.460089\pi$
$11$	0.829532	0.250113	0.125057	+	0.992150i	$0.460089\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	0.133176	0.0355928
$15$	−3.96271	−1.02317
$16$	1.00000	0.250000
$17$	−7.00392	−1.69870	−0.849350	−	0.527830i	$-0.823006\pi$
$17$	−7.00392	−1.69870	−0.849350	+	0.527830i	$0.823006\pi$
$18$	1.00000	0.235702
$19$	2.69311	0.617841	0.308921	−	0.951088i	$-0.400032\pi$
$19$	2.69311	0.617841	0.308921	+	0.951088i	$0.400032\pi$
$20$	−3.96271	−0.886088
$21$	0.133176	0.0290614
$22$	0.829532	0.176857
$23$	2.07146	0.431930	0.215965	−	0.976401i	$-0.430710\pi$
$23$	2.07146	0.431930	0.215965	+	0.976401i	$0.430710\pi$
$24$	1.00000	0.204124
$25$	10.7031	2.14061
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0.133176	0.0251679
$29$	0.727357	0.135067	0.0675334	−	0.997717i	$-0.478487\pi$
$29$	0.727357	0.135067	0.0675334	+	0.997717i	$0.478487\pi$
$30$	−3.96271	−0.723488
$31$	7.57160	1.35990	0.679950	−	0.733259i	$-0.262002\pi$
$31$	7.57160	1.35990	0.679950	+	0.733259i	$0.262002\pi$
$32$	1.00000	0.176777
$33$	0.829532	0.144403
$34$	−7.00392	−1.20116
$35$	−0.527737	−0.0892039
$36$	1.00000	0.166667
$37$	−6.98878	−1.14895	−0.574474	−	0.818523i	$-0.694793\pi$
$37$	−6.98878	−1.14895	−0.574474	+	0.818523i	$0.694793\pi$
$38$	2.69311	0.436880
$39$	−1.00000	−0.160128
$40$	−3.96271	−0.626559
$41$	−0.446893	−0.0697930	−0.0348965	−	0.999391i	$-0.511110\pi$
$41$	−0.446893	−0.0697930	−0.0348965	+	0.999391i	$0.511110\pi$
$42$	0.133176	0.0205495
$43$	10.3946	1.58516	0.792580	−	0.609767i	$-0.208737\pi$
$43$	10.3946	1.58516	0.792580	+	0.609767i	$0.208737\pi$
$44$	0.829532	0.125057
$45$	−3.96271	−0.590726
$46$	2.07146	0.305420
$47$	5.80531	0.846792	0.423396	−	0.905945i	$-0.360838\pi$
$47$	5.80531	0.846792	0.423396	+	0.905945i	$0.360838\pi$
$48$	1.00000	0.144338
$49$	−6.98226	−0.997466
$50$	10.7031	1.51364
$51$	−7.00392	−0.980745
$52$	−1.00000	−0.138675
$53$	−8.83345	−1.21337	−0.606684	−	0.794943i	$-0.707501\pi$
$53$	−8.83345	−1.21337	−0.606684	+	0.794943i	$0.707501\pi$
$54$	1.00000	0.136083
$55$	−3.28719	−0.443245
$56$	0.133176	0.0177964
$57$	2.69311	0.356711
$58$	0.727357	0.0955066
$59$	−10.1232	−1.31793	−0.658967	−	0.752172i	$-0.729006\pi$
$59$	−10.1232	−1.31793	−0.658967	+	0.752172i	$0.729006\pi$
$60$	−3.96271	−0.511583
$61$	5.99269	0.767285	0.383643	−	0.923482i	$-0.374669\pi$
$61$	5.99269	0.767285	0.383643	+	0.923482i	$0.374669\pi$
$62$	7.57160	0.961594
$63$	0.133176	0.0167786
$64$	1.00000	0.125000
$65$	3.96271	0.491513
$66$	0.829532	0.102108
$67$	−13.4078	−1.63802	−0.819011	−	0.573778i	$-0.805477\pi$
$67$	−13.4078	−1.63802	−0.819011	+	0.573778i	$0.805477\pi$
$68$	−7.00392	−0.849350
$69$	2.07146	0.249375
$70$	−0.527737	−0.0630767
$71$	−10.6971	−1.26951	−0.634757	−	0.772712i	$-0.718900\pi$
$71$	−10.6971	−1.26951	−0.634757	+	0.772712i	$0.718900\pi$
$72$	1.00000	0.117851
$73$	−8.51639	−0.996768	−0.498384	−	0.866956i	$-0.666073\pi$
$73$	−8.51639	−0.996768	−0.498384	+	0.866956i	$0.666073\pi$
$74$	−6.98878	−0.812429
$75$	10.7031	1.23588
$76$	2.69311	0.308921
$77$	0.110474	0.0125896
$78$	−1.00000	−0.113228
$79$	−7.01281	−0.789003	−0.394501	−	0.918895i	$-0.629083\pi$
$79$	−7.01281	−0.789003	−0.394501	+	0.918895i	$0.629083\pi$
$80$	−3.96271	−0.443044
$81$	1.00000	0.111111
$82$	−0.446893	−0.0493511
$83$	−1.00352	−0.110151	−0.0550754	−	0.998482i	$-0.517540\pi$
$83$	−1.00352	−0.110151	−0.0550754	+	0.998482i	$0.517540\pi$
$84$	0.133176	0.0145307
$85$	27.7545	3.01040
$86$	10.3946	1.12088
$87$	0.727357	0.0779808
$88$	0.829532	0.0884284
$89$	4.77140	0.505767	0.252883	−	0.967497i	$-0.418621\pi$
$89$	4.77140	0.505767	0.252883	+	0.967497i	$0.418621\pi$
$90$	−3.96271	−0.417706
$91$	−0.133176	−0.0139606
$92$	2.07146	0.215965
$93$	7.57160	0.785138
$94$	5.80531	0.598772
$95$	−10.6720	−1.09492
$96$	1.00000	0.102062
$97$	14.5759	1.47995	0.739977	−	0.672632i	$-0.234836\pi$
$97$	14.5759	1.47995	0.739977	+	0.672632i	$0.234836\pi$
$98$	−6.98226	−0.705315
$99$	0.829532	0.0833711
$100$	10.7031	1.07031
$101$	−5.59851	−0.557073	−0.278536	−	0.960426i	$-0.589849\pi$
$101$	−5.59851	−0.557073	−0.278536	+	0.960426i	$0.589849\pi$
$102$	−7.00392	−0.693491
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−0.527737	−0.0515019
$106$	−8.83345	−0.857981
$107$	−15.6929	−1.51709	−0.758545	−	0.651621i	$-0.774089\pi$
$107$	−15.6929	−1.51709	−0.758545	+	0.651621i	$0.774089\pi$
$108$	1.00000	0.0962250
$109$	−5.20681	−0.498722	−0.249361	−	0.968411i	$-0.580221\pi$
$109$	−5.20681	−0.498722	−0.249361	+	0.968411i	$0.580221\pi$
$110$	−3.28719	−0.313421
$111$	−6.98878	−0.663346
$112$	0.133176	0.0125839
$113$	−0.688656	−0.0647833	−0.0323917	−	0.999475i	$-0.510312\pi$
$113$	−0.688656	−0.0647833	−0.0323917	+	0.999475i	$0.510312\pi$
$114$	2.69311	0.252233
$115$	−8.20860	−0.765456
$116$	0.727357	0.0675334
$117$	−1.00000	−0.0924500
$118$	−10.1232	−0.931921
$119$	−0.932753	−0.0855054
$120$	−3.96271	−0.361744
$121$	−10.3119	−0.937443
$122$	5.99269	0.542553
$123$	−0.446893	−0.0402950
$124$	7.57160	0.679950
$125$	−22.5995	−2.02136
$126$	0.133176	0.0118643
$127$	−11.3586	−1.00791	−0.503955	−	0.863730i	$-0.668122\pi$
$127$	−11.3586	−1.00791	−0.503955	+	0.863730i	$0.668122\pi$
$128$	1.00000	0.0883883
$129$	10.3946	0.915193
$130$	3.96271	0.347552
$131$	−18.7011	−1.63393	−0.816963	−	0.576690i	$-0.804344\pi$
$131$	−18.7011	−1.63393	−0.816963	+	0.576690i	$0.804344\pi$
$132$	0.829532	0.0722015
$133$	0.358657	0.0310995
$134$	−13.4078	−1.15826
$135$	−3.96271	−0.341056
$136$	−7.00392	−0.600581
$137$	−13.1788	−1.12594	−0.562971	−	0.826477i	$-0.690342\pi$
$137$	−13.1788	−1.12594	−0.562971	+	0.826477i	$0.690342\pi$
$138$	2.07146	0.176335
$139$	−8.73296	−0.740720	−0.370360	−	0.928888i	$-0.620766\pi$
$139$	−8.73296	−0.740720	−0.370360	+	0.928888i	$0.620766\pi$
$140$	−0.527737	−0.0446019
$141$	5.80531	0.488896
$142$	−10.6971	−0.897682
$143$	−0.829532	−0.0693689
$144$	1.00000	0.0833333
$145$	−2.88230	−0.239362
$146$	−8.51639	−0.704821
$147$	−6.98226	−0.575887
$148$	−6.98878	−0.574474
$149$	−15.6248	−1.28004	−0.640018	−	0.768360i	$-0.721073\pi$
$149$	−15.6248	−1.28004	−0.640018	+	0.768360i	$0.721073\pi$
$150$	10.7031	0.873900
$151$	−4.60466	−0.374722	−0.187361	−	0.982291i	$-0.559993\pi$
$151$	−4.60466	−0.374722	−0.187361	+	0.982291i	$0.559993\pi$
$152$	2.69311	0.218440
$153$	−7.00392	−0.566233
$154$	0.110474	0.00890222
$155$	−30.0040	−2.40998
$156$	−1.00000	−0.0800641
$157$	7.73031	0.616946	0.308473	−	0.951233i	$-0.400182\pi$
$157$	7.73031	0.616946	0.308473	+	0.951233i	$0.400182\pi$
$158$	−7.01281	−0.557909
$159$	−8.83345	−0.700538
$160$	−3.96271	−0.313280
$161$	0.275869	0.0217415
$162$	1.00000	0.0785674
$163$	10.8081	0.846553	0.423276	−	0.906001i	$-0.360880\pi$
$163$	10.8081	0.846553	0.423276	+	0.906001i	$0.360880\pi$
$164$	−0.446893	−0.0348965
$165$	−3.28719	−0.255907
$166$	−1.00352	−0.0778884
$167$	−9.76395	−0.755557	−0.377779	−	0.925896i	$-0.623312\pi$
$167$	−9.76395	−0.755557	−0.377779	+	0.925896i	$0.623312\pi$
$168$	0.133176	0.0102747
$169$	1.00000	0.0769231
$170$	27.7545	2.12867
$171$	2.69311	0.205947
$172$	10.3946	0.792580
$173$	18.2114	1.38459	0.692294	−	0.721615i	$-0.256600\pi$
$173$	18.2114	1.38459	0.692294	+	0.721615i	$0.256600\pi$
$174$	0.727357	0.0551408
$175$	1.42539	0.107749
$176$	0.829532	0.0625283
$177$	−10.1232	−0.760910
$178$	4.77140	0.357631
$179$	25.5316	1.90832	0.954162	−	0.299290i	$-0.0967498\pi$
$179$	25.5316	1.90832	0.954162	+	0.299290i	$0.0967498\pi$
$180$	−3.96271	−0.295363
$181$	6.53741	0.485922	0.242961	−	0.970036i	$-0.421881\pi$
$181$	6.53741	0.485922	0.242961	+	0.970036i	$0.421881\pi$
$182$	−0.133176	−0.00987166
$183$	5.99269	0.442992
$184$	2.07146	0.152710
$185$	27.6945	2.03614
$186$	7.57160	0.555177
$187$	−5.80997	−0.424867
$188$	5.80531	0.423396
$189$	0.133176	0.00968712
$190$	−10.6720	−0.774228
$191$	24.4667	1.77035	0.885173	−	0.465262i	$-0.154040\pi$
$191$	24.4667	1.77035	0.885173	+	0.465262i	$0.154040\pi$
$192$	1.00000	0.0721688
$193$	−15.8174	−1.13856	−0.569281	−	0.822143i	$-0.692778\pi$
$193$	−15.8174	−1.13856	−0.569281	+	0.822143i	$0.692778\pi$
$194$	14.5759	1.04649
$195$	3.96271	0.283775
$196$	−6.98226	−0.498733
$197$	−6.37807	−0.454419	−0.227209	−	0.973846i	$-0.572960\pi$
$197$	−6.37807	−0.454419	−0.227209	+	0.973846i	$0.572960\pi$
$198$	0.829532	0.0589522
$199$	−1.53521	−0.108828	−0.0544140	−	0.998518i	$-0.517329\pi$
$199$	−1.53521	−0.108828	−0.0544140	+	0.998518i	$0.517329\pi$
$200$	10.7031	0.756820
$201$	−13.4078	−0.945712
$202$	−5.59851	−0.393910
$203$	0.0968664	0.00679869
$204$	−7.00392	−0.490372
$205$	1.77091	0.123686
$206$	−1.00000	−0.0696733
$207$	2.07146	0.143977
$208$	−1.00000	−0.0693375
$209$	2.23402	0.154530
$210$	−0.527737	−0.0364173
$211$	−26.9295	−1.85390	−0.926951	−	0.375182i	$-0.877580\pi$
$211$	−26.9295	−1.85390	−0.926951	+	0.375182i	$0.877580\pi$
$212$	−8.83345	−0.606684
$213$	−10.6971	−0.732954
$214$	−15.6929	−1.07274
$215$	−41.1907	−2.80918
$216$	1.00000	0.0680414
$217$	1.00835	0.0684516
$218$	−5.20681	−0.352650
$219$	−8.51639	−0.575484
$220$	−3.28719	−0.221622
$221$	7.00392	0.471135
$222$	−6.98878	−0.469056
$223$	10.3471	0.692894	0.346447	−	0.938070i	$-0.387388\pi$
$223$	10.3471	0.692894	0.346447	+	0.938070i	$0.387388\pi$
$224$	0.133176	0.00889819
$225$	10.7031	0.713537
$226$	−0.688656	−0.0458087
$227$	1.27278	0.0844771	0.0422386	−	0.999108i	$-0.486551\pi$
$227$	1.27278	0.0844771	0.0422386	+	0.999108i	$0.486551\pi$
$228$	2.69311	0.178355
$229$	−4.92528	−0.325472	−0.162736	−	0.986670i	$-0.552032\pi$
$229$	−4.92528	−0.325472	−0.162736	+	0.986670i	$0.552032\pi$
$230$	−8.20860	−0.541259
$231$	0.110474	0.00726863
$232$	0.727357	0.0477533
$233$	−22.4533	−1.47097	−0.735484	−	0.677542i	$-0.763045\pi$
$233$	−22.4533	−1.47097	−0.735484	+	0.677542i	$0.763045\pi$
$234$	−1.00000	−0.0653720
$235$	−23.0048	−1.50067
$236$	−10.1232	−0.658967
$237$	−7.01281	−0.455531
$238$	−0.932753	−0.0604614
$239$	−6.18920	−0.400346	−0.200173	−	0.979761i	$-0.564150\pi$
$239$	−6.18920	−0.400346	−0.200173	+	0.979761i	$0.564150\pi$
$240$	−3.96271	−0.255792
$241$	18.9753	1.22231	0.611155	−	0.791511i	$-0.290705\pi$
$241$	18.9753	1.22231	0.611155	+	0.791511i	$0.290705\pi$
$242$	−10.3119	−0.662873
$243$	1.00000	0.0641500
$244$	5.99269	0.383643
$245$	27.6687	1.76769
$246$	−0.446893	−0.0284929
$247$	−2.69311	−0.171358
$248$	7.57160	0.480797
$249$	−1.00352	−0.0635956
$250$	−22.5995	−1.42932
$251$	−8.58481	−0.541868	−0.270934	−	0.962598i	$-0.587333\pi$
$251$	−8.58481	−0.541868	−0.270934	+	0.962598i	$0.587333\pi$
$252$	0.133176	0.00838930
$253$	1.71834	0.108031
$254$	−11.3586	−0.712700
$255$	27.7545	1.73805
$256$	1.00000	0.0625000
$257$	−16.4098	−1.02362	−0.511808	−	0.859100i	$-0.671024\pi$
$257$	−16.4098	−1.02362	−0.511808	+	0.859100i	$0.671024\pi$
$258$	10.3946	0.647139
$259$	−0.930737	−0.0578332
$260$	3.96271	0.245757
$261$	0.727357	0.0450223
$262$	−18.7011	−1.15536
$263$	28.9252	1.78360	0.891801	−	0.452428i	$-0.149442\pi$
$263$	28.9252	1.78360	0.891801	+	0.452428i	$0.149442\pi$
$264$	0.829532	0.0510541
$265$	35.0044	2.15030
$266$	0.358657	0.0219907
$267$	4.77140	0.292005
$268$	−13.4078	−0.819011
$269$	20.8927	1.27385	0.636925	−	0.770926i	$-0.280206\pi$
$269$	20.8927	1.27385	0.636925	+	0.770926i	$0.280206\pi$
$270$	−3.96271	−0.241163
$271$	−0.311163	−0.0189018	−0.00945090	−	0.999955i	$-0.503008\pi$
$271$	−0.311163	−0.0189018	−0.00945090	+	0.999955i	$0.503008\pi$
$272$	−7.00392	−0.424675
$273$	−0.133176	−0.00806017
$274$	−13.1788	−0.796161
$275$	8.87852	0.535395
$276$	2.07146	0.124687
$277$	9.35681	0.562196	0.281098	−	0.959679i	$-0.409301\pi$
$277$	9.35681	0.562196	0.281098	+	0.959679i	$0.409301\pi$
$278$	−8.73296	−0.523768
$279$	7.57160	0.453300
$280$	−0.527737	−0.0315383
$281$	−12.7435	−0.760214	−0.380107	−	0.924942i	$-0.624113\pi$
$281$	−12.7435	−0.760214	−0.380107	+	0.924942i	$0.624113\pi$
$282$	5.80531	0.345701
$283$	11.6910	0.694960	0.347480	−	0.937687i	$-0.387037\pi$
$283$	11.6910	0.694960	0.347480	+	0.937687i	$0.387037\pi$
$284$	−10.6971	−0.634757
$285$	−10.6720	−0.632155
$286$	−0.829532	−0.0490512
$287$	−0.0595155	−0.00351309
$288$	1.00000	0.0589256
$289$	32.0549	1.88558
$290$	−2.88230	−0.169255
$291$	14.5759	0.854452
$292$	−8.51639	−0.498384
$293$	16.7907	0.980926	0.490463	−	0.871462i	$-0.336828\pi$
$293$	16.7907	0.980926	0.490463	+	0.871462i	$0.336828\pi$
$294$	−6.98226	−0.407214
$295$	40.1155	2.33561
$296$	−6.98878	−0.406215
$297$	0.829532	0.0481343
$298$	−15.6248	−0.905122
$299$	−2.07146	−0.119796
$300$	10.7031	0.617941
$301$	1.38431	0.0797903
$302$	−4.60466	−0.264968
$303$	−5.59851	−0.321626
$304$	2.69311	0.154460
$305$	−23.7473	−1.35976
$306$	−7.00392	−0.400387
$307$	−20.3688	−1.16251	−0.581253	−	0.813723i	$-0.697437\pi$
$307$	−20.3688	−1.16251	−0.581253	+	0.813723i	$0.697437\pi$
$308$	0.110474	0.00629482
$309$	−1.00000	−0.0568880
$310$	−30.0040	−1.70411
$311$	−14.9885	−0.849922	−0.424961	−	0.905212i	$-0.639712\pi$
$311$	−14.9885	−0.849922	−0.424961	+	0.905212i	$0.639712\pi$
$312$	−1.00000	−0.0566139
$313$	−2.06755	−0.116865	−0.0584325	−	0.998291i	$-0.518610\pi$
$313$	−2.06755	−0.116865	−0.0584325	+	0.998291i	$0.518610\pi$
$314$	7.73031	0.436247
$315$	−0.527737	−0.0297346
$316$	−7.01281	−0.394501
$317$	−0.106723	−0.00599417	−0.00299709	−	0.999996i	$-0.500954\pi$
$317$	−0.106723	−0.00599417	−0.00299709	+	0.999996i	$0.500954\pi$
$318$	−8.83345	−0.495355
$319$	0.603365	0.0337820
$320$	−3.96271	−0.221522
$321$	−15.6929	−0.875892
$322$	0.275869	0.0153736
$323$	−18.8623	−1.04953
$324$	1.00000	0.0555556
$325$	−10.7031	−0.593698
$326$	10.8081	0.598603
$327$	−5.20681	−0.287937
$328$	−0.446893	−0.0246756
$329$	0.773128	0.0426239
$330$	−3.28719	−0.180954
$331$	−5.51043	−0.302881	−0.151440	−	0.988466i	$-0.548391\pi$
$331$	−5.51043	−0.302881	−0.151440	+	0.988466i	$0.548391\pi$
$332$	−1.00352	−0.0550754
$333$	−6.98878	−0.382983
$334$	−9.76395	−0.534260
$335$	53.1311	2.90286
$336$	0.133176	0.00726534
$337$	−15.2036	−0.828192	−0.414096	−	0.910233i	$-0.635902\pi$
$337$	−15.2036	−0.828192	−0.414096	+	0.910233i	$0.635902\pi$
$338$	1.00000	0.0543928
$339$	−0.688656	−0.0374027
$340$	27.7545	1.50520
$341$	6.28088	0.340129
$342$	2.69311	0.145627
$343$	−1.86210	−0.100544
$344$	10.3946	0.560439
$345$	−8.20860	−0.441936
$346$	18.2114	0.979052
$347$	9.43539	0.506518	0.253259	−	0.967399i	$-0.418498\pi$
$347$	9.43539	0.506518	0.253259	+	0.967399i	$0.418498\pi$
$348$	0.727357	0.0389904
$349$	−34.7553	−1.86041	−0.930204	−	0.367044i	$-0.880370\pi$
$349$	−34.7553	−1.86041	−0.930204	+	0.367044i	$0.880370\pi$
$350$	1.42539	0.0761902
$351$	−1.00000	−0.0533761
$352$	0.829532	0.0442142
$353$	1.11441	0.0593143	0.0296571	−	0.999560i	$-0.490558\pi$
$353$	1.11441	0.0593143	0.0296571	+	0.999560i	$0.490558\pi$
$354$	−10.1232	−0.538045
$355$	42.3895	2.24980
$356$	4.77140	0.252883
$357$	−0.932753	−0.0493665
$358$	25.5316	1.34939
$359$	−7.02430	−0.370728	−0.185364	−	0.982670i	$-0.559346\pi$
$359$	−7.02430	−0.370728	−0.185364	+	0.982670i	$0.559346\pi$
$360$	−3.96271	−0.208853
$361$	−11.7472	−0.618272
$362$	6.53741	0.343598
$363$	−10.3119	−0.541233
$364$	−0.133176	−0.00698032
$365$	33.7480	1.76645
$366$	5.99269	0.313243
$367$	29.9449	1.56311	0.781555	−	0.623836i	$-0.214427\pi$
$367$	29.9449	1.56311	0.781555	+	0.623836i	$0.214427\pi$
$368$	2.07146	0.107982
$369$	−0.446893	−0.0232643
$370$	27.6945	1.43977
$371$	−1.17640	−0.0610758
$372$	7.57160	0.392569
$373$	15.9660	0.826686	0.413343	−	0.910575i	$-0.364361\pi$
$373$	15.9660	0.826686	0.413343	+	0.910575i	$0.364361\pi$
$374$	−5.80997	−0.300426
$375$	−22.5995	−1.16703
$376$	5.80531	0.299386
$377$	−0.727357	−0.0374608
$378$	0.133176	0.00684983
$379$	−37.5613	−1.92940	−0.964698	−	0.263357i	$-0.915170\pi$
$379$	−37.5613	−1.92940	−0.964698	+	0.263357i	$0.915170\pi$
$380$	−10.6720	−0.547462
$381$	−11.3586	−0.581917
$382$	24.4667	1.25182
$383$	6.98732	0.357035	0.178518	−	0.983937i	$-0.442870\pi$
$383$	6.98732	0.357035	0.178518	+	0.983937i	$0.442870\pi$
$384$	1.00000	0.0510310
$385$	−0.437775	−0.0223111
$386$	−15.8174	−0.805085
$387$	10.3946	0.528387
$388$	14.5759	0.739977
$389$	−13.4606	−0.682481	−0.341240	−	0.939976i	$-0.610847\pi$
$389$	−13.4606	−0.682481	−0.341240	+	0.939976i	$0.610847\pi$
$390$	3.96271	0.200659
$391$	−14.5083	−0.733719
$392$	−6.98226	−0.352658
$393$	−18.7011	−0.943348
$394$	−6.37807	−0.321323
$395$	27.7897	1.39825
$396$	0.829532	0.0416855
$397$	−18.6840	−0.937722	−0.468861	−	0.883272i	$-0.655336\pi$
$397$	−18.6840	−0.937722	−0.468861	+	0.883272i	$0.655336\pi$
$398$	−1.53521	−0.0769530
$399$	0.358657	0.0179553
$400$	10.7031	0.535153
$401$	5.16563	0.257959	0.128980	−	0.991647i	$-0.458830\pi$
$401$	5.16563	0.257959	0.128980	+	0.991647i	$0.458830\pi$
$402$	−13.4078	−0.668720
$403$	−7.57160	−0.377168
$404$	−5.59851	−0.278536
$405$	−3.96271	−0.196909
$406$	0.0968664	0.00480740
$407$	−5.79741	−0.287367
$408$	−7.00392	−0.346746
$409$	8.70455	0.430412	0.215206	−	0.976569i	$-0.430958\pi$
$409$	8.70455	0.430412	0.215206	+	0.976569i	$0.430958\pi$
$410$	1.77091	0.0874589
$411$	−13.1788	−0.650063
$412$	−1.00000	−0.0492665
$413$	−1.34817	−0.0663393
$414$	2.07146	0.101807
$415$	3.97666	0.195207
$416$	−1.00000	−0.0490290
$417$	−8.73296	−0.427655
$418$	2.23402	0.109269
$419$	25.9033	1.26546	0.632730	−	0.774372i	$-0.281934\pi$
$419$	25.9033	1.26546	0.632730	+	0.774372i	$0.281934\pi$
$420$	−0.527737	−0.0257509
$421$	37.0324	1.80485	0.902424	−	0.430849i	$-0.141786\pi$
$421$	37.0324	1.80485	0.902424	+	0.430849i	$0.141786\pi$
$422$	−26.9295	−1.31091
$423$	5.80531	0.282264
$424$	−8.83345	−0.428990
$425$	−74.9633	−3.63625
$426$	−10.6971	−0.518277
$427$	0.798082	0.0386219
$428$	−15.6929	−0.758545
$429$	−0.829532	−0.0400502
$430$	−41.1907	−1.98639
$431$	−14.4660	−0.696805	−0.348402	−	0.937345i	$-0.613276\pi$
$431$	−14.4660	−0.696805	−0.348402	+	0.937345i	$0.613276\pi$
$432$	1.00000	0.0481125
$433$	26.2026	1.25922	0.629608	−	0.776913i	$-0.283216\pi$
$433$	26.2026	1.25922	0.629608	+	0.776913i	$0.283216\pi$
$434$	1.00835	0.0484026
$435$	−2.88230	−0.138196
$436$	−5.20681	−0.249361
$437$	5.57867	0.266864
$438$	−8.51639	−0.406929
$439$	−7.36622	−0.351571	−0.175785	−	0.984429i	$-0.556246\pi$
$439$	−7.36622	−0.351571	−0.175785	+	0.984429i	$0.556246\pi$
$440$	−3.28719	−0.156711
$441$	−6.98226	−0.332489
$442$	7.00392	0.333142
$443$	−4.70488	−0.223535	−0.111768	−	0.993734i	$-0.535651\pi$
$443$	−4.70488	−0.223535	−0.111768	+	0.993734i	$0.535651\pi$
$444$	−6.98878	−0.331673
$445$	−18.9076	−0.896308
$446$	10.3471	0.489950
$447$	−15.6248	−0.739029
$448$	0.133176	0.00629197
$449$	−9.70001	−0.457772	−0.228886	−	0.973453i	$-0.573508\pi$
$449$	−9.70001	−0.457772	−0.228886	+	0.973453i	$0.573508\pi$
$450$	10.7031	0.504547
$451$	−0.370712	−0.0174562
$452$	−0.688656	−0.0323917
$453$	−4.60466	−0.216346
$454$	1.27278	0.0597344
$455$	0.527737	0.0247407
$456$	2.69311	0.126116
$457$	36.6423	1.71405	0.857026	−	0.515272i	$-0.172309\pi$
$457$	36.6423	1.71405	0.857026	+	0.515272i	$0.172309\pi$
$458$	−4.92528	−0.230143
$459$	−7.00392	−0.326915
$460$	−8.20860	−0.382728
$461$	−8.36398	−0.389549	−0.194775	−	0.980848i	$-0.562398\pi$
$461$	−8.36398	−0.389549	−0.194775	+	0.980848i	$0.562398\pi$
$462$	0.110474	0.00513970
$463$	−5.23002	−0.243060	−0.121530	−	0.992588i	$-0.538780\pi$
$463$	−5.23002	−0.243060	−0.121530	+	0.992588i	$0.538780\pi$
$464$	0.727357	0.0337667
$465$	−30.0040	−1.39140
$466$	−22.4533	−1.04013
$467$	−36.4755	−1.68789	−0.843943	−	0.536433i	$-0.819771\pi$
$467$	−36.4755	−1.68789	−0.843943	+	0.536433i	$0.819771\pi$
$468$	−1.00000	−0.0462250
$469$	−1.78559	−0.0824511
$470$	−23.0048	−1.06113
$471$	7.73031	0.356194
$472$	−10.1232	−0.465960
$473$	8.62264	0.396470
$474$	−7.01281	−0.322109
$475$	28.8245	1.32256
$476$	−0.932753	−0.0427527
$477$	−8.83345	−0.404456
$478$	−6.18920	−0.283087
$479$	−38.2795	−1.74904	−0.874518	−	0.484992i	$-0.838822\pi$
$479$	−38.2795	−1.74904	−0.874518	+	0.484992i	$0.838822\pi$
$480$	−3.96271	−0.180872
$481$	6.98878	0.318661
$482$	18.9753	0.864304
$483$	0.275869	0.0125525
$484$	−10.3119	−0.468722
$485$	−57.7599	−2.62274
$486$	1.00000	0.0453609
$487$	5.22127	0.236598	0.118299	−	0.992978i	$-0.462256\pi$
$487$	5.22127	0.236598	0.118299	+	0.992978i	$0.462256\pi$
$488$	5.99269	0.271276
$489$	10.8081	0.488757
$490$	27.6687	1.24994
$491$	−30.3389	−1.36918	−0.684588	−	0.728930i	$-0.740018\pi$
$491$	−30.3389	−1.36918	−0.684588	+	0.728930i	$0.740018\pi$
$492$	−0.446893	−0.0201475
$493$	−5.09435	−0.229438
$494$	−2.69311	−0.121169
$495$	−3.28719	−0.147748
$496$	7.57160	0.339975
$497$	−1.42460	−0.0639020
$498$	−1.00352	−0.0449689
$499$	−4.67825	−0.209427	−0.104714	−	0.994502i	$-0.533393\pi$
$499$	−4.67825	−0.209427	−0.104714	+	0.994502i	$0.533393\pi$
$500$	−22.5995	−1.01068
$501$	−9.76395	−0.436221
$502$	−8.58481	−0.383159
$503$	19.6279	0.875166	0.437583	−	0.899178i	$-0.355835\pi$
$503$	19.6279	0.875166	0.437583	+	0.899178i	$0.355835\pi$
$504$	0.133176	0.00593213
$505$	22.1853	0.987232
$506$	1.71834	0.0763897
$507$	1.00000	0.0444116
$508$	−11.3586	−0.503955
$509$	−39.5683	−1.75383	−0.876917	−	0.480642i	$-0.840404\pi$
$509$	−39.5683	−1.75383	−0.876917	+	0.480642i	$0.840404\pi$
$510$	27.7545	1.22899
$511$	−1.13418	−0.0501731
$512$	1.00000	0.0441942
$513$	2.69311	0.118904
$514$	−16.4098	−0.723806
$515$	3.96271	0.174618
$516$	10.3946	0.457596
$517$	4.81569	0.211794
$518$	−0.930737	−0.0408942
$519$	18.2114	0.799393
$520$	3.96271	0.173776
$521$	37.7768	1.65503	0.827516	−	0.561443i	$-0.189754\pi$
$521$	37.7768	1.65503	0.827516	+	0.561443i	$0.189754\pi$
$522$	0.727357	0.0318355
$523$	10.5766	0.462482	0.231241	−	0.972897i	$-0.425721\pi$
$523$	10.5766	0.462482	0.231241	+	0.972897i	$0.425721\pi$
$524$	−18.7011	−0.816963
$525$	1.42539	0.0622091
$526$	28.9252	1.26120
$527$	−53.0309	−2.31006
$528$	0.829532	0.0361007
$529$	−18.7090	−0.813437
$530$	35.0044	1.52049
$531$	−10.1232	−0.439312
$532$	0.358657	0.0155498
$533$	0.446893	0.0193571
$534$	4.77140	0.206479
$535$	62.1863	2.68855
$536$	−13.4078	−0.579128
$537$	25.5316	1.10177
$538$	20.8927	0.900748
$539$	−5.79201	−0.249479
$540$	−3.96271	−0.170528
$541$	−4.94989	−0.212812	−0.106406	−	0.994323i	$-0.533934\pi$
$541$	−4.94989	−0.212812	−0.106406	+	0.994323i	$0.533934\pi$
$542$	−0.311163	−0.0133656
$543$	6.53741	0.280547
$544$	−7.00392	−0.300291
$545$	20.6331	0.883824
$546$	−0.133176	−0.00569940
$547$	−13.8319	−0.591409	−0.295705	−	0.955279i	$-0.595554\pi$
$547$	−13.8319	−0.591409	−0.295705	+	0.955279i	$0.595554\pi$
$548$	−13.1788	−0.562971
$549$	5.99269	0.255762
$550$	8.87852	0.378581
$551$	1.95885	0.0834498
$552$	2.07146	0.0881673
$553$	−0.933937	−0.0397151
$554$	9.35681	0.397533
$555$	27.6945	1.17557
$556$	−8.73296	−0.370360
$557$	−6.16858	−0.261371	−0.130686	−	0.991424i	$-0.541718\pi$
$557$	−6.16858	−0.261371	−0.130686	+	0.991424i	$0.541718\pi$
$558$	7.57160	0.320531
$559$	−10.3946	−0.439644
$560$	−0.527737	−0.0223010
$561$	−5.80997	−0.245297
$562$	−12.7435	−0.537553
$563$	14.8925	0.627644	0.313822	−	0.949482i	$-0.398390\pi$
$563$	14.8925	0.627644	0.313822	+	0.949482i	$0.398390\pi$
$564$	5.80531	0.244448
$565$	2.72894	0.114807
$566$	11.6910	0.491411
$567$	0.133176	0.00559286
$568$	−10.6971	−0.448841
$569$	0.777737	0.0326044	0.0163022	−	0.999867i	$-0.494811\pi$
$569$	0.777737	0.0326044	0.0163022	+	0.999867i	$0.494811\pi$
$570$	−10.6720	−0.447001
$571$	−1.14647	−0.0479783	−0.0239891	−	0.999712i	$-0.507637\pi$
$571$	−1.14647	−0.0479783	−0.0239891	+	0.999712i	$0.507637\pi$
$572$	−0.829532	−0.0346845
$573$	24.4667	1.02211
$574$	−0.0595155	−0.00248413
$575$	22.1710	0.924593
$576$	1.00000	0.0416667
$577$	34.6368	1.44195	0.720974	−	0.692963i	$-0.243695\pi$
$577$	34.6368	1.44195	0.720974	+	0.692963i	$0.243695\pi$
$578$	32.0549	1.33331
$579$	−15.8174	−0.657349
$580$	−2.88230	−0.119681
$581$	−0.133645	−0.00554453
$582$	14.5759	0.604189
$583$	−7.32763	−0.303479
$584$	−8.51639	−0.352411
$585$	3.96271	0.163838
$586$	16.7907	0.693619
$587$	−5.05639	−0.208700	−0.104350	−	0.994541i	$-0.533276\pi$
$587$	−5.05639	−0.208700	−0.104350	+	0.994541i	$0.533276\pi$
$588$	−6.98226	−0.287944
$589$	20.3911	0.840202
$590$	40.1155	1.65153
$591$	−6.37807	−0.262359
$592$	−6.98878	−0.287237
$593$	−5.96202	−0.244831	−0.122415	−	0.992479i	$-0.539064\pi$
$593$	−5.96202	−0.244831	−0.122415	+	0.992479i	$0.539064\pi$
$594$	0.829532	0.0340361
$595$	3.69623	0.151531
$596$	−15.6248	−0.640018
$597$	−1.53521	−0.0628319
$598$	−2.07146	−0.0847084
$599$	−36.2499	−1.48113	−0.740564	−	0.671985i	$-0.765442\pi$
$599$	−36.2499	−1.48113	−0.740564	+	0.671985i	$0.765442\pi$
$600$	10.7031	0.436950
$601$	5.74387	0.234297	0.117149	−	0.993114i	$-0.462625\pi$
$601$	5.74387	0.234297	0.117149	+	0.993114i	$0.462625\pi$
$602$	1.38431	0.0564203
$603$	−13.4078	−0.546007
$604$	−4.60466	−0.187361
$605$	40.8630	1.66132
$606$	−5.59851	−0.227424
$607$	−30.3665	−1.23254	−0.616270	−	0.787535i	$-0.711357\pi$
$607$	−30.3665	−1.23254	−0.616270	+	0.787535i	$0.711357\pi$
$608$	2.69311	0.109220
$609$	0.0968664	0.00392523
$610$	−23.7473	−0.961499
$611$	−5.80531	−0.234858
$612$	−7.00392	−0.283117
$613$	24.8756	1.00472	0.502358	−	0.864660i	$-0.332466\pi$
$613$	24.8756	1.00472	0.502358	+	0.864660i	$0.332466\pi$
$614$	−20.3688	−0.822016
$615$	1.77091	0.0714099
$616$	0.110474	0.00445111
$617$	−27.0913	−1.09065	−0.545327	−	0.838223i	$-0.683595\pi$
$617$	−27.0913	−1.09065	−0.545327	+	0.838223i	$0.683595\pi$
$618$	−1.00000	−0.0402259
$619$	−30.4299	−1.22308	−0.611540	−	0.791214i	$-0.709450\pi$
$619$	−30.4299	−1.22308	−0.611540	+	0.791214i	$0.709450\pi$
$620$	−30.0040	−1.20499
$621$	2.07146	0.0831249
$622$	−14.9885	−0.600985
$623$	0.635435	0.0254582
$624$	−1.00000	−0.0400320
$625$	36.0400	1.44160
$626$	−2.06755	−0.0826360
$627$	2.23402	0.0892181
$628$	7.73031	0.308473
$629$	48.9488	1.95172
$630$	−0.527737	−0.0210256
$631$	−15.0756	−0.600148	−0.300074	−	0.953916i	$-0.597011\pi$
$631$	−15.0756	−0.600148	−0.300074	+	0.953916i	$0.597011\pi$
$632$	−7.01281	−0.278955
$633$	−26.9295	−1.07035
$634$	−0.106723	−0.00423852
$635$	45.0107	1.78620
$636$	−8.83345	−0.350269
$637$	6.98226	0.276647
$638$	0.603365	0.0238875
$639$	−10.6971	−0.423171
$640$	−3.96271	−0.156640
$641$	19.1025	0.754503	0.377252	−	0.926111i	$-0.376869\pi$
$641$	19.1025	0.754503	0.377252	+	0.926111i	$0.376869\pi$
$642$	−15.6929	−0.619349
$643$	−33.5846	−1.32445	−0.662223	−	0.749307i	$-0.730387\pi$
$643$	−33.5846	−1.32445	−0.662223	+	0.749307i	$0.730387\pi$
$644$	0.275869	0.0108708
$645$	−41.1907	−1.62188
$646$	−18.8623	−0.742128
$647$	10.8071	0.424873	0.212436	−	0.977175i	$-0.431860\pi$
$647$	10.8071	0.424873	0.212436	+	0.977175i	$0.431860\pi$
$648$	1.00000	0.0392837
$649$	−8.39755	−0.329633
$650$	−10.7031	−0.419808
$651$	1.00835	0.0395205
$652$	10.8081	0.423276
$653$	−33.1312	−1.29653	−0.648263	−	0.761417i	$-0.724504\pi$
$653$	−33.1312	−1.29653	−0.648263	+	0.761417i	$0.724504\pi$
$654$	−5.20681	−0.203602
$655$	74.1072	2.89561
$656$	−0.446893	−0.0174483
$657$	−8.51639	−0.332256
$658$	0.773128	0.0301397
$659$	8.54101	0.332711	0.166355	−	0.986066i	$-0.446800\pi$
$659$	8.54101	0.332711	0.166355	+	0.986066i	$0.446800\pi$
$660$	−3.28719	−0.127954
$661$	47.7810	1.85846	0.929232	−	0.369497i	$-0.120470\pi$
$661$	47.7810	1.85846	0.929232	+	0.369497i	$0.120470\pi$
$662$	−5.51043	−0.214169
$663$	7.00392	0.272010
$664$	−1.00352	−0.0389442
$665$	−1.42125	−0.0551138
$666$	−6.98878	−0.270810
$667$	1.50669	0.0583393
$668$	−9.76395	−0.377779
$669$	10.3471	0.400043
$670$	53.1311	2.05264
$671$	4.97112	0.191908
$672$	0.133176	0.00513737
$673$	25.9899	1.00184	0.500919	−	0.865494i	$-0.332995\pi$
$673$	25.9899	1.00184	0.500919	+	0.865494i	$0.332995\pi$
$674$	−15.2036	−0.585620
$675$	10.7031	0.411961
$676$	1.00000	0.0384615
$677$	33.3877	1.28319	0.641596	−	0.767042i	$-0.278272\pi$
$677$	33.3877	1.28319	0.641596	+	0.767042i	$0.278272\pi$
$678$	−0.688656	−0.0264477
$679$	1.94115	0.0744946
$680$	27.7545	1.06434
$681$	1.27278	0.0487729
$682$	6.28088	0.240507
$683$	−19.6432	−0.751628	−0.375814	−	0.926695i	$-0.622637\pi$
$683$	−19.6432	−0.751628	−0.375814	+	0.926695i	$0.622637\pi$
$684$	2.69311	0.102974
$685$	52.2238	1.99537
$686$	−1.86210	−0.0710954
$687$	−4.92528	−0.187911
$688$	10.3946	0.396290
$689$	8.83345	0.336528
$690$	−8.20860	−0.312496
$691$	2.83301	0.107773	0.0538864	−	0.998547i	$-0.482839\pi$
$691$	2.83301	0.107773	0.0538864	+	0.998547i	$0.482839\pi$
$692$	18.2114	0.692294
$693$	0.110474	0.00419655
$694$	9.43539	0.358162
$695$	34.6062	1.31269
$696$	0.727357	0.0275704
$697$	3.13001	0.118557
$698$	−34.7553	−1.31551
$699$	−22.4533	−0.849264
$700$	1.42539	0.0538746
$701$	18.0348	0.681165	0.340582	−	0.940215i	$-0.389376\pi$
$701$	18.0348	0.681165	0.340582	+	0.940215i	$0.389376\pi$
$702$	−1.00000	−0.0377426
$703$	−18.8215	−0.709868
$704$	0.829532	0.0312641
$705$	−23.0048	−0.866409
$706$	1.11441	0.0419415
$707$	−0.745587	−0.0280407
$708$	−10.1232	−0.380455
$709$	−38.7789	−1.45637	−0.728185	−	0.685380i	$-0.759636\pi$
$709$	−38.7789	−1.45637	−0.728185	+	0.685380i	$0.759636\pi$
$710$	42.3895	1.59085
$711$	−7.01281	−0.263001
$712$	4.77140	0.178816
$713$	15.6843	0.587381
$714$	−0.932753	−0.0349074
$715$	3.28719	0.122934
$716$	25.5316	0.954162
$717$	−6.18920	−0.231140
$718$	−7.02430	−0.262145
$719$	36.7385	1.37012	0.685058	−	0.728489i	$-0.259777\pi$
$719$	36.7385	1.37012	0.685058	+	0.728489i	$0.259777\pi$
$720$	−3.96271	−0.147681
$721$	−0.133176	−0.00495973
$722$	−11.7472	−0.437184
$723$	18.9753	0.705701
$724$	6.53741	0.242961
$725$	7.78494	0.289125
$726$	−10.3119	−0.382710
$727$	8.56467	0.317646	0.158823	−	0.987307i	$-0.449230\pi$
$727$	8.56467	0.317646	0.158823	+	0.987307i	$0.449230\pi$
$728$	−0.133176	−0.00493583
$729$	1.00000	0.0370370
$730$	33.7480	1.24907
$731$	−72.8029	−2.69271
$732$	5.99269	0.221496
$733$	−27.0616	−0.999543	−0.499771	−	0.866157i	$-0.666583\pi$
$733$	−27.0616	−0.999543	−0.499771	+	0.866157i	$0.666583\pi$
$734$	29.9449	1.10529
$735$	27.6687	1.02057
$736$	2.07146	0.0763551
$737$	−11.1222	−0.409691
$738$	−0.446893	−0.0164504
$739$	−35.7446	−1.31489	−0.657443	−	0.753504i	$-0.728362\pi$
$739$	−35.7446	−1.31489	−0.657443	+	0.753504i	$0.728362\pi$
$740$	27.6945	1.01807
$741$	−2.69311	−0.0989338
$742$	−1.17640	−0.0431871
$743$	24.4861	0.898308	0.449154	−	0.893454i	$-0.351726\pi$
$743$	24.4861	0.898308	0.449154	+	0.893454i	$0.351726\pi$
$744$	7.57160	0.277588
$745$	61.9166	2.26845
$746$	15.9660	0.584556
$747$	−1.00352	−0.0367170
$748$	−5.80997	−0.212434
$749$	−2.08992	−0.0763639
$750$	−22.5995	−0.825218
$751$	29.2811	1.06848	0.534242	−	0.845332i	$-0.320597\pi$
$751$	29.2811	1.06848	0.534242	+	0.845332i	$0.320597\pi$
$752$	5.80531	0.211698
$753$	−8.58481	−0.312848
$754$	−0.727357	−0.0264888
$755$	18.2469	0.664073
$756$	0.133176	0.00484356
$757$	52.6929	1.91516	0.957578	−	0.288174i	$-0.0930482\pi$
$757$	52.6929	1.91516	0.957578	+	0.288174i	$0.0930482\pi$
$758$	−37.5613	−1.36429
$759$	1.71834	0.0623719
$760$	−10.6720	−0.387114
$761$	−2.29681	−0.0832591	−0.0416296	−	0.999133i	$-0.513255\pi$
$761$	−2.29681	−0.0832591	−0.0416296	+	0.999133i	$0.513255\pi$
$762$	−11.3586	−0.411478
$763$	−0.693422	−0.0251036
$764$	24.4667	0.885173
$765$	27.7545	1.00347
$766$	6.98732	0.252462
$767$	10.1232	0.365529
$768$	1.00000	0.0360844
$769$	30.6844	1.10651	0.553253	−	0.833013i	$-0.313386\pi$
$769$	30.6844	1.10651	0.553253	+	0.833013i	$0.313386\pi$
$770$	−0.437775	−0.0157763
$771$	−16.4098	−0.590985
$772$	−15.8174	−0.569281
$773$	−14.0074	−0.503810	−0.251905	−	0.967752i	$-0.581057\pi$
$773$	−14.0074	−0.503810	−0.251905	+	0.967752i	$0.581057\pi$
$774$	10.3946	0.373626
$775$	81.0392	2.91101
$776$	14.5759	0.523243
$777$	−0.930737	−0.0333900
$778$	−13.4606	−0.482587
$779$	−1.20353	−0.0431210
$780$	3.96271	0.141888
$781$	−8.87360	−0.317522
$782$	−14.5083	−0.518818
$783$	0.727357	0.0259936
$784$	−6.98226	−0.249367
$785$	−30.6330	−1.09334
$786$	−18.7011	−0.667048
$787$	−40.5516	−1.44551	−0.722753	−	0.691106i	$-0.757124\pi$
$787$	−40.5516	−1.44551	−0.722753	+	0.691106i	$0.757124\pi$
$788$	−6.37807	−0.227209
$789$	28.9252	1.02976
$790$	27.7897	0.988713
$791$	−0.0917124	−0.00326092
$792$	0.829532	0.0294761
$793$	−5.99269	−0.212807
$794$	−18.6840	−0.663070
$795$	35.0044	1.24148
$796$	−1.53521	−0.0544140
$797$	13.1777	0.466777	0.233389	−	0.972384i	$-0.425019\pi$
$797$	13.1777	0.466777	0.233389	+	0.972384i	$0.425019\pi$
$798$	0.358657	0.0126963
$799$	−40.6599	−1.43845
$800$	10.7031	0.378410
$801$	4.77140	0.168589
$802$	5.16563	0.182405
$803$	−7.06461	−0.249305
$804$	−13.4078	−0.472856
$805$	−1.09319	−0.0385298
$806$	−7.57160	−0.266698
$807$	20.8927	0.735458
$808$	−5.59851	−0.196955
$809$	−46.6473	−1.64003	−0.820017	−	0.572340i	$-0.806036\pi$
$809$	−46.6473	−1.64003	−0.820017	+	0.572340i	$0.806036\pi$
$810$	−3.96271	−0.139235
$811$	17.8328	0.626193	0.313096	−	0.949721i	$-0.398634\pi$
$811$	17.8328	0.626193	0.313096	+	0.949721i	$0.398634\pi$
$812$	0.0968664	0.00339935
$813$	−0.311163	−0.0109130
$814$	−5.79741	−0.203199
$815$	−42.8292	−1.50024
$816$	−7.00392	−0.245186
$817$	27.9938	0.979378
$818$	8.70455	0.304347
$819$	−0.133176	−0.00465354
$820$	1.77091	0.0618428
$821$	20.9104	0.729778	0.364889	−	0.931051i	$-0.381107\pi$
$821$	20.9104	0.729778	0.364889	+	0.931051i	$0.381107\pi$
$822$	−13.1788	−0.459664
$823$	34.7728	1.21210	0.606052	−	0.795425i	$-0.292752\pi$
$823$	34.7728	1.21210	0.606052	+	0.795425i	$0.292752\pi$
$824$	−1.00000	−0.0348367
$825$	8.87852	0.309110
$826$	−1.34817	−0.0469089
$827$	27.8295	0.967727	0.483864	−	0.875143i	$-0.339233\pi$
$827$	27.8295	0.967727	0.483864	+	0.875143i	$0.339233\pi$
$828$	2.07146	0.0719883
$829$	49.1715	1.70780	0.853898	−	0.520440i	$-0.174232\pi$
$829$	49.1715	1.70780	0.853898	+	0.520440i	$0.174232\pi$
$830$	3.97666	0.138032
$831$	9.35681	0.324584
$832$	−1.00000	−0.0346688
$833$	48.9032	1.69440
$834$	−8.73296	−0.302398
$835$	38.6917	1.33898
$836$	2.23402	0.0772651
$837$	7.57160	0.261713
$838$	25.9033	0.894816
$839$	6.06274	0.209309	0.104655	−	0.994509i	$-0.466626\pi$
$839$	6.06274	0.209309	0.104655	+	0.994509i	$0.466626\pi$
$840$	−0.527737	−0.0182087
$841$	−28.4710	−0.981757
$842$	37.0324	1.27622
$843$	−12.7435	−0.438910
$844$	−26.9295	−0.926951
$845$	−3.96271	−0.136321
$846$	5.80531	0.199591
$847$	−1.37329	−0.0471869
$848$	−8.83345	−0.303342
$849$	11.6910	0.401235
$850$	−74.9633	−2.57122
$851$	−14.4770	−0.496265
$852$	−10.6971	−0.366477
$853$	33.1671	1.13562	0.567810	−	0.823160i	$-0.307791\pi$
$853$	33.1671	1.13562	0.567810	+	0.823160i	$0.307791\pi$
$854$	0.798082	0.0273098
$855$	−10.6720	−0.364975
$856$	−15.6929	−0.536372
$857$	9.02526	0.308297	0.154149	−	0.988048i	$-0.450737\pi$
$857$	9.02526	0.308297	0.154149	+	0.988048i	$0.450737\pi$
$858$	−0.829532	−0.0283197
$859$	31.7032	1.08170	0.540849	−	0.841120i	$-0.318103\pi$
$859$	31.7032	1.08170	0.540849	+	0.841120i	$0.318103\pi$
$860$	−41.1907	−1.40459
$861$	−0.0595155	−0.00202828
$862$	−14.4660	−0.492715
$863$	−9.33028	−0.317606	−0.158803	−	0.987310i	$-0.550764\pi$
$863$	−9.33028	−0.317606	−0.158803	+	0.987310i	$0.550764\pi$
$864$	1.00000	0.0340207
$865$	−72.1665	−2.45374
$866$	26.2026	0.890400
$867$	32.0549	1.08864
$868$	1.00835	0.0342258
$869$	−5.81735	−0.197340
$870$	−2.88230	−0.0977192
$871$	13.4078	0.454306
$872$	−5.20681	−0.176325
$873$	14.5759	0.493318
$874$	5.57867	0.188701
$875$	−3.00971	−0.101747
$876$	−8.51639	−0.287742
$877$	44.2797	1.49522	0.747609	−	0.664139i	$-0.231202\pi$
$877$	44.2797	1.49522	0.747609	+	0.664139i	$0.231202\pi$
$878$	−7.36622	−0.248598
$879$	16.7907	0.566338
$880$	−3.28719	−0.110811
$881$	−19.3614	−0.652301	−0.326151	−	0.945318i	$-0.605752\pi$
$881$	−19.3614	−0.652301	−0.326151	+	0.945318i	$0.605752\pi$
$882$	−6.98226	−0.235105
$883$	−12.0024	−0.403914	−0.201957	−	0.979394i	$-0.564730\pi$
$883$	−12.0024	−0.403914	−0.201957	+	0.979394i	$0.564730\pi$
$884$	7.00392	0.235567
$885$	40.1155	1.34847
$886$	−4.70488	−0.158063
$887$	23.9598	0.804491	0.402245	−	0.915532i	$-0.368230\pi$
$887$	23.9598	0.804491	0.402245	+	0.915532i	$0.368230\pi$
$888$	−6.98878	−0.234528
$889$	−1.51269	−0.0507339
$890$	−18.9076	−0.633786
$891$	0.829532	0.0277904
$892$	10.3471	0.346447
$893$	15.6343	0.523183
$894$	−15.6248	−0.522572
$895$	−101.174	−3.38189
$896$	0.133176	0.00444910
$897$	−2.07146	−0.0691641
$898$	−9.70001	−0.323693
$899$	5.50725	0.183677
$900$	10.7031	0.356768
$901$	61.8688	2.06115
$902$	−0.370712	−0.0123434
$903$	1.38431	0.0460669
$904$	−0.688656	−0.0229044
$905$	−25.9058	−0.861139
$906$	−4.60466	−0.152980
$907$	−27.0218	−0.897243	−0.448622	−	0.893722i	$-0.648085\pi$
$907$	−27.0218	−0.897243	−0.448622	+	0.893722i	$0.648085\pi$
$908$	1.27278	0.0422386
$909$	−5.59851	−0.185691
$910$	0.527737	0.0174943
$911$	40.6355	1.34632	0.673158	−	0.739499i	$-0.264938\pi$
$911$	40.6355	1.34632	0.673158	+	0.739499i	$0.264938\pi$
$912$	2.69311	0.0891777
$913$	−0.832453	−0.0275502
$914$	36.6423	1.21202
$915$	−23.7473	−0.785061
$916$	−4.92528	−0.162736
$917$	−2.49054	−0.0822449
$918$	−7.00392	−0.231164
$919$	−57.2580	−1.88877	−0.944384	−	0.328844i	$-0.893341\pi$
$919$	−57.2580	−1.88877	−0.944384	+	0.328844i	$0.893341\pi$
$920$	−8.20860	−0.270629
$921$	−20.3688	−0.671173
$922$	−8.36398	−0.275453
$923$	10.6971	0.352100
$924$	0.110474	0.00363432
$925$	−74.8013	−2.45945
$926$	−5.23002	−0.171869
$927$	−1.00000	−0.0328443
$928$	0.727357	0.0238767
$929$	26.0742	0.855467	0.427734	−	0.903905i	$-0.359312\pi$
$929$	26.0742	0.855467	0.427734	+	0.903905i	$0.359312\pi$
$930$	−30.0040	−0.983871
$931$	−18.8040	−0.616276
$932$	−22.4533	−0.735484
$933$	−14.9885	−0.490703
$934$	−36.4755	−1.19352
$935$	23.0232	0.752940
$936$	−1.00000	−0.0326860
$937$	39.0230	1.27483	0.637413	−	0.770523i	$-0.280005\pi$
$937$	39.0230	1.27483	0.637413	+	0.770523i	$0.280005\pi$
$938$	−1.78559	−0.0583017
$939$	−2.06755	−0.0674720
$940$	−23.0048	−0.750333
$941$	−41.9604	−1.36787	−0.683935	−	0.729543i	$-0.739733\pi$
$941$	−41.9604	−1.36787	−0.683935	+	0.729543i	$0.739733\pi$
$942$	7.73031	0.251867
$943$	−0.925723	−0.0301457
$944$	−10.1232	−0.329484
$945$	−0.527737	−0.0171673
$946$	8.62264	0.280346
$947$	50.7557	1.64934	0.824670	−	0.565614i	$-0.191361\pi$
$947$	50.7557	1.64934	0.824670	+	0.565614i	$0.191361\pi$
$948$	−7.01281	−0.227765
$949$	8.51639	0.276454
$950$	28.8245	0.935189
$951$	−0.106723	−0.00346074
$952$	−0.932753	−0.0302307
$953$	44.1844	1.43127	0.715637	−	0.698473i	$-0.246137\pi$
$953$	44.1844	1.43127	0.715637	+	0.698473i	$0.246137\pi$
$954$	−8.83345	−0.285994
$955$	−96.9542	−3.13737
$956$	−6.18920	−0.200173
$957$	0.603365	0.0195040
$958$	−38.2795	−1.23676
$959$	−1.75510	−0.0566752
$960$	−3.96271	−0.127896
$961$	26.3291	0.849326
$962$	6.98878	0.225327
$963$	−15.6929	−0.505696
$964$	18.9753	0.611155
$965$	62.6798	2.01773
$966$	0.275869	0.00887594
$967$	58.4134	1.87845	0.939224	−	0.343305i	$-0.111546\pi$
$967$	58.4134	1.87845	0.939224	+	0.343305i	$0.111546\pi$
$968$	−10.3119	−0.331436
$969$	−18.8623	−0.605945
$970$	−57.7599	−1.85456
$971$	−9.11649	−0.292562	−0.146281	−	0.989243i	$-0.546730\pi$
$971$	−9.11649	−0.292562	−0.146281	+	0.989243i	$0.546730\pi$
$972$	1.00000	0.0320750
$973$	−1.16302	−0.0372847
$974$	5.22127	0.167300
$975$	−10.7031	−0.342772
$976$	5.99269	0.191821
$977$	41.3721	1.32361	0.661806	−	0.749675i	$-0.269790\pi$
$977$	41.3721	1.32361	0.661806	+	0.749675i	$0.269790\pi$
$978$	10.8081	0.345604
$979$	3.95802	0.126499
$980$	27.6687	0.883843
$981$	−5.20681	−0.166241
$982$	−30.3389	−0.968154
$983$	55.5213	1.77086	0.885428	−	0.464777i	$-0.153865\pi$
$983$	55.5213	1.77086	0.885428	+	0.464777i	$0.153865\pi$
$984$	−0.446893	−0.0142464
$985$	25.2744	0.805310
$986$	−5.09435	−0.162237
$987$	0.773128	0.0246089
$988$	−2.69311	−0.0856792
$989$	21.5320	0.684678
$990$	−3.28719	−0.104474
$991$	−26.8575	−0.853158	−0.426579	−	0.904450i	$-0.640281\pi$
$991$	−26.8575	−0.853158	−0.426579	+	0.904450i	$0.640281\pi$
$992$	7.57160	0.240398
$993$	−5.51043	−0.174868
$994$	−1.42460	−0.0451855
$995$	6.08358	0.192862
$996$	−1.00352	−0.0317978
$997$	−22.8107	−0.722423	−0.361211	−	0.932484i	$-0.617637\pi$
$997$	−22.8107	−0.722423	−0.361211	+	0.932484i	$0.617637\pi$
$998$	−4.67825	−0.148087
$999$	−6.98878	−0.221115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.q.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.q.1.1	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.96271 q^{5} +1.00000 q^{6} +0.133176 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.96271 q^{5} +1.00000 q^{6} +0.133176 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.96271 q^{10} +0.829532 q^{11} +1.00000 q^{12} -1.00000 q^{13} +0.133176 q^{14} -3.96271 q^{15} +1.00000 q^{16} -7.00392 q^{17} +1.00000 q^{18} +2.69311 q^{19} -3.96271 q^{20} +0.133176 q^{21} +0.829532 q^{22} +2.07146 q^{23} +1.00000 q^{24} +10.7031 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.133176 q^{28} +0.727357 q^{29} -3.96271 q^{30} +7.57160 q^{31} +1.00000 q^{32} +0.829532 q^{33} -7.00392 q^{34} -0.527737 q^{35} +1.00000 q^{36} -6.98878 q^{37} +2.69311 q^{38} -1.00000 q^{39} -3.96271 q^{40} -0.446893 q^{41} +0.133176 q^{42} +10.3946 q^{43} +0.829532 q^{44} -3.96271 q^{45} +2.07146 q^{46} +5.80531 q^{47} +1.00000 q^{48} -6.98226 q^{49} +10.7031 q^{50} -7.00392 q^{51} -1.00000 q^{52} -8.83345 q^{53} +1.00000 q^{54} -3.28719 q^{55} +0.133176 q^{56} +2.69311 q^{57} +0.727357 q^{58} -10.1232 q^{59} -3.96271 q^{60} +5.99269 q^{61} +7.57160 q^{62} +0.133176 q^{63} +1.00000 q^{64} +3.96271 q^{65} +0.829532 q^{66} -13.4078 q^{67} -7.00392 q^{68} +2.07146 q^{69} -0.527737 q^{70} -10.6971 q^{71} +1.00000 q^{72} -8.51639 q^{73} -6.98878 q^{74} +10.7031 q^{75} +2.69311 q^{76} +0.110474 q^{77} -1.00000 q^{78} -7.01281 q^{79} -3.96271 q^{80} +1.00000 q^{81} -0.446893 q^{82} -1.00352 q^{83} +0.133176 q^{84} +27.7545 q^{85} +10.3946 q^{86} +0.727357 q^{87} +0.829532 q^{88} +4.77140 q^{89} -3.96271 q^{90} -0.133176 q^{91} +2.07146 q^{92} +7.57160 q^{93} +5.80531 q^{94} -10.6720 q^{95} +1.00000 q^{96} +14.5759 q^{97} -6.98226 q^{98} +0.829532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * q^99

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