LMFDB - Embedded newform 8034.2.a.p.1.8

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} - x^{7} - 12x^{6} + 12x^{5} + 43x^{4} - 38x^{3} - 49x^{2} + 23x + 20 $ x^8 - x^7 - 12x^6 + 12x^5 + 43x^4 - 38x^3 - 49x^2 + 23x + 20
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$1.80009$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.02511 q^{5} +1.00000 q^{6} -2.69336 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.02511 q^{5} +1.00000 q^{6} -2.69336 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.02511 q^{10} -2.27080 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.69336 q^{14} +3.02511 q^{15} +1.00000 q^{16} -6.46889 q^{17} +1.00000 q^{18} -5.63805 q^{19} +3.02511 q^{20} -2.69336 q^{21} -2.27080 q^{22} -4.09415 q^{23} +1.00000 q^{24} +4.15130 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.69336 q^{28} -8.69441 q^{29} +3.02511 q^{30} +0.130650 q^{31} +1.00000 q^{32} -2.27080 q^{33} -6.46889 q^{34} -8.14770 q^{35} +1.00000 q^{36} -5.91687 q^{37} -5.63805 q^{38} +1.00000 q^{39} +3.02511 q^{40} -3.27964 q^{41} -2.69336 q^{42} +2.43048 q^{43} -2.27080 q^{44} +3.02511 q^{45} -4.09415 q^{46} +2.53673 q^{47} +1.00000 q^{48} +0.254168 q^{49} +4.15130 q^{50} -6.46889 q^{51} +1.00000 q^{52} -10.7968 q^{53} +1.00000 q^{54} -6.86943 q^{55} -2.69336 q^{56} -5.63805 q^{57} -8.69441 q^{58} -1.40465 q^{59} +3.02511 q^{60} +2.06457 q^{61} +0.130650 q^{62} -2.69336 q^{63} +1.00000 q^{64} +3.02511 q^{65} -2.27080 q^{66} +3.30838 q^{67} -6.46889 q^{68} -4.09415 q^{69} -8.14770 q^{70} +3.12821 q^{71} +1.00000 q^{72} -6.65670 q^{73} -5.91687 q^{74} +4.15130 q^{75} -5.63805 q^{76} +6.11608 q^{77} +1.00000 q^{78} +15.1430 q^{79} +3.02511 q^{80} +1.00000 q^{81} -3.27964 q^{82} -0.455558 q^{83} -2.69336 q^{84} -19.5691 q^{85} +2.43048 q^{86} -8.69441 q^{87} -2.27080 q^{88} -12.6552 q^{89} +3.02511 q^{90} -2.69336 q^{91} -4.09415 q^{92} +0.130650 q^{93} +2.53673 q^{94} -17.0557 q^{95} +1.00000 q^{96} +18.9875 q^{97} +0.254168 q^{98} -2.27080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{10} - 7 q^{11} + 8 q^{12} + 8 q^{13} - 6 q^{14} - 8 q^{15} + 8 q^{16} - 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 6 q^{21} - 7 q^{22} - 14 q^{23} + 8 q^{24} - 2 q^{25} + 8 q^{26} + 8 q^{27} - 6 q^{28} - 25 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - 7 q^{33} - 20 q^{34} - 18 q^{35} + 8 q^{36} - 15 q^{37} - 12 q^{38} + 8 q^{39} - 8 q^{40} - 18 q^{41} - 6 q^{42} - 8 q^{43} - 7 q^{44} - 8 q^{45} - 14 q^{46} - 12 q^{47} + 8 q^{48} - 8 q^{49} - 2 q^{50} - 20 q^{51} + 8 q^{52} - 25 q^{53} + 8 q^{54} - 8 q^{55} - 6 q^{56} - 12 q^{57} - 25 q^{58} - 9 q^{59} - 8 q^{60} - 2 q^{61} - 12 q^{62} - 6 q^{63} + 8 q^{64} - 8 q^{65} - 7 q^{66} - 8 q^{67} - 20 q^{68} - 14 q^{69} - 18 q^{70} - 13 q^{71} + 8 q^{72} - 2 q^{73} - 15 q^{74} - 2 q^{75} - 12 q^{76} - 5 q^{77} + 8 q^{78} + q^{79} - 8 q^{80} + 8 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 5 q^{85} - 8 q^{86} - 25 q^{87} - 7 q^{88} - 17 q^{89} - 8 q^{90} - 6 q^{91} - 14 q^{92} - 12 q^{93} - 12 q^{94} + 10 q^{95} + 8 q^{96} + 19 q^{97} - 8 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9 - 8 * q^10 - 7 * q^11 + 8 * q^12 + 8 * q^13 - 6 * q^14 - 8 * q^15 + 8 * q^16 - 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 6 * q^21 - 7 * q^22 - 14 * q^23 + 8 * q^24 - 2 * q^25 + 8 * q^26 + 8 * q^27 - 6 * q^28 - 25 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - 7 * q^33 - 20 * q^34 - 18 * q^35 + 8 * q^36 - 15 * q^37 - 12 * q^38 + 8 * q^39 - 8 * q^40 - 18 * q^41 - 6 * q^42 - 8 * q^43 - 7 * q^44 - 8 * q^45 - 14 * q^46 - 12 * q^47 + 8 * q^48 - 8 * q^49 - 2 * q^50 - 20 * q^51 + 8 * q^52 - 25 * q^53 + 8 * q^54 - 8 * q^55 - 6 * q^56 - 12 * q^57 - 25 * q^58 - 9 * q^59 - 8 * q^60 - 2 * q^61 - 12 * q^62 - 6 * q^63 + 8 * q^64 - 8 * q^65 - 7 * q^66 - 8 * q^67 - 20 * q^68 - 14 * q^69 - 18 * q^70 - 13 * q^71 + 8 * q^72 - 2 * q^73 - 15 * q^74 - 2 * q^75 - 12 * q^76 - 5 * q^77 + 8 * q^78 + q^79 - 8 * q^80 + 8 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 5 * q^85 - 8 * q^86 - 25 * q^87 - 7 * q^88 - 17 * q^89 - 8 * q^90 - 6 * q^91 - 14 * q^92 - 12 * q^93 - 12 * q^94 + 10 * q^95 + 8 * q^96 + 19 * q^97 - 8 * q^98 - 7 * 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
$5$	3.02511	1.35287	0.676436	−	0.736502i	$-0.263524\pi$
$5$	3.02511	1.35287	0.676436	+	0.736502i	$0.263524\pi$
$6$	1.00000	0.408248
$7$	−2.69336	−1.01799	−0.508996	−	0.860769i	$-0.669983\pi$
$7$	−2.69336	−1.01799	−0.508996	+	0.860769i	$0.669983\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.02511	0.956624
$11$	−2.27080	−0.684673	−0.342336	−	0.939577i	$-0.611218\pi$
$11$	−2.27080	−0.684673	−0.342336	+	0.939577i	$0.611218\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.69336	−0.719830
$15$	3.02511	0.781081
$16$	1.00000	0.250000
$17$	−6.46889	−1.56894	−0.784468	−	0.620169i	$-0.787064\pi$
$17$	−6.46889	−1.56894	−0.784468	+	0.620169i	$0.787064\pi$
$18$	1.00000	0.235702
$19$	−5.63805	−1.29346	−0.646729	−	0.762720i	$-0.723863\pi$
$19$	−5.63805	−1.29346	−0.646729	+	0.762720i	$0.723863\pi$
$20$	3.02511	0.676436
$21$	−2.69336	−0.587739
$22$	−2.27080	−0.484137
$23$	−4.09415	−0.853690	−0.426845	−	0.904325i	$-0.640375\pi$
$23$	−4.09415	−0.853690	−0.426845	+	0.904325i	$0.640375\pi$
$24$	1.00000	0.204124
$25$	4.15130	0.830260
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−2.69336	−0.508996
$29$	−8.69441	−1.61451	−0.807256	−	0.590201i	$-0.799048\pi$
$29$	−8.69441	−1.61451	−0.807256	+	0.590201i	$0.799048\pi$
$30$	3.02511	0.552307
$31$	0.130650	0.0234655	0.0117327	−	0.999931i	$-0.496265\pi$
$31$	0.130650	0.0234655	0.0117327	+	0.999931i	$0.496265\pi$
$32$	1.00000	0.176777
$33$	−2.27080	−0.395296
$34$	−6.46889	−1.10941
$35$	−8.14770	−1.37721
$36$	1.00000	0.166667
$37$	−5.91687	−0.972727	−0.486363	−	0.873757i	$-0.661677\pi$
$37$	−5.91687	−0.972727	−0.486363	+	0.873757i	$0.661677\pi$
$38$	−5.63805	−0.914613
$39$	1.00000	0.160128
$40$	3.02511	0.478312
$41$	−3.27964	−0.512194	−0.256097	−	0.966651i	$-0.582437\pi$
$41$	−3.27964	−0.512194	−0.256097	+	0.966651i	$0.582437\pi$
$42$	−2.69336	−0.415594
$43$	2.43048	0.370645	0.185322	−	0.982678i	$-0.440667\pi$
$43$	2.43048	0.370645	0.185322	+	0.982678i	$0.440667\pi$
$44$	−2.27080	−0.342336
$45$	3.02511	0.450957
$46$	−4.09415	−0.603650
$47$	2.53673	0.370020	0.185010	−	0.982737i	$-0.440768\pi$
$47$	2.53673	0.370020	0.185010	+	0.982737i	$0.440768\pi$
$48$	1.00000	0.144338
$49$	0.254168	0.0363097
$50$	4.15130	0.587083
$51$	−6.46889	−0.905826
$52$	1.00000	0.138675
$53$	−10.7968	−1.48306	−0.741529	−	0.670920i	$-0.765899\pi$
$53$	−10.7968	−1.48306	−0.741529	+	0.670920i	$0.765899\pi$
$54$	1.00000	0.136083
$55$	−6.86943	−0.926274
$56$	−2.69336	−0.359915
$57$	−5.63805	−0.746778
$58$	−8.69441	−1.14163
$59$	−1.40465	−0.182870	−0.0914349	−	0.995811i	$-0.529145\pi$
$59$	−1.40465	−0.182870	−0.0914349	+	0.995811i	$0.529145\pi$
$60$	3.02511	0.390540
$61$	2.06457	0.264341	0.132170	−	0.991227i	$-0.457805\pi$
$61$	2.06457	0.264341	0.132170	+	0.991227i	$0.457805\pi$
$62$	0.130650	0.0165926
$63$	−2.69336	−0.339331
$64$	1.00000	0.125000
$65$	3.02511	0.375219
$66$	−2.27080	−0.279516
$67$	3.30838	0.404182	0.202091	−	0.979367i	$-0.435226\pi$
$67$	3.30838	0.404182	0.202091	+	0.979367i	$0.435226\pi$
$68$	−6.46889	−0.784468
$69$	−4.09415	−0.492878
$70$	−8.14770	−0.973837
$71$	3.12821	0.371250	0.185625	−	0.982621i	$-0.440569\pi$
$71$	3.12821	0.371250	0.185625	+	0.982621i	$0.440569\pi$
$72$	1.00000	0.117851
$73$	−6.65670	−0.779107	−0.389554	−	0.921004i	$-0.627371\pi$
$73$	−6.65670	−0.779107	−0.389554	+	0.921004i	$0.627371\pi$
$74$	−5.91687	−0.687822
$75$	4.15130	0.479351
$76$	−5.63805	−0.646729
$77$	6.11608	0.696992
$78$	1.00000	0.113228
$79$	15.1430	1.70372	0.851862	−	0.523766i	$-0.175473\pi$
$79$	15.1430	1.70372	0.851862	+	0.523766i	$0.175473\pi$
$80$	3.02511	0.338218
$81$	1.00000	0.111111
$82$	−3.27964	−0.362176
$83$	−0.455558	−0.0500040	−0.0250020	−	0.999687i	$-0.507959\pi$
$83$	−0.455558	−0.0500040	−0.0250020	+	0.999687i	$0.507959\pi$
$84$	−2.69336	−0.293869
$85$	−19.5691	−2.12257
$86$	2.43048	0.262086
$87$	−8.69441	−0.932139
$88$	−2.27080	−0.242068
$89$	−12.6552	−1.34145	−0.670727	−	0.741704i	$-0.734018\pi$
$89$	−12.6552	−1.34145	−0.670727	+	0.741704i	$0.734018\pi$
$90$	3.02511	0.318875
$91$	−2.69336	−0.282340
$92$	−4.09415	−0.426845
$93$	0.130650	0.0135478
$94$	2.53673	0.261644
$95$	−17.0557	−1.74988
$96$	1.00000	0.102062
$97$	18.9875	1.92789	0.963946	−	0.266097i	$-0.0857342\pi$
$97$	18.9875	1.92789	0.963946	+	0.266097i	$0.0857342\pi$
$98$	0.254168	0.0256748
$99$	−2.27080	−0.228224
$100$	4.15130	0.415130
$101$	4.95667	0.493207	0.246604	−	0.969116i	$-0.420685\pi$
$101$	4.95667	0.493207	0.246604	+	0.969116i	$0.420685\pi$
$102$	−6.46889	−0.640516
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−8.14770	−0.795134
$106$	−10.7968	−1.04868
$107$	−11.4347	−1.10544	−0.552719	−	0.833368i	$-0.686410\pi$
$107$	−11.4347	−1.10544	−0.552719	+	0.833368i	$0.686410\pi$
$108$	1.00000	0.0962250
$109$	6.60596	0.632736	0.316368	−	0.948636i	$-0.397537\pi$
$109$	6.60596	0.632736	0.316368	+	0.948636i	$0.397537\pi$
$110$	−6.86943	−0.654975
$111$	−5.91687	−0.561604
$112$	−2.69336	−0.254498
$113$	15.0535	1.41611	0.708056	−	0.706157i	$-0.249573\pi$
$113$	15.0535	1.41611	0.708056	+	0.706157i	$0.249573\pi$
$114$	−5.63805	−0.528052
$115$	−12.3853	−1.15493
$116$	−8.69441	−0.807256
$117$	1.00000	0.0924500
$118$	−1.40465	−0.129309
$119$	17.4230	1.59717
$120$	3.02511	0.276154
$121$	−5.84346	−0.531223
$122$	2.06457	0.186917
$123$	−3.27964	−0.295715
$124$	0.130650	0.0117327
$125$	−2.56741	−0.229636
$126$	−2.69336	−0.239943
$127$	−1.17643	−0.104391	−0.0521955	−	0.998637i	$-0.516622\pi$
$127$	−1.17643	−0.104391	−0.0521955	+	0.998637i	$0.516622\pi$
$128$	1.00000	0.0883883
$129$	2.43048	0.213992
$130$	3.02511	0.265320
$131$	8.19930	0.716377	0.358188	−	0.933649i	$-0.383395\pi$
$131$	8.19930	0.716377	0.358188	+	0.933649i	$0.383395\pi$
$132$	−2.27080	−0.197648
$133$	15.1853	1.31673
$134$	3.30838	0.285800
$135$	3.02511	0.260360
$136$	−6.46889	−0.554703
$137$	13.6611	1.16715	0.583573	−	0.812060i	$-0.301654\pi$
$137$	13.6611	1.16715	0.583573	+	0.812060i	$0.301654\pi$
$138$	−4.09415	−0.348518
$139$	11.8673	1.00657	0.503285	−	0.864120i	$-0.332125\pi$
$139$	11.8673	1.00657	0.503285	+	0.864120i	$0.332125\pi$
$140$	−8.14770	−0.688607
$141$	2.53673	0.213631
$142$	3.12821	0.262513
$143$	−2.27080	−0.189894
$144$	1.00000	0.0833333
$145$	−26.3016	−2.18423
$146$	−6.65670	−0.550912
$147$	0.254168	0.0209634
$148$	−5.91687	−0.486363
$149$	−4.56144	−0.373687	−0.186844	−	0.982390i	$-0.559826\pi$
$149$	−4.56144	−0.373687	−0.186844	+	0.982390i	$0.559826\pi$
$150$	4.15130	0.338952
$151$	3.11724	0.253677	0.126839	−	0.991923i	$-0.459517\pi$
$151$	3.11724	0.253677	0.126839	+	0.991923i	$0.459517\pi$
$152$	−5.63805	−0.457306
$153$	−6.46889	−0.522979
$154$	6.11608	0.492848
$155$	0.395231	0.0317457
$156$	1.00000	0.0800641
$157$	1.03792	0.0828348	0.0414174	−	0.999142i	$-0.486813\pi$
$157$	1.03792	0.0828348	0.0414174	+	0.999142i	$0.486813\pi$
$158$	15.1430	1.20472
$159$	−10.7968	−0.856244
$160$	3.02511	0.239156
$161$	11.0270	0.869051
$162$	1.00000	0.0785674
$163$	−3.15612	−0.247206	−0.123603	−	0.992332i	$-0.539445\pi$
$163$	−3.15612	−0.247206	−0.123603	+	0.992332i	$0.539445\pi$
$164$	−3.27964	−0.256097
$165$	−6.86943	−0.534785
$166$	−0.455558	−0.0353582
$167$	1.64094	0.126980	0.0634898	−	0.997982i	$-0.479777\pi$
$167$	1.64094	0.126980	0.0634898	+	0.997982i	$0.479777\pi$
$168$	−2.69336	−0.207797
$169$	1.00000	0.0769231
$170$	−19.5691	−1.50088
$171$	−5.63805	−0.431153
$172$	2.43048	0.185322
$173$	−2.13885	−0.162614	−0.0813068	−	0.996689i	$-0.525909\pi$
$173$	−2.13885	−0.162614	−0.0813068	+	0.996689i	$0.525909\pi$
$174$	−8.69441	−0.659122
$175$	−11.1809	−0.845199
$176$	−2.27080	−0.171168
$177$	−1.40465	−0.105580
$178$	−12.6552	−0.948551
$179$	−0.285828	−0.0213638	−0.0106819	−	0.999943i	$-0.503400\pi$
$179$	−0.285828	−0.0213638	−0.0106819	+	0.999943i	$0.503400\pi$
$180$	3.02511	0.225479
$181$	−5.81041	−0.431885	−0.215942	−	0.976406i	$-0.569282\pi$
$181$	−5.81041	−0.431885	−0.215942	+	0.976406i	$0.569282\pi$
$182$	−2.69336	−0.199645
$183$	2.06457	0.152617
$184$	−4.09415	−0.301825
$185$	−17.8992	−1.31597
$186$	0.130650	0.00957973
$187$	14.6896	1.07421
$188$	2.53673	0.185010
$189$	−2.69336	−0.195913
$190$	−17.0557	−1.23735
$191$	12.8426	0.929261	0.464630	−	0.885505i	$-0.346187\pi$
$191$	12.8426	0.929261	0.464630	+	0.885505i	$0.346187\pi$
$192$	1.00000	0.0721688
$193$	−2.93887	−0.211544	−0.105772	−	0.994390i	$-0.533731\pi$
$193$	−2.93887	−0.211544	−0.105772	+	0.994390i	$0.533731\pi$
$194$	18.9875	1.36323
$195$	3.02511	0.216633
$196$	0.254168	0.0181548
$197$	−3.88254	−0.276619	−0.138310	−	0.990389i	$-0.544167\pi$
$197$	−3.88254	−0.276619	−0.138310	+	0.990389i	$0.544167\pi$
$198$	−2.27080	−0.161379
$199$	13.3279	0.944793	0.472396	−	0.881386i	$-0.343389\pi$
$199$	13.3279	0.944793	0.472396	+	0.881386i	$0.343389\pi$
$200$	4.15130	0.293541
$201$	3.30838	0.233355
$202$	4.95667	0.348750
$203$	23.4172	1.64356
$204$	−6.46889	−0.452913
$205$	−9.92127	−0.692932
$206$	1.00000	0.0696733
$207$	−4.09415	−0.284563
$208$	1.00000	0.0693375
$209$	12.8029	0.885595
$210$	−8.14770	−0.562245
$211$	−16.2884	−1.12134	−0.560669	−	0.828040i	$-0.689456\pi$
$211$	−16.2884	−1.12134	−0.560669	+	0.828040i	$0.689456\pi$
$212$	−10.7968	−0.741529
$213$	3.12821	0.214341
$214$	−11.4347	−0.781663
$215$	7.35248	0.501435
$216$	1.00000	0.0680414
$217$	−0.351887	−0.0238877
$218$	6.60596	0.447412
$219$	−6.65670	−0.449818
$220$	−6.86943	−0.463137
$221$	−6.46889	−0.435145
$222$	−5.91687	−0.397114
$223$	11.6698	0.781465	0.390732	−	0.920504i	$-0.372222\pi$
$223$	11.6698	0.781465	0.390732	+	0.920504i	$0.372222\pi$
$224$	−2.69336	−0.179957
$225$	4.15130	0.276753
$226$	15.0535	1.00134
$227$	8.09096	0.537016	0.268508	−	0.963277i	$-0.413469\pi$
$227$	8.09096	0.537016	0.268508	+	0.963277i	$0.413469\pi$
$228$	−5.63805	−0.373389
$229$	−13.0652	−0.863373	−0.431687	−	0.902024i	$-0.642081\pi$
$229$	−13.0652	−0.863373	−0.431687	+	0.902024i	$0.642081\pi$
$230$	−12.3853	−0.816661
$231$	6.11608	0.402409
$232$	−8.69441	−0.570816
$233$	−5.71040	−0.374101	−0.187050	−	0.982350i	$-0.559893\pi$
$233$	−5.71040	−0.374101	−0.187050	+	0.982350i	$0.559893\pi$
$234$	1.00000	0.0653720
$235$	7.67389	0.500590
$236$	−1.40465	−0.0914349
$237$	15.1430	0.983646
$238$	17.4230	1.12937
$239$	4.16296	0.269280	0.134640	−	0.990895i	$-0.457012\pi$
$239$	4.16296	0.269280	0.134640	+	0.990895i	$0.457012\pi$
$240$	3.02511	0.195270
$241$	8.27876	0.533282	0.266641	−	0.963796i	$-0.414086\pi$
$241$	8.27876	0.533282	0.266641	+	0.963796i	$0.414086\pi$
$242$	−5.84346	−0.375632
$243$	1.00000	0.0641500
$244$	2.06457	0.132170
$245$	0.768886	0.0491223
$246$	−3.27964	−0.209102
$247$	−5.63805	−0.358741
$248$	0.130650	0.00829629
$249$	−0.455558	−0.0288698
$250$	−2.56741	−0.162377
$251$	22.5397	1.42270	0.711348	−	0.702840i	$-0.248085\pi$
$251$	22.5397	1.42270	0.711348	+	0.702840i	$0.248085\pi$
$252$	−2.69336	−0.169665
$253$	9.29702	0.584498
$254$	−1.17643	−0.0738156
$255$	−19.5691	−1.22547
$256$	1.00000	0.0625000
$257$	1.97789	0.123377	0.0616886	−	0.998095i	$-0.480351\pi$
$257$	1.97789	0.123377	0.0616886	+	0.998095i	$0.480351\pi$
$258$	2.43048	0.151315
$259$	15.9362	0.990229
$260$	3.02511	0.187609
$261$	−8.69441	−0.538171
$262$	8.19930	0.506555
$263$	23.7814	1.46642	0.733212	−	0.680000i	$-0.238020\pi$
$263$	23.7814	1.46642	0.733212	+	0.680000i	$0.238020\pi$
$264$	−2.27080	−0.139758
$265$	−32.6616	−2.00639
$266$	15.1853	0.931069
$267$	−12.6552	−0.774489
$268$	3.30838	0.202091
$269$	−14.2318	−0.867727	−0.433864	−	0.900979i	$-0.642850\pi$
$269$	−14.2318	−0.867727	−0.433864	+	0.900979i	$0.642850\pi$
$270$	3.02511	0.184102
$271$	−26.3938	−1.60331	−0.801654	−	0.597789i	$-0.796046\pi$
$271$	−26.3938	−1.60331	−0.801654	+	0.597789i	$0.796046\pi$
$272$	−6.46889	−0.392234
$273$	−2.69336	−0.163009
$274$	13.6611	0.825298
$275$	−9.42679	−0.568457
$276$	−4.09415	−0.246439
$277$	−10.2646	−0.616742	−0.308371	−	0.951266i	$-0.599784\pi$
$277$	−10.2646	−0.616742	−0.308371	+	0.951266i	$0.599784\pi$
$278$	11.8673	0.711753
$279$	0.130650	0.00782182
$280$	−8.14770	−0.486918
$281$	0.397057	0.0236864	0.0118432	−	0.999930i	$-0.496230\pi$
$281$	0.397057	0.0236864	0.0118432	+	0.999930i	$0.496230\pi$
$282$	2.53673	0.151060
$283$	−3.57610	−0.212577	−0.106289	−	0.994335i	$-0.533897\pi$
$283$	−3.57610	−0.212577	−0.106289	+	0.994335i	$0.533897\pi$
$284$	3.12821	0.185625
$285$	−17.0557	−1.01029
$286$	−2.27080	−0.134275
$287$	8.83324	0.521409
$288$	1.00000	0.0589256
$289$	24.8466	1.46156
$290$	−26.3016	−1.54448
$291$	18.9875	1.11307
$292$	−6.65670	−0.389554
$293$	−30.8097	−1.79992	−0.899960	−	0.435972i	$-0.856405\pi$
$293$	−30.8097	−1.79992	−0.899960	+	0.435972i	$0.856405\pi$
$294$	0.254168	0.0148234
$295$	−4.24922	−0.247399
$296$	−5.91687	−0.343911
$297$	−2.27080	−0.131765
$298$	−4.56144	−0.264237
$299$	−4.09415	−0.236771
$300$	4.15130	0.239675
$301$	−6.54615	−0.377314
$302$	3.11724	0.179377
$303$	4.95667	0.284753
$304$	−5.63805	−0.323364
$305$	6.24555	0.357619
$306$	−6.46889	−0.369802
$307$	−14.3149	−0.816992	−0.408496	−	0.912760i	$-0.633947\pi$
$307$	−14.3149	−0.816992	−0.408496	+	0.912760i	$0.633947\pi$
$308$	6.11608	0.348496
$309$	1.00000	0.0568880
$310$	0.395231	0.0224476
$311$	−4.06378	−0.230436	−0.115218	−	0.993340i	$-0.536757\pi$
$311$	−4.06378	−0.230436	−0.115218	+	0.993340i	$0.536757\pi$
$312$	1.00000	0.0566139
$313$	10.1702	0.574851	0.287426	−	0.957803i	$-0.407201\pi$
$313$	10.1702	0.574851	0.287426	+	0.957803i	$0.407201\pi$
$314$	1.03792	0.0585730
$315$	−8.14770	−0.459071
$316$	15.1430	0.851862
$317$	16.5651	0.930388	0.465194	−	0.885209i	$-0.345985\pi$
$317$	16.5651	0.930388	0.465194	+	0.885209i	$0.345985\pi$
$318$	−10.7968	−0.605456
$319$	19.7433	1.10541
$320$	3.02511	0.169109
$321$	−11.4347	−0.638225
$322$	11.0270	0.614512
$323$	36.4719	2.02935
$324$	1.00000	0.0555556
$325$	4.15130	0.230273
$326$	−3.15612	−0.174801
$327$	6.60596	0.365311
$328$	−3.27964	−0.181088
$329$	−6.83232	−0.376678
$330$	−6.86943	−0.378150
$331$	−15.5478	−0.854586	−0.427293	−	0.904113i	$-0.640533\pi$
$331$	−15.5478	−0.854586	−0.427293	+	0.904113i	$0.640533\pi$
$332$	−0.455558	−0.0250020
$333$	−5.91687	−0.324242
$334$	1.64094	0.0897882
$335$	10.0082	0.546807
$336$	−2.69336	−0.146935
$337$	4.81244	0.262151	0.131075	−	0.991372i	$-0.458157\pi$
$337$	4.81244	0.262151	0.131075	+	0.991372i	$0.458157\pi$
$338$	1.00000	0.0543928
$339$	15.0535	0.817592
$340$	−19.5691	−1.06128
$341$	−0.296681	−0.0160662
$342$	−5.63805	−0.304871
$343$	18.1689	0.981030
$344$	2.43048	0.131043
$345$	−12.3853	−0.666801
$346$	−2.13885	−0.114985
$347$	−16.4182	−0.881375	−0.440688	−	0.897660i	$-0.645265\pi$
$347$	−16.4182	−0.881375	−0.440688	+	0.897660i	$0.645265\pi$
$348$	−8.69441	−0.466069
$349$	−5.51363	−0.295138	−0.147569	−	0.989052i	$-0.547145\pi$
$349$	−5.51363	−0.295138	−0.147569	+	0.989052i	$0.547145\pi$
$350$	−11.1809	−0.597646
$351$	1.00000	0.0533761
$352$	−2.27080	−0.121034
$353$	−5.91505	−0.314827	−0.157413	−	0.987533i	$-0.550315\pi$
$353$	−5.91505	−0.314827	−0.157413	+	0.987533i	$0.550315\pi$
$354$	−1.40465	−0.0746563
$355$	9.46318	0.502254
$356$	−12.6552	−0.670727
$357$	17.4230	0.922124
$358$	−0.285828	−0.0151065
$359$	22.3773	1.18103	0.590513	−	0.807028i	$-0.298925\pi$
$359$	22.3773	1.18103	0.590513	+	0.807028i	$0.298925\pi$
$360$	3.02511	0.159437
$361$	12.7876	0.673033
$362$	−5.81041	−0.305389
$363$	−5.84346	−0.306702
$364$	−2.69336	−0.141170
$365$	−20.1373	−1.05403
$366$	2.06457	0.107917
$367$	−17.8087	−0.929606	−0.464803	−	0.885414i	$-0.653875\pi$
$367$	−17.8087	−0.929606	−0.464803	+	0.885414i	$0.653875\pi$
$368$	−4.09415	−0.213423
$369$	−3.27964	−0.170731
$370$	−17.8992	−0.930534
$371$	29.0797	1.50974
$372$	0.130650	0.00677389
$373$	3.12200	0.161651	0.0808255	−	0.996728i	$-0.474244\pi$
$373$	3.12200	0.161651	0.0808255	+	0.996728i	$0.474244\pi$
$374$	14.6896	0.759580
$375$	−2.56741	−0.132580
$376$	2.53673	0.130822
$377$	−8.69441	−0.447785
$378$	−2.69336	−0.138531
$379$	−24.8232	−1.27508	−0.637542	−	0.770415i	$-0.720049\pi$
$379$	−24.8232	−1.27508	−0.637542	+	0.770415i	$0.720049\pi$
$380$	−17.0557	−0.874941
$381$	−1.17643	−0.0602702
$382$	12.8426	0.657086
$383$	3.89727	0.199141	0.0995706	−	0.995030i	$-0.468253\pi$
$383$	3.89727	0.199141	0.0995706	+	0.995030i	$0.468253\pi$
$384$	1.00000	0.0510310
$385$	18.5018	0.942940
$386$	−2.93887	−0.149584
$387$	2.43048	0.123548
$388$	18.9875	0.963946
$389$	−7.75827	−0.393360	−0.196680	−	0.980468i	$-0.563016\pi$
$389$	−7.75827	−0.393360	−0.196680	+	0.980468i	$0.563016\pi$
$390$	3.02511	0.153182
$391$	26.4846	1.33939
$392$	0.254168	0.0128374
$393$	8.19930	0.413600
$394$	−3.88254	−0.195599
$395$	45.8094	2.30492
$396$	−2.27080	−0.114112
$397$	−11.2318	−0.563707	−0.281854	−	0.959457i	$-0.590949\pi$
$397$	−11.2318	−0.563707	−0.281854	+	0.959457i	$0.590949\pi$
$398$	13.3279	0.668069
$399$	15.1853	0.760215
$400$	4.15130	0.207565
$401$	−7.34904	−0.366994	−0.183497	−	0.983020i	$-0.558742\pi$
$401$	−7.34904	−0.366994	−0.183497	+	0.983020i	$0.558742\pi$
$402$	3.30838	0.165007
$403$	0.130650	0.00650815
$404$	4.95667	0.246604
$405$	3.02511	0.150319
$406$	23.4172	1.16217
$407$	13.4360	0.666000
$408$	−6.46889	−0.320258
$409$	7.48859	0.370287	0.185143	−	0.982712i	$-0.440725\pi$
$409$	7.48859	0.370287	0.185143	+	0.982712i	$0.440725\pi$
$410$	−9.92127	−0.489977
$411$	13.6611	0.673853
$412$	1.00000	0.0492665
$413$	3.78322	0.186160
$414$	−4.09415	−0.201217
$415$	−1.37811	−0.0676490
$416$	1.00000	0.0490290
$417$	11.8673	0.581144
$418$	12.8029	0.626210
$419$	−17.2875	−0.844551	−0.422275	−	0.906468i	$-0.638768\pi$
$419$	−17.2875	−0.844551	−0.422275	+	0.906468i	$0.638768\pi$
$420$	−8.14770	−0.397567
$421$	−30.8652	−1.50428	−0.752139	−	0.659004i	$-0.770978\pi$
$421$	−30.8652	−1.50428	−0.752139	+	0.659004i	$0.770978\pi$
$422$	−16.2884	−0.792905
$423$	2.53673	0.123340
$424$	−10.7968	−0.524340
$425$	−26.8543	−1.30263
$426$	3.12821	0.151562
$427$	−5.56061	−0.269097
$428$	−11.4347	−0.552719
$429$	−2.27080	−0.109635
$430$	7.35248	0.354568
$431$	−6.73390	−0.324361	−0.162180	−	0.986761i	$-0.551853\pi$
$431$	−6.73390	−0.324361	−0.162180	+	0.986761i	$0.551853\pi$
$432$	1.00000	0.0481125
$433$	11.0933	0.533111	0.266555	−	0.963820i	$-0.414115\pi$
$433$	11.0933	0.533111	0.266555	+	0.963820i	$0.414115\pi$
$434$	−0.351887	−0.0168911
$435$	−26.3016	−1.26106
$436$	6.60596	0.316368
$437$	23.0831	1.10421
$438$	−6.65670	−0.318069
$439$	−20.2320	−0.965621	−0.482810	−	0.875725i	$-0.660384\pi$
$439$	−20.2320	−0.965621	−0.482810	+	0.875725i	$0.660384\pi$
$440$	−6.86943	−0.327487
$441$	0.254168	0.0121032
$442$	−6.46889	−0.307694
$443$	−15.2905	−0.726472	−0.363236	−	0.931697i	$-0.618328\pi$
$443$	−15.2905	−0.726472	−0.363236	+	0.931697i	$0.618328\pi$
$444$	−5.91687	−0.280802
$445$	−38.2835	−1.81481
$446$	11.6698	0.552579
$447$	−4.56144	−0.215749
$448$	−2.69336	−0.127249
$449$	5.34215	0.252112	0.126056	−	0.992023i	$-0.459768\pi$
$449$	5.34215	0.252112	0.126056	+	0.992023i	$0.459768\pi$
$450$	4.15130	0.195694
$451$	7.44741	0.350685
$452$	15.0535	0.708056
$453$	3.11724	0.146461
$454$	8.09096	0.379728
$455$	−8.14770	−0.381970
$456$	−5.63805	−0.264026
$457$	−10.8520	−0.507635	−0.253817	−	0.967252i	$-0.581686\pi$
$457$	−10.8520	−0.507635	−0.253817	+	0.967252i	$0.581686\pi$
$458$	−13.0652	−0.610497
$459$	−6.46889	−0.301942
$460$	−12.3853	−0.577466
$461$	−16.6560	−0.775746	−0.387873	−	0.921713i	$-0.626790\pi$
$461$	−16.6560	−0.775746	−0.387873	+	0.921713i	$0.626790\pi$
$462$	6.11608	0.284546
$463$	20.7965	0.966496	0.483248	−	0.875483i	$-0.339457\pi$
$463$	20.7965	0.966496	0.483248	+	0.875483i	$0.339457\pi$
$464$	−8.69441	−0.403628
$465$	0.395231	0.0183284
$466$	−5.71040	−0.264529
$467$	−34.1900	−1.58212	−0.791062	−	0.611736i	$-0.790472\pi$
$467$	−34.1900	−1.58212	−0.791062	+	0.611736i	$0.790472\pi$
$468$	1.00000	0.0462250
$469$	−8.91064	−0.411455
$470$	7.67389	0.353970
$471$	1.03792	0.0478247
$472$	−1.40465	−0.0646543
$473$	−5.51914	−0.253770
$474$	15.1430	0.695543
$475$	−23.4052	−1.07391
$476$	17.4230	0.798583
$477$	−10.7968	−0.494353
$478$	4.16296	0.190410
$479$	−18.8894	−0.863077	−0.431538	−	0.902095i	$-0.642029\pi$
$479$	−18.8894	−0.863077	−0.431538	+	0.902095i	$0.642029\pi$
$480$	3.02511	0.138077
$481$	−5.91687	−0.269786
$482$	8.27876	0.377087
$483$	11.0270	0.501747
$484$	−5.84346	−0.265612
$485$	57.4394	2.60819
$486$	1.00000	0.0453609
$487$	5.83537	0.264426	0.132213	−	0.991221i	$-0.457792\pi$
$487$	5.83537	0.264426	0.132213	+	0.991221i	$0.457792\pi$
$488$	2.06457	0.0934586
$489$	−3.15612	−0.142725
$490$	0.768886	0.0347347
$491$	20.0931	0.906787	0.453394	−	0.891310i	$-0.350213\pi$
$491$	20.0931	0.906787	0.453394	+	0.891310i	$0.350213\pi$
$492$	−3.27964	−0.147858
$493$	56.2432	2.53307
$494$	−5.63805	−0.253668
$495$	−6.86943	−0.308758
$496$	0.130650	0.00586636
$497$	−8.42538	−0.377930
$498$	−0.455558	−0.0204140
$499$	10.0743	0.450985	0.225493	−	0.974245i	$-0.427601\pi$
$499$	10.0743	0.450985	0.225493	+	0.974245i	$0.427601\pi$
$500$	−2.56741	−0.114818
$501$	1.64094	0.0733117
$502$	22.5397	1.00600
$503$	4.00325	0.178496	0.0892481	−	0.996009i	$-0.471554\pi$
$503$	4.00325	0.178496	0.0892481	+	0.996009i	$0.471554\pi$
$504$	−2.69336	−0.119972
$505$	14.9945	0.667246
$506$	9.29702	0.413303
$507$	1.00000	0.0444116
$508$	−1.17643	−0.0521955
$509$	15.8657	0.703236	0.351618	−	0.936144i	$-0.385632\pi$
$509$	15.8657	0.703236	0.351618	+	0.936144i	$0.385632\pi$
$510$	−19.5691	−0.866535
$511$	17.9289	0.793126
$512$	1.00000	0.0441942
$513$	−5.63805	−0.248926
$514$	1.97789	0.0872408
$515$	3.02511	0.133302
$516$	2.43048	0.106996
$517$	−5.76041	−0.253343
$518$	15.9362	0.700198
$519$	−2.13885	−0.0938850
$520$	3.02511	0.132660
$521$	−11.4992	−0.503787	−0.251894	−	0.967755i	$-0.581053\pi$
$521$	−11.4992	−0.503787	−0.251894	+	0.967755i	$0.581053\pi$
$522$	−8.69441	−0.380544
$523$	−41.7804	−1.82693	−0.913464	−	0.406919i	$-0.866603\pi$
$523$	−41.7804	−1.82693	−0.913464	+	0.406919i	$0.866603\pi$
$524$	8.19930	0.358188
$525$	−11.1809	−0.487976
$526$	23.7814	1.03692
$527$	−0.845161	−0.0368158
$528$	−2.27080	−0.0988240
$529$	−6.23790	−0.271213
$530$	−32.6616	−1.41873
$531$	−1.40465	−0.0609566
$532$	15.1853	0.658365
$533$	−3.27964	−0.142057
$534$	−12.6552	−0.547646
$535$	−34.5914	−1.49552
$536$	3.30838	0.142900
$537$	−0.285828	−0.0123344
$538$	−14.2318	−0.613576
$539$	−0.577165	−0.0248602
$540$	3.02511	0.130180
$541$	−16.2931	−0.700496	−0.350248	−	0.936657i	$-0.613903\pi$
$541$	−16.2931	−0.700496	−0.350248	+	0.936657i	$0.613903\pi$
$542$	−26.3938	−1.13371
$543$	−5.81041	−0.249349
$544$	−6.46889	−0.277351
$545$	19.9838	0.856011
$546$	−2.69336	−0.115265
$547$	−40.1581	−1.71704	−0.858519	−	0.512781i	$-0.828615\pi$
$547$	−40.1581	−1.71704	−0.858519	+	0.512781i	$0.828615\pi$
$548$	13.6611	0.583573
$549$	2.06457	0.0881136
$550$	−9.42679	−0.401959
$551$	49.0195	2.08830
$552$	−4.09415	−0.174259
$553$	−40.7856	−1.73438
$554$	−10.2646	−0.436102
$555$	−17.8992	−0.759778
$556$	11.8673	0.503285
$557$	−33.1074	−1.40280	−0.701402	−	0.712766i	$-0.747442\pi$
$557$	−33.1074	−1.40280	−0.701402	+	0.712766i	$0.747442\pi$
$558$	0.130650	0.00553086
$559$	2.43048	0.102798
$560$	−8.14770	−0.344303
$561$	14.6896	0.620194
$562$	0.397057	0.0167488
$563$	33.2734	1.40231	0.701154	−	0.713010i	$-0.252668\pi$
$563$	33.2734	1.40231	0.701154	+	0.713010i	$0.252668\pi$
$564$	2.53673	0.106816
$565$	45.5384	1.91582
$566$	−3.57610	−0.150315
$567$	−2.69336	−0.113110
$568$	3.12821	0.131257
$569$	−28.4313	−1.19190	−0.595951	−	0.803021i	$-0.703225\pi$
$569$	−28.4313	−1.19190	−0.595951	+	0.803021i	$0.703225\pi$
$570$	−17.0557	−0.714386
$571$	12.4765	0.522125	0.261062	−	0.965322i	$-0.415927\pi$
$571$	12.4765	0.522125	0.261062	+	0.965322i	$0.415927\pi$
$572$	−2.27080	−0.0949470
$573$	12.8426	0.536509
$574$	8.83324	0.368692
$575$	−16.9961	−0.708785
$576$	1.00000	0.0416667
$577$	−0.203131	−0.00845647	−0.00422824	−	0.999991i	$-0.501346\pi$
$577$	−0.203131	−0.00845647	−0.00422824	+	0.999991i	$0.501346\pi$
$578$	24.8466	1.03348
$579$	−2.93887	−0.122135
$580$	−26.3016	−1.09211
$581$	1.22698	0.0509037
$582$	18.9875	0.787059
$583$	24.5175	1.01541
$584$	−6.65670	−0.275456
$585$	3.02511	0.125073
$586$	−30.8097	−1.27274
$587$	−1.83792	−0.0758590	−0.0379295	−	0.999280i	$-0.512076\pi$
$587$	−1.83792	−0.0758590	−0.0379295	+	0.999280i	$0.512076\pi$
$588$	0.254168	0.0104817
$589$	−0.736612	−0.0303516
$590$	−4.24922	−0.174938
$591$	−3.88254	−0.159706
$592$	−5.91687	−0.243182
$593$	39.4437	1.61976	0.809880	−	0.586596i	$-0.199532\pi$
$593$	39.4437	1.61976	0.809880	+	0.586596i	$0.199532\pi$
$594$	−2.27080	−0.0931722
$595$	52.7066	2.16076
$596$	−4.56144	−0.186844
$597$	13.3279	0.545476
$598$	−4.09415	−0.167422
$599$	4.23627	0.173089	0.0865445	−	0.996248i	$-0.472418\pi$
$599$	4.23627	0.173089	0.0865445	+	0.996248i	$0.472418\pi$
$600$	4.15130	0.169476
$601$	−3.47784	−0.141864	−0.0709321	−	0.997481i	$-0.522597\pi$
$601$	−3.47784	−0.141864	−0.0709321	+	0.997481i	$0.522597\pi$
$602$	−6.54615	−0.266801
$603$	3.30838	0.134727
$604$	3.11724	0.126839
$605$	−17.6771	−0.718677
$606$	4.95667	0.201351
$607$	−8.27441	−0.335848	−0.167924	−	0.985800i	$-0.553706\pi$
$607$	−8.27441	−0.335848	−0.167924	+	0.985800i	$0.553706\pi$
$608$	−5.63805	−0.228653
$609$	23.4172	0.948911
$610$	6.24555	0.252875
$611$	2.53673	0.102625
$612$	−6.46889	−0.261489
$613$	−18.5984	−0.751182	−0.375591	−	0.926785i	$-0.622560\pi$
$613$	−18.5984	−0.751182	−0.375591	+	0.926785i	$0.622560\pi$
$614$	−14.3149	−0.577700
$615$	−9.92127	−0.400064
$616$	6.11608	0.246424
$617$	7.44461	0.299709	0.149854	−	0.988708i	$-0.452120\pi$
$617$	7.44461	0.299709	0.149854	+	0.988708i	$0.452120\pi$
$618$	1.00000	0.0402259
$619$	32.5728	1.30921	0.654607	−	0.755970i	$-0.272834\pi$
$619$	32.5728	1.30921	0.654607	+	0.755970i	$0.272834\pi$
$620$	0.395231	0.0158729
$621$	−4.09415	−0.164293
$622$	−4.06378	−0.162943
$623$	34.0851	1.36559
$624$	1.00000	0.0400320
$625$	−28.5232	−1.14093
$626$	10.1702	0.406481
$627$	12.8029	0.511299
$628$	1.03792	0.0414174
$629$	38.2756	1.52615
$630$	−8.14770	−0.324612
$631$	−8.63751	−0.343854	−0.171927	−	0.985110i	$-0.554999\pi$
$631$	−8.63751	−0.343854	−0.171927	+	0.985110i	$0.554999\pi$
$632$	15.1430	0.602358
$633$	−16.2884	−0.647404
$634$	16.5651	0.657884
$635$	−3.55882	−0.141228
$636$	−10.7968	−0.428122
$637$	0.254168	0.0100705
$638$	19.7433	0.781645
$639$	3.12821	0.123750
$640$	3.02511	0.119578
$641$	−22.7313	−0.897831	−0.448916	−	0.893574i	$-0.648190\pi$
$641$	−22.7313	−0.897831	−0.448916	+	0.893574i	$0.648190\pi$
$642$	−11.4347	−0.451293
$643$	19.8080	0.781152	0.390576	−	0.920571i	$-0.372276\pi$
$643$	19.8080	0.781152	0.390576	+	0.920571i	$0.372276\pi$
$644$	11.0270	0.434525
$645$	7.35248	0.289503
$646$	36.4719	1.43497
$647$	−16.4113	−0.645193	−0.322597	−	0.946537i	$-0.604556\pi$
$647$	−16.4113	−0.645193	−0.322597	+	0.946537i	$0.604556\pi$
$648$	1.00000	0.0392837
$649$	3.18968	0.125206
$650$	4.15130	0.162827
$651$	−0.351887	−0.0137916
$652$	−3.15612	−0.123603
$653$	−9.80411	−0.383664	−0.191832	−	0.981428i	$-0.561443\pi$
$653$	−9.80411	−0.383664	−0.191832	+	0.981428i	$0.561443\pi$
$654$	6.60596	0.258314
$655$	24.8038	0.969165
$656$	−3.27964	−0.128048
$657$	−6.65670	−0.259702
$658$	−6.83232	−0.266352
$659$	18.3546	0.714996	0.357498	−	0.933914i	$-0.383630\pi$
$659$	18.3546	0.714996	0.357498	+	0.933914i	$0.383630\pi$
$660$	−6.86943	−0.267392
$661$	18.9376	0.736589	0.368294	−	0.929709i	$-0.379942\pi$
$661$	18.9376	0.736589	0.368294	+	0.929709i	$0.379942\pi$
$662$	−15.5478	−0.604284
$663$	−6.46889	−0.251231
$664$	−0.455558	−0.0176791
$665$	45.9372	1.78137
$666$	−5.91687	−0.229274
$667$	35.5963	1.37829
$668$	1.64094	0.0634898
$669$	11.6698	0.451179
$670$	10.0082	0.386651
$671$	−4.68822	−0.180987
$672$	−2.69336	−0.103898
$673$	6.43975	0.248234	0.124117	−	0.992268i	$-0.460390\pi$
$673$	6.43975	0.248234	0.124117	+	0.992268i	$0.460390\pi$
$674$	4.81244	0.185368
$675$	4.15130	0.159784
$676$	1.00000	0.0384615
$677$	−40.0589	−1.53959	−0.769795	−	0.638292i	$-0.779641\pi$
$677$	−40.0589	−1.53959	−0.769795	+	0.638292i	$0.779641\pi$
$678$	15.0535	0.578125
$679$	−51.1402	−1.96258
$680$	−19.5691	−0.750441
$681$	8.09096	0.310046
$682$	−0.296681	−0.0113605
$683$	6.39646	0.244754	0.122377	−	0.992484i	$-0.460948\pi$
$683$	6.39646	0.244754	0.122377	+	0.992484i	$0.460948\pi$
$684$	−5.63805	−0.215576
$685$	41.3264	1.57900
$686$	18.1689	0.693693
$687$	−13.0652	−0.498469
$688$	2.43048	0.0926612
$689$	−10.7968	−0.411326
$690$	−12.3853	−0.471499
$691$	27.5581	1.04836	0.524180	−	0.851607i	$-0.324372\pi$
$691$	27.5581	1.04836	0.524180	+	0.851607i	$0.324372\pi$
$692$	−2.13885	−0.0813068
$693$	6.11608	0.232331
$694$	−16.4182	−0.623227
$695$	35.8999	1.36176
$696$	−8.69441	−0.329561
$697$	21.2156	0.803599
$698$	−5.51363	−0.208694
$699$	−5.71040	−0.215987
$700$	−11.1809	−0.422600
$701$	−18.9310	−0.715014	−0.357507	−	0.933911i	$-0.616373\pi$
$701$	−18.9310	−0.715014	−0.357507	+	0.933911i	$0.616373\pi$
$702$	1.00000	0.0377426
$703$	33.3596	1.25818
$704$	−2.27080	−0.0855841
$705$	7.67389	0.289016
$706$	−5.91505	−0.222616
$707$	−13.3501	−0.502081
$708$	−1.40465	−0.0527900
$709$	8.39275	0.315196	0.157598	−	0.987503i	$-0.449625\pi$
$709$	8.39275	0.315196	0.157598	+	0.987503i	$0.449625\pi$
$710$	9.46318	0.355147
$711$	15.1430	0.567908
$712$	−12.6552	−0.474276
$713$	−0.534902	−0.0200322
$714$	17.4230	0.652040
$715$	−6.86943	−0.256902
$716$	−0.285828	−0.0106819
$717$	4.16296	0.155469
$718$	22.3773	0.835112
$719$	1.28309	0.0478512	0.0239256	−	0.999714i	$-0.492384\pi$
$719$	1.28309	0.0478512	0.0239256	+	0.999714i	$0.492384\pi$
$720$	3.02511	0.112739
$721$	−2.69336	−0.100306
$722$	12.7876	0.475906
$723$	8.27876	0.307890
$724$	−5.81041	−0.215942
$725$	−36.0931	−1.34047
$726$	−5.84346	−0.216871
$727$	38.0397	1.41082	0.705408	−	0.708802i	$-0.250764\pi$
$727$	38.0397	1.41082	0.705408	+	0.708802i	$0.250764\pi$
$728$	−2.69336	−0.0998224
$729$	1.00000	0.0370370
$730$	−20.1373	−0.745313
$731$	−15.7225	−0.581518
$732$	2.06457	0.0763086
$733$	14.5385	0.536992	0.268496	−	0.963281i	$-0.413473\pi$
$733$	14.5385	0.536992	0.268496	+	0.963281i	$0.413473\pi$
$734$	−17.8087	−0.657331
$735$	0.768886	0.0283608
$736$	−4.09415	−0.150913
$737$	−7.51267	−0.276733
$738$	−3.27964	−0.120725
$739$	19.0327	0.700130	0.350065	−	0.936726i	$-0.386160\pi$
$739$	19.0327	0.700130	0.350065	+	0.936726i	$0.386160\pi$
$740$	−17.8992	−0.657987
$741$	−5.63805	−0.207119
$742$	29.0797	1.06755
$743$	−27.5913	−1.01223	−0.506114	−	0.862467i	$-0.668918\pi$
$743$	−27.5913	−1.01223	−0.506114	+	0.862467i	$0.668918\pi$
$744$	0.130650	0.00478987
$745$	−13.7989	−0.505551
$746$	3.12200	0.114305
$747$	−0.455558	−0.0166680
$748$	14.6896	0.537104
$749$	30.7978	1.12533
$750$	−2.56741	−0.0937485
$751$	47.0617	1.71730	0.858652	−	0.512558i	$-0.171302\pi$
$751$	47.0617	1.71730	0.858652	+	0.512558i	$0.171302\pi$
$752$	2.53673	0.0925050
$753$	22.5397	0.821394
$754$	−8.69441	−0.316632
$755$	9.43000	0.343193
$756$	−2.69336	−0.0979564
$757$	7.65554	0.278245	0.139123	−	0.990275i	$-0.455572\pi$
$757$	7.65554	0.278245	0.139123	+	0.990275i	$0.455572\pi$
$758$	−24.8232	−0.901621
$759$	9.29702	0.337460
$760$	−17.0557	−0.618677
$761$	−45.7839	−1.65967	−0.829833	−	0.558012i	$-0.811564\pi$
$761$	−45.7839	−1.65967	−0.829833	+	0.558012i	$0.811564\pi$
$762$	−1.17643	−0.0426175
$763$	−17.7922	−0.644121
$764$	12.8426	0.464630
$765$	−19.5691	−0.707523
$766$	3.89727	0.140814
$767$	−1.40465	−0.0507190
$768$	1.00000	0.0360844
$769$	−25.4496	−0.917738	−0.458869	−	0.888504i	$-0.651745\pi$
$769$	−25.4496	−0.917738	−0.458869	+	0.888504i	$0.651745\pi$
$770$	18.5018	0.666760
$771$	1.97789	0.0712318
$772$	−2.93887	−0.105772
$773$	−38.8749	−1.39823	−0.699117	−	0.715007i	$-0.746423\pi$
$773$	−38.8749	−1.39823	−0.699117	+	0.715007i	$0.746423\pi$
$774$	2.43048	0.0873618
$775$	0.542368	0.0194824
$776$	18.9875	0.681613
$777$	15.9362	0.571709
$778$	−7.75827	−0.278147
$779$	18.4908	0.662501
$780$	3.02511	0.108316
$781$	−7.10354	−0.254185
$782$	26.4846	0.947089
$783$	−8.69441	−0.310713
$784$	0.254168	0.00907742
$785$	3.13982	0.112065
$786$	8.19930	0.292460
$787$	52.8387	1.88350	0.941749	−	0.336317i	$-0.109181\pi$
$787$	52.8387	1.88350	0.941749	+	0.336317i	$0.109181\pi$
$788$	−3.88254	−0.138310
$789$	23.7814	0.846641
$790$	45.8094	1.62982
$791$	−40.5444	−1.44159
$792$	−2.27080	−0.0806895
$793$	2.06457	0.0733149
$794$	−11.2318	−0.398601
$795$	−32.6616	−1.15839
$796$	13.3279	0.472396
$797$	−55.9505	−1.98187	−0.990933	−	0.134354i	$-0.957104\pi$
$797$	−55.9505	−1.98187	−0.990933	+	0.134354i	$0.957104\pi$
$798$	15.1853	0.537553
$799$	−16.4098	−0.580538
$800$	4.15130	0.146771
$801$	−12.6552	−0.447151
$802$	−7.34904	−0.259504
$803$	15.1160	0.533434
$804$	3.30838	0.116677
$805$	33.3580	1.17571
$806$	0.130650	0.00460195
$807$	−14.2318	−0.500983
$808$	4.95667	0.174375
$809$	9.83253	0.345693	0.172847	−	0.984949i	$-0.444703\pi$
$809$	9.83253	0.345693	0.172847	+	0.984949i	$0.444703\pi$
$810$	3.02511	0.106292
$811$	17.8095	0.625376	0.312688	−	0.949856i	$-0.398771\pi$
$811$	17.8095	0.625376	0.312688	+	0.949856i	$0.398771\pi$
$812$	23.4172	0.821781
$813$	−26.3938	−0.925670
$814$	13.4360	0.470933
$815$	−9.54762	−0.334439
$816$	−6.46889	−0.226456
$817$	−13.7032	−0.479413
$818$	7.48859	0.261832
$819$	−2.69336	−0.0941135
$820$	−9.92127	−0.346466
$821$	−48.4425	−1.69065	−0.845327	−	0.534250i	$-0.820594\pi$
$821$	−48.4425	−1.69065	−0.845327	+	0.534250i	$0.820594\pi$
$822$	13.6611	0.476486
$823$	−0.823522	−0.0287062	−0.0143531	−	0.999897i	$-0.504569\pi$
$823$	−0.823522	−0.0287062	−0.0143531	+	0.999897i	$0.504569\pi$
$824$	1.00000	0.0348367
$825$	−9.42679	−0.328199
$826$	3.78322	0.131635
$827$	−14.2434	−0.495293	−0.247646	−	0.968850i	$-0.579657\pi$
$827$	−14.2434	−0.495293	−0.247646	+	0.968850i	$0.579657\pi$
$828$	−4.09415	−0.142282
$829$	−44.8269	−1.55690	−0.778451	−	0.627705i	$-0.783994\pi$
$829$	−44.8269	−1.55690	−0.778451	+	0.627705i	$0.783994\pi$
$830$	−1.37811	−0.0478350
$831$	−10.2646	−0.356076
$832$	1.00000	0.0346688
$833$	−1.64418	−0.0569676
$834$	11.8673	0.410931
$835$	4.96402	0.171787
$836$	12.8029	0.442798
$837$	0.130650	0.00451593
$838$	−17.2875	−0.597188
$839$	−31.8684	−1.10022	−0.550109	−	0.835093i	$-0.685414\pi$
$839$	−31.8684	−1.10022	−0.550109	+	0.835093i	$0.685414\pi$
$840$	−8.14770	−0.281122
$841$	46.5928	1.60665
$842$	−30.8652	−1.06369
$843$	0.397057	0.0136754
$844$	−16.2884	−0.560669
$845$	3.02511	0.104067
$846$	2.53673	0.0872146
$847$	15.7385	0.540782
$848$	−10.7968	−0.370765
$849$	−3.57610	−0.122732
$850$	−26.8543	−0.921095
$851$	24.2246	0.830407
$852$	3.12821	0.107171
$853$	−32.8272	−1.12398	−0.561990	−	0.827144i	$-0.689964\pi$
$853$	−32.8272	−1.12398	−0.561990	+	0.827144i	$0.689964\pi$
$854$	−5.56061	−0.190280
$855$	−17.0557	−0.583294
$856$	−11.4347	−0.390831
$857$	−26.8784	−0.918147	−0.459074	−	0.888398i	$-0.651819\pi$
$857$	−26.8784	−0.918147	−0.459074	+	0.888398i	$0.651819\pi$
$858$	−2.27080	−0.0775239
$859$	−48.5608	−1.65687	−0.828436	−	0.560083i	$-0.810769\pi$
$859$	−48.5608	−1.65687	−0.828436	+	0.560083i	$0.810769\pi$
$860$	7.35248	0.250717
$861$	8.83324	0.301036
$862$	−6.73390	−0.229358
$863$	−5.66995	−0.193007	−0.0965036	−	0.995333i	$-0.530766\pi$
$863$	−5.66995	−0.193007	−0.0965036	+	0.995333i	$0.530766\pi$
$864$	1.00000	0.0340207
$865$	−6.47026	−0.219995
$866$	11.0933	0.376966
$867$	24.8466	0.843833
$868$	−0.351887	−0.0119438
$869$	−34.3868	−1.16649
$870$	−26.3016	−0.891707
$871$	3.30838	0.112100
$872$	6.60596	0.223706
$873$	18.9875	0.642631
$874$	23.0831	0.780796
$875$	6.91495	0.233768
$876$	−6.65670	−0.224909
$877$	24.4323	0.825021	0.412511	−	0.910953i	$-0.364652\pi$
$877$	24.4323	0.825021	0.412511	+	0.910953i	$0.364652\pi$
$878$	−20.2320	−0.682797
$879$	−30.8097	−1.03918
$880$	−6.86943	−0.231568
$881$	44.2179	1.48974	0.744869	−	0.667211i	$-0.232512\pi$
$881$	44.2179	1.48974	0.744869	+	0.667211i	$0.232512\pi$
$882$	0.254168	0.00855827
$883$	−18.6672	−0.628200	−0.314100	−	0.949390i	$-0.601703\pi$
$883$	−18.6672	−0.628200	−0.314100	+	0.949390i	$0.601703\pi$
$884$	−6.46889	−0.217572
$885$	−4.24922	−0.142836
$886$	−15.2905	−0.513693
$887$	−45.3389	−1.52233	−0.761166	−	0.648558i	$-0.775373\pi$
$887$	−45.3389	−1.52233	−0.761166	+	0.648558i	$0.775373\pi$
$888$	−5.91687	−0.198557
$889$	3.16854	0.106269
$890$	−38.2835	−1.28327
$891$	−2.27080	−0.0760747
$892$	11.6698	0.390732
$893$	−14.3022	−0.478605
$894$	−4.56144	−0.152557
$895$	−0.864662	−0.0289025
$896$	−2.69336	−0.0899787
$897$	−4.09415	−0.136700
$898$	5.34215	0.178270
$899$	−1.13593	−0.0378853
$900$	4.15130	0.138377
$901$	69.8435	2.32682
$902$	7.44741	0.247972
$903$	−6.54615	−0.217842
$904$	15.0535	0.500671
$905$	−17.5772	−0.584284
$906$	3.11724	0.103563
$907$	−16.0174	−0.531849	−0.265924	−	0.963994i	$-0.585677\pi$
$907$	−16.0174	−0.531849	−0.265924	+	0.963994i	$0.585677\pi$
$908$	8.09096	0.268508
$909$	4.95667	0.164402
$910$	−8.14770	−0.270094
$911$	32.7455	1.08491	0.542453	−	0.840086i	$-0.317496\pi$
$911$	32.7455	1.08491	0.542453	+	0.840086i	$0.317496\pi$
$912$	−5.63805	−0.186695
$913$	1.03448	0.0342364
$914$	−10.8520	−0.358952
$915$	6.24555	0.206471
$916$	−13.0652	−0.431687
$917$	−22.0836	−0.729266
$918$	−6.46889	−0.213505
$919$	−49.4309	−1.63058	−0.815288	−	0.579055i	$-0.803421\pi$
$919$	−49.4309	−1.63058	−0.815288	+	0.579055i	$0.803421\pi$
$920$	−12.3853	−0.408330
$921$	−14.3149	−0.471690
$922$	−16.6560	−0.548535
$923$	3.12821	0.102966
$924$	6.11608	0.201204
$925$	−24.5627	−0.807616
$926$	20.7965	0.683416
$927$	1.00000	0.0328443
$928$	−8.69441	−0.285408
$929$	−24.4798	−0.803155	−0.401578	−	0.915825i	$-0.631538\pi$
$929$	−24.4798	−0.803155	−0.401578	+	0.915825i	$0.631538\pi$
$930$	0.395231	0.0129601
$931$	−1.43301	−0.0469650
$932$	−5.71040	−0.187050
$933$	−4.06378	−0.133042
$934$	−34.1900	−1.11873
$935$	44.4376	1.45327
$936$	1.00000	0.0326860
$937$	−40.7413	−1.33096	−0.665480	−	0.746416i	$-0.731773\pi$
$937$	−40.7413	−1.33096	−0.665480	+	0.746416i	$0.731773\pi$
$938$	−8.91064	−0.290943
$939$	10.1702	0.331890
$940$	7.67389	0.250295
$941$	36.9860	1.20571	0.602854	−	0.797852i	$-0.294030\pi$
$941$	36.9860	1.20571	0.602854	+	0.797852i	$0.294030\pi$
$942$	1.03792	0.0338172
$943$	13.4273	0.437255
$944$	−1.40465	−0.0457175
$945$	−8.14770	−0.265045
$946$	−5.51914	−0.179443
$947$	−25.6692	−0.834136	−0.417068	−	0.908875i	$-0.636942\pi$
$947$	−25.6692	−0.834136	−0.417068	+	0.908875i	$0.636942\pi$
$948$	15.1430	0.491823
$949$	−6.65670	−0.216086
$950$	−23.4052	−0.759367
$951$	16.5651	0.537160
$952$	17.4230	0.564684
$953$	−47.0433	−1.52388	−0.761941	−	0.647647i	$-0.775753\pi$
$953$	−47.0433	−1.52388	−0.761941	+	0.647647i	$0.775753\pi$
$954$	−10.7968	−0.349560
$955$	38.8504	1.25717
$956$	4.16296	0.134640
$957$	19.7433	0.638210
$958$	−18.8894	−0.610288
$959$	−36.7942	−1.18815
$960$	3.02511	0.0976351
$961$	−30.9829	−0.999449
$962$	−5.91687	−0.190767
$963$	−11.4347	−0.368479
$964$	8.27876	0.266641
$965$	−8.89040	−0.286192
$966$	11.0270	0.354788
$967$	33.0500	1.06282	0.531408	−	0.847116i	$-0.321663\pi$
$967$	33.0500	1.06282	0.531408	+	0.847116i	$0.321663\pi$
$968$	−5.84346	−0.187816
$969$	36.4719	1.17165
$970$	57.4394	1.84427
$971$	6.35226	0.203854	0.101927	−	0.994792i	$-0.467499\pi$
$971$	6.35226	0.203854	0.101927	+	0.994792i	$0.467499\pi$
$972$	1.00000	0.0320750
$973$	−31.9628	−1.02468
$974$	5.83537	0.186977
$975$	4.15130	0.132948
$976$	2.06457	0.0660852
$977$	4.91867	0.157362	0.0786811	−	0.996900i	$-0.474929\pi$
$977$	4.91867	0.157362	0.0786811	+	0.996900i	$0.474929\pi$
$978$	−3.15612	−0.100922
$979$	28.7376	0.918457
$980$	0.768886	0.0245612
$981$	6.60596	0.210912
$982$	20.0931	0.641195
$983$	7.28466	0.232345	0.116172	−	0.993229i	$-0.462938\pi$
$983$	7.28466	0.232345	0.116172	+	0.993229i	$0.462938\pi$
$984$	−3.27964	−0.104551
$985$	−11.7451	−0.374230
$986$	56.2432	1.79115
$987$	−6.83232	−0.217475
$988$	−5.63805	−0.179370
$989$	−9.95076	−0.316416
$990$	−6.86943	−0.218325
$991$	13.5108	0.429184	0.214592	−	0.976704i	$-0.431158\pi$
$991$	13.5108	0.429184	0.214592	+	0.976704i	$0.431158\pi$
$992$	0.130650	0.00414815
$993$	−15.5478	−0.493396
$994$	−8.42538	−0.267237
$995$	40.3185	1.27818
$996$	−0.455558	−0.0144349
$997$	−29.3488	−0.929485	−0.464742	−	0.885446i	$-0.653853\pi$
$997$	−29.3488	−0.929485	−0.464742	+	0.885446i	$0.653853\pi$
$998$	10.0743	0.318895
$999$	−5.91687	−0.187201

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.p.1.8	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.p.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.02511 q^{5} +1.00000 q^{6} -2.69336 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.02511 q^{5} +1.00000 q^{6} -2.69336 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.02511 q^{10} -2.27080 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.69336 q^{14} +3.02511 q^{15} +1.00000 q^{16} -6.46889 q^{17} +1.00000 q^{18} -5.63805 q^{19} +3.02511 q^{20} -2.69336 q^{21} -2.27080 q^{22} -4.09415 q^{23} +1.00000 q^{24} +4.15130 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.69336 q^{28} -8.69441 q^{29} +3.02511 q^{30} +0.130650 q^{31} +1.00000 q^{32} -2.27080 q^{33} -6.46889 q^{34} -8.14770 q^{35} +1.00000 q^{36} -5.91687 q^{37} -5.63805 q^{38} +1.00000 q^{39} +3.02511 q^{40} -3.27964 q^{41} -2.69336 q^{42} +2.43048 q^{43} -2.27080 q^{44} +3.02511 q^{45} -4.09415 q^{46} +2.53673 q^{47} +1.00000 q^{48} +0.254168 q^{49} +4.15130 q^{50} -6.46889 q^{51} +1.00000 q^{52} -10.7968 q^{53} +1.00000 q^{54} -6.86943 q^{55} -2.69336 q^{56} -5.63805 q^{57} -8.69441 q^{58} -1.40465 q^{59} +3.02511 q^{60} +2.06457 q^{61} +0.130650 q^{62} -2.69336 q^{63} +1.00000 q^{64} +3.02511 q^{65} -2.27080 q^{66} +3.30838 q^{67} -6.46889 q^{68} -4.09415 q^{69} -8.14770 q^{70} +3.12821 q^{71} +1.00000 q^{72} -6.65670 q^{73} -5.91687 q^{74} +4.15130 q^{75} -5.63805 q^{76} +6.11608 q^{77} +1.00000 q^{78} +15.1430 q^{79} +3.02511 q^{80} +1.00000 q^{81} -3.27964 q^{82} -0.455558 q^{83} -2.69336 q^{84} -19.5691 q^{85} +2.43048 q^{86} -8.69441 q^{87} -2.27080 q^{88} -12.6552 q^{89} +3.02511 q^{90} -2.69336 q^{91} -4.09415 q^{92} +0.130650 q^{93} +2.53673 q^{94} -17.0557 q^{95} +1.00000 q^{96} +18.9875 q^{97} +0.254168 q^{98} -2.27080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{10} - 7 q^{11} + 8 q^{12} + 8 q^{13} - 6 q^{14} - 8 q^{15} + 8 q^{16} - 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 6 q^{21} - 7 q^{22} - 14 q^{23} + 8 q^{24} - 2 q^{25} + 8 q^{26} + 8 q^{27} - 6 q^{28} - 25 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - 7 q^{33} - 20 q^{34} - 18 q^{35} + 8 q^{36} - 15 q^{37} - 12 q^{38} + 8 q^{39} - 8 q^{40} - 18 q^{41} - 6 q^{42} - 8 q^{43} - 7 q^{44} - 8 q^{45} - 14 q^{46} - 12 q^{47} + 8 q^{48} - 8 q^{49} - 2 q^{50} - 20 q^{51} + 8 q^{52} - 25 q^{53} + 8 q^{54} - 8 q^{55} - 6 q^{56} - 12 q^{57} - 25 q^{58} - 9 q^{59} - 8 q^{60} - 2 q^{61} - 12 q^{62} - 6 q^{63} + 8 q^{64} - 8 q^{65} - 7 q^{66} - 8 q^{67} - 20 q^{68} - 14 q^{69} - 18 q^{70} - 13 q^{71} + 8 q^{72} - 2 q^{73} - 15 q^{74} - 2 q^{75} - 12 q^{76} - 5 q^{77} + 8 q^{78} + q^{79} - 8 q^{80} + 8 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 5 q^{85} - 8 q^{86} - 25 q^{87} - 7 q^{88} - 17 q^{89} - 8 q^{90} - 6 q^{91} - 14 q^{92} - 12 q^{93} - 12 q^{94} + 10 q^{95} + 8 q^{96} + 19 q^{97} - 8 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9 - 8 * q^10 - 7 * q^11 + 8 * q^12 + 8 * q^13 - 6 * q^14 - 8 * q^15 + 8 * q^16 - 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 6 * q^21 - 7 * q^22 - 14 * q^23 + 8 * q^24 - 2 * q^25 + 8 * q^26 + 8 * q^27 - 6 * q^28 - 25 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - 7 * q^33 - 20 * q^34 - 18 * q^35 + 8 * q^36 - 15 * q^37 - 12 * q^38 + 8 * q^39 - 8 * q^40 - 18 * q^41 - 6 * q^42 - 8 * q^43 - 7 * q^44 - 8 * q^45 - 14 * q^46 - 12 * q^47 + 8 * q^48 - 8 * q^49 - 2 * q^50 - 20 * q^51 + 8 * q^52 - 25 * q^53 + 8 * q^54 - 8 * q^55 - 6 * q^56 - 12 * q^57 - 25 * q^58 - 9 * q^59 - 8 * q^60 - 2 * q^61 - 12 * q^62 - 6 * q^63 + 8 * q^64 - 8 * q^65 - 7 * q^66 - 8 * q^67 - 20 * q^68 - 14 * q^69 - 18 * q^70 - 13 * q^71 + 8 * q^72 - 2 * q^73 - 15 * q^74 - 2 * q^75 - 12 * q^76 - 5 * q^77 + 8 * q^78 + q^79 - 8 * q^80 + 8 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 5 * q^85 - 8 * q^86 - 25 * q^87 - 7 * q^88 - 17 * q^89 - 8 * q^90 - 6 * q^91 - 14 * q^92 - 12 * q^93 - 12 * q^94 + 10 * q^95 + 8 * q^96 + 19 * q^97 - 8 * q^98 - 7 * q^99

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