LMFDB - Embedded newform 8034.2.a.o.1.3

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 $ x^7 - 3x^6 - 4x^5 + 14x^4 + 3x^3 - 12x^2 - 3x + 1
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			1.3
Root			$1.27539$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.55242 q^{5} +1.00000 q^{6} +1.37822 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.55242 q^{5} +1.00000 q^{6} +1.37822 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.55242 q^{10} +4.10597 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.37822 q^{14} +2.55242 q^{15} +1.00000 q^{16} +3.57390 q^{17} -1.00000 q^{18} +0.378218 q^{19} -2.55242 q^{20} -1.37822 q^{21} -4.10597 q^{22} +3.65040 q^{23} +1.00000 q^{24} +1.51486 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.37822 q^{28} -0.329406 q^{29} -2.55242 q^{30} -7.41763 q^{31} -1.00000 q^{32} -4.10597 q^{33} -3.57390 q^{34} -3.51779 q^{35} +1.00000 q^{36} -6.88409 q^{37} -0.378218 q^{38} -1.00000 q^{39} +2.55242 q^{40} -7.85728 q^{41} +1.37822 q^{42} -2.74031 q^{43} +4.10597 q^{44} -2.55242 q^{45} -3.65040 q^{46} -2.13101 q^{47} -1.00000 q^{48} -5.10052 q^{49} -1.51486 q^{50} -3.57390 q^{51} +1.00000 q^{52} -10.1230 q^{53} +1.00000 q^{54} -10.4802 q^{55} -1.37822 q^{56} -0.378218 q^{57} +0.329406 q^{58} +8.34165 q^{59} +2.55242 q^{60} -0.317128 q^{61} +7.41763 q^{62} +1.37822 q^{63} +1.00000 q^{64} -2.55242 q^{65} +4.10597 q^{66} +3.12773 q^{67} +3.57390 q^{68} -3.65040 q^{69} +3.51779 q^{70} +8.40081 q^{71} -1.00000 q^{72} +2.15179 q^{73} +6.88409 q^{74} -1.51486 q^{75} +0.378218 q^{76} +5.65892 q^{77} +1.00000 q^{78} -5.79457 q^{79} -2.55242 q^{80} +1.00000 q^{81} +7.85728 q^{82} -1.11990 q^{83} -1.37822 q^{84} -9.12209 q^{85} +2.74031 q^{86} +0.329406 q^{87} -4.10597 q^{88} +0.259370 q^{89} +2.55242 q^{90} +1.37822 q^{91} +3.65040 q^{92} +7.41763 q^{93} +2.13101 q^{94} -0.965372 q^{95} +1.00000 q^{96} +4.63686 q^{97} +5.10052 q^{98} +4.10597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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
$5$	−2.55242	−1.14148	−0.570739	−	0.821132i	$-0.693343\pi$
$5$	−2.55242	−1.14148	−0.570739	+	0.821132i	$0.693343\pi$
$6$	1.00000	0.408248
$7$	1.37822	0.520917	0.260459	−	0.965485i	$-0.416126\pi$
$7$	1.37822	0.520917	0.260459	+	0.965485i	$0.416126\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.55242	0.807147
$11$	4.10597	1.23800	0.618998	−	0.785392i	$-0.287539\pi$
$11$	4.10597	1.23800	0.618998	+	0.785392i	$0.287539\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.37822	−0.368344
$15$	2.55242	0.659033
$16$	1.00000	0.250000
$17$	3.57390	0.866797	0.433399	−	0.901202i	$-0.357314\pi$
$17$	3.57390	0.866797	0.433399	+	0.901202i	$0.357314\pi$
$18$	−1.00000	−0.235702
$19$	0.378218	0.0867691	0.0433846	−	0.999058i	$-0.486186\pi$
$19$	0.378218	0.0867691	0.0433846	+	0.999058i	$0.486186\pi$
$20$	−2.55242	−0.570739
$21$	−1.37822	−0.300752
$22$	−4.10597	−0.875396
$23$	3.65040	0.761161	0.380580	−	0.924748i	$-0.375724\pi$
$23$	3.65040	0.761161	0.380580	+	0.924748i	$0.375724\pi$
$24$	1.00000	0.204124
$25$	1.51486	0.302972
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.37822	0.260459
$29$	−0.329406	−0.0611692	−0.0305846	−	0.999532i	$-0.509737\pi$
$29$	−0.329406	−0.0611692	−0.0305846	+	0.999532i	$0.509737\pi$
$30$	−2.55242	−0.466006
$31$	−7.41763	−1.33225	−0.666123	−	0.745842i	$-0.732047\pi$
$31$	−7.41763	−1.33225	−0.666123	+	0.745842i	$0.732047\pi$
$32$	−1.00000	−0.176777
$33$	−4.10597	−0.714757
$34$	−3.57390	−0.612918
$35$	−3.51779	−0.594616
$36$	1.00000	0.166667
$37$	−6.88409	−1.13174	−0.565869	−	0.824495i	$-0.691459\pi$
$37$	−6.88409	−1.13174	−0.565869	+	0.824495i	$0.691459\pi$
$38$	−0.378218	−0.0613550
$39$	−1.00000	−0.160128
$40$	2.55242	0.403573
$41$	−7.85728	−1.22710	−0.613550	−	0.789656i	$-0.710259\pi$
$41$	−7.85728	−1.22710	−0.613550	+	0.789656i	$0.710259\pi$
$42$	1.37822	0.212664
$43$	−2.74031	−0.417893	−0.208947	−	0.977927i	$-0.567003\pi$
$43$	−2.74031	−0.417893	−0.208947	+	0.977927i	$0.567003\pi$
$44$	4.10597	0.618998
$45$	−2.55242	−0.380493
$46$	−3.65040	−0.538222
$47$	−2.13101	−0.310840	−0.155420	−	0.987849i	$-0.549673\pi$
$47$	−2.13101	−0.310840	−0.155420	+	0.987849i	$0.549673\pi$
$48$	−1.00000	−0.144338
$49$	−5.10052	−0.728645
$50$	−1.51486	−0.214234
$51$	−3.57390	−0.500446
$52$	1.00000	0.138675
$53$	−10.1230	−1.39050	−0.695251	−	0.718767i	$-0.744707\pi$
$53$	−10.1230	−1.39050	−0.695251	+	0.718767i	$0.744707\pi$
$54$	1.00000	0.136083
$55$	−10.4802	−1.41315
$56$	−1.37822	−0.184172
$57$	−0.378218	−0.0500962
$58$	0.329406	0.0432532
$59$	8.34165	1.08599	0.542995	−	0.839736i	$-0.317290\pi$
$59$	8.34165	1.08599	0.542995	+	0.839736i	$0.317290\pi$
$60$	2.55242	0.329516
$61$	−0.317128	−0.0406041	−0.0203020	−	0.999794i	$-0.506463\pi$
$61$	−0.317128	−0.0406041	−0.0203020	+	0.999794i	$0.506463\pi$
$62$	7.41763	0.942040
$63$	1.37822	0.173639
$64$	1.00000	0.125000
$65$	−2.55242	−0.316589
$66$	4.10597	0.505410
$67$	3.12773	0.382113	0.191056	−	0.981579i	$-0.438809\pi$
$67$	3.12773	0.382113	0.191056	+	0.981579i	$0.438809\pi$
$68$	3.57390	0.433399
$69$	−3.65040	−0.439456
$70$	3.51779	0.420457
$71$	8.40081	0.996992	0.498496	−	0.866892i	$-0.333886\pi$
$71$	8.40081	0.996992	0.498496	+	0.866892i	$0.333886\pi$
$72$	−1.00000	−0.117851
$73$	2.15179	0.251848	0.125924	−	0.992040i	$-0.459810\pi$
$73$	2.15179	0.251848	0.125924	+	0.992040i	$0.459810\pi$
$74$	6.88409	0.800259
$75$	−1.51486	−0.174921
$76$	0.378218	0.0433846
$77$	5.65892	0.644894
$78$	1.00000	0.113228
$79$	−5.79457	−0.651940	−0.325970	−	0.945380i	$-0.605691\pi$
$79$	−5.79457	−0.651940	−0.325970	+	0.945380i	$0.605691\pi$
$80$	−2.55242	−0.285370
$81$	1.00000	0.111111
$82$	7.85728	0.867691
$83$	−1.11990	−0.122925	−0.0614625	−	0.998109i	$-0.519576\pi$
$83$	−1.11990	−0.122925	−0.0614625	+	0.998109i	$0.519576\pi$
$84$	−1.37822	−0.150376
$85$	−9.12209	−0.989430
$86$	2.74031	0.295495
$87$	0.329406	0.0353161
$88$	−4.10597	−0.437698
$89$	0.259370	0.0274932	0.0137466	−	0.999906i	$-0.495624\pi$
$89$	0.259370	0.0274932	0.0137466	+	0.999906i	$0.495624\pi$
$90$	2.55242	0.269049
$91$	1.37822	0.144476
$92$	3.65040	0.380580
$93$	7.41763	0.769173
$94$	2.13101	0.219797
$95$	−0.965372	−0.0990451
$96$	1.00000	0.102062
$97$	4.63686	0.470802	0.235401	−	0.971898i	$-0.424360\pi$
$97$	4.63686	0.470802	0.235401	+	0.971898i	$0.424360\pi$
$98$	5.10052	0.515230
$99$	4.10597	0.412665
$100$	1.51486	0.151486
$101$	−15.5977	−1.55203	−0.776014	−	0.630715i	$-0.782762\pi$
$101$	−15.5977	−1.55203	−0.776014	+	0.630715i	$0.782762\pi$
$102$	3.57390	0.353868
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	3.51779	0.343302
$106$	10.1230	0.983233
$107$	10.0618	0.972714	0.486357	−	0.873760i	$-0.338325\pi$
$107$	10.0618	0.972714	0.486357	+	0.873760i	$0.338325\pi$
$108$	−1.00000	−0.0962250
$109$	11.4816	1.09974	0.549869	−	0.835251i	$-0.314678\pi$
$109$	11.4816	1.09974	0.549869	+	0.835251i	$0.314678\pi$
$110$	10.4802	0.999245
$111$	6.88409	0.653409
$112$	1.37822	0.130229
$113$	4.69080	0.441273	0.220637	−	0.975356i	$-0.429186\pi$
$113$	4.69080	0.441273	0.220637	+	0.975356i	$0.429186\pi$
$114$	0.378218	0.0354233
$115$	−9.31736	−0.868848
$116$	−0.329406	−0.0305846
$117$	1.00000	0.0924500
$118$	−8.34165	−0.767911
$119$	4.92561	0.451530
$120$	−2.55242	−0.233003
$121$	5.85898	0.532635
$122$	0.317128	0.0287114
$123$	7.85728	0.708467
$124$	−7.41763	−0.666123
$125$	8.89555	0.795642
$126$	−1.37822	−0.122781
$127$	−18.9176	−1.67867	−0.839335	−	0.543615i	$-0.817055\pi$
$127$	−18.9176	−1.67867	−0.839335	+	0.543615i	$0.817055\pi$
$128$	−1.00000	−0.0883883
$129$	2.74031	0.241271
$130$	2.55242	0.223862
$131$	14.9131	1.30297	0.651483	−	0.758663i	$-0.274147\pi$
$131$	14.9131	1.30297	0.651483	+	0.758663i	$0.274147\pi$
$132$	−4.10597	−0.357379
$133$	0.521267	0.0451995
$134$	−3.12773	−0.270194
$135$	2.55242	0.219678
$136$	−3.57390	−0.306459
$137$	17.1905	1.46868	0.734341	−	0.678781i	$-0.237491\pi$
$137$	17.1905	1.46868	0.734341	+	0.678781i	$0.237491\pi$
$138$	3.65040	0.310743
$139$	18.1741	1.54150	0.770752	−	0.637135i	$-0.219881\pi$
$139$	18.1741	1.54150	0.770752	+	0.637135i	$0.219881\pi$
$140$	−3.51779	−0.297308
$141$	2.13101	0.179463
$142$	−8.40081	−0.704980
$143$	4.10597	0.343358
$144$	1.00000	0.0833333
$145$	0.840784	0.0698233
$146$	−2.15179	−0.178083
$147$	5.10052	0.420683
$148$	−6.88409	−0.565869
$149$	−7.54334	−0.617975	−0.308987	−	0.951066i	$-0.599990\pi$
$149$	−7.54334	−0.617975	−0.308987	+	0.951066i	$0.599990\pi$
$150$	1.51486	0.123688
$151$	−22.2535	−1.81096	−0.905481	−	0.424386i	$-0.860490\pi$
$151$	−22.2535	−1.81096	−0.905481	+	0.424386i	$0.860490\pi$
$152$	−0.378218	−0.0306775
$153$	3.57390	0.288932
$154$	−5.65892	−0.456009
$155$	18.9329	1.52073
$156$	−1.00000	−0.0800641
$157$	−11.8126	−0.942746	−0.471373	−	0.881934i	$-0.656242\pi$
$157$	−11.8126	−0.942746	−0.471373	+	0.881934i	$0.656242\pi$
$158$	5.79457	0.460992
$159$	10.1230	0.802806
$160$	2.55242	0.201787
$161$	5.03104	0.396502
$162$	−1.00000	−0.0785674
$163$	−5.81167	−0.455205	−0.227603	−	0.973754i	$-0.573089\pi$
$163$	−5.81167	−0.455205	−0.227603	+	0.973754i	$0.573089\pi$
$164$	−7.85728	−0.613550
$165$	10.4802	0.815880
$166$	1.11990	0.0869211
$167$	−8.49879	−0.657656	−0.328828	−	0.944390i	$-0.606654\pi$
$167$	−8.49879	−0.657656	−0.328828	+	0.944390i	$0.606654\pi$
$168$	1.37822	0.106332
$169$	1.00000	0.0769231
$170$	9.12209	0.699632
$171$	0.378218	0.0289230
$172$	−2.74031	−0.208947
$173$	−16.5832	−1.26080	−0.630398	−	0.776272i	$-0.717108\pi$
$173$	−16.5832	−1.26080	−0.630398	+	0.776272i	$0.717108\pi$
$174$	−0.329406	−0.0249722
$175$	2.08781	0.157823
$176$	4.10597	0.309499
$177$	−8.34165	−0.626997
$178$	−0.259370	−0.0194406
$179$	−14.9667	−1.11866	−0.559331	−	0.828945i	$-0.688942\pi$
$179$	−14.9667	−1.11866	−0.559331	+	0.828945i	$0.688942\pi$
$180$	−2.55242	−0.190246
$181$	−15.9377	−1.18464	−0.592319	−	0.805704i	$-0.701787\pi$
$181$	−15.9377	−1.18464	−0.592319	+	0.805704i	$0.701787\pi$
$182$	−1.37822	−0.102160
$183$	0.317128	0.0234428
$184$	−3.65040	−0.269111
$185$	17.5711	1.29185
$186$	−7.41763	−0.543887
$187$	14.6743	1.07309
$188$	−2.13101	−0.155420
$189$	−1.37822	−0.100251
$190$	0.965372	0.0700354
$191$	14.0461	1.01634	0.508170	−	0.861257i	$-0.330322\pi$
$191$	14.0461	1.01634	0.508170	+	0.861257i	$0.330322\pi$
$192$	−1.00000	−0.0721688
$193$	−9.70946	−0.698902	−0.349451	−	0.936955i	$-0.613632\pi$
$193$	−9.70946	−0.698902	−0.349451	+	0.936955i	$0.613632\pi$
$194$	−4.63686	−0.332907
$195$	2.55242	0.182783
$196$	−5.10052	−0.364323
$197$	10.6953	0.762006	0.381003	−	0.924574i	$-0.375579\pi$
$197$	10.6953	0.762006	0.381003	+	0.924574i	$0.375579\pi$
$198$	−4.10597	−0.291799
$199$	−4.21109	−0.298516	−0.149258	−	0.988798i	$-0.547689\pi$
$199$	−4.21109	−0.298516	−0.149258	+	0.988798i	$0.547689\pi$
$200$	−1.51486	−0.107117
$201$	−3.12773	−0.220613
$202$	15.5977	1.09745
$203$	−0.453994	−0.0318641
$204$	−3.57390	−0.250223
$205$	20.0551	1.40071
$206$	−1.00000	−0.0696733
$207$	3.65040	0.253720
$208$	1.00000	0.0693375
$209$	1.55295	0.107420
$210$	−3.51779	−0.242751
$211$	−21.1987	−1.45938	−0.729690	−	0.683778i	$-0.760336\pi$
$211$	−21.1987	−1.45938	−0.729690	+	0.683778i	$0.760336\pi$
$212$	−10.1230	−0.695251
$213$	−8.40081	−0.575614
$214$	−10.0618	−0.687813
$215$	6.99442	0.477016
$216$	1.00000	0.0680414
$217$	−10.2231	−0.693990
$218$	−11.4816	−0.777632
$219$	−2.15179	−0.145405
$220$	−10.4802	−0.706573
$221$	3.57390	0.240406
$222$	−6.88409	−0.462030
$223$	9.75733	0.653399	0.326700	−	0.945128i	$-0.394063\pi$
$223$	9.75733	0.653399	0.326700	+	0.945128i	$0.394063\pi$
$224$	−1.37822	−0.0920861
$225$	1.51486	0.100991
$226$	−4.69080	−0.312027
$227$	26.6880	1.77135	0.885673	−	0.464310i	$-0.153698\pi$
$227$	26.6880	1.77135	0.885673	+	0.464310i	$0.153698\pi$
$228$	−0.378218	−0.0250481
$229$	−21.0379	−1.39022	−0.695112	−	0.718902i	$-0.744645\pi$
$229$	−21.0379	−1.39022	−0.695112	+	0.718902i	$0.744645\pi$
$230$	9.31736	0.614368
$231$	−5.65892	−0.372330
$232$	0.329406	0.0216266
$233$	−8.73734	−0.572402	−0.286201	−	0.958170i	$-0.592393\pi$
$233$	−8.73734	−0.572402	−0.286201	+	0.958170i	$0.592393\pi$
$234$	−1.00000	−0.0653720
$235$	5.43923	0.354816
$236$	8.34165	0.542995
$237$	5.79457	0.376398
$238$	−4.92561	−0.319280
$239$	−17.3130	−1.11988	−0.559942	−	0.828532i	$-0.689177\pi$
$239$	−17.3130	−1.11988	−0.559942	+	0.828532i	$0.689177\pi$
$240$	2.55242	0.164758
$241$	19.3299	1.24515	0.622574	−	0.782561i	$-0.286087\pi$
$241$	19.3299	1.24515	0.622574	+	0.782561i	$0.286087\pi$
$242$	−5.85898	−0.376630
$243$	−1.00000	−0.0641500
$244$	−0.317128	−0.0203020
$245$	13.0187	0.831732
$246$	−7.85728	−0.500962
$247$	0.378218	0.0240654
$248$	7.41763	0.471020
$249$	1.11990	0.0709708
$250$	−8.89555	−0.562604
$251$	11.1871	0.706125	0.353063	−	0.935600i	$-0.385140\pi$
$251$	11.1871	0.706125	0.353063	+	0.935600i	$0.385140\pi$
$252$	1.37822	0.0868196
$253$	14.9884	0.942314
$254$	18.9176	1.18700
$255$	9.12209	0.571248
$256$	1.00000	0.0625000
$257$	−25.3163	−1.57919	−0.789594	−	0.613629i	$-0.789709\pi$
$257$	−25.3163	−1.57919	−0.789594	+	0.613629i	$0.789709\pi$
$258$	−2.74031	−0.170604
$259$	−9.48777	−0.589542
$260$	−2.55242	−0.158295
$261$	−0.329406	−0.0203897
$262$	−14.9131	−0.921336
$263$	−22.2746	−1.37351	−0.686754	−	0.726890i	$-0.740965\pi$
$263$	−22.2746	−1.37351	−0.686754	+	0.726890i	$0.740965\pi$
$264$	4.10597	0.252705
$265$	25.8382	1.58723
$266$	−0.521267	−0.0319609
$267$	−0.259370	−0.0158732
$268$	3.12773	0.191056
$269$	23.4427	1.42933	0.714663	−	0.699469i	$-0.246580\pi$
$269$	23.4427	1.42933	0.714663	+	0.699469i	$0.246580\pi$
$270$	−2.55242	−0.155335
$271$	14.7770	0.897638	0.448819	−	0.893623i	$-0.351845\pi$
$271$	14.7770	0.897638	0.448819	+	0.893623i	$0.351845\pi$
$272$	3.57390	0.216699
$273$	−1.37822	−0.0834135
$274$	−17.1905	−1.03851
$275$	6.21997	0.375078
$276$	−3.65040	−0.219728
$277$	0.941275	0.0565557	0.0282779	−	0.999600i	$-0.490998\pi$
$277$	0.941275	0.0565557	0.0282779	+	0.999600i	$0.490998\pi$
$278$	−18.1741	−1.09001
$279$	−7.41763	−0.444082
$280$	3.51779	0.210228
$281$	−8.44093	−0.503543	−0.251772	−	0.967787i	$-0.581013\pi$
$281$	−8.44093	−0.503543	−0.251772	+	0.967787i	$0.581013\pi$
$282$	−2.13101	−0.126900
$283$	0.458757	0.0272703	0.0136351	−	0.999907i	$-0.495660\pi$
$283$	0.458757	0.0272703	0.0136351	+	0.999907i	$0.495660\pi$
$284$	8.40081	0.498496
$285$	0.965372	0.0571837
$286$	−4.10597	−0.242791
$287$	−10.8290	−0.639218
$288$	−1.00000	−0.0589256
$289$	−4.22727	−0.248663
$290$	−0.840784	−0.0493726
$291$	−4.63686	−0.271818
$292$	2.15179	0.125924
$293$	−5.81927	−0.339965	−0.169983	−	0.985447i	$-0.554371\pi$
$293$	−5.81927	−0.339965	−0.169983	+	0.985447i	$0.554371\pi$
$294$	−5.10052	−0.297468
$295$	−21.2914	−1.23963
$296$	6.88409	0.400130
$297$	−4.10597	−0.238252
$298$	7.54334	0.436974
$299$	3.65040	0.211108
$300$	−1.51486	−0.0874605
$301$	−3.77674	−0.217688
$302$	22.2535	1.28054
$303$	15.5977	0.896064
$304$	0.378218	0.0216923
$305$	0.809445	0.0463487
$306$	−3.57390	−0.204306
$307$	−15.4051	−0.879214	−0.439607	−	0.898190i	$-0.644882\pi$
$307$	−15.4051	−0.879214	−0.439607	+	0.898190i	$0.644882\pi$
$308$	5.65892	0.322447
$309$	−1.00000	−0.0568880
$310$	−18.9329	−1.07532
$311$	21.3489	1.21058	0.605292	−	0.796004i	$-0.293056\pi$
$311$	21.3489	1.21058	0.605292	+	0.796004i	$0.293056\pi$
$312$	1.00000	0.0566139
$313$	−0.467785	−0.0264408	−0.0132204	−	0.999913i	$-0.504208\pi$
$313$	−0.467785	−0.0264408	−0.0132204	+	0.999913i	$0.504208\pi$
$314$	11.8126	0.666622
$315$	−3.51779	−0.198205
$316$	−5.79457	−0.325970
$317$	17.6599	0.991881	0.495941	−	0.868356i	$-0.334823\pi$
$317$	17.6599	0.991881	0.495941	+	0.868356i	$0.334823\pi$
$318$	−10.1230	−0.567670
$319$	−1.35253	−0.0757273
$320$	−2.55242	−0.142685
$321$	−10.0618	−0.561597
$322$	−5.03104	−0.280369
$323$	1.35171	0.0752112
$324$	1.00000	0.0555556
$325$	1.51486	0.0840293
$326$	5.81167	0.321879
$327$	−11.4816	−0.634934
$328$	7.85728	0.433846
$329$	−2.93699	−0.161922
$330$	−10.4802	−0.576914
$331$	−14.5394	−0.799155	−0.399578	−	0.916699i	$-0.630843\pi$
$331$	−14.5394	−0.799155	−0.399578	+	0.916699i	$0.630843\pi$
$332$	−1.11990	−0.0614625
$333$	−6.88409	−0.377246
$334$	8.49879	0.465033
$335$	−7.98328	−0.436173
$336$	−1.37822	−0.0751879
$337$	−27.2491	−1.48435	−0.742177	−	0.670204i	$-0.766207\pi$
$337$	−27.2491	−1.48435	−0.742177	+	0.670204i	$0.766207\pi$
$338$	−1.00000	−0.0543928
$339$	−4.69080	−0.254769
$340$	−9.12209	−0.494715
$341$	−30.4566	−1.64932
$342$	−0.378218	−0.0204517
$343$	−16.6771	−0.900481
$344$	2.74031	0.147748
$345$	9.31736	0.501630
$346$	16.5832	0.891517
$347$	−6.74311	−0.361989	−0.180994	−	0.983484i	$-0.557932\pi$
$347$	−6.74311	−0.361989	−0.180994	+	0.983484i	$0.557932\pi$
$348$	0.329406	0.0176580
$349$	−9.28940	−0.497250	−0.248625	−	0.968600i	$-0.579979\pi$
$349$	−9.28940	−0.497250	−0.248625	+	0.968600i	$0.579979\pi$
$350$	−2.08781	−0.111598
$351$	−1.00000	−0.0533761
$352$	−4.10597	−0.218849
$353$	9.67070	0.514719	0.257360	−	0.966316i	$-0.417147\pi$
$353$	9.67070	0.514719	0.257360	+	0.966316i	$0.417147\pi$
$354$	8.34165	0.443354
$355$	−21.4424	−1.13804
$356$	0.259370	0.0137466
$357$	−4.92561	−0.260691
$358$	14.9667	0.791013
$359$	−3.21503	−0.169683	−0.0848413	−	0.996394i	$-0.527038\pi$
$359$	−3.21503	−0.169683	−0.0848413	+	0.996394i	$0.527038\pi$
$360$	2.55242	0.134524
$361$	−18.8570	−0.992471
$362$	15.9377	0.837666
$363$	−5.85898	−0.307517
$364$	1.37822	0.0722382
$365$	−5.49228	−0.287479
$366$	−0.317128	−0.0165766
$367$	13.5101	0.705224	0.352612	−	0.935770i	$-0.385294\pi$
$367$	13.5101	0.705224	0.352612	+	0.935770i	$0.385294\pi$
$368$	3.65040	0.190290
$369$	−7.85728	−0.409034
$370$	−17.5711	−0.913478
$371$	−13.9517	−0.724336
$372$	7.41763	0.384586
$373$	−8.16869	−0.422959	−0.211479	−	0.977382i	$-0.567828\pi$
$373$	−8.16869	−0.422959	−0.211479	+	0.977382i	$0.567828\pi$
$374$	−14.6743	−0.758790
$375$	−8.89555	−0.459364
$376$	2.13101	0.109898
$377$	−0.329406	−0.0169653
$378$	1.37822	0.0708879
$379$	−5.83245	−0.299593	−0.149797	−	0.988717i	$-0.547862\pi$
$379$	−5.83245	−0.299593	−0.149797	+	0.988717i	$0.547862\pi$
$380$	−0.965372	−0.0495225
$381$	18.9176	0.969180
$382$	−14.0461	−0.718661
$383$	10.4854	0.535779	0.267890	−	0.963450i	$-0.413674\pi$
$383$	10.4854	0.535779	0.267890	+	0.963450i	$0.413674\pi$
$384$	1.00000	0.0510310
$385$	−14.4440	−0.736132
$386$	9.70946	0.494199
$387$	−2.74031	−0.139298
$388$	4.63686	0.235401
$389$	−1.54358	−0.0782628	−0.0391314	−	0.999234i	$-0.512459\pi$
$389$	−1.54358	−0.0782628	−0.0391314	+	0.999234i	$0.512459\pi$
$390$	−2.55242	−0.129247
$391$	13.0461	0.659772
$392$	5.10052	0.257615
$393$	−14.9131	−0.752268
$394$	−10.6953	−0.538820
$395$	14.7902	0.744176
$396$	4.10597	0.206333
$397$	25.3759	1.27358	0.636790	−	0.771038i	$-0.280262\pi$
$397$	25.3759	1.27358	0.636790	+	0.771038i	$0.280262\pi$
$398$	4.21109	0.211083
$399$	−0.521267	−0.0260960
$400$	1.51486	0.0757430
$401$	−18.4808	−0.922887	−0.461444	−	0.887170i	$-0.652668\pi$
$401$	−18.4808	−0.922887	−0.461444	+	0.887170i	$0.652668\pi$
$402$	3.12773	0.155997
$403$	−7.41763	−0.369499
$404$	−15.5977	−0.776014
$405$	−2.55242	−0.126831
$406$	0.453994	0.0225313
$407$	−28.2659	−1.40109
$408$	3.57390	0.176934
$409$	5.38841	0.266440	0.133220	−	0.991086i	$-0.457468\pi$
$409$	5.38841	0.266440	0.133220	+	0.991086i	$0.457468\pi$
$410$	−20.0551	−0.990450
$411$	−17.1905	−0.847944
$412$	1.00000	0.0492665
$413$	11.4966	0.565711
$414$	−3.65040	−0.179407
$415$	2.85846	0.140316
$416$	−1.00000	−0.0490290
$417$	−18.1741	−0.889988
$418$	−1.55295	−0.0759573
$419$	−17.1706	−0.838840	−0.419420	−	0.907792i	$-0.637767\pi$
$419$	−17.1706	−0.838840	−0.419420	+	0.907792i	$0.637767\pi$
$420$	3.51779	0.171651
$421$	−27.6057	−1.34542	−0.672710	−	0.739906i	$-0.734870\pi$
$421$	−27.6057	−1.34542	−0.672710	+	0.739906i	$0.734870\pi$
$422$	21.1987	1.03194
$423$	−2.13101	−0.103613
$424$	10.1230	0.491616
$425$	5.41395	0.262615
$426$	8.40081	0.407020
$427$	−0.437072	−0.0211514
$428$	10.0618	0.486357
$429$	−4.10597	−0.198238
$430$	−6.99442	−0.337301
$431$	−6.25335	−0.301213	−0.150607	−	0.988594i	$-0.548123\pi$
$431$	−6.25335	−0.301213	−0.150607	+	0.988594i	$0.548123\pi$
$432$	−1.00000	−0.0481125
$433$	−15.4271	−0.741380	−0.370690	−	0.928757i	$-0.620879\pi$
$433$	−15.4271	−0.741380	−0.370690	+	0.928757i	$0.620879\pi$
$434$	10.2231	0.490725
$435$	−0.840784	−0.0403125
$436$	11.4816	0.549869
$437$	1.38065	0.0660453
$438$	2.15179	0.102817
$439$	10.2796	0.490617	0.245309	−	0.969445i	$-0.421111\pi$
$439$	10.2796	0.490617	0.245309	+	0.969445i	$0.421111\pi$
$440$	10.4802	0.499622
$441$	−5.10052	−0.242882
$442$	−3.57390	−0.169993
$443$	29.9234	1.42170	0.710852	−	0.703342i	$-0.248310\pi$
$443$	29.9234	1.42170	0.710852	+	0.703342i	$0.248310\pi$
$444$	6.88409	0.326704
$445$	−0.662023	−0.0313829
$446$	−9.75733	−0.462023
$447$	7.54334	0.356788
$448$	1.37822	0.0651147
$449$	−6.67530	−0.315027	−0.157513	−	0.987517i	$-0.550348\pi$
$449$	−6.67530	−0.315027	−0.157513	+	0.987517i	$0.550348\pi$
$450$	−1.51486	−0.0714112
$451$	−32.2617	−1.51915
$452$	4.69080	0.220637
$453$	22.2535	1.04556
$454$	−26.6880	−1.25253
$455$	−3.51779	−0.164917
$456$	0.378218	0.0177117
$457$	−5.76757	−0.269796	−0.134898	−	0.990860i	$-0.543071\pi$
$457$	−5.76757	−0.269796	−0.134898	+	0.990860i	$0.543071\pi$
$458$	21.0379	0.983036
$459$	−3.57390	−0.166815
$460$	−9.31736	−0.434424
$461$	10.8327	0.504528	0.252264	−	0.967658i	$-0.418825\pi$
$461$	10.8327	0.504528	0.252264	+	0.967658i	$0.418825\pi$
$462$	5.65892	0.263277
$463$	−11.7791	−0.547420	−0.273710	−	0.961812i	$-0.588251\pi$
$463$	−11.7791	−0.547420	−0.273710	+	0.961812i	$0.588251\pi$
$464$	−0.329406	−0.0152923
$465$	−18.9329	−0.877994
$466$	8.73734	0.404749
$467$	33.0283	1.52837	0.764184	−	0.644998i	$-0.223142\pi$
$467$	33.0283	1.52837	0.764184	+	0.644998i	$0.223142\pi$
$468$	1.00000	0.0462250
$469$	4.31069	0.199049
$470$	−5.43923	−0.250893
$471$	11.8126	0.544295
$472$	−8.34165	−0.383955
$473$	−11.2516	−0.517350
$474$	−5.79457	−0.266154
$475$	0.572947	0.0262886
$476$	4.92561	0.225765
$477$	−10.1230	−0.463500
$478$	17.3130	0.791877
$479$	−19.4169	−0.887179	−0.443589	−	0.896230i	$-0.646295\pi$
$479$	−19.4169	−0.887179	−0.443589	+	0.896230i	$0.646295\pi$
$480$	−2.55242	−0.116502
$481$	−6.88409	−0.313887
$482$	−19.3299	−0.880453
$483$	−5.03104	−0.228920
$484$	5.85898	0.266317
$485$	−11.8352	−0.537410
$486$	1.00000	0.0453609
$487$	12.6915	0.575107	0.287554	−	0.957765i	$-0.407158\pi$
$487$	12.6915	0.575107	0.287554	+	0.957765i	$0.407158\pi$
$488$	0.317128	0.0143557
$489$	5.81167	0.262813
$490$	−13.0187	−0.588124
$491$	−14.4170	−0.650629	−0.325315	−	0.945606i	$-0.605470\pi$
$491$	−14.4170	−0.650629	−0.325315	+	0.945606i	$0.605470\pi$
$492$	7.85728	0.354233
$493$	−1.17726	−0.0530213
$494$	−0.378218	−0.0170168
$495$	−10.4802	−0.471048
$496$	−7.41763	−0.333062
$497$	11.5781	0.519351
$498$	−1.11990	−0.0501839
$499$	13.4253	0.600998	0.300499	−	0.953782i	$-0.402847\pi$
$499$	13.4253	0.600998	0.300499	+	0.953782i	$0.402847\pi$
$500$	8.89555	0.397821
$501$	8.49879	0.379698
$502$	−11.1871	−0.499306
$503$	22.0217	0.981900	0.490950	−	0.871188i	$-0.336650\pi$
$503$	22.0217	0.981900	0.490950	+	0.871188i	$0.336650\pi$
$504$	−1.37822	−0.0613907
$505$	39.8119	1.77161
$506$	−14.9884	−0.666317
$507$	−1.00000	−0.0444116
$508$	−18.9176	−0.839335
$509$	−1.19058	−0.0527714	−0.0263857	−	0.999652i	$-0.508400\pi$
$509$	−1.19058	−0.0527714	−0.0263857	+	0.999652i	$0.508400\pi$
$510$	−9.12209	−0.403933
$511$	2.96564	0.131192
$512$	−1.00000	−0.0441942
$513$	−0.378218	−0.0166987
$514$	25.3163	1.11666
$515$	−2.55242	−0.112473
$516$	2.74031	0.120635
$517$	−8.74985	−0.384818
$518$	9.48777	0.416869
$519$	16.5832	0.727921
$520$	2.55242	0.111931
$521$	−14.7616	−0.646718	−0.323359	−	0.946276i	$-0.604812\pi$
$521$	−14.7616	−0.646718	−0.323359	+	0.946276i	$0.604812\pi$
$522$	0.329406	0.0144177
$523$	34.5063	1.50885	0.754427	−	0.656384i	$-0.227915\pi$
$523$	34.5063	1.50885	0.754427	+	0.656384i	$0.227915\pi$
$524$	14.9131	0.651483
$525$	−2.08781	−0.0911194
$526$	22.2746	0.971217
$527$	−26.5098	−1.15479
$528$	−4.10597	−0.178689
$529$	−9.67459	−0.420634
$530$	−25.8382	−1.12234
$531$	8.34165	0.361997
$532$	0.521267	0.0225998
$533$	−7.85728	−0.340336
$534$	0.259370	0.0112241
$535$	−25.6820	−1.11033
$536$	−3.12773	−0.135097
$537$	14.9667	0.645859
$538$	−23.4427	−1.01069
$539$	−20.9426	−0.902060
$540$	2.55242	0.109839
$541$	−17.0031	−0.731020	−0.365510	−	0.930807i	$-0.619105\pi$
$541$	−17.0031	−0.731020	−0.365510	+	0.930807i	$0.619105\pi$
$542$	−14.7770	−0.634726
$543$	15.9377	0.683951
$544$	−3.57390	−0.153230
$545$	−29.3059	−1.25533
$546$	1.37822	0.0589823
$547$	36.4996	1.56061	0.780306	−	0.625398i	$-0.215063\pi$
$547$	36.4996	1.56061	0.780306	+	0.625398i	$0.215063\pi$
$548$	17.1905	0.734341
$549$	−0.317128	−0.0135347
$550$	−6.21997	−0.265220
$551$	−0.124587	−0.00530760
$552$	3.65040	0.155371
$553$	−7.98618	−0.339607
$554$	−0.941275	−0.0399909
$555$	−17.5711	−0.745852
$556$	18.1741	0.770752
$557$	−43.3356	−1.83619	−0.918094	−	0.396363i	$-0.870272\pi$
$557$	−43.3356	−1.83619	−0.918094	+	0.396363i	$0.870272\pi$
$558$	7.41763	0.314013
$559$	−2.74031	−0.115903
$560$	−3.51779	−0.148654
$561$	−14.6743	−0.619550
$562$	8.44093	0.356059
$563$	−37.0062	−1.55962	−0.779812	−	0.626014i	$-0.784685\pi$
$563$	−37.0062	−1.55962	−0.779812	+	0.626014i	$0.784685\pi$
$564$	2.13101	0.0897316
$565$	−11.9729	−0.503704
$566$	−0.458757	−0.0192830
$567$	1.37822	0.0578797
$568$	−8.40081	−0.352490
$569$	−20.9891	−0.879910	−0.439955	−	0.898020i	$-0.645006\pi$
$569$	−20.9891	−0.879910	−0.439955	+	0.898020i	$0.645006\pi$
$570$	−0.965372	−0.0404350
$571$	−13.1783	−0.551495	−0.275748	−	0.961230i	$-0.588925\pi$
$571$	−13.1783	−0.551495	−0.275748	+	0.961230i	$0.588925\pi$
$572$	4.10597	0.171679
$573$	−14.0461	−0.586784
$574$	10.8290	0.451995
$575$	5.52984	0.230610
$576$	1.00000	0.0416667
$577$	−31.5512	−1.31349	−0.656746	−	0.754112i	$-0.728068\pi$
$577$	−31.5512	−1.31349	−0.656746	+	0.754112i	$0.728068\pi$
$578$	4.22727	0.175831
$579$	9.70946	0.403512
$580$	0.840784	0.0349117
$581$	−1.54347	−0.0640338
$582$	4.63686	0.192204
$583$	−41.5647	−1.72144
$584$	−2.15179	−0.0890417
$585$	−2.55242	−0.105530
$586$	5.81927	0.240392
$587$	−28.2823	−1.16734	−0.583668	−	0.811992i	$-0.698383\pi$
$587$	−28.2823	−1.16734	−0.583668	+	0.811992i	$0.698383\pi$
$588$	5.10052	0.210342
$589$	−2.80548	−0.115598
$590$	21.2914	0.876553
$591$	−10.6953	−0.439945
$592$	−6.88409	−0.282934
$593$	3.23446	0.132823	0.0664117	−	0.997792i	$-0.478845\pi$
$593$	3.23446	0.132823	0.0664117	+	0.997792i	$0.478845\pi$
$594$	4.10597	0.168470
$595$	−12.5722	−0.515411
$596$	−7.54334	−0.308987
$597$	4.21109	0.172348
$598$	−3.65040	−0.149276
$599$	−16.7633	−0.684930	−0.342465	−	0.939531i	$-0.611262\pi$
$599$	−16.7633	−0.684930	−0.342465	+	0.939531i	$0.611262\pi$
$600$	1.51486	0.0618439
$601$	28.5348	1.16396	0.581980	−	0.813203i	$-0.302278\pi$
$601$	28.5348	1.16396	0.581980	+	0.813203i	$0.302278\pi$
$602$	3.77674	0.153929
$603$	3.12773	0.127371
$604$	−22.2535	−0.905481
$605$	−14.9546	−0.607991
$606$	−15.5977	−0.633613
$607$	38.5489	1.56465	0.782327	−	0.622868i	$-0.214033\pi$
$607$	38.5489	1.56465	0.782327	+	0.622868i	$0.214033\pi$
$608$	−0.378218	−0.0153388
$609$	0.453994	0.0183968
$610$	−0.809445	−0.0327735
$611$	−2.13101	−0.0862114
$612$	3.57390	0.144466
$613$	23.7566	0.959522	0.479761	−	0.877399i	$-0.340723\pi$
$613$	23.7566	0.959522	0.479761	+	0.877399i	$0.340723\pi$
$614$	15.4051	0.621698
$615$	−20.0551	−0.808699
$616$	−5.65892	−0.228004
$617$	−2.88539	−0.116161	−0.0580807	−	0.998312i	$-0.518498\pi$
$617$	−2.88539	−0.116161	−0.0580807	+	0.998312i	$0.518498\pi$
$618$	1.00000	0.0402259
$619$	−25.6125	−1.02945	−0.514727	−	0.857354i	$-0.672107\pi$
$619$	−25.6125	−1.02945	−0.514727	+	0.857354i	$0.672107\pi$
$620$	18.9329	0.760365
$621$	−3.65040	−0.146485
$622$	−21.3489	−0.856012
$623$	0.357469	0.0143217
$624$	−1.00000	−0.0400320
$625$	−30.2795	−1.21118
$626$	0.467785	0.0186964
$627$	−1.55295	−0.0620189
$628$	−11.8126	−0.471373
$629$	−24.6030	−0.980987
$630$	3.51779	0.140152
$631$	−2.46911	−0.0982939	−0.0491469	−	0.998792i	$-0.515650\pi$
$631$	−2.46911	−0.0982939	−0.0491469	+	0.998792i	$0.515650\pi$
$632$	5.79457	0.230496
$633$	21.1987	0.842574
$634$	−17.6599	−0.701366
$635$	48.2858	1.91616
$636$	10.1230	0.401403
$637$	−5.10052	−0.202090
$638$	1.35253	0.0535473
$639$	8.40081	0.332331
$640$	2.55242	0.100893
$641$	41.5397	1.64072	0.820360	−	0.571847i	$-0.193773\pi$
$641$	41.5397	1.64072	0.820360	+	0.571847i	$0.193773\pi$
$642$	10.0618	0.397109
$643$	−6.01921	−0.237374	−0.118687	−	0.992932i	$-0.537869\pi$
$643$	−6.01921	−0.237374	−0.118687	+	0.992932i	$0.537869\pi$
$644$	5.03104	0.198251
$645$	−6.99442	−0.275405
$646$	−1.35171	−0.0531824
$647$	−6.66297	−0.261949	−0.130974	−	0.991386i	$-0.541811\pi$
$647$	−6.66297	−0.261949	−0.130974	+	0.991386i	$0.541811\pi$
$648$	−1.00000	−0.0392837
$649$	34.2505	1.34445
$650$	−1.51486	−0.0594177
$651$	10.2231	0.400675
$652$	−5.81167	−0.227603
$653$	44.0181	1.72256	0.861282	−	0.508128i	$-0.169662\pi$
$653$	44.0181	1.72256	0.861282	+	0.508128i	$0.169662\pi$
$654$	11.4816	0.448966
$655$	−38.0646	−1.48731
$656$	−7.85728	−0.306775
$657$	2.15179	0.0839494
$658$	2.93699	0.114496
$659$	36.7419	1.43126	0.715631	−	0.698479i	$-0.246139\pi$
$659$	36.7419	1.43126	0.715631	+	0.698479i	$0.246139\pi$
$660$	10.4802	0.407940
$661$	−19.5472	−0.760298	−0.380149	−	0.924925i	$-0.624127\pi$
$661$	−19.5472	−0.760298	−0.380149	+	0.924925i	$0.624127\pi$
$662$	14.5394	0.565088
$663$	−3.57390	−0.138799
$664$	1.11990	0.0434605
$665$	−1.33049	−0.0515943
$666$	6.88409	0.266753
$667$	−1.20246	−0.0465596
$668$	−8.49879	−0.328828
$669$	−9.75733	−0.377240
$670$	7.98328	0.308421
$671$	−1.30212	−0.0502677
$672$	1.37822	0.0531659
$673$	14.6908	0.566289	0.283144	−	0.959077i	$-0.408622\pi$
$673$	14.6908	0.566289	0.283144	+	0.959077i	$0.408622\pi$
$674$	27.2491	1.04960
$675$	−1.51486	−0.0583070
$676$	1.00000	0.0384615
$677$	26.6253	1.02329	0.511646	−	0.859196i	$-0.329036\pi$
$677$	26.6253	1.02329	0.511646	+	0.859196i	$0.329036\pi$
$678$	4.69080	0.180149
$679$	6.39061	0.245249
$680$	9.12209	0.349816
$681$	−26.6880	−1.02269
$682$	30.4566	1.16624
$683$	15.9055	0.608607	0.304303	−	0.952575i	$-0.401576\pi$
$683$	15.9055	0.608607	0.304303	+	0.952575i	$0.401576\pi$
$684$	0.378218	0.0144615
$685$	−43.8774	−1.67647
$686$	16.6771	0.636736
$687$	21.0379	0.802646
$688$	−2.74031	−0.104473
$689$	−10.1230	−0.385656
$690$	−9.31736	−0.354706
$691$	48.6228	1.84970	0.924849	−	0.380335i	$-0.124191\pi$
$691$	48.6228	1.84970	0.924849	+	0.380335i	$0.124191\pi$
$692$	−16.5832	−0.630398
$693$	5.65892	0.214965
$694$	6.74311	0.255965
$695$	−46.3879	−1.75959
$696$	−0.329406	−0.0124861
$697$	−28.0811	−1.06365
$698$	9.28940	0.351609
$699$	8.73734	0.330477
$700$	2.08781	0.0789117
$701$	−15.0542	−0.568588	−0.284294	−	0.958737i	$-0.591759\pi$
$701$	−15.0542	−0.568588	−0.284294	+	0.958737i	$0.591759\pi$
$702$	1.00000	0.0377426
$703$	−2.60369	−0.0981999
$704$	4.10597	0.154750
$705$	−5.43923	−0.204853
$706$	−9.67070	−0.363962
$707$	−21.4970	−0.808479
$708$	−8.34165	−0.313498
$709$	31.3168	1.17613	0.588063	−	0.808815i	$-0.299891\pi$
$709$	31.3168	1.17613	0.588063	+	0.808815i	$0.299891\pi$
$710$	21.4424	0.804719
$711$	−5.79457	−0.217313
$712$	−0.259370	−0.00972032
$713$	−27.0773	−1.01405
$714$	4.92561	0.184336
$715$	−10.4802	−0.391936
$716$	−14.9667	−0.559331
$717$	17.3130	0.646565
$718$	3.21503	0.119984
$719$	−52.9418	−1.97440	−0.987198	−	0.159500i	$-0.949012\pi$
$719$	−52.9418	−1.97440	−0.987198	+	0.159500i	$0.949012\pi$
$720$	−2.55242	−0.0951232
$721$	1.37822	0.0513275
$722$	18.8570	0.701783
$723$	−19.3299	−0.718886
$724$	−15.9377	−0.592319
$725$	−0.499005	−0.0185326
$726$	5.85898	0.217447
$727$	5.87787	0.217998	0.108999	−	0.994042i	$-0.465235\pi$
$727$	5.87787	0.217998	0.108999	+	0.994042i	$0.465235\pi$
$728$	−1.37822	−0.0510802
$729$	1.00000	0.0370370
$730$	5.49228	0.203278
$731$	−9.79358	−0.362229
$732$	0.317128	0.0117214
$733$	35.8254	1.32324	0.661622	−	0.749838i	$-0.269869\pi$
$733$	35.8254	1.32324	0.661622	+	0.749838i	$0.269869\pi$
$734$	−13.5101	−0.498668
$735$	−13.0187	−0.480201
$736$	−3.65040	−0.134555
$737$	12.8423	0.473054
$738$	7.85728	0.289230
$739$	−10.0672	−0.370327	−0.185164	−	0.982708i	$-0.559281\pi$
$739$	−10.0672	−0.370327	−0.185164	+	0.982708i	$0.559281\pi$
$740$	17.5711	0.645927
$741$	−0.378218	−0.0138942
$742$	13.9517	0.512183
$743$	24.4390	0.896580	0.448290	−	0.893888i	$-0.352033\pi$
$743$	24.4390	0.896580	0.448290	+	0.893888i	$0.352033\pi$
$744$	−7.41763	−0.271944
$745$	19.2538	0.705405
$746$	8.16869	0.299077
$747$	−1.11990	−0.0409750
$748$	14.6743	0.536546
$749$	13.8674	0.506704
$750$	8.89555	0.324820
$751$	−11.2872	−0.411874	−0.205937	−	0.978565i	$-0.566024\pi$
$751$	−11.2872	−0.411874	−0.205937	+	0.978565i	$0.566024\pi$
$752$	−2.13101	−0.0777099
$753$	−11.1871	−0.407682
$754$	0.329406	0.0119963
$755$	56.8003	2.06717
$756$	−1.37822	−0.0501253
$757$	−31.1159	−1.13093	−0.565464	−	0.824773i	$-0.691303\pi$
$757$	−31.1159	−1.13093	−0.565464	+	0.824773i	$0.691303\pi$
$758$	5.83245	0.211844
$759$	−14.9884	−0.544045
$760$	0.965372	0.0350177
$761$	43.0335	1.55996	0.779982	−	0.625802i	$-0.215228\pi$
$761$	43.0335	1.55996	0.779982	+	0.625802i	$0.215228\pi$
$762$	−18.9176	−0.685314
$763$	15.8241	0.572873
$764$	14.0461	0.508170
$765$	−9.12209	−0.329810
$766$	−10.4854	−0.378853
$767$	8.34165	0.301199
$768$	−1.00000	−0.0360844
$769$	6.89994	0.248818	0.124409	−	0.992231i	$-0.460296\pi$
$769$	6.89994	0.248818	0.124409	+	0.992231i	$0.460296\pi$
$770$	14.4440	0.520524
$771$	25.3163	0.911745
$772$	−9.70946	−0.349451
$773$	13.3315	0.479499	0.239750	−	0.970835i	$-0.422935\pi$
$773$	13.3315	0.479499	0.239750	+	0.970835i	$0.422935\pi$
$774$	2.74031	0.0984984
$775$	−11.2367	−0.403633
$776$	−4.63686	−0.166454
$777$	9.48777	0.340372
$778$	1.54358	0.0553402
$779$	−2.97176	−0.106474
$780$	2.55242	0.0913914
$781$	34.4935	1.23427
$782$	−13.0461	−0.466529
$783$	0.329406	0.0117720
$784$	−5.10052	−0.182161
$785$	30.1507	1.07612
$786$	14.9131	0.531934
$787$	−22.2913	−0.794597	−0.397299	−	0.917689i	$-0.630052\pi$
$787$	−22.2913	−0.794597	−0.397299	+	0.917689i	$0.630052\pi$
$788$	10.6953	0.381003
$789$	22.2746	0.792995
$790$	−14.7902	−0.526212
$791$	6.46495	0.229867
$792$	−4.10597	−0.145899
$793$	−0.317128	−0.0112615
$794$	−25.3759	−0.900556
$795$	−25.8382	−0.916386
$796$	−4.21109	−0.149258
$797$	−50.1769	−1.77736	−0.888678	−	0.458532i	$-0.848375\pi$
$797$	−50.1769	−1.77736	−0.888678	+	0.458532i	$0.848375\pi$
$798$	0.521267	0.0184526
$799$	−7.61600	−0.269435
$800$	−1.51486	−0.0535584
$801$	0.259370	0.00916441
$802$	18.4808	0.652580
$803$	8.83519	0.311787
$804$	−3.12773	−0.110306
$805$	−12.8414	−0.452598
$806$	7.41763	0.261275
$807$	−23.4427	−0.825221
$808$	15.5977	0.548725
$809$	−47.5700	−1.67247	−0.836235	−	0.548371i	$-0.815248\pi$
$809$	−47.5700	−1.67247	−0.836235	+	0.548371i	$0.815248\pi$
$810$	2.55242	0.0896830
$811$	−31.1647	−1.09434	−0.547171	−	0.837021i	$-0.684295\pi$
$811$	−31.1647	−1.09434	−0.547171	+	0.837021i	$0.684295\pi$
$812$	−0.453994	−0.0159321
$813$	−14.7770	−0.518251
$814$	28.2659	0.990718
$815$	14.8338	0.519607
$816$	−3.57390	−0.125111
$817$	−1.03643	−0.0362602
$818$	−5.38841	−0.188401
$819$	1.37822	0.0481588
$820$	20.0551	0.700354
$821$	−7.31853	−0.255418	−0.127709	−	0.991812i	$-0.540762\pi$
$821$	−7.31853	−0.255418	−0.127709	+	0.991812i	$0.540762\pi$
$822$	17.1905	0.599587
$823$	−14.1340	−0.492682	−0.246341	−	0.969183i	$-0.579228\pi$
$823$	−14.1340	−0.492682	−0.246341	+	0.969183i	$0.579228\pi$
$824$	−1.00000	−0.0348367
$825$	−6.21997	−0.216552
$826$	−11.4966	−0.400018
$827$	−32.4299	−1.12770	−0.563850	−	0.825877i	$-0.690680\pi$
$827$	−32.4299	−1.12770	−0.563850	+	0.825877i	$0.690680\pi$
$828$	3.65040	0.126860
$829$	20.4679	0.710881	0.355440	−	0.934699i	$-0.384331\pi$
$829$	20.4679	0.710881	0.355440	+	0.934699i	$0.384331\pi$
$830$	−2.85846	−0.0992185
$831$	−0.941275	−0.0326525
$832$	1.00000	0.0346688
$833$	−18.2287	−0.631587
$834$	18.1741	0.629316
$835$	21.6925	0.750700
$836$	1.55295	0.0537099
$837$	7.41763	0.256391
$838$	17.1706	0.593150
$839$	−13.3546	−0.461052	−0.230526	−	0.973066i	$-0.574045\pi$
$839$	−13.3546	−0.461052	−0.230526	+	0.973066i	$0.574045\pi$
$840$	−3.51779	−0.121375
$841$	−28.8915	−0.996258
$842$	27.6057	0.951356
$843$	8.44093	0.290721
$844$	−21.1987	−0.729690
$845$	−2.55242	−0.0878060
$846$	2.13101	0.0732656
$847$	8.07495	0.277459
$848$	−10.1230	−0.347625
$849$	−0.458757	−0.0157445
$850$	−5.41395	−0.185697
$851$	−25.1297	−0.861434
$852$	−8.40081	−0.287807
$853$	26.5489	0.909017	0.454508	−	0.890742i	$-0.349815\pi$
$853$	26.5489	0.909017	0.454508	+	0.890742i	$0.349815\pi$
$854$	0.437072	0.0149563
$855$	−0.965372	−0.0330150
$856$	−10.0618	−0.343906
$857$	−31.4250	−1.07346	−0.536728	−	0.843755i	$-0.680340\pi$
$857$	−31.4250	−1.07346	−0.536728	+	0.843755i	$0.680340\pi$
$858$	4.10597	0.140175
$859$	−34.3335	−1.17144	−0.585721	−	0.810513i	$-0.699189\pi$
$859$	−34.3335	−1.17144	−0.585721	+	0.810513i	$0.699189\pi$
$860$	6.99442	0.238508
$861$	10.8290	0.369053
$862$	6.25335	0.212990
$863$	−13.8241	−0.470577	−0.235289	−	0.971926i	$-0.575604\pi$
$863$	−13.8241	−0.470577	−0.235289	+	0.971926i	$0.575604\pi$
$864$	1.00000	0.0340207
$865$	42.3273	1.43917
$866$	15.4271	0.524235
$867$	4.22727	0.143566
$868$	−10.2231	−0.346995
$869$	−23.7923	−0.807100
$870$	0.840784	0.0285053
$871$	3.12773	0.105979
$872$	−11.4816	−0.388816
$873$	4.63686	0.156934
$874$	−1.38065	−0.0467010
$875$	12.2600	0.414464
$876$	−2.15179	−0.0727023
$877$	0.0399391	0.00134865	0.000674324	−	1.00000i	$-0.499785\pi$
$877$	0.0399391	0.00134865	0.000674324		1.00000i	$0.499785\pi$
$878$	−10.2796	−0.346919
$879$	5.81927	0.196279
$880$	−10.4802	−0.353286
$881$	−22.9628	−0.773638	−0.386819	−	0.922156i	$-0.626426\pi$
$881$	−22.9628	−0.773638	−0.386819	+	0.922156i	$0.626426\pi$
$882$	5.10052	0.171743
$883$	2.20731	0.0742821	0.0371410	−	0.999310i	$-0.488175\pi$
$883$	2.20731	0.0742821	0.0371410	+	0.999310i	$0.488175\pi$
$884$	3.57390	0.120203
$885$	21.2914	0.715703
$886$	−29.9234	−1.00530
$887$	−24.6791	−0.828644	−0.414322	−	0.910130i	$-0.635981\pi$
$887$	−24.6791	−0.828644	−0.414322	+	0.910130i	$0.635981\pi$
$888$	−6.88409	−0.231015
$889$	−26.0726	−0.874448
$890$	0.662023	0.0221911
$891$	4.10597	0.137555
$892$	9.75733	0.326700
$893$	−0.805985	−0.0269713
$894$	−7.54334	−0.252287
$895$	38.2013	1.27693
$896$	−1.37822	−0.0460430
$897$	−3.65040	−0.121883
$898$	6.67530	0.222758
$899$	2.44342	0.0814925
$900$	1.51486	0.0504953
$901$	−36.1786	−1.20528
$902$	32.2617	1.07420
$903$	3.77674	0.125682
$904$	−4.69080	−0.156014
$905$	40.6797	1.35224
$906$	−22.2535	−0.739322
$907$	−23.5663	−0.782508	−0.391254	−	0.920283i	$-0.627959\pi$
$907$	−23.5663	−0.782508	−0.391254	+	0.920283i	$0.627959\pi$
$908$	26.6880	0.885673
$909$	−15.5977	−0.517343
$910$	3.51779	0.116614
$911$	−28.0145	−0.928163	−0.464082	−	0.885792i	$-0.653616\pi$
$911$	−28.0145	−0.928163	−0.464082	+	0.885792i	$0.653616\pi$
$912$	−0.378218	−0.0125240
$913$	−4.59827	−0.152181
$914$	5.76757	0.190774
$915$	−0.809445	−0.0267594
$916$	−21.0379	−0.695112
$917$	20.5535	0.678738
$918$	3.57390	0.117956
$919$	−13.9310	−0.459542	−0.229771	−	0.973245i	$-0.573798\pi$
$919$	−13.9310	−0.459542	−0.229771	+	0.973245i	$0.573798\pi$
$920$	9.31736	0.307184
$921$	15.4051	0.507614
$922$	−10.8327	−0.356755
$923$	8.40081	0.276516
$924$	−5.65892	−0.186165
$925$	−10.4284	−0.342885
$926$	11.7791	0.387084
$927$	1.00000	0.0328443
$928$	0.329406	0.0108133
$929$	−55.5699	−1.82319	−0.911594	−	0.411091i	$-0.865148\pi$
$929$	−55.5699	−1.82319	−0.911594	+	0.411091i	$0.865148\pi$
$930$	18.9329	0.620835
$931$	−1.92911	−0.0632239
$932$	−8.73734	−0.286201
$933$	−21.3489	−0.698931
$934$	−33.0283	−1.08072
$935$	−37.4550	−1.22491
$936$	−1.00000	−0.0326860
$937$	16.7160	0.546088	0.273044	−	0.962002i	$-0.411969\pi$
$937$	16.7160	0.546088	0.273044	+	0.962002i	$0.411969\pi$
$938$	−4.31069	−0.140749
$939$	0.467785	0.0152656
$940$	5.43923	0.177408
$941$	−2.93553	−0.0956957	−0.0478478	−	0.998855i	$-0.515236\pi$
$941$	−2.93553	−0.0956957	−0.0478478	+	0.998855i	$0.515236\pi$
$942$	−11.8126	−0.384875
$943$	−28.6822	−0.934021
$944$	8.34165	0.271497
$945$	3.51779	0.114434
$946$	11.2516	0.365822
$947$	30.9142	1.00458	0.502288	−	0.864700i	$-0.332492\pi$
$947$	30.9142	1.00458	0.502288	+	0.864700i	$0.332492\pi$
$948$	5.79457	0.188199
$949$	2.15179	0.0698501
$950$	−0.572947	−0.0185889
$951$	−17.6599	−0.572663
$952$	−4.92561	−0.159640
$953$	−39.3113	−1.27342	−0.636709	−	0.771104i	$-0.719705\pi$
$953$	−39.3113	−1.27342	−0.636709	+	0.771104i	$0.719705\pi$
$954$	10.1230	0.327744
$955$	−35.8516	−1.16013
$956$	−17.3130	−0.559942
$957$	1.35253	0.0437212
$958$	19.4169	0.627330
$959$	23.6922	0.765062
$960$	2.55242	0.0823791
$961$	24.0213	0.774880
$962$	6.88409	0.221952
$963$	10.0618	0.324238
$964$	19.3299	0.622574
$965$	24.7827	0.797782
$966$	5.03104	0.161871
$967$	33.4298	1.07503	0.537515	−	0.843254i	$-0.319363\pi$
$967$	33.4298	1.07503	0.537515	+	0.843254i	$0.319363\pi$
$968$	−5.85898	−0.188315
$969$	−1.35171	−0.0434232
$970$	11.8352	0.380006
$971$	−1.90635	−0.0611778	−0.0305889	−	0.999532i	$-0.509738\pi$
$971$	−1.90635	−0.0611778	−0.0305889	+	0.999532i	$0.509738\pi$
$972$	−1.00000	−0.0320750
$973$	25.0478	0.802996
$974$	−12.6915	−0.406662
$975$	−1.51486	−0.0485144
$976$	−0.317128	−0.0101510
$977$	22.6232	0.723781	0.361891	−	0.932221i	$-0.382131\pi$
$977$	22.6232	0.723781	0.361891	+	0.932221i	$0.382131\pi$
$978$	−5.81167	−0.185837
$979$	1.06497	0.0340365
$980$	13.0187	0.415866
$981$	11.4816	0.366579
$982$	14.4170	0.460064
$983$	−35.9535	−1.14674	−0.573369	−	0.819297i	$-0.694364\pi$
$983$	−35.9535	−1.14674	−0.573369	+	0.819297i	$0.694364\pi$
$984$	−7.85728	−0.250481
$985$	−27.2988	−0.869814
$986$	1.17726	0.0374917
$987$	2.93699	0.0934855
$988$	0.378218	0.0120327
$989$	−10.0032	−0.318084
$990$	10.4802	0.333082
$991$	−47.8301	−1.51937	−0.759686	−	0.650290i	$-0.774647\pi$
$991$	−47.8301	−1.51937	−0.759686	+	0.650290i	$0.774647\pi$
$992$	7.41763	0.235510
$993$	14.5394	0.461392
$994$	−11.5781	−0.367236
$995$	10.7485	0.340750
$996$	1.11990	0.0354854
$997$	−44.1437	−1.39805	−0.699023	−	0.715099i	$-0.746381\pi$
$997$	−44.1437	−1.39805	−0.699023	+	0.715099i	$0.746381\pi$
$998$	−13.4253	−0.424970
$999$	6.88409	0.217803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.o.1.3	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.o.1.3	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.55242 q^{5} +1.00000 q^{6} +1.37822 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.55242 q^{5} +1.00000 q^{6} +1.37822 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.55242 q^{10} +4.10597 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.37822 q^{14} +2.55242 q^{15} +1.00000 q^{16} +3.57390 q^{17} -1.00000 q^{18} +0.378218 q^{19} -2.55242 q^{20} -1.37822 q^{21} -4.10597 q^{22} +3.65040 q^{23} +1.00000 q^{24} +1.51486 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.37822 q^{28} -0.329406 q^{29} -2.55242 q^{30} -7.41763 q^{31} -1.00000 q^{32} -4.10597 q^{33} -3.57390 q^{34} -3.51779 q^{35} +1.00000 q^{36} -6.88409 q^{37} -0.378218 q^{38} -1.00000 q^{39} +2.55242 q^{40} -7.85728 q^{41} +1.37822 q^{42} -2.74031 q^{43} +4.10597 q^{44} -2.55242 q^{45} -3.65040 q^{46} -2.13101 q^{47} -1.00000 q^{48} -5.10052 q^{49} -1.51486 q^{50} -3.57390 q^{51} +1.00000 q^{52} -10.1230 q^{53} +1.00000 q^{54} -10.4802 q^{55} -1.37822 q^{56} -0.378218 q^{57} +0.329406 q^{58} +8.34165 q^{59} +2.55242 q^{60} -0.317128 q^{61} +7.41763 q^{62} +1.37822 q^{63} +1.00000 q^{64} -2.55242 q^{65} +4.10597 q^{66} +3.12773 q^{67} +3.57390 q^{68} -3.65040 q^{69} +3.51779 q^{70} +8.40081 q^{71} -1.00000 q^{72} +2.15179 q^{73} +6.88409 q^{74} -1.51486 q^{75} +0.378218 q^{76} +5.65892 q^{77} +1.00000 q^{78} -5.79457 q^{79} -2.55242 q^{80} +1.00000 q^{81} +7.85728 q^{82} -1.11990 q^{83} -1.37822 q^{84} -9.12209 q^{85} +2.74031 q^{86} +0.329406 q^{87} -4.10597 q^{88} +0.259370 q^{89} +2.55242 q^{90} +1.37822 q^{91} +3.65040 q^{92} +7.41763 q^{93} +2.13101 q^{94} -0.965372 q^{95} +1.00000 q^{96} +4.63686 q^{97} +5.10052 q^{98} +4.10597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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