LMFDB - Embedded newform 8034.2.a.r.1.5

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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 45x^{6} + 7x^{5} - 123x^{4} + 37x^{3} + 87x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 45x^6 + 7x^5 - 123x^4 + 37x^3 + 87x^2 - 54x + 8
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			1.5
Root			$0.435443$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.435443 q^{5} -1.00000 q^{6} +1.91967 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.435443 q^{5} -1.00000 q^{6} +1.91967 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.435443 q^{10} +2.85320 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.91967 q^{14} +0.435443 q^{15} +1.00000 q^{16} -3.59019 q^{17} +1.00000 q^{18} -3.69491 q^{19} -0.435443 q^{20} -1.91967 q^{21} +2.85320 q^{22} -1.86832 q^{23} -1.00000 q^{24} -4.81039 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.91967 q^{28} -0.961428 q^{29} +0.435443 q^{30} -2.14442 q^{31} +1.00000 q^{32} -2.85320 q^{33} -3.59019 q^{34} -0.835905 q^{35} +1.00000 q^{36} -6.21204 q^{37} -3.69491 q^{38} -1.00000 q^{39} -0.435443 q^{40} -3.59132 q^{41} -1.91967 q^{42} -4.97924 q^{43} +2.85320 q^{44} -0.435443 q^{45} -1.86832 q^{46} +5.08864 q^{47} -1.00000 q^{48} -3.31489 q^{49} -4.81039 q^{50} +3.59019 q^{51} +1.00000 q^{52} -5.58096 q^{53} -1.00000 q^{54} -1.24241 q^{55} +1.91967 q^{56} +3.69491 q^{57} -0.961428 q^{58} -14.6828 q^{59} +0.435443 q^{60} +1.19089 q^{61} -2.14442 q^{62} +1.91967 q^{63} +1.00000 q^{64} -0.435443 q^{65} -2.85320 q^{66} -11.5845 q^{67} -3.59019 q^{68} +1.86832 q^{69} -0.835905 q^{70} -9.27413 q^{71} +1.00000 q^{72} +13.8968 q^{73} -6.21204 q^{74} +4.81039 q^{75} -3.69491 q^{76} +5.47719 q^{77} -1.00000 q^{78} +13.2308 q^{79} -0.435443 q^{80} +1.00000 q^{81} -3.59132 q^{82} +0.983189 q^{83} -1.91967 q^{84} +1.56333 q^{85} -4.97924 q^{86} +0.961428 q^{87} +2.85320 q^{88} +2.06273 q^{89} -0.435443 q^{90} +1.91967 q^{91} -1.86832 q^{92} +2.14442 q^{93} +5.08864 q^{94} +1.60893 q^{95} -1.00000 q^{96} +1.12706 q^{97} -3.31489 q^{98} +2.85320 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 5 q^{11} - 9 q^{12} + 9 q^{13} - 4 q^{14} + 4 q^{15} + 9 q^{16} - 6 q^{17} + 9 q^{18} - 4 q^{19} - 4 q^{20} + 4 q^{21} - 5 q^{22} - 6 q^{23} - 9 q^{24} - 11 q^{25} + 9 q^{26} - 9 q^{27} - 4 q^{28} - 19 q^{29} + 4 q^{30} - 6 q^{31} + 9 q^{32} + 5 q^{33} - 6 q^{34} + 10 q^{35} + 9 q^{36} - 13 q^{37} - 4 q^{38} - 9 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} - 20 q^{43} - 5 q^{44} - 4 q^{45} - 6 q^{46} + 14 q^{47} - 9 q^{48} - 3 q^{49} - 11 q^{50} + 6 q^{51} + 9 q^{52} - 3 q^{53} - 9 q^{54} - 4 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 9 q^{59} + 4 q^{60} - 24 q^{61} - 6 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 5 q^{66} - 4 q^{67} - 6 q^{68} + 6 q^{69} + 10 q^{70} - 9 q^{71} + 9 q^{72} - 24 q^{73} - 13 q^{74} + 11 q^{75} - 4 q^{76} + 3 q^{77} - 9 q^{78} - 15 q^{79} - 4 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} + 4 q^{84} - 31 q^{85} - 20 q^{86} + 19 q^{87} - 5 q^{88} + 3 q^{89} - 4 q^{90} - 4 q^{91} - 6 q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} - 9 q^{96} - 19 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 5 * q^11 - 9 * q^12 + 9 * q^13 - 4 * q^14 + 4 * q^15 + 9 * q^16 - 6 * q^17 + 9 * q^18 - 4 * q^19 - 4 * q^20 + 4 * q^21 - 5 * q^22 - 6 * q^23 - 9 * q^24 - 11 * q^25 + 9 * q^26 - 9 * q^27 - 4 * q^28 - 19 * q^29 + 4 * q^30 - 6 * q^31 + 9 * q^32 + 5 * q^33 - 6 * q^34 + 10 * q^35 + 9 * q^36 - 13 * q^37 - 4 * q^38 - 9 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 - 20 * q^43 - 5 * q^44 - 4 * q^45 - 6 * q^46 + 14 * q^47 - 9 * q^48 - 3 * q^49 - 11 * q^50 + 6 * q^51 + 9 * q^52 - 3 * q^53 - 9 * q^54 - 4 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 9 * q^59 + 4 * q^60 - 24 * q^61 - 6 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 5 * q^66 - 4 * q^67 - 6 * q^68 + 6 * q^69 + 10 * q^70 - 9 * q^71 + 9 * q^72 - 24 * q^73 - 13 * q^74 + 11 * q^75 - 4 * q^76 + 3 * q^77 - 9 * q^78 - 15 * q^79 - 4 * q^80 + 9 * q^81 - 18 * q^82 + 20 * q^83 + 4 * q^84 - 31 * q^85 - 20 * q^86 + 19 * q^87 - 5 * q^88 + 3 * q^89 - 4 * q^90 - 4 * q^91 - 6 * q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 - 9 * q^96 - 19 * q^97 - 3 * q^98 - 5 * 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
$5$	−0.435443	−0.194736	−0.0973681	−	0.995248i	$-0.531042\pi$
$5$	−0.435443	−0.194736	−0.0973681	+	0.995248i	$0.531042\pi$
$6$	−1.00000	−0.408248
$7$	1.91967	0.725565	0.362783	−	0.931874i	$-0.381827\pi$
$7$	1.91967	0.725565	0.362783	+	0.931874i	$0.381827\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.435443	−0.137699
$11$	2.85320	0.860273	0.430136	−	0.902764i	$-0.358465\pi$
$11$	2.85320	0.860273	0.430136	+	0.902764i	$0.358465\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.91967	0.513052
$15$	0.435443	0.112431
$16$	1.00000	0.250000
$17$	−3.59019	−0.870750	−0.435375	−	0.900249i	$-0.643384\pi$
$17$	−3.59019	−0.870750	−0.435375	+	0.900249i	$0.643384\pi$
$18$	1.00000	0.235702
$19$	−3.69491	−0.847672	−0.423836	−	0.905739i	$-0.639317\pi$
$19$	−3.69491	−0.847672	−0.423836	+	0.905739i	$0.639317\pi$
$20$	−0.435443	−0.0973681
$21$	−1.91967	−0.418905
$22$	2.85320	0.608305
$23$	−1.86832	−0.389571	−0.194785	−	0.980846i	$-0.562401\pi$
$23$	−1.86832	−0.389571	−0.194785	+	0.980846i	$0.562401\pi$
$24$	−1.00000	−0.204124
$25$	−4.81039	−0.962078
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.91967	0.362783
$29$	−0.961428	−0.178533	−0.0892663	−	0.996008i	$-0.528452\pi$
$29$	−0.961428	−0.178533	−0.0892663	+	0.996008i	$0.528452\pi$
$30$	0.435443	0.0795007
$31$	−2.14442	−0.385148	−0.192574	−	0.981282i	$-0.561684\pi$
$31$	−2.14442	−0.385148	−0.192574	+	0.981282i	$0.561684\pi$
$32$	1.00000	0.176777
$33$	−2.85320	−0.496679
$34$	−3.59019	−0.615713
$35$	−0.835905	−0.141294
$36$	1.00000	0.166667
$37$	−6.21204	−1.02125	−0.510627	−	0.859803i	$-0.670587\pi$
$37$	−6.21204	−1.02125	−0.510627	+	0.859803i	$0.670587\pi$
$38$	−3.69491	−0.599394
$39$	−1.00000	−0.160128
$40$	−0.435443	−0.0688496
$41$	−3.59132	−0.560870	−0.280435	−	0.959873i	$-0.590479\pi$
$41$	−3.59132	−0.560870	−0.280435	+	0.959873i	$0.590479\pi$
$42$	−1.91967	−0.296211
$43$	−4.97924	−0.759328	−0.379664	−	0.925125i	$-0.623960\pi$
$43$	−4.97924	−0.759328	−0.379664	+	0.925125i	$0.623960\pi$
$44$	2.85320	0.430136
$45$	−0.435443	−0.0649121
$46$	−1.86832	−0.275468
$47$	5.08864	0.742254	0.371127	−	0.928582i	$-0.378971\pi$
$47$	5.08864	0.742254	0.371127	+	0.928582i	$0.378971\pi$
$48$	−1.00000	−0.144338
$49$	−3.31489	−0.473555
$50$	−4.81039	−0.680292
$51$	3.59019	0.502728
$52$	1.00000	0.138675
$53$	−5.58096	−0.766603	−0.383302	−	0.923623i	$-0.625213\pi$
$53$	−5.58096	−0.766603	−0.383302	+	0.923623i	$0.625213\pi$
$54$	−1.00000	−0.136083
$55$	−1.24241	−0.167526
$56$	1.91967	0.256526
$57$	3.69491	0.489403
$58$	−0.961428	−0.126242
$59$	−14.6828	−1.91154	−0.955768	−	0.294123i	$-0.904973\pi$
$59$	−14.6828	−1.91154	−0.955768	+	0.294123i	$0.904973\pi$
$60$	0.435443	0.0562155
$61$	1.19089	0.152478	0.0762392	−	0.997090i	$-0.475709\pi$
$61$	1.19089	0.152478	0.0762392	+	0.997090i	$0.475709\pi$
$62$	−2.14442	−0.272341
$63$	1.91967	0.241855
$64$	1.00000	0.125000
$65$	−0.435443	−0.0540101
$66$	−2.85320	−0.351205
$67$	−11.5845	−1.41527	−0.707637	−	0.706576i	$-0.750239\pi$
$67$	−11.5845	−1.41527	−0.707637	+	0.706576i	$0.750239\pi$
$68$	−3.59019	−0.435375
$69$	1.86832	0.224919
$70$	−0.835905	−0.0999098
$71$	−9.27413	−1.10064	−0.550318	−	0.834955i	$-0.685494\pi$
$71$	−9.27413	−1.10064	−0.550318	+	0.834955i	$0.685494\pi$
$72$	1.00000	0.117851
$73$	13.8968	1.62649	0.813247	−	0.581919i	$-0.197698\pi$
$73$	13.8968	1.62649	0.813247	+	0.581919i	$0.197698\pi$
$74$	−6.21204	−0.722135
$75$	4.81039	0.555456
$76$	−3.69491	−0.423836
$77$	5.47719	0.624184
$78$	−1.00000	−0.113228
$79$	13.2308	1.48859	0.744293	−	0.667853i	$-0.232787\pi$
$79$	13.2308	1.48859	0.744293	+	0.667853i	$0.232787\pi$
$80$	−0.435443	−0.0486841
$81$	1.00000	0.111111
$82$	−3.59132	−0.396595
$83$	0.983189	0.107919	0.0539595	−	0.998543i	$-0.482816\pi$
$83$	0.983189	0.107919	0.0539595	+	0.998543i	$0.482816\pi$
$84$	−1.91967	−0.209453
$85$	1.56333	0.169567
$86$	−4.97924	−0.536926
$87$	0.961428	0.103076
$88$	2.85320	0.304152
$89$	2.06273	0.218649	0.109324	−	0.994006i	$-0.465131\pi$
$89$	2.06273	0.218649	0.109324	+	0.994006i	$0.465131\pi$
$90$	−0.435443	−0.0458998
$91$	1.91967	0.201236
$92$	−1.86832	−0.194785
$93$	2.14442	0.222366
$94$	5.08864	0.524853
$95$	1.60893	0.165072
$96$	−1.00000	−0.102062
$97$	1.12706	0.114436	0.0572180	−	0.998362i	$-0.481777\pi$
$97$	1.12706	0.114436	0.0572180	+	0.998362i	$0.481777\pi$
$98$	−3.31489	−0.334854
$99$	2.85320	0.286758
$100$	−4.81039	−0.481039
$101$	4.85161	0.482753	0.241377	−	0.970432i	$-0.422401\pi$
$101$	4.85161	0.482753	0.241377	+	0.970432i	$0.422401\pi$
$102$	3.59019	0.355482
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	0.835905	0.0815760
$106$	−5.58096	−0.542070
$107$	−4.59582	−0.444295	−0.222148	−	0.975013i	$-0.571307\pi$
$107$	−4.59582	−0.444295	−0.222148	+	0.975013i	$0.571307\pi$
$108$	−1.00000	−0.0962250
$109$	1.77584	0.170095	0.0850475	−	0.996377i	$-0.472896\pi$
$109$	1.77584	0.170095	0.0850475	+	0.996377i	$0.472896\pi$
$110$	−1.24241	−0.118459
$111$	6.21204	0.589621
$112$	1.91967	0.181391
$113$	−0.661262	−0.0622063	−0.0311031	−	0.999516i	$-0.509902\pi$
$113$	−0.661262	−0.0622063	−0.0311031	+	0.999516i	$0.509902\pi$
$114$	3.69491	0.346060
$115$	0.813546	0.0758636
$116$	−0.961428	−0.0892663
$117$	1.00000	0.0924500
$118$	−14.6828	−1.35166
$119$	−6.89197	−0.631786
$120$	0.435443	0.0397504
$121$	−2.85924	−0.259931
$122$	1.19089	0.107819
$123$	3.59132	0.323818
$124$	−2.14442	−0.192574
$125$	4.27187	0.382088
$126$	1.91967	0.171017
$127$	−9.57705	−0.849826	−0.424913	−	0.905234i	$-0.639695\pi$
$127$	−9.57705	−0.849826	−0.424913	+	0.905234i	$0.639695\pi$
$128$	1.00000	0.0883883
$129$	4.97924	0.438398
$130$	−0.435443	−0.0381909
$131$	4.59625	0.401576	0.200788	−	0.979635i	$-0.435650\pi$
$131$	4.59625	0.401576	0.200788	+	0.979635i	$0.435650\pi$
$132$	−2.85320	−0.248339
$133$	−7.09300	−0.615041
$134$	−11.5845	−1.00075
$135$	0.435443	0.0374770
$136$	−3.59019	−0.307857
$137$	19.5581	1.67096	0.835482	−	0.549517i	$-0.185188\pi$
$137$	19.5581	1.67096	0.835482	+	0.549517i	$0.185188\pi$
$138$	1.86832	0.159042
$139$	−13.2902	−1.12726	−0.563632	−	0.826026i	$-0.690596\pi$
$139$	−13.2902	−1.12726	−0.563632	+	0.826026i	$0.690596\pi$
$140$	−0.835905	−0.0706469
$141$	−5.08864	−0.428541
$142$	−9.27413	−0.778268
$143$	2.85320	0.238597
$144$	1.00000	0.0833333
$145$	0.418647	0.0347668
$146$	13.8968	1.15010
$147$	3.31489	0.273407
$148$	−6.21204	−0.510627
$149$	−2.44653	−0.200427	−0.100214	−	0.994966i	$-0.531953\pi$
$149$	−2.44653	−0.200427	−0.100214	+	0.994966i	$0.531953\pi$
$150$	4.81039	0.392767
$151$	−8.79598	−0.715807	−0.357903	−	0.933759i	$-0.616508\pi$
$151$	−8.79598	−0.715807	−0.357903	+	0.933759i	$0.616508\pi$
$152$	−3.69491	−0.299697
$153$	−3.59019	−0.290250
$154$	5.47719	0.441365
$155$	0.933772	0.0750023
$156$	−1.00000	−0.0800641
$157$	−19.1172	−1.52572	−0.762858	−	0.646566i	$-0.776205\pi$
$157$	−19.1172	−1.52572	−0.762858	+	0.646566i	$0.776205\pi$
$158$	13.2308	1.05259
$159$	5.58096	0.442599
$160$	−0.435443	−0.0344248
$161$	−3.58654	−0.282659
$162$	1.00000	0.0785674
$163$	20.0038	1.56682	0.783409	−	0.621506i	$-0.213479\pi$
$163$	20.0038	1.56682	0.783409	+	0.621506i	$0.213479\pi$
$164$	−3.59132	−0.280435
$165$	1.24241	0.0967213
$166$	0.983189	0.0763103
$167$	−9.82204	−0.760052	−0.380026	−	0.924976i	$-0.624085\pi$
$167$	−9.82204	−0.760052	−0.380026	+	0.924976i	$0.624085\pi$
$168$	−1.91967	−0.148105
$169$	1.00000	0.0769231
$170$	1.56333	0.119902
$171$	−3.69491	−0.282557
$172$	−4.97924	−0.379664
$173$	−11.9212	−0.906355	−0.453178	−	0.891420i	$-0.649710\pi$
$173$	−11.9212	−0.906355	−0.453178	+	0.891420i	$0.649710\pi$
$174$	0.961428	0.0728857
$175$	−9.23434	−0.698050
$176$	2.85320	0.215068
$177$	14.6828	1.10363
$178$	2.06273	0.154608
$179$	23.0540	1.72314	0.861569	−	0.507640i	$-0.169482\pi$
$179$	23.0540	1.72314	0.861569	+	0.507640i	$0.169482\pi$
$180$	−0.435443	−0.0324560
$181$	13.6865	1.01731	0.508655	−	0.860971i	$-0.330143\pi$
$181$	13.6865	1.01731	0.508655	+	0.860971i	$0.330143\pi$
$182$	1.91967	0.142295
$183$	−1.19089	−0.0880335
$184$	−1.86832	−0.137734
$185$	2.70499	0.198875
$186$	2.14442	0.157236
$187$	−10.2435	−0.749082
$188$	5.08864	0.371127
$189$	−1.91967	−0.139635
$190$	1.60893	0.116724
$191$	−17.6932	−1.28024	−0.640119	−	0.768276i	$-0.721115\pi$
$191$	−17.6932	−1.28024	−0.640119	+	0.768276i	$0.721115\pi$
$192$	−1.00000	−0.0721688
$193$	−6.71548	−0.483391	−0.241696	−	0.970352i	$-0.577704\pi$
$193$	−6.71548	−0.483391	−0.241696	+	0.970352i	$0.577704\pi$
$194$	1.12706	0.0809184
$195$	0.435443	0.0311827
$196$	−3.31489	−0.236778
$197$	17.1089	1.21896	0.609480	−	0.792802i	$-0.291378\pi$
$197$	17.1089	1.21896	0.609480	+	0.792802i	$0.291378\pi$
$198$	2.85320	0.202768
$199$	21.9091	1.55310	0.776548	−	0.630058i	$-0.216969\pi$
$199$	21.9091	1.55310	0.776548	+	0.630058i	$0.216969\pi$
$200$	−4.81039	−0.340146
$201$	11.5845	0.817109
$202$	4.85161	0.341358
$203$	−1.84562	−0.129537
$204$	3.59019	0.251364
$205$	1.56382	0.109222
$206$	−1.00000	−0.0696733
$207$	−1.86832	−0.129857
$208$	1.00000	0.0693375
$209$	−10.5423	−0.729229
$210$	0.835905	0.0576830
$211$	−25.4887	−1.75471	−0.877357	−	0.479838i	$-0.840695\pi$
$211$	−25.4887	−1.75471	−0.877357	+	0.479838i	$0.840695\pi$
$212$	−5.58096	−0.383302
$213$	9.27413	0.635453
$214$	−4.59582	−0.314164
$215$	2.16818	0.147869
$216$	−1.00000	−0.0680414
$217$	−4.11656	−0.279450
$218$	1.77584	0.120275
$219$	−13.8968	−0.939057
$220$	−1.24241	−0.0837631
$221$	−3.59019	−0.241503
$222$	6.21204	0.416925
$223$	−6.37624	−0.426984	−0.213492	−	0.976945i	$-0.568484\pi$
$223$	−6.37624	−0.426984	−0.213492	+	0.976945i	$0.568484\pi$
$224$	1.91967	0.128263
$225$	−4.81039	−0.320693
$226$	−0.661262	−0.0439865
$227$	−6.58905	−0.437331	−0.218665	−	0.975800i	$-0.570170\pi$
$227$	−6.58905	−0.437331	−0.218665	+	0.975800i	$0.570170\pi$
$228$	3.69491	0.244702
$229$	−13.8618	−0.916017	−0.458008	−	0.888948i	$-0.651437\pi$
$229$	−13.8618	−0.916017	−0.458008	+	0.888948i	$0.651437\pi$
$230$	0.813546	0.0536436
$231$	−5.47719	−0.360373
$232$	−0.961428	−0.0631208
$233$	4.29081	0.281101	0.140550	−	0.990074i	$-0.455113\pi$
$233$	4.29081	0.281101	0.140550	+	0.990074i	$0.455113\pi$
$234$	1.00000	0.0653720
$235$	−2.21581	−0.144544
$236$	−14.6828	−0.955768
$237$	−13.2308	−0.859436
$238$	−6.89197	−0.446740
$239$	15.0455	0.973214	0.486607	−	0.873621i	$-0.338234\pi$
$239$	15.0455	0.973214	0.486607	+	0.873621i	$0.338234\pi$
$240$	0.435443	0.0281077
$241$	7.07455	0.455712	0.227856	−	0.973695i	$-0.426828\pi$
$241$	7.07455	0.455712	0.227856	+	0.973695i	$0.426828\pi$
$242$	−2.85924	−0.183799
$243$	−1.00000	−0.0641500
$244$	1.19089	0.0762392
$245$	1.44345	0.0922183
$246$	3.59132	0.228974
$247$	−3.69491	−0.235102
$248$	−2.14442	−0.136171
$249$	−0.983189	−0.0623071
$250$	4.27187	0.270177
$251$	11.9732	0.755741	0.377871	−	0.925858i	$-0.376656\pi$
$251$	11.9732	0.755741	0.377871	+	0.925858i	$0.376656\pi$
$252$	1.91967	0.120928
$253$	−5.33068	−0.335137
$254$	−9.57705	−0.600918
$255$	−1.56333	−0.0978993
$256$	1.00000	0.0625000
$257$	25.1051	1.56601	0.783007	−	0.622013i	$-0.213685\pi$
$257$	25.1051	1.56601	0.783007	+	0.622013i	$0.213685\pi$
$258$	4.97924	0.309994
$259$	−11.9250	−0.740986
$260$	−0.435443	−0.0270051
$261$	−0.961428	−0.0595109
$262$	4.59625	0.283957
$263$	−17.1415	−1.05699	−0.528494	−	0.848937i	$-0.677243\pi$
$263$	−17.1415	−1.05699	−0.528494	+	0.848937i	$0.677243\pi$
$264$	−2.85320	−0.175602
$265$	2.43019	0.149285
$266$	−7.09300	−0.434900
$267$	−2.06273	−0.126237
$268$	−11.5845	−0.707637
$269$	23.0381	1.40466	0.702328	−	0.711853i	$-0.252144\pi$
$269$	23.0381	1.40466	0.702328	+	0.711853i	$0.252144\pi$
$270$	0.435443	0.0265002
$271$	18.8576	1.14552	0.572758	−	0.819724i	$-0.305873\pi$
$271$	18.8576	1.14552	0.572758	+	0.819724i	$0.305873\pi$
$272$	−3.59019	−0.217687
$273$	−1.91967	−0.116183
$274$	19.5581	1.18155
$275$	−13.7250	−0.827649
$276$	1.86832	0.112459
$277$	−22.6360	−1.36007	−0.680033	−	0.733181i	$-0.738035\pi$
$277$	−22.6360	−1.36007	−0.680033	+	0.733181i	$0.738035\pi$
$278$	−13.2902	−0.797096
$279$	−2.14442	−0.128383
$280$	−0.835905	−0.0499549
$281$	−28.6570	−1.70953	−0.854767	−	0.519012i	$-0.826300\pi$
$281$	−28.6570	−1.70953	−0.854767	+	0.519012i	$0.826300\pi$
$282$	−5.08864	−0.303024
$283$	28.3194	1.68342	0.841708	−	0.539933i	$-0.181550\pi$
$283$	28.3194	1.68342	0.841708	+	0.539933i	$0.181550\pi$
$284$	−9.27413	−0.550318
$285$	−1.60893	−0.0953046
$286$	2.85320	0.168713
$287$	−6.89413	−0.406947
$288$	1.00000	0.0589256
$289$	−4.11051	−0.241795
$290$	0.418647	0.0245838
$291$	−1.12706	−0.0660696
$292$	13.8968	0.813247
$293$	−11.5696	−0.675900	−0.337950	−	0.941164i	$-0.609734\pi$
$293$	−11.5696	−0.675900	−0.337950	+	0.941164i	$0.609734\pi$
$294$	3.31489	0.193328
$295$	6.39352	0.372245
$296$	−6.21204	−0.361068
$297$	−2.85320	−0.165560
$298$	−2.44653	−0.141724
$299$	−1.86832	−0.108048
$300$	4.81039	0.277728
$301$	−9.55848	−0.550942
$302$	−8.79598	−0.506152
$303$	−4.85161	−0.278718
$304$	−3.69491	−0.211918
$305$	−0.518567	−0.0296931
$306$	−3.59019	−0.205238
$307$	−2.02100	−0.115345	−0.0576724	−	0.998336i	$-0.518368\pi$
$307$	−2.02100	−0.115345	−0.0576724	+	0.998336i	$0.518368\pi$
$308$	5.47719	0.312092
$309$	1.00000	0.0568880
$310$	0.933772	0.0530347
$311$	−20.8655	−1.18318	−0.591588	−	0.806240i	$-0.701499\pi$
$311$	−20.8655	−1.18318	−0.591588	+	0.806240i	$0.701499\pi$
$312$	−1.00000	−0.0566139
$313$	11.7502	0.664159	0.332079	−	0.943251i	$-0.392250\pi$
$313$	11.7502	0.664159	0.332079	+	0.943251i	$0.392250\pi$
$314$	−19.1172	−1.07884
$315$	−0.835905	−0.0470979
$316$	13.2308	0.744293
$317$	−24.1089	−1.35409	−0.677046	−	0.735941i	$-0.736740\pi$
$317$	−24.1089	−1.35409	−0.677046	+	0.735941i	$0.736740\pi$
$318$	5.58096	0.312964
$319$	−2.74315	−0.153587
$320$	−0.435443	−0.0243420
$321$	4.59582	0.256514
$322$	−3.58654	−0.199870
$323$	13.2655	0.738110
$324$	1.00000	0.0555556
$325$	−4.81039	−0.266832
$326$	20.0038	1.10791
$327$	−1.77584	−0.0982044
$328$	−3.59132	−0.198297
$329$	9.76848	0.538554
$330$	1.24241	0.0683923
$331$	−9.55801	−0.525356	−0.262678	−	0.964884i	$-0.584606\pi$
$331$	−9.55801	−0.525356	−0.262678	+	0.964884i	$0.584606\pi$
$332$	0.983189	0.0539595
$333$	−6.21204	−0.340418
$334$	−9.82204	−0.537438
$335$	5.04440	0.275605
$336$	−1.91967	−0.104726
$337$	−14.4527	−0.787287	−0.393643	−	0.919263i	$-0.628786\pi$
$337$	−14.4527	−0.787287	−0.393643	+	0.919263i	$0.628786\pi$
$338$	1.00000	0.0543928
$339$	0.661262	0.0359148
$340$	1.56333	0.0847833
$341$	−6.11845	−0.331333
$342$	−3.69491	−0.199798
$343$	−19.8011	−1.06916
$344$	−4.97924	−0.268463
$345$	−0.813546	−0.0437999
$346$	−11.9212	−0.640890
$347$	35.7615	1.91978	0.959889	−	0.280379i	$-0.0904600\pi$
$347$	35.7615	1.91978	0.959889	+	0.280379i	$0.0904600\pi$
$348$	0.961428	0.0515379
$349$	−0.534690	−0.0286213	−0.0143106	−	0.999898i	$-0.504555\pi$
$349$	−0.534690	−0.0286213	−0.0143106	+	0.999898i	$0.504555\pi$
$350$	−9.23434	−0.493596
$351$	−1.00000	−0.0533761
$352$	2.85320	0.152076
$353$	−13.3704	−0.711637	−0.355818	−	0.934555i	$-0.615798\pi$
$353$	−13.3704	−0.711637	−0.355818	+	0.934555i	$0.615798\pi$
$354$	14.6828	0.780381
$355$	4.03836	0.214334
$356$	2.06273	0.109324
$357$	6.89197	0.364762
$358$	23.0540	1.21844
$359$	−17.8765	−0.943485	−0.471742	−	0.881736i	$-0.656375\pi$
$359$	−17.8765	−0.943485	−0.471742	+	0.881736i	$0.656375\pi$
$360$	−0.435443	−0.0229499
$361$	−5.34761	−0.281453
$362$	13.6865	0.719346
$363$	2.85924	0.150071
$364$	1.91967	0.100618
$365$	−6.05126	−0.316737
$366$	−1.19089	−0.0622491
$367$	−4.27224	−0.223009	−0.111505	−	0.993764i	$-0.535567\pi$
$367$	−4.27224	−0.223009	−0.111505	+	0.993764i	$0.535567\pi$
$368$	−1.86832	−0.0973927
$369$	−3.59132	−0.186957
$370$	2.70499	0.140626
$371$	−10.7136	−0.556221
$372$	2.14442	0.111183
$373$	−19.8892	−1.02982	−0.514912	−	0.857243i	$-0.672175\pi$
$373$	−19.8892	−1.02982	−0.514912	+	0.857243i	$0.672175\pi$
$374$	−10.2435	−0.529681
$375$	−4.27187	−0.220598
$376$	5.08864	0.262427
$377$	−0.961428	−0.0495161
$378$	−1.91967	−0.0987369
$379$	−20.9693	−1.07712	−0.538562	−	0.842586i	$-0.681032\pi$
$379$	−20.9693	−1.07712	−0.538562	+	0.842586i	$0.681032\pi$
$380$	1.60893	0.0825362
$381$	9.57705	0.490647
$382$	−17.6932	−0.905265
$383$	18.4552	0.943018	0.471509	−	0.881861i	$-0.343709\pi$
$383$	18.4552	0.943018	0.471509	+	0.881861i	$0.343709\pi$
$384$	−1.00000	−0.0510310
$385$	−2.38501	−0.121551
$386$	−6.71548	−0.341809
$387$	−4.97924	−0.253109
$388$	1.12706	0.0572180
$389$	16.5559	0.839417	0.419709	−	0.907659i	$-0.362132\pi$
$389$	16.5559	0.839417	0.419709	+	0.907659i	$0.362132\pi$
$390$	0.435443	0.0220495
$391$	6.70762	0.339219
$392$	−3.31489	−0.167427
$393$	−4.59625	−0.231850
$394$	17.1089	0.861935
$395$	−5.76128	−0.289882
$396$	2.85320	0.143379
$397$	5.58308	0.280207	0.140103	−	0.990137i	$-0.455257\pi$
$397$	5.58308	0.280207	0.140103	+	0.990137i	$0.455257\pi$
$398$	21.9091	1.09821
$399$	7.09300	0.355094
$400$	−4.81039	−0.240519
$401$	12.2927	0.613868	0.306934	−	0.951731i	$-0.400697\pi$
$401$	12.2927	0.613868	0.306934	+	0.951731i	$0.400697\pi$
$402$	11.5845	0.577783
$403$	−2.14442	−0.106821
$404$	4.85161	0.241377
$405$	−0.435443	−0.0216374
$406$	−1.84562	−0.0915966
$407$	−17.7242	−0.878556
$408$	3.59019	0.177741
$409$	−9.85431	−0.487264	−0.243632	−	0.969868i	$-0.578339\pi$
$409$	−9.85431	−0.487264	−0.243632	+	0.969868i	$0.578339\pi$
$410$	1.56382	0.0772313
$411$	−19.5581	−0.964732
$412$	−1.00000	−0.0492665
$413$	−28.1860	−1.38694
$414$	−1.86832	−0.0918228
$415$	−0.428123	−0.0210157
$416$	1.00000	0.0490290
$417$	13.2902	0.650826
$418$	−10.5423	−0.515643
$419$	25.1699	1.22963	0.614814	−	0.788672i	$-0.289231\pi$
$419$	25.1699	1.22963	0.614814	+	0.788672i	$0.289231\pi$
$420$	0.835905	0.0407880
$421$	−39.2159	−1.91127	−0.955633	−	0.294559i	$-0.904827\pi$
$421$	−39.2159	−1.91127	−0.955633	+	0.294559i	$0.904827\pi$
$422$	−25.4887	−1.24077
$423$	5.08864	0.247418
$424$	−5.58096	−0.271035
$425$	17.2702	0.837729
$426$	9.27413	0.449333
$427$	2.28612	0.110633
$428$	−4.59582	−0.222148
$429$	−2.85320	−0.137754
$430$	2.16818	0.104559
$431$	−3.65383	−0.175999	−0.0879994	−	0.996121i	$-0.528047\pi$
$431$	−3.65383	−0.175999	−0.0879994	+	0.996121i	$0.528047\pi$
$432$	−1.00000	−0.0481125
$433$	−39.2104	−1.88433	−0.942166	−	0.335146i	$-0.891214\pi$
$433$	−39.2104	−1.88433	−0.942166	+	0.335146i	$0.891214\pi$
$434$	−4.11656	−0.197601
$435$	−0.418647	−0.0200726
$436$	1.77584	0.0850475
$437$	6.90327	0.330228
$438$	−13.8968	−0.664013
$439$	−34.3154	−1.63779	−0.818893	−	0.573946i	$-0.805412\pi$
$439$	−34.3154	−1.63779	−0.818893	+	0.573946i	$0.805412\pi$
$440$	−1.24241	−0.0592295
$441$	−3.31489	−0.157852
$442$	−3.59019	−0.170768
$443$	−17.8103	−0.846192	−0.423096	−	0.906085i	$-0.639057\pi$
$443$	−17.8103	−0.846192	−0.423096	+	0.906085i	$0.639057\pi$
$444$	6.21204	0.294810
$445$	−0.898201	−0.0425788
$446$	−6.37624	−0.301923
$447$	2.44653	0.115717
$448$	1.91967	0.0906956
$449$	12.0579	0.569047	0.284524	−	0.958669i	$-0.408165\pi$
$449$	12.0579	0.569047	0.284524	+	0.958669i	$0.408165\pi$
$450$	−4.81039	−0.226764
$451$	−10.2468	−0.482501
$452$	−0.661262	−0.0311031
$453$	8.79598	0.413271
$454$	−6.58905	−0.309239
$455$	−0.835905	−0.0391879
$456$	3.69491	0.173030
$457$	−14.5303	−0.679697	−0.339848	−	0.940480i	$-0.610376\pi$
$457$	−14.5303	−0.679697	−0.339848	+	0.940480i	$0.610376\pi$
$458$	−13.8618	−0.647722
$459$	3.59019	0.167576
$460$	0.813546	0.0379318
$461$	−7.55984	−0.352097	−0.176049	−	0.984381i	$-0.556332\pi$
$461$	−7.55984	−0.352097	−0.176049	+	0.984381i	$0.556332\pi$
$462$	−5.47719	−0.254822
$463$	26.5738	1.23499	0.617495	−	0.786575i	$-0.288148\pi$
$463$	26.5738	1.23499	0.617495	+	0.786575i	$0.288148\pi$
$464$	−0.961428	−0.0446332
$465$	−0.933772	−0.0433026
$466$	4.29081	0.198768
$467$	−1.01733	−0.0470766	−0.0235383	−	0.999723i	$-0.507493\pi$
$467$	−1.01733	−0.0470766	−0.0235383	+	0.999723i	$0.507493\pi$
$468$	1.00000	0.0462250
$469$	−22.2384	−1.02687
$470$	−2.21581	−0.102208
$471$	19.1172	0.880873
$472$	−14.6828	−0.675830
$473$	−14.2068	−0.653229
$474$	−13.2308	−0.607713
$475$	17.7740	0.815526
$476$	−6.89197	−0.315893
$477$	−5.58096	−0.255534
$478$	15.0455	0.688166
$479$	14.8403	0.678072	0.339036	−	0.940773i	$-0.389899\pi$
$479$	14.8403	0.678072	0.339036	+	0.940773i	$0.389899\pi$
$480$	0.435443	0.0198752
$481$	−6.21204	−0.283245
$482$	7.07455	0.322237
$483$	3.58654	0.163193
$484$	−2.85924	−0.129965
$485$	−0.490772	−0.0222848
$486$	−1.00000	−0.0453609
$487$	−11.0288	−0.499762	−0.249881	−	0.968277i	$-0.580392\pi$
$487$	−11.0288	−0.499762	−0.249881	+	0.968277i	$0.580392\pi$
$488$	1.19089	0.0539093
$489$	−20.0038	−0.904603
$490$	1.44345	0.0652082
$491$	20.0599	0.905289	0.452644	−	0.891691i	$-0.350481\pi$
$491$	20.0599	0.905289	0.452644	+	0.891691i	$0.350481\pi$
$492$	3.59132	0.161909
$493$	3.45171	0.155457
$494$	−3.69491	−0.166242
$495$	−1.24241	−0.0558421
$496$	−2.14442	−0.0962871
$497$	−17.8032	−0.798584
$498$	−0.983189	−0.0440578
$499$	7.16865	0.320913	0.160456	−	0.987043i	$-0.448703\pi$
$499$	7.16865	0.320913	0.160456	+	0.987043i	$0.448703\pi$
$500$	4.27187	0.191044
$501$	9.82204	0.438816
$502$	11.9732	0.534390
$503$	7.65548	0.341341	0.170671	−	0.985328i	$-0.445407\pi$
$503$	7.65548	0.341341	0.170671	+	0.985328i	$0.445407\pi$
$504$	1.91967	0.0855087
$505$	−2.11260	−0.0940095
$506$	−5.33068	−0.236978
$507$	−1.00000	−0.0444116
$508$	−9.57705	−0.424913
$509$	−23.2451	−1.03032	−0.515160	−	0.857094i	$-0.672267\pi$
$509$	−23.2451	−1.03032	−0.515160	+	0.857094i	$0.672267\pi$
$510$	−1.56333	−0.0692252
$511$	26.6771	1.18013
$512$	1.00000	0.0441942
$513$	3.69491	0.163134
$514$	25.1051	1.10734
$515$	0.435443	0.0191879
$516$	4.97924	0.219199
$517$	14.5189	0.638541
$518$	−11.9250	−0.523956
$519$	11.9212	0.523284
$520$	−0.435443	−0.0190955
$521$	−12.0630	−0.528490	−0.264245	−	0.964456i	$-0.585123\pi$
$521$	−12.0630	−0.528490	−0.264245	+	0.964456i	$0.585123\pi$
$522$	−0.961428	−0.0420806
$523$	−4.04978	−0.177084	−0.0885422	−	0.996072i	$-0.528221\pi$
$523$	−4.04978	−0.177084	−0.0885422	+	0.996072i	$0.528221\pi$
$524$	4.59625	0.200788
$525$	9.23434	0.403019
$526$	−17.1415	−0.747404
$527$	7.69887	0.335368
$528$	−2.85320	−0.124170
$529$	−19.5094	−0.848234
$530$	2.43019	0.105561
$531$	−14.6828	−0.637178
$532$	−7.09300	−0.307520
$533$	−3.59132	−0.155557
$534$	−2.06273	−0.0892630
$535$	2.00122	0.0865203
$536$	−11.5845	−0.500375
$537$	−23.0540	−0.994854
$538$	23.0381	0.993242
$539$	−9.45804	−0.407387
$540$	0.435443	0.0187385
$541$	−38.6211	−1.66045	−0.830224	−	0.557429i	$-0.811788\pi$
$541$	−38.6211	−1.66045	−0.830224	+	0.557429i	$0.811788\pi$
$542$	18.8576	0.810003
$543$	−13.6865	−0.587344
$544$	−3.59019	−0.153928
$545$	−0.773280	−0.0331237
$546$	−1.91967	−0.0821541
$547$	26.9807	1.15361	0.576806	−	0.816881i	$-0.304299\pi$
$547$	26.9807	1.15361	0.576806	+	0.816881i	$0.304299\pi$
$548$	19.5581	0.835482
$549$	1.19089	0.0508261
$550$	−13.7250	−0.585236
$551$	3.55239	0.151337
$552$	1.86832	0.0795208
$553$	25.3988	1.08007
$554$	−22.6360	−0.961712
$555$	−2.70499	−0.114821
$556$	−13.2902	−0.563632
$557$	5.83424	0.247205	0.123602	−	0.992332i	$-0.460555\pi$
$557$	5.83424	0.247205	0.123602	+	0.992332i	$0.460555\pi$
$558$	−2.14442	−0.0907803
$559$	−4.97924	−0.210600
$560$	−0.835905	−0.0353235
$561$	10.2435	0.432483
$562$	−28.6570	−1.20882
$563$	−11.3301	−0.477505	−0.238753	−	0.971080i	$-0.576738\pi$
$563$	−11.3301	−0.477505	−0.238753	+	0.971080i	$0.576738\pi$
$564$	−5.08864	−0.214270
$565$	0.287942	0.0121138
$566$	28.3194	1.19035
$567$	1.91967	0.0806184
$568$	−9.27413	−0.389134
$569$	22.9363	0.961538	0.480769	−	0.876847i	$-0.340358\pi$
$569$	22.9363	0.961538	0.480769	+	0.876847i	$0.340358\pi$
$570$	−1.60893	−0.0673905
$571$	15.9369	0.666937	0.333469	−	0.942761i	$-0.391781\pi$
$571$	15.9369	0.666937	0.333469	+	0.942761i	$0.391781\pi$
$572$	2.85320	0.119298
$573$	17.6932	0.739146
$574$	−6.89413	−0.287755
$575$	8.98733	0.374798
$576$	1.00000	0.0416667
$577$	20.4819	0.852674	0.426337	−	0.904564i	$-0.359804\pi$
$577$	20.4819	0.852674	0.426337	+	0.904564i	$0.359804\pi$
$578$	−4.11051	−0.170975
$579$	6.71548	0.279086
$580$	0.418647	0.0173834
$581$	1.88739	0.0783023
$582$	−1.12706	−0.0467183
$583$	−15.9236	−0.659488
$584$	13.8968	0.575052
$585$	−0.435443	−0.0180034
$586$	−11.5696	−0.477934
$587$	−8.80968	−0.363614	−0.181807	−	0.983334i	$-0.558195\pi$
$587$	−8.80968	−0.363614	−0.181807	+	0.983334i	$0.558195\pi$
$588$	3.31489	0.136704
$589$	7.92343	0.326479
$590$	6.39352	0.263217
$591$	−17.1089	−0.703767
$592$	−6.21204	−0.255313
$593$	−2.93928	−0.120702	−0.0603508	−	0.998177i	$-0.519222\pi$
$593$	−2.93928	−0.120702	−0.0603508	+	0.998177i	$0.519222\pi$
$594$	−2.85320	−0.117068
$595$	3.00106	0.123032
$596$	−2.44653	−0.100214
$597$	−21.9091	−0.896681
$598$	−1.86832	−0.0764012
$599$	31.7805	1.29852	0.649258	−	0.760568i	$-0.275080\pi$
$599$	31.7805	1.29852	0.649258	+	0.760568i	$0.275080\pi$
$600$	4.81039	0.196383
$601$	29.2659	1.19378	0.596891	−	0.802322i	$-0.296403\pi$
$601$	29.2659	1.19378	0.596891	+	0.802322i	$0.296403\pi$
$602$	−9.55848	−0.389575
$603$	−11.5845	−0.471758
$604$	−8.79598	−0.357903
$605$	1.24504	0.0506180
$606$	−4.85161	−0.197083
$607$	−18.5058	−0.751126	−0.375563	−	0.926797i	$-0.622551\pi$
$607$	−18.5058	−0.751126	−0.375563	+	0.926797i	$0.622551\pi$
$608$	−3.69491	−0.149849
$609$	1.84562	0.0747883
$610$	−0.518567	−0.0209962
$611$	5.08864	0.205864
$612$	−3.59019	−0.145125
$613$	44.2527	1.78735	0.893675	−	0.448714i	$-0.148118\pi$
$613$	44.2527	1.78735	0.893675	+	0.448714i	$0.148118\pi$
$614$	−2.02100	−0.0815611
$615$	−1.56382	−0.0630591
$616$	5.47719	0.220682
$617$	23.2214	0.934860	0.467430	−	0.884030i	$-0.345180\pi$
$617$	23.2214	0.934860	0.467430	+	0.884030i	$0.345180\pi$
$618$	1.00000	0.0402259
$619$	43.9505	1.76652	0.883260	−	0.468884i	$-0.155344\pi$
$619$	43.9505	1.76652	0.883260	+	0.468884i	$0.155344\pi$
$620$	0.933772	0.0375012
$621$	1.86832	0.0749730
$622$	−20.8655	−0.836632
$623$	3.95975	0.158644
$624$	−1.00000	−0.0400320
$625$	22.1918	0.887672
$626$	11.7502	0.469631
$627$	10.5423	0.421020
$628$	−19.1172	−0.762858
$629$	22.3024	0.889256
$630$	−0.835905	−0.0333033
$631$	−20.8690	−0.830782	−0.415391	−	0.909643i	$-0.636355\pi$
$631$	−20.8690	−0.830782	−0.415391	+	0.909643i	$0.636355\pi$
$632$	13.2308	0.526295
$633$	25.4887	1.01308
$634$	−24.1089	−0.957487
$635$	4.17026	0.165492
$636$	5.58096	0.221299
$637$	−3.31489	−0.131341
$638$	−2.74315	−0.108602
$639$	−9.27413	−0.366879
$640$	−0.435443	−0.0172124
$641$	4.90029	0.193550	0.0967749	−	0.995306i	$-0.469147\pi$
$641$	4.90029	0.193550	0.0967749	+	0.995306i	$0.469147\pi$
$642$	4.59582	0.181383
$643$	14.4357	0.569289	0.284644	−	0.958633i	$-0.408124\pi$
$643$	14.4357	0.569289	0.284644	+	0.958633i	$0.408124\pi$
$644$	−3.58654	−0.141330
$645$	−2.16818	−0.0853720
$646$	13.2655	0.521922
$647$	27.2215	1.07019	0.535093	−	0.844793i	$-0.320277\pi$
$647$	27.2215	1.07019	0.535093	+	0.844793i	$0.320277\pi$
$648$	1.00000	0.0392837
$649$	−41.8929	−1.64444
$650$	−4.81039	−0.188679
$651$	4.11656	0.161341
$652$	20.0038	0.783409
$653$	44.9605	1.75944	0.879721	−	0.475491i	$-0.157730\pi$
$653$	44.9605	1.75944	0.879721	+	0.475491i	$0.157730\pi$
$654$	−1.77584	−0.0694410
$655$	−2.00141	−0.0782014
$656$	−3.59132	−0.140217
$657$	13.8968	0.542165
$658$	9.76848	0.380815
$659$	−15.1942	−0.591880	−0.295940	−	0.955206i	$-0.595633\pi$
$659$	−15.1942	−0.591880	−0.295940	+	0.955206i	$0.595633\pi$
$660$	1.24241	0.0483607
$661$	−31.1366	−1.21107	−0.605536	−	0.795818i	$-0.707041\pi$
$661$	−31.1366	−1.21107	−0.605536	+	0.795818i	$0.707041\pi$
$662$	−9.55801	−0.371482
$663$	3.59019	0.139432
$664$	0.983189	0.0381551
$665$	3.08860	0.119771
$666$	−6.21204	−0.240712
$667$	1.79625	0.0695511
$668$	−9.82204	−0.380026
$669$	6.37624	0.246520
$670$	5.04440	0.194882
$671$	3.39786	0.131173
$672$	−1.91967	−0.0740527
$673$	−30.3741	−1.17084	−0.585418	−	0.810731i	$-0.699070\pi$
$673$	−30.3741	−1.17084	−0.585418	+	0.810731i	$0.699070\pi$
$674$	−14.4527	−0.556696
$675$	4.81039	0.185152
$676$	1.00000	0.0384615
$677$	24.4810	0.940880	0.470440	−	0.882432i	$-0.344095\pi$
$677$	24.4810	0.940880	0.470440	+	0.882432i	$0.344095\pi$
$678$	0.661262	0.0253956
$679$	2.16358	0.0830308
$680$	1.56333	0.0599508
$681$	6.58905	0.252493
$682$	−6.11845	−0.234288
$683$	−3.97456	−0.152082	−0.0760412	−	0.997105i	$-0.524228\pi$
$683$	−3.97456	−0.152082	−0.0760412	+	0.997105i	$0.524228\pi$
$684$	−3.69491	−0.141279
$685$	−8.51646	−0.325397
$686$	−19.8011	−0.756011
$687$	13.8618	0.528863
$688$	−4.97924	−0.189832
$689$	−5.58096	−0.212617
$690$	−0.813546	−0.0309712
$691$	−37.6284	−1.43145	−0.715725	−	0.698382i	$-0.753904\pi$
$691$	−37.6284	−1.43145	−0.715725	+	0.698382i	$0.753904\pi$
$692$	−11.9212	−0.453178
$693$	5.47719	0.208061
$694$	35.7615	1.35749
$695$	5.78715	0.219519
$696$	0.961428	0.0364428
$697$	12.8935	0.488377
$698$	−0.534690	−0.0202383
$699$	−4.29081	−0.162293
$700$	−9.23434	−0.349025
$701$	26.4628	0.999487	0.499743	−	0.866174i	$-0.333428\pi$
$701$	26.4628	0.999487	0.499743	+	0.866174i	$0.333428\pi$
$702$	−1.00000	−0.0377426
$703$	22.9530	0.865687
$704$	2.85320	0.107534
$705$	2.21581	0.0834524
$706$	−13.3704	−0.503203
$707$	9.31346	0.350269
$708$	14.6828	0.551813
$709$	8.92096	0.335034	0.167517	−	0.985869i	$-0.446425\pi$
$709$	8.92096	0.335034	0.167517	+	0.985869i	$0.446425\pi$
$710$	4.03836	0.151557
$711$	13.2308	0.496195
$712$	2.06273	0.0773040
$713$	4.00645	0.150043
$714$	6.89197	0.257925
$715$	−1.24241	−0.0464634
$716$	23.0540	0.861569
$717$	−15.0455	−0.561885
$718$	−17.8765	−0.667144
$719$	−38.8301	−1.44812	−0.724059	−	0.689738i	$-0.757726\pi$
$719$	−38.8301	−1.44812	−0.724059	+	0.689738i	$0.757726\pi$
$720$	−0.435443	−0.0162280
$721$	−1.91967	−0.0714921
$722$	−5.34761	−0.199017
$723$	−7.07455	−0.263105
$724$	13.6865	0.508655
$725$	4.62484	0.171762
$726$	2.85924	0.106116
$727$	38.0465	1.41107	0.705534	−	0.708676i	$-0.250707\pi$
$727$	38.0465	1.41107	0.705534	+	0.708676i	$0.250707\pi$
$728$	1.91967	0.0711475
$729$	1.00000	0.0370370
$730$	−6.05126	−0.223967
$731$	17.8764	0.661184
$732$	−1.19089	−0.0440167
$733$	−26.2286	−0.968774	−0.484387	−	0.874854i	$-0.660957\pi$
$733$	−26.2286	−0.968774	−0.484387	+	0.874854i	$0.660957\pi$
$734$	−4.27224	−0.157691
$735$	−1.44345	−0.0532423
$736$	−1.86832	−0.0688671
$737$	−33.0530	−1.21752
$738$	−3.59132	−0.132198
$739$	10.5718	0.388891	0.194445	−	0.980913i	$-0.437709\pi$
$739$	10.5718	0.388891	0.194445	+	0.980913i	$0.437709\pi$
$740$	2.70499	0.0994375
$741$	3.69491	0.135736
$742$	−10.7136	−0.393307
$743$	−32.0142	−1.17449	−0.587244	−	0.809410i	$-0.699787\pi$
$743$	−32.0142	−1.17449	−0.587244	+	0.809410i	$0.699787\pi$
$744$	2.14442	0.0786181
$745$	1.06533	0.0390305
$746$	−19.8892	−0.728195
$747$	0.983189	0.0359730
$748$	−10.2435	−0.374541
$749$	−8.82244	−0.322365
$750$	−4.27187	−0.155987
$751$	8.25627	0.301276	0.150638	−	0.988589i	$-0.451867\pi$
$751$	8.25627	0.301276	0.150638	+	0.988589i	$0.451867\pi$
$752$	5.08864	0.185564
$753$	−11.9732	−0.436327
$754$	−0.961428	−0.0350131
$755$	3.83015	0.139393
$756$	−1.91967	−0.0698175
$757$	21.2231	0.771367	0.385683	−	0.922631i	$-0.373966\pi$
$757$	21.2231	0.771367	0.385683	+	0.922631i	$0.373966\pi$
$758$	−20.9693	−0.761641
$759$	5.33068	0.193492
$760$	1.60893	0.0583619
$761$	−23.4698	−0.850781	−0.425390	−	0.905010i	$-0.639863\pi$
$761$	−23.4698	−0.850781	−0.425390	+	0.905010i	$0.639863\pi$
$762$	9.57705	0.346940
$763$	3.40903	0.123415
$764$	−17.6932	−0.640119
$765$	1.56333	0.0565222
$766$	18.4552	0.666815
$767$	−14.6828	−0.530164
$768$	−1.00000	−0.0360844
$769$	12.5262	0.451705	0.225852	−	0.974162i	$-0.427483\pi$
$769$	12.5262	0.451705	0.225852	+	0.974162i	$0.427483\pi$
$770$	−2.38501	−0.0859497
$771$	−25.1051	−0.904138
$772$	−6.71548	−0.241696
$773$	−2.88554	−0.103786	−0.0518928	−	0.998653i	$-0.516525\pi$
$773$	−2.88554	−0.103786	−0.0518928	+	0.998653i	$0.516525\pi$
$774$	−4.97924	−0.178975
$775$	10.3155	0.370543
$776$	1.12706	0.0404592
$777$	11.9250	0.427808
$778$	16.5559	0.593558
$779$	13.2696	0.475433
$780$	0.435443	0.0155914
$781$	−26.4610	−0.946848
$782$	6.70762	0.239864
$783$	0.961428	0.0343586
$784$	−3.31489	−0.118389
$785$	8.32444	0.297112
$786$	−4.59625	−0.163943
$787$	−10.1891	−0.363204	−0.181602	−	0.983372i	$-0.558128\pi$
$787$	−10.1891	−0.363204	−0.181602	+	0.983372i	$0.558128\pi$
$788$	17.1089	0.609480
$789$	17.1415	0.610253
$790$	−5.76128	−0.204977
$791$	−1.26940	−0.0451347
$792$	2.85320	0.101384
$793$	1.19089	0.0422899
$794$	5.58308	0.198136
$795$	−2.43019	−0.0861900
$796$	21.9091	0.776548
$797$	−46.9047	−1.66145	−0.830725	−	0.556683i	$-0.812074\pi$
$797$	−46.9047	−1.66145	−0.830725	+	0.556683i	$0.812074\pi$
$798$	7.09300	0.251089
$799$	−18.2692	−0.646318
$800$	−4.81039	−0.170073
$801$	2.06273	0.0728829
$802$	12.2927	0.434070
$803$	39.6503	1.39923
$804$	11.5845	0.408554
$805$	1.56174	0.0550440
$806$	−2.14442	−0.0755338
$807$	−23.0381	−0.810979
$808$	4.85161	0.170679
$809$	−17.3103	−0.608598	−0.304299	−	0.952577i	$-0.598422\pi$
$809$	−17.3103	−0.608598	−0.304299	+	0.952577i	$0.598422\pi$
$810$	−0.435443	−0.0152999
$811$	38.4439	1.34995	0.674974	−	0.737842i	$-0.264155\pi$
$811$	38.4439	1.34995	0.674974	+	0.737842i	$0.264155\pi$
$812$	−1.84562	−0.0647685
$813$	−18.8576	−0.661365
$814$	−17.7242	−0.621233
$815$	−8.71052	−0.305116
$816$	3.59019	0.125682
$817$	18.3979	0.643660
$818$	−9.85431	−0.344548
$819$	1.91967	0.0670785
$820$	1.56382	0.0546108
$821$	−1.88080	−0.0656402	−0.0328201	−	0.999461i	$-0.510449\pi$
$821$	−1.88080	−0.0656402	−0.0328201	+	0.999461i	$0.510449\pi$
$822$	−19.5581	−0.682168
$823$	−1.76910	−0.0616668	−0.0308334	−	0.999525i	$-0.509816\pi$
$823$	−1.76910	−0.0616668	−0.0308334	+	0.999525i	$0.509816\pi$
$824$	−1.00000	−0.0348367
$825$	13.7250	0.477843
$826$	−28.1860	−0.980717
$827$	19.9243	0.692836	0.346418	−	0.938080i	$-0.387398\pi$
$827$	19.9243	0.692836	0.346418	+	0.938080i	$0.387398\pi$
$828$	−1.86832	−0.0649285
$829$	12.7098	0.441431	0.220716	−	0.975338i	$-0.429161\pi$
$829$	12.7098	0.441431	0.220716	+	0.975338i	$0.429161\pi$
$830$	−0.428123	−0.0148604
$831$	22.6360	0.785235
$832$	1.00000	0.0346688
$833$	11.9011	0.412348
$834$	13.2902	0.460204
$835$	4.27694	0.148010
$836$	−10.5423	−0.364614
$837$	2.14442	0.0741218
$838$	25.1699	0.869478
$839$	19.3957	0.669616	0.334808	−	0.942286i	$-0.391329\pi$
$839$	19.3957	0.669616	0.334808	+	0.942286i	$0.391329\pi$
$840$	0.835905	0.0288415
$841$	−28.0757	−0.968126
$842$	−39.2159	−1.35147
$843$	28.6570	0.987000
$844$	−25.4887	−0.877357
$845$	−0.435443	−0.0149797
$846$	5.08864	0.174951
$847$	−5.48878	−0.188597
$848$	−5.58096	−0.191651
$849$	−28.3194	−0.971921
$850$	17.2702	0.592364
$851$	11.6061	0.397851
$852$	9.27413	0.317726
$853$	−37.8794	−1.29697	−0.648483	−	0.761229i	$-0.724596\pi$
$853$	−37.8794	−1.29697	−0.648483	+	0.761229i	$0.724596\pi$
$854$	2.28612	0.0782294
$855$	1.60893	0.0550241
$856$	−4.59582	−0.157082
$857$	6.83432	0.233456	0.116728	−	0.993164i	$-0.462759\pi$
$857$	6.83432	0.233456	0.116728	+	0.993164i	$0.462759\pi$
$858$	−2.85320	−0.0974067
$859$	−43.8794	−1.49714	−0.748572	−	0.663053i	$-0.769260\pi$
$859$	−43.8794	−1.49714	−0.748572	+	0.663053i	$0.769260\pi$
$860$	2.16818	0.0739343
$861$	6.89413	0.234951
$862$	−3.65383	−0.124450
$863$	21.4793	0.731164	0.365582	−	0.930779i	$-0.380870\pi$
$863$	21.4793	0.731164	0.365582	+	0.930779i	$0.380870\pi$
$864$	−1.00000	−0.0340207
$865$	5.19102	0.176500
$866$	−39.2104	−1.33242
$867$	4.11051	0.139600
$868$	−4.11656	−0.139725
$869$	37.7503	1.28059
$870$	−0.418647	−0.0141935
$871$	−11.5845	−0.392526
$872$	1.77584	0.0601377
$873$	1.12706	0.0381453
$874$	6.90327	0.233507
$875$	8.20056	0.277229
$876$	−13.8968	−0.469528
$877$	37.0928	1.25253	0.626267	−	0.779608i	$-0.284582\pi$
$877$	37.0928	1.25253	0.626267	+	0.779608i	$0.284582\pi$
$878$	−34.3154	−1.15809
$879$	11.5696	0.390231
$880$	−1.24241	−0.0418816
$881$	41.9391	1.41297	0.706483	−	0.707730i	$-0.250281\pi$
$881$	41.9391	1.41297	0.706483	+	0.707730i	$0.250281\pi$
$882$	−3.31489	−0.111618
$883$	28.6777	0.965080	0.482540	−	0.875874i	$-0.339714\pi$
$883$	28.6777	0.965080	0.482540	+	0.875874i	$0.339714\pi$
$884$	−3.59019	−0.120751
$885$	−6.39352	−0.214916
$886$	−17.8103	−0.598348
$887$	38.1841	1.28210	0.641048	−	0.767501i	$-0.278500\pi$
$887$	38.1841	1.28210	0.641048	+	0.767501i	$0.278500\pi$
$888$	6.21204	0.208462
$889$	−18.3847	−0.616604
$890$	−0.898201	−0.0301078
$891$	2.85320	0.0955858
$892$	−6.37624	−0.213492
$893$	−18.8021	−0.629188
$894$	2.44653	0.0818242
$895$	−10.0387	−0.335557
$896$	1.91967	0.0641315
$897$	1.86832	0.0623813
$898$	12.0579	0.402377
$899$	2.06170	0.0687616
$900$	−4.81039	−0.160346
$901$	20.0367	0.667520
$902$	−10.2468	−0.341180
$903$	9.55848	0.318086
$904$	−0.661262	−0.0219932
$905$	−5.95969	−0.198107
$906$	8.79598	0.292227
$907$	−58.2817	−1.93521	−0.967606	−	0.252465i	$-0.918759\pi$
$907$	−58.2817	−1.93521	−0.967606	+	0.252465i	$0.918759\pi$
$908$	−6.58905	−0.218665
$909$	4.85161	0.160918
$910$	−0.835905	−0.0277100
$911$	−25.6731	−0.850587	−0.425294	−	0.905055i	$-0.639829\pi$
$911$	−25.6731	−0.850587	−0.425294	+	0.905055i	$0.639829\pi$
$912$	3.69491	0.122351
$913$	2.80524	0.0928398
$914$	−14.5303	−0.480618
$915$	0.518567	0.0171433
$916$	−13.8618	−0.458008
$917$	8.82326	0.291370
$918$	3.59019	0.118494
$919$	32.4735	1.07120	0.535601	−	0.844471i	$-0.320085\pi$
$919$	32.4735	1.07120	0.535601	+	0.844471i	$0.320085\pi$
$920$	0.813546	0.0268218
$921$	2.02100	0.0665943
$922$	−7.55984	−0.248970
$923$	−9.27413	−0.305262
$924$	−5.47719	−0.180186
$925$	29.8823	0.982525
$926$	26.5738	0.873269
$927$	−1.00000	−0.0328443
$928$	−0.961428	−0.0315604
$929$	8.12505	0.266574	0.133287	−	0.991077i	$-0.457447\pi$
$929$	8.12505	0.266574	0.133287	+	0.991077i	$0.457447\pi$
$930$	−0.933772	−0.0306196
$931$	12.2482	0.401419
$932$	4.29081	0.140550
$933$	20.8655	0.683107
$934$	−1.01733	−0.0332882
$935$	4.46048	0.145873
$936$	1.00000	0.0326860
$937$	53.0163	1.73197	0.865984	−	0.500071i	$-0.166693\pi$
$937$	53.0163	1.73197	0.865984	+	0.500071i	$0.166693\pi$
$938$	−22.2384	−0.726109
$939$	−11.7502	−0.383452
$940$	−2.21581	−0.0722719
$941$	−6.22348	−0.202880	−0.101440	−	0.994842i	$-0.532345\pi$
$941$	−6.22348	−0.202880	−0.101440	+	0.994842i	$0.532345\pi$
$942$	19.1172	0.622871
$943$	6.70972	0.218499
$944$	−14.6828	−0.477884
$945$	0.835905	0.0271920
$946$	−14.2068	−0.461903
$947$	−41.1840	−1.33830	−0.669149	−	0.743128i	$-0.733341\pi$
$947$	−41.1840	−1.33830	−0.669149	+	0.743128i	$0.733341\pi$
$948$	−13.2308	−0.429718
$949$	13.8968	0.451108
$950$	17.7740	0.576664
$951$	24.1089	0.781785
$952$	−6.89197	−0.223370
$953$	33.1197	1.07285	0.536426	−	0.843947i	$-0.319774\pi$
$953$	33.1197	1.07285	0.536426	+	0.843947i	$0.319774\pi$
$954$	−5.58096	−0.180690
$955$	7.70441	0.249309
$956$	15.0455	0.486607
$957$	2.74315	0.0886734
$958$	14.8403	0.479469
$959$	37.5451	1.21239
$960$	0.435443	0.0140539
$961$	−26.4015	−0.851661
$962$	−6.21204	−0.200284
$963$	−4.59582	−0.148098
$964$	7.07455	0.227856
$965$	2.92421	0.0941337
$966$	3.58654	0.115395
$967$	39.4750	1.26943	0.634715	−	0.772746i	$-0.281117\pi$
$967$	39.4750	1.26943	0.634715	+	0.772746i	$0.281117\pi$
$968$	−2.85924	−0.0918995
$969$	−13.2655	−0.426148
$970$	−0.490772	−0.0157578
$971$	4.12552	0.132394	0.0661971	−	0.997807i	$-0.478913\pi$
$971$	4.12552	0.132394	0.0661971	+	0.997807i	$0.478913\pi$
$972$	−1.00000	−0.0320750
$973$	−25.5128	−0.817904
$974$	−11.0288	−0.353385
$975$	4.81039	0.154056
$976$	1.19089	0.0381196
$977$	−53.1614	−1.70079	−0.850393	−	0.526149i	$-0.823636\pi$
$977$	−53.1614	−1.70079	−0.850393	+	0.526149i	$0.823636\pi$
$978$	−20.0038	−0.639651
$979$	5.88538	0.188098
$980$	1.44345	0.0461092
$981$	1.77584	0.0566984
$982$	20.0599	0.640136
$983$	−29.2183	−0.931919	−0.465960	−	0.884806i	$-0.654291\pi$
$983$	−29.2183	−0.931919	−0.465960	+	0.884806i	$0.654291\pi$
$984$	3.59132	0.114487
$985$	−7.44996	−0.237376
$986$	3.45171	0.109925
$987$	−9.76848	−0.310934
$988$	−3.69491	−0.117551
$989$	9.30281	0.295812
$990$	−1.24241	−0.0394863
$991$	−8.64776	−0.274705	−0.137353	−	0.990522i	$-0.543859\pi$
$991$	−8.64776	−0.274705	−0.137353	+	0.990522i	$0.543859\pi$
$992$	−2.14442	−0.0680853
$993$	9.55801	0.303314
$994$	−17.8032	−0.564684
$995$	−9.54019	−0.302444
$996$	−0.983189	−0.0311535
$997$	45.4141	1.43828	0.719140	−	0.694865i	$-0.244536\pi$
$997$	45.4141	1.43828	0.719140	+	0.694865i	$0.244536\pi$
$998$	7.16865	0.226920
$999$	6.21204	0.196540

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.r.1.5	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.r.1.5	✓	9	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.435443 q^{5} -1.00000 q^{6} +1.91967 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.435443 q^{5} -1.00000 q^{6} +1.91967 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.435443 q^{10} +2.85320 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.91967 q^{14} +0.435443 q^{15} +1.00000 q^{16} -3.59019 q^{17} +1.00000 q^{18} -3.69491 q^{19} -0.435443 q^{20} -1.91967 q^{21} +2.85320 q^{22} -1.86832 q^{23} -1.00000 q^{24} -4.81039 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.91967 q^{28} -0.961428 q^{29} +0.435443 q^{30} -2.14442 q^{31} +1.00000 q^{32} -2.85320 q^{33} -3.59019 q^{34} -0.835905 q^{35} +1.00000 q^{36} -6.21204 q^{37} -3.69491 q^{38} -1.00000 q^{39} -0.435443 q^{40} -3.59132 q^{41} -1.91967 q^{42} -4.97924 q^{43} +2.85320 q^{44} -0.435443 q^{45} -1.86832 q^{46} +5.08864 q^{47} -1.00000 q^{48} -3.31489 q^{49} -4.81039 q^{50} +3.59019 q^{51} +1.00000 q^{52} -5.58096 q^{53} -1.00000 q^{54} -1.24241 q^{55} +1.91967 q^{56} +3.69491 q^{57} -0.961428 q^{58} -14.6828 q^{59} +0.435443 q^{60} +1.19089 q^{61} -2.14442 q^{62} +1.91967 q^{63} +1.00000 q^{64} -0.435443 q^{65} -2.85320 q^{66} -11.5845 q^{67} -3.59019 q^{68} +1.86832 q^{69} -0.835905 q^{70} -9.27413 q^{71} +1.00000 q^{72} +13.8968 q^{73} -6.21204 q^{74} +4.81039 q^{75} -3.69491 q^{76} +5.47719 q^{77} -1.00000 q^{78} +13.2308 q^{79} -0.435443 q^{80} +1.00000 q^{81} -3.59132 q^{82} +0.983189 q^{83} -1.91967 q^{84} +1.56333 q^{85} -4.97924 q^{86} +0.961428 q^{87} +2.85320 q^{88} +2.06273 q^{89} -0.435443 q^{90} +1.91967 q^{91} -1.86832 q^{92} +2.14442 q^{93} +5.08864 q^{94} +1.60893 q^{95} -1.00000 q^{96} +1.12706 q^{97} -3.31489 q^{98} +2.85320 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} - 4 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 5 q^{11} - 9 q^{12} + 9 q^{13} - 4 q^{14} + 4 q^{15} + 9 q^{16} - 6 q^{17} + 9 q^{18} - 4 q^{19} - 4 q^{20} + 4 q^{21} - 5 q^{22} - 6 q^{23} - 9 q^{24} - 11 q^{25} + 9 q^{26} - 9 q^{27} - 4 q^{28} - 19 q^{29} + 4 q^{30} - 6 q^{31} + 9 q^{32} + 5 q^{33} - 6 q^{34} + 10 q^{35} + 9 q^{36} - 13 q^{37} - 4 q^{38} - 9 q^{39} - 4 q^{40} - 18 q^{41} + 4 q^{42} - 20 q^{43} - 5 q^{44} - 4 q^{45} - 6 q^{46} + 14 q^{47} - 9 q^{48} - 3 q^{49} - 11 q^{50} + 6 q^{51} + 9 q^{52} - 3 q^{53} - 9 q^{54} - 4 q^{55} - 4 q^{56} + 4 q^{57} - 19 q^{58} - 9 q^{59} + 4 q^{60} - 24 q^{61} - 6 q^{62} - 4 q^{63} + 9 q^{64} - 4 q^{65} + 5 q^{66} - 4 q^{67} - 6 q^{68} + 6 q^{69} + 10 q^{70} - 9 q^{71} + 9 q^{72} - 24 q^{73} - 13 q^{74} + 11 q^{75} - 4 q^{76} + 3 q^{77} - 9 q^{78} - 15 q^{79} - 4 q^{80} + 9 q^{81} - 18 q^{82} + 20 q^{83} + 4 q^{84} - 31 q^{85} - 20 q^{86} + 19 q^{87} - 5 q^{88} + 3 q^{89} - 4 q^{90} - 4 q^{91} - 6 q^{92} + 6 q^{93} + 14 q^{94} - 4 q^{95} - 9 q^{96} - 19 q^{97} - 3 q^{98} - 5 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 - 4 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 5 * q^11 - 9 * q^12 + 9 * q^13 - 4 * q^14 + 4 * q^15 + 9 * q^16 - 6 * q^17 + 9 * q^18 - 4 * q^19 - 4 * q^20 + 4 * q^21 - 5 * q^22 - 6 * q^23 - 9 * q^24 - 11 * q^25 + 9 * q^26 - 9 * q^27 - 4 * q^28 - 19 * q^29 + 4 * q^30 - 6 * q^31 + 9 * q^32 + 5 * q^33 - 6 * q^34 + 10 * q^35 + 9 * q^36 - 13 * q^37 - 4 * q^38 - 9 * q^39 - 4 * q^40 - 18 * q^41 + 4 * q^42 - 20 * q^43 - 5 * q^44 - 4 * q^45 - 6 * q^46 + 14 * q^47 - 9 * q^48 - 3 * q^49 - 11 * q^50 + 6 * q^51 + 9 * q^52 - 3 * q^53 - 9 * q^54 - 4 * q^55 - 4 * q^56 + 4 * q^57 - 19 * q^58 - 9 * q^59 + 4 * q^60 - 24 * q^61 - 6 * q^62 - 4 * q^63 + 9 * q^64 - 4 * q^65 + 5 * q^66 - 4 * q^67 - 6 * q^68 + 6 * q^69 + 10 * q^70 - 9 * q^71 + 9 * q^72 - 24 * q^73 - 13 * q^74 + 11 * q^75 - 4 * q^76 + 3 * q^77 - 9 * q^78 - 15 * q^79 - 4 * q^80 + 9 * q^81 - 18 * q^82 + 20 * q^83 + 4 * q^84 - 31 * q^85 - 20 * q^86 + 19 * q^87 - 5 * q^88 + 3 * q^89 - 4 * q^90 - 4 * q^91 - 6 * q^92 + 6 * q^93 + 14 * q^94 - 4 * q^95 - 9 * q^96 - 19 * q^97 - 3 * q^98 - 5 * q^99

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