LMFDB - Embedded newform 8034.2.a.u.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 18x^{9} + 64x^{8} + 85x^{7} - 249x^{6} - 109x^{5} + 230x^{4} + 97x^{3} - 53x^{2} - 32x - 4 $ x^11 - 4x^10 - 18x^9 + 64x^8 + 85x^7 - 249x^6 - 109x^5 + 230x^4 + 97x^3 - 53x^2 - 32x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-2.14636$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.41909 q^{5} -1.00000 q^{6} -0.663444 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.41909 q^{5} -1.00000 q^{6} -0.663444 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.41909 q^{10} +2.84618 q^{11} -1.00000 q^{12} -1.00000 q^{13} -0.663444 q^{14} -1.41909 q^{15} +1.00000 q^{16} +0.681547 q^{17} +1.00000 q^{18} +0.731632 q^{19} +1.41909 q^{20} +0.663444 q^{21} +2.84618 q^{22} -4.77050 q^{23} -1.00000 q^{24} -2.98619 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.663444 q^{28} -7.26722 q^{29} -1.41909 q^{30} -8.39326 q^{31} +1.00000 q^{32} -2.84618 q^{33} +0.681547 q^{34} -0.941485 q^{35} +1.00000 q^{36} -1.15896 q^{37} +0.731632 q^{38} +1.00000 q^{39} +1.41909 q^{40} -5.26351 q^{41} +0.663444 q^{42} -9.83608 q^{43} +2.84618 q^{44} +1.41909 q^{45} -4.77050 q^{46} +2.71118 q^{47} -1.00000 q^{48} -6.55984 q^{49} -2.98619 q^{50} -0.681547 q^{51} -1.00000 q^{52} +0.417418 q^{53} -1.00000 q^{54} +4.03897 q^{55} -0.663444 q^{56} -0.731632 q^{57} -7.26722 q^{58} -9.24350 q^{59} -1.41909 q^{60} +13.8272 q^{61} -8.39326 q^{62} -0.663444 q^{63} +1.00000 q^{64} -1.41909 q^{65} -2.84618 q^{66} +12.7544 q^{67} +0.681547 q^{68} +4.77050 q^{69} -0.941485 q^{70} -10.6711 q^{71} +1.00000 q^{72} -16.0490 q^{73} -1.15896 q^{74} +2.98619 q^{75} +0.731632 q^{76} -1.88828 q^{77} +1.00000 q^{78} +5.68580 q^{79} +1.41909 q^{80} +1.00000 q^{81} -5.26351 q^{82} -2.69083 q^{83} +0.663444 q^{84} +0.967175 q^{85} -9.83608 q^{86} +7.26722 q^{87} +2.84618 q^{88} +5.07803 q^{89} +1.41909 q^{90} +0.663444 q^{91} -4.77050 q^{92} +8.39326 q^{93} +2.71118 q^{94} +1.03825 q^{95} -1.00000 q^{96} -3.23767 q^{97} -6.55984 q^{98} +2.84618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.41909	0.634635	0.317317	−	0.948319i	$-0.397218\pi$
$5$	1.41909	0.634635	0.317317	+	0.948319i	$0.397218\pi$
$6$	−1.00000	−0.408248
$7$	−0.663444	−0.250758	−0.125379	−	0.992109i	$-0.540015\pi$
$7$	−0.663444	−0.250758	−0.125379	+	0.992109i	$0.540015\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.41909	0.448755
$11$	2.84618	0.858154	0.429077	−	0.903268i	$-0.358839\pi$
$11$	2.84618	0.858154	0.429077	+	0.903268i	$0.358839\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.663444	−0.177313
$15$	−1.41909	−0.366407
$16$	1.00000	0.250000
$17$	0.681547	0.165300	0.0826498	−	0.996579i	$-0.473662\pi$
$17$	0.681547	0.165300	0.0826498	+	0.996579i	$0.473662\pi$
$18$	1.00000	0.235702
$19$	0.731632	0.167848	0.0839240	−	0.996472i	$-0.473255\pi$
$19$	0.731632	0.167848	0.0839240	+	0.996472i	$0.473255\pi$
$20$	1.41909	0.317317
$21$	0.663444	0.144775
$22$	2.84618	0.606807
$23$	−4.77050	−0.994717	−0.497359	−	0.867545i	$-0.665697\pi$
$23$	−4.77050	−0.994717	−0.497359	+	0.867545i	$0.665697\pi$
$24$	−1.00000	−0.204124
$25$	−2.98619	−0.597239
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−0.663444	−0.125379
$29$	−7.26722	−1.34949	−0.674745	−	0.738051i	$-0.735746\pi$
$29$	−7.26722	−1.34949	−0.674745	+	0.738051i	$0.735746\pi$
$30$	−1.41909	−0.259089
$31$	−8.39326	−1.50747	−0.753737	−	0.657176i	$-0.771751\pi$
$31$	−8.39326	−1.50747	−0.753737	+	0.657176i	$0.771751\pi$
$32$	1.00000	0.176777
$33$	−2.84618	−0.495456
$34$	0.681547	0.116884
$35$	−0.941485	−0.159140
$36$	1.00000	0.166667
$37$	−1.15896	−0.190532	−0.0952658	−	0.995452i	$-0.530370\pi$
$37$	−1.15896	−0.190532	−0.0952658	+	0.995452i	$0.530370\pi$
$38$	0.731632	0.118686
$39$	1.00000	0.160128
$40$	1.41909	0.224377
$41$	−5.26351	−0.822023	−0.411011	−	0.911630i	$-0.634824\pi$
$41$	−5.26351	−0.822023	−0.411011	+	0.911630i	$0.634824\pi$
$42$	0.663444	0.102372
$43$	−9.83608	−1.49999	−0.749994	−	0.661444i	$-0.769944\pi$
$43$	−9.83608	−1.49999	−0.749994	+	0.661444i	$0.769944\pi$
$44$	2.84618	0.429077
$45$	1.41909	0.211545
$46$	−4.77050	−0.703371
$47$	2.71118	0.395467	0.197733	−	0.980256i	$-0.436642\pi$
$47$	2.71118	0.395467	0.197733	+	0.980256i	$0.436642\pi$
$48$	−1.00000	−0.144338
$49$	−6.55984	−0.937120
$50$	−2.98619	−0.422311
$51$	−0.681547	−0.0954357
$52$	−1.00000	−0.138675
$53$	0.417418	0.0573368	0.0286684	−	0.999589i	$-0.490873\pi$
$53$	0.417418	0.0573368	0.0286684	+	0.999589i	$0.490873\pi$
$54$	−1.00000	−0.136083
$55$	4.03897	0.544615
$56$	−0.663444	−0.0886565
$57$	−0.731632	−0.0969071
$58$	−7.26722	−0.954233
$59$	−9.24350	−1.20340	−0.601701	−	0.798722i	$-0.705510\pi$
$59$	−9.24350	−1.20340	−0.601701	+	0.798722i	$0.705510\pi$
$60$	−1.41909	−0.183203
$61$	13.8272	1.77039	0.885197	−	0.465217i	$-0.154024\pi$
$61$	13.8272	1.77039	0.885197	+	0.465217i	$0.154024\pi$
$62$	−8.39326	−1.06595
$63$	−0.663444	−0.0835861
$64$	1.00000	0.125000
$65$	−1.41909	−0.176016
$66$	−2.84618	−0.350340
$67$	12.7544	1.55819	0.779097	−	0.626904i	$-0.215678\pi$
$67$	12.7544	1.55819	0.779097	+	0.626904i	$0.215678\pi$
$68$	0.681547	0.0826498
$69$	4.77050	0.574300
$70$	−0.941485	−0.112529
$71$	−10.6711	−1.26642	−0.633211	−	0.773979i	$-0.718263\pi$
$71$	−10.6711	−1.26642	−0.633211	+	0.773979i	$0.718263\pi$
$72$	1.00000	0.117851
$73$	−16.0490	−1.87840	−0.939199	−	0.343374i	$-0.888430\pi$
$73$	−16.0490	−1.87840	−0.939199	+	0.343374i	$0.888430\pi$
$74$	−1.15896	−0.134726
$75$	2.98619	0.344816
$76$	0.731632	0.0839240
$77$	−1.88828	−0.215189
$78$	1.00000	0.113228
$79$	5.68580	0.639702	0.319851	−	0.947468i	$-0.396367\pi$
$79$	5.68580	0.639702	0.319851	+	0.947468i	$0.396367\pi$
$80$	1.41909	0.158659
$81$	1.00000	0.111111
$82$	−5.26351	−0.581258
$83$	−2.69083	−0.295357	−0.147679	−	0.989035i	$-0.547180\pi$
$83$	−2.69083	−0.295357	−0.147679	+	0.989035i	$0.547180\pi$
$84$	0.663444	0.0723877
$85$	0.967175	0.104905
$86$	−9.83608	−1.06065
$87$	7.26722	0.779128
$88$	2.84618	0.303403
$89$	5.07803	0.538271	0.269135	−	0.963102i	$-0.413262\pi$
$89$	5.07803	0.538271	0.269135	+	0.963102i	$0.413262\pi$
$90$	1.41909	0.149585
$91$	0.663444	0.0695479
$92$	−4.77050	−0.497359
$93$	8.39326	0.870341
$94$	2.71118	0.279637
$95$	1.03825	0.106522
$96$	−1.00000	−0.102062
$97$	−3.23767	−0.328736	−0.164368	−	0.986399i	$-0.552558\pi$
$97$	−3.23767	−0.328736	−0.164368	+	0.986399i	$0.552558\pi$
$98$	−6.55984	−0.662644
$99$	2.84618	0.286051
$100$	−2.98619	−0.298619
$101$	−8.57871	−0.853614	−0.426807	−	0.904343i	$-0.640362\pi$
$101$	−8.57871	−0.853614	−0.426807	+	0.904343i	$0.640362\pi$
$102$	−0.681547	−0.0674832
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	0.941485	0.0918795
$106$	0.417418	0.0405432
$107$	13.3773	1.29323	0.646614	−	0.762818i	$-0.276185\pi$
$107$	13.3773	1.29323	0.646614	+	0.762818i	$0.276185\pi$
$108$	−1.00000	−0.0962250
$109$	11.7111	1.12172	0.560861	−	0.827910i	$-0.310470\pi$
$109$	11.7111	1.12172	0.560861	+	0.827910i	$0.310470\pi$
$110$	4.03897	0.385101
$111$	1.15896	0.110003
$112$	−0.663444	−0.0626896
$113$	−12.3676	−1.16345	−0.581723	−	0.813387i	$-0.697621\pi$
$113$	−12.3676	−1.16345	−0.581723	+	0.813387i	$0.697621\pi$
$114$	−0.731632	−0.0685236
$115$	−6.76975	−0.631282
$116$	−7.26722	−0.674745
$117$	−1.00000	−0.0924500
$118$	−9.24350	−0.850933
$119$	−0.452169	−0.0414503
$120$	−1.41909	−0.129544
$121$	−2.89928	−0.263571
$122$	13.8272	1.25186
$123$	5.26351	0.474595
$124$	−8.39326	−0.753737
$125$	−11.3331	−1.01366
$126$	−0.663444	−0.0591043
$127$	5.46760	0.485171	0.242585	−	0.970130i	$-0.422005\pi$
$127$	5.46760	0.485171	0.242585	+	0.970130i	$0.422005\pi$
$128$	1.00000	0.0883883
$129$	9.83608	0.866019
$130$	−1.41909	−0.124462
$131$	20.9694	1.83211	0.916054	−	0.401055i	$-0.131356\pi$
$131$	20.9694	1.83211	0.916054	+	0.401055i	$0.131356\pi$
$132$	−2.84618	−0.247728
$133$	−0.485397	−0.0420893
$134$	12.7544	1.10181
$135$	−1.41909	−0.122136
$136$	0.681547	0.0584422
$137$	2.91313	0.248886	0.124443	−	0.992227i	$-0.460286\pi$
$137$	2.91313	0.248886	0.124443	+	0.992227i	$0.460286\pi$
$138$	4.77050	0.406092
$139$	5.52313	0.468466	0.234233	−	0.972181i	$-0.424742\pi$
$139$	5.52313	0.468466	0.234233	+	0.972181i	$0.424742\pi$
$140$	−0.941485	−0.0795700
$141$	−2.71118	−0.228323
$142$	−10.6711	−0.895495
$143$	−2.84618	−0.238009
$144$	1.00000	0.0833333
$145$	−10.3128	−0.856433
$146$	−16.0490	−1.32823
$147$	6.55984	0.541047
$148$	−1.15896	−0.0952658
$149$	4.68049	0.383441	0.191720	−	0.981450i	$-0.438593\pi$
$149$	4.68049	0.383441	0.191720	+	0.981450i	$0.438593\pi$
$150$	2.98619	0.243822
$151$	−7.12915	−0.580162	−0.290081	−	0.957002i	$-0.593682\pi$
$151$	−7.12915	−0.580162	−0.290081	+	0.957002i	$0.593682\pi$
$152$	0.731632	0.0593432
$153$	0.681547	0.0550998
$154$	−1.88828	−0.152162
$155$	−11.9108	−0.956696
$156$	1.00000	0.0800641
$157$	−6.15568	−0.491276	−0.245638	−	0.969362i	$-0.578998\pi$
$157$	−6.15568	−0.491276	−0.245638	+	0.969362i	$0.578998\pi$
$158$	5.68580	0.452338
$159$	−0.417418	−0.0331034
$160$	1.41909	0.112189
$161$	3.16496	0.249434
$162$	1.00000	0.0785674
$163$	4.24155	0.332224	0.166112	−	0.986107i	$-0.446879\pi$
$163$	4.24155	0.332224	0.166112	+	0.986107i	$0.446879\pi$
$164$	−5.26351	−0.411011
$165$	−4.03897	−0.314433
$166$	−2.69083	−0.208849
$167$	16.9619	1.31255	0.656277	−	0.754520i	$-0.272130\pi$
$167$	16.9619	1.31255	0.656277	+	0.754520i	$0.272130\pi$
$168$	0.663444	0.0511859
$169$	1.00000	0.0769231
$170$	0.967175	0.0741789
$171$	0.731632	0.0559493
$172$	−9.83608	−0.749994
$173$	−0.757763	−0.0576117	−0.0288058	−	0.999585i	$-0.509170\pi$
$173$	−0.757763	−0.0576117	−0.0288058	+	0.999585i	$0.509170\pi$
$174$	7.26722	0.550927
$175$	1.98117	0.149763
$176$	2.84618	0.214539
$177$	9.24350	0.694784
$178$	5.07803	0.380615
$179$	−13.6119	−1.01740	−0.508701	−	0.860943i	$-0.669874\pi$
$179$	−13.6119	−1.01740	−0.508701	+	0.860943i	$0.669874\pi$
$180$	1.41909	0.105772
$181$	0.502488	0.0373496	0.0186748	−	0.999826i	$-0.494055\pi$
$181$	0.502488	0.0373496	0.0186748	+	0.999826i	$0.494055\pi$
$182$	0.663444	0.0491778
$183$	−13.8272	−1.02214
$184$	−4.77050	−0.351686
$185$	−1.64466	−0.120918
$186$	8.39326	0.615424
$187$	1.93980	0.141852
$188$	2.71118	0.197733
$189$	0.663444	0.0482585
$190$	1.03825	0.0753225
$191$	−14.6616	−1.06088	−0.530439	−	0.847723i	$-0.677973\pi$
$191$	−14.6616	−1.06088	−0.530439	+	0.847723i	$0.677973\pi$
$192$	−1.00000	−0.0721688
$193$	−5.11853	−0.368440	−0.184220	−	0.982885i	$-0.558976\pi$
$193$	−5.11853	−0.368440	−0.184220	+	0.982885i	$0.558976\pi$
$194$	−3.23767	−0.232451
$195$	1.41909	0.101623
$196$	−6.55984	−0.468560
$197$	−14.7666	−1.05208	−0.526039	−	0.850460i	$-0.676324\pi$
$197$	−14.7666	−1.05208	−0.526039	+	0.850460i	$0.676324\pi$
$198$	2.84618	0.202269
$199$	12.1403	0.860605	0.430302	−	0.902685i	$-0.358407\pi$
$199$	12.1403	0.860605	0.430302	+	0.902685i	$0.358407\pi$
$200$	−2.98619	−0.211156
$201$	−12.7544	−0.899623
$202$	−8.57871	−0.603596
$203$	4.82140	0.338396
$204$	−0.681547	−0.0477179
$205$	−7.46938	−0.521684
$206$	1.00000	0.0696733
$207$	−4.77050	−0.331572
$208$	−1.00000	−0.0693375
$209$	2.08235	0.144039
$210$	0.941485	0.0649686
$211$	−6.35426	−0.437446	−0.218723	−	0.975787i	$-0.570189\pi$
$211$	−6.35426	−0.437446	−0.218723	+	0.975787i	$0.570189\pi$
$212$	0.417418	0.0286684
$213$	10.6711	0.731169
$214$	13.3773	0.914450
$215$	−13.9583	−0.951945
$216$	−1.00000	−0.0680414
$217$	5.56846	0.378012
$218$	11.7111	0.793177
$219$	16.0490	1.08449
$220$	4.03897	0.272307
$221$	−0.681547	−0.0458458
$222$	1.15896	0.0777842
$223$	−5.39336	−0.361166	−0.180583	−	0.983560i	$-0.557798\pi$
$223$	−5.39336	−0.361166	−0.180583	+	0.983560i	$0.557798\pi$
$224$	−0.663444	−0.0443282
$225$	−2.98619	−0.199080
$226$	−12.3676	−0.822681
$227$	23.4618	1.55722	0.778608	−	0.627511i	$-0.215926\pi$
$227$	23.4618	1.55722	0.778608	+	0.627511i	$0.215926\pi$
$228$	−0.731632	−0.0484535
$229$	−27.7556	−1.83414	−0.917069	−	0.398728i	$-0.869452\pi$
$229$	−27.7556	−1.83414	−0.917069	+	0.398728i	$0.869452\pi$
$230$	−6.76975	−0.446384
$231$	1.88828	0.124240
$232$	−7.26722	−0.477116
$233$	18.4178	1.20659	0.603294	−	0.797519i	$-0.293855\pi$
$233$	18.4178	1.20659	0.603294	+	0.797519i	$0.293855\pi$
$234$	−1.00000	−0.0653720
$235$	3.84740	0.250977
$236$	−9.24350	−0.601701
$237$	−5.68580	−0.369332
$238$	−0.452169	−0.0293098
$239$	−28.7478	−1.85954	−0.929769	−	0.368143i	$-0.879994\pi$
$239$	−28.7478	−1.85954	−0.929769	+	0.368143i	$0.879994\pi$
$240$	−1.41909	−0.0916016
$241$	15.7695	1.01580	0.507901	−	0.861415i	$-0.330422\pi$
$241$	15.7695	1.01580	0.507901	+	0.861415i	$0.330422\pi$
$242$	−2.89928	−0.186373
$243$	−1.00000	−0.0641500
$244$	13.8272	0.885197
$245$	−9.30898	−0.594729
$246$	5.26351	0.335589
$247$	−0.731632	−0.0465526
$248$	−8.39326	−0.532973
$249$	2.69083	0.170524
$250$	−11.3331	−0.716768
$251$	−14.7783	−0.932801	−0.466400	−	0.884574i	$-0.654449\pi$
$251$	−14.7783	−0.932801	−0.466400	+	0.884574i	$0.654449\pi$
$252$	−0.663444	−0.0417931
$253$	−13.5777	−0.853621
$254$	5.46760	0.343067
$255$	−0.967175	−0.0605668
$256$	1.00000	0.0625000
$257$	−8.94211	−0.557793	−0.278897	−	0.960321i	$-0.589969\pi$
$257$	−8.94211	−0.557793	−0.278897	+	0.960321i	$0.589969\pi$
$258$	9.83608	0.612368
$259$	0.768905	0.0477774
$260$	−1.41909	−0.0880080
$261$	−7.26722	−0.449830
$262$	20.9694	1.29550
$263$	−22.5134	−1.38823	−0.694117	−	0.719863i	$-0.744205\pi$
$263$	−22.5134	−1.38823	−0.694117	+	0.719863i	$0.744205\pi$
$264$	−2.84618	−0.175170
$265$	0.592352	0.0363879
$266$	−0.485397	−0.0297616
$267$	−5.07803	−0.310771
$268$	12.7544	0.779097
$269$	−23.4591	−1.43033	−0.715164	−	0.698957i	$-0.753648\pi$
$269$	−23.4591	−1.43033	−0.715164	+	0.698957i	$0.753648\pi$
$270$	−1.41909	−0.0863629
$271$	−3.57638	−0.217249	−0.108625	−	0.994083i	$-0.534645\pi$
$271$	−3.57638	−0.217249	−0.108625	+	0.994083i	$0.534645\pi$
$272$	0.681547	0.0413249
$273$	−0.663444	−0.0401535
$274$	2.91313	0.175989
$275$	−8.49923	−0.512523
$276$	4.77050	0.287150
$277$	31.1353	1.87074	0.935369	−	0.353672i	$-0.115067\pi$
$277$	31.1353	1.87074	0.935369	+	0.353672i	$0.115067\pi$
$278$	5.52313	0.331255
$279$	−8.39326	−0.502492
$280$	−0.941485	−0.0562645
$281$	7.88815	0.470568	0.235284	−	0.971927i	$-0.424398\pi$
$281$	7.88815	0.470568	0.235284	+	0.971927i	$0.424398\pi$
$282$	−2.71118	−0.161449
$283$	−16.4691	−0.978988	−0.489494	−	0.872007i	$-0.662819\pi$
$283$	−16.4691	−0.978988	−0.489494	+	0.872007i	$0.662819\pi$
$284$	−10.6711	−0.633211
$285$	−1.03825	−0.0615006
$286$	−2.84618	−0.168298
$287$	3.49205	0.206129
$288$	1.00000	0.0589256
$289$	−16.5355	−0.972676
$290$	−10.3128	−0.605589
$291$	3.23767	0.189796
$292$	−16.0490	−0.939199
$293$	9.65149	0.563846	0.281923	−	0.959437i	$-0.409028\pi$
$293$	9.65149	0.563846	0.281923	+	0.959437i	$0.409028\pi$
$294$	6.55984	0.382578
$295$	−13.1173	−0.763721
$296$	−1.15896	−0.0673631
$297$	−2.84618	−0.165152
$298$	4.68049	0.271133
$299$	4.77050	0.275885
$300$	2.98619	0.172408
$301$	6.52570	0.376135
$302$	−7.12915	−0.410237
$303$	8.57871	0.492834
$304$	0.731632	0.0419620
$305$	19.6220	1.12355
$306$	0.681547	0.0389615
$307$	3.30746	0.188767	0.0943833	−	0.995536i	$-0.469912\pi$
$307$	3.30746	0.188767	0.0943833	+	0.995536i	$0.469912\pi$
$308$	−1.88828	−0.107595
$309$	−1.00000	−0.0568880
$310$	−11.9108	−0.676486
$311$	−22.2595	−1.26222	−0.631111	−	0.775692i	$-0.717401\pi$
$311$	−22.2595	−1.26222	−0.631111	+	0.775692i	$0.717401\pi$
$312$	1.00000	0.0566139
$313$	3.47768	0.196570	0.0982851	−	0.995158i	$-0.468664\pi$
$313$	3.47768	0.196570	0.0982851	+	0.995158i	$0.468664\pi$
$314$	−6.15568	−0.347385
$315$	−0.941485	−0.0530467
$316$	5.68580	0.319851
$317$	−0.951562	−0.0534450	−0.0267225	−	0.999643i	$-0.508507\pi$
$317$	−0.951562	−0.0534450	−0.0267225	+	0.999643i	$0.508507\pi$
$318$	−0.417418	−0.0234076
$319$	−20.6838	−1.15807
$320$	1.41909	0.0793294
$321$	−13.3773	−0.746645
$322$	3.16496	0.176376
$323$	0.498642	0.0277452
$324$	1.00000	0.0555556
$325$	2.98619	0.165644
$326$	4.24155	0.234918
$327$	−11.7111	−0.647627
$328$	−5.26351	−0.290629
$329$	−1.79872	−0.0991666
$330$	−4.03897	−0.222338
$331$	32.1899	1.76932	0.884658	−	0.466241i	$-0.154392\pi$
$331$	32.1899	1.76932	0.884658	+	0.466241i	$0.154392\pi$
$332$	−2.69083	−0.147679
$333$	−1.15896	−0.0635105
$334$	16.9619	0.928115
$335$	18.0995	0.988884
$336$	0.663444	0.0361939
$337$	−33.1545	−1.80604	−0.903022	−	0.429595i	$-0.858656\pi$
$337$	−33.1545	−1.80604	−0.903022	+	0.429595i	$0.858656\pi$
$338$	1.00000	0.0543928
$339$	12.3676	0.671716
$340$	0.967175	0.0524524
$341$	−23.8887	−1.29365
$342$	0.731632	0.0395621
$343$	8.99620	0.485749
$344$	−9.83608	−0.530326
$345$	6.76975	0.364471
$346$	−0.757763	−0.0407376
$347$	−0.149929	−0.00804859	−0.00402430	−	0.999992i	$-0.501281\pi$
$347$	−0.149929	−0.00804859	−0.00402430	+	0.999992i	$0.501281\pi$
$348$	7.26722	0.389564
$349$	17.7769	0.951574	0.475787	−	0.879561i	$-0.342163\pi$
$349$	17.7769	0.951574	0.475787	+	0.879561i	$0.342163\pi$
$350$	1.98117	0.105898
$351$	1.00000	0.0533761
$352$	2.84618	0.151702
$353$	−28.9840	−1.54266	−0.771332	−	0.636433i	$-0.780409\pi$
$353$	−28.9840	−1.54266	−0.771332	+	0.636433i	$0.780409\pi$
$354$	9.24350	0.491287
$355$	−15.1432	−0.803715
$356$	5.07803	0.269135
$357$	0.452169	0.0239313
$358$	−13.6119	−0.719412
$359$	23.8241	1.25739	0.628693	−	0.777654i	$-0.283590\pi$
$359$	23.8241	1.25739	0.628693	+	0.777654i	$0.283590\pi$
$360$	1.41909	0.0747924
$361$	−18.4647	−0.971827
$362$	0.502488	0.0264102
$363$	2.89928	0.152173
$364$	0.663444	0.0347739
$365$	−22.7750	−1.19210
$366$	−13.8272	−0.722760
$367$	13.6338	0.711681	0.355840	−	0.934547i	$-0.384195\pi$
$367$	13.6338	0.711681	0.355840	+	0.934547i	$0.384195\pi$
$368$	−4.77050	−0.248679
$369$	−5.26351	−0.274008
$370$	−1.64466	−0.0855019
$371$	−0.276934	−0.0143777
$372$	8.39326	0.435170
$373$	16.3499	0.846564	0.423282	−	0.905998i	$-0.360878\pi$
$373$	16.3499	0.846564	0.423282	+	0.905998i	$0.360878\pi$
$374$	1.93980	0.100305
$375$	11.3331	0.585239
$376$	2.71118	0.139819
$377$	7.26722	0.374281
$378$	0.663444	0.0341239
$379$	19.5810	1.00581	0.502904	−	0.864342i	$-0.332265\pi$
$379$	19.5810	1.00581	0.502904	+	0.864342i	$0.332265\pi$
$380$	1.03825	0.0532611
$381$	−5.46760	−0.280113
$382$	−14.6616	−0.750154
$383$	6.08494	0.310926	0.155463	−	0.987842i	$-0.450313\pi$
$383$	6.08494	0.310926	0.155463	+	0.987842i	$0.450313\pi$
$384$	−1.00000	−0.0510310
$385$	−2.67963	−0.136567
$386$	−5.11853	−0.260526
$387$	−9.83608	−0.499996
$388$	−3.23767	−0.164368
$389$	38.4852	1.95127	0.975637	−	0.219389i	$-0.0704065\pi$
$389$	38.4852	1.95127	0.975637	+	0.219389i	$0.0704065\pi$
$390$	1.41909	0.0718582
$391$	−3.25132	−0.164426
$392$	−6.55984	−0.331322
$393$	−20.9694	−1.05777
$394$	−14.7666	−0.743932
$395$	8.06864	0.405977
$396$	2.84618	0.143026
$397$	−16.9039	−0.848384	−0.424192	−	0.905572i	$-0.639442\pi$
$397$	−16.9039	−0.848384	−0.424192	+	0.905572i	$0.639442\pi$
$398$	12.1403	0.608540
$399$	0.485397	0.0243003
$400$	−2.98619	−0.149310
$401$	7.47454	0.373260	0.186630	−	0.982430i	$-0.440243\pi$
$401$	7.47454	0.373260	0.186630	+	0.982430i	$0.440243\pi$
$402$	−12.7544	−0.636130
$403$	8.39326	0.418098
$404$	−8.57871	−0.426807
$405$	1.41909	0.0705150
$406$	4.82140	0.239282
$407$	−3.29860	−0.163505
$408$	−0.681547	−0.0337416
$409$	20.6003	1.01862	0.509309	−	0.860584i	$-0.329901\pi$
$409$	20.6003	1.01862	0.509309	+	0.860584i	$0.329901\pi$
$410$	−7.46938	−0.368886
$411$	−2.91313	−0.143694
$412$	1.00000	0.0492665
$413$	6.13255	0.301763
$414$	−4.77050	−0.234457
$415$	−3.81852	−0.187444
$416$	−1.00000	−0.0490290
$417$	−5.52313	−0.270469
$418$	2.08235	0.101851
$419$	−13.3982	−0.654546	−0.327273	−	0.944930i	$-0.606130\pi$
$419$	−13.3982	−0.654546	−0.327273	+	0.944930i	$0.606130\pi$
$420$	0.941485	0.0459398
$421$	−15.9984	−0.779715	−0.389858	−	0.920875i	$-0.627476\pi$
$421$	−15.9984	−0.779715	−0.389858	+	0.920875i	$0.627476\pi$
$422$	−6.35426	−0.309321
$423$	2.71118	0.131822
$424$	0.417418	0.0202716
$425$	−2.03523	−0.0987233
$426$	10.6711	0.517014
$427$	−9.17359	−0.443941
$428$	13.3773	0.646614
$429$	2.84618	0.137415
$430$	−13.9583	−0.673127
$431$	32.5389	1.56734	0.783672	−	0.621175i	$-0.213344\pi$
$431$	32.5389	1.56734	0.783672	+	0.621175i	$0.213344\pi$
$432$	−1.00000	−0.0481125
$433$	−7.10913	−0.341643	−0.170821	−	0.985302i	$-0.554642\pi$
$433$	−7.10913	−0.341643	−0.170821	+	0.985302i	$0.554642\pi$
$434$	5.56846	0.267295
$435$	10.3128	0.494462
$436$	11.7111	0.560861
$437$	−3.49025	−0.166961
$438$	16.0490	0.766853
$439$	−21.8721	−1.04390	−0.521950	−	0.852976i	$-0.674795\pi$
$439$	−21.8721	−1.04390	−0.521950	+	0.852976i	$0.674795\pi$
$440$	4.03897	0.192550
$441$	−6.55984	−0.312373
$442$	−0.681547	−0.0324179
$443$	36.1719	1.71858	0.859289	−	0.511491i	$-0.170907\pi$
$443$	36.1719	1.71858	0.859289	+	0.511491i	$0.170907\pi$
$444$	1.15896	0.0550017
$445$	7.20617	0.341605
$446$	−5.39336	−0.255383
$447$	−4.68049	−0.221380
$448$	−0.663444	−0.0313448
$449$	18.7947	0.886975	0.443488	−	0.896280i	$-0.353741\pi$
$449$	18.7947	0.886975	0.443488	+	0.896280i	$0.353741\pi$
$450$	−2.98619	−0.140770
$451$	−14.9809	−0.705422
$452$	−12.3676	−0.581723
$453$	7.12915	0.334957
$454$	23.4618	1.10112
$455$	0.941485	0.0441375
$456$	−0.731632	−0.0342618
$457$	−13.1669	−0.615920	−0.307960	−	0.951399i	$-0.599646\pi$
$457$	−13.1669	−0.615920	−0.307960	+	0.951399i	$0.599646\pi$
$458$	−27.7556	−1.29693
$459$	−0.681547	−0.0318119
$460$	−6.76975	−0.315641
$461$	12.1988	0.568155	0.284077	−	0.958801i	$-0.408313\pi$
$461$	12.1988	0.568155	0.284077	+	0.958801i	$0.408313\pi$
$462$	1.88828	0.0878507
$463$	−13.6491	−0.634326	−0.317163	−	0.948371i	$-0.602730\pi$
$463$	−13.6491	−0.634326	−0.317163	+	0.948371i	$0.602730\pi$
$464$	−7.26722	−0.337372
$465$	11.9108	0.552349
$466$	18.4178	0.853187
$467$	−24.7567	−1.14560	−0.572801	−	0.819694i	$-0.694143\pi$
$467$	−24.7567	−1.14560	−0.572801	+	0.819694i	$0.694143\pi$
$468$	−1.00000	−0.0462250
$469$	−8.46181	−0.390730
$470$	3.84740	0.177467
$471$	6.15568	0.283639
$472$	−9.24350	−0.425467
$473$	−27.9952	−1.28722
$474$	−5.68580	−0.261157
$475$	−2.18480	−0.100245
$476$	−0.452169	−0.0207251
$477$	0.417418	0.0191123
$478$	−28.7478	−1.31489
$479$	29.3848	1.34263	0.671313	−	0.741174i	$-0.265731\pi$
$479$	29.3848	1.34263	0.671313	+	0.741174i	$0.265731\pi$
$480$	−1.41909	−0.0647721
$481$	1.15896	0.0528440
$482$	15.7695	0.718281
$483$	−3.16496	−0.144011
$484$	−2.89928	−0.131786
$485$	−4.59454	−0.208627
$486$	−1.00000	−0.0453609
$487$	39.0027	1.76738	0.883691	−	0.468072i	$-0.155051\pi$
$487$	39.0027	1.76738	0.883691	+	0.468072i	$0.155051\pi$
$488$	13.8272	0.625929
$489$	−4.24155	−0.191809
$490$	−9.30898	−0.420537
$491$	−0.488438	−0.0220429	−0.0110214	−	0.999939i	$-0.503508\pi$
$491$	−0.488438	−0.0220429	−0.0110214	+	0.999939i	$0.503508\pi$
$492$	5.26351	0.237298
$493$	−4.95296	−0.223070
$494$	−0.731632	−0.0329177
$495$	4.03897	0.181538
$496$	−8.39326	−0.376869
$497$	7.07965	0.317566
$498$	2.69083	0.120579
$499$	−43.5949	−1.95158	−0.975788	−	0.218720i	$-0.929812\pi$
$499$	−43.5949	−1.95158	−0.975788	+	0.218720i	$0.929812\pi$
$500$	−11.3331	−0.506832
$501$	−16.9619	−0.757803
$502$	−14.7783	−0.659590
$503$	−6.13022	−0.273333	−0.136666	−	0.990617i	$-0.543639\pi$
$503$	−6.13022	−0.273333	−0.136666	+	0.990617i	$0.543639\pi$
$504$	−0.663444	−0.0295522
$505$	−12.1739	−0.541733
$506$	−13.5777	−0.603601
$507$	−1.00000	−0.0444116
$508$	5.46760	0.242585
$509$	25.6267	1.13588	0.567942	−	0.823068i	$-0.307740\pi$
$509$	25.6267	1.13588	0.567942	+	0.823068i	$0.307740\pi$
$510$	−0.967175	−0.0428272
$511$	10.6476	0.471024
$512$	1.00000	0.0441942
$513$	−0.731632	−0.0323024
$514$	−8.94211	−0.394420
$515$	1.41909	0.0625324
$516$	9.83608	0.433009
$517$	7.71650	0.339371
$518$	0.768905	0.0337837
$519$	0.757763	0.0332621
$520$	−1.41909	−0.0622311
$521$	0.419142	0.0183629	0.00918147	−	0.999958i	$-0.497077\pi$
$521$	0.419142	0.0183629	0.00918147	+	0.999958i	$0.497077\pi$
$522$	−7.26722	−0.318078
$523$	33.6778	1.47263	0.736314	−	0.676640i	$-0.236565\pi$
$523$	33.6778	1.47263	0.736314	+	0.676640i	$0.236565\pi$
$524$	20.9694	0.916054
$525$	−1.98117	−0.0864655
$526$	−22.5134	−0.981629
$527$	−5.72041	−0.249185
$528$	−2.84618	−0.123864
$529$	−0.242359	−0.0105374
$530$	0.592352	0.0257301
$531$	−9.24350	−0.401134
$532$	−0.485397	−0.0210446
$533$	5.26351	0.227988
$534$	−5.07803	−0.219748
$535$	18.9835	0.820727
$536$	12.7544	0.550904
$537$	13.6119	0.587397
$538$	−23.4591	−1.01139
$539$	−18.6705	−0.804194
$540$	−1.41909	−0.0610678
$541$	21.1858	0.910849	0.455425	−	0.890274i	$-0.349487\pi$
$541$	21.1858	0.910849	0.455425	+	0.890274i	$0.349487\pi$
$542$	−3.57638	−0.153619
$543$	−0.502488	−0.0215638
$544$	0.681547	0.0292211
$545$	16.6191	0.711884
$546$	−0.663444	−0.0283928
$547$	−28.8386	−1.23305	−0.616525	−	0.787335i	$-0.711460\pi$
$547$	−28.8386	−1.23305	−0.616525	+	0.787335i	$0.711460\pi$
$548$	2.91313	0.124443
$549$	13.8272	0.590131
$550$	−8.49923	−0.362408
$551$	−5.31693	−0.226509
$552$	4.77050	0.203046
$553$	−3.77221	−0.160411
$554$	31.1353	1.32281
$555$	1.64466	0.0698120
$556$	5.52313	0.234233
$557$	−34.0041	−1.44080	−0.720399	−	0.693560i	$-0.756041\pi$
$557$	−34.0041	−1.44080	−0.720399	+	0.693560i	$0.756041\pi$
$558$	−8.39326	−0.355315
$559$	9.83608	0.416022
$560$	−0.941485	−0.0397850
$561$	−1.93980	−0.0818986
$562$	7.88815	0.332742
$563$	13.5761	0.572165	0.286083	−	0.958205i	$-0.407647\pi$
$563$	13.5761	0.572165	0.286083	+	0.958205i	$0.407647\pi$
$564$	−2.71118	−0.114161
$565$	−17.5507	−0.738364
$566$	−16.4691	−0.692249
$567$	−0.663444	−0.0278620
$568$	−10.6711	−0.447748
$569$	−12.5370	−0.525579	−0.262789	−	0.964853i	$-0.584642\pi$
$569$	−12.5370	−0.525579	−0.262789	+	0.964853i	$0.584642\pi$
$570$	−1.03825	−0.0434875
$571$	11.8625	0.496432	0.248216	−	0.968705i	$-0.420156\pi$
$571$	11.8625	0.496432	0.248216	+	0.968705i	$0.420156\pi$
$572$	−2.84618	−0.119005
$573$	14.6616	0.612498
$574$	3.49205	0.145755
$575$	14.2456	0.594084
$576$	1.00000	0.0416667
$577$	−16.3051	−0.678790	−0.339395	−	0.940644i	$-0.610222\pi$
$577$	−16.3051	−0.678790	−0.339395	+	0.940644i	$0.610222\pi$
$578$	−16.5355	−0.687786
$579$	5.11853	0.212719
$580$	−10.3128	−0.428216
$581$	1.78522	0.0740633
$582$	3.23767	0.134206
$583$	1.18805	0.0492038
$584$	−16.0490	−0.664114
$585$	−1.41909	−0.0586720
$586$	9.65149	0.398699
$587$	29.4027	1.21358	0.606789	−	0.794863i	$-0.292457\pi$
$587$	29.4027	1.21358	0.606789	+	0.794863i	$0.292457\pi$
$588$	6.55984	0.270523
$589$	−6.14078	−0.253027
$590$	−13.1173	−0.540032
$591$	14.7666	0.607418
$592$	−1.15896	−0.0476329
$593$	39.2504	1.61182	0.805911	−	0.592036i	$-0.201676\pi$
$593$	39.2504	1.61182	0.805911	+	0.592036i	$0.201676\pi$
$594$	−2.84618	−0.116780
$595$	−0.641667	−0.0263058
$596$	4.68049	0.191720
$597$	−12.1403	−0.496870
$598$	4.77050	0.195080
$599$	−35.5418	−1.45220	−0.726100	−	0.687589i	$-0.758669\pi$
$599$	−35.5418	−1.45220	−0.726100	+	0.687589i	$0.758669\pi$
$600$	2.98619	0.121911
$601$	−24.0793	−0.982217	−0.491108	−	0.871098i	$-0.663408\pi$
$601$	−24.0793	−0.982217	−0.491108	+	0.871098i	$0.663408\pi$
$602$	6.52570	0.265968
$603$	12.7544	0.519398
$604$	−7.12915	−0.290081
$605$	−4.11433	−0.167271
$606$	8.57871	0.348486
$607$	12.4356	0.504746	0.252373	−	0.967630i	$-0.418789\pi$
$607$	12.4356	0.504746	0.252373	+	0.967630i	$0.418789\pi$
$608$	0.731632	0.0296716
$609$	−4.82140	−0.195373
$610$	19.6220	0.794472
$611$	−2.71118	−0.109683
$612$	0.681547	0.0275499
$613$	−30.9741	−1.25103	−0.625515	−	0.780212i	$-0.715111\pi$
$613$	−30.9741	−1.25103	−0.625515	+	0.780212i	$0.715111\pi$
$614$	3.30746	0.133478
$615$	7.46938	0.301195
$616$	−1.88828	−0.0760809
$617$	−49.4754	−1.99180	−0.995902	−	0.0904339i	$-0.971175\pi$
$617$	−49.4754	−1.99180	−0.995902	+	0.0904339i	$0.971175\pi$
$618$	−1.00000	−0.0402259
$619$	−33.6218	−1.35137	−0.675687	−	0.737189i	$-0.736153\pi$
$619$	−33.6218	−1.35137	−0.675687	+	0.737189i	$0.736153\pi$
$620$	−11.9108	−0.478348
$621$	4.77050	0.191433
$622$	−22.2595	−0.892526
$623$	−3.36899	−0.134976
$624$	1.00000	0.0400320
$625$	−1.15168	−0.0460674
$626$	3.47768	0.138996
$627$	−2.08235	−0.0831612
$628$	−6.15568	−0.245638
$629$	−0.789885	−0.0314948
$630$	−0.941485	−0.0375097
$631$	−42.2140	−1.68051	−0.840257	−	0.542189i	$-0.817596\pi$
$631$	−42.2140	−1.68051	−0.840257	+	0.542189i	$0.817596\pi$
$632$	5.68580	0.226169
$633$	6.35426	0.252559
$634$	−0.951562	−0.0377913
$635$	7.75899	0.307906
$636$	−0.417418	−0.0165517
$637$	6.55984	0.259910
$638$	−20.6838	−0.818879
$639$	−10.6711	−0.422141
$640$	1.41909	0.0560943
$641$	−42.0429	−1.66059	−0.830297	−	0.557321i	$-0.811829\pi$
$641$	−42.0429	−1.66059	−0.830297	+	0.557321i	$0.811829\pi$
$642$	−13.3773	−0.527958
$643$	−47.5818	−1.87644	−0.938221	−	0.346038i	$-0.887527\pi$
$643$	−47.5818	−1.87644	−0.938221	+	0.346038i	$0.887527\pi$
$644$	3.16496	0.124717
$645$	13.9583	0.549606
$646$	0.498642	0.0196188
$647$	14.5102	0.570454	0.285227	−	0.958460i	$-0.407931\pi$
$647$	14.5102	0.570454	0.285227	+	0.958460i	$0.407931\pi$
$648$	1.00000	0.0392837
$649$	−26.3086	−1.03270
$650$	2.98619	0.117128
$651$	−5.56846	−0.218245
$652$	4.24155	0.166112
$653$	13.9062	0.544191	0.272095	−	0.962270i	$-0.412283\pi$
$653$	13.9062	0.544191	0.272095	+	0.962270i	$0.412283\pi$
$654$	−11.7111	−0.457941
$655$	29.7574	1.16272
$656$	−5.26351	−0.205506
$657$	−16.0490	−0.626133
$658$	−1.79872	−0.0701214
$659$	−0.146787	−0.00571801	−0.00285900	−	0.999996i	$-0.500910\pi$
$659$	−0.146787	−0.00571801	−0.00285900	+	0.999996i	$0.500910\pi$
$660$	−4.03897	−0.157217
$661$	−6.92396	−0.269311	−0.134655	−	0.990892i	$-0.542993\pi$
$661$	−6.92396	−0.269311	−0.134655	+	0.990892i	$0.542993\pi$
$662$	32.1899	1.25110
$663$	0.681547	0.0264691
$664$	−2.69083	−0.104424
$665$	−0.688821	−0.0267113
$666$	−1.15896	−0.0449087
$667$	34.6683	1.34236
$668$	16.9619	0.656277
$669$	5.39336	0.208519
$670$	18.0995	0.699246
$671$	39.3547	1.51927
$672$	0.663444	0.0255929
$673$	−41.2148	−1.58871	−0.794357	−	0.607451i	$-0.792192\pi$
$673$	−41.2148	−1.58871	−0.794357	+	0.607451i	$0.792192\pi$
$674$	−33.1545	−1.27707
$675$	2.98619	0.114939
$676$	1.00000	0.0384615
$677$	11.1025	0.426705	0.213352	−	0.976975i	$-0.431562\pi$
$677$	11.1025	0.426705	0.213352	+	0.976975i	$0.431562\pi$
$678$	12.3676	0.474975
$679$	2.14802	0.0824333
$680$	0.967175	0.0370895
$681$	−23.4618	−0.899059
$682$	−23.8887	−0.914746
$683$	−9.03475	−0.345705	−0.172853	−	0.984948i	$-0.555298\pi$
$683$	−9.03475	−0.345705	−0.172853	+	0.984948i	$0.555298\pi$
$684$	0.731632	0.0279747
$685$	4.13399	0.157951
$686$	8.99620	0.343477
$687$	27.7556	1.05894
$688$	−9.83608	−0.374997
$689$	−0.417418	−0.0159024
$690$	6.76975	0.257720
$691$	−2.77354	−0.105511	−0.0527553	−	0.998607i	$-0.516800\pi$
$691$	−2.77354	−0.105511	−0.0527553	+	0.998607i	$0.516800\pi$
$692$	−0.757763	−0.0288058
$693$	−1.88828	−0.0717298
$694$	−0.149929	−0.00569121
$695$	7.83780	0.297305
$696$	7.26722	0.275463
$697$	−3.58733	−0.135880
$698$	17.7769	0.672864
$699$	−18.4178	−0.696624
$700$	1.98117	0.0748813
$701$	−14.1849	−0.535757	−0.267879	−	0.963453i	$-0.586323\pi$
$701$	−14.1849	−0.535757	−0.267879	+	0.963453i	$0.586323\pi$
$702$	1.00000	0.0377426
$703$	−0.847931	−0.0319803
$704$	2.84618	0.107269
$705$	−3.84740	−0.144902
$706$	−28.9840	−1.09083
$707$	5.69150	0.214051
$708$	9.24350	0.347392
$709$	−39.8532	−1.49672	−0.748360	−	0.663293i	$-0.769158\pi$
$709$	−39.8532	−1.49672	−0.748360	+	0.663293i	$0.769158\pi$
$710$	−15.1432	−0.568313
$711$	5.68580	0.213234
$712$	5.07803	0.190307
$713$	40.0400	1.49951
$714$	0.452169	0.0169220
$715$	−4.03897	−0.151049
$716$	−13.6119	−0.508701
$717$	28.7478	1.07360
$718$	23.8241	0.889106
$719$	−15.4983	−0.577989	−0.288994	−	0.957331i	$-0.593321\pi$
$719$	−15.4983	−0.577989	−0.288994	+	0.957331i	$0.593321\pi$
$720$	1.41909	0.0528862
$721$	−0.663444	−0.0247080
$722$	−18.4647	−0.687186
$723$	−15.7695	−0.586474
$724$	0.502488	0.0186748
$725$	21.7013	0.805967
$726$	2.89928	0.107603
$727$	38.5482	1.42967	0.714837	−	0.699292i	$-0.246501\pi$
$727$	38.5482	1.42967	0.714837	+	0.699292i	$0.246501\pi$
$728$	0.663444	0.0245889
$729$	1.00000	0.0370370
$730$	−22.7750	−0.842940
$731$	−6.70376	−0.247947
$732$	−13.8272	−0.511069
$733$	8.09704	0.299071	0.149535	−	0.988756i	$-0.452222\pi$
$733$	8.09704	0.299071	0.149535	+	0.988756i	$0.452222\pi$
$734$	13.6338	0.503234
$735$	9.30898	0.343367
$736$	−4.77050	−0.175843
$737$	36.3012	1.33717
$738$	−5.26351	−0.193753
$739$	45.6712	1.68004	0.840022	−	0.542552i	$-0.182542\pi$
$739$	45.6712	1.68004	0.840022	+	0.542552i	$0.182542\pi$
$740$	−1.64466	−0.0604590
$741$	0.731632	0.0268772
$742$	−0.276934	−0.0101666
$743$	25.4855	0.934972	0.467486	−	0.884000i	$-0.345160\pi$
$743$	25.4855	0.934972	0.467486	+	0.884000i	$0.345160\pi$
$744$	8.39326	0.307712
$745$	6.64202	0.243345
$746$	16.3499	0.598611
$747$	−2.69083	−0.0984523
$748$	1.93980	0.0709262
$749$	−8.87506	−0.324288
$750$	11.3331	0.413826
$751$	44.8041	1.63493	0.817463	−	0.575981i	$-0.195380\pi$
$751$	44.8041	1.63493	0.817463	+	0.575981i	$0.195380\pi$
$752$	2.71118	0.0988666
$753$	14.7783	0.538553
$754$	7.26722	0.264657
$755$	−10.1169	−0.368191
$756$	0.663444	0.0241292
$757$	23.8420	0.866552	0.433276	−	0.901261i	$-0.357358\pi$
$757$	23.8420	0.866552	0.433276	+	0.901261i	$0.357358\pi$
$758$	19.5810	0.711214
$759$	13.5777	0.492838
$760$	1.03825	0.0376613
$761$	35.3504	1.28145	0.640726	−	0.767770i	$-0.278634\pi$
$761$	35.3504	1.28145	0.640726	+	0.767770i	$0.278634\pi$
$762$	−5.46760	−0.198070
$763$	−7.76968	−0.281281
$764$	−14.6616	−0.530439
$765$	0.967175	0.0349683
$766$	6.08494	0.219858
$767$	9.24350	0.333764
$768$	−1.00000	−0.0360844
$769$	26.0952	0.941016	0.470508	−	0.882396i	$-0.344071\pi$
$769$	26.0952	0.941016	0.470508	+	0.882396i	$0.344071\pi$
$770$	−2.67963	−0.0965672
$771$	8.94211	0.322042
$772$	−5.11853	−0.184220
$773$	−11.1103	−0.399610	−0.199805	−	0.979836i	$-0.564031\pi$
$773$	−11.1103	−0.399610	−0.199805	+	0.979836i	$0.564031\pi$
$774$	−9.83608	−0.353551
$775$	25.0639	0.900322
$776$	−3.23767	−0.116226
$777$	−0.768905	−0.0275843
$778$	38.4852	1.37976
$779$	−3.85096	−0.137975
$780$	1.41909	0.0508115
$781$	−30.3717	−1.08679
$782$	−3.25132	−0.116267
$783$	7.26722	0.259709
$784$	−6.55984	−0.234280
$785$	−8.73544	−0.311781
$786$	−20.9694	−0.747955
$787$	−24.1979	−0.862564	−0.431282	−	0.902217i	$-0.641939\pi$
$787$	−24.1979	−0.862564	−0.431282	+	0.902217i	$0.641939\pi$
$788$	−14.7666	−0.526039
$789$	22.5134	0.801497
$790$	8.06864	0.287069
$791$	8.20522	0.291744
$792$	2.84618	0.101134
$793$	−13.8272	−0.491019
$794$	−16.9039	−0.599898
$795$	−0.592352	−0.0210086
$796$	12.1403	0.430302
$797$	8.15513	0.288869	0.144435	−	0.989514i	$-0.453864\pi$
$797$	8.15513	0.288869	0.144435	+	0.989514i	$0.453864\pi$
$798$	0.485397	0.0171829
$799$	1.84780	0.0653704
$800$	−2.98619	−0.105578
$801$	5.07803	0.179424
$802$	7.47454	0.263935
$803$	−45.6784	−1.61196
$804$	−12.7544	−0.449812
$805$	4.49135	0.158299
$806$	8.39326	0.295640
$807$	23.4591	0.825800
$808$	−8.57871	−0.301798
$809$	−30.4770	−1.07152	−0.535758	−	0.844372i	$-0.679974\pi$
$809$	−30.4770	−1.07152	−0.535758	+	0.844372i	$0.679974\pi$
$810$	1.41909	0.0498616
$811$	−11.2851	−0.396272	−0.198136	−	0.980174i	$-0.563489\pi$
$811$	−11.2851	−0.396272	−0.198136	+	0.980174i	$0.563489\pi$
$812$	4.82140	0.169198
$813$	3.57638	0.125429
$814$	−3.29860	−0.115616
$815$	6.01912	0.210841
$816$	−0.681547	−0.0238589
$817$	−7.19640	−0.251770
$818$	20.6003	0.720271
$819$	0.663444	0.0231826
$820$	−7.46938	−0.260842
$821$	−2.29477	−0.0800879	−0.0400439	−	0.999198i	$-0.512750\pi$
$821$	−2.29477	−0.0800879	−0.0400439	+	0.999198i	$0.512750\pi$
$822$	−2.91313	−0.101607
$823$	30.7765	1.07280	0.536401	−	0.843963i	$-0.319784\pi$
$823$	30.7765	1.07280	0.536401	+	0.843963i	$0.319784\pi$
$824$	1.00000	0.0348367
$825$	8.49923	0.295905
$826$	6.13255	0.213379
$827$	−40.1467	−1.39604	−0.698019	−	0.716079i	$-0.745935\pi$
$827$	−40.1467	−1.39604	−0.698019	+	0.716079i	$0.745935\pi$
$828$	−4.77050	−0.165786
$829$	8.47614	0.294388	0.147194	−	0.989108i	$-0.452976\pi$
$829$	8.47614	0.294388	0.147194	+	0.989108i	$0.452976\pi$
$830$	−3.81852	−0.132543
$831$	−31.1353	−1.08007
$832$	−1.00000	−0.0346688
$833$	−4.47084	−0.154906
$834$	−5.52313	−0.191250
$835$	24.0704	0.832992
$836$	2.08235	0.0720197
$837$	8.39326	0.290114
$838$	−13.3982	−0.462834
$839$	13.7357	0.474208	0.237104	−	0.971484i	$-0.423802\pi$
$839$	13.7357	0.474208	0.237104	+	0.971484i	$0.423802\pi$
$840$	0.941485	0.0324843
$841$	23.8125	0.821121
$842$	−15.9984	−0.551342
$843$	−7.88815	−0.271682
$844$	−6.35426	−0.218723
$845$	1.41909	0.0488181
$846$	2.71118	0.0932124
$847$	1.92351	0.0660927
$848$	0.417418	0.0143342
$849$	16.4691	0.565219
$850$	−2.03523	−0.0698079
$851$	5.52881	0.189525
$852$	10.6711	0.365584
$853$	10.1241	0.346644	0.173322	−	0.984865i	$-0.444550\pi$
$853$	10.1241	0.346644	0.173322	+	0.984865i	$0.444550\pi$
$854$	−9.17359	−0.313914
$855$	1.03825	0.0355074
$856$	13.3773	0.457225
$857$	−22.7162	−0.775969	−0.387985	−	0.921666i	$-0.626829\pi$
$857$	−22.7162	−0.775969	−0.387985	+	0.921666i	$0.626829\pi$
$858$	2.84618	0.0971668
$859$	11.3582	0.387538	0.193769	−	0.981047i	$-0.437929\pi$
$859$	11.3582	0.387538	0.193769	+	0.981047i	$0.437929\pi$
$860$	−13.9583	−0.475973
$861$	−3.49205	−0.119009
$862$	32.5389	1.10828
$863$	−30.3938	−1.03462	−0.517308	−	0.855799i	$-0.673066\pi$
$863$	−30.3938	−1.03462	−0.517308	+	0.855799i	$0.673066\pi$
$864$	−1.00000	−0.0340207
$865$	−1.07533	−0.0365624
$866$	−7.10913	−0.241578
$867$	16.5355	0.561575
$868$	5.56846	0.189006
$869$	16.1828	0.548963
$870$	10.3128	0.349637
$871$	−12.7544	−0.432165
$872$	11.7111	0.396589
$873$	−3.23767	−0.109579
$874$	−3.49025	−0.118059
$875$	7.51888	0.254185
$876$	16.0490	0.542247
$877$	39.2790	1.32636	0.663179	−	0.748461i	$-0.269207\pi$
$877$	39.2790	1.32636	0.663179	+	0.748461i	$0.269207\pi$
$878$	−21.8721	−0.738148
$879$	−9.65149	−0.325537
$880$	4.03897	0.136154
$881$	−9.24308	−0.311407	−0.155704	−	0.987804i	$-0.549764\pi$
$881$	−9.24308	−0.311407	−0.155704	+	0.987804i	$0.549764\pi$
$882$	−6.55984	−0.220881
$883$	17.4183	0.586174	0.293087	−	0.956086i	$-0.405317\pi$
$883$	17.4183	0.586174	0.293087	+	0.956086i	$0.405317\pi$
$884$	−0.681547	−0.0229229
$885$	13.1173	0.440934
$886$	36.1719	1.21522
$887$	20.8660	0.700613	0.350306	−	0.936635i	$-0.386077\pi$
$887$	20.8660	0.700613	0.350306	+	0.936635i	$0.386077\pi$
$888$	1.15896	0.0388921
$889$	−3.62745	−0.121661
$890$	7.20617	0.241551
$891$	2.84618	0.0953505
$892$	−5.39336	−0.180583
$893$	1.98359	0.0663783
$894$	−4.68049	−0.156539
$895$	−19.3165	−0.645679
$896$	−0.663444	−0.0221641
$897$	−4.77050	−0.159282
$898$	18.7947	0.627186
$899$	60.9957	2.03432
$900$	−2.98619	−0.0995398
$901$	0.284490	0.00947774
$902$	−14.9809	−0.498809
$903$	−6.52570	−0.217162
$904$	−12.3676	−0.411341
$905$	0.713074	0.0237034
$906$	7.12915	0.236850
$907$	4.16688	0.138359	0.0691795	−	0.997604i	$-0.477962\pi$
$907$	4.16688	0.138359	0.0691795	+	0.997604i	$0.477962\pi$
$908$	23.4618	0.778608
$909$	−8.57871	−0.284538
$910$	0.941485	0.0312099
$911$	45.1831	1.49698	0.748491	−	0.663145i	$-0.230779\pi$
$911$	45.1831	1.49698	0.748491	+	0.663145i	$0.230779\pi$
$912$	−0.731632	−0.0242268
$913$	−7.65858	−0.253462
$914$	−13.1669	−0.435522
$915$	−19.6220	−0.648684
$916$	−27.7556	−0.917069
$917$	−13.9121	−0.459417
$918$	−0.681547	−0.0224944
$919$	−43.2412	−1.42640	−0.713198	−	0.700963i	$-0.752754\pi$
$919$	−43.2412	−1.42640	−0.713198	+	0.700963i	$0.752754\pi$
$920$	−6.76975	−0.223192
$921$	−3.30746	−0.108984
$922$	12.1988	0.401746
$923$	10.6711	0.351242
$924$	1.88828	0.0621198
$925$	3.46087	0.113793
$926$	−13.6491	−0.448536
$927$	1.00000	0.0328443
$928$	−7.26722	−0.238558
$929$	59.6953	1.95854	0.979270	−	0.202560i	$-0.0649260\pi$
$929$	59.6953	1.95854	0.979270	+	0.202560i	$0.0649260\pi$
$930$	11.9108	0.390569
$931$	−4.79939	−0.157294
$932$	18.4178	0.603294
$933$	22.2595	0.728744
$934$	−24.7567	−0.810063
$935$	2.75275	0.0900245
$936$	−1.00000	−0.0326860
$937$	−14.6744	−0.479391	−0.239696	−	0.970848i	$-0.577048\pi$
$937$	−14.6744	−0.479391	−0.239696	+	0.970848i	$0.577048\pi$
$938$	−8.46181	−0.276288
$939$	−3.47768	−0.113490
$940$	3.84740	0.125488
$941$	−6.23944	−0.203400	−0.101700	−	0.994815i	$-0.532428\pi$
$941$	−6.23944	−0.203400	−0.101700	+	0.994815i	$0.532428\pi$
$942$	6.15568	0.200563
$943$	25.1096	0.817680
$944$	−9.24350	−0.300850
$945$	0.941485	0.0306265
$946$	−27.9952	−0.910203
$947$	26.4286	0.858813	0.429406	−	0.903111i	$-0.358723\pi$
$947$	26.4286	0.858813	0.429406	+	0.903111i	$0.358723\pi$
$948$	−5.68580	−0.184666
$949$	16.0490	0.520974
$950$	−2.18480	−0.0708841
$951$	0.951562	0.0308565
$952$	−0.452169	−0.0146549
$953$	−1.08754	−0.0352287	−0.0176144	−	0.999845i	$-0.505607\pi$
$953$	−1.08754	−0.0352287	−0.0176144	+	0.999845i	$0.505607\pi$
$954$	0.417418	0.0135144
$955$	−20.8061	−0.673270
$956$	−28.7478	−0.929769
$957$	20.6838	0.668612
$958$	29.3848	0.949380
$959$	−1.93270	−0.0624102
$960$	−1.41909	−0.0458008
$961$	39.4469	1.27248
$962$	1.15896	0.0373663
$963$	13.3773	0.431076
$964$	15.7695	0.507901
$965$	−7.26364	−0.233825
$966$	−3.16496	−0.101831
$967$	−10.0737	−0.323949	−0.161975	−	0.986795i	$-0.551786\pi$
$967$	−10.0737	−0.323949	−0.161975	+	0.986795i	$0.551786\pi$
$968$	−2.89928	−0.0931865
$969$	−0.498642	−0.0160187
$970$	−4.59454	−0.147522
$971$	−10.3301	−0.331508	−0.165754	−	0.986167i	$-0.553006\pi$
$971$	−10.3301	−0.331508	−0.165754	+	0.986167i	$0.553006\pi$
$972$	−1.00000	−0.0320750
$973$	−3.66429	−0.117472
$974$	39.0027	1.24973
$975$	−2.98619	−0.0956347
$976$	13.8272	0.442598
$977$	15.0604	0.481825	0.240913	−	0.970547i	$-0.422553\pi$
$977$	15.0604	0.481825	0.240913	+	0.970547i	$0.422553\pi$
$978$	−4.24155	−0.135630
$979$	14.4530	0.461919
$980$	−9.30898	−0.297365
$981$	11.7111	0.373907
$982$	−0.488438	−0.0155867
$983$	23.1020	0.736840	0.368420	−	0.929660i	$-0.379899\pi$
$983$	23.1020	0.736840	0.368420	+	0.929660i	$0.379899\pi$
$984$	5.26351	0.167795
$985$	−20.9551	−0.667686
$986$	−4.95296	−0.157734
$987$	1.79872	0.0572539
$988$	−0.731632	−0.0232763
$989$	46.9230	1.49206
$990$	4.03897	0.128367
$991$	−12.8243	−0.407377	−0.203689	−	0.979036i	$-0.565293\pi$
$991$	−12.8243	−0.407377	−0.203689	+	0.979036i	$0.565293\pi$
$992$	−8.39326	−0.266486
$993$	−32.1899	−1.02151
$994$	7.07965	0.224553
$995$	17.2282	0.546170
$996$	2.69083	0.0852622
$997$	−18.8083	−0.595664	−0.297832	−	0.954618i	$-0.596263\pi$
$997$	−18.8083	−0.595664	−0.297832	+	0.954618i	$0.596263\pi$
$998$	−43.5949	−1.37997
$999$	1.15896	0.0366678

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.u.1.8	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.u.1.8	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.41909 q^{5} -1.00000 q^{6} -0.663444 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.41909 q^{5} -1.00000 q^{6} -0.663444 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.41909 q^{10} +2.84618 q^{11} -1.00000 q^{12} -1.00000 q^{13} -0.663444 q^{14} -1.41909 q^{15} +1.00000 q^{16} +0.681547 q^{17} +1.00000 q^{18} +0.731632 q^{19} +1.41909 q^{20} +0.663444 q^{21} +2.84618 q^{22} -4.77050 q^{23} -1.00000 q^{24} -2.98619 q^{25} -1.00000 q^{26} -1.00000 q^{27} -0.663444 q^{28} -7.26722 q^{29} -1.41909 q^{30} -8.39326 q^{31} +1.00000 q^{32} -2.84618 q^{33} +0.681547 q^{34} -0.941485 q^{35} +1.00000 q^{36} -1.15896 q^{37} +0.731632 q^{38} +1.00000 q^{39} +1.41909 q^{40} -5.26351 q^{41} +0.663444 q^{42} -9.83608 q^{43} +2.84618 q^{44} +1.41909 q^{45} -4.77050 q^{46} +2.71118 q^{47} -1.00000 q^{48} -6.55984 q^{49} -2.98619 q^{50} -0.681547 q^{51} -1.00000 q^{52} +0.417418 q^{53} -1.00000 q^{54} +4.03897 q^{55} -0.663444 q^{56} -0.731632 q^{57} -7.26722 q^{58} -9.24350 q^{59} -1.41909 q^{60} +13.8272 q^{61} -8.39326 q^{62} -0.663444 q^{63} +1.00000 q^{64} -1.41909 q^{65} -2.84618 q^{66} +12.7544 q^{67} +0.681547 q^{68} +4.77050 q^{69} -0.941485 q^{70} -10.6711 q^{71} +1.00000 q^{72} -16.0490 q^{73} -1.15896 q^{74} +2.98619 q^{75} +0.731632 q^{76} -1.88828 q^{77} +1.00000 q^{78} +5.68580 q^{79} +1.41909 q^{80} +1.00000 q^{81} -5.26351 q^{82} -2.69083 q^{83} +0.663444 q^{84} +0.967175 q^{85} -9.83608 q^{86} +7.26722 q^{87} +2.84618 q^{88} +5.07803 q^{89} +1.41909 q^{90} +0.663444 q^{91} -4.77050 q^{92} +8.39326 q^{93} +2.71118 q^{94} +1.03825 q^{95} -1.00000 q^{96} -3.23767 q^{97} -6.55984 q^{98} +2.84618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} - 2 q^{5} - 11 q^{6} - 2 q^{7} + 11 q^{8} + 11 q^{9} - 2 q^{10} - 10 q^{11} - 11 q^{12} - 11 q^{13} - 2 q^{14} + 2 q^{15} + 11 q^{16} + 6 q^{17} + 11 q^{18} - 3 q^{19} - 2 q^{20} + 2 q^{21} - 10 q^{22} + 3 q^{23} - 11 q^{24} - q^{25} - 11 q^{26} - 11 q^{27} - 2 q^{28} - 22 q^{29} + 2 q^{30} - 5 q^{31} + 11 q^{32} + 10 q^{33} + 6 q^{34} - 20 q^{35} + 11 q^{36} - 26 q^{37} - 3 q^{38} + 11 q^{39} - 2 q^{40} - 6 q^{41} + 2 q^{42} - 8 q^{43} - 10 q^{44} - 2 q^{45} + 3 q^{46} + 6 q^{47} - 11 q^{48} - 5 q^{49} - q^{50} - 6 q^{51} - 11 q^{52} - 25 q^{53} - 11 q^{54} - 2 q^{56} + 3 q^{57} - 22 q^{58} + 7 q^{59} + 2 q^{60} - 36 q^{61} - 5 q^{62} - 2 q^{63} + 11 q^{64} + 2 q^{65} + 10 q^{66} - 12 q^{67} + 6 q^{68} - 3 q^{69} - 20 q^{70} - 15 q^{71} + 11 q^{72} - 12 q^{73} - 26 q^{74} + q^{75} - 3 q^{76} - q^{77} + 11 q^{78} - 15 q^{79} - 2 q^{80} + 11 q^{81} - 6 q^{82} - 16 q^{83} + 2 q^{84} - 25 q^{85} - 8 q^{86} + 22 q^{87} - 10 q^{88} - 2 q^{89} - 2 q^{90} + 2 q^{91} + 3 q^{92} + 5 q^{93} + 6 q^{94} + 16 q^{95} - 11 q^{96} - 10 q^{97} - 5 q^{98} - 10 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 - 2 * q^5 - 11 * q^6 - 2 * q^7 + 11 * q^8 + 11 * q^9 - 2 * q^10 - 10 * q^11 - 11 * q^12 - 11 * q^13 - 2 * q^14 + 2 * q^15 + 11 * q^16 + 6 * q^17 + 11 * q^18 - 3 * q^19 - 2 * q^20 + 2 * q^21 - 10 * q^22 + 3 * q^23 - 11 * q^24 - q^25 - 11 * q^26 - 11 * q^27 - 2 * q^28 - 22 * q^29 + 2 * q^30 - 5 * q^31 + 11 * q^32 + 10 * q^33 + 6 * q^34 - 20 * q^35 + 11 * q^36 - 26 * q^37 - 3 * q^38 + 11 * q^39 - 2 * q^40 - 6 * q^41 + 2 * q^42 - 8 * q^43 - 10 * q^44 - 2 * q^45 + 3 * q^46 + 6 * q^47 - 11 * q^48 - 5 * q^49 - q^50 - 6 * q^51 - 11 * q^52 - 25 * q^53 - 11 * q^54 - 2 * q^56 + 3 * q^57 - 22 * q^58 + 7 * q^59 + 2 * q^60 - 36 * q^61 - 5 * q^62 - 2 * q^63 + 11 * q^64 + 2 * q^65 + 10 * q^66 - 12 * q^67 + 6 * q^68 - 3 * q^69 - 20 * q^70 - 15 * q^71 + 11 * q^72 - 12 * q^73 - 26 * q^74 + q^75 - 3 * q^76 - q^77 + 11 * q^78 - 15 * q^79 - 2 * q^80 + 11 * q^81 - 6 * q^82 - 16 * q^83 + 2 * q^84 - 25 * q^85 - 8 * q^86 + 22 * q^87 - 10 * q^88 - 2 * q^89 - 2 * q^90 + 2 * q^91 + 3 * q^92 + 5 * q^93 + 6 * q^94 + 16 * q^95 - 11 * q^96 - 10 * q^97 - 5 * q^98 - 10 * q^99

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