LMFDB - Embedded newform 8030.2.a.bc.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8030,2,Mod(1,8030)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8030, 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("8030.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8030 = 2 \cdot 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8030.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:	$64.1198728231$
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} - 5 x^{10} - 10 x^{9} + 71 x^{8} + 28 x^{7} - 360 x^{6} - 60 x^{5} + 788 x^{4} + 309 x^{3} + \cdots - 95 $ x^11 - 5x^10 - 10x^9 + 71x^8 + 28x^7 - 360x^6 - 60x^5 + 788x^4 + 309x^3 - 632x^2 - 503x - 95
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			1.4
Root			$2.29138$ of defining polynomial
Character	$\chi$	$=$	8030.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.29138 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.29138 q^{6} +3.99723 q^{7} -1.00000 q^{8} +2.25044 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.29138 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.29138 q^{6} +3.99723 q^{7} -1.00000 q^{8} +2.25044 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.29138 q^{12} -5.89738 q^{13} -3.99723 q^{14} -2.29138 q^{15} +1.00000 q^{16} +0.342682 q^{17} -2.25044 q^{18} -3.73006 q^{19} +1.00000 q^{20} -9.15920 q^{21} -1.00000 q^{22} -3.30961 q^{23} +2.29138 q^{24} +1.00000 q^{25} +5.89738 q^{26} +1.71753 q^{27} +3.99723 q^{28} +8.32042 q^{29} +2.29138 q^{30} +2.97439 q^{31} -1.00000 q^{32} -2.29138 q^{33} -0.342682 q^{34} +3.99723 q^{35} +2.25044 q^{36} +0.181197 q^{37} +3.73006 q^{38} +13.5132 q^{39} -1.00000 q^{40} +0.916462 q^{41} +9.15920 q^{42} -0.526104 q^{43} +1.00000 q^{44} +2.25044 q^{45} +3.30961 q^{46} -11.3649 q^{47} -2.29138 q^{48} +8.97787 q^{49} -1.00000 q^{50} -0.785217 q^{51} -5.89738 q^{52} -3.06385 q^{53} -1.71753 q^{54} +1.00000 q^{55} -3.99723 q^{56} +8.54699 q^{57} -8.32042 q^{58} +3.32278 q^{59} -2.29138 q^{60} -7.98125 q^{61} -2.97439 q^{62} +8.99554 q^{63} +1.00000 q^{64} -5.89738 q^{65} +2.29138 q^{66} +13.6513 q^{67} +0.342682 q^{68} +7.58358 q^{69} -3.99723 q^{70} +1.58137 q^{71} -2.25044 q^{72} -1.00000 q^{73} -0.181197 q^{74} -2.29138 q^{75} -3.73006 q^{76} +3.99723 q^{77} -13.5132 q^{78} -8.19081 q^{79} +1.00000 q^{80} -10.6868 q^{81} -0.916462 q^{82} +5.60247 q^{83} -9.15920 q^{84} +0.342682 q^{85} +0.526104 q^{86} -19.0653 q^{87} -1.00000 q^{88} -16.5957 q^{89} -2.25044 q^{90} -23.5732 q^{91} -3.30961 q^{92} -6.81547 q^{93} +11.3649 q^{94} -3.73006 q^{95} +2.29138 q^{96} +9.79365 q^{97} -8.97787 q^{98} +2.25044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * 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
$3$	−2.29138	−1.32293	−0.661466	−	0.749976i	$-0.730065\pi$
$3$	−2.29138	−1.32293	−0.661466	+	0.749976i	$0.730065\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.29138	0.935454
$7$	3.99723	1.51081	0.755406	−	0.655257i	$-0.227440\pi$
$7$	3.99723	1.51081	0.755406	+	0.655257i	$0.227440\pi$
$8$	−1.00000	−0.353553
$9$	2.25044	0.750147
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.29138	−0.661466
$13$	−5.89738	−1.63564	−0.817820	−	0.575474i	$-0.804818\pi$
$13$	−5.89738	−1.63564	−0.817820	+	0.575474i	$0.804818\pi$
$14$	−3.99723	−1.06831
$15$	−2.29138	−0.591633
$16$	1.00000	0.250000
$17$	0.342682	0.0831127	0.0415564	−	0.999136i	$-0.486768\pi$
$17$	0.342682	0.0831127	0.0415564	+	0.999136i	$0.486768\pi$
$18$	−2.25044	−0.530434
$19$	−3.73006	−0.855734	−0.427867	−	0.903842i	$-0.640735\pi$
$19$	−3.73006	−0.855734	−0.427867	+	0.903842i	$0.640735\pi$
$20$	1.00000	0.223607
$21$	−9.15920	−1.99870
$22$	−1.00000	−0.213201
$23$	−3.30961	−0.690101	−0.345050	−	0.938584i	$-0.612138\pi$
$23$	−3.30961	−0.690101	−0.345050	+	0.938584i	$0.612138\pi$
$24$	2.29138	0.467727
$25$	1.00000	0.200000
$26$	5.89738	1.15657
$27$	1.71753	0.330538
$28$	3.99723	0.755406
$29$	8.32042	1.54506	0.772532	−	0.634976i	$-0.218990\pi$
$29$	8.32042	1.54506	0.772532	+	0.634976i	$0.218990\pi$
$30$	2.29138	0.418348
$31$	2.97439	0.534216	0.267108	−	0.963667i	$-0.413932\pi$
$31$	2.97439	0.534216	0.267108	+	0.963667i	$0.413932\pi$
$32$	−1.00000	−0.176777
$33$	−2.29138	−0.398879
$34$	−0.342682	−0.0587696
$35$	3.99723	0.675656
$36$	2.25044	0.375073
$37$	0.181197	0.0297886	0.0148943	−	0.999889i	$-0.495259\pi$
$37$	0.181197	0.0297886	0.0148943	+	0.999889i	$0.495259\pi$
$38$	3.73006	0.605095
$39$	13.5132	2.16384
$40$	−1.00000	−0.158114
$41$	0.916462	0.143127	0.0715637	−	0.997436i	$-0.477201\pi$
$41$	0.916462	0.143127	0.0715637	+	0.997436i	$0.477201\pi$
$42$	9.15920	1.41329
$43$	−0.526104	−0.0802301	−0.0401151	−	0.999195i	$-0.512772\pi$
$43$	−0.526104	−0.0802301	−0.0401151	+	0.999195i	$0.512772\pi$
$44$	1.00000	0.150756
$45$	2.25044	0.335476
$46$	3.30961	0.487975
$47$	−11.3649	−1.65774	−0.828868	−	0.559444i	$-0.811015\pi$
$47$	−11.3649	−1.65774	−0.828868	+	0.559444i	$0.811015\pi$
$48$	−2.29138	−0.330733
$49$	8.97787	1.28255
$50$	−1.00000	−0.141421
$51$	−0.785217	−0.109952
$52$	−5.89738	−0.817820
$53$	−3.06385	−0.420852	−0.210426	−	0.977610i	$-0.567485\pi$
$53$	−3.06385	−0.420852	−0.210426	+	0.977610i	$0.567485\pi$
$54$	−1.71753	−0.233726
$55$	1.00000	0.134840
$56$	−3.99723	−0.534153
$57$	8.54699	1.13208
$58$	−8.32042	−1.09253
$59$	3.32278	0.432589	0.216294	−	0.976328i	$-0.430603\pi$
$59$	3.32278	0.432589	0.216294	+	0.976328i	$0.430603\pi$
$60$	−2.29138	−0.295816
$61$	−7.98125	−1.02189	−0.510947	−	0.859612i	$-0.670705\pi$
$61$	−7.98125	−1.02189	−0.510947	+	0.859612i	$0.670705\pi$
$62$	−2.97439	−0.377748
$63$	8.99554	1.13333
$64$	1.00000	0.125000
$65$	−5.89738	−0.731481
$66$	2.29138	0.282050
$67$	13.6513	1.66777	0.833886	−	0.551937i	$-0.186111\pi$
$67$	13.6513	1.66777	0.833886	+	0.551937i	$0.186111\pi$
$68$	0.342682	0.0415564
$69$	7.58358	0.912956
$70$	−3.99723	−0.477761
$71$	1.58137	0.187674	0.0938368	−	0.995588i	$-0.470087\pi$
$71$	1.58137	0.187674	0.0938368	+	0.995588i	$0.470087\pi$
$72$	−2.25044	−0.265217
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−0.181197	−0.0210637
$75$	−2.29138	−0.264586
$76$	−3.73006	−0.427867
$77$	3.99723	0.455527
$78$	−13.5132	−1.53007
$79$	−8.19081	−0.921538	−0.460769	−	0.887520i	$-0.652426\pi$
$79$	−8.19081	−0.921538	−0.460769	+	0.887520i	$0.652426\pi$
$80$	1.00000	0.111803
$81$	−10.6868	−1.18743
$82$	−0.916462	−0.101206
$83$	5.60247	0.614951	0.307475	−	0.951556i	$-0.400516\pi$
$83$	5.60247	0.614951	0.307475	+	0.951556i	$0.400516\pi$
$84$	−9.15920	−0.999350
$85$	0.342682	0.0371691
$86$	0.526104	0.0567313
$87$	−19.0653	−2.04401
$88$	−1.00000	−0.106600
$89$	−16.5957	−1.75914	−0.879572	−	0.475765i	$-0.842171\pi$
$89$	−16.5957	−1.75914	−0.879572	+	0.475765i	$0.842171\pi$
$90$	−2.25044	−0.237217
$91$	−23.5732	−2.47114
$92$	−3.30961	−0.345050
$93$	−6.81547	−0.706731
$94$	11.3649	1.17220
$95$	−3.73006	−0.382696
$96$	2.29138	0.233863
$97$	9.79365	0.994394	0.497197	−	0.867638i	$-0.334363\pi$
$97$	9.79365	0.994394	0.497197	+	0.867638i	$0.334363\pi$
$98$	−8.97787	−0.906902
$99$	2.25044	0.226178
$100$	1.00000	0.100000
$101$	11.3362	1.12799	0.563995	−	0.825778i	$-0.309264\pi$
$101$	11.3362	1.12799	0.563995	+	0.825778i	$0.309264\pi$
$102$	0.785217	0.0777481
$103$	−6.90293	−0.680166	−0.340083	−	0.940395i	$-0.610455\pi$
$103$	−6.90293	−0.680166	−0.340083	+	0.940395i	$0.610455\pi$
$104$	5.89738	0.578286
$105$	−9.15920	−0.893846
$106$	3.06385	0.297588
$107$	−11.5612	−1.11766	−0.558831	−	0.829282i	$-0.688750\pi$
$107$	−11.5612	−1.11766	−0.558831	+	0.829282i	$0.688750\pi$
$108$	1.71753	0.165269
$109$	4.57338	0.438050	0.219025	−	0.975719i	$-0.429712\pi$
$109$	4.57338	0.438050	0.219025	+	0.975719i	$0.429712\pi$
$110$	−1.00000	−0.0953463
$111$	−0.415192	−0.0394083
$112$	3.99723	0.377703
$113$	2.99798	0.282026	0.141013	−	0.990008i	$-0.454964\pi$
$113$	2.99798	0.282026	0.141013	+	0.990008i	$0.454964\pi$
$114$	−8.54699	−0.800499
$115$	−3.30961	−0.308623
$116$	8.32042	0.772532
$117$	−13.2717	−1.22697
$118$	−3.32278	−0.305886
$119$	1.36978	0.125568
$120$	2.29138	0.209174
$121$	1.00000	0.0909091
$122$	7.98125	0.722589
$123$	−2.09997	−0.189348
$124$	2.97439	0.267108
$125$	1.00000	0.0894427
$126$	−8.99554	−0.801386
$127$	−14.0797	−1.24937	−0.624686	−	0.780876i	$-0.714773\pi$
$127$	−14.0797	−1.24937	−0.624686	+	0.780876i	$0.714773\pi$
$128$	−1.00000	−0.0883883
$129$	1.20551	0.106139
$130$	5.89738	0.517235
$131$	−16.6850	−1.45778	−0.728888	−	0.684632i	$-0.759963\pi$
$131$	−16.6850	−1.45778	−0.728888	+	0.684632i	$0.759963\pi$
$132$	−2.29138	−0.199439
$133$	−14.9099	−1.29285
$134$	−13.6513	−1.17929
$135$	1.71753	0.147821
$136$	−0.342682	−0.0293848
$137$	−17.3651	−1.48360	−0.741800	−	0.670621i	$-0.766028\pi$
$137$	−17.3651	−1.48360	−0.741800	+	0.670621i	$0.766028\pi$
$138$	−7.58358	−0.645557
$139$	5.64148	0.478504	0.239252	−	0.970957i	$-0.423098\pi$
$139$	5.64148	0.478504	0.239252	+	0.970957i	$0.423098\pi$
$140$	3.99723	0.337828
$141$	26.0413	2.19307
$142$	−1.58137	−0.132705
$143$	−5.89738	−0.493164
$144$	2.25044	0.187537
$145$	8.32042	0.690974
$146$	1.00000	0.0827606
$147$	−20.5717	−1.69673
$148$	0.181197	0.0148943
$149$	9.92464	0.813058	0.406529	−	0.913638i	$-0.366739\pi$
$149$	9.92464	0.813058	0.406529	+	0.913638i	$0.366739\pi$
$150$	2.29138	0.187091
$151$	−1.01353	−0.0824797	−0.0412399	−	0.999149i	$-0.513131\pi$
$151$	−1.01353	−0.0824797	−0.0412399	+	0.999149i	$0.513131\pi$
$152$	3.73006	0.302548
$153$	0.771187	0.0623467
$154$	−3.99723	−0.322106
$155$	2.97439	0.238909
$156$	13.5132	1.08192
$157$	−11.4714	−0.915518	−0.457759	−	0.889076i	$-0.651348\pi$
$157$	−11.4714	−0.915518	−0.457759	+	0.889076i	$0.651348\pi$
$158$	8.19081	0.651626
$159$	7.02046	0.556759
$160$	−1.00000	−0.0790569
$161$	−13.2293	−1.04261
$162$	10.6868	0.839637
$163$	−25.3855	−1.98835	−0.994173	−	0.107793i	$-0.965622\pi$
$163$	−25.3855	−1.98835	−0.994173	+	0.107793i	$0.965622\pi$
$164$	0.916462	0.0715637
$165$	−2.29138	−0.178384
$166$	−5.60247	−0.434836
$167$	−4.66214	−0.360767	−0.180383	−	0.983596i	$-0.557734\pi$
$167$	−4.66214	−0.360767	−0.180383	+	0.983596i	$0.557734\pi$
$168$	9.15920	0.706647
$169$	21.7791	1.67532
$170$	−0.342682	−0.0262825
$171$	−8.39427	−0.641926
$172$	−0.526104	−0.0401151
$173$	2.85656	0.217180	0.108590	−	0.994087i	$-0.465366\pi$
$173$	2.85656	0.217180	0.108590	+	0.994087i	$0.465366\pi$
$174$	19.0653	1.44534
$175$	3.99723	0.302162
$176$	1.00000	0.0753778
$177$	−7.61375	−0.572285
$178$	16.5957	1.24390
$179$	24.4413	1.82683	0.913413	−	0.407034i	$-0.133437\pi$
$179$	24.4413	1.82683	0.913413	+	0.407034i	$0.133437\pi$
$180$	2.25044	0.167738
$181$	1.71240	0.127282	0.0636409	−	0.997973i	$-0.479729\pi$
$181$	1.71240	0.127282	0.0636409	+	0.997973i	$0.479729\pi$
$182$	23.5732	1.74736
$183$	18.2881	1.35190
$184$	3.30961	0.243988
$185$	0.181197	0.0133219
$186$	6.81547	0.499735
$187$	0.342682	0.0250594
$188$	−11.3649	−0.828868
$189$	6.86536	0.499381
$190$	3.73006	0.270607
$191$	−17.4883	−1.26541	−0.632706	−	0.774392i	$-0.718056\pi$
$191$	−17.4883	−1.26541	−0.632706	+	0.774392i	$0.718056\pi$
$192$	−2.29138	−0.165366
$193$	17.2605	1.24244	0.621220	−	0.783636i	$-0.286637\pi$
$193$	17.2605	1.24244	0.621220	+	0.783636i	$0.286637\pi$
$194$	−9.79365	−0.703143
$195$	13.5132	0.967698
$196$	8.97787	0.641276
$197$	−13.3442	−0.950735	−0.475367	−	0.879787i	$-0.657685\pi$
$197$	−13.3442	−0.950735	−0.475367	+	0.879787i	$0.657685\pi$
$198$	−2.25044	−0.159932
$199$	26.2503	1.86083	0.930417	−	0.366503i	$-0.119445\pi$
$199$	26.2503	1.86083	0.930417	+	0.366503i	$0.119445\pi$
$200$	−1.00000	−0.0707107
$201$	−31.2804	−2.20635
$202$	−11.3362	−0.797609
$203$	33.2587	2.33430
$204$	−0.785217	−0.0549762
$205$	0.916462	0.0640085
$206$	6.90293	0.480950
$207$	−7.44808	−0.517677
$208$	−5.89738	−0.408910
$209$	−3.73006	−0.258013
$210$	9.15920	0.632045
$211$	6.26661	0.431411	0.215706	−	0.976458i	$-0.430795\pi$
$211$	6.26661	0.431411	0.215706	+	0.976458i	$0.430795\pi$
$212$	−3.06385	−0.210426
$213$	−3.62352	−0.248279
$214$	11.5612	0.790306
$215$	−0.526104	−0.0358800
$216$	−1.71753	−0.116863
$217$	11.8893	0.807100
$218$	−4.57338	−0.309748
$219$	2.29138	0.154837
$220$	1.00000	0.0674200
$221$	−2.02093	−0.135942
$222$	0.415192	0.0278659
$223$	−15.0305	−1.00652	−0.503259	−	0.864136i	$-0.667866\pi$
$223$	−15.0305	−1.00652	−0.503259	+	0.864136i	$0.667866\pi$
$224$	−3.99723	−0.267076
$225$	2.25044	0.150029
$226$	−2.99798	−0.199422
$227$	7.69759	0.510907	0.255453	−	0.966821i	$-0.417775\pi$
$227$	7.69759	0.510907	0.255453	+	0.966821i	$0.417775\pi$
$228$	8.54699	0.566039
$229$	−8.83782	−0.584020	−0.292010	−	0.956415i	$-0.594324\pi$
$229$	−8.83782	−0.584020	−0.292010	+	0.956415i	$0.594324\pi$
$230$	3.30961	0.218229
$231$	−9.15920	−0.602631
$232$	−8.32042	−0.546263
$233$	4.15939	0.272491	0.136245	−	0.990675i	$-0.456496\pi$
$233$	4.15939	0.272491	0.136245	+	0.990675i	$0.456496\pi$
$234$	13.2717	0.867599
$235$	−11.3649	−0.741362
$236$	3.32278	0.216294
$237$	18.7683	1.21913
$238$	−1.36978	−0.0887898
$239$	12.4304	0.804056	0.402028	−	0.915627i	$-0.368305\pi$
$239$	12.4304	0.804056	0.402028	+	0.915627i	$0.368305\pi$
$240$	−2.29138	−0.147908
$241$	−22.0798	−1.42229	−0.711144	−	0.703046i	$-0.751823\pi$
$241$	−22.0798	−1.42229	−0.711144	+	0.703046i	$0.751823\pi$
$242$	−1.00000	−0.0642824
$243$	19.3351	1.24035
$244$	−7.98125	−0.510947
$245$	8.97787	0.573575
$246$	2.09997	0.133889
$247$	21.9976	1.39967
$248$	−2.97439	−0.188874
$249$	−12.8374	−0.813538
$250$	−1.00000	−0.0632456
$251$	5.21406	0.329108	0.164554	−	0.986368i	$-0.447381\pi$
$251$	5.21406	0.329108	0.164554	+	0.986368i	$0.447381\pi$
$252$	8.99554	0.566665
$253$	−3.30961	−0.208073
$254$	14.0797	0.883439
$255$	−0.785217	−0.0491722
$256$	1.00000	0.0625000
$257$	20.6043	1.28526	0.642629	−	0.766177i	$-0.277844\pi$
$257$	20.6043	1.28526	0.642629	+	0.766177i	$0.277844\pi$
$258$	−1.20551	−0.0750516
$259$	0.724287	0.0450050
$260$	−5.89738	−0.365740
$261$	18.7246	1.15902
$262$	16.6850	1.03080
$263$	31.6164	1.94955	0.974775	−	0.223190i	$-0.0716469\pi$
$263$	31.6164	1.94955	0.974775	+	0.223190i	$0.0716469\pi$
$264$	2.29138	0.141025
$265$	−3.06385	−0.188211
$266$	14.9099	0.914185
$267$	38.0272	2.32723
$268$	13.6513	0.833886
$269$	8.30535	0.506386	0.253193	−	0.967416i	$-0.418519\pi$
$269$	8.30535	0.506386	0.253193	+	0.967416i	$0.418519\pi$
$270$	−1.71753	−0.104525
$271$	3.61113	0.219361	0.109680	−	0.993967i	$-0.465017\pi$
$271$	3.61113	0.219361	0.109680	+	0.993967i	$0.465017\pi$
$272$	0.342682	0.0207782
$273$	54.0153	3.26915
$274$	17.3651	1.04906
$275$	1.00000	0.0603023
$276$	7.58358	0.456478
$277$	23.8459	1.43276	0.716381	−	0.697709i	$-0.245797\pi$
$277$	23.8459	1.43276	0.716381	+	0.697709i	$0.245797\pi$
$278$	−5.64148	−0.338354
$279$	6.69369	0.400741
$280$	−3.99723	−0.238880
$281$	−0.801712	−0.0478261	−0.0239131	−	0.999714i	$-0.507612\pi$
$281$	−0.801712	−0.0478261	−0.0239131	+	0.999714i	$0.507612\pi$
$282$	−26.0413	−1.55074
$283$	0.0670592	0.00398626	0.00199313	−	0.999998i	$-0.499366\pi$
$283$	0.0670592	0.00398626	0.00199313	+	0.999998i	$0.499366\pi$
$284$	1.58137	0.0938368
$285$	8.54699	0.506280
$286$	5.89738	0.348720
$287$	3.66331	0.216238
$288$	−2.25044	−0.132608
$289$	−16.8826	−0.993092
$290$	−8.32042	−0.488592
$291$	−22.4410	−1.31552
$292$	−1.00000	−0.0585206
$293$	−11.0458	−0.645303	−0.322652	−	0.946518i	$-0.604574\pi$
$293$	−11.0458	−0.645303	−0.322652	+	0.946518i	$0.604574\pi$
$294$	20.5717	1.19977
$295$	3.32278	0.193459
$296$	−0.181197	−0.0105319
$297$	1.71753	0.0996611
$298$	−9.92464	−0.574919
$299$	19.5180	1.12876
$300$	−2.29138	−0.132293
$301$	−2.10296	−0.121213
$302$	1.01353	0.0583220
$303$	−25.9755	−1.49225
$304$	−3.73006	−0.213933
$305$	−7.98125	−0.457005
$306$	−0.771187	−0.0440858
$307$	−19.8683	−1.13394	−0.566972	−	0.823737i	$-0.691885\pi$
$307$	−19.8683	−1.13394	−0.566972	+	0.823737i	$0.691885\pi$
$308$	3.99723	0.227763
$309$	15.8173	0.899813
$310$	−2.97439	−0.168934
$311$	−23.5556	−1.33572	−0.667858	−	0.744288i	$-0.732789\pi$
$311$	−23.5556	−1.33572	−0.667858	+	0.744288i	$0.732789\pi$
$312$	−13.5132	−0.765033
$313$	−33.1423	−1.87331	−0.936657	−	0.350249i	$-0.886097\pi$
$313$	−33.1423	−1.87331	−0.936657	+	0.350249i	$0.886097\pi$
$314$	11.4714	0.647369
$315$	8.99554	0.506841
$316$	−8.19081	−0.460769
$317$	−19.3282	−1.08558	−0.542789	−	0.839869i	$-0.682632\pi$
$317$	−19.3282	−1.08558	−0.542789	+	0.839869i	$0.682632\pi$
$318$	−7.02046	−0.393688
$319$	8.32042	0.465854
$320$	1.00000	0.0559017
$321$	26.4911	1.47859
$322$	13.2293	0.737239
$323$	−1.27823	−0.0711224
$324$	−10.6868	−0.593713
$325$	−5.89738	−0.327128
$326$	25.3855	1.40597
$327$	−10.4794	−0.579511
$328$	−0.916462	−0.0506032
$329$	−45.4280	−2.50453
$330$	2.29138	0.126137
$331$	29.4924	1.62105	0.810525	−	0.585704i	$-0.199182\pi$
$331$	29.4924	1.62105	0.810525	+	0.585704i	$0.199182\pi$
$332$	5.60247	0.307475
$333$	0.407773	0.0223458
$334$	4.66214	0.255101
$335$	13.6513	0.745850
$336$	−9.15920	−0.499675
$337$	−23.3262	−1.27066	−0.635331	−	0.772240i	$-0.719136\pi$
$337$	−23.3262	−1.27066	−0.635331	+	0.772240i	$0.719136\pi$
$338$	−21.7791	−1.18463
$339$	−6.86951	−0.373101
$340$	0.342682	0.0185846
$341$	2.97439	0.161072
$342$	8.39427	0.453910
$343$	7.90601	0.426884
$344$	0.526104	0.0283656
$345$	7.58358	0.408286
$346$	−2.85656	−0.153570
$347$	7.22040	0.387612	0.193806	−	0.981040i	$-0.437917\pi$
$347$	7.22040	0.387612	0.193806	+	0.981040i	$0.437917\pi$
$348$	−19.0653	−1.02201
$349$	−17.4248	−0.932728	−0.466364	−	0.884593i	$-0.654436\pi$
$349$	−17.4248	−0.932728	−0.466364	+	0.884593i	$0.654436\pi$
$350$	−3.99723	−0.213661
$351$	−10.1289	−0.540642
$352$	−1.00000	−0.0533002
$353$	11.8334	0.629830	0.314915	−	0.949120i	$-0.398024\pi$
$353$	11.8334	0.629830	0.314915	+	0.949120i	$0.398024\pi$
$354$	7.61375	0.404667
$355$	1.58137	0.0839302
$356$	−16.5957	−0.879572
$357$	−3.13870	−0.166117
$358$	−24.4413	−1.29176
$359$	10.1810	0.537332	0.268666	−	0.963233i	$-0.413417\pi$
$359$	10.1810	0.537332	0.268666	+	0.963233i	$0.413417\pi$
$360$	−2.25044	−0.118609
$361$	−5.08667	−0.267719
$362$	−1.71240	−0.0900018
$363$	−2.29138	−0.120266
$364$	−23.5732	−1.23557
$365$	−1.00000	−0.0523424
$366$	−18.2881	−0.955935
$367$	−12.2471	−0.639292	−0.319646	−	0.947537i	$-0.603564\pi$
$367$	−12.2471	−0.639292	−0.319646	+	0.947537i	$0.603564\pi$
$368$	−3.30961	−0.172525
$369$	2.06244	0.107367
$370$	−0.181197	−0.00941999
$371$	−12.2469	−0.635829
$372$	−6.81547	−0.353366
$373$	−25.1095	−1.30012	−0.650060	−	0.759883i	$-0.725256\pi$
$373$	−25.1095	−1.30012	−0.650060	+	0.759883i	$0.725256\pi$
$374$	−0.342682	−0.0177197
$375$	−2.29138	−0.118327
$376$	11.3649	0.586098
$377$	−49.0687	−2.52717
$378$	−6.86536	−0.353116
$379$	9.00049	0.462324	0.231162	−	0.972915i	$-0.425747\pi$
$379$	9.00049	0.462324	0.231162	+	0.972915i	$0.425747\pi$
$380$	−3.73006	−0.191348
$381$	32.2620	1.65283
$382$	17.4883	0.894782
$383$	−3.77890	−0.193093	−0.0965464	−	0.995328i	$-0.530780\pi$
$383$	−3.77890	−0.193093	−0.0965464	+	0.995328i	$0.530780\pi$
$384$	2.29138	0.116932
$385$	3.99723	0.203718
$386$	−17.2605	−0.878538
$387$	−1.18397	−0.0601844
$388$	9.79365	0.497197
$389$	−8.21748	−0.416643	−0.208321	−	0.978060i	$-0.566800\pi$
$389$	−8.21748	−0.416643	−0.208321	+	0.978060i	$0.566800\pi$
$390$	−13.5132	−0.684266
$391$	−1.13414	−0.0573562
$392$	−8.97787	−0.453451
$393$	38.2318	1.92854
$394$	13.3442	0.672271
$395$	−8.19081	−0.412124
$396$	2.25044	0.113089
$397$	−12.2142	−0.613013	−0.306507	−	0.951869i	$-0.599160\pi$
$397$	−12.2142	−0.613013	−0.306507	+	0.951869i	$0.599160\pi$
$398$	−26.2503	−1.31581
$399$	34.1643	1.71036
$400$	1.00000	0.0500000
$401$	1.08058	0.0539617	0.0269809	−	0.999636i	$-0.491411\pi$
$401$	1.08058	0.0539617	0.0269809	+	0.999636i	$0.491411\pi$
$402$	31.2804	1.56012
$403$	−17.5411	−0.873786
$404$	11.3362	0.563995
$405$	−10.6868	−0.531033
$406$	−33.2587	−1.65060
$407$	0.181197	0.00898161
$408$	0.785217	0.0388740
$409$	−9.69607	−0.479440	−0.239720	−	0.970842i	$-0.577056\pi$
$409$	−9.69607	−0.479440	−0.239720	+	0.970842i	$0.577056\pi$
$410$	−0.916462	−0.0452608
$411$	39.7901	1.96270
$412$	−6.90293	−0.340083
$413$	13.2819	0.653560
$414$	7.44808	0.366053
$415$	5.60247	0.275014
$416$	5.89738	0.289143
$417$	−12.9268	−0.633028
$418$	3.73006	0.182443
$419$	−6.95727	−0.339885	−0.169942	−	0.985454i	$-0.554358\pi$
$419$	−6.95727	−0.339885	−0.169942	+	0.985454i	$0.554358\pi$
$420$	−9.15920	−0.446923
$421$	−11.8235	−0.576240	−0.288120	−	0.957594i	$-0.593030\pi$
$421$	−11.8235	−0.576240	−0.288120	+	0.957594i	$0.593030\pi$
$422$	−6.26661	−0.305054
$423$	−25.5760	−1.24355
$424$	3.06385	0.148794
$425$	0.342682	0.0166225
$426$	3.62352	0.175560
$427$	−31.9029	−1.54389
$428$	−11.5612	−0.558831
$429$	13.5132	0.652422
$430$	0.526104	0.0253710
$431$	1.33137	0.0641299	0.0320649	−	0.999486i	$-0.489792\pi$
$431$	1.33137	0.0641299	0.0320649	+	0.999486i	$0.489792\pi$
$432$	1.71753	0.0826346
$433$	−25.0102	−1.20191	−0.600956	−	0.799282i	$-0.705213\pi$
$433$	−25.0102	−1.20191	−0.600956	+	0.799282i	$0.705213\pi$
$434$	−11.8893	−0.570706
$435$	−19.0653	−0.914111
$436$	4.57338	0.219025
$437$	12.3450	0.590543
$438$	−2.29138	−0.109487
$439$	2.73101	0.130344	0.0651721	−	0.997874i	$-0.479240\pi$
$439$	2.73101	0.130344	0.0651721	+	0.997874i	$0.479240\pi$
$440$	−1.00000	−0.0476731
$441$	20.2042	0.962103
$442$	2.02093	0.0961259
$443$	−22.8468	−1.08548	−0.542741	−	0.839900i	$-0.682613\pi$
$443$	−22.8468	−1.08548	−0.542741	+	0.839900i	$0.682613\pi$
$444$	−0.415192	−0.0197041
$445$	−16.5957	−0.786714
$446$	15.0305	0.711715
$447$	−22.7412	−1.07562
$448$	3.99723	0.188851
$449$	−8.32217	−0.392748	−0.196374	−	0.980529i	$-0.562917\pi$
$449$	−8.32217	−0.392748	−0.196374	+	0.980529i	$0.562917\pi$
$450$	−2.25044	−0.106087
$451$	0.916462	0.0431545
$452$	2.99798	0.141013
$453$	2.32238	0.109115
$454$	−7.69759	−0.361266
$455$	−23.5732	−1.10513
$456$	−8.54699	−0.400250
$457$	−31.3373	−1.46590	−0.732949	−	0.680283i	$-0.761857\pi$
$457$	−31.3373	−1.46590	−0.732949	+	0.680283i	$0.761857\pi$
$458$	8.83782	0.412964
$459$	0.588567	0.0274719
$460$	−3.30961	−0.154311
$461$	24.1527	1.12490	0.562452	−	0.826830i	$-0.309858\pi$
$461$	24.1527	1.12490	0.562452	+	0.826830i	$0.309858\pi$
$462$	9.15920	0.426124
$463$	9.10157	0.422986	0.211493	−	0.977380i	$-0.432167\pi$
$463$	9.10157	0.422986	0.211493	+	0.977380i	$0.432167\pi$
$464$	8.32042	0.386266
$465$	−6.81547	−0.316060
$466$	−4.15939	−0.192680
$467$	14.3421	0.663671	0.331836	−	0.943337i	$-0.392332\pi$
$467$	14.3421	0.663671	0.331836	+	0.943337i	$0.392332\pi$
$468$	−13.2717	−0.613485
$469$	54.5674	2.51969
$470$	11.3649	0.524222
$471$	26.2854	1.21117
$472$	−3.32278	−0.152943
$473$	−0.526104	−0.0241903
$474$	−18.7683	−0.862056
$475$	−3.73006	−0.171147
$476$	1.36978	0.0627838
$477$	−6.89502	−0.315701
$478$	−12.4304	−0.568554
$479$	4.24365	0.193897	0.0969486	−	0.995289i	$-0.469092\pi$
$479$	4.24365	0.193897	0.0969486	+	0.995289i	$0.469092\pi$
$480$	2.29138	0.104587
$481$	−1.06859	−0.0487235
$482$	22.0798	1.00571
$483$	30.3133	1.37930
$484$	1.00000	0.0454545
$485$	9.79365	0.444707
$486$	−19.3351	−0.877056
$487$	−5.32276	−0.241197	−0.120599	−	0.992701i	$-0.538481\pi$
$487$	−5.32276	−0.241197	−0.120599	+	0.992701i	$0.538481\pi$
$488$	7.98125	0.361294
$489$	58.1680	2.63045
$490$	−8.97787	−0.405579
$491$	−11.8656	−0.535487	−0.267744	−	0.963490i	$-0.586278\pi$
$491$	−11.8656	−0.535487	−0.267744	+	0.963490i	$0.586278\pi$
$492$	−2.09997	−0.0946738
$493$	2.85126	0.128414
$494$	−21.9976	−0.989718
$495$	2.25044	0.101150
$496$	2.97439	0.133554
$497$	6.32109	0.283540
$498$	12.8374	0.575258
$499$	28.0055	1.25370	0.626849	−	0.779141i	$-0.284344\pi$
$499$	28.0055	1.25370	0.626849	+	0.779141i	$0.284344\pi$
$500$	1.00000	0.0447214
$501$	10.6827	0.477270
$502$	−5.21406	−0.232715
$503$	19.8086	0.883223	0.441611	−	0.897206i	$-0.354407\pi$
$503$	19.8086	0.883223	0.441611	+	0.897206i	$0.354407\pi$
$504$	−8.99554	−0.400693
$505$	11.3362	0.504452
$506$	3.30961	0.147130
$507$	−49.9044	−2.21633
$508$	−14.0797	−0.624686
$509$	10.5088	0.465794	0.232897	−	0.972501i	$-0.425180\pi$
$509$	10.5088	0.465794	0.232897	+	0.972501i	$0.425180\pi$
$510$	0.785217	0.0347700
$511$	−3.99723	−0.176827
$512$	−1.00000	−0.0441942
$513$	−6.40648	−0.282853
$514$	−20.6043	−0.908815
$515$	−6.90293	−0.304179
$516$	1.20551	0.0530695
$517$	−11.3649	−0.499826
$518$	−0.724287	−0.0318233
$519$	−6.54547	−0.287314
$520$	5.89738	0.258617
$521$	−11.3674	−0.498016	−0.249008	−	0.968501i	$-0.580104\pi$
$521$	−11.3674	−0.498016	−0.249008	+	0.968501i	$0.580104\pi$
$522$	−18.7246	−0.819554
$523$	−33.9647	−1.48517	−0.742586	−	0.669751i	$-0.766401\pi$
$523$	−33.9647	−1.48517	−0.742586	+	0.669751i	$0.766401\pi$
$524$	−16.6850	−0.728888
$525$	−9.15920	−0.399740
$526$	−31.6164	−1.37854
$527$	1.01927	0.0444002
$528$	−2.29138	−0.0997197
$529$	−12.0465	−0.523761
$530$	3.06385	0.133085
$531$	7.47771	0.324505
$532$	−14.9099	−0.646427
$533$	−5.40473	−0.234105
$534$	−38.0272	−1.64560
$535$	−11.5612	−0.499833
$536$	−13.6513	−0.589646
$537$	−56.0043	−2.41676
$538$	−8.30535	−0.358069
$539$	8.97787	0.386704
$540$	1.71753	0.0739106
$541$	16.4990	0.709348	0.354674	−	0.934990i	$-0.384592\pi$
$541$	16.4990	0.709348	0.354674	+	0.934990i	$0.384592\pi$
$542$	−3.61113	−0.155112
$543$	−3.92377	−0.168385
$544$	−0.342682	−0.0146924
$545$	4.57338	0.195902
$546$	−54.0153	−2.31164
$547$	38.0637	1.62748	0.813742	−	0.581226i	$-0.197427\pi$
$547$	38.0637	1.62748	0.813742	+	0.581226i	$0.197427\pi$
$548$	−17.3651	−0.741800
$549$	−17.9613	−0.766571
$550$	−1.00000	−0.0426401
$551$	−31.0357	−1.32216
$552$	−7.58358	−0.322779
$553$	−32.7406	−1.39227
$554$	−23.8459	−1.01312
$555$	−0.415192	−0.0176239
$556$	5.64148	0.239252
$557$	−3.41454	−0.144679	−0.0723394	−	0.997380i	$-0.523046\pi$
$557$	−3.41454	−0.144679	−0.0723394	+	0.997380i	$0.523046\pi$
$558$	−6.69369	−0.283367
$559$	3.10264	0.131228
$560$	3.99723	0.168914
$561$	−0.785217	−0.0331519
$562$	0.801712	0.0338182
$563$	−29.8711	−1.25892	−0.629458	−	0.777034i	$-0.716723\pi$
$563$	−29.8711	−1.25892	−0.629458	+	0.777034i	$0.716723\pi$
$564$	26.0413	1.09654
$565$	2.99798	0.126126
$566$	−0.0670592	−0.00281871
$567$	−42.7178	−1.79398
$568$	−1.58137	−0.0663526
$569$	4.55331	0.190885	0.0954424	−	0.995435i	$-0.469573\pi$
$569$	4.55331	0.190885	0.0954424	+	0.995435i	$0.469573\pi$
$570$	−8.54699	−0.357994
$571$	−25.0464	−1.04816	−0.524079	−	0.851669i	$-0.675590\pi$
$571$	−25.0464	−1.04816	−0.524079	+	0.851669i	$0.675590\pi$
$572$	−5.89738	−0.246582
$573$	40.0725	1.67405
$574$	−3.66331	−0.152904
$575$	−3.30961	−0.138020
$576$	2.25044	0.0937684
$577$	−15.5690	−0.648145	−0.324072	−	0.946032i	$-0.605052\pi$
$577$	−15.5690	−0.648145	−0.324072	+	0.946032i	$0.605052\pi$
$578$	16.8826	0.702222
$579$	−39.5505	−1.64366
$580$	8.32042	0.345487
$581$	22.3944	0.929075
$582$	22.4410	0.930210
$583$	−3.06385	−0.126892
$584$	1.00000	0.0413803
$585$	−13.2717	−0.548718
$586$	11.0458	0.456298
$587$	26.7609	1.10454	0.552271	−	0.833665i	$-0.313761\pi$
$587$	26.7609	1.10454	0.552271	+	0.833665i	$0.313761\pi$
$588$	−20.5717	−0.848365
$589$	−11.0946	−0.457147
$590$	−3.32278	−0.136797
$591$	30.5767	1.25776
$592$	0.181197	0.00744716
$593$	−16.4764	−0.676603	−0.338302	−	0.941038i	$-0.609852\pi$
$593$	−16.4764	−0.676603	−0.338302	+	0.941038i	$0.609852\pi$
$594$	−1.71753	−0.0704710
$595$	1.36978	0.0561556
$596$	9.92464	0.406529
$597$	−60.1495	−2.46175
$598$	−19.5180	−0.798152
$599$	14.1353	0.577551	0.288776	−	0.957397i	$-0.406752\pi$
$599$	14.1353	0.577551	0.288776	+	0.957397i	$0.406752\pi$
$600$	2.29138	0.0935454
$601$	−4.34227	−0.177125	−0.0885624	−	0.996071i	$-0.528227\pi$
$601$	−4.34227	−0.177125	−0.0885624	+	0.996071i	$0.528227\pi$
$602$	2.10296	0.0857103
$603$	30.7214	1.25107
$604$	−1.01353	−0.0412399
$605$	1.00000	0.0406558
$606$	25.9755	1.05518
$607$	−8.16056	−0.331227	−0.165614	−	0.986191i	$-0.552960\pi$
$607$	−8.16056	−0.331227	−0.165614	+	0.986191i	$0.552960\pi$
$608$	3.73006	0.151274
$609$	−76.2084	−3.08812
$610$	7.98125	0.323151
$611$	67.0230	2.71146
$612$	0.771187	0.0311734
$613$	−34.6202	−1.39830	−0.699149	−	0.714976i	$-0.746438\pi$
$613$	−34.6202	−1.39830	−0.699149	+	0.714976i	$0.746438\pi$
$614$	19.8683	0.801820
$615$	−2.09997	−0.0846788
$616$	−3.99723	−0.161053
$617$	20.1835	0.812556	0.406278	−	0.913750i	$-0.366827\pi$
$617$	20.1835	0.812556	0.406278	+	0.913750i	$0.366827\pi$
$618$	−15.8173	−0.636264
$619$	−25.9737	−1.04397	−0.521985	−	0.852955i	$-0.674808\pi$
$619$	−25.9737	−1.04397	−0.521985	+	0.852955i	$0.674808\pi$
$620$	2.97439	0.119454
$621$	−5.68434	−0.228105
$622$	23.5556	0.944494
$623$	−66.3370	−2.65774
$624$	13.5132	0.540960
$625$	1.00000	0.0400000
$626$	33.1423	1.32463
$627$	8.54699	0.341334
$628$	−11.4714	−0.457759
$629$	0.0620931	0.00247581
$630$	−8.99554	−0.358391
$631$	−22.4183	−0.892457	−0.446229	−	0.894919i	$-0.647233\pi$
$631$	−22.4183	−0.892457	−0.446229	+	0.894919i	$0.647233\pi$
$632$	8.19081	0.325813
$633$	−14.3592	−0.570727
$634$	19.3282	0.767620
$635$	−14.0797	−0.558736
$636$	7.02046	0.278379
$637$	−52.9460	−2.09780
$638$	−8.32042	−0.329409
$639$	3.55877	0.140783
$640$	−1.00000	−0.0395285
$641$	−13.0496	−0.515426	−0.257713	−	0.966221i	$-0.582969\pi$
$641$	−13.0496	−0.515426	−0.257713	+	0.966221i	$0.582969\pi$
$642$	−26.4911	−1.04552
$643$	17.8838	0.705269	0.352634	−	0.935761i	$-0.385286\pi$
$643$	17.8838	0.705269	0.352634	+	0.935761i	$0.385286\pi$
$644$	−13.2293	−0.521306
$645$	1.20551	0.0474668
$646$	1.27823	0.0502911
$647$	−3.46161	−0.136090	−0.0680449	−	0.997682i	$-0.521676\pi$
$647$	−3.46161	−0.136090	−0.0680449	+	0.997682i	$0.521676\pi$
$648$	10.6868	0.419819
$649$	3.32278	0.130430
$650$	5.89738	0.231314
$651$	−27.2430	−1.06774
$652$	−25.3855	−0.994173
$653$	35.4338	1.38663	0.693316	−	0.720633i	$-0.256149\pi$
$653$	35.4338	1.38663	0.693316	+	0.720633i	$0.256149\pi$
$654$	10.4794	0.409776
$655$	−16.6850	−0.651938
$656$	0.916462	0.0357818
$657$	−2.25044	−0.0877981
$658$	45.4280	1.77097
$659$	−18.6726	−0.727383	−0.363691	−	0.931520i	$-0.618484\pi$
$659$	−18.6726	−0.727383	−0.363691	+	0.931520i	$0.618484\pi$
$660$	−2.29138	−0.0891920
$661$	−29.4619	−1.14593	−0.572967	−	0.819578i	$-0.694208\pi$
$661$	−29.4619	−1.14593	−0.572967	+	0.819578i	$0.694208\pi$
$662$	−29.4924	−1.14626
$663$	4.63073	0.179843
$664$	−5.60247	−0.217418
$665$	−14.9099	−0.578181
$666$	−0.407773	−0.0158009
$667$	−27.5373	−1.06625
$668$	−4.66214	−0.180383
$669$	34.4407	1.33155
$670$	−13.6513	−0.527396
$671$	−7.98125	−0.308113
$672$	9.15920	0.353324
$673$	−48.2504	−1.85992	−0.929958	−	0.367665i	$-0.880157\pi$
$673$	−48.2504	−1.85992	−0.929958	+	0.367665i	$0.880157\pi$
$674$	23.3262	0.898493
$675$	1.71753	0.0661077
$676$	21.7791	0.837659
$677$	39.4971	1.51800	0.758998	−	0.651093i	$-0.225689\pi$
$677$	39.4971	1.51800	0.758998	+	0.651093i	$0.225689\pi$
$678$	6.86951	0.263822
$679$	39.1475	1.50234
$680$	−0.342682	−0.0131413
$681$	−17.6381	−0.675895
$682$	−2.97439	−0.113895
$683$	−23.2945	−0.891341	−0.445670	−	0.895197i	$-0.647035\pi$
$683$	−23.2945	−0.891341	−0.445670	+	0.895197i	$0.647035\pi$
$684$	−8.39427	−0.320963
$685$	−17.3651	−0.663486
$686$	−7.90601	−0.301853
$687$	20.2508	0.772618
$688$	−0.526104	−0.0200575
$689$	18.0687	0.688363
$690$	−7.58358	−0.288702
$691$	34.6364	1.31763	0.658815	−	0.752305i	$-0.271058\pi$
$691$	34.6364	1.31763	0.658815	+	0.752305i	$0.271058\pi$
$692$	2.85656	0.108590
$693$	8.99554	0.341712
$694$	−7.22040	−0.274083
$695$	5.64148	0.213994
$696$	19.0653	0.722668
$697$	0.314055	0.0118957
$698$	17.4248	0.659539
$699$	−9.53076	−0.360486
$700$	3.99723	0.151081
$701$	42.3474	1.59944	0.799720	−	0.600373i	$-0.204981\pi$
$701$	42.3474	1.59944	0.799720	+	0.600373i	$0.204981\pi$
$702$	10.1289	0.382292
$703$	−0.675876	−0.0254911
$704$	1.00000	0.0376889
$705$	26.0413	0.980771
$706$	−11.8334	−0.445357
$707$	45.3132	1.70418
$708$	−7.61375	−0.286142
$709$	−38.6621	−1.45199	−0.725993	−	0.687703i	$-0.758619\pi$
$709$	−38.6621	−1.45199	−0.725993	+	0.687703i	$0.758619\pi$
$710$	−1.58137	−0.0593476
$711$	−18.4329	−0.691289
$712$	16.5957	0.621952
$713$	−9.84407	−0.368663
$714$	3.13870	0.117463
$715$	−5.89738	−0.220550
$716$	24.4413	0.913413
$717$	−28.4828	−1.06371
$718$	−10.1810	−0.379951
$719$	−0.647098	−0.0241327	−0.0120663	−	0.999927i	$-0.503841\pi$
$719$	−0.647098	−0.0241327	−0.0120663	+	0.999927i	$0.503841\pi$
$720$	2.25044	0.0838690
$721$	−27.5926	−1.02760
$722$	5.08667	0.189306
$723$	50.5934	1.88159
$724$	1.71240	0.0636409
$725$	8.32042	0.309013
$726$	2.29138	0.0850412
$727$	−5.87830	−0.218014	−0.109007	−	0.994041i	$-0.534767\pi$
$727$	−5.87830	−0.218014	−0.109007	+	0.994041i	$0.534767\pi$
$728$	23.5732	0.873682
$729$	−12.2435	−0.453465
$730$	1.00000	0.0370117
$731$	−0.180287	−0.00666814
$732$	18.2881	0.675948
$733$	−26.4511	−0.976992	−0.488496	−	0.872566i	$-0.662454\pi$
$733$	−26.4511	−0.976992	−0.488496	+	0.872566i	$0.662454\pi$
$734$	12.2471	0.452047
$735$	−20.5717	−0.758800
$736$	3.30961	0.121994
$737$	13.6513	0.502852
$738$	−2.06244	−0.0759196
$739$	29.9862	1.10306	0.551530	−	0.834155i	$-0.314044\pi$
$739$	29.9862	1.10306	0.551530	+	0.834155i	$0.314044\pi$
$740$	0.181197	0.00666094
$741$	−50.4049	−1.85167
$742$	12.2469	0.449599
$743$	−3.97233	−0.145731	−0.0728653	−	0.997342i	$-0.523214\pi$
$743$	−3.97233	−0.145731	−0.0728653	+	0.997342i	$0.523214\pi$
$744$	6.81547	0.249867
$745$	9.92464	0.363611
$746$	25.1095	0.919324
$747$	12.6080	0.461304
$748$	0.342682	0.0125297
$749$	−46.2127	−1.68858
$750$	2.29138	0.0836695
$751$	49.5975	1.80984	0.904919	−	0.425584i	$-0.139931\pi$
$751$	49.5975	1.80984	0.904919	+	0.425584i	$0.139931\pi$
$752$	−11.3649	−0.414434
$753$	−11.9474	−0.435388
$754$	49.0687	1.78698
$755$	−1.01353	−0.0368861
$756$	6.86536	0.249691
$757$	−46.3020	−1.68287	−0.841437	−	0.540355i	$-0.818290\pi$
$757$	−46.3020	−1.68287	−0.841437	+	0.540355i	$0.818290\pi$
$758$	−9.00049	−0.326913
$759$	7.58358	0.275267
$760$	3.73006	0.135303
$761$	−39.6711	−1.43808	−0.719038	−	0.694971i	$-0.755417\pi$
$761$	−39.6711	−1.43808	−0.719038	+	0.694971i	$0.755417\pi$
$762$	−32.2620	−1.16873
$763$	18.2809	0.661812
$764$	−17.4883	−0.632706
$765$	0.771187	0.0278823
$766$	3.77890	0.136537
$767$	−19.5957	−0.707559
$768$	−2.29138	−0.0826832
$769$	−39.0595	−1.40852	−0.704261	−	0.709941i	$-0.748722\pi$
$769$	−39.0595	−1.40852	−0.704261	+	0.709941i	$0.748722\pi$
$770$	−3.99723	−0.144050
$771$	−47.2123	−1.70031
$772$	17.2605	0.621220
$773$	27.1481	0.976451	0.488225	−	0.872718i	$-0.337644\pi$
$773$	27.1481	0.976451	0.488225	+	0.872718i	$0.337644\pi$
$774$	1.18397	0.0425568
$775$	2.97439	0.106843
$776$	−9.79365	−0.351572
$777$	−1.65962	−0.0595385
$778$	8.21748	0.294611
$779$	−3.41846	−0.122479
$780$	13.5132	0.483849
$781$	1.58137	0.0565857
$782$	1.13414	0.0405569
$783$	14.2906	0.510703
$784$	8.97787	0.320638
$785$	−11.4714	−0.409432
$786$	−38.2318	−1.36368
$787$	−5.33508	−0.190175	−0.0950876	−	0.995469i	$-0.530313\pi$
$787$	−5.33508	−0.190175	−0.0950876	+	0.995469i	$0.530313\pi$
$788$	−13.3442	−0.475367
$789$	−72.4453	−2.57912
$790$	8.19081	0.291416
$791$	11.9836	0.426088
$792$	−2.25044	−0.0799659
$793$	47.0685	1.67145
$794$	12.2142	0.433466
$795$	7.02046	0.248990
$796$	26.2503	0.930417
$797$	−4.76765	−0.168879	−0.0844394	−	0.996429i	$-0.526910\pi$
$797$	−4.76765	−0.168879	−0.0844394	+	0.996429i	$0.526910\pi$
$798$	−34.1643	−1.20940
$799$	−3.89454	−0.137779
$800$	−1.00000	−0.0353553
$801$	−37.3477	−1.31962
$802$	−1.08058	−0.0381567
$803$	−1.00000	−0.0352892
$804$	−31.2804	−1.10317
$805$	−13.2293	−0.466271
$806$	17.5411	0.617860
$807$	−19.0308	−0.669914
$808$	−11.3362	−0.398804
$809$	−43.1208	−1.51605	−0.758023	−	0.652228i	$-0.773834\pi$
$809$	−43.1208	−1.51605	−0.758023	+	0.652228i	$0.773834\pi$
$810$	10.6868	0.375497
$811$	−31.8379	−1.11798	−0.558990	−	0.829174i	$-0.688811\pi$
$811$	−31.8379	−1.11798	−0.558990	+	0.829174i	$0.688811\pi$
$812$	33.2587	1.16715
$813$	−8.27450	−0.290199
$814$	−0.181197	−0.00635096
$815$	−25.3855	−0.889216
$816$	−0.785217	−0.0274881
$817$	1.96240	0.0686557
$818$	9.69607	0.339015
$819$	−53.0501	−1.85372
$820$	0.916462	0.0320042
$821$	20.0722	0.700526	0.350263	−	0.936651i	$-0.386092\pi$
$821$	20.0722	0.700526	0.350263	+	0.936651i	$0.386092\pi$
$822$	−39.7901	−1.38784
$823$	−44.3948	−1.54751	−0.773753	−	0.633488i	$-0.781623\pi$
$823$	−44.3948	−1.54751	−0.773753	+	0.633488i	$0.781623\pi$
$824$	6.90293	0.240475
$825$	−2.29138	−0.0797758
$826$	−13.2819	−0.462137
$827$	24.0435	0.836076	0.418038	−	0.908430i	$-0.362718\pi$
$827$	24.0435	0.836076	0.418038	+	0.908430i	$0.362718\pi$
$828$	−7.44808	−0.258839
$829$	36.6581	1.27319	0.636595	−	0.771198i	$-0.280342\pi$
$829$	36.6581	1.27319	0.636595	+	0.771198i	$0.280342\pi$
$830$	−5.60247	−0.194465
$831$	−54.6402	−1.89545
$832$	−5.89738	−0.204455
$833$	3.07656	0.106596
$834$	12.9268	0.447618
$835$	−4.66214	−0.161340
$836$	−3.73006	−0.129007
$837$	5.10860	0.176579
$838$	6.95727	0.240335
$839$	52.3312	1.80667	0.903337	−	0.428931i	$-0.141110\pi$
$839$	52.3312	1.80667	0.903337	+	0.428931i	$0.141110\pi$
$840$	9.15920	0.316022
$841$	40.2295	1.38722
$842$	11.8235	0.407463
$843$	1.83703	0.0632707
$844$	6.26661	0.215706
$845$	21.7791	0.749225
$846$	25.5760	0.879320
$847$	3.99723	0.137347
$848$	−3.06385	−0.105213
$849$	−0.153658	−0.00527355
$850$	−0.342682	−0.0117539
$851$	−0.599691	−0.0205572
$852$	−3.62352	−0.124140
$853$	−23.7792	−0.814185	−0.407093	−	0.913387i	$-0.633457\pi$
$853$	−23.7792	−0.814185	−0.407093	+	0.913387i	$0.633457\pi$
$854$	31.9029	1.09170
$855$	−8.39427	−0.287078
$856$	11.5612	0.395153
$857$	−36.2566	−1.23850	−0.619250	−	0.785194i	$-0.712563\pi$
$857$	−36.2566	−1.23850	−0.619250	+	0.785194i	$0.712563\pi$
$858$	−13.5132	−0.461332
$859$	−7.73115	−0.263783	−0.131892	−	0.991264i	$-0.542105\pi$
$859$	−7.73115	−0.263783	−0.131892	+	0.991264i	$0.542105\pi$
$860$	−0.526104	−0.0179400
$861$	−8.39406	−0.286069
$862$	−1.33137	−0.0453467
$863$	−38.8300	−1.32179	−0.660894	−	0.750479i	$-0.729823\pi$
$863$	−38.8300	−1.32179	−0.660894	+	0.750479i	$0.729823\pi$
$864$	−1.71753	−0.0584315
$865$	2.85656	0.0971259
$866$	25.0102	0.849880
$867$	38.6844	1.31379
$868$	11.8893	0.403550
$869$	−8.19081	−0.277854
$870$	19.0653	0.646374
$871$	−80.5069	−2.72787
$872$	−4.57338	−0.154874
$873$	22.0400	0.745942
$874$	−12.3450	−0.417577
$875$	3.99723	0.135131
$876$	2.29138	0.0774187
$877$	34.1534	1.15328	0.576639	−	0.816999i	$-0.304364\pi$
$877$	34.1534	1.15328	0.576639	+	0.816999i	$0.304364\pi$
$878$	−2.73101	−0.0921672
$879$	25.3102	0.853692
$880$	1.00000	0.0337100
$881$	−43.7801	−1.47499	−0.737495	−	0.675353i	$-0.763991\pi$
$881$	−43.7801	−1.47499	−0.737495	+	0.675353i	$0.763991\pi$
$882$	−20.2042	−0.680310
$883$	39.5408	1.33065	0.665327	−	0.746552i	$-0.268292\pi$
$883$	39.5408	1.33065	0.665327	+	0.746552i	$0.268292\pi$
$884$	−2.02093	−0.0679712
$885$	−7.61375	−0.255934
$886$	22.8468	0.767552
$887$	0.320000	0.0107446	0.00537228	−	0.999986i	$-0.498290\pi$
$887$	0.320000	0.0107446	0.00537228	+	0.999986i	$0.498290\pi$
$888$	0.415192	0.0139329
$889$	−56.2799	−1.88757
$890$	16.5957	0.556290
$891$	−10.6868	−0.358023
$892$	−15.0305	−0.503259
$893$	42.3916	1.41858
$894$	22.7412	0.760578
$895$	24.4413	0.816981
$896$	−3.99723	−0.133538
$897$	−44.7233	−1.49327
$898$	8.32217	0.277715
$899$	24.7482	0.825398
$900$	2.25044	0.0750147
$901$	−1.04993	−0.0349782
$902$	−0.916462	−0.0305149
$903$	4.81869	0.160356
$904$	−2.99798	−0.0997112
$905$	1.71240	0.0569221
$906$	−2.32238	−0.0771560
$907$	−33.7322	−1.12006	−0.560030	−	0.828472i	$-0.689211\pi$
$907$	−33.7322	−1.12006	−0.560030	+	0.828472i	$0.689211\pi$
$908$	7.69759	0.255453
$909$	25.5113	0.846158
$910$	23.5732	0.781445
$911$	2.99156	0.0991147	0.0495573	−	0.998771i	$-0.484219\pi$
$911$	2.99156	0.0991147	0.0495573	+	0.998771i	$0.484219\pi$
$912$	8.54699	0.283019
$913$	5.60247	0.185415
$914$	31.3373	1.03655
$915$	18.2881	0.604586
$916$	−8.83782	−0.292010
$917$	−66.6939	−2.20243
$918$	−0.588567	−0.0194256
$919$	−42.0031	−1.38555	−0.692777	−	0.721152i	$-0.743613\pi$
$919$	−42.0031	−1.38555	−0.692777	+	0.721152i	$0.743613\pi$
$920$	3.30961	0.109115
$921$	45.5260	1.50013
$922$	−24.1527	−0.795427
$923$	−9.32592	−0.306966
$924$	−9.15920	−0.301315
$925$	0.181197	0.00595772
$926$	−9.10157	−0.299096
$927$	−15.5346	−0.510224
$928$	−8.32042	−0.273131
$929$	20.4967	0.672476	0.336238	−	0.941777i	$-0.390845\pi$
$929$	20.4967	0.672476	0.336238	+	0.941777i	$0.390845\pi$
$930$	6.81547	0.223488
$931$	−33.4880	−1.09752
$932$	4.15939	0.136245
$933$	53.9750	1.76706
$934$	−14.3421	−0.469286
$935$	0.342682	0.0112069
$936$	13.2717	0.433800
$937$	14.4188	0.471041	0.235520	−	0.971869i	$-0.424321\pi$
$937$	14.4188	0.471041	0.235520	+	0.971869i	$0.424321\pi$
$938$	−54.5674	−1.78169
$939$	75.9417	2.47826
$940$	−11.3649	−0.370681
$941$	23.3390	0.760829	0.380414	−	0.924816i	$-0.375781\pi$
$941$	23.3390	0.760829	0.380414	+	0.924816i	$0.375781\pi$
$942$	−26.2854	−0.856424
$943$	−3.03313	−0.0987723
$944$	3.32278	0.108147
$945$	6.86536	0.223330
$946$	0.526104	0.0171051
$947$	−23.5265	−0.764509	−0.382255	−	0.924057i	$-0.624852\pi$
$947$	−23.5265	−0.764509	−0.382255	+	0.924057i	$0.624852\pi$
$948$	18.7683	0.609566
$949$	5.89738	0.191437
$950$	3.73006	0.121019
$951$	44.2883	1.43615
$952$	−1.36978	−0.0443949
$953$	55.6965	1.80419	0.902093	−	0.431542i	$-0.142030\pi$
$953$	55.6965	1.80419	0.902093	+	0.431542i	$0.142030\pi$
$954$	6.89502	0.223234
$955$	−17.4883	−0.565910
$956$	12.4304	0.402028
$957$	−19.0653	−0.616293
$958$	−4.24365	−0.137106
$959$	−69.4123	−2.24144
$960$	−2.29138	−0.0739541
$961$	−22.1530	−0.714613
$962$	1.06859	0.0344527
$963$	−26.0178	−0.838410
$964$	−22.0798	−0.711144
$965$	17.2605	0.555637
$966$	−30.3133	−0.975316
$967$	−36.4464	−1.17204	−0.586019	−	0.810297i	$-0.699306\pi$
$967$	−36.4464	−1.17204	−0.586019	+	0.810297i	$0.699306\pi$
$968$	−1.00000	−0.0321412
$969$	2.92891	0.0940900
$970$	−9.79365	−0.314455
$971$	29.4772	0.945968	0.472984	−	0.881071i	$-0.343177\pi$
$971$	29.4772	0.945968	0.472984	+	0.881071i	$0.343177\pi$
$972$	19.3351	0.620173
$973$	22.5503	0.722930
$974$	5.32276	0.170552
$975$	13.5132	0.432768
$976$	−7.98125	−0.255474
$977$	−16.5112	−0.528241	−0.264120	−	0.964490i	$-0.585082\pi$
$977$	−16.5112	−0.528241	−0.264120	+	0.964490i	$0.585082\pi$
$978$	−58.1680	−1.86001
$979$	−16.5957	−0.530402
$980$	8.97787	0.286788
$981$	10.2921	0.328602
$982$	11.8656	0.378647
$983$	−15.2062	−0.485004	−0.242502	−	0.970151i	$-0.577968\pi$
$983$	−15.2062	−0.485004	−0.242502	+	0.970151i	$0.577968\pi$
$984$	2.09997	0.0669445
$985$	−13.3442	−0.425182
$986$	−2.85126	−0.0908027
$987$	104.093	3.31332
$988$	21.9976	0.699836
$989$	1.74120	0.0553669
$990$	−2.25044	−0.0715237
$991$	45.2659	1.43792	0.718960	−	0.695052i	$-0.244619\pi$
$991$	45.2659	1.43792	0.718960	+	0.695052i	$0.244619\pi$
$992$	−2.97439	−0.0944370
$993$	−67.5785	−2.14454
$994$	−6.32109	−0.200493
$995$	26.2503	0.832190
$996$	−12.8374	−0.406769
$997$	−25.4794	−0.806942	−0.403471	−	0.914993i	$-0.632196\pi$
$997$	−25.4794	−0.806942	−0.403471	+	0.914993i	$0.632196\pi$
$998$	−28.0055	−0.886498
$999$	0.311211	0.00984628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8030.2.a.bc.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8030.2.a.bc.1.4	✓	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:	\( N \)	\(=\)	\( 8030 = 2 \cdot 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8030.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.29138 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.29138 q^{6} +3.99723 q^{7} -1.00000 q^{8} +2.25044 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.29138 q^{3} +1.00000 q^{4} +1.00000 q^{5} +2.29138 q^{6} +3.99723 q^{7} -1.00000 q^{8} +2.25044 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.29138 q^{12} -5.89738 q^{13} -3.99723 q^{14} -2.29138 q^{15} +1.00000 q^{16} +0.342682 q^{17} -2.25044 q^{18} -3.73006 q^{19} +1.00000 q^{20} -9.15920 q^{21} -1.00000 q^{22} -3.30961 q^{23} +2.29138 q^{24} +1.00000 q^{25} +5.89738 q^{26} +1.71753 q^{27} +3.99723 q^{28} +8.32042 q^{29} +2.29138 q^{30} +2.97439 q^{31} -1.00000 q^{32} -2.29138 q^{33} -0.342682 q^{34} +3.99723 q^{35} +2.25044 q^{36} +0.181197 q^{37} +3.73006 q^{38} +13.5132 q^{39} -1.00000 q^{40} +0.916462 q^{41} +9.15920 q^{42} -0.526104 q^{43} +1.00000 q^{44} +2.25044 q^{45} +3.30961 q^{46} -11.3649 q^{47} -2.29138 q^{48} +8.97787 q^{49} -1.00000 q^{50} -0.785217 q^{51} -5.89738 q^{52} -3.06385 q^{53} -1.71753 q^{54} +1.00000 q^{55} -3.99723 q^{56} +8.54699 q^{57} -8.32042 q^{58} +3.32278 q^{59} -2.29138 q^{60} -7.98125 q^{61} -2.97439 q^{62} +8.99554 q^{63} +1.00000 q^{64} -5.89738 q^{65} +2.29138 q^{66} +13.6513 q^{67} +0.342682 q^{68} +7.58358 q^{69} -3.99723 q^{70} +1.58137 q^{71} -2.25044 q^{72} -1.00000 q^{73} -0.181197 q^{74} -2.29138 q^{75} -3.73006 q^{76} +3.99723 q^{77} -13.5132 q^{78} -8.19081 q^{79} +1.00000 q^{80} -10.6868 q^{81} -0.916462 q^{82} +5.60247 q^{83} -9.15920 q^{84} +0.342682 q^{85} +0.526104 q^{86} -19.0653 q^{87} -1.00000 q^{88} -16.5957 q^{89} -2.25044 q^{90} -23.5732 q^{91} -3.30961 q^{92} -6.81547 q^{93} +11.3649 q^{94} -3.73006 q^{95} +2.29138 q^{96} +9.79365 q^{97} -8.97787 q^{98} +2.25044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - 5 q^{3} + 11 q^{4} + 11 q^{5} + 5 q^{6} - q^{7} - 11 q^{8} + 12 q^{9} - 11 q^{10} + 11 q^{11} - 5 q^{12} - 8 q^{13} + q^{14} - 5 q^{15} + 11 q^{16} - 15 q^{17} - 12 q^{18} + 5 q^{19} + 11 q^{20} - 11 q^{22} - 24 q^{23} + 5 q^{24} + 11 q^{25} + 8 q^{26} - 32 q^{27} - q^{28} + 10 q^{29} + 5 q^{30} + 7 q^{31} - 11 q^{32} - 5 q^{33} + 15 q^{34} - q^{35} + 12 q^{36} - 24 q^{37} - 5 q^{38} + 3 q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} + 11 q^{44} + 12 q^{45} + 24 q^{46} - 8 q^{47} - 5 q^{48} - 18 q^{49} - 11 q^{50} + 22 q^{51} - 8 q^{52} - 30 q^{53} + 32 q^{54} + 11 q^{55} + q^{56} - 32 q^{57} - 10 q^{58} + 8 q^{59} - 5 q^{60} - 26 q^{61} - 7 q^{62} - 5 q^{63} + 11 q^{64} - 8 q^{65} + 5 q^{66} - 24 q^{67} - 15 q^{68} - 25 q^{69} + q^{70} + 16 q^{71} - 12 q^{72} - 11 q^{73} + 24 q^{74} - 5 q^{75} + 5 q^{76} - q^{77} - 3 q^{78} + 4 q^{79} + 11 q^{80} - 13 q^{81} - 10 q^{82} - 2 q^{83} - 15 q^{85} + 14 q^{86} - 17 q^{87} - 11 q^{88} - 11 q^{89} - 12 q^{90} - 41 q^{91} - 24 q^{92} - 15 q^{93} + 8 q^{94} + 5 q^{95} + 5 q^{96} - 37 q^{97} + 18 q^{98} + 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 5 * q^3 + 11 * q^4 + 11 * q^5 + 5 * q^6 - q^7 - 11 * q^8 + 12 * q^9 - 11 * q^10 + 11 * q^11 - 5 * q^12 - 8 * q^13 + q^14 - 5 * q^15 + 11 * q^16 - 15 * q^17 - 12 * q^18 + 5 * q^19 + 11 * q^20 - 11 * q^22 - 24 * q^23 + 5 * q^24 + 11 * q^25 + 8 * q^26 - 32 * q^27 - q^28 + 10 * q^29 + 5 * q^30 + 7 * q^31 - 11 * q^32 - 5 * q^33 + 15 * q^34 - q^35 + 12 * q^36 - 24 * q^37 - 5 * q^38 + 3 * q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 + 11 * q^44 + 12 * q^45 + 24 * q^46 - 8 * q^47 - 5 * q^48 - 18 * q^49 - 11 * q^50 + 22 * q^51 - 8 * q^52 - 30 * q^53 + 32 * q^54 + 11 * q^55 + q^56 - 32 * q^57 - 10 * q^58 + 8 * q^59 - 5 * q^60 - 26 * q^61 - 7 * q^62 - 5 * q^63 + 11 * q^64 - 8 * q^65 + 5 * q^66 - 24 * q^67 - 15 * q^68 - 25 * q^69 + q^70 + 16 * q^71 - 12 * q^72 - 11 * q^73 + 24 * q^74 - 5 * q^75 + 5 * q^76 - q^77 - 3 * q^78 + 4 * q^79 + 11 * q^80 - 13 * q^81 - 10 * q^82 - 2 * q^83 - 15 * q^85 + 14 * q^86 - 17 * q^87 - 11 * q^88 - 11 * q^89 - 12 * q^90 - 41 * q^91 - 24 * q^92 - 15 * q^93 + 8 * q^94 + 5 * q^95 + 5 * q^96 - 37 * q^97 + 18 * q^98 + 12 * q^99

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