LMFDB - Embedded newform 1334.2.a.k.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 $ x^10 - 5x^9 - 8x^8 + 60x^7 + 13x^6 - 241x^5 + 6x^4 + 346x^3 + 16x^2 - 64*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.20998$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} -1.11783 q^{5} -1.20998 q^{6} -0.129988 q^{7} +1.00000 q^{8} -1.53596 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} -1.11783 q^{5} -1.20998 q^{6} -0.129988 q^{7} +1.00000 q^{8} -1.53596 q^{9} -1.11783 q^{10} +3.11750 q^{11} -1.20998 q^{12} +6.27035 q^{13} -0.129988 q^{14} +1.35255 q^{15} +1.00000 q^{16} -1.75169 q^{17} -1.53596 q^{18} -5.63256 q^{19} -1.11783 q^{20} +0.157283 q^{21} +3.11750 q^{22} +1.00000 q^{23} -1.20998 q^{24} -3.75046 q^{25} +6.27035 q^{26} +5.48840 q^{27} -0.129988 q^{28} +1.00000 q^{29} +1.35255 q^{30} +10.4681 q^{31} +1.00000 q^{32} -3.77210 q^{33} -1.75169 q^{34} +0.145304 q^{35} -1.53596 q^{36} +8.19710 q^{37} -5.63256 q^{38} -7.58698 q^{39} -1.11783 q^{40} +7.36357 q^{41} +0.157283 q^{42} +0.205564 q^{43} +3.11750 q^{44} +1.71694 q^{45} +1.00000 q^{46} +2.32196 q^{47} -1.20998 q^{48} -6.98310 q^{49} -3.75046 q^{50} +2.11951 q^{51} +6.27035 q^{52} +4.62519 q^{53} +5.48840 q^{54} -3.48483 q^{55} -0.129988 q^{56} +6.81527 q^{57} +1.00000 q^{58} +6.32600 q^{59} +1.35255 q^{60} +9.72943 q^{61} +10.4681 q^{62} +0.199656 q^{63} +1.00000 q^{64} -7.00918 q^{65} -3.77210 q^{66} +11.4742 q^{67} -1.75169 q^{68} -1.20998 q^{69} +0.145304 q^{70} +2.68556 q^{71} -1.53596 q^{72} +10.4380 q^{73} +8.19710 q^{74} +4.53797 q^{75} -5.63256 q^{76} -0.405238 q^{77} -7.58698 q^{78} +0.00107576 q^{79} -1.11783 q^{80} -2.03296 q^{81} +7.36357 q^{82} -9.48695 q^{83} +0.157283 q^{84} +1.95809 q^{85} +0.205564 q^{86} -1.20998 q^{87} +3.11750 q^{88} -8.32545 q^{89} +1.71694 q^{90} -0.815071 q^{91} +1.00000 q^{92} -12.6662 q^{93} +2.32196 q^{94} +6.29624 q^{95} -1.20998 q^{96} -18.4768 q^{97} -6.98310 q^{98} -4.78835 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) $ 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * 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
$3$	−1.20998	−0.698580	−0.349290	−	0.937015i	$-0.613577\pi$
$3$	−1.20998	−0.698580	−0.349290	+	0.937015i	$0.613577\pi$
$4$	1.00000	0.500000
$5$	−1.11783	−0.499908	−0.249954	−	0.968258i	$-0.580416\pi$
$5$	−1.11783	−0.499908	−0.249954	+	0.968258i	$0.580416\pi$
$6$	−1.20998	−0.493971
$7$	−0.129988	−0.0491309	−0.0245654	−	0.999698i	$-0.507820\pi$
$7$	−0.129988	−0.0491309	−0.0245654	+	0.999698i	$0.507820\pi$
$8$	1.00000	0.353553
$9$	−1.53596	−0.511986
$10$	−1.11783	−0.353488
$11$	3.11750	0.939962	0.469981	−	0.882676i	$-0.344261\pi$
$11$	3.11750	0.939962	0.469981	+	0.882676i	$0.344261\pi$
$12$	−1.20998	−0.349290
$13$	6.27035	1.73908	0.869541	−	0.493860i	$-0.164415\pi$
$13$	6.27035	1.73908	0.869541	+	0.493860i	$0.164415\pi$
$14$	−0.129988	−0.0347408
$15$	1.35255	0.349226
$16$	1.00000	0.250000
$17$	−1.75169	−0.424848	−0.212424	−	0.977178i	$-0.568136\pi$
$17$	−1.75169	−0.424848	−0.212424	+	0.977178i	$0.568136\pi$
$18$	−1.53596	−0.362029
$19$	−5.63256	−1.29220	−0.646099	−	0.763253i	$-0.723601\pi$
$19$	−5.63256	−1.29220	−0.646099	+	0.763253i	$0.723601\pi$
$20$	−1.11783	−0.249954
$21$	0.157283	0.0343219
$22$	3.11750	0.664654
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.20998	−0.246985
$25$	−3.75046	−0.750092
$26$	6.27035	1.22972
$27$	5.48840	1.05624
$28$	−0.129988	−0.0245654
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.35255	0.246940
$31$	10.4681	1.88013	0.940067	−	0.340990i	$-0.110762\pi$
$31$	10.4681	1.88013	0.940067	+	0.340990i	$0.110762\pi$
$32$	1.00000	0.176777
$33$	−3.77210	−0.656639
$34$	−1.75169	−0.300413
$35$	0.145304	0.0245609
$36$	−1.53596	−0.255993
$37$	8.19710	1.34759	0.673797	−	0.738916i	$-0.264662\pi$
$37$	8.19710	1.34759	0.673797	+	0.738916i	$0.264662\pi$
$38$	−5.63256	−0.913722
$39$	−7.58698	−1.21489
$40$	−1.11783	−0.176744
$41$	7.36357	1.15000	0.574999	−	0.818154i	$-0.305003\pi$
$41$	7.36357	1.15000	0.574999	+	0.818154i	$0.305003\pi$
$42$	0.157283	0.0242692
$43$	0.205564	0.0313482	0.0156741	−	0.999877i	$-0.495011\pi$
$43$	0.205564	0.0313482	0.0156741	+	0.999877i	$0.495011\pi$
$44$	3.11750	0.469981
$45$	1.71694	0.255946
$46$	1.00000	0.147442
$47$	2.32196	0.338693	0.169347	−	0.985557i	$-0.445834\pi$
$47$	2.32196	0.338693	0.169347	+	0.985557i	$0.445834\pi$
$48$	−1.20998	−0.174645
$49$	−6.98310	−0.997586
$50$	−3.75046	−0.530395
$51$	2.11951	0.296791
$52$	6.27035	0.869541
$53$	4.62519	0.635319	0.317659	−	0.948205i	$-0.397103\pi$
$53$	4.62519	0.635319	0.317659	+	0.948205i	$0.397103\pi$
$54$	5.48840	0.746877
$55$	−3.48483	−0.469895
$56$	−0.129988	−0.0173704
$57$	6.81527	0.902704
$58$	1.00000	0.131306
$59$	6.32600	0.823575	0.411788	−	0.911280i	$-0.364905\pi$
$59$	6.32600	0.823575	0.411788	+	0.911280i	$0.364905\pi$
$60$	1.35255	0.174613
$61$	9.72943	1.24573	0.622863	−	0.782331i	$-0.285969\pi$
$61$	9.72943	1.24573	0.622863	+	0.782331i	$0.285969\pi$
$62$	10.4681	1.32946
$63$	0.199656	0.0251543
$64$	1.00000	0.125000
$65$	−7.00918	−0.869381
$66$	−3.77210	−0.464314
$67$	11.4742	1.40180	0.700898	−	0.713262i	$-0.252783\pi$
$67$	11.4742	1.40180	0.700898	+	0.713262i	$0.252783\pi$
$68$	−1.75169	−0.212424
$69$	−1.20998	−0.145664
$70$	0.145304	0.0173672
$71$	2.68556	0.318717	0.159358	−	0.987221i	$-0.449057\pi$
$71$	2.68556	0.318717	0.159358	+	0.987221i	$0.449057\pi$
$72$	−1.53596	−0.181014
$73$	10.4380	1.22168	0.610838	−	0.791755i	$-0.290833\pi$
$73$	10.4380	1.22168	0.610838	+	0.791755i	$0.290833\pi$
$74$	8.19710	0.952893
$75$	4.53797	0.523999
$76$	−5.63256	−0.646099
$77$	−0.405238	−0.0461812
$78$	−7.58698	−0.859056
$79$	0.00107576	0.000121032 0	6.05160e−5	−	1.00000i	$-0.499981\pi$
$79$	0.00107576	0.000121032 0	6.05160e−5		1.00000i	$0.499981\pi$
$80$	−1.11783	−0.124977
$81$	−2.03296	−0.225885
$82$	7.36357	0.813171
$83$	−9.48695	−1.04133	−0.520664	−	0.853762i	$-0.674316\pi$
$83$	−9.48695	−1.04133	−0.520664	+	0.853762i	$0.674316\pi$
$84$	0.157283	0.0171609
$85$	1.95809	0.212385
$86$	0.205564	0.0221665
$87$	−1.20998	−0.129723
$88$	3.11750	0.332327
$89$	−8.32545	−0.882496	−0.441248	−	0.897385i	$-0.645464\pi$
$89$	−8.32545	−0.882496	−0.441248	+	0.897385i	$0.645464\pi$
$90$	1.71694	0.180981
$91$	−0.815071	−0.0854427
$92$	1.00000	0.104257
$93$	−12.6662	−1.31342
$94$	2.32196	0.239492
$95$	6.29624	0.645981
$96$	−1.20998	−0.123493
$97$	−18.4768	−1.87603	−0.938016	−	0.346592i	$-0.887339\pi$
$97$	−18.4768	−1.87603	−0.938016	+	0.346592i	$0.887339\pi$
$98$	−6.98310	−0.705400
$99$	−4.78835	−0.481247
$100$	−3.75046	−0.375046
$101$	−4.80247	−0.477863	−0.238932	−	0.971036i	$-0.576797\pi$
$101$	−4.80247	−0.477863	−0.238932	+	0.971036i	$0.576797\pi$
$102$	2.11951	0.209863
$103$	5.75833	0.567386	0.283693	−	0.958915i	$-0.408440\pi$
$103$	5.75833	0.567386	0.283693	+	0.958915i	$0.408440\pi$
$104$	6.27035	0.614858
$105$	−0.175815	−0.0171578
$106$	4.62519	0.449238
$107$	−1.95838	−0.189324	−0.0946619	−	0.995509i	$-0.530177\pi$
$107$	−1.95838	−0.189324	−0.0946619	+	0.995509i	$0.530177\pi$
$108$	5.48840	0.528122
$109$	−12.2243	−1.17088	−0.585440	−	0.810716i	$-0.699078\pi$
$109$	−12.2243	−1.17088	−0.585440	+	0.810716i	$0.699078\pi$
$110$	−3.48483	−0.332266
$111$	−9.91829	−0.941403
$112$	−0.129988	−0.0122827
$113$	−10.3190	−0.970726	−0.485363	−	0.874313i	$-0.661312\pi$
$113$	−10.3190	−0.970726	−0.485363	+	0.874313i	$0.661312\pi$
$114$	6.81527	0.638308
$115$	−1.11783	−0.104238
$116$	1.00000	0.0928477
$117$	−9.63099	−0.890385
$118$	6.32600	0.582356
$119$	0.227699	0.0208732
$120$	1.35255	0.123470
$121$	−1.28118	−0.116471
$122$	9.72943	0.880861
$123$	−8.90975	−0.803365
$124$	10.4681	0.940067
$125$	9.78151	0.874885
$126$	0.199656	0.0177868
$127$	8.79882	0.780769	0.390385	−	0.920652i	$-0.372342\pi$
$127$	8.79882	0.780769	0.390385	+	0.920652i	$0.372342\pi$
$128$	1.00000	0.0883883
$129$	−0.248728	−0.0218992
$130$	−7.00918	−0.614746
$131$	−5.88354	−0.514047	−0.257024	−	0.966405i	$-0.582742\pi$
$131$	−5.88354	−0.514047	−0.257024	+	0.966405i	$0.582742\pi$
$132$	−3.77210	−0.328319
$133$	0.732166	0.0634869
$134$	11.4742	0.991219
$135$	−6.13509	−0.528025
$136$	−1.75169	−0.150207
$137$	−12.9394	−1.10549	−0.552744	−	0.833351i	$-0.686419\pi$
$137$	−12.9394	−1.10549	−0.552744	+	0.833351i	$0.686419\pi$
$138$	−1.20998	−0.103000
$139$	−0.743944	−0.0631005	−0.0315503	−	0.999502i	$-0.510044\pi$
$139$	−0.743944	−0.0631005	−0.0315503	+	0.999502i	$0.510044\pi$
$140$	0.145304	0.0122805
$141$	−2.80952	−0.236604
$142$	2.68556	0.225367
$143$	19.5478	1.63467
$144$	−1.53596	−0.127996
$145$	−1.11783	−0.0928306
$146$	10.4380	0.863856
$147$	8.44939	0.696894
$148$	8.19710	0.673797
$149$	7.32776	0.600314	0.300157	−	0.953890i	$-0.402961\pi$
$149$	7.32776	0.600314	0.300157	+	0.953890i	$0.402961\pi$
$150$	4.53797	0.370523
$151$	−0.202927	−0.0165140	−0.00825699	−	0.999966i	$-0.502628\pi$
$151$	−0.202927	−0.0165140	−0.00825699	+	0.999966i	$0.502628\pi$
$152$	−5.63256	−0.456861
$153$	2.69053	0.217516
$154$	−0.405238	−0.0326550
$155$	−11.7016	−0.939894
$156$	−7.58698	−0.607444
$157$	13.8790	1.10766	0.553832	−	0.832628i	$-0.313165\pi$
$157$	13.8790	1.10766	0.553832	+	0.832628i	$0.313165\pi$
$158$	0.00107576	8.55826e−5 0
$159$	−5.59637	−0.443821
$160$	−1.11783	−0.0883721
$161$	−0.129988	−0.0102445
$162$	−2.03296	−0.159725
$163$	−21.5244	−1.68592	−0.842959	−	0.537978i	$-0.819188\pi$
$163$	−21.5244	−1.68592	−0.842959	+	0.537978i	$0.819188\pi$
$164$	7.36357	0.574999
$165$	4.21657	0.328259
$166$	−9.48695	−0.736330
$167$	7.56506	0.585402	0.292701	−	0.956204i	$-0.405446\pi$
$167$	7.56506	0.585402	0.292701	+	0.956204i	$0.405446\pi$
$168$	0.157283	0.0121346
$169$	26.3173	2.02441
$170$	1.95809	0.150179
$171$	8.65138	0.661587
$172$	0.205564	0.0156741
$173$	−12.4347	−0.945390	−0.472695	−	0.881226i	$-0.656719\pi$
$173$	−12.4347	−0.945390	−0.472695	+	0.881226i	$0.656719\pi$
$174$	−1.20998	−0.0917281
$175$	0.487515	0.0368527
$176$	3.11750	0.234991
$177$	−7.65431	−0.575333
$178$	−8.32545	−0.624019
$179$	−4.24327	−0.317157	−0.158579	−	0.987346i	$-0.550691\pi$
$179$	−4.24327	−0.317157	−0.158579	+	0.987346i	$0.550691\pi$
$180$	1.71694	0.127973
$181$	−8.14770	−0.605614	−0.302807	−	0.953052i	$-0.597924\pi$
$181$	−8.14770	−0.605614	−0.302807	+	0.953052i	$0.597924\pi$
$182$	−0.815071	−0.0604171
$183$	−11.7724	−0.870239
$184$	1.00000	0.0737210
$185$	−9.16295	−0.673673
$186$	−12.6662	−0.928731
$187$	−5.46091	−0.399341
$188$	2.32196	0.169347
$189$	−0.713427	−0.0518942
$190$	6.29624	0.456777
$191$	−5.46141	−0.395174	−0.197587	−	0.980285i	$-0.563311\pi$
$191$	−5.46141	−0.395174	−0.197587	+	0.980285i	$0.563311\pi$
$192$	−1.20998	−0.0873225
$193$	13.2028	0.950355	0.475177	−	0.879890i	$-0.342384\pi$
$193$	13.2028	0.950355	0.475177	+	0.879890i	$0.342384\pi$
$194$	−18.4768	−1.32655
$195$	8.48094	0.607333
$196$	−6.98310	−0.498793
$197$	−13.3018	−0.947715	−0.473858	−	0.880602i	$-0.657139\pi$
$197$	−13.3018	−0.947715	−0.473858	+	0.880602i	$0.657139\pi$
$198$	−4.78835	−0.340293
$199$	14.9536	1.06003	0.530016	−	0.847987i	$-0.322186\pi$
$199$	14.9536	1.06003	0.530016	+	0.847987i	$0.322186\pi$
$200$	−3.75046	−0.265198
$201$	−13.8835	−0.979267
$202$	−4.80247	−0.337900
$203$	−0.129988	−0.00912338
$204$	2.11951	0.148395
$205$	−8.23121	−0.574893
$206$	5.75833	0.401202
$207$	−1.53596	−0.106756
$208$	6.27035	0.434771
$209$	−17.5595	−1.21462
$210$	−0.175815	−0.0121324
$211$	−1.07548	−0.0740391	−0.0370196	−	0.999315i	$-0.511786\pi$
$211$	−1.07548	−0.0740391	−0.0370196	+	0.999315i	$0.511786\pi$
$212$	4.62519	0.317659
$213$	−3.24946	−0.222649
$214$	−1.95838	−0.133872
$215$	−0.229785	−0.0156712
$216$	5.48840	0.373438
$217$	−1.36073	−0.0923726
$218$	−12.2243	−0.827937
$219$	−12.6297	−0.853439
$220$	−3.48483	−0.234947
$221$	−10.9837	−0.738846
$222$	−9.91829	−0.665672
$223$	20.6032	1.37969	0.689846	−	0.723956i	$-0.257678\pi$
$223$	20.6032	1.37969	0.689846	+	0.723956i	$0.257678\pi$
$224$	−0.129988	−0.00868520
$225$	5.76054	0.384036
$226$	−10.3190	−0.686407
$227$	7.44211	0.493950	0.246975	−	0.969022i	$-0.420563\pi$
$227$	7.44211	0.493950	0.246975	+	0.969022i	$0.420563\pi$
$228$	6.81527	0.451352
$229$	−1.58178	−0.104527	−0.0522633	−	0.998633i	$-0.516644\pi$
$229$	−1.58178	−0.104527	−0.0522633	+	0.998633i	$0.516644\pi$
$230$	−1.11783	−0.0737074
$231$	0.490329	0.0322613
$232$	1.00000	0.0656532
$233$	9.41846	0.617024	0.308512	−	0.951220i	$-0.400169\pi$
$233$	9.41846	0.617024	0.308512	+	0.951220i	$0.400169\pi$
$234$	−9.63099	−0.629597
$235$	−2.59556	−0.169316
$236$	6.32600	0.411788
$237$	−0.00130164	−8.45506e−5 0
$238$	0.227699	0.0147596
$239$	7.67049	0.496163	0.248082	−	0.968739i	$-0.420200\pi$
$239$	7.67049	0.496163	0.248082	+	0.968739i	$0.420200\pi$
$240$	1.35255	0.0873065
$241$	−6.50395	−0.418957	−0.209478	−	0.977813i	$-0.567177\pi$
$241$	−6.50395	−0.418957	−0.209478	+	0.977813i	$0.567177\pi$
$242$	−1.28118	−0.0823576
$243$	−14.0054	−0.898445
$244$	9.72943	0.622863
$245$	7.80591	0.498701
$246$	−8.90975	−0.568065
$247$	−35.3181	−2.24724
$248$	10.4681	0.664728
$249$	11.4790	0.727451
$250$	9.78151	0.618637
$251$	13.5122	0.852880	0.426440	−	0.904516i	$-0.359768\pi$
$251$	13.5122	0.852880	0.426440	+	0.904516i	$0.359768\pi$
$252$	0.199656	0.0125772
$253$	3.11750	0.195996
$254$	8.79882	0.552087
$255$	−2.36925	−0.148368
$256$	1.00000	0.0625000
$257$	−8.45016	−0.527107	−0.263553	−	0.964645i	$-0.584895\pi$
$257$	−8.45016	−0.527107	−0.263553	+	0.964645i	$0.584895\pi$
$258$	−0.248728	−0.0154851
$259$	−1.06553	−0.0662085
$260$	−7.00918	−0.434691
$261$	−1.53596	−0.0950734
$262$	−5.88354	−0.363486
$263$	−9.63906	−0.594370	−0.297185	−	0.954820i	$-0.596048\pi$
$263$	−9.63906	−0.594370	−0.297185	+	0.954820i	$0.596048\pi$
$264$	−3.77210	−0.232157
$265$	−5.17017	−0.317601
$266$	0.732166	0.0448920
$267$	10.0736	0.616494
$268$	11.4742	0.700898
$269$	−4.03549	−0.246048	−0.123024	−	0.992404i	$-0.539259\pi$
$269$	−4.03549	−0.246048	−0.123024	+	0.992404i	$0.539259\pi$
$270$	−6.13509	−0.373370
$271$	−3.13889	−0.190674	−0.0953369	−	0.995445i	$-0.530393\pi$
$271$	−3.13889	−0.190674	−0.0953369	+	0.995445i	$0.530393\pi$
$272$	−1.75169	−0.106212
$273$	0.986217	0.0596886
$274$	−12.9394	−0.781698
$275$	−11.6921	−0.705058
$276$	−1.20998	−0.0728320
$277$	−3.44283	−0.206860	−0.103430	−	0.994637i	$-0.532982\pi$
$277$	−3.44283	−0.206860	−0.103430	+	0.994637i	$0.532982\pi$
$278$	−0.743944	−0.0446188
$279$	−16.0786	−0.962602
$280$	0.145304	0.00868360
$281$	−18.4002	−1.09766	−0.548832	−	0.835932i	$-0.684928\pi$
$281$	−18.4002	−1.09766	−0.548832	+	0.835932i	$0.684928\pi$
$282$	−2.80952	−0.167305
$283$	23.6918	1.40833	0.704167	−	0.710035i	$-0.251321\pi$
$283$	23.6918	1.40833	0.704167	+	0.710035i	$0.251321\pi$
$284$	2.68556	0.159358
$285$	−7.61830	−0.451269
$286$	19.5478	1.15589
$287$	−0.957177	−0.0565004
$288$	−1.53596	−0.0905071
$289$	−13.9316	−0.819504
$290$	−1.11783	−0.0656412
$291$	22.3565	1.31056
$292$	10.4380	0.610838
$293$	−19.0411	−1.11239	−0.556195	−	0.831052i	$-0.687739\pi$
$293$	−19.0411	−1.11239	−0.556195	+	0.831052i	$0.687739\pi$
$294$	8.44939	0.492778
$295$	−7.07138	−0.411712
$296$	8.19710	0.476447
$297$	17.1101	0.992829
$298$	7.32776	0.424486
$299$	6.27035	0.362624
$300$	4.53797	0.262000
$301$	−0.0267209	−0.00154017
$302$	−0.202927	−0.0116772
$303$	5.81087	0.333826
$304$	−5.63256	−0.323050
$305$	−10.8758	−0.622749
$306$	2.69053	0.153807
$307$	4.50182	0.256933	0.128466	−	0.991714i	$-0.458995\pi$
$307$	4.50182	0.256933	0.128466	+	0.991714i	$0.458995\pi$
$308$	−0.405238	−0.0230906
$309$	−6.96745	−0.396364
$310$	−11.7016	−0.664606
$311$	29.0796	1.64895	0.824477	−	0.565896i	$-0.191470\pi$
$311$	29.0796	1.64895	0.824477	+	0.565896i	$0.191470\pi$
$312$	−7.58698	−0.429528
$313$	27.8636	1.57494	0.787472	−	0.616350i	$-0.211389\pi$
$313$	27.8636	1.57494	0.787472	+	0.616350i	$0.211389\pi$
$314$	13.8790	0.783237
$315$	−0.223181	−0.0125748
$316$	0.00107576	6.05160e−5 0
$317$	−32.5230	−1.82667	−0.913335	−	0.407208i	$-0.866502\pi$
$317$	−32.5230	−1.82667	−0.913335	+	0.407208i	$0.866502\pi$
$318$	−5.59637	−0.313829
$319$	3.11750	0.174547
$320$	−1.11783	−0.0624885
$321$	2.36959	0.132258
$322$	−0.129988	−0.00724395
$323$	9.86653	0.548988
$324$	−2.03296	−0.112942
$325$	−23.5167	−1.30447
$326$	−21.5244	−1.19212
$327$	14.7912	0.817953
$328$	7.36357	0.406585
$329$	−0.301828	−0.0166403
$330$	4.21657	0.232114
$331$	−15.5546	−0.854958	−0.427479	−	0.904025i	$-0.640598\pi$
$331$	−15.5546	−0.854958	−0.427479	+	0.904025i	$0.640598\pi$
$332$	−9.48695	−0.520664
$333$	−12.5904	−0.689949
$334$	7.56506	0.413942
$335$	−12.8262	−0.700769
$336$	0.157283	0.00858047
$337$	−12.4105	−0.676040	−0.338020	−	0.941139i	$-0.609757\pi$
$337$	−12.4105	−0.676040	−0.338020	+	0.941139i	$0.609757\pi$
$338$	26.3173	1.43147
$339$	12.4857	0.678130
$340$	1.95809	0.106193
$341$	32.6345	1.76725
$342$	8.65138	0.467813
$343$	1.81764	0.0981432
$344$	0.205564	0.0110833
$345$	1.35255	0.0728186
$346$	−12.4347	−0.668491
$347$	0.491982	0.0264110	0.0132055	−	0.999913i	$-0.495796\pi$
$347$	0.491982	0.0264110	0.0132055	+	0.999913i	$0.495796\pi$
$348$	−1.20998	−0.0648615
$349$	−16.0347	−0.858317	−0.429159	−	0.903229i	$-0.641190\pi$
$349$	−16.0347	−0.858317	−0.429159	+	0.903229i	$0.641190\pi$
$350$	0.487515	0.0260588
$351$	34.4142	1.83689
$352$	3.11750	0.166163
$353$	−22.7357	−1.21010	−0.605051	−	0.796187i	$-0.706847\pi$
$353$	−22.7357	−1.21010	−0.605051	+	0.796187i	$0.706847\pi$
$354$	−7.65431	−0.406822
$355$	−3.00199	−0.159329
$356$	−8.32545	−0.441248
$357$	−0.275511	−0.0145816
$358$	−4.24327	−0.224264
$359$	26.1918	1.38235	0.691175	−	0.722687i	$-0.257093\pi$
$359$	26.1918	1.38235	0.691175	+	0.722687i	$0.257093\pi$
$360$	1.71694	0.0904905
$361$	12.7258	0.669778
$362$	−8.14770	−0.428234
$363$	1.55020	0.0813645
$364$	−0.815071	−0.0427213
$365$	−11.6679	−0.610726
$366$	−11.7724	−0.615352
$367$	−20.0708	−1.04769	−0.523843	−	0.851815i	$-0.675502\pi$
$367$	−20.0708	−1.04769	−0.523843	+	0.851815i	$0.675502\pi$
$368$	1.00000	0.0521286
$369$	−11.3101	−0.588782
$370$	−9.16295	−0.476359
$371$	−0.601220	−0.0312138
$372$	−12.6662	−0.656712
$373$	−24.1133	−1.24854	−0.624269	−	0.781210i	$-0.714603\pi$
$373$	−24.1133	−1.24854	−0.624269	+	0.781210i	$0.714603\pi$
$374$	−5.46091	−0.282377
$375$	−11.8354	−0.611177
$376$	2.32196	0.119746
$377$	6.27035	0.322939
$378$	−0.713427	−0.0366947
$379$	−17.2909	−0.888173	−0.444087	−	0.895984i	$-0.646472\pi$
$379$	−17.2909	−0.888173	−0.444087	+	0.895984i	$0.646472\pi$
$380$	6.29624	0.322990
$381$	−10.6464	−0.545430
$382$	−5.46141	−0.279430
$383$	−26.4282	−1.35042	−0.675210	−	0.737626i	$-0.735947\pi$
$383$	−26.4282	−1.35042	−0.675210	+	0.737626i	$0.735947\pi$
$384$	−1.20998	−0.0617463
$385$	0.452987	0.0230863
$386$	13.2028	0.672002
$387$	−0.315737	−0.0160498
$388$	−18.4768	−0.938016
$389$	−17.3344	−0.878888	−0.439444	−	0.898270i	$-0.644824\pi$
$389$	−17.3344	−0.878888	−0.439444	+	0.898270i	$0.644824\pi$
$390$	8.48094	0.429449
$391$	−1.75169	−0.0885870
$392$	−6.98310	−0.352700
$393$	7.11894	0.359103
$394$	−13.3018	−0.670136
$395$	−0.00120251	−6.05049e−5 0
$396$	−4.78835	−0.240624
$397$	31.5186	1.58187	0.790936	−	0.611899i	$-0.209594\pi$
$397$	31.5186	1.58187	0.790936	+	0.611899i	$0.209594\pi$
$398$	14.9536	0.749556
$399$	−0.885904	−0.0443507
$400$	−3.75046	−0.187523
$401$	−20.8432	−1.04086	−0.520430	−	0.853904i	$-0.674228\pi$
$401$	−20.8432	−1.04086	−0.520430	+	0.853904i	$0.674228\pi$
$402$	−13.8835	−0.692446
$403$	65.6389	3.26971
$404$	−4.80247	−0.238932
$405$	2.27251	0.112922
$406$	−0.129988	−0.00645120
$407$	25.5545	1.26669
$408$	2.11951	0.104931
$409$	19.3519	0.956890	0.478445	−	0.878117i	$-0.341201\pi$
$409$	19.3519	0.956890	0.478445	+	0.878117i	$0.341201\pi$
$410$	−8.23121	−0.406511
$411$	15.6564	0.772272
$412$	5.75833	0.283693
$413$	−0.822305	−0.0404630
$414$	−1.53596	−0.0754882
$415$	10.6048	0.520568
$416$	6.27035	0.307429
$417$	0.900155	0.0440808
$418$	−17.5595	−0.858865
$419$	28.1828	1.37682	0.688411	−	0.725321i	$-0.258309\pi$
$419$	28.1828	1.37682	0.688411	+	0.725321i	$0.258309\pi$
$420$	−0.175815	−0.00857889
$421$	15.9374	0.776742	0.388371	−	0.921503i	$-0.373038\pi$
$421$	15.9374	0.776742	0.388371	+	0.921503i	$0.373038\pi$
$422$	−1.07548	−0.0523536
$423$	−3.56644	−0.173406
$424$	4.62519	0.224619
$425$	6.56966	0.318675
$426$	−3.24946	−0.157437
$427$	−1.26471	−0.0612036
$428$	−1.95838	−0.0946619
$429$	−23.6524	−1.14195
$430$	−0.229785	−0.0110812
$431$	13.5139	0.650942	0.325471	−	0.945552i	$-0.394477\pi$
$431$	13.5139	0.650942	0.325471	+	0.945552i	$0.394477\pi$
$432$	5.48840	0.264061
$433$	20.1564	0.968654	0.484327	−	0.874887i	$-0.339065\pi$
$433$	20.1564	0.968654	0.484327	+	0.874887i	$0.339065\pi$
$434$	−1.36073	−0.0653173
$435$	1.35255	0.0648496
$436$	−12.2243	−0.585440
$437$	−5.63256	−0.269442
$438$	−12.6297	−0.603472
$439$	31.6966	1.51280	0.756399	−	0.654110i	$-0.226957\pi$
$439$	31.6966	1.51280	0.756399	+	0.654110i	$0.226957\pi$
$440$	−3.48483	−0.166133
$441$	10.7257	0.510750
$442$	−10.9837	−0.522443
$443$	−37.8585	−1.79871	−0.899355	−	0.437220i	$-0.855963\pi$
$443$	−37.8585	−1.79871	−0.899355	+	0.437220i	$0.855963\pi$
$444$	−9.91829	−0.470701
$445$	9.30643	0.441167
$446$	20.6032	0.975589
$447$	−8.86642	−0.419367
$448$	−0.129988	−0.00614136
$449$	−39.3313	−1.85616	−0.928080	−	0.372381i	$-0.878542\pi$
$449$	−39.3313	−1.85616	−0.928080	+	0.372381i	$0.878542\pi$
$450$	5.76054	0.271555
$451$	22.9560	1.08095
$452$	−10.3190	−0.485363
$453$	0.245537	0.0115363
$454$	7.44211	0.349276
$455$	0.911110	0.0427135
$456$	6.81527	0.319154
$457$	−13.7231	−0.641941	−0.320971	−	0.947089i	$-0.604009\pi$
$457$	−13.7231	−0.641941	−0.320971	+	0.947089i	$0.604009\pi$
$458$	−1.58178	−0.0739115
$459$	−9.61400	−0.448743
$460$	−1.11783	−0.0521190
$461$	−7.28087	−0.339104	−0.169552	−	0.985521i	$-0.554232\pi$
$461$	−7.28087	−0.339104	−0.169552	+	0.985521i	$0.554232\pi$
$462$	0.490329	0.0228122
$463$	8.25788	0.383776	0.191888	−	0.981417i	$-0.438539\pi$
$463$	8.25788	0.383776	0.191888	+	0.981417i	$0.438539\pi$
$464$	1.00000	0.0464238
$465$	14.1586	0.656592
$466$	9.41846	0.436302
$467$	42.7781	1.97953	0.989767	−	0.142691i	$-0.0455754\pi$
$467$	42.7781	1.97953	0.989767	+	0.142691i	$0.0455754\pi$
$468$	−9.63099	−0.445193
$469$	−1.49151	−0.0688715
$470$	−2.59556	−0.119724
$471$	−16.7933	−0.773792
$472$	6.32600	0.291178
$473$	0.640846	0.0294661
$474$	−0.00130164	−5.97863e−5 0
$475$	21.1247	0.969268
$476$	0.227699	0.0104366
$477$	−7.10409	−0.325274
$478$	7.67049	0.350840
$479$	5.60274	0.255996	0.127998	−	0.991774i	$-0.459145\pi$
$479$	5.60274	0.255996	0.127998	+	0.991774i	$0.459145\pi$
$480$	1.35255	0.0617350
$481$	51.3987	2.34358
$482$	−6.50395	−0.296247
$483$	0.157283	0.00715660
$484$	−1.28118	−0.0582356
$485$	20.6539	0.937844
$486$	−14.0054	−0.635296
$487$	−18.9679	−0.859516	−0.429758	−	0.902944i	$-0.641401\pi$
$487$	−18.9679	−0.859516	−0.429758	+	0.902944i	$0.641401\pi$
$488$	9.72943	0.440431
$489$	26.0440	1.17775
$490$	7.80591	0.352635
$491$	27.7760	1.25351	0.626756	−	0.779216i	$-0.284382\pi$
$491$	27.7760	1.25351	0.626756	+	0.779216i	$0.284382\pi$
$492$	−8.90975	−0.401683
$493$	−1.75169	−0.0788923
$494$	−35.3181	−1.58904
$495$	5.35255	0.240579
$496$	10.4681	0.470033
$497$	−0.349091	−0.0156588
$498$	11.4790	0.514386
$499$	14.1434	0.633147	0.316574	−	0.948568i	$-0.397468\pi$
$499$	14.1434	0.633147	0.316574	+	0.948568i	$0.397468\pi$
$500$	9.78151	0.437443
$501$	−9.15355	−0.408950
$502$	13.5122	0.603077
$503$	−4.61513	−0.205778	−0.102889	−	0.994693i	$-0.532809\pi$
$503$	−4.61513	−0.205778	−0.102889	+	0.994693i	$0.532809\pi$
$504$	0.199656	0.00889339
$505$	5.36834	0.238888
$506$	3.11750	0.138590
$507$	−31.8433	−1.41421
$508$	8.79882	0.390385
$509$	12.6506	0.560728	0.280364	−	0.959894i	$-0.409545\pi$
$509$	12.6506	0.560728	0.280364	+	0.959894i	$0.409545\pi$
$510$	−2.36925	−0.104912
$511$	−1.35682	−0.0600220
$512$	1.00000	0.0441942
$513$	−30.9138	−1.36488
$514$	−8.45016	−0.372721
$515$	−6.43683	−0.283641
$516$	−0.248728	−0.0109496
$517$	7.23873	0.318359
$518$	−1.06553	−0.0468165
$519$	15.0456	0.660430
$520$	−7.00918	−0.307373
$521$	24.9533	1.09322	0.546611	−	0.837387i	$-0.315918\pi$
$521$	24.9533	1.09322	0.546611	+	0.837387i	$0.315918\pi$
$522$	−1.53596	−0.0672270
$523$	−28.9770	−1.26708	−0.633538	−	0.773711i	$-0.718398\pi$
$523$	−28.9770	−1.26708	−0.633538	+	0.773711i	$0.718398\pi$
$524$	−5.88354	−0.257024
$525$	−0.589882	−0.0257446
$526$	−9.63906	−0.420283
$527$	−18.3370	−0.798772
$528$	−3.77210	−0.164160
$529$	1.00000	0.0434783
$530$	−5.17017	−0.224578
$531$	−9.71647	−0.421659
$532$	0.732166	0.0317434
$533$	46.1722	1.99994
$534$	10.0736	0.435927
$535$	2.18913	0.0946445
$536$	11.4742	0.495610
$537$	5.13426	0.221560
$538$	−4.03549	−0.173982
$539$	−21.7698	−0.937693
$540$	−6.13509	−0.264012
$541$	43.3429	1.86346	0.931729	−	0.363154i	$-0.118300\pi$
$541$	43.3429	1.86346	0.931729	+	0.363154i	$0.118300\pi$
$542$	−3.13889	−0.134827
$543$	9.85852	0.423070
$544$	−1.75169	−0.0751033
$545$	13.6647	0.585332
$546$	0.986217	0.0422062
$547$	2.71083	0.115907	0.0579533	−	0.998319i	$-0.481543\pi$
$547$	2.71083	0.115907	0.0579533	+	0.998319i	$0.481543\pi$
$548$	−12.9394	−0.552744
$549$	−14.9440	−0.637794
$550$	−11.6921	−0.498551
$551$	−5.63256	−0.239955
$552$	−1.20998	−0.0515000
$553$	−0.000139836 0	−5.94641e−6 0
$554$	−3.44283	−0.146272
$555$	11.0870	0.470615
$556$	−0.743944	−0.0315503
$557$	−11.8398	−0.501667	−0.250833	−	0.968030i	$-0.580705\pi$
$557$	−11.8398	−0.501667	−0.250833	+	0.968030i	$0.580705\pi$
$558$	−16.0786	−0.680662
$559$	1.28896	0.0545171
$560$	0.145304	0.00614023
$561$	6.60757	0.278972
$562$	−18.4002	−0.776166
$563$	−34.3605	−1.44812	−0.724062	−	0.689735i	$-0.757727\pi$
$563$	−34.3605	−1.44812	−0.724062	+	0.689735i	$0.757727\pi$
$564$	−2.80952	−0.118302
$565$	11.5348	0.485274
$566$	23.6918	0.995842
$567$	0.264261	0.0110979
$568$	2.68556	0.112683
$569$	−7.34971	−0.308116	−0.154058	−	0.988062i	$-0.549234\pi$
$569$	−7.34971	−0.308116	−0.154058	+	0.988062i	$0.549234\pi$
$570$	−7.61830	−0.319096
$571$	23.4104	0.979694	0.489847	−	0.871808i	$-0.337053\pi$
$571$	23.4104	0.979694	0.489847	+	0.871808i	$0.337053\pi$
$572$	19.5478	0.817336
$573$	6.60818	0.276061
$574$	−0.957177	−0.0399518
$575$	−3.75046	−0.156405
$576$	−1.53596	−0.0639982
$577$	38.0675	1.58477	0.792385	−	0.610021i	$-0.208839\pi$
$577$	38.0675	1.58477	0.792385	+	0.610021i	$0.208839\pi$
$578$	−13.9316	−0.579477
$579$	−15.9750	−0.663899
$580$	−1.11783	−0.0464153
$581$	1.23319	0.0511614
$582$	22.3565	0.926705
$583$	14.4190	0.597175
$584$	10.4380	0.431928
$585$	10.7658	0.445111
$586$	−19.0411	−0.786579
$587$	−26.4211	−1.09052	−0.545258	−	0.838268i	$-0.683568\pi$
$587$	−26.4211	−1.09052	−0.545258	+	0.838268i	$0.683568\pi$
$588$	8.44939	0.348447
$589$	−58.9625	−2.42951
$590$	−7.07138	−0.291124
$591$	16.0949	0.662055
$592$	8.19710	0.336899
$593$	16.2700	0.668129	0.334064	−	0.942550i	$-0.391580\pi$
$593$	16.2700	0.668129	0.334064	+	0.942550i	$0.391580\pi$
$594$	17.1101	0.702036
$595$	−0.254529	−0.0104347
$596$	7.32776	0.300157
$597$	−18.0935	−0.740518
$598$	6.27035	0.256414
$599$	16.3449	0.667836	0.333918	−	0.942602i	$-0.391629\pi$
$599$	16.3449	0.667836	0.333918	+	0.942602i	$0.391629\pi$
$600$	4.53797	0.185262
$601$	36.4550	1.48703	0.743515	−	0.668719i	$-0.233157\pi$
$601$	36.4550	1.48703	0.743515	+	0.668719i	$0.233157\pi$
$602$	−0.0267209	−0.00108906
$603$	−17.6239	−0.717699
$604$	−0.202927	−0.00825699
$605$	1.43214	0.0582249
$606$	5.81087	0.236051
$607$	−17.5069	−0.710583	−0.355292	−	0.934756i	$-0.615618\pi$
$607$	−17.5069	−0.710583	−0.355292	+	0.934756i	$0.615618\pi$
$608$	−5.63256	−0.228431
$609$	0.157283	0.00637341
$610$	−10.8758	−0.440350
$611$	14.5595	0.589015
$612$	2.69053	0.108758
$613$	14.8398	0.599374	0.299687	−	0.954038i	$-0.403118\pi$
$613$	14.8398	0.599374	0.299687	+	0.954038i	$0.403118\pi$
$614$	4.50182	0.181679
$615$	9.95958	0.401609
$616$	−0.405238	−0.0163275
$617$	−49.1250	−1.97770	−0.988849	−	0.148925i	$-0.952419\pi$
$617$	−49.1250	−1.97770	−0.988849	+	0.148925i	$0.952419\pi$
$618$	−6.96745	−0.280272
$619$	−34.9426	−1.40446	−0.702232	−	0.711949i	$-0.747813\pi$
$619$	−34.9426	−1.40446	−0.702232	+	0.711949i	$0.747813\pi$
$620$	−11.7016	−0.469947
$621$	5.48840	0.220242
$622$	29.0796	1.16599
$623$	1.08221	0.0433578
$624$	−7.58698	−0.303722
$625$	7.81824	0.312730
$626$	27.8636	1.11365
$627$	21.2466	0.848508
$628$	13.8790	0.553832
$629$	−14.3588	−0.572523
$630$	−0.223181	−0.00889176
$631$	−19.2504	−0.766348	−0.383174	−	0.923676i	$-0.625169\pi$
$631$	−19.2504	−0.766348	−0.383174	+	0.923676i	$0.625169\pi$
$632$	0.00107576	4.27913e−5 0
$633$	1.30131	0.0517223
$634$	−32.5230	−1.29165
$635$	−9.83558	−0.390313
$636$	−5.59637	−0.221911
$637$	−43.7865	−1.73488
$638$	3.11750	0.123423
$639$	−4.12490	−0.163179
$640$	−1.11783	−0.0441861
$641$	8.51957	0.336503	0.168251	−	0.985744i	$-0.446188\pi$
$641$	8.51957	0.336503	0.168251	+	0.985744i	$0.446188\pi$
$642$	2.36959	0.0935204
$643$	−36.6520	−1.44541	−0.722707	−	0.691155i	$-0.757102\pi$
$643$	−36.6520	−1.44541	−0.722707	+	0.691155i	$0.757102\pi$
$644$	−0.129988	−0.00512225
$645$	0.278035	0.0109476
$646$	9.86653	0.388193
$647$	19.2288	0.755962	0.377981	−	0.925813i	$-0.376618\pi$
$647$	19.2288	0.755962	0.377981	+	0.925813i	$0.376618\pi$
$648$	−2.03296	−0.0798624
$649$	19.7213	0.774129
$650$	−23.5167	−0.922401
$651$	1.64646	0.0645297
$652$	−21.5244	−0.842959
$653$	31.2769	1.22396	0.611981	−	0.790873i	$-0.290373\pi$
$653$	31.2769	1.22396	0.611981	+	0.790873i	$0.290373\pi$
$654$	14.7912	0.578380
$655$	6.57679	0.256976
$656$	7.36357	0.287499
$657$	−16.0323	−0.625481
$658$	−0.301828	−0.0117665
$659$	39.6668	1.54520	0.772600	−	0.634893i	$-0.218956\pi$
$659$	39.6668	1.54520	0.772600	+	0.634893i	$0.218956\pi$
$660$	4.21657	0.164130
$661$	−15.0237	−0.584355	−0.292177	−	0.956364i	$-0.594380\pi$
$661$	−15.0237	−0.584355	−0.292177	+	0.956364i	$0.594380\pi$
$662$	−15.5546	−0.604547
$663$	13.2901	0.516143
$664$	−9.48695	−0.368165
$665$	−0.818437	−0.0317376
$666$	−12.5904	−0.487868
$667$	1.00000	0.0387202
$668$	7.56506	0.292701
$669$	−24.9294	−0.963825
$670$	−12.8262	−0.495519
$671$	30.3315	1.17094
$672$	0.157283	0.00606731
$673$	23.5472	0.907679	0.453840	−	0.891083i	$-0.350054\pi$
$673$	23.5472	0.907679	0.453840	+	0.891083i	$0.350054\pi$
$674$	−12.4105	−0.478033
$675$	−20.5840	−0.792279
$676$	26.3173	1.01220
$677$	−45.0443	−1.73119	−0.865596	−	0.500742i	$-0.833060\pi$
$677$	−45.0443	−1.73119	−0.865596	+	0.500742i	$0.833060\pi$
$678$	12.4857	0.479510
$679$	2.40176	0.0921711
$680$	1.95809	0.0750895
$681$	−9.00478	−0.345064
$682$	32.6345	1.24964
$683$	6.64033	0.254085	0.127043	−	0.991897i	$-0.459452\pi$
$683$	6.64033	0.254085	0.127043	+	0.991897i	$0.459452\pi$
$684$	8.65138	0.330794
$685$	14.4640	0.552642
$686$	1.81764	0.0693977
$687$	1.91391	0.0730203
$688$	0.205564	0.00783705
$689$	29.0016	1.10487
$690$	1.35255	0.0514906
$691$	−9.17472	−0.349023	−0.174511	−	0.984655i	$-0.555835\pi$
$691$	−9.17472	−0.349023	−0.174511	+	0.984655i	$0.555835\pi$
$692$	−12.4347	−0.472695
$693$	0.622428	0.0236441
$694$	0.491982	0.0186754
$695$	0.831602	0.0315445
$696$	−1.20998	−0.0458640
$697$	−12.8987	−0.488574
$698$	−16.0347	−0.606922
$699$	−11.3961	−0.431041
$700$	0.487515	0.0184263
$701$	−16.1406	−0.609621	−0.304810	−	0.952413i	$-0.598593\pi$
$701$	−16.1406	−0.609621	−0.304810	+	0.952413i	$0.598593\pi$
$702$	34.4142	1.29888
$703$	−46.1707	−1.74136
$704$	3.11750	0.117495
$705$	3.14056	0.118280
$706$	−22.7357	−0.855671
$707$	0.624264	0.0234779
$708$	−7.65431	−0.287667
$709$	−15.0241	−0.564240	−0.282120	−	0.959379i	$-0.591038\pi$
$709$	−15.0241	−0.564240	−0.282120	+	0.959379i	$0.591038\pi$
$710$	−3.00199	−0.112663
$711$	−0.00165232	−6.19667e−5 0
$712$	−8.32545	−0.312010
$713$	10.4681	0.392035
$714$	−0.275511	−0.0103107
$715$	−21.8511	−0.817186
$716$	−4.24327	−0.158579
$717$	−9.28112	−0.346610
$718$	26.1918	0.977469
$719$	18.3513	0.684390	0.342195	−	0.939629i	$-0.388830\pi$
$719$	18.3513	0.684390	0.342195	+	0.939629i	$0.388830\pi$
$720$	1.71694	0.0639865
$721$	−0.748515	−0.0278762
$722$	12.7258	0.473604
$723$	7.86963	0.292675
$724$	−8.14770	−0.302807
$725$	−3.75046	−0.139289
$726$	1.55020	0.0575334
$727$	−9.98544	−0.370340	−0.185170	−	0.982707i	$-0.559283\pi$
$727$	−9.98544	−0.370340	−0.185170	+	0.982707i	$0.559283\pi$
$728$	−0.815071	−0.0302085
$729$	23.0451	0.853520
$730$	−11.6679	−0.431849
$731$	−0.360085	−0.0133182
$732$	−11.7724	−0.435120
$733$	−39.2000	−1.44789	−0.723943	−	0.689860i	$-0.757672\pi$
$733$	−39.2000	−1.44789	−0.723943	+	0.689860i	$0.757672\pi$
$734$	−20.0708	−0.740826
$735$	−9.44497	−0.348383
$736$	1.00000	0.0368605
$737$	35.7708	1.31763
$738$	−11.3101	−0.416332
$739$	8.05438	0.296285	0.148143	−	0.988966i	$-0.452671\pi$
$739$	8.05438	0.296285	0.148143	+	0.988966i	$0.452671\pi$
$740$	−9.16295	−0.336837
$741$	42.7341	1.56988
$742$	−0.601220	−0.0220715
$743$	29.6175	1.08656	0.543280	−	0.839552i	$-0.317182\pi$
$743$	29.6175	1.08656	0.543280	+	0.839552i	$0.317182\pi$
$744$	−12.6662	−0.464366
$745$	−8.19118	−0.300102
$746$	−24.1133	−0.882849
$747$	14.5716	0.533145
$748$	−5.46091	−0.199671
$749$	0.254566	0.00930165
$750$	−11.8354	−0.432168
$751$	6.33981	0.231343	0.115671	−	0.993288i	$-0.463098\pi$
$751$	6.33981	0.231343	0.115671	+	0.993288i	$0.463098\pi$
$752$	2.32196	0.0846733
$753$	−16.3494	−0.595805
$754$	6.27035	0.228353
$755$	0.226838	0.00825548
$756$	−0.713427	−0.0259471
$757$	−15.0133	−0.545669	−0.272835	−	0.962061i	$-0.587961\pi$
$757$	−15.0133	−0.545669	−0.272835	+	0.962061i	$0.587961\pi$
$758$	−17.2909	−0.628033
$759$	−3.77210	−0.136919
$760$	6.29624	0.228389
$761$	−21.7840	−0.789669	−0.394835	−	0.918752i	$-0.629198\pi$
$761$	−21.7840	−0.789669	−0.394835	+	0.918752i	$0.629198\pi$
$762$	−10.6464	−0.385677
$763$	1.58902	0.0575264
$764$	−5.46141	−0.197587
$765$	−3.00755	−0.108738
$766$	−26.4282	−0.954891
$767$	39.6662	1.43226
$768$	−1.20998	−0.0436613
$769$	4.40517	0.158854	0.0794272	−	0.996841i	$-0.474691\pi$
$769$	4.40517	0.158854	0.0794272	+	0.996841i	$0.474691\pi$
$770$	0.452987	0.0163245
$771$	10.2245	0.368226
$772$	13.2028	0.475177
$773$	−6.17844	−0.222223	−0.111112	−	0.993808i	$-0.535441\pi$
$773$	−6.17844	−0.222223	−0.111112	+	0.993808i	$0.535441\pi$
$774$	−0.315737	−0.0113489
$775$	−39.2603	−1.41027
$776$	−18.4768	−0.663277
$777$	1.28926	0.0462520
$778$	−17.3344	−0.621468
$779$	−41.4758	−1.48602
$780$	8.48094	0.303666
$781$	8.37223	0.299582
$782$	−1.75169	−0.0626405
$783$	5.48840	0.196139
$784$	−6.98310	−0.249397
$785$	−15.5143	−0.553730
$786$	7.11894	0.253924
$787$	47.5861	1.69626	0.848131	−	0.529787i	$-0.177728\pi$
$787$	47.5861	1.69626	0.848131	+	0.529787i	$0.177728\pi$
$788$	−13.3018	−0.473858
$789$	11.6630	0.415215
$790$	−0.00120251	−4.27835e−5 0
$791$	1.34134	0.0476926
$792$	−4.78835	−0.170147
$793$	61.0069	2.16642
$794$	31.5186	1.11855
$795$	6.25578	0.221870
$796$	14.9536	0.530016
$797$	−27.5025	−0.974190	−0.487095	−	0.873349i	$-0.661943\pi$
$797$	−27.5025	−0.974190	−0.487095	+	0.873349i	$0.661943\pi$
$798$	−0.885904	−0.0313607
$799$	−4.06737	−0.143893
$800$	−3.75046	−0.132599
$801$	12.7875	0.451825
$802$	−20.8432	−0.736000
$803$	32.5405	1.14833
$804$	−13.8835	−0.489633
$805$	0.145304	0.00512131
$806$	65.6389	2.31203
$807$	4.88285	0.171884
$808$	−4.80247	−0.168950
$809$	−49.8785	−1.75364	−0.876818	−	0.480823i	$-0.840338\pi$
$809$	−49.8785	−1.75364	−0.876818	+	0.480823i	$0.840338\pi$
$810$	2.27251	0.0798477
$811$	−26.9903	−0.947759	−0.473880	−	0.880590i	$-0.657147\pi$
$811$	−26.9903	−0.947759	−0.473880	+	0.880590i	$0.657147\pi$
$812$	−0.129988	−0.00456169
$813$	3.79798	0.133201
$814$	25.5545	0.895683
$815$	24.0605	0.842804
$816$	2.11951	0.0741976
$817$	−1.15785	−0.0405081
$818$	19.3519	0.676624
$819$	1.25191	0.0437454
$820$	−8.23121	−0.287446
$821$	36.9614	1.28996	0.644981	−	0.764199i	$-0.276865\pi$
$821$	36.9614	1.28996	0.644981	+	0.764199i	$0.276865\pi$
$822$	15.6564	0.546079
$823$	−6.79864	−0.236986	−0.118493	−	0.992955i	$-0.537806\pi$
$823$	−6.79864	−0.236986	−0.118493	+	0.992955i	$0.537806\pi$
$824$	5.75833	0.200601
$825$	14.1471	0.492539
$826$	−0.822305	−0.0286116
$827$	−50.7784	−1.76574	−0.882869	−	0.469620i	$-0.844391\pi$
$827$	−50.7784	−1.76574	−0.882869	+	0.469620i	$0.844391\pi$
$828$	−1.53596	−0.0533782
$829$	−1.09593	−0.0380631	−0.0190316	−	0.999819i	$-0.506058\pi$
$829$	−1.09593	−0.0380631	−0.0190316	+	0.999819i	$0.506058\pi$
$830$	10.6048	0.368098
$831$	4.16575	0.144508
$832$	6.27035	0.217385
$833$	12.2323	0.423823
$834$	0.900155	0.0311698
$835$	−8.45645	−0.292647
$836$	−17.5595	−0.607309
$837$	57.4534	1.98588
$838$	28.1828	0.973560
$839$	24.8576	0.858179	0.429090	−	0.903262i	$-0.358834\pi$
$839$	24.8576	0.858179	0.429090	+	0.903262i	$0.358834\pi$
$840$	−0.175815	−0.00606619
$841$	1.00000	0.0344828
$842$	15.9374	0.549240
$843$	22.2638	0.766807
$844$	−1.07548	−0.0370196
$845$	−29.4182	−1.01202
$846$	−3.56644	−0.122617
$847$	0.166539	0.00572233
$848$	4.62519	0.158830
$849$	−28.6666	−0.983834
$850$	6.56966	0.225337
$851$	8.19710	0.280993
$852$	−3.24946	−0.111325
$853$	14.4999	0.496468	0.248234	−	0.968700i	$-0.420150\pi$
$853$	14.4999	0.496468	0.248234	+	0.968700i	$0.420150\pi$
$854$	−1.26471	−0.0432775
$855$	−9.67076	−0.330733
$856$	−1.95838	−0.0669361
$857$	49.7359	1.69894	0.849472	−	0.527633i	$-0.176920\pi$
$857$	49.7359	1.69894	0.849472	+	0.527633i	$0.176920\pi$
$858$	−23.6524	−0.807480
$859$	46.6069	1.59021	0.795104	−	0.606473i	$-0.207416\pi$
$859$	46.6069	1.59021	0.795104	+	0.606473i	$0.207416\pi$
$860$	−0.229785	−0.00783562
$861$	1.15816	0.0394700
$862$	13.5139	0.460285
$863$	28.4740	0.969267	0.484633	−	0.874717i	$-0.338953\pi$
$863$	28.4740	0.969267	0.484633	+	0.874717i	$0.338953\pi$
$864$	5.48840	0.186719
$865$	13.8998	0.472608
$866$	20.1564	0.684942
$867$	16.8569	0.572489
$868$	−1.36073	−0.0461863
$869$	0.00335367	0.000113766 0
$870$	1.35255	0.0458556
$871$	71.9472	2.43784
$872$	−12.2243	−0.413968
$873$	28.3795	0.960502
$874$	−5.63256	−0.190524
$875$	−1.27148	−0.0429839
$876$	−12.6297	−0.426719
$877$	−36.5247	−1.23335	−0.616676	−	0.787217i	$-0.711521\pi$
$877$	−36.5247	−1.23335	−0.616676	+	0.787217i	$0.711521\pi$
$878$	31.6966	1.06971
$879$	23.0392	0.777094
$880$	−3.48483	−0.117474
$881$	−36.4569	−1.22826	−0.614132	−	0.789203i	$-0.710494\pi$
$881$	−36.4569	−1.22826	−0.614132	+	0.789203i	$0.710494\pi$
$882$	10.7257	0.361155
$883$	−46.0951	−1.55122	−0.775611	−	0.631211i	$-0.782558\pi$
$883$	−46.0951	−1.55122	−0.775611	+	0.631211i	$0.782558\pi$
$884$	−10.9837	−0.369423
$885$	8.55621	0.287614
$886$	−37.8585	−1.27188
$887$	−31.0325	−1.04197	−0.520984	−	0.853566i	$-0.674435\pi$
$887$	−31.0325	−1.04197	−0.520984	+	0.853566i	$0.674435\pi$
$888$	−9.91829	−0.332836
$889$	−1.14374	−0.0383599
$890$	9.30643	0.311952
$891$	−6.33777	−0.212323
$892$	20.6032	0.689846
$893$	−13.0786	−0.437659
$894$	−8.86642	−0.296537
$895$	4.74325	0.158549
$896$	−0.129988	−0.00434260
$897$	−7.58698	−0.253322
$898$	−39.3313	−1.31250
$899$	10.4681	0.349132
$900$	5.76054	0.192018
$901$	−8.10192	−0.269914
$902$	22.9560	0.764350
$903$	0.0323316	0.00107593
$904$	−10.3190	−0.343203
$905$	9.10773	0.302751
$906$	0.245537	0.00815743
$907$	20.7902	0.690326	0.345163	−	0.938543i	$-0.387824\pi$
$907$	20.7902	0.690326	0.345163	+	0.938543i	$0.387824\pi$
$908$	7.44211	0.246975
$909$	7.37639	0.244659
$910$	0.911110	0.0302030
$911$	−6.47884	−0.214654	−0.107327	−	0.994224i	$-0.534229\pi$
$911$	−6.47884	−0.214654	−0.107327	+	0.994224i	$0.534229\pi$
$912$	6.81527	0.225676
$913$	−29.5756	−0.978809
$914$	−13.7231	−0.453921
$915$	13.1595	0.435040
$916$	−1.58178	−0.0522633
$917$	0.764790	0.0252556
$918$	−9.61400	−0.317309
$919$	16.2594	0.536348	0.268174	−	0.963371i	$-0.413580\pi$
$919$	16.2594	0.536348	0.268174	+	0.963371i	$0.413580\pi$
$920$	−1.11783	−0.0368537
$921$	−5.44710	−0.179488
$922$	−7.28087	−0.239783
$923$	16.8394	0.554275
$924$	0.490329	0.0161306
$925$	−30.7429	−1.01082
$926$	8.25788	0.271371
$927$	−8.84456	−0.290493
$928$	1.00000	0.0328266
$929$	−22.3623	−0.733684	−0.366842	−	0.930283i	$-0.619561\pi$
$929$	−22.3623	−0.733684	−0.366842	+	0.930283i	$0.619561\pi$
$930$	14.1586	0.464280
$931$	39.3328	1.28908
$932$	9.41846	0.308512
$933$	−35.1856	−1.15193
$934$	42.7781	1.39974
$935$	6.10436	0.199634
$936$	−9.63099	−0.314799
$937$	−0.661967	−0.0216255	−0.0108128	−	0.999942i	$-0.503442\pi$
$937$	−0.661967	−0.0216255	−0.0108128	+	0.999942i	$0.503442\pi$
$938$	−1.49151	−0.0486995
$939$	−33.7143	−1.10022
$940$	−2.59556	−0.0846578
$941$	−30.3762	−0.990234	−0.495117	−	0.868826i	$-0.664875\pi$
$941$	−30.3762	−0.990234	−0.495117	+	0.868826i	$0.664875\pi$
$942$	−16.7933	−0.547154
$943$	7.36357	0.239791
$944$	6.32600	0.205894
$945$	0.797489	0.0259423
$946$	0.640846	0.0208357
$947$	−50.0348	−1.62591	−0.812957	−	0.582324i	$-0.802144\pi$
$947$	−50.0348	−1.62591	−0.812957	+	0.582324i	$0.802144\pi$
$948$	−0.00130164	−4.22753e−5 0
$949$	65.4500	2.12460
$950$	21.1247	0.685376
$951$	39.3520	1.27608
$952$	0.227699	0.00737978
$953$	−29.8518	−0.966996	−0.483498	−	0.875345i	$-0.660634\pi$
$953$	−29.8518	−0.966996	−0.483498	+	0.875345i	$0.660634\pi$
$954$	−7.10409	−0.230004
$955$	6.10493	0.197551
$956$	7.67049	0.248082
$957$	−3.77210	−0.121935
$958$	5.60274	0.181016
$959$	1.68197	0.0543136
$960$	1.35255	0.0436532
$961$	78.5820	2.53490
$962$	51.3987	1.65716
$963$	3.00799	0.0969311
$964$	−6.50395	−0.209478
$965$	−14.7584	−0.475090
$966$	0.157283	0.00506048
$967$	14.4523	0.464755	0.232378	−	0.972626i	$-0.425350\pi$
$967$	14.4523	0.464755	0.232378	+	0.972626i	$0.425350\pi$
$968$	−1.28118	−0.0411788
$969$	−11.9383	−0.383512
$970$	20.6539	0.663156
$971$	−27.3582	−0.877968	−0.438984	−	0.898495i	$-0.644661\pi$
$971$	−27.3582	−0.877968	−0.438984	+	0.898495i	$0.644661\pi$
$972$	−14.0054	−0.449222
$973$	0.0967039	0.00310018
$974$	−18.9679	−0.607770
$975$	28.4546	0.911278
$976$	9.72943	0.311431
$977$	5.59583	0.179027	0.0895133	−	0.995986i	$-0.471469\pi$
$977$	5.59583	0.179027	0.0895133	+	0.995986i	$0.471469\pi$
$978$	26.0440	0.832794
$979$	−25.9546	−0.829513
$980$	7.80591	0.249351
$981$	18.7761	0.599474
$982$	27.7760	0.886367
$983$	16.6795	0.531992	0.265996	−	0.963974i	$-0.414299\pi$
$983$	16.6795	0.531992	0.265996	+	0.963974i	$0.414299\pi$
$984$	−8.90975	−0.284033
$985$	14.8692	0.473771
$986$	−1.75169	−0.0557853
$987$	0.365204	0.0116246
$988$	−35.3181	−1.12362
$989$	0.205564	0.00653656
$990$	5.35255	0.170115
$991$	−25.3492	−0.805244	−0.402622	−	0.915366i	$-0.631901\pi$
$991$	−25.3492	−0.805244	−0.402622	+	0.915366i	$0.631901\pi$
$992$	10.4681	0.332364
$993$	18.8207	0.597257
$994$	−0.349091	−0.0110725
$995$	−16.7156	−0.529919
$996$	11.4790	0.363726
$997$	−50.3646	−1.59506	−0.797532	−	0.603277i	$-0.793861\pi$
$997$	−50.3646	−1.59506	−0.797532	+	0.603277i	$0.793861\pi$
$998$	14.1434	0.447703
$999$	44.9890	1.42339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.k.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.k.1.3	✓	10	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} -1.11783 q^{5} -1.20998 q^{6} -0.129988 q^{7} +1.00000 q^{8} -1.53596 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.20998 q^{3} +1.00000 q^{4} -1.11783 q^{5} -1.20998 q^{6} -0.129988 q^{7} +1.00000 q^{8} -1.53596 q^{9} -1.11783 q^{10} +3.11750 q^{11} -1.20998 q^{12} +6.27035 q^{13} -0.129988 q^{14} +1.35255 q^{15} +1.00000 q^{16} -1.75169 q^{17} -1.53596 q^{18} -5.63256 q^{19} -1.11783 q^{20} +0.157283 q^{21} +3.11750 q^{22} +1.00000 q^{23} -1.20998 q^{24} -3.75046 q^{25} +6.27035 q^{26} +5.48840 q^{27} -0.129988 q^{28} +1.00000 q^{29} +1.35255 q^{30} +10.4681 q^{31} +1.00000 q^{32} -3.77210 q^{33} -1.75169 q^{34} +0.145304 q^{35} -1.53596 q^{36} +8.19710 q^{37} -5.63256 q^{38} -7.58698 q^{39} -1.11783 q^{40} +7.36357 q^{41} +0.157283 q^{42} +0.205564 q^{43} +3.11750 q^{44} +1.71694 q^{45} +1.00000 q^{46} +2.32196 q^{47} -1.20998 q^{48} -6.98310 q^{49} -3.75046 q^{50} +2.11951 q^{51} +6.27035 q^{52} +4.62519 q^{53} +5.48840 q^{54} -3.48483 q^{55} -0.129988 q^{56} +6.81527 q^{57} +1.00000 q^{58} +6.32600 q^{59} +1.35255 q^{60} +9.72943 q^{61} +10.4681 q^{62} +0.199656 q^{63} +1.00000 q^{64} -7.00918 q^{65} -3.77210 q^{66} +11.4742 q^{67} -1.75169 q^{68} -1.20998 q^{69} +0.145304 q^{70} +2.68556 q^{71} -1.53596 q^{72} +10.4380 q^{73} +8.19710 q^{74} +4.53797 q^{75} -5.63256 q^{76} -0.405238 q^{77} -7.58698 q^{78} +0.00107576 q^{79} -1.11783 q^{80} -2.03296 q^{81} +7.36357 q^{82} -9.48695 q^{83} +0.157283 q^{84} +1.95809 q^{85} +0.205564 q^{86} -1.20998 q^{87} +3.11750 q^{88} -8.32545 q^{89} +1.71694 q^{90} -0.815071 q^{91} +1.00000 q^{92} -12.6662 q^{93} +2.32196 q^{94} +6.29624 q^{95} -1.20998 q^{96} -18.4768 q^{97} -6.98310 q^{98} -4.78835 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9}+O(q^{10}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9	\( 10 q + 10 q^{2} + 5 q^{3} + 10 q^{4} - q^{5} + 5 q^{6} + 2 q^{7} + 10 q^{8} + 11 q^{9} - q^{10} + q^{11} + 5 q^{12} + 9 q^{13} + 2 q^{14} + 5 q^{15} + 10 q^{16} + 11 q^{18} + 20 q^{19} - q^{20} + 14 q^{21} + q^{22} + 10 q^{23} + 5 q^{24} + 23 q^{25} + 9 q^{26} + 23 q^{27} + 2 q^{28} + 10 q^{29} + 5 q^{30} + 21 q^{31} + 10 q^{32} + q^{33} + 2 q^{35} + 11 q^{36} - 8 q^{37} + 20 q^{38} + 23 q^{39} - q^{40} - 4 q^{41} + 14 q^{42} - 3 q^{43} + q^{44} - 18 q^{45} + 10 q^{46} - q^{47} + 5 q^{48} + 18 q^{49} + 23 q^{50} - 6 q^{51} + 9 q^{52} - 13 q^{53} + 23 q^{54} + 13 q^{55} + 2 q^{56} - 22 q^{57} + 10 q^{58} + 14 q^{59} + 5 q^{60} + 12 q^{61} + 21 q^{62} - 26 q^{63} + 10 q^{64} - 25 q^{65} + q^{66} + 6 q^{67} + 5 q^{69} + 2 q^{70} + 8 q^{71} + 11 q^{72} + 16 q^{73} - 8 q^{74} + 8 q^{75} + 20 q^{76} - 16 q^{77} + 23 q^{78} + 7 q^{79} - q^{80} - 2 q^{81} - 4 q^{82} + 18 q^{83} + 14 q^{84} + 8 q^{85} - 3 q^{86} + 5 q^{87} + q^{88} + 2 q^{89} - 18 q^{90} + 8 q^{91} + 10 q^{92} - 41 q^{93} - q^{94} - 16 q^{95} + 5 q^{96} + 6 q^{97} + 18 q^{98} - 22 q^{99}+O(q^{100}) \) 10 * q + 10 * q^2 + 5 * q^3 + 10 * q^4 - q^5 + 5 * q^6 + 2 * q^7 + 10 * q^8 + 11 * q^9 - q^10 + q^11 + 5 * q^12 + 9 * q^13 + 2 * q^14 + 5 * q^15 + 10 * q^16 + 11 * q^18 + 20 * q^19 - q^20 + 14 * q^21 + q^22 + 10 * q^23 + 5 * q^24 + 23 * q^25 + 9 * q^26 + 23 * q^27 + 2 * q^28 + 10 * q^29 + 5 * q^30 + 21 * q^31 + 10 * q^32 + q^33 + 2 * q^35 + 11 * q^36 - 8 * q^37 + 20 * q^38 + 23 * q^39 - q^40 - 4 * q^41 + 14 * q^42 - 3 * q^43 + q^44 - 18 * q^45 + 10 * q^46 - q^47 + 5 * q^48 + 18 * q^49 + 23 * q^50 - 6 * q^51 + 9 * q^52 - 13 * q^53 + 23 * q^54 + 13 * q^55 + 2 * q^56 - 22 * q^57 + 10 * q^58 + 14 * q^59 + 5 * q^60 + 12 * q^61 + 21 * q^62 - 26 * q^63 + 10 * q^64 - 25 * q^65 + q^66 + 6 * q^67 + 5 * q^69 + 2 * q^70 + 8 * q^71 + 11 * q^72 + 16 * q^73 - 8 * q^74 + 8 * q^75 + 20 * q^76 - 16 * q^77 + 23 * q^78 + 7 * q^79 - q^80 - 2 * q^81 - 4 * q^82 + 18 * q^83 + 14 * q^84 + 8 * q^85 - 3 * q^86 + 5 * q^87 + q^88 + 2 * q^89 - 18 * q^90 + 8 * q^91 + 10 * q^92 - 41 * q^93 - q^94 - 16 * q^95 + 5 * q^96 + 6 * q^97 + 18 * q^98 - 22 * q^99

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