LMFDB - Embedded newform 8022.2.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 39 x^{11} + 67 x^{10} + 588 x^{9} - 823 x^{8} - 4265 x^{7} + 4419 x^{6} + 14926 x^{5} + \cdots - 984 $ x^13 - 2x^12 - 39x^11 + 67x^10 + 588x^9 - 823x^8 - 4265x^7 + 4419x^6 + 14926x^5 - 9090x^4 - 21330x^3 + 2178x^2 + 5892x - 984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.997264$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.997264 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.997264 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.997264 q^{10} -3.11756 q^{11} +1.00000 q^{12} -0.0342787 q^{13} +1.00000 q^{14} +0.997264 q^{15} +1.00000 q^{16} -1.85519 q^{17} -1.00000 q^{18} +5.81960 q^{19} +0.997264 q^{20} -1.00000 q^{21} +3.11756 q^{22} -9.38995 q^{23} -1.00000 q^{24} -4.00547 q^{25} +0.0342787 q^{26} +1.00000 q^{27} -1.00000 q^{28} -8.20061 q^{29} -0.997264 q^{30} -3.82943 q^{31} -1.00000 q^{32} -3.11756 q^{33} +1.85519 q^{34} -0.997264 q^{35} +1.00000 q^{36} +6.37019 q^{37} -5.81960 q^{38} -0.0342787 q^{39} -0.997264 q^{40} -6.95633 q^{41} +1.00000 q^{42} +3.59869 q^{43} -3.11756 q^{44} +0.997264 q^{45} +9.38995 q^{46} +3.17273 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.00547 q^{50} -1.85519 q^{51} -0.0342787 q^{52} +11.0948 q^{53} -1.00000 q^{54} -3.10903 q^{55} +1.00000 q^{56} +5.81960 q^{57} +8.20061 q^{58} +4.14376 q^{59} +0.997264 q^{60} +14.7318 q^{61} +3.82943 q^{62} -1.00000 q^{63} +1.00000 q^{64} -0.0341849 q^{65} +3.11756 q^{66} +1.17263 q^{67} -1.85519 q^{68} -9.38995 q^{69} +0.997264 q^{70} +13.8670 q^{71} -1.00000 q^{72} +16.3602 q^{73} -6.37019 q^{74} -4.00547 q^{75} +5.81960 q^{76} +3.11756 q^{77} +0.0342787 q^{78} +1.04051 q^{79} +0.997264 q^{80} +1.00000 q^{81} +6.95633 q^{82} -0.388553 q^{83} -1.00000 q^{84} -1.85012 q^{85} -3.59869 q^{86} -8.20061 q^{87} +3.11756 q^{88} +13.2495 q^{89} -0.997264 q^{90} +0.0342787 q^{91} -9.38995 q^{92} -3.82943 q^{93} -3.17273 q^{94} +5.80368 q^{95} -1.00000 q^{96} +0.345628 q^{97} -1.00000 q^{98} -3.11756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 2 q^{10} - q^{11} + 13 q^{12} + 14 q^{13} + 13 q^{14} - 2 q^{15} + 13 q^{16} + 7 q^{17} - 13 q^{18} - 2 q^{20} - 13 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 17 q^{25} - 14 q^{26} + 13 q^{27} - 13 q^{28} + 5 q^{29} + 2 q^{30} - 7 q^{31} - 13 q^{32} - q^{33} - 7 q^{34} + 2 q^{35} + 13 q^{36} + 15 q^{37} + 14 q^{39} + 2 q^{40} - 10 q^{41} + 13 q^{42} + 15 q^{43} - q^{44} - 2 q^{45} - 11 q^{46} - 7 q^{47} + 13 q^{48} + 13 q^{49} - 17 q^{50} + 7 q^{51} + 14 q^{52} + 14 q^{53} - 13 q^{54} + 19 q^{55} + 13 q^{56} - 5 q^{58} - 18 q^{59} - 2 q^{60} + 27 q^{61} + 7 q^{62} - 13 q^{63} + 13 q^{64} + 18 q^{65} + q^{66} + 7 q^{67} + 7 q^{68} + 11 q^{69} - 2 q^{70} - 4 q^{71} - 13 q^{72} + 26 q^{73} - 15 q^{74} + 17 q^{75} + q^{77} - 14 q^{78} + 20 q^{79} - 2 q^{80} + 13 q^{81} + 10 q^{82} + q^{83} - 13 q^{84} + 34 q^{85} - 15 q^{86} + 5 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} - 14 q^{91} + 11 q^{92} - 7 q^{93} + 7 q^{94} + 24 q^{95} - 13 q^{96} + 18 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 2 * q^10 - q^11 + 13 * q^12 + 14 * q^13 + 13 * q^14 - 2 * q^15 + 13 * q^16 + 7 * q^17 - 13 * q^18 - 2 * q^20 - 13 * q^21 + q^22 + 11 * q^23 - 13 * q^24 + 17 * q^25 - 14 * q^26 + 13 * q^27 - 13 * q^28 + 5 * q^29 + 2 * q^30 - 7 * q^31 - 13 * q^32 - q^33 - 7 * q^34 + 2 * q^35 + 13 * q^36 + 15 * q^37 + 14 * q^39 + 2 * q^40 - 10 * q^41 + 13 * q^42 + 15 * q^43 - q^44 - 2 * q^45 - 11 * q^46 - 7 * q^47 + 13 * q^48 + 13 * q^49 - 17 * q^50 + 7 * q^51 + 14 * q^52 + 14 * q^53 - 13 * q^54 + 19 * q^55 + 13 * q^56 - 5 * q^58 - 18 * q^59 - 2 * q^60 + 27 * q^61 + 7 * q^62 - 13 * q^63 + 13 * q^64 + 18 * q^65 + q^66 + 7 * q^67 + 7 * q^68 + 11 * q^69 - 2 * q^70 - 4 * q^71 - 13 * q^72 + 26 * q^73 - 15 * q^74 + 17 * q^75 + q^77 - 14 * q^78 + 20 * q^79 - 2 * q^80 + 13 * q^81 + 10 * q^82 + q^83 - 13 * q^84 + 34 * q^85 - 15 * q^86 + 5 * q^87 + q^88 - 15 * q^89 + 2 * q^90 - 14 * q^91 + 11 * q^92 - 7 * q^93 + 7 * q^94 + 24 * q^95 - 13 * q^96 + 18 * q^97 - 13 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	0.997264	0.445990	0.222995	−	0.974820i	$-0.428417\pi$
$5$	0.997264	0.445990	0.222995	+	0.974820i	$0.428417\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.997264	−0.315362
$11$	−3.11756	−0.939980	−0.469990	−	0.882672i	$-0.655742\pi$
$11$	−3.11756	−0.939980	−0.469990	+	0.882672i	$0.655742\pi$
$12$	1.00000	0.288675
$13$	−0.0342787	−0.00950720	−0.00475360	−	0.999989i	$-0.501513\pi$
$13$	−0.0342787	−0.00950720	−0.00475360	+	0.999989i	$0.501513\pi$
$14$	1.00000	0.267261
$15$	0.997264	0.257492
$16$	1.00000	0.250000
$17$	−1.85519	−0.449951	−0.224975	−	0.974364i	$-0.572230\pi$
$17$	−1.85519	−0.449951	−0.224975	+	0.974364i	$0.572230\pi$
$18$	−1.00000	−0.235702
$19$	5.81960	1.33511	0.667554	−	0.744561i	$-0.267341\pi$
$19$	5.81960	1.33511	0.667554	+	0.744561i	$0.267341\pi$
$20$	0.997264	0.222995
$21$	−1.00000	−0.218218
$22$	3.11756	0.664666
$23$	−9.38995	−1.95794	−0.978970	−	0.204002i	$-0.934605\pi$
$23$	−9.38995	−1.95794	−0.978970	+	0.204002i	$0.934605\pi$
$24$	−1.00000	−0.204124
$25$	−4.00547	−0.801093
$26$	0.0342787	0.00672260
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	−8.20061	−1.52281	−0.761407	−	0.648274i	$-0.775491\pi$
$29$	−8.20061	−1.52281	−0.761407	+	0.648274i	$0.775491\pi$
$30$	−0.997264	−0.182075
$31$	−3.82943	−0.687786	−0.343893	−	0.939009i	$-0.611746\pi$
$31$	−3.82943	−0.687786	−0.343893	+	0.939009i	$0.611746\pi$
$32$	−1.00000	−0.176777
$33$	−3.11756	−0.542697
$34$	1.85519	0.318163
$35$	−0.997264	−0.168568
$36$	1.00000	0.166667
$37$	6.37019	1.04725	0.523626	−	0.851948i	$-0.324579\pi$
$37$	6.37019	1.04725	0.523626	+	0.851948i	$0.324579\pi$
$38$	−5.81960	−0.944064
$39$	−0.0342787	−0.00548898
$40$	−0.997264	−0.157681
$41$	−6.95633	−1.08640	−0.543198	−	0.839605i	$-0.682787\pi$
$41$	−6.95633	−1.08640	−0.543198	+	0.839605i	$0.682787\pi$
$42$	1.00000	0.154303
$43$	3.59869	0.548795	0.274397	−	0.961616i	$-0.411522\pi$
$43$	3.59869	0.548795	0.274397	+	0.961616i	$0.411522\pi$
$44$	−3.11756	−0.469990
$45$	0.997264	0.148663
$46$	9.38995	1.38447
$47$	3.17273	0.462790	0.231395	−	0.972860i	$-0.425671\pi$
$47$	3.17273	0.462790	0.231395	+	0.972860i	$0.425671\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	4.00547	0.566458
$51$	−1.85519	−0.259779
$52$	−0.0342787	−0.00475360
$53$	11.0948	1.52399	0.761994	−	0.647584i	$-0.224220\pi$
$53$	11.0948	1.52399	0.761994	+	0.647584i	$0.224220\pi$
$54$	−1.00000	−0.136083
$55$	−3.10903	−0.419221
$56$	1.00000	0.133631
$57$	5.81960	0.770825
$58$	8.20061	1.07679
$59$	4.14376	0.539472	0.269736	−	0.962934i	$-0.413064\pi$
$59$	4.14376	0.539472	0.269736	+	0.962934i	$0.413064\pi$
$60$	0.997264	0.128746
$61$	14.7318	1.88621	0.943106	−	0.332491i	$-0.107889\pi$
$61$	14.7318	1.88621	0.943106	+	0.332491i	$0.107889\pi$
$62$	3.82943	0.486338
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	−0.0341849	−0.00424011
$66$	3.11756	0.383745
$67$	1.17263	0.143260	0.0716298	−	0.997431i	$-0.477180\pi$
$67$	1.17263	0.143260	0.0716298	+	0.997431i	$0.477180\pi$
$68$	−1.85519	−0.224975
$69$	−9.38995	−1.13042
$70$	0.997264	0.119196
$71$	13.8670	1.64571	0.822857	−	0.568249i	$-0.192379\pi$
$71$	13.8670	1.64571	0.822857	+	0.568249i	$0.192379\pi$
$72$	−1.00000	−0.117851
$73$	16.3602	1.91481	0.957406	−	0.288746i	$-0.0932384\pi$
$73$	16.3602	1.91481	0.957406	+	0.288746i	$0.0932384\pi$
$74$	−6.37019	−0.740519
$75$	−4.00547	−0.462511
$76$	5.81960	0.667554
$77$	3.11756	0.355279
$78$	0.0342787	0.00388130
$79$	1.04051	0.117067	0.0585335	−	0.998285i	$-0.481358\pi$
$79$	1.04051	0.117067	0.0585335	+	0.998285i	$0.481358\pi$
$80$	0.997264	0.111497
$81$	1.00000	0.111111
$82$	6.95633	0.768198
$83$	−0.388553	−0.0426492	−0.0213246	−	0.999773i	$-0.506788\pi$
$83$	−0.388553	−0.0426492	−0.0213246	+	0.999773i	$0.506788\pi$
$84$	−1.00000	−0.109109
$85$	−1.85012	−0.200673
$86$	−3.59869	−0.388057
$87$	−8.20061	−0.879197
$88$	3.11756	0.332333
$89$	13.2495	1.40444	0.702221	−	0.711959i	$-0.252192\pi$
$89$	13.2495	1.40444	0.702221	+	0.711959i	$0.252192\pi$
$90$	−0.997264	−0.105121
$91$	0.0342787	0.00359338
$92$	−9.38995	−0.978970
$93$	−3.82943	−0.397093
$94$	−3.17273	−0.327242
$95$	5.80368	0.595445
$96$	−1.00000	−0.102062
$97$	0.345628	0.0350932	0.0175466	−	0.999846i	$-0.494414\pi$
$97$	0.345628	0.0350932	0.0175466	+	0.999846i	$0.494414\pi$
$98$	−1.00000	−0.101015
$99$	−3.11756	−0.313327
$100$	−4.00547	−0.400547
$101$	−1.69199	−0.168359	−0.0841797	−	0.996451i	$-0.526827\pi$
$101$	−1.69199	−0.168359	−0.0841797	+	0.996451i	$0.526827\pi$
$102$	1.85519	0.183692
$103$	−5.90002	−0.581346	−0.290673	−	0.956822i	$-0.593879\pi$
$103$	−5.90002	−0.581346	−0.290673	+	0.956822i	$0.593879\pi$
$104$	0.0342787	0.00336130
$105$	−0.997264	−0.0973230
$106$	−11.0948	−1.07762
$107$	9.58062	0.926194	0.463097	−	0.886308i	$-0.346738\pi$
$107$	9.58062	0.926194	0.463097	+	0.886308i	$0.346738\pi$
$108$	1.00000	0.0962250
$109$	−7.95227	−0.761689	−0.380845	−	0.924639i	$-0.624367\pi$
$109$	−7.95227	−0.761689	−0.380845	+	0.924639i	$0.624367\pi$
$110$	3.10903	0.296434
$111$	6.37019	0.604632
$112$	−1.00000	−0.0944911
$113$	16.6563	1.56689	0.783446	−	0.621460i	$-0.213460\pi$
$113$	16.6563	1.56689	0.783446	+	0.621460i	$0.213460\pi$
$114$	−5.81960	−0.545056
$115$	−9.36426	−0.873222
$116$	−8.20061	−0.761407
$117$	−0.0342787	−0.00316907
$118$	−4.14376	−0.381464
$119$	1.85519	0.170065
$120$	−0.997264	−0.0910373
$121$	−1.28082	−0.116438
$122$	−14.7318	−1.33375
$123$	−6.95633	−0.627231
$124$	−3.82943	−0.343893
$125$	−8.98082	−0.803269
$126$	1.00000	0.0890871
$127$	−5.89840	−0.523398	−0.261699	−	0.965150i	$-0.584283\pi$
$127$	−5.89840	−0.523398	−0.261699	+	0.965150i	$0.584283\pi$
$128$	−1.00000	−0.0883883
$129$	3.59869	0.316847
$130$	0.0341849	0.00299821
$131$	6.72501	0.587567	0.293784	−	0.955872i	$-0.405086\pi$
$131$	6.72501	0.587567	0.293784	+	0.955872i	$0.405086\pi$
$132$	−3.11756	−0.271349
$133$	−5.81960	−0.504623
$134$	−1.17263	−0.101300
$135$	0.997264	0.0858308
$136$	1.85519	0.159082
$137$	−17.9145	−1.53054	−0.765269	−	0.643711i	$-0.777394\pi$
$137$	−17.9145	−1.53054	−0.765269	+	0.643711i	$0.777394\pi$
$138$	9.38995	0.799326
$139$	20.5532	1.74330	0.871651	−	0.490126i	$-0.163049\pi$
$139$	20.5532	1.74330	0.871651	+	0.490126i	$0.163049\pi$
$140$	−0.997264	−0.0842842
$141$	3.17273	0.267192
$142$	−13.8670	−1.16370
$143$	0.106866	0.00893657
$144$	1.00000	0.0833333
$145$	−8.17816	−0.679160
$146$	−16.3602	−1.35398
$147$	1.00000	0.0824786
$148$	6.37019	0.523626
$149$	22.1758	1.81671	0.908355	−	0.418199i	$-0.137339\pi$
$149$	22.1758	1.81671	0.908355	+	0.418199i	$0.137339\pi$
$150$	4.00547	0.327045
$151$	17.4710	1.42177	0.710885	−	0.703309i	$-0.248295\pi$
$151$	17.4710	1.42177	0.710885	+	0.703309i	$0.248295\pi$
$152$	−5.81960	−0.472032
$153$	−1.85519	−0.149984
$154$	−3.11756	−0.251220
$155$	−3.81895	−0.306746
$156$	−0.0342787	−0.00274449
$157$	13.2620	1.05842	0.529211	−	0.848490i	$-0.322488\pi$
$157$	13.2620	1.05842	0.529211	+	0.848490i	$0.322488\pi$
$158$	−1.04051	−0.0827788
$159$	11.0948	0.879875
$160$	−0.997264	−0.0788406
$161$	9.38995	0.740032
$162$	−1.00000	−0.0785674
$163$	−11.9360	−0.934896	−0.467448	−	0.884021i	$-0.654827\pi$
$163$	−11.9360	−0.934896	−0.467448	+	0.884021i	$0.654827\pi$
$164$	−6.95633	−0.543198
$165$	−3.10903	−0.242038
$166$	0.388553	0.0301575
$167$	14.0698	1.08876	0.544378	−	0.838840i	$-0.316766\pi$
$167$	14.0698	1.08876	0.544378	+	0.838840i	$0.316766\pi$
$168$	1.00000	0.0771517
$169$	−12.9988	−0.999910
$170$	1.85012	0.141898
$171$	5.81960	0.445036
$172$	3.59869	0.274397
$173$	6.96753	0.529732	0.264866	−	0.964285i	$-0.414672\pi$
$173$	6.96753	0.529732	0.264866	+	0.964285i	$0.414672\pi$
$174$	8.20061	0.621686
$175$	4.00547	0.302785
$176$	−3.11756	−0.234995
$177$	4.14376	0.311464
$178$	−13.2495	−0.993090
$179$	−12.0313	−0.899260	−0.449630	−	0.893215i	$-0.648444\pi$
$179$	−12.0313	−0.899260	−0.449630	+	0.893215i	$0.648444\pi$
$180$	0.997264	0.0743316
$181$	−1.55209	−0.115366	−0.0576829	−	0.998335i	$-0.518371\pi$
$181$	−1.55209	−0.115366	−0.0576829	+	0.998335i	$0.518371\pi$
$182$	−0.0342787	−0.00254091
$183$	14.7318	1.08901
$184$	9.38995	0.692237
$185$	6.35276	0.467064
$186$	3.82943	0.280787
$187$	5.78368	0.422944
$188$	3.17273	0.231395
$189$	−1.00000	−0.0727393
$190$	−5.80368	−0.421043
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	7.57531	0.545283	0.272641	−	0.962116i	$-0.412103\pi$
$193$	7.57531	0.545283	0.272641	+	0.962116i	$0.412103\pi$
$194$	−0.345628	−0.0248146
$195$	−0.0341849	−0.00244803
$196$	1.00000	0.0714286
$197$	−13.4794	−0.960367	−0.480183	−	0.877168i	$-0.659430\pi$
$197$	−13.4794	−0.960367	−0.480183	+	0.877168i	$0.659430\pi$
$198$	3.11756	0.221555
$199$	11.2135	0.794902	0.397451	−	0.917623i	$-0.369895\pi$
$199$	11.2135	0.794902	0.397451	+	0.917623i	$0.369895\pi$
$200$	4.00547	0.283229
$201$	1.17263	0.0827109
$202$	1.69199	0.119048
$203$	8.20061	0.575570
$204$	−1.85519	−0.129890
$205$	−6.93729	−0.484522
$206$	5.90002	0.411074
$207$	−9.38995	−0.652647
$208$	−0.0342787	−0.00237680
$209$	−18.1430	−1.25497
$210$	0.997264	0.0688177
$211$	−18.6307	−1.28259	−0.641295	−	0.767294i	$-0.721603\pi$
$211$	−18.6307	−1.28259	−0.641295	+	0.767294i	$0.721603\pi$
$212$	11.0948	0.761994
$213$	13.8670	0.950153
$214$	−9.58062	−0.654918
$215$	3.58884	0.244757
$216$	−1.00000	−0.0680414
$217$	3.82943	0.259959
$218$	7.95227	0.538595
$219$	16.3602	1.10552
$220$	−3.10903	−0.209611
$221$	0.0635936	0.00427777
$222$	−6.37019	−0.427539
$223$	23.2062	1.55400	0.777001	−	0.629499i	$-0.216740\pi$
$223$	23.2062	1.55400	0.777001	+	0.629499i	$0.216740\pi$
$224$	1.00000	0.0668153
$225$	−4.00547	−0.267031
$226$	−16.6563	−1.10796
$227$	−4.79183	−0.318045	−0.159022	−	0.987275i	$-0.550834\pi$
$227$	−4.79183	−0.318045	−0.159022	+	0.987275i	$0.550834\pi$
$228$	5.81960	0.385412
$229$	17.9043	1.18315	0.591573	−	0.806251i	$-0.298507\pi$
$229$	17.9043	1.18315	0.591573	+	0.806251i	$0.298507\pi$
$230$	9.36426	0.617461
$231$	3.11756	0.205120
$232$	8.20061	0.538396
$233$	1.25242	0.0820487	0.0410243	−	0.999158i	$-0.486938\pi$
$233$	1.25242	0.0820487	0.0410243	+	0.999158i	$0.486938\pi$
$234$	0.0342787	0.00224087
$235$	3.16405	0.206400
$236$	4.14376	0.269736
$237$	1.04051	0.0675886
$238$	−1.85519	−0.120254
$239$	−6.32606	−0.409199	−0.204600	−	0.978846i	$-0.565589\pi$
$239$	−6.32606	−0.409199	−0.204600	+	0.978846i	$0.565589\pi$
$240$	0.997264	0.0643731
$241$	20.1858	1.30028	0.650141	−	0.759814i	$-0.274710\pi$
$241$	20.1858	1.30028	0.650141	+	0.759814i	$0.274710\pi$
$242$	1.28082	0.0823343
$243$	1.00000	0.0641500
$244$	14.7318	0.943106
$245$	0.997264	0.0637128
$246$	6.95633	0.443519
$247$	−0.199488	−0.0126931
$248$	3.82943	0.243169
$249$	−0.388553	−0.0246235
$250$	8.98082	0.567997
$251$	−5.62102	−0.354795	−0.177398	−	0.984139i	$-0.556768\pi$
$251$	−5.62102	−0.354795	−0.177398	+	0.984139i	$0.556768\pi$
$252$	−1.00000	−0.0629941
$253$	29.2737	1.84042
$254$	5.89840	0.370098
$255$	−1.85012	−0.115859
$256$	1.00000	0.0625000
$257$	20.6107	1.28566	0.642830	−	0.766008i	$-0.277760\pi$
$257$	20.6107	1.28566	0.642830	+	0.766008i	$0.277760\pi$
$258$	−3.59869	−0.224045
$259$	−6.37019	−0.395824
$260$	−0.0341849	−0.00212006
$261$	−8.20061	−0.507605
$262$	−6.72501	−0.415473
$263$	5.64224	0.347916	0.173958	−	0.984753i	$-0.444344\pi$
$263$	5.64224	0.347916	0.173958	+	0.984753i	$0.444344\pi$
$264$	3.11756	0.191873
$265$	11.0644	0.679683
$266$	5.81960	0.356823
$267$	13.2495	0.810855
$268$	1.17263	0.0716298
$269$	−18.6716	−1.13843	−0.569215	−	0.822189i	$-0.692753\pi$
$269$	−18.6716	−1.13843	−0.569215	+	0.822189i	$0.692753\pi$
$270$	−0.997264	−0.0606915
$271$	7.23623	0.439569	0.219785	−	0.975548i	$-0.429465\pi$
$271$	7.23623	0.439569	0.219785	+	0.975548i	$0.429465\pi$
$272$	−1.85519	−0.112488
$273$	0.0342787	0.00207464
$274$	17.9145	1.08225
$275$	12.4873	0.753011
$276$	−9.38995	−0.565209
$277$	−18.0569	−1.08493	−0.542466	−	0.840078i	$-0.682509\pi$
$277$	−18.0569	−1.08493	−0.542466	+	0.840078i	$0.682509\pi$
$278$	−20.5532	−1.23270
$279$	−3.82943	−0.229262
$280$	0.997264	0.0595979
$281$	−21.3845	−1.27569	−0.637846	−	0.770164i	$-0.720174\pi$
$281$	−21.3845	−1.27569	−0.637846	+	0.770164i	$0.720174\pi$
$282$	−3.17273	−0.188933
$283$	−24.0321	−1.42856	−0.714280	−	0.699860i	$-0.753246\pi$
$283$	−24.0321	−1.42856	−0.714280	+	0.699860i	$0.753246\pi$
$284$	13.8670	0.822857
$285$	5.80368	0.343780
$286$	−0.106866	−0.00631911
$287$	6.95633	0.410619
$288$	−1.00000	−0.0589256
$289$	−13.5583	−0.797544
$290$	8.17816	0.480238
$291$	0.345628	0.0202610
$292$	16.3602	0.957406
$293$	−12.2777	−0.717269	−0.358635	−	0.933478i	$-0.616758\pi$
$293$	−12.2777	−0.717269	−0.358635	+	0.933478i	$0.616758\pi$
$294$	−1.00000	−0.0583212
$295$	4.13243	0.240599
$296$	−6.37019	−0.370260
$297$	−3.11756	−0.180899
$298$	−22.1758	−1.28461
$299$	0.321875	0.0186145
$300$	−4.00547	−0.231256
$301$	−3.59869	−0.207425
$302$	−17.4710	−1.00534
$303$	−1.69199	−0.0972024
$304$	5.81960	0.333777
$305$	14.6915	0.841232
$306$	1.85519	0.106054
$307$	1.45692	0.0831511	0.0415755	−	0.999135i	$-0.486762\pi$
$307$	1.45692	0.0831511	0.0415755	+	0.999135i	$0.486762\pi$
$308$	3.11756	0.177639
$309$	−5.90002	−0.335640
$310$	3.81895	0.216902
$311$	1.82022	0.103215	0.0516075	−	0.998667i	$-0.483566\pi$
$311$	1.82022	0.103215	0.0516075	+	0.998667i	$0.483566\pi$
$312$	0.0342787	0.00194065
$313$	20.7542	1.17310	0.586548	−	0.809915i	$-0.300487\pi$
$313$	20.7542	1.17310	0.586548	+	0.809915i	$0.300487\pi$
$314$	−13.2620	−0.748418
$315$	−0.997264	−0.0561894
$316$	1.04051	0.0585335
$317$	20.4478	1.14846	0.574231	−	0.818694i	$-0.305301\pi$
$317$	20.4478	1.14846	0.574231	+	0.818694i	$0.305301\pi$
$318$	−11.0948	−0.622166
$319$	25.5659	1.43141
$320$	0.997264	0.0557487
$321$	9.58062	0.534738
$322$	−9.38995	−0.523282
$323$	−10.7965	−0.600733
$324$	1.00000	0.0555556
$325$	0.137302	0.00761615
$326$	11.9360	0.661071
$327$	−7.95227	−0.439761
$328$	6.95633	0.384099
$329$	−3.17273	−0.174918
$330$	3.10903	0.171146
$331$	−29.1939	−1.60464	−0.802320	−	0.596894i	$-0.796401\pi$
$331$	−29.1939	−1.60464	−0.802320	+	0.596894i	$0.796401\pi$
$332$	−0.388553	−0.0213246
$333$	6.37019	0.349084
$334$	−14.0698	−0.769867
$335$	1.16942	0.0638923
$336$	−1.00000	−0.0545545
$337$	−16.6660	−0.907854	−0.453927	−	0.891039i	$-0.649977\pi$
$337$	−16.6660	−0.907854	−0.453927	+	0.891039i	$0.649977\pi$
$338$	12.9988	0.707043
$339$	16.6563	0.904646
$340$	−1.85012	−0.100337
$341$	11.9385	0.646505
$342$	−5.81960	−0.314688
$343$	−1.00000	−0.0539949
$344$	−3.59869	−0.194028
$345$	−9.36426	−0.504155
$346$	−6.96753	−0.374577
$347$	−16.9854	−0.911826	−0.455913	−	0.890024i	$-0.650687\pi$
$347$	−16.9854	−0.911826	−0.455913	+	0.890024i	$0.650687\pi$
$348$	−8.20061	−0.439599
$349$	12.8259	0.686557	0.343279	−	0.939234i	$-0.388462\pi$
$349$	12.8259	0.686557	0.343279	+	0.939234i	$0.388462\pi$
$350$	−4.00547	−0.214101
$351$	−0.0342787	−0.00182966
$352$	3.11756	0.166166
$353$	20.6643	1.09985	0.549924	−	0.835214i	$-0.314656\pi$
$353$	20.6643	1.09985	0.549924	+	0.835214i	$0.314656\pi$
$354$	−4.14376	−0.220239
$355$	13.8291	0.733972
$356$	13.2495	0.702221
$357$	1.85519	0.0981873
$358$	12.0313	0.635873
$359$	−12.4178	−0.655385	−0.327692	−	0.944784i	$-0.606271\pi$
$359$	−12.4178	−0.655385	−0.327692	+	0.944784i	$0.606271\pi$
$360$	−0.997264	−0.0525604
$361$	14.8677	0.782513
$362$	1.55209	0.0815759
$363$	−1.28082	−0.0672257
$364$	0.0342787	0.00179669
$365$	16.3154	0.853986
$366$	−14.7318	−0.770043
$367$	−15.2207	−0.794516	−0.397258	−	0.917707i	$-0.630038\pi$
$367$	−15.2207	−0.794516	−0.397258	+	0.917707i	$0.630038\pi$
$368$	−9.38995	−0.489485
$369$	−6.95633	−0.362132
$370$	−6.35276	−0.330264
$371$	−11.0948	−0.576014
$372$	−3.82943	−0.198547
$373$	−15.5897	−0.807204	−0.403602	−	0.914935i	$-0.632242\pi$
$373$	−15.5897	−0.807204	−0.403602	+	0.914935i	$0.632242\pi$
$374$	−5.78368	−0.299067
$375$	−8.98082	−0.463768
$376$	−3.17273	−0.163621
$377$	0.281106	0.0144777
$378$	1.00000	0.0514344
$379$	8.45863	0.434491	0.217245	−	0.976117i	$-0.430293\pi$
$379$	8.45863	0.434491	0.217245	+	0.976117i	$0.430293\pi$
$380$	5.80368	0.297722
$381$	−5.89840	−0.302184
$382$	1.00000	0.0511645
$383$	−21.2296	−1.08478	−0.542391	−	0.840126i	$-0.682481\pi$
$383$	−21.2296	−1.08478	−0.542391	+	0.840126i	$0.682481\pi$
$384$	−1.00000	−0.0510310
$385$	3.10903	0.158451
$386$	−7.57531	−0.385573
$387$	3.59869	0.182932
$388$	0.345628	0.0175466
$389$	28.3954	1.43970	0.719851	−	0.694129i	$-0.244210\pi$
$389$	28.3954	1.43970	0.719851	+	0.694129i	$0.244210\pi$
$390$	0.0341849	0.00173102
$391$	17.4202	0.880977
$392$	−1.00000	−0.0505076
$393$	6.72501	0.339232
$394$	13.4794	0.679082
$395$	1.03767	0.0522107
$396$	−3.11756	−0.156663
$397$	−14.0049	−0.702884	−0.351442	−	0.936210i	$-0.614308\pi$
$397$	−14.0049	−0.702884	−0.351442	+	0.936210i	$0.614308\pi$
$398$	−11.2135	−0.562080
$399$	−5.81960	−0.291344
$400$	−4.00547	−0.200273
$401$	−33.2815	−1.66200	−0.831000	−	0.556272i	$-0.812231\pi$
$401$	−33.2815	−1.66200	−0.831000	+	0.556272i	$0.812231\pi$
$402$	−1.17263	−0.0584855
$403$	0.131268	0.00653892
$404$	−1.69199	−0.0841797
$405$	0.997264	0.0495544
$406$	−8.20061	−0.406989
$407$	−19.8594	−0.984396
$408$	1.85519	0.0918458
$409$	25.4724	1.25953	0.629764	−	0.776787i	$-0.283152\pi$
$409$	25.4724	1.25953	0.629764	+	0.776787i	$0.283152\pi$
$410$	6.93729	0.342609
$411$	−17.9145	−0.883657
$412$	−5.90002	−0.290673
$413$	−4.14376	−0.203901
$414$	9.38995	0.461491
$415$	−0.387490	−0.0190211
$416$	0.0342787	0.00168065
$417$	20.5532	1.00650
$418$	18.1430	0.887401
$419$	0.567056	0.0277025	0.0138512	−	0.999904i	$-0.495591\pi$
$419$	0.567056	0.0277025	0.0138512	+	0.999904i	$0.495591\pi$
$420$	−0.997264	−0.0486615
$421$	−26.4078	−1.28704	−0.643520	−	0.765429i	$-0.722527\pi$
$421$	−26.4078	−1.28704	−0.643520	+	0.765429i	$0.722527\pi$
$422$	18.6307	0.906928
$423$	3.17273	0.154263
$424$	−11.0948	−0.538811
$425$	7.43092	0.360452
$426$	−13.8670	−0.671860
$427$	−14.7318	−0.712921
$428$	9.58062	0.463097
$429$	0.106866	0.00515953
$430$	−3.58884	−0.173069
$431$	−4.58604	−0.220902	−0.110451	−	0.993882i	$-0.535229\pi$
$431$	−4.58604	−0.220902	−0.110451	+	0.993882i	$0.535229\pi$
$432$	1.00000	0.0481125
$433$	39.3437	1.89074	0.945368	−	0.326004i	$-0.105702\pi$
$433$	39.3437	1.89074	0.945368	+	0.326004i	$0.105702\pi$
$434$	−3.82943	−0.183819
$435$	−8.17816	−0.392113
$436$	−7.95227	−0.380845
$437$	−54.6458	−2.61406
$438$	−16.3602	−0.781718
$439$	−7.13980	−0.340764	−0.170382	−	0.985378i	$-0.554500\pi$
$439$	−7.13980	−0.340764	−0.170382	+	0.985378i	$0.554500\pi$
$440$	3.10903	0.148217
$441$	1.00000	0.0476190
$442$	−0.0635936	−0.00302484
$443$	−37.8864	−1.80004	−0.900019	−	0.435850i	$-0.856448\pi$
$443$	−37.8864	−1.80004	−0.900019	+	0.435850i	$0.856448\pi$
$444$	6.37019	0.302316
$445$	13.2132	0.626367
$446$	−23.2062	−1.09885
$447$	22.1758	1.04888
$448$	−1.00000	−0.0472456
$449$	6.57743	0.310408	0.155204	−	0.987882i	$-0.450396\pi$
$449$	6.57743	0.310408	0.155204	+	0.987882i	$0.450396\pi$
$450$	4.00547	0.188819
$451$	21.6868	1.02119
$452$	16.6563	0.783446
$453$	17.4710	0.820859
$454$	4.79183	0.224892
$455$	0.0341849	0.00160261
$456$	−5.81960	−0.272528
$457$	0.0810198	0.00378995	0.00189497	−	0.999998i	$-0.499397\pi$
$457$	0.0810198	0.00378995	0.00189497	+	0.999998i	$0.499397\pi$
$458$	−17.9043	−0.836611
$459$	−1.85519	−0.0865930
$460$	−9.36426	−0.436611
$461$	24.1379	1.12421	0.562107	−	0.827064i	$-0.309991\pi$
$461$	24.1379	1.12421	0.562107	+	0.827064i	$0.309991\pi$
$462$	−3.11756	−0.145042
$463$	39.2942	1.82616	0.913079	−	0.407783i	$-0.133698\pi$
$463$	39.2942	1.82616	0.913079	+	0.407783i	$0.133698\pi$
$464$	−8.20061	−0.380704
$465$	−3.81895	−0.177100
$466$	−1.25242	−0.0580172
$467$	−13.7394	−0.635782	−0.317891	−	0.948127i	$-0.602975\pi$
$467$	−13.7394	−0.635782	−0.317891	+	0.948127i	$0.602975\pi$
$468$	−0.0342787	−0.00158453
$469$	−1.17263	−0.0541470
$470$	−3.16405	−0.145947
$471$	13.2620	0.611081
$472$	−4.14376	−0.190732
$473$	−11.2191	−0.515856
$474$	−1.04051	−0.0477924
$475$	−23.3102	−1.06955
$476$	1.85519	0.0850327
$477$	11.0948	0.507996
$478$	6.32606	0.289347
$479$	9.98679	0.456308	0.228154	−	0.973625i	$-0.426731\pi$
$479$	9.98679	0.456308	0.228154	+	0.973625i	$0.426731\pi$
$480$	−0.997264	−0.0455186
$481$	−0.218362	−0.00995644
$482$	−20.1858	−0.919438
$483$	9.38995	0.427258
$484$	−1.28082	−0.0582191
$485$	0.344682	0.0156512
$486$	−1.00000	−0.0453609
$487$	26.5560	1.20337	0.601684	−	0.798735i	$-0.294497\pi$
$487$	26.5560	1.20337	0.601684	+	0.798735i	$0.294497\pi$
$488$	−14.7318	−0.666877
$489$	−11.9360	−0.539763
$490$	−0.997264	−0.0450518
$491$	−15.9684	−0.720642	−0.360321	−	0.932828i	$-0.617333\pi$
$491$	−15.9684	−0.720642	−0.360321	+	0.932828i	$0.617333\pi$
$492$	−6.95633	−0.313616
$493$	15.2137	0.685191
$494$	0.199488	0.00897540
$495$	−3.10903	−0.139740
$496$	−3.82943	−0.171947
$497$	−13.8670	−0.622021
$498$	0.388553	0.0174115
$499$	−6.55541	−0.293460	−0.146730	−	0.989177i	$-0.546875\pi$
$499$	−6.55541	−0.293460	−0.146730	+	0.989177i	$0.546875\pi$
$500$	−8.98082	−0.401635
$501$	14.0698	0.628594
$502$	5.62102	0.250878
$503$	−5.28667	−0.235721	−0.117860	−	0.993030i	$-0.537604\pi$
$503$	−5.28667	−0.235721	−0.117860	+	0.993030i	$0.537604\pi$
$504$	1.00000	0.0445435
$505$	−1.68736	−0.0750866
$506$	−29.2737	−1.30138
$507$	−12.9988	−0.577298
$508$	−5.89840	−0.261699
$509$	−19.5478	−0.866442	−0.433221	−	0.901288i	$-0.642623\pi$
$509$	−19.5478	−0.866442	−0.433221	+	0.901288i	$0.642623\pi$
$510$	1.85012	0.0819246
$511$	−16.3602	−0.723731
$512$	−1.00000	−0.0441942
$513$	5.81960	0.256942
$514$	−20.6107	−0.909100
$515$	−5.88387	−0.259274
$516$	3.59869	0.158423
$517$	−9.89118	−0.435014
$518$	6.37019	0.279890
$519$	6.96753	0.305841
$520$	0.0341849	0.00149911
$521$	8.10406	0.355045	0.177523	−	0.984117i	$-0.443192\pi$
$521$	8.10406	0.355045	0.177523	+	0.984117i	$0.443192\pi$
$522$	8.20061	0.358931
$523$	−7.43852	−0.325264	−0.162632	−	0.986687i	$-0.551998\pi$
$523$	−7.43852	−0.325264	−0.162632	+	0.986687i	$0.551998\pi$
$524$	6.72501	0.293784
$525$	4.00547	0.174813
$526$	−5.64224	−0.246014
$527$	7.10434	0.309470
$528$	−3.11756	−0.135674
$529$	65.1712	2.83353
$530$	−11.0644	−0.480609
$531$	4.14376	0.179824
$532$	−5.81960	−0.252312
$533$	0.238454	0.0103286
$534$	−13.2495	−0.573361
$535$	9.55440	0.413073
$536$	−1.17263	−0.0506499
$537$	−12.0313	−0.519188
$538$	18.6716	0.804992
$539$	−3.11756	−0.134283
$540$	0.997264	0.0429154
$541$	−4.66590	−0.200603	−0.100301	−	0.994957i	$-0.531981\pi$
$541$	−4.66590	−0.200603	−0.100301	+	0.994957i	$0.531981\pi$
$542$	−7.23623	−0.310823
$543$	−1.55209	−0.0666065
$544$	1.85519	0.0795408
$545$	−7.93051	−0.339706
$546$	−0.0342787	−0.00146699
$547$	13.7045	0.585961	0.292980	−	0.956118i	$-0.405353\pi$
$547$	13.7045	0.585961	0.292980	+	0.956118i	$0.405353\pi$
$548$	−17.9145	−0.765269
$549$	14.7318	0.628738
$550$	−12.4873	−0.532459
$551$	−47.7242	−2.03312
$552$	9.38995	0.399663
$553$	−1.04051	−0.0442471
$554$	18.0569	0.767162
$555$	6.35276	0.269660
$556$	20.5532	0.871651
$557$	41.6220	1.76358	0.881790	−	0.471643i	$-0.156339\pi$
$557$	41.6220	1.76358	0.881790	+	0.471643i	$0.156339\pi$
$558$	3.82943	0.162113
$559$	−0.123358	−0.00521750
$560$	−0.997264	−0.0421421
$561$	5.78368	0.244187
$562$	21.3845	0.902050
$563$	−1.52162	−0.0641287	−0.0320644	−	0.999486i	$-0.510208\pi$
$563$	−1.52162	−0.0641287	−0.0320644	+	0.999486i	$0.510208\pi$
$564$	3.17273	0.133596
$565$	16.6107	0.698818
$566$	24.0321	1.01014
$567$	−1.00000	−0.0419961
$568$	−13.8670	−0.581848
$569$	−2.33941	−0.0980732	−0.0490366	−	0.998797i	$-0.515615\pi$
$569$	−2.33941	−0.0980732	−0.0490366	+	0.998797i	$0.515615\pi$
$570$	−5.80368	−0.243089
$571$	−6.55158	−0.274175	−0.137087	−	0.990559i	$-0.543774\pi$
$571$	−6.55158	−0.274175	−0.137087	+	0.990559i	$0.543774\pi$
$572$	0.106866	0.00446829
$573$	−1.00000	−0.0417756
$574$	−6.95633	−0.290352
$575$	37.6111	1.56849
$576$	1.00000	0.0416667
$577$	21.2819	0.885975	0.442988	−	0.896528i	$-0.353919\pi$
$577$	21.2819	0.885975	0.442988	+	0.896528i	$0.353919\pi$
$578$	13.5583	0.563949
$579$	7.57531	0.314819
$580$	−8.17816	−0.339580
$581$	0.388553	0.0161199
$582$	−0.345628	−0.0143267
$583$	−34.5887	−1.43252
$584$	−16.3602	−0.676988
$585$	−0.0341849	−0.00141337
$586$	12.2777	0.507186
$587$	−37.7516	−1.55818	−0.779088	−	0.626915i	$-0.784317\pi$
$587$	−37.7516	−1.55818	−0.779088	+	0.626915i	$0.784317\pi$
$588$	1.00000	0.0412393
$589$	−22.2858	−0.918269
$590$	−4.13243	−0.170129
$591$	−13.4794	−0.554468
$592$	6.37019	0.261813
$593$	30.1554	1.23833	0.619167	−	0.785260i	$-0.287471\pi$
$593$	30.1554	1.23833	0.619167	+	0.785260i	$0.287471\pi$
$594$	3.11756	0.127915
$595$	1.85012	0.0758474
$596$	22.1758	0.908355
$597$	11.2135	0.458937
$598$	−0.321875	−0.0131625
$599$	18.5297	0.757103	0.378552	−	0.925580i	$-0.376422\pi$
$599$	18.5297	0.757103	0.378552	+	0.925580i	$0.376422\pi$
$600$	4.00547	0.163522
$601$	−20.7708	−0.847257	−0.423628	−	0.905836i	$-0.639244\pi$
$601$	−20.7708	−0.847257	−0.423628	+	0.905836i	$0.639244\pi$
$602$	3.59869	0.146672
$603$	1.17263	0.0477532
$604$	17.4710	0.710885
$605$	−1.27732	−0.0519303
$606$	1.69199	0.0687325
$607$	12.6574	0.513746	0.256873	−	0.966445i	$-0.417308\pi$
$607$	12.6574	0.513746	0.256873	+	0.966445i	$0.417308\pi$
$608$	−5.81960	−0.236016
$609$	8.20061	0.332305
$610$	−14.6915	−0.594841
$611$	−0.108757	−0.00439984
$612$	−1.85519	−0.0749918
$613$	−7.66405	−0.309548	−0.154774	−	0.987950i	$-0.549465\pi$
$613$	−7.66405	−0.309548	−0.154774	+	0.987950i	$0.549465\pi$
$614$	−1.45692	−0.0587967
$615$	−6.93729	−0.279739
$616$	−3.11756	−0.125610
$617$	41.7691	1.68156	0.840780	−	0.541377i	$-0.182097\pi$
$617$	41.7691	1.68156	0.840780	+	0.541377i	$0.182097\pi$
$618$	5.90002	0.237333
$619$	−4.85712	−0.195224	−0.0976121	−	0.995225i	$-0.531120\pi$
$619$	−4.85712	−0.195224	−0.0976121	+	0.995225i	$0.531120\pi$
$620$	−3.81895	−0.153373
$621$	−9.38995	−0.376806
$622$	−1.82022	−0.0729840
$623$	−13.2495	−0.530829
$624$	−0.0342787	−0.00137225
$625$	11.0711	0.442843
$626$	−20.7542	−0.829503
$627$	−18.1430	−0.724560
$628$	13.2620	0.529211
$629$	−11.8179	−0.471212
$630$	0.997264	0.0397319
$631$	22.5617	0.898166	0.449083	−	0.893490i	$-0.351751\pi$
$631$	22.5617	0.898166	0.449083	+	0.893490i	$0.351751\pi$
$632$	−1.04051	−0.0413894
$633$	−18.6307	−0.740504
$634$	−20.4478	−0.812085
$635$	−5.88226	−0.233430
$636$	11.0948	0.439938
$637$	−0.0342787	−0.00135817
$638$	−25.5659	−1.01216
$639$	13.8670	0.548571
$640$	−0.997264	−0.0394203
$641$	−4.49272	−0.177452	−0.0887260	−	0.996056i	$-0.528280\pi$
$641$	−4.49272	−0.177452	−0.0887260	+	0.996056i	$0.528280\pi$
$642$	−9.58062	−0.378117
$643$	9.24636	0.364641	0.182320	−	0.983239i	$-0.441639\pi$
$643$	9.24636	0.364641	0.182320	+	0.983239i	$0.441639\pi$
$644$	9.38995	0.370016
$645$	3.58884	0.141310
$646$	10.7965	0.424782
$647$	8.79765	0.345871	0.172936	−	0.984933i	$-0.444675\pi$
$647$	8.79765	0.345871	0.172936	+	0.984933i	$0.444675\pi$
$648$	−1.00000	−0.0392837
$649$	−12.9184	−0.507093
$650$	−0.137302	−0.00538543
$651$	3.82943	0.150087
$652$	−11.9360	−0.467448
$653$	−14.0595	−0.550190	−0.275095	−	0.961417i	$-0.588709\pi$
$653$	−14.0595	−0.550190	−0.275095	+	0.961417i	$0.588709\pi$
$654$	7.95227	0.310958
$655$	6.70661	0.262049
$656$	−6.95633	−0.271599
$657$	16.3602	0.638270
$658$	3.17273	0.123686
$659$	10.3781	0.404274	0.202137	−	0.979357i	$-0.435211\pi$
$659$	10.3781	0.404274	0.202137	+	0.979357i	$0.435211\pi$
$660$	−3.10903	−0.121019
$661$	−30.4122	−1.18290	−0.591449	−	0.806342i	$-0.701444\pi$
$661$	−30.4122	−1.18290	−0.591449	+	0.806342i	$0.701444\pi$
$662$	29.1939	1.13465
$663$	0.0635936	0.00246977
$664$	0.388553	0.0150788
$665$	−5.80368	−0.225057
$666$	−6.37019	−0.246840
$667$	77.0033	2.98158
$668$	14.0698	0.544378
$669$	23.2062	0.897204
$670$	−1.16942	−0.0451787
$671$	−45.9272	−1.77300
$672$	1.00000	0.0385758
$673$	−7.33497	−0.282742	−0.141371	−	0.989957i	$-0.545151\pi$
$673$	−7.33497	−0.282742	−0.141371	+	0.989957i	$0.545151\pi$
$674$	16.6660	0.641950
$675$	−4.00547	−0.154170
$676$	−12.9988	−0.499955
$677$	17.5361	0.673967	0.336983	−	0.941511i	$-0.390593\pi$
$677$	17.5361	0.673967	0.336983	+	0.941511i	$0.390593\pi$
$678$	−16.6563	−0.639681
$679$	−0.345628	−0.0132640
$680$	1.85012	0.0709488
$681$	−4.79183	−0.183623
$682$	−11.9385	−0.457148
$683$	13.9477	0.533693	0.266847	−	0.963739i	$-0.414018\pi$
$683$	13.9477	0.533693	0.266847	+	0.963739i	$0.414018\pi$
$684$	5.81960	0.222518
$685$	−17.8655	−0.682604
$686$	1.00000	0.0381802
$687$	17.9043	0.683090
$688$	3.59869	0.137199
$689$	−0.380315	−0.0144889
$690$	9.36426	0.356491
$691$	−14.1890	−0.539776	−0.269888	−	0.962892i	$-0.586987\pi$
$691$	−14.1890	−0.539776	−0.269888	+	0.962892i	$0.586987\pi$
$692$	6.96753	0.264866
$693$	3.11756	0.118426
$694$	16.9854	0.644759
$695$	20.4970	0.777495
$696$	8.20061	0.310843
$697$	12.9053	0.488825
$698$	−12.8259	−0.485469
$699$	1.25242	0.0473708
$700$	4.00547	0.151392
$701$	−18.5138	−0.699255	−0.349627	−	0.936889i	$-0.613692\pi$
$701$	−18.5138	−0.699255	−0.349627	+	0.936889i	$0.613692\pi$
$702$	0.0342787	0.00129377
$703$	37.0720	1.39820
$704$	−3.11756	−0.117497
$705$	3.16405	0.119165
$706$	−20.6643	−0.777711
$707$	1.69199	0.0636339
$708$	4.14376	0.155732
$709$	−43.2071	−1.62268	−0.811338	−	0.584577i	$-0.801260\pi$
$709$	−43.2071	−1.62268	−0.811338	+	0.584577i	$0.801260\pi$
$710$	−13.8291	−0.518996
$711$	1.04051	0.0390223
$712$	−13.2495	−0.496545
$713$	35.9582	1.34664
$714$	−1.85519	−0.0694289
$715$	0.106573	0.00398562
$716$	−12.0313	−0.449630
$717$	−6.32606	−0.236251
$718$	12.4178	0.463427
$719$	17.9581	0.669724	0.334862	−	0.942267i	$-0.391310\pi$
$719$	17.9581	0.669724	0.334862	+	0.942267i	$0.391310\pi$
$720$	0.997264	0.0371658
$721$	5.90002	0.219728
$722$	−14.8677	−0.553320
$723$	20.1858	0.750718
$724$	−1.55209	−0.0576829
$725$	32.8472	1.21992
$726$	1.28082	0.0475357
$727$	−12.7749	−0.473796	−0.236898	−	0.971535i	$-0.576131\pi$
$727$	−12.7749	−0.473796	−0.236898	+	0.971535i	$0.576131\pi$
$728$	−0.0342787	−0.00127045
$729$	1.00000	0.0370370
$730$	−16.3154	−0.603860
$731$	−6.67627	−0.246931
$732$	14.7318	0.544503
$733$	24.1118	0.890589	0.445295	−	0.895384i	$-0.353099\pi$
$733$	24.1118	0.890589	0.445295	+	0.895384i	$0.353099\pi$
$734$	15.2207	0.561807
$735$	0.997264	0.0367846
$736$	9.38995	0.346118
$737$	−3.65574	−0.134661
$738$	6.95633	0.256066
$739$	21.5088	0.791215	0.395607	−	0.918420i	$-0.370534\pi$
$739$	21.5088	0.791215	0.395607	+	0.918420i	$0.370534\pi$
$740$	6.35276	0.233532
$741$	−0.199488	−0.00732839
$742$	11.0948	0.407303
$743$	−37.1756	−1.36384	−0.681919	−	0.731427i	$-0.738855\pi$
$743$	−37.1756	−1.36384	−0.681919	+	0.731427i	$0.738855\pi$
$744$	3.82943	0.140394
$745$	22.1151	0.810234
$746$	15.5897	0.570779
$747$	−0.388553	−0.0142164
$748$	5.78368	0.211472
$749$	−9.58062	−0.350068
$750$	8.98082	0.327933
$751$	−9.30329	−0.339482	−0.169741	−	0.985489i	$-0.554293\pi$
$751$	−9.30329	−0.339482	−0.169741	+	0.985489i	$0.554293\pi$
$752$	3.17273	0.115698
$753$	−5.62102	−0.204841
$754$	−0.281106	−0.0102373
$755$	17.4232	0.634095
$756$	−1.00000	−0.0363696
$757$	24.3351	0.884476	0.442238	−	0.896898i	$-0.354185\pi$
$757$	24.3351	0.884476	0.442238	+	0.896898i	$0.354185\pi$
$758$	−8.45863	−0.307231
$759$	29.2737	1.06257
$760$	−5.80368	−0.210521
$761$	−12.7899	−0.463634	−0.231817	−	0.972759i	$-0.574467\pi$
$761$	−12.7899	−0.463634	−0.231817	+	0.972759i	$0.574467\pi$
$762$	5.89840	0.213676
$763$	7.95227	0.287891
$764$	−1.00000	−0.0361787
$765$	−1.85012	−0.0668911
$766$	21.2296	0.767057
$767$	−0.142043	−0.00512887
$768$	1.00000	0.0360844
$769$	−12.4233	−0.447997	−0.223999	−	0.974589i	$-0.571911\pi$
$769$	−12.4233	−0.447997	−0.223999	+	0.974589i	$0.571911\pi$
$770$	−3.10903	−0.112042
$771$	20.6107	0.742277
$772$	7.57531	0.272641
$773$	54.9328	1.97580	0.987898	−	0.155106i	$-0.0495719\pi$
$773$	54.9328	1.97580	0.987898	+	0.155106i	$0.0495719\pi$
$774$	−3.59869	−0.129352
$775$	15.3387	0.550981
$776$	−0.345628	−0.0124073
$777$	−6.37019	−0.228529
$778$	−28.3954	−1.01802
$779$	−40.4831	−1.45046
$780$	−0.0341849	−0.00122402
$781$	−43.2313	−1.54694
$782$	−17.4202	−0.622945
$783$	−8.20061	−0.293066
$784$	1.00000	0.0357143
$785$	13.2257	0.472046
$786$	−6.72501	−0.239873
$787$	11.1278	0.396665	0.198332	−	0.980135i	$-0.436447\pi$
$787$	11.1278	0.396665	0.198332	+	0.980135i	$0.436447\pi$
$788$	−13.4794	−0.480183
$789$	5.64224	0.200869
$790$	−1.03767	−0.0369185
$791$	−16.6563	−0.592230
$792$	3.11756	0.110778
$793$	−0.504987	−0.0179326
$794$	14.0049	0.497014
$795$	11.0644	0.392415
$796$	11.2135	0.397451
$797$	1.90136	0.0673497	0.0336748	−	0.999433i	$-0.489279\pi$
$797$	1.90136	0.0673497	0.0336748	+	0.999433i	$0.489279\pi$
$798$	5.81960	0.206012
$799$	−5.88603	−0.208233
$800$	4.00547	0.141615
$801$	13.2495	0.468147
$802$	33.2815	1.17521
$803$	−51.0038	−1.79988
$804$	1.17263	0.0413555
$805$	9.36426	0.330047
$806$	−0.131268	−0.00462371
$807$	−18.6716	−0.657273
$808$	1.69199	0.0595241
$809$	−10.9048	−0.383394	−0.191697	−	0.981454i	$-0.561399\pi$
$809$	−10.9048	−0.383394	−0.191697	+	0.981454i	$0.561399\pi$
$810$	−0.997264	−0.0350403
$811$	42.1292	1.47935	0.739677	−	0.672962i	$-0.234978\pi$
$811$	42.1292	1.47935	0.739677	+	0.672962i	$0.234978\pi$
$812$	8.20061	0.287785
$813$	7.23623	0.253786
$814$	19.8594	0.696073
$815$	−11.9033	−0.416954
$816$	−1.85519	−0.0649448
$817$	20.9429	0.732700
$818$	−25.4724	−0.890620
$819$	0.0342787	0.00119779
$820$	−6.93729	−0.242261
$821$	11.8371	0.413119	0.206560	−	0.978434i	$-0.433773\pi$
$821$	11.8371	0.413119	0.206560	+	0.978434i	$0.433773\pi$
$822$	17.9145	0.624840
$823$	−5.04421	−0.175830	−0.0879151	−	0.996128i	$-0.528020\pi$
$823$	−5.04421	−0.175830	−0.0879151	+	0.996128i	$0.528020\pi$
$824$	5.90002	0.205537
$825$	12.4873	0.434751
$826$	4.14376	0.144180
$827$	16.2682	0.565699	0.282850	−	0.959164i	$-0.408720\pi$
$827$	16.2682	0.565699	0.282850	+	0.959164i	$0.408720\pi$
$828$	−9.38995	−0.326323
$829$	−5.82047	−0.202153	−0.101077	−	0.994879i	$-0.532229\pi$
$829$	−5.82047	−0.202153	−0.101077	+	0.994879i	$0.532229\pi$
$830$	0.387490	0.0134500
$831$	−18.0569	−0.626385
$832$	−0.0342787	−0.00118840
$833$	−1.85519	−0.0642787
$834$	−20.5532	−0.711700
$835$	14.0313	0.485574
$836$	−18.1430	−0.627487
$837$	−3.82943	−0.132364
$838$	−0.567056	−0.0195886
$839$	−34.0494	−1.17551	−0.587757	−	0.809037i	$-0.699989\pi$
$839$	−34.0494	−1.17551	−0.587757	+	0.809037i	$0.699989\pi$
$840$	0.997264	0.0344089
$841$	38.2499	1.31896
$842$	26.4078	0.910074
$843$	−21.3845	−0.736521
$844$	−18.6307	−0.641295
$845$	−12.9633	−0.445949
$846$	−3.17273	−0.109081
$847$	1.28082	0.0440095
$848$	11.0948	0.380997
$849$	−24.0321	−0.824780
$850$	−7.43092	−0.254878
$851$	−59.8158	−2.05046
$852$	13.8670	0.475077
$853$	−15.6645	−0.536343	−0.268171	−	0.963371i	$-0.586419\pi$
$853$	−15.6645	−0.536343	−0.268171	+	0.963371i	$0.586419\pi$
$854$	14.7318	0.504112
$855$	5.80368	0.198482
$856$	−9.58062	−0.327459
$857$	−2.90781	−0.0993290	−0.0496645	−	0.998766i	$-0.515815\pi$
$857$	−2.90781	−0.0993290	−0.0496645	+	0.998766i	$0.515815\pi$
$858$	−0.106866	−0.00364834
$859$	−35.6671	−1.21695	−0.608473	−	0.793575i	$-0.708218\pi$
$859$	−35.6671	−1.21695	−0.608473	+	0.793575i	$0.708218\pi$
$860$	3.58884	0.122378
$861$	6.95633	0.237071
$862$	4.58604	0.156201
$863$	−13.1584	−0.447917	−0.223958	−	0.974599i	$-0.571898\pi$
$863$	−13.1584	−0.447917	−0.223958	+	0.974599i	$0.571898\pi$
$864$	−1.00000	−0.0340207
$865$	6.94847	0.236255
$866$	−39.3437	−1.33695
$867$	−13.5583	−0.460462
$868$	3.82943	0.129979
$869$	−3.24386	−0.110041
$870$	8.17816	0.277266
$871$	−0.0401962	−0.00136200
$872$	7.95227	0.269298
$873$	0.345628	0.0116977
$874$	54.6458	1.84842
$875$	8.98082	0.303607
$876$	16.3602	0.552758
$877$	28.5637	0.964529	0.482265	−	0.876026i	$-0.339814\pi$
$877$	28.5637	0.964529	0.482265	+	0.876026i	$0.339814\pi$
$878$	7.13980	0.240957
$879$	−12.2777	−0.414116
$880$	−3.10903	−0.104805
$881$	−36.2758	−1.22216	−0.611082	−	0.791567i	$-0.709265\pi$
$881$	−36.2758	−1.22216	−0.611082	+	0.791567i	$0.709265\pi$
$882$	−1.00000	−0.0336718
$883$	22.7442	0.765403	0.382701	−	0.923872i	$-0.374994\pi$
$883$	22.7442	0.765403	0.382701	+	0.923872i	$0.374994\pi$
$884$	0.0635936	0.00213889
$885$	4.13243	0.138910
$886$	37.8864	1.27282
$887$	8.58822	0.288364	0.144182	−	0.989551i	$-0.453945\pi$
$887$	8.58822	0.288364	0.144182	+	0.989551i	$0.453945\pi$
$888$	−6.37019	−0.213770
$889$	5.89840	0.197826
$890$	−13.2132	−0.442908
$891$	−3.11756	−0.104442
$892$	23.2062	0.777001
$893$	18.4640	0.617875
$894$	−22.1758	−0.741669
$895$	−11.9984	−0.401061
$896$	1.00000	0.0334077
$897$	0.321875	0.0107471
$898$	−6.57743	−0.219492
$899$	31.4036	1.04737
$900$	−4.00547	−0.133516
$901$	−20.5830	−0.685720
$902$	−21.6868	−0.722091
$903$	−3.59869	−0.119757
$904$	−16.6563	−0.553980
$905$	−1.54784	−0.0514520
$906$	−17.4710	−0.580435
$907$	−31.7910	−1.05560	−0.527802	−	0.849368i	$-0.676984\pi$
$907$	−31.7910	−1.05560	−0.527802	+	0.849368i	$0.676984\pi$
$908$	−4.79183	−0.159022
$909$	−1.69199	−0.0561198
$910$	−0.0341849	−0.00113322
$911$	−25.8509	−0.856478	−0.428239	−	0.903665i	$-0.640866\pi$
$911$	−25.8509	−0.856478	−0.428239	+	0.903665i	$0.640866\pi$
$912$	5.81960	0.192706
$913$	1.21134	0.0400894
$914$	−0.0810198	−0.00267990
$915$	14.6915	0.485685
$916$	17.9043	0.591573
$917$	−6.72501	−0.222080
$918$	1.85519	0.0612305
$919$	5.59901	0.184694	0.0923472	−	0.995727i	$-0.470563\pi$
$919$	5.59901	0.184694	0.0923472	+	0.995727i	$0.470563\pi$
$920$	9.36426	0.308730
$921$	1.45692	0.0480073
$922$	−24.1379	−0.794940
$923$	−0.475344	−0.0156461
$924$	3.11756	0.102560
$925$	−25.5156	−0.838947
$926$	−39.2942	−1.29129
$927$	−5.90002	−0.193782
$928$	8.20061	0.269198
$929$	24.6230	0.807854	0.403927	−	0.914791i	$-0.367645\pi$
$929$	24.6230	0.807854	0.403927	+	0.914791i	$0.367645\pi$
$930$	3.81895	0.125228
$931$	5.81960	0.190730
$932$	1.25242	0.0410243
$933$	1.82022	0.0595912
$934$	13.7394	0.449566
$935$	5.76785	0.188629
$936$	0.0342787	0.00112043
$937$	−5.79461	−0.189302	−0.0946509	−	0.995511i	$-0.530173\pi$
$937$	−5.79461	−0.189302	−0.0946509	+	0.995511i	$0.530173\pi$
$938$	1.17263	0.0382877
$939$	20.7542	0.677287
$940$	3.16405	0.103200
$941$	−60.7043	−1.97890	−0.989451	−	0.144866i	$-0.953725\pi$
$941$	−60.7043	−1.97890	−0.989451	+	0.144866i	$0.953725\pi$
$942$	−13.2620	−0.432099
$943$	65.3196	2.12710
$944$	4.14376	0.134868
$945$	−0.997264	−0.0324410
$946$	11.2191	0.364765
$947$	1.41102	0.0458521	0.0229261	−	0.999737i	$-0.492702\pi$
$947$	1.41102	0.0458521	0.0229261	+	0.999737i	$0.492702\pi$
$948$	1.04051	0.0337943
$949$	−0.560805	−0.0182045
$950$	23.3102	0.756283
$951$	20.4478	0.663064
$952$	−1.85519	−0.0601272
$953$	−3.31068	−0.107244	−0.0536218	−	0.998561i	$-0.517077\pi$
$953$	−3.31068	−0.107244	−0.0536218	+	0.998561i	$0.517077\pi$
$954$	−11.0948	−0.359208
$955$	−0.997264	−0.0322707
$956$	−6.32606	−0.204600
$957$	25.5659	0.826427
$958$	−9.98679	−0.322659
$959$	17.9145	0.578489
$960$	0.997264	0.0321865
$961$	−16.3355	−0.526950
$962$	0.218362	0.00704027
$963$	9.58062	0.308731
$964$	20.1858	0.650141
$965$	7.55458	0.243191
$966$	−9.38995	−0.302117
$967$	−5.61704	−0.180632	−0.0903159	−	0.995913i	$-0.528788\pi$
$967$	−5.61704	−0.180632	−0.0903159	+	0.995913i	$0.528788\pi$
$968$	1.28082	0.0411671
$969$	−10.7965	−0.346833
$970$	−0.344682	−0.0110671
$971$	−31.4793	−1.01022	−0.505110	−	0.863055i	$-0.668548\pi$
$971$	−31.4793	−1.01022	−0.505110	+	0.863055i	$0.668548\pi$
$972$	1.00000	0.0320750
$973$	−20.5532	−0.658907
$974$	−26.5560	−0.850909
$975$	0.137302	0.00439719
$976$	14.7318	0.471553
$977$	−48.8353	−1.56238	−0.781190	−	0.624294i	$-0.785387\pi$
$977$	−48.8353	−1.56238	−0.781190	+	0.624294i	$0.785387\pi$
$978$	11.9360	0.381670
$979$	−41.3060	−1.32015
$980$	0.997264	0.0318564
$981$	−7.95227	−0.253896
$982$	15.9684	0.509571
$983$	32.6838	1.04245	0.521226	−	0.853419i	$-0.325475\pi$
$983$	32.6838	1.04245	0.521226	+	0.853419i	$0.325475\pi$
$984$	6.95633	0.221760
$985$	−13.4425	−0.428314
$986$	−15.2137	−0.484503
$987$	−3.17273	−0.100989
$988$	−0.199488	−0.00634657
$989$	−33.7915	−1.07451
$990$	3.10903	0.0988114
$991$	12.7778	0.405902	0.202951	−	0.979189i	$-0.434947\pi$
$991$	12.7778	0.405902	0.202951	+	0.979189i	$0.434947\pi$
$992$	3.82943	0.121585
$993$	−29.1939	−0.926440
$994$	13.8670	0.439836
$995$	11.1828	0.354518
$996$	−0.388553	−0.0123118
$997$	57.6567	1.82601	0.913003	−	0.407952i	$-0.133757\pi$
$997$	57.6567	1.82601	0.913003	+	0.407952i	$0.133757\pi$
$998$	6.55541	0.207508
$999$	6.37019	0.201544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.w.1.9	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.w.1.9	✓	13	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.997264 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.997264 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.997264 q^{10} -3.11756 q^{11} +1.00000 q^{12} -0.0342787 q^{13} +1.00000 q^{14} +0.997264 q^{15} +1.00000 q^{16} -1.85519 q^{17} -1.00000 q^{18} +5.81960 q^{19} +0.997264 q^{20} -1.00000 q^{21} +3.11756 q^{22} -9.38995 q^{23} -1.00000 q^{24} -4.00547 q^{25} +0.0342787 q^{26} +1.00000 q^{27} -1.00000 q^{28} -8.20061 q^{29} -0.997264 q^{30} -3.82943 q^{31} -1.00000 q^{32} -3.11756 q^{33} +1.85519 q^{34} -0.997264 q^{35} +1.00000 q^{36} +6.37019 q^{37} -5.81960 q^{38} -0.0342787 q^{39} -0.997264 q^{40} -6.95633 q^{41} +1.00000 q^{42} +3.59869 q^{43} -3.11756 q^{44} +0.997264 q^{45} +9.38995 q^{46} +3.17273 q^{47} +1.00000 q^{48} +1.00000 q^{49} +4.00547 q^{50} -1.85519 q^{51} -0.0342787 q^{52} +11.0948 q^{53} -1.00000 q^{54} -3.10903 q^{55} +1.00000 q^{56} +5.81960 q^{57} +8.20061 q^{58} +4.14376 q^{59} +0.997264 q^{60} +14.7318 q^{61} +3.82943 q^{62} -1.00000 q^{63} +1.00000 q^{64} -0.0341849 q^{65} +3.11756 q^{66} +1.17263 q^{67} -1.85519 q^{68} -9.38995 q^{69} +0.997264 q^{70} +13.8670 q^{71} -1.00000 q^{72} +16.3602 q^{73} -6.37019 q^{74} -4.00547 q^{75} +5.81960 q^{76} +3.11756 q^{77} +0.0342787 q^{78} +1.04051 q^{79} +0.997264 q^{80} +1.00000 q^{81} +6.95633 q^{82} -0.388553 q^{83} -1.00000 q^{84} -1.85012 q^{85} -3.59869 q^{86} -8.20061 q^{87} +3.11756 q^{88} +13.2495 q^{89} -0.997264 q^{90} +0.0342787 q^{91} -9.38995 q^{92} -3.82943 q^{93} -3.17273 q^{94} +5.80368 q^{95} -1.00000 q^{96} +0.345628 q^{97} -1.00000 q^{98} -3.11756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 2 q^{10} - q^{11} + 13 q^{12} + 14 q^{13} + 13 q^{14} - 2 q^{15} + 13 q^{16} + 7 q^{17} - 13 q^{18} - 2 q^{20} - 13 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 17 q^{25} - 14 q^{26} + 13 q^{27} - 13 q^{28} + 5 q^{29} + 2 q^{30} - 7 q^{31} - 13 q^{32} - q^{33} - 7 q^{34} + 2 q^{35} + 13 q^{36} + 15 q^{37} + 14 q^{39} + 2 q^{40} - 10 q^{41} + 13 q^{42} + 15 q^{43} - q^{44} - 2 q^{45} - 11 q^{46} - 7 q^{47} + 13 q^{48} + 13 q^{49} - 17 q^{50} + 7 q^{51} + 14 q^{52} + 14 q^{53} - 13 q^{54} + 19 q^{55} + 13 q^{56} - 5 q^{58} - 18 q^{59} - 2 q^{60} + 27 q^{61} + 7 q^{62} - 13 q^{63} + 13 q^{64} + 18 q^{65} + q^{66} + 7 q^{67} + 7 q^{68} + 11 q^{69} - 2 q^{70} - 4 q^{71} - 13 q^{72} + 26 q^{73} - 15 q^{74} + 17 q^{75} + q^{77} - 14 q^{78} + 20 q^{79} - 2 q^{80} + 13 q^{81} + 10 q^{82} + q^{83} - 13 q^{84} + 34 q^{85} - 15 q^{86} + 5 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} - 14 q^{91} + 11 q^{92} - 7 q^{93} + 7 q^{94} + 24 q^{95} - 13 q^{96} + 18 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 2 * q^10 - q^11 + 13 * q^12 + 14 * q^13 + 13 * q^14 - 2 * q^15 + 13 * q^16 + 7 * q^17 - 13 * q^18 - 2 * q^20 - 13 * q^21 + q^22 + 11 * q^23 - 13 * q^24 + 17 * q^25 - 14 * q^26 + 13 * q^27 - 13 * q^28 + 5 * q^29 + 2 * q^30 - 7 * q^31 - 13 * q^32 - q^33 - 7 * q^34 + 2 * q^35 + 13 * q^36 + 15 * q^37 + 14 * q^39 + 2 * q^40 - 10 * q^41 + 13 * q^42 + 15 * q^43 - q^44 - 2 * q^45 - 11 * q^46 - 7 * q^47 + 13 * q^48 + 13 * q^49 - 17 * q^50 + 7 * q^51 + 14 * q^52 + 14 * q^53 - 13 * q^54 + 19 * q^55 + 13 * q^56 - 5 * q^58 - 18 * q^59 - 2 * q^60 + 27 * q^61 + 7 * q^62 - 13 * q^63 + 13 * q^64 + 18 * q^65 + q^66 + 7 * q^67 + 7 * q^68 + 11 * q^69 - 2 * q^70 - 4 * q^71 - 13 * q^72 + 26 * q^73 - 15 * q^74 + 17 * q^75 + q^77 - 14 * q^78 + 20 * q^79 - 2 * q^80 + 13 * q^81 + 10 * q^82 + q^83 - 13 * q^84 + 34 * q^85 - 15 * q^86 + 5 * q^87 + q^88 - 15 * q^89 + 2 * q^90 - 14 * q^91 + 11 * q^92 - 7 * q^93 + 7 * q^94 + 24 * q^95 - 13 * q^96 + 18 * q^97 - 13 * q^98 - q^99

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