LMFDB - Embedded newform 8034.2.a.s.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$10$
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} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 $ x^10 - 4x^9 - 15x^8 + 72x^7 - 27x^6 - 115x^5 + 54x^4 + 68x^3 - 15x^2 - 15*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$0.757747$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.284726 q^{5} +1.00000 q^{6} -1.57147 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.284726 q^{5} +1.00000 q^{6} -1.57147 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.284726 q^{10} +4.76651 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.57147 q^{14} +0.284726 q^{15} +1.00000 q^{16} +0.813724 q^{17} -1.00000 q^{18} +5.65410 q^{19} -0.284726 q^{20} +1.57147 q^{21} -4.76651 q^{22} -0.125604 q^{23} +1.00000 q^{24} -4.91893 q^{25} +1.00000 q^{26} -1.00000 q^{27} -1.57147 q^{28} -4.38859 q^{29} -0.284726 q^{30} -7.23875 q^{31} -1.00000 q^{32} -4.76651 q^{33} -0.813724 q^{34} +0.447438 q^{35} +1.00000 q^{36} +9.11727 q^{37} -5.65410 q^{38} +1.00000 q^{39} +0.284726 q^{40} +0.508199 q^{41} -1.57147 q^{42} +1.30632 q^{43} +4.76651 q^{44} -0.284726 q^{45} +0.125604 q^{46} -1.48340 q^{47} -1.00000 q^{48} -4.53048 q^{49} +4.91893 q^{50} -0.813724 q^{51} -1.00000 q^{52} -10.7769 q^{53} +1.00000 q^{54} -1.35715 q^{55} +1.57147 q^{56} -5.65410 q^{57} +4.38859 q^{58} -8.72531 q^{59} +0.284726 q^{60} -13.6296 q^{61} +7.23875 q^{62} -1.57147 q^{63} +1.00000 q^{64} +0.284726 q^{65} +4.76651 q^{66} +14.2771 q^{67} +0.813724 q^{68} +0.125604 q^{69} -0.447438 q^{70} -14.8763 q^{71} -1.00000 q^{72} +15.7662 q^{73} -9.11727 q^{74} +4.91893 q^{75} +5.65410 q^{76} -7.49043 q^{77} -1.00000 q^{78} -1.39634 q^{79} -0.284726 q^{80} +1.00000 q^{81} -0.508199 q^{82} +14.5499 q^{83} +1.57147 q^{84} -0.231688 q^{85} -1.30632 q^{86} +4.38859 q^{87} -4.76651 q^{88} +7.82081 q^{89} +0.284726 q^{90} +1.57147 q^{91} -0.125604 q^{92} +7.23875 q^{93} +1.48340 q^{94} -1.60987 q^{95} +1.00000 q^{96} -9.35333 q^{97} +4.53048 q^{98} +4.76651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * 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
$5$	−0.284726	−0.127333	−0.0636666	−	0.997971i	$-0.520279\pi$
$5$	−0.284726	−0.127333	−0.0636666	+	0.997971i	$0.520279\pi$
$6$	1.00000	0.408248
$7$	−1.57147	−0.593960	−0.296980	−	0.954884i	$-0.595980\pi$
$7$	−1.57147	−0.593960	−0.296980	+	0.954884i	$0.595980\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.284726	0.0900382
$11$	4.76651	1.43716	0.718578	−	0.695447i	$-0.244793\pi$
$11$	4.76651	1.43716	0.718578	+	0.695447i	$0.244793\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.57147	0.419993
$15$	0.284726	0.0735159
$16$	1.00000	0.250000
$17$	0.813724	0.197357	0.0986786	−	0.995119i	$-0.468538\pi$
$17$	0.813724	0.197357	0.0986786	+	0.995119i	$0.468538\pi$
$18$	−1.00000	−0.235702
$19$	5.65410	1.29714	0.648570	−	0.761155i	$-0.275367\pi$
$19$	5.65410	1.29714	0.648570	+	0.761155i	$0.275367\pi$
$20$	−0.284726	−0.0636666
$21$	1.57147	0.342923
$22$	−4.76651	−1.01622
$23$	−0.125604	−0.0261903	−0.0130951	−	0.999914i	$-0.504168\pi$
$23$	−0.125604	−0.0261903	−0.0130951	+	0.999914i	$0.504168\pi$
$24$	1.00000	0.204124
$25$	−4.91893	−0.983786
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−1.57147	−0.296980
$29$	−4.38859	−0.814941	−0.407470	−	0.913218i	$-0.633589\pi$
$29$	−4.38859	−0.814941	−0.407470	+	0.913218i	$0.633589\pi$
$30$	−0.284726	−0.0519836
$31$	−7.23875	−1.30012	−0.650059	−	0.759884i	$-0.725256\pi$
$31$	−7.23875	−1.30012	−0.650059	+	0.759884i	$0.725256\pi$
$32$	−1.00000	−0.176777
$33$	−4.76651	−0.829742
$34$	−0.813724	−0.139553
$35$	0.447438	0.0756309
$36$	1.00000	0.166667
$37$	9.11727	1.49887	0.749435	−	0.662078i	$-0.230325\pi$
$37$	9.11727	1.49887	0.749435	+	0.662078i	$0.230325\pi$
$38$	−5.65410	−0.917217
$39$	1.00000	0.160128
$40$	0.284726	0.0450191
$41$	0.508199	0.0793673	0.0396837	−	0.999212i	$-0.487365\pi$
$41$	0.508199	0.0793673	0.0396837	+	0.999212i	$0.487365\pi$
$42$	−1.57147	−0.242483
$43$	1.30632	0.199211	0.0996056	−	0.995027i	$-0.468242\pi$
$43$	1.30632	0.199211	0.0996056	+	0.995027i	$0.468242\pi$
$44$	4.76651	0.718578
$45$	−0.284726	−0.0424444
$46$	0.125604	0.0185193
$47$	−1.48340	−0.216377	−0.108188	−	0.994130i	$-0.534505\pi$
$47$	−1.48340	−0.216377	−0.108188	+	0.994130i	$0.534505\pi$
$48$	−1.00000	−0.144338
$49$	−4.53048	−0.647211
$50$	4.91893	0.695642
$51$	−0.813724	−0.113944
$52$	−1.00000	−0.138675
$53$	−10.7769	−1.48032	−0.740159	−	0.672432i	$-0.765250\pi$
$53$	−10.7769	−1.48032	−0.740159	+	0.672432i	$0.765250\pi$
$54$	1.00000	0.136083
$55$	−1.35715	−0.182998
$56$	1.57147	0.209997
$57$	−5.65410	−0.748904
$58$	4.38859	0.576250
$59$	−8.72531	−1.13594	−0.567970	−	0.823050i	$-0.692271\pi$
$59$	−8.72531	−1.13594	−0.567970	+	0.823050i	$0.692271\pi$
$60$	0.284726	0.0367579
$61$	−13.6296	−1.74509	−0.872544	−	0.488535i	$-0.837531\pi$
$61$	−13.6296	−1.74509	−0.872544	+	0.488535i	$0.837531\pi$
$62$	7.23875	0.919322
$63$	−1.57147	−0.197987
$64$	1.00000	0.125000
$65$	0.284726	0.0353159
$66$	4.76651	0.586716
$67$	14.2771	1.74423	0.872115	−	0.489301i	$-0.162748\pi$
$67$	14.2771	1.74423	0.872115	+	0.489301i	$0.162748\pi$
$68$	0.813724	0.0986786
$69$	0.125604	0.0151210
$70$	−0.447438	−0.0534791
$71$	−14.8763	−1.76549	−0.882747	−	0.469848i	$-0.844309\pi$
$71$	−14.8763	−1.76549	−0.882747	+	0.469848i	$0.844309\pi$
$72$	−1.00000	−0.117851
$73$	15.7662	1.84529	0.922646	−	0.385647i	$-0.126022\pi$
$73$	15.7662	1.84529	0.922646	+	0.385647i	$0.126022\pi$
$74$	−9.11727	−1.05986
$75$	4.91893	0.567989
$76$	5.65410	0.648570
$77$	−7.49043	−0.853614
$78$	−1.00000	−0.113228
$79$	−1.39634	−0.157101	−0.0785504	−	0.996910i	$-0.525029\pi$
$79$	−1.39634	−0.157101	−0.0785504	+	0.996910i	$0.525029\pi$
$80$	−0.284726	−0.0318333
$81$	1.00000	0.111111
$82$	−0.508199	−0.0561212
$83$	14.5499	1.59706	0.798528	−	0.601957i	$-0.205612\pi$
$83$	14.5499	1.59706	0.798528	+	0.601957i	$0.205612\pi$
$84$	1.57147	0.171462
$85$	−0.231688	−0.0251301
$86$	−1.30632	−0.140864
$87$	4.38859	0.470506
$88$	−4.76651	−0.508111
$89$	7.82081	0.829004	0.414502	−	0.910048i	$-0.363956\pi$
$89$	7.82081	0.829004	0.414502	+	0.910048i	$0.363956\pi$
$90$	0.284726	0.0300127
$91$	1.57147	0.164735
$92$	−0.125604	−0.0130951
$93$	7.23875	0.750623
$94$	1.48340	0.153002
$95$	−1.60987	−0.165169
$96$	1.00000	0.102062
$97$	−9.35333	−0.949686	−0.474843	−	0.880070i	$-0.657495\pi$
$97$	−9.35333	−0.949686	−0.474843	+	0.880070i	$0.657495\pi$
$98$	4.53048	0.457647
$99$	4.76651	0.479052
$100$	−4.91893	−0.491893
$101$	12.1478	1.20875	0.604374	−	0.796700i	$-0.293423\pi$
$101$	12.1478	1.20875	0.604374	+	0.796700i	$0.293423\pi$
$102$	0.813724	0.0805707
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−0.447438	−0.0436655
$106$	10.7769	1.04674
$107$	−19.8210	−1.91617	−0.958086	−	0.286479i	$-0.907515\pi$
$107$	−19.8210	−1.91617	−0.958086	+	0.286479i	$0.907515\pi$
$108$	−1.00000	−0.0962250
$109$	−18.2787	−1.75078	−0.875391	−	0.483416i	$-0.839396\pi$
$109$	−18.2787	−1.75078	−0.875391	+	0.483416i	$0.839396\pi$
$110$	1.35715	0.129399
$111$	−9.11727	−0.865373
$112$	−1.57147	−0.148490
$113$	8.50569	0.800148	0.400074	−	0.916483i	$-0.368984\pi$
$113$	8.50569	0.800148	0.400074	+	0.916483i	$0.368984\pi$
$114$	5.65410	0.529555
$115$	0.0357628	0.00333489
$116$	−4.38859	−0.407470
$117$	−1.00000	−0.0924500
$118$	8.72531	0.803230
$119$	−1.27874	−0.117222
$120$	−0.284726	−0.0259918
$121$	11.7196	1.06542
$122$	13.6296	1.23396
$123$	−0.508199	−0.0458228
$124$	−7.23875	−0.650059
$125$	2.82417	0.252602
$126$	1.57147	0.139998
$127$	7.40900	0.657442	0.328721	−	0.944427i	$-0.393382\pi$
$127$	7.40900	0.657442	0.328721	+	0.944427i	$0.393382\pi$
$128$	−1.00000	−0.0883883
$129$	−1.30632	−0.115015
$130$	−0.284726	−0.0249721
$131$	16.2594	1.42059	0.710296	−	0.703903i	$-0.248561\pi$
$131$	16.2594	1.42059	0.710296	+	0.703903i	$0.248561\pi$
$132$	−4.76651	−0.414871
$133$	−8.88526	−0.770450
$134$	−14.2771	−1.23336
$135$	0.284726	0.0245053
$136$	−0.813724	−0.0697763
$137$	20.0970	1.71700	0.858502	−	0.512811i	$-0.171396\pi$
$137$	20.0970	1.71700	0.858502	+	0.512811i	$0.171396\pi$
$138$	−0.125604	−0.0106921
$139$	2.23216	0.189330	0.0946649	−	0.995509i	$-0.469822\pi$
$139$	2.23216	0.189330	0.0946649	+	0.995509i	$0.469822\pi$
$140$	0.447438	0.0378154
$141$	1.48340	0.124925
$142$	14.8763	1.24839
$143$	−4.76651	−0.398595
$144$	1.00000	0.0833333
$145$	1.24954	0.103769
$146$	−15.7662	−1.30482
$147$	4.53048	0.373667
$148$	9.11727	0.749435
$149$	0.158544	0.0129884	0.00649421	−	0.999979i	$-0.497933\pi$
$149$	0.158544	0.0129884	0.00649421	+	0.999979i	$0.497933\pi$
$150$	−4.91893	−0.401629
$151$	7.15544	0.582302	0.291151	−	0.956677i	$-0.405962\pi$
$151$	7.15544	0.582302	0.291151	+	0.956677i	$0.405962\pi$
$152$	−5.65410	−0.458608
$153$	0.813724	0.0657857
$154$	7.49043	0.603596
$155$	2.06106	0.165548
$156$	1.00000	0.0800641
$157$	−14.6855	−1.17203	−0.586015	−	0.810300i	$-0.699304\pi$
$157$	−14.6855	−1.17203	−0.586015	+	0.810300i	$0.699304\pi$
$158$	1.39634	0.111087
$159$	10.7769	0.854662
$160$	0.284726	0.0225095
$161$	0.197384	0.0155560
$162$	−1.00000	−0.0785674
$163$	−16.1529	−1.26519	−0.632595	−	0.774482i	$-0.718010\pi$
$163$	−16.1529	−1.26519	−0.632595	+	0.774482i	$0.718010\pi$
$164$	0.508199	0.0396837
$165$	1.35715	0.105654
$166$	−14.5499	−1.12929
$167$	−3.52477	−0.272755	−0.136377	−	0.990657i	$-0.543546\pi$
$167$	−3.52477	−0.272755	−0.136377	+	0.990657i	$0.543546\pi$
$168$	−1.57147	−0.121242
$169$	1.00000	0.0769231
$170$	0.231688	0.0177697
$171$	5.65410	0.432380
$172$	1.30632	0.0996056
$173$	4.01572	0.305310	0.152655	−	0.988280i	$-0.451218\pi$
$173$	4.01572	0.305310	0.152655	+	0.988280i	$0.451218\pi$
$174$	−4.38859	−0.332698
$175$	7.72996	0.584330
$176$	4.76651	0.359289
$177$	8.72531	0.655835
$178$	−7.82081	−0.586195
$179$	12.8088	0.957376	0.478688	−	0.877985i	$-0.341113\pi$
$179$	12.8088	0.957376	0.478688	+	0.877985i	$0.341113\pi$
$180$	−0.284726	−0.0212222
$181$	−23.0612	−1.71413	−0.857064	−	0.515210i	$-0.827714\pi$
$181$	−23.0612	−1.71413	−0.857064	+	0.515210i	$0.827714\pi$
$182$	−1.57147	−0.116485
$183$	13.6296	1.00753
$184$	0.125604	0.00925967
$185$	−2.59592	−0.190856
$186$	−7.23875	−0.530771
$187$	3.87862	0.283633
$188$	−1.48340	−0.108188
$189$	1.57147	0.114308
$190$	1.60987	0.116792
$191$	10.0552	0.727570	0.363785	−	0.931483i	$-0.381484\pi$
$191$	10.0552	0.727570	0.363785	+	0.931483i	$0.381484\pi$
$192$	−1.00000	−0.0721688
$193$	10.3248	0.743195	0.371597	−	0.928394i	$-0.378810\pi$
$193$	10.3248	0.743195	0.371597	+	0.928394i	$0.378810\pi$
$194$	9.35333	0.671530
$195$	−0.284726	−0.0203896
$196$	−4.53048	−0.323605
$197$	−21.2280	−1.51243	−0.756215	−	0.654324i	$-0.772953\pi$
$197$	−21.2280	−1.51243	−0.756215	+	0.654324i	$0.772953\pi$
$198$	−4.76651	−0.338741
$199$	−7.77491	−0.551149	−0.275574	−	0.961280i	$-0.588868\pi$
$199$	−7.77491	−0.551149	−0.275574	+	0.961280i	$0.588868\pi$
$200$	4.91893	0.347821
$201$	−14.2771	−1.00703
$202$	−12.1478	−0.854715
$203$	6.89654	0.484043
$204$	−0.813724	−0.0569721
$205$	−0.144697	−0.0101061
$206$	1.00000	0.0696733
$207$	−0.125604	−0.00873010
$208$	−1.00000	−0.0693375
$209$	26.9503	1.86419
$210$	0.447438	0.0308762
$211$	−9.17382	−0.631552	−0.315776	−	0.948834i	$-0.602265\pi$
$211$	−9.17382	−0.631552	−0.315776	+	0.948834i	$0.602265\pi$
$212$	−10.7769	−0.740159
$213$	14.8763	1.01931
$214$	19.8210	1.35494
$215$	−0.371941	−0.0253662
$216$	1.00000	0.0680414
$217$	11.3755	0.772219
$218$	18.2787	1.23799
$219$	−15.7662	−1.06538
$220$	−1.35715	−0.0914988
$221$	−0.813724	−0.0547370
$222$	9.11727	0.611911
$223$	−14.1408	−0.946935	−0.473468	−	0.880811i	$-0.656998\pi$
$223$	−14.1408	−0.946935	−0.473468	+	0.880811i	$0.656998\pi$
$224$	1.57147	0.104998
$225$	−4.91893	−0.327929
$226$	−8.50569	−0.565790
$227$	27.9922	1.85791	0.928953	−	0.370199i	$-0.120710\pi$
$227$	27.9922	1.85791	0.928953	+	0.370199i	$0.120710\pi$
$228$	−5.65410	−0.374452
$229$	−14.2973	−0.944791	−0.472396	−	0.881387i	$-0.656611\pi$
$229$	−14.2973	−0.944791	−0.472396	+	0.881387i	$0.656611\pi$
$230$	−0.0357628	−0.00235813
$231$	7.49043	0.492834
$232$	4.38859	0.288125
$233$	−20.6934	−1.35567	−0.677833	−	0.735216i	$-0.737081\pi$
$233$	−20.6934	−1.35567	−0.677833	+	0.735216i	$0.737081\pi$
$234$	1.00000	0.0653720
$235$	0.422363	0.0275520
$236$	−8.72531	−0.567970
$237$	1.39634	0.0907022
$238$	1.27874	0.0828887
$239$	7.80979	0.505173	0.252587	−	0.967574i	$-0.418719\pi$
$239$	7.80979	0.505173	0.252587	+	0.967574i	$0.418719\pi$
$240$	0.284726	0.0183790
$241$	0.197841	0.0127441	0.00637203	−	0.999980i	$-0.497972\pi$
$241$	0.197841	0.0127441	0.00637203	+	0.999980i	$0.497972\pi$
$242$	−11.7196	−0.753363
$243$	−1.00000	−0.0641500
$244$	−13.6296	−0.872544
$245$	1.28994	0.0824114
$246$	0.508199	0.0324016
$247$	−5.65410	−0.359762
$248$	7.23875	0.459661
$249$	−14.5499	−0.922061
$250$	−2.82417	−0.178616
$251$	−18.6073	−1.17448	−0.587241	−	0.809412i	$-0.699786\pi$
$251$	−18.6073	−1.17448	−0.587241	+	0.809412i	$0.699786\pi$
$252$	−1.57147	−0.0989934
$253$	−0.598693	−0.0376395
$254$	−7.40900	−0.464882
$255$	0.231688	0.0145089
$256$	1.00000	0.0625000
$257$	30.0237	1.87282	0.936412	−	0.350902i	$-0.114125\pi$
$257$	30.0237	1.87282	0.936412	+	0.350902i	$0.114125\pi$
$258$	1.30632	0.0813276
$259$	−14.3275	−0.890270
$260$	0.284726	0.0176579
$261$	−4.38859	−0.271647
$262$	−16.2594	−1.00451
$263$	16.8580	1.03951	0.519754	−	0.854316i	$-0.326024\pi$
$263$	16.8580	1.03951	0.519754	+	0.854316i	$0.326024\pi$
$264$	4.76651	0.293358
$265$	3.06845	0.188494
$266$	8.88526	0.544790
$267$	−7.82081	−0.478626
$268$	14.2771	0.872115
$269$	3.44100	0.209801	0.104901	−	0.994483i	$-0.466548\pi$
$269$	3.44100	0.209801	0.104901	+	0.994483i	$0.466548\pi$
$270$	−0.284726	−0.0173279
$271$	−32.9010	−1.99860	−0.999298	−	0.0374593i	$-0.988074\pi$
$271$	−32.9010	−1.99860	−0.999298	+	0.0374593i	$0.988074\pi$
$272$	0.813724	0.0493393
$273$	−1.57147	−0.0951098
$274$	−20.0970	−1.21410
$275$	−23.4461	−1.41385
$276$	0.125604	0.00756049
$277$	7.91129	0.475343	0.237672	−	0.971346i	$-0.423616\pi$
$277$	7.91129	0.475343	0.237672	+	0.971346i	$0.423616\pi$
$278$	−2.23216	−0.133876
$279$	−7.23875	−0.433373
$280$	−0.447438	−0.0267396
$281$	−10.9550	−0.653521	−0.326760	−	0.945107i	$-0.605957\pi$
$281$	−10.9550	−0.653521	−0.326760	+	0.945107i	$0.605957\pi$
$282$	−1.48340	−0.0883355
$283$	−16.4960	−0.980588	−0.490294	−	0.871557i	$-0.663111\pi$
$283$	−16.4960	−0.980588	−0.490294	+	0.871557i	$0.663111\pi$
$284$	−14.8763	−0.882747
$285$	1.60987	0.0953604
$286$	4.76651	0.281849
$287$	−0.798620	−0.0471411
$288$	−1.00000	−0.0589256
$289$	−16.3379	−0.961050
$290$	−1.24954	−0.0733758
$291$	9.35333	0.548302
$292$	15.7662	0.922646
$293$	−22.4481	−1.31143	−0.655717	−	0.755007i	$-0.727633\pi$
$293$	−22.4481	−1.31143	−0.655717	+	0.755007i	$0.727633\pi$
$294$	−4.53048	−0.264223
$295$	2.48432	0.144643
$296$	−9.11727	−0.529931
$297$	−4.76651	−0.276581
$298$	−0.158544	−0.00918420
$299$	0.125604	0.00726388
$300$	4.91893	0.283995
$301$	−2.05284	−0.118324
$302$	−7.15544	−0.411749
$303$	−12.1478	−0.697872
$304$	5.65410	0.324285
$305$	3.88069	0.222208
$306$	−0.813724	−0.0465175
$307$	−23.2601	−1.32752	−0.663762	−	0.747944i	$-0.731041\pi$
$307$	−23.2601	−1.32752	−0.663762	+	0.747944i	$0.731041\pi$
$308$	−7.49043	−0.426807
$309$	1.00000	0.0568880
$310$	−2.06106	−0.117060
$311$	−13.7959	−0.782292	−0.391146	−	0.920329i	$-0.627921\pi$
$311$	−13.7959	−0.782292	−0.391146	+	0.920329i	$0.627921\pi$
$312$	−1.00000	−0.0566139
$313$	13.7894	0.779421	0.389710	−	0.920937i	$-0.372575\pi$
$313$	13.7894	0.779421	0.389710	+	0.920937i	$0.372575\pi$
$314$	14.6855	0.828750
$315$	0.447438	0.0252103
$316$	−1.39634	−0.0785504
$317$	−17.8126	−1.00046	−0.500228	−	0.865893i	$-0.666751\pi$
$317$	−17.8126	−1.00046	−0.500228	+	0.865893i	$0.666751\pi$
$318$	−10.7769	−0.604337
$319$	−20.9182	−1.17120
$320$	−0.284726	−0.0159166
$321$	19.8210	1.10630
$322$	−0.197384	−0.0109998
$323$	4.60088	0.256000
$324$	1.00000	0.0555556
$325$	4.91893	0.272853
$326$	16.1529	0.894625
$327$	18.2787	1.01081
$328$	−0.508199	−0.0280606
$329$	2.33113	0.128519
$330$	−1.35715	−0.0747085
$331$	−31.1397	−1.71159	−0.855797	−	0.517311i	$-0.826933\pi$
$331$	−31.1397	−1.71159	−0.855797	+	0.517311i	$0.826933\pi$
$332$	14.5499	0.798528
$333$	9.11727	0.499623
$334$	3.52477	0.192867
$335$	−4.06507	−0.222098
$336$	1.57147	0.0857308
$337$	21.3537	1.16321	0.581606	−	0.813470i	$-0.302424\pi$
$337$	21.3537	1.16321	0.581606	+	0.813470i	$0.302424\pi$
$338$	−1.00000	−0.0543928
$339$	−8.50569	−0.461966
$340$	−0.231688	−0.0125651
$341$	−34.5035	−1.86847
$342$	−5.65410	−0.305739
$343$	18.1198	0.978378
$344$	−1.30632	−0.0704318
$345$	−0.0357628	−0.00192540
$346$	−4.01572	−0.215886
$347$	−11.0140	−0.591262	−0.295631	−	0.955302i	$-0.595530\pi$
$347$	−11.0140	−0.591262	−0.295631	+	0.955302i	$0.595530\pi$
$348$	4.38859	0.235253
$349$	−0.620411	−0.0332098	−0.0166049	−	0.999862i	$-0.505286\pi$
$349$	−0.620411	−0.0332098	−0.0166049	+	0.999862i	$0.505286\pi$
$350$	−7.72996	−0.413184
$351$	1.00000	0.0533761
$352$	−4.76651	−0.254056
$353$	−2.23649	−0.119036	−0.0595182	−	0.998227i	$-0.518956\pi$
$353$	−2.23649	−0.119036	−0.0595182	+	0.998227i	$0.518956\pi$
$354$	−8.72531	−0.463745
$355$	4.23567	0.224806
$356$	7.82081	0.414502
$357$	1.27874	0.0676784
$358$	−12.8088	−0.676967
$359$	20.4277	1.07814	0.539068	−	0.842263i	$-0.318777\pi$
$359$	20.4277	1.07814	0.539068	+	0.842263i	$0.318777\pi$
$360$	0.284726	0.0150064
$361$	12.9689	0.682573
$362$	23.0612	1.21207
$363$	−11.7196	−0.615118
$364$	1.57147	0.0823675
$365$	−4.48904	−0.234967
$366$	−13.6296	−0.712429
$367$	−9.79762	−0.511432	−0.255716	−	0.966752i	$-0.582311\pi$
$367$	−9.79762	−0.511432	−0.255716	+	0.966752i	$0.582311\pi$
$368$	−0.125604	−0.00654757
$369$	0.508199	0.0264558
$370$	2.59592	0.134956
$371$	16.9356	0.879250
$372$	7.23875	0.375312
$373$	10.5182	0.544612	0.272306	−	0.962211i	$-0.412214\pi$
$373$	10.5182	0.544612	0.272306	+	0.962211i	$0.412214\pi$
$374$	−3.87862	−0.200559
$375$	−2.82417	−0.145840
$376$	1.48340	0.0765008
$377$	4.38859	0.226024
$378$	−1.57147	−0.0808278
$379$	0.525304	0.0269830	0.0134915	−	0.999909i	$-0.495705\pi$
$379$	0.525304	0.0269830	0.0134915	+	0.999909i	$0.495705\pi$
$380$	−1.60987	−0.0825845
$381$	−7.40900	−0.379575
$382$	−10.0552	−0.514470
$383$	6.82429	0.348705	0.174353	−	0.984683i	$-0.444217\pi$
$383$	6.82429	0.348705	0.174353	+	0.984683i	$0.444217\pi$
$384$	1.00000	0.0510310
$385$	2.13272	0.108693
$386$	−10.3248	−0.525518
$387$	1.30632	0.0664037
$388$	−9.35333	−0.474843
$389$	15.5685	0.789353	0.394676	−	0.918820i	$-0.370857\pi$
$389$	15.5685	0.789353	0.394676	+	0.918820i	$0.370857\pi$
$390$	0.284726	0.0144176
$391$	−0.102207	−0.00516884
$392$	4.53048	0.228824
$393$	−16.2594	−0.820179
$394$	21.2280	1.06945
$395$	0.397575	0.0200042
$396$	4.76651	0.239526
$397$	13.3157	0.668294	0.334147	−	0.942521i	$-0.391552\pi$
$397$	13.3157	0.668294	0.334147	+	0.942521i	$0.391552\pi$
$398$	7.77491	0.389721
$399$	8.88526	0.444820
$400$	−4.91893	−0.245947
$401$	−5.32006	−0.265671	−0.132836	−	0.991138i	$-0.542408\pi$
$401$	−5.32006	−0.265671	−0.132836	+	0.991138i	$0.542408\pi$
$402$	14.2771	0.712079
$403$	7.23875	0.360588
$404$	12.1478	0.604374
$405$	−0.284726	−0.0141481
$406$	−6.89654	−0.342270
$407$	43.4575	2.15411
$408$	0.813724	0.0402854
$409$	7.46473	0.369107	0.184554	−	0.982822i	$-0.440916\pi$
$409$	7.46473	0.369107	0.184554	+	0.982822i	$0.440916\pi$
$410$	0.144697	0.00714609
$411$	−20.0970	−0.991313
$412$	−1.00000	−0.0492665
$413$	13.7116	0.674703
$414$	0.125604	0.00617311
$415$	−4.14272	−0.203358
$416$	1.00000	0.0490290
$417$	−2.23216	−0.109310
$418$	−26.9503	−1.31818
$419$	11.8973	0.581223	0.290612	−	0.956841i	$-0.406141\pi$
$419$	11.8973	0.581223	0.290612	+	0.956841i	$0.406141\pi$
$420$	−0.447438	−0.0218328
$421$	12.6697	0.617484	0.308742	−	0.951146i	$-0.400092\pi$
$421$	12.6697	0.617484	0.308742	+	0.951146i	$0.400092\pi$
$422$	9.17382	0.446575
$423$	−1.48340	−0.0721256
$424$	10.7769	0.523371
$425$	−4.00265	−0.194157
$426$	−14.8763	−0.720760
$427$	21.4185	1.03651
$428$	−19.8210	−0.958086
$429$	4.76651	0.230129
$430$	0.371941	0.0179366
$431$	−9.01033	−0.434012	−0.217006	−	0.976170i	$-0.569629\pi$
$431$	−9.01033	−0.434012	−0.217006	+	0.976170i	$0.569629\pi$
$432$	−1.00000	−0.0481125
$433$	6.23323	0.299550	0.149775	−	0.988720i	$-0.452145\pi$
$433$	6.23323	0.299550	0.149775	+	0.988720i	$0.452145\pi$
$434$	−11.3755	−0.546041
$435$	−1.24954	−0.0599111
$436$	−18.2787	−0.875391
$437$	−0.710179	−0.0339725
$438$	15.7662	0.753338
$439$	−31.9196	−1.52344	−0.761719	−	0.647908i	$-0.775644\pi$
$439$	−31.9196	−1.52344	−0.761719	+	0.647908i	$0.775644\pi$
$440$	1.35715	0.0646994
$441$	−4.53048	−0.215737
$442$	0.813724	0.0387049
$443$	−27.4935	−1.30625	−0.653127	−	0.757248i	$-0.726543\pi$
$443$	−27.4935	−1.30625	−0.653127	+	0.757248i	$0.726543\pi$
$444$	−9.11727	−0.432687
$445$	−2.22679	−0.105560
$446$	14.1408	0.669584
$447$	−0.158544	−0.00749887
$448$	−1.57147	−0.0742451
$449$	−8.41394	−0.397078	−0.198539	−	0.980093i	$-0.563620\pi$
$449$	−8.41394	−0.397078	−0.198539	+	0.980093i	$0.563620\pi$
$450$	4.91893	0.231881
$451$	2.42233	0.114063
$452$	8.50569	0.400074
$453$	−7.15544	−0.336192
$454$	−27.9922	−1.31374
$455$	−0.447438	−0.0209762
$456$	5.65410	0.264778
$457$	1.08417	0.0507155	0.0253577	−	0.999678i	$-0.491928\pi$
$457$	1.08417	0.0507155	0.0253577	+	0.999678i	$0.491928\pi$
$458$	14.2973	0.668068
$459$	−0.813724	−0.0379814
$460$	0.0357628	0.00166745
$461$	32.6531	1.52081	0.760403	−	0.649451i	$-0.225001\pi$
$461$	32.6531	1.52081	0.760403	+	0.649451i	$0.225001\pi$
$462$	−7.49043	−0.348486
$463$	6.48173	0.301232	0.150616	−	0.988592i	$-0.451874\pi$
$463$	6.48173	0.301232	0.150616	+	0.988592i	$0.451874\pi$
$464$	−4.38859	−0.203735
$465$	−2.06106	−0.0955793
$466$	20.6934	0.958601
$467$	27.0871	1.25344	0.626720	−	0.779245i	$-0.284397\pi$
$467$	27.0871	1.25344	0.626720	+	0.779245i	$0.284397\pi$
$468$	−1.00000	−0.0462250
$469$	−22.4361	−1.03600
$470$	−0.422363	−0.0194822
$471$	14.6855	0.676672
$472$	8.72531	0.401615
$473$	6.22656	0.286297
$474$	−1.39634	−0.0641362
$475$	−27.8121	−1.27611
$476$	−1.27874	−0.0586112
$477$	−10.7769	−0.493439
$478$	−7.80979	−0.357211
$479$	−23.3440	−1.06662	−0.533308	−	0.845921i	$-0.679051\pi$
$479$	−23.3440	−1.06662	−0.533308	+	0.845921i	$0.679051\pi$
$480$	−0.284726	−0.0129959
$481$	−9.11727	−0.415712
$482$	−0.197841	−0.00901141
$483$	−0.197384	−0.00898126
$484$	11.7196	0.532708
$485$	2.66313	0.120927
$486$	1.00000	0.0453609
$487$	−20.9287	−0.948368	−0.474184	−	0.880426i	$-0.657257\pi$
$487$	−20.9287	−0.948368	−0.474184	+	0.880426i	$0.657257\pi$
$488$	13.6296	0.616982
$489$	16.1529	0.730458
$490$	−1.28994	−0.0582737
$491$	−3.17633	−0.143346	−0.0716728	−	0.997428i	$-0.522834\pi$
$491$	−3.17633	−0.143346	−0.0716728	+	0.997428i	$0.522834\pi$
$492$	−0.508199	−0.0229114
$493$	−3.57110	−0.160834
$494$	5.65410	0.254390
$495$	−1.35715	−0.0609992
$496$	−7.23875	−0.325029
$497$	23.3777	1.04863
$498$	14.5499	0.651996
$499$	−8.10963	−0.363037	−0.181518	−	0.983388i	$-0.558101\pi$
$499$	−8.10963	−0.363037	−0.181518	+	0.983388i	$0.558101\pi$
$500$	2.82417	0.126301
$501$	3.52477	0.157475
$502$	18.6073	0.830485
$503$	32.2053	1.43596	0.717981	−	0.696063i	$-0.245066\pi$
$503$	32.2053	1.43596	0.717981	+	0.696063i	$0.245066\pi$
$504$	1.57147	0.0699989
$505$	−3.45878	−0.153914
$506$	0.598693	0.0266152
$507$	−1.00000	−0.0444116
$508$	7.40900	0.328721
$509$	−21.7818	−0.965461	−0.482730	−	0.875769i	$-0.660355\pi$
$509$	−21.7818	−0.965461	−0.482730	+	0.875769i	$0.660355\pi$
$510$	−0.231688	−0.0102593
$511$	−24.7761	−1.09603
$512$	−1.00000	−0.0441942
$513$	−5.65410	−0.249635
$514$	−30.0237	−1.32429
$515$	0.284726	0.0125465
$516$	−1.30632	−0.0575073
$517$	−7.07066	−0.310967
$518$	14.3275	0.629516
$519$	−4.01572	−0.176271
$520$	−0.284726	−0.0124860
$521$	−17.8371	−0.781457	−0.390729	−	0.920506i	$-0.627777\pi$
$521$	−17.8371	−0.781457	−0.390729	+	0.920506i	$0.627777\pi$
$522$	4.38859	0.192083
$523$	25.3408	1.10808	0.554038	−	0.832491i	$-0.313086\pi$
$523$	25.3408	1.10808	0.554038	+	0.832491i	$0.313086\pi$
$524$	16.2594	0.710296
$525$	−7.72996	−0.337363
$526$	−16.8580	−0.735043
$527$	−5.89035	−0.256588
$528$	−4.76651	−0.207436
$529$	−22.9842	−0.999314
$530$	−3.06845	−0.133285
$531$	−8.72531	−0.378646
$532$	−8.88526	−0.385225
$533$	−0.508199	−0.0220125
$534$	7.82081	0.338440
$535$	5.64356	0.243992
$536$	−14.2771	−0.616678
$537$	−12.8088	−0.552741
$538$	−3.44100	−0.148352
$539$	−21.5945	−0.930143
$540$	0.284726	0.0122526
$541$	−34.0239	−1.46280	−0.731401	−	0.681948i	$-0.761133\pi$
$541$	−34.0239	−1.46280	−0.731401	+	0.681948i	$0.761133\pi$
$542$	32.9010	1.41322
$543$	23.0612	0.989653
$544$	−0.813724	−0.0348881
$545$	5.20442	0.222933
$546$	1.57147	0.0672528
$547$	−27.8322	−1.19002	−0.595009	−	0.803719i	$-0.702851\pi$
$547$	−27.8322	−1.19002	−0.595009	+	0.803719i	$0.702851\pi$
$548$	20.0970	0.858502
$549$	−13.6296	−0.581696
$550$	23.4461	0.999746
$551$	−24.8135	−1.05709
$552$	−0.125604	−0.00534607
$553$	2.19431	0.0933117
$554$	−7.91129	−0.336118
$555$	2.59592	0.110191
$556$	2.23216	0.0946649
$557$	0.760098	0.0322064	0.0161032	−	0.999870i	$-0.494874\pi$
$557$	0.760098	0.0322064	0.0161032	+	0.999870i	$0.494874\pi$
$558$	7.23875	0.306441
$559$	−1.30632	−0.0552512
$560$	0.447438	0.0189077
$561$	−3.87862	−0.163756
$562$	10.9550	0.462109
$563$	−1.91503	−0.0807087	−0.0403544	−	0.999185i	$-0.512849\pi$
$563$	−1.91503	−0.0807087	−0.0403544	+	0.999185i	$0.512849\pi$
$564$	1.48340	0.0624626
$565$	−2.42179	−0.101885
$566$	16.4960	0.693380
$567$	−1.57147	−0.0659956
$568$	14.8763	0.624196
$569$	−17.0314	−0.713994	−0.356997	−	0.934106i	$-0.616199\pi$
$569$	−17.0314	−0.713994	−0.356997	+	0.934106i	$0.616199\pi$
$570$	−1.60987	−0.0674300
$571$	6.11663	0.255973	0.127986	−	0.991776i	$-0.459149\pi$
$571$	6.11663	0.255973	0.127986	+	0.991776i	$0.459149\pi$
$572$	−4.76651	−0.199298
$573$	−10.0552	−0.420063
$574$	0.798620	0.0333338
$575$	0.617839	0.0257657
$576$	1.00000	0.0416667
$577$	−30.2815	−1.26063	−0.630317	−	0.776338i	$-0.717075\pi$
$577$	−30.2815	−1.26063	−0.630317	+	0.776338i	$0.717075\pi$
$578$	16.3379	0.679565
$579$	−10.3248	−0.429084
$580$	1.24954	0.0518845
$581$	−22.8647	−0.948589
$582$	−9.35333	−0.387708
$583$	−51.3680	−2.12745
$584$	−15.7662	−0.652410
$585$	0.284726	0.0117720
$586$	22.4481	0.927323
$587$	12.8548	0.530574	0.265287	−	0.964170i	$-0.414533\pi$
$587$	12.8548	0.530574	0.265287	+	0.964170i	$0.414533\pi$
$588$	4.53048	0.186834
$589$	−40.9286	−1.68644
$590$	−2.48432	−0.102278
$591$	21.2280	0.873202
$592$	9.11727	0.374718
$593$	−14.9040	−0.612035	−0.306018	−	0.952026i	$-0.598997\pi$
$593$	−14.9040	−0.612035	−0.306018	+	0.952026i	$0.598997\pi$
$594$	4.76651	0.195572
$595$	0.364092	0.0149263
$596$	0.158544	0.00649421
$597$	7.77491	0.318206
$598$	−0.125604	−0.00513634
$599$	29.0452	1.18675	0.593377	−	0.804924i	$-0.297794\pi$
$599$	29.0452	1.18675	0.593377	+	0.804924i	$0.297794\pi$
$600$	−4.91893	−0.200815
$601$	−23.7722	−0.969689	−0.484844	−	0.874600i	$-0.661124\pi$
$601$	−23.7722	−0.969689	−0.484844	+	0.874600i	$0.661124\pi$
$602$	2.05284	0.0836674
$603$	14.2771	0.581410
$604$	7.15544	0.291151
$605$	−3.33686	−0.135663
$606$	12.1478	0.493470
$607$	−14.3408	−0.582075	−0.291037	−	0.956712i	$-0.594000\pi$
$607$	−14.3408	−0.582075	−0.291037	+	0.956712i	$0.594000\pi$
$608$	−5.65410	−0.229304
$609$	−6.89654	−0.279462
$610$	−3.88069	−0.157125
$611$	1.48340	0.0600121
$612$	0.813724	0.0328929
$613$	0.480369	0.0194019	0.00970097	−	0.999953i	$-0.496912\pi$
$613$	0.480369	0.0194019	0.00970097	+	0.999953i	$0.496912\pi$
$614$	23.2601	0.938701
$615$	0.144697	0.00583476
$616$	7.49043	0.301798
$617$	−13.8941	−0.559353	−0.279677	−	0.960094i	$-0.590227\pi$
$617$	−13.8941	−0.559353	−0.279677	+	0.960094i	$0.590227\pi$
$618$	−1.00000	−0.0402259
$619$	−12.1476	−0.488254	−0.244127	−	0.969743i	$-0.578501\pi$
$619$	−12.1476	−0.488254	−0.244127	+	0.969743i	$0.578501\pi$
$620$	2.06106	0.0827741
$621$	0.125604	0.00504033
$622$	13.7959	0.553164
$623$	−12.2902	−0.492396
$624$	1.00000	0.0400320
$625$	23.7905	0.951622
$626$	−13.7894	−0.551134
$627$	−26.9503	−1.07629
$628$	−14.6855	−0.586015
$629$	7.41895	0.295813
$630$	−0.447438	−0.0178264
$631$	−16.5952	−0.660643	−0.330322	−	0.943868i	$-0.607157\pi$
$631$	−16.5952	−0.660643	−0.330322	+	0.943868i	$0.607157\pi$
$632$	1.39634	0.0555435
$633$	9.17382	0.364627
$634$	17.8126	0.707430
$635$	−2.10953	−0.0837142
$636$	10.7769	0.427331
$637$	4.53048	0.179504
$638$	20.9182	0.828161
$639$	−14.8763	−0.588498
$640$	0.284726	0.0112548
$641$	−2.47627	−0.0978066	−0.0489033	−	0.998804i	$-0.515573\pi$
$641$	−2.47627	−0.0978066	−0.0489033	+	0.998804i	$0.515573\pi$
$642$	−19.8210	−0.782274
$643$	−46.4608	−1.83223	−0.916117	−	0.400912i	$-0.868693\pi$
$643$	−46.4608	−1.83223	−0.916117	+	0.400912i	$0.868693\pi$
$644$	0.197384	0.00777800
$645$	0.371941	0.0146452
$646$	−4.60088	−0.181019
$647$	−26.8615	−1.05603	−0.528017	−	0.849234i	$-0.677064\pi$
$647$	−26.8615	−1.05603	−0.528017	+	0.849234i	$0.677064\pi$
$648$	−1.00000	−0.0392837
$649$	−41.5893	−1.63252
$650$	−4.91893	−0.192936
$651$	−11.3755	−0.445841
$652$	−16.1529	−0.632595
$653$	−3.04852	−0.119298	−0.0596490	−	0.998219i	$-0.518998\pi$
$653$	−3.04852	−0.119298	−0.0596490	+	0.998219i	$0.518998\pi$
$654$	−18.2787	−0.714754
$655$	−4.62947	−0.180888
$656$	0.508199	0.0198418
$657$	15.7662	0.615098
$658$	−2.33113	−0.0908769
$659$	−42.2274	−1.64495	−0.822473	−	0.568804i	$-0.807406\pi$
$659$	−42.2274	−1.64495	−0.822473	+	0.568804i	$0.807406\pi$
$660$	1.35715	0.0528269
$661$	40.6078	1.57946	0.789729	−	0.613455i	$-0.210221\pi$
$661$	40.6078	1.57946	0.789729	+	0.613455i	$0.210221\pi$
$662$	31.1397	1.21028
$663$	0.813724	0.0316024
$664$	−14.5499	−0.564645
$665$	2.52986	0.0981039
$666$	−9.11727	−0.353287
$667$	0.551226	0.0213435
$668$	−3.52477	−0.136377
$669$	14.1408	0.546713
$670$	4.06507	0.157047
$671$	−64.9654	−2.50796
$672$	−1.57147	−0.0606208
$673$	38.1682	1.47128	0.735639	−	0.677374i	$-0.236882\pi$
$673$	38.1682	1.47128	0.735639	+	0.677374i	$0.236882\pi$
$674$	−21.3537	−0.822515
$675$	4.91893	0.189330
$676$	1.00000	0.0384615
$677$	4.81868	0.185197	0.0925984	−	0.995704i	$-0.470483\pi$
$677$	4.81868	0.185197	0.0925984	+	0.995704i	$0.470483\pi$
$678$	8.50569	0.326659
$679$	14.6985	0.564076
$680$	0.231688	0.00888484
$681$	−27.9922	−1.07266
$682$	34.5035	1.32121
$683$	−21.7817	−0.833454	−0.416727	−	0.909032i	$-0.636823\pi$
$683$	−21.7817	−0.833454	−0.416727	+	0.909032i	$0.636823\pi$
$684$	5.65410	0.216190
$685$	−5.72214	−0.218632
$686$	−18.1198	−0.691818
$687$	14.2973	0.545476
$688$	1.30632	0.0498028
$689$	10.7769	0.410566
$690$	0.0357628	0.00136147
$691$	−30.1413	−1.14663	−0.573314	−	0.819335i	$-0.694343\pi$
$691$	−30.1413	−1.14663	−0.573314	+	0.819335i	$0.694343\pi$
$692$	4.01572	0.152655
$693$	−7.49043	−0.284538
$694$	11.0140	0.418085
$695$	−0.635555	−0.0241080
$696$	−4.38859	−0.166349
$697$	0.413534	0.0156637
$698$	0.620411	0.0234829
$699$	20.6934	0.782694
$700$	7.72996	0.292165
$701$	−1.05511	−0.0398510	−0.0199255	−	0.999801i	$-0.506343\pi$
$701$	−1.05511	−0.0398510	−0.0199255	+	0.999801i	$0.506343\pi$
$702$	−1.00000	−0.0377426
$703$	51.5500	1.94424
$704$	4.76651	0.179644
$705$	−0.422363	−0.0159071
$706$	2.23649	0.0841715
$707$	−19.0899	−0.717949
$708$	8.72531	0.327917
$709$	31.8883	1.19759	0.598795	−	0.800902i	$-0.295646\pi$
$709$	31.8883	1.19759	0.598795	+	0.800902i	$0.295646\pi$
$710$	−4.23567	−0.158962
$711$	−1.39634	−0.0523669
$712$	−7.82081	−0.293097
$713$	0.909218	0.0340505
$714$	−1.27874	−0.0478558
$715$	1.35715	0.0507544
$716$	12.8088	0.478688
$717$	−7.80979	−0.291662
$718$	−20.4277	−0.762357
$719$	8.33035	0.310670	0.155335	−	0.987862i	$-0.450354\pi$
$719$	8.33035	0.310670	0.155335	+	0.987862i	$0.450354\pi$
$720$	−0.284726	−0.0106111
$721$	1.57147	0.0585247
$722$	−12.9689	−0.482652
$723$	−0.197841	−0.00735778
$724$	−23.0612	−0.857064
$725$	21.5872	0.801727
$726$	11.7196	0.434954
$727$	−11.9461	−0.443056	−0.221528	−	0.975154i	$-0.571104\pi$
$727$	−11.9461	−0.443056	−0.221528	+	0.975154i	$0.571104\pi$
$728$	−1.57147	−0.0582426
$729$	1.00000	0.0370370
$730$	4.48904	0.166147
$731$	1.06298	0.0393158
$732$	13.6296	0.503764
$733$	20.6118	0.761314	0.380657	−	0.924716i	$-0.375698\pi$
$733$	20.6118	0.761314	0.380657	+	0.924716i	$0.375698\pi$
$734$	9.79762	0.361637
$735$	−1.28994	−0.0475803
$736$	0.125604	0.00462983
$737$	68.0521	2.50673
$738$	−0.508199	−0.0187071
$739$	−21.6577	−0.796691	−0.398346	−	0.917235i	$-0.630416\pi$
$739$	−21.6577	−0.796691	−0.398346	+	0.917235i	$0.630416\pi$
$740$	−2.59592	−0.0954280
$741$	5.65410	0.207709
$742$	−16.9356	−0.621724
$743$	−7.95496	−0.291839	−0.145920	−	0.989296i	$-0.546614\pi$
$743$	−7.95496	−0.291839	−0.145920	+	0.989296i	$0.546614\pi$
$744$	−7.23875	−0.265385
$745$	−0.0451415	−0.00165386
$746$	−10.5182	−0.385099
$747$	14.5499	0.532352
$748$	3.87862	0.141816
$749$	31.1482	1.13813
$750$	2.82417	0.103124
$751$	−17.4191	−0.635631	−0.317815	−	0.948153i	$-0.602949\pi$
$751$	−17.4191	−0.635631	−0.317815	+	0.948153i	$0.602949\pi$
$752$	−1.48340	−0.0540942
$753$	18.6073	0.678088
$754$	−4.38859	−0.159823
$755$	−2.03734	−0.0741463
$756$	1.57147	0.0571539
$757$	18.4445	0.670377	0.335188	−	0.942151i	$-0.391200\pi$
$757$	18.4445	0.670377	0.335188	+	0.942151i	$0.391200\pi$
$758$	−0.525304	−0.0190799
$759$	0.598693	0.0217312
$760$	1.60987	0.0583961
$761$	−14.2359	−0.516053	−0.258026	−	0.966138i	$-0.583072\pi$
$761$	−14.2359	−0.516053	−0.258026	+	0.966138i	$0.583072\pi$
$762$	7.40900	0.268400
$763$	28.7245	1.03990
$764$	10.0552	0.363785
$765$	−0.231688	−0.00837671
$766$	−6.82429	−0.246572
$767$	8.72531	0.315053
$768$	−1.00000	−0.0360844
$769$	42.8472	1.54511	0.772555	−	0.634947i	$-0.218978\pi$
$769$	42.8472	1.54511	0.772555	+	0.634947i	$0.218978\pi$
$770$	−2.13272	−0.0768578
$771$	−30.0237	−1.08128
$772$	10.3248	0.371597
$773$	−15.8858	−0.571372	−0.285686	−	0.958323i	$-0.592221\pi$
$773$	−15.8858	−0.571372	−0.285686	+	0.958323i	$0.592221\pi$
$774$	−1.30632	−0.0469545
$775$	35.6069	1.27904
$776$	9.35333	0.335765
$777$	14.3275	0.513997
$778$	−15.5685	−0.558157
$779$	2.87341	0.102951
$780$	−0.284726	−0.0101948
$781$	−70.9081	−2.53729
$782$	0.102207	0.00365492
$783$	4.38859	0.156835
$784$	−4.53048	−0.161803
$785$	4.18134	0.149238
$786$	16.2594	0.579954
$787$	−7.57441	−0.269999	−0.134999	−	0.990846i	$-0.543103\pi$
$787$	−7.57441	−0.269999	−0.134999	+	0.990846i	$0.543103\pi$
$788$	−21.2280	−0.756215
$789$	−16.8580	−0.600160
$790$	−0.397575	−0.0141451
$791$	−13.3664	−0.475256
$792$	−4.76651	−0.169370
$793$	13.6296	0.484000
$794$	−13.3157	−0.472555
$795$	−3.06845	−0.108827
$796$	−7.77491	−0.275574
$797$	6.64042	0.235216	0.117608	−	0.993060i	$-0.462477\pi$
$797$	6.64042	0.235216	0.117608	+	0.993060i	$0.462477\pi$
$798$	−8.88526	−0.314535
$799$	−1.20708	−0.0427035
$800$	4.91893	0.173910
$801$	7.82081	0.276335
$802$	5.32006	0.187858
$803$	75.1496	2.65197
$804$	−14.2771	−0.503516
$805$	−0.0562002	−0.00198080
$806$	−7.23875	−0.254974
$807$	−3.44100	−0.121129
$808$	−12.1478	−0.427357
$809$	−45.2928	−1.59241	−0.796205	−	0.605026i	$-0.793163\pi$
$809$	−45.2928	−1.59241	−0.796205	+	0.605026i	$0.793163\pi$
$810$	0.284726	0.0100042
$811$	−25.3544	−0.890314	−0.445157	−	0.895452i	$-0.646852\pi$
$811$	−25.3544	−0.890314	−0.445157	+	0.895452i	$0.646852\pi$
$812$	6.89654	0.242021
$813$	32.9010	1.15389
$814$	−43.4575	−1.52319
$815$	4.59914	0.161101
$816$	−0.813724	−0.0284861
$817$	7.38604	0.258405
$818$	−7.46473	−0.260998
$819$	1.57147	0.0549117
$820$	−0.144697	−0.00505305
$821$	41.7920	1.45855	0.729276	−	0.684219i	$-0.239857\pi$
$821$	41.7920	1.45855	0.729276	+	0.684219i	$0.239857\pi$
$822$	20.0970	0.700964
$823$	19.6881	0.686285	0.343142	−	0.939283i	$-0.388509\pi$
$823$	19.6881	0.686285	0.343142	+	0.939283i	$0.388509\pi$
$824$	1.00000	0.0348367
$825$	23.4461	0.816289
$826$	−13.7116	−0.477087
$827$	36.0711	1.25432	0.627158	−	0.778892i	$-0.284218\pi$
$827$	36.0711	1.25432	0.627158	+	0.778892i	$0.284218\pi$
$828$	−0.125604	−0.00436505
$829$	−37.2829	−1.29489	−0.647444	−	0.762113i	$-0.724162\pi$
$829$	−37.2829	−1.29489	−0.647444	+	0.762113i	$0.724162\pi$
$830$	4.14272	0.143796
$831$	−7.91129	−0.274439
$832$	−1.00000	−0.0346688
$833$	−3.68656	−0.127732
$834$	2.23216	0.0772936
$835$	1.00359	0.0347307
$836$	26.9503	0.932096
$837$	7.23875	0.250208
$838$	−11.8973	−0.410987
$839$	−43.7850	−1.51162	−0.755812	−	0.654788i	$-0.772758\pi$
$839$	−43.7850	−1.51162	−0.755812	+	0.654788i	$0.772758\pi$
$840$	0.447438	0.0154381
$841$	−9.74028	−0.335872
$842$	−12.6697	−0.436627
$843$	10.9550	0.377310
$844$	−9.17382	−0.315776
$845$	−0.284726	−0.00979486
$846$	1.48340	0.0510005
$847$	−18.4170	−0.632815
$848$	−10.7769	−0.370079
$849$	16.4960	0.566143
$850$	4.00265	0.137290
$851$	−1.14517	−0.0392559
$852$	14.8763	0.509654
$853$	17.5113	0.599575	0.299788	−	0.954006i	$-0.403084\pi$
$853$	17.5113	0.599575	0.299788	+	0.954006i	$0.403084\pi$
$854$	−21.4185	−0.732926
$855$	−1.60987	−0.0550563
$856$	19.8210	0.677469
$857$	−17.9140	−0.611929	−0.305965	−	0.952043i	$-0.598979\pi$
$857$	−17.9140	−0.611929	−0.305965	+	0.952043i	$0.598979\pi$
$858$	−4.76651	−0.162726
$859$	−35.8532	−1.22330	−0.611648	−	0.791130i	$-0.709493\pi$
$859$	−35.8532	−1.22330	−0.611648	+	0.791130i	$0.709493\pi$
$860$	−0.371941	−0.0126831
$861$	0.798620	0.0272169
$862$	9.01033	0.306893
$863$	−43.5805	−1.48350	−0.741749	−	0.670678i	$-0.766003\pi$
$863$	−43.5805	−1.48350	−0.741749	+	0.670678i	$0.766003\pi$
$864$	1.00000	0.0340207
$865$	−1.14338	−0.0388760
$866$	−6.23323	−0.211814
$867$	16.3379	0.554863
$868$	11.3755	0.386109
$869$	−6.65568	−0.225778
$870$	1.24954	0.0423635
$871$	−14.2771	−0.483762
$872$	18.2787	0.618995
$873$	−9.35333	−0.316562
$874$	0.710179	0.0240222
$875$	−4.43811	−0.150036
$876$	−15.7662	−0.532690
$877$	−34.7716	−1.17415	−0.587076	−	0.809532i	$-0.699721\pi$
$877$	−34.7716	−1.17415	−0.587076	+	0.809532i	$0.699721\pi$
$878$	31.9196	1.07723
$879$	22.4481	0.757156
$880$	−1.35715	−0.0457494
$881$	−17.4703	−0.588590	−0.294295	−	0.955715i	$-0.595085\pi$
$881$	−17.4703	−0.588590	−0.294295	+	0.955715i	$0.595085\pi$
$882$	4.53048	0.152549
$883$	−20.9498	−0.705018	−0.352509	−	0.935808i	$-0.614671\pi$
$883$	−20.9498	−0.705018	−0.352509	+	0.935808i	$0.614671\pi$
$884$	−0.813724	−0.0273685
$885$	−2.48432	−0.0835095
$886$	27.4935	0.923661
$887$	−16.6414	−0.558763	−0.279382	−	0.960180i	$-0.590129\pi$
$887$	−16.6414	−0.558763	−0.279382	+	0.960180i	$0.590129\pi$
$888$	9.11727	0.305956
$889$	−11.6430	−0.390495
$890$	2.22679	0.0746420
$891$	4.76651	0.159684
$892$	−14.1408	−0.473468
$893$	−8.38732	−0.280671
$894$	0.158544	0.00530250
$895$	−3.64700	−0.121906
$896$	1.57147	0.0524992
$897$	−0.125604	−0.00419380
$898$	8.41394	0.280777
$899$	31.7679	1.05952
$900$	−4.91893	−0.163964
$901$	−8.76941	−0.292151
$902$	−2.42233	−0.0806549
$903$	2.05284	0.0683141
$904$	−8.50569	−0.282895
$905$	6.56613	0.218265
$906$	7.15544	0.237724
$907$	−42.1953	−1.40107	−0.700536	−	0.713617i	$-0.747056\pi$
$907$	−42.1953	−1.40107	−0.700536	+	0.713617i	$0.747056\pi$
$908$	27.9922	0.928953
$909$	12.1478	0.402916
$910$	0.447438	0.0148324
$911$	−48.6991	−1.61347	−0.806737	−	0.590910i	$-0.798769\pi$
$911$	−48.6991	−1.61347	−0.806737	+	0.590910i	$0.798769\pi$
$912$	−5.65410	−0.187226
$913$	69.3521	2.29522
$914$	−1.08417	−0.0358613
$915$	−3.88069	−0.128292
$916$	−14.2973	−0.472396
$917$	−25.5512	−0.843775
$918$	0.813724	0.0268569
$919$	7.47172	0.246469	0.123235	−	0.992378i	$-0.460673\pi$
$919$	7.47172	0.246469	0.123235	+	0.992378i	$0.460673\pi$
$920$	−0.0357628	−0.00117906
$921$	23.2601	0.766446
$922$	−32.6531	−1.07537
$923$	14.8763	0.489660
$924$	7.49043	0.246417
$925$	−44.8472	−1.47457
$926$	−6.48173	−0.213003
$927$	−1.00000	−0.0328443
$928$	4.38859	0.144063
$929$	20.6018	0.675924	0.337962	−	0.941160i	$-0.390262\pi$
$929$	20.6018	0.675924	0.337962	+	0.941160i	$0.390262\pi$
$930$	2.06106	0.0675848
$931$	−25.6158	−0.839523
$932$	−20.6934	−0.677833
$933$	13.7959	0.451656
$934$	−27.0871	−0.886316
$935$	−1.10434	−0.0361159
$936$	1.00000	0.0326860
$937$	0.0426215	0.00139238	0.000696191	−	1.00000i	$-0.499778\pi$
$937$	0.0426215	0.00139238	0.000696191		1.00000i	$0.499778\pi$
$938$	22.4361	0.732565
$939$	−13.7894	−0.449999
$940$	0.422363	0.0137760
$941$	54.4307	1.77439	0.887195	−	0.461396i	$-0.152651\pi$
$941$	54.4307	1.77439	0.887195	+	0.461396i	$0.152651\pi$
$942$	−14.6855	−0.478479
$943$	−0.0638320	−0.00207865
$944$	−8.72531	−0.283985
$945$	−0.447438	−0.0145552
$946$	−6.22656	−0.202443
$947$	1.95021	0.0633733	0.0316867	−	0.999498i	$-0.489912\pi$
$947$	1.95021	0.0633733	0.0316867	+	0.999498i	$0.489912\pi$
$948$	1.39634	0.0453511
$949$	−15.7662	−0.511792
$950$	27.8121	0.902345
$951$	17.8126	0.577614
$952$	1.27874	0.0414444
$953$	−29.5525	−0.957298	−0.478649	−	0.878006i	$-0.658873\pi$
$953$	−29.5525	−0.957298	−0.478649	+	0.878006i	$0.658873\pi$
$954$	10.7769	0.348914
$955$	−2.86298	−0.0926438
$956$	7.80979	0.252587
$957$	20.9182	0.676191
$958$	23.3440	0.754211
$959$	−31.5819	−1.01983
$960$	0.284726	0.00918948
$961$	21.3995	0.690307
$962$	9.11727	0.293953
$963$	−19.8210	−0.638724
$964$	0.197841	0.00637203
$965$	−2.93973	−0.0946334
$966$	0.197384	0.00635071
$967$	−32.7342	−1.05266	−0.526331	−	0.850280i	$-0.676433\pi$
$967$	−32.7342	−1.05266	−0.526331	+	0.850280i	$0.676433\pi$
$968$	−11.7196	−0.376681
$969$	−4.60088	−0.147802
$970$	−2.66313	−0.0855080
$971$	6.79283	0.217992	0.108996	−	0.994042i	$-0.465236\pi$
$971$	6.79283	0.217992	0.108996	+	0.994042i	$0.465236\pi$
$972$	−1.00000	−0.0320750
$973$	−3.50778	−0.112454
$974$	20.9287	0.670598
$975$	−4.91893	−0.157532
$976$	−13.6296	−0.436272
$977$	−12.7452	−0.407754	−0.203877	−	0.978996i	$-0.565354\pi$
$977$	−12.7452	−0.407754	−0.203877	+	0.978996i	$0.565354\pi$
$978$	−16.1529	−0.516512
$979$	37.2779	1.19141
$980$	1.28994	0.0412057
$981$	−18.2787	−0.583594
$982$	3.17633	0.101361
$983$	−39.1126	−1.24750	−0.623749	−	0.781625i	$-0.714391\pi$
$983$	−39.1126	−1.24750	−0.623749	+	0.781625i	$0.714391\pi$
$984$	0.508199	0.0162008
$985$	6.04414	0.192582
$986$	3.57110	0.113727
$987$	−2.33113	−0.0742007
$988$	−5.65410	−0.179881
$989$	−0.164079	−0.00521740
$990$	1.35715	0.0431329
$991$	−35.8145	−1.13768	−0.568842	−	0.822447i	$-0.692608\pi$
$991$	−35.8145	−1.13768	−0.568842	+	0.822447i	$0.692608\pi$
$992$	7.23875	0.229831
$993$	31.1397	0.988190
$994$	−23.3777	−0.741496
$995$	2.21372	0.0701796
$996$	−14.5499	−0.461031
$997$	−23.0014	−0.728462	−0.364231	−	0.931309i	$-0.618668\pi$
$997$	−23.0014	−0.728462	−0.364231	+	0.931309i	$0.618668\pi$
$998$	8.10963	0.256706
$999$	−9.11727	−0.288458

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.s.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.s.1.4	✓	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.284726 q^{5} +1.00000 q^{6} -1.57147 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.284726 q^{5} +1.00000 q^{6} -1.57147 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.284726 q^{10} +4.76651 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.57147 q^{14} +0.284726 q^{15} +1.00000 q^{16} +0.813724 q^{17} -1.00000 q^{18} +5.65410 q^{19} -0.284726 q^{20} +1.57147 q^{21} -4.76651 q^{22} -0.125604 q^{23} +1.00000 q^{24} -4.91893 q^{25} +1.00000 q^{26} -1.00000 q^{27} -1.57147 q^{28} -4.38859 q^{29} -0.284726 q^{30} -7.23875 q^{31} -1.00000 q^{32} -4.76651 q^{33} -0.813724 q^{34} +0.447438 q^{35} +1.00000 q^{36} +9.11727 q^{37} -5.65410 q^{38} +1.00000 q^{39} +0.284726 q^{40} +0.508199 q^{41} -1.57147 q^{42} +1.30632 q^{43} +4.76651 q^{44} -0.284726 q^{45} +0.125604 q^{46} -1.48340 q^{47} -1.00000 q^{48} -4.53048 q^{49} +4.91893 q^{50} -0.813724 q^{51} -1.00000 q^{52} -10.7769 q^{53} +1.00000 q^{54} -1.35715 q^{55} +1.57147 q^{56} -5.65410 q^{57} +4.38859 q^{58} -8.72531 q^{59} +0.284726 q^{60} -13.6296 q^{61} +7.23875 q^{62} -1.57147 q^{63} +1.00000 q^{64} +0.284726 q^{65} +4.76651 q^{66} +14.2771 q^{67} +0.813724 q^{68} +0.125604 q^{69} -0.447438 q^{70} -14.8763 q^{71} -1.00000 q^{72} +15.7662 q^{73} -9.11727 q^{74} +4.91893 q^{75} +5.65410 q^{76} -7.49043 q^{77} -1.00000 q^{78} -1.39634 q^{79} -0.284726 q^{80} +1.00000 q^{81} -0.508199 q^{82} +14.5499 q^{83} +1.57147 q^{84} -0.231688 q^{85} -1.30632 q^{86} +4.38859 q^{87} -4.76651 q^{88} +7.82081 q^{89} +0.284726 q^{90} +1.57147 q^{91} -0.125604 q^{92} +7.23875 q^{93} +1.48340 q^{94} -1.60987 q^{95} +1.00000 q^{96} -9.35333 q^{97} +4.53048 q^{98} +4.76651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

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