LMFDB - Embedded newform 2006.2.a.t.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2006,2,Mod(1,2006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2006 = 2 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2006.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:	$16.0179906455$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 13x^{6} + 24x^{5} + 50x^{4} - 50x^{3} - 62x^{2} + 28x + 24 $ x^8 - 3x^7 - 13x^6 + 24x^5 + 50x^4 - 50x^3 - 62x^2 + 28*x + 24
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$4.27543$ of defining polynomial
Character	$\chi$	$=$	2006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.94000 q^{3} +1.00000 q^{4} -3.29166 q^{5} -1.94000 q^{6} -4.13061 q^{7} +1.00000 q^{8} +0.763600 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.94000 q^{3} +1.00000 q^{4} -3.29166 q^{5} -1.94000 q^{6} -4.13061 q^{7} +1.00000 q^{8} +0.763600 q^{9} -3.29166 q^{10} -1.37530 q^{11} -1.94000 q^{12} -4.99195 q^{13} -4.13061 q^{14} +6.38583 q^{15} +1.00000 q^{16} -1.00000 q^{17} +0.763600 q^{18} +7.53781 q^{19} -3.29166 q^{20} +8.01337 q^{21} -1.37530 q^{22} -8.63886 q^{23} -1.94000 q^{24} +5.83505 q^{25} -4.99195 q^{26} +4.33862 q^{27} -4.13061 q^{28} -8.59892 q^{29} +6.38583 q^{30} -7.14275 q^{31} +1.00000 q^{32} +2.66808 q^{33} -1.00000 q^{34} +13.5966 q^{35} +0.763600 q^{36} +7.68302 q^{37} +7.53781 q^{38} +9.68439 q^{39} -3.29166 q^{40} +5.60962 q^{41} +8.01337 q^{42} -9.03690 q^{43} -1.37530 q^{44} -2.51351 q^{45} -8.63886 q^{46} +10.3875 q^{47} -1.94000 q^{48} +10.0619 q^{49} +5.83505 q^{50} +1.94000 q^{51} -4.99195 q^{52} -4.82323 q^{53} +4.33862 q^{54} +4.52703 q^{55} -4.13061 q^{56} -14.6233 q^{57} -8.59892 q^{58} -1.00000 q^{59} +6.38583 q^{60} +13.7258 q^{61} -7.14275 q^{62} -3.15413 q^{63} +1.00000 q^{64} +16.4318 q^{65} +2.66808 q^{66} +5.22849 q^{67} -1.00000 q^{68} +16.7594 q^{69} +13.5966 q^{70} +10.0395 q^{71} +0.763600 q^{72} +0.929411 q^{73} +7.68302 q^{74} -11.3200 q^{75} +7.53781 q^{76} +5.68083 q^{77} +9.68439 q^{78} +0.584753 q^{79} -3.29166 q^{80} -10.7077 q^{81} +5.60962 q^{82} -8.14442 q^{83} +8.01337 q^{84} +3.29166 q^{85} -9.03690 q^{86} +16.6819 q^{87} -1.37530 q^{88} -4.62435 q^{89} -2.51351 q^{90} +20.6198 q^{91} -8.63886 q^{92} +13.8569 q^{93} +10.3875 q^{94} -24.8119 q^{95} -1.94000 q^{96} -11.5680 q^{97} +10.0619 q^{98} -1.05018 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9} - 5 q^{10} - 5 q^{11} + 5 q^{12} + q^{13} + 9 q^{15} + 8 q^{16} - 8 q^{17} + 17 q^{18} + 8 q^{19} - 5 q^{20} + 13 q^{21} - 5 q^{22} - 8 q^{23} + 5 q^{24} + 29 q^{25} + q^{26} + 44 q^{27} + 20 q^{29} + 9 q^{30} + 18 q^{31} + 8 q^{32} - 23 q^{33} - 8 q^{34} + 9 q^{35} + 17 q^{36} - 7 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 12 q^{41} + 13 q^{42} - 8 q^{43} - 5 q^{44} + 5 q^{45} - 8 q^{46} + 30 q^{47} + 5 q^{48} + 28 q^{49} + 29 q^{50} - 5 q^{51} + q^{52} - 5 q^{53} + 44 q^{54} + 23 q^{55} + 13 q^{57} + 20 q^{58} - 8 q^{59} + 9 q^{60} + 12 q^{61} + 18 q^{62} + 21 q^{63} + 8 q^{64} - 52 q^{65} - 23 q^{66} - 4 q^{67} - 8 q^{68} + 24 q^{69} + 9 q^{70} + 4 q^{71} + 17 q^{72} - 18 q^{73} - 7 q^{74} - 49 q^{75} + 8 q^{76} - 13 q^{77} + 6 q^{78} - 17 q^{79} - 5 q^{80} + 12 q^{81} + 12 q^{82} + 9 q^{83} + 13 q^{84} + 5 q^{85} - 8 q^{86} + 48 q^{87} - 5 q^{88} - 12 q^{89} + 5 q^{90} + 31 q^{91} - 8 q^{92} - 3 q^{93} + 30 q^{94} - 7 q^{95} + 5 q^{96} - 11 q^{97} + 28 q^{98} - 27 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9 - 5 * q^10 - 5 * q^11 + 5 * q^12 + q^13 + 9 * q^15 + 8 * q^16 - 8 * q^17 + 17 * q^18 + 8 * q^19 - 5 * q^20 + 13 * q^21 - 5 * q^22 - 8 * q^23 + 5 * q^24 + 29 * q^25 + q^26 + 44 * q^27 + 20 * q^29 + 9 * q^30 + 18 * q^31 + 8 * q^32 - 23 * q^33 - 8 * q^34 + 9 * q^35 + 17 * q^36 - 7 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 12 * q^41 + 13 * q^42 - 8 * q^43 - 5 * q^44 + 5 * q^45 - 8 * q^46 + 30 * q^47 + 5 * q^48 + 28 * q^49 + 29 * q^50 - 5 * q^51 + q^52 - 5 * q^53 + 44 * q^54 + 23 * q^55 + 13 * q^57 + 20 * q^58 - 8 * q^59 + 9 * q^60 + 12 * q^61 + 18 * q^62 + 21 * q^63 + 8 * q^64 - 52 * q^65 - 23 * q^66 - 4 * q^67 - 8 * q^68 + 24 * q^69 + 9 * q^70 + 4 * q^71 + 17 * q^72 - 18 * q^73 - 7 * q^74 - 49 * q^75 + 8 * q^76 - 13 * q^77 + 6 * q^78 - 17 * q^79 - 5 * q^80 + 12 * q^81 + 12 * q^82 + 9 * q^83 + 13 * q^84 + 5 * q^85 - 8 * q^86 + 48 * q^87 - 5 * q^88 - 12 * q^89 + 5 * q^90 + 31 * q^91 - 8 * q^92 - 3 * q^93 + 30 * q^94 - 7 * q^95 + 5 * q^96 - 11 * q^97 + 28 * q^98 - 27 * 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
$3$	−1.94000	−1.12006	−0.560030	−	0.828472i	$-0.689210\pi$
$3$	−1.94000	−1.12006	−0.560030	+	0.828472i	$0.689210\pi$
$4$	1.00000	0.500000
$5$	−3.29166	−1.47208	−0.736038	−	0.676940i	$-0.763306\pi$
$5$	−3.29166	−1.47208	−0.736038	+	0.676940i	$0.763306\pi$
$6$	−1.94000	−0.792002
$7$	−4.13061	−1.56122	−0.780611	−	0.625017i	$-0.785092\pi$
$7$	−4.13061	−1.56122	−0.780611	+	0.625017i	$0.785092\pi$
$8$	1.00000	0.353553
$9$	0.763600	0.254533
$10$	−3.29166	−1.04092
$11$	−1.37530	−0.414669	−0.207334	−	0.978270i	$-0.566479\pi$
$11$	−1.37530	−0.414669	−0.207334	+	0.978270i	$0.566479\pi$
$12$	−1.94000	−0.560030
$13$	−4.99195	−1.38452	−0.692259	−	0.721649i	$-0.743385\pi$
$13$	−4.99195	−1.38452	−0.692259	+	0.721649i	$0.743385\pi$
$14$	−4.13061	−1.10395
$15$	6.38583	1.64881
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.763600	0.179982
$19$	7.53781	1.72929	0.864646	−	0.502382i	$-0.167543\pi$
$19$	7.53781	1.72929	0.864646	+	0.502382i	$0.167543\pi$
$20$	−3.29166	−0.736038
$21$	8.01337	1.74866
$22$	−1.37530	−0.293215
$23$	−8.63886	−1.80133	−0.900664	−	0.434517i	$-0.856919\pi$
$23$	−8.63886	−1.80133	−0.900664	+	0.434517i	$0.856919\pi$
$24$	−1.94000	−0.396001
$25$	5.83505	1.16701
$26$	−4.99195	−0.979002
$27$	4.33862	0.834967
$28$	−4.13061	−0.780611
$29$	−8.59892	−1.59678	−0.798390	−	0.602141i	$-0.794314\pi$
$29$	−8.59892	−1.59678	−0.798390	+	0.602141i	$0.794314\pi$
$30$	6.38583	1.16589
$31$	−7.14275	−1.28288	−0.641438	−	0.767175i	$-0.721662\pi$
$31$	−7.14275	−1.28288	−0.641438	+	0.767175i	$0.721662\pi$
$32$	1.00000	0.176777
$33$	2.66808	0.464454
$34$	−1.00000	−0.171499
$35$	13.5966	2.29824
$36$	0.763600	0.127267
$37$	7.68302	1.26308	0.631540	−	0.775343i	$-0.282423\pi$
$37$	7.68302	1.26308	0.631540	+	0.775343i	$0.282423\pi$
$38$	7.53781	1.22279
$39$	9.68439	1.55074
$40$	−3.29166	−0.520458
$41$	5.60962	0.876076	0.438038	−	0.898956i	$-0.355674\pi$
$41$	5.60962	0.876076	0.438038	+	0.898956i	$0.355674\pi$
$42$	8.01337	1.23649
$43$	−9.03690	−1.37811	−0.689057	−	0.724707i	$-0.741975\pi$
$43$	−9.03690	−1.37811	−0.689057	+	0.724707i	$0.741975\pi$
$44$	−1.37530	−0.207334
$45$	−2.51351	−0.374693
$46$	−8.63886	−1.27373
$47$	10.3875	1.51517	0.757584	−	0.652738i	$-0.226380\pi$
$47$	10.3875	1.51517	0.757584	+	0.652738i	$0.226380\pi$
$48$	−1.94000	−0.280015
$49$	10.0619	1.43741
$50$	5.83505	0.825201
$51$	1.94000	0.271654
$52$	−4.99195	−0.692259
$53$	−4.82323	−0.662522	−0.331261	−	0.943539i	$-0.607474\pi$
$53$	−4.82323	−0.662522	−0.331261	+	0.943539i	$0.607474\pi$
$54$	4.33862	0.590411
$55$	4.52703	0.610425
$56$	−4.13061	−0.551975
$57$	−14.6233	−1.93691
$58$	−8.59892	−1.12909
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	6.38583	0.824407
$61$	13.7258	1.75741	0.878706	−	0.477363i	$-0.158407\pi$
$61$	13.7258	1.75741	0.878706	+	0.477363i	$0.158407\pi$
$62$	−7.14275	−0.907130
$63$	−3.15413	−0.397383
$64$	1.00000	0.125000
$65$	16.4318	2.03812
$66$	2.66808	0.328418
$67$	5.22849	0.638762	0.319381	−	0.947626i	$-0.396525\pi$
$67$	5.22849	0.638762	0.319381	+	0.947626i	$0.396525\pi$
$68$	−1.00000	−0.121268
$69$	16.7594	2.01759
$70$	13.5966	1.62510
$71$	10.0395	1.19147	0.595735	−	0.803181i	$-0.296861\pi$
$71$	10.0395	1.19147	0.595735	+	0.803181i	$0.296861\pi$
$72$	0.763600	0.0899911
$73$	0.929411	0.108779	0.0543897	−	0.998520i	$-0.482679\pi$
$73$	0.929411	0.108779	0.0543897	+	0.998520i	$0.482679\pi$
$74$	7.68302	0.893133
$75$	−11.3200	−1.30712
$76$	7.53781	0.864646
$77$	5.68083	0.647390
$78$	9.68439	1.09654
$79$	0.584753	0.0657898	0.0328949	−	0.999459i	$-0.489527\pi$
$79$	0.584753	0.0657898	0.0328949	+	0.999459i	$0.489527\pi$
$80$	−3.29166	−0.368019
$81$	−10.7077	−1.18975
$82$	5.60962	0.619479
$83$	−8.14442	−0.893967	−0.446983	−	0.894542i	$-0.647502\pi$
$83$	−8.14442	−0.893967	−0.446983	+	0.894542i	$0.647502\pi$
$84$	8.01337	0.874331
$85$	3.29166	0.357031
$86$	−9.03690	−0.974474
$87$	16.6819	1.78849
$88$	−1.37530	−0.146608
$89$	−4.62435	−0.490180	−0.245090	−	0.969500i	$-0.578817\pi$
$89$	−4.62435	−0.490180	−0.245090	+	0.969500i	$0.578817\pi$
$90$	−2.51351	−0.264948
$91$	20.6198	2.16154
$92$	−8.63886	−0.900664
$93$	13.8569	1.43690
$94$	10.3875	1.07139
$95$	−24.8119	−2.54565
$96$	−1.94000	−0.198000
$97$	−11.5680	−1.17455	−0.587276	−	0.809386i	$-0.699800\pi$
$97$	−11.5680	−1.17455	−0.587276	+	0.809386i	$0.699800\pi$
$98$	10.0619	1.01641
$99$	−1.05018	−0.105547
$100$	5.83505	0.583505
$101$	−13.5881	−1.35207	−0.676035	−	0.736869i	$-0.736303\pi$
$101$	−13.5881	−1.35207	−0.676035	+	0.736869i	$0.736303\pi$
$102$	1.94000	0.192089
$103$	7.68360	0.757087	0.378544	−	0.925583i	$-0.376425\pi$
$103$	7.68360	0.757087	0.378544	+	0.925583i	$0.376425\pi$
$104$	−4.99195	−0.489501
$105$	−26.3773	−2.57416
$106$	−4.82323	−0.468474
$107$	−11.1651	−1.07937	−0.539685	−	0.841867i	$-0.681457\pi$
$107$	−11.1651	−1.07937	−0.539685	+	0.841867i	$0.681457\pi$
$108$	4.33862	0.417484
$109$	−3.01105	−0.288406	−0.144203	−	0.989548i	$-0.546062\pi$
$109$	−3.01105	−0.288406	−0.144203	+	0.989548i	$0.546062\pi$
$110$	4.52703	0.431635
$111$	−14.9051	−1.41473
$112$	−4.13061	−0.390306
$113$	−1.23307	−0.115997	−0.0579985	−	0.998317i	$-0.518472\pi$
$113$	−1.23307	−0.115997	−0.0579985	+	0.998317i	$0.518472\pi$
$114$	−14.6233	−1.36960
$115$	28.4362	2.65169
$116$	−8.59892	−0.798390
$117$	−3.81185	−0.352406
$118$	−1.00000	−0.0920575
$119$	4.13061	0.378652
$120$	6.38583	0.582944
$121$	−9.10855	−0.828050
$122$	13.7258	1.24268
$123$	−10.8827	−0.981257
$124$	−7.14275	−0.641438
$125$	−2.74871	−0.245853
$126$	−3.15413	−0.280992
$127$	−10.4049	−0.923282	−0.461641	−	0.887067i	$-0.652739\pi$
$127$	−10.4049	−0.923282	−0.461641	+	0.887067i	$0.652739\pi$
$128$	1.00000	0.0883883
$129$	17.5316	1.54357
$130$	16.4318	1.44117
$131$	18.1412	1.58500	0.792502	−	0.609869i	$-0.208778\pi$
$131$	18.1412	1.58500	0.792502	+	0.609869i	$0.208778\pi$
$132$	2.66808	0.232227
$133$	−31.1357	−2.69981
$134$	5.22849	0.451673
$135$	−14.2813	−1.22914
$136$	−1.00000	−0.0857493
$137$	16.1319	1.37824	0.689121	−	0.724646i	$-0.257997\pi$
$137$	16.1319	1.37824	0.689121	+	0.724646i	$0.257997\pi$
$138$	16.7594	1.42665
$139$	2.62325	0.222501	0.111251	−	0.993792i	$-0.464514\pi$
$139$	2.62325	0.222501	0.111251	+	0.993792i	$0.464514\pi$
$140$	13.5966	1.14912
$141$	−20.1517	−1.69708
$142$	10.0395	0.842496
$143$	6.86544	0.574117
$144$	0.763600	0.0636333
$145$	28.3048	2.35058
$146$	0.929411	0.0769186
$147$	−19.5201	−1.60999
$148$	7.68302	0.631540
$149$	−12.1078	−0.991910	−0.495955	−	0.868348i	$-0.665182\pi$
$149$	−12.1078	−0.991910	−0.495955	+	0.868348i	$0.665182\pi$
$150$	−11.3200	−0.924274
$151$	13.5720	1.10448	0.552239	−	0.833686i	$-0.313774\pi$
$151$	13.5720	1.10448	0.552239	+	0.833686i	$0.313774\pi$
$152$	7.53781	0.611397
$153$	−0.763600	−0.0617334
$154$	5.68083	0.457774
$155$	23.5115	1.88849
$156$	9.68439	0.775372
$157$	−23.8640	−1.90455	−0.952276	−	0.305239i	$-0.901264\pi$
$157$	−23.8640	−1.90455	−0.952276	+	0.305239i	$0.901264\pi$
$158$	0.584753	0.0465204
$159$	9.35707	0.742064
$160$	−3.29166	−0.260229
$161$	35.6837	2.81227
$162$	−10.7077	−0.841278
$163$	−1.79867	−0.140883	−0.0704415	−	0.997516i	$-0.522441\pi$
$163$	−1.79867	−0.140883	−0.0704415	+	0.997516i	$0.522441\pi$
$164$	5.60962	0.438038
$165$	−8.78244	−0.683712
$166$	−8.14442	−0.632130
$167$	13.5797	1.05083	0.525415	−	0.850846i	$-0.323910\pi$
$167$	13.5797	1.05083	0.525415	+	0.850846i	$0.323910\pi$
$168$	8.01337	0.618245
$169$	11.9196	0.916892
$170$	3.29166	0.252459
$171$	5.75587	0.440162
$172$	−9.03690	−0.689057
$173$	−15.0435	−1.14374	−0.571869	−	0.820345i	$-0.693781\pi$
$173$	−15.0435	−1.14374	−0.571869	+	0.820345i	$0.693781\pi$
$174$	16.6819	1.26465
$175$	−24.1023	−1.82196
$176$	−1.37530	−0.103667
$177$	1.94000	0.145819
$178$	−4.62435	−0.346609
$179$	5.61651	0.419798	0.209899	−	0.977723i	$-0.432686\pi$
$179$	5.61651	0.419798	0.209899	+	0.977723i	$0.432686\pi$
$180$	−2.51351	−0.187346
$181$	6.95661	0.517081	0.258540	−	0.966000i	$-0.416758\pi$
$181$	6.95661	0.517081	0.258540	+	0.966000i	$0.416758\pi$
$182$	20.6198	1.52844
$183$	−26.6281	−1.96841
$184$	−8.63886	−0.636866
$185$	−25.2899	−1.85935
$186$	13.8569	1.01604
$187$	1.37530	0.100572
$188$	10.3875	0.757584
$189$	−17.9211	−1.30357
$190$	−24.8119	−1.80005
$191$	−18.3988	−1.33129	−0.665647	−	0.746267i	$-0.731844\pi$
$191$	−18.3988	−1.33129	−0.665647	+	0.746267i	$0.731844\pi$
$192$	−1.94000	−0.140007
$193$	13.0769	0.941299	0.470650	−	0.882320i	$-0.344020\pi$
$193$	13.0769	0.941299	0.470650	+	0.882320i	$0.344020\pi$
$194$	−11.5680	−0.830534
$195$	−31.8778	−2.28281
$196$	10.0619	0.718707
$197$	5.77738	0.411621	0.205811	−	0.978592i	$-0.434017\pi$
$197$	5.77738	0.411621	0.205811	+	0.978592i	$0.434017\pi$
$198$	−1.05018	−0.0746330
$199$	13.6146	0.965115	0.482557	−	0.875864i	$-0.339708\pi$
$199$	13.6146	0.965115	0.482557	+	0.875864i	$0.339708\pi$
$200$	5.83505	0.412601
$201$	−10.1433	−0.715451
$202$	−13.5881	−0.956058
$203$	35.5187	2.49293
$204$	1.94000	0.135827
$205$	−18.4650	−1.28965
$206$	7.68360	0.535342
$207$	−6.59664	−0.458498
$208$	−4.99195	−0.346130
$209$	−10.3668	−0.717083
$210$	−26.3773	−1.82021
$211$	−4.32695	−0.297879	−0.148940	−	0.988846i	$-0.547586\pi$
$211$	−4.32695	−0.297879	−0.148940	+	0.988846i	$0.547586\pi$
$212$	−4.82323	−0.331261
$213$	−19.4766	−1.33452
$214$	−11.1651	−0.763231
$215$	29.7464	2.02869
$216$	4.33862	0.295205
$217$	29.5039	2.00285
$218$	−3.01105	−0.203934
$219$	−1.80306	−0.121839
$220$	4.52703	0.305212
$221$	4.99195	0.335795
$222$	−14.9051	−1.00036
$223$	0.284365	0.0190425	0.00952126	−	0.999955i	$-0.496969\pi$
$223$	0.284365	0.0190425	0.00952126	+	0.999955i	$0.496969\pi$
$224$	−4.13061	−0.275988
$225$	4.45565	0.297043
$226$	−1.23307	−0.0820223
$227$	12.8084	0.850123	0.425061	−	0.905165i	$-0.360253\pi$
$227$	12.8084	0.850123	0.425061	+	0.905165i	$0.360253\pi$
$228$	−14.6233	−0.968455
$229$	−25.8249	−1.70656	−0.853279	−	0.521455i	$-0.825389\pi$
$229$	−25.8249	−1.70656	−0.853279	+	0.521455i	$0.825389\pi$
$230$	28.4362	1.87503
$231$	−11.0208	−0.725116
$232$	−8.59892	−0.564547
$233$	−9.10564	−0.596531	−0.298265	−	0.954483i	$-0.596408\pi$
$233$	−9.10564	−0.596531	−0.298265	+	0.954483i	$0.596408\pi$
$234$	−3.81185	−0.249189
$235$	−34.1921	−2.23044
$236$	−1.00000	−0.0650945
$237$	−1.13442	−0.0736885
$238$	4.13061	0.267747
$239$	0.637883	0.0412613	0.0206306	−	0.999787i	$-0.493433\pi$
$239$	0.637883	0.0412613	0.0206306	+	0.999787i	$0.493433\pi$
$240$	6.38583	0.412203
$241$	6.48602	0.417801	0.208901	−	0.977937i	$-0.433011\pi$
$241$	6.48602	0.417801	0.208901	+	0.977937i	$0.433011\pi$
$242$	−9.10855	−0.585520
$243$	7.75712	0.497619
$244$	13.7258	0.878706
$245$	−33.1204	−2.11599
$246$	−10.8827	−0.693854
$247$	−37.6284	−2.39424
$248$	−7.14275	−0.453565
$249$	15.8002	1.00130
$250$	−2.74871	−0.173844
$251$	1.49442	0.0943269	0.0471635	−	0.998887i	$-0.484982\pi$
$251$	1.49442	0.0943269	0.0471635	+	0.998887i	$0.484982\pi$
$252$	−3.15413	−0.198692
$253$	11.8810	0.746955
$254$	−10.4049	−0.652859
$255$	−6.38583	−0.399896
$256$	1.00000	0.0625000
$257$	10.4452	0.651554	0.325777	−	0.945447i	$-0.394374\pi$
$257$	10.4452	0.651554	0.325777	+	0.945447i	$0.394374\pi$
$258$	17.5316	1.09147
$259$	−31.7355	−1.97195
$260$	16.4318	1.01906
$261$	−6.56613	−0.406433
$262$	18.1412	1.12077
$263$	4.68368	0.288808	0.144404	−	0.989519i	$-0.453873\pi$
$263$	4.68368	0.288808	0.144404	+	0.989519i	$0.453873\pi$
$264$	2.66808	0.164209
$265$	15.8765	0.975284
$266$	−31.1357	−1.90905
$267$	8.97123	0.549030
$268$	5.22849	0.319381
$269$	−18.8135	−1.14708	−0.573540	−	0.819178i	$-0.694430\pi$
$269$	−18.8135	−1.14708	−0.573540	+	0.819178i	$0.694430\pi$
$270$	−14.2813	−0.869130
$271$	14.0815	0.855391	0.427696	−	0.903923i	$-0.359325\pi$
$271$	14.0815	0.855391	0.427696	+	0.903923i	$0.359325\pi$
$272$	−1.00000	−0.0606339
$273$	−40.0024	−2.42105
$274$	16.1319	0.974564
$275$	−8.02496	−0.483923
$276$	16.7594	1.00880
$277$	−16.1722	−0.971692	−0.485846	−	0.874044i	$-0.661488\pi$
$277$	−16.1722	−0.971692	−0.485846	+	0.874044i	$0.661488\pi$
$278$	2.62325	0.157332
$279$	−5.45420	−0.326535
$280$	13.5966	0.812550
$281$	−15.8181	−0.943628	−0.471814	−	0.881698i	$-0.656401\pi$
$281$	−15.8181	−0.943628	−0.471814	+	0.881698i	$0.656401\pi$
$282$	−20.1517	−1.20002
$283$	31.1434	1.85128	0.925640	−	0.378404i	$-0.123527\pi$
$283$	31.1434	1.85128	0.925640	+	0.378404i	$0.123527\pi$
$284$	10.0395	0.595735
$285$	48.1351	2.85128
$286$	6.86544	0.405962
$287$	−23.1711	−1.36775
$288$	0.763600	0.0449956
$289$	1.00000	0.0588235
$290$	28.3048	1.66211
$291$	22.4419	1.31557
$292$	0.929411	0.0543897
$293$	−18.9273	−1.10574	−0.552872	−	0.833266i	$-0.686468\pi$
$293$	−18.9273	−1.10574	−0.552872	+	0.833266i	$0.686468\pi$
$294$	−19.5201	−1.13843
$295$	3.29166	0.191648
$296$	7.68302	0.446566
$297$	−5.96690	−0.346235
$298$	−12.1078	−0.701387
$299$	43.1248	2.49397
$300$	−11.3200	−0.653561
$301$	37.3279	2.15154
$302$	13.5720	0.780983
$303$	26.3610	1.51440
$304$	7.53781	0.432323
$305$	−45.1808	−2.58705
$306$	−0.763600	−0.0436521
$307$	−2.11320	−0.120607	−0.0603034	−	0.998180i	$-0.519207\pi$
$307$	−2.11320	−0.120607	−0.0603034	+	0.998180i	$0.519207\pi$
$308$	5.68083	0.323695
$309$	−14.9062	−0.847983
$310$	23.5115	1.33537
$311$	9.13783	0.518159	0.259079	−	0.965856i	$-0.416581\pi$
$311$	9.13783	0.518159	0.259079	+	0.965856i	$0.416581\pi$
$312$	9.68439	0.548271
$313$	−21.9472	−1.24053	−0.620266	−	0.784392i	$-0.712975\pi$
$313$	−21.9472	−1.24053	−0.620266	+	0.784392i	$0.712975\pi$
$314$	−23.8640	−1.34672
$315$	10.3823	0.584978
$316$	0.584753	0.0328949
$317$	−8.76195	−0.492120	−0.246060	−	0.969255i	$-0.579136\pi$
$317$	−8.76195	−0.492120	−0.246060	+	0.969255i	$0.579136\pi$
$318$	9.35707	0.524719
$319$	11.8261	0.662135
$320$	−3.29166	−0.184010
$321$	21.6603	1.20896
$322$	35.6837	1.98858
$323$	−7.53781	−0.419415
$324$	−10.7077	−0.594873
$325$	−29.1283	−1.61575
$326$	−1.79867	−0.0996193
$327$	5.84143	0.323032
$328$	5.60962	0.309740
$329$	−42.9065	−2.36551
$330$	−8.78244	−0.483457
$331$	15.4599	0.849755	0.424878	−	0.905251i	$-0.360317\pi$
$331$	15.4599	0.849755	0.424878	+	0.905251i	$0.360317\pi$
$332$	−8.14442	−0.446983
$333$	5.86675	0.321496
$334$	13.5797	0.743048
$335$	−17.2104	−0.940306
$336$	8.01337	0.437165
$337$	0.245643	0.0133810	0.00669051	−	0.999978i	$-0.497870\pi$
$337$	0.245643	0.0133810	0.00669051	+	0.999978i	$0.497870\pi$
$338$	11.9196	0.648340
$339$	2.39215	0.129924
$340$	3.29166	0.178516
$341$	9.82343	0.531969
$342$	5.75587	0.311242
$343$	−12.6475	−0.682902
$344$	−9.03690	−0.487237
$345$	−55.1663	−2.97005
$346$	−15.0435	−0.808745
$347$	−22.2440	−1.19412	−0.597061	−	0.802196i	$-0.703665\pi$
$347$	−22.2440	−1.19412	−0.597061	+	0.802196i	$0.703665\pi$
$348$	16.6819	0.894244
$349$	18.5179	0.991242	0.495621	−	0.868539i	$-0.334941\pi$
$349$	18.5179	0.991242	0.495621	+	0.868539i	$0.334941\pi$
$350$	−24.1023	−1.28832
$351$	−21.6582	−1.15603
$352$	−1.37530	−0.0733038
$353$	−19.7592	−1.05168	−0.525839	−	0.850584i	$-0.676249\pi$
$353$	−19.7592	−1.05168	−0.525839	+	0.850584i	$0.676249\pi$
$354$	1.94000	0.103110
$355$	−33.0467	−1.75393
$356$	−4.62435	−0.245090
$357$	−8.01337	−0.424113
$358$	5.61651	0.296842
$359$	19.1975	1.01321	0.506603	−	0.862179i	$-0.330901\pi$
$359$	19.1975	1.01321	0.506603	+	0.862179i	$0.330901\pi$
$360$	−2.51351	−0.132474
$361$	37.8185	1.99045
$362$	6.95661	0.365631
$363$	17.6706	0.927465
$364$	20.6198	1.08077
$365$	−3.05931	−0.160132
$366$	−26.6281	−1.39187
$367$	9.09868	0.474947	0.237474	−	0.971394i	$-0.423681\pi$
$367$	9.09868	0.474947	0.237474	+	0.971394i	$0.423681\pi$
$368$	−8.63886	−0.450332
$369$	4.28351	0.222990
$370$	−25.2899	−1.31476
$371$	19.9229	1.03434
$372$	13.8569	0.718449
$373$	−15.3374	−0.794141	−0.397071	−	0.917788i	$-0.629973\pi$
$373$	−15.3374	−0.794141	−0.397071	+	0.917788i	$0.629973\pi$
$374$	1.37530	0.0711151
$375$	5.33251	0.275369
$376$	10.3875	0.535693
$377$	42.9254	2.21077
$378$	−17.9211	−0.921763
$379$	2.79569	0.143605	0.0718025	−	0.997419i	$-0.477125\pi$
$379$	2.79569	0.143605	0.0718025	+	0.997419i	$0.477125\pi$
$380$	−24.8119	−1.27282
$381$	20.1854	1.03413
$382$	−18.3988	−0.941367
$383$	1.64336	0.0839717	0.0419858	−	0.999118i	$-0.486632\pi$
$383$	1.64336	0.0839717	0.0419858	+	0.999118i	$0.486632\pi$
$384$	−1.94000	−0.0990002
$385$	−18.6994	−0.953008
$386$	13.0769	0.665599
$387$	−6.90058	−0.350776
$388$	−11.5680	−0.587276
$389$	26.2876	1.33283	0.666416	−	0.745580i	$-0.267827\pi$
$389$	26.2876	1.33283	0.666416	+	0.745580i	$0.267827\pi$
$390$	−31.8778	−1.61419
$391$	8.63886	0.436886
$392$	10.0619	0.508203
$393$	−35.1939	−1.77530
$394$	5.77738	0.291060
$395$	−1.92481	−0.0968477
$396$	−1.05018	−0.0527735
$397$	12.1636	0.610475	0.305238	−	0.952276i	$-0.401264\pi$
$397$	12.1636	0.610475	0.305238	+	0.952276i	$0.401264\pi$
$398$	13.6146	0.682439
$399$	60.4033	3.02395
$400$	5.83505	0.291753
$401$	−2.92169	−0.145902	−0.0729512	−	0.997336i	$-0.523242\pi$
$401$	−2.92169	−0.145902	−0.0729512	+	0.997336i	$0.523242\pi$
$402$	−10.1433	−0.505900
$403$	35.6563	1.77617
$404$	−13.5881	−0.676035
$405$	35.2462	1.75140
$406$	35.5187	1.76277
$407$	−10.5665	−0.523760
$408$	1.94000	0.0960443
$409$	29.0484	1.43635	0.718175	−	0.695862i	$-0.244978\pi$
$409$	29.0484	1.43635	0.718175	+	0.695862i	$0.244978\pi$
$410$	−18.4650	−0.911921
$411$	−31.2959	−1.54371
$412$	7.68360	0.378544
$413$	4.13061	0.203254
$414$	−6.59664	−0.324207
$415$	26.8087	1.31599
$416$	−4.99195	−0.244751
$417$	−5.08911	−0.249215
$418$	−10.3668	−0.507054
$419$	11.1303	0.543750	0.271875	−	0.962333i	$-0.412356\pi$
$419$	11.1303	0.543750	0.271875	+	0.962333i	$0.412356\pi$
$420$	−26.3773	−1.28708
$421$	6.71494	0.327266	0.163633	−	0.986521i	$-0.447679\pi$
$421$	6.71494	0.327266	0.163633	+	0.986521i	$0.447679\pi$
$422$	−4.32695	−0.210633
$423$	7.93187	0.385661
$424$	−4.82323	−0.234237
$425$	−5.83505	−0.283042
$426$	−19.4766	−0.943646
$427$	−56.6960	−2.74371
$428$	−11.1651	−0.539685
$429$	−13.3190	−0.643045
$430$	29.7464	1.43450
$431$	1.99594	0.0961412	0.0480706	−	0.998844i	$-0.484693\pi$
$431$	1.99594	0.0961412	0.0480706	+	0.998844i	$0.484693\pi$
$432$	4.33862	0.208742
$433$	15.5147	0.745589	0.372794	−	0.927914i	$-0.378400\pi$
$433$	15.5147	0.745589	0.372794	+	0.927914i	$0.378400\pi$
$434$	29.5039	1.41623
$435$	−54.9112	−2.63279
$436$	−3.01105	−0.144203
$437$	−65.1181	−3.11502
$438$	−1.80306	−0.0861534
$439$	24.0677	1.14869	0.574344	−	0.818614i	$-0.305257\pi$
$439$	24.0677	1.14869	0.574344	+	0.818614i	$0.305257\pi$
$440$	4.52703	0.215818
$441$	7.68327	0.365870
$442$	4.99195	0.237443
$443$	−27.2209	−1.29330	−0.646652	−	0.762785i	$-0.723831\pi$
$443$	−27.2209	−1.29330	−0.646652	+	0.762785i	$0.723831\pi$
$444$	−14.9051	−0.707363
$445$	15.2218	0.721582
$446$	0.284365	0.0134651
$447$	23.4892	1.11100
$448$	−4.13061	−0.195153
$449$	−20.5988	−0.972116	−0.486058	−	0.873926i	$-0.661566\pi$
$449$	−20.5988	−0.972116	−0.486058	+	0.873926i	$0.661566\pi$
$450$	4.45565	0.210041
$451$	−7.71492	−0.363281
$452$	−1.23307	−0.0579985
$453$	−26.3298	−1.23708
$454$	12.8084	0.601127
$455$	−67.8734	−3.18195
$456$	−14.6233	−0.684801
$457$	18.6422	0.872045	0.436023	−	0.899936i	$-0.356387\pi$
$457$	18.6422	0.872045	0.436023	+	0.899936i	$0.356387\pi$
$458$	−25.8249	−1.20672
$459$	−4.33862	−0.202509
$460$	28.4362	1.32585
$461$	4.32434	0.201405	0.100702	−	0.994917i	$-0.467891\pi$
$461$	4.32434	0.201405	0.100702	+	0.994917i	$0.467891\pi$
$462$	−11.0208	−0.512734
$463$	−12.1451	−0.564429	−0.282215	−	0.959351i	$-0.591069\pi$
$463$	−12.1451	−0.564429	−0.282215	+	0.959351i	$0.591069\pi$
$464$	−8.59892	−0.399195
$465$	−45.6124	−2.11522
$466$	−9.10564	−0.421811
$467$	28.8348	1.33432	0.667159	−	0.744916i	$-0.267510\pi$
$467$	28.8348	1.33432	0.667159	+	0.744916i	$0.267510\pi$
$468$	−3.81185	−0.176203
$469$	−21.5968	−0.997249
$470$	−34.1921	−1.57716
$471$	46.2961	2.13321
$472$	−1.00000	−0.0460287
$473$	12.4285	0.571461
$474$	−1.13442	−0.0521057
$475$	43.9835	2.01810
$476$	4.13061	0.189326
$477$	−3.68302	−0.168634
$478$	0.637883	0.0291761
$479$	11.1823	0.510931	0.255465	−	0.966818i	$-0.417771\pi$
$479$	11.1823	0.510931	0.255465	+	0.966818i	$0.417771\pi$
$480$	6.38583	0.291472
$481$	−38.3533	−1.74876
$482$	6.48602	0.295430
$483$	−69.2265	−3.14991
$484$	−9.10855	−0.414025
$485$	38.0780	1.72903
$486$	7.75712	0.351870
$487$	−25.8318	−1.17055	−0.585276	−	0.810834i	$-0.699014\pi$
$487$	−25.8318	−1.17055	−0.585276	+	0.810834i	$0.699014\pi$
$488$	13.7258	0.621339
$489$	3.48943	0.157797
$490$	−33.1204	−1.49623
$491$	−20.2673	−0.914649	−0.457325	−	0.889300i	$-0.651192\pi$
$491$	−20.2673	−0.914649	−0.457325	+	0.889300i	$0.651192\pi$
$492$	−10.8827	−0.490629
$493$	8.59892	0.387276
$494$	−37.6284	−1.69298
$495$	3.45684	0.155373
$496$	−7.14275	−0.320719
$497$	−41.4692	−1.86015
$498$	15.8002	0.708023
$499$	−24.7462	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$499$	−24.7462	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$500$	−2.74871	−0.122926
$501$	−26.3446	−1.17699
$502$	1.49442	0.0666992
$503$	−11.0299	−0.491801	−0.245901	−	0.969295i	$-0.579084\pi$
$503$	−11.0299	−0.491801	−0.245901	+	0.969295i	$0.579084\pi$
$504$	−3.15413	−0.140496
$505$	44.7276	1.99035
$506$	11.8810	0.528177
$507$	−23.1240	−1.02697
$508$	−10.4049	−0.461641
$509$	−13.8444	−0.613642	−0.306821	−	0.951767i	$-0.599265\pi$
$509$	−13.8444	−0.613642	−0.306821	+	0.951767i	$0.599265\pi$
$510$	−6.38583	−0.282769
$511$	−3.83903	−0.169829
$512$	1.00000	0.0441942
$513$	32.7036	1.44390
$514$	10.4452	0.460718
$515$	−25.2918	−1.11449
$516$	17.5316	0.771785
$517$	−14.2859	−0.628293
$518$	−31.7355	−1.39438
$519$	29.1844	1.28105
$520$	16.4318	0.720584
$521$	35.3623	1.54925	0.774625	−	0.632420i	$-0.217938\pi$
$521$	35.3623	1.54925	0.774625	+	0.632420i	$0.217938\pi$
$522$	−6.56613	−0.287392
$523$	9.56391	0.418201	0.209100	−	0.977894i	$-0.432946\pi$
$523$	9.56391	0.418201	0.209100	+	0.977894i	$0.432946\pi$
$524$	18.1412	0.792502
$525$	46.7585	2.04071
$526$	4.68368	0.204218
$527$	7.14275	0.311143
$528$	2.66808	0.116113
$529$	51.6300	2.24478
$530$	15.8765	0.689630
$531$	−0.763600	−0.0331374
$532$	−31.1357	−1.34990
$533$	−28.0030	−1.21294
$534$	8.97123	0.388223
$535$	36.7518	1.58892
$536$	5.22849	0.225836
$537$	−10.8960	−0.470199
$538$	−18.8135	−0.811108
$539$	−13.8381	−0.596051
$540$	−14.2813	−0.614568
$541$	−6.38297	−0.274426	−0.137213	−	0.990542i	$-0.543814\pi$
$541$	−6.38297	−0.274426	−0.137213	+	0.990542i	$0.543814\pi$
$542$	14.0815	0.604853
$543$	−13.4958	−0.579161
$544$	−1.00000	−0.0428746
$545$	9.91136	0.424556
$546$	−40.0024	−1.71194
$547$	8.94468	0.382447	0.191223	−	0.981547i	$-0.438755\pi$
$547$	8.94468	0.382447	0.191223	+	0.981547i	$0.438755\pi$
$548$	16.1319	0.689121
$549$	10.4810	0.447320
$550$	−8.02496	−0.342185
$551$	−64.8170	−2.76130
$552$	16.7594	0.713327
$553$	−2.41538	−0.102713
$554$	−16.1722	−0.687090
$555$	49.0625	2.08259
$556$	2.62325	0.111251
$557$	27.0169	1.14474	0.572371	−	0.819995i	$-0.306024\pi$
$557$	27.0169	1.14474	0.572371	+	0.819995i	$0.306024\pi$
$558$	−5.45420	−0.230895
$559$	45.1118	1.90802
$560$	13.5966	0.574560
$561$	−2.66808	−0.112647
$562$	−15.8181	−0.667246
$563$	−40.6376	−1.71267	−0.856336	−	0.516419i	$-0.827265\pi$
$563$	−40.6376	−1.71267	−0.856336	+	0.516419i	$0.827265\pi$
$564$	−20.1517	−0.848539
$565$	4.05884	0.170757
$566$	31.1434	1.30905
$567$	44.2293	1.85746
$568$	10.0395	0.421248
$569$	2.59942	0.108973	0.0544867	−	0.998514i	$-0.482648\pi$
$569$	2.59942	0.108973	0.0544867	+	0.998514i	$0.482648\pi$
$570$	48.1351	2.01616
$571$	21.3736	0.894459	0.447229	−	0.894419i	$-0.352411\pi$
$571$	21.3736	0.894459	0.447229	+	0.894419i	$0.352411\pi$
$572$	6.86544	0.287058
$573$	35.6938	1.49113
$574$	−23.1711	−0.967145
$575$	−50.4082	−2.10217
$576$	0.763600	0.0318167
$577$	39.4895	1.64397	0.821984	−	0.569511i	$-0.192867\pi$
$577$	39.4895	1.64397	0.821984	+	0.569511i	$0.192867\pi$
$578$	1.00000	0.0415945
$579$	−25.3693	−1.05431
$580$	28.3048	1.17529
$581$	33.6414	1.39568
$582$	22.4419	0.930248
$583$	6.63340	0.274727
$584$	0.929411	0.0384593
$585$	12.5473	0.518769
$586$	−18.9273	−0.781879
$587$	4.69341	0.193718	0.0968590	−	0.995298i	$-0.469120\pi$
$587$	4.69341	0.193718	0.0968590	+	0.995298i	$0.469120\pi$
$588$	−19.5201	−0.804995
$589$	−53.8407	−2.21847
$590$	3.29166	0.135516
$591$	−11.2081	−0.461040
$592$	7.68302	0.315770
$593$	−27.8920	−1.14539	−0.572693	−	0.819770i	$-0.694101\pi$
$593$	−27.8920	−1.14539	−0.572693	+	0.819770i	$0.694101\pi$
$594$	−5.96690	−0.244825
$595$	−13.5966	−0.557405
$596$	−12.1078	−0.495955
$597$	−26.4124	−1.08099
$598$	43.1248	1.76350
$599$	32.3517	1.32185	0.660927	−	0.750451i	$-0.270163\pi$
$599$	32.3517	1.32185	0.660927	+	0.750451i	$0.270163\pi$
$600$	−11.3200	−0.462137
$601$	18.9319	0.772248	0.386124	−	0.922447i	$-0.373814\pi$
$601$	18.9319	0.772248	0.386124	+	0.922447i	$0.373814\pi$
$602$	37.3279	1.52137
$603$	3.99247	0.162586
$604$	13.5720	0.552239
$605$	29.9823	1.21895
$606$	26.3610	1.07084
$607$	−28.9030	−1.17313	−0.586567	−	0.809900i	$-0.699521\pi$
$607$	−28.9030	−1.17313	−0.586567	+	0.809900i	$0.699521\pi$
$608$	7.53781	0.305698
$609$	−68.9064	−2.79223
$610$	−45.1808	−1.82932
$611$	−51.8538	−2.09778
$612$	−0.763600	−0.0308667
$613$	24.9684	1.00846	0.504231	−	0.863569i	$-0.331776\pi$
$613$	24.9684	1.00846	0.504231	+	0.863569i	$0.331776\pi$
$614$	−2.11320	−0.0852820
$615$	35.8221	1.44449
$616$	5.68083	0.228887
$617$	14.2024	0.571768	0.285884	−	0.958264i	$-0.407713\pi$
$617$	14.2024	0.571768	0.285884	+	0.958264i	$0.407713\pi$
$618$	−14.9062	−0.599614
$619$	−10.4411	−0.419664	−0.209832	−	0.977737i	$-0.567292\pi$
$619$	−10.4411	−0.419664	−0.209832	+	0.977737i	$0.567292\pi$
$620$	23.5115	0.944246
$621$	−37.4807	−1.50405
$622$	9.13783	0.366394
$623$	19.1013	0.765279
$624$	9.68439	0.387686
$625$	−20.1274	−0.805097
$626$	−21.9472	−0.877188
$627$	20.1115	0.803176
$628$	−23.8640	−0.952276
$629$	−7.68302	−0.306342
$630$	10.3823	0.413642
$631$	41.2199	1.64094	0.820469	−	0.571691i	$-0.193712\pi$
$631$	41.2199	1.64094	0.820469	+	0.571691i	$0.193712\pi$
$632$	0.584753	0.0232602
$633$	8.39428	0.333643
$634$	−8.76195	−0.347981
$635$	34.2493	1.35914
$636$	9.35707	0.371032
$637$	−50.2285	−1.99013
$638$	11.8261	0.468200
$639$	7.66616	0.303269
$640$	−3.29166	−0.130114
$641$	31.8196	1.25680	0.628399	−	0.777891i	$-0.283711\pi$
$641$	31.8196	1.25680	0.628399	+	0.777891i	$0.283711\pi$
$642$	21.6603	0.854864
$643$	4.41118	0.173960	0.0869799	−	0.996210i	$-0.472278\pi$
$643$	4.41118	0.173960	0.0869799	+	0.996210i	$0.472278\pi$
$644$	35.6837	1.40614
$645$	−57.7081	−2.27225
$646$	−7.53781	−0.296571
$647$	29.5730	1.16264	0.581318	−	0.813676i	$-0.302537\pi$
$647$	29.5730	1.16264	0.581318	+	0.813676i	$0.302537\pi$
$648$	−10.7077	−0.420639
$649$	1.37530	0.0539853
$650$	−29.1283	−1.14251
$651$	−57.2375	−2.24332
$652$	−1.79867	−0.0704415
$653$	−32.7891	−1.28314	−0.641569	−	0.767066i	$-0.721716\pi$
$653$	−32.7891	−1.28314	−0.641569	+	0.767066i	$0.721716\pi$
$654$	5.84143	0.228418
$655$	−59.7148	−2.33325
$656$	5.60962	0.219019
$657$	0.709698	0.0276880
$658$	−42.9065	−1.67267
$659$	−18.8639	−0.734833	−0.367416	−	0.930057i	$-0.619758\pi$
$659$	−18.8639	−0.734833	−0.367416	+	0.930057i	$0.619758\pi$
$660$	−8.78244	−0.341856
$661$	−0.114001	−0.00443412	−0.00221706	−	0.999998i	$-0.500706\pi$
$661$	−0.114001	−0.00443412	−0.00221706	+	0.999998i	$0.500706\pi$
$662$	15.4599	0.600868
$663$	−9.68439	−0.376110
$664$	−8.14442	−0.316065
$665$	102.488	3.97432
$666$	5.86675	0.227332
$667$	74.2849	2.87632
$668$	13.5797	0.525415
$669$	−0.551669	−0.0213287
$670$	−17.2104	−0.664897
$671$	−18.8771	−0.728744
$672$	8.01337	0.309123
$673$	43.7882	1.68791	0.843955	−	0.536414i	$-0.180221\pi$
$673$	43.7882	1.68791	0.843955	+	0.536414i	$0.180221\pi$
$674$	0.245643	0.00946180
$675$	25.3161	0.974415
$676$	11.9196	0.458446
$677$	31.5043	1.21081	0.605404	−	0.795918i	$-0.293012\pi$
$677$	31.5043	1.21081	0.605404	+	0.795918i	$0.293012\pi$
$678$	2.39215	0.0918699
$679$	47.7829	1.83374
$680$	3.29166	0.126230
$681$	−24.8483	−0.952188
$682$	9.82343	0.376159
$683$	14.7566	0.564645	0.282323	−	0.959320i	$-0.408895\pi$
$683$	14.7566	0.564645	0.282323	+	0.959320i	$0.408895\pi$
$684$	5.75587	0.220081
$685$	−53.1008	−2.02888
$686$	−12.6475	−0.482884
$687$	50.1003	1.91145
$688$	−9.03690	−0.344529
$689$	24.0774	0.917274
$690$	−55.1663	−2.10015
$691$	−6.63879	−0.252552	−0.126276	−	0.991995i	$-0.540302\pi$
$691$	−6.63879	−0.252552	−0.126276	+	0.991995i	$0.540302\pi$
$692$	−15.0435	−0.571869
$693$	4.33788	0.164782
$694$	−22.2440	−0.844372
$695$	−8.63486	−0.327539
$696$	16.6819	0.632326
$697$	−5.60962	−0.212480
$698$	18.5179	0.700914
$699$	17.6649	0.668150
$700$	−24.1023	−0.910981
$701$	−26.6420	−1.00626	−0.503128	−	0.864212i	$-0.667817\pi$
$701$	−26.6420	−1.00626	−0.503128	+	0.864212i	$0.667817\pi$
$702$	−21.6582	−0.817435
$703$	57.9131	2.18423
$704$	−1.37530	−0.0518336
$705$	66.3326	2.49823
$706$	−19.7592	−0.743649
$707$	56.1272	2.11088
$708$	1.94000	0.0729097
$709$	−31.3989	−1.17921	−0.589604	−	0.807692i	$-0.700716\pi$
$709$	−31.3989	−1.17921	−0.589604	+	0.807692i	$0.700716\pi$
$710$	−33.0467	−1.24022
$711$	0.446517	0.0167457
$712$	−4.62435	−0.173305
$713$	61.7052	2.31088
$714$	−8.01337	−0.299893
$715$	−22.5987	−0.845144
$716$	5.61651	0.209899
$717$	−1.23749	−0.0462151
$718$	19.1975	0.716445
$719$	−35.6866	−1.33088	−0.665442	−	0.746449i	$-0.731757\pi$
$719$	−35.6866	−1.33088	−0.665442	+	0.746449i	$0.731757\pi$
$720$	−2.51351	−0.0936732
$721$	−31.7379	−1.18198
$722$	37.8185	1.40746
$723$	−12.5829	−0.467962
$724$	6.95661	0.258540
$725$	−50.1751	−1.86346
$726$	17.6706	0.655817
$727$	−14.0021	−0.519308	−0.259654	−	0.965702i	$-0.583608\pi$
$727$	−14.0021	−0.519308	−0.259654	+	0.965702i	$0.583608\pi$
$728$	20.6198	0.764220
$729$	17.0743	0.632383
$730$	−3.05931	−0.113230
$731$	9.03690	0.334242
$732$	−26.6281	−0.984203
$733$	19.8661	0.733771	0.366885	−	0.930266i	$-0.380424\pi$
$733$	19.8661	0.733771	0.366885	+	0.930266i	$0.380424\pi$
$734$	9.09868	0.335838
$735$	64.2536	2.37003
$736$	−8.63886	−0.318433
$737$	−7.19075	−0.264875
$738$	4.28351	0.157678
$739$	−1.89954	−0.0698756	−0.0349378	−	0.999389i	$-0.511123\pi$
$739$	−1.89954	−0.0698756	−0.0349378	+	0.999389i	$0.511123\pi$
$740$	−25.2899	−0.929676
$741$	72.9990	2.68169
$742$	19.9229	0.731392
$743$	32.0874	1.17717	0.588587	−	0.808434i	$-0.299685\pi$
$743$	32.0874	1.17717	0.588587	+	0.808434i	$0.299685\pi$
$744$	13.8569	0.508020
$745$	39.8548	1.46017
$746$	−15.3374	−0.561543
$747$	−6.21908	−0.227544
$748$	1.37530	0.0502860
$749$	46.1186	1.68514
$750$	5.33251	0.194716
$751$	−17.5791	−0.641469	−0.320735	−	0.947169i	$-0.603930\pi$
$751$	−17.5791	−0.641469	−0.320735	+	0.947169i	$0.603930\pi$
$752$	10.3875	0.378792
$753$	−2.89917	−0.105652
$754$	42.9254	1.56325
$755$	−44.6746	−1.62588
$756$	−17.9211	−0.651785
$757$	−9.46682	−0.344077	−0.172039	−	0.985090i	$-0.555035\pi$
$757$	−9.46682	−0.344077	−0.172039	+	0.985090i	$0.555035\pi$
$758$	2.79569	0.101544
$759$	−23.0492	−0.836634
$760$	−24.8119	−0.900023
$761$	10.8279	0.392513	0.196256	−	0.980553i	$-0.437122\pi$
$761$	10.8279	0.392513	0.196256	+	0.980553i	$0.437122\pi$
$762$	20.1854	0.731241
$763$	12.4375	0.450266
$764$	−18.3988	−0.665647
$765$	2.51351	0.0908763
$766$	1.64336	0.0593769
$767$	4.99195	0.180249
$768$	−1.94000	−0.0700037
$769$	−5.31191	−0.191552	−0.0957761	−	0.995403i	$-0.530533\pi$
$769$	−5.31191	−0.191552	−0.0957761	+	0.995403i	$0.530533\pi$
$770$	−18.6994	−0.673879
$771$	−20.2637	−0.729779
$772$	13.0769	0.470650
$773$	15.6933	0.564448	0.282224	−	0.959349i	$-0.408928\pi$
$773$	15.6933	0.564448	0.282224	+	0.959349i	$0.408928\pi$
$774$	−6.90058	−0.248036
$775$	−41.6783	−1.49713
$776$	−11.5680	−0.415267
$777$	61.5669	2.20870
$778$	26.2876	0.942455
$779$	42.2842	1.51499
$780$	−31.8778	−1.14141
$781$	−13.8073	−0.494065
$782$	8.63886	0.308925
$783$	−37.3074	−1.33326
$784$	10.0619	0.359354
$785$	78.5521	2.80365
$786$	−35.1939	−1.25533
$787$	11.0330	0.393284	0.196642	−	0.980475i	$-0.436996\pi$
$787$	11.0330	0.393284	0.196642	+	0.980475i	$0.436996\pi$
$788$	5.77738	0.205811
$789$	−9.08634	−0.323482
$790$	−1.92481	−0.0684817
$791$	5.09331	0.181097
$792$	−1.05018	−0.0373165
$793$	−68.5187	−2.43317
$794$	12.1636	0.431671
$795$	−30.8003	−1.09238
$796$	13.6146	0.482557
$797$	8.42233	0.298334	0.149167	−	0.988812i	$-0.452341\pi$
$797$	8.42233	0.298334	0.149167	+	0.988812i	$0.452341\pi$
$798$	60.4033	2.13825
$799$	−10.3875	−0.367482
$800$	5.83505	0.206300
$801$	−3.53115	−0.124767
$802$	−2.92169	−0.103169
$803$	−1.27822	−0.0451074
$804$	−10.1433	−0.357726
$805$	−117.459	−4.13988
$806$	35.6563	1.25594
$807$	36.4982	1.28480
$808$	−13.5881	−0.478029
$809$	−36.8157	−1.29437	−0.647185	−	0.762333i	$-0.724054\pi$
$809$	−36.8157	−1.29437	−0.647185	+	0.762333i	$0.724054\pi$
$810$	35.2462	1.23843
$811$	1.81633	0.0637799	0.0318899	−	0.999491i	$-0.489847\pi$
$811$	1.81633	0.0637799	0.0318899	+	0.999491i	$0.489847\pi$
$812$	35.5187	1.24646
$813$	−27.3181	−0.958089
$814$	−10.5665	−0.370355
$815$	5.92063	0.207391
$816$	1.94000	0.0679136
$817$	−68.1184	−2.38316
$818$	29.0484	1.01565
$819$	15.7453	0.550184
$820$	−18.4650	−0.644826
$821$	−45.2515	−1.57929	−0.789644	−	0.613565i	$-0.789735\pi$
$821$	−45.2515	−1.57929	−0.789644	+	0.613565i	$0.789735\pi$
$822$	−31.2959	−1.09157
$823$	−1.96041	−0.0683357	−0.0341679	−	0.999416i	$-0.510878\pi$
$823$	−1.96041	−0.0683357	−0.0341679	+	0.999416i	$0.510878\pi$
$824$	7.68360	0.267671
$825$	15.5684	0.542023
$826$	4.13061	0.143722
$827$	−27.2083	−0.946126	−0.473063	−	0.881029i	$-0.656852\pi$
$827$	−27.2083	−0.946126	−0.473063	+	0.881029i	$0.656852\pi$
$828$	−6.59664	−0.229249
$829$	45.4914	1.57998	0.789990	−	0.613120i	$-0.210086\pi$
$829$	45.4914	1.57998	0.789990	+	0.613120i	$0.210086\pi$
$830$	26.8087	0.930544
$831$	31.3740	1.08835
$832$	−4.99195	−0.173065
$833$	−10.0619	−0.348624
$834$	−5.08911	−0.176221
$835$	−44.6998	−1.54690
$836$	−10.3668	−0.358542
$837$	−30.9896	−1.07116
$838$	11.1303	0.384490
$839$	36.2702	1.25219	0.626093	−	0.779748i	$-0.284653\pi$
$839$	36.2702	1.25219	0.626093	+	0.779748i	$0.284653\pi$
$840$	−26.3773	−0.910105
$841$	44.9414	1.54970
$842$	6.71494	0.231412
$843$	30.6871	1.05692
$844$	−4.32695	−0.148940
$845$	−39.2353	−1.34974
$846$	7.93187	0.272703
$847$	37.6238	1.29277
$848$	−4.82323	−0.165631
$849$	−60.4181	−2.07354
$850$	−5.83505	−0.200141
$851$	−66.3726	−2.27522
$852$	−19.4766	−0.667258
$853$	48.3054	1.65395	0.826973	−	0.562242i	$-0.190061\pi$
$853$	48.3054	1.65395	0.826973	+	0.562242i	$0.190061\pi$
$854$	−56.6960	−1.94010
$855$	−18.9464	−0.647953
$856$	−11.1651	−0.381615
$857$	−1.96373	−0.0670797	−0.0335398	−	0.999437i	$-0.510678\pi$
$857$	−1.96373	−0.0670797	−0.0335398	+	0.999437i	$0.510678\pi$
$858$	−13.3190	−0.454702
$859$	32.1622	1.09736	0.548680	−	0.836033i	$-0.315131\pi$
$859$	32.1622	1.09736	0.548680	+	0.836033i	$0.315131\pi$
$860$	29.7464	1.01435
$861$	44.9520	1.53196
$862$	1.99594	0.0679821
$863$	11.0130	0.374888	0.187444	−	0.982275i	$-0.439980\pi$
$863$	11.0130	0.374888	0.187444	+	0.982275i	$0.439980\pi$
$864$	4.33862	0.147603
$865$	49.5182	1.68367
$866$	15.5147	0.527211
$867$	−1.94000	−0.0658859
$868$	29.5039	1.00143
$869$	−0.804211	−0.0272810
$870$	−54.9112	−1.86166
$871$	−26.1004	−0.884377
$872$	−3.01105	−0.101967
$873$	−8.83333	−0.298963
$874$	−65.1181	−2.20265
$875$	11.3539	0.383830
$876$	−1.80306	−0.0609197
$877$	−1.51495	−0.0511561	−0.0255781	−	0.999673i	$-0.508143\pi$
$877$	−1.51495	−0.0511561	−0.0255781	+	0.999673i	$0.508143\pi$
$878$	24.0677	0.812245
$879$	36.7189	1.23850
$880$	4.52703	0.152606
$881$	−40.7260	−1.37210	−0.686048	−	0.727557i	$-0.740656\pi$
$881$	−40.7260	−1.37210	−0.686048	+	0.727557i	$0.740656\pi$
$882$	7.68327	0.258709
$883$	28.6039	0.962598	0.481299	−	0.876557i	$-0.340165\pi$
$883$	28.6039	0.962598	0.481299	+	0.876557i	$0.340165\pi$
$884$	4.99195	0.167898
$885$	−6.38583	−0.214657
$886$	−27.2209	−0.914504
$887$	37.7689	1.26816	0.634078	−	0.773269i	$-0.281380\pi$
$887$	37.7689	1.26816	0.634078	+	0.773269i	$0.281380\pi$
$888$	−14.9051	−0.500181
$889$	42.9784	1.44145
$890$	15.2218	0.510236
$891$	14.7263	0.493351
$892$	0.284365	0.00952126
$893$	78.2987	2.62017
$894$	23.4892	0.785595
$895$	−18.4877	−0.617975
$896$	−4.13061	−0.137994
$897$	−83.6621	−2.79340
$898$	−20.5988	−0.687390
$899$	61.4199	2.04847
$900$	4.45565	0.148522
$901$	4.82323	0.160685
$902$	−7.71492	−0.256879
$903$	−72.4161	−2.40986
$904$	−1.23307	−0.0410111
$905$	−22.8988	−0.761183
$906$	−26.3298	−0.874748
$907$	−23.7501	−0.788610	−0.394305	−	0.918980i	$-0.629015\pi$
$907$	−23.7501	−0.788610	−0.394305	+	0.918980i	$0.629015\pi$
$908$	12.8084	0.425061
$909$	−10.3759	−0.344147
$910$	−67.8734	−2.24998
$911$	−42.5580	−1.41001	−0.705005	−	0.709202i	$-0.749055\pi$
$911$	−42.5580	−1.41001	−0.705005	+	0.709202i	$0.749055\pi$
$912$	−14.6233	−0.484227
$913$	11.2010	0.370700
$914$	18.6422	0.616629
$915$	87.6508	2.89765
$916$	−25.8249	−0.853279
$917$	−74.9342	−2.47454
$918$	−4.33862	−0.143196
$919$	45.6984	1.50745	0.753725	−	0.657190i	$-0.228255\pi$
$919$	45.6984	1.50745	0.753725	+	0.657190i	$0.228255\pi$
$920$	28.4362	0.937515
$921$	4.09961	0.135087
$922$	4.32434	0.142415
$923$	−50.1167	−1.64961
$924$	−11.0208	−0.362558
$925$	44.8308	1.47403
$926$	−12.1451	−0.399112
$927$	5.86719	0.192704
$928$	−8.59892	−0.282273
$929$	−27.1263	−0.889986	−0.444993	−	0.895534i	$-0.646794\pi$
$929$	−27.1263	−0.889986	−0.444993	+	0.895534i	$0.646794\pi$
$930$	−45.6124	−1.49569
$931$	75.8447	2.48571
$932$	−9.10564	−0.298265
$933$	−17.7274	−0.580369
$934$	28.8348	0.943505
$935$	−4.52703	−0.148050
$936$	−3.81185	−0.124594
$937$	47.4814	1.55115	0.775575	−	0.631255i	$-0.217460\pi$
$937$	47.4814	1.55115	0.775575	+	0.631255i	$0.217460\pi$
$938$	−21.5968	−0.705161
$939$	42.5776	1.38947
$940$	−34.1921	−1.11522
$941$	−13.2032	−0.430411	−0.215206	−	0.976569i	$-0.569042\pi$
$941$	−13.2032	−0.430411	−0.215206	+	0.976569i	$0.569042\pi$
$942$	46.2961	1.50841
$943$	−48.4608	−1.57810
$944$	−1.00000	−0.0325472
$945$	58.9903	1.91895
$946$	12.4285	0.404084
$947$	10.9750	0.356638	0.178319	−	0.983973i	$-0.442934\pi$
$947$	10.9750	0.356638	0.178319	+	0.983973i	$0.442934\pi$
$948$	−1.13442	−0.0368443
$949$	−4.63958	−0.150607
$950$	43.9835	1.42701
$951$	16.9982	0.551204
$952$	4.13061	0.133874
$953$	−53.0085	−1.71711	−0.858556	−	0.512720i	$-0.828638\pi$
$953$	−53.0085	−1.71711	−0.858556	+	0.512720i	$0.828638\pi$
$954$	−3.68302	−0.119242
$955$	60.5628	1.95977
$956$	0.637883	0.0206306
$957$	−22.9426	−0.741630
$958$	11.1823	0.361283
$959$	−66.6346	−2.15174
$960$	6.38583	0.206102
$961$	20.0189	0.645770
$962$	−38.3533	−1.23656
$963$	−8.52567	−0.274736
$964$	6.48602	0.208901
$965$	−43.0449	−1.38566
$966$	−69.2265	−2.22732
$967$	12.2638	0.394379	0.197189	−	0.980365i	$-0.436819\pi$
$967$	12.2638	0.394379	0.197189	+	0.980365i	$0.436819\pi$
$968$	−9.10855	−0.292760
$969$	14.6233	0.469769
$970$	38.0780	1.22261
$971$	−8.04180	−0.258074	−0.129037	−	0.991640i	$-0.541189\pi$
$971$	−8.04180	−0.258074	−0.129037	+	0.991640i	$0.541189\pi$
$972$	7.75712	0.248810
$973$	−10.8356	−0.347374
$974$	−25.8318	−0.827706
$975$	56.5089	1.80973
$976$	13.7258	0.439353
$977$	−19.1974	−0.614178	−0.307089	−	0.951681i	$-0.599355\pi$
$977$	−19.1974	−0.614178	−0.307089	+	0.951681i	$0.599355\pi$
$978$	3.48943	0.111580
$979$	6.35987	0.203262
$980$	−33.1204	−1.05799
$981$	−2.29924	−0.0734090
$982$	−20.2673	−0.646755
$983$	−8.89362	−0.283662	−0.141831	−	0.989891i	$-0.545299\pi$
$983$	−8.89362	−0.283662	−0.141831	+	0.989891i	$0.545299\pi$
$984$	−10.8827	−0.346927
$985$	−19.0172	−0.605938
$986$	8.59892	0.273845
$987$	83.2387	2.64952
$988$	−37.6284	−1.19712
$989$	78.0685	2.48244
$990$	3.45684	0.109866
$991$	45.0187	1.43007	0.715033	−	0.699091i	$-0.246412\pi$
$991$	45.0187	1.43007	0.715033	+	0.699091i	$0.246412\pi$
$992$	−7.14275	−0.226783
$993$	−29.9923	−0.951776
$994$	−41.4692	−1.31532
$995$	−44.8147	−1.42072
$996$	15.8002	0.500648
$997$	7.38955	0.234029	0.117015	−	0.993130i	$-0.462668\pi$
$997$	7.38955	0.234029	0.117015	+	0.993130i	$0.462668\pi$
$998$	−24.7462	−0.783328
$999$	33.3337	1.05463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2006.2.a.t.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2006.2.a.t.1.1	✓	8	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:	\( N \)	\(=\)	\( 2006 = 2 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.94000 q^{3} +1.00000 q^{4} -3.29166 q^{5} -1.94000 q^{6} -4.13061 q^{7} +1.00000 q^{8} +0.763600 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.94000 q^{3} +1.00000 q^{4} -3.29166 q^{5} -1.94000 q^{6} -4.13061 q^{7} +1.00000 q^{8} +0.763600 q^{9} -3.29166 q^{10} -1.37530 q^{11} -1.94000 q^{12} -4.99195 q^{13} -4.13061 q^{14} +6.38583 q^{15} +1.00000 q^{16} -1.00000 q^{17} +0.763600 q^{18} +7.53781 q^{19} -3.29166 q^{20} +8.01337 q^{21} -1.37530 q^{22} -8.63886 q^{23} -1.94000 q^{24} +5.83505 q^{25} -4.99195 q^{26} +4.33862 q^{27} -4.13061 q^{28} -8.59892 q^{29} +6.38583 q^{30} -7.14275 q^{31} +1.00000 q^{32} +2.66808 q^{33} -1.00000 q^{34} +13.5966 q^{35} +0.763600 q^{36} +7.68302 q^{37} +7.53781 q^{38} +9.68439 q^{39} -3.29166 q^{40} +5.60962 q^{41} +8.01337 q^{42} -9.03690 q^{43} -1.37530 q^{44} -2.51351 q^{45} -8.63886 q^{46} +10.3875 q^{47} -1.94000 q^{48} +10.0619 q^{49} +5.83505 q^{50} +1.94000 q^{51} -4.99195 q^{52} -4.82323 q^{53} +4.33862 q^{54} +4.52703 q^{55} -4.13061 q^{56} -14.6233 q^{57} -8.59892 q^{58} -1.00000 q^{59} +6.38583 q^{60} +13.7258 q^{61} -7.14275 q^{62} -3.15413 q^{63} +1.00000 q^{64} +16.4318 q^{65} +2.66808 q^{66} +5.22849 q^{67} -1.00000 q^{68} +16.7594 q^{69} +13.5966 q^{70} +10.0395 q^{71} +0.763600 q^{72} +0.929411 q^{73} +7.68302 q^{74} -11.3200 q^{75} +7.53781 q^{76} +5.68083 q^{77} +9.68439 q^{78} +0.584753 q^{79} -3.29166 q^{80} -10.7077 q^{81} +5.60962 q^{82} -8.14442 q^{83} +8.01337 q^{84} +3.29166 q^{85} -9.03690 q^{86} +16.6819 q^{87} -1.37530 q^{88} -4.62435 q^{89} -2.51351 q^{90} +20.6198 q^{91} -8.63886 q^{92} +13.8569 q^{93} +10.3875 q^{94} -24.8119 q^{95} -1.94000 q^{96} -11.5680 q^{97} +10.0619 q^{98} -1.05018 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9	\( 8 q + 8 q^{2} + 5 q^{3} + 8 q^{4} - 5 q^{5} + 5 q^{6} + 8 q^{8} + 17 q^{9} - 5 q^{10} - 5 q^{11} + 5 q^{12} + q^{13} + 9 q^{15} + 8 q^{16} - 8 q^{17} + 17 q^{18} + 8 q^{19} - 5 q^{20} + 13 q^{21} - 5 q^{22} - 8 q^{23} + 5 q^{24} + 29 q^{25} + q^{26} + 44 q^{27} + 20 q^{29} + 9 q^{30} + 18 q^{31} + 8 q^{32} - 23 q^{33} - 8 q^{34} + 9 q^{35} + 17 q^{36} - 7 q^{37} + 8 q^{38} + 6 q^{39} - 5 q^{40} + 12 q^{41} + 13 q^{42} - 8 q^{43} - 5 q^{44} + 5 q^{45} - 8 q^{46} + 30 q^{47} + 5 q^{48} + 28 q^{49} + 29 q^{50} - 5 q^{51} + q^{52} - 5 q^{53} + 44 q^{54} + 23 q^{55} + 13 q^{57} + 20 q^{58} - 8 q^{59} + 9 q^{60} + 12 q^{61} + 18 q^{62} + 21 q^{63} + 8 q^{64} - 52 q^{65} - 23 q^{66} - 4 q^{67} - 8 q^{68} + 24 q^{69} + 9 q^{70} + 4 q^{71} + 17 q^{72} - 18 q^{73} - 7 q^{74} - 49 q^{75} + 8 q^{76} - 13 q^{77} + 6 q^{78} - 17 q^{79} - 5 q^{80} + 12 q^{81} + 12 q^{82} + 9 q^{83} + 13 q^{84} + 5 q^{85} - 8 q^{86} + 48 q^{87} - 5 q^{88} - 12 q^{89} + 5 q^{90} + 31 q^{91} - 8 q^{92} - 3 q^{93} + 30 q^{94} - 7 q^{95} + 5 q^{96} - 11 q^{97} + 28 q^{98} - 27 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 5 * q^3 + 8 * q^4 - 5 * q^5 + 5 * q^6 + 8 * q^8 + 17 * q^9 - 5 * q^10 - 5 * q^11 + 5 * q^12 + q^13 + 9 * q^15 + 8 * q^16 - 8 * q^17 + 17 * q^18 + 8 * q^19 - 5 * q^20 + 13 * q^21 - 5 * q^22 - 8 * q^23 + 5 * q^24 + 29 * q^25 + q^26 + 44 * q^27 + 20 * q^29 + 9 * q^30 + 18 * q^31 + 8 * q^32 - 23 * q^33 - 8 * q^34 + 9 * q^35 + 17 * q^36 - 7 * q^37 + 8 * q^38 + 6 * q^39 - 5 * q^40 + 12 * q^41 + 13 * q^42 - 8 * q^43 - 5 * q^44 + 5 * q^45 - 8 * q^46 + 30 * q^47 + 5 * q^48 + 28 * q^49 + 29 * q^50 - 5 * q^51 + q^52 - 5 * q^53 + 44 * q^54 + 23 * q^55 + 13 * q^57 + 20 * q^58 - 8 * q^59 + 9 * q^60 + 12 * q^61 + 18 * q^62 + 21 * q^63 + 8 * q^64 - 52 * q^65 - 23 * q^66 - 4 * q^67 - 8 * q^68 + 24 * q^69 + 9 * q^70 + 4 * q^71 + 17 * q^72 - 18 * q^73 - 7 * q^74 - 49 * q^75 + 8 * q^76 - 13 * q^77 + 6 * q^78 - 17 * q^79 - 5 * q^80 + 12 * q^81 + 12 * q^82 + 9 * q^83 + 13 * q^84 + 5 * q^85 - 8 * q^86 + 48 * q^87 - 5 * q^88 - 12 * q^89 + 5 * q^90 + 31 * q^91 - 8 * q^92 - 3 * q^93 + 30 * q^94 - 7 * q^95 + 5 * q^96 - 11 * q^97 + 28 * q^98 - 27 * q^99

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