LMFDB - Embedded newform 1502.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1502,2,Mod(1,1502)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1502, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1502.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1502 = 2 \cdot 751 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1502.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:	$11.9935303836$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4x^{10} - 9x^{9} + 58x^{8} - 40x^{7} - 146x^{6} + 237x^{5} - 47x^{4} - 89x^{3} + 39x^{2} - 1 $ x^11 - 4x^10 - 9x^9 + 58x^8 - 40x^7 - 146x^6 + 237x^5 - 47x^4 - 89x^3 + 39*x^2 - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.23340$ of defining polynomial
Character	$\chi$	$=$	1502.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.27345 q^{3} +1.00000 q^{4} -1.29537 q^{5} -2.27345 q^{6} -2.53574 q^{7} -1.00000 q^{8} +2.16859 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.27345 q^{3} +1.00000 q^{4} -1.29537 q^{5} -2.27345 q^{6} -2.53574 q^{7} -1.00000 q^{8} +2.16859 q^{9} +1.29537 q^{10} -0.130403 q^{11} +2.27345 q^{12} -0.185725 q^{13} +2.53574 q^{14} -2.94497 q^{15} +1.00000 q^{16} -0.0597223 q^{17} -2.16859 q^{18} -4.43119 q^{19} -1.29537 q^{20} -5.76490 q^{21} +0.130403 q^{22} -2.35691 q^{23} -2.27345 q^{24} -3.32201 q^{25} +0.185725 q^{26} -1.89016 q^{27} -2.53574 q^{28} +7.14624 q^{29} +2.94497 q^{30} +8.33125 q^{31} -1.00000 q^{32} -0.296464 q^{33} +0.0597223 q^{34} +3.28474 q^{35} +2.16859 q^{36} -9.75035 q^{37} +4.43119 q^{38} -0.422237 q^{39} +1.29537 q^{40} -6.74252 q^{41} +5.76490 q^{42} -0.618782 q^{43} -0.130403 q^{44} -2.80914 q^{45} +2.35691 q^{46} -9.33195 q^{47} +2.27345 q^{48} -0.570001 q^{49} +3.32201 q^{50} -0.135776 q^{51} -0.185725 q^{52} -8.64141 q^{53} +1.89016 q^{54} +0.168920 q^{55} +2.53574 q^{56} -10.0741 q^{57} -7.14624 q^{58} -11.2119 q^{59} -2.94497 q^{60} +7.09541 q^{61} -8.33125 q^{62} -5.49900 q^{63} +1.00000 q^{64} +0.240583 q^{65} +0.296464 q^{66} -2.14117 q^{67} -0.0597223 q^{68} -5.35833 q^{69} -3.28474 q^{70} +14.6649 q^{71} -2.16859 q^{72} -11.2560 q^{73} +9.75035 q^{74} -7.55243 q^{75} -4.43119 q^{76} +0.330668 q^{77} +0.422237 q^{78} -12.8840 q^{79} -1.29537 q^{80} -10.8030 q^{81} +6.74252 q^{82} +1.15515 q^{83} -5.76490 q^{84} +0.0773627 q^{85} +0.618782 q^{86} +16.2467 q^{87} +0.130403 q^{88} +6.87269 q^{89} +2.80914 q^{90} +0.470951 q^{91} -2.35691 q^{92} +18.9407 q^{93} +9.33195 q^{94} +5.74005 q^{95} -2.27345 q^{96} -6.52769 q^{97} +0.570001 q^{98} -0.282790 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.27345	1.31258	0.656290	−	0.754509i	$-0.272125\pi$
$3$	2.27345	1.31258	0.656290	+	0.754509i	$0.272125\pi$
$4$	1.00000	0.500000
$5$	−1.29537	−0.579309	−0.289654	−	0.957131i	$-0.593540\pi$
$5$	−1.29537	−0.579309	−0.289654	+	0.957131i	$0.593540\pi$
$6$	−2.27345	−0.928134
$7$	−2.53574	−0.958421	−0.479211	−	0.877700i	$-0.659077\pi$
$7$	−2.53574	−0.958421	−0.479211	+	0.877700i	$0.659077\pi$
$8$	−1.00000	−0.353553
$9$	2.16859	0.722865
$10$	1.29537	0.409633
$11$	−0.130403	−0.0393179	−0.0196589	−	0.999807i	$-0.506258\pi$
$11$	−0.130403	−0.0393179	−0.0196589	+	0.999807i	$0.506258\pi$
$12$	2.27345	0.656290
$13$	−0.185725	−0.0515108	−0.0257554	−	0.999668i	$-0.508199\pi$
$13$	−0.185725	−0.0515108	−0.0257554	+	0.999668i	$0.508199\pi$
$14$	2.53574	0.677706
$15$	−2.94497	−0.760389
$16$	1.00000	0.250000
$17$	−0.0597223	−0.0144848	−0.00724239	−	0.999974i	$-0.502305\pi$
$17$	−0.0597223	−0.0144848	−0.00724239	+	0.999974i	$0.502305\pi$
$18$	−2.16859	−0.511143
$19$	−4.43119	−1.01658	−0.508292	−	0.861185i	$-0.669723\pi$
$19$	−4.43119	−1.01658	−0.508292	+	0.861185i	$0.669723\pi$
$20$	−1.29537	−0.289654
$21$	−5.76490	−1.25800
$22$	0.130403	0.0278019
$23$	−2.35691	−0.491450	−0.245725	−	0.969340i	$-0.579026\pi$
$23$	−2.35691	−0.491450	−0.245725	+	0.969340i	$0.579026\pi$
$24$	−2.27345	−0.464067
$25$	−3.32201	−0.664401
$26$	0.185725	0.0364237
$27$	−1.89016	−0.363762
$28$	−2.53574	−0.479211
$29$	7.14624	1.32702	0.663512	−	0.748166i	$-0.269065\pi$
$29$	7.14624	1.32702	0.663512	+	0.748166i	$0.269065\pi$
$30$	2.94497	0.537676
$31$	8.33125	1.49634	0.748168	−	0.663509i	$-0.230934\pi$
$31$	8.33125	1.49634	0.748168	+	0.663509i	$0.230934\pi$
$32$	−1.00000	−0.176777
$33$	−0.296464	−0.0516078
$34$	0.0597223	0.0102423
$35$	3.28474	0.555222
$36$	2.16859	0.361432
$37$	−9.75035	−1.60295	−0.801474	−	0.598030i	$-0.795950\pi$
$37$	−9.75035	−1.60295	−0.801474	+	0.598030i	$0.795950\pi$
$38$	4.43119	0.718834
$39$	−0.422237	−0.0676121
$40$	1.29537	0.204817
$41$	−6.74252	−1.05300	−0.526502	−	0.850174i	$-0.676497\pi$
$41$	−6.74252	−1.05300	−0.526502	+	0.850174i	$0.676497\pi$
$42$	5.76490	0.889543
$43$	−0.618782	−0.0943634	−0.0471817	−	0.998886i	$-0.515024\pi$
$43$	−0.618782	−0.0943634	−0.0471817	+	0.998886i	$0.515024\pi$
$44$	−0.130403	−0.0196589
$45$	−2.80914	−0.418762
$46$	2.35691	0.347508
$47$	−9.33195	−1.36121	−0.680603	−	0.732653i	$-0.738282\pi$
$47$	−9.33195	−1.36121	−0.680603	+	0.732653i	$0.738282\pi$
$48$	2.27345	0.328145
$49$	−0.570001	−0.0814287
$50$	3.32201	0.469803
$51$	−0.135776	−0.0190124
$52$	−0.185725	−0.0257554
$53$	−8.64141	−1.18699	−0.593494	−	0.804838i	$-0.702252\pi$
$53$	−8.64141	−1.18699	−0.593494	+	0.804838i	$0.702252\pi$
$54$	1.89016	0.257219
$55$	0.168920	0.0227772
$56$	2.53574	0.338853
$57$	−10.0741	−1.33435
$58$	−7.14624	−0.938348
$59$	−11.2119	−1.45967	−0.729833	−	0.683625i	$-0.760402\pi$
$59$	−11.2119	−1.45967	−0.729833	+	0.683625i	$0.760402\pi$
$60$	−2.94497	−0.380195
$61$	7.09541	0.908474	0.454237	−	0.890881i	$-0.349912\pi$
$61$	7.09541	0.908474	0.454237	+	0.890881i	$0.349912\pi$
$62$	−8.33125	−1.05807
$63$	−5.49900	−0.692809
$64$	1.00000	0.125000
$65$	0.240583	0.0298407
$66$	0.296464	0.0364923
$67$	−2.14117	−0.261586	−0.130793	−	0.991410i	$-0.541752\pi$
$67$	−2.14117	−0.261586	−0.130793	+	0.991410i	$0.541752\pi$
$68$	−0.0597223	−0.00724239
$69$	−5.35833	−0.645067
$70$	−3.28474	−0.392601
$71$	14.6649	1.74041	0.870203	−	0.492694i	$-0.163988\pi$
$71$	14.6649	1.74041	0.870203	+	0.492694i	$0.163988\pi$
$72$	−2.16859	−0.255571
$73$	−11.2560	−1.31741	−0.658705	−	0.752401i	$-0.728895\pi$
$73$	−11.2560	−1.31741	−0.658705	+	0.752401i	$0.728895\pi$
$74$	9.75035	1.13346
$75$	−7.55243	−0.872079
$76$	−4.43119	−0.508292
$77$	0.330668	0.0376831
$78$	0.422237	0.0478090
$79$	−12.8840	−1.44956	−0.724780	−	0.688981i	$-0.758058\pi$
$79$	−12.8840	−1.44956	−0.724780	+	0.688981i	$0.758058\pi$
$80$	−1.29537	−0.144827
$81$	−10.8030	−1.20033
$82$	6.74252	0.744586
$83$	1.15515	0.126794	0.0633971	−	0.997988i	$-0.479807\pi$
$83$	1.15515	0.126794	0.0633971	+	0.997988i	$0.479807\pi$
$84$	−5.76490	−0.629002
$85$	0.0773627	0.00839116
$86$	0.618782	0.0667250
$87$	16.2467	1.74182
$88$	0.130403	0.0139010
$89$	6.87269	0.728503	0.364252	−	0.931301i	$-0.381325\pi$
$89$	6.87269	0.728503	0.364252	+	0.931301i	$0.381325\pi$
$90$	2.80914	0.296110
$91$	0.470951	0.0493691
$92$	−2.35691	−0.245725
$93$	18.9407	1.96406
$94$	9.33195	0.962518
$95$	5.74005	0.588917
$96$	−2.27345	−0.232033
$97$	−6.52769	−0.662787	−0.331393	−	0.943493i	$-0.607519\pi$
$97$	−6.52769	−0.662787	−0.331393	+	0.943493i	$0.607519\pi$
$98$	0.570001	0.0575788
$99$	−0.282790	−0.0284215
$100$	−3.32201	−0.332201
$101$	−4.73117	−0.470769	−0.235384	−	0.971902i	$-0.575635\pi$
$101$	−4.73117	−0.470769	−0.235384	+	0.971902i	$0.575635\pi$
$102$	0.135776	0.0134438
$103$	7.32999	0.722246	0.361123	−	0.932518i	$-0.382393\pi$
$103$	7.32999	0.722246	0.361123	+	0.932518i	$0.382393\pi$
$104$	0.185725	0.0182118
$105$	7.46770	0.728773
$106$	8.64141	0.839328
$107$	16.1536	1.56162	0.780812	−	0.624766i	$-0.214806\pi$
$107$	16.1536	1.56162	0.780812	+	0.624766i	$0.214806\pi$
$108$	−1.89016	−0.181881
$109$	9.58293	0.917878	0.458939	−	0.888468i	$-0.348230\pi$
$109$	9.58293	0.917878	0.458939	+	0.888468i	$0.348230\pi$
$110$	−0.168920	−0.0161059
$111$	−22.1670	−2.10400
$112$	−2.53574	−0.239605
$113$	17.1386	1.61227	0.806134	−	0.591733i	$-0.201556\pi$
$113$	17.1386	1.61227	0.806134	+	0.591733i	$0.201556\pi$
$114$	10.0741	0.943527
$115$	3.05308	0.284702
$116$	7.14624	0.663512
$117$	−0.402762	−0.0372354
$118$	11.2119	1.03214
$119$	0.151440	0.0138825
$120$	2.94497	0.268838
$121$	−10.9830	−0.998454
$122$	−7.09541	−0.642388
$123$	−15.3288	−1.38215
$124$	8.33125	0.748168
$125$	10.7801	0.964202
$126$	5.49900	0.489890
$127$	−11.3389	−1.00617	−0.503083	−	0.864238i	$-0.667801\pi$
$127$	−11.3389	−1.00617	−0.503083	+	0.864238i	$0.667801\pi$
$128$	−1.00000	−0.0883883
$129$	−1.40677	−0.123859
$130$	−0.240583	−0.0211006
$131$	20.4969	1.79082	0.895411	−	0.445241i	$-0.146882\pi$
$131$	20.4969	1.79082	0.895411	+	0.445241i	$0.146882\pi$
$132$	−0.296464	−0.0258039
$133$	11.2364	0.974316
$134$	2.14117	0.184969
$135$	2.44847	0.210731
$136$	0.0597223	0.00512114
$137$	7.11331	0.607731	0.303866	−	0.952715i	$-0.401723\pi$
$137$	7.11331	0.607731	0.303866	+	0.952715i	$0.401723\pi$
$138$	5.35833	0.456132
$139$	−16.5254	−1.40167	−0.700835	−	0.713324i	$-0.747189\pi$
$139$	−16.5254	−1.40167	−0.700835	+	0.713324i	$0.747189\pi$
$140$	3.28474	0.277611
$141$	−21.2158	−1.78669
$142$	−14.6649	−1.23065
$143$	0.0242190	0.00202530
$144$	2.16859	0.180716
$145$	−9.25706	−0.768757
$146$	11.2560	0.931549
$147$	−1.29587	−0.106882
$148$	−9.75035	−0.801474
$149$	−17.8938	−1.46592	−0.732958	−	0.680274i	$-0.761861\pi$
$149$	−17.8938	−1.46592	−0.732958	+	0.680274i	$0.761861\pi$
$150$	7.55243	0.616653
$151$	18.8242	1.53190	0.765948	−	0.642903i	$-0.222270\pi$
$151$	18.8242	1.53190	0.765948	+	0.642903i	$0.222270\pi$
$152$	4.43119	0.359417
$153$	−0.129513	−0.0104705
$154$	−0.330668	−0.0266460
$155$	−10.7921	−0.866841
$156$	−0.422237	−0.0338060
$157$	0.407105	0.0324905	0.0162453	−	0.999868i	$-0.494829\pi$
$157$	0.407105	0.0324905	0.0162453	+	0.999868i	$0.494829\pi$
$158$	12.8840	1.02499
$159$	−19.6458	−1.55802
$160$	1.29537	0.102408
$161$	5.97653	0.471016
$162$	10.8030	0.848762
$163$	−22.4759	−1.76045	−0.880224	−	0.474559i	$-0.842608\pi$
$163$	−22.4759	−1.76045	−0.880224	+	0.474559i	$0.842608\pi$
$164$	−6.74252	−0.526502
$165$	0.384032	0.0298969
$166$	−1.15515	−0.0896570
$167$	−8.16941	−0.632168	−0.316084	−	0.948731i	$-0.602368\pi$
$167$	−8.16941	−0.632168	−0.316084	+	0.948731i	$0.602368\pi$
$168$	5.76490	0.444772
$169$	−12.9655	−0.997347
$170$	−0.0773627	−0.00593345
$171$	−9.60945	−0.734853
$172$	−0.618782	−0.0471817
$173$	10.1896	0.774699	0.387349	−	0.921933i	$-0.373391\pi$
$173$	10.1896	0.774699	0.387349	+	0.921933i	$0.373391\pi$
$174$	−16.2467	−1.23166
$175$	8.42376	0.636776
$176$	−0.130403	−0.00982947
$177$	−25.4898	−1.91593
$178$	−6.87269	−0.515130
$179$	5.79627	0.433234	0.216617	−	0.976257i	$-0.430498\pi$
$179$	5.79627	0.433234	0.216617	+	0.976257i	$0.430498\pi$
$180$	−2.80914	−0.209381
$181$	17.8865	1.32950	0.664748	−	0.747067i	$-0.268539\pi$
$181$	17.8865	1.32950	0.664748	+	0.747067i	$0.268539\pi$
$182$	−0.470951	−0.0349092
$183$	16.1311	1.19244
$184$	2.35691	0.173754
$185$	12.6304	0.928602
$186$	−18.9407	−1.38880
$187$	0.00778794	0.000569511 0
$188$	−9.33195	−0.680603
$189$	4.79297	0.348637
$190$	−5.74005	−0.416427
$191$	17.7663	1.28552	0.642762	−	0.766066i	$-0.277789\pi$
$191$	17.7663	1.28552	0.642762	+	0.766066i	$0.277789\pi$
$192$	2.27345	0.164072
$193$	4.92689	0.354645	0.177323	−	0.984153i	$-0.443256\pi$
$193$	4.92689	0.354645	0.177323	+	0.984153i	$0.443256\pi$
$194$	6.52769	0.468661
$195$	0.546955	0.0391683
$196$	−0.570001	−0.0407144
$197$	14.5597	1.03733	0.518667	−	0.854977i	$-0.326429\pi$
$197$	14.5597	1.03733	0.518667	+	0.854977i	$0.326429\pi$
$198$	0.282790	0.0200970
$199$	−6.18992	−0.438792	−0.219396	−	0.975636i	$-0.570409\pi$
$199$	−6.18992	−0.438792	−0.219396	+	0.975636i	$0.570409\pi$
$200$	3.32201	0.234901
$201$	−4.86786	−0.343352
$202$	4.73117	0.332884
$203$	−18.1210	−1.27185
$204$	−0.135776	−0.00950621
$205$	8.73408	0.610015
$206$	−7.32999	−0.510705
$207$	−5.11119	−0.355252
$208$	−0.185725	−0.0128777
$209$	0.577839	0.0399700
$210$	−7.46770	−0.515320
$211$	−9.29319	−0.639770	−0.319885	−	0.947456i	$-0.603644\pi$
$211$	−9.29319	−0.639770	−0.319885	+	0.947456i	$0.603644\pi$
$212$	−8.64141	−0.593494
$213$	33.3400	2.28442
$214$	−16.1536	−1.10424
$215$	0.801554	0.0546655
$216$	1.89016	0.128609
$217$	−21.1259	−1.43412
$218$	−9.58293	−0.649038
$219$	−25.5899	−1.72921
$220$	0.168920	0.0113886
$221$	0.0110919	0.000746123 0
$222$	22.1670	1.48775
$223$	8.90555	0.596360	0.298180	−	0.954510i	$-0.403620\pi$
$223$	8.90555	0.596360	0.298180	+	0.954510i	$0.403620\pi$
$224$	2.53574	0.169427
$225$	−7.20408	−0.480272
$226$	−17.1386	−1.14005
$227$	−5.78561	−0.384004	−0.192002	−	0.981395i	$-0.561498\pi$
$227$	−5.78561	−0.384004	−0.192002	+	0.981395i	$0.561498\pi$
$228$	−10.0741	−0.667174
$229$	−12.6946	−0.838882	−0.419441	−	0.907783i	$-0.637774\pi$
$229$	−12.6946	−0.838882	−0.419441	+	0.907783i	$0.637774\pi$
$230$	−3.05308	−0.201314
$231$	0.751758	0.0494621
$232$	−7.14624	−0.469174
$233$	18.1472	1.18886	0.594430	−	0.804148i	$-0.297378\pi$
$233$	18.1472	1.18886	0.594430	+	0.804148i	$0.297378\pi$
$234$	0.402762	0.0263294
$235$	12.0884	0.788558
$236$	−11.2119	−0.729833
$237$	−29.2911	−1.90266
$238$	−0.151440	−0.00981643
$239$	−16.9046	−1.09347	−0.546734	−	0.837306i	$-0.684129\pi$
$239$	−16.9046	−1.09347	−0.546734	+	0.837306i	$0.684129\pi$
$240$	−2.94497	−0.190097
$241$	13.4296	0.865079	0.432540	−	0.901615i	$-0.357618\pi$
$241$	13.4296	0.865079	0.432540	+	0.901615i	$0.357618\pi$
$242$	10.9830	0.706014
$243$	−18.8896	−1.21177
$244$	7.09541	0.454237
$245$	0.738365	0.0471724
$246$	15.3288	0.977329
$247$	0.822983	0.0523651
$248$	−8.33125	−0.529035
$249$	2.62618	0.166427
$250$	−10.7801	−0.681794
$251$	−15.2054	−0.959755	−0.479877	−	0.877336i	$-0.659319\pi$
$251$	−15.2054	−0.959755	−0.479877	+	0.877336i	$0.659319\pi$
$252$	−5.49900	−0.346405
$253$	0.307348	0.0193228
$254$	11.3389	0.711466
$255$	0.175881	0.0110141
$256$	1.00000	0.0625000
$257$	−14.3746	−0.896661	−0.448331	−	0.893868i	$-0.647981\pi$
$257$	−14.3746	−0.896661	−0.448331	+	0.893868i	$0.647981\pi$
$258$	1.40677	0.0875818
$259$	24.7244	1.53630
$260$	0.240583	0.0149203
$261$	15.4973	0.959259
$262$	−20.4969	−1.26630
$263$	2.03908	0.125735	0.0628674	−	0.998022i	$-0.479975\pi$
$263$	2.03908	0.125735	0.0628674	+	0.998022i	$0.479975\pi$
$264$	0.296464	0.0182461
$265$	11.1939	0.687633
$266$	−11.2364	−0.688946
$267$	15.6247	0.956219
$268$	−2.14117	−0.130793
$269$	9.55225	0.582411	0.291206	−	0.956660i	$-0.405944\pi$
$269$	9.55225	0.582411	0.291206	+	0.956660i	$0.405944\pi$
$270$	−2.44847	−0.149009
$271$	8.82342	0.535985	0.267992	−	0.963421i	$-0.413640\pi$
$271$	8.82342	0.535985	0.267992	+	0.963421i	$0.413640\pi$
$272$	−0.0597223	−0.00362120
$273$	1.07069	0.0648008
$274$	−7.11331	−0.429731
$275$	0.433198	0.0261228
$276$	−5.35833	−0.322534
$277$	−1.29172	−0.0776121	−0.0388060	−	0.999247i	$-0.512355\pi$
$277$	−1.29172	−0.0776121	−0.0388060	+	0.999247i	$0.512355\pi$
$278$	16.5254	0.991130
$279$	18.0671	1.08165
$280$	−3.28474	−0.196301
$281$	−17.6376	−1.05217	−0.526084	−	0.850432i	$-0.676340\pi$
$281$	−17.6376	−1.05217	−0.526084	+	0.850432i	$0.676340\pi$
$282$	21.2158	1.26338
$283$	14.5869	0.867103	0.433552	−	0.901129i	$-0.357260\pi$
$283$	14.5869	0.867103	0.433552	+	0.901129i	$0.357260\pi$
$284$	14.6649	0.870203
$285$	13.0497	0.773000
$286$	−0.0242190	−0.00143210
$287$	17.0973	1.00922
$288$	−2.16859	−0.127786
$289$	−16.9964	−0.999790
$290$	9.25706	0.543593
$291$	−14.8404	−0.869960
$292$	−11.2560	−0.658705
$293$	−26.6094	−1.55454	−0.777268	−	0.629170i	$-0.783395\pi$
$293$	−26.6094	−1.55454	−0.777268	+	0.629170i	$0.783395\pi$
$294$	1.29587	0.0755767
$295$	14.5236	0.845598
$296$	9.75035	0.566728
$297$	0.246482	0.0143023
$298$	17.8938	1.03656
$299$	0.437738	0.0253150
$300$	−7.55243	−0.436040
$301$	1.56907	0.0904399
$302$	−18.8242	−1.08321
$303$	−10.7561	−0.617921
$304$	−4.43119	−0.254146
$305$	−9.19121	−0.526287
$306$	0.129513	0.00740379
$307$	−2.54566	−0.145289	−0.0726443	−	0.997358i	$-0.523144\pi$
$307$	−2.54566	−0.145289	−0.0726443	+	0.997358i	$0.523144\pi$
$308$	0.330668	0.0188415
$309$	16.6644	0.948005
$310$	10.7921	0.612949
$311$	8.64313	0.490107	0.245053	−	0.969510i	$-0.421194\pi$
$311$	8.64313	0.490107	0.245053	+	0.969510i	$0.421194\pi$
$312$	0.422237	0.0239045
$313$	−17.0889	−0.965919	−0.482960	−	0.875643i	$-0.660438\pi$
$313$	−17.0889	−0.965919	−0.482960	+	0.875643i	$0.660438\pi$
$314$	−0.407105	−0.0229743
$315$	7.12326	0.401350
$316$	−12.8840	−0.724780
$317$	−3.58865	−0.201559	−0.100779	−	0.994909i	$-0.532134\pi$
$317$	−3.58865	−0.201559	−0.100779	+	0.994909i	$0.532134\pi$
$318$	19.6458	1.10168
$319$	−0.931889	−0.0521758
$320$	−1.29537	−0.0724136
$321$	36.7244	2.04976
$322$	−5.97653	−0.333059
$323$	0.264641	0.0147250
$324$	−10.8030	−0.600166
$325$	0.616979	0.0342239
$326$	22.4759	1.24482
$327$	21.7863	1.20479
$328$	6.74252	0.372293
$329$	23.6634	1.30461
$330$	−0.384032	−0.0211403
$331$	−18.0837	−0.993971	−0.496985	−	0.867759i	$-0.665560\pi$
$331$	−18.0837	−0.993971	−0.496985	+	0.867759i	$0.665560\pi$
$332$	1.15515	0.0633971
$333$	−21.1446	−1.15871
$334$	8.16941	0.447010
$335$	2.77362	0.151539
$336$	−5.76490	−0.314501
$337$	18.2806	0.995806	0.497903	−	0.867233i	$-0.334104\pi$
$337$	18.2806	0.995806	0.497903	+	0.867233i	$0.334104\pi$
$338$	12.9655	0.705231
$339$	38.9639	2.11623
$340$	0.0773627	0.00419558
$341$	−1.08642	−0.0588328
$342$	9.60945	0.519620
$343$	19.1956	1.03646
$344$	0.618782	0.0333625
$345$	6.94105	0.373693
$346$	−10.1896	−0.547795
$347$	35.1213	1.88541	0.942706	−	0.333625i	$-0.108272\pi$
$347$	35.1213	1.88541	0.942706	+	0.333625i	$0.108272\pi$
$348$	16.2467	0.870912
$349$	22.9927	1.23077	0.615386	−	0.788226i	$-0.289000\pi$
$349$	22.9927	1.23077	0.615386	+	0.788226i	$0.289000\pi$
$350$	−8.42376	−0.450269
$351$	0.351050	0.0187377
$352$	0.130403	0.00695048
$353$	−8.26524	−0.439914	−0.219957	−	0.975510i	$-0.570592\pi$
$353$	−8.26524	−0.439914	−0.219957	+	0.975510i	$0.570592\pi$
$354$	25.4898	1.35477
$355$	−18.9966	−1.00823
$356$	6.87269	0.364252
$357$	0.344293	0.0182219
$358$	−5.79627	−0.306342
$359$	4.53500	0.239348	0.119674	−	0.992813i	$-0.461815\pi$
$359$	4.53500	0.239348	0.119674	+	0.992813i	$0.461815\pi$
$360$	2.80914	0.148055
$361$	0.635441	0.0334443
$362$	−17.8865	−0.940096
$363$	−24.9693	−1.31055
$364$	0.470951	0.0246845
$365$	14.5807	0.763187
$366$	−16.1311	−0.843185
$367$	−30.5542	−1.59492	−0.797458	−	0.603374i	$-0.793822\pi$
$367$	−30.5542	−1.59492	−0.797458	+	0.603374i	$0.793822\pi$
$368$	−2.35691	−0.122863
$369$	−14.6218	−0.761180
$370$	−12.6304	−0.656621
$371$	21.9124	1.13764
$372$	18.9407	0.982030
$373$	−13.6940	−0.709049	−0.354524	−	0.935047i	$-0.615357\pi$
$373$	−13.6940	−0.709049	−0.354524	+	0.935047i	$0.615357\pi$
$374$	−0.00778794	−0.000402705 0
$375$	24.5081	1.26559
$376$	9.33195	0.481259
$377$	−1.32724	−0.0683561
$378$	−4.79297	−0.246524
$379$	11.2087	0.575751	0.287876	−	0.957668i	$-0.407051\pi$
$379$	11.2087	0.575751	0.287876	+	0.957668i	$0.407051\pi$
$380$	5.74005	0.294458
$381$	−25.7785	−1.32067
$382$	−17.7663	−0.909002
$383$	16.4097	0.838498	0.419249	−	0.907871i	$-0.362293\pi$
$383$	16.4097	0.838498	0.419249	+	0.907871i	$0.362293\pi$
$384$	−2.27345	−0.116017
$385$	−0.428339	−0.0218302
$386$	−4.92689	−0.250772
$387$	−1.34189	−0.0682120
$388$	−6.52769	−0.331393
$389$	36.3036	1.84067	0.920334	−	0.391134i	$-0.127917\pi$
$389$	36.3036	1.84067	0.920334	+	0.391134i	$0.127917\pi$
$390$	−0.546955	−0.0276962
$391$	0.140760	0.00711855
$392$	0.570001	0.0287894
$393$	46.5987	2.35060
$394$	−14.5597	−0.733505
$395$	16.6896	0.839743
$396$	−0.282790	−0.0142108
$397$	−33.5693	−1.68480	−0.842398	−	0.538856i	$-0.818857\pi$
$397$	−33.5693	−1.68480	−0.842398	+	0.538856i	$0.818857\pi$
$398$	6.18992	0.310273
$399$	25.5454	1.27887
$400$	−3.32201	−0.166100
$401$	−12.8228	−0.640340	−0.320170	−	0.947360i	$-0.603740\pi$
$401$	−12.8228	−0.640340	−0.320170	+	0.947360i	$0.603740\pi$
$402$	4.86786	0.242787
$403$	−1.54732	−0.0770775
$404$	−4.73117	−0.235384
$405$	13.9939	0.695363
$406$	18.1210	0.899332
$407$	1.27147	0.0630245
$408$	0.135776	0.00672191
$409$	17.2395	0.852440	0.426220	−	0.904619i	$-0.359845\pi$
$409$	17.2395	0.852440	0.426220	+	0.904619i	$0.359845\pi$
$410$	−8.73408	−0.431346
$411$	16.1718	0.797696
$412$	7.32999	0.361123
$413$	28.4305	1.39898
$414$	5.11119	0.251201
$415$	−1.49635	−0.0734530
$416$	0.185725	0.00910592
$417$	−37.5698	−1.83980
$418$	−0.577839	−0.0282630
$419$	40.3102	1.96928	0.984641	−	0.174589i	$-0.0558595\pi$
$419$	40.3102	1.96928	0.984641	+	0.174589i	$0.0558595\pi$
$420$	7.46770	0.364387
$421$	29.7857	1.45167	0.725834	−	0.687870i	$-0.241454\pi$
$421$	29.7857	1.45167	0.725834	+	0.687870i	$0.241454\pi$
$422$	9.29319	0.452386
$423$	−20.2372	−0.983968
$424$	8.64141	0.419664
$425$	0.198398	0.00962370
$426$	−33.3400	−1.61533
$427$	−17.9921	−0.870701
$428$	16.1536	0.780812
$429$	0.0550609	0.00265836
$430$	−0.801554	−0.0386544
$431$	26.3225	1.26791	0.633955	−	0.773370i	$-0.281431\pi$
$431$	26.3225	1.26791	0.633955	+	0.773370i	$0.281431\pi$
$432$	−1.89016	−0.0909405
$433$	26.1462	1.25650	0.628252	−	0.778010i	$-0.283771\pi$
$433$	26.1462	1.25650	0.628252	+	0.778010i	$0.283771\pi$
$434$	21.1259	1.01408
$435$	−21.0455	−1.00905
$436$	9.58293	0.458939
$437$	10.4439	0.499601
$438$	25.5899	1.22273
$439$	−6.02361	−0.287491	−0.143746	−	0.989615i	$-0.545915\pi$
$439$	−6.02361	−0.287491	−0.143746	+	0.989615i	$0.545915\pi$
$440$	−0.168920	−0.00805296
$441$	−1.23610	−0.0588619
$442$	−0.0110919	−0.000527589 0
$443$	−35.0847	−1.66692	−0.833462	−	0.552576i	$-0.813645\pi$
$443$	−35.0847	−1.66692	−0.833462	+	0.552576i	$0.813645\pi$
$444$	−22.1670	−1.05200
$445$	−8.90270	−0.422029
$446$	−8.90555	−0.421690
$447$	−40.6807	−1.92413
$448$	−2.53574	−0.119803
$449$	−14.2296	−0.671538	−0.335769	−	0.941944i	$-0.608996\pi$
$449$	−14.2296	−0.671538	−0.335769	+	0.941944i	$0.608996\pi$
$450$	7.20408	0.339604
$451$	0.879242	0.0414019
$452$	17.1386	0.806134
$453$	42.7961	2.01073
$454$	5.78561	0.271532
$455$	−0.610058	−0.0286000
$456$	10.0741	0.471763
$457$	−4.32660	−0.202390	−0.101195	−	0.994867i	$-0.532267\pi$
$457$	−4.32660	−0.202390	−0.101195	+	0.994867i	$0.532267\pi$
$458$	12.6946	0.593179
$459$	0.112885	0.00526901
$460$	3.05308	0.142351
$461$	−16.1118	−0.750400	−0.375200	−	0.926944i	$-0.622426\pi$
$461$	−16.1118	−0.750400	−0.375200	+	0.926944i	$0.622426\pi$
$462$	−0.751758	−0.0349750
$463$	8.27134	0.384402	0.192201	−	0.981356i	$-0.438438\pi$
$463$	8.27134	0.384402	0.192201	+	0.981356i	$0.438438\pi$
$464$	7.14624	0.331756
$465$	−24.5353	−1.13780
$466$	−18.1472	−0.840651
$467$	−9.25175	−0.428120	−0.214060	−	0.976821i	$-0.568669\pi$
$467$	−9.25175	−0.428120	−0.214060	+	0.976821i	$0.568669\pi$
$468$	−0.402762	−0.0186177
$469$	5.42946	0.250709
$470$	−12.0884	−0.557595
$471$	0.925535	0.0426464
$472$	11.2119	0.516070
$473$	0.0806908	0.00371017
$474$	29.2911	1.34539
$475$	14.7204	0.675420
$476$	0.151440	0.00694126
$477$	−18.7397	−0.858032
$478$	16.9046	0.773199
$479$	23.2797	1.06368	0.531839	−	0.846845i	$-0.321501\pi$
$479$	23.2797	1.06368	0.531839	+	0.846845i	$0.321501\pi$
$480$	2.94497	0.134419
$481$	1.81088	0.0825692
$482$	−13.4296	−0.611703
$483$	13.5874	0.618246
$484$	−10.9830	−0.499227
$485$	8.45580	0.383958
$486$	18.8896	0.856850
$487$	9.15437	0.414824	0.207412	−	0.978254i	$-0.433496\pi$
$487$	9.15437	0.414824	0.207412	+	0.978254i	$0.433496\pi$
$488$	−7.09541	−0.321194
$489$	−51.0979	−2.31073
$490$	−0.738365	−0.0333559
$491$	20.8618	0.941480	0.470740	−	0.882272i	$-0.343987\pi$
$491$	20.8618	0.941480	0.470740	+	0.882272i	$0.343987\pi$
$492$	−15.3288	−0.691076
$493$	−0.426790	−0.0192217
$494$	−0.822983	−0.0370277
$495$	0.366319	0.0164648
$496$	8.33125	0.374084
$497$	−37.1865	−1.66804
$498$	−2.62618	−0.117682
$499$	−43.7208	−1.95721	−0.978606	−	0.205744i	$-0.934039\pi$
$499$	−43.7208	−1.95721	−0.978606	+	0.205744i	$0.934039\pi$
$500$	10.7801	0.482101
$501$	−18.5728	−0.829770
$502$	15.2054	0.678649
$503$	11.1745	0.498246	0.249123	−	0.968472i	$-0.419858\pi$
$503$	11.1745	0.498246	0.249123	+	0.968472i	$0.419858\pi$
$504$	5.49900	0.244945
$505$	6.12863	0.272721
$506$	−0.307348	−0.0136633
$507$	−29.4765	−1.30910
$508$	−11.3389	−0.503083
$509$	−40.5301	−1.79646	−0.898232	−	0.439522i	$-0.855148\pi$
$509$	−40.5301	−1.79646	−0.898232	+	0.439522i	$0.855148\pi$
$510$	−0.175881	−0.00778812
$511$	28.5422	1.26263
$512$	−1.00000	−0.0441942
$513$	8.37567	0.369795
$514$	14.3746	0.634035
$515$	−9.49508	−0.418403
$516$	−1.40677	−0.0619297
$517$	1.21691	0.0535197
$518$	−24.7244	−1.08633
$519$	23.1655	1.01685
$520$	−0.240583	−0.0105503
$521$	−24.0520	−1.05374	−0.526869	−	0.849947i	$-0.676634\pi$
$521$	−24.0520	−1.05374	−0.526869	+	0.849947i	$0.676634\pi$
$522$	−15.4973	−0.678299
$523$	5.69976	0.249233	0.124617	−	0.992205i	$-0.460230\pi$
$523$	5.69976	0.249233	0.124617	+	0.992205i	$0.460230\pi$
$524$	20.4969	0.895411
$525$	19.1510	0.835819
$526$	−2.03908	−0.0889080
$527$	−0.497561	−0.0216741
$528$	−0.296464	−0.0129020
$529$	−17.4450	−0.758477
$530$	−11.1939	−0.486230
$531$	−24.3141	−1.05514
$532$	11.2364	0.487158
$533$	1.25225	0.0542411
$534$	−15.6247	−0.676149
$535$	−20.9249	−0.904663
$536$	2.14117	0.0924845
$537$	13.1776	0.568654
$538$	−9.55225	−0.411827
$539$	0.0743296	0.00320160
$540$	2.44847	0.105365
$541$	10.8421	0.466139	0.233070	−	0.972460i	$-0.425123\pi$
$541$	10.8421	0.466139	0.233070	+	0.972460i	$0.425123\pi$
$542$	−8.82342	−0.378998
$543$	40.6642	1.74507
$544$	0.0597223	0.00256057
$545$	−12.4135	−0.531735
$546$	−1.07069	−0.0458211
$547$	−33.6410	−1.43838	−0.719192	−	0.694812i	$-0.755488\pi$
$547$	−33.6410	−1.43838	−0.719192	+	0.694812i	$0.755488\pi$
$548$	7.11331	0.303866
$549$	15.3871	0.656704
$550$	−0.433198	−0.0184716
$551$	−31.6664	−1.34903
$552$	5.35833	0.228066
$553$	32.6704	1.38929
$554$	1.29172	0.0548800
$555$	28.7145	1.21886
$556$	−16.5254	−0.700835
$557$	−18.0383	−0.764306	−0.382153	−	0.924099i	$-0.624817\pi$
$557$	−18.0383	−0.764306	−0.382153	+	0.924099i	$0.624817\pi$
$558$	−18.0671	−0.764841
$559$	0.114923	0.00486074
$560$	3.28474	0.138806
$561$	0.0177055	0.000747528 0
$562$	17.6376	0.743996
$563$	32.4494	1.36758	0.683789	−	0.729680i	$-0.260331\pi$
$563$	32.4494	1.36758	0.683789	+	0.729680i	$0.260331\pi$
$564$	−21.2158	−0.893345
$565$	−22.2010	−0.934002
$566$	−14.5869	−0.613135
$567$	27.3936	1.15042
$568$	−14.6649	−0.615326
$569$	8.65846	0.362982	0.181491	−	0.983393i	$-0.441908\pi$
$569$	8.65846	0.362982	0.181491	+	0.983393i	$0.441908\pi$
$570$	−13.0497	−0.546593
$571$	−3.32351	−0.139084	−0.0695422	−	0.997579i	$-0.522154\pi$
$571$	−3.32351	−0.139084	−0.0695422	+	0.997579i	$0.522154\pi$
$572$	0.0242190	0.00101265
$573$	40.3908	1.68735
$574$	−17.0973	−0.713627
$575$	7.82968	0.326520
$576$	2.16859	0.0903581
$577$	−3.72070	−0.154895	−0.0774473	−	0.996996i	$-0.524677\pi$
$577$	−3.72070	−0.154895	−0.0774473	+	0.996996i	$0.524677\pi$
$578$	16.9964	0.706958
$579$	11.2011	0.465500
$580$	−9.25706	−0.384378
$581$	−2.92916	−0.121522
$582$	14.8404	0.615155
$583$	1.12686	0.0466699
$584$	11.2560	0.465775
$585$	0.521728	0.0215708
$586$	26.6094	1.09922
$587$	−41.6665	−1.71976	−0.859880	−	0.510496i	$-0.829462\pi$
$587$	−41.6665	−1.71976	−0.859880	+	0.510496i	$0.829462\pi$
$588$	−1.29587	−0.0534408
$589$	−36.9173	−1.52115
$590$	−14.5236	−0.597928
$591$	33.1007	1.36158
$592$	−9.75035	−0.400737
$593$	−35.2490	−1.44750	−0.723751	−	0.690062i	$-0.757583\pi$
$593$	−35.2490	−1.44750	−0.723751	+	0.690062i	$0.757583\pi$
$594$	−0.246482	−0.0101133
$595$	−0.196172	−0.00804227
$596$	−17.8938	−0.732958
$597$	−14.0725	−0.575949
$598$	−0.437738	−0.0179004
$599$	9.87582	0.403515	0.201758	−	0.979435i	$-0.435335\pi$
$599$	9.87582	0.403515	0.201758	+	0.979435i	$0.435335\pi$
$600$	7.55243	0.308327
$601$	−23.5286	−0.959753	−0.479876	−	0.877336i	$-0.659319\pi$
$601$	−23.5286	−0.959753	−0.479876	+	0.877336i	$0.659319\pi$
$602$	−1.56907	−0.0639506
$603$	−4.64333	−0.189091
$604$	18.8242	0.765948
$605$	14.2271	0.578413
$606$	10.7561	0.436936
$607$	32.8147	1.33191	0.665954	−	0.745993i	$-0.268025\pi$
$607$	32.8147	1.33191	0.665954	+	0.745993i	$0.268025\pi$
$608$	4.43119	0.179708
$609$	−41.1974	−1.66940
$610$	9.19121	0.372141
$611$	1.73318	0.0701168
$612$	−0.129513	−0.00523527
$613$	4.92010	0.198721	0.0993605	−	0.995052i	$-0.468320\pi$
$613$	4.92010	0.198721	0.0993605	+	0.995052i	$0.468320\pi$
$614$	2.54566	0.102735
$615$	19.8565	0.800693
$616$	−0.330668	−0.0133230
$617$	20.6490	0.831298	0.415649	−	0.909525i	$-0.363554\pi$
$617$	20.6490	0.831298	0.415649	+	0.909525i	$0.363554\pi$
$618$	−16.6644	−0.670341
$619$	−0.0386946	−0.00155527	−0.000777633	−	1.00000i	$-0.500248\pi$
$619$	−0.0386946	−0.00155527	−0.000777633		1.00000i	$0.500248\pi$
$620$	−10.7921	−0.433420
$621$	4.45495	0.178771
$622$	−8.64313	−0.346558
$623$	−17.4274	−0.698213
$624$	−0.422237	−0.0169030
$625$	2.64575	0.105830
$626$	17.0889	0.683008
$627$	1.31369	0.0524637
$628$	0.407105	0.0162453
$629$	0.582313	0.0232183
$630$	−7.12326	−0.283798
$631$	−23.6083	−0.939833	−0.469917	−	0.882711i	$-0.655716\pi$
$631$	−23.6083	−0.939833	−0.469917	+	0.882711i	$0.655716\pi$
$632$	12.8840	0.512497
$633$	−21.1277	−0.839749
$634$	3.58865	0.142524
$635$	14.6881	0.582881
$636$	−19.6458	−0.779009
$637$	0.105863	0.00419446
$638$	0.931889	0.0368938
$639$	31.8023	1.25808
$640$	1.29537	0.0512042
$641$	−41.0542	−1.62154	−0.810771	−	0.585363i	$-0.800952\pi$
$641$	−41.0542	−1.62154	−0.810771	+	0.585363i	$0.800952\pi$
$642$	−36.7244	−1.44940
$643$	−7.48359	−0.295124	−0.147562	−	0.989053i	$-0.547143\pi$
$643$	−7.48359	−0.295124	−0.147562	+	0.989053i	$0.547143\pi$
$644$	5.97653	0.235508
$645$	1.82230	0.0717529
$646$	−0.264641	−0.0104122
$647$	38.4914	1.51325	0.756626	−	0.653847i	$-0.226846\pi$
$647$	38.4914	1.51325	0.756626	+	0.653847i	$0.226846\pi$
$648$	10.8030	0.424381
$649$	1.46206	0.0573910
$650$	−0.616979	−0.0241999
$651$	−48.0288	−1.88240
$652$	−22.4759	−0.880224
$653$	6.07190	0.237612	0.118806	−	0.992918i	$-0.462093\pi$
$653$	6.07190	0.237612	0.118806	+	0.992918i	$0.462093\pi$
$654$	−21.7863	−0.851913
$655$	−26.5511	−1.03744
$656$	−6.74252	−0.263251
$657$	−24.4096	−0.952309
$658$	−23.6634	−0.922497
$659$	−28.8523	−1.12392	−0.561962	−	0.827163i	$-0.689953\pi$
$659$	−28.8523	−1.12392	−0.561962	+	0.827163i	$0.689953\pi$
$660$	0.384032	0.0149484
$661$	3.15864	0.122857	0.0614284	−	0.998111i	$-0.480434\pi$
$661$	3.15864	0.122857	0.0614284	+	0.998111i	$0.480434\pi$
$662$	18.0837	0.702843
$663$	0.0252170	0.000979346 0
$664$	−1.15515	−0.0448285
$665$	−14.5553	−0.564430
$666$	21.1446	0.819335
$667$	−16.8431	−0.652166
$668$	−8.16941	−0.316084
$669$	20.2464	0.782770
$670$	−2.77362	−0.107154
$671$	−0.925260	−0.0357193
$672$	5.76490	0.222386
$673$	6.83610	0.263512	0.131756	−	0.991282i	$-0.457938\pi$
$673$	6.83610	0.263512	0.131756	+	0.991282i	$0.457938\pi$
$674$	−18.2806	−0.704141
$675$	6.27913	0.241684
$676$	−12.9655	−0.498673
$677$	0.172947	0.00664691	0.00332345	−	0.999994i	$-0.498942\pi$
$677$	0.172947	0.00664691	0.00332345	+	0.999994i	$0.498942\pi$
$678$	−38.9639	−1.49640
$679$	16.5526	0.635229
$680$	−0.0773627	−0.00296672
$681$	−13.1533	−0.504036
$682$	1.08642	0.0416010
$683$	13.8386	0.529520	0.264760	−	0.964314i	$-0.414707\pi$
$683$	13.8386	0.529520	0.264760	+	0.964314i	$0.414707\pi$
$684$	−9.60945	−0.367427
$685$	−9.21440	−0.352064
$686$	−19.1956	−0.732891
$687$	−28.8606	−1.10110
$688$	−0.618782	−0.0235908
$689$	1.60493	0.0611428
$690$	−6.94105	−0.264241
$691$	−4.86979	−0.185256	−0.0926279	−	0.995701i	$-0.529527\pi$
$691$	−4.86979	−0.185256	−0.0926279	+	0.995701i	$0.529527\pi$
$692$	10.1896	0.387349
$693$	0.717084	0.0272398
$694$	−35.1213	−1.33319
$695$	21.4066	0.812000
$696$	−16.2467	−0.615828
$697$	0.402678	0.0152525
$698$	−22.9927	−0.870288
$699$	41.2567	1.56047
$700$	8.42376	0.318388
$701$	10.2925	0.388742	0.194371	−	0.980928i	$-0.437733\pi$
$701$	10.2925	0.388742	0.194371	+	0.980928i	$0.437733\pi$
$702$	−0.351050	−0.0132495
$703$	43.2056	1.62953
$704$	−0.130403	−0.00491473
$705$	27.4824	1.03505
$706$	8.26524	0.311066
$707$	11.9970	0.451195
$708$	−25.4898	−0.957964
$709$	−16.1652	−0.607097	−0.303548	−	0.952816i	$-0.598171\pi$
$709$	−16.1652	−0.607097	−0.303548	+	0.952816i	$0.598171\pi$
$710$	18.9966	0.712928
$711$	−27.9401	−1.04784
$712$	−6.87269	−0.257565
$713$	−19.6360	−0.735375
$714$	−0.344293	−0.0128848
$715$	−0.0313727	−0.00117327
$716$	5.79627	0.216617
$717$	−38.4319	−1.43526
$718$	−4.53500	−0.169245
$719$	30.1623	1.12487	0.562433	−	0.826843i	$-0.309865\pi$
$719$	30.1623	1.12487	0.562433	+	0.826843i	$0.309865\pi$
$720$	−2.80914	−0.104691
$721$	−18.5870	−0.692216
$722$	−0.635441	−0.0236487
$723$	30.5317	1.13549
$724$	17.8865	0.664748
$725$	−23.7399	−0.881676
$726$	24.9693	0.926699
$727$	−44.1102	−1.63596	−0.817979	−	0.575249i	$-0.804905\pi$
$727$	−44.1102	−1.63596	−0.817979	+	0.575249i	$0.804905\pi$
$728$	−0.470951	−0.0174546
$729$	−10.5357	−0.390211
$730$	−14.5807	−0.539655
$731$	0.0369551	0.00136683
$732$	16.1311	0.596222
$733$	−39.0332	−1.44173	−0.720863	−	0.693078i	$-0.756254\pi$
$733$	−39.0332	−1.44173	−0.720863	+	0.693078i	$0.756254\pi$
$734$	30.5542	1.12778
$735$	1.67864	0.0619175
$736$	2.35691	0.0868769
$737$	0.279214	0.0102850
$738$	14.6218	0.538235
$739$	20.4307	0.751555	0.375778	−	0.926710i	$-0.377376\pi$
$739$	20.4307	0.751555	0.375778	+	0.926710i	$0.377376\pi$
$740$	12.6304	0.464301
$741$	1.87101	0.0687334
$742$	−21.9124	−0.804430
$743$	15.7493	0.577787	0.288893	−	0.957361i	$-0.406713\pi$
$743$	15.7493	0.577787	0.288893	+	0.957361i	$0.406713\pi$
$744$	−18.9407	−0.694400
$745$	23.1791	0.849218
$746$	13.6940	0.501373
$747$	2.50505	0.0916551
$748$	0.00778794	0.000284755 0
$749$	−40.9613	−1.49669
$750$	−24.5081	−0.894909
$751$	−1.00000	−0.0364905
$751$	−1.00000	−0.0364905
$752$	−9.33195	−0.340301
$753$	−34.5687	−1.25975
$754$	1.32724	0.0483351
$755$	−24.3844	−0.887441
$756$	4.79297	0.174319
$757$	−21.8653	−0.794709	−0.397354	−	0.917665i	$-0.630072\pi$
$757$	−21.8653	−0.794709	−0.397354	+	0.917665i	$0.630072\pi$
$758$	−11.2087	−0.407118
$759$	0.698741	0.0253627
$760$	−5.74005	−0.208213
$761$	−43.4144	−1.57377	−0.786885	−	0.617100i	$-0.788307\pi$
$761$	−43.4144	−1.57377	−0.786885	+	0.617100i	$0.788307\pi$
$762$	25.7785	0.933856
$763$	−24.2998	−0.879714
$764$	17.7663	0.642762
$765$	0.167768	0.00606568
$766$	−16.4097	−0.592908
$767$	2.08233	0.0751886
$768$	2.27345	0.0820362
$769$	40.5922	1.46379	0.731895	−	0.681417i	$-0.238636\pi$
$769$	40.5922	1.46379	0.731895	+	0.681417i	$0.238636\pi$
$770$	0.428339	0.0154362
$771$	−32.6799	−1.17694
$772$	4.92689	0.177323
$773$	−19.5153	−0.701916	−0.350958	−	0.936391i	$-0.614144\pi$
$773$	−19.5153	−0.701916	−0.350958	+	0.936391i	$0.614144\pi$
$774$	1.34189	0.0482331
$775$	−27.6764	−0.994167
$776$	6.52769	0.234330
$777$	56.2098	2.01651
$778$	−36.3036	−1.30155
$779$	29.8774	1.07047
$780$	0.546955	0.0195841
$781$	−1.91234	−0.0684290
$782$	−0.140760	−0.00503357
$783$	−13.5076	−0.482721
$784$	−0.570001	−0.0203572
$785$	−0.527354	−0.0188221
$786$	−46.5987	−1.66212
$787$	47.1561	1.68094	0.840468	−	0.541862i	$-0.182280\pi$
$787$	47.1561	1.68094	0.840468	+	0.541862i	$0.182280\pi$
$788$	14.5597	0.518667
$789$	4.63575	0.165037
$790$	−16.6896	−0.593788
$791$	−43.4592	−1.54523
$792$	0.282790	0.0100485
$793$	−1.31779	−0.0467962
$794$	33.5693	1.19133
$795$	25.4487	0.902573
$796$	−6.18992	−0.219396
$797$	−23.9240	−0.847431	−0.423715	−	0.905795i	$-0.639274\pi$
$797$	−23.9240	−0.847431	−0.423715	+	0.905795i	$0.639274\pi$
$798$	−25.5454	−0.904296
$799$	0.557326	0.0197168
$800$	3.32201	0.117451
$801$	14.9041	0.526609
$802$	12.8228	0.452789
$803$	1.46781	0.0517978
$804$	−4.86786	−0.171676
$805$	−7.74184	−0.272864
$806$	1.54732	0.0545020
$807$	21.7166	0.764461
$808$	4.73117	0.166442
$809$	−21.4385	−0.753739	−0.376869	−	0.926266i	$-0.622999\pi$
$809$	−21.4385	−0.753739	−0.376869	+	0.926266i	$0.622999\pi$
$810$	−13.9939	−0.491696
$811$	42.3509	1.48714	0.743571	−	0.668657i	$-0.233131\pi$
$811$	42.3509	1.48714	0.743571	+	0.668657i	$0.233131\pi$
$812$	−18.1210	−0.635924
$813$	20.0596	0.703522
$814$	−1.27147	−0.0445651
$815$	29.1147	1.01984
$816$	−0.135776	−0.00475311
$817$	2.74194	0.0959283
$818$	−17.2395	−0.602766
$819$	1.02130	0.0356872
$820$	8.73408	0.305007
$821$	−23.0054	−0.802895	−0.401448	−	0.915882i	$-0.631493\pi$
$821$	−23.0054	−0.802895	−0.401448	+	0.915882i	$0.631493\pi$
$822$	−16.1718	−0.564056
$823$	9.56777	0.333511	0.166756	−	0.985998i	$-0.446671\pi$
$823$	9.56777	0.333511	0.166756	+	0.985998i	$0.446671\pi$
$824$	−7.32999	−0.255352
$825$	0.984857	0.0342883
$826$	−28.4305	−0.989225
$827$	15.6581	0.544487	0.272243	−	0.962228i	$-0.412234\pi$
$827$	15.6581	0.544487	0.272243	+	0.962228i	$0.412234\pi$
$828$	−5.11119	−0.177626
$829$	−11.7239	−0.407187	−0.203594	−	0.979055i	$-0.565262\pi$
$829$	−11.7239	−0.407187	−0.203594	+	0.979055i	$0.565262\pi$
$830$	1.49635	0.0519391
$831$	−2.93667	−0.101872
$832$	−0.185725	−0.00643885
$833$	0.0340418	0.00117948
$834$	37.5698	1.30094
$835$	10.5824	0.366220
$836$	0.577839	0.0199850
$837$	−15.7474	−0.544310
$838$	−40.3102	−1.39249
$839$	0.743555	0.0256704	0.0128352	−	0.999918i	$-0.495914\pi$
$839$	0.743555	0.0256704	0.0128352	+	0.999918i	$0.495914\pi$
$840$	−7.46770	−0.257660
$841$	22.0688	0.760993
$842$	−29.7857	−1.02648
$843$	−40.0982	−1.38105
$844$	−9.29319	−0.319885
$845$	16.7952	0.577772
$846$	20.2372	0.695770
$847$	27.8501	0.956940
$848$	−8.64141	−0.296747
$849$	33.1627	1.13814
$850$	−0.198398	−0.00680499
$851$	22.9807	0.787769
$852$	33.3400	1.14221
$853$	−41.0568	−1.40576	−0.702879	−	0.711309i	$-0.748102\pi$
$853$	−41.0568	−1.40576	−0.702879	+	0.711309i	$0.748102\pi$
$854$	17.9921	0.615678
$855$	12.4478	0.425707
$856$	−16.1536	−0.552118
$857$	−39.9038	−1.36309	−0.681543	−	0.731778i	$-0.738691\pi$
$857$	−39.9038	−1.36309	−0.681543	+	0.731778i	$0.738691\pi$
$858$	−0.0550609	−0.00187975
$859$	−37.9956	−1.29639	−0.648196	−	0.761473i	$-0.724476\pi$
$859$	−37.9956	−1.29639	−0.648196	+	0.761473i	$0.724476\pi$
$860$	0.801554	0.0273328
$861$	38.8699	1.32468
$862$	−26.3225	−0.896547
$863$	−38.6213	−1.31469	−0.657343	−	0.753592i	$-0.728320\pi$
$863$	−38.6213	−1.31469	−0.657343	+	0.753592i	$0.728320\pi$
$864$	1.89016	0.0643046
$865$	−13.1993	−0.448790
$866$	−26.1462	−0.888483
$867$	−38.6406	−1.31230
$868$	−21.1259	−0.717060
$869$	1.68010	0.0569936
$870$	21.0455	0.713509
$871$	0.397669	0.0134745
$872$	−9.58293	−0.324519
$873$	−14.1559	−0.479105
$874$	−10.4439	−0.353271
$875$	−27.3356	−0.924112
$876$	−25.5899	−0.864603
$877$	5.23050	0.176621	0.0883107	−	0.996093i	$-0.471853\pi$
$877$	5.23050	0.176621	0.0883107	+	0.996093i	$0.471853\pi$
$878$	6.02361	0.203287
$879$	−60.4952	−2.04045
$880$	0.168920	0.00569430
$881$	−55.8451	−1.88147	−0.940734	−	0.339145i	$-0.889862\pi$
$881$	−55.8451	−1.88147	−0.940734	+	0.339145i	$0.889862\pi$
$882$	1.23610	0.0416217
$883$	37.1788	1.25117	0.625583	−	0.780158i	$-0.284861\pi$
$883$	37.1788	1.25117	0.625583	+	0.780158i	$0.284861\pi$
$884$	0.0110919	0.000373062 0
$885$	33.0188	1.10991
$886$	35.0847	1.17869
$887$	39.7068	1.33322	0.666612	−	0.745405i	$-0.267744\pi$
$887$	39.7068	1.33322	0.666612	+	0.745405i	$0.267744\pi$
$888$	22.1670	0.743875
$889$	28.7526	0.964330
$890$	8.90270	0.298419
$891$	1.40874	0.0471945
$892$	8.90555	0.298180
$893$	41.3517	1.38378
$894$	40.6807	1.36057
$895$	−7.50834	−0.250976
$896$	2.53574	0.0847133
$897$	0.995176	0.0332280
$898$	14.2296	0.474849
$899$	59.5371	1.98567
$900$	−7.20408	−0.240136
$901$	0.516085	0.0171933
$902$	−0.879242	−0.0292756
$903$	3.56722	0.118709
$904$	−17.1386	−0.570023
$905$	−23.1698	−0.770189
$906$	−42.7961	−1.42180
$907$	6.42228	0.213248	0.106624	−	0.994299i	$-0.465996\pi$
$907$	6.42228	0.213248	0.106624	+	0.994299i	$0.465996\pi$
$908$	−5.78561	−0.192002
$909$	−10.2600	−0.340302
$910$	0.610058	0.0202232
$911$	−21.9036	−0.725698	−0.362849	−	0.931848i	$-0.618196\pi$
$911$	−21.9036	−0.725698	−0.362849	+	0.931848i	$0.618196\pi$
$912$	−10.0741	−0.333587
$913$	−0.150635	−0.00498528
$914$	4.32660	0.143111
$915$	−20.8958	−0.690793
$916$	−12.6946	−0.419441
$917$	−51.9749	−1.71636
$918$	−0.112885	−0.00372575
$919$	−11.7781	−0.388525	−0.194263	−	0.980950i	$-0.562231\pi$
$919$	−11.7781	−0.388525	−0.194263	+	0.980950i	$0.562231\pi$
$920$	−3.05308	−0.100657
$921$	−5.78745	−0.190703
$922$	16.1118	0.530613
$923$	−2.72364	−0.0896497
$924$	0.751758	0.0247310
$925$	32.3907	1.06500
$926$	−8.27134	−0.271813
$927$	15.8958	0.522086
$928$	−7.14624	−0.234587
$929$	44.8980	1.47305	0.736527	−	0.676408i	$-0.236464\pi$
$929$	44.8980	1.47305	0.736527	+	0.676408i	$0.236464\pi$
$930$	24.5353	0.804544
$931$	2.52578	0.0827792
$932$	18.1472	0.594430
$933$	19.6498	0.643304
$934$	9.25175	0.302727
$935$	−0.0100883	−0.000329923 0
$936$	0.402762	0.0131647
$937$	−32.0131	−1.04582	−0.522911	−	0.852387i	$-0.675154\pi$
$937$	−32.0131	−1.04582	−0.522911	+	0.852387i	$0.675154\pi$
$938$	−5.42946	−0.177278
$939$	−38.8507	−1.26785
$940$	12.0884	0.394279
$941$	13.8811	0.452510	0.226255	−	0.974068i	$-0.427352\pi$
$941$	13.8811	0.452510	0.226255	+	0.974068i	$0.427352\pi$
$942$	−0.925535	−0.0301556
$943$	15.8915	0.517499
$944$	−11.2119	−0.364917
$945$	−6.20869	−0.201969
$946$	−0.0806908	−0.00262348
$947$	−2.29837	−0.0746870	−0.0373435	−	0.999302i	$-0.511890\pi$
$947$	−2.29837	−0.0746870	−0.0373435	+	0.999302i	$0.511890\pi$
$948$	−29.2911	−0.951331
$949$	2.09051	0.0678609
$950$	−14.7204	−0.477594
$951$	−8.15863	−0.264562
$952$	−0.151440	−0.00490821
$953$	−12.2636	−0.397256	−0.198628	−	0.980075i	$-0.563649\pi$
$953$	−12.2636	−0.397256	−0.198628	+	0.980075i	$0.563649\pi$
$954$	18.7397	0.606721
$955$	−23.0140	−0.744715
$956$	−16.9046	−0.546734
$957$	−2.11861	−0.0684848
$958$	−23.2797	−0.752134
$959$	−18.0375	−0.582463
$960$	−2.94497	−0.0950486
$961$	38.4097	1.23902
$962$	−1.81088	−0.0583852
$963$	35.0305	1.12884
$964$	13.4296	0.432540
$965$	−6.38216	−0.205449
$966$	−13.5874	−0.437166
$967$	−34.3803	−1.10560	−0.552798	−	0.833315i	$-0.686440\pi$
$967$	−34.3803	−1.10560	−0.552798	+	0.833315i	$0.686440\pi$
$968$	10.9830	0.353007
$969$	0.601649	0.0193277
$970$	−8.45580	−0.271499
$971$	39.3186	1.26179	0.630896	−	0.775867i	$-0.282687\pi$
$971$	39.3186	1.26179	0.630896	+	0.775867i	$0.282687\pi$
$972$	−18.8896	−0.605884
$973$	41.9043	1.34339
$974$	−9.15437	−0.293325
$975$	1.40267	0.0449215
$976$	7.09541	0.227118
$977$	−11.8871	−0.380303	−0.190152	−	0.981755i	$-0.560898\pi$
$977$	−11.8871	−0.380303	−0.190152	+	0.981755i	$0.560898\pi$
$978$	51.0979	1.63393
$979$	−0.896217	−0.0286432
$980$	0.738365	0.0235862
$981$	20.7815	0.663502
$982$	−20.8618	−0.665727
$983$	−41.7894	−1.33287	−0.666437	−	0.745561i	$-0.732182\pi$
$983$	−41.7894	−1.33287	−0.666437	+	0.745561i	$0.732182\pi$
$984$	15.3288	0.488664
$985$	−18.8602	−0.600937
$986$	0.426790	0.0135918
$987$	53.7978	1.71240
$988$	0.822983	0.0261826
$989$	1.45841	0.0463749
$990$	−0.366319	−0.0116424
$991$	14.6691	0.465978	0.232989	−	0.972479i	$-0.425149\pi$
$991$	14.6691	0.465978	0.232989	+	0.972479i	$0.425149\pi$
$992$	−8.33125	−0.264517
$993$	−41.1125	−1.30467
$994$	37.1865	1.17948
$995$	8.01826	0.254196
$996$	2.62618	0.0832137
$997$	−16.7406	−0.530179	−0.265089	−	0.964224i	$-0.585401\pi$
$997$	−16.7406	−0.530179	−0.265089	+	0.964224i	$0.585401\pi$
$998$	43.7208	1.38396
$999$	18.4297	0.583091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1502.2.a.e.1.11	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1502.2.a.e.1.11	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1502 = 2 \cdot 751 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1502.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.27345 q^{3} +1.00000 q^{4} -1.29537 q^{5} -2.27345 q^{6} -2.53574 q^{7} -1.00000 q^{8} +2.16859 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.27345 q^{3} +1.00000 q^{4} -1.29537 q^{5} -2.27345 q^{6} -2.53574 q^{7} -1.00000 q^{8} +2.16859 q^{9} +1.29537 q^{10} -0.130403 q^{11} +2.27345 q^{12} -0.185725 q^{13} +2.53574 q^{14} -2.94497 q^{15} +1.00000 q^{16} -0.0597223 q^{17} -2.16859 q^{18} -4.43119 q^{19} -1.29537 q^{20} -5.76490 q^{21} +0.130403 q^{22} -2.35691 q^{23} -2.27345 q^{24} -3.32201 q^{25} +0.185725 q^{26} -1.89016 q^{27} -2.53574 q^{28} +7.14624 q^{29} +2.94497 q^{30} +8.33125 q^{31} -1.00000 q^{32} -0.296464 q^{33} +0.0597223 q^{34} +3.28474 q^{35} +2.16859 q^{36} -9.75035 q^{37} +4.43119 q^{38} -0.422237 q^{39} +1.29537 q^{40} -6.74252 q^{41} +5.76490 q^{42} -0.618782 q^{43} -0.130403 q^{44} -2.80914 q^{45} +2.35691 q^{46} -9.33195 q^{47} +2.27345 q^{48} -0.570001 q^{49} +3.32201 q^{50} -0.135776 q^{51} -0.185725 q^{52} -8.64141 q^{53} +1.89016 q^{54} +0.168920 q^{55} +2.53574 q^{56} -10.0741 q^{57} -7.14624 q^{58} -11.2119 q^{59} -2.94497 q^{60} +7.09541 q^{61} -8.33125 q^{62} -5.49900 q^{63} +1.00000 q^{64} +0.240583 q^{65} +0.296464 q^{66} -2.14117 q^{67} -0.0597223 q^{68} -5.35833 q^{69} -3.28474 q^{70} +14.6649 q^{71} -2.16859 q^{72} -11.2560 q^{73} +9.75035 q^{74} -7.55243 q^{75} -4.43119 q^{76} +0.330668 q^{77} +0.422237 q^{78} -12.8840 q^{79} -1.29537 q^{80} -10.8030 q^{81} +6.74252 q^{82} +1.15515 q^{83} -5.76490 q^{84} +0.0773627 q^{85} +0.618782 q^{86} +16.2467 q^{87} +0.130403 q^{88} +6.87269 q^{89} +2.80914 q^{90} +0.470951 q^{91} -2.35691 q^{92} +18.9407 q^{93} +9.33195 q^{94} +5.74005 q^{95} -2.27345 q^{96} -6.52769 q^{97} +0.570001 q^{98} -0.282790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9	\( 11 q - 11 q^{2} - 4 q^{3} + 11 q^{4} + q^{5} + 4 q^{6} - 6 q^{7} - 11 q^{8} + 3 q^{9} - q^{10} + 4 q^{11} - 4 q^{12} - 19 q^{13} + 6 q^{14} + q^{15} + 11 q^{16} - 8 q^{17} - 3 q^{18} - 9 q^{19} + q^{20} - 6 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 2 q^{25} + 19 q^{26} - 16 q^{27} - 6 q^{28} + 13 q^{29} - q^{30} - 19 q^{31} - 11 q^{32} - 37 q^{33} + 8 q^{34} + 3 q^{35} + 3 q^{36} - 29 q^{37} + 9 q^{38} + 8 q^{39} - q^{40} - 23 q^{41} + 6 q^{42} - 13 q^{43} + 4 q^{44} - 6 q^{45} - 2 q^{46} - 16 q^{47} - 4 q^{48} - 5 q^{49} + 2 q^{50} + 33 q^{51} - 19 q^{52} - 25 q^{53} + 16 q^{54} - 14 q^{55} + 6 q^{56} + 4 q^{57} - 13 q^{58} + 6 q^{59} + q^{60} + 10 q^{61} + 19 q^{62} - 7 q^{63} + 11 q^{64} - 19 q^{65} + 37 q^{66} - 16 q^{67} - 8 q^{68} - 25 q^{69} - 3 q^{70} + 8 q^{71} - 3 q^{72} - 56 q^{73} + 29 q^{74} - 50 q^{75} - 9 q^{76} - 7 q^{77} - 8 q^{78} + 2 q^{79} + q^{80} - 5 q^{81} + 23 q^{82} + 21 q^{83} - 6 q^{84} - 55 q^{85} + 13 q^{86} - 11 q^{87} - 4 q^{88} - 24 q^{89} + 6 q^{90} - 43 q^{91} + 2 q^{92} + 10 q^{93} + 16 q^{94} + 25 q^{95} + 4 q^{96} - 84 q^{97} + 5 q^{98} + 14 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - 4 * q^3 + 11 * q^4 + q^5 + 4 * q^6 - 6 * q^7 - 11 * q^8 + 3 * q^9 - q^10 + 4 * q^11 - 4 * q^12 - 19 * q^13 + 6 * q^14 + q^15 + 11 * q^16 - 8 * q^17 - 3 * q^18 - 9 * q^19 + q^20 - 6 * q^21 - 4 * q^22 + 2 * q^23 + 4 * q^24 - 2 * q^25 + 19 * q^26 - 16 * q^27 - 6 * q^28 + 13 * q^29 - q^30 - 19 * q^31 - 11 * q^32 - 37 * q^33 + 8 * q^34 + 3 * q^35 + 3 * q^36 - 29 * q^37 + 9 * q^38 + 8 * q^39 - q^40 - 23 * q^41 + 6 * q^42 - 13 * q^43 + 4 * q^44 - 6 * q^45 - 2 * q^46 - 16 * q^47 - 4 * q^48 - 5 * q^49 + 2 * q^50 + 33 * q^51 - 19 * q^52 - 25 * q^53 + 16 * q^54 - 14 * q^55 + 6 * q^56 + 4 * q^57 - 13 * q^58 + 6 * q^59 + q^60 + 10 * q^61 + 19 * q^62 - 7 * q^63 + 11 * q^64 - 19 * q^65 + 37 * q^66 - 16 * q^67 - 8 * q^68 - 25 * q^69 - 3 * q^70 + 8 * q^71 - 3 * q^72 - 56 * q^73 + 29 * q^74 - 50 * q^75 - 9 * q^76 - 7 * q^77 - 8 * q^78 + 2 * q^79 + q^80 - 5 * q^81 + 23 * q^82 + 21 * q^83 - 6 * q^84 - 55 * q^85 + 13 * q^86 - 11 * q^87 - 4 * q^88 - 24 * q^89 + 6 * q^90 - 43 * q^91 + 2 * q^92 + 10 * q^93 + 16 * q^94 + 25 * q^95 + 4 * q^96 - 84 * q^97 + 5 * q^98 + 14 * q^99

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