LMFDB - Embedded newform 4730.2.a.bf.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 32 x^{11} - 5 x^{10} + 376 x^{9} + 100 x^{8} - 1985 x^{7} - 576 x^{6} + 4708 x^{5} + 889 x^{4} + \cdots - 128 $ x^13 - 32x^11 - 5x^10 + 376x^9 + 100x^8 - 1985x^7 - 576x^6 + 4708x^5 + 889x^4 - 4774x^3 - 296x^2 + 1648*x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.15443$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.15443 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.15443 q^{6} +5.20049 q^{7} +1.00000 q^{8} +1.64159 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.15443 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.15443 q^{6} +5.20049 q^{7} +1.00000 q^{8} +1.64159 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.15443 q^{12} -3.69356 q^{13} +5.20049 q^{14} -2.15443 q^{15} +1.00000 q^{16} +2.28911 q^{17} +1.64159 q^{18} +3.91291 q^{19} -1.00000 q^{20} +11.2041 q^{21} +1.00000 q^{22} -7.46477 q^{23} +2.15443 q^{24} +1.00000 q^{25} -3.69356 q^{26} -2.92661 q^{27} +5.20049 q^{28} +8.04319 q^{29} -2.15443 q^{30} -2.87929 q^{31} +1.00000 q^{32} +2.15443 q^{33} +2.28911 q^{34} -5.20049 q^{35} +1.64159 q^{36} +10.2217 q^{37} +3.91291 q^{38} -7.95753 q^{39} -1.00000 q^{40} +3.12737 q^{41} +11.2041 q^{42} +1.00000 q^{43} +1.00000 q^{44} -1.64159 q^{45} -7.46477 q^{46} -9.31889 q^{47} +2.15443 q^{48} +20.0451 q^{49} +1.00000 q^{50} +4.93173 q^{51} -3.69356 q^{52} -0.670647 q^{53} -2.92661 q^{54} -1.00000 q^{55} +5.20049 q^{56} +8.43011 q^{57} +8.04319 q^{58} +6.55249 q^{59} -2.15443 q^{60} +7.70264 q^{61} -2.87929 q^{62} +8.53706 q^{63} +1.00000 q^{64} +3.69356 q^{65} +2.15443 q^{66} -4.29126 q^{67} +2.28911 q^{68} -16.0824 q^{69} -5.20049 q^{70} -8.54294 q^{71} +1.64159 q^{72} -9.80369 q^{73} +10.2217 q^{74} +2.15443 q^{75} +3.91291 q^{76} +5.20049 q^{77} -7.95753 q^{78} +11.4945 q^{79} -1.00000 q^{80} -11.2300 q^{81} +3.12737 q^{82} -6.18517 q^{83} +11.2041 q^{84} -2.28911 q^{85} +1.00000 q^{86} +17.3285 q^{87} +1.00000 q^{88} -5.34397 q^{89} -1.64159 q^{90} -19.2083 q^{91} -7.46477 q^{92} -6.20325 q^{93} -9.31889 q^{94} -3.91291 q^{95} +2.15443 q^{96} +5.40206 q^{97} +20.0451 q^{98} +1.64159 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9	$ 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9} - 13 q^{10} + 13 q^{11} + 11 q^{13} + 7 q^{14} + 13 q^{16} - 2 q^{17} + 25 q^{18} + 7 q^{19} - 13 q^{20} + 12 q^{21} + 13 q^{22} + 12 q^{23} + 13 q^{25} + 11 q^{26} - 15 q^{27} + 7 q^{28} + 14 q^{29} + 20 q^{31} + 13 q^{32} - 2 q^{34} - 7 q^{35} + 25 q^{36} + 17 q^{37} + 7 q^{38} - 4 q^{39} - 13 q^{40} + 9 q^{41} + 12 q^{42} + 13 q^{43} + 13 q^{44} - 25 q^{45} + 12 q^{46} - 9 q^{47} + 30 q^{49} + 13 q^{50} - 3 q^{51} + 11 q^{52} + 22 q^{53} - 15 q^{54} - 13 q^{55} + 7 q^{56} + 17 q^{57} + 14 q^{58} + 19 q^{59} + 2 q^{61} + 20 q^{62} + 12 q^{63} + 13 q^{64} - 11 q^{65} + 9 q^{67} - 2 q^{68} - 6 q^{69} - 7 q^{70} + 6 q^{71} + 25 q^{72} + 7 q^{73} + 17 q^{74} + 7 q^{76} + 7 q^{77} - 4 q^{78} + 50 q^{79} - 13 q^{80} + 85 q^{81} + 9 q^{82} + q^{83} + 12 q^{84} + 2 q^{85} + 13 q^{86} - 21 q^{87} + 13 q^{88} + 5 q^{89} - 25 q^{90} + 5 q^{91} + 12 q^{92} + 3 q^{93} - 9 q^{94} - 7 q^{95} + 20 q^{97} + 30 q^{98} + 25 q^{99}+O(q^{100}) $ 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9 - 13 * q^10 + 13 * q^11 + 11 * q^13 + 7 * q^14 + 13 * q^16 - 2 * q^17 + 25 * q^18 + 7 * q^19 - 13 * q^20 + 12 * q^21 + 13 * q^22 + 12 * q^23 + 13 * q^25 + 11 * q^26 - 15 * q^27 + 7 * q^28 + 14 * q^29 + 20 * q^31 + 13 * q^32 - 2 * q^34 - 7 * q^35 + 25 * q^36 + 17 * q^37 + 7 * q^38 - 4 * q^39 - 13 * q^40 + 9 * q^41 + 12 * q^42 + 13 * q^43 + 13 * q^44 - 25 * q^45 + 12 * q^46 - 9 * q^47 + 30 * q^49 + 13 * q^50 - 3 * q^51 + 11 * q^52 + 22 * q^53 - 15 * q^54 - 13 * q^55 + 7 * q^56 + 17 * q^57 + 14 * q^58 + 19 * q^59 + 2 * q^61 + 20 * q^62 + 12 * q^63 + 13 * q^64 - 11 * q^65 + 9 * q^67 - 2 * q^68 - 6 * q^69 - 7 * q^70 + 6 * q^71 + 25 * q^72 + 7 * q^73 + 17 * q^74 + 7 * q^76 + 7 * q^77 - 4 * q^78 + 50 * q^79 - 13 * q^80 + 85 * q^81 + 9 * q^82 + q^83 + 12 * q^84 + 2 * q^85 + 13 * q^86 - 21 * q^87 + 13 * q^88 + 5 * q^89 - 25 * q^90 + 5 * q^91 + 12 * q^92 + 3 * q^93 - 9 * q^94 - 7 * q^95 + 20 * q^97 + 30 * q^98 + 25 * 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
$3$	2.15443	1.24386	0.621932	−	0.783071i	$-0.286348\pi$
$3$	2.15443	1.24386	0.621932	+	0.783071i	$0.286348\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.15443	0.879544
$7$	5.20049	1.96560	0.982800	−	0.184674i	$-0.0591230\pi$
$7$	5.20049	1.96560	0.982800	+	0.184674i	$0.0591230\pi$
$8$	1.00000	0.353553
$9$	1.64159	0.547196
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.15443	0.621932
$13$	−3.69356	−1.02441	−0.512204	−	0.858864i	$-0.671171\pi$
$13$	−3.69356	−1.02441	−0.512204	+	0.858864i	$0.671171\pi$
$14$	5.20049	1.38989
$15$	−2.15443	−0.556273
$16$	1.00000	0.250000
$17$	2.28911	0.555190	0.277595	−	0.960698i	$-0.410463\pi$
$17$	2.28911	0.555190	0.277595	+	0.960698i	$0.410463\pi$
$18$	1.64159	0.386926
$19$	3.91291	0.897684	0.448842	−	0.893611i	$-0.351837\pi$
$19$	3.91291	0.897684	0.448842	+	0.893611i	$0.351837\pi$
$20$	−1.00000	−0.223607
$21$	11.2041	2.44494
$22$	1.00000	0.213201
$23$	−7.46477	−1.55651	−0.778256	−	0.627948i	$-0.783895\pi$
$23$	−7.46477	−1.55651	−0.778256	+	0.627948i	$0.783895\pi$
$24$	2.15443	0.439772
$25$	1.00000	0.200000
$26$	−3.69356	−0.724366
$27$	−2.92661	−0.563226
$28$	5.20049	0.982800
$29$	8.04319	1.49358	0.746791	−	0.665058i	$-0.231593\pi$
$29$	8.04319	1.49358	0.746791	+	0.665058i	$0.231593\pi$
$30$	−2.15443	−0.393344
$31$	−2.87929	−0.517136	−0.258568	−	0.965993i	$-0.583251\pi$
$31$	−2.87929	−0.517136	−0.258568	+	0.965993i	$0.583251\pi$
$32$	1.00000	0.176777
$33$	2.15443	0.375039
$34$	2.28911	0.392579
$35$	−5.20049	−0.879043
$36$	1.64159	0.273598
$37$	10.2217	1.68043	0.840216	−	0.542253i	$-0.182428\pi$
$37$	10.2217	1.68043	0.840216	+	0.542253i	$0.182428\pi$
$38$	3.91291	0.634758
$39$	−7.95753	−1.27422
$40$	−1.00000	−0.158114
$41$	3.12737	0.488413	0.244206	−	0.969723i	$-0.421473\pi$
$41$	3.12737	0.488413	0.244206	+	0.969723i	$0.421473\pi$
$42$	11.2041	1.72883
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−1.64159	−0.244714
$46$	−7.46477	−1.10062
$47$	−9.31889	−1.35930	−0.679650	−	0.733536i	$-0.737868\pi$
$47$	−9.31889	−1.35930	−0.679650	+	0.733536i	$0.737868\pi$
$48$	2.15443	0.310966
$49$	20.0451	2.86358
$50$	1.00000	0.141421
$51$	4.93173	0.690581
$52$	−3.69356	−0.512204
$53$	−0.670647	−0.0921205	−0.0460602	−	0.998939i	$-0.514667\pi$
$53$	−0.670647	−0.0921205	−0.0460602	+	0.998939i	$0.514667\pi$
$54$	−2.92661	−0.398261
$55$	−1.00000	−0.134840
$56$	5.20049	0.694944
$57$	8.43011	1.11660
$58$	8.04319	1.05612
$59$	6.55249	0.853062	0.426531	−	0.904473i	$-0.359736\pi$
$59$	6.55249	0.853062	0.426531	+	0.904473i	$0.359736\pi$
$60$	−2.15443	−0.278136
$61$	7.70264	0.986221	0.493111	−	0.869967i	$-0.335860\pi$
$61$	7.70264	0.986221	0.493111	+	0.869967i	$0.335860\pi$
$62$	−2.87929	−0.365671
$63$	8.53706	1.07557
$64$	1.00000	0.125000
$65$	3.69356	0.458129
$66$	2.15443	0.265193
$67$	−4.29126	−0.524261	−0.262131	−	0.965032i	$-0.584425\pi$
$67$	−4.29126	−0.524261	−0.262131	+	0.965032i	$0.584425\pi$
$68$	2.28911	0.277595
$69$	−16.0824	−1.93609
$70$	−5.20049	−0.621577
$71$	−8.54294	−1.01386	−0.506930	−	0.861987i	$-0.669220\pi$
$71$	−8.54294	−1.01386	−0.506930	+	0.861987i	$0.669220\pi$
$72$	1.64159	0.193463
$73$	−9.80369	−1.14743	−0.573717	−	0.819053i	$-0.694499\pi$
$73$	−9.80369	−1.14743	−0.573717	+	0.819053i	$0.694499\pi$
$74$	10.2217	1.18824
$75$	2.15443	0.248773
$76$	3.91291	0.448842
$77$	5.20049	0.592651
$78$	−7.95753	−0.901012
$79$	11.4945	1.29323	0.646614	−	0.762818i	$-0.276185\pi$
$79$	11.4945	1.29323	0.646614	+	0.762818i	$0.276185\pi$
$80$	−1.00000	−0.111803
$81$	−11.2300	−1.24777
$82$	3.12737	0.345360
$83$	−6.18517	−0.678910	−0.339455	−	0.940622i	$-0.610243\pi$
$83$	−6.18517	−0.678910	−0.339455	+	0.940622i	$0.610243\pi$
$84$	11.2041	1.22247
$85$	−2.28911	−0.248289
$86$	1.00000	0.107833
$87$	17.3285	1.85781
$88$	1.00000	0.106600
$89$	−5.34397	−0.566460	−0.283230	−	0.959052i	$-0.591406\pi$
$89$	−5.34397	−0.566460	−0.283230	+	0.959052i	$0.591406\pi$
$90$	−1.64159	−0.173039
$91$	−19.2083	−2.01358
$92$	−7.46477	−0.778256
$93$	−6.20325	−0.643247
$94$	−9.31889	−0.961170
$95$	−3.91291	−0.401456
$96$	2.15443	0.219886
$97$	5.40206	0.548496	0.274248	−	0.961659i	$-0.411571\pi$
$97$	5.40206	0.548496	0.274248	+	0.961659i	$0.411571\pi$
$98$	20.0451	2.02486
$99$	1.64159	0.164986
$100$	1.00000	0.100000
$101$	16.4334	1.63518	0.817591	−	0.575799i	$-0.195309\pi$
$101$	16.4334	1.63518	0.817591	+	0.575799i	$0.195309\pi$
$102$	4.93173	0.488314
$103$	−12.9541	−1.27640	−0.638201	−	0.769870i	$-0.720321\pi$
$103$	−12.9541	−1.27640	−0.638201	+	0.769870i	$0.720321\pi$
$104$	−3.69356	−0.362183
$105$	−11.2041	−1.09341
$106$	−0.670647	−0.0651390
$107$	−16.3514	−1.58075	−0.790373	−	0.612626i	$-0.790113\pi$
$107$	−16.3514	−1.58075	−0.790373	+	0.612626i	$0.790113\pi$
$108$	−2.92661	−0.281613
$109$	16.8177	1.61084	0.805419	−	0.592705i	$-0.201940\pi$
$109$	16.8177	1.61084	0.805419	+	0.592705i	$0.201940\pi$
$110$	−1.00000	−0.0953463
$111$	22.0219	2.09023
$112$	5.20049	0.491400
$113$	−5.65787	−0.532248	−0.266124	−	0.963939i	$-0.585743\pi$
$113$	−5.65787	−0.532248	−0.266124	+	0.963939i	$0.585743\pi$
$114$	8.43011	0.789553
$115$	7.46477	0.696093
$116$	8.04319	0.746791
$117$	−6.06330	−0.560552
$118$	6.55249	0.603206
$119$	11.9045	1.09128
$120$	−2.15443	−0.196672
$121$	1.00000	0.0909091
$122$	7.70264	0.697364
$123$	6.73771	0.607519
$124$	−2.87929	−0.258568
$125$	−1.00000	−0.0894427
$126$	8.53706	0.760542
$127$	−17.6856	−1.56934	−0.784670	−	0.619914i	$-0.787167\pi$
$127$	−17.6856	−1.56934	−0.784670	+	0.619914i	$0.787167\pi$
$128$	1.00000	0.0883883
$129$	2.15443	0.189687
$130$	3.69356	0.323946
$131$	−16.4398	−1.43635	−0.718176	−	0.695861i	$-0.755023\pi$
$131$	−16.4398	−1.43635	−0.718176	+	0.695861i	$0.755023\pi$
$132$	2.15443	0.187519
$133$	20.3491	1.76449
$134$	−4.29126	−0.370709
$135$	2.92661	0.251882
$136$	2.28911	0.196289
$137$	−4.54096	−0.387960	−0.193980	−	0.981005i	$-0.562140\pi$
$137$	−4.54096	−0.387960	−0.193980	+	0.981005i	$0.562140\pi$
$138$	−16.0824	−1.36902
$139$	17.7324	1.50404	0.752021	−	0.659139i	$-0.229079\pi$
$139$	17.7324	1.50404	0.752021	+	0.659139i	$0.229079\pi$
$140$	−5.20049	−0.439521
$141$	−20.0769	−1.69078
$142$	−8.54294	−0.716908
$143$	−3.69356	−0.308871
$144$	1.64159	0.136799
$145$	−8.04319	−0.667950
$146$	−9.80369	−0.811359
$147$	43.1858	3.56190
$148$	10.2217	0.840216
$149$	−2.59038	−0.212212	−0.106106	−	0.994355i	$-0.533838\pi$
$149$	−2.59038	−0.212212	−0.106106	+	0.994355i	$0.533838\pi$
$150$	2.15443	0.175909
$151$	20.9220	1.70261	0.851304	−	0.524673i	$-0.175813\pi$
$151$	20.9220	1.70261	0.851304	+	0.524673i	$0.175813\pi$
$152$	3.91291	0.317379
$153$	3.75777	0.303798
$154$	5.20049	0.419067
$155$	2.87929	0.231270
$156$	−7.95753	−0.637112
$157$	−13.6347	−1.08817	−0.544083	−	0.839031i	$-0.683122\pi$
$157$	−13.6347	−1.08817	−0.544083	+	0.839031i	$0.683122\pi$
$158$	11.4945	0.914450
$159$	−1.44487	−0.114585
$160$	−1.00000	−0.0790569
$161$	−38.8204	−3.05948
$162$	−11.2300	−0.882308
$163$	−18.6569	−1.46133	−0.730663	−	0.682739i	$-0.760789\pi$
$163$	−18.6569	−1.46133	−0.730663	+	0.682739i	$0.760789\pi$
$164$	3.12737	0.244206
$165$	−2.15443	−0.167723
$166$	−6.18517	−0.480062
$167$	2.47973	0.191887	0.0959435	−	0.995387i	$-0.469413\pi$
$167$	2.47973	0.191887	0.0959435	+	0.995387i	$0.469413\pi$
$168$	11.2041	0.864416
$169$	0.642357	0.0494121
$170$	−2.28911	−0.175567
$171$	6.42339	0.491209
$172$	1.00000	0.0762493
$173$	−2.91913	−0.221937	−0.110968	−	0.993824i	$-0.535395\pi$
$173$	−2.91913	−0.221937	−0.110968	+	0.993824i	$0.535395\pi$
$174$	17.3285	1.31367
$175$	5.20049	0.393120
$176$	1.00000	0.0753778
$177$	14.1169	1.06109
$178$	−5.34397	−0.400548
$179$	−13.7699	−1.02921	−0.514606	−	0.857427i	$-0.672062\pi$
$179$	−13.7699	−1.02921	−0.514606	+	0.857427i	$0.672062\pi$
$180$	−1.64159	−0.122357
$181$	−9.50722	−0.706666	−0.353333	−	0.935498i	$-0.614952\pi$
$181$	−9.50722	−0.706666	−0.353333	+	0.935498i	$0.614952\pi$
$182$	−19.2083	−1.42381
$183$	16.5948	1.22672
$184$	−7.46477	−0.550310
$185$	−10.2217	−0.751512
$186$	−6.20325	−0.454844
$187$	2.28911	0.167396
$188$	−9.31889	−0.679650
$189$	−15.2198	−1.10708
$190$	−3.91291	−0.283873
$191$	22.3373	1.61627	0.808134	−	0.588998i	$-0.200477\pi$
$191$	22.3373	1.61627	0.808134	+	0.588998i	$0.200477\pi$
$192$	2.15443	0.155483
$193$	5.77134	0.415430	0.207715	−	0.978189i	$-0.433397\pi$
$193$	5.77134	0.415430	0.207715	+	0.978189i	$0.433397\pi$
$194$	5.40206	0.387845
$195$	7.95753	0.569850
$196$	20.0451	1.43179
$197$	7.78147	0.554407	0.277203	−	0.960811i	$-0.410592\pi$
$197$	7.78147	0.554407	0.277203	+	0.960811i	$0.410592\pi$
$198$	1.64159	0.116663
$199$	−17.2211	−1.22077	−0.610387	−	0.792104i	$-0.708986\pi$
$199$	−17.2211	−1.22077	−0.610387	+	0.792104i	$0.708986\pi$
$200$	1.00000	0.0707107
$201$	−9.24525	−0.652109
$202$	16.4334	1.15625
$203$	41.8285	2.93579
$204$	4.93173	0.345290
$205$	−3.12737	−0.218425
$206$	−12.9541	−0.902552
$207$	−12.2541	−0.851717
$208$	−3.69356	−0.256102
$209$	3.91291	0.270662
$210$	−11.2041	−0.773157
$211$	−2.25780	−0.155434	−0.0777168	−	0.996975i	$-0.524763\pi$
$211$	−2.25780	−0.155434	−0.0777168	+	0.996975i	$0.524763\pi$
$212$	−0.670647	−0.0460602
$213$	−18.4052	−1.26110
$214$	−16.3514	−1.11776
$215$	−1.00000	−0.0681994
$216$	−2.92661	−0.199131
$217$	−14.9737	−1.01648
$218$	16.8177	1.13904
$219$	−21.1214	−1.42725
$220$	−1.00000	−0.0674200
$221$	−8.45495	−0.568741
$222$	22.0219	1.47801
$223$	−5.70292	−0.381896	−0.190948	−	0.981600i	$-0.561156\pi$
$223$	−5.70292	−0.381896	−0.190948	+	0.981600i	$0.561156\pi$
$224$	5.20049	0.347472
$225$	1.64159	0.109439
$226$	−5.65787	−0.376356
$227$	−1.85378	−0.123040	−0.0615199	−	0.998106i	$-0.519595\pi$
$227$	−1.85378	−0.123040	−0.0615199	+	0.998106i	$0.519595\pi$
$228$	8.43011	0.558298
$229$	−12.0610	−0.797014	−0.398507	−	0.917165i	$-0.630472\pi$
$229$	−12.0610	−0.797014	−0.398507	+	0.917165i	$0.630472\pi$
$230$	7.46477	0.492212
$231$	11.2041	0.737176
$232$	8.04319	0.528061
$233$	6.65456	0.435955	0.217977	−	0.975954i	$-0.430054\pi$
$233$	6.65456	0.435955	0.217977	+	0.975954i	$0.430054\pi$
$234$	−6.06330	−0.396370
$235$	9.31889	0.607898
$236$	6.55249	0.426531
$237$	24.7641	1.60860
$238$	11.9045	0.771653
$239$	−15.6396	−1.01164	−0.505819	−	0.862639i	$-0.668810\pi$
$239$	−15.6396	−1.01164	−0.505819	+	0.862639i	$0.668810\pi$
$240$	−2.15443	−0.139068
$241$	−0.896388	−0.0577414	−0.0288707	−	0.999583i	$-0.509191\pi$
$241$	−0.896388	−0.0577414	−0.0288707	+	0.999583i	$0.509191\pi$
$242$	1.00000	0.0642824
$243$	−15.4144	−0.988832
$244$	7.70264	0.493111
$245$	−20.0451	−1.28063
$246$	6.73771	0.429581
$247$	−14.4526	−0.919595
$248$	−2.87929	−0.182835
$249$	−13.3255	−0.844471
$250$	−1.00000	−0.0632456
$251$	3.71338	0.234387	0.117193	−	0.993109i	$-0.462610\pi$
$251$	3.71338	0.234387	0.117193	+	0.993109i	$0.462610\pi$
$252$	8.53706	0.537784
$253$	−7.46477	−0.469306
$254$	−17.6856	−1.10969
$255$	−4.93173	−0.308837
$256$	1.00000	0.0625000
$257$	5.07711	0.316701	0.158351	−	0.987383i	$-0.449382\pi$
$257$	5.07711	0.316701	0.158351	+	0.987383i	$0.449382\pi$
$258$	2.15443	0.134129
$259$	53.1576	3.30305
$260$	3.69356	0.229065
$261$	13.2036	0.817283
$262$	−16.4398	−1.01565
$263$	27.1172	1.67212	0.836058	−	0.548641i	$-0.184855\pi$
$263$	27.1172	1.67212	0.836058	+	0.548641i	$0.184855\pi$
$264$	2.15443	0.132596
$265$	0.670647	0.0411975
$266$	20.3491	1.24768
$267$	−11.5132	−0.704599
$268$	−4.29126	−0.262131
$269$	−2.78067	−0.169540	−0.0847702	−	0.996401i	$-0.527016\pi$
$269$	−2.78067	−0.169540	−0.0847702	+	0.996401i	$0.527016\pi$
$270$	2.92661	0.178108
$271$	−12.6460	−0.768189	−0.384094	−	0.923294i	$-0.625486\pi$
$271$	−12.6460	−0.768189	−0.384094	+	0.923294i	$0.625486\pi$
$272$	2.28911	0.138798
$273$	−41.3830	−2.50461
$274$	−4.54096	−0.274329
$275$	1.00000	0.0603023
$276$	−16.0824	−0.968044
$277$	−6.74725	−0.405403	−0.202701	−	0.979241i	$-0.564972\pi$
$277$	−6.74725	−0.405403	−0.202701	+	0.979241i	$0.564972\pi$
$278$	17.7324	1.06352
$279$	−4.72661	−0.282975
$280$	−5.20049	−0.310789
$281$	−5.29405	−0.315816	−0.157908	−	0.987454i	$-0.550475\pi$
$281$	−5.29405	−0.315816	−0.157908	+	0.987454i	$0.550475\pi$
$282$	−20.0769	−1.19556
$283$	−0.938443	−0.0557846	−0.0278923	−	0.999611i	$-0.508880\pi$
$283$	−0.938443	−0.0557846	−0.0278923	+	0.999611i	$0.508880\pi$
$284$	−8.54294	−0.506930
$285$	−8.43011	−0.499357
$286$	−3.69356	−0.218405
$287$	16.2638	0.960024
$288$	1.64159	0.0967315
$289$	−11.7600	−0.691764
$290$	−8.04319	−0.472312
$291$	11.6384	0.682254
$292$	−9.80369	−0.573717
$293$	25.1151	1.46724	0.733620	−	0.679560i	$-0.237829\pi$
$293$	25.1151	1.46724	0.733620	+	0.679560i	$0.237829\pi$
$294$	43.1858	2.51865
$295$	−6.55249	−0.381501
$296$	10.2217	0.594122
$297$	−2.92661	−0.169819
$298$	−2.59038	−0.150057
$299$	27.5715	1.59450
$300$	2.15443	0.124386
$301$	5.20049	0.299751
$302$	20.9220	1.20393
$303$	35.4046	2.03394
$304$	3.91291	0.224421
$305$	−7.70264	−0.441052
$306$	3.75777	0.214818
$307$	−11.3935	−0.650262	−0.325131	−	0.945669i	$-0.605408\pi$
$307$	−11.3935	−0.650262	−0.325131	+	0.945669i	$0.605408\pi$
$308$	5.20049	0.296325
$309$	−27.9087	−1.58767
$310$	2.87929	0.163533
$311$	−4.64254	−0.263254	−0.131627	−	0.991299i	$-0.542020\pi$
$311$	−4.64254	−0.263254	−0.131627	+	0.991299i	$0.542020\pi$
$312$	−7.95753	−0.450506
$313$	−7.23924	−0.409186	−0.204593	−	0.978847i	$-0.565587\pi$
$313$	−7.23924	−0.409186	−0.204593	+	0.978847i	$0.565587\pi$
$314$	−13.6347	−0.769450
$315$	−8.53706	−0.481009
$316$	11.4945	0.646614
$317$	13.1816	0.740353	0.370176	−	0.928961i	$-0.379297\pi$
$317$	13.1816	0.740353	0.370176	+	0.928961i	$0.379297\pi$
$318$	−1.44487	−0.0810240
$319$	8.04319	0.450332
$320$	−1.00000	−0.0559017
$321$	−35.2280	−1.96623
$322$	−38.8204	−2.16338
$323$	8.95708	0.498385
$324$	−11.2300	−0.623886
$325$	−3.69356	−0.204882
$326$	−18.6569	−1.03331
$327$	36.2325	2.00366
$328$	3.12737	0.172680
$329$	−48.4628	−2.67184
$330$	−2.15443	−0.118598
$331$	5.45659	0.299921	0.149961	−	0.988692i	$-0.452085\pi$
$331$	5.45659	0.299921	0.149961	+	0.988692i	$0.452085\pi$
$332$	−6.18517	−0.339455
$333$	16.7798	0.919525
$334$	2.47973	0.135685
$335$	4.29126	0.234457
$336$	11.2041	0.611234
$337$	23.7542	1.29397	0.646987	−	0.762501i	$-0.276029\pi$
$337$	23.7542	1.29397	0.646987	+	0.762501i	$0.276029\pi$
$338$	0.642357	0.0349396
$339$	−12.1895	−0.662044
$340$	−2.28911	−0.124144
$341$	−2.87929	−0.155922
$342$	6.42339	0.347337
$343$	67.8407	3.66306
$344$	1.00000	0.0539164
$345$	16.0824	0.865845
$346$	−2.91913	−0.156933
$347$	−27.5506	−1.47899	−0.739497	−	0.673160i	$-0.764937\pi$
$347$	−27.5506	−1.47899	−0.739497	+	0.673160i	$0.764937\pi$
$348$	17.3285	0.928906
$349$	19.1046	1.02264	0.511322	−	0.859389i	$-0.329156\pi$
$349$	19.1046	1.02264	0.511322	+	0.859389i	$0.329156\pi$
$350$	5.20049	0.277978
$351$	10.8096	0.576973
$352$	1.00000	0.0533002
$353$	−19.9199	−1.06023	−0.530114	−	0.847926i	$-0.677851\pi$
$353$	−19.9199	−1.06023	−0.530114	+	0.847926i	$0.677851\pi$
$354$	14.1169	0.750306
$355$	8.54294	0.453412
$356$	−5.34397	−0.283230
$357$	25.6474	1.35741
$358$	−13.7699	−0.727763
$359$	−6.69249	−0.353216	−0.176608	−	0.984281i	$-0.556512\pi$
$359$	−6.69249	−0.353216	−0.176608	+	0.984281i	$0.556512\pi$
$360$	−1.64159	−0.0865193
$361$	−3.68911	−0.194164
$362$	−9.50722	−0.499688
$363$	2.15443	0.113078
$364$	−19.2083	−1.00679
$365$	9.80369	0.513149
$366$	16.5948	0.867425
$367$	−10.2267	−0.533827	−0.266914	−	0.963720i	$-0.586004\pi$
$367$	−10.2267	−0.533827	−0.266914	+	0.963720i	$0.586004\pi$
$368$	−7.46477	−0.389128
$369$	5.13385	0.267258
$370$	−10.2217	−0.531399
$371$	−3.48769	−0.181072
$372$	−6.20325	−0.321623
$373$	18.4363	0.954594	0.477297	−	0.878742i	$-0.341617\pi$
$373$	18.4363	0.954594	0.477297	+	0.878742i	$0.341617\pi$
$374$	2.28911	0.118367
$375$	−2.15443	−0.111255
$376$	−9.31889	−0.480585
$377$	−29.7080	−1.53004
$378$	−15.2198	−0.782822
$379$	2.83712	0.145733	0.0728666	−	0.997342i	$-0.476785\pi$
$379$	2.83712	0.145733	0.0728666	+	0.997342i	$0.476785\pi$
$380$	−3.91291	−0.200728
$381$	−38.1024	−1.95204
$382$	22.3373	1.14287
$383$	13.9972	0.715223	0.357612	−	0.933870i	$-0.383591\pi$
$383$	13.9972	0.715223	0.357612	+	0.933870i	$0.383591\pi$
$384$	2.15443	0.109943
$385$	−5.20049	−0.265041
$386$	5.77134	0.293753
$387$	1.64159	0.0834466
$388$	5.40206	0.274248
$389$	−3.40004	−0.172389	−0.0861944	−	0.996278i	$-0.527471\pi$
$389$	−3.40004	−0.172389	−0.0861944	+	0.996278i	$0.527471\pi$
$390$	7.95753	0.402945
$391$	−17.0877	−0.864160
$392$	20.0451	1.01243
$393$	−35.4185	−1.78663
$394$	7.78147	0.392025
$395$	−11.4945	−0.578349
$396$	1.64159	0.0824929
$397$	19.0532	0.956251	0.478125	−	0.878292i	$-0.341316\pi$
$397$	19.0532	0.956251	0.478125	+	0.878292i	$0.341316\pi$
$398$	−17.2211	−0.863217
$399$	43.8407	2.19478
$400$	1.00000	0.0500000
$401$	6.62751	0.330962	0.165481	−	0.986213i	$-0.447082\pi$
$401$	6.62751	0.330962	0.165481	+	0.986213i	$0.447082\pi$
$402$	−9.24525	−0.461111
$403$	10.6348	0.529759
$404$	16.4334	0.817591
$405$	11.2300	0.558021
$406$	41.8285	2.07591
$407$	10.2217	0.506669
$408$	4.93173	0.244157
$409$	−26.0155	−1.28638	−0.643192	−	0.765705i	$-0.722390\pi$
$409$	−26.0155	−1.28638	−0.643192	+	0.765705i	$0.722390\pi$
$410$	−3.12737	−0.154450
$411$	−9.78319	−0.482569
$412$	−12.9541	−0.638201
$413$	34.0762	1.67678
$414$	−12.2541	−0.602255
$415$	6.18517	0.303618
$416$	−3.69356	−0.181091
$417$	38.2033	1.87082
$418$	3.91291	0.191387
$419$	17.7419	0.866747	0.433373	−	0.901214i	$-0.357323\pi$
$419$	17.7419	0.866747	0.433373	+	0.901214i	$0.357323\pi$
$420$	−11.2041	−0.546705
$421$	7.77410	0.378886	0.189443	−	0.981892i	$-0.439332\pi$
$421$	7.77410	0.378886	0.189443	+	0.981892i	$0.439332\pi$
$422$	−2.25780	−0.109908
$423$	−15.2978	−0.743804
$424$	−0.670647	−0.0325695
$425$	2.28911	0.111038
$426$	−18.4052	−0.891735
$427$	40.0575	1.93852
$428$	−16.3514	−0.790373
$429$	−7.95753	−0.384193
$430$	−1.00000	−0.0482243
$431$	24.8823	1.19854	0.599270	−	0.800547i	$-0.295458\pi$
$431$	24.8823	1.19854	0.599270	+	0.800547i	$0.295458\pi$
$432$	−2.92661	−0.140807
$433$	32.3003	1.55226	0.776128	−	0.630576i	$-0.217181\pi$
$433$	32.3003	1.55226	0.776128	+	0.630576i	$0.217181\pi$
$434$	−14.9737	−0.718762
$435$	−17.3285	−0.830839
$436$	16.8177	0.805419
$437$	−29.2090	−1.39725
$438$	−21.1214	−1.00922
$439$	−33.5844	−1.60290	−0.801448	−	0.598064i	$-0.795937\pi$
$439$	−33.5844	−1.60290	−0.801448	+	0.598064i	$0.795937\pi$
$440$	−1.00000	−0.0476731
$441$	32.9058	1.56694
$442$	−8.45495	−0.402161
$443$	−26.5635	−1.26207	−0.631036	−	0.775754i	$-0.717370\pi$
$443$	−26.5635	−1.26207	−0.631036	+	0.775754i	$0.717370\pi$
$444$	22.0219	1.04511
$445$	5.34397	0.253329
$446$	−5.70292	−0.270041
$447$	−5.58080	−0.263963
$448$	5.20049	0.245700
$449$	36.7589	1.73476	0.867379	−	0.497648i	$-0.165803\pi$
$449$	36.7589	1.73476	0.867379	+	0.497648i	$0.165803\pi$
$450$	1.64159	0.0773852
$451$	3.12737	0.147262
$452$	−5.65787	−0.266124
$453$	45.0751	2.11781
$454$	−1.85378	−0.0870022
$455$	19.2083	0.900499
$456$	8.43011	0.394776
$457$	24.9793	1.16848	0.584241	−	0.811581i	$-0.301392\pi$
$457$	24.9793	1.16848	0.584241	+	0.811581i	$0.301392\pi$
$458$	−12.0610	−0.563574
$459$	−6.69932	−0.312698
$460$	7.46477	0.348047
$461$	−28.6874	−1.33610	−0.668052	−	0.744115i	$-0.732872\pi$
$461$	−28.6874	−1.33610	−0.668052	+	0.744115i	$0.732872\pi$
$462$	11.2041	0.521262
$463$	−6.94892	−0.322944	−0.161472	−	0.986877i	$-0.551624\pi$
$463$	−6.94892	−0.322944	−0.161472	+	0.986877i	$0.551624\pi$
$464$	8.04319	0.373396
$465$	6.20325	0.287669
$466$	6.65456	0.308267
$467$	−25.0640	−1.15982	−0.579911	−	0.814680i	$-0.696913\pi$
$467$	−25.0640	−1.15982	−0.579911	+	0.814680i	$0.696913\pi$
$468$	−6.06330	−0.280276
$469$	−22.3167	−1.03049
$470$	9.31889	0.429848
$471$	−29.3750	−1.35353
$472$	6.55249	0.301603
$473$	1.00000	0.0459800
$474$	24.7641	1.13745
$475$	3.91291	0.179537
$476$	11.9045	0.545641
$477$	−1.10093	−0.0504080
$478$	−15.6396	−0.715337
$479$	−24.7063	−1.12886	−0.564429	−	0.825482i	$-0.690904\pi$
$479$	−24.7063	−1.12886	−0.564429	+	0.825482i	$0.690904\pi$
$480$	−2.15443	−0.0983360
$481$	−37.7543	−1.72145
$482$	−0.896388	−0.0408294
$483$	−83.6361	−3.80557
$484$	1.00000	0.0454545
$485$	−5.40206	−0.245295
$486$	−15.4144	−0.699210
$487$	−27.4194	−1.24249	−0.621245	−	0.783617i	$-0.713373\pi$
$487$	−27.4194	−1.24249	−0.621245	+	0.783617i	$0.713373\pi$
$488$	7.70264	0.348682
$489$	−40.1952	−1.81769
$490$	−20.0451	−0.905544
$491$	−26.8303	−1.21084	−0.605418	−	0.795907i	$-0.706994\pi$
$491$	−26.8303	−1.21084	−0.605418	+	0.795907i	$0.706994\pi$
$492$	6.73771	0.303759
$493$	18.4117	0.829223
$494$	−14.4526	−0.650252
$495$	−1.64159	−0.0737839
$496$	−2.87929	−0.129284
$497$	−44.4275	−1.99284
$498$	−13.3255	−0.597131
$499$	−19.6464	−0.879495	−0.439748	−	0.898121i	$-0.644932\pi$
$499$	−19.6464	−0.879495	−0.439748	+	0.898121i	$0.644932\pi$
$500$	−1.00000	−0.0447214
$501$	5.34241	0.238681
$502$	3.71338	0.165736
$503$	−21.2482	−0.947409	−0.473705	−	0.880684i	$-0.657084\pi$
$503$	−21.2482	−0.947409	−0.473705	+	0.880684i	$0.657084\pi$
$504$	8.53706	0.380271
$505$	−16.4334	−0.731276
$506$	−7.46477	−0.331849
$507$	1.38392	0.0614619
$508$	−17.6856	−0.784670
$509$	−13.9210	−0.617036	−0.308518	−	0.951219i	$-0.599833\pi$
$509$	−13.9210	−0.617036	−0.308518	+	0.951219i	$0.599833\pi$
$510$	−4.93173	−0.218381
$511$	−50.9840	−2.25540
$512$	1.00000	0.0441942
$513$	−11.4516	−0.505599
$514$	5.07711	0.223942
$515$	12.9541	0.570824
$516$	2.15443	0.0948437
$517$	−9.31889	−0.409844
$518$	53.1576	2.33561
$519$	−6.28906	−0.276059
$520$	3.69356	0.161973
$521$	40.9486	1.79399	0.896995	−	0.442041i	$-0.145745\pi$
$521$	40.9486	1.79399	0.896995	+	0.442041i	$0.145745\pi$
$522$	13.2036	0.577906
$523$	21.5173	0.940887	0.470444	−	0.882430i	$-0.344094\pi$
$523$	21.5173	0.940887	0.470444	+	0.882430i	$0.344094\pi$
$524$	−16.4398	−0.718176
$525$	11.2041	0.488987
$526$	27.1172	1.18236
$527$	−6.59101	−0.287109
$528$	2.15443	0.0937597
$529$	32.7227	1.42273
$530$	0.670647	0.0291310
$531$	10.7565	0.466792
$532$	20.3491	0.882243
$533$	−11.5511	−0.500334
$534$	−11.5132	−0.498227
$535$	16.3514	0.706931
$536$	−4.29126	−0.185354
$537$	−29.6664	−1.28020
$538$	−2.78067	−0.119883
$539$	20.0451	0.863402
$540$	2.92661	0.125941
$541$	25.3884	1.09153	0.545766	−	0.837938i	$-0.316239\pi$
$541$	25.3884	1.09153	0.545766	+	0.837938i	$0.316239\pi$
$542$	−12.6460	−0.543191
$543$	−20.4827	−0.878996
$544$	2.28911	0.0981447
$545$	−16.8177	−0.720389
$546$	−41.3830	−1.77103
$547$	−27.2451	−1.16492	−0.582458	−	0.812861i	$-0.697909\pi$
$547$	−27.2451	−1.16492	−0.582458	+	0.812861i	$0.697909\pi$
$548$	−4.54096	−0.193980
$549$	12.6446	0.539657
$550$	1.00000	0.0426401
$551$	31.4723	1.34076
$552$	−16.0824	−0.684510
$553$	59.7768	2.54197
$554$	−6.74725	−0.286663
$555$	−22.0219	−0.934778
$556$	17.7324	0.752021
$557$	−38.6556	−1.63789	−0.818945	−	0.573872i	$-0.805441\pi$
$557$	−38.6556	−1.63789	−0.818945	+	0.573872i	$0.805441\pi$
$558$	−4.72661	−0.200094
$559$	−3.69356	−0.156221
$560$	−5.20049	−0.219761
$561$	4.93173	0.208218
$562$	−5.29405	−0.223316
$563$	−10.9047	−0.459579	−0.229790	−	0.973240i	$-0.573804\pi$
$563$	−10.9047	−0.459579	−0.229790	+	0.973240i	$0.573804\pi$
$564$	−20.0769	−0.845392
$565$	5.65787	0.238028
$566$	−0.938443	−0.0394457
$567$	−58.4012	−2.45262
$568$	−8.54294	−0.358454
$569$	−42.4101	−1.77792	−0.888961	−	0.457982i	$-0.848572\pi$
$569$	−42.4101	−1.77792	−0.888961	+	0.457982i	$0.848572\pi$
$570$	−8.43011	−0.353099
$571$	0.618946	0.0259021	0.0129510	−	0.999916i	$-0.495877\pi$
$571$	0.618946	0.0259021	0.0129510	+	0.999916i	$0.495877\pi$
$572$	−3.69356	−0.154435
$573$	48.1242	2.01042
$574$	16.2638	0.678839
$575$	−7.46477	−0.311302
$576$	1.64159	0.0683995
$577$	−27.3660	−1.13926	−0.569630	−	0.821901i	$-0.692914\pi$
$577$	−27.3660	−1.13926	−0.569630	+	0.821901i	$0.692914\pi$
$578$	−11.7600	−0.489151
$579$	12.4340	0.516738
$580$	−8.04319	−0.333975
$581$	−32.1659	−1.33447
$582$	11.6384	0.482426
$583$	−0.670647	−0.0277754
$584$	−9.80369	−0.405680
$585$	6.06330	0.250687
$586$	25.1151	1.03750
$587$	3.63605	0.150076	0.0750380	−	0.997181i	$-0.476092\pi$
$587$	3.63605	0.150076	0.0750380	+	0.997181i	$0.476092\pi$
$588$	43.1858	1.78095
$589$	−11.2664	−0.464225
$590$	−6.55249	−0.269762
$591$	16.7647	0.689606
$592$	10.2217	0.420108
$593$	2.40157	0.0986206	0.0493103	−	0.998784i	$-0.484298\pi$
$593$	2.40157	0.0986206	0.0493103	+	0.998784i	$0.484298\pi$
$594$	−2.92661	−0.120080
$595$	−11.9045	−0.488036
$596$	−2.59038	−0.106106
$597$	−37.1018	−1.51848
$598$	27.5715	1.12748
$599$	−21.5690	−0.881284	−0.440642	−	0.897683i	$-0.645249\pi$
$599$	−21.5690	−0.881284	−0.440642	+	0.897683i	$0.645249\pi$
$600$	2.15443	0.0879544
$601$	25.5815	1.04349	0.521745	−	0.853101i	$-0.325281\pi$
$601$	25.5815	1.04349	0.521745	+	0.853101i	$0.325281\pi$
$602$	5.20049	0.211956
$603$	−7.04449	−0.286874
$604$	20.9220	0.851304
$605$	−1.00000	−0.0406558
$606$	35.4046	1.43822
$607$	−16.2877	−0.661097	−0.330548	−	0.943789i	$-0.607234\pi$
$607$	−16.2877	−0.661097	−0.330548	+	0.943789i	$0.607234\pi$
$608$	3.91291	0.158690
$609$	90.1168	3.65172
$610$	−7.70264	−0.311871
$611$	34.4199	1.39248
$612$	3.75777	0.151899
$613$	−4.91861	−0.198661	−0.0993304	−	0.995055i	$-0.531670\pi$
$613$	−4.91861	−0.198661	−0.0993304	+	0.995055i	$0.531670\pi$
$614$	−11.3935	−0.459805
$615$	−6.73771	−0.271691
$616$	5.20049	0.209534
$617$	−18.4337	−0.742114	−0.371057	−	0.928610i	$-0.621004\pi$
$617$	−18.4337	−0.742114	−0.371057	+	0.928610i	$0.621004\pi$
$618$	−27.9087	−1.12265
$619$	26.7959	1.07702	0.538509	−	0.842620i	$-0.318988\pi$
$619$	26.7959	1.07702	0.538509	+	0.842620i	$0.318988\pi$
$620$	2.87929	0.115635
$621$	21.8464	0.876668
$622$	−4.64254	−0.186149
$623$	−27.7913	−1.11343
$624$	−7.95753	−0.318556
$625$	1.00000	0.0400000
$626$	−7.23924	−0.289338
$627$	8.43011	0.336666
$628$	−13.6347	−0.544083
$629$	23.3985	0.932959
$630$	−8.53706	−0.340125
$631$	−3.76933	−0.150055	−0.0750273	−	0.997181i	$-0.523904\pi$
$631$	−3.76933	−0.150055	−0.0750273	+	0.997181i	$0.523904\pi$
$632$	11.4945	0.457225
$633$	−4.86429	−0.193338
$634$	13.1816	0.523508
$635$	17.6856	0.701830
$636$	−1.44487	−0.0572926
$637$	−74.0376	−2.93348
$638$	8.04319	0.318433
$639$	−14.0240	−0.554781
$640$	−1.00000	−0.0395285
$641$	33.5915	1.32678	0.663392	−	0.748272i	$-0.269116\pi$
$641$	33.5915	1.32678	0.663392	+	0.748272i	$0.269116\pi$
$642$	−35.2280	−1.39034
$643$	−25.2666	−0.996417	−0.498208	−	0.867057i	$-0.666009\pi$
$643$	−25.2666	−0.996417	−0.498208	+	0.867057i	$0.666009\pi$
$644$	−38.8204	−1.52974
$645$	−2.15443	−0.0848308
$646$	8.95708	0.352412
$647$	38.3656	1.50831	0.754154	−	0.656698i	$-0.228047\pi$
$647$	38.3656	1.50831	0.754154	+	0.656698i	$0.228047\pi$
$648$	−11.2300	−0.441154
$649$	6.55249	0.257208
$650$	−3.69356	−0.144873
$651$	−32.2599	−1.26437
$652$	−18.6569	−0.730663
$653$	−13.4101	−0.524777	−0.262388	−	0.964962i	$-0.584510\pi$
$653$	−13.4101	−0.524777	−0.262388	+	0.964962i	$0.584510\pi$
$654$	36.2325	1.41680
$655$	16.4398	0.642357
$656$	3.12737	0.122103
$657$	−16.0936	−0.627872
$658$	−48.4628	−1.88928
$659$	−13.5960	−0.529624	−0.264812	−	0.964300i	$-0.585310\pi$
$659$	−13.5960	−0.529624	−0.264812	+	0.964300i	$0.585310\pi$
$660$	−2.15443	−0.0838613
$661$	−14.5741	−0.566868	−0.283434	−	0.958992i	$-0.591474\pi$
$661$	−14.5741	−0.566868	−0.283434	+	0.958992i	$0.591474\pi$
$662$	5.45659	0.212076
$663$	−18.2156	−0.707437
$664$	−6.18517	−0.240031
$665$	−20.3491	−0.789102
$666$	16.7798	0.650203
$667$	−60.0405	−2.32478
$668$	2.47973	0.0959435
$669$	−12.2866	−0.475026
$670$	4.29126	0.165786
$671$	7.70264	0.297357
$672$	11.2041	0.432208
$673$	20.4531	0.788408	0.394204	−	0.919023i	$-0.371020\pi$
$673$	20.4531	0.788408	0.394204	+	0.919023i	$0.371020\pi$
$674$	23.7542	0.914978
$675$	−2.92661	−0.112645
$676$	0.642357	0.0247061
$677$	−23.6276	−0.908082	−0.454041	−	0.890981i	$-0.650018\pi$
$677$	−23.6276	−0.908082	−0.454041	+	0.890981i	$0.650018\pi$
$678$	−12.1895	−0.468136
$679$	28.0933	1.07812
$680$	−2.28911	−0.0877833
$681$	−3.99385	−0.153045
$682$	−2.87929	−0.110254
$683$	−20.3160	−0.777371	−0.388685	−	0.921371i	$-0.627071\pi$
$683$	−20.3160	−0.777371	−0.388685	+	0.921371i	$0.627071\pi$
$684$	6.42339	0.245605
$685$	4.54096	0.173501
$686$	67.8407	2.59017
$687$	−25.9847	−0.991376
$688$	1.00000	0.0381246
$689$	2.47707	0.0943690
$690$	16.0824	0.612245
$691$	−33.7100	−1.28239	−0.641194	−	0.767379i	$-0.721561\pi$
$691$	−33.7100	−1.28239	−0.641194	+	0.767379i	$0.721561\pi$
$692$	−2.91913	−0.110968
$693$	8.53706	0.324296
$694$	−27.5506	−1.04581
$695$	−17.7324	−0.672628
$696$	17.3285	0.656836
$697$	7.15888	0.271162
$698$	19.1046	0.723119
$699$	14.3368	0.542268
$700$	5.20049	0.196560
$701$	−25.8681	−0.977025	−0.488513	−	0.872557i	$-0.662460\pi$
$701$	−25.8681	−0.977025	−0.488513	+	0.872557i	$0.662460\pi$
$702$	10.8096	0.407982
$703$	39.9965	1.50850
$704$	1.00000	0.0376889
$705$	20.0769	0.756141
$706$	−19.9199	−0.749694
$707$	85.4616	3.21411
$708$	14.1169	0.530546
$709$	31.4230	1.18012	0.590058	−	0.807361i	$-0.299105\pi$
$709$	31.4230	1.18012	0.590058	+	0.807361i	$0.299105\pi$
$710$	8.54294	0.320611
$711$	18.8692	0.707649
$712$	−5.34397	−0.200274
$713$	21.4933	0.804929
$714$	25.6474	0.959831
$715$	3.69356	0.138131
$716$	−13.7699	−0.514606
$717$	−33.6944	−1.25834
$718$	−6.69249	−0.249761
$719$	−9.03068	−0.336787	−0.168394	−	0.985720i	$-0.553858\pi$
$719$	−9.03068	−0.336787	−0.168394	+	0.985720i	$0.553858\pi$
$720$	−1.64159	−0.0611784
$721$	−67.3674	−2.50889
$722$	−3.68911	−0.137295
$723$	−1.93121	−0.0718225
$724$	−9.50722	−0.353333
$725$	8.04319	0.298717
$726$	2.15443	0.0799586
$727$	−3.98733	−0.147882	−0.0739410	−	0.997263i	$-0.523558\pi$
$727$	−3.98733	−0.147882	−0.0739410	+	0.997263i	$0.523558\pi$
$728$	−19.2083	−0.711907
$729$	0.480600	0.0178000
$730$	9.80369	0.362851
$731$	2.28911	0.0846657
$732$	16.5948	0.613362
$733$	−22.6962	−0.838303	−0.419151	−	0.907916i	$-0.637672\pi$
$733$	−22.6962	−0.838303	−0.419151	+	0.907916i	$0.637672\pi$
$734$	−10.2267	−0.377473
$735$	−43.1858	−1.59293
$736$	−7.46477	−0.275155
$737$	−4.29126	−0.158071
$738$	5.13385	0.188980
$739$	33.6588	1.23816	0.619079	−	0.785328i	$-0.287506\pi$
$739$	33.6588	1.23816	0.619079	+	0.785328i	$0.287506\pi$
$740$	−10.2217	−0.375756
$741$	−31.1371	−1.14385
$742$	−3.48769	−0.128037
$743$	−9.34944	−0.342998	−0.171499	−	0.985184i	$-0.554861\pi$
$743$	−9.34944	−0.342998	−0.171499	+	0.985184i	$0.554861\pi$
$744$	−6.20325	−0.227422
$745$	2.59038	0.0949042
$746$	18.4363	0.675000
$747$	−10.1535	−0.371497
$748$	2.28911	0.0836981
$749$	−85.0351	−3.10711
$750$	−2.15443	−0.0786688
$751$	52.3542	1.91043	0.955216	−	0.295908i	$-0.0956223\pi$
$751$	52.3542	1.91043	0.955216	+	0.295908i	$0.0956223\pi$
$752$	−9.31889	−0.339825
$753$	8.00024	0.291545
$754$	−29.7080	−1.08190
$755$	−20.9220	−0.761429
$756$	−15.2198	−0.553539
$757$	38.6890	1.40618	0.703088	−	0.711103i	$-0.251804\pi$
$757$	38.6890	1.40618	0.703088	+	0.711103i	$0.251804\pi$
$758$	2.83712	0.103049
$759$	−16.0824	−0.583752
$760$	−3.91291	−0.141936
$761$	−20.6832	−0.749765	−0.374882	−	0.927072i	$-0.622317\pi$
$761$	−20.6832	−0.749765	−0.374882	+	0.927072i	$0.622317\pi$
$762$	−38.1024	−1.38030
$763$	87.4600	3.16626
$764$	22.3373	0.808134
$765$	−3.75777	−0.135863
$766$	13.9972	0.505739
$767$	−24.2020	−0.873884
$768$	2.15443	0.0777415
$769$	6.62323	0.238840	0.119420	−	0.992844i	$-0.461897\pi$
$769$	6.62323	0.238840	0.119420	+	0.992844i	$0.461897\pi$
$770$	−5.20049	−0.187413
$771$	10.9383	0.393933
$772$	5.77134	0.207715
$773$	−44.9087	−1.61525	−0.807627	−	0.589694i	$-0.799248\pi$
$773$	−44.9087	−1.61525	−0.807627	+	0.589694i	$0.799248\pi$
$774$	1.64159	0.0590057
$775$	−2.87929	−0.103427
$776$	5.40206	0.193923
$777$	114.525	4.10855
$778$	−3.40004	−0.121897
$779$	12.2371	0.438440
$780$	7.95753	0.284925
$781$	−8.54294	−0.305690
$782$	−17.0877	−0.611053
$783$	−23.5393	−0.841225
$784$	20.0451	0.715895
$785$	13.6347	0.486643
$786$	−35.4185	−1.26334
$787$	10.4312	0.371832	0.185916	−	0.982566i	$-0.440475\pi$
$787$	10.4312	0.371832	0.185916	+	0.982566i	$0.440475\pi$
$788$	7.78147	0.277203
$789$	58.4222	2.07988
$790$	−11.4945	−0.408954
$791$	−29.4237	−1.04619
$792$	1.64159	0.0583313
$793$	−28.4501	−1.01029
$794$	19.0532	0.676172
$795$	1.44487	0.0512441
$796$	−17.2211	−0.610387
$797$	32.0697	1.13597	0.567983	−	0.823040i	$-0.307724\pi$
$797$	32.0697	1.13597	0.567983	+	0.823040i	$0.307724\pi$
$798$	43.8407	1.55194
$799$	−21.3320	−0.754670
$800$	1.00000	0.0353553
$801$	−8.77260	−0.309965
$802$	6.62751	0.234026
$803$	−9.80369	−0.345965
$804$	−9.24525	−0.326055
$805$	38.8204	1.36824
$806$	10.6348	0.374596
$807$	−5.99077	−0.210885
$808$	16.4334	0.578124
$809$	−10.9308	−0.384308	−0.192154	−	0.981365i	$-0.561547\pi$
$809$	−10.9308	−0.384308	−0.192154	+	0.981365i	$0.561547\pi$
$810$	11.2300	0.394580
$811$	9.65584	0.339063	0.169531	−	0.985525i	$-0.445775\pi$
$811$	9.65584	0.339063	0.169531	+	0.985525i	$0.445775\pi$
$812$	41.8285	1.46789
$813$	−27.2449	−0.955522
$814$	10.2217	0.358269
$815$	18.6569	0.653524
$816$	4.93173	0.172645
$817$	3.91291	0.136895
$818$	−26.0155	−0.909611
$819$	−31.5321	−1.10182
$820$	−3.12737	−0.109212
$821$	−27.9243	−0.974565	−0.487283	−	0.873244i	$-0.662012\pi$
$821$	−27.9243	−0.974565	−0.487283	+	0.873244i	$0.662012\pi$
$822$	−9.78319	−0.341228
$823$	−18.5996	−0.648341	−0.324170	−	0.945999i	$-0.605085\pi$
$823$	−18.5996	−0.648341	−0.324170	+	0.945999i	$0.605085\pi$
$824$	−12.9541	−0.451276
$825$	2.15443	0.0750078
$826$	34.0762	1.18566
$827$	45.5295	1.58322	0.791608	−	0.611030i	$-0.209244\pi$
$827$	45.5295	1.58322	0.791608	+	0.611030i	$0.209244\pi$
$828$	−12.2541	−0.425859
$829$	44.6185	1.54967	0.774833	−	0.632166i	$-0.217834\pi$
$829$	44.6185	1.54967	0.774833	+	0.632166i	$0.217834\pi$
$830$	6.18517	0.214690
$831$	−14.5365	−0.504266
$832$	−3.69356	−0.128051
$833$	45.8853	1.58983
$834$	38.2033	1.32287
$835$	−2.47973	−0.0858145
$836$	3.91291	0.135331
$837$	8.42656	0.291265
$838$	17.7419	0.612883
$839$	−6.02623	−0.208048	−0.104024	−	0.994575i	$-0.533172\pi$
$839$	−6.02623	−0.208048	−0.104024	+	0.994575i	$0.533172\pi$
$840$	−11.2041	−0.386579
$841$	35.6929	1.23079
$842$	7.77410	0.267913
$843$	−11.4057	−0.392832
$844$	−2.25780	−0.0777168
$845$	−0.642357	−0.0220978
$846$	−15.2978	−0.525949
$847$	5.20049	0.178691
$848$	−0.670647	−0.0230301
$849$	−2.02181	−0.0693884
$850$	2.28911	0.0785158
$851$	−76.3023	−2.61561
$852$	−18.4052	−0.630552
$853$	37.9163	1.29823	0.649116	−	0.760690i	$-0.275139\pi$
$853$	37.9163	1.29823	0.649116	+	0.760690i	$0.275139\pi$
$854$	40.0575	1.37074
$855$	−6.42339	−0.219675
$856$	−16.3514	−0.558878
$857$	9.15268	0.312650	0.156325	−	0.987706i	$-0.450035\pi$
$857$	9.15268	0.312650	0.156325	+	0.987706i	$0.450035\pi$
$858$	−7.95753	−0.271665
$859$	−6.50679	−0.222009	−0.111004	−	0.993820i	$-0.535407\pi$
$859$	−6.50679	−0.222009	−0.111004	+	0.993820i	$0.535407\pi$
$860$	−1.00000	−0.0340997
$861$	35.0394	1.19414
$862$	24.8823	0.847495
$863$	−12.9822	−0.441918	−0.220959	−	0.975283i	$-0.570919\pi$
$863$	−12.9822	−0.441918	−0.220959	+	0.975283i	$0.570919\pi$
$864$	−2.92661	−0.0995653
$865$	2.91913	0.0992532
$866$	32.3003	1.09761
$867$	−25.3361	−0.860460
$868$	−14.9737	−0.508242
$869$	11.4945	0.389923
$870$	−17.3285	−0.587492
$871$	15.8500	0.537057
$872$	16.8177	0.569518
$873$	8.86796	0.300135
$874$	−29.2090	−0.988008
$875$	−5.20049	−0.175809
$876$	−21.1214	−0.713626
$877$	−15.6834	−0.529592	−0.264796	−	0.964305i	$-0.585305\pi$
$877$	−15.6834	−0.529592	−0.264796	+	0.964305i	$0.585305\pi$
$878$	−33.5844	−1.13342
$879$	54.1089	1.82505
$880$	−1.00000	−0.0337100
$881$	−33.4494	−1.12694	−0.563469	−	0.826137i	$-0.690533\pi$
$881$	−33.4494	−1.12694	−0.563469	+	0.826137i	$0.690533\pi$
$882$	32.9058	1.10799
$883$	−57.8360	−1.94634	−0.973168	−	0.230098i	$-0.926095\pi$
$883$	−57.8360	−1.94634	−0.973168	+	0.230098i	$0.926095\pi$
$884$	−8.45495	−0.284371
$885$	−14.1169	−0.474535
$886$	−26.5635	−0.892419
$887$	9.92486	0.333244	0.166622	−	0.986021i	$-0.446714\pi$
$887$	9.92486	0.333244	0.166622	+	0.986021i	$0.446714\pi$
$888$	22.0219	0.739007
$889$	−91.9735	−3.08469
$890$	5.34397	0.179130
$891$	−11.2300	−0.376218
$892$	−5.70292	−0.190948
$893$	−36.4640	−1.22022
$894$	−5.58080	−0.186650
$895$	13.7699	0.460278
$896$	5.20049	0.173736
$897$	59.4011	1.98334
$898$	36.7589	1.22666
$899$	−23.1587	−0.772386
$900$	1.64159	0.0547196
$901$	−1.53518	−0.0511444
$902$	3.12737	0.104130
$903$	11.2041	0.372849
$904$	−5.65787	−0.188178
$905$	9.50722	0.316031
$906$	45.0751	1.49752
$907$	48.1403	1.59847	0.799236	−	0.601017i	$-0.205238\pi$
$907$	48.1403	1.59847	0.799236	+	0.601017i	$0.205238\pi$
$908$	−1.85378	−0.0615199
$909$	26.9768	0.894765
$910$	19.2083	0.636749
$911$	40.6760	1.34766	0.673829	−	0.738888i	$-0.264649\pi$
$911$	40.6760	1.34766	0.673829	+	0.738888i	$0.264649\pi$
$912$	8.43011	0.279149
$913$	−6.18517	−0.204699
$914$	24.9793	0.826241
$915$	−16.5948	−0.548608
$916$	−12.0610	−0.398507
$917$	−85.4950	−2.82329
$918$	−6.69932	−0.221111
$919$	33.9679	1.12050	0.560249	−	0.828324i	$-0.310705\pi$
$919$	33.9679	1.12050	0.560249	+	0.828324i	$0.310705\pi$
$920$	7.46477	0.246106
$921$	−24.5466	−0.808837
$922$	−28.6874	−0.944768
$923$	31.5538	1.03861
$924$	11.2041	0.368588
$925$	10.2217	0.336086
$926$	−6.94892	−0.228356
$927$	−21.2652	−0.698442
$928$	8.04319	0.264031
$929$	10.5337	0.345600	0.172800	−	0.984957i	$-0.444718\pi$
$929$	10.5337	0.345600	0.172800	+	0.984957i	$0.444718\pi$
$930$	6.20325	0.203413
$931$	78.4346	2.57059
$932$	6.65456	0.217977
$933$	−10.0021	−0.327453
$934$	−25.0640	−0.820118
$935$	−2.28911	−0.0748618
$936$	−6.06330	−0.198185
$937$	5.91694	0.193298	0.0966490	−	0.995319i	$-0.469188\pi$
$937$	5.91694	0.193298	0.0966490	+	0.995319i	$0.469188\pi$
$938$	−22.3167	−0.728665
$939$	−15.5965	−0.508972
$940$	9.31889	0.303949
$941$	−26.3145	−0.857829	−0.428914	−	0.903345i	$-0.641104\pi$
$941$	−26.3145	−0.857829	−0.428914	+	0.903345i	$0.641104\pi$
$942$	−29.3750	−0.957090
$943$	−23.3451	−0.760220
$944$	6.55249	0.213265
$945$	15.2198	0.495100
$946$	1.00000	0.0325128
$947$	−44.4225	−1.44354	−0.721769	−	0.692134i	$-0.756671\pi$
$947$	−44.4225	−1.44354	−0.721769	+	0.692134i	$0.756671\pi$
$948$	24.7641	0.804299
$949$	36.2105	1.17544
$950$	3.91291	0.126952
$951$	28.3989	0.920898
$952$	11.9045	0.385826
$953$	31.1009	1.00746	0.503729	−	0.863862i	$-0.331961\pi$
$953$	31.1009	1.00746	0.503729	+	0.863862i	$0.331961\pi$
$954$	−1.10093	−0.0356438
$955$	−22.3373	−0.722817
$956$	−15.6396	−0.505819
$957$	17.3285	0.560152
$958$	−24.7063	−0.798223
$959$	−23.6152	−0.762574
$960$	−2.15443	−0.0695341
$961$	−22.7097	−0.732570
$962$	−37.7543	−1.21725
$963$	−26.8422	−0.864979
$964$	−0.896388	−0.0288707
$965$	−5.77134	−0.185786
$966$	−83.6361	−2.69095
$967$	42.4769	1.36596	0.682982	−	0.730435i	$-0.260683\pi$
$967$	42.4769	1.36596	0.682982	+	0.730435i	$0.260683\pi$
$968$	1.00000	0.0321412
$969$	19.2974	0.619923
$970$	−5.40206	−0.173450
$971$	−17.2183	−0.552562	−0.276281	−	0.961077i	$-0.589102\pi$
$971$	−17.2183	−0.552562	−0.276281	+	0.961077i	$0.589102\pi$
$972$	−15.4144	−0.494416
$973$	92.2171	2.95635
$974$	−27.4194	−0.878573
$975$	−7.95753	−0.254845
$976$	7.70264	0.246555
$977$	9.75852	0.312203	0.156101	−	0.987741i	$-0.450107\pi$
$977$	9.75852	0.312203	0.156101	+	0.987741i	$0.450107\pi$
$978$	−40.1952	−1.28530
$979$	−5.34397	−0.170794
$980$	−20.0451	−0.640316
$981$	27.6077	0.881445
$982$	−26.8303	−0.856191
$983$	45.8749	1.46318	0.731591	−	0.681744i	$-0.238778\pi$
$983$	45.8749	1.46318	0.731591	+	0.681744i	$0.238778\pi$
$984$	6.73771	0.214790
$985$	−7.78147	−0.247938
$986$	18.4117	0.586349
$987$	−104.410	−3.32340
$988$	−14.4526	−0.459797
$989$	−7.46477	−0.237366
$990$	−1.64159	−0.0521731
$991$	−14.7351	−0.468077	−0.234039	−	0.972227i	$-0.575194\pi$
$991$	−14.7351	−0.468077	−0.234039	+	0.972227i	$0.575194\pi$
$992$	−2.87929	−0.0914177
$993$	11.7559	0.373061
$994$	−44.4275	−1.40915
$995$	17.2211	0.545946
$996$	−13.3255	−0.422236
$997$	11.3414	0.359185	0.179592	−	0.983741i	$-0.442522\pi$
$997$	11.3414	0.359185	0.179592	+	0.983741i	$0.442522\pi$
$998$	−19.6464	−0.621897
$999$	−29.9148	−0.946463

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.10	✓	13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.15443 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.15443 q^{6} +5.20049 q^{7} +1.00000 q^{8} +1.64159 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.15443 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.15443 q^{6} +5.20049 q^{7} +1.00000 q^{8} +1.64159 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.15443 q^{12} -3.69356 q^{13} +5.20049 q^{14} -2.15443 q^{15} +1.00000 q^{16} +2.28911 q^{17} +1.64159 q^{18} +3.91291 q^{19} -1.00000 q^{20} +11.2041 q^{21} +1.00000 q^{22} -7.46477 q^{23} +2.15443 q^{24} +1.00000 q^{25} -3.69356 q^{26} -2.92661 q^{27} +5.20049 q^{28} +8.04319 q^{29} -2.15443 q^{30} -2.87929 q^{31} +1.00000 q^{32} +2.15443 q^{33} +2.28911 q^{34} -5.20049 q^{35} +1.64159 q^{36} +10.2217 q^{37} +3.91291 q^{38} -7.95753 q^{39} -1.00000 q^{40} +3.12737 q^{41} +11.2041 q^{42} +1.00000 q^{43} +1.00000 q^{44} -1.64159 q^{45} -7.46477 q^{46} -9.31889 q^{47} +2.15443 q^{48} +20.0451 q^{49} +1.00000 q^{50} +4.93173 q^{51} -3.69356 q^{52} -0.670647 q^{53} -2.92661 q^{54} -1.00000 q^{55} +5.20049 q^{56} +8.43011 q^{57} +8.04319 q^{58} +6.55249 q^{59} -2.15443 q^{60} +7.70264 q^{61} -2.87929 q^{62} +8.53706 q^{63} +1.00000 q^{64} +3.69356 q^{65} +2.15443 q^{66} -4.29126 q^{67} +2.28911 q^{68} -16.0824 q^{69} -5.20049 q^{70} -8.54294 q^{71} +1.64159 q^{72} -9.80369 q^{73} +10.2217 q^{74} +2.15443 q^{75} +3.91291 q^{76} +5.20049 q^{77} -7.95753 q^{78} +11.4945 q^{79} -1.00000 q^{80} -11.2300 q^{81} +3.12737 q^{82} -6.18517 q^{83} +11.2041 q^{84} -2.28911 q^{85} +1.00000 q^{86} +17.3285 q^{87} +1.00000 q^{88} -5.34397 q^{89} -1.64159 q^{90} -19.2083 q^{91} -7.46477 q^{92} -6.20325 q^{93} -9.31889 q^{94} -3.91291 q^{95} +2.15443 q^{96} +5.40206 q^{97} +20.0451 q^{98} +1.64159 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9} - 13 q^{10} + 13 q^{11} + 11 q^{13} + 7 q^{14} + 13 q^{16} - 2 q^{17} + 25 q^{18} + 7 q^{19} - 13 q^{20} + 12 q^{21} + 13 q^{22} + 12 q^{23} + 13 q^{25} + 11 q^{26} - 15 q^{27} + 7 q^{28} + 14 q^{29} + 20 q^{31} + 13 q^{32} - 2 q^{34} - 7 q^{35} + 25 q^{36} + 17 q^{37} + 7 q^{38} - 4 q^{39} - 13 q^{40} + 9 q^{41} + 12 q^{42} + 13 q^{43} + 13 q^{44} - 25 q^{45} + 12 q^{46} - 9 q^{47} + 30 q^{49} + 13 q^{50} - 3 q^{51} + 11 q^{52} + 22 q^{53} - 15 q^{54} - 13 q^{55} + 7 q^{56} + 17 q^{57} + 14 q^{58} + 19 q^{59} + 2 q^{61} + 20 q^{62} + 12 q^{63} + 13 q^{64} - 11 q^{65} + 9 q^{67} - 2 q^{68} - 6 q^{69} - 7 q^{70} + 6 q^{71} + 25 q^{72} + 7 q^{73} + 17 q^{74} + 7 q^{76} + 7 q^{77} - 4 q^{78} + 50 q^{79} - 13 q^{80} + 85 q^{81} + 9 q^{82} + q^{83} + 12 q^{84} + 2 q^{85} + 13 q^{86} - 21 q^{87} + 13 q^{88} + 5 q^{89} - 25 q^{90} + 5 q^{91} + 12 q^{92} + 3 q^{93} - 9 q^{94} - 7 q^{95} + 20 q^{97} + 30 q^{98} + 25 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9 - 13 * q^10 + 13 * q^11 + 11 * q^13 + 7 * q^14 + 13 * q^16 - 2 * q^17 + 25 * q^18 + 7 * q^19 - 13 * q^20 + 12 * q^21 + 13 * q^22 + 12 * q^23 + 13 * q^25 + 11 * q^26 - 15 * q^27 + 7 * q^28 + 14 * q^29 + 20 * q^31 + 13 * q^32 - 2 * q^34 - 7 * q^35 + 25 * q^36 + 17 * q^37 + 7 * q^38 - 4 * q^39 - 13 * q^40 + 9 * q^41 + 12 * q^42 + 13 * q^43 + 13 * q^44 - 25 * q^45 + 12 * q^46 - 9 * q^47 + 30 * q^49 + 13 * q^50 - 3 * q^51 + 11 * q^52 + 22 * q^53 - 15 * q^54 - 13 * q^55 + 7 * q^56 + 17 * q^57 + 14 * q^58 + 19 * q^59 + 2 * q^61 + 20 * q^62 + 12 * q^63 + 13 * q^64 - 11 * q^65 + 9 * q^67 - 2 * q^68 - 6 * q^69 - 7 * q^70 + 6 * q^71 + 25 * q^72 + 7 * q^73 + 17 * q^74 + 7 * q^76 + 7 * q^77 - 4 * q^78 + 50 * q^79 - 13 * q^80 + 85 * q^81 + 9 * q^82 + q^83 + 12 * q^84 + 2 * q^85 + 13 * q^86 - 21 * q^87 + 13 * q^88 + 5 * q^89 - 25 * q^90 + 5 * q^91 + 12 * q^92 + 3 * q^93 - 9 * q^94 - 7 * q^95 + 20 * q^97 + 30 * q^98 + 25 * q^99

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