LMFDB - Embedded newform 4730.2.a.bf.1.2

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			1.2
Root			$3.26258$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -3.26258 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.26258 q^{6} +2.73152 q^{7} +1.00000 q^{8} +7.64446 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.26258 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.26258 q^{6} +2.73152 q^{7} +1.00000 q^{8} +7.64446 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.26258 q^{12} +6.11752 q^{13} +2.73152 q^{14} +3.26258 q^{15} +1.00000 q^{16} +7.48258 q^{17} +7.64446 q^{18} -7.78028 q^{19} -1.00000 q^{20} -8.91182 q^{21} +1.00000 q^{22} +8.88984 q^{23} -3.26258 q^{24} +1.00000 q^{25} +6.11752 q^{26} -15.1529 q^{27} +2.73152 q^{28} +6.36025 q^{29} +3.26258 q^{30} +6.01389 q^{31} +1.00000 q^{32} -3.26258 q^{33} +7.48258 q^{34} -2.73152 q^{35} +7.64446 q^{36} -0.607804 q^{37} -7.78028 q^{38} -19.9589 q^{39} -1.00000 q^{40} +2.66769 q^{41} -8.91182 q^{42} +1.00000 q^{43} +1.00000 q^{44} -7.64446 q^{45} +8.88984 q^{46} +0.852378 q^{47} -3.26258 q^{48} +0.461206 q^{49} +1.00000 q^{50} -24.4126 q^{51} +6.11752 q^{52} -9.54066 q^{53} -15.1529 q^{54} -1.00000 q^{55} +2.73152 q^{56} +25.3838 q^{57} +6.36025 q^{58} -1.12856 q^{59} +3.26258 q^{60} +9.95844 q^{61} +6.01389 q^{62} +20.8810 q^{63} +1.00000 q^{64} -6.11752 q^{65} -3.26258 q^{66} -11.0418 q^{67} +7.48258 q^{68} -29.0039 q^{69} -2.73152 q^{70} -4.13401 q^{71} +7.64446 q^{72} -13.2485 q^{73} -0.607804 q^{74} -3.26258 q^{75} -7.78028 q^{76} +2.73152 q^{77} -19.9589 q^{78} -2.52486 q^{79} -1.00000 q^{80} +26.5044 q^{81} +2.66769 q^{82} -12.7935 q^{83} -8.91182 q^{84} -7.48258 q^{85} +1.00000 q^{86} -20.7509 q^{87} +1.00000 q^{88} +1.91784 q^{89} -7.64446 q^{90} +16.7101 q^{91} +8.88984 q^{92} -19.6208 q^{93} +0.852378 q^{94} +7.78028 q^{95} -3.26258 q^{96} +12.9532 q^{97} +0.461206 q^{98} +7.64446 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.26258	−1.88365	−0.941827	−	0.336098i	$-0.890893\pi$
$3$	−3.26258	−1.88365	−0.941827	+	0.336098i	$0.890893\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−3.26258	−1.33194
$7$	2.73152	1.03242	0.516209	−	0.856463i	$-0.327343\pi$
$7$	2.73152	1.03242	0.516209	+	0.856463i	$0.327343\pi$
$8$	1.00000	0.353553
$9$	7.64446	2.54815
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.26258	−0.941827
$13$	6.11752	1.69670	0.848348	−	0.529439i	$-0.177598\pi$
$13$	6.11752	1.69670	0.848348	+	0.529439i	$0.177598\pi$
$14$	2.73152	0.730030
$15$	3.26258	0.842396
$16$	1.00000	0.250000
$17$	7.48258	1.81479	0.907396	−	0.420276i	$-0.138067\pi$
$17$	7.48258	1.81479	0.907396	+	0.420276i	$0.138067\pi$
$18$	7.64446	1.80182
$19$	−7.78028	−1.78492	−0.892459	−	0.451128i	$-0.851022\pi$
$19$	−7.78028	−1.78492	−0.892459	+	0.451128i	$0.851022\pi$
$20$	−1.00000	−0.223607
$21$	−8.91182	−1.94472
$22$	1.00000	0.213201
$23$	8.88984	1.85366	0.926830	−	0.375481i	$-0.122523\pi$
$23$	8.88984	1.85366	0.926830	+	0.375481i	$0.122523\pi$
$24$	−3.26258	−0.665972
$25$	1.00000	0.200000
$26$	6.11752	1.19974
$27$	−15.1529	−2.91618
$28$	2.73152	0.516209
$29$	6.36025	1.18107	0.590534	−	0.807012i	$-0.298917\pi$
$29$	6.36025	1.18107	0.590534	+	0.807012i	$0.298917\pi$
$30$	3.26258	0.595664
$31$	6.01389	1.08013	0.540064	−	0.841624i	$-0.318400\pi$
$31$	6.01389	1.08013	0.540064	+	0.841624i	$0.318400\pi$
$32$	1.00000	0.176777
$33$	−3.26258	−0.567943
$34$	7.48258	1.28325
$35$	−2.73152	−0.461711
$36$	7.64446	1.27408
$37$	−0.607804	−0.0999224	−0.0499612	−	0.998751i	$-0.515910\pi$
$37$	−0.607804	−0.0999224	−0.0499612	+	0.998751i	$0.515910\pi$
$38$	−7.78028	−1.26213
$39$	−19.9589	−3.19599
$40$	−1.00000	−0.158114
$41$	2.66769	0.416624	0.208312	−	0.978062i	$-0.433203\pi$
$41$	2.66769	0.416624	0.208312	+	0.978062i	$0.433203\pi$
$42$	−8.91182	−1.37512
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−7.64446	−1.13957
$46$	8.88984	1.31074
$47$	0.852378	0.124332	0.0621660	−	0.998066i	$-0.480199\pi$
$47$	0.852378	0.124332	0.0621660	+	0.998066i	$0.480199\pi$
$48$	−3.26258	−0.470914
$49$	0.461206	0.0658865
$50$	1.00000	0.141421
$51$	−24.4126	−3.41844
$52$	6.11752	0.848348
$53$	−9.54066	−1.31051	−0.655255	−	0.755408i	$-0.727439\pi$
$53$	−9.54066	−1.31051	−0.655255	+	0.755408i	$0.727439\pi$
$54$	−15.1529	−2.06205
$55$	−1.00000	−0.134840
$56$	2.73152	0.365015
$57$	25.3838	3.36217
$58$	6.36025	0.835142
$59$	−1.12856	−0.146926	−0.0734632	−	0.997298i	$-0.523405\pi$
$59$	−1.12856	−0.146926	−0.0734632	+	0.997298i	$0.523405\pi$
$60$	3.26258	0.421198
$61$	9.95844	1.27505	0.637524	−	0.770431i	$-0.279959\pi$
$61$	9.95844	1.27505	0.637524	+	0.770431i	$0.279959\pi$
$62$	6.01389	0.763765
$63$	20.8810	2.63076
$64$	1.00000	0.125000
$65$	−6.11752	−0.758785
$66$	−3.26258	−0.401596
$67$	−11.0418	−1.34897	−0.674487	−	0.738286i	$-0.735635\pi$
$67$	−11.0418	−1.34897	−0.674487	+	0.738286i	$0.735635\pi$
$68$	7.48258	0.907396
$69$	−29.0039	−3.49165
$70$	−2.73152	−0.326479
$71$	−4.13401	−0.490616	−0.245308	−	0.969445i	$-0.578889\pi$
$71$	−4.13401	−0.490616	−0.245308	+	0.969445i	$0.578889\pi$
$72$	7.64446	0.900908
$73$	−13.2485	−1.55062	−0.775309	−	0.631582i	$-0.782406\pi$
$73$	−13.2485	−1.55062	−0.775309	+	0.631582i	$0.782406\pi$
$74$	−0.607804	−0.0706558
$75$	−3.26258	−0.376731
$76$	−7.78028	−0.892459
$77$	2.73152	0.311286
$78$	−19.9589	−2.25990
$79$	−2.52486	−0.284069	−0.142034	−	0.989862i	$-0.545364\pi$
$79$	−2.52486	−0.284069	−0.142034	+	0.989862i	$0.545364\pi$
$80$	−1.00000	−0.111803
$81$	26.5044	2.94493
$82$	2.66769	0.294597
$83$	−12.7935	−1.40427	−0.702135	−	0.712043i	$-0.747770\pi$
$83$	−12.7935	−1.40427	−0.702135	+	0.712043i	$0.747770\pi$
$84$	−8.91182	−0.972359
$85$	−7.48258	−0.811600
$86$	1.00000	0.107833
$87$	−20.7509	−2.22473
$88$	1.00000	0.106600
$89$	1.91784	0.203290	0.101645	−	0.994821i	$-0.467589\pi$
$89$	1.91784	0.203290	0.101645	+	0.994821i	$0.467589\pi$
$90$	−7.64446	−0.805797
$91$	16.7101	1.75170
$92$	8.88984	0.926830
$93$	−19.6208	−2.03459
$94$	0.852378	0.0879160
$95$	7.78028	0.798240
$96$	−3.26258	−0.332986
$97$	12.9532	1.31520	0.657601	−	0.753366i	$-0.271571\pi$
$97$	12.9532	1.31520	0.657601	+	0.753366i	$0.271571\pi$
$98$	0.461206	0.0465888
$99$	7.64446	0.768297
$100$	1.00000	0.100000
$101$	3.60944	0.359152	0.179576	−	0.983744i	$-0.442527\pi$
$101$	3.60944	0.359152	0.179576	+	0.983744i	$0.442527\pi$
$102$	−24.4126	−2.41720
$103$	−1.89824	−0.187039	−0.0935197	−	0.995617i	$-0.529812\pi$
$103$	−1.89824	−0.187039	−0.0935197	+	0.995617i	$0.529812\pi$
$104$	6.11752	0.599872
$105$	8.91182	0.869704
$106$	−9.54066	−0.926670
$107$	3.55840	0.344003	0.172002	−	0.985097i	$-0.444977\pi$
$107$	3.55840	0.344003	0.172002	+	0.985097i	$0.444977\pi$
$108$	−15.1529	−1.45809
$109$	6.28847	0.602326	0.301163	−	0.953573i	$-0.402625\pi$
$109$	6.28847	0.602326	0.301163	+	0.953573i	$0.402625\pi$
$110$	−1.00000	−0.0953463
$111$	1.98301	0.188219
$112$	2.73152	0.258104
$113$	−4.24313	−0.399160	−0.199580	−	0.979882i	$-0.563958\pi$
$113$	−4.24313	−0.399160	−0.199580	+	0.979882i	$0.563958\pi$
$114$	25.3838	2.37741
$115$	−8.88984	−0.828982
$116$	6.36025	0.590534
$117$	46.7652	4.32344
$118$	−1.12856	−0.103893
$119$	20.4388	1.87362
$120$	3.26258	0.297832
$121$	1.00000	0.0909091
$122$	9.95844	0.901595
$123$	−8.70358	−0.784775
$124$	6.01389	0.540064
$125$	−1.00000	−0.0894427
$126$	20.8810	1.86023
$127$	−1.72903	−0.153426	−0.0767132	−	0.997053i	$-0.524443\pi$
$127$	−1.72903	−0.153426	−0.0767132	+	0.997053i	$0.524443\pi$
$128$	1.00000	0.0883883
$129$	−3.26258	−0.287255
$130$	−6.11752	−0.536542
$131$	−17.4710	−1.52645	−0.763223	−	0.646135i	$-0.776384\pi$
$131$	−17.4710	−1.52645	−0.763223	+	0.646135i	$0.776384\pi$
$132$	−3.26258	−0.283972
$133$	−21.2520	−1.84278
$134$	−11.0418	−0.953869
$135$	15.1529	1.30416
$136$	7.48258	0.641626
$137$	−0.759375	−0.0648778	−0.0324389	−	0.999474i	$-0.510327\pi$
$137$	−0.759375	−0.0648778	−0.0324389	+	0.999474i	$0.510327\pi$
$138$	−29.0039	−2.46897
$139$	−4.51146	−0.382657	−0.191328	−	0.981526i	$-0.561280\pi$
$139$	−4.51146	−0.382657	−0.191328	+	0.981526i	$0.561280\pi$
$140$	−2.73152	−0.230856
$141$	−2.78095	−0.234199
$142$	−4.13401	−0.346918
$143$	6.11752	0.511573
$144$	7.64446	0.637038
$145$	−6.36025	−0.528190
$146$	−13.2485	−1.09645
$147$	−1.50472	−0.124107
$148$	−0.607804	−0.0499612
$149$	6.08570	0.498560	0.249280	−	0.968431i	$-0.419806\pi$
$149$	6.08570	0.498560	0.249280	+	0.968431i	$0.419806\pi$
$150$	−3.26258	−0.266389
$151$	8.36366	0.680625	0.340312	−	0.940312i	$-0.389467\pi$
$151$	8.36366	0.680625	0.340312	+	0.940312i	$0.389467\pi$
$152$	−7.78028	−0.631064
$153$	57.2003	4.62437
$154$	2.73152	0.220112
$155$	−6.01389	−0.483048
$156$	−19.9589	−1.59799
$157$	−6.68607	−0.533606	−0.266803	−	0.963751i	$-0.585967\pi$
$157$	−6.68607	−0.533606	−0.266803	+	0.963751i	$0.585967\pi$
$158$	−2.52486	−0.200867
$159$	31.1272	2.46855
$160$	−1.00000	−0.0790569
$161$	24.2828	1.91375
$162$	26.5044	2.08238
$163$	22.5617	1.76717	0.883585	−	0.468270i	$-0.155123\pi$
$163$	22.5617	1.76717	0.883585	+	0.468270i	$0.155123\pi$
$164$	2.66769	0.208312
$165$	3.26258	0.253992
$166$	−12.7935	−0.992969
$167$	−14.7906	−1.14453	−0.572267	−	0.820067i	$-0.693936\pi$
$167$	−14.7906	−1.14453	−0.572267	+	0.820067i	$0.693936\pi$
$168$	−8.91182	−0.687562
$169$	24.4241	1.87878
$170$	−7.48258	−0.573888
$171$	−59.4760	−4.54825
$172$	1.00000	0.0762493
$173$	−5.80673	−0.441478	−0.220739	−	0.975333i	$-0.570847\pi$
$173$	−5.80673	−0.441478	−0.220739	+	0.975333i	$0.570847\pi$
$174$	−20.7509	−1.57312
$175$	2.73152	0.206484
$176$	1.00000	0.0753778
$177$	3.68203	0.276759
$178$	1.91784	0.143748
$179$	9.00912	0.673373	0.336687	−	0.941617i	$-0.390694\pi$
$179$	9.00912	0.673373	0.336687	+	0.941617i	$0.390694\pi$
$180$	−7.64446	−0.569784
$181$	−20.2234	−1.50319	−0.751597	−	0.659623i	$-0.770716\pi$
$181$	−20.2234	−1.50319	−0.751597	+	0.659623i	$0.770716\pi$
$182$	16.7101	1.23864
$183$	−32.4903	−2.40175
$184$	8.88984	0.655368
$185$	0.607804	0.0446866
$186$	−19.6208	−1.43867
$187$	7.48258	0.547181
$188$	0.852378	0.0621660
$189$	−41.3906	−3.01072
$190$	7.78028	0.564441
$191$	16.1486	1.16847	0.584237	−	0.811583i	$-0.301394\pi$
$191$	16.1486	1.16847	0.584237	+	0.811583i	$0.301394\pi$
$192$	−3.26258	−0.235457
$193$	11.6496	0.838558	0.419279	−	0.907857i	$-0.362283\pi$
$193$	11.6496	0.838558	0.419279	+	0.907857i	$0.362283\pi$
$194$	12.9532	0.929988
$195$	19.9589	1.42929
$196$	0.461206	0.0329433
$197$	15.2043	1.08326	0.541630	−	0.840617i	$-0.317808\pi$
$197$	15.2043	1.08326	0.541630	+	0.840617i	$0.317808\pi$
$198$	7.64446	0.543268
$199$	−2.21588	−0.157079	−0.0785396	−	0.996911i	$-0.525026\pi$
$199$	−2.21588	−0.157079	−0.0785396	+	0.996911i	$0.525026\pi$
$200$	1.00000	0.0707107
$201$	36.0249	2.54100
$202$	3.60944	0.253959
$203$	17.3732	1.21936
$204$	−24.4126	−1.70922
$205$	−2.66769	−0.186320
$206$	−1.89824	−0.132257
$207$	67.9580	4.72341
$208$	6.11752	0.424174
$209$	−7.78028	−0.538173
$210$	8.91182	0.614974
$211$	12.3897	0.852939	0.426470	−	0.904502i	$-0.359757\pi$
$211$	12.3897	0.852939	0.426470	+	0.904502i	$0.359757\pi$
$212$	−9.54066	−0.655255
$213$	13.4875	0.924152
$214$	3.55840	0.243247
$215$	−1.00000	−0.0681994
$216$	−15.1529	−1.03103
$217$	16.4271	1.11514
$218$	6.28847	0.425909
$219$	43.2243	2.92083
$220$	−1.00000	−0.0674200
$221$	45.7749	3.07915
$222$	1.98301	0.133091
$223$	−3.05848	−0.204811	−0.102405	−	0.994743i	$-0.532654\pi$
$223$	−3.05848	−0.204811	−0.102405	+	0.994743i	$0.532654\pi$
$224$	2.73152	0.182507
$225$	7.64446	0.509631
$226$	−4.24313	−0.282249
$227$	14.6877	0.974860	0.487430	−	0.873162i	$-0.337934\pi$
$227$	14.6877	0.974860	0.487430	+	0.873162i	$0.337934\pi$
$228$	25.3838	1.68108
$229$	−13.4531	−0.889008	−0.444504	−	0.895777i	$-0.646620\pi$
$229$	−13.4531	−0.889008	−0.444504	+	0.895777i	$0.646620\pi$
$230$	−8.88984	−0.586179
$231$	−8.91182	−0.586355
$232$	6.36025	0.417571
$233$	−17.1819	−1.12562	−0.562811	−	0.826586i	$-0.690280\pi$
$233$	−17.1819	−1.12562	−0.562811	+	0.826586i	$0.690280\pi$
$234$	46.7652	3.05713
$235$	−0.852378	−0.0556030
$236$	−1.12856	−0.0734632
$237$	8.23757	0.535088
$238$	20.4388	1.32485
$239$	17.8779	1.15643	0.578213	−	0.815886i	$-0.303750\pi$
$239$	17.8779	1.15643	0.578213	+	0.815886i	$0.303750\pi$
$240$	3.26258	0.210599
$241$	−23.9789	−1.54462	−0.772308	−	0.635249i	$-0.780898\pi$
$241$	−23.9789	−1.54462	−0.772308	+	0.635249i	$0.780898\pi$
$242$	1.00000	0.0642824
$243$	−41.0139	−2.63105
$244$	9.95844	0.637524
$245$	−0.461206	−0.0294653
$246$	−8.70358	−0.554920
$247$	−47.5960	−3.02846
$248$	6.01389	0.381883
$249$	41.7399	2.64516
$250$	−1.00000	−0.0632456
$251$	12.1141	0.764633	0.382316	−	0.924031i	$-0.375126\pi$
$251$	12.1141	0.764633	0.382316	+	0.924031i	$0.375126\pi$
$252$	20.8810	1.31538
$253$	8.88984	0.558899
$254$	−1.72903	−0.108489
$255$	24.4126	1.52877
$256$	1.00000	0.0625000
$257$	12.6375	0.788305	0.394152	−	0.919045i	$-0.371038\pi$
$257$	12.6375	0.788305	0.394152	+	0.919045i	$0.371038\pi$
$258$	−3.26258	−0.203120
$259$	−1.66023	−0.103162
$260$	−6.11752	−0.379393
$261$	48.6207	3.00954
$262$	−17.4710	−1.07936
$263$	−30.8809	−1.90420	−0.952099	−	0.305790i	$-0.901079\pi$
$263$	−30.8809	−1.90420	−0.952099	+	0.305790i	$0.901079\pi$
$264$	−3.26258	−0.200798
$265$	9.54066	0.586078
$266$	−21.2520	−1.30304
$267$	−6.25711	−0.382929
$268$	−11.0418	−0.674487
$269$	−18.0663	−1.10152	−0.550762	−	0.834662i	$-0.685663\pi$
$269$	−18.0663	−1.10152	−0.550762	+	0.834662i	$0.685663\pi$
$270$	15.1529	0.922179
$271$	21.2955	1.29361	0.646805	−	0.762656i	$-0.276105\pi$
$271$	21.2955	1.29361	0.646805	+	0.762656i	$0.276105\pi$
$272$	7.48258	0.453698
$273$	−54.5182	−3.29959
$274$	−0.759375	−0.0458755
$275$	1.00000	0.0603023
$276$	−29.0039	−1.74583
$277$	8.04461	0.483354	0.241677	−	0.970357i	$-0.422303\pi$
$277$	8.04461	0.483354	0.241677	+	0.970357i	$0.422303\pi$
$278$	−4.51146	−0.270579
$279$	45.9730	2.75233
$280$	−2.73152	−0.163240
$281$	−29.1658	−1.73988	−0.869942	−	0.493154i	$-0.835844\pi$
$281$	−29.1658	−1.73988	−0.869942	+	0.493154i	$0.835844\pi$
$282$	−2.78095	−0.165603
$283$	−5.12601	−0.304710	−0.152355	−	0.988326i	$-0.548686\pi$
$283$	−5.12601	−0.304710	−0.152355	+	0.988326i	$0.548686\pi$
$284$	−4.13401	−0.245308
$285$	−25.3838	−1.50361
$286$	6.11752	0.361737
$287$	7.28686	0.430130
$288$	7.64446	0.450454
$289$	38.9891	2.29347
$290$	−6.36025	−0.373487
$291$	−42.2610	−2.47739
$292$	−13.2485	−0.775309
$293$	−17.4294	−1.01824	−0.509118	−	0.860697i	$-0.670028\pi$
$293$	−17.4294	−1.01824	−0.509118	+	0.860697i	$0.670028\pi$
$294$	−1.50472	−0.0877572
$295$	1.12856	0.0657075
$296$	−0.607804	−0.0353279
$297$	−15.1529	−0.879263
$298$	6.08570	0.352535
$299$	54.3838	3.14510
$300$	−3.26258	−0.188365
$301$	2.73152	0.157442
$302$	8.36366	0.481274
$303$	−11.7761	−0.676519
$304$	−7.78028	−0.446230
$305$	−9.95844	−0.570219
$306$	57.2003	3.26992
$307$	11.6324	0.663898	0.331949	−	0.943297i	$-0.392294\pi$
$307$	11.6324	0.663898	0.331949	+	0.943297i	$0.392294\pi$
$308$	2.73152	0.155643
$309$	6.19317	0.352317
$310$	−6.01389	−0.341566
$311$	−6.14313	−0.348345	−0.174172	−	0.984715i	$-0.555725\pi$
$311$	−6.14313	−0.348345	−0.174172	+	0.984715i	$0.555725\pi$
$312$	−19.9589	−1.12995
$313$	−24.6979	−1.39601	−0.698003	−	0.716095i	$-0.745928\pi$
$313$	−24.6979	−1.39601	−0.698003	+	0.716095i	$0.745928\pi$
$314$	−6.68607	−0.377316
$315$	−20.8810	−1.17651
$316$	−2.52486	−0.142034
$317$	8.66426	0.486633	0.243317	−	0.969947i	$-0.421765\pi$
$317$	8.66426	0.486633	0.243317	+	0.969947i	$0.421765\pi$
$318$	31.1272	1.74553
$319$	6.36025	0.356106
$320$	−1.00000	−0.0559017
$321$	−11.6096	−0.647983
$322$	24.2828	1.35323
$323$	−58.2166	−3.23926
$324$	26.5044	1.47247
$325$	6.11752	0.339339
$326$	22.5617	1.24958
$327$	−20.5167	−1.13457
$328$	2.66769	0.147299
$329$	2.32829	0.128363
$330$	3.26258	0.179599
$331$	35.9138	1.97400	0.986999	−	0.160724i	$-0.0513828\pi$
$331$	35.9138	1.97400	0.986999	+	0.160724i	$0.0513828\pi$
$332$	−12.7935	−0.702135
$333$	−4.64633	−0.254617
$334$	−14.7906	−0.809307
$335$	11.0418	0.603280
$336$	−8.91182	−0.486180
$337$	0.835503	0.0455128	0.0227564	−	0.999741i	$-0.492756\pi$
$337$	0.835503	0.0455128	0.0227564	+	0.999741i	$0.492756\pi$
$338$	24.4241	1.32850
$339$	13.8436	0.751880
$340$	−7.48258	−0.405800
$341$	6.01389	0.325671
$342$	−59.4760	−3.21610
$343$	−17.8609	−0.964395
$344$	1.00000	0.0539164
$345$	29.0039	1.56152
$346$	−5.80673	−0.312172
$347$	−1.30007	−0.0697913	−0.0348956	−	0.999391i	$-0.511110\pi$
$347$	−1.30007	−0.0697913	−0.0348956	+	0.999391i	$0.511110\pi$
$348$	−20.7509	−1.11236
$349$	26.2403	1.40461	0.702306	−	0.711875i	$-0.252154\pi$
$349$	26.2403	1.40461	0.702306	+	0.711875i	$0.252154\pi$
$350$	2.73152	0.146006
$351$	−92.6985	−4.94788
$352$	1.00000	0.0533002
$353$	9.93627	0.528854	0.264427	−	0.964406i	$-0.414817\pi$
$353$	9.93627	0.528854	0.264427	+	0.964406i	$0.414817\pi$
$354$	3.68203	0.195698
$355$	4.13401	0.219410
$356$	1.91784	0.101645
$357$	−66.6834	−3.52926
$358$	9.00912	0.476147
$359$	−28.8363	−1.52192	−0.760962	−	0.648797i	$-0.775272\pi$
$359$	−28.8363	−1.52192	−0.760962	+	0.648797i	$0.775272\pi$
$360$	−7.64446	−0.402898
$361$	41.5328	2.18594
$362$	−20.2234	−1.06292
$363$	−3.26258	−0.171241
$364$	16.7101	0.875849
$365$	13.2485	0.693458
$366$	−32.4903	−1.69829
$367$	−36.6213	−1.91162	−0.955808	−	0.293992i	$-0.905016\pi$
$367$	−36.6213	−1.91162	−0.955808	+	0.293992i	$0.905016\pi$
$368$	8.88984	0.463415
$369$	20.3931	1.06162
$370$	0.607804	0.0315982
$371$	−26.0605	−1.35299
$372$	−19.6208	−1.01729
$373$	13.8817	0.718766	0.359383	−	0.933190i	$-0.382987\pi$
$373$	13.8817	0.718766	0.359383	+	0.933190i	$0.382987\pi$
$374$	7.48258	0.386915
$375$	3.26258	0.168479
$376$	0.852378	0.0439580
$377$	38.9090	2.00391
$378$	−41.3906	−2.12890
$379$	−7.18540	−0.369089	−0.184545	−	0.982824i	$-0.559081\pi$
$379$	−7.18540	−0.369089	−0.184545	+	0.982824i	$0.559081\pi$
$380$	7.78028	0.399120
$381$	5.64110	0.289002
$382$	16.1486	0.826236
$383$	−28.7845	−1.47082	−0.735410	−	0.677622i	$-0.763011\pi$
$383$	−28.7845	−1.47082	−0.735410	+	0.677622i	$0.763011\pi$
$384$	−3.26258	−0.166493
$385$	−2.73152	−0.139211
$386$	11.6496	0.592950
$387$	7.64446	0.388590
$388$	12.9532	0.657601
$389$	0.309694	0.0157021	0.00785106	−	0.999969i	$-0.497501\pi$
$389$	0.309694	0.0157021	0.00785106	+	0.999969i	$0.497501\pi$
$390$	19.9589	1.01066
$391$	66.5190	3.36401
$392$	0.461206	0.0232944
$393$	57.0005	2.87530
$394$	15.2043	0.765980
$395$	2.52486	0.127039
$396$	7.64446	0.384149
$397$	−29.8800	−1.49964	−0.749818	−	0.661644i	$-0.769859\pi$
$397$	−29.8800	−1.49964	−0.749818	+	0.661644i	$0.769859\pi$
$398$	−2.21588	−0.111072
$399$	69.3364	3.47116
$400$	1.00000	0.0500000
$401$	−7.23252	−0.361175	−0.180587	−	0.983559i	$-0.557800\pi$
$401$	−7.23252	−0.361175	−0.180587	+	0.983559i	$0.557800\pi$
$402$	36.0249	1.79676
$403$	36.7901	1.83265
$404$	3.60944	0.179576
$405$	−26.5044	−1.31701
$406$	17.3732	0.862215
$407$	−0.607804	−0.0301277
$408$	−24.4126	−1.20860
$409$	12.8063	0.633229	0.316615	−	0.948554i	$-0.397454\pi$
$409$	12.8063	0.633229	0.316615	+	0.948554i	$0.397454\pi$
$410$	−2.66769	−0.131748
$411$	2.47752	0.122207
$412$	−1.89824	−0.0935197
$413$	−3.08269	−0.151689
$414$	67.9580	3.33995
$415$	12.7935	0.628009
$416$	6.11752	0.299936
$417$	14.7190	0.720793
$418$	−7.78028	−0.380546
$419$	2.39313	0.116912	0.0584561	−	0.998290i	$-0.481382\pi$
$419$	2.39313	0.116912	0.0584561	+	0.998290i	$0.481382\pi$
$420$	8.91182	0.434852
$421$	6.58937	0.321146	0.160573	−	0.987024i	$-0.448666\pi$
$421$	6.58937	0.321146	0.160573	+	0.987024i	$0.448666\pi$
$422$	12.3897	0.603119
$423$	6.51597	0.316817
$424$	−9.54066	−0.463335
$425$	7.48258	0.362959
$426$	13.4875	0.653474
$427$	27.2017	1.31638
$428$	3.55840	0.172002
$429$	−19.9589	−0.963627
$430$	−1.00000	−0.0482243
$431$	−38.2689	−1.84335	−0.921674	−	0.387965i	$-0.873178\pi$
$431$	−38.2689	−1.84335	−0.921674	+	0.387965i	$0.873178\pi$
$432$	−15.1529	−0.729046
$433$	−26.5851	−1.27760	−0.638799	−	0.769374i	$-0.720568\pi$
$433$	−26.5851	−1.27760	−0.638799	+	0.769374i	$0.720568\pi$
$434$	16.4271	0.788525
$435$	20.7509	0.994927
$436$	6.28847	0.301163
$437$	−69.1655	−3.30863
$438$	43.2243	2.06534
$439$	5.69352	0.271737	0.135868	−	0.990727i	$-0.456618\pi$
$439$	5.69352	0.271737	0.135868	+	0.990727i	$0.456618\pi$
$440$	−1.00000	−0.0476731
$441$	3.52567	0.167889
$442$	45.7749	2.17729
$443$	−21.1563	−1.00516	−0.502582	−	0.864529i	$-0.667617\pi$
$443$	−21.1563	−1.00516	−0.502582	+	0.864529i	$0.667617\pi$
$444$	1.98301	0.0941096
$445$	−1.91784	−0.0909143
$446$	−3.05848	−0.144823
$447$	−19.8551	−0.939114
$448$	2.73152	0.129052
$449$	−8.72132	−0.411585	−0.205792	−	0.978596i	$-0.565977\pi$
$449$	−8.72132	−0.411585	−0.205792	+	0.978596i	$0.565977\pi$
$450$	7.64446	0.360363
$451$	2.66769	0.125617
$452$	−4.24313	−0.199580
$453$	−27.2871	−1.28206
$454$	14.6877	0.689330
$455$	−16.7101	−0.783383
$456$	25.3838	1.18871
$457$	0.125694	0.00587973	0.00293987	−	0.999996i	$-0.499064\pi$
$457$	0.125694	0.00587973	0.00293987	+	0.999996i	$0.499064\pi$
$458$	−13.4531	−0.628623
$459$	−113.383	−5.29227
$460$	−8.88984	−0.414491
$461$	3.91909	0.182530	0.0912651	−	0.995827i	$-0.470909\pi$
$461$	3.91909	0.182530	0.0912651	+	0.995827i	$0.470909\pi$
$462$	−8.91182	−0.414615
$463$	−18.4445	−0.857187	−0.428594	−	0.903497i	$-0.640991\pi$
$463$	−18.4445	−0.857187	−0.428594	+	0.903497i	$0.640991\pi$
$464$	6.36025	0.295267
$465$	19.6208	0.909894
$466$	−17.1819	−0.795935
$467$	−19.7612	−0.914440	−0.457220	−	0.889354i	$-0.651155\pi$
$467$	−19.7612	−0.914440	−0.457220	+	0.889354i	$0.651155\pi$
$468$	46.7652	2.16172
$469$	−30.1610	−1.39271
$470$	−0.852378	−0.0393172
$471$	21.8139	1.00513
$472$	−1.12856	−0.0519463
$473$	1.00000	0.0459800
$474$	8.23757	0.378364
$475$	−7.78028	−0.356984
$476$	20.4388	0.936812
$477$	−72.9331	−3.33938
$478$	17.8779	0.817716
$479$	39.0414	1.78385	0.891924	−	0.452185i	$-0.149355\pi$
$479$	39.0414	1.78385	0.891924	+	0.452185i	$0.149355\pi$
$480$	3.26258	0.148916
$481$	−3.71825	−0.169538
$482$	−23.9789	−1.09221
$483$	−79.2246	−3.60485
$484$	1.00000	0.0454545
$485$	−12.9532	−0.588176
$486$	−41.0139	−1.86043
$487$	23.8887	1.08250	0.541251	−	0.840861i	$-0.317951\pi$
$487$	23.8887	1.08250	0.541251	+	0.840861i	$0.317951\pi$
$488$	9.95844	0.450797
$489$	−73.6095	−3.32874
$490$	−0.461206	−0.0208351
$491$	−23.3319	−1.05295	−0.526477	−	0.850189i	$-0.676487\pi$
$491$	−23.3319	−1.05295	−0.526477	+	0.850189i	$0.676487\pi$
$492$	−8.70358	−0.392388
$493$	47.5911	2.14340
$494$	−47.5960	−2.14145
$495$	−7.64446	−0.343593
$496$	6.01389	0.270032
$497$	−11.2921	−0.506521
$498$	41.7399	1.87041
$499$	−28.8772	−1.29272	−0.646361	−	0.763032i	$-0.723710\pi$
$499$	−28.8772	−1.29272	−0.646361	+	0.763032i	$0.723710\pi$
$500$	−1.00000	−0.0447214
$501$	48.2557	2.15591
$502$	12.1141	0.540677
$503$	−38.5921	−1.72074	−0.860369	−	0.509671i	$-0.829767\pi$
$503$	−38.5921	−1.72074	−0.860369	+	0.509671i	$0.829767\pi$
$504$	20.8810	0.930114
$505$	−3.60944	−0.160618
$506$	8.88984	0.395202
$507$	−79.6857	−3.53896
$508$	−1.72903	−0.0767132
$509$	−4.40494	−0.195245	−0.0976227	−	0.995223i	$-0.531124\pi$
$509$	−4.40494	−0.195245	−0.0976227	+	0.995223i	$0.531124\pi$
$510$	24.4126	1.08101
$511$	−36.1885	−1.60089
$512$	1.00000	0.0441942
$513$	117.894	5.20515
$514$	12.6375	0.557416
$515$	1.89824	0.0836465
$516$	−3.26258	−0.143627
$517$	0.852378	0.0374875
$518$	−1.66023	−0.0729463
$519$	18.9450	0.831591
$520$	−6.11752	−0.268271
$521$	−22.1098	−0.968646	−0.484323	−	0.874889i	$-0.660934\pi$
$521$	−22.1098	−0.968646	−0.484323	+	0.874889i	$0.660934\pi$
$522$	48.6207	2.12807
$523$	−4.11099	−0.179761	−0.0898805	−	0.995953i	$-0.528649\pi$
$523$	−4.11099	−0.179761	−0.0898805	+	0.995953i	$0.528649\pi$
$524$	−17.4710	−0.763223
$525$	−8.91182	−0.388944
$526$	−30.8809	−1.34647
$527$	44.9995	1.96021
$528$	−3.26258	−0.141986
$529$	56.0293	2.43606
$530$	9.54066	0.414420
$531$	−8.62726	−0.374391
$532$	−21.2520	−0.921391
$533$	16.3197	0.706884
$534$	−6.25711	−0.270772
$535$	−3.55840	−0.153843
$536$	−11.0418	−0.476935
$537$	−29.3930	−1.26840
$538$	−18.0663	−0.778895
$539$	0.461206	0.0198655
$540$	15.1529	0.652079
$541$	10.5245	0.452482	0.226241	−	0.974071i	$-0.427356\pi$
$541$	10.5245	0.452482	0.226241	+	0.974071i	$0.427356\pi$
$542$	21.2955	0.914720
$543$	65.9806	2.83150
$544$	7.48258	0.320813
$545$	−6.28847	−0.269369
$546$	−54.5182	−2.33317
$547$	37.3005	1.59486	0.797428	−	0.603414i	$-0.206193\pi$
$547$	37.3005	1.59486	0.797428	+	0.603414i	$0.206193\pi$
$548$	−0.759375	−0.0324389
$549$	76.1269	3.24902
$550$	1.00000	0.0426401
$551$	−49.4845	−2.10811
$552$	−29.0039	−1.23449
$553$	−6.89671	−0.293278
$554$	8.04461	0.341783
$555$	−1.98301	−0.0841742
$556$	−4.51146	−0.191328
$557$	−14.8754	−0.630293	−0.315146	−	0.949043i	$-0.602054\pi$
$557$	−14.8754	−0.630293	−0.315146	+	0.949043i	$0.602054\pi$
$558$	45.9730	1.94619
$559$	6.11752	0.258744
$560$	−2.73152	−0.115428
$561$	−24.4126	−1.03070
$562$	−29.1658	−1.23028
$563$	18.4913	0.779315	0.389658	−	0.920960i	$-0.372593\pi$
$563$	18.4913	0.779315	0.389658	+	0.920960i	$0.372593\pi$
$564$	−2.78095	−0.117099
$565$	4.24313	0.178510
$566$	−5.12601	−0.215462
$567$	72.3972	3.04040
$568$	−4.13401	−0.173459
$569$	8.73588	0.366227	0.183114	−	0.983092i	$-0.441382\pi$
$569$	8.73588	0.366227	0.183114	+	0.983092i	$0.441382\pi$
$570$	−25.3838	−1.06321
$571$	−0.811948	−0.0339790	−0.0169895	−	0.999856i	$-0.505408\pi$
$571$	−0.811948	−0.0339790	−0.0169895	+	0.999856i	$0.505408\pi$
$572$	6.11752	0.255786
$573$	−52.6863	−2.20100
$574$	7.28686	0.304148
$575$	8.88984	0.370732
$576$	7.64446	0.318519
$577$	20.7394	0.863393	0.431696	−	0.902019i	$-0.357915\pi$
$577$	20.7394	0.863393	0.431696	+	0.902019i	$0.357915\pi$
$578$	38.9891	1.62173
$579$	−38.0079	−1.57955
$580$	−6.36025	−0.264095
$581$	−34.9458	−1.44979
$582$	−42.2610	−1.75178
$583$	−9.54066	−0.395134
$584$	−13.2485	−0.548226
$585$	−46.7652	−1.93350
$586$	−17.4294	−0.720001
$587$	22.0637	0.910668	0.455334	−	0.890321i	$-0.349520\pi$
$587$	22.0637	0.910668	0.455334	+	0.890321i	$0.349520\pi$
$588$	−1.50472	−0.0620537
$589$	−46.7898	−1.92794
$590$	1.12856	0.0464622
$591$	−49.6052	−2.04049
$592$	−0.607804	−0.0249806
$593$	42.7997	1.75757	0.878786	−	0.477216i	$-0.158354\pi$
$593$	42.7997	1.75757	0.878786	+	0.477216i	$0.158354\pi$
$594$	−15.1529	−0.621733
$595$	−20.4388	−0.837910
$596$	6.08570	0.249280
$597$	7.22948	0.295883
$598$	54.3838	2.22392
$599$	−44.3238	−1.81102	−0.905511	−	0.424323i	$-0.860512\pi$
$599$	−44.3238	−1.81102	−0.905511	+	0.424323i	$0.860512\pi$
$600$	−3.26258	−0.133194
$601$	34.5402	1.40893	0.704463	−	0.709741i	$-0.251188\pi$
$601$	34.5402	1.40893	0.704463	+	0.709741i	$0.251188\pi$
$602$	2.73152	0.111328
$603$	−84.4089	−3.43739
$604$	8.36366	0.340312
$605$	−1.00000	−0.0406558
$606$	−11.7761	−0.478371
$607$	−21.4937	−0.872402	−0.436201	−	0.899849i	$-0.643676\pi$
$607$	−21.4937	−0.872402	−0.436201	+	0.899849i	$0.643676\pi$
$608$	−7.78028	−0.315532
$609$	−56.6814	−2.29685
$610$	−9.95844	−0.403205
$611$	5.21444	0.210954
$612$	57.2003	2.31219
$613$	−2.16333	−0.0873761	−0.0436881	−	0.999045i	$-0.513911\pi$
$613$	−2.16333	−0.0873761	−0.0436881	+	0.999045i	$0.513911\pi$
$614$	11.6324	0.469446
$615$	8.70358	0.350962
$616$	2.73152	0.110056
$617$	24.5899	0.989950	0.494975	−	0.868907i	$-0.335177\pi$
$617$	24.5899	0.989950	0.494975	+	0.868907i	$0.335177\pi$
$618$	6.19317	0.249126
$619$	15.5361	0.624447	0.312223	−	0.950009i	$-0.398926\pi$
$619$	15.5361	0.624447	0.312223	+	0.950009i	$0.398926\pi$
$620$	−6.01389	−0.241524
$621$	−134.707	−5.40561
$622$	−6.14313	−0.246317
$623$	5.23862	0.209881
$624$	−19.9589	−0.798997
$625$	1.00000	0.0400000
$626$	−24.6979	−0.987125
$627$	25.3838	1.01373
$628$	−6.68607	−0.266803
$629$	−4.54794	−0.181338
$630$	−20.8810	−0.831919
$631$	35.2931	1.40500	0.702498	−	0.711686i	$-0.252068\pi$
$631$	35.2931	1.40500	0.702498	+	0.711686i	$0.252068\pi$
$632$	−2.52486	−0.100434
$633$	−40.4223	−1.60664
$634$	8.66426	0.344102
$635$	1.72903	0.0686144
$636$	31.1272	1.23427
$637$	2.82144	0.111789
$638$	6.36025	0.251805
$639$	−31.6022	−1.25017
$640$	−1.00000	−0.0395285
$641$	−8.95945	−0.353877	−0.176939	−	0.984222i	$-0.556619\pi$
$641$	−8.95945	−0.353877	−0.176939	+	0.984222i	$0.556619\pi$
$642$	−11.6096	−0.458193
$643$	11.3438	0.447356	0.223678	−	0.974663i	$-0.428194\pi$
$643$	11.3438	0.447356	0.223678	+	0.974663i	$0.428194\pi$
$644$	24.2828	0.956876
$645$	3.26258	0.128464
$646$	−58.2166	−2.29050
$647$	−26.8885	−1.05710	−0.528548	−	0.848903i	$-0.677263\pi$
$647$	−26.8885	−1.05710	−0.528548	+	0.848903i	$0.677263\pi$
$648$	26.5044	1.04119
$649$	−1.12856	−0.0443000
$650$	6.11752	0.239949
$651$	−53.5947	−2.10054
$652$	22.5617	0.883585
$653$	17.2333	0.674393	0.337196	−	0.941434i	$-0.390521\pi$
$653$	17.2333	0.674393	0.337196	+	0.941434i	$0.390521\pi$
$654$	−20.5167	−0.802265
$655$	17.4710	0.682647
$656$	2.66769	0.104156
$657$	−101.278	−3.95121
$658$	2.32829	0.0907661
$659$	2.81633	0.109709	0.0548543	−	0.998494i	$-0.482531\pi$
$659$	2.81633	0.109709	0.0548543	+	0.998494i	$0.482531\pi$
$660$	3.26258	0.126996
$661$	13.2691	0.516110	0.258055	−	0.966130i	$-0.416918\pi$
$661$	13.2691	0.516110	0.258055	+	0.966130i	$0.416918\pi$
$662$	35.9138	1.39583
$663$	−149.344	−5.80006
$664$	−12.7935	−0.496485
$665$	21.2520	0.824117
$666$	−4.64633	−0.180042
$667$	56.5416	2.18930
$668$	−14.7906	−0.572267
$669$	9.97854	0.385793
$670$	11.0418	0.426583
$671$	9.95844	0.384441
$672$	−8.91182	−0.343781
$673$	−7.65905	−0.295235	−0.147617	−	0.989045i	$-0.547160\pi$
$673$	−7.65905	−0.295235	−0.147617	+	0.989045i	$0.547160\pi$
$674$	0.835503	0.0321824
$675$	−15.1529	−0.583237
$676$	24.4241	0.939388
$677$	24.9266	0.958007	0.479004	−	0.877813i	$-0.340998\pi$
$677$	24.9266	0.958007	0.479004	+	0.877813i	$0.340998\pi$
$678$	13.8436	0.531659
$679$	35.3820	1.35784
$680$	−7.48258	−0.286944
$681$	−47.9200	−1.83630
$682$	6.01389	0.230284
$683$	−0.841780	−0.0322098	−0.0161049	−	0.999870i	$-0.505127\pi$
$683$	−0.841780	−0.0322098	−0.0161049	+	0.999870i	$0.505127\pi$
$684$	−59.4760	−2.27412
$685$	0.759375	0.0290142
$686$	−17.8609	−0.681931
$687$	43.8920	1.67458
$688$	1.00000	0.0381246
$689$	−58.3652	−2.22354
$690$	29.0039	1.10416
$691$	26.1079	0.993191	0.496596	−	0.867982i	$-0.334583\pi$
$691$	26.1079	0.993191	0.496596	+	0.867982i	$0.334583\pi$
$692$	−5.80673	−0.220739
$693$	20.8810	0.793204
$694$	−1.30007	−0.0493499
$695$	4.51146	0.171129
$696$	−20.7509	−0.786559
$697$	19.9612	0.756086
$698$	26.2403	0.993211
$699$	56.0573	2.12028
$700$	2.73152	0.103242
$701$	18.2442	0.689074	0.344537	−	0.938773i	$-0.388036\pi$
$701$	18.2442	0.689074	0.344537	+	0.938773i	$0.388036\pi$
$702$	−92.6985	−3.49868
$703$	4.72889	0.178353
$704$	1.00000	0.0376889
$705$	2.78095	0.104737
$706$	9.93627	0.373956
$707$	9.85925	0.370795
$708$	3.68203	0.138379
$709$	9.38743	0.352552	0.176276	−	0.984341i	$-0.443595\pi$
$709$	9.38743	0.352552	0.176276	+	0.984341i	$0.443595\pi$
$710$	4.13401	0.155147
$711$	−19.3012	−0.723851
$712$	1.91784	0.0718740
$713$	53.4625	2.00219
$714$	−66.6834	−2.49556
$715$	−6.11752	−0.228782
$716$	9.00912	0.336687
$717$	−58.3282	−2.17831
$718$	−28.8363	−1.07616
$719$	−34.7065	−1.29433	−0.647166	−	0.762349i	$-0.724046\pi$
$719$	−34.7065	−1.29433	−0.647166	+	0.762349i	$0.724046\pi$
$720$	−7.64446	−0.284892
$721$	−5.18509	−0.193103
$722$	41.5328	1.54569
$723$	78.2331	2.90952
$724$	−20.2234	−0.751597
$725$	6.36025	0.236214
$726$	−3.26258	−0.121086
$727$	−2.61803	−0.0970975	−0.0485487	−	0.998821i	$-0.515460\pi$
$727$	−2.61803	−0.0970975	−0.0485487	+	0.998821i	$0.515460\pi$
$728$	16.7101	0.619319
$729$	54.2983	2.01105
$730$	13.2485	0.490349
$731$	7.48258	0.276753
$732$	−32.4903	−1.20087
$733$	−25.9663	−0.959087	−0.479544	−	0.877518i	$-0.659198\pi$
$733$	−25.9663	−0.959087	−0.479544	+	0.877518i	$0.659198\pi$
$734$	−36.6213	−1.35172
$735$	1.50472	0.0555025
$736$	8.88984	0.327684
$737$	−11.0418	−0.406731
$738$	20.3931	0.750679
$739$	1.38279	0.0508668	0.0254334	−	0.999677i	$-0.491903\pi$
$739$	1.38279	0.0508668	0.0254334	+	0.999677i	$0.491903\pi$
$740$	0.607804	0.0223433
$741$	155.286	5.70458
$742$	−26.0605	−0.956711
$743$	1.68351	0.0617621	0.0308811	−	0.999523i	$-0.490169\pi$
$743$	1.68351	0.0617621	0.0308811	+	0.999523i	$0.490169\pi$
$744$	−19.6208	−0.719335
$745$	−6.08570	−0.222963
$746$	13.8817	0.508244
$747$	−97.7995	−3.57830
$748$	7.48258	0.273590
$749$	9.71983	0.355155
$750$	3.26258	0.119133
$751$	7.26875	0.265241	0.132620	−	0.991167i	$-0.457661\pi$
$751$	7.26875	0.265241	0.132620	+	0.991167i	$0.457661\pi$
$752$	0.852378	0.0310830
$753$	−39.5232	−1.44030
$754$	38.9090	1.41698
$755$	−8.36366	−0.304385
$756$	−41.3906	−1.50536
$757$	38.3526	1.39395	0.696975	−	0.717096i	$-0.254529\pi$
$757$	38.3526	1.39395	0.696975	+	0.717096i	$0.254529\pi$
$758$	−7.18540	−0.260985
$759$	−29.0039	−1.05277
$760$	7.78028	0.282220
$761$	−17.3124	−0.627574	−0.313787	−	0.949493i	$-0.601598\pi$
$761$	−17.3124	−0.627574	−0.313787	+	0.949493i	$0.601598\pi$
$762$	5.64110	0.204356
$763$	17.1771	0.621852
$764$	16.1486	0.584237
$765$	−57.2003	−2.06808
$766$	−28.7845	−1.04003
$767$	−6.90401	−0.249289
$768$	−3.26258	−0.117728
$769$	5.07471	0.182999	0.0914994	−	0.995805i	$-0.470834\pi$
$769$	5.07471	0.182999	0.0914994	+	0.995805i	$0.470834\pi$
$770$	−2.73152	−0.0984372
$771$	−41.2309	−1.48489
$772$	11.6496	0.419279
$773$	−22.6272	−0.813845	−0.406922	−	0.913463i	$-0.633398\pi$
$773$	−22.6272	−0.813845	−0.406922	+	0.913463i	$0.633398\pi$
$774$	7.64446	0.274774
$775$	6.01389	0.216025
$776$	12.9532	0.464994
$777$	5.41664	0.194321
$778$	0.309694	0.0111031
$779$	−20.7554	−0.743640
$780$	19.9589	0.714645
$781$	−4.13401	−0.147926
$782$	66.5190	2.37871
$783$	−96.3765	−3.44421
$784$	0.461206	0.0164716
$785$	6.68607	0.238636
$786$	57.0005	2.03314
$787$	−9.94530	−0.354512	−0.177256	−	0.984165i	$-0.556722\pi$
$787$	−9.94530	−0.354512	−0.177256	+	0.984165i	$0.556722\pi$
$788$	15.2043	0.541630
$789$	100.752	3.58685
$790$	2.52486	0.0898305
$791$	−11.5902	−0.412100
$792$	7.64446	0.271634
$793$	60.9210	2.16337
$794$	−29.8800	−1.06040
$795$	−31.1272	−1.10397
$796$	−2.21588	−0.0785396
$797$	−7.89423	−0.279628	−0.139814	−	0.990178i	$-0.544650\pi$
$797$	−7.89423	−0.279628	−0.139814	+	0.990178i	$0.544650\pi$
$798$	69.3364	2.45448
$799$	6.37799	0.225637
$800$	1.00000	0.0353553
$801$	14.6608	0.518015
$802$	−7.23252	−0.255389
$803$	−13.2485	−0.467529
$804$	36.0249	1.27050
$805$	−24.2828	−0.855856
$806$	36.7901	1.29588
$807$	58.9429	2.07489
$808$	3.60944	0.126980
$809$	15.9642	0.561271	0.280635	−	0.959814i	$-0.409455\pi$
$809$	15.9642	0.561271	0.280635	+	0.959814i	$0.409455\pi$
$810$	−26.5044	−0.931269
$811$	−9.47545	−0.332728	−0.166364	−	0.986064i	$-0.553203\pi$
$811$	−9.47545	−0.332728	−0.166364	+	0.986064i	$0.553203\pi$
$812$	17.3732	0.609678
$813$	−69.4783	−2.43671
$814$	−0.607804	−0.0213035
$815$	−22.5617	−0.790303
$816$	−24.4126	−0.854611
$817$	−7.78028	−0.272198
$818$	12.8063	0.447761
$819$	127.740	4.46360
$820$	−2.66769	−0.0931599
$821$	38.8017	1.35419	0.677094	−	0.735896i	$-0.263239\pi$
$821$	38.8017	1.35419	0.677094	+	0.735896i	$0.263239\pi$
$822$	2.47752	0.0864136
$823$	−4.72647	−0.164754	−0.0823772	−	0.996601i	$-0.526251\pi$
$823$	−4.72647	−0.164754	−0.0823772	+	0.996601i	$0.526251\pi$
$824$	−1.89824	−0.0661284
$825$	−3.26258	−0.113589
$826$	−3.08269	−0.107261
$827$	−49.4963	−1.72116	−0.860578	−	0.509319i	$-0.829897\pi$
$827$	−49.4963	−1.72116	−0.860578	+	0.509319i	$0.829897\pi$
$828$	67.9580	2.36170
$829$	18.0650	0.627423	0.313712	−	0.949518i	$-0.398428\pi$
$829$	18.0650	0.627423	0.313712	+	0.949518i	$0.398428\pi$
$830$	12.7935	0.444069
$831$	−26.2462	−0.910471
$832$	6.11752	0.212087
$833$	3.45101	0.119570
$834$	14.7190	0.509678
$835$	14.7906	0.511851
$836$	−7.78028	−0.269087
$837$	−91.1282	−3.14985
$838$	2.39313	0.0826693
$839$	13.5439	0.467587	0.233793	−	0.972286i	$-0.424886\pi$
$839$	13.5439	0.467587	0.233793	+	0.972286i	$0.424886\pi$
$840$	8.91182	0.307487
$841$	11.4528	0.394923
$842$	6.58937	0.227085
$843$	95.1558	3.27734
$844$	12.3897	0.426470
$845$	−24.4241	−0.840214
$846$	6.51597	0.224023
$847$	2.73152	0.0938562
$848$	−9.54066	−0.327627
$849$	16.7240	0.573968
$850$	7.48258	0.256650
$851$	−5.40328	−0.185222
$852$	13.4875	0.462076
$853$	13.4081	0.459085	0.229543	−	0.973299i	$-0.426277\pi$
$853$	13.4081	0.459085	0.229543	+	0.973299i	$0.426277\pi$
$854$	27.2017	0.930822
$855$	59.4760	2.03404
$856$	3.55840	0.121623
$857$	−2.10280	−0.0718302	−0.0359151	−	0.999355i	$-0.511435\pi$
$857$	−2.10280	−0.0718302	−0.0359151	+	0.999355i	$0.511435\pi$
$858$	−19.9589	−0.681387
$859$	−7.01321	−0.239288	−0.119644	−	0.992817i	$-0.538175\pi$
$859$	−7.01321	−0.239288	−0.119644	+	0.992817i	$0.538175\pi$
$860$	−1.00000	−0.0340997
$861$	−23.7740	−0.810216
$862$	−38.2689	−1.30344
$863$	32.2177	1.09670	0.548352	−	0.836247i	$-0.315255\pi$
$863$	32.2177	1.09670	0.548352	+	0.836247i	$0.315255\pi$
$864$	−15.1529	−0.515513
$865$	5.80673	0.197435
$866$	−26.5851	−0.903398
$867$	−127.205	−4.32011
$868$	16.4271	0.557571
$869$	−2.52486	−0.0856500
$870$	20.7509	0.703520
$871$	−67.5487	−2.28880
$872$	6.28847	0.212955
$873$	99.0205	3.35134
$874$	−69.1655	−2.33956
$875$	−2.73152	−0.0923423
$876$	43.2243	1.46041
$877$	−30.7262	−1.03755	−0.518776	−	0.854910i	$-0.673612\pi$
$877$	−30.7262	−1.03755	−0.518776	+	0.854910i	$0.673612\pi$
$878$	5.69352	0.192147
$879$	56.8648	1.91800
$880$	−1.00000	−0.0337100
$881$	41.3315	1.39249	0.696247	−	0.717803i	$-0.254852\pi$
$881$	41.3315	1.39249	0.696247	+	0.717803i	$0.254852\pi$
$882$	3.52567	0.118715
$883$	5.38708	0.181290	0.0906448	−	0.995883i	$-0.471107\pi$
$883$	5.38708	0.181290	0.0906448	+	0.995883i	$0.471107\pi$
$884$	45.7749	1.53958
$885$	−3.68203	−0.123770
$886$	−21.1563	−0.710759
$887$	40.0017	1.34313	0.671563	−	0.740947i	$-0.265623\pi$
$887$	40.0017	1.34313	0.671563	+	0.740947i	$0.265623\pi$
$888$	1.98301	0.0665455
$889$	−4.72288	−0.158400
$890$	−1.91784	−0.0642861
$891$	26.5044	0.887930
$892$	−3.05848	−0.102405
$893$	−6.63174	−0.221923
$894$	−19.8551	−0.664054
$895$	−9.00912	−0.301142
$896$	2.73152	0.0912537
$897$	−177.432	−5.92427
$898$	−8.72132	−0.291034
$899$	38.2499	1.27570
$900$	7.64446	0.254815
$901$	−71.3887	−2.37830
$902$	2.66769	0.0888245
$903$	−8.91182	−0.296567
$904$	−4.24313	−0.141124
$905$	20.2234	0.672249
$906$	−27.2871	−0.906555
$907$	−22.5610	−0.749125	−0.374562	−	0.927202i	$-0.622207\pi$
$907$	−22.5610	−0.749125	−0.374562	+	0.927202i	$0.622207\pi$
$908$	14.6877	0.487430
$909$	27.5922	0.915175
$910$	−16.7101	−0.553936
$911$	11.6888	0.387266	0.193633	−	0.981074i	$-0.437973\pi$
$911$	11.6888	0.387266	0.193633	+	0.981074i	$0.437973\pi$
$912$	25.3838	0.840542
$913$	−12.7935	−0.423404
$914$	0.125694	0.00415760
$915$	32.4903	1.07409
$916$	−13.4531	−0.444504
$917$	−47.7223	−1.57593
$918$	−113.383	−3.74220
$919$	36.6817	1.21002	0.605009	−	0.796218i	$-0.293169\pi$
$919$	36.6817	1.21002	0.605009	+	0.796218i	$0.293169\pi$
$920$	−8.88984	−0.293089
$921$	−37.9518	−1.25055
$922$	3.91909	0.129068
$923$	−25.2899	−0.832427
$924$	−8.91182	−0.293177
$925$	−0.607804	−0.0199845
$926$	−18.4445	−0.606123
$927$	−14.5110	−0.476605
$928$	6.36025	0.208785
$929$	−17.6418	−0.578808	−0.289404	−	0.957207i	$-0.593457\pi$
$929$	−17.6418	−0.578808	−0.289404	+	0.957207i	$0.593457\pi$
$930$	19.6208	0.643393
$931$	−3.58831	−0.117602
$932$	−17.1819	−0.562811
$933$	20.0425	0.656161
$934$	−19.7612	−0.646607
$935$	−7.48258	−0.244707
$936$	46.7652	1.52857
$937$	6.40942	0.209387	0.104693	−	0.994505i	$-0.466614\pi$
$937$	6.40942	0.209387	0.104693	+	0.994505i	$0.466614\pi$
$938$	−30.1610	−0.984792
$939$	80.5788	2.62959
$940$	−0.852378	−0.0278015
$941$	−6.93849	−0.226188	−0.113094	−	0.993584i	$-0.536076\pi$
$941$	−6.93849	−0.226188	−0.113094	+	0.993584i	$0.536076\pi$
$942$	21.8139	0.710734
$943$	23.7154	0.772279
$944$	−1.12856	−0.0367316
$945$	41.3906	1.34644
$946$	1.00000	0.0325128
$947$	−10.1517	−0.329887	−0.164944	−	0.986303i	$-0.552744\pi$
$947$	−10.1517	−0.329887	−0.164944	+	0.986303i	$0.552744\pi$
$948$	8.23757	0.267544
$949$	−81.0479	−2.63093
$950$	−7.78028	−0.252426
$951$	−28.2679	−0.916649
$952$	20.4388	0.662426
$953$	−16.4986	−0.534443	−0.267221	−	0.963635i	$-0.586105\pi$
$953$	−16.4986	−0.534443	−0.267221	+	0.963635i	$0.586105\pi$
$954$	−72.9331	−2.36130
$955$	−16.1486	−0.522557
$956$	17.8779	0.578213
$957$	−20.7509	−0.670780
$958$	39.0414	1.26137
$959$	−2.07425	−0.0669810
$960$	3.26258	0.105299
$961$	5.16691	0.166674
$962$	−3.71825	−0.119881
$963$	27.2020	0.876573
$964$	−23.9789	−0.772308
$965$	−11.6496	−0.375015
$966$	−79.2246	−2.54901
$967$	48.6597	1.56479	0.782396	−	0.622781i	$-0.213997\pi$
$967$	48.6597	1.56479	0.782396	+	0.622781i	$0.213997\pi$
$968$	1.00000	0.0321412
$969$	189.937	6.10164
$970$	−12.9532	−0.415903
$971$	2.38795	0.0766330	0.0383165	−	0.999266i	$-0.487800\pi$
$971$	2.38795	0.0766330	0.0383165	+	0.999266i	$0.487800\pi$
$972$	−41.0139	−1.31552
$973$	−12.3231	−0.395062
$974$	23.8887	0.765444
$975$	−19.9589	−0.639198
$976$	9.95844	0.318762
$977$	−38.4820	−1.23115	−0.615575	−	0.788079i	$-0.711076\pi$
$977$	−38.4820	−1.23115	−0.615575	+	0.788079i	$0.711076\pi$
$978$	−73.6095	−2.35377
$979$	1.91784	0.0612944
$980$	−0.461206	−0.0147327
$981$	48.0720	1.53482
$982$	−23.3319	−0.744551
$983$	−49.1853	−1.56877	−0.784384	−	0.620275i	$-0.787021\pi$
$983$	−49.1853	−1.56877	−0.784384	+	0.620275i	$0.787021\pi$
$984$	−8.70358	−0.277460
$985$	−15.2043	−0.484448
$986$	47.5911	1.51561
$987$	−7.59623	−0.241791
$988$	−47.5960	−1.51423
$989$	8.88984	0.282680
$990$	−7.64446	−0.242957
$991$	−19.9159	−0.632649	−0.316325	−	0.948651i	$-0.602449\pi$
$991$	−19.9159	−0.632649	−0.316325	+	0.948651i	$0.602449\pi$
$992$	6.01389	0.190941
$993$	−117.172	−3.71833
$994$	−11.2921	−0.358165
$995$	2.21588	0.0702480
$996$	41.7399	1.32258
$997$	1.91558	0.0606670	0.0303335	−	0.999540i	$-0.490343\pi$
$997$	1.91558	0.0606670	0.0303335	+	0.999540i	$0.490343\pi$
$998$	−28.8772	−0.914093
$999$	9.21002	0.291392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.2	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.26258 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.26258 q^{6} +2.73152 q^{7} +1.00000 q^{8} +7.64446 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.26258 q^{3} +1.00000 q^{4} -1.00000 q^{5} -3.26258 q^{6} +2.73152 q^{7} +1.00000 q^{8} +7.64446 q^{9} -1.00000 q^{10} +1.00000 q^{11} -3.26258 q^{12} +6.11752 q^{13} +2.73152 q^{14} +3.26258 q^{15} +1.00000 q^{16} +7.48258 q^{17} +7.64446 q^{18} -7.78028 q^{19} -1.00000 q^{20} -8.91182 q^{21} +1.00000 q^{22} +8.88984 q^{23} -3.26258 q^{24} +1.00000 q^{25} +6.11752 q^{26} -15.1529 q^{27} +2.73152 q^{28} +6.36025 q^{29} +3.26258 q^{30} +6.01389 q^{31} +1.00000 q^{32} -3.26258 q^{33} +7.48258 q^{34} -2.73152 q^{35} +7.64446 q^{36} -0.607804 q^{37} -7.78028 q^{38} -19.9589 q^{39} -1.00000 q^{40} +2.66769 q^{41} -8.91182 q^{42} +1.00000 q^{43} +1.00000 q^{44} -7.64446 q^{45} +8.88984 q^{46} +0.852378 q^{47} -3.26258 q^{48} +0.461206 q^{49} +1.00000 q^{50} -24.4126 q^{51} +6.11752 q^{52} -9.54066 q^{53} -15.1529 q^{54} -1.00000 q^{55} +2.73152 q^{56} +25.3838 q^{57} +6.36025 q^{58} -1.12856 q^{59} +3.26258 q^{60} +9.95844 q^{61} +6.01389 q^{62} +20.8810 q^{63} +1.00000 q^{64} -6.11752 q^{65} -3.26258 q^{66} -11.0418 q^{67} +7.48258 q^{68} -29.0039 q^{69} -2.73152 q^{70} -4.13401 q^{71} +7.64446 q^{72} -13.2485 q^{73} -0.607804 q^{74} -3.26258 q^{75} -7.78028 q^{76} +2.73152 q^{77} -19.9589 q^{78} -2.52486 q^{79} -1.00000 q^{80} +26.5044 q^{81} +2.66769 q^{82} -12.7935 q^{83} -8.91182 q^{84} -7.48258 q^{85} +1.00000 q^{86} -20.7509 q^{87} +1.00000 q^{88} +1.91784 q^{89} -7.64446 q^{90} +16.7101 q^{91} +8.88984 q^{92} -19.6208 q^{93} +0.852378 q^{94} +7.78028 q^{95} -3.26258 q^{96} +12.9532 q^{97} +0.461206 q^{98} +7.64446 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 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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