LMFDB - Embedded newform 4730.2.a.be.1.7

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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 $ x^12 - 3x^11 - 26x^10 + 79x^9 + 247x^8 - 766x^7 - 1023x^6 + 3281x^5 + 1634x^4 - 5557x^3 - 483x^2 + 1648*x + 392
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.769997$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.769997 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.769997 q^{6} +4.71912 q^{7} +1.00000 q^{8} -2.40710 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.769997 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.769997 q^{6} +4.71912 q^{7} +1.00000 q^{8} -2.40710 q^{9} +1.00000 q^{10} -1.00000 q^{11} +0.769997 q^{12} +4.82049 q^{13} +4.71912 q^{14} +0.769997 q^{15} +1.00000 q^{16} +6.87326 q^{17} -2.40710 q^{18} -6.08969 q^{19} +1.00000 q^{20} +3.63371 q^{21} -1.00000 q^{22} -2.82049 q^{23} +0.769997 q^{24} +1.00000 q^{25} +4.82049 q^{26} -4.16346 q^{27} +4.71912 q^{28} +0.648686 q^{29} +0.769997 q^{30} +8.04887 q^{31} +1.00000 q^{32} -0.769997 q^{33} +6.87326 q^{34} +4.71912 q^{35} -2.40710 q^{36} +1.84432 q^{37} -6.08969 q^{38} +3.71176 q^{39} +1.00000 q^{40} -5.87951 q^{41} +3.63371 q^{42} +1.00000 q^{43} -1.00000 q^{44} -2.40710 q^{45} -2.82049 q^{46} -12.3087 q^{47} +0.769997 q^{48} +15.2701 q^{49} +1.00000 q^{50} +5.29239 q^{51} +4.82049 q^{52} +8.05623 q^{53} -4.16346 q^{54} -1.00000 q^{55} +4.71912 q^{56} -4.68904 q^{57} +0.648686 q^{58} -12.7272 q^{59} +0.769997 q^{60} +11.5570 q^{61} +8.04887 q^{62} -11.3594 q^{63} +1.00000 q^{64} +4.82049 q^{65} -0.769997 q^{66} +2.87102 q^{67} +6.87326 q^{68} -2.17177 q^{69} +4.71912 q^{70} +2.63811 q^{71} -2.40710 q^{72} +1.83057 q^{73} +1.84432 q^{74} +0.769997 q^{75} -6.08969 q^{76} -4.71912 q^{77} +3.71176 q^{78} -9.14301 q^{79} +1.00000 q^{80} +4.01546 q^{81} -5.87951 q^{82} -2.49005 q^{83} +3.63371 q^{84} +6.87326 q^{85} +1.00000 q^{86} +0.499486 q^{87} -1.00000 q^{88} -6.18484 q^{89} -2.40710 q^{90} +22.7485 q^{91} -2.82049 q^{92} +6.19761 q^{93} -12.3087 q^{94} -6.08969 q^{95} +0.769997 q^{96} +8.98364 q^{97} +15.2701 q^{98} +2.40710 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * 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
$3$	0.769997	0.444558	0.222279	−	0.974983i	$-0.428650\pi$
$3$	0.769997	0.444558	0.222279	+	0.974983i	$0.428650\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.769997	0.314350
$7$	4.71912	1.78366	0.891830	−	0.452370i	$-0.149422\pi$
$7$	4.71912	1.78366	0.891830	+	0.452370i	$0.149422\pi$
$8$	1.00000	0.353553
$9$	−2.40710	−0.802368
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.769997	0.222279
$13$	4.82049	1.33696	0.668481	−	0.743729i	$-0.266945\pi$
$13$	4.82049	1.33696	0.668481	+	0.743729i	$0.266945\pi$
$14$	4.71912	1.26124
$15$	0.769997	0.198812
$16$	1.00000	0.250000
$17$	6.87326	1.66701	0.833506	−	0.552511i	$-0.186330\pi$
$17$	6.87326	1.66701	0.833506	+	0.552511i	$0.186330\pi$
$18$	−2.40710	−0.567360
$19$	−6.08969	−1.39707	−0.698535	−	0.715576i	$-0.746164\pi$
$19$	−6.08969	−1.39707	−0.698535	+	0.715576i	$0.746164\pi$
$20$	1.00000	0.223607
$21$	3.63371	0.792941
$22$	−1.00000	−0.213201
$23$	−2.82049	−0.588112	−0.294056	−	0.955788i	$-0.595005\pi$
$23$	−2.82049	−0.588112	−0.294056	+	0.955788i	$0.595005\pi$
$24$	0.769997	0.157175
$25$	1.00000	0.200000
$26$	4.82049	0.945375
$27$	−4.16346	−0.801257
$28$	4.71912	0.891830
$29$	0.648686	0.120458	0.0602290	−	0.998185i	$-0.480817\pi$
$29$	0.648686	0.120458	0.0602290	+	0.998185i	$0.480817\pi$
$30$	0.769997	0.140582
$31$	8.04887	1.44562	0.722810	−	0.691047i	$-0.242850\pi$
$31$	8.04887	1.44562	0.722810	+	0.691047i	$0.242850\pi$
$32$	1.00000	0.176777
$33$	−0.769997	−0.134039
$34$	6.87326	1.17875
$35$	4.71912	0.797677
$36$	−2.40710	−0.401184
$37$	1.84432	0.303205	0.151602	−	0.988442i	$-0.451557\pi$
$37$	1.84432	0.303205	0.151602	+	0.988442i	$0.451557\pi$
$38$	−6.08969	−0.987878
$39$	3.71176	0.594358
$40$	1.00000	0.158114
$41$	−5.87951	−0.918225	−0.459112	−	0.888378i	$-0.651832\pi$
$41$	−5.87951	−0.918225	−0.459112	+	0.888378i	$0.651832\pi$
$42$	3.63371	0.560694
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	−2.40710	−0.358830
$46$	−2.82049	−0.415858
$47$	−12.3087	−1.79541	−0.897706	−	0.440595i	$-0.854768\pi$
$47$	−12.3087	−1.79541	−0.897706	+	0.440595i	$0.854768\pi$
$48$	0.769997	0.111140
$49$	15.2701	2.18144
$50$	1.00000	0.141421
$51$	5.29239	0.741083
$52$	4.82049	0.668481
$53$	8.05623	1.10661	0.553304	−	0.832979i	$-0.313367\pi$
$53$	8.05623	1.10661	0.553304	+	0.832979i	$0.313367\pi$
$54$	−4.16346	−0.566575
$55$	−1.00000	−0.134840
$56$	4.71912	0.630619
$57$	−4.68904	−0.621079
$58$	0.648686	0.0851766
$59$	−12.7272	−1.65693	−0.828467	−	0.560037i	$-0.810787\pi$
$59$	−12.7272	−1.65693	−0.828467	+	0.560037i	$0.810787\pi$
$60$	0.769997	0.0994062
$61$	11.5570	1.47972	0.739860	−	0.672761i	$-0.234892\pi$
$61$	11.5570	1.47972	0.739860	+	0.672761i	$0.234892\pi$
$62$	8.04887	1.02221
$63$	−11.3594	−1.43115
$64$	1.00000	0.125000
$65$	4.82049	0.597908
$66$	−0.769997	−0.0947801
$67$	2.87102	0.350750	0.175375	−	0.984502i	$-0.443886\pi$
$67$	2.87102	0.350750	0.175375	+	0.984502i	$0.443886\pi$
$68$	6.87326	0.833506
$69$	−2.17177	−0.261450
$70$	4.71912	0.564043
$71$	2.63811	0.313086	0.156543	−	0.987671i	$-0.449965\pi$
$71$	2.63811	0.313086	0.156543	+	0.987671i	$0.449965\pi$
$72$	−2.40710	−0.283680
$73$	1.83057	0.214252	0.107126	−	0.994245i	$-0.465835\pi$
$73$	1.83057	0.214252	0.107126	+	0.994245i	$0.465835\pi$
$74$	1.84432	0.214398
$75$	0.769997	0.0889116
$76$	−6.08969	−0.698535
$77$	−4.71912	−0.537794
$78$	3.71176	0.420274
$79$	−9.14301	−1.02867	−0.514334	−	0.857590i	$-0.671961\pi$
$79$	−9.14301	−1.02867	−0.514334	+	0.857590i	$0.671961\pi$
$80$	1.00000	0.111803
$81$	4.01546	0.446162
$82$	−5.87951	−0.649283
$83$	−2.49005	−0.273318	−0.136659	−	0.990618i	$-0.543636\pi$
$83$	−2.49005	−0.273318	−0.136659	+	0.990618i	$0.543636\pi$
$84$	3.63371	0.396470
$85$	6.87326	0.745510
$86$	1.00000	0.107833
$87$	0.499486	0.0535506
$88$	−1.00000	−0.106600
$89$	−6.18484	−0.655592	−0.327796	−	0.944749i	$-0.606306\pi$
$89$	−6.18484	−0.655592	−0.327796	+	0.944749i	$0.606306\pi$
$90$	−2.40710	−0.253731
$91$	22.7485	2.38469
$92$	−2.82049	−0.294056
$93$	6.19761	0.642662
$94$	−12.3087	−1.26955
$95$	−6.08969	−0.624789
$96$	0.769997	0.0785875
$97$	8.98364	0.912150	0.456075	−	0.889941i	$-0.349255\pi$
$97$	8.98364	0.912150	0.456075	+	0.889941i	$0.349255\pi$
$98$	15.2701	1.54251
$99$	2.40710	0.241923
$100$	1.00000	0.100000
$101$	−7.55809	−0.752058	−0.376029	−	0.926608i	$-0.622711\pi$
$101$	−7.55809	−0.752058	−0.376029	+	0.926608i	$0.622711\pi$
$102$	5.29239	0.524025
$103$	3.23968	0.319215	0.159607	−	0.987181i	$-0.448977\pi$
$103$	3.23968	0.319215	0.159607	+	0.987181i	$0.448977\pi$
$104$	4.82049	0.472688
$105$	3.63371	0.354614
$106$	8.05623	0.782490
$107$	−18.1188	−1.75161	−0.875805	−	0.482665i	$-0.839669\pi$
$107$	−18.1188	−1.75161	−0.875805	+	0.482665i	$0.839669\pi$
$108$	−4.16346	−0.400629
$109$	−10.1215	−0.969464	−0.484732	−	0.874663i	$-0.661083\pi$
$109$	−10.1215	−0.969464	−0.484732	+	0.874663i	$0.661083\pi$
$110$	−1.00000	−0.0953463
$111$	1.42012	0.134792
$112$	4.71912	0.445915
$113$	−4.53172	−0.426309	−0.213154	−	0.977019i	$-0.568374\pi$
$113$	−4.53172	−0.426309	−0.213154	+	0.977019i	$0.568374\pi$
$114$	−4.68904	−0.439169
$115$	−2.82049	−0.263012
$116$	0.648686	0.0602290
$117$	−11.6034	−1.07274
$118$	−12.7272	−1.17163
$119$	32.4358	2.97338
$120$	0.769997	0.0702908
$121$	1.00000	0.0909091
$122$	11.5570	1.04632
$123$	−4.52720	−0.408204
$124$	8.04887	0.722810
$125$	1.00000	0.0894427
$126$	−11.3594	−1.01198
$127$	−13.1291	−1.16502	−0.582511	−	0.812823i	$-0.697930\pi$
$127$	−13.1291	−1.16502	−0.582511	+	0.812823i	$0.697930\pi$
$128$	1.00000	0.0883883
$129$	0.769997	0.0677945
$130$	4.82049	0.422785
$131$	19.3773	1.69301	0.846503	−	0.532384i	$-0.178704\pi$
$131$	19.3773	1.69301	0.846503	+	0.532384i	$0.178704\pi$
$132$	−0.769997	−0.0670197
$133$	−28.7380	−2.49190
$134$	2.87102	0.248018
$135$	−4.16346	−0.358333
$136$	6.87326	0.589377
$137$	11.6852	0.998331	0.499165	−	0.866507i	$-0.333640\pi$
$137$	11.6852	0.998331	0.499165	+	0.866507i	$0.333640\pi$
$138$	−2.17177	−0.184873
$139$	0.0272877	0.00231451	0.00115726	−	0.999999i	$-0.499632\pi$
$139$	0.0272877	0.00231451	0.00115726	+	0.999999i	$0.499632\pi$
$140$	4.71912	0.398839
$141$	−9.47769	−0.798165
$142$	2.63811	0.221385
$143$	−4.82049	−0.403109
$144$	−2.40710	−0.200592
$145$	0.648686	0.0538704
$146$	1.83057	0.151499
$147$	11.7579	0.969779
$148$	1.84432	0.151602
$149$	22.0490	1.80632	0.903161	−	0.429303i	$-0.141241\pi$
$149$	22.0490	1.80632	0.903161	+	0.429303i	$0.141241\pi$
$150$	0.769997	0.0628700
$151$	5.00624	0.407402	0.203701	−	0.979033i	$-0.434703\pi$
$151$	5.00624	0.407402	0.203701	+	0.979033i	$0.434703\pi$
$152$	−6.08969	−0.493939
$153$	−16.5447	−1.33756
$154$	−4.71912	−0.380278
$155$	8.04887	0.646501
$156$	3.71176	0.297179
$157$	−3.27661	−0.261502	−0.130751	−	0.991415i	$-0.541739\pi$
$157$	−3.27661	−0.261502	−0.130751	+	0.991415i	$0.541739\pi$
$158$	−9.14301	−0.727378
$159$	6.20327	0.491952
$160$	1.00000	0.0790569
$161$	−13.3102	−1.04899
$162$	4.01546	0.315484
$163$	1.81470	0.142139	0.0710693	−	0.997471i	$-0.477359\pi$
$163$	1.81470	0.142139	0.0710693	+	0.997471i	$0.477359\pi$
$164$	−5.87951	−0.459112
$165$	−0.769997	−0.0599442
$166$	−2.49005	−0.193265
$167$	−19.9902	−1.54689	−0.773443	−	0.633866i	$-0.781467\pi$
$167$	−19.9902	−1.54689	−0.773443	+	0.633866i	$0.781467\pi$
$168$	3.63371	0.280347
$169$	10.2371	0.787469
$170$	6.87326	0.527155
$171$	14.6585	1.12096
$172$	1.00000	0.0762493
$173$	14.1771	1.07787	0.538933	−	0.842348i	$-0.318827\pi$
$173$	14.1771	1.07787	0.538933	+	0.842348i	$0.318827\pi$
$174$	0.499486	0.0378660
$175$	4.71912	0.356732
$176$	−1.00000	−0.0753778
$177$	−9.79988	−0.736604
$178$	−6.18484	−0.463573
$179$	−24.3657	−1.82117	−0.910587	−	0.413317i	$-0.864370\pi$
$179$	−24.3657	−1.82117	−0.910587	+	0.413317i	$0.864370\pi$
$180$	−2.40710	−0.179415
$181$	19.6016	1.45697	0.728487	−	0.685060i	$-0.240224\pi$
$181$	19.6016	1.45697	0.728487	+	0.685060i	$0.240224\pi$
$182$	22.7485	1.68623
$183$	8.89885	0.657822
$184$	−2.82049	−0.207929
$185$	1.84432	0.135597
$186$	6.19761	0.454431
$187$	−6.87326	−0.502623
$188$	−12.3087	−0.897706
$189$	−19.6479	−1.42917
$190$	−6.08969	−0.441792
$191$	8.97018	0.649060	0.324530	−	0.945875i	$-0.394794\pi$
$191$	8.97018	0.649060	0.324530	+	0.945875i	$0.394794\pi$
$192$	0.769997	0.0555698
$193$	−18.6940	−1.34562	−0.672812	−	0.739813i	$-0.734914\pi$
$193$	−18.6940	−1.34562	−0.672812	+	0.739813i	$0.734914\pi$
$194$	8.98364	0.644988
$195$	3.71176	0.265805
$196$	15.2701	1.09072
$197$	−20.2277	−1.44116	−0.720581	−	0.693371i	$-0.756125\pi$
$197$	−20.2277	−1.44116	−0.720581	+	0.693371i	$0.756125\pi$
$198$	2.40710	0.171065
$199$	10.2488	0.726516	0.363258	−	0.931689i	$-0.381664\pi$
$199$	10.2488	0.726516	0.363258	+	0.931689i	$0.381664\pi$
$200$	1.00000	0.0707107
$201$	2.21067	0.155929
$202$	−7.55809	−0.531785
$203$	3.06123	0.214856
$204$	5.29239	0.370542
$205$	−5.87951	−0.410643
$206$	3.23968	0.225719
$207$	6.78921	0.471882
$208$	4.82049	0.334241
$209$	6.08969	0.421232
$210$	3.63371	0.250750
$211$	−20.1549	−1.38752	−0.693762	−	0.720204i	$-0.744048\pi$
$211$	−20.1549	−1.38752	−0.693762	+	0.720204i	$0.744048\pi$
$212$	8.05623	0.553304
$213$	2.03134	0.139185
$214$	−18.1188	−1.23858
$215$	1.00000	0.0681994
$216$	−4.16346	−0.283287
$217$	37.9836	2.57849
$218$	−10.1215	−0.685514
$219$	1.40953	0.0952475
$220$	−1.00000	−0.0674200
$221$	33.1325	2.22873
$222$	1.42012	0.0953124
$223$	−2.95695	−0.198012	−0.0990060	−	0.995087i	$-0.531566\pi$
$223$	−2.95695	−0.198012	−0.0990060	+	0.995087i	$0.531566\pi$
$224$	4.71912	0.315310
$225$	−2.40710	−0.160474
$226$	−4.53172	−0.301446
$227$	10.2629	0.681171	0.340585	−	0.940214i	$-0.389375\pi$
$227$	10.2629	0.681171	0.340585	+	0.940214i	$0.389375\pi$
$228$	−4.68904	−0.310539
$229$	8.63226	0.570436	0.285218	−	0.958463i	$-0.407934\pi$
$229$	8.63226	0.570436	0.285218	+	0.958463i	$0.407934\pi$
$230$	−2.82049	−0.185977
$231$	−3.63371	−0.239081
$232$	0.648686	0.0425883
$233$	15.5796	1.02066	0.510328	−	0.859980i	$-0.329524\pi$
$233$	15.5796	1.02066	0.510328	+	0.859980i	$0.329524\pi$
$234$	−11.6034	−0.758539
$235$	−12.3087	−0.802933
$236$	−12.7272	−0.828467
$237$	−7.04009	−0.457303
$238$	32.4358	2.10250
$239$	13.1299	0.849302	0.424651	−	0.905357i	$-0.360397\pi$
$239$	13.1299	0.849302	0.424651	+	0.905357i	$0.360397\pi$
$240$	0.769997	0.0497031
$241$	−11.1282	−0.716829	−0.358415	−	0.933562i	$-0.616683\pi$
$241$	−11.1282	−0.716829	−0.358415	+	0.933562i	$0.616683\pi$
$242$	1.00000	0.0642824
$243$	15.5823	0.999603
$244$	11.5570	0.739860
$245$	15.2701	0.975571
$246$	−4.52720	−0.288644
$247$	−29.3553	−1.86783
$248$	8.04887	0.511104
$249$	−1.91733	−0.121506
$250$	1.00000	0.0632456
$251$	17.4341	1.10043	0.550217	−	0.835022i	$-0.314545\pi$
$251$	17.4341	1.10043	0.550217	+	0.835022i	$0.314545\pi$
$252$	−11.3594	−0.715576
$253$	2.82049	0.177322
$254$	−13.1291	−0.823795
$255$	5.29239	0.331423
$256$	1.00000	0.0625000
$257$	−19.2926	−1.20344	−0.601720	−	0.798707i	$-0.705518\pi$
$257$	−19.2926	−1.20344	−0.601720	+	0.798707i	$0.705518\pi$
$258$	0.769997	0.0479379
$259$	8.70358	0.540814
$260$	4.82049	0.298954
$261$	−1.56145	−0.0966516
$262$	19.3773	1.19714
$263$	19.1093	1.17833	0.589165	−	0.808012i	$-0.299457\pi$
$263$	19.1093	1.17833	0.589165	+	0.808012i	$0.299457\pi$
$264$	−0.769997	−0.0473901
$265$	8.05623	0.494890
$266$	−28.7380	−1.76204
$267$	−4.76231	−0.291449
$268$	2.87102	0.175375
$269$	−20.2582	−1.23517	−0.617583	−	0.786505i	$-0.711888\pi$
$269$	−20.2582	−1.23517	−0.617583	+	0.786505i	$0.711888\pi$
$270$	−4.16346	−0.253380
$271$	−26.0211	−1.58067	−0.790334	−	0.612677i	$-0.790093\pi$
$271$	−26.0211	−1.58067	−0.790334	+	0.612677i	$0.790093\pi$
$272$	6.87326	0.416753
$273$	17.5163	1.06013
$274$	11.6852	0.705926
$275$	−1.00000	−0.0603023
$276$	−2.17177	−0.130725
$277$	−16.0212	−0.962622	−0.481311	−	0.876550i	$-0.659839\pi$
$277$	−16.0212	−0.962622	−0.481311	+	0.876550i	$0.659839\pi$
$278$	0.0272877	0.00163661
$279$	−19.3745	−1.15992
$280$	4.71912	0.282021
$281$	−3.66414	−0.218584	−0.109292	−	0.994010i	$-0.534858\pi$
$281$	−3.66414	−0.218584	−0.109292	+	0.994010i	$0.534858\pi$
$282$	−9.47769	−0.564388
$283$	4.36373	0.259397	0.129698	−	0.991553i	$-0.458599\pi$
$283$	4.36373	0.259397	0.129698	+	0.991553i	$0.458599\pi$
$284$	2.63811	0.156543
$285$	−4.68904	−0.277755
$286$	−4.82049	−0.285041
$287$	−27.7461	−1.63780
$288$	−2.40710	−0.141840
$289$	30.2417	1.77893
$290$	0.648686	0.0380921
$291$	6.91738	0.405504
$292$	1.83057	0.107126
$293$	−5.41921	−0.316593	−0.158297	−	0.987392i	$-0.550600\pi$
$293$	−5.41921	−0.316593	−0.158297	+	0.987392i	$0.550600\pi$
$294$	11.7579	0.685737
$295$	−12.7272	−0.741004
$296$	1.84432	0.107199
$297$	4.16346	0.241588
$298$	22.0490	1.27726
$299$	−13.5961	−0.786284
$300$	0.769997	0.0444558
$301$	4.71912	0.272006
$302$	5.00624	0.288077
$303$	−5.81971	−0.334334
$304$	−6.08969	−0.349267
$305$	11.5570	0.661751
$306$	−16.5447	−0.945795
$307$	9.54656	0.544851	0.272426	−	0.962177i	$-0.412174\pi$
$307$	9.54656	0.544851	0.272426	+	0.962177i	$0.412174\pi$
$308$	−4.71912	−0.268897
$309$	2.49454	0.141910
$310$	8.04887	0.457145
$311$	16.9195	0.959417	0.479709	−	0.877428i	$-0.340742\pi$
$311$	16.9195	0.959417	0.479709	+	0.877428i	$0.340742\pi$
$312$	3.71176	0.210137
$313$	−19.9949	−1.13018	−0.565090	−	0.825029i	$-0.691159\pi$
$313$	−19.9949	−1.13018	−0.565090	+	0.825029i	$0.691159\pi$
$314$	−3.27661	−0.184910
$315$	−11.3594	−0.640031
$316$	−9.14301	−0.514334
$317$	−28.6527	−1.60930	−0.804648	−	0.593752i	$-0.797646\pi$
$317$	−28.6527	−1.60930	−0.804648	+	0.593752i	$0.797646\pi$
$318$	6.20327	0.347862
$319$	−0.648686	−0.0363194
$320$	1.00000	0.0559017
$321$	−13.9514	−0.778693
$322$	−13.3102	−0.741750
$323$	−41.8560	−2.32893
$324$	4.01546	0.223081
$325$	4.82049	0.267392
$326$	1.81470	0.100507
$327$	−7.79353	−0.430983
$328$	−5.87951	−0.324641
$329$	−58.0864	−3.20241
$330$	−0.769997	−0.0423870
$331$	−16.3489	−0.898618	−0.449309	−	0.893376i	$-0.648330\pi$
$331$	−16.3489	−0.898618	−0.449309	+	0.893376i	$0.648330\pi$
$332$	−2.49005	−0.136659
$333$	−4.43947	−0.243282
$334$	−19.9902	−1.09381
$335$	2.87102	0.156860
$336$	3.63371	0.198235
$337$	17.2707	0.940794	0.470397	−	0.882455i	$-0.344111\pi$
$337$	17.2707	0.940794	0.470397	+	0.882455i	$0.344111\pi$
$338$	10.2371	0.556824
$339$	−3.48941	−0.189519
$340$	6.87326	0.372755
$341$	−8.04887	−0.435871
$342$	14.6585	0.792641
$343$	39.0276	2.10729
$344$	1.00000	0.0539164
$345$	−2.17177	−0.116924
$346$	14.1771	0.762167
$347$	15.2519	0.818765	0.409382	−	0.912363i	$-0.365744\pi$
$347$	15.2519	0.818765	0.409382	+	0.912363i	$0.365744\pi$
$348$	0.499486	0.0267753
$349$	−27.0659	−1.44880	−0.724401	−	0.689378i	$-0.757884\pi$
$349$	−27.0659	−1.44880	−0.724401	+	0.689378i	$0.757884\pi$
$350$	4.71912	0.252248
$351$	−20.0699	−1.07125
$352$	−1.00000	−0.0533002
$353$	25.4907	1.35673	0.678366	−	0.734724i	$-0.262689\pi$
$353$	25.4907	1.35673	0.678366	+	0.734724i	$0.262689\pi$
$354$	−9.79988	−0.520858
$355$	2.63811	0.140016
$356$	−6.18484	−0.327796
$357$	24.9755	1.32184
$358$	−24.3657	−1.28776
$359$	13.1171	0.692294	0.346147	−	0.938180i	$-0.387490\pi$
$359$	13.1171	0.692294	0.346147	+	0.938180i	$0.387490\pi$
$360$	−2.40710	−0.126866
$361$	18.0843	0.951804
$362$	19.6016	1.03024
$363$	0.769997	0.0404144
$364$	22.7485	1.19234
$365$	1.83057	0.0958164
$366$	8.89885	0.465150
$367$	3.78574	0.197614	0.0988071	−	0.995107i	$-0.468497\pi$
$367$	3.78574	0.197614	0.0988071	+	0.995107i	$0.468497\pi$
$368$	−2.82049	−0.147028
$369$	14.1526	0.736754
$370$	1.84432	0.0958817
$371$	38.0183	1.97381
$372$	6.19761	0.321331
$373$	−34.9268	−1.80844	−0.904221	−	0.427064i	$-0.859548\pi$
$373$	−34.9268	−1.80844	−0.904221	+	0.427064i	$0.859548\pi$
$374$	−6.87326	−0.355408
$375$	0.769997	0.0397625
$376$	−12.3087	−0.634774
$377$	3.12698	0.161048
$378$	−19.6479	−1.01058
$379$	34.4499	1.76957	0.884786	−	0.465997i	$-0.154304\pi$
$379$	34.4499	1.76957	0.884786	+	0.465997i	$0.154304\pi$
$380$	−6.08969	−0.312394
$381$	−10.1094	−0.517920
$382$	8.97018	0.458955
$383$	−31.8557	−1.62775	−0.813874	−	0.581042i	$-0.802645\pi$
$383$	−31.8557	−1.62775	−0.813874	+	0.581042i	$0.802645\pi$
$384$	0.769997	0.0392938
$385$	−4.71912	−0.240509
$386$	−18.6940	−0.951500
$387$	−2.40710	−0.122360
$388$	8.98364	0.456075
$389$	−5.70481	−0.289246	−0.144623	−	0.989487i	$-0.546197\pi$
$389$	−5.70481	−0.289246	−0.144623	+	0.989487i	$0.546197\pi$
$390$	3.71176	0.187952
$391$	−19.3859	−0.980390
$392$	15.2701	0.771257
$393$	14.9205	0.752640
$394$	−20.2277	−1.01906
$395$	−9.14301	−0.460035
$396$	2.40710	0.120962
$397$	−18.1068	−0.908754	−0.454377	−	0.890810i	$-0.650138\pi$
$397$	−18.1068	−0.908754	−0.454377	+	0.890810i	$0.650138\pi$
$398$	10.2488	0.513724
$399$	−22.1282	−1.10779
$400$	1.00000	0.0500000
$401$	13.1359	0.655977	0.327988	−	0.944682i	$-0.393629\pi$
$401$	13.1359	0.655977	0.327988	+	0.944682i	$0.393629\pi$
$402$	2.21067	0.110258
$403$	38.7995	1.93274
$404$	−7.55809	−0.376029
$405$	4.01546	0.199530
$406$	3.06123	0.151926
$407$	−1.84432	−0.0914196
$408$	5.29239	0.262013
$409$	27.9862	1.38383	0.691915	−	0.721979i	$-0.256767\pi$
$409$	27.9862	1.38383	0.691915	+	0.721979i	$0.256767\pi$
$410$	−5.87951	−0.290368
$411$	8.99754	0.443816
$412$	3.23968	0.159607
$413$	−60.0610	−2.95541
$414$	6.78921	0.333671
$415$	−2.49005	−0.122232
$416$	4.82049	0.236344
$417$	0.0210114	0.00102893
$418$	6.08969	0.297856
$419$	8.90520	0.435047	0.217524	−	0.976055i	$-0.430202\pi$
$419$	8.90520	0.435047	0.217524	+	0.976055i	$0.430202\pi$
$420$	3.63371	0.177307
$421$	10.4484	0.509222	0.254611	−	0.967044i	$-0.418053\pi$
$421$	10.4484	0.509222	0.254611	+	0.967044i	$0.418053\pi$
$422$	−20.1549	−0.981127
$423$	29.6284	1.44058
$424$	8.05623	0.391245
$425$	6.87326	0.333402
$426$	2.03134	0.0984186
$427$	54.5388	2.63932
$428$	−18.1188	−0.875805
$429$	−3.71176	−0.179206
$430$	1.00000	0.0482243
$431$	−4.68303	−0.225574	−0.112787	−	0.993619i	$-0.535978\pi$
$431$	−4.68303	−0.225574	−0.112787	+	0.993619i	$0.535978\pi$
$432$	−4.16346	−0.200314
$433$	26.6316	1.27983	0.639917	−	0.768444i	$-0.278969\pi$
$433$	26.6316	1.27983	0.639917	+	0.768444i	$0.278969\pi$
$434$	37.9836	1.82327
$435$	0.499486	0.0239485
$436$	−10.1215	−0.484732
$437$	17.1759	0.821634
$438$	1.40953	0.0673501
$439$	−18.6380	−0.889543	−0.444772	−	0.895644i	$-0.646715\pi$
$439$	−18.6380	−0.889543	−0.444772	+	0.895644i	$0.646715\pi$
$440$	−1.00000	−0.0476731
$441$	−36.7567	−1.75032
$442$	33.1325	1.57595
$443$	−17.5322	−0.832981	−0.416491	−	0.909140i	$-0.636740\pi$
$443$	−17.5322	−0.832981	−0.416491	+	0.909140i	$0.636740\pi$
$444$	1.42012	0.0673961
$445$	−6.18484	−0.293190
$446$	−2.95695	−0.140016
$447$	16.9776	0.803015
$448$	4.71912	0.222958
$449$	−12.0831	−0.570236	−0.285118	−	0.958492i	$-0.592033\pi$
$449$	−12.0831	−0.570236	−0.285118	+	0.958492i	$0.592033\pi$
$450$	−2.40710	−0.113472
$451$	5.87951	0.276855
$452$	−4.53172	−0.213154
$453$	3.85479	0.181114
$454$	10.2629	0.481660
$455$	22.7485	1.06646
$456$	−4.68904	−0.219585
$457$	5.06828	0.237084	0.118542	−	0.992949i	$-0.462178\pi$
$457$	5.06828	0.237084	0.118542	+	0.992949i	$0.462178\pi$
$458$	8.63226	0.403359
$459$	−28.6165	−1.33571
$460$	−2.82049	−0.131506
$461$	10.2649	0.478082	0.239041	−	0.971009i	$-0.423167\pi$
$461$	10.2649	0.478082	0.239041	+	0.971009i	$0.423167\pi$
$462$	−3.63371	−0.169056
$463$	−15.8848	−0.738229	−0.369115	−	0.929384i	$-0.620339\pi$
$463$	−15.8848	−0.738229	−0.369115	+	0.929384i	$0.620339\pi$
$464$	0.648686	0.0301145
$465$	6.19761	0.287407
$466$	15.5796	0.721712
$467$	28.6315	1.32491	0.662455	−	0.749102i	$-0.269515\pi$
$467$	28.6315	1.32491	0.662455	+	0.749102i	$0.269515\pi$
$468$	−11.6034	−0.536368
$469$	13.5487	0.625619
$470$	−12.3087	−0.567759
$471$	−2.52298	−0.116253
$472$	−12.7272	−0.585815
$473$	−1.00000	−0.0459800
$474$	−7.04009	−0.323362
$475$	−6.08969	−0.279414
$476$	32.4358	1.48669
$477$	−19.3922	−0.887907
$478$	13.1299	0.600547
$479$	4.26885	0.195049	0.0975244	−	0.995233i	$-0.468908\pi$
$479$	4.26885	0.195049	0.0975244	+	0.995233i	$0.468908\pi$
$480$	0.769997	0.0351454
$481$	8.89053	0.405373
$482$	−11.1282	−0.506875
$483$	−10.2488	−0.466338
$484$	1.00000	0.0454545
$485$	8.98364	0.407926
$486$	15.5823	0.706826
$487$	22.1475	1.00360	0.501800	−	0.864983i	$-0.332671\pi$
$487$	22.1475	1.00360	0.501800	+	0.864983i	$0.332671\pi$
$488$	11.5570	0.523160
$489$	1.39732	0.0631889
$490$	15.2701	0.689833
$491$	−25.1815	−1.13642	−0.568212	−	0.822882i	$-0.692365\pi$
$491$	−25.1815	−1.13642	−0.568212	+	0.822882i	$0.692365\pi$
$492$	−4.52720	−0.204102
$493$	4.45859	0.200805
$494$	−29.3553	−1.32076
$495$	2.40710	0.108191
$496$	8.04887	0.361405
$497$	12.4496	0.558439
$498$	−1.91733	−0.0859176
$499$	25.1495	1.12585	0.562924	−	0.826509i	$-0.309676\pi$
$499$	25.1495	1.12585	0.562924	+	0.826509i	$0.309676\pi$
$500$	1.00000	0.0447214
$501$	−15.3924	−0.687681
$502$	17.4341	0.778124
$503$	24.0806	1.07370	0.536850	−	0.843678i	$-0.319614\pi$
$503$	24.0806	1.07370	0.536850	+	0.843678i	$0.319614\pi$
$504$	−11.3594	−0.505989
$505$	−7.55809	−0.336331
$506$	2.82049	0.125386
$507$	7.88253	0.350076
$508$	−13.1291	−0.582511
$509$	−40.4523	−1.79302	−0.896509	−	0.443025i	$-0.853905\pi$
$509$	−40.4523	−1.79302	−0.896509	+	0.443025i	$0.853905\pi$
$510$	5.29239	0.234351
$511$	8.63868	0.382153
$512$	1.00000	0.0441942
$513$	25.3541	1.11941
$514$	−19.2926	−0.850960
$515$	3.23968	0.142757
$516$	0.769997	0.0338972
$517$	12.3087	0.541337
$518$	8.70358	0.382413
$519$	10.9163	0.479175
$520$	4.82049	0.211392
$521$	13.8543	0.606968	0.303484	−	0.952837i	$-0.401850\pi$
$521$	13.8543	0.606968	0.303484	+	0.952837i	$0.401850\pi$
$522$	−1.56145	−0.0683430
$523$	23.0481	1.00783	0.503913	−	0.863755i	$-0.331893\pi$
$523$	23.0481	1.00783	0.503913	+	0.863755i	$0.331893\pi$
$524$	19.3773	0.846503
$525$	3.63371	0.158588
$526$	19.1093	0.833206
$527$	55.3220	2.40986
$528$	−0.769997	−0.0335098
$529$	−15.0449	−0.654124
$530$	8.05623	0.349940
$531$	30.6356	1.32947
$532$	−28.7380	−1.24595
$533$	−28.3421	−1.22763
$534$	−4.76231	−0.206085
$535$	−18.1188	−0.783344
$536$	2.87102	0.124009
$537$	−18.7615	−0.809618
$538$	−20.2582	−0.873395
$539$	−15.2701	−0.657730
$540$	−4.16346	−0.179167
$541$	−5.81427	−0.249975	−0.124987	−	0.992158i	$-0.539889\pi$
$541$	−5.81427	−0.249975	−0.124987	+	0.992158i	$0.539889\pi$
$542$	−26.0211	−1.11770
$543$	15.0932	0.647710
$544$	6.87326	0.294689
$545$	−10.1215	−0.433557
$546$	17.5163	0.749627
$547$	−6.90073	−0.295054	−0.147527	−	0.989058i	$-0.547131\pi$
$547$	−6.90073	−0.295054	−0.147527	+	0.989058i	$0.547131\pi$
$548$	11.6852	0.499165
$549$	−27.8189	−1.18728
$550$	−1.00000	−0.0426401
$551$	−3.95029	−0.168288
$552$	−2.17177	−0.0924366
$553$	−43.1470	−1.83480
$554$	−16.0212	−0.680677
$555$	1.42012	0.0602809
$556$	0.0272877	0.00115726
$557$	−20.8179	−0.882081	−0.441041	−	0.897487i	$-0.645390\pi$
$557$	−20.8179	−0.882081	−0.441041	+	0.897487i	$0.645390\pi$
$558$	−19.3745	−0.820187
$559$	4.82049	0.203885
$560$	4.71912	0.199419
$561$	−5.29239	−0.223445
$562$	−3.66414	−0.154562
$563$	−31.0099	−1.30691	−0.653456	−	0.756964i	$-0.726682\pi$
$563$	−31.0099	−1.30691	−0.653456	+	0.756964i	$0.726682\pi$
$564$	−9.47769	−0.399083
$565$	−4.53172	−0.190651
$566$	4.36373	0.183421
$567$	18.9495	0.795802
$568$	2.63811	0.110693
$569$	−10.7850	−0.452130	−0.226065	−	0.974112i	$-0.572586\pi$
$569$	−10.7850	−0.452130	−0.226065	+	0.974112i	$0.572586\pi$
$570$	−4.68904	−0.196402
$571$	0.800396	0.0334955	0.0167478	−	0.999860i	$-0.494669\pi$
$571$	0.800396	0.0334955	0.0167478	+	0.999860i	$0.494669\pi$
$572$	−4.82049	−0.201555
$573$	6.90702	0.288545
$574$	−27.7461	−1.15810
$575$	−2.82049	−0.117622
$576$	−2.40710	−0.100296
$577$	21.0496	0.876308	0.438154	−	0.898900i	$-0.355632\pi$
$577$	21.0496	0.876308	0.438154	+	0.898900i	$0.355632\pi$
$578$	30.2417	1.25789
$579$	−14.3943	−0.598208
$580$	0.648686	0.0269352
$581$	−11.7508	−0.487507
$582$	6.91738	0.286735
$583$	−8.05623	−0.333655
$584$	1.83057	0.0757495
$585$	−11.6034	−0.479742
$586$	−5.41921	−0.223865
$587$	−21.5013	−0.887452	−0.443726	−	0.896163i	$-0.646344\pi$
$587$	−21.5013	−0.887452	−0.443726	+	0.896163i	$0.646344\pi$
$588$	11.7579	0.484889
$589$	−49.0151	−2.01963
$590$	−12.7272	−0.523969
$591$	−15.5753	−0.640681
$592$	1.84432	0.0758012
$593$	33.7120	1.38439	0.692194	−	0.721712i	$-0.256644\pi$
$593$	33.7120	1.38439	0.692194	+	0.721712i	$0.256644\pi$
$594$	4.16346	0.170829
$595$	32.4358	1.32974
$596$	22.0490	0.903161
$597$	7.89153	0.322979
$598$	−13.5961	−0.555987
$599$	−16.7109	−0.682787	−0.341394	−	0.939920i	$-0.610899\pi$
$599$	−16.7109	−0.682787	−0.341394	+	0.939920i	$0.610899\pi$
$600$	0.769997	0.0314350
$601$	−21.5232	−0.877950	−0.438975	−	0.898499i	$-0.644658\pi$
$601$	−21.5232	−0.877950	−0.438975	+	0.898499i	$0.644658\pi$
$602$	4.71912	0.192337
$603$	−6.91083	−0.281431
$604$	5.00624	0.203701
$605$	1.00000	0.0406558
$606$	−5.81971	−0.236410
$607$	42.2614	1.71534	0.857669	−	0.514202i	$-0.171912\pi$
$607$	42.2614	1.71534	0.857669	+	0.514202i	$0.171912\pi$
$608$	−6.08969	−0.246969
$609$	2.35714	0.0955160
$610$	11.5570	0.467928
$611$	−59.3340	−2.40040
$612$	−16.5447	−0.668778
$613$	2.85831	0.115446	0.0577231	−	0.998333i	$-0.481616\pi$
$613$	2.85831	0.115446	0.0577231	+	0.998333i	$0.481616\pi$
$614$	9.54656	0.385268
$615$	−4.52720	−0.182555
$616$	−4.71912	−0.190139
$617$	15.3058	0.616189	0.308094	−	0.951356i	$-0.400309\pi$
$617$	15.3058	0.616189	0.308094	+	0.951356i	$0.400309\pi$
$618$	2.49454	0.100345
$619$	−12.5129	−0.502936	−0.251468	−	0.967866i	$-0.580913\pi$
$619$	−12.5129	−0.502936	−0.251468	+	0.967866i	$0.580913\pi$
$620$	8.04887	0.323250
$621$	11.7430	0.471229
$622$	16.9195	0.678410
$623$	−29.1870	−1.16935
$624$	3.71176	0.148589
$625$	1.00000	0.0400000
$626$	−19.9949	−0.799158
$627$	4.68904	0.187262
$628$	−3.27661	−0.130751
$629$	12.6765	0.505446
$630$	−11.3594	−0.452570
$631$	−38.2723	−1.52359	−0.761797	−	0.647815i	$-0.775683\pi$
$631$	−38.2723	−1.52359	−0.761797	+	0.647815i	$0.775683\pi$
$632$	−9.14301	−0.363689
$633$	−15.5193	−0.616835
$634$	−28.6527	−1.13794
$635$	−13.1291	−0.521013
$636$	6.20327	0.245976
$637$	73.6093	2.91651
$638$	−0.648686	−0.0256817
$639$	−6.35020	−0.251210
$640$	1.00000	0.0395285
$641$	−29.2175	−1.15402	−0.577012	−	0.816736i	$-0.695781\pi$
$641$	−29.2175	−1.15402	−0.577012	+	0.816736i	$0.695781\pi$
$642$	−13.9514	−0.550619
$643$	−13.4890	−0.531953	−0.265977	−	0.963980i	$-0.585694\pi$
$643$	−13.4890	−0.531953	−0.265977	+	0.963980i	$0.585694\pi$
$644$	−13.3102	−0.524496
$645$	0.769997	0.0303186
$646$	−41.8560	−1.64680
$647$	−14.9960	−0.589554	−0.294777	−	0.955566i	$-0.595245\pi$
$647$	−14.9960	−0.589554	−0.294777	+	0.955566i	$0.595245\pi$
$648$	4.01546	0.157742
$649$	12.7272	0.499585
$650$	4.82049	0.189075
$651$	29.2473	1.14629
$652$	1.81470	0.0710693
$653$	−37.8833	−1.48249	−0.741245	−	0.671235i	$-0.765764\pi$
$653$	−37.8833	−1.48249	−0.741245	+	0.671235i	$0.765764\pi$
$654$	−7.79353	−0.304751
$655$	19.3773	0.757135
$656$	−5.87951	−0.229556
$657$	−4.40637	−0.171909
$658$	−58.0864	−2.26444
$659$	−37.3822	−1.45620	−0.728101	−	0.685470i	$-0.759597\pi$
$659$	−37.3822	−1.45620	−0.728101	+	0.685470i	$0.759597\pi$
$660$	−0.769997	−0.0299721
$661$	28.8056	1.12041	0.560204	−	0.828355i	$-0.310723\pi$
$661$	28.8056	1.12041	0.560204	+	0.828355i	$0.310723\pi$
$662$	−16.3489	−0.635419
$663$	25.5119	0.990801
$664$	−2.49005	−0.0966326
$665$	−28.7380	−1.11441
$666$	−4.43947	−0.172026
$667$	−1.82961	−0.0708428
$668$	−19.9902	−0.773443
$669$	−2.27684	−0.0880279
$670$	2.87102	0.110917
$671$	−11.5570	−0.446152
$672$	3.63371	0.140173
$673$	−17.9961	−0.693697	−0.346849	−	0.937921i	$-0.612748\pi$
$673$	−17.9961	−0.693697	−0.346849	+	0.937921i	$0.612748\pi$
$674$	17.2707	0.665242
$675$	−4.16346	−0.160251
$676$	10.2371	0.393734
$677$	−21.2437	−0.816463	−0.408231	−	0.912879i	$-0.633854\pi$
$677$	−21.2437	−0.816463	−0.408231	+	0.912879i	$0.633854\pi$
$678$	−3.48941	−0.134010
$679$	42.3949	1.62697
$680$	6.87326	0.263578
$681$	7.90238	0.302820
$682$	−8.04887	−0.308207
$683$	35.5322	1.35960	0.679800	−	0.733397i	$-0.262067\pi$
$683$	35.5322	1.35960	0.679800	+	0.733397i	$0.262067\pi$
$684$	14.6585	0.560482
$685$	11.6852	0.446467
$686$	39.0276	1.49008
$687$	6.64682	0.253592
$688$	1.00000	0.0381246
$689$	38.8349	1.47949
$690$	−2.17177	−0.0826778
$691$	4.62012	0.175758	0.0878788	−	0.996131i	$-0.471991\pi$
$691$	4.62012	0.175758	0.0878788	+	0.996131i	$0.471991\pi$
$692$	14.1771	0.538933
$693$	11.3594	0.431509
$694$	15.2519	0.578954
$695$	0.0272877	0.00103508
$696$	0.499486	0.0189330
$697$	−40.4114	−1.53069
$698$	−27.0659	−1.02446
$699$	11.9963	0.453741
$700$	4.71912	0.178366
$701$	−11.5919	−0.437821	−0.218910	−	0.975745i	$-0.570250\pi$
$701$	−11.5919	−0.437821	−0.218910	+	0.975745i	$0.570250\pi$
$702$	−20.0699	−0.757489
$703$	−11.2313	−0.423598
$704$	−1.00000	−0.0376889
$705$	−9.47769	−0.356950
$706$	25.4907	0.959354
$707$	−35.6675	−1.34142
$708$	−9.79988	−0.368302
$709$	−1.41006	−0.0529560	−0.0264780	−	0.999649i	$-0.508429\pi$
$709$	−1.41006	−0.0529560	−0.0264780	+	0.999649i	$0.508429\pi$
$710$	2.63811	0.0990065
$711$	22.0082	0.825371
$712$	−6.18484	−0.231787
$713$	−22.7017	−0.850187
$714$	24.9755	0.934683
$715$	−4.82049	−0.180276
$716$	−24.3657	−0.910587
$717$	10.1100	0.377564
$718$	13.1171	0.489526
$719$	−26.6089	−0.992346	−0.496173	−	0.868224i	$-0.665262\pi$
$719$	−26.6089	−0.992346	−0.496173	+	0.868224i	$0.665262\pi$
$720$	−2.40710	−0.0897075
$721$	15.2884	0.569371
$722$	18.0843	0.673027
$723$	−8.56867	−0.318672
$724$	19.6016	0.728487
$725$	0.648686	0.0240916
$726$	0.769997	0.0285773
$727$	11.2988	0.419050	0.209525	−	0.977803i	$-0.432808\pi$
$727$	11.2988	0.419050	0.209525	+	0.977803i	$0.432808\pi$
$728$	22.7485	0.843114
$729$	−0.0480836	−0.00178087
$730$	1.83057	0.0677524
$731$	6.87326	0.254217
$732$	8.89885	0.328911
$733$	−16.7737	−0.619550	−0.309775	−	0.950810i	$-0.600254\pi$
$733$	−16.7737	−0.619550	−0.309775	+	0.950810i	$0.600254\pi$
$734$	3.78574	0.139734
$735$	11.7579	0.433698
$736$	−2.82049	−0.103965
$737$	−2.87102	−0.105755
$738$	14.1526	0.520964
$739$	10.3739	0.381612	0.190806	−	0.981628i	$-0.438890\pi$
$739$	10.3739	0.381612	0.190806	+	0.981628i	$0.438890\pi$
$740$	1.84432	0.0677986
$741$	−22.6035	−0.830359
$742$	38.0183	1.39570
$743$	−34.3670	−1.26080	−0.630401	−	0.776270i	$-0.717110\pi$
$743$	−34.3670	−1.26080	−0.630401	+	0.776270i	$0.717110\pi$
$744$	6.19761	0.227215
$745$	22.0490	0.807811
$746$	−34.9268	−1.27876
$747$	5.99380	0.219302
$748$	−6.87326	−0.251311
$749$	−85.5048	−3.12428
$750$	0.769997	0.0281163
$751$	−32.1192	−1.17204	−0.586022	−	0.810295i	$-0.699307\pi$
$751$	−32.1192	−1.17204	−0.586022	+	0.810295i	$0.699307\pi$
$752$	−12.3087	−0.448853
$753$	13.4242	0.489207
$754$	3.12698	0.113878
$755$	5.00624	0.182196
$756$	−19.6479	−0.714586
$757$	27.0969	0.984854	0.492427	−	0.870354i	$-0.336110\pi$
$757$	27.0969	0.984854	0.492427	+	0.870354i	$0.336110\pi$
$758$	34.4499	1.25128
$759$	2.17177	0.0788302
$760$	−6.08969	−0.220896
$761$	10.0722	0.365119	0.182559	−	0.983195i	$-0.441562\pi$
$761$	10.0722	0.365119	0.182559	+	0.983195i	$0.441562\pi$
$762$	−10.1094	−0.366225
$763$	−47.7646	−1.72919
$764$	8.97018	0.324530
$765$	−16.5447	−0.598173
$766$	−31.8557	−1.15099
$767$	−61.3511	−2.21526
$768$	0.769997	0.0277849
$769$	−4.43828	−0.160049	−0.0800243	−	0.996793i	$-0.525500\pi$
$769$	−4.43828	−0.160049	−0.0800243	+	0.996793i	$0.525500\pi$
$770$	−4.71912	−0.170065
$771$	−14.8553	−0.534999
$772$	−18.6940	−0.672812
$773$	−27.3865	−0.985025	−0.492512	−	0.870305i	$-0.663921\pi$
$773$	−27.3865	−0.985025	−0.492512	+	0.870305i	$0.663921\pi$
$774$	−2.40710	−0.0865216
$775$	8.04887	0.289124
$776$	8.98364	0.322494
$777$	6.70173	0.240423
$778$	−5.70481	−0.204527
$779$	35.8044	1.28282
$780$	3.71176	0.132902
$781$	−2.63811	−0.0943990
$782$	−19.3859	−0.693240
$783$	−2.70077	−0.0965178
$784$	15.2701	0.545361
$785$	−3.27661	−0.116947
$786$	14.9205	0.532197
$787$	10.7649	0.383729	0.191864	−	0.981421i	$-0.438547\pi$
$787$	10.7649	0.383729	0.191864	+	0.981421i	$0.438547\pi$
$788$	−20.2277	−0.720581
$789$	14.7141	0.523837
$790$	−9.14301	−0.325294
$791$	−21.3858	−0.760390
$792$	2.40710	0.0855327
$793$	55.7103	1.97833
$794$	−18.1068	−0.642586
$795$	6.20327	0.220007
$796$	10.2488	0.363258
$797$	−36.8519	−1.30536	−0.652681	−	0.757633i	$-0.726356\pi$
$797$	−36.8519	−1.30536	−0.652681	+	0.757633i	$0.726356\pi$
$798$	−22.1282	−0.783328
$799$	−84.6011	−2.99297
$800$	1.00000	0.0353553
$801$	14.8876	0.526026
$802$	13.1359	0.463846
$803$	−1.83057	−0.0645994
$804$	2.21067	0.0779645
$805$	−13.3102	−0.469124
$806$	38.7995	1.36665
$807$	−15.5988	−0.549103
$808$	−7.55809	−0.265893
$809$	−7.39980	−0.260163	−0.130082	−	0.991503i	$-0.541524\pi$
$809$	−7.39980	−0.260163	−0.130082	+	0.991503i	$0.541524\pi$
$810$	4.01546	0.141089
$811$	4.59768	0.161447	0.0807233	−	0.996737i	$-0.474277\pi$
$811$	4.59768	0.161447	0.0807233	+	0.996737i	$0.474277\pi$
$812$	3.06123	0.107428
$813$	−20.0362	−0.702699
$814$	−1.84432	−0.0646435
$815$	1.81470	0.0635663
$816$	5.29239	0.185271
$817$	−6.08969	−0.213051
$818$	27.9862	0.978516
$819$	−54.7579	−1.91340
$820$	−5.87951	−0.205321
$821$	4.88804	0.170594	0.0852969	−	0.996356i	$-0.472816\pi$
$821$	4.88804	0.170594	0.0852969	+	0.996356i	$0.472816\pi$
$822$	8.99754	0.313825
$823$	−24.8907	−0.867635	−0.433817	−	0.901001i	$-0.642834\pi$
$823$	−24.8907	−0.867635	−0.433817	+	0.901001i	$0.642834\pi$
$824$	3.23968	0.112859
$825$	−0.769997	−0.0268079
$826$	−60.0610	−2.08979
$827$	−57.2563	−1.99100	−0.995498	−	0.0947800i	$-0.969785\pi$
$827$	−57.2563	−1.99100	−0.995498	+	0.0947800i	$0.969785\pi$
$828$	6.78921	0.235941
$829$	−4.93618	−0.171440	−0.0857202	−	0.996319i	$-0.527319\pi$
$829$	−4.93618	−0.171440	−0.0857202	+	0.996319i	$0.527319\pi$
$830$	−2.49005	−0.0864308
$831$	−12.3363	−0.427942
$832$	4.82049	0.167120
$833$	104.955	3.63649
$834$	0.0210114	0.000727567 0
$835$	−19.9902	−0.691788
$836$	6.08969	0.210616
$837$	−33.5111	−1.15831
$838$	8.90520	0.307625
$839$	26.0555	0.899537	0.449769	−	0.893145i	$-0.351506\pi$
$839$	26.0555	0.899537	0.449769	+	0.893145i	$0.351506\pi$
$840$	3.63371	0.125375
$841$	−28.5792	−0.985490
$842$	10.4484	0.360074
$843$	−2.82138	−0.0971734
$844$	−20.1549	−0.693762
$845$	10.2371	0.352167
$846$	29.6284	1.01864
$847$	4.71912	0.162151
$848$	8.05623	0.276652
$849$	3.36006	0.115317
$850$	6.87326	0.235751
$851$	−5.20189	−0.178318
$852$	2.03134	0.0695925
$853$	57.1833	1.95792	0.978959	−	0.204059i	$-0.0654133\pi$
$853$	57.1833	1.95792	0.978959	+	0.204059i	$0.0654133\pi$
$854$	54.5388	1.86628
$855$	14.6585	0.501310
$856$	−18.1188	−0.619288
$857$	−12.8285	−0.438215	−0.219107	−	0.975701i	$-0.570314\pi$
$857$	−12.8285	−0.438215	−0.219107	+	0.975701i	$0.570314\pi$
$858$	−3.71176	−0.126717
$859$	−45.2051	−1.54238	−0.771189	−	0.636606i	$-0.780338\pi$
$859$	−45.2051	−1.54238	−0.771189	+	0.636606i	$0.780338\pi$
$860$	1.00000	0.0340997
$861$	−21.3644	−0.728098
$862$	−4.68303	−0.159505
$863$	−18.5139	−0.630222	−0.315111	−	0.949055i	$-0.602042\pi$
$863$	−18.5139	−0.630222	−0.315111	+	0.949055i	$0.602042\pi$
$864$	−4.16346	−0.141644
$865$	14.1771	0.482037
$866$	26.6316	0.904979
$867$	23.2861	0.790836
$868$	37.9836	1.28925
$869$	9.14301	0.310155
$870$	0.499486	0.0169342
$871$	13.8397	0.468940
$872$	−10.1215	−0.342757
$873$	−21.6246	−0.731880
$874$	17.1759	0.580983
$875$	4.71912	0.159535
$876$	1.40953	0.0476237
$877$	−30.7168	−1.03723	−0.518617	−	0.855007i	$-0.673553\pi$
$877$	−30.7168	−1.03723	−0.518617	+	0.855007i	$0.673553\pi$
$878$	−18.6380	−0.629002
$879$	−4.17278	−0.140744
$880$	−1.00000	−0.0337100
$881$	34.9784	1.17845	0.589226	−	0.807968i	$-0.299433\pi$
$881$	34.9784	1.17845	0.589226	+	0.807968i	$0.299433\pi$
$882$	−36.7567	−1.23766
$883$	−42.1301	−1.41779	−0.708895	−	0.705314i	$-0.750806\pi$
$883$	−42.1301	−1.41779	−0.708895	+	0.705314i	$0.750806\pi$
$884$	33.1325	1.11437
$885$	−9.79988	−0.329419
$886$	−17.5322	−0.589007
$887$	0.315696	0.0106000	0.00530001	−	0.999986i	$-0.498313\pi$
$887$	0.315696	0.0106000	0.00530001	+	0.999986i	$0.498313\pi$
$888$	1.42012	0.0476562
$889$	−61.9579	−2.07800
$890$	−6.18484	−0.207316
$891$	−4.01546	−0.134523
$892$	−2.95695	−0.0990060
$893$	74.9563	2.50832
$894$	16.9776	0.567817
$895$	−24.3657	−0.814454
$896$	4.71912	0.157655
$897$	−10.4690	−0.349549
$898$	−12.0831	−0.403218
$899$	5.22119	0.174136
$900$	−2.40710	−0.0802368
$901$	55.3726	1.84473
$902$	5.87951	0.195766
$903$	3.63371	0.120922
$904$	−4.53172	−0.150723
$905$	19.6016	0.651579
$906$	3.85479	0.128067
$907$	3.77433	0.125325	0.0626624	−	0.998035i	$-0.480041\pi$
$907$	3.77433	0.125325	0.0626624	+	0.998035i	$0.480041\pi$
$908$	10.2629	0.340585
$909$	18.1931	0.603427
$910$	22.7485	0.754104
$911$	−0.0501735	−0.00166232	−0.000831162	−	1.00000i	$-0.500265\pi$
$911$	−0.0501735	−0.00166232	−0.000831162		1.00000i	$0.500265\pi$
$912$	−4.68904	−0.155270
$913$	2.49005	0.0824085
$914$	5.06828	0.167644
$915$	8.89885	0.294187
$916$	8.63226	0.285218
$917$	91.4440	3.01975
$918$	−28.6165	−0.944486
$919$	−22.5653	−0.744359	−0.372180	−	0.928161i	$-0.621389\pi$
$919$	−22.5653	−0.744359	−0.372180	+	0.928161i	$0.621389\pi$
$920$	−2.82049	−0.0929887
$921$	7.35083	0.242218
$922$	10.2649	0.338055
$923$	12.7170	0.418584
$924$	−3.63371	−0.119540
$925$	1.84432	0.0606409
$926$	−15.8848	−0.522007
$927$	−7.79823	−0.256128
$928$	0.648686	0.0212942
$929$	41.4602	1.36027	0.680133	−	0.733089i	$-0.261922\pi$
$929$	41.4602	1.36027	0.680133	+	0.733089i	$0.261922\pi$
$930$	6.19761	0.203228
$931$	−92.9902	−3.04763
$932$	15.5796	0.510328
$933$	13.0280	0.426517
$934$	28.6315	0.936853
$935$	−6.87326	−0.224780
$936$	−11.6034	−0.379269
$937$	−7.37921	−0.241068	−0.120534	−	0.992709i	$-0.538461\pi$
$937$	−7.37921	−0.241068	−0.120534	+	0.992709i	$0.538461\pi$
$938$	13.5487	0.442380
$939$	−15.3960	−0.502431
$940$	−12.3087	−0.401466
$941$	0.272822	0.00889373	0.00444686	−	0.999990i	$-0.498585\pi$
$941$	0.272822	0.00889373	0.00444686	+	0.999990i	$0.498585\pi$
$942$	−2.52298	−0.0822033
$943$	16.5831	0.540019
$944$	−12.7272	−0.414234
$945$	−19.6479	−0.639145
$946$	−1.00000	−0.0325128
$947$	3.59408	0.116792	0.0583960	−	0.998293i	$-0.481401\pi$
$947$	3.59408	0.116792	0.0583960	+	0.998293i	$0.481401\pi$
$948$	−7.04009	−0.228652
$949$	8.82424	0.286447
$950$	−6.08969	−0.197576
$951$	−22.0625	−0.715426
$952$	32.4358	1.05125
$953$	9.92898	0.321631	0.160816	−	0.986984i	$-0.448588\pi$
$953$	9.92898	0.321631	0.160816	+	0.986984i	$0.448588\pi$
$954$	−19.3922	−0.627845
$955$	8.97018	0.290268
$956$	13.1299	0.424651
$957$	−0.499486	−0.0161461
$958$	4.26885	0.137920
$959$	55.1437	1.78068
$960$	0.769997	0.0248516
$961$	33.7843	1.08982
$962$	8.89053	0.286642
$963$	43.6138	1.40544
$964$	−11.1282	−0.358415
$965$	−18.6940	−0.601782
$966$	−10.2488	−0.329751
$967$	19.6010	0.630327	0.315163	−	0.949037i	$-0.397941\pi$
$967$	19.6010	0.630327	0.315163	+	0.949037i	$0.397941\pi$
$968$	1.00000	0.0321412
$969$	−32.2290	−1.03535
$970$	8.98364	0.288447
$971$	−27.5075	−0.882757	−0.441378	−	0.897321i	$-0.645510\pi$
$971$	−27.5075	−0.882757	−0.441378	+	0.897321i	$0.645510\pi$
$972$	15.5823	0.499801
$973$	0.128774	0.00412830
$974$	22.1475	0.709653
$975$	3.71176	0.118872
$976$	11.5570	0.369930
$977$	51.1229	1.63557	0.817783	−	0.575527i	$-0.195203\pi$
$977$	51.1229	1.63557	0.817783	+	0.575527i	$0.195203\pi$
$978$	1.39732	0.0446813
$979$	6.18484	0.197668
$980$	15.2701	0.487786
$981$	24.3635	0.777867
$982$	−25.1815	−0.803573
$983$	32.4526	1.03508	0.517539	−	0.855660i	$-0.326848\pi$
$983$	32.4526	1.03508	0.517539	+	0.855660i	$0.326848\pi$
$984$	−4.52720	−0.144322
$985$	−20.2277	−0.644507
$986$	4.45859	0.141990
$987$	−44.7264	−1.42366
$988$	−29.3553	−0.933915
$989$	−2.82049	−0.0896863
$990$	2.40710	0.0765028
$991$	15.4066	0.489408	0.244704	−	0.969598i	$-0.421309\pi$
$991$	15.4066	0.489408	0.244704	+	0.969598i	$0.421309\pi$
$992$	8.04887	0.255552
$993$	−12.5886	−0.399488
$994$	12.4496	0.394876
$995$	10.2488	0.324908
$996$	−1.91733	−0.0607529
$997$	−12.2555	−0.388136	−0.194068	−	0.980988i	$-0.562168\pi$
$997$	−12.2555	−0.388136	−0.194068	+	0.980988i	$0.562168\pi$
$998$	25.1495	0.796095
$999$	−7.67875	−0.242945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.be.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.be.1.7	✓	12	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.769997 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.769997 q^{6} +4.71912 q^{7} +1.00000 q^{8} -2.40710 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.769997 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.769997 q^{6} +4.71912 q^{7} +1.00000 q^{8} -2.40710 q^{9} +1.00000 q^{10} -1.00000 q^{11} +0.769997 q^{12} +4.82049 q^{13} +4.71912 q^{14} +0.769997 q^{15} +1.00000 q^{16} +6.87326 q^{17} -2.40710 q^{18} -6.08969 q^{19} +1.00000 q^{20} +3.63371 q^{21} -1.00000 q^{22} -2.82049 q^{23} +0.769997 q^{24} +1.00000 q^{25} +4.82049 q^{26} -4.16346 q^{27} +4.71912 q^{28} +0.648686 q^{29} +0.769997 q^{30} +8.04887 q^{31} +1.00000 q^{32} -0.769997 q^{33} +6.87326 q^{34} +4.71912 q^{35} -2.40710 q^{36} +1.84432 q^{37} -6.08969 q^{38} +3.71176 q^{39} +1.00000 q^{40} -5.87951 q^{41} +3.63371 q^{42} +1.00000 q^{43} -1.00000 q^{44} -2.40710 q^{45} -2.82049 q^{46} -12.3087 q^{47} +0.769997 q^{48} +15.2701 q^{49} +1.00000 q^{50} +5.29239 q^{51} +4.82049 q^{52} +8.05623 q^{53} -4.16346 q^{54} -1.00000 q^{55} +4.71912 q^{56} -4.68904 q^{57} +0.648686 q^{58} -12.7272 q^{59} +0.769997 q^{60} +11.5570 q^{61} +8.04887 q^{62} -11.3594 q^{63} +1.00000 q^{64} +4.82049 q^{65} -0.769997 q^{66} +2.87102 q^{67} +6.87326 q^{68} -2.17177 q^{69} +4.71912 q^{70} +2.63811 q^{71} -2.40710 q^{72} +1.83057 q^{73} +1.84432 q^{74} +0.769997 q^{75} -6.08969 q^{76} -4.71912 q^{77} +3.71176 q^{78} -9.14301 q^{79} +1.00000 q^{80} +4.01546 q^{81} -5.87951 q^{82} -2.49005 q^{83} +3.63371 q^{84} +6.87326 q^{85} +1.00000 q^{86} +0.499486 q^{87} -1.00000 q^{88} -6.18484 q^{89} -2.40710 q^{90} +22.7485 q^{91} -2.82049 q^{92} +6.19761 q^{93} -12.3087 q^{94} -6.08969 q^{95} +0.769997 q^{96} +8.98364 q^{97} +15.2701 q^{98} +2.40710 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9	\( 12 q + 12 q^{2} + 3 q^{3} + 12 q^{4} + 12 q^{5} + 3 q^{6} + 8 q^{7} + 12 q^{8} + 25 q^{9} + 12 q^{10} - 12 q^{11} + 3 q^{12} + 16 q^{13} + 8 q^{14} + 3 q^{15} + 12 q^{16} + 18 q^{17} + 25 q^{18} - 4 q^{19} + 12 q^{20} + 4 q^{21} - 12 q^{22} + 8 q^{23} + 3 q^{24} + 12 q^{25} + 16 q^{26} + 6 q^{27} + 8 q^{28} + 20 q^{29} + 3 q^{30} + 5 q^{31} + 12 q^{32} - 3 q^{33} + 18 q^{34} + 8 q^{35} + 25 q^{36} + 19 q^{37} - 4 q^{38} + 6 q^{39} + 12 q^{40} + 16 q^{41} + 4 q^{42} + 12 q^{43} - 12 q^{44} + 25 q^{45} + 8 q^{46} - q^{47} + 3 q^{48} + 52 q^{49} + 12 q^{50} + q^{51} + 16 q^{52} + 11 q^{53} + 6 q^{54} - 12 q^{55} + 8 q^{56} + 9 q^{57} + 20 q^{58} - 11 q^{59} + 3 q^{60} + 18 q^{61} + 5 q^{62} + 15 q^{63} + 12 q^{64} + 16 q^{65} - 3 q^{66} - 10 q^{67} + 18 q^{68} + 8 q^{70} - 2 q^{71} + 25 q^{72} + 29 q^{73} + 19 q^{74} + 3 q^{75} - 4 q^{76} - 8 q^{77} + 6 q^{78} + 2 q^{79} + 12 q^{80} - 8 q^{81} + 16 q^{82} + 26 q^{83} + 4 q^{84} + 18 q^{85} + 12 q^{86} - 4 q^{87} - 12 q^{88} + 41 q^{89} + 25 q^{90} - 4 q^{91} + 8 q^{92} + 5 q^{93} - q^{94} - 4 q^{95} + 3 q^{96} - 7 q^{97} + 52 q^{98} - 25 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 3 * q^3 + 12 * q^4 + 12 * q^5 + 3 * q^6 + 8 * q^7 + 12 * q^8 + 25 * q^9 + 12 * q^10 - 12 * q^11 + 3 * q^12 + 16 * q^13 + 8 * q^14 + 3 * q^15 + 12 * q^16 + 18 * q^17 + 25 * q^18 - 4 * q^19 + 12 * q^20 + 4 * q^21 - 12 * q^22 + 8 * q^23 + 3 * q^24 + 12 * q^25 + 16 * q^26 + 6 * q^27 + 8 * q^28 + 20 * q^29 + 3 * q^30 + 5 * q^31 + 12 * q^32 - 3 * q^33 + 18 * q^34 + 8 * q^35 + 25 * q^36 + 19 * q^37 - 4 * q^38 + 6 * q^39 + 12 * q^40 + 16 * q^41 + 4 * q^42 + 12 * q^43 - 12 * q^44 + 25 * q^45 + 8 * q^46 - q^47 + 3 * q^48 + 52 * q^49 + 12 * q^50 + q^51 + 16 * q^52 + 11 * q^53 + 6 * q^54 - 12 * q^55 + 8 * q^56 + 9 * q^57 + 20 * q^58 - 11 * q^59 + 3 * q^60 + 18 * q^61 + 5 * q^62 + 15 * q^63 + 12 * q^64 + 16 * q^65 - 3 * q^66 - 10 * q^67 + 18 * q^68 + 8 * q^70 - 2 * q^71 + 25 * q^72 + 29 * q^73 + 19 * q^74 + 3 * q^75 - 4 * q^76 - 8 * q^77 + 6 * q^78 + 2 * q^79 + 12 * q^80 - 8 * q^81 + 16 * q^82 + 26 * q^83 + 4 * q^84 + 18 * q^85 + 12 * q^86 - 4 * q^87 - 12 * q^88 + 41 * q^89 + 25 * q^90 - 4 * q^91 + 8 * q^92 + 5 * q^93 - q^94 - 4 * q^95 + 3 * q^96 - 7 * q^97 + 52 * q^98 - 25 * q^99

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