LMFDB - Embedded newform 2415.2.a.v.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2415,2,Mod(1,2415)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("2415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2415 = 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2415.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:	$19.2838720881$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 16x^{8} + 30x^{7} + 83x^{6} - 137x^{5} - 164x^{4} + 208x^{3} + 108x^{2} - 83x - 12 $ x^10 - 2x^9 - 16x^8 + 30x^7 + 83x^6 - 137x^5 - 164x^4 + 208x^3 + 108x^2 - 83*x - 12
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.24070$ of defining polynomial
Character	$\chi$	$=$	2415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.24070 q^{2} +1.00000 q^{3} +3.02074 q^{4} +1.00000 q^{5} +2.24070 q^{6} -1.00000 q^{7} +2.28717 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.24070 q^{2} +1.00000 q^{3} +3.02074 q^{4} +1.00000 q^{5} +2.24070 q^{6} -1.00000 q^{7} +2.28717 q^{8} +1.00000 q^{9} +2.24070 q^{10} +1.84108 q^{11} +3.02074 q^{12} +5.37031 q^{13} -2.24070 q^{14} +1.00000 q^{15} -0.916621 q^{16} -4.29412 q^{17} +2.24070 q^{18} -1.36463 q^{19} +3.02074 q^{20} -1.00000 q^{21} +4.12530 q^{22} +1.00000 q^{23} +2.28717 q^{24} +1.00000 q^{25} +12.0332 q^{26} +1.00000 q^{27} -3.02074 q^{28} +7.26140 q^{29} +2.24070 q^{30} +10.4659 q^{31} -6.62821 q^{32} +1.84108 q^{33} -9.62183 q^{34} -1.00000 q^{35} +3.02074 q^{36} +8.15031 q^{37} -3.05772 q^{38} +5.37031 q^{39} +2.28717 q^{40} +2.01488 q^{41} -2.24070 q^{42} -10.2779 q^{43} +5.56141 q^{44} +1.00000 q^{45} +2.24070 q^{46} -1.65313 q^{47} -0.916621 q^{48} +1.00000 q^{49} +2.24070 q^{50} -4.29412 q^{51} +16.2223 q^{52} -2.66988 q^{53} +2.24070 q^{54} +1.84108 q^{55} -2.28717 q^{56} -1.36463 q^{57} +16.2706 q^{58} -9.10026 q^{59} +3.02074 q^{60} +2.51269 q^{61} +23.4509 q^{62} -1.00000 q^{63} -13.0186 q^{64} +5.37031 q^{65} +4.12530 q^{66} -7.21545 q^{67} -12.9714 q^{68} +1.00000 q^{69} -2.24070 q^{70} -13.5922 q^{71} +2.28717 q^{72} -5.73002 q^{73} +18.2624 q^{74} +1.00000 q^{75} -4.12218 q^{76} -1.84108 q^{77} +12.0332 q^{78} -2.11985 q^{79} -0.916621 q^{80} +1.00000 q^{81} +4.51475 q^{82} -0.975069 q^{83} -3.02074 q^{84} -4.29412 q^{85} -23.0298 q^{86} +7.26140 q^{87} +4.21085 q^{88} -15.0699 q^{89} +2.24070 q^{90} -5.37031 q^{91} +3.02074 q^{92} +10.4659 q^{93} -3.70417 q^{94} -1.36463 q^{95} -6.62821 q^{96} -13.7843 q^{97} +2.24070 q^{98} +1.84108 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 - 10 * q^7 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} - q^{11} + 16 q^{12} - 2 q^{13} - 2 q^{14} + 10 q^{15} + 36 q^{16} + 8 q^{17} + 2 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{21} + 10 q^{23} + 6 q^{24} + 10 q^{25} + 15 q^{26} + 10 q^{27} - 16 q^{28} + 6 q^{29} + 2 q^{30} + 16 q^{31} - q^{32} - q^{33} + 21 q^{34} - 10 q^{35} + 16 q^{36} - 6 q^{38} - 2 q^{39} + 6 q^{40} + 23 q^{41} - 2 q^{42} + 4 q^{43} - q^{44} + 10 q^{45} + 2 q^{46} + 21 q^{47} + 36 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 10 q^{52} - q^{53} + 2 q^{54} - q^{55} - 6 q^{56} + 11 q^{57} + 8 q^{58} + 15 q^{59} + 16 q^{60} + 29 q^{61} + 12 q^{62} - 10 q^{63} + 80 q^{64} - 2 q^{65} + 32 q^{67} - 28 q^{68} + 10 q^{69} - 2 q^{70} - 4 q^{71} + 6 q^{72} + 18 q^{73} - 49 q^{74} + 10 q^{75} + 49 q^{76} + q^{77} + 15 q^{78} + 8 q^{79} + 36 q^{80} + 10 q^{81} + 6 q^{82} + 2 q^{83} - 16 q^{84} + 8 q^{85} - 14 q^{86} + 6 q^{87} - 69 q^{88} + 6 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{92} + 16 q^{93} - 2 q^{94} + 11 q^{95} - q^{96} - 2 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 - 10 * q^7 + 6 * q^8 + 10 * q^9 + 2 * q^10 - q^11 + 16 * q^12 - 2 * q^13 - 2 * q^14 + 10 * q^15 + 36 * q^16 + 8 * q^17 + 2 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^21 + 10 * q^23 + 6 * q^24 + 10 * q^25 + 15 * q^26 + 10 * q^27 - 16 * q^28 + 6 * q^29 + 2 * q^30 + 16 * q^31 - q^32 - q^33 + 21 * q^34 - 10 * q^35 + 16 * q^36 - 6 * q^38 - 2 * q^39 + 6 * q^40 + 23 * q^41 - 2 * q^42 + 4 * q^43 - q^44 + 10 * q^45 + 2 * q^46 + 21 * q^47 + 36 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 10 * q^52 - q^53 + 2 * q^54 - q^55 - 6 * q^56 + 11 * q^57 + 8 * q^58 + 15 * q^59 + 16 * q^60 + 29 * q^61 + 12 * q^62 - 10 * q^63 + 80 * q^64 - 2 * q^65 + 32 * q^67 - 28 * q^68 + 10 * q^69 - 2 * q^70 - 4 * q^71 + 6 * q^72 + 18 * q^73 - 49 * q^74 + 10 * q^75 + 49 * q^76 + q^77 + 15 * q^78 + 8 * q^79 + 36 * q^80 + 10 * q^81 + 6 * q^82 + 2 * q^83 - 16 * q^84 + 8 * q^85 - 14 * q^86 + 6 * q^87 - 69 * q^88 + 6 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^92 + 16 * q^93 - 2 * q^94 + 11 * q^95 - q^96 - 2 * q^97 + 2 * q^98 - 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 $

$2$	2.24070	1.58441	0.792207	−	0.610252i	$-0.208932\pi$
$2$	2.24070	1.58441	0.792207	+	0.610252i	$0.208932\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.02074	1.51037
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.24070	0.914762
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.28717	0.808635
$9$	1.00000	0.333333
$10$	2.24070	0.708572
$11$	1.84108	0.555106	0.277553	−	0.960710i	$-0.410477\pi$
$11$	1.84108	0.555106	0.277553	+	0.960710i	$0.410477\pi$
$12$	3.02074	0.872012
$13$	5.37031	1.48946	0.744728	−	0.667368i	$-0.232579\pi$
$13$	5.37031	1.48946	0.744728	+	0.667368i	$0.232579\pi$
$14$	−2.24070	−0.598852
$15$	1.00000	0.258199
$16$	−0.916621	−0.229155
$17$	−4.29412	−1.04148	−0.520739	−	0.853716i	$-0.674343\pi$
$17$	−4.29412	−1.04148	−0.520739	+	0.853716i	$0.674343\pi$
$18$	2.24070	0.528138
$19$	−1.36463	−0.313067	−0.156534	−	0.987673i	$-0.550032\pi$
$19$	−1.36463	−0.313067	−0.156534	+	0.987673i	$0.550032\pi$
$20$	3.02074	0.675457
$21$	−1.00000	−0.218218
$22$	4.12530	0.879518
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.28717	0.466866
$25$	1.00000	0.200000
$26$	12.0332	2.35991
$27$	1.00000	0.192450
$28$	−3.02074	−0.570866
$29$	7.26140	1.34841	0.674204	−	0.738545i	$-0.264487\pi$
$29$	7.26140	1.34841	0.674204	+	0.738545i	$0.264487\pi$
$30$	2.24070	0.409094
$31$	10.4659	1.87973	0.939865	−	0.341547i	$-0.110951\pi$
$31$	10.4659	1.87973	0.939865	+	0.341547i	$0.110951\pi$
$32$	−6.62821	−1.17171
$33$	1.84108	0.320491
$34$	−9.62183	−1.65013
$35$	−1.00000	−0.169031
$36$	3.02074	0.503456
$37$	8.15031	1.33990	0.669951	−	0.742405i	$-0.266315\pi$
$37$	8.15031	1.33990	0.669951	+	0.742405i	$0.266315\pi$
$38$	−3.05772	−0.496028
$39$	5.37031	0.859937
$40$	2.28717	0.361633
$41$	2.01488	0.314672	0.157336	−	0.987545i	$-0.449709\pi$
$41$	2.01488	0.314672	0.157336	+	0.987545i	$0.449709\pi$
$42$	−2.24070	−0.345748
$43$	−10.2779	−1.56737	−0.783686	−	0.621157i	$-0.786663\pi$
$43$	−10.2779	−1.56737	−0.783686	+	0.621157i	$0.786663\pi$
$44$	5.56141	0.838415
$45$	1.00000	0.149071
$46$	2.24070	0.330373
$47$	−1.65313	−0.241134	−0.120567	−	0.992705i	$-0.538471\pi$
$47$	−1.65313	−0.241134	−0.120567	+	0.992705i	$0.538471\pi$
$48$	−0.916621	−0.132303
$49$	1.00000	0.142857
$50$	2.24070	0.316883
$51$	−4.29412	−0.601297
$52$	16.2223	2.24963
$53$	−2.66988	−0.366736	−0.183368	−	0.983044i	$-0.558700\pi$
$53$	−2.66988	−0.366736	−0.183368	+	0.983044i	$0.558700\pi$
$54$	2.24070	0.304921
$55$	1.84108	0.248251
$56$	−2.28717	−0.305635
$57$	−1.36463	−0.180749
$58$	16.2706	2.13644
$59$	−9.10026	−1.18475	−0.592376	−	0.805661i	$-0.701810\pi$
$59$	−9.10026	−1.18475	−0.592376	+	0.805661i	$0.701810\pi$
$60$	3.02074	0.389975
$61$	2.51269	0.321716	0.160858	−	0.986978i	$-0.448574\pi$
$61$	2.51269	0.321716	0.160858	+	0.986978i	$0.448574\pi$
$62$	23.4509	2.97827
$63$	−1.00000	−0.125988
$64$	−13.0186	−1.62732
$65$	5.37031	0.666105
$66$	4.12530	0.507790
$67$	−7.21545	−0.881507	−0.440754	−	0.897628i	$-0.645289\pi$
$67$	−7.21545	−0.881507	−0.440754	+	0.897628i	$0.645289\pi$
$68$	−12.9714	−1.57301
$69$	1.00000	0.120386
$70$	−2.24070	−0.267815
$71$	−13.5922	−1.61310	−0.806549	−	0.591167i	$-0.798667\pi$
$71$	−13.5922	−1.61310	−0.806549	+	0.591167i	$0.798667\pi$
$72$	2.28717	0.269545
$73$	−5.73002	−0.670649	−0.335324	−	0.942103i	$-0.608846\pi$
$73$	−5.73002	−0.670649	−0.335324	+	0.942103i	$0.608846\pi$
$74$	18.2624	2.12296
$75$	1.00000	0.115470
$76$	−4.12218	−0.472847
$77$	−1.84108	−0.209810
$78$	12.0332	1.36250
$79$	−2.11985	−0.238502	−0.119251	−	0.992864i	$-0.538049\pi$
$79$	−2.11985	−0.238502	−0.119251	+	0.992864i	$0.538049\pi$
$80$	−0.916621	−0.102481
$81$	1.00000	0.111111
$82$	4.51475	0.498571
$83$	−0.975069	−0.107028	−0.0535139	−	0.998567i	$-0.517042\pi$
$83$	−0.975069	−0.107028	−0.0535139	+	0.998567i	$0.517042\pi$
$84$	−3.02074	−0.329589
$85$	−4.29412	−0.465763
$86$	−23.0298	−2.48337
$87$	7.26140	0.778504
$88$	4.21085	0.448878
$89$	−15.0699	−1.59740	−0.798701	−	0.601728i	$-0.794479\pi$
$89$	−15.0699	−1.59740	−0.798701	+	0.601728i	$0.794479\pi$
$90$	2.24070	0.236191
$91$	−5.37031	−0.562961
$92$	3.02074	0.314934
$93$	10.4659	1.08526
$94$	−3.70417	−0.382056
$95$	−1.36463	−0.140008
$96$	−6.62821	−0.676488
$97$	−13.7843	−1.39958	−0.699791	−	0.714348i	$-0.746723\pi$
$97$	−13.7843	−1.39958	−0.699791	+	0.714348i	$0.746723\pi$
$98$	2.24070	0.226345
$99$	1.84108	0.185035
$100$	3.02074	0.302074
$101$	5.06319	0.503806	0.251903	−	0.967753i	$-0.418944\pi$
$101$	5.06319	0.503806	0.251903	+	0.967753i	$0.418944\pi$
$102$	−9.62183	−0.952704
$103$	13.6984	1.34974	0.674872	−	0.737935i	$-0.264199\pi$
$103$	13.6984	1.34974	0.674872	+	0.737935i	$0.264199\pi$
$104$	12.2828	1.20443
$105$	−1.00000	−0.0975900
$106$	−5.98239	−0.581061
$107$	−4.81282	−0.465273	−0.232637	−	0.972564i	$-0.574735\pi$
$107$	−4.81282	−0.465273	−0.232637	+	0.972564i	$0.574735\pi$
$108$	3.02074	0.290671
$109$	4.62075	0.442588	0.221294	−	0.975207i	$-0.428972\pi$
$109$	4.62075	0.442588	0.221294	+	0.975207i	$0.428972\pi$
$110$	4.12530	0.393332
$111$	8.15031	0.773593
$112$	0.916621	0.0866126
$113$	7.62295	0.717107	0.358554	−	0.933509i	$-0.383270\pi$
$113$	7.62295	0.717107	0.358554	+	0.933509i	$0.383270\pi$
$114$	−3.05772	−0.286382
$115$	1.00000	0.0932505
$116$	21.9348	2.03659
$117$	5.37031	0.496485
$118$	−20.3910	−1.87714
$119$	4.29412	0.393641
$120$	2.28717	0.208789
$121$	−7.61043	−0.691857
$122$	5.63018	0.509732
$123$	2.01488	0.181676
$124$	31.6147	2.83908
$125$	1.00000	0.0894427
$126$	−2.24070	−0.199617
$127$	−19.4957	−1.72996	−0.864981	−	0.501805i	$-0.832670\pi$
$127$	−19.4957	−1.72996	−0.864981	+	0.501805i	$0.832670\pi$
$128$	−15.9143	−1.40664
$129$	−10.2779	−0.904923
$130$	12.0332	1.05539
$131$	16.7034	1.45938	0.729692	−	0.683775i	$-0.239663\pi$
$131$	16.7034	1.45938	0.729692	+	0.683775i	$0.239663\pi$
$132$	5.56141	0.484059
$133$	1.36463	0.118328
$134$	−16.1677	−1.39667
$135$	1.00000	0.0860663
$136$	−9.82136	−0.842175
$137$	10.1491	0.867099	0.433550	−	0.901130i	$-0.357261\pi$
$137$	10.1491	0.867099	0.433550	+	0.901130i	$0.357261\pi$
$138$	2.24070	0.190741
$139$	22.1683	1.88029	0.940145	−	0.340776i	$-0.110690\pi$
$139$	22.1683	1.88029	0.940145	+	0.340776i	$0.110690\pi$
$140$	−3.02074	−0.255299
$141$	−1.65313	−0.139219
$142$	−30.4561	−2.55582
$143$	9.88716	0.826806
$144$	−0.916621	−0.0763851
$145$	7.26140	0.603026
$146$	−12.8393	−1.06259
$147$	1.00000	0.0824786
$148$	24.6199	2.02375
$149$	−0.933442	−0.0764706	−0.0382353	−	0.999269i	$-0.512174\pi$
$149$	−0.933442	−0.0764706	−0.0382353	+	0.999269i	$0.512174\pi$
$150$	2.24070	0.182952
$151$	−2.53317	−0.206146	−0.103073	−	0.994674i	$-0.532868\pi$
$151$	−2.53317	−0.206146	−0.103073	+	0.994674i	$0.532868\pi$
$152$	−3.12113	−0.253157
$153$	−4.29412	−0.347159
$154$	−4.12530	−0.332427
$155$	10.4659	0.840641
$156$	16.2223	1.29882
$157$	−8.18306	−0.653079	−0.326540	−	0.945184i	$-0.605883\pi$
$157$	−8.18306	−0.653079	−0.326540	+	0.945184i	$0.605883\pi$
$158$	−4.74994	−0.377885
$159$	−2.66988	−0.211735
$160$	−6.62821	−0.524006
$161$	−1.00000	−0.0788110
$162$	2.24070	0.176046
$163$	−1.32049	−0.103429	−0.0517145	−	0.998662i	$-0.516469\pi$
$163$	−1.32049	−0.103429	−0.0517145	+	0.998662i	$0.516469\pi$
$164$	6.08644	0.475271
$165$	1.84108	0.143328
$166$	−2.18484	−0.169576
$167$	−1.24890	−0.0966431	−0.0483215	−	0.998832i	$-0.515387\pi$
$167$	−1.24890	−0.0966431	−0.0483215	+	0.998832i	$0.515387\pi$
$168$	−2.28717	−0.176459
$169$	15.8402	1.21848
$170$	−9.62183	−0.737961
$171$	−1.36463	−0.104356
$172$	−31.0470	−2.36731
$173$	−0.405247	−0.0308103	−0.0154052	−	0.999881i	$-0.504904\pi$
$173$	−0.405247	−0.0308103	−0.0154052	+	0.999881i	$0.504904\pi$
$174$	16.2706	1.23347
$175$	−1.00000	−0.0755929
$176$	−1.68757	−0.127206
$177$	−9.10026	−0.684017
$178$	−33.7670	−2.53095
$179$	−18.7384	−1.40058	−0.700288	−	0.713860i	$-0.746945\pi$
$179$	−18.7384	−1.40058	−0.700288	+	0.713860i	$0.746945\pi$
$180$	3.02074	0.225152
$181$	−4.13400	−0.307278	−0.153639	−	0.988127i	$-0.549099\pi$
$181$	−4.13400	−0.307278	−0.153639	+	0.988127i	$0.549099\pi$
$182$	−12.0332	−0.891964
$183$	2.51269	0.185743
$184$	2.28717	0.168612
$185$	8.15031	0.599223
$186$	23.4509	1.71951
$187$	−7.90581	−0.578130
$188$	−4.99368	−0.364201
$189$	−1.00000	−0.0727393
$190$	−3.05772	−0.221830
$191$	−8.91571	−0.645118	−0.322559	−	0.946549i	$-0.604543\pi$
$191$	−8.91571	−0.645118	−0.322559	+	0.946549i	$0.604543\pi$
$192$	−13.0186	−0.939535
$193$	−15.2404	−1.09703	−0.548516	−	0.836140i	$-0.684807\pi$
$193$	−15.2404	−1.09703	−0.548516	+	0.836140i	$0.684807\pi$
$194$	−30.8864	−2.21752
$195$	5.37031	0.384576
$196$	3.02074	0.215767
$197$	0.244594	0.0174266	0.00871331	−	0.999962i	$-0.497226\pi$
$197$	0.244594	0.0174266	0.00871331	+	0.999962i	$0.497226\pi$
$198$	4.12530	0.293173
$199$	9.18780	0.651306	0.325653	−	0.945489i	$-0.394416\pi$
$199$	9.18780	0.651306	0.325653	+	0.945489i	$0.394416\pi$
$200$	2.28717	0.161727
$201$	−7.21545	−0.508938
$202$	11.3451	0.798237
$203$	−7.26140	−0.509650
$204$	−12.9714	−0.908180
$205$	2.01488	0.140726
$206$	30.6940	2.13855
$207$	1.00000	0.0695048
$208$	−4.92254	−0.341317
$209$	−2.51239	−0.173785
$210$	−2.24070	−0.154623
$211$	−10.1947	−0.701835	−0.350917	−	0.936406i	$-0.614130\pi$
$211$	−10.1947	−0.701835	−0.350917	+	0.936406i	$0.614130\pi$
$212$	−8.06499	−0.553906
$213$	−13.5922	−0.931323
$214$	−10.7841	−0.737185
$215$	−10.2779	−0.700950
$216$	2.28717	0.155622
$217$	−10.4659	−0.710471
$218$	10.3537	0.701242
$219$	−5.73002	−0.387199
$220$	5.56141	0.374950
$221$	−23.0607	−1.55123
$222$	18.2624	1.22569
$223$	17.9706	1.20340	0.601700	−	0.798722i	$-0.294490\pi$
$223$	17.9706	1.20340	0.601700	+	0.798722i	$0.294490\pi$
$224$	6.62821	0.442866
$225$	1.00000	0.0666667
$226$	17.0808	1.13619
$227$	−25.9347	−1.72135	−0.860674	−	0.509157i	$-0.829957\pi$
$227$	−25.9347	−1.72135	−0.860674	+	0.509157i	$0.829957\pi$
$228$	−4.12218	−0.272998
$229$	19.0337	1.25778	0.628892	−	0.777492i	$-0.283509\pi$
$229$	19.0337	1.25778	0.628892	+	0.777492i	$0.283509\pi$
$230$	2.24070	0.147747
$231$	−1.84108	−0.121134
$232$	16.6080	1.09037
$233$	2.41293	0.158076	0.0790382	−	0.996872i	$-0.474815\pi$
$233$	2.41293	0.158076	0.0790382	+	0.996872i	$0.474815\pi$
$234$	12.0332	0.786638
$235$	−1.65313	−0.107838
$236$	−27.4895	−1.78941
$237$	−2.11985	−0.137699
$238$	9.62183	0.623691
$239$	14.7799	0.956033	0.478017	−	0.878351i	$-0.341356\pi$
$239$	14.7799	0.956033	0.478017	+	0.878351i	$0.341356\pi$
$240$	−0.916621	−0.0591676
$241$	−12.5015	−0.805295	−0.402648	−	0.915355i	$-0.631910\pi$
$241$	−12.5015	−0.805295	−0.402648	+	0.915355i	$0.631910\pi$
$242$	−17.0527	−1.09619
$243$	1.00000	0.0641500
$244$	7.59016	0.485910
$245$	1.00000	0.0638877
$246$	4.51475	0.287850
$247$	−7.32847	−0.466300
$248$	23.9372	1.52002
$249$	−0.975069	−0.0617925
$250$	2.24070	0.141714
$251$	−23.6248	−1.49119	−0.745593	−	0.666402i	$-0.767834\pi$
$251$	−23.6248	−1.49119	−0.745593	+	0.666402i	$0.767834\pi$
$252$	−3.02074	−0.190289
$253$	1.84108	0.115748
$254$	−43.6840	−2.74098
$255$	−4.29412	−0.268908
$256$	−9.62206	−0.601379
$257$	−1.00978	−0.0629883	−0.0314942	−	0.999504i	$-0.510027\pi$
$257$	−1.00978	−0.0629883	−0.0314942	+	0.999504i	$0.510027\pi$
$258$	−23.0298	−1.43377
$259$	−8.15031	−0.506435
$260$	16.2223	1.00606
$261$	7.26140	0.449469
$262$	37.4274	2.31227
$263$	−5.64970	−0.348375	−0.174188	−	0.984712i	$-0.555730\pi$
$263$	−5.64970	−0.348375	−0.174188	+	0.984712i	$0.555730\pi$
$264$	4.21085	0.259160
$265$	−2.66988	−0.164009
$266$	3.05772	0.187481
$267$	−15.0699	−0.922261
$268$	−21.7960	−1.33140
$269$	2.11790	0.129130	0.0645652	−	0.997913i	$-0.479434\pi$
$269$	2.11790	0.129130	0.0645652	+	0.997913i	$0.479434\pi$
$270$	2.24070	0.136365
$271$	8.99760	0.546565	0.273282	−	0.961934i	$-0.411891\pi$
$271$	8.99760	0.546565	0.273282	+	0.961934i	$0.411891\pi$
$272$	3.93608	0.238660
$273$	−5.37031	−0.325026
$274$	22.7412	1.37384
$275$	1.84108	0.111021
$276$	3.02074	0.181827
$277$	−13.6390	−0.819487	−0.409743	−	0.912201i	$-0.634382\pi$
$277$	−13.6390	−0.819487	−0.409743	+	0.912201i	$0.634382\pi$
$278$	49.6725	2.97916
$279$	10.4659	0.626576
$280$	−2.28717	−0.136684
$281$	−1.38635	−0.0827025	−0.0413513	−	0.999145i	$-0.513166\pi$
$281$	−1.38635	−0.0827025	−0.0413513	+	0.999145i	$0.513166\pi$
$282$	−3.70417	−0.220580
$283$	24.2611	1.44217	0.721085	−	0.692847i	$-0.243644\pi$
$283$	24.2611	1.44217	0.721085	+	0.692847i	$0.243644\pi$
$284$	−41.0585	−2.43637
$285$	−1.36463	−0.0808336
$286$	22.1542	1.31000
$287$	−2.01488	−0.118935
$288$	−6.62821	−0.390571
$289$	1.43946	0.0846744
$290$	16.2706	0.955444
$291$	−13.7843	−0.808049
$292$	−17.3089	−1.01293
$293$	29.1609	1.70360	0.851799	−	0.523869i	$-0.175512\pi$
$293$	29.1609	1.70360	0.851799	+	0.523869i	$0.175512\pi$
$294$	2.24070	0.130680
$295$	−9.10026	−0.529838
$296$	18.6411	1.08349
$297$	1.84108	0.106830
$298$	−2.09156	−0.121161
$299$	5.37031	0.310573
$300$	3.02074	0.174402
$301$	10.2779	0.592411
$302$	−5.67608	−0.326621
$303$	5.06319	0.290872
$304$	1.25085	0.0717410
$305$	2.51269	0.143876
$306$	−9.62183	−0.550044
$307$	−26.5719	−1.51654	−0.758268	−	0.651943i	$-0.773954\pi$
$307$	−26.5719	−1.51654	−0.758268	+	0.651943i	$0.773954\pi$
$308$	−5.56141	−0.316891
$309$	13.6984	0.779275
$310$	23.4509	1.33192
$311$	20.2658	1.14917	0.574584	−	0.818445i	$-0.305164\pi$
$311$	20.2658	1.14917	0.574584	+	0.818445i	$0.305164\pi$
$312$	12.2828	0.695376
$313$	9.01468	0.509540	0.254770	−	0.967002i	$-0.418000\pi$
$313$	9.01468	0.509540	0.254770	+	0.967002i	$0.418000\pi$
$314$	−18.3358	−1.03475
$315$	−1.00000	−0.0563436
$316$	−6.40350	−0.360225
$317$	19.6506	1.10369	0.551844	−	0.833947i	$-0.313924\pi$
$317$	19.6506	1.10369	0.551844	+	0.833947i	$0.313924\pi$
$318$	−5.98239	−0.335476
$319$	13.3688	0.748510
$320$	−13.0186	−0.727761
$321$	−4.81282	−0.268626
$322$	−2.24070	−0.124869
$323$	5.85988	0.326052
$324$	3.02074	0.167819
$325$	5.37031	0.297891
$326$	−2.95883	−0.163874
$327$	4.62075	0.255528
$328$	4.60838	0.254455
$329$	1.65313	0.0911401
$330$	4.12530	0.227091
$331$	−19.2746	−1.05943	−0.529715	−	0.848176i	$-0.677701\pi$
$331$	−19.2746	−1.05943	−0.529715	+	0.848176i	$0.677701\pi$
$332$	−2.94543	−0.161651
$333$	8.15031	0.446634
$334$	−2.79842	−0.153123
$335$	−7.21545	−0.394222
$336$	0.916621	0.0500058
$337$	−5.85176	−0.318765	−0.159383	−	0.987217i	$-0.550950\pi$
$337$	−5.85176	−0.318765	−0.159383	+	0.987217i	$0.550950\pi$
$338$	35.4931	1.93057
$339$	7.62295	0.414022
$340$	−12.9714	−0.703473
$341$	19.2685	1.04345
$342$	−3.05772	−0.165343
$343$	−1.00000	−0.0539949
$344$	−23.5074	−1.26743
$345$	1.00000	0.0538382
$346$	−0.908036	−0.0488163
$347$	2.86621	0.153866	0.0769332	−	0.997036i	$-0.475487\pi$
$347$	2.86621	0.153866	0.0769332	+	0.997036i	$0.475487\pi$
$348$	21.9348	1.17583
$349$	35.1597	1.88206	0.941028	−	0.338329i	$-0.109862\pi$
$349$	35.1597	1.88206	0.941028	+	0.338329i	$0.109862\pi$
$350$	−2.24070	−0.119770
$351$	5.37031	0.286646
$352$	−12.2030	−0.650425
$353$	7.81798	0.416109	0.208055	−	0.978117i	$-0.433287\pi$
$353$	7.81798	0.416109	0.208055	+	0.978117i	$0.433287\pi$
$354$	−20.3910	−1.08377
$355$	−13.5922	−0.721399
$356$	−45.5221	−2.41267
$357$	4.29412	0.227269
$358$	−41.9872	−2.21909
$359$	−35.8124	−1.89010	−0.945052	−	0.326919i	$-0.893990\pi$
$359$	−35.8124	−1.89010	−0.945052	+	0.326919i	$0.893990\pi$
$360$	2.28717	0.120544
$361$	−17.1378	−0.901989
$362$	−9.26306	−0.486856
$363$	−7.61043	−0.399444
$364$	−16.2223	−0.850279
$365$	−5.73002	−0.299923
$366$	5.63018	0.294294
$367$	18.7259	0.977483	0.488741	−	0.872429i	$-0.337456\pi$
$367$	18.7259	0.977483	0.488741	+	0.872429i	$0.337456\pi$
$368$	−0.916621	−0.0477822
$369$	2.01488	0.104891
$370$	18.2624	0.949417
$371$	2.66988	0.138613
$372$	31.6147	1.63915
$373$	−7.68127	−0.397721	−0.198860	−	0.980028i	$-0.563724\pi$
$373$	−7.68127	−0.397721	−0.198860	+	0.980028i	$0.563724\pi$
$374$	−17.7146	−0.915998
$375$	1.00000	0.0516398
$376$	−3.78099	−0.194990
$377$	38.9960	2.00839
$378$	−2.24070	−0.115249
$379$	12.6629	0.650449	0.325224	−	0.945637i	$-0.394560\pi$
$379$	12.6629	0.650449	0.325224	+	0.945637i	$0.394560\pi$
$380$	−4.12218	−0.211464
$381$	−19.4957	−0.998794
$382$	−19.9774	−1.02213
$383$	−37.0664	−1.89401	−0.947003	−	0.321226i	$-0.895905\pi$
$383$	−37.0664	−1.89401	−0.947003	+	0.321226i	$0.895905\pi$
$384$	−15.9143	−0.812124
$385$	−1.84108	−0.0938300
$386$	−34.1493	−1.73815
$387$	−10.2779	−0.522457
$388$	−41.6387	−2.11388
$389$	−15.9429	−0.808335	−0.404168	−	0.914685i	$-0.632439\pi$
$389$	−15.9429	−0.808335	−0.404168	+	0.914685i	$0.632439\pi$
$390$	12.0332	0.609327
$391$	−4.29412	−0.217163
$392$	2.28717	0.115519
$393$	16.7034	0.842576
$394$	0.548062	0.0276110
$395$	−2.11985	−0.106661
$396$	5.56141	0.279472
$397$	20.3938	1.02354	0.511768	−	0.859123i	$-0.328991\pi$
$397$	20.3938	1.02354	0.511768	+	0.859123i	$0.328991\pi$
$398$	20.5871	1.03194
$399$	1.36463	0.0683168
$400$	−0.916621	−0.0458311
$401$	4.23611	0.211541	0.105771	−	0.994391i	$-0.466269\pi$
$401$	4.23611	0.211541	0.105771	+	0.994391i	$0.466269\pi$
$402$	−16.1677	−0.806369
$403$	56.2051	2.79977
$404$	15.2946	0.760932
$405$	1.00000	0.0496904
$406$	−16.2706	−0.807497
$407$	15.0054	0.743788
$408$	−9.82136	−0.486230
$409$	−12.9047	−0.638096	−0.319048	−	0.947739i	$-0.603363\pi$
$409$	−12.9047	−0.638096	−0.319048	+	0.947739i	$0.603363\pi$
$410$	4.51475	0.222968
$411$	10.1491	0.500620
$412$	41.3793	2.03861
$413$	9.10026	0.447794
$414$	2.24070	0.110124
$415$	−0.975069	−0.0478643
$416$	−35.5955	−1.74521
$417$	22.1683	1.08559
$418$	−5.62951	−0.275348
$419$	−15.4019	−0.752432	−0.376216	−	0.926532i	$-0.622775\pi$
$419$	−15.4019	−0.752432	−0.376216	+	0.926532i	$0.622775\pi$
$420$	−3.02074	−0.147397
$421$	0.323203	0.0157520	0.00787599	−	0.999969i	$-0.497493\pi$
$421$	0.323203	0.0157520	0.00787599	+	0.999969i	$0.497493\pi$
$422$	−22.8433	−1.11200
$423$	−1.65313	−0.0803780
$424$	−6.10645	−0.296555
$425$	−4.29412	−0.208295
$426$	−30.4561	−1.47560
$427$	−2.51269	−0.121597
$428$	−14.5383	−0.702734
$429$	9.88716	0.477356
$430$	−23.0298	−1.11060
$431$	14.6975	0.707955	0.353977	−	0.935254i	$-0.384829\pi$
$431$	14.6975	0.707955	0.353977	+	0.935254i	$0.384829\pi$
$432$	−0.916621	−0.0441010
$433$	21.8802	1.05149	0.525747	−	0.850641i	$-0.323786\pi$
$433$	21.8802	1.05149	0.525747	+	0.850641i	$0.323786\pi$
$434$	−23.4509	−1.12568
$435$	7.26140	0.348158
$436$	13.9581	0.668471
$437$	−1.36463	−0.0652790
$438$	−12.8393	−0.613484
$439$	12.1200	0.578456	0.289228	−	0.957260i	$-0.406601\pi$
$439$	12.1200	0.578456	0.289228	+	0.957260i	$0.406601\pi$
$440$	4.21085	0.200744
$441$	1.00000	0.0476190
$442$	−51.6722	−2.45780
$443$	24.3085	1.15493	0.577467	−	0.816414i	$-0.304041\pi$
$443$	24.3085	1.15493	0.577467	+	0.816414i	$0.304041\pi$
$444$	24.6199	1.16841
$445$	−15.0699	−0.714380
$446$	40.2667	1.90669
$447$	−0.933442	−0.0441503
$448$	13.0186	0.615070
$449$	31.7963	1.50056	0.750280	−	0.661120i	$-0.229919\pi$
$449$	31.7963	1.50056	0.750280	+	0.661120i	$0.229919\pi$
$450$	2.24070	0.105628
$451$	3.70956	0.174676
$452$	23.0269	1.08310
$453$	−2.53317	−0.119019
$454$	−58.1119	−2.72733
$455$	−5.37031	−0.251764
$456$	−3.12113	−0.146160
$457$	−29.3237	−1.37170	−0.685852	−	0.727741i	$-0.740570\pi$
$457$	−29.3237	−1.37170	−0.685852	+	0.727741i	$0.740570\pi$
$458$	42.6489	1.99285
$459$	−4.29412	−0.200432
$460$	3.02074	0.140843
$461$	−27.8589	−1.29752	−0.648758	−	0.760994i	$-0.724711\pi$
$461$	−27.8589	−1.29752	−0.648758	+	0.760994i	$0.724711\pi$
$462$	−4.12530	−0.191927
$463$	−13.4739	−0.626185	−0.313093	−	0.949723i	$-0.601365\pi$
$463$	−13.4739	−0.626185	−0.313093	+	0.949723i	$0.601365\pi$
$464$	−6.65595	−0.308995
$465$	10.4659	0.485344
$466$	5.40665	0.250458
$467$	−9.54918	−0.441883	−0.220942	−	0.975287i	$-0.570913\pi$
$467$	−9.54918	−0.441883	−0.220942	+	0.975287i	$0.570913\pi$
$468$	16.2223	0.749876
$469$	7.21545	0.333178
$470$	−3.70417	−0.170861
$471$	−8.18306	−0.377055
$472$	−20.8138	−0.958033
$473$	−18.9225	−0.870058
$474$	−4.74994	−0.218172
$475$	−1.36463	−0.0626134
$476$	12.9714	0.594543
$477$	−2.66988	−0.122245
$478$	33.1174	1.51475
$479$	9.84621	0.449885	0.224942	−	0.974372i	$-0.427781\pi$
$479$	9.84621	0.449885	0.224942	+	0.974372i	$0.427781\pi$
$480$	−6.62821	−0.302535
$481$	43.7697	1.99572
$482$	−28.0122	−1.27592
$483$	−1.00000	−0.0455016
$484$	−22.9891	−1.04496
$485$	−13.7843	−0.625912
$486$	2.24070	0.101640
$487$	−23.0870	−1.04617	−0.523085	−	0.852281i	$-0.675219\pi$
$487$	−23.0870	−1.04617	−0.523085	+	0.852281i	$0.675219\pi$
$488$	5.74693	0.260151
$489$	−1.32049	−0.0597148
$490$	2.24070	0.101225
$491$	16.3914	0.739732	0.369866	−	0.929085i	$-0.379404\pi$
$491$	16.3914	0.739732	0.369866	+	0.929085i	$0.379404\pi$
$492$	6.08644	0.274398
$493$	−31.1813	−1.40434
$494$	−16.4209	−0.738812
$495$	1.84108	0.0827503
$496$	−9.59326	−0.430750
$497$	13.5922	0.609694
$498$	−2.18484	−0.0979049
$499$	−2.29412	−0.102699	−0.0513495	−	0.998681i	$-0.516352\pi$
$499$	−2.29412	−0.102699	−0.0513495	+	0.998681i	$0.516352\pi$
$500$	3.02074	0.135091
$501$	−1.24890	−0.0557969
$502$	−52.9361	−2.36266
$503$	−13.2902	−0.592581	−0.296290	−	0.955098i	$-0.595750\pi$
$503$	−13.2902	−0.592581	−0.296290	+	0.955098i	$0.595750\pi$
$504$	−2.28717	−0.101878
$505$	5.06319	0.225309
$506$	4.12530	0.183392
$507$	15.8402	0.703488
$508$	−58.8913	−2.61288
$509$	31.4847	1.39554	0.697768	−	0.716324i	$-0.254177\pi$
$509$	31.4847	1.39554	0.697768	+	0.716324i	$0.254177\pi$
$510$	−9.62183	−0.426062
$511$	5.73002	0.253481
$512$	10.2685	0.453807
$513$	−1.36463	−0.0602498
$514$	−2.26261	−0.0997996
$515$	13.6984	0.603624
$516$	−31.0470	−1.36677
$517$	−3.04355	−0.133855
$518$	−18.2624	−0.802404
$519$	−0.405247	−0.0177884
$520$	12.2828	0.538636
$521$	12.7102	0.556842	0.278421	−	0.960459i	$-0.410189\pi$
$521$	12.7102	0.556842	0.278421	+	0.960459i	$0.410189\pi$
$522$	16.2706	0.712146
$523$	37.5981	1.64405	0.822026	−	0.569450i	$-0.192844\pi$
$523$	37.5981	1.64405	0.822026	+	0.569450i	$0.192844\pi$
$524$	50.4567	2.20421
$525$	−1.00000	−0.0436436
$526$	−12.6593	−0.551971
$527$	−44.9418	−1.95769
$528$	−1.68757	−0.0734421
$529$	1.00000	0.0434783
$530$	−5.98239	−0.259858
$531$	−9.10026	−0.394918
$532$	4.12218	0.178719
$533$	10.8206	0.468690
$534$	−33.7670	−1.46124
$535$	−4.81282	−0.208076
$536$	−16.5029	−0.712818
$537$	−18.7384	−0.808623
$538$	4.74557	0.204596
$539$	1.84108	0.0793009
$540$	3.02074	0.129992
$541$	9.57300	0.411576	0.205788	−	0.978597i	$-0.434024\pi$
$541$	9.57300	0.411576	0.205788	+	0.978597i	$0.434024\pi$
$542$	20.1609	0.865985
$543$	−4.13400	−0.177407
$544$	28.4623	1.22031
$545$	4.62075	0.197931
$546$	−12.0332	−0.514976
$547$	25.1401	1.07491	0.537455	−	0.843292i	$-0.319386\pi$
$547$	25.1401	1.07491	0.537455	+	0.843292i	$0.319386\pi$
$548$	30.6579	1.30964
$549$	2.51269	0.107239
$550$	4.12530	0.175904
$551$	−9.90911	−0.422142
$552$	2.28717	0.0973482
$553$	2.11985	0.0901451
$554$	−30.5609	−1.29841
$555$	8.15031	0.345961
$556$	66.9646	2.83993
$557$	−30.1362	−1.27691	−0.638456	−	0.769658i	$-0.720427\pi$
$557$	−30.1362	−1.27691	−0.638456	+	0.769658i	$0.720427\pi$
$558$	23.4509	0.992757
$559$	−55.1957	−2.33453
$560$	0.916621	0.0387343
$561$	−7.90581	−0.333784
$562$	−3.10639	−0.131035
$563$	7.18835	0.302953	0.151476	−	0.988461i	$-0.451597\pi$
$563$	7.18835	0.302953	0.151476	+	0.988461i	$0.451597\pi$
$564$	−4.99368	−0.210272
$565$	7.62295	0.320700
$566$	54.3617	2.28499
$567$	−1.00000	−0.0419961
$568$	−31.0876	−1.30441
$569$	−19.6755	−0.824841	−0.412421	−	0.910994i	$-0.635317\pi$
$569$	−19.6755	−0.824841	−0.412421	+	0.910994i	$0.635317\pi$
$570$	−3.05772	−0.128074
$571$	45.4489	1.90198	0.950988	−	0.309228i	$-0.100071\pi$
$571$	45.4489	1.90198	0.950988	+	0.309228i	$0.100071\pi$
$572$	29.8665	1.24878
$573$	−8.91571	−0.372459
$574$	−4.51475	−0.188442
$575$	1.00000	0.0417029
$576$	−13.0186	−0.542441
$577$	−10.1234	−0.421441	−0.210720	−	0.977546i	$-0.567581\pi$
$577$	−10.1234	−0.421441	−0.210720	+	0.977546i	$0.567581\pi$
$578$	3.22541	0.134159
$579$	−15.2404	−0.633371
$580$	21.9348	0.910792
$581$	0.975069	0.0404527
$582$	−30.8864	−1.28028
$583$	−4.91545	−0.203577
$584$	−13.1055	−0.542310
$585$	5.37031	0.222035
$586$	65.3408	2.69921
$587$	−30.3470	−1.25255	−0.626277	−	0.779600i	$-0.715422\pi$
$587$	−30.3470	−1.25255	−0.626277	+	0.779600i	$0.715422\pi$
$588$	3.02074	0.124573
$589$	−14.2820	−0.588481
$590$	−20.3910	−0.839482
$591$	0.244594	0.0100613
$592$	−7.47075	−0.307046
$593$	−14.8285	−0.608934	−0.304467	−	0.952523i	$-0.598478\pi$
$593$	−14.8285	−0.608934	−0.304467	+	0.952523i	$0.598478\pi$
$594$	4.12530	0.169263
$595$	4.29412	0.176042
$596$	−2.81968	−0.115499
$597$	9.18780	0.376032
$598$	12.0332	0.492076
$599$	−31.9264	−1.30448	−0.652239	−	0.758014i	$-0.726170\pi$
$599$	−31.9264	−1.30448	−0.652239	+	0.758014i	$0.726170\pi$
$600$	2.28717	0.0933732
$601$	−12.9927	−0.529982	−0.264991	−	0.964251i	$-0.585369\pi$
$601$	−12.9927	−0.529982	−0.264991	+	0.964251i	$0.585369\pi$
$602$	23.0298	0.938624
$603$	−7.21545	−0.293836
$604$	−7.65204	−0.311357
$605$	−7.61043	−0.309408
$606$	11.3451	0.460862
$607$	44.9942	1.82626	0.913129	−	0.407671i	$-0.133659\pi$
$607$	44.9942	1.82626	0.913129	+	0.407671i	$0.133659\pi$
$608$	9.04503	0.366825
$609$	−7.26140	−0.294247
$610$	5.63018	0.227959
$611$	−8.87783	−0.359158
$612$	−12.9714	−0.524338
$613$	20.7151	0.836674	0.418337	−	0.908292i	$-0.362613\pi$
$613$	20.7151	0.836674	0.418337	+	0.908292i	$0.362613\pi$
$614$	−59.5396	−2.40282
$615$	2.01488	0.0812480
$616$	−4.21085	−0.169660
$617$	36.3840	1.46476	0.732382	−	0.680894i	$-0.238409\pi$
$617$	36.3840	1.46476	0.732382	+	0.680894i	$0.238409\pi$
$618$	30.6940	1.23469
$619$	−19.9578	−0.802172	−0.401086	−	0.916040i	$-0.631367\pi$
$619$	−19.9578	−0.802172	−0.401086	+	0.916040i	$0.631367\pi$
$620$	31.6147	1.26968
$621$	1.00000	0.0401286
$622$	45.4096	1.82076
$623$	15.0699	0.603761
$624$	−4.92254	−0.197059
$625$	1.00000	0.0400000
$626$	20.1992	0.807322
$627$	−2.51239	−0.100335
$628$	−24.7189	−0.986390
$629$	−34.9984	−1.39548
$630$	−2.24070	−0.0892716
$631$	−28.6474	−1.14044	−0.570218	−	0.821493i	$-0.693141\pi$
$631$	−28.6474	−1.14044	−0.570218	+	0.821493i	$0.693141\pi$
$632$	−4.84844	−0.192861
$633$	−10.1947	−0.405204
$634$	44.0311	1.74870
$635$	−19.4957	−0.773663
$636$	−8.06499	−0.319798
$637$	5.37031	0.212779
$638$	29.9555	1.18595
$639$	−13.5922	−0.537699
$640$	−15.9143	−0.629069
$641$	−48.2390	−1.90532	−0.952662	−	0.304031i	$-0.901667\pi$
$641$	−48.2390	−1.90532	−0.952662	+	0.304031i	$0.901667\pi$
$642$	−10.7841	−0.425614
$643$	38.3756	1.51339	0.756693	−	0.653770i	$-0.226814\pi$
$643$	38.3756	1.51339	0.756693	+	0.653770i	$0.226814\pi$
$644$	−3.02074	−0.119034
$645$	−10.2779	−0.404694
$646$	13.1302	0.516602
$647$	−37.5480	−1.47616	−0.738082	−	0.674711i	$-0.764268\pi$
$647$	−37.5480	−1.47616	−0.738082	+	0.674711i	$0.764268\pi$
$648$	2.28717	0.0898484
$649$	−16.7543	−0.657663
$650$	12.0332	0.471983
$651$	−10.4659	−0.410191
$652$	−3.98886	−0.156216
$653$	20.3812	0.797579	0.398789	−	0.917043i	$-0.369430\pi$
$653$	20.3812	0.797579	0.398789	+	0.917043i	$0.369430\pi$
$654$	10.3537	0.404862
$655$	16.7034	0.652657
$656$	−1.84689	−0.0721088
$657$	−5.73002	−0.223550
$658$	3.70417	0.144404
$659$	36.9106	1.43783	0.718916	−	0.695097i	$-0.244638\pi$
$659$	36.9106	1.43783	0.718916	+	0.695097i	$0.244638\pi$
$660$	5.56141	0.216478
$661$	42.6530	1.65901	0.829505	−	0.558499i	$-0.188622\pi$
$661$	42.6530	1.65901	0.829505	+	0.558499i	$0.188622\pi$
$662$	−43.1887	−1.67857
$663$	−23.0607	−0.895605
$664$	−2.23014	−0.0865464
$665$	1.36463	0.0529180
$666$	18.2624	0.707653
$667$	7.26140	0.281163
$668$	−3.77261	−0.145967
$669$	17.9706	0.694784
$670$	−16.1677	−0.624611
$671$	4.62605	0.178587
$672$	6.62821	0.255689
$673$	13.5845	0.523645	0.261823	−	0.965116i	$-0.415676\pi$
$673$	13.5845	0.523645	0.261823	+	0.965116i	$0.415676\pi$
$674$	−13.1120	−0.505056
$675$	1.00000	0.0384900
$676$	47.8491	1.84035
$677$	−26.7636	−1.02861	−0.514304	−	0.857608i	$-0.671950\pi$
$677$	−26.7636	−1.02861	−0.514304	+	0.857608i	$0.671950\pi$
$678$	17.0808	0.655982
$679$	13.7843	0.528992
$680$	−9.82136	−0.376632
$681$	−25.9347	−0.993821
$682$	43.1750	1.65326
$683$	−27.8788	−1.06675	−0.533376	−	0.845879i	$-0.679077\pi$
$683$	−27.8788	−1.06675	−0.533376	+	0.845879i	$0.679077\pi$
$684$	−4.12218	−0.157616
$685$	10.1491	0.387779
$686$	−2.24070	−0.0855503
$687$	19.0337	0.726182
$688$	9.42098	0.359172
$689$	−14.3381	−0.546236
$690$	2.24070	0.0853020
$691$	37.7038	1.43432	0.717160	−	0.696908i	$-0.245442\pi$
$691$	37.7038	1.43432	0.717160	+	0.696908i	$0.245442\pi$
$692$	−1.22414	−0.0465350
$693$	−1.84108	−0.0699368
$694$	6.42232	0.243788
$695$	22.1683	0.840891
$696$	16.6080	0.629526
$697$	−8.65216	−0.327724
$698$	78.7823	2.98196
$699$	2.41293	0.0912654
$700$	−3.02074	−0.114173
$701$	−7.14336	−0.269801	−0.134901	−	0.990859i	$-0.543071\pi$
$701$	−7.14336	−0.269801	−0.134901	+	0.990859i	$0.543071\pi$
$702$	12.0332	0.454166
$703$	−11.1221	−0.419479
$704$	−23.9682	−0.903336
$705$	−1.65313	−0.0622606
$706$	17.5178	0.659289
$707$	−5.06319	−0.190421
$708$	−27.4895	−1.03312
$709$	44.7578	1.68091	0.840457	−	0.541879i	$-0.182287\pi$
$709$	44.7578	1.68091	0.840457	+	0.541879i	$0.182287\pi$
$710$	−30.4561	−1.14300
$711$	−2.11985	−0.0795005
$712$	−34.4673	−1.29172
$713$	10.4659	0.391951
$714$	9.62183	0.360088
$715$	9.88716	0.369759
$716$	−56.6039	−2.11539
$717$	14.7799	0.551966
$718$	−80.2448	−2.99471
$719$	9.64093	0.359546	0.179773	−	0.983708i	$-0.442464\pi$
$719$	9.64093	0.359546	0.179773	+	0.983708i	$0.442464\pi$
$720$	−0.916621	−0.0341605
$721$	−13.6984	−0.510155
$722$	−38.4006	−1.42912
$723$	−12.5015	−0.464938
$724$	−12.4877	−0.464103
$725$	7.26140	0.269682
$726$	−17.0527	−0.632885
$727$	−16.3347	−0.605821	−0.302911	−	0.953019i	$-0.597958\pi$
$727$	−16.3347	−0.605821	−0.302911	+	0.953019i	$0.597958\pi$
$728$	−12.2828	−0.455230
$729$	1.00000	0.0370370
$730$	−12.8393	−0.475203
$731$	44.1347	1.63238
$732$	7.59016	0.280540
$733$	8.73756	0.322729	0.161365	−	0.986895i	$-0.448410\pi$
$733$	8.73756	0.322729	0.161365	+	0.986895i	$0.448410\pi$
$734$	41.9591	1.54874
$735$	1.00000	0.0368856
$736$	−6.62821	−0.244319
$737$	−13.2842	−0.489330
$738$	4.51475	0.166190
$739$	16.5849	0.610086	0.305043	−	0.952339i	$-0.401329\pi$
$739$	16.5849	0.610086	0.305043	+	0.952339i	$0.401329\pi$
$740$	24.6199	0.905047
$741$	−7.32847	−0.269218
$742$	5.98239	0.219620
$743$	−23.5199	−0.862860	−0.431430	−	0.902146i	$-0.641991\pi$
$743$	−23.5199	−0.862860	−0.431430	+	0.902146i	$0.641991\pi$
$744$	23.9372	0.877581
$745$	−0.933442	−0.0341987
$746$	−17.2114	−0.630155
$747$	−0.975069	−0.0356759
$748$	−23.8814	−0.873190
$749$	4.81282	0.175857
$750$	2.24070	0.0818188
$751$	25.7451	0.939451	0.469726	−	0.882812i	$-0.344353\pi$
$751$	25.7451	0.939451	0.469726	+	0.882812i	$0.344353\pi$
$752$	1.51530	0.0552572
$753$	−23.6248	−0.860936
$754$	87.3782	3.18213
$755$	−2.53317	−0.0921915
$756$	−3.02074	−0.109863
$757$	30.7195	1.11652	0.558260	−	0.829666i	$-0.311469\pi$
$757$	30.7195	1.11652	0.558260	+	0.829666i	$0.311469\pi$
$758$	28.3737	1.03058
$759$	1.84108	0.0668269
$760$	−3.12113	−0.113215
$761$	45.1515	1.63674	0.818370	−	0.574691i	$-0.194878\pi$
$761$	45.1515	1.63674	0.818370	+	0.574691i	$0.194878\pi$
$762$	−43.6840	−1.58250
$763$	−4.62075	−0.167282
$764$	−26.9320	−0.974366
$765$	−4.29412	−0.155254
$766$	−83.0547	−3.00089
$767$	−48.8712	−1.76464
$768$	−9.62206	−0.347206
$769$	−33.4314	−1.20557	−0.602783	−	0.797905i	$-0.705942\pi$
$769$	−33.4314	−1.20557	−0.602783	+	0.797905i	$0.705942\pi$
$770$	−4.12530	−0.148666
$771$	−1.00978	−0.0363663
$772$	−46.0374	−1.65692
$773$	−17.8333	−0.641418	−0.320709	−	0.947178i	$-0.603921\pi$
$773$	−17.8333	−0.641418	−0.320709	+	0.947178i	$0.603921\pi$
$774$	−23.0298	−0.827789
$775$	10.4659	0.375946
$776$	−31.5269	−1.13175
$777$	−8.15031	−0.292391
$778$	−35.7232	−1.28074
$779$	−2.74957	−0.0985135
$780$	16.2223	0.580851
$781$	−25.0243	−0.895440
$782$	−9.62183	−0.344076
$783$	7.26140	0.259501
$784$	−0.916621	−0.0327365
$785$	−8.18306	−0.292066
$786$	37.4274	1.33499
$787$	−23.4022	−0.834198	−0.417099	−	0.908861i	$-0.636953\pi$
$787$	−23.4022	−0.834198	−0.417099	+	0.908861i	$0.636953\pi$
$788$	0.738855	0.0263206
$789$	−5.64970	−0.201134
$790$	−4.74994	−0.168995
$791$	−7.62295	−0.271041
$792$	4.21085	0.149626
$793$	13.4939	0.479182
$794$	45.6964	1.62171
$795$	−2.66988	−0.0946907
$796$	27.7539	0.983712
$797$	−5.65897	−0.200451	−0.100226	−	0.994965i	$-0.531956\pi$
$797$	−5.65897	−0.200451	−0.100226	+	0.994965i	$0.531956\pi$
$798$	3.05772	0.108242
$799$	7.09875	0.251136
$800$	−6.62821	−0.234342
$801$	−15.0699	−0.532467
$802$	9.49185	0.335169
$803$	−10.5494	−0.372281
$804$	−21.7960	−0.768684
$805$	−1.00000	−0.0352454
$806$	125.939	4.43600
$807$	2.11790	0.0745535
$808$	11.5803	0.407395
$809$	−50.2791	−1.76772	−0.883859	−	0.467754i	$-0.845063\pi$
$809$	−50.2791	−1.76772	−0.883859	+	0.467754i	$0.845063\pi$
$810$	2.24070	0.0787302
$811$	−11.5641	−0.406070	−0.203035	−	0.979171i	$-0.565081\pi$
$811$	−11.5641	−0.406070	−0.203035	+	0.979171i	$0.565081\pi$
$812$	−21.9348	−0.769760
$813$	8.99760	0.315559
$814$	33.6225	1.17847
$815$	−1.32049	−0.0462549
$816$	3.93608	0.137790
$817$	14.0256	0.490693
$818$	−28.9155	−1.01101
$819$	−5.37031	−0.187654
$820$	6.08644	0.212548
$821$	3.35083	0.116945	0.0584724	−	0.998289i	$-0.481377\pi$
$821$	3.35083	0.116945	0.0584724	+	0.998289i	$0.481377\pi$
$822$	22.7412	0.793190
$823$	23.3900	0.815326	0.407663	−	0.913133i	$-0.366344\pi$
$823$	23.3900	0.815326	0.407663	+	0.913133i	$0.366344\pi$
$824$	31.3305	1.09145
$825$	1.84108	0.0640981
$826$	20.3910	0.709492
$827$	35.3873	1.23054	0.615268	−	0.788318i	$-0.289048\pi$
$827$	35.3873	1.23054	0.615268	+	0.788318i	$0.289048\pi$
$828$	3.02074	0.104978
$829$	46.9831	1.63179	0.815894	−	0.578201i	$-0.196245\pi$
$829$	46.9831	1.63179	0.815894	+	0.578201i	$0.196245\pi$
$830$	−2.18484	−0.0758368
$831$	−13.6390	−0.473131
$832$	−69.9138	−2.42382
$833$	−4.29412	−0.148782
$834$	49.6725	1.72002
$835$	−1.24890	−0.0432201
$836$	−7.58926	−0.262480
$837$	10.4659	0.361754
$838$	−34.5110	−1.19216
$839$	−39.8240	−1.37488	−0.687438	−	0.726243i	$-0.741265\pi$
$839$	−39.8240	−1.37488	−0.687438	+	0.726243i	$0.741265\pi$
$840$	−2.28717	−0.0789147
$841$	23.7279	0.818205
$842$	0.724202	0.0249576
$843$	−1.38635	−0.0477483
$844$	−30.7956	−1.06003
$845$	15.8402	0.544920
$846$	−3.70417	−0.127352
$847$	7.61043	0.261497
$848$	2.44726	0.0840394
$849$	24.2611	0.832637
$850$	−9.62183	−0.330026
$851$	8.15031	0.279389
$852$	−41.0585	−1.40664
$853$	−10.8803	−0.372535	−0.186267	−	0.982499i	$-0.559639\pi$
$853$	−10.8803	−0.372535	−0.186267	+	0.982499i	$0.559639\pi$
$854$	−5.63018	−0.192661
$855$	−1.36463	−0.0466693
$856$	−11.0077	−0.376236
$857$	31.2773	1.06841	0.534206	−	0.845354i	$-0.320611\pi$
$857$	31.2773	1.06841	0.534206	+	0.845354i	$0.320611\pi$
$858$	22.1542	0.756330
$859$	52.1465	1.77921	0.889607	−	0.456726i	$-0.150978\pi$
$859$	52.1465	1.77921	0.889607	+	0.456726i	$0.150978\pi$
$860$	−31.0470	−1.05869
$861$	−2.01488	−0.0686671
$862$	32.9327	1.12169
$863$	31.9865	1.08883	0.544417	−	0.838815i	$-0.316751\pi$
$863$	31.9865	1.08883	0.544417	+	0.838815i	$0.316751\pi$
$864$	−6.62821	−0.225496
$865$	−0.405247	−0.0137788
$866$	49.0269	1.66600
$867$	1.43946	0.0488868
$868$	−31.6147	−1.07307
$869$	−3.90281	−0.132394
$870$	16.2706	0.551626
$871$	−38.7492	−1.31297
$872$	10.5684	0.357892
$873$	−13.7843	−0.466527
$874$	−3.05772	−0.103429
$875$	−1.00000	−0.0338062
$876$	−17.3089	−0.584813
$877$	46.3793	1.56612	0.783059	−	0.621947i	$-0.213658\pi$
$877$	46.3793	1.56612	0.783059	+	0.621947i	$0.213658\pi$
$878$	27.1573	0.916514
$879$	29.1609	0.983573
$880$	−1.68757	−0.0568880
$881$	43.5226	1.46632	0.733158	−	0.680059i	$-0.238046\pi$
$881$	43.5226	1.46632	0.733158	+	0.680059i	$0.238046\pi$
$882$	2.24070	0.0754483
$883$	12.1382	0.408482	0.204241	−	0.978921i	$-0.434527\pi$
$883$	12.1382	0.408482	0.204241	+	0.978921i	$0.434527\pi$
$884$	−69.6604	−2.34293
$885$	−9.10026	−0.305902
$886$	54.4682	1.82989
$887$	−2.26569	−0.0760745	−0.0380373	−	0.999276i	$-0.512111\pi$
$887$	−2.26569	−0.0760745	−0.0380373	+	0.999276i	$0.512111\pi$
$888$	18.6411	0.625555
$889$	19.4957	0.653864
$890$	−33.7670	−1.13187
$891$	1.84108	0.0616785
$892$	54.2845	1.81758
$893$	2.25591	0.0754912
$894$	−2.09156	−0.0699524
$895$	−18.7384	−0.626357
$896$	15.9143	0.531660
$897$	5.37031	0.179309
$898$	71.2460	2.37751
$899$	75.9970	2.53464
$900$	3.02074	0.100691
$901$	11.4648	0.381947
$902$	8.31201	0.276760
$903$	10.2779	0.342029
$904$	17.4350	0.579878
$905$	−4.13400	−0.137419
$906$	−5.67608	−0.188575
$907$	40.4339	1.34259	0.671293	−	0.741192i	$-0.265739\pi$
$907$	40.4339	1.34259	0.671293	+	0.741192i	$0.265739\pi$
$908$	−78.3420	−2.59987
$909$	5.06319	0.167935
$910$	−12.0332	−0.398898
$911$	−3.17457	−0.105178	−0.0525891	−	0.998616i	$-0.516747\pi$
$911$	−3.17457	−0.105178	−0.0525891	+	0.998616i	$0.516747\pi$
$912$	1.25085	0.0414197
$913$	−1.79518	−0.0594117
$914$	−65.7056	−2.17335
$915$	2.51269	0.0830668
$916$	57.4959	1.89972
$917$	−16.7034	−0.551596
$918$	−9.62183	−0.317568
$919$	21.6635	0.714614	0.357307	−	0.933987i	$-0.383695\pi$
$919$	21.6635	0.714614	0.357307	+	0.933987i	$0.383695\pi$
$920$	2.28717	0.0754056
$921$	−26.5719	−0.875573
$922$	−62.4234	−2.05580
$923$	−72.9943	−2.40264
$924$	−5.56141	−0.182957
$925$	8.15031	0.267980
$926$	−30.1910	−0.992137
$927$	13.6984	0.449915
$928$	−48.1301	−1.57995
$929$	−1.61108	−0.0528579	−0.0264289	−	0.999651i	$-0.508414\pi$
$929$	−1.61108	−0.0528579	−0.0264289	+	0.999651i	$0.508414\pi$
$930$	23.4509	0.768986
$931$	−1.36463	−0.0447239
$932$	7.28883	0.238753
$933$	20.2658	0.663473
$934$	−21.3968	−0.700126
$935$	−7.90581	−0.258548
$936$	12.2828	0.401475
$937$	−42.4240	−1.38593	−0.692967	−	0.720970i	$-0.743697\pi$
$937$	−42.4240	−1.38593	−0.692967	+	0.720970i	$0.743697\pi$
$938$	16.1677	0.527893
$939$	9.01468	0.294183
$940$	−4.99368	−0.162876
$941$	−20.3143	−0.662226	−0.331113	−	0.943591i	$-0.607424\pi$
$941$	−20.3143	−0.662226	−0.331113	+	0.943591i	$0.607424\pi$
$942$	−18.3358	−0.597412
$943$	2.01488	0.0656137
$944$	8.34149	0.271492
$945$	−1.00000	−0.0325300
$946$	−42.3997	−1.37853
$947$	−30.7786	−1.00017	−0.500085	−	0.865976i	$-0.666698\pi$
$947$	−30.7786	−1.00017	−0.500085	+	0.865976i	$0.666698\pi$
$948$	−6.40350	−0.207976
$949$	−30.7720	−0.998901
$950$	−3.05772	−0.0992056
$951$	19.6506	0.637214
$952$	9.82136	0.318312
$953$	−3.02877	−0.0981114	−0.0490557	−	0.998796i	$-0.515621\pi$
$953$	−3.02877	−0.0981114	−0.0490557	+	0.998796i	$0.515621\pi$
$954$	−5.98239	−0.193687
$955$	−8.91571	−0.288506
$956$	44.6462	1.44396
$957$	13.3688	0.432152
$958$	22.0624	0.712804
$959$	−10.1491	−0.327733
$960$	−13.0186	−0.420173
$961$	78.5349	2.53338
$962$	98.0747	3.16205
$963$	−4.81282	−0.155091
$964$	−37.7639	−1.21629
$965$	−15.2404	−0.490607
$966$	−2.24070	−0.0720933
$967$	−9.98590	−0.321125	−0.160562	−	0.987026i	$-0.551331\pi$
$967$	−9.98590	−0.321125	−0.160562	+	0.987026i	$0.551331\pi$
$968$	−17.4063	−0.559460
$969$	5.85988	0.188246
$970$	−30.8864	−0.991703
$971$	45.1229	1.44806	0.724031	−	0.689768i	$-0.242287\pi$
$971$	45.1229	1.44806	0.724031	+	0.689768i	$0.242287\pi$
$972$	3.02074	0.0968902
$973$	−22.1683	−0.710683
$974$	−51.7309	−1.65757
$975$	5.37031	0.171987
$976$	−2.30318	−0.0737230
$977$	18.4007	0.588692	0.294346	−	0.955699i	$-0.404898\pi$
$977$	18.4007	0.588692	0.294346	+	0.955699i	$0.404898\pi$
$978$	−2.95883	−0.0946129
$979$	−27.7448	−0.886728
$980$	3.02074	0.0964939
$981$	4.62075	0.147529
$982$	36.7282	1.17204
$983$	9.18930	0.293093	0.146546	−	0.989204i	$-0.453184\pi$
$983$	9.18930	0.293093	0.146546	+	0.989204i	$0.453184\pi$
$984$	4.60838	0.146910
$985$	0.244594	0.00779342
$986$	−69.8680	−2.22505
$987$	1.65313	0.0526198
$988$	−22.1374	−0.704284
$989$	−10.2779	−0.326820
$990$	4.12530	0.131111
$991$	21.4378	0.680994	0.340497	−	0.940246i	$-0.389405\pi$
$991$	21.4378	0.680994	0.340497	+	0.940246i	$0.389405\pi$
$992$	−69.3701	−2.20250
$993$	−19.2746	−0.611662
$994$	30.4561	0.966007
$995$	9.18780	0.291273
$996$	−2.94543	−0.0933294
$997$	−10.3284	−0.327105	−0.163552	−	0.986535i	$-0.552295\pi$
$997$	−10.3284	−0.327105	−0.163552	+	0.986535i	$0.552295\pi$
$998$	−5.14043	−0.162718
$999$	8.15031	0.257864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2415.2.a.v.1.8	✓	10
3.2	odd	2		7245.2.a.bu.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2415.2.a.v.1.8	✓	10	1.1	even	1	trivial
7245.2.a.bu.1.3		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 2415 = 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2415.a (trivial)

\(f(q)\)	\(=\)	\(q+2.24070 q^{2} +1.00000 q^{3} +3.02074 q^{4} +1.00000 q^{5} +2.24070 q^{6} -1.00000 q^{7} +2.28717 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.24070 q^{2} +1.00000 q^{3} +3.02074 q^{4} +1.00000 q^{5} +2.24070 q^{6} -1.00000 q^{7} +2.28717 q^{8} +1.00000 q^{9} +2.24070 q^{10} +1.84108 q^{11} +3.02074 q^{12} +5.37031 q^{13} -2.24070 q^{14} +1.00000 q^{15} -0.916621 q^{16} -4.29412 q^{17} +2.24070 q^{18} -1.36463 q^{19} +3.02074 q^{20} -1.00000 q^{21} +4.12530 q^{22} +1.00000 q^{23} +2.28717 q^{24} +1.00000 q^{25} +12.0332 q^{26} +1.00000 q^{27} -3.02074 q^{28} +7.26140 q^{29} +2.24070 q^{30} +10.4659 q^{31} -6.62821 q^{32} +1.84108 q^{33} -9.62183 q^{34} -1.00000 q^{35} +3.02074 q^{36} +8.15031 q^{37} -3.05772 q^{38} +5.37031 q^{39} +2.28717 q^{40} +2.01488 q^{41} -2.24070 q^{42} -10.2779 q^{43} +5.56141 q^{44} +1.00000 q^{45} +2.24070 q^{46} -1.65313 q^{47} -0.916621 q^{48} +1.00000 q^{49} +2.24070 q^{50} -4.29412 q^{51} +16.2223 q^{52} -2.66988 q^{53} +2.24070 q^{54} +1.84108 q^{55} -2.28717 q^{56} -1.36463 q^{57} +16.2706 q^{58} -9.10026 q^{59} +3.02074 q^{60} +2.51269 q^{61} +23.4509 q^{62} -1.00000 q^{63} -13.0186 q^{64} +5.37031 q^{65} +4.12530 q^{66} -7.21545 q^{67} -12.9714 q^{68} +1.00000 q^{69} -2.24070 q^{70} -13.5922 q^{71} +2.28717 q^{72} -5.73002 q^{73} +18.2624 q^{74} +1.00000 q^{75} -4.12218 q^{76} -1.84108 q^{77} +12.0332 q^{78} -2.11985 q^{79} -0.916621 q^{80} +1.00000 q^{81} +4.51475 q^{82} -0.975069 q^{83} -3.02074 q^{84} -4.29412 q^{85} -23.0298 q^{86} +7.26140 q^{87} +4.21085 q^{88} -15.0699 q^{89} +2.24070 q^{90} -5.37031 q^{91} +3.02074 q^{92} +10.4659 q^{93} -3.70417 q^{94} -1.36463 q^{95} -6.62821 q^{96} -13.7843 q^{97} +2.24070 q^{98} +1.84108 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 - 10 * q^7 + 6 * q^8 + 10 * q^9	\( 10 q + 2 q^{2} + 10 q^{3} + 16 q^{4} + 10 q^{5} + 2 q^{6} - 10 q^{7} + 6 q^{8} + 10 q^{9} + 2 q^{10} - q^{11} + 16 q^{12} - 2 q^{13} - 2 q^{14} + 10 q^{15} + 36 q^{16} + 8 q^{17} + 2 q^{18} + 11 q^{19} + 16 q^{20} - 10 q^{21} + 10 q^{23} + 6 q^{24} + 10 q^{25} + 15 q^{26} + 10 q^{27} - 16 q^{28} + 6 q^{29} + 2 q^{30} + 16 q^{31} - q^{32} - q^{33} + 21 q^{34} - 10 q^{35} + 16 q^{36} - 6 q^{38} - 2 q^{39} + 6 q^{40} + 23 q^{41} - 2 q^{42} + 4 q^{43} - q^{44} + 10 q^{45} + 2 q^{46} + 21 q^{47} + 36 q^{48} + 10 q^{49} + 2 q^{50} + 8 q^{51} + 10 q^{52} - q^{53} + 2 q^{54} - q^{55} - 6 q^{56} + 11 q^{57} + 8 q^{58} + 15 q^{59} + 16 q^{60} + 29 q^{61} + 12 q^{62} - 10 q^{63} + 80 q^{64} - 2 q^{65} + 32 q^{67} - 28 q^{68} + 10 q^{69} - 2 q^{70} - 4 q^{71} + 6 q^{72} + 18 q^{73} - 49 q^{74} + 10 q^{75} + 49 q^{76} + q^{77} + 15 q^{78} + 8 q^{79} + 36 q^{80} + 10 q^{81} + 6 q^{82} + 2 q^{83} - 16 q^{84} + 8 q^{85} - 14 q^{86} + 6 q^{87} - 69 q^{88} + 6 q^{89} + 2 q^{90} + 2 q^{91} + 16 q^{92} + 16 q^{93} - 2 q^{94} + 11 q^{95} - q^{96} - 2 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 10 * q^3 + 16 * q^4 + 10 * q^5 + 2 * q^6 - 10 * q^7 + 6 * q^8 + 10 * q^9 + 2 * q^10 - q^11 + 16 * q^12 - 2 * q^13 - 2 * q^14 + 10 * q^15 + 36 * q^16 + 8 * q^17 + 2 * q^18 + 11 * q^19 + 16 * q^20 - 10 * q^21 + 10 * q^23 + 6 * q^24 + 10 * q^25 + 15 * q^26 + 10 * q^27 - 16 * q^28 + 6 * q^29 + 2 * q^30 + 16 * q^31 - q^32 - q^33 + 21 * q^34 - 10 * q^35 + 16 * q^36 - 6 * q^38 - 2 * q^39 + 6 * q^40 + 23 * q^41 - 2 * q^42 + 4 * q^43 - q^44 + 10 * q^45 + 2 * q^46 + 21 * q^47 + 36 * q^48 + 10 * q^49 + 2 * q^50 + 8 * q^51 + 10 * q^52 - q^53 + 2 * q^54 - q^55 - 6 * q^56 + 11 * q^57 + 8 * q^58 + 15 * q^59 + 16 * q^60 + 29 * q^61 + 12 * q^62 - 10 * q^63 + 80 * q^64 - 2 * q^65 + 32 * q^67 - 28 * q^68 + 10 * q^69 - 2 * q^70 - 4 * q^71 + 6 * q^72 + 18 * q^73 - 49 * q^74 + 10 * q^75 + 49 * q^76 + q^77 + 15 * q^78 + 8 * q^79 + 36 * q^80 + 10 * q^81 + 6 * q^82 + 2 * q^83 - 16 * q^84 + 8 * q^85 - 14 * q^86 + 6 * q^87 - 69 * q^88 + 6 * q^89 + 2 * q^90 + 2 * q^91 + 16 * q^92 + 16 * q^93 - 2 * q^94 + 11 * q^95 - q^96 - 2 * q^97 + 2 * q^98 - q^99

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