LMFDB - Embedded newform 6045.2.a.w.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 15 x^{9} + 29 x^{8} + 81 x^{7} - 151 x^{6} - 192 x^{5} + 345 x^{4} + 199 x^{3} + \cdots + 118 $ x^11 - 2x^10 - 15x^9 + 29x^8 + 81x^7 - 151x^6 - 192x^5 + 345x^4 + 199x^3 - 344x^2 - 70x + 118
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.65932$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.65932 q^{2} -1.00000 q^{3} +0.753351 q^{4} -1.00000 q^{5} -1.65932 q^{6} -0.633348 q^{7} -2.06859 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.65932 q^{2} -1.00000 q^{3} +0.753351 q^{4} -1.00000 q^{5} -1.65932 q^{6} -0.633348 q^{7} -2.06859 q^{8} +1.00000 q^{9} -1.65932 q^{10} +2.37237 q^{11} -0.753351 q^{12} -1.00000 q^{13} -1.05093 q^{14} +1.00000 q^{15} -4.93916 q^{16} -0.303780 q^{17} +1.65932 q^{18} +0.492015 q^{19} -0.753351 q^{20} +0.633348 q^{21} +3.93653 q^{22} +8.17027 q^{23} +2.06859 q^{24} +1.00000 q^{25} -1.65932 q^{26} -1.00000 q^{27} -0.477134 q^{28} +0.889763 q^{29} +1.65932 q^{30} -1.00000 q^{31} -4.05848 q^{32} -2.37237 q^{33} -0.504069 q^{34} +0.633348 q^{35} +0.753351 q^{36} -1.86370 q^{37} +0.816412 q^{38} +1.00000 q^{39} +2.06859 q^{40} -2.92585 q^{41} +1.05093 q^{42} +5.91830 q^{43} +1.78723 q^{44} -1.00000 q^{45} +13.5571 q^{46} -1.52652 q^{47} +4.93916 q^{48} -6.59887 q^{49} +1.65932 q^{50} +0.303780 q^{51} -0.753351 q^{52} -7.63719 q^{53} -1.65932 q^{54} -2.37237 q^{55} +1.31014 q^{56} -0.492015 q^{57} +1.47640 q^{58} -9.55789 q^{59} +0.753351 q^{60} -5.23955 q^{61} -1.65932 q^{62} -0.633348 q^{63} +3.14400 q^{64} +1.00000 q^{65} -3.93653 q^{66} +5.70782 q^{67} -0.228853 q^{68} -8.17027 q^{69} +1.05093 q^{70} +10.5764 q^{71} -2.06859 q^{72} -7.76362 q^{73} -3.09248 q^{74} -1.00000 q^{75} +0.370660 q^{76} -1.50254 q^{77} +1.65932 q^{78} +15.9956 q^{79} +4.93916 q^{80} +1.00000 q^{81} -4.85494 q^{82} -14.0090 q^{83} +0.477134 q^{84} +0.303780 q^{85} +9.82037 q^{86} -0.889763 q^{87} -4.90747 q^{88} -11.4226 q^{89} -1.65932 q^{90} +0.633348 q^{91} +6.15508 q^{92} +1.00000 q^{93} -2.53298 q^{94} -0.492015 q^{95} +4.05848 q^{96} +5.02137 q^{97} -10.9497 q^{98} +2.37237 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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 $

$2$	1.65932	1.17332	0.586659	−	0.809834i	$-0.300443\pi$
$2$	1.65932	1.17332	0.586659	+	0.809834i	$0.300443\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.753351	0.376676
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.65932	−0.677416
$7$	−0.633348	−0.239383	−0.119692	−	0.992811i	$-0.538191\pi$
$7$	−0.633348	−0.239383	−0.119692	+	0.992811i	$0.538191\pi$
$8$	−2.06859	−0.731358
$9$	1.00000	0.333333
$10$	−1.65932	−0.524724
$11$	2.37237	0.715297	0.357649	−	0.933856i	$-0.383579\pi$
$11$	2.37237	0.715297	0.357649	+	0.933856i	$0.383579\pi$
$12$	−0.753351	−0.217474
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.05093	−0.280873
$15$	1.00000	0.258199
$16$	−4.93916	−1.23479
$17$	−0.303780	−0.0736775	−0.0368388	−	0.999321i	$-0.511729\pi$
$17$	−0.303780	−0.0736775	−0.0368388	+	0.999321i	$0.511729\pi$
$18$	1.65932	0.391106
$19$	0.492015	0.112876	0.0564380	−	0.998406i	$-0.482026\pi$
$19$	0.492015	0.112876	0.0564380	+	0.998406i	$0.482026\pi$
$20$	−0.753351	−0.168454
$21$	0.633348	0.138208
$22$	3.93653	0.839271
$23$	8.17027	1.70362	0.851809	−	0.523852i	$-0.175505\pi$
$23$	8.17027	1.70362	0.851809	+	0.523852i	$0.175505\pi$
$24$	2.06859	0.422250
$25$	1.00000	0.200000
$26$	−1.65932	−0.325420
$27$	−1.00000	−0.192450
$28$	−0.477134	−0.0901698
$29$	0.889763	0.165225	0.0826124	−	0.996582i	$-0.473674\pi$
$29$	0.889763	0.165225	0.0826124	+	0.996582i	$0.473674\pi$
$30$	1.65932	0.302949
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.05848	−0.717445
$33$	−2.37237	−0.412977
$34$	−0.504069	−0.0864472
$35$	0.633348	0.107055
$36$	0.753351	0.125559
$37$	−1.86370	−0.306391	−0.153195	−	0.988196i	$-0.548956\pi$
$37$	−1.86370	−0.306391	−0.153195	+	0.988196i	$0.548956\pi$
$38$	0.816412	0.132439
$39$	1.00000	0.160128
$40$	2.06859	0.327073
$41$	−2.92585	−0.456942	−0.228471	−	0.973551i	$-0.573373\pi$
$41$	−2.92585	−0.456942	−0.228471	+	0.973551i	$0.573373\pi$
$42$	1.05093	0.162162
$43$	5.91830	0.902532	0.451266	−	0.892389i	$-0.350972\pi$
$43$	5.91830	0.902532	0.451266	+	0.892389i	$0.350972\pi$
$44$	1.78723	0.269435
$45$	−1.00000	−0.149071
$46$	13.5571	1.99889
$47$	−1.52652	−0.222665	−0.111333	−	0.993783i	$-0.535512\pi$
$47$	−1.52652	−0.222665	−0.111333	+	0.993783i	$0.535512\pi$
$48$	4.93916	0.712907
$49$	−6.59887	−0.942696
$50$	1.65932	0.234664
$51$	0.303780	0.0425377
$52$	−0.753351	−0.104471
$53$	−7.63719	−1.04905	−0.524525	−	0.851395i	$-0.675757\pi$
$53$	−7.63719	−1.04905	−0.524525	+	0.851395i	$0.675757\pi$
$54$	−1.65932	−0.225805
$55$	−2.37237	−0.319891
$56$	1.31014	0.175075
$57$	−0.492015	−0.0651690
$58$	1.47640	0.193861
$59$	−9.55789	−1.24433	−0.622165	−	0.782886i	$-0.713747\pi$
$59$	−9.55789	−1.24433	−0.622165	+	0.782886i	$0.713747\pi$
$60$	0.753351	0.0972572
$61$	−5.23955	−0.670856	−0.335428	−	0.942066i	$-0.608881\pi$
$61$	−5.23955	−0.670856	−0.335428	+	0.942066i	$0.608881\pi$
$62$	−1.65932	−0.210734
$63$	−0.633348	−0.0797944
$64$	3.14400	0.393000
$65$	1.00000	0.124035
$66$	−3.93653	−0.484554
$67$	5.70782	0.697322	0.348661	−	0.937249i	$-0.386637\pi$
$67$	5.70782	0.697322	0.348661	+	0.937249i	$0.386637\pi$
$68$	−0.228853	−0.0277525
$69$	−8.17027	−0.983585
$70$	1.05093	0.125610
$71$	10.5764	1.25519	0.627594	−	0.778541i	$-0.284040\pi$
$71$	10.5764	1.25519	0.627594	+	0.778541i	$0.284040\pi$
$72$	−2.06859	−0.243786
$73$	−7.76362	−0.908663	−0.454332	−	0.890833i	$-0.650122\pi$
$73$	−7.76362	−0.908663	−0.454332	+	0.890833i	$0.650122\pi$
$74$	−3.09248	−0.359494
$75$	−1.00000	−0.115470
$76$	0.370660	0.0425176
$77$	−1.50254	−0.171230
$78$	1.65932	0.187881
$79$	15.9956	1.79965	0.899824	−	0.436254i	$-0.143695\pi$
$79$	15.9956	1.79965	0.899824	+	0.436254i	$0.143695\pi$
$80$	4.93916	0.552215
$81$	1.00000	0.111111
$82$	−4.85494	−0.536138
$83$	−14.0090	−1.53769	−0.768843	−	0.639438i	$-0.779167\pi$
$83$	−14.0090	−1.53769	−0.768843	+	0.639438i	$0.779167\pi$
$84$	0.477134	0.0520595
$85$	0.303780	0.0329496
$86$	9.82037	1.05896
$87$	−0.889763	−0.0953926
$88$	−4.90747	−0.523138
$89$	−11.4226	−1.21079	−0.605395	−	0.795925i	$-0.706985\pi$
$89$	−11.4226	−1.21079	−0.605395	+	0.795925i	$0.706985\pi$
$90$	−1.65932	−0.174908
$91$	0.633348	0.0663929
$92$	6.15508	0.641712
$93$	1.00000	0.103695
$94$	−2.53298	−0.261257
$95$	−0.492015	−0.0504797
$96$	4.05848	0.414217
$97$	5.02137	0.509843	0.254922	−	0.966962i	$-0.417950\pi$
$97$	5.02137	0.509843	0.254922	+	0.966962i	$0.417950\pi$
$98$	−10.9497	−1.10608
$99$	2.37237	0.238432
$100$	0.753351	0.0753351
$101$	−12.1094	−1.20493	−0.602464	−	0.798146i	$-0.705814\pi$
$101$	−12.1094	−1.20493	−0.602464	+	0.798146i	$0.705814\pi$
$102$	0.504069	0.0499103
$103$	−3.96372	−0.390557	−0.195279	−	0.980748i	$-0.562561\pi$
$103$	−3.96372	−0.390557	−0.195279	+	0.980748i	$0.562561\pi$
$104$	2.06859	0.202842
$105$	−0.633348	−0.0618085
$106$	−12.6726	−1.23087
$107$	4.37197	0.422654	0.211327	−	0.977415i	$-0.432221\pi$
$107$	4.37197	0.422654	0.211327	+	0.977415i	$0.432221\pi$
$108$	−0.753351	−0.0724913
$109$	−7.59144	−0.727128	−0.363564	−	0.931569i	$-0.618440\pi$
$109$	−7.59144	−0.727128	−0.363564	+	0.931569i	$0.618440\pi$
$110$	−3.93653	−0.375334
$111$	1.86370	0.176895
$112$	3.12821	0.295588
$113$	−16.9512	−1.59464	−0.797320	−	0.603557i	$-0.793749\pi$
$113$	−16.9512	−1.59464	−0.797320	+	0.603557i	$0.793749\pi$
$114$	−0.816412	−0.0764640
$115$	−8.17027	−0.761882
$116$	0.670304	0.0622362
$117$	−1.00000	−0.0924500
$118$	−15.8596	−1.46000
$119$	0.192399	0.0176372
$120$	−2.06859	−0.188836
$121$	−5.37185	−0.488350
$122$	−8.69411	−0.787127
$123$	2.92585	0.263815
$124$	−0.753351	−0.0676529
$125$	−1.00000	−0.0894427
$126$	−1.05093	−0.0936242
$127$	−13.6814	−1.21403	−0.607013	−	0.794692i	$-0.707632\pi$
$127$	−13.6814	−1.21403	−0.607013	+	0.794692i	$0.707632\pi$
$128$	13.3339	1.17856
$129$	−5.91830	−0.521077
$130$	1.65932	0.145532
$131$	−13.6411	−1.19183	−0.595916	−	0.803047i	$-0.703211\pi$
$131$	−13.6411	−1.19183	−0.595916	+	0.803047i	$0.703211\pi$
$132$	−1.78723	−0.155558
$133$	−0.311617	−0.0270206
$134$	9.47112	0.818180
$135$	1.00000	0.0860663
$136$	0.628397	0.0538846
$137$	12.9693	1.10804	0.554022	−	0.832502i	$-0.313092\pi$
$137$	12.9693	1.10804	0.554022	+	0.832502i	$0.313092\pi$
$138$	−13.5571	−1.15406
$139$	12.9373	1.09733	0.548664	−	0.836043i	$-0.315137\pi$
$139$	12.9373	1.09733	0.548664	+	0.836043i	$0.315137\pi$
$140$	0.477134	0.0403252
$141$	1.52652	0.128556
$142$	17.5497	1.47273
$143$	−2.37237	−0.198388
$144$	−4.93916	−0.411597
$145$	−0.889763	−0.0738908
$146$	−12.8824	−1.06615
$147$	6.59887	0.544266
$148$	−1.40402	−0.115410
$149$	−5.75744	−0.471668	−0.235834	−	0.971793i	$-0.575782\pi$
$149$	−5.75744	−0.471668	−0.235834	+	0.971793i	$0.575782\pi$
$150$	−1.65932	−0.135483
$151$	−14.3830	−1.17047	−0.585237	−	0.810862i	$-0.698999\pi$
$151$	−14.3830	−1.17047	−0.585237	+	0.810862i	$0.698999\pi$
$152$	−1.01778	−0.0825528
$153$	−0.303780	−0.0245592
$154$	−2.49320	−0.200907
$155$	1.00000	0.0803219
$156$	0.753351	0.0603164
$157$	−14.4101	−1.15005	−0.575025	−	0.818136i	$-0.695008\pi$
$157$	−14.4101	−1.15005	−0.575025	+	0.818136i	$0.695008\pi$
$158$	26.5419	2.11156
$159$	7.63719	0.605669
$160$	4.05848	0.320851
$161$	−5.17463	−0.407818
$162$	1.65932	0.130369
$163$	−3.88613	−0.304385	−0.152193	−	0.988351i	$-0.548633\pi$
$163$	−3.88613	−0.304385	−0.152193	+	0.988351i	$0.548633\pi$
$164$	−2.20420	−0.172119
$165$	2.37237	0.184689
$166$	−23.2454	−1.80419
$167$	−7.02275	−0.543437	−0.271718	−	0.962377i	$-0.587592\pi$
$167$	−7.02275	−0.543437	−0.271718	+	0.962377i	$0.587592\pi$
$168$	−1.31014	−0.101079
$169$	1.00000	0.0769231
$170$	0.504069	0.0386603
$171$	0.492015	0.0376253
$172$	4.45856	0.339962
$173$	−10.8354	−0.823799	−0.411899	−	0.911229i	$-0.635134\pi$
$173$	−10.8354	−0.823799	−0.411899	+	0.911229i	$0.635134\pi$
$174$	−1.47640	−0.111926
$175$	−0.633348	−0.0478766
$176$	−11.7175	−0.883243
$177$	9.55789	0.718415
$178$	−18.9537	−1.42064
$179$	−1.86535	−0.139423	−0.0697115	−	0.997567i	$-0.522208\pi$
$179$	−1.86535	−0.139423	−0.0697115	+	0.997567i	$0.522208\pi$
$180$	−0.753351	−0.0561515
$181$	16.2684	1.20922	0.604610	−	0.796522i	$-0.293329\pi$
$181$	16.2684	1.20922	0.604610	+	0.796522i	$0.293329\pi$
$182$	1.05093	0.0779000
$183$	5.23955	0.387319
$184$	−16.9010	−1.24596
$185$	1.86370	0.137022
$186$	1.65932	0.121667
$187$	−0.720680	−0.0527013
$188$	−1.15000	−0.0838726
$189$	0.633348	0.0460693
$190$	−0.816412	−0.0592287
$191$	−22.3096	−1.61426	−0.807132	−	0.590371i	$-0.798982\pi$
$191$	−22.3096	−1.61426	−0.807132	+	0.590371i	$0.798982\pi$
$192$	−3.14400	−0.226899
$193$	5.88842	0.423858	0.211929	−	0.977285i	$-0.432025\pi$
$193$	5.88842	0.423858	0.211929	+	0.977285i	$0.432025\pi$
$194$	8.33208	0.598208
$195$	−1.00000	−0.0716115
$196$	−4.97127	−0.355090
$197$	9.37271	0.667778	0.333889	−	0.942612i	$-0.391639\pi$
$197$	9.37271	0.667778	0.333889	+	0.942612i	$0.391639\pi$
$198$	3.93653	0.279757
$199$	−12.8883	−0.913629	−0.456814	−	0.889562i	$-0.651010\pi$
$199$	−12.8883	−0.913629	−0.456814	+	0.889562i	$0.651010\pi$
$200$	−2.06859	−0.146272
$201$	−5.70782	−0.402599
$202$	−20.0933	−1.41376
$203$	−0.563530	−0.0395520
$204$	0.228853	0.0160229
$205$	2.92585	0.204351
$206$	−6.57709	−0.458248
$207$	8.17027	0.567873
$208$	4.93916	0.342469
$209$	1.16724	0.0807399
$210$	−1.05093	−0.0725210
$211$	−25.5114	−1.75628	−0.878139	−	0.478406i	$-0.841215\pi$
$211$	−25.5114	−1.75628	−0.878139	+	0.478406i	$0.841215\pi$
$212$	−5.75349	−0.395151
$213$	−10.5764	−0.724683
$214$	7.25451	0.495908
$215$	−5.91830	−0.403625
$216$	2.06859	0.140750
$217$	0.633348	0.0429945
$218$	−12.5966	−0.853153
$219$	7.76362	0.524617
$220$	−1.78723	−0.120495
$221$	0.303780	0.0204345
$222$	3.09248	0.207554
$223$	15.2117	1.01865	0.509326	−	0.860574i	$-0.329895\pi$
$223$	15.2117	1.01865	0.509326	+	0.860574i	$0.329895\pi$
$224$	2.57043	0.171744
$225$	1.00000	0.0666667
$226$	−28.1276	−1.87102
$227$	8.78179	0.582868	0.291434	−	0.956591i	$-0.405868\pi$
$227$	8.78179	0.582868	0.291434	+	0.956591i	$0.405868\pi$
$228$	−0.370660	−0.0245476
$229$	−10.5164	−0.694944	−0.347472	−	0.937690i	$-0.612960\pi$
$229$	−10.5164	−0.694944	−0.347472	+	0.937690i	$0.612960\pi$
$230$	−13.5571	−0.893930
$231$	1.50254	0.0988597
$232$	−1.84056	−0.120838
$233$	1.48009	0.0969639	0.0484819	−	0.998824i	$-0.484562\pi$
$233$	1.48009	0.0969639	0.0484819	+	0.998824i	$0.484562\pi$
$234$	−1.65932	−0.108473
$235$	1.52652	0.0995789
$236$	−7.20045	−0.468709
$237$	−15.9956	−1.03903
$238$	0.319251	0.0206940
$239$	18.1131	1.17164	0.585820	−	0.810441i	$-0.300773\pi$
$239$	18.1131	1.17164	0.585820	+	0.810441i	$0.300773\pi$
$240$	−4.93916	−0.318822
$241$	−3.35958	−0.216410	−0.108205	−	0.994129i	$-0.534510\pi$
$241$	−3.35958	−0.216410	−0.108205	+	0.994129i	$0.534510\pi$
$242$	−8.91363	−0.572990
$243$	−1.00000	−0.0641500
$244$	−3.94722	−0.252695
$245$	6.59887	0.421586
$246$	4.85494	0.309539
$247$	−0.492015	−0.0313062
$248$	2.06859	0.131356
$249$	14.0090	0.887783
$250$	−1.65932	−0.104945
$251$	11.4054	0.719901	0.359951	−	0.932971i	$-0.382794\pi$
$251$	11.4054	0.719901	0.359951	+	0.932971i	$0.382794\pi$
$252$	−0.477134	−0.0300566
$253$	19.3829	1.21859
$254$	−22.7018	−1.42444
$255$	−0.303780	−0.0190235
$256$	15.8372	0.989825
$257$	12.6063	0.786362	0.393181	−	0.919461i	$-0.371375\pi$
$257$	12.6063	0.786362	0.393181	+	0.919461i	$0.371375\pi$
$258$	−9.82037	−0.611390
$259$	1.18037	0.0733448
$260$	0.753351	0.0467209
$261$	0.889763	0.0550749
$262$	−22.6351	−1.39840
$263$	−16.6775	−1.02838	−0.514190	−	0.857676i	$-0.671907\pi$
$263$	−16.6775	−1.02838	−0.514190	+	0.857676i	$0.671907\pi$
$264$	4.90747	0.302034
$265$	7.63719	0.469149
$266$	−0.517073	−0.0317038
$267$	11.4226	0.699050
$268$	4.30000	0.262664
$269$	28.0235	1.70863	0.854313	−	0.519759i	$-0.173978\pi$
$269$	28.0235	1.70863	0.854313	+	0.519759i	$0.173978\pi$
$270$	1.65932	0.100983
$271$	−2.38896	−0.145119	−0.0725596	−	0.997364i	$-0.523117\pi$
$271$	−2.38896	−0.145119	−0.0725596	+	0.997364i	$0.523117\pi$
$272$	1.50042	0.0909763
$273$	−0.633348	−0.0383320
$274$	21.5203	1.30009
$275$	2.37237	0.143059
$276$	−6.15508	−0.370492
$277$	9.75423	0.586075	0.293037	−	0.956101i	$-0.405334\pi$
$277$	9.75423	0.586075	0.293037	+	0.956101i	$0.405334\pi$
$278$	21.4672	1.28751
$279$	−1.00000	−0.0598684
$280$	−1.31014	−0.0782958
$281$	20.3335	1.21299	0.606497	−	0.795086i	$-0.292574\pi$
$281$	20.3335	1.21299	0.606497	+	0.795086i	$0.292574\pi$
$282$	2.53298	0.150837
$283$	−25.5799	−1.52057	−0.760284	−	0.649590i	$-0.774940\pi$
$283$	−25.5799	−1.52057	−0.760284	+	0.649590i	$0.774940\pi$
$284$	7.96774	0.472799
$285$	0.492015	0.0291445
$286$	−3.93653	−0.232772
$287$	1.85309	0.109384
$288$	−4.05848	−0.239148
$289$	−16.9077	−0.994572
$290$	−1.47640	−0.0866974
$291$	−5.02137	−0.294358
$292$	−5.84873	−0.342271
$293$	13.3441	0.779573	0.389786	−	0.920905i	$-0.372549\pi$
$293$	13.3441	0.779573	0.389786	+	0.920905i	$0.372549\pi$
$294$	10.9497	0.638597
$295$	9.55789	0.556482
$296$	3.85524	0.224081
$297$	−2.37237	−0.137659
$298$	−9.55345	−0.553416
$299$	−8.17027	−0.472499
$300$	−0.753351	−0.0434948
$301$	−3.74835	−0.216051
$302$	−23.8661	−1.37334
$303$	12.1094	0.695665
$304$	−2.43014	−0.139378
$305$	5.23955	0.300016
$306$	−0.504069	−0.0288157
$307$	4.84234	0.276367	0.138184	−	0.990407i	$-0.455874\pi$
$307$	4.84234	0.276367	0.138184	+	0.990407i	$0.455874\pi$
$308$	−1.13194	−0.0644982
$309$	3.96372	0.225488
$310$	1.65932	0.0942432
$311$	−24.2720	−1.37634	−0.688168	−	0.725551i	$-0.741585\pi$
$311$	−24.2720	−1.37634	−0.688168	+	0.725551i	$0.741585\pi$
$312$	−2.06859	−0.117111
$313$	4.31190	0.243723	0.121862	−	0.992547i	$-0.461114\pi$
$313$	4.31190	0.243723	0.121862	+	0.992547i	$0.461114\pi$
$314$	−23.9110	−1.34937
$315$	0.633348	0.0356851
$316$	12.0503	0.677883
$317$	−7.76955	−0.436382	−0.218191	−	0.975906i	$-0.570015\pi$
$317$	−7.76955	−0.436382	−0.218191	+	0.975906i	$0.570015\pi$
$318$	12.6726	0.710642
$319$	2.11085	0.118185
$320$	−3.14400	−0.175755
$321$	−4.37197	−0.244020
$322$	−8.58637	−0.478500
$323$	−0.149464	−0.00831643
$324$	0.753351	0.0418528
$325$	−1.00000	−0.0554700
$326$	−6.44834	−0.357141
$327$	7.59144	0.419808
$328$	6.05240	0.334188
$329$	0.966816	0.0533023
$330$	3.93653	0.216699
$331$	−19.7323	−1.08458	−0.542291	−	0.840191i	$-0.682443\pi$
$331$	−19.7323	−1.08458	−0.542291	+	0.840191i	$0.682443\pi$
$332$	−10.5537	−0.579209
$333$	−1.86370	−0.102130
$334$	−11.6530	−0.637624
$335$	−5.70782	−0.311852
$336$	−3.12821	−0.170658
$337$	21.7137	1.18282	0.591409	−	0.806371i	$-0.298572\pi$
$337$	21.7137	1.18282	0.591409	+	0.806371i	$0.298572\pi$
$338$	1.65932	0.0902552
$339$	16.9512	0.920665
$340$	0.228853	0.0124113
$341$	−2.37237	−0.128471
$342$	0.816412	0.0441465
$343$	8.61282	0.465049
$344$	−12.2426	−0.660074
$345$	8.17027	0.439873
$346$	−17.9794	−0.966578
$347$	−3.77458	−0.202630	−0.101315	−	0.994854i	$-0.532305\pi$
$347$	−3.77458	−0.202630	−0.101315	+	0.994854i	$0.532305\pi$
$348$	−0.670304	−0.0359321
$349$	−33.0775	−1.77060	−0.885298	−	0.465023i	$-0.846046\pi$
$349$	−33.0775	−1.77060	−0.885298	+	0.465023i	$0.846046\pi$
$350$	−1.05093	−0.0561745
$351$	1.00000	0.0533761
$352$	−9.62823	−0.513186
$353$	18.3281	0.975506	0.487753	−	0.872982i	$-0.337817\pi$
$353$	18.3281	0.975506	0.487753	+	0.872982i	$0.337817\pi$
$354$	15.8596	0.842929
$355$	−10.5764	−0.561337
$356$	−8.60520	−0.456075
$357$	−0.192399	−0.0101828
$358$	−3.09522	−0.163588
$359$	−1.41740	−0.0748075	−0.0374038	−	0.999300i	$-0.511909\pi$
$359$	−1.41740	−0.0748075	−0.0374038	+	0.999300i	$0.511909\pi$
$360$	2.06859	0.109024
$361$	−18.7579	−0.987259
$362$	26.9945	1.41880
$363$	5.37185	0.281949
$364$	0.477134	0.0250086
$365$	7.76362	0.406367
$366$	8.69411	0.454448
$367$	22.1553	1.15650	0.578249	−	0.815861i	$-0.303736\pi$
$367$	22.1553	1.15650	0.578249	+	0.815861i	$0.303736\pi$
$368$	−40.3543	−2.10361
$369$	−2.92585	−0.152314
$370$	3.09248	0.160771
$371$	4.83700	0.251125
$372$	0.753351	0.0390594
$373$	−18.6522	−0.965773	−0.482886	−	0.875683i	$-0.660412\pi$
$373$	−18.6522	−0.965773	−0.482886	+	0.875683i	$0.660412\pi$
$374$	−1.19584	−0.0618354
$375$	1.00000	0.0516398
$376$	3.15774	0.162848
$377$	−0.889763	−0.0458251
$378$	1.05093	0.0540540
$379$	−3.18739	−0.163725	−0.0818625	−	0.996644i	$-0.526087\pi$
$379$	−3.18739	−0.163725	−0.0818625	+	0.996644i	$0.526087\pi$
$380$	−0.370660	−0.0190145
$381$	13.6814	0.700918
$382$	−37.0188	−1.89405
$383$	−17.0908	−0.873301	−0.436651	−	0.899631i	$-0.643835\pi$
$383$	−17.0908	−0.873301	−0.436651	+	0.899631i	$0.643835\pi$
$384$	−13.3339	−0.680441
$385$	1.50254	0.0765764
$386$	9.77079	0.497320
$387$	5.91830	0.300844
$388$	3.78286	0.192046
$389$	−20.2872	−1.02860	−0.514302	−	0.857609i	$-0.671949\pi$
$389$	−20.2872	−1.02860	−0.514302	+	0.857609i	$0.671949\pi$
$390$	−1.65932	−0.0840231
$391$	−2.48197	−0.125518
$392$	13.6504	0.689448
$393$	13.6411	0.688105
$394$	15.5523	0.783516
$395$	−15.9956	−0.804827
$396$	1.78723	0.0898117
$397$	11.9169	0.598094	0.299047	−	0.954238i	$-0.403331\pi$
$397$	11.9169	0.598094	0.299047	+	0.954238i	$0.403331\pi$
$398$	−21.3859	−1.07198
$399$	0.311617	0.0156004
$400$	−4.93916	−0.246958
$401$	−35.0389	−1.74976	−0.874880	−	0.484340i	$-0.839060\pi$
$401$	−35.0389	−1.74976	−0.874880	+	0.484340i	$0.839060\pi$
$402$	−9.47112	−0.472377
$403$	1.00000	0.0498135
$404$	−9.12261	−0.453867
$405$	−1.00000	−0.0496904
$406$	−0.935078	−0.0464071
$407$	−4.42140	−0.219160
$408$	−0.628397	−0.0311103
$409$	18.5345	0.916472	0.458236	−	0.888830i	$-0.348481\pi$
$409$	18.5345	0.916472	0.458236	+	0.888830i	$0.348481\pi$
$410$	4.85494	0.239768
$411$	−12.9693	−0.639730
$412$	−2.98607	−0.147113
$413$	6.05347	0.297872
$414$	13.5571	0.666296
$415$	14.0090	0.687674
$416$	4.05848	0.198983
$417$	−12.9373	−0.633543
$418$	1.93683	0.0947336
$419$	20.6274	1.00772	0.503858	−	0.863787i	$-0.331913\pi$
$419$	20.6274	1.00772	0.503858	+	0.863787i	$0.331913\pi$
$420$	−0.477134	−0.0232817
$421$	−30.7434	−1.49834	−0.749172	−	0.662376i	$-0.769548\pi$
$421$	−30.7434	−1.49834	−0.749172	+	0.662376i	$0.769548\pi$
$422$	−42.3317	−2.06067
$423$	−1.52652	−0.0742218
$424$	15.7982	0.767230
$425$	−0.303780	−0.0147355
$426$	−17.5497	−0.850284
$427$	3.31846	0.160592
$428$	3.29363	0.159204
$429$	2.37237	0.114539
$430$	−9.82037	−0.473580
$431$	15.5154	0.747350	0.373675	−	0.927560i	$-0.378098\pi$
$431$	15.5154	0.747350	0.373675	+	0.927560i	$0.378098\pi$
$432$	4.93916	0.237636
$433$	−28.2326	−1.35677	−0.678387	−	0.734705i	$-0.737320\pi$
$433$	−28.2326	−1.35677	−0.678387	+	0.734705i	$0.737320\pi$
$434$	1.05093	0.0504462
$435$	0.889763	0.0426609
$436$	−5.71902	−0.273891
$437$	4.01990	0.192298
$438$	12.8824	0.615543
$439$	−27.3737	−1.30647	−0.653237	−	0.757153i	$-0.726589\pi$
$439$	−27.3737	−1.30647	−0.653237	+	0.757153i	$0.726589\pi$
$440$	4.90747	0.233955
$441$	−6.59887	−0.314232
$442$	0.504069	0.0239761
$443$	0.994668	0.0472581	0.0236291	−	0.999721i	$-0.492478\pi$
$443$	0.994668	0.0472581	0.0236291	+	0.999721i	$0.492478\pi$
$444$	1.40402	0.0666320
$445$	11.4226	0.541482
$446$	25.2411	1.19520
$447$	5.75744	0.272317
$448$	−1.99125	−0.0940775
$449$	11.8799	0.560648	0.280324	−	0.959905i	$-0.409558\pi$
$449$	11.8799	0.560648	0.280324	+	0.959905i	$0.409558\pi$
$450$	1.65932	0.0782212
$451$	−6.94122	−0.326849
$452$	−12.7702	−0.600662
$453$	14.3830	0.675774
$454$	14.5718	0.683889
$455$	−0.633348	−0.0296918
$456$	1.01778	0.0476619
$457$	27.9831	1.30900	0.654498	−	0.756064i	$-0.272880\pi$
$457$	27.9831	1.30900	0.654498	+	0.756064i	$0.272880\pi$
$458$	−17.4501	−0.815391
$459$	0.303780	0.0141792
$460$	−6.15508	−0.286982
$461$	−39.8872	−1.85773	−0.928865	−	0.370418i	$-0.879214\pi$
$461$	−39.8872	−1.85773	−0.928865	+	0.370418i	$0.879214\pi$
$462$	2.49320	0.115994
$463$	−25.3912	−1.18003	−0.590015	−	0.807392i	$-0.700878\pi$
$463$	−25.3912	−1.18003	−0.590015	+	0.807392i	$0.700878\pi$
$464$	−4.39469	−0.204018
$465$	−1.00000	−0.0463739
$466$	2.45595	0.113769
$467$	4.27172	0.197671	0.0988357	−	0.995104i	$-0.468488\pi$
$467$	4.27172	0.197671	0.0988357	+	0.995104i	$0.468488\pi$
$468$	−0.753351	−0.0348237
$469$	−3.61504	−0.166927
$470$	2.53298	0.116838
$471$	14.4101	0.663981
$472$	19.7714	0.910051
$473$	14.0404	0.645579
$474$	−26.5419	−1.21911
$475$	0.492015	0.0225752
$476$	0.144944	0.00664349
$477$	−7.63719	−0.349683
$478$	30.0555	1.37471
$479$	5.98418	0.273424	0.136712	−	0.990611i	$-0.456347\pi$
$479$	5.98418	0.273424	0.136712	+	0.990611i	$0.456347\pi$
$480$	−4.05848	−0.185243
$481$	1.86370	0.0849775
$482$	−5.57463	−0.253918
$483$	5.17463	0.235454
$484$	−4.04689	−0.183949
$485$	−5.02137	−0.228009
$486$	−1.65932	−0.0752684
$487$	0.383880	0.0173953	0.00869763	−	0.999962i	$-0.497231\pi$
$487$	0.383880	0.0173953	0.00869763	+	0.999962i	$0.497231\pi$
$488$	10.8385	0.490636
$489$	3.88613	0.175737
$490$	10.9497	0.494655
$491$	7.60888	0.343384	0.171692	−	0.985151i	$-0.445077\pi$
$491$	7.60888	0.343384	0.171692	+	0.985151i	$0.445077\pi$
$492$	2.20420	0.0993728
$493$	−0.270292	−0.0121734
$494$	−0.816412	−0.0367321
$495$	−2.37237	−0.106630
$496$	4.93916	0.221775
$497$	−6.69854	−0.300471
$498$	23.2454	1.04165
$499$	7.55487	0.338202	0.169101	−	0.985599i	$-0.445914\pi$
$499$	7.55487	0.338202	0.169101	+	0.985599i	$0.445914\pi$
$500$	−0.753351	−0.0336909
$501$	7.02275	0.313753
$502$	18.9252	0.844673
$503$	19.4090	0.865406	0.432703	−	0.901536i	$-0.357560\pi$
$503$	19.4090	0.865406	0.432703	+	0.901536i	$0.357560\pi$
$504$	1.31014	0.0583582
$505$	12.1094	0.538860
$506$	32.1625	1.42980
$507$	−1.00000	−0.0444116
$508$	−10.3069	−0.457294
$509$	6.53484	0.289652	0.144826	−	0.989457i	$-0.453738\pi$
$509$	6.53484	0.289652	0.144826	+	0.989457i	$0.453738\pi$
$510$	−0.504069	−0.0223206
$511$	4.91708	0.217519
$512$	−0.388728	−0.0171795
$513$	−0.492015	−0.0217230
$514$	20.9180	0.922653
$515$	3.96372	0.174662
$516$	−4.45856	−0.196277
$517$	−3.62147	−0.159272
$518$	1.95862	0.0860568
$519$	10.8354	0.475620
$520$	−2.06859	−0.0907138
$521$	28.7238	1.25841	0.629207	−	0.777238i	$-0.283380\pi$
$521$	28.7238	1.25841	0.629207	+	0.777238i	$0.283380\pi$
$522$	1.47640	0.0646204
$523$	−38.9530	−1.70329	−0.851647	−	0.524115i	$-0.824396\pi$
$523$	−38.9530	−1.70329	−0.851647	+	0.524115i	$0.824396\pi$
$524$	−10.2766	−0.448934
$525$	0.633348	0.0276416
$526$	−27.6734	−1.20662
$527$	0.303780	0.0132329
$528$	11.7175	0.509940
$529$	43.7533	1.90232
$530$	12.6726	0.550461
$531$	−9.55789	−0.414777
$532$	−0.234757	−0.0101780
$533$	2.92585	0.126733
$534$	18.9537	0.820208
$535$	−4.37197	−0.189017
$536$	−11.8072	−0.509992
$537$	1.86535	0.0804959
$538$	46.5001	2.00476
$539$	−15.6550	−0.674308
$540$	0.753351	0.0324191
$541$	44.9979	1.93461	0.967306	−	0.253613i	$-0.0816188\pi$
$541$	44.9979	1.93461	0.967306	+	0.253613i	$0.0816188\pi$
$542$	−3.96406	−0.170271
$543$	−16.2684	−0.698143
$544$	1.23289	0.0528596
$545$	7.59144	0.325182
$546$	−1.05093	−0.0449756
$547$	29.5357	1.26285	0.631427	−	0.775435i	$-0.282469\pi$
$547$	29.5357	1.26285	0.631427	+	0.775435i	$0.282469\pi$
$548$	9.77046	0.417373
$549$	−5.23955	−0.223619
$550$	3.93653	0.167854
$551$	0.437777	0.0186499
$552$	16.9010	0.719353
$553$	−10.1308	−0.430805
$554$	16.1854	0.687652
$555$	−1.86370	−0.0791098
$556$	9.74633	0.413337
$557$	41.5440	1.76028	0.880138	−	0.474719i	$-0.157450\pi$
$557$	41.5440	1.76028	0.880138	+	0.474719i	$0.157450\pi$
$558$	−1.65932	−0.0702447
$559$	−5.91830	−0.250317
$560$	−3.12821	−0.132191
$561$	0.720680	0.0304271
$562$	33.7398	1.42323
$563$	40.6361	1.71261	0.856303	−	0.516473i	$-0.172755\pi$
$563$	40.6361	1.71261	0.856303	+	0.516473i	$0.172755\pi$
$564$	1.15000	0.0484239
$565$	16.9512	0.713144
$566$	−42.4453	−1.78411
$567$	−0.633348	−0.0265981
$568$	−21.8783	−0.917991
$569$	11.2342	0.470964	0.235482	−	0.971879i	$-0.424333\pi$
$569$	11.2342	0.470964	0.235482	+	0.971879i	$0.424333\pi$
$570$	0.816412	0.0341957
$571$	−47.3021	−1.97953	−0.989765	−	0.142706i	$-0.954420\pi$
$571$	−47.3021	−1.97953	−0.989765	+	0.142706i	$0.954420\pi$
$572$	−1.78723	−0.0747278
$573$	22.3096	0.931996
$574$	3.07487	0.128342
$575$	8.17027	0.340724
$576$	3.14400	0.131000
$577$	−17.7023	−0.736955	−0.368477	−	0.929637i	$-0.620121\pi$
$577$	−17.7023	−0.736955	−0.368477	+	0.929637i	$0.620121\pi$
$578$	−28.0554	−1.16695
$579$	−5.88842	−0.244715
$580$	−0.670304	−0.0278329
$581$	8.87257	0.368096
$582$	−8.33208	−0.345376
$583$	−18.1183	−0.750382
$584$	16.0598	0.664558
$585$	1.00000	0.0413449
$586$	22.1422	0.914687
$587$	13.9475	0.575676	0.287838	−	0.957679i	$-0.407063\pi$
$587$	13.9475	0.575676	0.287838	+	0.957679i	$0.407063\pi$
$588$	4.97127	0.205012
$589$	−0.492015	−0.0202731
$590$	15.8596	0.652930
$591$	−9.37271	−0.385542
$592$	9.20513	0.378329
$593$	35.4312	1.45498	0.727492	−	0.686116i	$-0.240686\pi$
$593$	35.4312	1.45498	0.727492	+	0.686116i	$0.240686\pi$
$594$	−3.93653	−0.161518
$595$	−0.192399	−0.00788758
$596$	−4.33737	−0.177666
$597$	12.8883	0.527484
$598$	−13.5571	−0.554392
$599$	−16.5066	−0.674441	−0.337221	−	0.941426i	$-0.609487\pi$
$599$	−16.5066	−0.674441	−0.337221	+	0.941426i	$0.609487\pi$
$600$	2.06859	0.0844499
$601$	−33.9470	−1.38473	−0.692364	−	0.721549i	$-0.743431\pi$
$601$	−33.9470	−1.38473	−0.692364	+	0.721549i	$0.743431\pi$
$602$	−6.21971	−0.253497
$603$	5.70782	0.232441
$604$	−10.8355	−0.440889
$605$	5.37185	0.218397
$606$	20.0933	0.816236
$607$	41.0415	1.66582	0.832911	−	0.553407i	$-0.186672\pi$
$607$	41.0415	1.66582	0.832911	+	0.553407i	$0.186672\pi$
$608$	−1.99683	−0.0809823
$609$	0.563530	0.0228354
$610$	8.69411	0.352014
$611$	1.52652	0.0617562
$612$	−0.228853	−0.00925084
$613$	−37.7416	−1.52437	−0.762184	−	0.647361i	$-0.775873\pi$
$613$	−37.7416	−1.52437	−0.762184	+	0.647361i	$0.775873\pi$
$614$	8.03501	0.324266
$615$	−2.92585	−0.117982
$616$	3.10814	0.125230
$617$	−28.2056	−1.13551	−0.567757	−	0.823196i	$-0.692189\pi$
$617$	−28.2056	−1.13551	−0.567757	+	0.823196i	$0.692189\pi$
$618$	6.57709	0.264569
$619$	38.1562	1.53363	0.766814	−	0.641869i	$-0.221841\pi$
$619$	38.1562	1.53363	0.766814	+	0.641869i	$0.221841\pi$
$620$	0.753351	0.0302553
$621$	−8.17027	−0.327862
$622$	−40.2750	−1.61488
$623$	7.23446	0.289843
$624$	−4.93916	−0.197725
$625$	1.00000	0.0400000
$626$	7.15483	0.285965
$627$	−1.16724	−0.0466152
$628$	−10.8558	−0.433195
$629$	0.566156	0.0225741
$630$	1.05093	0.0418700
$631$	30.9010	1.23015	0.615075	−	0.788469i	$-0.289126\pi$
$631$	30.9010	1.23015	0.615075	+	0.788469i	$0.289126\pi$
$632$	−33.0884	−1.31619
$633$	25.5114	1.01399
$634$	−12.8922	−0.512014
$635$	13.6814	0.542929
$636$	5.75349	0.228141
$637$	6.59887	0.261457
$638$	3.50258	0.138668
$639$	10.5764	0.418396
$640$	−13.3339	−0.527068
$641$	6.70430	0.264804	0.132402	−	0.991196i	$-0.457731\pi$
$641$	6.70430	0.264804	0.132402	+	0.991196i	$0.457731\pi$
$642$	−7.25451	−0.286313
$643$	−32.6348	−1.28699	−0.643495	−	0.765450i	$-0.722516\pi$
$643$	−32.6348	−1.28699	−0.643495	+	0.765450i	$0.722516\pi$
$644$	−3.89831	−0.153615
$645$	5.91830	0.233033
$646$	−0.248010	−0.00975781
$647$	−10.4168	−0.409526	−0.204763	−	0.978812i	$-0.565642\pi$
$647$	−10.4168	−0.409526	−0.204763	+	0.978812i	$0.565642\pi$
$648$	−2.06859	−0.0812620
$649$	−22.6749	−0.890066
$650$	−1.65932	−0.0650840
$651$	−0.633348	−0.0248229
$652$	−2.92762	−0.114654
$653$	−20.4225	−0.799193	−0.399597	−	0.916691i	$-0.630850\pi$
$653$	−20.4225	−0.799193	−0.399597	+	0.916691i	$0.630850\pi$
$654$	12.5966	0.492568
$655$	13.6411	0.533004
$656$	14.4513	0.564228
$657$	−7.76362	−0.302888
$658$	1.60426	0.0625406
$659$	−11.2038	−0.436438	−0.218219	−	0.975900i	$-0.570025\pi$
$659$	−11.2038	−0.436438	−0.218219	+	0.975900i	$0.570025\pi$
$660$	1.78723	0.0695678
$661$	30.6781	1.19324	0.596620	−	0.802524i	$-0.296510\pi$
$661$	30.6781	1.19324	0.596620	+	0.802524i	$0.296510\pi$
$662$	−32.7422	−1.27256
$663$	−0.303780	−0.0117978
$664$	28.9789	1.12460
$665$	0.311617	0.0120840
$666$	−3.09248	−0.119831
$667$	7.26960	0.281480
$668$	−5.29060	−0.204699
$669$	−15.2117	−0.588119
$670$	−9.47112	−0.365901
$671$	−12.4302	−0.479861
$672$	−2.57043	−0.0991566
$673$	26.7814	1.03235	0.516173	−	0.856484i	$-0.327356\pi$
$673$	26.7814	1.03235	0.516173	+	0.856484i	$0.327356\pi$
$674$	36.0300	1.38782
$675$	−1.00000	−0.0384900
$676$	0.753351	0.0289750
$677$	−11.1940	−0.430222	−0.215111	−	0.976590i	$-0.569011\pi$
$677$	−11.1940	−0.430222	−0.215111	+	0.976590i	$0.569011\pi$
$678$	28.1276	1.08023
$679$	−3.18028	−0.122048
$680$	−0.628397	−0.0240979
$681$	−8.78179	−0.336519
$682$	−3.93653	−0.150738
$683$	35.4131	1.35504	0.677522	−	0.735502i	$-0.263054\pi$
$683$	35.4131	1.35504	0.677522	+	0.735502i	$0.263054\pi$
$684$	0.370660	0.0141725
$685$	−12.9693	−0.495532
$686$	14.2914	0.545650
$687$	10.5164	0.401226
$688$	−29.2315	−1.11444
$689$	7.63719	0.290954
$690$	13.5571	0.516110
$691$	−3.02126	−0.114934	−0.0574671	−	0.998347i	$-0.518302\pi$
$691$	−3.02126	−0.114934	−0.0574671	+	0.998347i	$0.518302\pi$
$692$	−8.16285	−0.310305
$693$	−1.50254	−0.0570767
$694$	−6.26325	−0.237750
$695$	−12.9373	−0.490740
$696$	1.84056	0.0697661
$697$	0.888817	0.0336663
$698$	−54.8862	−2.07747
$699$	−1.48009	−0.0559821
$700$	−0.477134	−0.0180340
$701$	−3.13527	−0.118418	−0.0592088	−	0.998246i	$-0.518858\pi$
$701$	−3.13527	−0.118418	−0.0592088	+	0.998246i	$0.518858\pi$
$702$	1.65932	0.0626271
$703$	−0.916970	−0.0345842
$704$	7.45874	0.281112
$705$	−1.52652	−0.0574919
$706$	30.4122	1.14458
$707$	7.66945	0.288439
$708$	7.20045	0.270609
$709$	−48.5519	−1.82340	−0.911702	−	0.410852i	$-0.865231\pi$
$709$	−48.5519	−1.82340	−0.911702	+	0.410852i	$0.865231\pi$
$710$	−17.5497	−0.658627
$711$	15.9956	0.599882
$712$	23.6286	0.885520
$713$	−8.17027	−0.305979
$714$	−0.319251	−0.0119477
$715$	2.37237	0.0887217
$716$	−1.40527	−0.0525173
$717$	−18.1131	−0.676447
$718$	−2.35192	−0.0877730
$719$	−0.347224	−0.0129493	−0.00647463	−	0.999979i	$-0.502061\pi$
$719$	−0.347224	−0.0129493	−0.00647463	+	0.999979i	$0.502061\pi$
$720$	4.93916	0.184072
$721$	2.51042	0.0934928
$722$	−31.1254	−1.15837
$723$	3.35958	0.124944
$724$	12.2558	0.455483
$725$	0.889763	0.0330450
$726$	8.91363	0.330816
$727$	33.9449	1.25895	0.629473	−	0.777023i	$-0.283271\pi$
$727$	33.9449	1.25895	0.629473	+	0.777023i	$0.283271\pi$
$728$	−1.31014	−0.0485570
$729$	1.00000	0.0370370
$730$	12.8824	0.476797
$731$	−1.79786	−0.0664963
$732$	3.94722	0.145894
$733$	−27.6357	−1.02075	−0.510373	−	0.859953i	$-0.670493\pi$
$733$	−27.6357	−1.02075	−0.510373	+	0.859953i	$0.670493\pi$
$734$	36.7628	1.35694
$735$	−6.59887	−0.243403
$736$	−33.1589	−1.22225
$737$	13.5411	0.498792
$738$	−4.85494	−0.178713
$739$	19.4569	0.715735	0.357868	−	0.933772i	$-0.383504\pi$
$739$	19.4569	0.715735	0.357868	+	0.933772i	$0.383504\pi$
$740$	1.40402	0.0516129
$741$	0.492015	0.0180746
$742$	8.02615	0.294649
$743$	−39.2959	−1.44163	−0.720813	−	0.693130i	$-0.756231\pi$
$743$	−39.2959	−1.44163	−0.720813	+	0.693130i	$0.756231\pi$
$744$	−2.06859	−0.0758383
$745$	5.75744	0.210936
$746$	−30.9500	−1.13316
$747$	−14.0090	−0.512562
$748$	−0.542925	−0.0198513
$749$	−2.76898	−0.101176
$750$	1.65932	0.0605899
$751$	37.8017	1.37940	0.689702	−	0.724093i	$-0.257741\pi$
$751$	37.8017	1.37940	0.689702	+	0.724093i	$0.257741\pi$
$752$	7.53972	0.274945
$753$	−11.4054	−0.415635
$754$	−1.47640	−0.0537674
$755$	14.3830	0.523452
$756$	0.477134	0.0173532
$757$	−31.1807	−1.13328	−0.566642	−	0.823964i	$-0.691758\pi$
$757$	−31.1807	−1.13328	−0.566642	+	0.823964i	$0.691758\pi$
$758$	−5.28890	−0.192102
$759$	−19.3829	−0.703556
$760$	1.01778	0.0369187
$761$	−21.8704	−0.792800	−0.396400	−	0.918078i	$-0.629741\pi$
$761$	−21.8704	−0.792800	−0.396400	+	0.918078i	$0.629741\pi$
$762$	22.7018	0.822400
$763$	4.80803	0.174062
$764$	−16.8069	−0.608054
$765$	0.303780	0.0109832
$766$	−28.3592	−1.02466
$767$	9.55789	0.345115
$768$	−15.8372	−0.571476
$769$	23.6139	0.851539	0.425769	−	0.904832i	$-0.360003\pi$
$769$	23.6139	0.851539	0.425769	+	0.904832i	$0.360003\pi$
$770$	2.49320	0.0898485
$771$	−12.6063	−0.454006
$772$	4.43605	0.159657
$773$	43.8522	1.57725	0.788627	−	0.614872i	$-0.210792\pi$
$773$	43.8522	1.57725	0.788627	+	0.614872i	$0.210792\pi$
$774$	9.82037	0.352986
$775$	−1.00000	−0.0359211
$776$	−10.3872	−0.372878
$777$	−1.18037	−0.0423456
$778$	−33.6631	−1.20688
$779$	−1.43956	−0.0515778
$780$	−0.753351	−0.0269743
$781$	25.0912	0.897832
$782$	−4.11838	−0.147273
$783$	−0.889763	−0.0317975
$784$	32.5929	1.16403
$785$	14.4101	0.514318
$786$	22.6351	0.807366
$787$	21.1080	0.752419	0.376209	−	0.926535i	$-0.377227\pi$
$787$	21.1080	0.752419	0.376209	+	0.926535i	$0.377227\pi$
$788$	7.06094	0.251536
$789$	16.6775	0.593735
$790$	−26.5419	−0.944318
$791$	10.7360	0.381730
$792$	−4.90747	−0.174379
$793$	5.23955	0.186062
$794$	19.7740	0.701755
$795$	−7.63719	−0.270863
$796$	−9.70943	−0.344142
$797$	−23.2950	−0.825150	−0.412575	−	0.910924i	$-0.635370\pi$
$797$	−23.2950	−0.825150	−0.412575	+	0.910924i	$0.635370\pi$
$798$	0.517073	0.0183042
$799$	0.463725	0.0164054
$800$	−4.05848	−0.143489
$801$	−11.4226	−0.403597
$802$	−58.1409	−2.05303
$803$	−18.4182	−0.649964
$804$	−4.30000	−0.151649
$805$	5.17463	0.182382
$806$	1.65932	0.0584471
$807$	−28.0235	−0.986475
$808$	25.0493	0.881233
$809$	33.6423	1.18280	0.591400	−	0.806378i	$-0.298575\pi$
$809$	33.6423	1.18280	0.591400	+	0.806378i	$0.298575\pi$
$810$	−1.65932	−0.0583026
$811$	−40.5494	−1.42388	−0.711940	−	0.702240i	$-0.752183\pi$
$811$	−40.5494	−1.42388	−0.711940	+	0.702240i	$0.752183\pi$
$812$	−0.424536	−0.0148983
$813$	2.38896	0.0837846
$814$	−7.33652	−0.257145
$815$	3.88613	0.136125
$816$	−1.50042	−0.0525252
$817$	2.91189	0.101874
$818$	30.7547	1.07531
$819$	0.633348	0.0221310
$820$	2.20420	0.0769739
$821$	36.3395	1.26826	0.634129	−	0.773228i	$-0.281359\pi$
$821$	36.3395	1.26826	0.634129	+	0.773228i	$0.281359\pi$
$822$	−21.5203	−0.750606
$823$	54.0931	1.88557	0.942783	−	0.333406i	$-0.108198\pi$
$823$	54.0931	1.88557	0.942783	+	0.333406i	$0.108198\pi$
$824$	8.19933	0.285637
$825$	−2.37237	−0.0825954
$826$	10.0447	0.349498
$827$	−47.9552	−1.66757	−0.833783	−	0.552092i	$-0.813830\pi$
$827$	−47.9552	−1.66757	−0.833783	+	0.552092i	$0.813830\pi$
$828$	6.15508	0.213904
$829$	−27.2790	−0.947438	−0.473719	−	0.880676i	$-0.657089\pi$
$829$	−27.2790	−0.947438	−0.473719	+	0.880676i	$0.657089\pi$
$830$	23.2454	0.806860
$831$	−9.75423	−0.338371
$832$	−3.14400	−0.108999
$833$	2.00461	0.0694555
$834$	−21.4672	−0.743347
$835$	7.02275	0.243032
$836$	0.879344	0.0304128
$837$	1.00000	0.0345651
$838$	34.2276	1.18237
$839$	−12.3739	−0.427194	−0.213597	−	0.976922i	$-0.568518\pi$
$839$	−12.3739	−0.427194	−0.213597	+	0.976922i	$0.568518\pi$
$840$	1.31014	0.0452041
$841$	−28.2083	−0.972701
$842$	−51.0133	−1.75803
$843$	−20.3335	−0.700322
$844$	−19.2191	−0.661547
$845$	−1.00000	−0.0344010
$846$	−2.53298	−0.0870857
$847$	3.40225	0.116903
$848$	37.7214	1.29536
$849$	25.5799	0.877901
$850$	−0.504069	−0.0172894
$851$	−15.2270	−0.521973
$852$	−7.96774	−0.272970
$853$	28.7392	0.984011	0.492005	−	0.870592i	$-0.336264\pi$
$853$	28.7392	0.984011	0.492005	+	0.870592i	$0.336264\pi$
$854$	5.50640	0.188425
$855$	−0.492015	−0.0168266
$856$	−9.04382	−0.309112
$857$	29.7235	1.01534	0.507668	−	0.861553i	$-0.330508\pi$
$857$	29.7235	1.01534	0.507668	+	0.861553i	$0.330508\pi$
$858$	3.93653	0.134391
$859$	−19.6158	−0.669283	−0.334642	−	0.942345i	$-0.608615\pi$
$859$	−19.6158	−0.669283	−0.334642	+	0.942345i	$0.608615\pi$
$860$	−4.45856	−0.152036
$861$	−1.85309	−0.0631530
$862$	25.7450	0.876879
$863$	−56.3099	−1.91681	−0.958406	−	0.285409i	$-0.907871\pi$
$863$	−56.3099	−1.91681	−0.958406	+	0.285409i	$0.907871\pi$
$864$	4.05848	0.138072
$865$	10.8354	0.368414
$866$	−46.8470	−1.59193
$867$	16.9077	0.574216
$868$	0.477134	0.0161950
$869$	37.9476	1.28728
$870$	1.47640	0.0500548
$871$	−5.70782	−0.193402
$872$	15.7036	0.531791
$873$	5.02137	0.169948
$874$	6.67031	0.225626
$875$	0.633348	0.0214111
$876$	5.84873	0.197610
$877$	52.0716	1.75833	0.879167	−	0.476515i	$-0.158100\pi$
$877$	52.0716	1.75833	0.879167	+	0.476515i	$0.158100\pi$
$878$	−45.4217	−1.53291
$879$	−13.3441	−0.450086
$880$	11.7175	0.394998
$881$	9.02354	0.304011	0.152005	−	0.988380i	$-0.451427\pi$
$881$	9.02354	0.304011	0.152005	+	0.988380i	$0.451427\pi$
$882$	−10.9497	−0.368694
$883$	17.5622	0.591016	0.295508	−	0.955340i	$-0.404511\pi$
$883$	17.5622	0.591016	0.295508	+	0.955340i	$0.404511\pi$
$884$	0.228853	0.00769716
$885$	−9.55789	−0.321285
$886$	1.65048	0.0554488
$887$	−26.1460	−0.877895	−0.438948	−	0.898513i	$-0.644649\pi$
$887$	−26.1460	−0.877895	−0.438948	+	0.898513i	$0.644649\pi$
$888$	−3.85524	−0.129373
$889$	8.66507	0.290617
$890$	18.9537	0.635330
$891$	2.37237	0.0794775
$892$	11.4598	0.383701
$893$	−0.751069	−0.0251336
$894$	9.55345	0.319515
$895$	1.86535	0.0623519
$896$	−8.44498	−0.282127
$897$	8.17027	0.272797
$898$	19.7126	0.657819
$899$	−0.889763	−0.0296753
$900$	0.753351	0.0251117
$901$	2.32003	0.0772913
$902$	−11.5177	−0.383498
$903$	3.74835	0.124737
$904$	35.0652	1.16625
$905$	−16.2684	−0.540779
$906$	23.8661	0.792898
$907$	−14.7560	−0.489966	−0.244983	−	0.969527i	$-0.578782\pi$
$907$	−14.7560	−0.489966	−0.244983	+	0.969527i	$0.578782\pi$
$908$	6.61577	0.219552
$909$	−12.1094	−0.401642
$910$	−1.05093	−0.0348380
$911$	16.1559	0.535269	0.267634	−	0.963521i	$-0.413758\pi$
$911$	16.1559	0.535269	0.267634	+	0.963521i	$0.413758\pi$
$912$	2.43014	0.0804701
$913$	−33.2345	−1.09990
$914$	46.4330	1.53587
$915$	−5.23955	−0.173214
$916$	−7.92255	−0.261769
$917$	8.63959	0.285305
$918$	0.504069	0.0166368
$919$	28.2732	0.932646	0.466323	−	0.884614i	$-0.345578\pi$
$919$	28.2732	0.932646	0.466323	+	0.884614i	$0.345578\pi$
$920$	16.9010	0.557208
$921$	−4.84234	−0.159561
$922$	−66.1857	−2.17971
$923$	−10.5764	−0.348126
$924$	1.13194	0.0372381
$925$	−1.86370	−0.0612782
$926$	−42.1322	−1.38455
$927$	−3.96372	−0.130186
$928$	−3.61109	−0.118540
$929$	30.1560	0.989387	0.494693	−	0.869068i	$-0.335280\pi$
$929$	30.1560	0.989387	0.494693	+	0.869068i	$0.335280\pi$
$930$	−1.65932	−0.0544113
$931$	−3.24674	−0.106408
$932$	1.11503	0.0365239
$933$	24.2720	0.794628
$934$	7.08815	0.231932
$935$	0.720680	0.0235687
$936$	2.06859	0.0676141
$937$	−37.2465	−1.21679	−0.608395	−	0.793634i	$-0.708186\pi$
$937$	−37.2465	−1.21679	−0.608395	+	0.793634i	$0.708186\pi$
$938$	−5.99852	−0.195859
$939$	−4.31190	−0.140714
$940$	1.15000	0.0375090
$941$	9.24506	0.301380	0.150690	−	0.988581i	$-0.451850\pi$
$941$	9.24506	0.301380	0.150690	+	0.988581i	$0.451850\pi$
$942$	23.9110	0.779061
$943$	−23.9050	−0.778455
$944$	47.2080	1.53649
$945$	−0.633348	−0.0206028
$946$	23.2976	0.757470
$947$	−4.19516	−0.136324	−0.0681622	−	0.997674i	$-0.521714\pi$
$947$	−4.19516	−0.136324	−0.0681622	+	0.997674i	$0.521714\pi$
$948$	−12.0503	−0.391376
$949$	7.76362	0.252018
$950$	0.816412	0.0264879
$951$	7.76955	0.251945
$952$	−0.397994	−0.0128991
$953$	−26.2177	−0.849274	−0.424637	−	0.905364i	$-0.639598\pi$
$953$	−26.2177	−0.849274	−0.424637	+	0.905364i	$0.639598\pi$
$954$	−12.6726	−0.410290
$955$	22.3096	0.721921
$956$	13.6455	0.441328
$957$	−2.11085	−0.0682341
$958$	9.92968	0.320813
$959$	−8.21410	−0.265247
$960$	3.14400	0.101472
$961$	1.00000	0.0322581
$962$	3.09248	0.0997057
$963$	4.37197	0.140885
$964$	−2.53095	−0.0815163
$965$	−5.88842	−0.189555
$966$	8.58637	0.276262
$967$	−17.0826	−0.549341	−0.274670	−	0.961538i	$-0.588569\pi$
$967$	−17.0826	−0.549341	−0.274670	+	0.961538i	$0.588569\pi$
$968$	11.1122	0.357158
$969$	0.149464	0.00480149
$970$	−8.33208	−0.267527
$971$	2.83493	0.0909773	0.0454887	−	0.998965i	$-0.485516\pi$
$971$	2.83493	0.0909773	0.0454887	+	0.998965i	$0.485516\pi$
$972$	−0.753351	−0.0241638
$973$	−8.19382	−0.262682
$974$	0.636980	0.0204102
$975$	1.00000	0.0320256
$976$	25.8790	0.828367
$977$	−13.3590	−0.427391	−0.213696	−	0.976900i	$-0.568550\pi$
$977$	−13.3590	−0.427391	−0.213696	+	0.976900i	$0.568550\pi$
$978$	6.44834	0.206195
$979$	−27.0986	−0.866074
$980$	4.97127	0.158801
$981$	−7.59144	−0.242376
$982$	12.6256	0.402899
$983$	7.75896	0.247473	0.123736	−	0.992315i	$-0.460512\pi$
$983$	7.75896	0.247473	0.123736	+	0.992315i	$0.460512\pi$
$984$	−6.05240	−0.192944
$985$	−9.37271	−0.298639
$986$	−0.448502	−0.0142832
$987$	−0.966816	−0.0307741
$988$	−0.370660	−0.0117923
$989$	48.3541	1.53757
$990$	−3.93653	−0.125111
$991$	1.64172	0.0521511	0.0260755	−	0.999660i	$-0.491699\pi$
$991$	1.64172	0.0521511	0.0260755	+	0.999660i	$0.491699\pi$
$992$	4.05848	0.128857
$993$	19.7323	0.626184
$994$	−11.1150	−0.352548
$995$	12.8883	0.408587
$996$	10.5537	0.334406
$997$	−48.3006	−1.52970	−0.764848	−	0.644211i	$-0.777186\pi$
$997$	−48.3006	−1.52970	−0.764848	+	0.644211i	$0.777186\pi$
$998$	12.5360	0.396819
$999$	1.86370	0.0589649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.w.1.9	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.w.1.9	✓	11	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+1.65932 q^{2} -1.00000 q^{3} +0.753351 q^{4} -1.00000 q^{5} -1.65932 q^{6} -0.633348 q^{7} -2.06859 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.65932 q^{2} -1.00000 q^{3} +0.753351 q^{4} -1.00000 q^{5} -1.65932 q^{6} -0.633348 q^{7} -2.06859 q^{8} +1.00000 q^{9} -1.65932 q^{10} +2.37237 q^{11} -0.753351 q^{12} -1.00000 q^{13} -1.05093 q^{14} +1.00000 q^{15} -4.93916 q^{16} -0.303780 q^{17} +1.65932 q^{18} +0.492015 q^{19} -0.753351 q^{20} +0.633348 q^{21} +3.93653 q^{22} +8.17027 q^{23} +2.06859 q^{24} +1.00000 q^{25} -1.65932 q^{26} -1.00000 q^{27} -0.477134 q^{28} +0.889763 q^{29} +1.65932 q^{30} -1.00000 q^{31} -4.05848 q^{32} -2.37237 q^{33} -0.504069 q^{34} +0.633348 q^{35} +0.753351 q^{36} -1.86370 q^{37} +0.816412 q^{38} +1.00000 q^{39} +2.06859 q^{40} -2.92585 q^{41} +1.05093 q^{42} +5.91830 q^{43} +1.78723 q^{44} -1.00000 q^{45} +13.5571 q^{46} -1.52652 q^{47} +4.93916 q^{48} -6.59887 q^{49} +1.65932 q^{50} +0.303780 q^{51} -0.753351 q^{52} -7.63719 q^{53} -1.65932 q^{54} -2.37237 q^{55} +1.31014 q^{56} -0.492015 q^{57} +1.47640 q^{58} -9.55789 q^{59} +0.753351 q^{60} -5.23955 q^{61} -1.65932 q^{62} -0.633348 q^{63} +3.14400 q^{64} +1.00000 q^{65} -3.93653 q^{66} +5.70782 q^{67} -0.228853 q^{68} -8.17027 q^{69} +1.05093 q^{70} +10.5764 q^{71} -2.06859 q^{72} -7.76362 q^{73} -3.09248 q^{74} -1.00000 q^{75} +0.370660 q^{76} -1.50254 q^{77} +1.65932 q^{78} +15.9956 q^{79} +4.93916 q^{80} +1.00000 q^{81} -4.85494 q^{82} -14.0090 q^{83} +0.477134 q^{84} +0.303780 q^{85} +9.82037 q^{86} -0.889763 q^{87} -4.90747 q^{88} -11.4226 q^{89} -1.65932 q^{90} +0.633348 q^{91} +6.15508 q^{92} +1.00000 q^{93} -2.53298 q^{94} -0.492015 q^{95} +4.05848 q^{96} +5.02137 q^{97} -10.9497 q^{98} +2.37237 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 12 q^{4} - 11 q^{5} - 2 q^{6} + 4 q^{7} + 3 q^{8} + 11 q^{9} - 2 q^{10} - 12 q^{12} - 11 q^{13} + 5 q^{14} + 11 q^{15} - 10 q^{16} - 3 q^{17} + 2 q^{18} - 8 q^{19} - 12 q^{20} - 4 q^{21} - 3 q^{22} + 11 q^{23} - 3 q^{24} + 11 q^{25} - 2 q^{26} - 11 q^{27} + 14 q^{28} - 14 q^{29} + 2 q^{30} - 11 q^{31} + 8 q^{32} - 11 q^{34} - 4 q^{35} + 12 q^{36} + 7 q^{37} + 8 q^{38} + 11 q^{39} - 3 q^{40} + 22 q^{41} - 5 q^{42} - 5 q^{43} - 13 q^{44} - 11 q^{45} - 22 q^{46} + 5 q^{47} + 10 q^{48} - 33 q^{49} + 2 q^{50} + 3 q^{51} - 12 q^{52} + 4 q^{53} - 2 q^{54} - 13 q^{56} + 8 q^{57} - 18 q^{58} - 3 q^{59} + 12 q^{60} - 28 q^{61} - 2 q^{62} + 4 q^{63} + 3 q^{64} + 11 q^{65} + 3 q^{66} - 11 q^{67} - 9 q^{68} - 11 q^{69} - 5 q^{70} + 5 q^{71} + 3 q^{72} - 3 q^{73} - 12 q^{74} - 11 q^{75} - 36 q^{76} + 18 q^{77} + 2 q^{78} - 43 q^{79} + 10 q^{80} + 11 q^{81} - 15 q^{82} - 28 q^{83} - 14 q^{84} + 3 q^{85} + 10 q^{86} + 14 q^{87} - 43 q^{88} - 25 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 11 q^{93} - 16 q^{94} + 8 q^{95} - 8 q^{96} - 6 q^{97} - 14 q^{98}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 12 * q^4 - 11 * q^5 - 2 * q^6 + 4 * q^7 + 3 * q^8 + 11 * q^9 - 2 * q^10 - 12 * q^12 - 11 * q^13 + 5 * q^14 + 11 * q^15 - 10 * q^16 - 3 * q^17 + 2 * q^18 - 8 * q^19 - 12 * q^20 - 4 * q^21 - 3 * q^22 + 11 * q^23 - 3 * q^24 + 11 * q^25 - 2 * q^26 - 11 * q^27 + 14 * q^28 - 14 * q^29 + 2 * q^30 - 11 * q^31 + 8 * q^32 - 11 * q^34 - 4 * q^35 + 12 * q^36 + 7 * q^37 + 8 * q^38 + 11 * q^39 - 3 * q^40 + 22 * q^41 - 5 * q^42 - 5 * q^43 - 13 * q^44 - 11 * q^45 - 22 * q^46 + 5 * q^47 + 10 * q^48 - 33 * q^49 + 2 * q^50 + 3 * q^51 - 12 * q^52 + 4 * q^53 - 2 * q^54 - 13 * q^56 + 8 * q^57 - 18 * q^58 - 3 * q^59 + 12 * q^60 - 28 * q^61 - 2 * q^62 + 4 * q^63 + 3 * q^64 + 11 * q^65 + 3 * q^66 - 11 * q^67 - 9 * q^68 - 11 * q^69 - 5 * q^70 + 5 * q^71 + 3 * q^72 - 3 * q^73 - 12 * q^74 - 11 * q^75 - 36 * q^76 + 18 * q^77 + 2 * q^78 - 43 * q^79 + 10 * q^80 + 11 * q^81 - 15 * q^82 - 28 * q^83 - 14 * q^84 + 3 * q^85 + 10 * q^86 + 14 * q^87 - 43 * q^88 - 25 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 11 * q^93 - 16 * q^94 + 8 * q^95 - 8 * q^96 - 6 * q^97 - 14 * q^98

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