LMFDB - Embedded newform 2667.2.a.q.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2667,2,Mod(1,2667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2667, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2667 = 3 \cdot 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2667.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:	$21.2961022191$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 22 x^{17} + 101 x^{16} + 178 x^{15} - 1035 x^{14} - 583 x^{13} + 5572 x^{12} + \cdots + 210 $ x^19 - 4x^18 - 22x^17 + 101x^16 + 178x^15 - 1035x^14 - 583x^13 + 5572x^12 + 21x^11 - 17032x^10 + 4985x^9 + 29792x^8 - 13249x^7 - 28600x^6 + 14000x^5 + 13725x^4 - 5723x^3 - 2913x^2 + 608x + 210
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			1.17
Root			$2.42782$ of defining polynomial
Character	$\chi$	$=$	2667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.42782 q^{2} +1.00000 q^{3} +3.89430 q^{4} +4.13136 q^{5} +2.42782 q^{6} +1.00000 q^{7} +4.59902 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.42782 q^{2} +1.00000 q^{3} +3.89430 q^{4} +4.13136 q^{5} +2.42782 q^{6} +1.00000 q^{7} +4.59902 q^{8} +1.00000 q^{9} +10.0302 q^{10} -4.39665 q^{11} +3.89430 q^{12} +0.702420 q^{13} +2.42782 q^{14} +4.13136 q^{15} +3.37699 q^{16} -0.979615 q^{17} +2.42782 q^{18} -7.50347 q^{19} +16.0888 q^{20} +1.00000 q^{21} -10.6743 q^{22} -4.28424 q^{23} +4.59902 q^{24} +12.0682 q^{25} +1.70535 q^{26} +1.00000 q^{27} +3.89430 q^{28} +8.97712 q^{29} +10.0302 q^{30} -0.872190 q^{31} -0.999336 q^{32} -4.39665 q^{33} -2.37833 q^{34} +4.13136 q^{35} +3.89430 q^{36} +6.83153 q^{37} -18.2171 q^{38} +0.702420 q^{39} +19.0002 q^{40} -4.36586 q^{41} +2.42782 q^{42} -6.34656 q^{43} -17.1219 q^{44} +4.13136 q^{45} -10.4014 q^{46} +2.85801 q^{47} +3.37699 q^{48} +1.00000 q^{49} +29.2993 q^{50} -0.979615 q^{51} +2.73544 q^{52} -5.93310 q^{53} +2.42782 q^{54} -18.1642 q^{55} +4.59902 q^{56} -7.50347 q^{57} +21.7948 q^{58} +5.83624 q^{59} +16.0888 q^{60} +0.431173 q^{61} -2.11752 q^{62} +1.00000 q^{63} -9.18018 q^{64} +2.90195 q^{65} -10.6743 q^{66} +1.64991 q^{67} -3.81492 q^{68} -4.28424 q^{69} +10.0302 q^{70} -15.5767 q^{71} +4.59902 q^{72} -3.79200 q^{73} +16.5857 q^{74} +12.0682 q^{75} -29.2208 q^{76} -4.39665 q^{77} +1.70535 q^{78} +14.6779 q^{79} +13.9516 q^{80} +1.00000 q^{81} -10.5995 q^{82} -5.45195 q^{83} +3.89430 q^{84} -4.04715 q^{85} -15.4083 q^{86} +8.97712 q^{87} -20.2203 q^{88} -12.1433 q^{89} +10.0302 q^{90} +0.702420 q^{91} -16.6841 q^{92} -0.872190 q^{93} +6.93874 q^{94} -30.9996 q^{95} -0.999336 q^{96} +9.29248 q^{97} +2.42782 q^{98} -4.39665 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9}+O(q^{10}) $ 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20} + 19 q^{21} - 3 q^{22} - 17 q^{23} + 9 q^{24} + 38 q^{25} + 28 q^{26} + 19 q^{27} + 22 q^{28} + 2 q^{29} + 16 q^{31} + 17 q^{32} - 9 q^{33} + 29 q^{34} + 5 q^{35} + 22 q^{36} + 56 q^{37} + 2 q^{38} + 24 q^{39} - 13 q^{40} - 7 q^{41} + 4 q^{42} + 19 q^{43} - 29 q^{44} + 5 q^{45} + 10 q^{46} + 25 q^{47} + 20 q^{48} + 19 q^{49} - 9 q^{50} + 17 q^{51} + 16 q^{52} + 18 q^{53} + 4 q^{54} + 10 q^{55} + 9 q^{56} + 23 q^{57} + 31 q^{58} + 11 q^{59} + 5 q^{60} + 26 q^{61} + 26 q^{62} + 19 q^{63} + 45 q^{64} + 27 q^{65} - 3 q^{66} + 24 q^{67} + 14 q^{68} - 17 q^{69} - 32 q^{71} + 9 q^{72} + 51 q^{73} + 38 q^{75} + 12 q^{76} - 9 q^{77} + 28 q^{78} + 30 q^{79} - 30 q^{80} + 19 q^{81} - 52 q^{82} + q^{83} + 22 q^{84} + 44 q^{85} - 24 q^{86} + 2 q^{87} - 30 q^{88} + 5 q^{89} + 24 q^{91} - 88 q^{92} + 16 q^{93} + 7 q^{94} - 24 q^{95} + 17 q^{96} + 5 q^{97} + 4 q^{98} - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * 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 $

$2$	2.42782	1.71673	0.858363	−	0.513042i	$-0.171482\pi$
$2$	2.42782	1.71673	0.858363	+	0.513042i	$0.171482\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.89430	1.94715
$5$	4.13136	1.84760	0.923801	−	0.382873i	$-0.125065\pi$
$5$	4.13136	1.84760	0.923801	+	0.382873i	$0.125065\pi$
$6$	2.42782	0.991153
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	4.59902	1.62600
$9$	1.00000	0.333333
$10$	10.0302	3.17183
$11$	−4.39665	−1.32564	−0.662820	−	0.748779i	$-0.730641\pi$
$11$	−4.39665	−1.32564	−0.662820	+	0.748779i	$0.730641\pi$
$12$	3.89430	1.12419
$13$	0.702420	0.194816	0.0974081	−	0.995245i	$-0.468945\pi$
$13$	0.702420	0.194816	0.0974081	+	0.995245i	$0.468945\pi$
$14$	2.42782	0.648862
$15$	4.13136	1.06671
$16$	3.37699	0.844246
$17$	−0.979615	−0.237592	−0.118796	−	0.992919i	$-0.537903\pi$
$17$	−0.979615	−0.237592	−0.118796	+	0.992919i	$0.537903\pi$
$18$	2.42782	0.572242
$19$	−7.50347	−1.72141	−0.860707	−	0.509100i	$-0.829978\pi$
$19$	−7.50347	−1.72141	−0.860707	+	0.509100i	$0.829978\pi$
$20$	16.0888	3.59756
$21$	1.00000	0.218218
$22$	−10.6743	−2.27576
$23$	−4.28424	−0.893326	−0.446663	−	0.894702i	$-0.647388\pi$
$23$	−4.28424	−0.893326	−0.446663	+	0.894702i	$0.647388\pi$
$24$	4.59902	0.938771
$25$	12.0682	2.41363
$26$	1.70535	0.334446
$27$	1.00000	0.192450
$28$	3.89430	0.735954
$29$	8.97712	1.66701	0.833505	−	0.552513i	$-0.186331\pi$
$29$	8.97712	1.66701	0.833505	+	0.552513i	$0.186331\pi$
$30$	10.0302	1.83126
$31$	−0.872190	−0.156650	−0.0783249	−	0.996928i	$-0.524957\pi$
$31$	−0.872190	−0.156650	−0.0783249	+	0.996928i	$0.524957\pi$
$32$	−0.999336	−0.176659
$33$	−4.39665	−0.765359
$34$	−2.37833	−0.407880
$35$	4.13136	0.698328
$36$	3.89430	0.649050
$37$	6.83153	1.12310	0.561548	−	0.827444i	$-0.310206\pi$
$37$	6.83153	1.12310	0.561548	+	0.827444i	$0.310206\pi$
$38$	−18.2171	−2.95520
$39$	0.702420	0.112477
$40$	19.0002	3.00420
$41$	−4.36586	−0.681833	−0.340917	−	0.940094i	$-0.610737\pi$
$41$	−4.36586	−0.681833	−0.340917	+	0.940094i	$0.610737\pi$
$42$	2.42782	0.374621
$43$	−6.34656	−0.967841	−0.483921	−	0.875112i	$-0.660788\pi$
$43$	−6.34656	−0.967841	−0.483921	+	0.875112i	$0.660788\pi$
$44$	−17.1219	−2.58122
$45$	4.13136	0.615867
$46$	−10.4014	−1.53360
$47$	2.85801	0.416884	0.208442	−	0.978035i	$-0.433161\pi$
$47$	2.85801	0.416884	0.208442	+	0.978035i	$0.433161\pi$
$48$	3.37699	0.487426
$49$	1.00000	0.142857
$50$	29.2993	4.14355
$51$	−0.979615	−0.137174
$52$	2.73544	0.379337
$53$	−5.93310	−0.814974	−0.407487	−	0.913211i	$-0.633595\pi$
$53$	−5.93310	−0.814974	−0.407487	+	0.913211i	$0.633595\pi$
$54$	2.42782	0.330384
$55$	−18.1642	−2.44926
$56$	4.59902	0.614570
$57$	−7.50347	−0.993859
$58$	21.7948	2.86180
$59$	5.83624	0.759814	0.379907	−	0.925025i	$-0.375956\pi$
$59$	5.83624	0.759814	0.379907	+	0.925025i	$0.375956\pi$
$60$	16.0888	2.07705
$61$	0.431173	0.0552061	0.0276030	−	0.999619i	$-0.491213\pi$
$61$	0.431173	0.0552061	0.0276030	+	0.999619i	$0.491213\pi$
$62$	−2.11752	−0.268925
$63$	1.00000	0.125988
$64$	−9.18018	−1.14752
$65$	2.90195	0.359943
$66$	−10.6743	−1.31391
$67$	1.64991	0.201568	0.100784	−	0.994908i	$-0.467865\pi$
$67$	1.64991	0.201568	0.100784	+	0.994908i	$0.467865\pi$
$68$	−3.81492	−0.462627
$69$	−4.28424	−0.515762
$70$	10.0302	1.19884
$71$	−15.5767	−1.84862	−0.924309	−	0.381645i	$-0.875358\pi$
$71$	−15.5767	−1.84862	−0.924309	+	0.381645i	$0.875358\pi$
$72$	4.59902	0.542000
$73$	−3.79200	−0.443821	−0.221910	−	0.975067i	$-0.571229\pi$
$73$	−3.79200	−0.443821	−0.221910	+	0.975067i	$0.571229\pi$
$74$	16.5857	1.92805
$75$	12.0682	1.39351
$76$	−29.2208	−3.35185
$77$	−4.39665	−0.501045
$78$	1.70535	0.193093
$79$	14.6779	1.65139	0.825697	−	0.564114i	$-0.190782\pi$
$79$	14.6779	1.65139	0.825697	+	0.564114i	$0.190782\pi$
$80$	13.9516	1.55983
$81$	1.00000	0.111111
$82$	−10.5995	−1.17052
$83$	−5.45195	−0.598429	−0.299215	−	0.954186i	$-0.596725\pi$
$83$	−5.45195	−0.598429	−0.299215	+	0.954186i	$0.596725\pi$
$84$	3.89430	0.424903
$85$	−4.04715	−0.438975
$86$	−15.4083	−1.66152
$87$	8.97712	0.962448
$88$	−20.2203	−2.15549
$89$	−12.1433	−1.28719	−0.643593	−	0.765368i	$-0.722557\pi$
$89$	−12.1433	−1.28719	−0.643593	+	0.765368i	$0.722557\pi$
$90$	10.0302	1.05728
$91$	0.702420	0.0736336
$92$	−16.6841	−1.73944
$93$	−0.872190	−0.0904418
$94$	6.93874	0.715676
$95$	−30.9996	−3.18049
$96$	−0.999336	−0.101994
$97$	9.29248	0.943509	0.471754	−	0.881730i	$-0.343621\pi$
$97$	9.29248	0.943509	0.471754	+	0.881730i	$0.343621\pi$
$98$	2.42782	0.245247
$99$	−4.39665	−0.441880
$100$	46.9971	4.69971
$101$	10.0187	0.996893	0.498447	−	0.866920i	$-0.333904\pi$
$101$	10.0187	0.996893	0.498447	+	0.866920i	$0.333904\pi$
$102$	−2.37833	−0.235490
$103$	−10.3855	−1.02332	−0.511659	−	0.859189i	$-0.670969\pi$
$103$	−10.3855	−1.02332	−0.511659	+	0.859189i	$0.670969\pi$
$104$	3.23045	0.316771
$105$	4.13136	0.403180
$106$	−14.4045	−1.39909
$107$	−12.3554	−1.19445	−0.597223	−	0.802075i	$-0.703729\pi$
$107$	−12.3554	−1.19445	−0.597223	+	0.802075i	$0.703729\pi$
$108$	3.89430	0.374729
$109$	−12.4746	−1.19485	−0.597423	−	0.801926i	$-0.703809\pi$
$109$	−12.4746	−1.19485	−0.597423	+	0.801926i	$0.703809\pi$
$110$	−44.0993	−4.20470
$111$	6.83153	0.648420
$112$	3.37699	0.319095
$113$	17.5483	1.65080	0.825400	−	0.564548i	$-0.190949\pi$
$113$	17.5483	1.65080	0.825400	+	0.564548i	$0.190949\pi$
$114$	−18.2171	−1.70618
$115$	−17.6998	−1.65051
$116$	34.9596	3.24592
$117$	0.702420	0.0649388
$118$	14.1693	1.30439
$119$	−0.979615	−0.0898012
$120$	19.0002	1.73448
$121$	8.33054	0.757322
$122$	1.04681	0.0947738
$123$	−4.36586	−0.393657
$124$	−3.39657	−0.305021
$125$	29.2011	2.61183
$126$	2.42782	0.216287
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−20.2891	−1.79332
$129$	−6.34656	−0.558783
$130$	7.04541	0.617924
$131$	1.03408	0.0903480	0.0451740	−	0.998979i	$-0.485616\pi$
$131$	1.03408	0.0903480	0.0451740	+	0.998979i	$0.485616\pi$
$132$	−17.1219	−1.49027
$133$	−7.50347	−0.650633
$134$	4.00567	0.346037
$135$	4.13136	0.355571
$136$	−4.50527	−0.386324
$137$	10.4831	0.895629	0.447815	−	0.894126i	$-0.352202\pi$
$137$	10.4831	0.895629	0.447815	+	0.894126i	$0.352202\pi$
$138$	−10.4014	−0.885423
$139$	9.23389	0.783208	0.391604	−	0.920134i	$-0.371920\pi$
$139$	9.23389	0.783208	0.391604	+	0.920134i	$0.371920\pi$
$140$	16.0888	1.35975
$141$	2.85801	0.240688
$142$	−37.8175	−3.17357
$143$	−3.08830	−0.258256
$144$	3.37699	0.281415
$145$	37.0877	3.07997
$146$	−9.20630	−0.761919
$147$	1.00000	0.0824786
$148$	26.6040	2.18684
$149$	11.0699	0.906885	0.453442	−	0.891286i	$-0.350196\pi$
$149$	11.0699	0.906885	0.453442	+	0.891286i	$0.350196\pi$
$150$	29.2993	2.39228
$151$	12.6210	1.02708	0.513540	−	0.858066i	$-0.328334\pi$
$151$	12.6210	1.02708	0.513540	+	0.858066i	$0.328334\pi$
$152$	−34.5086	−2.79902
$153$	−0.979615	−0.0791972
$154$	−10.6743	−0.860157
$155$	−3.60333	−0.289427
$156$	2.73544	0.219010
$157$	−0.436970	−0.0348740	−0.0174370	−	0.999848i	$-0.505551\pi$
$157$	−0.436970	−0.0348740	−0.0174370	+	0.999848i	$0.505551\pi$
$158$	35.6353	2.83499
$159$	−5.93310	−0.470526
$160$	−4.12862	−0.326396
$161$	−4.28424	−0.337646
$162$	2.42782	0.190747
$163$	−11.0335	−0.864209	−0.432105	−	0.901824i	$-0.642229\pi$
$163$	−11.0335	−0.864209	−0.432105	+	0.901824i	$0.642229\pi$
$164$	−17.0020	−1.32763
$165$	−18.1642	−1.41408
$166$	−13.2363	−1.02734
$167$	22.0805	1.70864	0.854321	−	0.519746i	$-0.173973\pi$
$167$	22.0805	1.70864	0.854321	+	0.519746i	$0.173973\pi$
$168$	4.59902	0.354822
$169$	−12.5066	−0.962047
$170$	−9.82574	−0.753600
$171$	−7.50347	−0.573805
$172$	−24.7154	−1.88453
$173$	7.62698	0.579868	0.289934	−	0.957047i	$-0.406367\pi$
$173$	7.62698	0.579868	0.289934	+	0.957047i	$0.406367\pi$
$174$	21.7948	1.65226
$175$	12.0682	0.912267
$176$	−14.8474	−1.11917
$177$	5.83624	0.438679
$178$	−29.4817	−2.20975
$179$	−8.74055	−0.653299	−0.326650	−	0.945146i	$-0.605920\pi$
$179$	−8.74055	−0.653299	−0.326650	+	0.945146i	$0.605920\pi$
$180$	16.0888	1.19919
$181$	1.99890	0.148577	0.0742884	−	0.997237i	$-0.476331\pi$
$181$	1.99890	0.148577	0.0742884	+	0.997237i	$0.476331\pi$
$182$	1.70535	0.126409
$183$	0.431173	0.0318733
$184$	−19.7033	−1.45255
$185$	28.2235	2.07504
$186$	−2.11752	−0.155264
$187$	4.30703	0.314961
$188$	11.1300	0.811736
$189$	1.00000	0.0727393
$190$	−75.2613	−5.46003
$191$	−5.03588	−0.364383	−0.182192	−	0.983263i	$-0.558319\pi$
$191$	−5.03588	−0.364383	−0.182192	+	0.983263i	$0.558319\pi$
$192$	−9.18018	−0.662522
$193$	4.96100	0.357101	0.178550	−	0.983931i	$-0.442859\pi$
$193$	4.96100	0.357101	0.178550	+	0.983931i	$0.442859\pi$
$194$	22.5605	1.61975
$195$	2.90195	0.207813
$196$	3.89430	0.278164
$197$	3.19173	0.227401	0.113701	−	0.993515i	$-0.463729\pi$
$197$	3.19173	0.227401	0.113701	+	0.993515i	$0.463729\pi$
$198$	−10.6743	−0.758587
$199$	−7.96090	−0.564333	−0.282167	−	0.959365i	$-0.591053\pi$
$199$	−7.96090	−0.564333	−0.282167	+	0.959365i	$0.591053\pi$
$200$	55.5017	3.92457
$201$	1.64991	0.116375
$202$	24.3235	1.71139
$203$	8.97712	0.630070
$204$	−3.81492	−0.267098
$205$	−18.0370	−1.25976
$206$	−25.2142	−1.75676
$207$	−4.28424	−0.297775
$208$	2.37206	0.164473
$209$	32.9901	2.28198
$210$	10.0302	0.692149
$211$	−14.3101	−0.985151	−0.492575	−	0.870270i	$-0.663944\pi$
$211$	−14.3101	−0.985151	−0.492575	+	0.870270i	$0.663944\pi$
$212$	−23.1053	−1.58688
$213$	−15.5767	−1.06730
$214$	−29.9968	−2.05054
$215$	−26.2199	−1.78819
$216$	4.59902	0.312924
$217$	−0.872190	−0.0592081
$218$	−30.2860	−2.05123
$219$	−3.79200	−0.256240
$220$	−70.7367	−4.76907
$221$	−0.688101	−0.0462867
$222$	16.5857	1.11316
$223$	13.2261	0.885686	0.442843	−	0.896599i	$-0.353970\pi$
$223$	13.2261	0.885686	0.442843	+	0.896599i	$0.353970\pi$
$224$	−0.999336	−0.0667709
$225$	12.0682	0.804544
$226$	42.6040	2.83397
$227$	29.5131	1.95885	0.979426	−	0.201805i	$-0.0646807\pi$
$227$	29.5131	1.95885	0.979426	+	0.201805i	$0.0646807\pi$
$228$	−29.2208	−1.93519
$229$	−15.5215	−1.02569	−0.512845	−	0.858481i	$-0.671409\pi$
$229$	−15.5215	−1.02569	−0.512845	+	0.858481i	$0.671409\pi$
$230$	−42.9718	−2.83348
$231$	−4.39665	−0.289278
$232$	41.2860	2.71056
$233$	−6.88255	−0.450891	−0.225445	−	0.974256i	$-0.572384\pi$
$233$	−6.88255	−0.450891	−0.225445	+	0.974256i	$0.572384\pi$
$234$	1.70535	0.111482
$235$	11.8075	0.770236
$236$	22.7281	1.47947
$237$	14.6779	0.953432
$238$	−2.37833	−0.154164
$239$	5.00111	0.323495	0.161747	−	0.986832i	$-0.448287\pi$
$239$	5.00111	0.323495	0.161747	+	0.986832i	$0.448287\pi$
$240$	13.9516	0.900569
$241$	15.5508	1.00171	0.500856	−	0.865530i	$-0.333019\pi$
$241$	15.5508	1.00171	0.500856	+	0.865530i	$0.333019\pi$
$242$	20.2250	1.30011
$243$	1.00000	0.0641500
$244$	1.67912	0.107495
$245$	4.13136	0.263943
$246$	−10.5995	−0.675801
$247$	−5.27059	−0.335360
$248$	−4.01122	−0.254713
$249$	−5.45195	−0.345503
$250$	70.8950	4.48380
$251$	24.6173	1.55383	0.776916	−	0.629605i	$-0.216783\pi$
$251$	24.6173	1.55383	0.776916	+	0.629605i	$0.216783\pi$
$252$	3.89430	0.245318
$253$	18.8363	1.18423
$254$	2.42782	0.152335
$255$	−4.04715	−0.253442
$256$	−30.8980	−1.93112
$257$	10.9511	0.683108	0.341554	−	0.939862i	$-0.389047\pi$
$257$	10.9511	0.683108	0.341554	+	0.939862i	$0.389047\pi$
$258$	−15.4083	−0.959279
$259$	6.83153	0.424491
$260$	11.3011	0.700863
$261$	8.97712	0.555670
$262$	2.51056	0.155103
$263$	−23.9422	−1.47634	−0.738171	−	0.674614i	$-0.764310\pi$
$263$	−23.9422	−1.47634	−0.738171	+	0.674614i	$0.764310\pi$
$264$	−20.2203	−1.24447
$265$	−24.5118	−1.50575
$266$	−18.2171	−1.11696
$267$	−12.1433	−0.743157
$268$	6.42523	0.392484
$269$	−17.5905	−1.07251	−0.536257	−	0.844055i	$-0.680162\pi$
$269$	−17.5905	−1.07251	−0.536257	+	0.844055i	$0.680162\pi$
$270$	10.0302	0.610418
$271$	7.00655	0.425617	0.212809	−	0.977094i	$-0.431739\pi$
$271$	7.00655	0.425617	0.212809	+	0.977094i	$0.431739\pi$
$272$	−3.30815	−0.200586
$273$	0.702420	0.0425124
$274$	25.4510	1.53755
$275$	−53.0595	−3.19961
$276$	−16.6841	−1.00427
$277$	7.00516	0.420899	0.210449	−	0.977605i	$-0.432507\pi$
$277$	7.00516	0.420899	0.210449	+	0.977605i	$0.432507\pi$
$278$	22.4182	1.34455
$279$	−0.872190	−0.0522166
$280$	19.0002	1.13548
$281$	−23.2539	−1.38721	−0.693607	−	0.720354i	$-0.743979\pi$
$281$	−23.2539	−1.38721	−0.693607	+	0.720354i	$0.743979\pi$
$282$	6.93874	0.413196
$283$	30.2416	1.79768	0.898840	−	0.438278i	$-0.144411\pi$
$283$	30.2416	1.79768	0.898840	+	0.438278i	$0.144411\pi$
$284$	−60.6605	−3.59954
$285$	−30.9996	−1.83626
$286$	−7.49782	−0.443355
$287$	−4.36586	−0.257709
$288$	−0.999336	−0.0588864
$289$	−16.0404	−0.943550
$290$	90.0423	5.28747
$291$	9.29248	0.544735
$292$	−14.7672	−0.864186
$293$	−15.6762	−0.915812	−0.457906	−	0.889001i	$-0.651400\pi$
$293$	−15.6762	−0.915812	−0.457906	+	0.889001i	$0.651400\pi$
$294$	2.42782	0.141593
$295$	24.1116	1.40383
$296$	31.4184	1.82616
$297$	−4.39665	−0.255120
$298$	26.8758	1.55687
$299$	−3.00934	−0.174034
$300$	46.9971	2.71338
$301$	−6.34656	−0.365810
$302$	30.6414	1.76321
$303$	10.0187	0.575557
$304$	−25.3391	−1.45330
$305$	1.78133	0.101999
$306$	−2.37833	−0.135960
$307$	−8.13944	−0.464543	−0.232271	−	0.972651i	$-0.574616\pi$
$307$	−8.13944	−0.464543	−0.232271	+	0.972651i	$0.574616\pi$
$308$	−17.1219	−0.975610
$309$	−10.3855	−0.590812
$310$	−8.74823	−0.496866
$311$	10.5758	0.599698	0.299849	−	0.953987i	$-0.403064\pi$
$311$	10.5758	0.599698	0.299849	+	0.953987i	$0.403064\pi$
$312$	3.23045	0.182888
$313$	−21.2622	−1.20181	−0.600904	−	0.799321i	$-0.705193\pi$
$313$	−21.2622	−1.20181	−0.600904	+	0.799321i	$0.705193\pi$
$314$	−1.06088	−0.0598692
$315$	4.13136	0.232776
$316$	57.1602	3.21551
$317$	−17.7625	−0.997641	−0.498820	−	0.866705i	$-0.666233\pi$
$317$	−17.7625	−0.997641	−0.498820	+	0.866705i	$0.666233\pi$
$318$	−14.4045	−0.807764
$319$	−39.4693	−2.20985
$320$	−37.9266	−2.12016
$321$	−12.3554	−0.689614
$322$	−10.4014	−0.579645
$323$	7.35052	0.408994
$324$	3.89430	0.216350
$325$	8.47692	0.470215
$326$	−26.7873	−1.48361
$327$	−12.4746	−0.689845
$328$	−20.0787	−1.10866
$329$	2.85801	0.157567
$330$	−44.0993	−2.42759
$331$	−0.606407	−0.0333312	−0.0166656	−	0.999861i	$-0.505305\pi$
$331$	−0.606407	−0.0333312	−0.0166656	+	0.999861i	$0.505305\pi$
$332$	−21.2315	−1.16523
$333$	6.83153	0.374366
$334$	53.6075	2.93327
$335$	6.81636	0.372418
$336$	3.37699	0.184230
$337$	19.3425	1.05365	0.526827	−	0.849973i	$-0.323382\pi$
$337$	19.3425	1.05365	0.526827	+	0.849973i	$0.323382\pi$
$338$	−30.3638	−1.65157
$339$	17.5483	0.953090
$340$	−15.7608	−0.854750
$341$	3.83471	0.207661
$342$	−18.2171	−0.985066
$343$	1.00000	0.0539949
$344$	−29.1880	−1.57371
$345$	−17.6998	−0.952923
$346$	18.5169	0.995475
$347$	17.3328	0.930472	0.465236	−	0.885187i	$-0.345969\pi$
$347$	17.3328	0.930472	0.465236	+	0.885187i	$0.345969\pi$
$348$	34.9596	1.87403
$349$	28.3170	1.51578	0.757888	−	0.652385i	$-0.226231\pi$
$349$	28.3170	1.51578	0.757888	+	0.652385i	$0.226231\pi$
$350$	29.2993	1.56611
$351$	0.702420	0.0374924
$352$	4.39373	0.234187
$353$	−9.94061	−0.529085	−0.264543	−	0.964374i	$-0.585221\pi$
$353$	−9.94061	−0.529085	−0.264543	+	0.964374i	$0.585221\pi$
$354$	14.1693	0.753091
$355$	−64.3531	−3.41551
$356$	−47.2896	−2.50635
$357$	−0.979615	−0.0518467
$358$	−21.2205	−1.12154
$359$	12.6698	0.668689	0.334344	−	0.942451i	$-0.391485\pi$
$359$	12.6698	0.668689	0.334344	+	0.942451i	$0.391485\pi$
$360$	19.0002	1.00140
$361$	37.3021	1.96327
$362$	4.85296	0.255066
$363$	8.33054	0.437240
$364$	2.73544	0.143376
$365$	−15.6661	−0.820004
$366$	1.04681	0.0547177
$367$	13.6547	0.712772	0.356386	−	0.934339i	$-0.384009\pi$
$367$	13.6547	0.712772	0.356386	+	0.934339i	$0.384009\pi$
$368$	−14.4678	−0.754187
$369$	−4.36586	−0.227278
$370$	68.5216	3.56227
$371$	−5.93310	−0.308031
$372$	−3.39657	−0.176104
$373$	−9.79015	−0.506915	−0.253457	−	0.967347i	$-0.581568\pi$
$373$	−9.79015	−0.506915	−0.253457	+	0.967347i	$0.581568\pi$
$374$	10.4567	0.540702
$375$	29.2011	1.50794
$376$	13.1441	0.677853
$377$	6.30571	0.324761
$378$	2.42782	0.124874
$379$	−2.07864	−0.106772	−0.0533862	−	0.998574i	$-0.517001\pi$
$379$	−2.07864	−0.106772	−0.0533862	+	0.998574i	$0.517001\pi$
$380$	−120.722	−6.19289
$381$	1.00000	0.0512316
$382$	−12.2262	−0.625546
$383$	−6.32519	−0.323202	−0.161601	−	0.986856i	$-0.551666\pi$
$383$	−6.32519	−0.323202	−0.161601	+	0.986856i	$0.551666\pi$
$384$	−20.2891	−1.03538
$385$	−18.1642	−0.925731
$386$	12.0444	0.613044
$387$	−6.34656	−0.322614
$388$	36.1877	1.83715
$389$	−10.0363	−0.508859	−0.254429	−	0.967091i	$-0.581888\pi$
$389$	−10.0363	−0.508859	−0.254429	+	0.967091i	$0.581888\pi$
$390$	7.04541	0.356758
$391$	4.19691	0.212247
$392$	4.59902	0.232286
$393$	1.03408	0.0521624
$394$	7.74895	0.390386
$395$	60.6398	3.05112
$396$	−17.1219	−0.860407
$397$	−34.9023	−1.75170	−0.875848	−	0.482588i	$-0.839697\pi$
$397$	−34.9023	−1.75170	−0.875848	+	0.482588i	$0.839697\pi$
$398$	−19.3276	−0.968806
$399$	−7.50347	−0.375643
$400$	40.7540	2.03770
$401$	−22.2029	−1.10876	−0.554380	−	0.832264i	$-0.687045\pi$
$401$	−22.2029	−1.10876	−0.554380	+	0.832264i	$0.687045\pi$
$402$	4.00567	0.199785
$403$	−0.612643	−0.0305179
$404$	39.0157	1.94110
$405$	4.13136	0.205289
$406$	21.7948	1.08166
$407$	−30.0359	−1.48882
$408$	−4.50527	−0.223044
$409$	30.9983	1.53277	0.766384	−	0.642383i	$-0.222054\pi$
$409$	30.9983	1.53277	0.766384	+	0.642383i	$0.222054\pi$
$410$	−43.7905	−2.16266
$411$	10.4831	0.517092
$412$	−40.4444	−1.99255
$413$	5.83624	0.287183
$414$	−10.4014	−0.511199
$415$	−22.5240	−1.10566
$416$	−0.701953	−0.0344161
$417$	9.23389	0.452185
$418$	80.0941	3.91753
$419$	21.8162	1.06579	0.532894	−	0.846182i	$-0.321104\pi$
$419$	21.8162	1.06579	0.532894	+	0.846182i	$0.321104\pi$
$420$	16.0888	0.785052
$421$	0.803041	0.0391378	0.0195689	−	0.999809i	$-0.493771\pi$
$421$	0.803041	0.0391378	0.0195689	+	0.999809i	$0.493771\pi$
$422$	−34.7424	−1.69123
$423$	2.85801	0.138961
$424$	−27.2865	−1.32515
$425$	−11.8222	−0.573459
$426$	−37.8175	−1.83226
$427$	0.431173	0.0208659
$428$	−48.1158	−2.32577
$429$	−3.08830	−0.149104
$430$	−63.6573	−3.06983
$431$	−26.8778	−1.29466	−0.647328	−	0.762211i	$-0.724114\pi$
$431$	−26.8778	−1.29466	−0.647328	+	0.762211i	$0.724114\pi$
$432$	3.37699	0.162475
$433$	−0.181842	−0.00873876	−0.00436938	−	0.999990i	$-0.501391\pi$
$433$	−0.181842	−0.00873876	−0.00436938	+	0.999990i	$0.501391\pi$
$434$	−2.11752	−0.101644
$435$	37.0877	1.77822
$436$	−48.5797	−2.32655
$437$	32.1467	1.53778
$438$	−9.20630	−0.439894
$439$	40.9576	1.95480	0.977401	−	0.211395i	$-0.0678008\pi$
$439$	40.9576	1.95480	0.977401	+	0.211395i	$0.0678008\pi$
$440$	−83.5374	−3.98249
$441$	1.00000	0.0476190
$442$	−1.67059	−0.0794616
$443$	2.65537	0.126161	0.0630803	−	0.998008i	$-0.479908\pi$
$443$	2.65537	0.126161	0.0630803	+	0.998008i	$0.479908\pi$
$444$	26.6040	1.26257
$445$	−50.1683	−2.37821
$446$	32.1106	1.52048
$447$	11.0699	0.523590
$448$	−9.18018	−0.433723
$449$	41.8175	1.97349	0.986744	−	0.162285i	$-0.0518863\pi$
$449$	41.8175	1.97349	0.986744	+	0.162285i	$0.0518863\pi$
$450$	29.2993	1.38118
$451$	19.1952	0.903865
$452$	68.3382	3.21436
$453$	12.6210	0.592984
$454$	71.6524	3.36281
$455$	2.90195	0.136046
$456$	−34.5086	−1.61601
$457$	−8.99792	−0.420905	−0.210452	−	0.977604i	$-0.567494\pi$
$457$	−8.99792	−0.420905	−0.210452	+	0.977604i	$0.567494\pi$
$458$	−37.6834	−1.76083
$459$	−0.979615	−0.0457245
$460$	−68.9282	−3.21379
$461$	−8.15332	−0.379738	−0.189869	−	0.981809i	$-0.560806\pi$
$461$	−8.15332	−0.379738	−0.189869	+	0.981809i	$0.560806\pi$
$462$	−10.6743	−0.496612
$463$	−19.5221	−0.907270	−0.453635	−	0.891188i	$-0.649873\pi$
$463$	−19.5221	−0.907270	−0.453635	+	0.891188i	$0.649873\pi$
$464$	30.3156	1.40737
$465$	−3.60333	−0.167101
$466$	−16.7096	−0.774057
$467$	18.3081	0.847197	0.423598	−	0.905850i	$-0.360767\pi$
$467$	18.3081	0.847197	0.423598	+	0.905850i	$0.360767\pi$
$468$	2.73544	0.126446
$469$	1.64991	0.0761856
$470$	28.6664	1.32228
$471$	−0.436970	−0.0201345
$472$	26.8410	1.23546
$473$	27.9036	1.28301
$474$	35.6353	1.63678
$475$	−90.5531	−4.15486
$476$	−3.81492	−0.174856
$477$	−5.93310	−0.271658
$478$	12.1418	0.555352
$479$	20.4221	0.933111	0.466555	−	0.884492i	$-0.345495\pi$
$479$	20.4221	0.933111	0.466555	+	0.884492i	$0.345495\pi$
$480$	−4.12862	−0.188445
$481$	4.79860	0.218798
$482$	37.7544	1.71967
$483$	−4.28424	−0.194940
$484$	32.4416	1.47462
$485$	38.3906	1.74323
$486$	2.42782	0.110128
$487$	−27.4355	−1.24322	−0.621610	−	0.783327i	$-0.713521\pi$
$487$	−27.4355	−1.24322	−0.621610	+	0.783327i	$0.713521\pi$
$488$	1.98298	0.0897651
$489$	−11.0335	−0.498951
$490$	10.0302	0.453118
$491$	18.0466	0.814431	0.407215	−	0.913332i	$-0.366500\pi$
$491$	18.0466	0.814431	0.407215	+	0.913332i	$0.366500\pi$
$492$	−17.0020	−0.766509
$493$	−8.79412	−0.396067
$494$	−12.7960	−0.575721
$495$	−18.1642	−0.816418
$496$	−2.94537	−0.132251
$497$	−15.5767	−0.698712
$498$	−13.2363	−0.593135
$499$	24.6544	1.10368	0.551842	−	0.833949i	$-0.313925\pi$
$499$	24.6544	1.10368	0.551842	+	0.833949i	$0.313925\pi$
$500$	113.718	5.08563
$501$	22.0805	0.986485
$502$	59.7664	2.66750
$503$	−13.5368	−0.603577	−0.301789	−	0.953375i	$-0.597584\pi$
$503$	−13.5368	−0.603577	−0.301789	+	0.953375i	$0.597584\pi$
$504$	4.59902	0.204857
$505$	41.3907	1.84186
$506$	45.7312	2.03300
$507$	−12.5066	−0.555438
$508$	3.89430	0.172782
$509$	−44.1678	−1.95770	−0.978851	−	0.204576i	$-0.934419\pi$
$509$	−44.1678	−1.95770	−0.978851	+	0.204576i	$0.934419\pi$
$510$	−9.82574	−0.435091
$511$	−3.79200	−0.167748
$512$	−34.4364	−1.52189
$513$	−7.50347	−0.331286
$514$	26.5872	1.17271
$515$	−42.9064	−1.89068
$516$	−24.7154	−1.08804
$517$	−12.5657	−0.552638
$518$	16.5857	0.728735
$519$	7.62698	0.334787
$520$	13.3461	0.585267
$521$	−44.2787	−1.93989	−0.969943	−	0.243331i	$-0.921760\pi$
$521$	−44.2787	−1.93989	−0.969943	+	0.243331i	$0.921760\pi$
$522$	21.7948	0.953933
$523$	0.707142	0.0309212	0.0154606	−	0.999880i	$-0.495079\pi$
$523$	0.707142	0.0309212	0.0154606	+	0.999880i	$0.495079\pi$
$524$	4.02702	0.175921
$525$	12.0682	0.526698
$526$	−58.1274	−2.53448
$527$	0.854410	0.0372187
$528$	−14.8474	−0.646151
$529$	−4.64527	−0.201968
$530$	−59.5102	−2.58496
$531$	5.83624	0.253271
$532$	−29.2208	−1.26688
$533$	−3.06667	−0.132832
$534$	−29.4817	−1.27580
$535$	−51.0448	−2.20686
$536$	7.58796	0.327750
$537$	−8.74055	−0.377182
$538$	−42.7066	−1.84121
$539$	−4.39665	−0.189377
$540$	16.0888	0.692351
$541$	29.3076	1.26003	0.630015	−	0.776583i	$-0.283049\pi$
$541$	29.3076	1.26003	0.630015	+	0.776583i	$0.283049\pi$
$542$	17.0106	0.730669
$543$	1.99890	0.0857809
$544$	0.978964	0.0419728
$545$	−51.5370	−2.20760
$546$	1.70535	0.0729822
$547$	34.9550	1.49457	0.747285	−	0.664504i	$-0.231357\pi$
$547$	34.9550	1.49457	0.747285	+	0.664504i	$0.231357\pi$
$548$	40.8242	1.74393
$549$	0.431173	0.0184020
$550$	−128.819	−5.49285
$551$	−67.3595	−2.86961
$552$	−19.7033	−0.838629
$553$	14.6779	0.624168
$554$	17.0072	0.722569
$555$	28.2235	1.19802
$556$	35.9596	1.52502
$557$	−0.580975	−0.0246167	−0.0123083	−	0.999924i	$-0.503918\pi$
$557$	−0.580975	−0.0246167	−0.0123083	+	0.999924i	$0.503918\pi$
$558$	−2.11752	−0.0896417
$559$	−4.45795	−0.188551
$560$	13.9516	0.589561
$561$	4.30703	0.181843
$562$	−56.4563	−2.38147
$563$	−17.2618	−0.727497	−0.363748	−	0.931497i	$-0.618503\pi$
$563$	−17.2618	−0.727497	−0.363748	+	0.931497i	$0.618503\pi$
$564$	11.1300	0.468656
$565$	72.4982	3.05002
$566$	73.4212	3.08612
$567$	1.00000	0.0419961
$568$	−71.6377	−3.00585
$569$	13.6965	0.574188	0.287094	−	0.957902i	$-0.407311\pi$
$569$	13.6965	0.574188	0.287094	+	0.957902i	$0.407311\pi$
$570$	−75.2613	−3.15235
$571$	−40.5296	−1.69611	−0.848055	−	0.529909i	$-0.822226\pi$
$571$	−40.5296	−1.69611	−0.848055	+	0.529909i	$0.822226\pi$
$572$	−12.0268	−0.502864
$573$	−5.03588	−0.210377
$574$	−10.5995	−0.442415
$575$	−51.7029	−2.15616
$576$	−9.18018	−0.382507
$577$	−19.5066	−0.812069	−0.406035	−	0.913858i	$-0.633089\pi$
$577$	−19.5066	−0.812069	−0.406035	+	0.913858i	$0.633089\pi$
$578$	−38.9431	−1.61982
$579$	4.96100	0.206172
$580$	144.431	5.99716
$581$	−5.45195	−0.226185
$582$	22.5605	0.935161
$583$	26.0858	1.08036
$584$	−17.4395	−0.721652
$585$	2.90195	0.119981
$586$	−38.0589	−1.57220
$587$	20.5249	0.847155	0.423578	−	0.905860i	$-0.360774\pi$
$587$	20.5249	0.847155	0.423578	+	0.905860i	$0.360774\pi$
$588$	3.89430	0.160598
$589$	6.54445	0.269659
$590$	58.5387	2.41000
$591$	3.19173	0.131290
$592$	23.0700	0.948170
$593$	−24.3206	−0.998726	−0.499363	−	0.866393i	$-0.666433\pi$
$593$	−24.3206	−0.998726	−0.499363	+	0.866393i	$0.666433\pi$
$594$	−10.6743	−0.437971
$595$	−4.04715	−0.165917
$596$	43.1097	1.76584
$597$	−7.96090	−0.325818
$598$	−7.30612	−0.298770
$599$	−38.6834	−1.58056	−0.790280	−	0.612746i	$-0.790065\pi$
$599$	−38.6834	−1.58056	−0.790280	+	0.612746i	$0.790065\pi$
$600$	55.5017	2.26585
$601$	19.4855	0.794831	0.397416	−	0.917639i	$-0.369907\pi$
$601$	19.4855	0.794831	0.397416	+	0.917639i	$0.369907\pi$
$602$	−15.4083	−0.627995
$603$	1.64991	0.0671894
$604$	49.1498	1.99988
$605$	34.4165	1.39923
$606$	24.3235	0.988074
$607$	−28.3703	−1.15152	−0.575758	−	0.817620i	$-0.695293\pi$
$607$	−28.3703	−1.15152	−0.575758	+	0.817620i	$0.695293\pi$
$608$	7.49849	0.304104
$609$	8.97712	0.363771
$610$	4.32475	0.175104
$611$	2.00753	0.0812158
$612$	−3.81492	−0.154209
$613$	29.5222	1.19239	0.596196	−	0.802839i	$-0.296678\pi$
$613$	29.5222	1.19239	0.596196	+	0.802839i	$0.296678\pi$
$614$	−19.7611	−0.797493
$615$	−18.0370	−0.727320
$616$	−20.2203	−0.814699
$617$	−31.1688	−1.25481	−0.627405	−	0.778693i	$-0.715883\pi$
$617$	−31.1688	−1.25481	−0.627405	+	0.778693i	$0.715883\pi$
$618$	−25.2142	−1.01426
$619$	11.1738	0.449113	0.224556	−	0.974461i	$-0.427907\pi$
$619$	11.1738	0.449113	0.224556	+	0.974461i	$0.427907\pi$
$620$	−14.0325	−0.563557
$621$	−4.28424	−0.171921
$622$	25.6761	1.02952
$623$	−12.1433	−0.486511
$624$	2.37206	0.0949585
$625$	60.2997	2.41199
$626$	−51.6207	−2.06318
$627$	32.9901	1.31750
$628$	−1.70169	−0.0679050
$629$	−6.69227	−0.266838
$630$	10.0302	0.399613
$631$	7.63983	0.304137	0.152068	−	0.988370i	$-0.451407\pi$
$631$	7.63983	0.304137	0.152068	+	0.988370i	$0.451407\pi$
$632$	67.5040	2.68517
$633$	−14.3101	−0.568777
$634$	−43.1241	−1.71268
$635$	4.13136	0.163948
$636$	−23.1053	−0.916184
$637$	0.702420	0.0278309
$638$	−95.8242	−3.79372
$639$	−15.5767	−0.616206
$640$	−83.8218	−3.31335
$641$	11.2917	0.445994	0.222997	−	0.974819i	$-0.428416\pi$
$641$	11.2917	0.445994	0.222997	+	0.974819i	$0.428416\pi$
$642$	−29.9968	−1.18388
$643$	−20.4181	−0.805212	−0.402606	−	0.915373i	$-0.631896\pi$
$643$	−20.4181	−0.805212	−0.402606	+	0.915373i	$0.631896\pi$
$644$	−16.6841	−0.657447
$645$	−26.2199	−1.03241
$646$	17.8457	0.702130
$647$	−25.7217	−1.01122	−0.505612	−	0.862761i	$-0.668733\pi$
$647$	−25.7217	−1.01122	−0.505612	+	0.862761i	$0.668733\pi$
$648$	4.59902	0.180667
$649$	−25.6599	−1.00724
$650$	20.5804	0.807230
$651$	−0.872190	−0.0341838
$652$	−42.9677	−1.68275
$653$	−23.4539	−0.917821	−0.458910	−	0.888483i	$-0.651760\pi$
$653$	−23.4539	−0.917821	−0.458910	+	0.888483i	$0.651760\pi$
$654$	−30.2860	−1.18428
$655$	4.27216	0.166927
$656$	−14.7435	−0.575635
$657$	−3.79200	−0.147940
$658$	6.93874	0.270500
$659$	−5.91947	−0.230590	−0.115295	−	0.993331i	$-0.536781\pi$
$659$	−5.91947	−0.230590	−0.115295	+	0.993331i	$0.536781\pi$
$660$	−70.7367	−2.75342
$661$	37.2744	1.44981	0.724903	−	0.688851i	$-0.241885\pi$
$661$	37.2744	1.44981	0.724903	+	0.688851i	$0.241885\pi$
$662$	−1.47225	−0.0572205
$663$	−0.688101	−0.0267236
$664$	−25.0736	−0.973046
$665$	−30.9996	−1.20211
$666$	16.5857	0.642683
$667$	−38.4601	−1.48918
$668$	85.9882	3.32698
$669$	13.2261	0.511351
$670$	16.5489	0.639339
$671$	−1.89572	−0.0731834
$672$	−0.999336	−0.0385502
$673$	−19.6036	−0.755662	−0.377831	−	0.925875i	$-0.623330\pi$
$673$	−19.6036	−0.755662	−0.377831	+	0.925875i	$0.623330\pi$
$674$	46.9601	1.80884
$675$	12.0682	0.464504
$676$	−48.7045	−1.87325
$677$	−17.6369	−0.677839	−0.338920	−	0.940815i	$-0.610061\pi$
$677$	−17.6369	−0.677839	−0.338920	+	0.940815i	$0.610061\pi$
$678$	42.6040	1.63620
$679$	9.29248	0.356613
$680$	−18.6129	−0.713773
$681$	29.5131	1.13094
$682$	9.30999	0.356498
$683$	23.3875	0.894896	0.447448	−	0.894310i	$-0.352333\pi$
$683$	23.3875	0.894896	0.447448	+	0.894310i	$0.352333\pi$
$684$	−29.2208	−1.11728
$685$	43.3094	1.65477
$686$	2.42782	0.0926945
$687$	−15.5215	−0.592183
$688$	−21.4322	−0.817097
$689$	−4.16753	−0.158770
$690$	−42.9718	−1.63591
$691$	47.8622	1.82077	0.910383	−	0.413767i	$-0.135787\pi$
$691$	47.8622	1.82077	0.910383	+	0.413767i	$0.135787\pi$
$692$	29.7018	1.12909
$693$	−4.39665	−0.167015
$694$	42.0808	1.59737
$695$	38.1485	1.44706
$696$	41.2860	1.56494
$697$	4.27687	0.161998
$698$	68.7486	2.60217
$699$	−6.88255	−0.260322
$700$	46.9971	1.77632
$701$	−18.8401	−0.711580	−0.355790	−	0.934566i	$-0.615788\pi$
$701$	−18.8401	−0.711580	−0.355790	+	0.934566i	$0.615788\pi$
$702$	1.70535	0.0643642
$703$	−51.2602	−1.93331
$704$	40.3620	1.52120
$705$	11.8075	0.444696
$706$	−24.1340	−0.908295
$707$	10.0187	0.376790
$708$	22.7281	0.854174
$709$	−17.4274	−0.654499	−0.327250	−	0.944938i	$-0.606122\pi$
$709$	−17.4274	−0.654499	−0.327250	+	0.944938i	$0.606122\pi$
$710$	−156.238	−5.86350
$711$	14.6779	0.550464
$712$	−55.8473	−2.09296
$713$	3.73667	0.139939
$714$	−2.37833	−0.0890067
$715$	−12.7589	−0.477155
$716$	−34.0383	−1.27207
$717$	5.00111	0.186770
$718$	30.7601	1.14796
$719$	28.3723	1.05811	0.529055	−	0.848588i	$-0.322547\pi$
$719$	28.3723	1.05811	0.529055	+	0.848588i	$0.322547\pi$
$720$	13.9516	0.519944
$721$	−10.3855	−0.386778
$722$	90.5627	3.37039
$723$	15.5508	0.578339
$724$	7.78431	0.289302
$725$	108.337	4.02355
$726$	20.2250	0.750622
$727$	−39.0293	−1.44752	−0.723758	−	0.690054i	$-0.757587\pi$
$727$	−39.0293	−1.44752	−0.723758	+	0.690054i	$0.757587\pi$
$728$	3.23045	0.119728
$729$	1.00000	0.0370370
$730$	−38.0346	−1.40772
$731$	6.21719	0.229951
$732$	1.67912	0.0620620
$733$	−39.4181	−1.45594	−0.727970	−	0.685609i	$-0.759536\pi$
$733$	−39.4181	−1.45594	−0.727970	+	0.685609i	$0.759536\pi$
$734$	33.1512	1.22363
$735$	4.13136	0.152388
$736$	4.28140	0.157814
$737$	−7.25406	−0.267207
$738$	−10.5995	−0.390174
$739$	39.0447	1.43628	0.718141	−	0.695897i	$-0.244993\pi$
$739$	39.0447	1.43628	0.718141	+	0.695897i	$0.244993\pi$
$740$	109.911	4.04041
$741$	−5.27059	−0.193620
$742$	−14.4045	−0.528806
$743$	49.4864	1.81548	0.907741	−	0.419532i	$-0.137806\pi$
$743$	49.4864	1.81548	0.907741	+	0.419532i	$0.137806\pi$
$744$	−4.01122	−0.147058
$745$	45.7339	1.67556
$746$	−23.7687	−0.870234
$747$	−5.45195	−0.199476
$748$	16.7729	0.613277
$749$	−12.3554	−0.451458
$750$	70.8950	2.58872
$751$	19.6553	0.717231	0.358616	−	0.933485i	$-0.383249\pi$
$751$	19.6553	0.717231	0.358616	+	0.933485i	$0.383249\pi$
$752$	9.65147	0.351953
$753$	24.6173	0.897105
$754$	15.3091	0.557525
$755$	52.1418	1.89763
$756$	3.89430	0.141634
$757$	−31.7636	−1.15447	−0.577234	−	0.816579i	$-0.695868\pi$
$757$	−31.7636	−1.15447	−0.577234	+	0.816579i	$0.695868\pi$
$758$	−5.04655	−0.183299
$759$	18.8363	0.683715
$760$	−142.568	−5.17147
$761$	−17.6652	−0.640365	−0.320182	−	0.947356i	$-0.603744\pi$
$761$	−17.6652	−0.640365	−0.320182	+	0.947356i	$0.603744\pi$
$762$	2.42782	0.0879506
$763$	−12.4746	−0.451610
$764$	−19.6112	−0.709509
$765$	−4.04715	−0.146325
$766$	−15.3564	−0.554850
$767$	4.09949	0.148024
$768$	−30.8980	−1.11493
$769$	45.2679	1.63240	0.816201	−	0.577769i	$-0.196076\pi$
$769$	45.2679	1.63240	0.816201	+	0.577769i	$0.196076\pi$
$770$	−44.0993	−1.58923
$771$	10.9511	0.394392
$772$	19.3196	0.695329
$773$	−12.0686	−0.434079	−0.217039	−	0.976163i	$-0.569640\pi$
$773$	−12.0686	−0.434079	−0.217039	+	0.976163i	$0.569640\pi$
$774$	−15.4083	−0.553840
$775$	−10.5257	−0.378095
$776$	42.7363	1.53415
$777$	6.83153	0.245080
$778$	−24.3662	−0.873572
$779$	32.7591	1.17372
$780$	11.3011	0.404644
$781$	68.4855	2.45060
$782$	10.1893	0.364370
$783$	8.97712	0.320816
$784$	3.37699	0.120607
$785$	−1.80528	−0.0644333
$786$	2.51056	0.0895487
$787$	24.7311	0.881569	0.440785	−	0.897613i	$-0.354700\pi$
$787$	24.7311	0.881569	0.440785	+	0.897613i	$0.354700\pi$
$788$	12.4296	0.442785
$789$	−23.9422	−0.852366
$790$	147.222	5.23793
$791$	17.5483	0.623944
$792$	−20.2203	−0.718497
$793$	0.302865	0.0107550
$794$	−84.7364	−3.00718
$795$	−24.5118	−0.869344
$796$	−31.0022	−1.09884
$797$	−16.3346	−0.578603	−0.289301	−	0.957238i	$-0.593423\pi$
$797$	−16.3346	−0.578603	−0.289301	+	0.957238i	$0.593423\pi$
$798$	−18.2171	−0.644877
$799$	−2.79975	−0.0990482
$800$	−12.0601	−0.426390
$801$	−12.1433	−0.429062
$802$	−53.9046	−1.90344
$803$	16.6721	0.588346
$804$	6.42523	0.226601
$805$	−17.6998	−0.623834
$806$	−1.48739	−0.0523910
$807$	−17.5905	−0.619216
$808$	46.0760	1.62095
$809$	−48.7035	−1.71232	−0.856162	−	0.516707i	$-0.827157\pi$
$809$	−48.7035	−1.71232	−0.856162	+	0.516707i	$0.827157\pi$
$810$	10.0302	0.352425
$811$	5.69549	0.199996	0.0999978	−	0.994988i	$-0.468116\pi$
$811$	5.69549	0.199996	0.0999978	+	0.994988i	$0.468116\pi$
$812$	34.9596	1.22684
$813$	7.00655	0.245730
$814$	−72.9216	−2.55590
$815$	−45.5833	−1.59671
$816$	−3.30815	−0.115808
$817$	47.6212	1.66606
$818$	75.2582	2.63134
$819$	0.702420	0.0245445
$820$	−70.2414	−2.45294
$821$	−30.3036	−1.05760	−0.528802	−	0.848745i	$-0.677359\pi$
$821$	−30.3036	−1.05760	−0.528802	+	0.848745i	$0.677359\pi$
$822$	25.4510	0.887705
$823$	−1.13612	−0.0396027	−0.0198014	−	0.999804i	$-0.506303\pi$
$823$	−1.13612	−0.0396027	−0.0198014	+	0.999804i	$0.506303\pi$
$824$	−47.7633	−1.66391
$825$	−53.0595	−1.84729
$826$	14.1693	0.493014
$827$	−34.1644	−1.18801	−0.594006	−	0.804460i	$-0.702455\pi$
$827$	−34.1644	−1.18801	−0.594006	+	0.804460i	$0.702455\pi$
$828$	−16.6841	−0.579814
$829$	−16.2966	−0.566004	−0.283002	−	0.959119i	$-0.591330\pi$
$829$	−16.2966	−0.566004	−0.283002	+	0.959119i	$0.591330\pi$
$830$	−54.6842	−1.89811
$831$	7.00516	0.243006
$832$	−6.44834	−0.223556
$833$	−0.979615	−0.0339417
$834$	22.4182	0.776279
$835$	91.2227	3.15689
$836$	128.474	4.44335
$837$	−0.872190	−0.0301473
$838$	52.9657	1.82967
$839$	26.2732	0.907053	0.453526	−	0.891243i	$-0.350166\pi$
$839$	26.2732	0.907053	0.453526	+	0.891243i	$0.350166\pi$
$840$	19.0002	0.655570
$841$	51.5887	1.77892
$842$	1.94964	0.0671890
$843$	−23.2539	−0.800908
$844$	−55.7280	−1.91824
$845$	−51.6693	−1.77748
$846$	6.93874	0.238559
$847$	8.33054	0.286241
$848$	−20.0360	−0.688039
$849$	30.2416	1.03789
$850$	−28.7020	−0.984472
$851$	−29.2679	−1.00329
$852$	−60.6605	−2.07819
$853$	49.7979	1.70505	0.852524	−	0.522689i	$-0.175071\pi$
$853$	49.7979	1.70505	0.852524	+	0.522689i	$0.175071\pi$
$854$	1.04681	0.0358211
$855$	−30.9996	−1.06016
$856$	−56.8230	−1.94217
$857$	31.7264	1.08375	0.541877	−	0.840458i	$-0.317714\pi$
$857$	31.7264	1.08375	0.541877	+	0.840458i	$0.317714\pi$
$858$	−7.49782	−0.255971
$859$	2.93883	0.100272	0.0501359	−	0.998742i	$-0.484035\pi$
$859$	2.93883	0.100272	0.0501359	+	0.998742i	$0.484035\pi$
$860$	−102.108	−3.48187
$861$	−4.36586	−0.148788
$862$	−65.2543	−2.22257
$863$	48.0520	1.63571	0.817854	−	0.575425i	$-0.195163\pi$
$863$	48.0520	1.63571	0.817854	+	0.575425i	$0.195163\pi$
$864$	−0.999336	−0.0339981
$865$	31.5098	1.07137
$866$	−0.441479	−0.0150021
$867$	−16.0404	−0.544759
$868$	−3.39657	−0.115287
$869$	−64.5336	−2.18915
$870$	90.0423	3.05272
$871$	1.15893	0.0392688
$872$	−57.3708	−1.94282
$873$	9.29248	0.314503
$874$	78.0463	2.63996
$875$	29.2011	0.987178
$876$	−14.7672	−0.498938
$877$	1.45427	0.0491073	0.0245537	−	0.999699i	$-0.492184\pi$
$877$	1.45427	0.0491073	0.0245537	+	0.999699i	$0.492184\pi$
$878$	99.4377	3.35586
$879$	−15.6762	−0.528744
$880$	−61.3401	−2.06777
$881$	54.9217	1.85036	0.925179	−	0.379530i	$-0.123914\pi$
$881$	54.9217	1.85036	0.925179	+	0.379530i	$0.123914\pi$
$882$	2.42782	0.0817489
$883$	47.7578	1.60718	0.803590	−	0.595184i	$-0.202921\pi$
$883$	47.7578	1.60718	0.803590	+	0.595184i	$0.202921\pi$
$884$	−2.67968	−0.0901272
$885$	24.1116	0.810503
$886$	6.44676	0.216583
$887$	−13.5209	−0.453987	−0.226994	−	0.973896i	$-0.572890\pi$
$887$	−13.5209	−0.453987	−0.226994	+	0.973896i	$0.572890\pi$
$888$	31.4184	1.05433
$889$	1.00000	0.0335389
$890$	−121.800	−4.08273
$891$	−4.39665	−0.147293
$892$	51.5065	1.72456
$893$	−21.4450	−0.717630
$894$	26.8758	0.898861
$895$	−36.1104	−1.20704
$896$	−20.2891	−0.677812
$897$	−3.00934	−0.100479
$898$	101.525	3.38794
$899$	−7.82975	−0.261137
$900$	46.9971	1.56657
$901$	5.81216	0.193631
$902$	46.6024	1.55169
$903$	−6.34656	−0.211200
$904$	80.7048	2.68420
$905$	8.25817	0.274511
$906$	30.6414	1.01799
$907$	−51.1164	−1.69729	−0.848646	−	0.528962i	$-0.822581\pi$
$907$	−51.1164	−1.69729	−0.848646	+	0.528962i	$0.822581\pi$
$908$	114.933	3.81418
$909$	10.0187	0.332298
$910$	7.04541	0.233553
$911$	−33.9841	−1.12594	−0.562972	−	0.826476i	$-0.690342\pi$
$911$	−33.9841	−1.12594	−0.562972	+	0.826476i	$0.690342\pi$
$912$	−25.3391	−0.839062
$913$	23.9703	0.793302
$914$	−21.8453	−0.722579
$915$	1.78133	0.0588891
$916$	−60.4455	−1.99717
$917$	1.03408	0.0341483
$918$	−2.37833	−0.0784965
$919$	35.3987	1.16770	0.583848	−	0.811863i	$-0.301546\pi$
$919$	35.3987	1.16770	0.583848	+	0.811863i	$0.301546\pi$
$920$	−81.4016	−2.68373
$921$	−8.13944	−0.268204
$922$	−19.7948	−0.651907
$923$	−10.9414	−0.360141
$924$	−17.1219	−0.563269
$925$	82.4440	2.71074
$926$	−47.3962	−1.55754
$927$	−10.3855	−0.341106
$928$	−8.97115	−0.294493
$929$	−24.3384	−0.798518	−0.399259	−	0.916838i	$-0.630733\pi$
$929$	−24.3384	−0.798518	−0.399259	+	0.916838i	$0.630733\pi$
$930$	−8.74823	−0.286866
$931$	−7.50347	−0.245916
$932$	−26.8027	−0.877953
$933$	10.5758	0.346236
$934$	44.4487	1.45441
$935$	17.7939	0.581922
$936$	3.23045	0.105590
$937$	6.36212	0.207841	0.103921	−	0.994586i	$-0.466861\pi$
$937$	6.36212	0.207841	0.103921	+	0.994586i	$0.466861\pi$
$938$	4.00567	0.130790
$939$	−21.2622	−0.693864
$940$	45.9819	1.49977
$941$	−21.9441	−0.715358	−0.357679	−	0.933845i	$-0.616432\pi$
$941$	−21.9441	−0.715358	−0.357679	+	0.933845i	$0.616432\pi$
$942$	−1.06088	−0.0345655
$943$	18.7044	0.609099
$944$	19.7089	0.641470
$945$	4.13136	0.134393
$946$	67.7449	2.20258
$947$	−25.7408	−0.836463	−0.418232	−	0.908340i	$-0.637350\pi$
$947$	−25.7408	−0.836463	−0.418232	+	0.908340i	$0.637350\pi$
$948$	57.1602	1.85648
$949$	−2.66358	−0.0864635
$950$	−219.846	−7.13276
$951$	−17.7625	−0.575988
$952$	−4.50527	−0.146017
$953$	9.17939	0.297350	0.148675	−	0.988886i	$-0.452499\pi$
$953$	9.17939	0.297350	0.148675	+	0.988886i	$0.452499\pi$
$954$	−14.4045	−0.466363
$955$	−20.8050	−0.673235
$956$	19.4758	0.629893
$957$	−39.4693	−1.27586
$958$	49.5812	1.60190
$959$	10.4831	0.338516
$960$	−37.9266	−1.22408
$961$	−30.2393	−0.975461
$962$	11.6501	0.375616
$963$	−12.3554	−0.398149
$964$	60.5594	1.95049
$965$	20.4957	0.659780
$966$	−10.4014	−0.334658
$967$	57.5730	1.85142	0.925711	−	0.378231i	$-0.123467\pi$
$967$	57.5730	1.85142	0.925711	+	0.378231i	$0.123467\pi$
$968$	38.3123	1.23141
$969$	7.35052	0.236133
$970$	93.2055	2.99265
$971$	−9.99471	−0.320745	−0.160373	−	0.987057i	$-0.551270\pi$
$971$	−9.99471	−0.320745	−0.160373	+	0.987057i	$0.551270\pi$
$972$	3.89430	0.124910
$973$	9.23389	0.296025
$974$	−66.6084	−2.13427
$975$	8.47692	0.271479
$976$	1.45607	0.0466075
$977$	21.4270	0.685510	0.342755	−	0.939425i	$-0.388640\pi$
$977$	21.4270	0.685510	0.342755	+	0.939425i	$0.388640\pi$
$978$	−26.7873	−0.856563
$979$	53.3898	1.70635
$980$	16.0888	0.513937
$981$	−12.4746	−0.398282
$982$	43.8138	1.39816
$983$	−5.16510	−0.164741	−0.0823705	−	0.996602i	$-0.526249\pi$
$983$	−5.16510	−0.164741	−0.0823705	+	0.996602i	$0.526249\pi$
$984$	−20.0787	−0.640085
$985$	13.1862	0.420147
$986$	−21.3505	−0.679940
$987$	2.85801	0.0909716
$988$	−20.5253	−0.652996
$989$	27.1902	0.864598
$990$	−44.0993	−1.40157
$991$	47.8521	1.52007	0.760036	−	0.649881i	$-0.225181\pi$
$991$	47.8521	1.52007	0.760036	+	0.649881i	$0.225181\pi$
$992$	0.871610	0.0276736
$993$	−0.606407	−0.0192438
$994$	−37.8175	−1.19950
$995$	−32.8894	−1.04266
$996$	−21.2315	−0.672747
$997$	21.8952	0.693429	0.346714	−	0.937971i	$-0.387297\pi$
$997$	21.8952	0.693429	0.346714	+	0.937971i	$0.387297\pi$
$998$	59.8564	1.89472
$999$	6.83153	0.216140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2667.2.a.q.1.17	✓	19
3.2	odd	2		8001.2.a.v.1.3		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2667.2.a.q.1.17	✓	19	1.1	even	1	trivial
8001.2.a.v.1.3		19	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:	\( N \)	\(=\)	\( 2667 = 3 \cdot 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2667.a (trivial)

\(f(q)\)	\(=\)	\(q+2.42782 q^{2} +1.00000 q^{3} +3.89430 q^{4} +4.13136 q^{5} +2.42782 q^{6} +1.00000 q^{7} +4.59902 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.42782 q^{2} +1.00000 q^{3} +3.89430 q^{4} +4.13136 q^{5} +2.42782 q^{6} +1.00000 q^{7} +4.59902 q^{8} +1.00000 q^{9} +10.0302 q^{10} -4.39665 q^{11} +3.89430 q^{12} +0.702420 q^{13} +2.42782 q^{14} +4.13136 q^{15} +3.37699 q^{16} -0.979615 q^{17} +2.42782 q^{18} -7.50347 q^{19} +16.0888 q^{20} +1.00000 q^{21} -10.6743 q^{22} -4.28424 q^{23} +4.59902 q^{24} +12.0682 q^{25} +1.70535 q^{26} +1.00000 q^{27} +3.89430 q^{28} +8.97712 q^{29} +10.0302 q^{30} -0.872190 q^{31} -0.999336 q^{32} -4.39665 q^{33} -2.37833 q^{34} +4.13136 q^{35} +3.89430 q^{36} +6.83153 q^{37} -18.2171 q^{38} +0.702420 q^{39} +19.0002 q^{40} -4.36586 q^{41} +2.42782 q^{42} -6.34656 q^{43} -17.1219 q^{44} +4.13136 q^{45} -10.4014 q^{46} +2.85801 q^{47} +3.37699 q^{48} +1.00000 q^{49} +29.2993 q^{50} -0.979615 q^{51} +2.73544 q^{52} -5.93310 q^{53} +2.42782 q^{54} -18.1642 q^{55} +4.59902 q^{56} -7.50347 q^{57} +21.7948 q^{58} +5.83624 q^{59} +16.0888 q^{60} +0.431173 q^{61} -2.11752 q^{62} +1.00000 q^{63} -9.18018 q^{64} +2.90195 q^{65} -10.6743 q^{66} +1.64991 q^{67} -3.81492 q^{68} -4.28424 q^{69} +10.0302 q^{70} -15.5767 q^{71} +4.59902 q^{72} -3.79200 q^{73} +16.5857 q^{74} +12.0682 q^{75} -29.2208 q^{76} -4.39665 q^{77} +1.70535 q^{78} +14.6779 q^{79} +13.9516 q^{80} +1.00000 q^{81} -10.5995 q^{82} -5.45195 q^{83} +3.89430 q^{84} -4.04715 q^{85} -15.4083 q^{86} +8.97712 q^{87} -20.2203 q^{88} -12.1433 q^{89} +10.0302 q^{90} +0.702420 q^{91} -16.6841 q^{92} -0.872190 q^{93} +6.93874 q^{94} -30.9996 q^{95} -0.999336 q^{96} +9.29248 q^{97} +2.42782 q^{98} -4.39665 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9}+O(q^{10}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9	\( 19 q + 4 q^{2} + 19 q^{3} + 22 q^{4} + 5 q^{5} + 4 q^{6} + 19 q^{7} + 9 q^{8} + 19 q^{9} - 9 q^{11} + 22 q^{12} + 24 q^{13} + 4 q^{14} + 5 q^{15} + 20 q^{16} + 17 q^{17} + 4 q^{18} + 23 q^{19} + 5 q^{20} + 19 q^{21} - 3 q^{22} - 17 q^{23} + 9 q^{24} + 38 q^{25} + 28 q^{26} + 19 q^{27} + 22 q^{28} + 2 q^{29} + 16 q^{31} + 17 q^{32} - 9 q^{33} + 29 q^{34} + 5 q^{35} + 22 q^{36} + 56 q^{37} + 2 q^{38} + 24 q^{39} - 13 q^{40} - 7 q^{41} + 4 q^{42} + 19 q^{43} - 29 q^{44} + 5 q^{45} + 10 q^{46} + 25 q^{47} + 20 q^{48} + 19 q^{49} - 9 q^{50} + 17 q^{51} + 16 q^{52} + 18 q^{53} + 4 q^{54} + 10 q^{55} + 9 q^{56} + 23 q^{57} + 31 q^{58} + 11 q^{59} + 5 q^{60} + 26 q^{61} + 26 q^{62} + 19 q^{63} + 45 q^{64} + 27 q^{65} - 3 q^{66} + 24 q^{67} + 14 q^{68} - 17 q^{69} - 32 q^{71} + 9 q^{72} + 51 q^{73} + 38 q^{75} + 12 q^{76} - 9 q^{77} + 28 q^{78} + 30 q^{79} - 30 q^{80} + 19 q^{81} - 52 q^{82} + q^{83} + 22 q^{84} + 44 q^{85} - 24 q^{86} + 2 q^{87} - 30 q^{88} + 5 q^{89} + 24 q^{91} - 88 q^{92} + 16 q^{93} + 7 q^{94} - 24 q^{95} + 17 q^{96} + 5 q^{97} + 4 q^{98} - 9 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 19 * q^3 + 22 * q^4 + 5 * q^5 + 4 * q^6 + 19 * q^7 + 9 * q^8 + 19 * q^9 - 9 * q^11 + 22 * q^12 + 24 * q^13 + 4 * q^14 + 5 * q^15 + 20 * q^16 + 17 * q^17 + 4 * q^18 + 23 * q^19 + 5 * q^20 + 19 * q^21 - 3 * q^22 - 17 * q^23 + 9 * q^24 + 38 * q^25 + 28 * q^26 + 19 * q^27 + 22 * q^28 + 2 * q^29 + 16 * q^31 + 17 * q^32 - 9 * q^33 + 29 * q^34 + 5 * q^35 + 22 * q^36 + 56 * q^37 + 2 * q^38 + 24 * q^39 - 13 * q^40 - 7 * q^41 + 4 * q^42 + 19 * q^43 - 29 * q^44 + 5 * q^45 + 10 * q^46 + 25 * q^47 + 20 * q^48 + 19 * q^49 - 9 * q^50 + 17 * q^51 + 16 * q^52 + 18 * q^53 + 4 * q^54 + 10 * q^55 + 9 * q^56 + 23 * q^57 + 31 * q^58 + 11 * q^59 + 5 * q^60 + 26 * q^61 + 26 * q^62 + 19 * q^63 + 45 * q^64 + 27 * q^65 - 3 * q^66 + 24 * q^67 + 14 * q^68 - 17 * q^69 - 32 * q^71 + 9 * q^72 + 51 * q^73 + 38 * q^75 + 12 * q^76 - 9 * q^77 + 28 * q^78 + 30 * q^79 - 30 * q^80 + 19 * q^81 - 52 * q^82 + q^83 + 22 * q^84 + 44 * q^85 - 24 * q^86 + 2 * q^87 - 30 * q^88 + 5 * q^89 + 24 * q^91 - 88 * q^92 + 16 * q^93 + 7 * q^94 - 24 * q^95 + 17 * q^96 + 5 * q^97 + 4 * q^98 - 9 * q^99

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