LMFDB - Embedded newform 6010.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 $ x^16 - 8x^15 + 9x^14 + 75x^13 - 178x^12 - 232x^11 + 872x^10 + 228x^9 - 1986x^8 + 164x^7 + 2332x^6 - 440x^5 - 1344x^4 + 244x^3 + 295x^2 - 41*x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$1.74152$ of defining polynomial
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.741521 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.741521 q^{6} -2.92320 q^{7} +1.00000 q^{8} -2.45015 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.741521 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.741521 q^{6} -2.92320 q^{7} +1.00000 q^{8} -2.45015 q^{9} +1.00000 q^{10} +3.78605 q^{11} +0.741521 q^{12} -1.20674 q^{13} -2.92320 q^{14} +0.741521 q^{15} +1.00000 q^{16} +2.24040 q^{17} -2.45015 q^{18} -6.75626 q^{19} +1.00000 q^{20} -2.16761 q^{21} +3.78605 q^{22} -2.16212 q^{23} +0.741521 q^{24} +1.00000 q^{25} -1.20674 q^{26} -4.04140 q^{27} -2.92320 q^{28} -7.43472 q^{29} +0.741521 q^{30} +2.54924 q^{31} +1.00000 q^{32} +2.80743 q^{33} +2.24040 q^{34} -2.92320 q^{35} -2.45015 q^{36} -2.16013 q^{37} -6.75626 q^{38} -0.894820 q^{39} +1.00000 q^{40} -4.79426 q^{41} -2.16761 q^{42} +2.62620 q^{43} +3.78605 q^{44} -2.45015 q^{45} -2.16212 q^{46} -9.28939 q^{47} +0.741521 q^{48} +1.54507 q^{49} +1.00000 q^{50} +1.66131 q^{51} -1.20674 q^{52} -4.24197 q^{53} -4.04140 q^{54} +3.78605 q^{55} -2.92320 q^{56} -5.00990 q^{57} -7.43472 q^{58} -2.50293 q^{59} +0.741521 q^{60} -2.21161 q^{61} +2.54924 q^{62} +7.16226 q^{63} +1.00000 q^{64} -1.20674 q^{65} +2.80743 q^{66} -6.47843 q^{67} +2.24040 q^{68} -1.60326 q^{69} -2.92320 q^{70} +3.13750 q^{71} -2.45015 q^{72} +7.55686 q^{73} -2.16013 q^{74} +0.741521 q^{75} -6.75626 q^{76} -11.0674 q^{77} -0.894820 q^{78} -7.16658 q^{79} +1.00000 q^{80} +4.35366 q^{81} -4.79426 q^{82} +14.7455 q^{83} -2.16761 q^{84} +2.24040 q^{85} +2.62620 q^{86} -5.51300 q^{87} +3.78605 q^{88} +10.3519 q^{89} -2.45015 q^{90} +3.52753 q^{91} -2.16212 q^{92} +1.89031 q^{93} -9.28939 q^{94} -6.75626 q^{95} +0.741521 q^{96} -6.45797 q^{97} +1.54507 q^{98} -9.27637 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.741521	0.428117	0.214059	−	0.976821i	$-0.431332\pi$
$3$	0.741521	0.428117	0.214059	+	0.976821i	$0.431332\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.741521	0.302725
$7$	−2.92320	−1.10486	−0.552432	−	0.833558i	$-0.686300\pi$
$7$	−2.92320	−1.10486	−0.552432	+	0.833558i	$0.686300\pi$
$8$	1.00000	0.353553
$9$	−2.45015	−0.816716
$10$	1.00000	0.316228
$11$	3.78605	1.14154	0.570768	−	0.821111i	$-0.306646\pi$
$11$	3.78605	1.14154	0.570768	+	0.821111i	$0.306646\pi$
$12$	0.741521	0.214059
$13$	−1.20674	−0.334688	−0.167344	−	0.985899i	$-0.553519\pi$
$13$	−1.20674	−0.334688	−0.167344	+	0.985899i	$0.553519\pi$
$14$	−2.92320	−0.781257
$15$	0.741521	0.191460
$16$	1.00000	0.250000
$17$	2.24040	0.543378	0.271689	−	0.962385i	$-0.412418\pi$
$17$	2.24040	0.543378	0.271689	+	0.962385i	$0.412418\pi$
$18$	−2.45015	−0.577505
$19$	−6.75626	−1.54999	−0.774996	−	0.631967i	$-0.782248\pi$
$19$	−6.75626	−1.54999	−0.774996	+	0.631967i	$0.782248\pi$
$20$	1.00000	0.223607
$21$	−2.16761	−0.473011
$22$	3.78605	0.807188
$23$	−2.16212	−0.450833	−0.225416	−	0.974263i	$-0.572374\pi$
$23$	−2.16212	−0.450833	−0.225416	+	0.974263i	$0.572374\pi$
$24$	0.741521	0.151362
$25$	1.00000	0.200000
$26$	−1.20674	−0.236660
$27$	−4.04140	−0.777767
$28$	−2.92320	−0.552432
$29$	−7.43472	−1.38059	−0.690297	−	0.723527i	$-0.742520\pi$
$29$	−7.43472	−1.38059	−0.690297	+	0.723527i	$0.742520\pi$
$30$	0.741521	0.135383
$31$	2.54924	0.457856	0.228928	−	0.973443i	$-0.426478\pi$
$31$	2.54924	0.457856	0.228928	+	0.973443i	$0.426478\pi$
$32$	1.00000	0.176777
$33$	2.80743	0.488711
$34$	2.24040	0.384226
$35$	−2.92320	−0.494110
$36$	−2.45015	−0.408358
$37$	−2.16013	−0.355124	−0.177562	−	0.984110i	$-0.556821\pi$
$37$	−2.16013	−0.355124	−0.177562	+	0.984110i	$0.556821\pi$
$38$	−6.75626	−1.09601
$39$	−0.894820	−0.143286
$40$	1.00000	0.158114
$41$	−4.79426	−0.748737	−0.374369	−	0.927280i	$-0.622141\pi$
$41$	−4.79426	−0.748737	−0.374369	+	0.927280i	$0.622141\pi$
$42$	−2.16761	−0.334470
$43$	2.62620	0.400492	0.200246	−	0.979746i	$-0.435826\pi$
$43$	2.62620	0.400492	0.200246	+	0.979746i	$0.435826\pi$
$44$	3.78605	0.570768
$45$	−2.45015	−0.365246
$46$	−2.16212	−0.318787
$47$	−9.28939	−1.35500	−0.677499	−	0.735524i	$-0.736936\pi$
$47$	−9.28939	−1.35500	−0.677499	+	0.735524i	$0.736936\pi$
$48$	0.741521	0.107029
$49$	1.54507	0.220724
$50$	1.00000	0.141421
$51$	1.66131	0.232629
$52$	−1.20674	−0.167344
$53$	−4.24197	−0.582680	−0.291340	−	0.956620i	$-0.594101\pi$
$53$	−4.24197	−0.582680	−0.291340	+	0.956620i	$0.594101\pi$
$54$	−4.04140	−0.549965
$55$	3.78605	0.510510
$56$	−2.92320	−0.390628
$57$	−5.00990	−0.663578
$58$	−7.43472	−0.976227
$59$	−2.50293	−0.325854	−0.162927	−	0.986638i	$-0.552094\pi$
$59$	−2.50293	−0.325854	−0.162927	+	0.986638i	$0.552094\pi$
$60$	0.741521	0.0957299
$61$	−2.21161	−0.283167	−0.141584	−	0.989926i	$-0.545219\pi$
$61$	−2.21161	−0.283167	−0.141584	+	0.989926i	$0.545219\pi$
$62$	2.54924	0.323753
$63$	7.16226	0.902359
$64$	1.00000	0.125000
$65$	−1.20674	−0.149677
$66$	2.80743	0.345571
$67$	−6.47843	−0.791467	−0.395733	−	0.918365i	$-0.629510\pi$
$67$	−6.47843	−0.791467	−0.395733	+	0.918365i	$0.629510\pi$
$68$	2.24040	0.271689
$69$	−1.60326	−0.193009
$70$	−2.92320	−0.349389
$71$	3.13750	0.372352	0.186176	−	0.982516i	$-0.440390\pi$
$71$	3.13750	0.372352	0.186176	+	0.982516i	$0.440390\pi$
$72$	−2.45015	−0.288753
$73$	7.55686	0.884464	0.442232	−	0.896901i	$-0.354187\pi$
$73$	7.55686	0.884464	0.442232	+	0.896901i	$0.354187\pi$
$74$	−2.16013	−0.251110
$75$	0.741521	0.0856235
$76$	−6.75626	−0.774996
$77$	−11.0674	−1.26124
$78$	−0.894820	−0.101318
$79$	−7.16658	−0.806303	−0.403152	−	0.915133i	$-0.632085\pi$
$79$	−7.16658	−0.806303	−0.403152	+	0.915133i	$0.632085\pi$
$80$	1.00000	0.111803
$81$	4.35366	0.483740
$82$	−4.79426	−0.529437
$83$	14.7455	1.61852	0.809262	−	0.587447i	$-0.199867\pi$
$83$	14.7455	1.61852	0.809262	+	0.587447i	$0.199867\pi$
$84$	−2.16761	−0.236506
$85$	2.24040	0.243006
$86$	2.62620	0.283191
$87$	−5.51300	−0.591056
$88$	3.78605	0.403594
$89$	10.3519	1.09730	0.548652	−	0.836051i	$-0.315141\pi$
$89$	10.3519	1.09730	0.548652	+	0.836051i	$0.315141\pi$
$90$	−2.45015	−0.258268
$91$	3.52753	0.369785
$92$	−2.16212	−0.225416
$93$	1.89031	0.196016
$94$	−9.28939	−0.958128
$95$	−6.75626	−0.693177
$96$	0.741521	0.0756812
$97$	−6.45797	−0.655708	−0.327854	−	0.944728i	$-0.606325\pi$
$97$	−6.45797	−0.655708	−0.327854	+	0.944728i	$0.606325\pi$
$98$	1.54507	0.156076
$99$	−9.27637	−0.932310
$100$	1.00000	0.100000
$101$	3.69551	0.367717	0.183858	−	0.982953i	$-0.441141\pi$
$101$	3.69551	0.367717	0.183858	+	0.982953i	$0.441141\pi$
$102$	1.66131	0.164494
$103$	6.19576	0.610487	0.305243	−	0.952274i	$-0.401262\pi$
$103$	6.19576	0.610487	0.305243	+	0.952274i	$0.401262\pi$
$104$	−1.20674	−0.118330
$105$	−2.16761	−0.211537
$106$	−4.24197	−0.412017
$107$	−4.26814	−0.412617	−0.206309	−	0.978487i	$-0.566145\pi$
$107$	−4.26814	−0.412617	−0.206309	+	0.978487i	$0.566145\pi$
$108$	−4.04140	−0.388884
$109$	−6.78094	−0.649496	−0.324748	−	0.945800i	$-0.605280\pi$
$109$	−6.78094	−0.649496	−0.324748	+	0.945800i	$0.605280\pi$
$110$	3.78605	0.360985
$111$	−1.60178	−0.152035
$112$	−2.92320	−0.276216
$113$	−12.8387	−1.20776	−0.603881	−	0.797075i	$-0.706380\pi$
$113$	−12.8387	−1.20776	−0.603881	+	0.797075i	$0.706380\pi$
$114$	−5.00990	−0.469221
$115$	−2.16212	−0.201619
$116$	−7.43472	−0.690297
$117$	2.95668	0.273345
$118$	−2.50293	−0.230414
$119$	−6.54914	−0.600358
$120$	0.741521	0.0676913
$121$	3.33415	0.303105
$122$	−2.21161	−0.200229
$123$	−3.55504	−0.320547
$124$	2.54924	0.228928
$125$	1.00000	0.0894427
$126$	7.16226	0.638065
$127$	−21.5834	−1.91522	−0.957610	−	0.288069i	$-0.906987\pi$
$127$	−21.5834	−1.91522	−0.957610	+	0.288069i	$0.906987\pi$
$128$	1.00000	0.0883883
$129$	1.94739	0.171458
$130$	−1.20674	−0.105838
$131$	−1.86617	−0.163048	−0.0815242	−	0.996671i	$-0.525979\pi$
$131$	−1.86617	−0.163048	−0.0815242	+	0.996671i	$0.525979\pi$
$132$	2.80743	0.244356
$133$	19.7499	1.71253
$134$	−6.47843	−0.559651
$135$	−4.04140	−0.347828
$136$	2.24040	0.192113
$137$	16.5456	1.41358	0.706792	−	0.707421i	$-0.250141\pi$
$137$	16.5456	1.41358	0.706792	+	0.707421i	$0.250141\pi$
$138$	−1.60326	−0.136478
$139$	17.7109	1.50222	0.751111	−	0.660176i	$-0.229518\pi$
$139$	17.7109	1.50222	0.751111	+	0.660176i	$0.229518\pi$
$140$	−2.92320	−0.247055
$141$	−6.88828	−0.580098
$142$	3.13750	0.263293
$143$	−4.56876	−0.382059
$144$	−2.45015	−0.204179
$145$	−7.43472	−0.617420
$146$	7.55686	0.625410
$147$	1.14570	0.0944958
$148$	−2.16013	−0.177562
$149$	−6.38704	−0.523246	−0.261623	−	0.965170i	$-0.584258\pi$
$149$	−6.38704	−0.523246	−0.261623	+	0.965170i	$0.584258\pi$
$150$	0.741521	0.0605449
$151$	−3.63992	−0.296213	−0.148106	−	0.988971i	$-0.547318\pi$
$151$	−3.63992	−0.296213	−0.148106	+	0.988971i	$0.547318\pi$
$152$	−6.75626	−0.548005
$153$	−5.48932	−0.443785
$154$	−11.0674	−0.891833
$155$	2.54924	0.204760
$156$	−0.894820	−0.0716430
$157$	−3.48148	−0.277852	−0.138926	−	0.990303i	$-0.544365\pi$
$157$	−3.48148	−0.277852	−0.138926	+	0.990303i	$0.544365\pi$
$158$	−7.16658	−0.570142
$159$	−3.14551	−0.249455
$160$	1.00000	0.0790569
$161$	6.32029	0.498109
$162$	4.35366	0.342056
$163$	−7.48872	−0.586562	−0.293281	−	0.956026i	$-0.594747\pi$
$163$	−7.48872	−0.586562	−0.293281	+	0.956026i	$0.594747\pi$
$164$	−4.79426	−0.374369
$165$	2.80743	0.218558
$166$	14.7455	1.14447
$167$	0.756944	0.0585741	0.0292870	−	0.999571i	$-0.490676\pi$
$167$	0.756944	0.0585741	0.0292870	+	0.999571i	$0.490676\pi$
$168$	−2.16761	−0.167235
$169$	−11.5438	−0.887984
$170$	2.24040	0.171831
$171$	16.5538	1.26590
$172$	2.62620	0.200246
$173$	−18.3173	−1.39264	−0.696321	−	0.717730i	$-0.745181\pi$
$173$	−18.3173	−1.39264	−0.696321	+	0.717730i	$0.745181\pi$
$174$	−5.51300	−0.417940
$175$	−2.92320	−0.220973
$176$	3.78605	0.285384
$177$	−1.85598	−0.139504
$178$	10.3519	0.775911
$179$	2.24990	0.168166	0.0840829	−	0.996459i	$-0.473204\pi$
$179$	2.24990	0.168166	0.0840829	+	0.996459i	$0.473204\pi$
$180$	−2.45015	−0.182623
$181$	−9.62422	−0.715363	−0.357681	−	0.933844i	$-0.616433\pi$
$181$	−9.62422	−0.715363	−0.357681	+	0.933844i	$0.616433\pi$
$182$	3.52753	0.261478
$183$	−1.63995	−0.121229
$184$	−2.16212	−0.159393
$185$	−2.16013	−0.158816
$186$	1.89031	0.138604
$187$	8.48227	0.620285
$188$	−9.28939	−0.677499
$189$	11.8138	0.859327
$190$	−6.75626	−0.490150
$191$	1.03740	0.0750638	0.0375319	−	0.999295i	$-0.488050\pi$
$191$	1.03740	0.0750638	0.0375319	+	0.999295i	$0.488050\pi$
$192$	0.741521	0.0535147
$193$	−12.0456	−0.867064	−0.433532	−	0.901138i	$-0.642733\pi$
$193$	−12.0456	−0.867064	−0.433532	+	0.901138i	$0.642733\pi$
$194$	−6.45797	−0.463656
$195$	−0.894820	−0.0640794
$196$	1.54507	0.110362
$197$	15.0764	1.07415	0.537073	−	0.843536i	$-0.319530\pi$
$197$	15.0764	1.07415	0.537073	+	0.843536i	$0.319530\pi$
$198$	−9.27637	−0.659243
$199$	0.396256	0.0280899	0.0140449	−	0.999901i	$-0.495529\pi$
$199$	0.396256	0.0280899	0.0140449	+	0.999901i	$0.495529\pi$
$200$	1.00000	0.0707107
$201$	−4.80390	−0.338841
$202$	3.69551	0.260015
$203$	21.7331	1.52537
$204$	1.66131	0.116315
$205$	−4.79426	−0.334846
$206$	6.19576	0.431679
$207$	5.29751	0.368202
$208$	−1.20674	−0.0836721
$209$	−25.5795	−1.76937
$210$	−2.16761	−0.149579
$211$	18.2045	1.25325	0.626624	−	0.779322i	$-0.284436\pi$
$211$	18.2045	1.25325	0.626624	+	0.779322i	$0.284436\pi$
$212$	−4.24197	−0.291340
$213$	2.32652	0.159410
$214$	−4.26814	−0.291764
$215$	2.62620	0.179106
$216$	−4.04140	−0.274982
$217$	−7.45192	−0.505869
$218$	−6.78094	−0.459263
$219$	5.60357	0.378654
$220$	3.78605	0.255255
$221$	−2.70358	−0.181862
$222$	−1.60178	−0.107505
$223$	−9.99886	−0.669573	−0.334787	−	0.942294i	$-0.608664\pi$
$223$	−9.99886	−0.669573	−0.334787	+	0.942294i	$0.608664\pi$
$224$	−2.92320	−0.195314
$225$	−2.45015	−0.163343
$226$	−12.8387	−0.854016
$227$	−8.02690	−0.532764	−0.266382	−	0.963868i	$-0.585828\pi$
$227$	−8.02690	−0.532764	−0.266382	+	0.963868i	$0.585828\pi$
$228$	−5.00990	−0.331789
$229$	−25.6126	−1.69253	−0.846264	−	0.532763i	$-0.821154\pi$
$229$	−25.6126	−1.69253	−0.846264	+	0.532763i	$0.821154\pi$
$230$	−2.16212	−0.142566
$231$	−8.20667	−0.539960
$232$	−7.43472	−0.488113
$233$	8.36069	0.547727	0.273864	−	0.961769i	$-0.411698\pi$
$233$	8.36069	0.547727	0.273864	+	0.961769i	$0.411698\pi$
$234$	2.95668	0.193284
$235$	−9.28939	−0.605973
$236$	−2.50293	−0.162927
$237$	−5.31417	−0.345192
$238$	−6.54914	−0.424517
$239$	−5.94177	−0.384341	−0.192171	−	0.981362i	$-0.561553\pi$
$239$	−5.94177	−0.384341	−0.192171	+	0.981362i	$0.561553\pi$
$240$	0.741521	0.0478650
$241$	−28.2635	−1.82061	−0.910307	−	0.413933i	$-0.864155\pi$
$241$	−28.2635	−1.82061	−0.910307	+	0.413933i	$0.864155\pi$
$242$	3.33415	0.214327
$243$	15.3525	0.984865
$244$	−2.21161	−0.141584
$245$	1.54507	0.0987108
$246$	−3.55504	−0.226661
$247$	8.15302	0.518764
$248$	2.54924	0.161877
$249$	10.9341	0.692919
$250$	1.00000	0.0632456
$251$	1.54250	0.0973619	0.0486810	−	0.998814i	$-0.484498\pi$
$251$	1.54250	0.0973619	0.0486810	+	0.998814i	$0.484498\pi$
$252$	7.16226	0.451180
$253$	−8.18588	−0.514642
$254$	−21.5834	−1.35426
$255$	1.66131	0.104035
$256$	1.00000	0.0625000
$257$	12.2344	0.763159	0.381580	−	0.924336i	$-0.375380\pi$
$257$	12.2344	0.763159	0.381580	+	0.924336i	$0.375380\pi$
$258$	1.94739	0.121239
$259$	6.31449	0.392363
$260$	−1.20674	−0.0748386
$261$	18.2162	1.12755
$262$	−1.86617	−0.115293
$263$	6.05174	0.373167	0.186583	−	0.982439i	$-0.440259\pi$
$263$	6.05174	0.373167	0.186583	+	0.982439i	$0.440259\pi$
$264$	2.80743	0.172786
$265$	−4.24197	−0.260582
$266$	19.7499	1.21094
$267$	7.67618	0.469775
$268$	−6.47843	−0.395733
$269$	15.8007	0.963388	0.481694	−	0.876339i	$-0.340022\pi$
$269$	15.8007	0.963388	0.481694	+	0.876339i	$0.340022\pi$
$270$	−4.04140	−0.245952
$271$	5.49046	0.333522	0.166761	−	0.985997i	$-0.446669\pi$
$271$	5.49046	0.333522	0.166761	+	0.985997i	$0.446669\pi$
$272$	2.24040	0.135844
$273$	2.61573	0.158311
$274$	16.5456	0.999556
$275$	3.78605	0.228307
$276$	−1.60326	−0.0965046
$277$	12.6922	0.762601	0.381301	−	0.924451i	$-0.375476\pi$
$277$	12.6922	0.762601	0.381301	+	0.924451i	$0.375476\pi$
$278$	17.7109	1.06223
$279$	−6.24600	−0.373938
$280$	−2.92320	−0.174694
$281$	−11.4113	−0.680739	−0.340369	−	0.940292i	$-0.610552\pi$
$281$	−11.4113	−0.680739	−0.340369	+	0.940292i	$0.610552\pi$
$282$	−6.88828	−0.410191
$283$	−2.68041	−0.159334	−0.0796668	−	0.996822i	$-0.525386\pi$
$283$	−2.68041	−0.159334	−0.0796668	+	0.996822i	$0.525386\pi$
$284$	3.13750	0.186176
$285$	−5.00990	−0.296761
$286$	−4.56876	−0.270156
$287$	14.0146	0.827253
$288$	−2.45015	−0.144376
$289$	−11.9806	−0.704741
$290$	−7.43472	−0.436582
$291$	−4.78872	−0.280720
$292$	7.55686	0.442232
$293$	20.4478	1.19457	0.597285	−	0.802029i	$-0.296246\pi$
$293$	20.4478	1.19457	0.597285	+	0.802029i	$0.296246\pi$
$294$	1.14570	0.0668187
$295$	−2.50293	−0.145726
$296$	−2.16013	−0.125555
$297$	−15.3009	−0.887850
$298$	−6.38704	−0.369991
$299$	2.60911	0.150888
$300$	0.741521	0.0428117
$301$	−7.67691	−0.442490
$302$	−3.63992	−0.209454
$303$	2.74030	0.157426
$304$	−6.75626	−0.387498
$305$	−2.21161	−0.126636
$306$	−5.48932	−0.313803
$307$	−21.7246	−1.23989	−0.619943	−	0.784647i	$-0.712844\pi$
$307$	−21.7246	−1.23989	−0.619943	+	0.784647i	$0.712844\pi$
$308$	−11.0674	−0.630621
$309$	4.59429	0.261360
$310$	2.54924	0.144787
$311$	−21.9236	−1.24317	−0.621586	−	0.783346i	$-0.713511\pi$
$311$	−21.9236	−1.24317	−0.621586	+	0.783346i	$0.713511\pi$
$312$	−0.894820	−0.0506592
$313$	−13.4995	−0.763039	−0.381520	−	0.924361i	$-0.624599\pi$
$313$	−13.4995	−0.763039	−0.381520	+	0.924361i	$0.624599\pi$
$314$	−3.48148	−0.196471
$315$	7.16226	0.403547
$316$	−7.16658	−0.403152
$317$	22.9412	1.28851	0.644254	−	0.764811i	$-0.277168\pi$
$317$	22.9412	1.28851	0.644254	+	0.764811i	$0.277168\pi$
$318$	−3.14551	−0.176391
$319$	−28.1482	−1.57600
$320$	1.00000	0.0559017
$321$	−3.16492	−0.176649
$322$	6.32029	0.352216
$323$	−15.1367	−0.842231
$324$	4.35366	0.241870
$325$	−1.20674	−0.0669377
$326$	−7.48872	−0.414762
$327$	−5.02821	−0.278061
$328$	−4.79426	−0.264719
$329$	27.1547	1.49709
$330$	2.80743	0.154544
$331$	−20.8164	−1.14417	−0.572086	−	0.820194i	$-0.693866\pi$
$331$	−20.8164	−1.14417	−0.572086	+	0.820194i	$0.693866\pi$
$332$	14.7455	0.809262
$333$	5.29264	0.290035
$334$	0.756944	0.0414181
$335$	−6.47843	−0.353955
$336$	−2.16761	−0.118253
$337$	13.2746	0.723114	0.361557	−	0.932350i	$-0.382245\pi$
$337$	13.2746	0.723114	0.361557	+	0.932350i	$0.382245\pi$
$338$	−11.5438	−0.627899
$339$	−9.52015	−0.517063
$340$	2.24040	0.121503
$341$	9.65153	0.522660
$342$	16.5538	0.895128
$343$	15.9458	0.860994
$344$	2.62620	0.141595
$345$	−1.60326	−0.0863164
$346$	−18.3173	−0.984747
$347$	2.90152	0.155762	0.0778809	−	0.996963i	$-0.475185\pi$
$347$	2.90152	0.155762	0.0778809	+	0.996963i	$0.475185\pi$
$348$	−5.51300	−0.295528
$349$	−2.22064	−0.118868	−0.0594341	−	0.998232i	$-0.518930\pi$
$349$	−2.22064	−0.118868	−0.0594341	+	0.998232i	$0.518930\pi$
$350$	−2.92320	−0.156251
$351$	4.87690	0.260310
$352$	3.78605	0.201797
$353$	18.6751	0.993974	0.496987	−	0.867758i	$-0.334440\pi$
$353$	18.6751	0.993974	0.496987	+	0.867758i	$0.334440\pi$
$354$	−1.85598	−0.0986441
$355$	3.13750	0.166521
$356$	10.3519	0.548652
$357$	−4.85632	−0.257024
$358$	2.24990	0.118911
$359$	10.0962	0.532856	0.266428	−	0.963855i	$-0.414157\pi$
$359$	10.0962	0.532856	0.266428	+	0.963855i	$0.414157\pi$
$360$	−2.45015	−0.129134
$361$	26.6470	1.40247
$362$	−9.62422	−0.505838
$363$	2.47234	0.129764
$364$	3.52753	0.184893
$365$	7.55686	0.395544
$366$	−1.63995	−0.0857217
$367$	13.3188	0.695236	0.347618	−	0.937636i	$-0.386991\pi$
$367$	13.3188	0.695236	0.347618	+	0.937636i	$0.386991\pi$
$368$	−2.16212	−0.112708
$369$	11.7466	0.611505
$370$	−2.16013	−0.112300
$371$	12.4001	0.643782
$372$	1.89031	0.0980081
$373$	−7.01034	−0.362981	−0.181491	−	0.983393i	$-0.558092\pi$
$373$	−7.01034	−0.362981	−0.181491	+	0.983393i	$0.558092\pi$
$374$	8.48227	0.438608
$375$	0.741521	0.0382920
$376$	−9.28939	−0.479064
$377$	8.97175	0.462069
$378$	11.8138	0.607636
$379$	−11.3530	−0.583166	−0.291583	−	0.956546i	$-0.594182\pi$
$379$	−11.3530	−0.583166	−0.291583	+	0.956546i	$0.594182\pi$
$380$	−6.75626	−0.346589
$381$	−16.0046	−0.819939
$382$	1.03740	0.0530781
$383$	−1.90171	−0.0971729	−0.0485865	−	0.998819i	$-0.515472\pi$
$383$	−1.90171	−0.0971729	−0.0485865	+	0.998819i	$0.515472\pi$
$384$	0.741521	0.0378406
$385$	−11.0674	−0.564045
$386$	−12.0456	−0.613107
$387$	−6.43459	−0.327088
$388$	−6.45797	−0.327854
$389$	16.4178	0.832418	0.416209	−	0.909269i	$-0.363358\pi$
$389$	16.4178	0.832418	0.416209	+	0.909269i	$0.363358\pi$
$390$	−0.894820	−0.0453110
$391$	−4.84402	−0.244972
$392$	1.54507	0.0780378
$393$	−1.38381	−0.0698038
$394$	15.0764	0.759536
$395$	−7.16658	−0.360590
$396$	−9.27637	−0.466155
$397$	0.399823	0.0200666	0.0100333	−	0.999950i	$-0.496806\pi$
$397$	0.399823	0.0200666	0.0100333	+	0.999950i	$0.496806\pi$
$398$	0.396256	0.0198625
$399$	14.6449	0.733163
$400$	1.00000	0.0500000
$401$	12.1723	0.607856	0.303928	−	0.952695i	$-0.401702\pi$
$401$	12.1723	0.607856	0.303928	+	0.952695i	$0.401702\pi$
$402$	−4.80390	−0.239597
$403$	−3.07626	−0.153239
$404$	3.69551	0.183858
$405$	4.35366	0.216335
$406$	21.7331	1.07860
$407$	−8.17836	−0.405386
$408$	1.66131	0.0822469
$409$	−33.4856	−1.65575	−0.827877	−	0.560909i	$-0.810452\pi$
$409$	−33.4856	−1.65575	−0.827877	+	0.560909i	$0.810452\pi$
$410$	−4.79426	−0.236772
$411$	12.2689	0.605180
$412$	6.19576	0.305243
$413$	7.31656	0.360025
$414$	5.29751	0.260358
$415$	14.7455	0.723826
$416$	−1.20674	−0.0591651
$417$	13.1330	0.643127
$418$	−25.5795	−1.25113
$419$	9.60020	0.469001	0.234500	−	0.972116i	$-0.424655\pi$
$419$	9.60020	0.469001	0.234500	+	0.972116i	$0.424655\pi$
$420$	−2.16761	−0.105769
$421$	−5.78529	−0.281958	−0.140979	−	0.990013i	$-0.545025\pi$
$421$	−5.78529	−0.281958	−0.140979	+	0.990013i	$0.545025\pi$
$422$	18.2045	0.886180
$423$	22.7604	1.10665
$424$	−4.24197	−0.206008
$425$	2.24040	0.108676
$426$	2.32652	0.112720
$427$	6.46496	0.312861
$428$	−4.26814	−0.206309
$429$	−3.38783	−0.163566
$430$	2.62620	0.126647
$431$	19.4632	0.937509	0.468754	−	0.883329i	$-0.344703\pi$
$431$	19.4632	0.937509	0.468754	+	0.883329i	$0.344703\pi$
$432$	−4.04140	−0.194442
$433$	−2.27704	−0.109428	−0.0547138	−	0.998502i	$-0.517425\pi$
$433$	−2.27704	−0.109428	−0.0547138	+	0.998502i	$0.517425\pi$
$434$	−7.45192	−0.357703
$435$	−5.51300	−0.264328
$436$	−6.78094	−0.324748
$437$	14.6078	0.698787
$438$	5.60357	0.267749
$439$	4.72610	0.225565	0.112782	−	0.993620i	$-0.464024\pi$
$439$	4.72610	0.225565	0.112782	+	0.993620i	$0.464024\pi$
$440$	3.78605	0.180493
$441$	−3.78565	−0.180269
$442$	−2.70358	−0.128596
$443$	26.4606	1.25718	0.628590	−	0.777736i	$-0.283632\pi$
$443$	26.4606	1.25718	0.628590	+	0.777736i	$0.283632\pi$
$444$	−1.60178	−0.0760173
$445$	10.3519	0.490729
$446$	−9.99886	−0.473460
$447$	−4.73612	−0.224011
$448$	−2.92320	−0.138108
$449$	6.77324	0.319649	0.159825	−	0.987145i	$-0.448907\pi$
$449$	6.77324	0.319649	0.159825	+	0.987145i	$0.448907\pi$
$450$	−2.45015	−0.115501
$451$	−18.1513	−0.854711
$452$	−12.8387	−0.603881
$453$	−2.69908	−0.126814
$454$	−8.02690	−0.376721
$455$	3.52753	0.165373
$456$	−5.00990	−0.234610
$457$	26.8513	1.25605	0.628026	−	0.778193i	$-0.283863\pi$
$457$	26.8513	1.25605	0.628026	+	0.778193i	$0.283863\pi$
$458$	−25.6126	−1.19680
$459$	−9.05436	−0.422621
$460$	−2.16212	−0.100809
$461$	−5.33116	−0.248297	−0.124148	−	0.992264i	$-0.539620\pi$
$461$	−5.33116	−0.248297	−0.124148	+	0.992264i	$0.539620\pi$
$462$	−8.20667	−0.381809
$463$	23.2851	1.08215	0.541076	−	0.840974i	$-0.318017\pi$
$463$	23.2851	1.08215	0.541076	+	0.840974i	$0.318017\pi$
$464$	−7.43472	−0.345148
$465$	1.89031	0.0876611
$466$	8.36069	0.387302
$467$	−3.15723	−0.146099	−0.0730495	−	0.997328i	$-0.523273\pi$
$467$	−3.15723	−0.146099	−0.0730495	+	0.997328i	$0.523273\pi$
$468$	2.95668	0.136673
$469$	18.9377	0.874463
$470$	−9.28939	−0.428488
$471$	−2.58159	−0.118953
$472$	−2.50293	−0.115207
$473$	9.94293	0.457177
$474$	−5.31417	−0.244088
$475$	−6.75626	−0.309998
$476$	−6.54914	−0.300179
$477$	10.3935	0.475883
$478$	−5.94177	−0.271770
$479$	17.2512	0.788226	0.394113	−	0.919062i	$-0.371052\pi$
$479$	17.2512	0.788226	0.394113	+	0.919062i	$0.371052\pi$
$480$	0.741521	0.0338456
$481$	2.60671	0.118856
$482$	−28.2635	−1.28737
$483$	4.68663	0.213249
$484$	3.33415	0.151552
$485$	−6.45797	−0.293242
$486$	15.3525	0.696405
$487$	14.1137	0.639555	0.319777	−	0.947493i	$-0.396392\pi$
$487$	14.1137	0.639555	0.319777	+	0.947493i	$0.396392\pi$
$488$	−2.21161	−0.100115
$489$	−5.55305	−0.251117
$490$	1.54507	0.0697991
$491$	5.58698	0.252137	0.126068	−	0.992022i	$-0.459764\pi$
$491$	5.58698	0.252137	0.126068	+	0.992022i	$0.459764\pi$
$492$	−3.55504	−0.160274
$493$	−16.6568	−0.750184
$494$	8.15302	0.366822
$495$	−9.27637	−0.416942
$496$	2.54924	0.114464
$497$	−9.17151	−0.411399
$498$	10.9341	0.489967
$499$	31.5338	1.41165	0.705824	−	0.708387i	$-0.250577\pi$
$499$	31.5338	1.41165	0.705824	+	0.708387i	$0.250577\pi$
$500$	1.00000	0.0447214
$501$	0.561290	0.0250766
$502$	1.54250	0.0688453
$503$	−33.9558	−1.51402	−0.757008	−	0.653406i	$-0.773339\pi$
$503$	−33.9558	−1.51402	−0.757008	+	0.653406i	$0.773339\pi$
$504$	7.16226	0.319032
$505$	3.69551	0.164448
$506$	−8.18588	−0.363907
$507$	−8.55996	−0.380161
$508$	−21.5834	−0.957610
$509$	−25.9636	−1.15081	−0.575407	−	0.817867i	$-0.695156\pi$
$509$	−25.9636	−1.15081	−0.575407	+	0.817867i	$0.695156\pi$
$510$	1.66131	0.0735639
$511$	−22.0902	−0.977212
$512$	1.00000	0.0441942
$513$	27.3047	1.20553
$514$	12.2344	0.539635
$515$	6.19576	0.273018
$516$	1.94739	0.0857289
$517$	−35.1701	−1.54678
$518$	6.31449	0.277443
$519$	−13.5827	−0.596214
$520$	−1.20674	−0.0529189
$521$	19.3369	0.847165	0.423582	−	0.905858i	$-0.360772\pi$
$521$	19.3369	0.847165	0.423582	+	0.905858i	$0.360772\pi$
$522$	18.2162	0.797300
$523$	21.9848	0.961328	0.480664	−	0.876905i	$-0.340396\pi$
$523$	21.9848	0.961328	0.480664	+	0.876905i	$0.340396\pi$
$524$	−1.86617	−0.0815242
$525$	−2.16761	−0.0946023
$526$	6.05174	0.263869
$527$	5.71132	0.248789
$528$	2.80743	0.122178
$529$	−18.3252	−0.796750
$530$	−4.24197	−0.184259
$531$	6.13256	0.266130
$532$	19.7499	0.856265
$533$	5.78541	0.250594
$534$	7.67618	0.332181
$535$	−4.26814	−0.184528
$536$	−6.47843	−0.279826
$537$	1.66835	0.0719947
$538$	15.8007	0.681218
$539$	5.84970	0.251965
$540$	−4.04140	−0.173914
$541$	−1.17590	−0.0505558	−0.0252779	−	0.999680i	$-0.508047\pi$
$541$	−1.17590	−0.0505558	−0.0252779	+	0.999680i	$0.508047\pi$
$542$	5.49046	0.235835
$543$	−7.13656	−0.306259
$544$	2.24040	0.0960565
$545$	−6.78094	−0.290464
$546$	2.61573	0.111943
$547$	−1.59787	−0.0683201	−0.0341601	−	0.999416i	$-0.510876\pi$
$547$	−1.59787	−0.0683201	−0.0341601	+	0.999416i	$0.510876\pi$
$548$	16.5456	0.706792
$549$	5.41876	0.231267
$550$	3.78605	0.161438
$551$	50.2309	2.13991
$552$	−1.60326	−0.0682391
$553$	20.9493	0.890855
$554$	12.6922	0.539241
$555$	−1.60178	−0.0679919
$556$	17.7109	0.751111
$557$	6.99965	0.296585	0.148292	−	0.988944i	$-0.452622\pi$
$557$	6.99965	0.296585	0.148292	+	0.988944i	$0.452622\pi$
$558$	−6.24600	−0.264414
$559$	−3.16914	−0.134040
$560$	−2.92320	−0.123528
$561$	6.28978	0.265555
$562$	−11.4113	−0.481355
$563$	−0.539470	−0.0227359	−0.0113680	−	0.999935i	$-0.503619\pi$
$563$	−0.539470	−0.0227359	−0.0113680	+	0.999935i	$0.503619\pi$
$564$	−6.88828	−0.290049
$565$	−12.8387	−0.540127
$566$	−2.68041	−0.112666
$567$	−12.7266	−0.534467
$568$	3.13750	0.131646
$569$	−21.5821	−0.904770	−0.452385	−	0.891823i	$-0.649427\pi$
$569$	−21.5821	−0.904770	−0.452385	+	0.891823i	$0.649427\pi$
$570$	−5.00990	−0.209842
$571$	28.9663	1.21220	0.606102	−	0.795387i	$-0.292732\pi$
$571$	28.9663	1.21220	0.606102	+	0.795387i	$0.292732\pi$
$572$	−4.56876	−0.191029
$573$	0.769255	0.0321361
$574$	14.0146	0.584956
$575$	−2.16212	−0.0901665
$576$	−2.45015	−0.102089
$577$	28.1175	1.17055	0.585273	−	0.810837i	$-0.300987\pi$
$577$	28.1175	1.17055	0.585273	+	0.810837i	$0.300987\pi$
$578$	−11.9806	−0.498327
$579$	−8.93209	−0.371205
$580$	−7.43472	−0.308710
$581$	−43.1039	−1.78825
$582$	−4.78872	−0.198499
$583$	−16.0603	−0.665150
$584$	7.55686	0.312705
$585$	2.95668	0.122244
$586$	20.4478	0.844689
$587$	5.04201	0.208106	0.104053	−	0.994572i	$-0.466819\pi$
$587$	5.04201	0.208106	0.104053	+	0.994572i	$0.466819\pi$
$588$	1.14570	0.0472479
$589$	−17.2233	−0.709673
$590$	−2.50293	−0.103044
$591$	11.1794	0.459861
$592$	−2.16013	−0.0887809
$593$	15.1369	0.621597	0.310799	−	0.950476i	$-0.399403\pi$
$593$	15.1369	0.621597	0.310799	+	0.950476i	$0.399403\pi$
$594$	−15.3009	−0.627804
$595$	−6.54914	−0.268488
$596$	−6.38704	−0.261623
$597$	0.293832	0.0120258
$598$	2.60911	0.106694
$599$	20.9884	0.857563	0.428782	−	0.903408i	$-0.358943\pi$
$599$	20.9884	0.857563	0.428782	+	0.903408i	$0.358943\pi$
$600$	0.741521	0.0302725
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	−7.67691	−0.312887
$603$	15.8731	0.646403
$604$	−3.63992	−0.148106
$605$	3.33415	0.135552
$606$	2.74030	0.111317
$607$	26.7289	1.08489	0.542446	−	0.840091i	$-0.317498\pi$
$607$	26.7289	1.08489	0.542446	+	0.840091i	$0.317498\pi$
$608$	−6.75626	−0.274002
$609$	16.1156	0.653036
$610$	−2.21161	−0.0895453
$611$	11.2098	0.453502
$612$	−5.48932	−0.221893
$613$	5.68225	0.229504	0.114752	−	0.993394i	$-0.463393\pi$
$613$	5.68225	0.229504	0.114752	+	0.993394i	$0.463393\pi$
$614$	−21.7246	−0.876732
$615$	−3.55504	−0.143353
$616$	−11.0674	−0.445916
$617$	37.6119	1.51420	0.757099	−	0.653300i	$-0.226616\pi$
$617$	37.6119	1.51420	0.757099	+	0.653300i	$0.226616\pi$
$618$	4.59429	0.184809
$619$	20.0050	0.804069	0.402035	−	0.915624i	$-0.368303\pi$
$619$	20.0050	0.804069	0.402035	+	0.915624i	$0.368303\pi$
$620$	2.54924	0.102380
$621$	8.73798	0.350643
$622$	−21.9236	−0.879055
$623$	−30.2607	−1.21237
$624$	−0.894820	−0.0358215
$625$	1.00000	0.0400000
$626$	−13.4995	−0.539550
$627$	−18.9677	−0.757498
$628$	−3.48148	−0.138926
$629$	−4.83957	−0.192966
$630$	7.16226	0.285351
$631$	0.0444024	0.00176763	0.000883817	−	1.00000i	$-0.499719\pi$
$631$	0.0444024	0.00176763	0.000883817		1.00000i	$0.499719\pi$
$632$	−7.16658	−0.285071
$633$	13.4990	0.536537
$634$	22.9412	0.911113
$635$	−21.5834	−0.856512
$636$	−3.14551	−0.124728
$637$	−1.86449	−0.0738738
$638$	−28.1482	−1.11440
$639$	−7.68733	−0.304106
$640$	1.00000	0.0395285
$641$	−23.1116	−0.912852	−0.456426	−	0.889761i	$-0.650871\pi$
$641$	−23.1116	−0.912852	−0.456426	+	0.889761i	$0.650871\pi$
$642$	−3.16492	−0.124909
$643$	−6.57273	−0.259203	−0.129602	−	0.991566i	$-0.541370\pi$
$643$	−6.57273	−0.259203	−0.129602	+	0.991566i	$0.541370\pi$
$644$	6.32029	0.249054
$645$	1.94739	0.0766782
$646$	−15.1367	−0.595547
$647$	−16.7970	−0.660359	−0.330180	−	0.943918i	$-0.607109\pi$
$647$	−16.7970	−0.660359	−0.330180	+	0.943918i	$0.607109\pi$
$648$	4.35366	0.171028
$649$	−9.47622	−0.371974
$650$	−1.20674	−0.0473321
$651$	−5.52575	−0.216571
$652$	−7.48872	−0.293281
$653$	−20.2827	−0.793722	−0.396861	−	0.917879i	$-0.629901\pi$
$653$	−20.2827	−0.793722	−0.396861	+	0.917879i	$0.629901\pi$
$654$	−5.02821	−0.196619
$655$	−1.86617	−0.0729174
$656$	−4.79426	−0.187184
$657$	−18.5154	−0.722355
$658$	27.1547	1.05860
$659$	8.34781	0.325185	0.162592	−	0.986693i	$-0.448014\pi$
$659$	8.34781	0.325185	0.162592	+	0.986693i	$0.448014\pi$
$660$	2.80743	0.109279
$661$	−17.1480	−0.666981	−0.333490	−	0.942754i	$-0.608226\pi$
$661$	−17.1480	−0.666981	−0.333490	+	0.942754i	$0.608226\pi$
$662$	−20.8164	−0.809052
$663$	−2.00476	−0.0778584
$664$	14.7455	0.572235
$665$	19.7499	0.765866
$666$	5.29264	0.205086
$667$	16.0747	0.622417
$668$	0.756944	0.0292870
$669$	−7.41436	−0.286656
$670$	−6.47843	−0.250284
$671$	−8.37325	−0.323246
$672$	−2.16761	−0.0836174
$673$	−0.527550	−0.0203356	−0.0101678	−	0.999948i	$-0.503237\pi$
$673$	−0.527550	−0.0203356	−0.0101678	+	0.999948i	$0.503237\pi$
$674$	13.2746	0.511319
$675$	−4.04140	−0.155553
$676$	−11.5438	−0.443992
$677$	−21.8328	−0.839105	−0.419552	−	0.907731i	$-0.637813\pi$
$677$	−21.8328	−0.839105	−0.419552	+	0.907731i	$0.637813\pi$
$678$	−9.52015	−0.365619
$679$	18.8779	0.724468
$680$	2.24040	0.0859156
$681$	−5.95211	−0.228085
$682$	9.65153	0.369576
$683$	−25.5697	−0.978398	−0.489199	−	0.872172i	$-0.662711\pi$
$683$	−25.5697	−0.978398	−0.489199	+	0.872172i	$0.662711\pi$
$684$	16.5538	0.632951
$685$	16.5456	0.632174
$686$	15.9458	0.608814
$687$	−18.9923	−0.724601
$688$	2.62620	0.100123
$689$	5.11894	0.195016
$690$	−1.60326	−0.0610349
$691$	39.4532	1.50087	0.750436	−	0.660943i	$-0.229844\pi$
$691$	39.4532	1.50087	0.750436	+	0.660943i	$0.229844\pi$
$692$	−18.3173	−0.696321
$693$	27.1166	1.03008
$694$	2.90152	0.110140
$695$	17.7109	0.671814
$696$	−5.51300	−0.208970
$697$	−10.7411	−0.406847
$698$	−2.22064	−0.0840526
$699$	6.19963	0.234491
$700$	−2.92320	−0.110486
$701$	15.2977	0.577785	0.288893	−	0.957361i	$-0.406713\pi$
$701$	15.2977	0.577785	0.288893	+	0.957361i	$0.406713\pi$
$702$	4.87690	0.184067
$703$	14.5944	0.550438
$704$	3.78605	0.142692
$705$	−6.88828	−0.259428
$706$	18.6751	0.702846
$707$	−10.8027	−0.406277
$708$	−1.85598	−0.0697519
$709$	−8.37724	−0.314614	−0.157307	−	0.987550i	$-0.550281\pi$
$709$	−8.37724	−0.314614	−0.157307	+	0.987550i	$0.550281\pi$
$710$	3.13750	0.117748
$711$	17.5592	0.658520
$712$	10.3519	0.387955
$713$	−5.51175	−0.206417
$714$	−4.85632	−0.181743
$715$	−4.56876	−0.170862
$716$	2.24990	0.0840829
$717$	−4.40595	−0.164543
$718$	10.0962	0.376786
$719$	20.9443	0.781090	0.390545	−	0.920584i	$-0.372287\pi$
$719$	20.9443	0.781090	0.390545	+	0.920584i	$0.372287\pi$
$720$	−2.45015	−0.0913116
$721$	−18.1114	−0.674505
$722$	26.6470	0.991698
$723$	−20.9580	−0.779437
$724$	−9.62422	−0.357681
$725$	−7.43472	−0.276119
$726$	2.47234	0.0917572
$727$	−23.8660	−0.885140	−0.442570	−	0.896734i	$-0.645933\pi$
$727$	−23.8660	−0.885140	−0.442570	+	0.896734i	$0.645933\pi$
$728$	3.52753	0.130739
$729$	−1.67676	−0.0621021
$730$	7.55686	0.279692
$731$	5.88376	0.217619
$732$	−1.63995	−0.0606144
$733$	14.3164	0.528787	0.264394	−	0.964415i	$-0.414828\pi$
$733$	14.3164	0.528787	0.264394	+	0.964415i	$0.414828\pi$
$734$	13.3188	0.491606
$735$	1.14570	0.0422598
$736$	−2.16212	−0.0796967
$737$	−24.5277	−0.903488
$738$	11.7466	0.432400
$739$	−41.9894	−1.54461	−0.772303	−	0.635255i	$-0.780895\pi$
$739$	−41.9894	−1.54461	−0.772303	+	0.635255i	$0.780895\pi$
$740$	−2.16013	−0.0794080
$741$	6.04563	0.222092
$742$	12.4001	0.455222
$743$	2.19212	0.0804212	0.0402106	−	0.999191i	$-0.487197\pi$
$743$	2.19212	0.0804212	0.0402106	+	0.999191i	$0.487197\pi$
$744$	1.89031	0.0693022
$745$	−6.38704	−0.234003
$746$	−7.01034	−0.256667
$747$	−36.1285	−1.32187
$748$	8.48227	0.310143
$749$	12.4766	0.455886
$750$	0.741521	0.0270765
$751$	−6.65765	−0.242941	−0.121470	−	0.992595i	$-0.538761\pi$
$751$	−6.65765	−0.242941	−0.121470	+	0.992595i	$0.538761\pi$
$752$	−9.28939	−0.338749
$753$	1.14380	0.0416823
$754$	8.97175	0.326732
$755$	−3.63992	−0.132470
$756$	11.8138	0.429664
$757$	−8.18191	−0.297377	−0.148688	−	0.988884i	$-0.547505\pi$
$757$	−8.18191	−0.297377	−0.148688	+	0.988884i	$0.547505\pi$
$758$	−11.3530	−0.412361
$759$	−6.07000	−0.220327
$760$	−6.75626	−0.245075
$761$	−46.9481	−1.70187	−0.850934	−	0.525272i	$-0.823964\pi$
$761$	−46.9481	−1.70187	−0.850934	+	0.525272i	$0.823964\pi$
$762$	−16.0046	−0.579784
$763$	19.8220	0.717605
$764$	1.03740	0.0375319
$765$	−5.48932	−0.198467
$766$	−1.90171	−0.0687116
$767$	3.02038	0.109060
$768$	0.741521	0.0267573
$769$	−41.5242	−1.49740	−0.748700	−	0.662909i	$-0.769322\pi$
$769$	−41.5242	−1.49740	−0.748700	+	0.662909i	$0.769322\pi$
$770$	−11.0674	−0.398840
$771$	9.07204	0.326722
$772$	−12.0456	−0.433532
$773$	−11.1666	−0.401635	−0.200818	−	0.979629i	$-0.564360\pi$
$773$	−11.1666	−0.401635	−0.200818	+	0.979629i	$0.564360\pi$
$774$	−6.43459	−0.231286
$775$	2.54924	0.0915713
$776$	−6.45797	−0.231828
$777$	4.68232	0.167977
$778$	16.4178	0.588608
$779$	32.3912	1.16054
$780$	−0.894820	−0.0320397
$781$	11.8787	0.425054
$782$	−4.84402	−0.173222
$783$	30.0467	1.07378
$784$	1.54507	0.0551810
$785$	−3.48148	−0.124259
$786$	−1.38381	−0.0493588
$787$	18.9384	0.675081	0.337540	−	0.941311i	$-0.390405\pi$
$787$	18.9384	0.675081	0.337540	+	0.941311i	$0.390405\pi$
$788$	15.0764	0.537073
$789$	4.48750	0.159759
$790$	−7.16658	−0.254975
$791$	37.5300	1.33441
$792$	−9.27637	−0.329621
$793$	2.66883	0.0947728
$794$	0.399823	0.0141892
$795$	−3.14551	−0.111560
$796$	0.396256	0.0140449
$797$	−45.5372	−1.61301	−0.806506	−	0.591226i	$-0.798644\pi$
$797$	−45.5372	−1.61301	−0.806506	+	0.591226i	$0.798644\pi$
$798$	14.6449	0.518425
$799$	−20.8120	−0.736275
$800$	1.00000	0.0353553
$801$	−25.3638	−0.896185
$802$	12.1723	0.429819
$803$	28.6106	1.00965
$804$	−4.80390	−0.169420
$805$	6.32029	0.222761
$806$	−3.07626	−0.108357
$807$	11.7166	0.412443
$808$	3.69551	0.130008
$809$	13.0849	0.460041	0.230021	−	0.973186i	$-0.426121\pi$
$809$	13.0849	0.460041	0.230021	+	0.973186i	$0.426121\pi$
$810$	4.35366	0.152972
$811$	−52.3893	−1.83964	−0.919819	−	0.392343i	$-0.871665\pi$
$811$	−52.3893	−1.83964	−0.919819	+	0.392343i	$0.871665\pi$
$812$	21.7331	0.762684
$813$	4.07129	0.142786
$814$	−8.17836	−0.286651
$815$	−7.48872	−0.262319
$816$	1.66131	0.0581574
$817$	−17.7433	−0.620760
$818$	−33.4856	−1.17080
$819$	−8.64295	−0.302009
$820$	−4.79426	−0.167423
$821$	−53.0479	−1.85138	−0.925691	−	0.378280i	$-0.876516\pi$
$821$	−53.0479	−1.85138	−0.925691	+	0.378280i	$0.876516\pi$
$822$	12.2689	0.427927
$823$	50.1815	1.74922	0.874608	−	0.484830i	$-0.161119\pi$
$823$	50.1815	1.74922	0.874608	+	0.484830i	$0.161119\pi$
$824$	6.19576	0.215840
$825$	2.80743	0.0977423
$826$	7.31656	0.254576
$827$	−37.8153	−1.31497	−0.657483	−	0.753470i	$-0.728379\pi$
$827$	−37.8153	−1.31497	−0.657483	+	0.753470i	$0.728379\pi$
$828$	5.29751	0.184101
$829$	39.7175	1.37945	0.689723	−	0.724074i	$-0.257732\pi$
$829$	39.7175	1.37945	0.689723	+	0.724074i	$0.257732\pi$
$830$	14.7455	0.511823
$831$	9.41154	0.326483
$832$	−1.20674	−0.0418361
$833$	3.46158	0.119937
$834$	13.1330	0.454760
$835$	0.756944	0.0261951
$836$	−25.5795	−0.884685
$837$	−10.3025	−0.356106
$838$	9.60020	0.331634
$839$	−32.3825	−1.11797	−0.558985	−	0.829178i	$-0.688809\pi$
$839$	−32.3825	−1.11797	−0.558985	+	0.829178i	$0.688809\pi$
$840$	−2.16761	−0.0747897
$841$	26.2751	0.906038
$842$	−5.78529	−0.199374
$843$	−8.46169	−0.291436
$844$	18.2045	0.626624
$845$	−11.5438	−0.397118
$846$	22.7604	0.782518
$847$	−9.74637	−0.334889
$848$	−4.24197	−0.145670
$849$	−1.98758	−0.0682135
$850$	2.24040	0.0768452
$851$	4.67046	0.160101
$852$	2.32652	0.0797052
$853$	4.06971	0.139344	0.0696720	−	0.997570i	$-0.477805\pi$
$853$	4.06971	0.139344	0.0696720	+	0.997570i	$0.477805\pi$
$854$	6.46496	0.221226
$855$	16.5538	0.566129
$856$	−4.26814	−0.145882
$857$	44.2655	1.51208	0.756039	−	0.654526i	$-0.227132\pi$
$857$	44.2655	1.51208	0.756039	+	0.654526i	$0.227132\pi$
$858$	−3.38783	−0.115659
$859$	−36.6492	−1.25046	−0.625228	−	0.780442i	$-0.714994\pi$
$859$	−36.6492	−1.25046	−0.625228	+	0.780442i	$0.714994\pi$
$860$	2.62620	0.0895528
$861$	10.3921	0.354161
$862$	19.4632	0.662919
$863$	−36.5565	−1.24440	−0.622198	−	0.782860i	$-0.713760\pi$
$863$	−36.5565	−1.24440	−0.622198	+	0.782860i	$0.713760\pi$
$864$	−4.04140	−0.137491
$865$	−18.3173	−0.622809
$866$	−2.27704	−0.0773770
$867$	−8.88386	−0.301712
$868$	−7.45192	−0.252935
$869$	−27.1330	−0.920424
$870$	−5.51300	−0.186908
$871$	7.81776	0.264895
$872$	−6.78094	−0.229632
$873$	15.8230	0.535527
$874$	14.6078	0.494117
$875$	−2.92320	−0.0988220
$876$	5.60357	0.189327
$877$	−36.0907	−1.21870	−0.609349	−	0.792902i	$-0.708569\pi$
$877$	−36.0907	−1.21870	−0.609349	+	0.792902i	$0.708569\pi$
$878$	4.72610	0.159498
$879$	15.1624	0.511416
$880$	3.78605	0.127628
$881$	32.4769	1.09417	0.547087	−	0.837076i	$-0.315737\pi$
$881$	32.4769	1.09417	0.547087	+	0.837076i	$0.315737\pi$
$882$	−3.78565	−0.127469
$883$	28.1173	0.946223	0.473111	−	0.881003i	$-0.343131\pi$
$883$	28.1173	0.946223	0.473111	+	0.881003i	$0.343131\pi$
$884$	−2.70358	−0.0909311
$885$	−1.85598	−0.0623880
$886$	26.4606	0.888961
$887$	−31.1536	−1.04604	−0.523018	−	0.852321i	$-0.675194\pi$
$887$	−31.1536	−1.04604	−0.523018	+	0.852321i	$0.675194\pi$
$888$	−1.60178	−0.0537523
$889$	63.0926	2.11606
$890$	10.3519	0.346998
$891$	16.4832	0.552206
$892$	−9.99886	−0.334787
$893$	62.7615	2.10023
$894$	−4.73612	−0.158400
$895$	2.24990	0.0752060
$896$	−2.92320	−0.0976571
$897$	1.93471	0.0645980
$898$	6.77324	0.226026
$899$	−18.9529	−0.632113
$900$	−2.45015	−0.0816716
$901$	−9.50373	−0.316615
$902$	−18.1513	−0.604372
$903$	−5.69259	−0.189437
$904$	−12.8387	−0.427008
$905$	−9.62422	−0.319920
$906$	−2.69908	−0.0896708
$907$	1.65719	0.0550262	0.0275131	−	0.999621i	$-0.491241\pi$
$907$	1.65719	0.0550262	0.0275131	+	0.999621i	$0.491241\pi$
$908$	−8.02690	−0.266382
$909$	−9.05454	−0.300320
$910$	3.52753	0.116936
$911$	−32.9676	−1.09227	−0.546133	−	0.837698i	$-0.683901\pi$
$911$	−32.9676	−1.09227	−0.546133	+	0.837698i	$0.683901\pi$
$912$	−5.00990	−0.165895
$913$	55.8270	1.84760
$914$	26.8513	0.888163
$915$	−1.63995	−0.0542152
$916$	−25.6126	−0.846264
$917$	5.45519	0.180146
$918$	−9.05436	−0.298839
$919$	31.2474	1.03076	0.515379	−	0.856963i	$-0.327651\pi$
$919$	31.2474	1.03076	0.515379	+	0.856963i	$0.327651\pi$
$920$	−2.16212	−0.0712829
$921$	−16.1092	−0.530817
$922$	−5.33116	−0.175572
$923$	−3.78613	−0.124622
$924$	−8.20667	−0.269980
$925$	−2.16013	−0.0710247
$926$	23.2851	0.765197
$927$	−15.1805	−0.498594
$928$	−7.43472	−0.244057
$929$	−25.9809	−0.852404	−0.426202	−	0.904628i	$-0.640149\pi$
$929$	−25.9809	−0.852404	−0.426202	+	0.904628i	$0.640149\pi$
$930$	1.89031	0.0619858
$931$	−10.4389	−0.342121
$932$	8.36069	0.273864
$933$	−16.2568	−0.532224
$934$	−3.15723	−0.103308
$935$	8.48227	0.277400
$936$	2.95668	0.0966421
$937$	−54.3313	−1.77492	−0.887462	−	0.460880i	$-0.847534\pi$
$937$	−54.3313	−1.77492	−0.887462	+	0.460880i	$0.847534\pi$
$938$	18.9377	0.618339
$939$	−10.0102	−0.326670
$940$	−9.28939	−0.302987
$941$	−0.654760	−0.0213446	−0.0106723	−	0.999943i	$-0.503397\pi$
$941$	−0.654760	−0.0213446	−0.0106723	+	0.999943i	$0.503397\pi$
$942$	−2.58159	−0.0841128
$943$	10.3658	0.337555
$944$	−2.50293	−0.0814636
$945$	11.8138	0.384303
$946$	9.94293	0.323273
$947$	19.0893	0.620318	0.310159	−	0.950685i	$-0.399618\pi$
$947$	19.0893	0.620318	0.310159	+	0.950685i	$0.399618\pi$
$948$	−5.31417	−0.172596
$949$	−9.11914	−0.296020
$950$	−6.75626	−0.219202
$951$	17.0114	0.551633
$952$	−6.54914	−0.212259
$953$	−53.7847	−1.74226	−0.871129	−	0.491054i	$-0.836612\pi$
$953$	−53.7847	−1.74226	−0.871129	+	0.491054i	$0.836612\pi$
$954$	10.3935	0.336500
$955$	1.03740	0.0335695
$956$	−5.94177	−0.192171
$957$	−20.8725	−0.674712
$958$	17.2512	0.557360
$959$	−48.3660	−1.56182
$960$	0.741521	0.0239325
$961$	−24.5014	−0.790368
$962$	2.60671	0.0840437
$963$	10.4576	0.336991
$964$	−28.2635	−0.910307
$965$	−12.0456	−0.387763
$966$	4.68663	0.150790
$967$	−26.8623	−0.863835	−0.431917	−	0.901913i	$-0.642163\pi$
$967$	−26.8623	−0.863835	−0.431917	+	0.901913i	$0.642163\pi$
$968$	3.33415	0.107164
$969$	−11.2242	−0.360574
$970$	−6.45797	−0.207353
$971$	54.4207	1.74644	0.873222	−	0.487322i	$-0.162026\pi$
$971$	54.4207	1.74644	0.873222	+	0.487322i	$0.162026\pi$
$972$	15.3525	0.492432
$973$	−51.7725	−1.65975
$974$	14.1137	0.452233
$975$	−0.894820	−0.0286572
$976$	−2.21161	−0.0707918
$977$	18.4818	0.591284	0.295642	−	0.955299i	$-0.404466\pi$
$977$	18.4818	0.591284	0.295642	+	0.955299i	$0.404466\pi$
$978$	−5.55305	−0.177567
$979$	39.1929	1.25261
$980$	1.54507	0.0493554
$981$	16.6143	0.530454
$982$	5.58698	0.178288
$983$	31.3006	0.998333	0.499166	−	0.866506i	$-0.333640\pi$
$983$	31.3006	0.998333	0.499166	+	0.866506i	$0.333640\pi$
$984$	−3.55504	−0.113331
$985$	15.0764	0.480373
$986$	−16.6568	−0.530460
$987$	20.1358	0.640929
$988$	8.15302	0.259382
$989$	−5.67816	−0.180555
$990$	−9.27637	−0.294822
$991$	0.691328	0.0219608	0.0109804	−	0.999940i	$-0.496505\pi$
$991$	0.691328	0.0219608	0.0109804	+	0.999940i	$0.496505\pi$
$992$	2.54924	0.0809383
$993$	−15.4358	−0.489840
$994$	−9.17151	−0.290903
$995$	0.396256	0.0125622
$996$	10.9341	0.346459
$997$	−28.0981	−0.889877	−0.444938	−	0.895561i	$-0.646774\pi$
$997$	−28.0981	−0.889877	−0.444938	+	0.895561i	$0.646774\pi$
$998$	31.5338	0.998186
$999$	8.72995	0.276203

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.c.1.12	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.c.1.12	✓	16	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.741521 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.741521 q^{6} -2.92320 q^{7} +1.00000 q^{8} -2.45015 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.741521 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.741521 q^{6} -2.92320 q^{7} +1.00000 q^{8} -2.45015 q^{9} +1.00000 q^{10} +3.78605 q^{11} +0.741521 q^{12} -1.20674 q^{13} -2.92320 q^{14} +0.741521 q^{15} +1.00000 q^{16} +2.24040 q^{17} -2.45015 q^{18} -6.75626 q^{19} +1.00000 q^{20} -2.16761 q^{21} +3.78605 q^{22} -2.16212 q^{23} +0.741521 q^{24} +1.00000 q^{25} -1.20674 q^{26} -4.04140 q^{27} -2.92320 q^{28} -7.43472 q^{29} +0.741521 q^{30} +2.54924 q^{31} +1.00000 q^{32} +2.80743 q^{33} +2.24040 q^{34} -2.92320 q^{35} -2.45015 q^{36} -2.16013 q^{37} -6.75626 q^{38} -0.894820 q^{39} +1.00000 q^{40} -4.79426 q^{41} -2.16761 q^{42} +2.62620 q^{43} +3.78605 q^{44} -2.45015 q^{45} -2.16212 q^{46} -9.28939 q^{47} +0.741521 q^{48} +1.54507 q^{49} +1.00000 q^{50} +1.66131 q^{51} -1.20674 q^{52} -4.24197 q^{53} -4.04140 q^{54} +3.78605 q^{55} -2.92320 q^{56} -5.00990 q^{57} -7.43472 q^{58} -2.50293 q^{59} +0.741521 q^{60} -2.21161 q^{61} +2.54924 q^{62} +7.16226 q^{63} +1.00000 q^{64} -1.20674 q^{65} +2.80743 q^{66} -6.47843 q^{67} +2.24040 q^{68} -1.60326 q^{69} -2.92320 q^{70} +3.13750 q^{71} -2.45015 q^{72} +7.55686 q^{73} -2.16013 q^{74} +0.741521 q^{75} -6.75626 q^{76} -11.0674 q^{77} -0.894820 q^{78} -7.16658 q^{79} +1.00000 q^{80} +4.35366 q^{81} -4.79426 q^{82} +14.7455 q^{83} -2.16761 q^{84} +2.24040 q^{85} +2.62620 q^{86} -5.51300 q^{87} +3.78605 q^{88} +10.3519 q^{89} -2.45015 q^{90} +3.52753 q^{91} -2.16212 q^{92} +1.89031 q^{93} -9.28939 q^{94} -6.75626 q^{95} +0.741521 q^{96} -6.45797 q^{97} +1.54507 q^{98} -9.27637 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9	\( 16 q + 16 q^{2} - 8 q^{3} + 16 q^{4} + 16 q^{5} - 8 q^{6} - 10 q^{7} + 16 q^{8} - 2 q^{9} + 16 q^{10} - 14 q^{11} - 8 q^{12} - 20 q^{13} - 10 q^{14} - 8 q^{15} + 16 q^{16} - 27 q^{17} - 2 q^{18} - 17 q^{19} + 16 q^{20} - 12 q^{21} - 14 q^{22} - 9 q^{23} - 8 q^{24} + 16 q^{25} - 20 q^{26} - 11 q^{27} - 10 q^{28} - 23 q^{29} - 8 q^{30} - 21 q^{31} + 16 q^{32} - 9 q^{33} - 27 q^{34} - 10 q^{35} - 2 q^{36} - 16 q^{37} - 17 q^{38} - 6 q^{39} + 16 q^{40} - 35 q^{41} - 12 q^{42} + 3 q^{43} - 14 q^{44} - 2 q^{45} - 9 q^{46} - 25 q^{47} - 8 q^{48} - 24 q^{49} + 16 q^{50} - q^{51} - 20 q^{52} - 39 q^{53} - 11 q^{54} - 14 q^{55} - 10 q^{56} - 6 q^{57} - 23 q^{58} - 32 q^{59} - 8 q^{60} - 38 q^{61} - 21 q^{62} + q^{63} + 16 q^{64} - 20 q^{65} - 9 q^{66} + 5 q^{67} - 27 q^{68} - 25 q^{69} - 10 q^{70} - 16 q^{71} - 2 q^{72} - 17 q^{73} - 16 q^{74} - 8 q^{75} - 17 q^{76} - 34 q^{77} - 6 q^{78} - 40 q^{79} + 16 q^{80} - 28 q^{81} - 35 q^{82} - 22 q^{83} - 12 q^{84} - 27 q^{85} + 3 q^{86} + 10 q^{87} - 14 q^{88} - 46 q^{89} - 2 q^{90} - q^{91} - 9 q^{92} + 14 q^{93} - 25 q^{94} - 17 q^{95} - 8 q^{96} - 21 q^{97} - 24 q^{98} + 15 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 - 8 * q^3 + 16 * q^4 + 16 * q^5 - 8 * q^6 - 10 * q^7 + 16 * q^8 - 2 * q^9 + 16 * q^10 - 14 * q^11 - 8 * q^12 - 20 * q^13 - 10 * q^14 - 8 * q^15 + 16 * q^16 - 27 * q^17 - 2 * q^18 - 17 * q^19 + 16 * q^20 - 12 * q^21 - 14 * q^22 - 9 * q^23 - 8 * q^24 + 16 * q^25 - 20 * q^26 - 11 * q^27 - 10 * q^28 - 23 * q^29 - 8 * q^30 - 21 * q^31 + 16 * q^32 - 9 * q^33 - 27 * q^34 - 10 * q^35 - 2 * q^36 - 16 * q^37 - 17 * q^38 - 6 * q^39 + 16 * q^40 - 35 * q^41 - 12 * q^42 + 3 * q^43 - 14 * q^44 - 2 * q^45 - 9 * q^46 - 25 * q^47 - 8 * q^48 - 24 * q^49 + 16 * q^50 - q^51 - 20 * q^52 - 39 * q^53 - 11 * q^54 - 14 * q^55 - 10 * q^56 - 6 * q^57 - 23 * q^58 - 32 * q^59 - 8 * q^60 - 38 * q^61 - 21 * q^62 + q^63 + 16 * q^64 - 20 * q^65 - 9 * q^66 + 5 * q^67 - 27 * q^68 - 25 * q^69 - 10 * q^70 - 16 * q^71 - 2 * q^72 - 17 * q^73 - 16 * q^74 - 8 * q^75 - 17 * q^76 - 34 * q^77 - 6 * q^78 - 40 * q^79 + 16 * q^80 - 28 * q^81 - 35 * q^82 - 22 * q^83 - 12 * q^84 - 27 * q^85 + 3 * q^86 + 10 * q^87 - 14 * q^88 - 46 * q^89 - 2 * q^90 - q^91 - 9 * q^92 + 14 * q^93 - 25 * q^94 - 17 * q^95 - 8 * q^96 - 21 * q^97 - 24 * q^98 + 15 * q^99

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