LMFDB - Embedded newform 6042.2.a.bg.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, 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("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5 x^{11} - 34 x^{10} + 169 x^{9} + 453 x^{8} - 2095 x^{7} - 3056 x^{6} + 11545 x^{5} + \cdots + 7848 $ x^12 - 5x^11 - 34x^10 + 169x^9 + 453x^8 - 2095x^7 - 3056x^6 + 11545x^5 + 11014x^4 - 26766x^3 - 19370x^2 + 18296*x + 7848
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			1.5
Root			$-1.52770$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52770 q^{5} +1.00000 q^{6} -0.0681258 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52770 q^{5} +1.00000 q^{6} -0.0681258 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.52770 q^{10} +1.29338 q^{11} +1.00000 q^{12} -3.23428 q^{13} -0.0681258 q^{14} -1.52770 q^{15} +1.00000 q^{16} -1.90931 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.52770 q^{20} -0.0681258 q^{21} +1.29338 q^{22} +1.17399 q^{23} +1.00000 q^{24} -2.66615 q^{25} -3.23428 q^{26} +1.00000 q^{27} -0.0681258 q^{28} +7.56794 q^{29} -1.52770 q^{30} +7.36175 q^{31} +1.00000 q^{32} +1.29338 q^{33} -1.90931 q^{34} +0.104076 q^{35} +1.00000 q^{36} +3.84085 q^{37} -1.00000 q^{38} -3.23428 q^{39} -1.52770 q^{40} +4.30962 q^{41} -0.0681258 q^{42} +8.37693 q^{43} +1.29338 q^{44} -1.52770 q^{45} +1.17399 q^{46} +2.13981 q^{47} +1.00000 q^{48} -6.99536 q^{49} -2.66615 q^{50} -1.90931 q^{51} -3.23428 q^{52} +1.00000 q^{53} +1.00000 q^{54} -1.97589 q^{55} -0.0681258 q^{56} -1.00000 q^{57} +7.56794 q^{58} +10.4939 q^{59} -1.52770 q^{60} -5.69868 q^{61} +7.36175 q^{62} -0.0681258 q^{63} +1.00000 q^{64} +4.94099 q^{65} +1.29338 q^{66} +9.45747 q^{67} -1.90931 q^{68} +1.17399 q^{69} +0.104076 q^{70} -9.67811 q^{71} +1.00000 q^{72} +2.39646 q^{73} +3.84085 q^{74} -2.66615 q^{75} -1.00000 q^{76} -0.0881124 q^{77} -3.23428 q^{78} +9.59379 q^{79} -1.52770 q^{80} +1.00000 q^{81} +4.30962 q^{82} -3.04920 q^{83} -0.0681258 q^{84} +2.91684 q^{85} +8.37693 q^{86} +7.56794 q^{87} +1.29338 q^{88} +7.34216 q^{89} -1.52770 q^{90} +0.220338 q^{91} +1.17399 q^{92} +7.36175 q^{93} +2.13981 q^{94} +1.52770 q^{95} +1.00000 q^{96} +13.0877 q^{97} -6.99536 q^{98} +1.29338 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−1.52770	−0.683206	−0.341603	−	0.939844i	$-0.610970\pi$
$5$	−1.52770	−0.683206	−0.341603	+	0.939844i	$0.610970\pi$
$6$	1.00000	0.408248
$7$	−0.0681258	−0.0257491	−0.0128746	−	0.999917i	$-0.504098\pi$
$7$	−0.0681258	−0.0257491	−0.0128746	+	0.999917i	$0.504098\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.52770	−0.483100
$11$	1.29338	0.389968	0.194984	−	0.980806i	$-0.437535\pi$
$11$	1.29338	0.389968	0.194984	+	0.980806i	$0.437535\pi$
$12$	1.00000	0.288675
$13$	−3.23428	−0.897027	−0.448513	−	0.893776i	$-0.648046\pi$
$13$	−3.23428	−0.897027	−0.448513	+	0.893776i	$0.648046\pi$
$14$	−0.0681258	−0.0182074
$15$	−1.52770	−0.394449
$16$	1.00000	0.250000
$17$	−1.90931	−0.463075	−0.231538	−	0.972826i	$-0.574376\pi$
$17$	−1.90931	−0.463075	−0.231538	+	0.972826i	$0.574376\pi$
$18$	1.00000	0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.52770	−0.341603
$21$	−0.0681258	−0.0148663
$22$	1.29338	0.275749
$23$	1.17399	0.244794	0.122397	−	0.992481i	$-0.460942\pi$
$23$	1.17399	0.244794	0.122397	+	0.992481i	$0.460942\pi$
$24$	1.00000	0.204124
$25$	−2.66615	−0.533229
$26$	−3.23428	−0.634294
$27$	1.00000	0.192450
$28$	−0.0681258	−0.0128746
$29$	7.56794	1.40533	0.702665	−	0.711520i	$-0.251993\pi$
$29$	7.56794	1.40533	0.702665	+	0.711520i	$0.251993\pi$
$30$	−1.52770	−0.278918
$31$	7.36175	1.32221	0.661105	−	0.750294i	$-0.270088\pi$
$31$	7.36175	1.32221	0.661105	+	0.750294i	$0.270088\pi$
$32$	1.00000	0.176777
$33$	1.29338	0.225148
$34$	−1.90931	−0.327444
$35$	0.104076	0.0175920
$36$	1.00000	0.166667
$37$	3.84085	0.631431	0.315716	−	0.948854i	$-0.397755\pi$
$37$	3.84085	0.631431	0.315716	+	0.948854i	$0.397755\pi$
$38$	−1.00000	−0.162221
$39$	−3.23428	−0.517899
$40$	−1.52770	−0.241550
$41$	4.30962	0.673049	0.336525	−	0.941675i	$-0.390748\pi$
$41$	4.30962	0.673049	0.336525	+	0.941675i	$0.390748\pi$
$42$	−0.0681258	−0.0105120
$43$	8.37693	1.27747	0.638735	−	0.769427i	$-0.279458\pi$
$43$	8.37693	1.27747	0.638735	+	0.769427i	$0.279458\pi$
$44$	1.29338	0.194984
$45$	−1.52770	−0.227735
$46$	1.17399	0.173096
$47$	2.13981	0.312123	0.156061	−	0.987747i	$-0.450120\pi$
$47$	2.13981	0.312123	0.156061	+	0.987747i	$0.450120\pi$
$48$	1.00000	0.144338
$49$	−6.99536	−0.999337
$50$	−2.66615	−0.377050
$51$	−1.90931	−0.267357
$52$	−3.23428	−0.448513
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	−1.97589	−0.266428
$56$	−0.0681258	−0.00910370
$57$	−1.00000	−0.132453
$58$	7.56794	0.993719
$59$	10.4939	1.36619	0.683096	−	0.730328i	$-0.260633\pi$
$59$	10.4939	1.36619	0.683096	+	0.730328i	$0.260633\pi$
$60$	−1.52770	−0.197225
$61$	−5.69868	−0.729641	−0.364820	−	0.931078i	$-0.618870\pi$
$61$	−5.69868	−0.729641	−0.364820	+	0.931078i	$0.618870\pi$
$62$	7.36175	0.934943
$63$	−0.0681258	−0.00858305
$64$	1.00000	0.125000
$65$	4.94099	0.612854
$66$	1.29338	0.159204
$67$	9.45747	1.15541	0.577707	−	0.816244i	$-0.303948\pi$
$67$	9.45747	1.15541	0.577707	+	0.816244i	$0.303948\pi$
$68$	−1.90931	−0.231538
$69$	1.17399	0.141332
$70$	0.104076	0.0124394
$71$	−9.67811	−1.14858	−0.574290	−	0.818652i	$-0.694722\pi$
$71$	−9.67811	−1.14858	−0.574290	+	0.818652i	$0.694722\pi$
$72$	1.00000	0.117851
$73$	2.39646	0.280485	0.140242	−	0.990117i	$-0.455212\pi$
$73$	2.39646	0.280485	0.140242	+	0.990117i	$0.455212\pi$
$74$	3.84085	0.446489
$75$	−2.66615	−0.307860
$76$	−1.00000	−0.114708
$77$	−0.0881124	−0.0100413
$78$	−3.23428	−0.366210
$79$	9.59379	1.07939	0.539693	−	0.841862i	$-0.318540\pi$
$79$	9.59379	1.07939	0.539693	+	0.841862i	$0.318540\pi$
$80$	−1.52770	−0.170802
$81$	1.00000	0.111111
$82$	4.30962	0.475918
$83$	−3.04920	−0.334694	−0.167347	−	0.985898i	$-0.553520\pi$
$83$	−3.04920	−0.334694	−0.167347	+	0.985898i	$0.553520\pi$
$84$	−0.0681258	−0.00743314
$85$	2.91684	0.316376
$86$	8.37693	0.903307
$87$	7.56794	0.811368
$88$	1.29338	0.137874
$89$	7.34216	0.778267	0.389134	−	0.921181i	$-0.372774\pi$
$89$	7.34216	0.778267	0.389134	+	0.921181i	$0.372774\pi$
$90$	−1.52770	−0.161033
$91$	0.220338	0.0230977
$92$	1.17399	0.122397
$93$	7.36175	0.763378
$94$	2.13981	0.220704
$95$	1.52770	0.156738
$96$	1.00000	0.102062
$97$	13.0877	1.32886	0.664429	−	0.747351i	$-0.268675\pi$
$97$	13.0877	1.32886	0.664429	+	0.747351i	$0.268675\pi$
$98$	−6.99536	−0.706638
$99$	1.29338	0.129989
$100$	−2.66615	−0.266615
$101$	9.31767	0.927142	0.463571	−	0.886060i	$-0.346568\pi$
$101$	9.31767	0.927142	0.463571	+	0.886060i	$0.346568\pi$
$102$	−1.90931	−0.189050
$103$	3.51765	0.346605	0.173302	−	0.984869i	$-0.444556\pi$
$103$	3.51765	0.346605	0.173302	+	0.984869i	$0.444556\pi$
$104$	−3.23428	−0.317147
$105$	0.104076	0.0101567
$106$	1.00000	0.0971286
$107$	3.00389	0.290397	0.145199	−	0.989403i	$-0.453618\pi$
$107$	3.00389	0.290397	0.145199	+	0.989403i	$0.453618\pi$
$108$	1.00000	0.0962250
$109$	0.0186969	0.00179084	0.000895421	−	1.00000i	$-0.499715\pi$
$109$	0.0186969	0.00179084	0.000895421		1.00000i	$0.499715\pi$
$110$	−1.97589	−0.188393
$111$	3.84085	0.364557
$112$	−0.0681258	−0.00643729
$113$	−4.61544	−0.434184	−0.217092	−	0.976151i	$-0.569657\pi$
$113$	−4.61544	−0.434184	−0.217092	+	0.976151i	$0.569657\pi$
$114$	−1.00000	−0.0936586
$115$	−1.79350	−0.167245
$116$	7.56794	0.702665
$117$	−3.23428	−0.299009
$118$	10.4939	0.966044
$119$	0.130073	0.0119238
$120$	−1.52770	−0.139459
$121$	−9.32718	−0.847925
$122$	−5.69868	−0.515934
$123$	4.30962	0.388585
$124$	7.36175	0.661105
$125$	11.7115	1.04751
$126$	−0.0681258	−0.00606913
$127$	11.0759	0.982832	0.491416	−	0.870925i	$-0.336480\pi$
$127$	11.0759	0.982832	0.491416	+	0.870925i	$0.336480\pi$
$128$	1.00000	0.0883883
$129$	8.37693	0.737547
$130$	4.94099	0.433353
$131$	3.14137	0.274462	0.137231	−	0.990539i	$-0.456180\pi$
$131$	3.14137	0.274462	0.137231	+	0.990539i	$0.456180\pi$
$132$	1.29338	0.112574
$133$	0.0681258	0.00590726
$134$	9.45747	0.817001
$135$	−1.52770	−0.131483
$136$	−1.90931	−0.163722
$137$	−22.0056	−1.88006	−0.940032	−	0.341087i	$-0.889205\pi$
$137$	−22.0056	−1.88006	−0.940032	+	0.341087i	$0.889205\pi$
$138$	1.17399	0.0999369
$139$	−0.343421	−0.0291286	−0.0145643	−	0.999894i	$-0.504636\pi$
$139$	−0.343421	−0.0291286	−0.0145643	+	0.999894i	$0.504636\pi$
$140$	0.104076	0.00879599
$141$	2.13981	0.180204
$142$	−9.67811	−0.812169
$143$	−4.18314	−0.349812
$144$	1.00000	0.0833333
$145$	−11.5615	−0.960131
$146$	2.39646	0.198333
$147$	−6.99536	−0.576967
$148$	3.84085	0.315716
$149$	1.48529	0.121680	0.0608398	−	0.998148i	$-0.480622\pi$
$149$	1.48529	0.121680	0.0608398	+	0.998148i	$0.480622\pi$
$150$	−2.66615	−0.217690
$151$	4.36079	0.354876	0.177438	−	0.984132i	$-0.443219\pi$
$151$	4.36079	0.354876	0.177438	+	0.984132i	$0.443219\pi$
$152$	−1.00000	−0.0811107
$153$	−1.90931	−0.154358
$154$	−0.0881124	−0.00710030
$155$	−11.2465	−0.903342
$156$	−3.23428	−0.258949
$157$	−14.3207	−1.14292	−0.571459	−	0.820631i	$-0.693622\pi$
$157$	−14.3207	−1.14292	−0.571459	+	0.820631i	$0.693622\pi$
$158$	9.59379	0.763241
$159$	1.00000	0.0793052
$160$	−1.52770	−0.120775
$161$	−0.0799793	−0.00630325
$162$	1.00000	0.0785674
$163$	8.84544	0.692828	0.346414	−	0.938082i	$-0.387399\pi$
$163$	8.84544	0.692828	0.346414	+	0.938082i	$0.387399\pi$
$164$	4.30962	0.336525
$165$	−1.97589	−0.153823
$166$	−3.04920	−0.236664
$167$	17.9365	1.38797	0.693983	−	0.719992i	$-0.255854\pi$
$167$	17.9365	1.38797	0.693983	+	0.719992i	$0.255854\pi$
$168$	−0.0681258	−0.00525602
$169$	−2.53946	−0.195343
$170$	2.91684	0.223712
$171$	−1.00000	−0.0764719
$172$	8.37693	0.638735
$173$	1.42910	0.108652	0.0543261	−	0.998523i	$-0.482699\pi$
$173$	1.42910	0.108652	0.0543261	+	0.998523i	$0.482699\pi$
$174$	7.56794	0.573724
$175$	0.181633	0.0137302
$176$	1.29338	0.0974920
$177$	10.4939	0.788772
$178$	7.34216	0.550318
$179$	7.50014	0.560587	0.280293	−	0.959914i	$-0.409568\pi$
$179$	7.50014	0.560587	0.280293	+	0.959914i	$0.409568\pi$
$180$	−1.52770	−0.113868
$181$	1.73826	0.129204	0.0646021	−	0.997911i	$-0.479422\pi$
$181$	1.73826	0.129204	0.0646021	+	0.997911i	$0.479422\pi$
$182$	0.220338	0.0163325
$183$	−5.69868	−0.421258
$184$	1.17399	0.0865479
$185$	−5.86764	−0.431398
$186$	7.36175	0.539790
$187$	−2.46946	−0.180584
$188$	2.13981	0.156061
$189$	−0.0681258	−0.00495543
$190$	1.52770	0.110831
$191$	−11.4689	−0.829863	−0.414931	−	0.909853i	$-0.636194\pi$
$191$	−11.4689	−0.829863	−0.414931	+	0.909853i	$0.636194\pi$
$192$	1.00000	0.0721688
$193$	−2.15672	−0.155244	−0.0776219	−	0.996983i	$-0.524733\pi$
$193$	−2.15672	−0.155244	−0.0776219	+	0.996983i	$0.524733\pi$
$194$	13.0877	0.939645
$195$	4.94099	0.353831
$196$	−6.99536	−0.499668
$197$	−26.0427	−1.85547	−0.927733	−	0.373245i	$-0.878245\pi$
$197$	−26.0427	−1.85547	−0.927733	+	0.373245i	$0.878245\pi$
$198$	1.29338	0.0919163
$199$	−19.9903	−1.41708	−0.708538	−	0.705672i	$-0.750645\pi$
$199$	−19.9903	−1.41708	−0.708538	+	0.705672i	$0.750645\pi$
$200$	−2.66615	−0.188525
$201$	9.45747	0.667079
$202$	9.31767	0.655589
$203$	−0.515572	−0.0361861
$204$	−1.90931	−0.133678
$205$	−6.58378	−0.459831
$206$	3.51765	0.245086
$207$	1.17399	0.0815981
$208$	−3.23428	−0.224257
$209$	−1.29338	−0.0894648
$210$	0.104076	0.00718190
$211$	−18.4221	−1.26823	−0.634115	−	0.773239i	$-0.718635\pi$
$211$	−18.4221	−1.26823	−0.634115	+	0.773239i	$0.718635\pi$
$212$	1.00000	0.0686803
$213$	−9.67811	−0.663133
$214$	3.00389	0.205342
$215$	−12.7974	−0.872775
$216$	1.00000	0.0680414
$217$	−0.501525	−0.0340458
$218$	0.0186969	0.00126632
$219$	2.39646	0.161938
$220$	−1.97589	−0.133214
$221$	6.17523	0.415391
$222$	3.84085	0.257781
$223$	25.6910	1.72039	0.860197	−	0.509962i	$-0.170340\pi$
$223$	25.6910	1.72039	0.860197	+	0.509962i	$0.170340\pi$
$224$	−0.0681258	−0.00455185
$225$	−2.66615	−0.177743
$226$	−4.61544	−0.307014
$227$	−3.16166	−0.209847	−0.104923	−	0.994480i	$-0.533460\pi$
$227$	−3.16166	−0.209847	−0.104923	+	0.994480i	$0.533460\pi$
$228$	−1.00000	−0.0662266
$229$	21.1045	1.39463	0.697313	−	0.716766i	$-0.254379\pi$
$229$	21.1045	1.39463	0.697313	+	0.716766i	$0.254379\pi$
$230$	−1.79350	−0.118260
$231$	−0.0881124	−0.00579737
$232$	7.56794	0.496860
$233$	−16.3521	−1.07126	−0.535632	−	0.844451i	$-0.679927\pi$
$233$	−16.3521	−1.07126	−0.535632	+	0.844451i	$0.679927\pi$
$234$	−3.23428	−0.211431
$235$	−3.26897	−0.213244
$236$	10.4939	0.683096
$237$	9.59379	0.623183
$238$	0.130073	0.00843140
$239$	−19.7813	−1.27954	−0.639772	−	0.768565i	$-0.720971\pi$
$239$	−19.7813	−1.27954	−0.639772	+	0.768565i	$0.720971\pi$
$240$	−1.52770	−0.0986123
$241$	21.0738	1.35748	0.678740	−	0.734378i	$-0.262526\pi$
$241$	21.0738	1.35748	0.678740	+	0.734378i	$0.262526\pi$
$242$	−9.32718	−0.599574
$243$	1.00000	0.0641500
$244$	−5.69868	−0.364820
$245$	10.6868	0.682753
$246$	4.30962	0.274771
$247$	3.23428	0.205792
$248$	7.36175	0.467472
$249$	−3.04920	−0.193235
$250$	11.7115	0.740703
$251$	10.8755	0.686453	0.343227	−	0.939253i	$-0.388480\pi$
$251$	10.8755	0.686453	0.343227	+	0.939253i	$0.388480\pi$
$252$	−0.0681258	−0.00429152
$253$	1.51842	0.0954620
$254$	11.0759	0.694967
$255$	2.91684	0.182660
$256$	1.00000	0.0625000
$257$	23.9409	1.49339	0.746696	−	0.665165i	$-0.231639\pi$
$257$	23.9409	1.49339	0.746696	+	0.665165i	$0.231639\pi$
$258$	8.37693	0.521525
$259$	−0.261661	−0.0162588
$260$	4.94099	0.306427
$261$	7.56794	0.468444
$262$	3.14137	0.194074
$263$	−15.2400	−0.939738	−0.469869	−	0.882736i	$-0.655699\pi$
$263$	−15.2400	−0.939738	−0.469869	+	0.882736i	$0.655699\pi$
$264$	1.29338	0.0796019
$265$	−1.52770	−0.0938456
$266$	0.0681258	0.00417706
$267$	7.34216	0.449333
$268$	9.45747	0.577707
$269$	−19.7567	−1.20459	−0.602293	−	0.798275i	$-0.705746\pi$
$269$	−19.7567	−1.20459	−0.602293	+	0.798275i	$0.705746\pi$
$270$	−1.52770	−0.0929726
$271$	24.2613	1.47377	0.736884	−	0.676020i	$-0.236297\pi$
$271$	24.2613	1.47377	0.736884	+	0.676020i	$0.236297\pi$
$272$	−1.90931	−0.115769
$273$	0.220338	0.0133354
$274$	−22.0056	−1.32941
$275$	−3.44833	−0.207942
$276$	1.17399	0.0706661
$277$	0.188962	0.0113536	0.00567680	−	0.999984i	$-0.498193\pi$
$277$	0.188962	0.0113536	0.00567680	+	0.999984i	$0.498193\pi$
$278$	−0.343421	−0.0205970
$279$	7.36175	0.440736
$280$	0.104076	0.00621970
$281$	−11.3631	−0.677866	−0.338933	−	0.940811i	$-0.610066\pi$
$281$	−11.3631	−0.677866	−0.338933	+	0.940811i	$0.610066\pi$
$282$	2.13981	0.127424
$283$	25.0251	1.48759	0.743795	−	0.668408i	$-0.233024\pi$
$283$	25.0251	1.48759	0.743795	+	0.668408i	$0.233024\pi$
$284$	−9.67811	−0.574290
$285$	1.52770	0.0904929
$286$	−4.18314	−0.247354
$287$	−0.293596	−0.0173304
$288$	1.00000	0.0589256
$289$	−13.3545	−0.785561
$290$	−11.5615	−0.678915
$291$	13.0877	0.767217
$292$	2.39646	0.140242
$293$	−0.551917	−0.0322434	−0.0161217	−	0.999870i	$-0.505132\pi$
$293$	−0.551917	−0.0322434	−0.0161217	+	0.999870i	$0.505132\pi$
$294$	−6.99536	−0.407978
$295$	−16.0315	−0.933391
$296$	3.84085	0.223245
$297$	1.29338	0.0750494
$298$	1.48529	0.0860405
$299$	−3.79702	−0.219587
$300$	−2.66615	−0.153930
$301$	−0.570685	−0.0328937
$302$	4.36079	0.250935
$303$	9.31767	0.535286
$304$	−1.00000	−0.0573539
$305$	8.70584	0.498495
$306$	−1.90931	−0.109148
$307$	−21.5916	−1.23230	−0.616150	−	0.787629i	$-0.711309\pi$
$307$	−21.5916	−1.23230	−0.616150	+	0.787629i	$0.711309\pi$
$308$	−0.0881124	−0.00502067
$309$	3.51765	0.200112
$310$	−11.2465	−0.638759
$311$	13.2568	0.751724	0.375862	−	0.926676i	$-0.377347\pi$
$311$	13.2568	0.751724	0.375862	+	0.926676i	$0.377347\pi$
$312$	−3.23428	−0.183105
$313$	1.04046	0.0588103	0.0294051	−	0.999568i	$-0.490639\pi$
$313$	1.04046	0.0588103	0.0294051	+	0.999568i	$0.490639\pi$
$314$	−14.3207	−0.808165
$315$	0.104076	0.00586399
$316$	9.59379	0.539693
$317$	10.3642	0.582109	0.291054	−	0.956706i	$-0.405994\pi$
$317$	10.3642	0.582109	0.291054	+	0.956706i	$0.405994\pi$
$318$	1.00000	0.0560772
$319$	9.78820	0.548034
$320$	−1.52770	−0.0854008
$321$	3.00389	0.167661
$322$	−0.0799793	−0.00445707
$323$	1.90931	0.106237
$324$	1.00000	0.0555556
$325$	8.62305	0.478321
$326$	8.84544	0.489904
$327$	0.0186969	0.00103394
$328$	4.30962	0.237959
$329$	−0.145776	−0.00803690
$330$	−1.97589	−0.108769
$331$	−4.38505	−0.241024	−0.120512	−	0.992712i	$-0.538454\pi$
$331$	−4.38505	−0.241024	−0.120512	+	0.992712i	$0.538454\pi$
$332$	−3.04920	−0.167347
$333$	3.84085	0.210477
$334$	17.9365	0.981440
$335$	−14.4481	−0.789386
$336$	−0.0681258	−0.00371657
$337$	8.58002	0.467383	0.233692	−	0.972311i	$-0.424919\pi$
$337$	8.58002	0.467383	0.233692	+	0.972311i	$0.424919\pi$
$338$	−2.53946	−0.138129
$339$	−4.61544	−0.250676
$340$	2.91684	0.158188
$341$	9.52152	0.515619
$342$	−1.00000	−0.0540738
$343$	0.953446	0.0514812
$344$	8.37693	0.451654
$345$	−1.79350	−0.0965590
$346$	1.42910	0.0768287
$347$	3.98583	0.213971	0.106985	−	0.994261i	$-0.465880\pi$
$347$	3.98583	0.213971	0.106985	+	0.994261i	$0.465880\pi$
$348$	7.56794	0.405684
$349$	24.3568	1.30379	0.651896	−	0.758309i	$-0.273974\pi$
$349$	24.3568	1.30379	0.651896	+	0.758309i	$0.273974\pi$
$350$	0.181633	0.00970872
$351$	−3.23428	−0.172633
$352$	1.29338	0.0689372
$353$	−24.9852	−1.32983	−0.664915	−	0.746919i	$-0.731532\pi$
$353$	−24.9852	−1.32983	−0.664915	+	0.746919i	$0.731532\pi$
$354$	10.4939	0.557746
$355$	14.7852	0.784718
$356$	7.34216	0.389134
$357$	0.130073	0.00688421
$358$	7.50014	0.396395
$359$	−27.5465	−1.45385	−0.726925	−	0.686717i	$-0.759051\pi$
$359$	−27.5465	−1.45385	−0.726925	+	0.686717i	$0.759051\pi$
$360$	−1.52770	−0.0805166
$361$	1.00000	0.0526316
$362$	1.73826	0.0913611
$363$	−9.32718	−0.489550
$364$	0.220338	0.0115488
$365$	−3.66106	−0.191629
$366$	−5.69868	−0.297875
$367$	−13.7475	−0.717614	−0.358807	−	0.933412i	$-0.616816\pi$
$367$	−13.7475	−0.717614	−0.358807	+	0.933412i	$0.616816\pi$
$368$	1.17399	0.0611986
$369$	4.30962	0.224350
$370$	−5.86764	−0.305044
$371$	−0.0681258	−0.00353692
$372$	7.36175	0.381689
$373$	11.0746	0.573423	0.286712	−	0.958017i	$-0.407438\pi$
$373$	11.0746	0.573423	0.286712	+	0.958017i	$0.407438\pi$
$374$	−2.46946	−0.127693
$375$	11.7115	0.604781
$376$	2.13981	0.110352
$377$	−24.4768	−1.26062
$378$	−0.0681258	−0.00350402
$379$	15.2957	0.785689	0.392844	−	0.919605i	$-0.371491\pi$
$379$	15.2957	0.785689	0.392844	+	0.919605i	$0.371491\pi$
$380$	1.52770	0.0783691
$381$	11.0759	0.567438
$382$	−11.4689	−0.586802
$383$	25.2421	1.28981	0.644907	−	0.764261i	$-0.276896\pi$
$383$	25.2421	1.28981	0.644907	+	0.764261i	$0.276896\pi$
$384$	1.00000	0.0510310
$385$	0.134609	0.00686031
$386$	−2.15672	−0.109774
$387$	8.37693	0.425823
$388$	13.0877	0.664429
$389$	5.16687	0.261971	0.130985	−	0.991384i	$-0.458186\pi$
$389$	5.16687	0.261971	0.130985	+	0.991384i	$0.458186\pi$
$390$	4.94099	0.250197
$391$	−2.24151	−0.113358
$392$	−6.99536	−0.353319
$393$	3.14137	0.158461
$394$	−26.0427	−1.31201
$395$	−14.6564	−0.737443
$396$	1.29338	0.0649946
$397$	−36.1350	−1.81356	−0.906782	−	0.421600i	$-0.861469\pi$
$397$	−36.1350	−1.81356	−0.906782	+	0.421600i	$0.861469\pi$
$398$	−19.9903	−1.00202
$399$	0.0681258	0.00341056
$400$	−2.66615	−0.133307
$401$	−35.5422	−1.77489	−0.887447	−	0.460910i	$-0.847523\pi$
$401$	−35.5422	−1.77489	−0.887447	+	0.460910i	$0.847523\pi$
$402$	9.45747	0.471696
$403$	−23.8099	−1.18606
$404$	9.31767	0.463571
$405$	−1.52770	−0.0759118
$406$	−0.515572	−0.0255874
$407$	4.96766	0.246238
$408$	−1.90931	−0.0945249
$409$	11.7161	0.579326	0.289663	−	0.957129i	$-0.406457\pi$
$409$	11.7161	0.579326	0.289663	+	0.957129i	$0.406457\pi$
$410$	−6.58378	−0.325150
$411$	−22.0056	−1.08546
$412$	3.51765	0.173302
$413$	−0.714908	−0.0351783
$414$	1.17399	0.0576986
$415$	4.65826	0.228665
$416$	−3.23428	−0.158573
$417$	−0.343421	−0.0168174
$418$	−1.29338	−0.0632611
$419$	−4.57412	−0.223460	−0.111730	−	0.993739i	$-0.535639\pi$
$419$	−4.57412	−0.223460	−0.111730	+	0.993739i	$0.535639\pi$
$420$	0.104076	0.00507837
$421$	23.8507	1.16241	0.581207	−	0.813756i	$-0.302581\pi$
$421$	23.8507	1.16241	0.581207	+	0.813756i	$0.302581\pi$
$422$	−18.4221	−0.896773
$423$	2.13981	0.104041
$424$	1.00000	0.0485643
$425$	5.09050	0.246925
$426$	−9.67811	−0.468906
$427$	0.388227	0.0187876
$428$	3.00389	0.145199
$429$	−4.18314	−0.201964
$430$	−12.7974	−0.617145
$431$	15.7431	0.758317	0.379159	−	0.925332i	$-0.376213\pi$
$431$	15.7431	0.758317	0.379159	+	0.925332i	$0.376213\pi$
$432$	1.00000	0.0481125
$433$	−4.00252	−0.192349	−0.0961744	−	0.995364i	$-0.530661\pi$
$433$	−4.00252	−0.192349	−0.0961744	+	0.995364i	$0.530661\pi$
$434$	−0.501525	−0.0240740
$435$	−11.5615	−0.554332
$436$	0.0186969	0.000895421 0
$437$	−1.17399	−0.0561597
$438$	2.39646	0.114507
$439$	−16.5821	−0.791423	−0.395711	−	0.918375i	$-0.629502\pi$
$439$	−16.5821	−0.791423	−0.395711	+	0.918375i	$0.629502\pi$
$440$	−1.97589	−0.0941967
$441$	−6.99536	−0.333112
$442$	6.17523	0.293726
$443$	−2.10295	−0.0999141	−0.0499570	−	0.998751i	$-0.515908\pi$
$443$	−2.10295	−0.0999141	−0.0499570	+	0.998751i	$0.515908\pi$
$444$	3.84085	0.182279
$445$	−11.2166	−0.531717
$446$	25.6910	1.21650
$447$	1.48529	0.0702518
$448$	−0.0681258	−0.00321864
$449$	−10.4051	−0.491048	−0.245524	−	0.969390i	$-0.578960\pi$
$449$	−10.4051	−0.491048	−0.245524	+	0.969390i	$0.578960\pi$
$450$	−2.66615	−0.125683
$451$	5.57396	0.262468
$452$	−4.61544	−0.217092
$453$	4.36079	0.204888
$454$	−3.16166	−0.148384
$455$	−0.336609	−0.0157805
$456$	−1.00000	−0.0468293
$457$	24.9695	1.16802	0.584011	−	0.811745i	$-0.301482\pi$
$457$	24.9695	1.16802	0.584011	+	0.811745i	$0.301482\pi$
$458$	21.1045	0.986150
$459$	−1.90931	−0.0891189
$460$	−1.79350	−0.0836225
$461$	−13.3209	−0.620415	−0.310208	−	0.950669i	$-0.600399\pi$
$461$	−13.3209	−0.620415	−0.310208	+	0.950669i	$0.600399\pi$
$462$	−0.0881124	−0.00409936
$463$	24.1044	1.12023	0.560114	−	0.828416i	$-0.310757\pi$
$463$	24.1044	1.12023	0.560114	+	0.828416i	$0.310757\pi$
$464$	7.56794	0.351333
$465$	−11.2465	−0.521545
$466$	−16.3521	−0.757499
$467$	40.6908	1.88295	0.941473	−	0.337088i	$-0.109442\pi$
$467$	40.6908	1.88295	0.941473	+	0.337088i	$0.109442\pi$
$468$	−3.23428	−0.149504
$469$	−0.644298	−0.0297509
$470$	−3.26897	−0.150786
$471$	−14.3207	−0.659864
$472$	10.4939	0.483022
$473$	10.8345	0.498172
$474$	9.59379	0.440657
$475$	2.66615	0.122331
$476$	0.130073	0.00596190
$477$	1.00000	0.0457869
$478$	−19.7813	−0.904774
$479$	19.6217	0.896540	0.448270	−	0.893898i	$-0.352040\pi$
$479$	19.6217	0.896540	0.448270	+	0.893898i	$0.352040\pi$
$480$	−1.52770	−0.0697294
$481$	−12.4224	−0.566411
$482$	21.0738	0.959884
$483$	−0.0799793	−0.00363918
$484$	−9.32718	−0.423963
$485$	−19.9941	−0.907884
$486$	1.00000	0.0453609
$487$	26.9202	1.21987	0.609936	−	0.792451i	$-0.291195\pi$
$487$	26.9202	1.21987	0.609936	+	0.792451i	$0.291195\pi$
$488$	−5.69868	−0.257967
$489$	8.84544	0.400005
$490$	10.6868	0.482779
$491$	−25.8994	−1.16882	−0.584412	−	0.811457i	$-0.698675\pi$
$491$	−25.8994	−1.16882	−0.584412	+	0.811457i	$0.698675\pi$
$492$	4.30962	0.194293
$493$	−14.4495	−0.650774
$494$	3.23428	0.145517
$495$	−1.97589	−0.0888095
$496$	7.36175	0.330552
$497$	0.659330	0.0295750
$498$	−3.04920	−0.136638
$499$	6.92366	0.309946	0.154973	−	0.987919i	$-0.450471\pi$
$499$	6.92366	0.309946	0.154973	+	0.987919i	$0.450471\pi$
$500$	11.7115	0.523756
$501$	17.9365	0.801342
$502$	10.8755	0.485396
$503$	39.1759	1.74677	0.873384	−	0.487032i	$-0.161920\pi$
$503$	39.1759	1.74677	0.873384	+	0.487032i	$0.161920\pi$
$504$	−0.0681258	−0.00303457
$505$	−14.2346	−0.633429
$506$	1.51842	0.0675018
$507$	−2.53946	−0.112782
$508$	11.0759	0.491416
$509$	−42.8150	−1.89774	−0.948872	−	0.315662i	$-0.897773\pi$
$509$	−42.8150	−1.89774	−0.948872	+	0.315662i	$0.897773\pi$
$510$	2.91684	0.129160
$511$	−0.163261	−0.00722224
$512$	1.00000	0.0441942
$513$	−1.00000	−0.0441511
$514$	23.9409	1.05599
$515$	−5.37390	−0.236802
$516$	8.37693	0.368774
$517$	2.76758	0.121718
$518$	−0.261661	−0.0114967
$519$	1.42910	0.0627304
$520$	4.94099	0.216677
$521$	−10.7558	−0.471219	−0.235609	−	0.971848i	$-0.575709\pi$
$521$	−10.7558	−0.471219	−0.235609	+	0.971848i	$0.575709\pi$
$522$	7.56794	0.331240
$523$	19.6456	0.859040	0.429520	−	0.903057i	$-0.358683\pi$
$523$	19.6456	0.859040	0.429520	+	0.903057i	$0.358683\pi$
$524$	3.14137	0.137231
$525$	0.181633	0.00792714
$526$	−15.2400	−0.664495
$527$	−14.0559	−0.612283
$528$	1.29338	0.0562870
$529$	−21.6217	−0.940076
$530$	−1.52770	−0.0663589
$531$	10.4939	0.455398
$532$	0.0681258	0.00295363
$533$	−13.9385	−0.603743
$534$	7.34216	0.317726
$535$	−4.58903	−0.198401
$536$	9.45747	0.408501
$537$	7.50014	0.323655
$538$	−19.7567	−0.851771
$539$	−9.04764	−0.389709
$540$	−1.52770	−0.0657415
$541$	−11.3046	−0.486024	−0.243012	−	0.970023i	$-0.578136\pi$
$541$	−11.3046	−0.486024	−0.243012	+	0.970023i	$0.578136\pi$
$542$	24.2613	1.04211
$543$	1.73826	0.0745960
$544$	−1.90931	−0.0818609
$545$	−0.0285632	−0.00122351
$546$	0.220338	0.00942958
$547$	−6.83882	−0.292407	−0.146203	−	0.989255i	$-0.546705\pi$
$547$	−6.83882	−0.292407	−0.146203	+	0.989255i	$0.546705\pi$
$548$	−22.0056	−0.940032
$549$	−5.69868	−0.243214
$550$	−3.44833	−0.147037
$551$	−7.56794	−0.322405
$552$	1.17399	0.0499685
$553$	−0.653585	−0.0277933
$554$	0.188962	0.00802821
$555$	−5.86764	−0.249068
$556$	−0.343421	−0.0145643
$557$	−7.85497	−0.332826	−0.166413	−	0.986056i	$-0.553218\pi$
$557$	−7.85497	−0.332826	−0.166413	+	0.986056i	$0.553218\pi$
$558$	7.36175	0.311648
$559$	−27.0933	−1.14592
$560$	0.104076	0.00439799
$561$	−2.46946	−0.104261
$562$	−11.3631	−0.479324
$563$	−44.0002	−1.85439	−0.927194	−	0.374582i	$-0.877786\pi$
$563$	−44.0002	−1.85439	−0.927194	+	0.374582i	$0.877786\pi$
$564$	2.13981	0.0901021
$565$	7.05098	0.296637
$566$	25.0251	1.05188
$567$	−0.0681258	−0.00286102
$568$	−9.67811	−0.406085
$569$	−31.5877	−1.32423	−0.662113	−	0.749404i	$-0.730340\pi$
$569$	−31.5877	−1.32423	−0.662113	+	0.749404i	$0.730340\pi$
$570$	1.52770	0.0639881
$571$	−44.2344	−1.85115	−0.925577	−	0.378560i	$-0.876419\pi$
$571$	−44.2344	−1.85115	−0.925577	+	0.378560i	$0.876419\pi$
$572$	−4.18314	−0.174906
$573$	−11.4689	−0.479121
$574$	−0.293596	−0.0122545
$575$	−3.13004	−0.130532
$576$	1.00000	0.0416667
$577$	−22.6583	−0.943276	−0.471638	−	0.881792i	$-0.656337\pi$
$577$	−22.6583	−0.943276	−0.471638	+	0.881792i	$0.656337\pi$
$578$	−13.3545	−0.555476
$579$	−2.15672	−0.0896301
$580$	−11.5615	−0.480065
$581$	0.207730	0.00861808
$582$	13.0877	0.542504
$583$	1.29338	0.0535662
$584$	2.39646	0.0991663
$585$	4.94099	0.204285
$586$	−0.551917	−0.0227995
$587$	20.1398	0.831259	0.415629	−	0.909534i	$-0.363561\pi$
$587$	20.1398	0.831259	0.415629	+	0.909534i	$0.363561\pi$
$588$	−6.99536	−0.288484
$589$	−7.36175	−0.303336
$590$	−16.0315	−0.660007
$591$	−26.0427	−1.07125
$592$	3.84085	0.157858
$593$	12.6438	0.519219	0.259609	−	0.965714i	$-0.416406\pi$
$593$	12.6438	0.519219	0.259609	+	0.965714i	$0.416406\pi$
$594$	1.29338	0.0530679
$595$	−0.198712	−0.00814641
$596$	1.48529	0.0608398
$597$	−19.9903	−0.818150
$598$	−3.79702	−0.155272
$599$	−5.90058	−0.241091	−0.120546	−	0.992708i	$-0.538464\pi$
$599$	−5.90058	−0.241091	−0.120546	+	0.992708i	$0.538464\pi$
$600$	−2.66615	−0.108845
$601$	46.3586	1.89100	0.945502	−	0.325615i	$-0.105571\pi$
$601$	46.3586	1.89100	0.945502	+	0.325615i	$0.105571\pi$
$602$	−0.570685	−0.0232594
$603$	9.45747	0.385138
$604$	4.36079	0.177438
$605$	14.2491	0.579308
$606$	9.31767	0.378504
$607$	−22.4981	−0.913170	−0.456585	−	0.889680i	$-0.650927\pi$
$607$	−22.4981	−0.913170	−0.456585	+	0.889680i	$0.650927\pi$
$608$	−1.00000	−0.0405554
$609$	−0.515572	−0.0208920
$610$	8.70584	0.352489
$611$	−6.92072	−0.279983
$612$	−1.90931	−0.0771792
$613$	27.7369	1.12028	0.560142	−	0.828396i	$-0.310746\pi$
$613$	27.7369	1.12028	0.560142	+	0.828396i	$0.310746\pi$
$614$	−21.5916	−0.871368
$615$	−6.58378	−0.265484
$616$	−0.0881124	−0.00355015
$617$	28.9064	1.16373	0.581864	−	0.813286i	$-0.302324\pi$
$617$	28.9064	1.16373	0.581864	+	0.813286i	$0.302324\pi$
$618$	3.51765	0.141501
$619$	24.2423	0.974381	0.487190	−	0.873296i	$-0.338022\pi$
$619$	24.2423	0.974381	0.487190	+	0.873296i	$0.338022\pi$
$620$	−11.2465	−0.451671
$621$	1.17399	0.0471107
$622$	13.2568	0.531549
$623$	−0.500191	−0.0200397
$624$	−3.23428	−0.129475
$625$	−4.56093	−0.182437
$626$	1.04046	0.0415852
$627$	−1.29338	−0.0516525
$628$	−14.3207	−0.571459
$629$	−7.33336	−0.292400
$630$	0.104076	0.00414647
$631$	−36.9752	−1.47196	−0.735979	−	0.677005i	$-0.763278\pi$
$631$	−36.9752	−1.47196	−0.735979	+	0.677005i	$0.763278\pi$
$632$	9.59379	0.381620
$633$	−18.4221	−0.732212
$634$	10.3642	0.411613
$635$	−16.9207	−0.671477
$636$	1.00000	0.0396526
$637$	22.6249	0.896432
$638$	9.78820	0.387519
$639$	−9.67811	−0.382860
$640$	−1.52770	−0.0603875
$641$	−21.3141	−0.841855	−0.420928	−	0.907094i	$-0.638295\pi$
$641$	−21.3141	−0.841855	−0.420928	+	0.907094i	$0.638295\pi$
$642$	3.00389	0.118554
$643$	−23.9792	−0.945646	−0.472823	−	0.881157i	$-0.656765\pi$
$643$	−23.9792	−0.945646	−0.472823	+	0.881157i	$0.656765\pi$
$644$	−0.0799793	−0.00315162
$645$	−12.7974	−0.503897
$646$	1.90931	0.0751207
$647$	28.3968	1.11639	0.558197	−	0.829708i	$-0.311493\pi$
$647$	28.3968	1.11639	0.558197	+	0.829708i	$0.311493\pi$
$648$	1.00000	0.0392837
$649$	13.5726	0.532771
$650$	8.62305	0.338224
$651$	−0.501525	−0.0196563
$652$	8.84544	0.346414
$653$	19.9891	0.782235	0.391118	−	0.920341i	$-0.372089\pi$
$653$	19.9891	0.782235	0.391118	+	0.920341i	$0.372089\pi$
$654$	0.0186969	0.000731108 0
$655$	−4.79905	−0.187514
$656$	4.30962	0.168262
$657$	2.39646	0.0934949
$658$	−0.145776	−0.00568295
$659$	−34.9826	−1.36273	−0.681365	−	0.731944i	$-0.738613\pi$
$659$	−34.9826	−1.36273	−0.681365	+	0.731944i	$0.738613\pi$
$660$	−1.97589	−0.0769113
$661$	−8.70535	−0.338599	−0.169299	−	0.985565i	$-0.554150\pi$
$661$	−8.70535	−0.338599	−0.169299	+	0.985565i	$0.554150\pi$
$662$	−4.38505	−0.170430
$663$	6.17523	0.239826
$664$	−3.04920	−0.118332
$665$	−0.104076	−0.00403588
$666$	3.84085	0.148830
$667$	8.88471	0.344017
$668$	17.9365	0.693983
$669$	25.6910	0.993270
$670$	−14.4481	−0.558180
$671$	−7.37054	−0.284537
$672$	−0.0681258	−0.00262801
$673$	21.2536	0.819265	0.409632	−	0.912251i	$-0.365657\pi$
$673$	21.2536	0.819265	0.409632	+	0.912251i	$0.365657\pi$
$674$	8.58002	0.330490
$675$	−2.66615	−0.102620
$676$	−2.53946	−0.0976717
$677$	−41.3985	−1.59107	−0.795537	−	0.605906i	$-0.792811\pi$
$677$	−41.3985	−1.59107	−0.795537	+	0.605906i	$0.792811\pi$
$678$	−4.61544	−0.177255
$679$	−0.891613	−0.0342170
$680$	2.91684	0.111856
$681$	−3.16166	−0.121155
$682$	9.52152	0.364598
$683$	−24.0624	−0.920721	−0.460360	−	0.887732i	$-0.652280\pi$
$683$	−24.0624	−0.920721	−0.460360	+	0.887732i	$0.652280\pi$
$684$	−1.00000	−0.0382360
$685$	33.6178	1.28447
$686$	0.953446	0.0364027
$687$	21.1045	0.805188
$688$	8.37693	0.319367
$689$	−3.23428	−0.123216
$690$	−1.79350	−0.0682775
$691$	10.7529	0.409060	0.204530	−	0.978860i	$-0.434433\pi$
$691$	10.7529	0.409060	0.204530	+	0.978860i	$0.434433\pi$
$692$	1.42910	0.0543261
$693$	−0.0881124	−0.00334711
$694$	3.98583	0.151300
$695$	0.524643	0.0199008
$696$	7.56794	0.286862
$697$	−8.22839	−0.311673
$698$	24.3568	0.921920
$699$	−16.3521	−0.618495
$700$	0.181633	0.00686510
$701$	−25.3075	−0.955851	−0.477926	−	0.878400i	$-0.658611\pi$
$701$	−25.3075	−0.955851	−0.477926	+	0.878400i	$0.658611\pi$
$702$	−3.23428	−0.122070
$703$	−3.84085	−0.144860
$704$	1.29338	0.0487460
$705$	−3.26897	−0.123117
$706$	−24.9852	−0.940331
$707$	−0.634774	−0.0238731
$708$	10.4939	0.394386
$709$	−35.0559	−1.31655	−0.658276	−	0.752776i	$-0.728714\pi$
$709$	−35.0559	−1.31655	−0.658276	+	0.752776i	$0.728714\pi$
$710$	14.7852	0.554879
$711$	9.59379	0.359795
$712$	7.34216	0.275159
$713$	8.64264	0.323669
$714$	0.130073	0.00486787
$715$	6.39056	0.238993
$716$	7.50014	0.280293
$717$	−19.7813	−0.738745
$718$	−27.5465	−1.02803
$719$	6.41886	0.239383	0.119692	−	0.992811i	$-0.461809\pi$
$719$	6.41886	0.239383	0.119692	+	0.992811i	$0.461809\pi$
$720$	−1.52770	−0.0569338
$721$	−0.239643	−0.00892477
$722$	1.00000	0.0372161
$723$	21.0738	0.783742
$724$	1.73826	0.0646021
$725$	−20.1772	−0.749364
$726$	−9.32718	−0.346164
$727$	−48.8562	−1.81198	−0.905988	−	0.423304i	$-0.860870\pi$
$727$	−48.8562	−1.81198	−0.905988	+	0.423304i	$0.860870\pi$
$728$	0.220338	0.00816626
$729$	1.00000	0.0370370
$730$	−3.66106	−0.135502
$731$	−15.9941	−0.591564
$732$	−5.69868	−0.210629
$733$	39.2790	1.45080	0.725401	−	0.688327i	$-0.241654\pi$
$733$	39.2790	1.45080	0.725401	+	0.688327i	$0.241654\pi$
$734$	−13.7475	−0.507430
$735$	10.6868	0.394188
$736$	1.17399	0.0432740
$737$	12.2321	0.450574
$738$	4.30962	0.158639
$739$	13.9935	0.514757	0.257379	−	0.966311i	$-0.417141\pi$
$739$	13.9935	0.514757	0.257379	+	0.966311i	$0.417141\pi$
$740$	−5.86764	−0.215699
$741$	3.23428	0.118814
$742$	−0.0681258	−0.00250098
$743$	−41.3737	−1.51785	−0.758926	−	0.651177i	$-0.774276\pi$
$743$	−41.3737	−1.51785	−0.758926	+	0.651177i	$0.774276\pi$
$744$	7.36175	0.269895
$745$	−2.26907	−0.0831323
$746$	11.0746	0.405471
$747$	−3.04920	−0.111565
$748$	−2.46946	−0.0902922
$749$	−0.204643	−0.00747748
$750$	11.7115	0.427645
$751$	52.9775	1.93317	0.966587	−	0.256337i	$-0.0825157\pi$
$751$	52.9775	1.93317	0.966587	+	0.256337i	$0.0825157\pi$
$752$	2.13981	0.0780307
$753$	10.8755	0.396324
$754$	−24.4768	−0.891392
$755$	−6.66196	−0.242453
$756$	−0.0681258	−0.00247771
$757$	−15.6650	−0.569355	−0.284678	−	0.958623i	$-0.591887\pi$
$757$	−15.6650	−0.569355	−0.284678	+	0.958623i	$0.591887\pi$
$758$	15.2957	0.555566
$759$	1.51842	0.0551150
$760$	1.52770	0.0554153
$761$	−8.81271	−0.319460	−0.159730	−	0.987161i	$-0.551062\pi$
$761$	−8.81271	−0.319460	−0.159730	+	0.987161i	$0.551062\pi$
$762$	11.0759	0.401239
$763$	−0.00127375	−4.61127e−5 0
$764$	−11.4689	−0.414931
$765$	2.91684	0.105459
$766$	25.2421	0.912036
$767$	−33.9402	−1.22551
$768$	1.00000	0.0360844
$769$	4.93487	0.177956	0.0889780	−	0.996034i	$-0.471640\pi$
$769$	4.93487	0.177956	0.0889780	+	0.996034i	$0.471640\pi$
$770$	0.134609	0.00485097
$771$	23.9409	0.862210
$772$	−2.15672	−0.0776219
$773$	−11.3139	−0.406931	−0.203466	−	0.979082i	$-0.565221\pi$
$773$	−11.3139	−0.406931	−0.203466	+	0.979082i	$0.565221\pi$
$774$	8.37693	0.301102
$775$	−19.6275	−0.705041
$776$	13.0877	0.469822
$777$	−0.261661	−0.00938703
$778$	5.16687	0.185241
$779$	−4.30962	−0.154408
$780$	4.94099	0.176916
$781$	−12.5175	−0.447910
$782$	−2.24151	−0.0801564
$783$	7.56794	0.270456
$784$	−6.99536	−0.249834
$785$	21.8777	0.780849
$786$	3.14137	0.112049
$787$	−47.3949	−1.68945	−0.844723	−	0.535203i	$-0.820235\pi$
$787$	−47.3949	−1.68945	−0.844723	+	0.535203i	$0.820235\pi$
$788$	−26.0427	−0.927733
$789$	−15.2400	−0.542558
$790$	−14.6564	−0.521451
$791$	0.314431	0.0111799
$792$	1.29338	0.0459582
$793$	18.4311	0.654507
$794$	−36.1350	−1.28238
$795$	−1.52770	−0.0541818
$796$	−19.9903	−0.708538
$797$	55.2716	1.95782	0.978910	−	0.204290i	$-0.0654886\pi$
$797$	55.2716	1.95782	0.978910	+	0.204290i	$0.0654886\pi$
$798$	0.0681258	0.00241163
$799$	−4.08555	−0.144536
$800$	−2.66615	−0.0942625
$801$	7.34216	0.259422
$802$	−35.5422	−1.25504
$803$	3.09953	0.109380
$804$	9.45747	0.333539
$805$	0.122184	0.00430642
$806$	−23.8099	−0.838669
$807$	−19.7567	−0.695468
$808$	9.31767	0.327794
$809$	−2.91656	−0.102541	−0.0512705	−	0.998685i	$-0.516327\pi$
$809$	−2.91656	−0.102541	−0.0512705	+	0.998685i	$0.516327\pi$
$810$	−1.52770	−0.0536777
$811$	−23.1295	−0.812186	−0.406093	−	0.913832i	$-0.633109\pi$
$811$	−23.1295	−0.812186	−0.406093	+	0.913832i	$0.633109\pi$
$812$	−0.515572	−0.0180930
$813$	24.2613	0.850880
$814$	4.96766	0.174117
$815$	−13.5131	−0.473345
$816$	−1.90931	−0.0668392
$817$	−8.37693	−0.293072
$818$	11.7161	0.409645
$819$	0.220338	0.00769922
$820$	−6.58378	−0.229916
$821$	−22.5004	−0.785269	−0.392634	−	0.919695i	$-0.628436\pi$
$821$	−22.5004	−0.785269	−0.392634	+	0.919695i	$0.628436\pi$
$822$	−22.0056	−0.767533
$823$	38.9631	1.35817	0.679084	−	0.734061i	$-0.262377\pi$
$823$	38.9631	1.35817	0.679084	+	0.734061i	$0.262377\pi$
$824$	3.51765	0.122543
$825$	−3.44833	−0.120056
$826$	−0.714908	−0.0248748
$827$	24.5069	0.852187	0.426093	−	0.904679i	$-0.359889\pi$
$827$	24.5069	0.852187	0.426093	+	0.904679i	$0.359889\pi$
$828$	1.17399	0.0407991
$829$	−7.16311	−0.248785	−0.124392	−	0.992233i	$-0.539698\pi$
$829$	−7.16311	−0.248785	−0.124392	+	0.992233i	$0.539698\pi$
$830$	4.65826	0.161690
$831$	0.188962	0.00655500
$832$	−3.23428	−0.112128
$833$	13.3563	0.462768
$834$	−0.343421	−0.0118917
$835$	−27.4015	−0.948267
$836$	−1.29338	−0.0447324
$837$	7.36175	0.254459
$838$	−4.57412	−0.158010
$839$	−12.2660	−0.423469	−0.211734	−	0.977327i	$-0.567911\pi$
$839$	−12.2660	−0.423469	−0.211734	+	0.977327i	$0.567911\pi$
$840$	0.104076	0.00359095
$841$	28.2737	0.974955
$842$	23.8507	0.821950
$843$	−11.3631	−0.391366
$844$	−18.4221	−0.634115
$845$	3.87953	0.133460
$846$	2.13981	0.0735681
$847$	0.635422	0.0218333
$848$	1.00000	0.0343401
$849$	25.0251	0.858860
$850$	5.09050	0.174603
$851$	4.50913	0.154571
$852$	−9.67811	−0.331567
$853$	−26.5456	−0.908903	−0.454452	−	0.890771i	$-0.650165\pi$
$853$	−26.5456	−0.908903	−0.454452	+	0.890771i	$0.650165\pi$
$854$	0.388227	0.0132849
$855$	1.52770	0.0522461
$856$	3.00389	0.102671
$857$	−6.78792	−0.231871	−0.115935	−	0.993257i	$-0.536987\pi$
$857$	−6.78792	−0.231871	−0.115935	+	0.993257i	$0.536987\pi$
$858$	−4.18314	−0.142810
$859$	−19.3125	−0.658932	−0.329466	−	0.944167i	$-0.606869\pi$
$859$	−19.3125	−0.658932	−0.329466	+	0.944167i	$0.606869\pi$
$860$	−12.7974	−0.436387
$861$	−0.293596	−0.0100057
$862$	15.7431	0.536211
$863$	26.4376	0.899945	0.449972	−	0.893042i	$-0.351434\pi$
$863$	26.4376	0.899945	0.449972	+	0.893042i	$0.351434\pi$
$864$	1.00000	0.0340207
$865$	−2.18322	−0.0742319
$866$	−4.00252	−0.136011
$867$	−13.3545	−0.453544
$868$	−0.501525	−0.0170229
$869$	12.4084	0.420926
$870$	−11.5615	−0.391972
$871$	−30.5881	−1.03644
$872$	0.0186969	0.000633158 0
$873$	13.0877	0.442953
$874$	−1.17399	−0.0397109
$875$	−0.797858	−0.0269725
$876$	2.39646	0.0809689
$877$	−3.50800	−0.118457	−0.0592284	−	0.998244i	$-0.518864\pi$
$877$	−3.50800	−0.118457	−0.0592284	+	0.998244i	$0.518864\pi$
$878$	−16.5821	−0.559620
$879$	−0.551917	−0.0186157
$880$	−1.97589	−0.0666071
$881$	−14.4406	−0.486517	−0.243258	−	0.969962i	$-0.578216\pi$
$881$	−14.4406	−0.486517	−0.243258	+	0.969962i	$0.578216\pi$
$882$	−6.99536	−0.235546
$883$	−26.8303	−0.902912	−0.451456	−	0.892293i	$-0.649095\pi$
$883$	−26.8303	−0.902912	−0.451456	+	0.892293i	$0.649095\pi$
$884$	6.17523	0.207695
$885$	−16.0315	−0.538894
$886$	−2.10295	−0.0706499
$887$	−3.47022	−0.116519	−0.0582594	−	0.998301i	$-0.518555\pi$
$887$	−3.47022	−0.116519	−0.0582594	+	0.998301i	$0.518555\pi$
$888$	3.84085	0.128890
$889$	−0.754558	−0.0253071
$890$	−11.2166	−0.375981
$891$	1.29338	0.0433298
$892$	25.6910	0.860197
$893$	−2.13981	−0.0716059
$894$	1.48529	0.0496755
$895$	−11.4579	−0.382996
$896$	−0.0681258	−0.00227592
$897$	−3.79702	−0.126779
$898$	−10.4051	−0.347224
$899$	55.7133	1.85814
$900$	−2.66615	−0.0888716
$901$	−1.90931	−0.0636083
$902$	5.57396	0.185593
$903$	−0.570685	−0.0189912
$904$	−4.61544	−0.153507
$905$	−2.65554	−0.0882731
$906$	4.36079	0.144877
$907$	−13.1639	−0.437101	−0.218551	−	0.975826i	$-0.570133\pi$
$907$	−13.1639	−0.437101	−0.218551	+	0.975826i	$0.570133\pi$
$908$	−3.16166	−0.104923
$909$	9.31767	0.309047
$910$	−0.336609	−0.0111585
$911$	−15.9738	−0.529234	−0.264617	−	0.964354i	$-0.585246\pi$
$911$	−15.9738	−0.529234	−0.264617	+	0.964354i	$0.585246\pi$
$912$	−1.00000	−0.0331133
$913$	−3.94377	−0.130520
$914$	24.9695	0.825917
$915$	8.70584	0.287806
$916$	21.1045	0.697313
$917$	−0.214008	−0.00706718
$918$	−1.90931	−0.0630166
$919$	22.2199	0.732968	0.366484	−	0.930424i	$-0.380561\pi$
$919$	22.2199	0.732968	0.366484	+	0.930424i	$0.380561\pi$
$920$	−1.79350	−0.0591301
$921$	−21.5916	−0.711469
$922$	−13.3209	−0.438700
$923$	31.3017	1.03031
$924$	−0.0881124	−0.00289869
$925$	−10.2403	−0.336698
$926$	24.1044	0.792121
$927$	3.51765	0.115535
$928$	7.56794	0.248430
$929$	−29.4782	−0.967148	−0.483574	−	0.875304i	$-0.660662\pi$
$929$	−29.4782	−0.967148	−0.483574	+	0.875304i	$0.660662\pi$
$930$	−11.2465	−0.368788
$931$	6.99536	0.229264
$932$	−16.3521	−0.535632
$933$	13.2568	0.434008
$934$	40.6908	1.33144
$935$	3.77258	0.123376
$936$	−3.23428	−0.105716
$937$	−39.5043	−1.29055	−0.645274	−	0.763951i	$-0.723257\pi$
$937$	−39.5043	−1.29055	−0.645274	+	0.763951i	$0.723257\pi$
$938$	−0.644298	−0.0210371
$939$	1.04046	0.0339541
$940$	−3.26897	−0.106622
$941$	31.6346	1.03126	0.515629	−	0.856812i	$-0.327558\pi$
$941$	31.6346	1.03126	0.515629	+	0.856812i	$0.327558\pi$
$942$	−14.3207	−0.466594
$943$	5.05946	0.164759
$944$	10.4939	0.341548
$945$	0.104076	0.00338558
$946$	10.8345	0.352261
$947$	−9.44211	−0.306827	−0.153414	−	0.988162i	$-0.549027\pi$
$947$	−9.44211	−0.306827	−0.153414	+	0.988162i	$0.549027\pi$
$948$	9.59379	0.311592
$949$	−7.75082	−0.251602
$950$	2.66615	0.0865012
$951$	10.3642	0.336081
$952$	0.130073	0.00421570
$953$	−19.1869	−0.621525	−0.310762	−	0.950488i	$-0.600584\pi$
$953$	−19.1869	−0.621525	−0.310762	+	0.950488i	$0.600584\pi$
$954$	1.00000	0.0323762
$955$	17.5210	0.566967
$956$	−19.7813	−0.639772
$957$	9.78820	0.316408
$958$	19.6217	0.633949
$959$	1.49915	0.0484100
$960$	−1.52770	−0.0493062
$961$	23.1954	0.748238
$962$	−12.4224	−0.400513
$963$	3.00389	0.0967990
$964$	21.0738	0.678740
$965$	3.29481	0.106064
$966$	−0.0799793	−0.00257329
$967$	−36.2088	−1.16440	−0.582198	−	0.813047i	$-0.697807\pi$
$967$	−36.2088	−1.16440	−0.582198	+	0.813047i	$0.697807\pi$
$968$	−9.32718	−0.299787
$969$	1.90931	0.0613358
$970$	−19.9941	−0.641971
$971$	20.7791	0.666832	0.333416	−	0.942780i	$-0.391799\pi$
$971$	20.7791	0.666832	0.333416	+	0.942780i	$0.391799\pi$
$972$	1.00000	0.0320750
$973$	0.0233958	0.000750036 0
$974$	26.9202	0.862580
$975$	8.62305	0.276159
$976$	−5.69868	−0.182410
$977$	6.50516	0.208119	0.104059	−	0.994571i	$-0.466817\pi$
$977$	6.50516	0.208119	0.104059	+	0.994571i	$0.466817\pi$
$978$	8.84544	0.282846
$979$	9.49618	0.303499
$980$	10.6868	0.341377
$981$	0.0186969	0.000596948 0
$982$	−25.8994	−0.826484
$983$	−25.3177	−0.807508	−0.403754	−	0.914868i	$-0.632295\pi$
$983$	−25.3177	−0.807508	−0.403754	+	0.914868i	$0.632295\pi$
$984$	4.30962	0.137386
$985$	39.7853	1.26767
$986$	−14.4495	−0.460167
$987$	−0.145776	−0.00464011
$988$	3.23428	0.102896
$989$	9.83445	0.312717
$990$	−1.97589	−0.0627978
$991$	−34.3614	−1.09153	−0.545763	−	0.837939i	$-0.683760\pi$
$991$	−34.3614	−1.09153	−0.545763	+	0.837939i	$0.683760\pi$
$992$	7.36175	0.233736
$993$	−4.38505	−0.139155
$994$	0.659330	0.0209127
$995$	30.5391	0.968155
$996$	−3.04920	−0.0966177
$997$	−19.9309	−0.631217	−0.315608	−	0.948890i	$-0.602209\pi$
$997$	−19.9309	−0.631217	−0.315608	+	0.948890i	$0.602209\pi$
$998$	6.92366	0.219165
$999$	3.84085	0.121519

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bg.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bg.1.5	✓	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52770 q^{5} +1.00000 q^{6} -0.0681258 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.52770 q^{5} +1.00000 q^{6} -0.0681258 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.52770 q^{10} +1.29338 q^{11} +1.00000 q^{12} -3.23428 q^{13} -0.0681258 q^{14} -1.52770 q^{15} +1.00000 q^{16} -1.90931 q^{17} +1.00000 q^{18} -1.00000 q^{19} -1.52770 q^{20} -0.0681258 q^{21} +1.29338 q^{22} +1.17399 q^{23} +1.00000 q^{24} -2.66615 q^{25} -3.23428 q^{26} +1.00000 q^{27} -0.0681258 q^{28} +7.56794 q^{29} -1.52770 q^{30} +7.36175 q^{31} +1.00000 q^{32} +1.29338 q^{33} -1.90931 q^{34} +0.104076 q^{35} +1.00000 q^{36} +3.84085 q^{37} -1.00000 q^{38} -3.23428 q^{39} -1.52770 q^{40} +4.30962 q^{41} -0.0681258 q^{42} +8.37693 q^{43} +1.29338 q^{44} -1.52770 q^{45} +1.17399 q^{46} +2.13981 q^{47} +1.00000 q^{48} -6.99536 q^{49} -2.66615 q^{50} -1.90931 q^{51} -3.23428 q^{52} +1.00000 q^{53} +1.00000 q^{54} -1.97589 q^{55} -0.0681258 q^{56} -1.00000 q^{57} +7.56794 q^{58} +10.4939 q^{59} -1.52770 q^{60} -5.69868 q^{61} +7.36175 q^{62} -0.0681258 q^{63} +1.00000 q^{64} +4.94099 q^{65} +1.29338 q^{66} +9.45747 q^{67} -1.90931 q^{68} +1.17399 q^{69} +0.104076 q^{70} -9.67811 q^{71} +1.00000 q^{72} +2.39646 q^{73} +3.84085 q^{74} -2.66615 q^{75} -1.00000 q^{76} -0.0881124 q^{77} -3.23428 q^{78} +9.59379 q^{79} -1.52770 q^{80} +1.00000 q^{81} +4.30962 q^{82} -3.04920 q^{83} -0.0681258 q^{84} +2.91684 q^{85} +8.37693 q^{86} +7.56794 q^{87} +1.29338 q^{88} +7.34216 q^{89} -1.52770 q^{90} +0.220338 q^{91} +1.17399 q^{92} +7.36175 q^{93} +2.13981 q^{94} +1.52770 q^{95} +1.00000 q^{96} +13.0877 q^{97} -6.99536 q^{98} +1.29338 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9	\( 12 q + 12 q^{2} + 12 q^{3} + 12 q^{4} + 5 q^{5} + 12 q^{6} + 6 q^{7} + 12 q^{8} + 12 q^{9} + 5 q^{10} + 7 q^{11} + 12 q^{12} + 9 q^{13} + 6 q^{14} + 5 q^{15} + 12 q^{16} + 25 q^{17} + 12 q^{18} - 12 q^{19} + 5 q^{20} + 6 q^{21} + 7 q^{22} + 22 q^{23} + 12 q^{24} + 33 q^{25} + 9 q^{26} + 12 q^{27} + 6 q^{28} + q^{29} + 5 q^{30} + 23 q^{31} + 12 q^{32} + 7 q^{33} + 25 q^{34} + 5 q^{35} + 12 q^{36} - q^{37} - 12 q^{38} + 9 q^{39} + 5 q^{40} - 15 q^{41} + 6 q^{42} + 2 q^{43} + 7 q^{44} + 5 q^{45} + 22 q^{46} + 11 q^{47} + 12 q^{48} + 36 q^{49} + 33 q^{50} + 25 q^{51} + 9 q^{52} + 12 q^{53} + 12 q^{54} - 4 q^{55} + 6 q^{56} - 12 q^{57} + q^{58} + 3 q^{59} + 5 q^{60} + 16 q^{61} + 23 q^{62} + 6 q^{63} + 12 q^{64} + 7 q^{65} + 7 q^{66} - 2 q^{67} + 25 q^{68} + 22 q^{69} + 5 q^{70} - 4 q^{71} + 12 q^{72} + 35 q^{73} - q^{74} + 33 q^{75} - 12 q^{76} + 11 q^{77} + 9 q^{78} + 4 q^{79} + 5 q^{80} + 12 q^{81} - 15 q^{82} + 39 q^{83} + 6 q^{84} + 10 q^{85} + 2 q^{86} + q^{87} + 7 q^{88} + 11 q^{89} + 5 q^{90} - 18 q^{91} + 22 q^{92} + 23 q^{93} + 11 q^{94} - 5 q^{95} + 12 q^{96} - 21 q^{97} + 36 q^{98} + 7 q^{99}+O(q^{100}) \) 12 * q + 12 * q^2 + 12 * q^3 + 12 * q^4 + 5 * q^5 + 12 * q^6 + 6 * q^7 + 12 * q^8 + 12 * q^9 + 5 * q^10 + 7 * q^11 + 12 * q^12 + 9 * q^13 + 6 * q^14 + 5 * q^15 + 12 * q^16 + 25 * q^17 + 12 * q^18 - 12 * q^19 + 5 * q^20 + 6 * q^21 + 7 * q^22 + 22 * q^23 + 12 * q^24 + 33 * q^25 + 9 * q^26 + 12 * q^27 + 6 * q^28 + q^29 + 5 * q^30 + 23 * q^31 + 12 * q^32 + 7 * q^33 + 25 * q^34 + 5 * q^35 + 12 * q^36 - q^37 - 12 * q^38 + 9 * q^39 + 5 * q^40 - 15 * q^41 + 6 * q^42 + 2 * q^43 + 7 * q^44 + 5 * q^45 + 22 * q^46 + 11 * q^47 + 12 * q^48 + 36 * q^49 + 33 * q^50 + 25 * q^51 + 9 * q^52 + 12 * q^53 + 12 * q^54 - 4 * q^55 + 6 * q^56 - 12 * q^57 + q^58 + 3 * q^59 + 5 * q^60 + 16 * q^61 + 23 * q^62 + 6 * q^63 + 12 * q^64 + 7 * q^65 + 7 * q^66 - 2 * q^67 + 25 * q^68 + 22 * q^69 + 5 * q^70 - 4 * q^71 + 12 * q^72 + 35 * q^73 - q^74 + 33 * q^75 - 12 * q^76 + 11 * q^77 + 9 * q^78 + 4 * q^79 + 5 * q^80 + 12 * q^81 - 15 * q^82 + 39 * q^83 + 6 * q^84 + 10 * q^85 + 2 * q^86 + q^87 + 7 * q^88 + 11 * q^89 + 5 * q^90 - 18 * q^91 + 22 * q^92 + 23 * q^93 + 11 * q^94 - 5 * q^95 + 12 * q^96 - 21 * q^97 + 36 * q^98 + 7 * q^99

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