LMFDB - Embedded newform 6042.2.a.bh.1.7

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 40 x^{11} + 123 x^{10} + 537 x^{9} - 1707 x^{8} - 2914 x^{7} + 9639 x^{6} + \cdots + 1200 $ x^13 - 3x^12 - 40x^11 + 123x^10 + 537x^9 - 1707x^8 - 2914x^7 + 9639x^6 + 6938x^5 - 22200x^4 - 9466x^3 + 16812x^2 + 9304x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.229612$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.229612 q^{5} +1.00000 q^{6} +2.69176 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.229612 q^{5} +1.00000 q^{6} +2.69176 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.229612 q^{10} +3.73454 q^{11} +1.00000 q^{12} +2.15700 q^{13} +2.69176 q^{14} -0.229612 q^{15} +1.00000 q^{16} +5.34710 q^{17} +1.00000 q^{18} +1.00000 q^{19} -0.229612 q^{20} +2.69176 q^{21} +3.73454 q^{22} -1.94418 q^{23} +1.00000 q^{24} -4.94728 q^{25} +2.15700 q^{26} +1.00000 q^{27} +2.69176 q^{28} -5.72170 q^{29} -0.229612 q^{30} +10.3589 q^{31} +1.00000 q^{32} +3.73454 q^{33} +5.34710 q^{34} -0.618059 q^{35} +1.00000 q^{36} -7.91788 q^{37} +1.00000 q^{38} +2.15700 q^{39} -0.229612 q^{40} -4.50346 q^{41} +2.69176 q^{42} +9.41549 q^{43} +3.73454 q^{44} -0.229612 q^{45} -1.94418 q^{46} +5.70918 q^{47} +1.00000 q^{48} +0.245558 q^{49} -4.94728 q^{50} +5.34710 q^{51} +2.15700 q^{52} -1.00000 q^{53} +1.00000 q^{54} -0.857494 q^{55} +2.69176 q^{56} +1.00000 q^{57} -5.72170 q^{58} -11.8621 q^{59} -0.229612 q^{60} -12.4990 q^{61} +10.3589 q^{62} +2.69176 q^{63} +1.00000 q^{64} -0.495273 q^{65} +3.73454 q^{66} +4.80167 q^{67} +5.34710 q^{68} -1.94418 q^{69} -0.618059 q^{70} +4.70195 q^{71} +1.00000 q^{72} -2.77825 q^{73} -7.91788 q^{74} -4.94728 q^{75} +1.00000 q^{76} +10.0525 q^{77} +2.15700 q^{78} +9.77405 q^{79} -0.229612 q^{80} +1.00000 q^{81} -4.50346 q^{82} -7.84819 q^{83} +2.69176 q^{84} -1.22776 q^{85} +9.41549 q^{86} -5.72170 q^{87} +3.73454 q^{88} -3.87222 q^{89} -0.229612 q^{90} +5.80613 q^{91} -1.94418 q^{92} +10.3589 q^{93} +5.70918 q^{94} -0.229612 q^{95} +1.00000 q^{96} -6.33978 q^{97} +0.245558 q^{98} +3.73454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * 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
$5$	−0.229612	−0.102685	−0.0513427	−	0.998681i	$-0.516350\pi$
$5$	−0.229612	−0.102685	−0.0513427	+	0.998681i	$0.516350\pi$
$6$	1.00000	0.408248
$7$	2.69176	1.01739	0.508694	−	0.860947i	$-0.330128\pi$
$7$	2.69176	1.01739	0.508694	+	0.860947i	$0.330128\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.229612	−0.0726096
$11$	3.73454	1.12601	0.563003	−	0.826455i	$-0.309646\pi$
$11$	3.73454	1.12601	0.563003	+	0.826455i	$0.309646\pi$
$12$	1.00000	0.288675
$13$	2.15700	0.598245	0.299123	−	0.954215i	$-0.403306\pi$
$13$	2.15700	0.598245	0.299123	+	0.954215i	$0.403306\pi$
$14$	2.69176	0.719402
$15$	−0.229612	−0.0592855
$16$	1.00000	0.250000
$17$	5.34710	1.29686	0.648431	−	0.761274i	$-0.275426\pi$
$17$	5.34710	1.29686	0.648431	+	0.761274i	$0.275426\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−0.229612	−0.0513427
$21$	2.69176	0.587390
$22$	3.73454	0.796206
$23$	−1.94418	−0.405389	−0.202695	−	0.979242i	$-0.564970\pi$
$23$	−1.94418	−0.405389	−0.202695	+	0.979242i	$0.564970\pi$
$24$	1.00000	0.204124
$25$	−4.94728	−0.989456
$26$	2.15700	0.423023
$27$	1.00000	0.192450
$28$	2.69176	0.508694
$29$	−5.72170	−1.06249	−0.531247	−	0.847217i	$-0.678276\pi$
$29$	−5.72170	−1.06249	−0.531247	+	0.847217i	$0.678276\pi$
$30$	−0.229612	−0.0419212
$31$	10.3589	1.86052	0.930260	−	0.366900i	$-0.119581\pi$
$31$	10.3589	1.86052	0.930260	+	0.366900i	$0.119581\pi$
$32$	1.00000	0.176777
$33$	3.73454	0.650100
$34$	5.34710	0.917020
$35$	−0.618059	−0.104471
$36$	1.00000	0.166667
$37$	−7.91788	−1.30169	−0.650846	−	0.759210i	$-0.725585\pi$
$37$	−7.91788	−1.30169	−0.650846	+	0.759210i	$0.725585\pi$
$38$	1.00000	0.162221
$39$	2.15700	0.345397
$40$	−0.229612	−0.0363048
$41$	−4.50346	−0.703323	−0.351662	−	0.936127i	$-0.614383\pi$
$41$	−4.50346	−0.703323	−0.351662	+	0.936127i	$0.614383\pi$
$42$	2.69176	0.415347
$43$	9.41549	1.43585	0.717924	−	0.696121i	$-0.245092\pi$
$43$	9.41549	1.43585	0.717924	+	0.696121i	$0.245092\pi$
$44$	3.73454	0.563003
$45$	−0.229612	−0.0342285
$46$	−1.94418	−0.286653
$47$	5.70918	0.832770	0.416385	−	0.909188i	$-0.363297\pi$
$47$	5.70918	0.832770	0.416385	+	0.909188i	$0.363297\pi$
$48$	1.00000	0.144338
$49$	0.245558	0.0350797
$50$	−4.94728	−0.699651
$51$	5.34710	0.748743
$52$	2.15700	0.299123
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	−0.857494	−0.115624
$56$	2.69176	0.359701
$57$	1.00000	0.132453
$58$	−5.72170	−0.751297
$59$	−11.8621	−1.54431	−0.772154	−	0.635435i	$-0.780821\pi$
$59$	−11.8621	−1.54431	−0.772154	+	0.635435i	$0.780821\pi$
$60$	−0.229612	−0.0296427
$61$	−12.4990	−1.60034	−0.800169	−	0.599774i	$-0.795257\pi$
$61$	−12.4990	−1.60034	−0.800169	+	0.599774i	$0.795257\pi$
$62$	10.3589	1.31559
$63$	2.69176	0.339130
$64$	1.00000	0.125000
$65$	−0.495273	−0.0614311
$66$	3.73454	0.459690
$67$	4.80167	0.586617	0.293309	−	0.956018i	$-0.405244\pi$
$67$	4.80167	0.586617	0.293309	+	0.956018i	$0.405244\pi$
$68$	5.34710	0.648431
$69$	−1.94418	−0.234051
$70$	−0.618059	−0.0738722
$71$	4.70195	0.558019	0.279010	−	0.960288i	$-0.409994\pi$
$71$	4.70195	0.558019	0.279010	+	0.960288i	$0.409994\pi$
$72$	1.00000	0.117851
$73$	−2.77825	−0.325170	−0.162585	−	0.986695i	$-0.551983\pi$
$73$	−2.77825	−0.325170	−0.162585	+	0.986695i	$0.551983\pi$
$74$	−7.91788	−0.920435
$75$	−4.94728	−0.571263
$76$	1.00000	0.114708
$77$	10.0525	1.14559
$78$	2.15700	0.244233
$79$	9.77405	1.09967	0.549833	−	0.835275i	$-0.314691\pi$
$79$	9.77405	1.09967	0.549833	+	0.835275i	$0.314691\pi$
$80$	−0.229612	−0.0256714
$81$	1.00000	0.111111
$82$	−4.50346	−0.497324
$83$	−7.84819	−0.861450	−0.430725	−	0.902483i	$-0.641742\pi$
$83$	−7.84819	−0.861450	−0.430725	+	0.902483i	$0.641742\pi$
$84$	2.69176	0.293695
$85$	−1.22776	−0.133169
$86$	9.41549	1.01530
$87$	−5.72170	−0.613431
$88$	3.73454	0.398103
$89$	−3.87222	−0.410454	−0.205227	−	0.978714i	$-0.565793\pi$
$89$	−3.87222	−0.410454	−0.205227	+	0.978714i	$0.565793\pi$
$90$	−0.229612	−0.0242032
$91$	5.80613	0.608648
$92$	−1.94418	−0.202695
$93$	10.3589	1.07417
$94$	5.70918	0.588857
$95$	−0.229612	−0.0235577
$96$	1.00000	0.102062
$97$	−6.33978	−0.643707	−0.321854	−	0.946789i	$-0.604306\pi$
$97$	−6.33978	−0.643707	−0.321854	+	0.946789i	$0.604306\pi$
$98$	0.245558	0.0248051
$99$	3.73454	0.375335
$100$	−4.94728	−0.494728
$101$	−1.22246	−0.121640	−0.0608199	−	0.998149i	$-0.519372\pi$
$101$	−1.22246	−0.121640	−0.0608199	+	0.998149i	$0.519372\pi$
$102$	5.34710	0.529442
$103$	4.59661	0.452917	0.226458	−	0.974021i	$-0.427285\pi$
$103$	4.59661	0.452917	0.226458	+	0.974021i	$0.427285\pi$
$104$	2.15700	0.211512
$105$	−0.618059	−0.0603164
$106$	−1.00000	−0.0971286
$107$	−5.51466	−0.533123	−0.266561	−	0.963818i	$-0.585888\pi$
$107$	−5.51466	−0.533123	−0.266561	+	0.963818i	$0.585888\pi$
$108$	1.00000	0.0962250
$109$	−11.4302	−1.09481	−0.547407	−	0.836866i	$-0.684385\pi$
$109$	−11.4302	−1.09481	−0.547407	+	0.836866i	$0.684385\pi$
$110$	−0.857494	−0.0817588
$111$	−7.91788	−0.751532
$112$	2.69176	0.254347
$113$	11.7260	1.10309	0.551547	−	0.834144i	$-0.314038\pi$
$113$	11.7260	1.10309	0.551547	+	0.834144i	$0.314038\pi$
$114$	1.00000	0.0936586
$115$	0.446406	0.0416276
$116$	−5.72170	−0.531247
$117$	2.15700	0.199415
$118$	−11.8621	−1.09199
$119$	14.3931	1.31941
$120$	−0.229612	−0.0209606
$121$	2.94678	0.267889
$122$	−12.4990	−1.13161
$123$	−4.50346	−0.406064
$124$	10.3589	0.930260
$125$	2.28401	0.204288
$126$	2.69176	0.239801
$127$	−13.6692	−1.21294	−0.606472	−	0.795105i	$-0.707416\pi$
$127$	−13.6692	−1.21294	−0.606472	+	0.795105i	$0.707416\pi$
$128$	1.00000	0.0883883
$129$	9.41549	0.828987
$130$	−0.495273	−0.0434383
$131$	−9.59689	−0.838484	−0.419242	−	0.907874i	$-0.637704\pi$
$131$	−9.59689	−0.838484	−0.419242	+	0.907874i	$0.637704\pi$
$132$	3.73454	0.325050
$133$	2.69176	0.233405
$134$	4.80167	0.414801
$135$	−0.229612	−0.0197618
$136$	5.34710	0.458510
$137$	−4.82995	−0.412651	−0.206325	−	0.978483i	$-0.566151\pi$
$137$	−4.82995	−0.412651	−0.206325	+	0.978483i	$0.566151\pi$
$138$	−1.94418	−0.165499
$139$	13.9359	1.18203	0.591016	−	0.806660i	$-0.298727\pi$
$139$	13.9359	1.18203	0.591016	+	0.806660i	$0.298727\pi$
$140$	−0.618059	−0.0522355
$141$	5.70918	0.480800
$142$	4.70195	0.394579
$143$	8.05542	0.673628
$144$	1.00000	0.0833333
$145$	1.31377	0.109103
$146$	−2.77825	−0.229930
$147$	0.245558	0.0202533
$148$	−7.91788	−0.650846
$149$	−5.66620	−0.464193	−0.232096	−	0.972693i	$-0.574558\pi$
$149$	−5.66620	−0.464193	−0.232096	+	0.972693i	$0.574558\pi$
$150$	−4.94728	−0.403944
$151$	10.3781	0.844562	0.422281	−	0.906465i	$-0.361230\pi$
$151$	10.3781	0.844562	0.422281	+	0.906465i	$0.361230\pi$
$152$	1.00000	0.0811107
$153$	5.34710	0.432287
$154$	10.0525	0.810051
$155$	−2.37853	−0.191048
$156$	2.15700	0.172699
$157$	−16.0621	−1.28189	−0.640946	−	0.767586i	$-0.721458\pi$
$157$	−16.0621	−1.28189	−0.640946	+	0.767586i	$0.721458\pi$
$158$	9.77405	0.777581
$159$	−1.00000	−0.0793052
$160$	−0.229612	−0.0181524
$161$	−5.23325	−0.412438
$162$	1.00000	0.0785674
$163$	−21.9437	−1.71876	−0.859382	−	0.511334i	$-0.829151\pi$
$163$	−21.9437	−1.71876	−0.859382	+	0.511334i	$0.829151\pi$
$164$	−4.50346	−0.351662
$165$	−0.857494	−0.0667558
$166$	−7.84819	−0.609137
$167$	−4.71860	−0.365136	−0.182568	−	0.983193i	$-0.558441\pi$
$167$	−4.71860	−0.365136	−0.182568	+	0.983193i	$0.558441\pi$
$168$	2.69176	0.207674
$169$	−8.34733	−0.642102
$170$	−1.22776	−0.0941646
$171$	1.00000	0.0764719
$172$	9.41549	0.717924
$173$	15.8350	1.20391	0.601957	−	0.798528i	$-0.294388\pi$
$173$	15.8350	1.20391	0.601957	+	0.798528i	$0.294388\pi$
$174$	−5.72170	−0.433761
$175$	−13.3169	−1.00666
$176$	3.73454	0.281501
$177$	−11.8621	−0.891607
$178$	−3.87222	−0.290235
$179$	23.7752	1.77704	0.888521	−	0.458836i	$-0.151734\pi$
$179$	23.7752	1.77704	0.888521	+	0.458836i	$0.151734\pi$
$180$	−0.229612	−0.0171142
$181$	−0.00461300	−0.000342882 0	−0.000171441	−	1.00000i	$-0.500055\pi$
$181$	−0.00461300	−0.000342882 0	−0.000171441		1.00000i	$0.500055\pi$
$182$	5.80613	0.430379
$183$	−12.4990	−0.923956
$184$	−1.94418	−0.143327
$185$	1.81804	0.133665
$186$	10.3589	0.759554
$187$	19.9689	1.46027
$188$	5.70918	0.416385
$189$	2.69176	0.195797
$190$	−0.229612	−0.0166578
$191$	7.04012	0.509405	0.254703	−	0.967019i	$-0.418022\pi$
$191$	7.04012	0.509405	0.254703	+	0.967019i	$0.418022\pi$
$192$	1.00000	0.0721688
$193$	14.1207	1.01643	0.508215	−	0.861230i	$-0.330306\pi$
$193$	14.1207	1.01643	0.508215	+	0.861230i	$0.330306\pi$
$194$	−6.33978	−0.455170
$195$	−0.495273	−0.0354673
$196$	0.245558	0.0175399
$197$	−8.35483	−0.595257	−0.297629	−	0.954682i	$-0.596196\pi$
$197$	−8.35483	−0.595257	−0.297629	+	0.954682i	$0.596196\pi$
$198$	3.73454	0.265402
$199$	7.14212	0.506291	0.253146	−	0.967428i	$-0.418535\pi$
$199$	7.14212	0.506291	0.253146	+	0.967428i	$0.418535\pi$
$200$	−4.94728	−0.349825
$201$	4.80167	0.338684
$202$	−1.22246	−0.0860123
$203$	−15.4014	−1.08097
$204$	5.34710	0.374372
$205$	1.03405	0.0722210
$206$	4.59661	0.320261
$207$	−1.94418	−0.135130
$208$	2.15700	0.149561
$209$	3.73454	0.258323
$210$	−0.618059	−0.0426501
$211$	22.6837	1.56161	0.780805	−	0.624774i	$-0.214809\pi$
$211$	22.6837	1.56161	0.780805	+	0.624774i	$0.214809\pi$
$212$	−1.00000	−0.0686803
$213$	4.70195	0.322173
$214$	−5.51466	−0.376975
$215$	−2.16191	−0.147441
$216$	1.00000	0.0680414
$217$	27.8838	1.89287
$218$	−11.4302	−0.774151
$219$	−2.77825	−0.187737
$220$	−0.857494	−0.0578122
$221$	11.5337	0.775842
$222$	−7.91788	−0.531413
$223$	15.0523	1.00798	0.503989	−	0.863710i	$-0.331865\pi$
$223$	15.0523	1.00798	0.503989	+	0.863710i	$0.331865\pi$
$224$	2.69176	0.179851
$225$	−4.94728	−0.329819
$226$	11.7260	0.780005
$227$	−10.8269	−0.718609	−0.359304	−	0.933220i	$-0.616986\pi$
$227$	−10.8269	−0.718609	−0.359304	+	0.933220i	$0.616986\pi$
$228$	1.00000	0.0662266
$229$	22.5205	1.48820	0.744098	−	0.668071i	$-0.232880\pi$
$229$	22.5205	1.48820	0.744098	+	0.668071i	$0.232880\pi$
$230$	0.446406	0.0294351
$231$	10.0525	0.661404
$232$	−5.72170	−0.375648
$233$	23.0077	1.50729	0.753643	−	0.657284i	$-0.228295\pi$
$233$	23.0077	1.50729	0.753643	+	0.657284i	$0.228295\pi$
$234$	2.15700	0.141008
$235$	−1.31089	−0.0855134
$236$	−11.8621	−0.772154
$237$	9.77405	0.634893
$238$	14.3931	0.932965
$239$	−12.9454	−0.837367	−0.418683	−	0.908132i	$-0.637508\pi$
$239$	−12.9454	−0.837367	−0.418683	+	0.908132i	$0.637508\pi$
$240$	−0.229612	−0.0148214
$241$	17.3166	1.11546	0.557729	−	0.830023i	$-0.311673\pi$
$241$	17.3166	1.11546	0.557729	+	0.830023i	$0.311673\pi$
$242$	2.94678	0.189426
$243$	1.00000	0.0641500
$244$	−12.4990	−0.800169
$245$	−0.0563830	−0.00360218
$246$	−4.50346	−0.287130
$247$	2.15700	0.137247
$248$	10.3589	0.657793
$249$	−7.84819	−0.497359
$250$	2.28401	0.144454
$251$	−19.2404	−1.21444	−0.607220	−	0.794534i	$-0.707715\pi$
$251$	−19.2404	−1.21444	−0.607220	+	0.794534i	$0.707715\pi$
$252$	2.69176	0.169565
$253$	−7.26061	−0.456470
$254$	−13.6692	−0.857681
$255$	−1.22776	−0.0768851
$256$	1.00000	0.0625000
$257$	−22.6942	−1.41563	−0.707813	−	0.706399i	$-0.750318\pi$
$257$	−22.6942	−1.41563	−0.707813	+	0.706399i	$0.750318\pi$
$258$	9.41549	0.586183
$259$	−21.3130	−1.32433
$260$	−0.495273	−0.0307155
$261$	−5.72170	−0.354165
$262$	−9.59689	−0.592898
$263$	14.1756	0.874107	0.437053	−	0.899436i	$-0.356022\pi$
$263$	14.1756	0.874107	0.437053	+	0.899436i	$0.356022\pi$
$264$	3.73454	0.229845
$265$	0.229612	0.0141049
$266$	2.69176	0.165042
$267$	−3.87222	−0.236976
$268$	4.80167	0.293309
$269$	−13.1766	−0.803393	−0.401696	−	0.915773i	$-0.631579\pi$
$269$	−13.1766	−0.803393	−0.401696	+	0.915773i	$0.631579\pi$
$270$	−0.229612	−0.0139737
$271$	20.1979	1.22694	0.613468	−	0.789720i	$-0.289774\pi$
$271$	20.1979	1.22694	0.613468	+	0.789720i	$0.289774\pi$
$272$	5.34710	0.324215
$273$	5.80613	0.351403
$274$	−4.82995	−0.291788
$275$	−18.4758	−1.11413
$276$	−1.94418	−0.117026
$277$	−1.07872	−0.0648141	−0.0324070	−	0.999475i	$-0.510317\pi$
$277$	−1.07872	−0.0648141	−0.0324070	+	0.999475i	$0.510317\pi$
$278$	13.9359	0.835822
$279$	10.3589	0.620174
$280$	−0.618059	−0.0369361
$281$	4.52544	0.269965	0.134983	−	0.990848i	$-0.456902\pi$
$281$	4.52544	0.269965	0.134983	+	0.990848i	$0.456902\pi$
$282$	5.70918	0.339977
$283$	−12.6156	−0.749921	−0.374960	−	0.927041i	$-0.622344\pi$
$283$	−12.6156	−0.749921	−0.374960	+	0.927041i	$0.622344\pi$
$284$	4.70195	0.279010
$285$	−0.229612	−0.0136010
$286$	8.05542	0.476327
$287$	−12.1222	−0.715553
$288$	1.00000	0.0589256
$289$	11.5915	0.681850
$290$	1.31377	0.0771472
$291$	−6.33978	−0.371644
$292$	−2.77825	−0.162585
$293$	9.63524	0.562897	0.281449	−	0.959576i	$-0.409185\pi$
$293$	9.63524	0.562897	0.281449	+	0.959576i	$0.409185\pi$
$294$	0.245558	0.0143212
$295$	2.72367	0.158578
$296$	−7.91788	−0.460217
$297$	3.73454	0.216700
$298$	−5.66620	−0.328234
$299$	−4.19360	−0.242522
$300$	−4.94728	−0.285631
$301$	25.3442	1.46082
$302$	10.3781	0.597195
$303$	−1.22246	−0.0702287
$304$	1.00000	0.0573539
$305$	2.86993	0.164331
$306$	5.34710	0.305673
$307$	6.79595	0.387865	0.193933	−	0.981015i	$-0.437876\pi$
$307$	6.79595	0.387865	0.193933	+	0.981015i	$0.437876\pi$
$308$	10.0525	0.572793
$309$	4.59661	0.261492
$310$	−2.37853	−0.135092
$311$	−7.85807	−0.445590	−0.222795	−	0.974865i	$-0.571518\pi$
$311$	−7.85807	−0.445590	−0.222795	+	0.974865i	$0.571518\pi$
$312$	2.15700	0.122116
$313$	2.18896	0.123727	0.0618636	−	0.998085i	$-0.480296\pi$
$313$	2.18896	0.123727	0.0618636	+	0.998085i	$0.480296\pi$
$314$	−16.0621	−0.906435
$315$	−0.618059	−0.0348237
$316$	9.77405	0.549833
$317$	−12.7877	−0.718229	−0.359114	−	0.933294i	$-0.616921\pi$
$317$	−12.7877	−0.718229	−0.359114	+	0.933294i	$0.616921\pi$
$318$	−1.00000	−0.0560772
$319$	−21.3679	−1.19637
$320$	−0.229612	−0.0128357
$321$	−5.51466	−0.307799
$322$	−5.23325	−0.291638
$323$	5.34710	0.297520
$324$	1.00000	0.0555556
$325$	−10.6713	−0.591937
$326$	−21.9437	−1.21535
$327$	−11.4302	−0.632091
$328$	−4.50346	−0.248662
$329$	15.3677	0.847251
$330$	−0.857494	−0.0472035
$331$	28.1550	1.54754	0.773770	−	0.633466i	$-0.218369\pi$
$331$	28.1550	1.54754	0.773770	+	0.633466i	$0.218369\pi$
$332$	−7.84819	−0.430725
$333$	−7.91788	−0.433897
$334$	−4.71860	−0.258190
$335$	−1.10252	−0.0602371
$336$	2.69176	0.146847
$337$	1.65805	0.0903197	0.0451598	−	0.998980i	$-0.485620\pi$
$337$	1.65805	0.0903197	0.0451598	+	0.998980i	$0.485620\pi$
$338$	−8.34733	−0.454035
$339$	11.7260	0.636871
$340$	−1.22776	−0.0665844
$341$	38.6859	2.09496
$342$	1.00000	0.0540738
$343$	−18.1813	−0.981699
$344$	9.41549	0.507649
$345$	0.446406	0.0240337
$346$	15.8350	0.851296
$347$	−6.90793	−0.370837	−0.185419	−	0.982660i	$-0.559364\pi$
$347$	−6.90793	−0.370837	−0.185419	+	0.982660i	$0.559364\pi$
$348$	−5.72170	−0.306716
$349$	−15.1715	−0.812110	−0.406055	−	0.913849i	$-0.633096\pi$
$349$	−15.1715	−0.812110	−0.406055	+	0.913849i	$0.633096\pi$
$350$	−13.3169	−0.711817
$351$	2.15700	0.115132
$352$	3.73454	0.199052
$353$	−32.1958	−1.71361	−0.856804	−	0.515642i	$-0.827554\pi$
$353$	−32.1958	−1.71361	−0.856804	+	0.515642i	$0.827554\pi$
$354$	−11.8621	−0.630461
$355$	−1.07962	−0.0573004
$356$	−3.87222	−0.205227
$357$	14.3931	0.761763
$358$	23.7752	1.25656
$359$	28.6016	1.50953	0.754766	−	0.655994i	$-0.227750\pi$
$359$	28.6016	1.50953	0.754766	+	0.655994i	$0.227750\pi$
$360$	−0.229612	−0.0121016
$361$	1.00000	0.0526316
$362$	−0.00461300	−0.000242454 0
$363$	2.94678	0.154666
$364$	5.80613	0.304324
$365$	0.637919	0.0333902
$366$	−12.4990	−0.653335
$367$	−0.00646546	−0.000337494 0	−0.000168747	−	1.00000i	$-0.500054\pi$
$367$	−0.00646546	−0.000337494 0	−0.000168747		1.00000i	$0.500054\pi$
$368$	−1.94418	−0.101347
$369$	−4.50346	−0.234441
$370$	1.81804	0.0945152
$371$	−2.69176	−0.139749
$372$	10.3589	0.537086
$373$	4.76016	0.246472	0.123236	−	0.992377i	$-0.460673\pi$
$373$	4.76016	0.246472	0.123236	+	0.992377i	$0.460673\pi$
$374$	19.9689	1.03257
$375$	2.28401	0.117946
$376$	5.70918	0.294429
$377$	−12.3417	−0.635632
$378$	2.69176	0.138449
$379$	5.98301	0.307327	0.153663	−	0.988123i	$-0.450893\pi$
$379$	5.98301	0.307327	0.153663	+	0.988123i	$0.450893\pi$
$380$	−0.229612	−0.0117788
$381$	−13.6692	−0.700293
$382$	7.04012	0.360204
$383$	0.299468	0.0153021	0.00765105	−	0.999971i	$-0.497565\pi$
$383$	0.299468	0.0153021	0.00765105	+	0.999971i	$0.497565\pi$
$384$	1.00000	0.0510310
$385$	−2.30816	−0.117635
$386$	14.1207	0.718725
$387$	9.41549	0.478616
$388$	−6.33978	−0.321854
$389$	−26.5395	−1.34561	−0.672803	−	0.739821i	$-0.734910\pi$
$389$	−26.5395	−1.34561	−0.672803	+	0.739821i	$0.734910\pi$
$390$	−0.495273	−0.0250791
$391$	−10.3957	−0.525734
$392$	0.245558	0.0124026
$393$	−9.59689	−0.484099
$394$	−8.35483	−0.420910
$395$	−2.24423	−0.112920
$396$	3.73454	0.187668
$397$	2.93022	0.147063	0.0735317	−	0.997293i	$-0.476573\pi$
$397$	2.93022	0.147063	0.0735317	+	0.997293i	$0.476573\pi$
$398$	7.14212	0.358002
$399$	2.69176	0.134756
$400$	−4.94728	−0.247364
$401$	−34.2138	−1.70855	−0.854277	−	0.519818i	$-0.826000\pi$
$401$	−34.2138	−1.70855	−0.854277	+	0.519818i	$0.826000\pi$
$402$	4.80167	0.239486
$403$	22.3443	1.11305
$404$	−1.22246	−0.0608199
$405$	−0.229612	−0.0114095
$406$	−15.4014	−0.764361
$407$	−29.5696	−1.46571
$408$	5.34710	0.264721
$409$	−34.9044	−1.72591	−0.862957	−	0.505278i	$-0.831390\pi$
$409$	−34.9044	−1.72591	−0.862957	+	0.505278i	$0.831390\pi$
$410$	1.03405	0.0510680
$411$	−4.82995	−0.238244
$412$	4.59661	0.226458
$413$	−31.9298	−1.57116
$414$	−1.94418	−0.0955511
$415$	1.80203	0.0884584
$416$	2.15700	0.105756
$417$	13.9359	0.682446
$418$	3.73454	0.182662
$419$	12.7336	0.622075	0.311038	−	0.950398i	$-0.399323\pi$
$419$	12.7336	0.622075	0.311038	+	0.950398i	$0.399323\pi$
$420$	−0.618059	−0.0301582
$421$	36.5934	1.78345	0.891727	−	0.452573i	$-0.149494\pi$
$421$	36.5934	1.78345	0.891727	+	0.452573i	$0.149494\pi$
$422$	22.6837	1.10423
$423$	5.70918	0.277590
$424$	−1.00000	−0.0485643
$425$	−26.4536	−1.28319
$426$	4.70195	0.227810
$427$	−33.6444	−1.62817
$428$	−5.51466	−0.266561
$429$	8.05542	0.388919
$430$	−2.16191	−0.104256
$431$	−8.98839	−0.432956	−0.216478	−	0.976288i	$-0.569457\pi$
$431$	−8.98839	−0.432956	−0.216478	+	0.976288i	$0.569457\pi$
$432$	1.00000	0.0481125
$433$	28.4141	1.36549	0.682746	−	0.730655i	$-0.260785\pi$
$433$	28.4141	1.36549	0.682746	+	0.730655i	$0.260785\pi$
$434$	27.8838	1.33846
$435$	1.31377	0.0629904
$436$	−11.4302	−0.547407
$437$	−1.94418	−0.0930026
$438$	−2.77825	−0.132750
$439$	15.4087	0.735417	0.367709	−	0.929941i	$-0.380142\pi$
$439$	15.4087	0.735417	0.367709	+	0.929941i	$0.380142\pi$
$440$	−0.857494	−0.0408794
$441$	0.245558	0.0116932
$442$	11.5337	0.548603
$443$	11.6577	0.553874	0.276937	−	0.960888i	$-0.410681\pi$
$443$	11.6577	0.553874	0.276937	+	0.960888i	$0.410681\pi$
$444$	−7.91788	−0.375766
$445$	0.889106	0.0421477
$446$	15.0523	0.712748
$447$	−5.66620	−0.268002
$448$	2.69176	0.127174
$449$	15.9998	0.755076	0.377538	−	0.925994i	$-0.376771\pi$
$449$	15.9998	0.755076	0.377538	+	0.925994i	$0.376771\pi$
$450$	−4.94728	−0.233217
$451$	−16.8184	−0.791946
$452$	11.7260	0.551547
$453$	10.3781	0.487608
$454$	−10.8269	−0.508133
$455$	−1.33316	−0.0624993
$456$	1.00000	0.0468293
$457$	−28.4371	−1.33023	−0.665116	−	0.746740i	$-0.731618\pi$
$457$	−28.4371	−1.33023	−0.665116	+	0.746740i	$0.731618\pi$
$458$	22.5205	1.05231
$459$	5.34710	0.249581
$460$	0.446406	0.0208138
$461$	−27.3361	−1.27317	−0.636585	−	0.771207i	$-0.719653\pi$
$461$	−27.3361	−1.27317	−0.636585	+	0.771207i	$0.719653\pi$
$462$	10.0525	0.467683
$463$	24.5052	1.13885	0.569427	−	0.822042i	$-0.307165\pi$
$463$	24.5052	1.13885	0.569427	+	0.822042i	$0.307165\pi$
$464$	−5.72170	−0.265623
$465$	−2.37853	−0.110302
$466$	23.0077	1.06581
$467$	−2.50695	−0.116008	−0.0580040	−	0.998316i	$-0.518474\pi$
$467$	−2.50695	−0.116008	−0.0580040	+	0.998316i	$0.518474\pi$
$468$	2.15700	0.0997076
$469$	12.9249	0.596818
$470$	−1.31089	−0.0604671
$471$	−16.0621	−0.740101
$472$	−11.8621	−0.545995
$473$	35.1625	1.61677
$474$	9.77405	0.448937
$475$	−4.94728	−0.226997
$476$	14.3931	0.659706
$477$	−1.00000	−0.0457869
$478$	−12.9454	−0.592108
$479$	20.3482	0.929734	0.464867	−	0.885381i	$-0.346102\pi$
$479$	20.3482	0.929734	0.464867	+	0.885381i	$0.346102\pi$
$480$	−0.229612	−0.0104803
$481$	−17.0789	−0.778731
$482$	17.3166	0.788748
$483$	−5.23325	−0.238121
$484$	2.94678	0.133945
$485$	1.45569	0.0660993
$486$	1.00000	0.0453609
$487$	11.4351	0.518172	0.259086	−	0.965854i	$-0.416579\pi$
$487$	11.4351	0.518172	0.259086	+	0.965854i	$0.416579\pi$
$488$	−12.4990	−0.565805
$489$	−21.9437	−0.992329
$490$	−0.0563830	−0.00254712
$491$	−19.1590	−0.864636	−0.432318	−	0.901721i	$-0.642304\pi$
$491$	−19.1590	−0.864636	−0.432318	+	0.901721i	$0.642304\pi$
$492$	−4.50346	−0.203032
$493$	−30.5945	−1.37791
$494$	2.15700	0.0970482
$495$	−0.857494	−0.0385415
$496$	10.3589	0.465130
$497$	12.6565	0.567722
$498$	−7.84819	−0.351686
$499$	−21.1516	−0.946877	−0.473439	−	0.880827i	$-0.656987\pi$
$499$	−21.1516	−0.946877	−0.473439	+	0.880827i	$0.656987\pi$
$500$	2.28401	0.102144
$501$	−4.71860	−0.210812
$502$	−19.2404	−0.858739
$503$	19.4754	0.868365	0.434182	−	0.900825i	$-0.357037\pi$
$503$	19.4754	0.868365	0.434182	+	0.900825i	$0.357037\pi$
$504$	2.69176	0.119900
$505$	0.280692	0.0124906
$506$	−7.26061	−0.322773
$507$	−8.34733	−0.370718
$508$	−13.6692	−0.606472
$509$	−1.47522	−0.0653878	−0.0326939	−	0.999465i	$-0.510409\pi$
$509$	−1.47522	−0.0653878	−0.0326939	+	0.999465i	$0.510409\pi$
$510$	−1.22776	−0.0543659
$511$	−7.47838	−0.330824
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	−22.6942	−1.00100
$515$	−1.05543	−0.0465080
$516$	9.41549	0.414494
$517$	21.3212	0.937704
$518$	−21.3130	−0.936440
$519$	15.8350	0.695080
$520$	−0.495273	−0.0217192
$521$	−42.5214	−1.86290	−0.931448	−	0.363873i	$-0.881454\pi$
$521$	−42.5214	−1.86290	−0.931448	+	0.363873i	$0.881454\pi$
$522$	−5.72170	−0.250432
$523$	−10.6578	−0.466033	−0.233016	−	0.972473i	$-0.574860\pi$
$523$	−10.6578	−0.466033	−0.233016	+	0.972473i	$0.574860\pi$
$524$	−9.59689	−0.419242
$525$	−13.3169	−0.581196
$526$	14.1756	0.618087
$527$	55.3903	2.41284
$528$	3.73454	0.162525
$529$	−19.2202	−0.835660
$530$	0.229612	0.00997369
$531$	−11.8621	−0.514769
$532$	2.69176	0.116702
$533$	−9.71399	−0.420760
$534$	−3.87222	−0.167567
$535$	1.26623	0.0547439
$536$	4.80167	0.207401
$537$	23.7752	1.02598
$538$	−13.1766	−0.568085
$539$	0.917046	0.0395000
$540$	−0.229612	−0.00988091
$541$	−31.0140	−1.33340	−0.666699	−	0.745327i	$-0.732293\pi$
$541$	−31.0140	−1.33340	−0.666699	+	0.745327i	$0.732293\pi$
$542$	20.1979	0.867574
$543$	−0.00461300	−0.000197963 0
$544$	5.34710	0.229255
$545$	2.62451	0.112421
$546$	5.80613	0.248480
$547$	−42.1041	−1.80024	−0.900121	−	0.435640i	$-0.856522\pi$
$547$	−42.1041	−1.80024	−0.900121	+	0.435640i	$0.856522\pi$
$548$	−4.82995	−0.206325
$549$	−12.4990	−0.533446
$550$	−18.4758	−0.787811
$551$	−5.72170	−0.243753
$552$	−1.94418	−0.0827497
$553$	26.3094	1.11879
$554$	−1.07872	−0.0458305
$555$	1.81804	0.0771714
$556$	13.9359	0.591016
$557$	4.22375	0.178966	0.0894830	−	0.995988i	$-0.471479\pi$
$557$	4.22375	0.178966	0.0894830	+	0.995988i	$0.471479\pi$
$558$	10.3589	0.438529
$559$	20.3092	0.858990
$560$	−0.618059	−0.0261178
$561$	19.9689	0.843090
$562$	4.52544	0.190894
$563$	0.916245	0.0386151	0.0193076	−	0.999814i	$-0.493854\pi$
$563$	0.916245	0.0386151	0.0193076	+	0.999814i	$0.493854\pi$
$564$	5.70918	0.240400
$565$	−2.69244	−0.113272
$566$	−12.6156	−0.530274
$567$	2.69176	0.113043
$568$	4.70195	0.197290
$569$	31.9053	1.33754	0.668770	−	0.743469i	$-0.266821\pi$
$569$	31.9053	1.33754	0.668770	+	0.743469i	$0.266821\pi$
$570$	−0.229612	−0.00961737
$571$	5.33358	0.223203	0.111602	−	0.993753i	$-0.464402\pi$
$571$	5.33358	0.223203	0.111602	+	0.993753i	$0.464402\pi$
$572$	8.05542	0.336814
$573$	7.04012	0.294105
$574$	−12.1222	−0.505972
$575$	9.61839	0.401114
$576$	1.00000	0.0416667
$577$	4.68583	0.195074	0.0975368	−	0.995232i	$-0.468904\pi$
$577$	4.68583	0.195074	0.0975368	+	0.995232i	$0.468904\pi$
$578$	11.5915	0.482141
$579$	14.1207	0.586836
$580$	1.31377	0.0545513
$581$	−21.1254	−0.876430
$582$	−6.33978	−0.262792
$583$	−3.73454	−0.154669
$584$	−2.77825	−0.114965
$585$	−0.495273	−0.0204770
$586$	9.63524	0.398028
$587$	−8.52345	−0.351801	−0.175900	−	0.984408i	$-0.556284\pi$
$587$	−8.52345	−0.351801	−0.175900	+	0.984408i	$0.556284\pi$
$588$	0.245558	0.0101266
$589$	10.3589	0.426833
$590$	2.72367	0.112132
$591$	−8.35483	−0.343672
$592$	−7.91788	−0.325423
$593$	−9.14584	−0.375575	−0.187787	−	0.982210i	$-0.560132\pi$
$593$	−9.14584	−0.375575	−0.187787	+	0.982210i	$0.560132\pi$
$594$	3.73454	0.153230
$595$	−3.30482	−0.135484
$596$	−5.66620	−0.232096
$597$	7.14212	0.292308
$598$	−4.19360	−0.171489
$599$	−8.70052	−0.355493	−0.177747	−	0.984076i	$-0.556881\pi$
$599$	−8.70052	−0.355493	−0.177747	+	0.984076i	$0.556881\pi$
$600$	−4.94728	−0.201972
$601$	−23.4994	−0.958561	−0.479281	−	0.877662i	$-0.659102\pi$
$601$	−23.4994	−0.958561	−0.479281	+	0.877662i	$0.659102\pi$
$602$	25.3442	1.03295
$603$	4.80167	0.195539
$604$	10.3781	0.422281
$605$	−0.676615	−0.0275083
$606$	−1.22246	−0.0496592
$607$	42.3157	1.71754	0.858771	−	0.512359i	$-0.171228\pi$
$607$	42.3157	1.71754	0.858771	+	0.512359i	$0.171228\pi$
$608$	1.00000	0.0405554
$609$	−15.4014	−0.624098
$610$	2.86993	0.116200
$611$	12.3147	0.498201
$612$	5.34710	0.216144
$613$	40.8315	1.64917	0.824585	−	0.565739i	$-0.191409\pi$
$613$	40.8315	1.64917	0.824585	+	0.565739i	$0.191409\pi$
$614$	6.79595	0.274262
$615$	1.03405	0.0416968
$616$	10.0525	0.405026
$617$	−47.4801	−1.91148	−0.955739	−	0.294215i	$-0.904942\pi$
$617$	−47.4801	−1.91148	−0.955739	+	0.294215i	$0.904942\pi$
$618$	4.59661	0.184903
$619$	39.8664	1.60237	0.801183	−	0.598420i	$-0.204204\pi$
$619$	39.8664	1.60237	0.801183	+	0.598420i	$0.204204\pi$
$620$	−2.37853	−0.0955242
$621$	−1.94418	−0.0780172
$622$	−7.85807	−0.315080
$623$	−10.4231	−0.417592
$624$	2.15700	0.0863493
$625$	24.2120	0.968478
$626$	2.18896	0.0874884
$627$	3.73454	0.149143
$628$	−16.0621	−0.640946
$629$	−42.3377	−1.68811
$630$	−0.618059	−0.0246241
$631$	−25.0116	−0.995696	−0.497848	−	0.867264i	$-0.665876\pi$
$631$	−25.0116	−0.995696	−0.497848	+	0.867264i	$0.665876\pi$
$632$	9.77405	0.388791
$633$	22.6837	0.901596
$634$	−12.7877	−0.507864
$635$	3.13860	0.124552
$636$	−1.00000	−0.0396526
$637$	0.529670	0.0209863
$638$	−21.3679	−0.845964
$639$	4.70195	0.186006
$640$	−0.229612	−0.00907620
$641$	1.18853	0.0469443	0.0234721	−	0.999724i	$-0.492528\pi$
$641$	1.18853	0.0469443	0.0234721	+	0.999724i	$0.492528\pi$
$642$	−5.51466	−0.217646
$643$	−0.944982	−0.0372664	−0.0186332	−	0.999826i	$-0.505931\pi$
$643$	−0.944982	−0.0372664	−0.0186332	+	0.999826i	$0.505931\pi$
$644$	−5.23325	−0.206219
$645$	−2.16191	−0.0851249
$646$	5.34710	0.210379
$647$	−42.7889	−1.68221	−0.841103	−	0.540876i	$-0.818093\pi$
$647$	−42.7889	−1.68221	−0.841103	+	0.540876i	$0.818093\pi$
$648$	1.00000	0.0392837
$649$	−44.2993	−1.73890
$650$	−10.6713	−0.418563
$651$	27.8838	1.09285
$652$	−21.9437	−0.859382
$653$	24.9932	0.978061	0.489030	−	0.872267i	$-0.337351\pi$
$653$	24.9932	0.978061	0.489030	+	0.872267i	$0.337351\pi$
$654$	−11.4302	−0.446956
$655$	2.20356	0.0861002
$656$	−4.50346	−0.175831
$657$	−2.77825	−0.108390
$658$	15.3677	0.599097
$659$	3.89623	0.151776	0.0758878	−	0.997116i	$-0.475821\pi$
$659$	3.89623	0.151776	0.0758878	+	0.997116i	$0.475821\pi$
$660$	−0.857494	−0.0333779
$661$	29.3876	1.14304	0.571522	−	0.820587i	$-0.306353\pi$
$661$	29.3876	1.14304	0.571522	+	0.820587i	$0.306353\pi$
$662$	28.1550	1.09428
$663$	11.5337	0.447932
$664$	−7.84819	−0.304569
$665$	−0.618059	−0.0239673
$666$	−7.91788	−0.306812
$667$	11.1240	0.430723
$668$	−4.71860	−0.182568
$669$	15.0523	0.581956
$670$	−1.10252	−0.0425940
$671$	−46.6782	−1.80199
$672$	2.69176	0.103837
$673$	−17.2743	−0.665877	−0.332939	−	0.942949i	$-0.608040\pi$
$673$	−17.2743	−0.665877	−0.332939	+	0.942949i	$0.608040\pi$
$674$	1.65805	0.0638656
$675$	−4.94728	−0.190421
$676$	−8.34733	−0.321051
$677$	−9.78253	−0.375973	−0.187987	−	0.982172i	$-0.560196\pi$
$677$	−9.78253	−0.375973	−0.187987	+	0.982172i	$0.560196\pi$
$678$	11.7260	0.450336
$679$	−17.0651	−0.654900
$680$	−1.22776	−0.0470823
$681$	−10.8269	−0.414889
$682$	38.6859	1.48136
$683$	9.95344	0.380858	0.190429	−	0.981701i	$-0.439012\pi$
$683$	9.95344	0.380858	0.190429	+	0.981701i	$0.439012\pi$
$684$	1.00000	0.0382360
$685$	1.10901	0.0423732
$686$	−18.1813	−0.694166
$687$	22.5205	0.859210
$688$	9.41549	0.358962
$689$	−2.15700	−0.0821753
$690$	0.446406	0.0169944
$691$	−26.9096	−1.02369	−0.511845	−	0.859078i	$-0.671038\pi$
$691$	−26.9096	−1.02369	−0.511845	+	0.859078i	$0.671038\pi$
$692$	15.8350	0.601957
$693$	10.0525	0.381862
$694$	−6.90793	−0.262222
$695$	−3.19986	−0.121377
$696$	−5.72170	−0.216881
$697$	−24.0805	−0.912113
$698$	−15.1715	−0.574249
$699$	23.0077	0.870232
$700$	−13.3169	−0.503331
$701$	−18.4344	−0.696257	−0.348128	−	0.937447i	$-0.613183\pi$
$701$	−18.4344	−0.696257	−0.348128	+	0.937447i	$0.613183\pi$
$702$	2.15700	0.0814109
$703$	−7.91788	−0.298628
$704$	3.73454	0.140751
$705$	−1.31089	−0.0493712
$706$	−32.1958	−1.21170
$707$	−3.29058	−0.123755
$708$	−11.8621	−0.445803
$709$	−25.0032	−0.939014	−0.469507	−	0.882929i	$-0.655568\pi$
$709$	−25.0032	−0.939014	−0.469507	+	0.882929i	$0.655568\pi$
$710$	−1.07962	−0.0405175
$711$	9.77405	0.366555
$712$	−3.87222	−0.145118
$713$	−20.1396	−0.754235
$714$	14.3931	0.538648
$715$	−1.84962	−0.0691718
$716$	23.7752	0.888521
$717$	−12.9454	−0.483454
$718$	28.6016	1.06740
$719$	7.80105	0.290930	0.145465	−	0.989363i	$-0.453532\pi$
$719$	7.80105	0.290930	0.145465	+	0.989363i	$0.453532\pi$
$720$	−0.229612	−0.00855712
$721$	12.3729	0.460793
$722$	1.00000	0.0372161
$723$	17.3166	0.644010
$724$	−0.00461300	−0.000171441 0
$725$	28.3069	1.05129
$726$	2.94678	0.109365
$727$	−20.7644	−0.770108	−0.385054	−	0.922894i	$-0.625817\pi$
$727$	−20.7644	−0.770108	−0.385054	+	0.922894i	$0.625817\pi$
$728$	5.80613	0.215190
$729$	1.00000	0.0370370
$730$	0.637919	0.0236104
$731$	50.3455	1.86210
$732$	−12.4990	−0.461978
$733$	−26.1303	−0.965143	−0.482572	−	0.875856i	$-0.660297\pi$
$733$	−26.1303	−0.965143	−0.482572	+	0.875856i	$0.660297\pi$
$734$	−0.00646546	−0.000238644 0
$735$	−0.0563830	−0.00207972
$736$	−1.94418	−0.0716633
$737$	17.9320	0.660535
$738$	−4.50346	−0.165775
$739$	−28.3574	−1.04314	−0.521572	−	0.853207i	$-0.674654\pi$
$739$	−28.3574	−1.04314	−0.521572	+	0.853207i	$0.674654\pi$
$740$	1.81804	0.0668324
$741$	2.15700	0.0792395
$742$	−2.69176	−0.0988175
$743$	−27.1280	−0.995230	−0.497615	−	0.867398i	$-0.665791\pi$
$743$	−27.1280	−0.995230	−0.497615	+	0.867398i	$0.665791\pi$
$744$	10.3589	0.379777
$745$	1.30102	0.0476658
$746$	4.76016	0.174282
$747$	−7.84819	−0.287150
$748$	19.9689	0.730137
$749$	−14.8441	−0.542393
$750$	2.28401	0.0834003
$751$	8.09526	0.295400	0.147700	−	0.989032i	$-0.452813\pi$
$751$	8.09526	0.295400	0.147700	+	0.989032i	$0.452813\pi$
$752$	5.70918	0.208192
$753$	−19.2404	−0.701158
$754$	−12.3417	−0.449460
$755$	−2.38294	−0.0867242
$756$	2.69176	0.0978983
$757$	2.73340	0.0993471	0.0496736	−	0.998766i	$-0.484182\pi$
$757$	2.73340	0.0993471	0.0496736	+	0.998766i	$0.484182\pi$
$758$	5.98301	0.217313
$759$	−7.26061	−0.263543
$760$	−0.229612	−0.00832889
$761$	−43.1916	−1.56569	−0.782846	−	0.622215i	$-0.786233\pi$
$761$	−43.1916	−1.56569	−0.782846	+	0.622215i	$0.786233\pi$
$762$	−13.6692	−0.495182
$763$	−30.7673	−1.11385
$764$	7.04012	0.254703
$765$	−1.22776	−0.0443896
$766$	0.299468	0.0108202
$767$	−25.5865	−0.923875
$768$	1.00000	0.0360844
$769$	−20.3465	−0.733712	−0.366856	−	0.930278i	$-0.619566\pi$
$769$	−20.3465	−0.733712	−0.366856	+	0.930278i	$0.619566\pi$
$770$	−2.30816	−0.0831805
$771$	−22.6942	−0.817313
$772$	14.1207	0.508215
$773$	−0.497463	−0.0178925	−0.00894625	−	0.999960i	$-0.502848\pi$
$773$	−0.497463	−0.0178925	−0.00894625	+	0.999960i	$0.502848\pi$
$774$	9.41549	0.338433
$775$	−51.2486	−1.84090
$776$	−6.33978	−0.227585
$777$	−21.3130	−0.764600
$778$	−26.5395	−0.951488
$779$	−4.50346	−0.161353
$780$	−0.495273	−0.0177336
$781$	17.5596	0.628333
$782$	−10.3957	−0.371750
$783$	−5.72170	−0.204477
$784$	0.245558	0.00876993
$785$	3.68804	0.131632
$786$	−9.59689	−0.342310
$787$	23.2751	0.829668	0.414834	−	0.909897i	$-0.363840\pi$
$787$	23.2751	0.829668	0.414834	+	0.909897i	$0.363840\pi$
$788$	−8.35483	−0.297629
$789$	14.1756	0.504666
$790$	−2.24423	−0.0798463
$791$	31.5637	1.12227
$792$	3.73454	0.132701
$793$	−26.9605	−0.957395
$794$	2.93022	0.103990
$795$	0.229612	0.00814349
$796$	7.14212	0.253146
$797$	−2.04031	−0.0722715	−0.0361357	−	0.999347i	$-0.511505\pi$
$797$	−2.04031	−0.0722715	−0.0361357	+	0.999347i	$0.511505\pi$
$798$	2.69176	0.0952872
$799$	30.5276	1.07999
$800$	−4.94728	−0.174913
$801$	−3.87222	−0.136818
$802$	−34.2138	−1.20813
$803$	−10.3755	−0.366143
$804$	4.80167	0.169342
$805$	1.20162	0.0423514
$806$	22.3443	0.787044
$807$	−13.1766	−0.463839
$808$	−1.22246	−0.0430061
$809$	−3.95127	−0.138919	−0.0694597	−	0.997585i	$-0.522128\pi$
$809$	−3.95127	−0.138919	−0.0694597	+	0.997585i	$0.522128\pi$
$810$	−0.229612	−0.00806773
$811$	−18.7285	−0.657645	−0.328823	−	0.944392i	$-0.606652\pi$
$811$	−18.7285	−0.657645	−0.328823	+	0.944392i	$0.606652\pi$
$812$	−15.4014	−0.540485
$813$	20.1979	0.708371
$814$	−29.5696	−1.03641
$815$	5.03853	0.176492
$816$	5.34710	0.187186
$817$	9.41549	0.329406
$818$	−34.9044	−1.22040
$819$	5.80613	0.202883
$820$	1.03405	0.0361105
$821$	8.24151	0.287631	0.143815	−	0.989605i	$-0.454063\pi$
$821$	8.24151	0.287631	0.143815	+	0.989605i	$0.454063\pi$
$822$	−4.82995	−0.168464
$823$	−11.1697	−0.389351	−0.194676	−	0.980868i	$-0.562365\pi$
$823$	−11.1697	−0.389351	−0.194676	+	0.980868i	$0.562365\pi$
$824$	4.59661	0.160130
$825$	−18.4758	−0.643245
$826$	−31.9298	−1.11098
$827$	−55.5124	−1.93036	−0.965178	−	0.261596i	$-0.915751\pi$
$827$	−55.5124	−1.93036	−0.965178	+	0.261596i	$0.915751\pi$
$828$	−1.94418	−0.0675648
$829$	−19.0239	−0.660728	−0.330364	−	0.943854i	$-0.607172\pi$
$829$	−19.0239	−0.660728	−0.330364	+	0.943854i	$0.607172\pi$
$830$	1.80203	0.0625495
$831$	−1.07872	−0.0374204
$832$	2.15700	0.0747807
$833$	1.31302	0.0454935
$834$	13.9359	0.482562
$835$	1.08345	0.0374942
$836$	3.73454	0.129162
$837$	10.3589	0.358057
$838$	12.7336	0.439874
$839$	−14.2581	−0.492243	−0.246122	−	0.969239i	$-0.579156\pi$
$839$	−14.2581	−0.492243	−0.246122	+	0.969239i	$0.579156\pi$
$840$	−0.618059	−0.0213251
$841$	3.73790	0.128893
$842$	36.5934	1.26109
$843$	4.52544	0.155865
$844$	22.6837	0.780805
$845$	1.91664	0.0659346
$846$	5.70918	0.196286
$847$	7.93202	0.272547
$848$	−1.00000	−0.0343401
$849$	−12.6156	−0.432967
$850$	−26.4536	−0.907350
$851$	15.3938	0.527691
$852$	4.70195	0.161086
$853$	15.3974	0.527198	0.263599	−	0.964632i	$-0.415090\pi$
$853$	15.3974	0.527198	0.263599	+	0.964632i	$0.415090\pi$
$854$	−33.6444	−1.15129
$855$	−0.229612	−0.00785255
$856$	−5.51466	−0.188487
$857$	20.6854	0.706601	0.353300	−	0.935510i	$-0.385059\pi$
$857$	20.6854	0.706601	0.353300	+	0.935510i	$0.385059\pi$
$858$	8.05542	0.275007
$859$	29.4659	1.00536	0.502681	−	0.864472i	$-0.332347\pi$
$859$	29.4659	1.00536	0.502681	+	0.864472i	$0.332347\pi$
$860$	−2.16191	−0.0737204
$861$	−12.1222	−0.413125
$862$	−8.98839	−0.306146
$863$	12.3578	0.420663	0.210332	−	0.977630i	$-0.432546\pi$
$863$	12.3578	0.420663	0.210332	+	0.977630i	$0.432546\pi$
$864$	1.00000	0.0340207
$865$	−3.63591	−0.123625
$866$	28.4141	0.965549
$867$	11.5915	0.393666
$868$	27.8838	0.946436
$869$	36.5016	1.23823
$870$	1.31377	0.0445410
$871$	10.3572	0.350941
$872$	−11.4302	−0.387075
$873$	−6.33978	−0.214569
$874$	−1.94418	−0.0657628
$875$	6.14800	0.207840
$876$	−2.77825	−0.0938684
$877$	17.8497	0.602741	0.301370	−	0.953507i	$-0.402556\pi$
$877$	17.8497	0.602741	0.301370	+	0.953507i	$0.402556\pi$
$878$	15.4087	0.520018
$879$	9.63524	0.324989
$880$	−0.857494	−0.0289061
$881$	−32.1261	−1.08236	−0.541179	−	0.840908i	$-0.682022\pi$
$881$	−32.1261	−1.08236	−0.541179	+	0.840908i	$0.682022\pi$
$882$	0.245558	0.00826837
$883$	21.5541	0.725354	0.362677	−	0.931915i	$-0.381863\pi$
$883$	21.5541	0.725354	0.362677	+	0.931915i	$0.381863\pi$
$884$	11.5337	0.387921
$885$	2.72367	0.0915550
$886$	11.6577	0.391648
$887$	4.80272	0.161259	0.0806297	−	0.996744i	$-0.474307\pi$
$887$	4.80272	0.161259	0.0806297	+	0.996744i	$0.474307\pi$
$888$	−7.91788	−0.265707
$889$	−36.7941	−1.23404
$890$	0.889106	0.0298029
$891$	3.73454	0.125112
$892$	15.0523	0.503989
$893$	5.70918	0.191051
$894$	−5.66620	−0.189506
$895$	−5.45906	−0.182476
$896$	2.69176	0.0899253
$897$	−4.19360	−0.140020
$898$	15.9998	0.533920
$899$	−59.2708	−1.97679
$900$	−4.94728	−0.164909
$901$	−5.34710	−0.178138
$902$	−16.8184	−0.559990
$903$	25.3442	0.843402
$904$	11.7260	0.390002
$905$	0.00105920	3.52090e−5 0
$906$	10.3781	0.344791
$907$	4.79925	0.159357	0.0796783	−	0.996821i	$-0.474611\pi$
$907$	4.79925	0.159357	0.0796783	+	0.996821i	$0.474611\pi$
$908$	−10.8269	−0.359304
$909$	−1.22246	−0.0405466
$910$	−1.33316	−0.0441937
$911$	−16.8603	−0.558608	−0.279304	−	0.960203i	$-0.590104\pi$
$911$	−16.8603	−0.558608	−0.279304	+	0.960203i	$0.590104\pi$
$912$	1.00000	0.0331133
$913$	−29.3094	−0.969998
$914$	−28.4371	−0.940616
$915$	2.86993	0.0948768
$916$	22.5205	0.744098
$917$	−25.8325	−0.853065
$918$	5.34710	0.176481
$919$	42.7302	1.40954	0.704769	−	0.709437i	$-0.251050\pi$
$919$	42.7302	1.40954	0.704769	+	0.709437i	$0.251050\pi$
$920$	0.446406	0.0147176
$921$	6.79595	0.223934
$922$	−27.3361	−0.900267
$923$	10.1421	0.333832
$924$	10.0525	0.330702
$925$	39.1719	1.28797
$926$	24.5052	0.805292
$927$	4.59661	0.150972
$928$	−5.72170	−0.187824
$929$	49.7191	1.63123	0.815616	−	0.578594i	$-0.196398\pi$
$929$	49.7191	1.63123	0.815616	+	0.578594i	$0.196398\pi$
$930$	−2.37853	−0.0779952
$931$	0.245558	0.00804784
$932$	23.0077	0.753643
$933$	−7.85807	−0.257262
$934$	−2.50695	−0.0820301
$935$	−4.58510	−0.149949
$936$	2.15700	0.0705039
$937$	2.25483	0.0736620	0.0368310	−	0.999322i	$-0.488274\pi$
$937$	2.25483	0.0736620	0.0368310	+	0.999322i	$0.488274\pi$
$938$	12.9249	0.422014
$939$	2.18896	0.0714340
$940$	−1.31089	−0.0427567
$941$	48.1776	1.57054	0.785272	−	0.619151i	$-0.212523\pi$
$941$	48.1776	1.57054	0.785272	+	0.619151i	$0.212523\pi$
$942$	−16.0621	−0.523330
$943$	8.75553	0.285119
$944$	−11.8621	−0.386077
$945$	−0.618059	−0.0201055
$946$	35.1625	1.14323
$947$	−5.44115	−0.176814	−0.0884068	−	0.996084i	$-0.528178\pi$
$947$	−5.44115	−0.176814	−0.0884068	+	0.996084i	$0.528178\pi$
$948$	9.77405	0.317446
$949$	−5.99270	−0.194531
$950$	−4.94728	−0.160511
$951$	−12.7877	−0.414670
$952$	14.3931	0.466483
$953$	−61.3373	−1.98691	−0.993455	−	0.114225i	$-0.963562\pi$
$953$	−61.3373	−1.98691	−0.993455	+	0.114225i	$0.963562\pi$
$954$	−1.00000	−0.0323762
$955$	−1.61649	−0.0523085
$956$	−12.9454	−0.418683
$957$	−21.3679	−0.690727
$958$	20.3482	0.657421
$959$	−13.0011	−0.419826
$960$	−0.229612	−0.00741068
$961$	76.3077	2.46154
$962$	−17.0789	−0.550646
$963$	−5.51466	−0.177708
$964$	17.3166	0.557729
$965$	−3.24228	−0.104373
$966$	−5.23325	−0.168377
$967$	2.69077	0.0865292	0.0432646	−	0.999064i	$-0.486224\pi$
$967$	2.69077	0.0865292	0.0432646	+	0.999064i	$0.486224\pi$
$968$	2.94678	0.0947131
$969$	5.34710	0.171774
$970$	1.45569	0.0467393
$971$	56.1775	1.80282	0.901411	−	0.432964i	$-0.142532\pi$
$971$	56.1775	1.80282	0.901411	+	0.432964i	$0.142532\pi$
$972$	1.00000	0.0320750
$973$	37.5122	1.20259
$974$	11.4351	0.366403
$975$	−10.6713	−0.341755
$976$	−12.4990	−0.400085
$977$	−18.5907	−0.594769	−0.297384	−	0.954758i	$-0.596114\pi$
$977$	−18.5907	−0.594769	−0.297384	+	0.954758i	$0.596114\pi$
$978$	−21.9437	−0.701682
$979$	−14.4610	−0.462174
$980$	−0.0563830	−0.00180109
$981$	−11.4302	−0.364938
$982$	−19.1590	−0.611390
$983$	18.0467	0.575601	0.287800	−	0.957690i	$-0.407076\pi$
$983$	18.0467	0.575601	0.287800	+	0.957690i	$0.407076\pi$
$984$	−4.50346	−0.143565
$985$	1.91837	0.0611242
$986$	−30.5945	−0.974328
$987$	15.3677	0.489160
$988$	2.15700	0.0686235
$989$	−18.3054	−0.582077
$990$	−0.857494	−0.0272529
$991$	−57.4095	−1.82367	−0.911836	−	0.410555i	$-0.865335\pi$
$991$	−57.4095	−1.82367	−0.911836	+	0.410555i	$0.865335\pi$
$992$	10.3589	0.328897
$993$	28.1550	0.893473
$994$	12.6565	0.401440
$995$	−1.63991	−0.0519888
$996$	−7.84819	−0.248679
$997$	−0.488947	−0.0154851	−0.00774255	−	0.999970i	$-0.502465\pi$
$997$	−0.488947	−0.0154851	−0.00774255	+	0.999970i	$0.502465\pi$
$998$	−21.1516	−0.669543
$999$	−7.91788	−0.250511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bh.1.7	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bh.1.7	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.229612 q^{5} +1.00000 q^{6} +2.69176 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.229612 q^{5} +1.00000 q^{6} +2.69176 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.229612 q^{10} +3.73454 q^{11} +1.00000 q^{12} +2.15700 q^{13} +2.69176 q^{14} -0.229612 q^{15} +1.00000 q^{16} +5.34710 q^{17} +1.00000 q^{18} +1.00000 q^{19} -0.229612 q^{20} +2.69176 q^{21} +3.73454 q^{22} -1.94418 q^{23} +1.00000 q^{24} -4.94728 q^{25} +2.15700 q^{26} +1.00000 q^{27} +2.69176 q^{28} -5.72170 q^{29} -0.229612 q^{30} +10.3589 q^{31} +1.00000 q^{32} +3.73454 q^{33} +5.34710 q^{34} -0.618059 q^{35} +1.00000 q^{36} -7.91788 q^{37} +1.00000 q^{38} +2.15700 q^{39} -0.229612 q^{40} -4.50346 q^{41} +2.69176 q^{42} +9.41549 q^{43} +3.73454 q^{44} -0.229612 q^{45} -1.94418 q^{46} +5.70918 q^{47} +1.00000 q^{48} +0.245558 q^{49} -4.94728 q^{50} +5.34710 q^{51} +2.15700 q^{52} -1.00000 q^{53} +1.00000 q^{54} -0.857494 q^{55} +2.69176 q^{56} +1.00000 q^{57} -5.72170 q^{58} -11.8621 q^{59} -0.229612 q^{60} -12.4990 q^{61} +10.3589 q^{62} +2.69176 q^{63} +1.00000 q^{64} -0.495273 q^{65} +3.73454 q^{66} +4.80167 q^{67} +5.34710 q^{68} -1.94418 q^{69} -0.618059 q^{70} +4.70195 q^{71} +1.00000 q^{72} -2.77825 q^{73} -7.91788 q^{74} -4.94728 q^{75} +1.00000 q^{76} +10.0525 q^{77} +2.15700 q^{78} +9.77405 q^{79} -0.229612 q^{80} +1.00000 q^{81} -4.50346 q^{82} -7.84819 q^{83} +2.69176 q^{84} -1.22776 q^{85} +9.41549 q^{86} -5.72170 q^{87} +3.73454 q^{88} -3.87222 q^{89} -0.229612 q^{90} +5.80613 q^{91} -1.94418 q^{92} +10.3589 q^{93} +5.70918 q^{94} -0.229612 q^{95} +1.00000 q^{96} -6.33978 q^{97} +0.245558 q^{98} +3.73454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * q^99

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