LMFDB - Embedded newform 6034.2.a.l.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$-1.78235$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.78235 q^{3} +1.00000 q^{4} -0.422890 q^{5} +1.78235 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.176787 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.78235 q^{3} +1.00000 q^{4} -0.422890 q^{5} +1.78235 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.176787 q^{9} -0.422890 q^{10} -4.03659 q^{11} +1.78235 q^{12} +3.52451 q^{13} -1.00000 q^{14} -0.753739 q^{15} +1.00000 q^{16} -4.14306 q^{17} +0.176787 q^{18} +0.963265 q^{19} -0.422890 q^{20} -1.78235 q^{21} -4.03659 q^{22} -5.41079 q^{23} +1.78235 q^{24} -4.82116 q^{25} +3.52451 q^{26} -5.03197 q^{27} -1.00000 q^{28} -2.60435 q^{29} -0.753739 q^{30} +9.81130 q^{31} +1.00000 q^{32} -7.19463 q^{33} -4.14306 q^{34} +0.422890 q^{35} +0.176787 q^{36} -10.7725 q^{37} +0.963265 q^{38} +6.28192 q^{39} -0.422890 q^{40} +3.77025 q^{41} -1.78235 q^{42} -8.90254 q^{43} -4.03659 q^{44} -0.0747613 q^{45} -5.41079 q^{46} -3.03453 q^{47} +1.78235 q^{48} +1.00000 q^{49} -4.82116 q^{50} -7.38441 q^{51} +3.52451 q^{52} -0.619030 q^{53} -5.03197 q^{54} +1.70703 q^{55} -1.00000 q^{56} +1.71688 q^{57} -2.60435 q^{58} +5.81038 q^{59} -0.753739 q^{60} -7.09467 q^{61} +9.81130 q^{62} -0.176787 q^{63} +1.00000 q^{64} -1.49048 q^{65} -7.19463 q^{66} -5.95361 q^{67} -4.14306 q^{68} -9.64394 q^{69} +0.422890 q^{70} +1.45430 q^{71} +0.176787 q^{72} +11.0953 q^{73} -10.7725 q^{74} -8.59302 q^{75} +0.963265 q^{76} +4.03659 q^{77} +6.28192 q^{78} -7.96550 q^{79} -0.422890 q^{80} -9.49911 q^{81} +3.77025 q^{82} -6.25940 q^{83} -1.78235 q^{84} +1.75206 q^{85} -8.90254 q^{86} -4.64187 q^{87} -4.03659 q^{88} +6.63706 q^{89} -0.0747613 q^{90} -3.52451 q^{91} -5.41079 q^{92} +17.4872 q^{93} -3.03453 q^{94} -0.407355 q^{95} +1.78235 q^{96} +13.5480 q^{97} +1.00000 q^{98} -0.713615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	1.78235	1.02904	0.514521	−	0.857478i	$-0.327970\pi$
$3$	1.78235	1.02904	0.514521	+	0.857478i	$0.327970\pi$
$4$	1.00000	0.500000
$5$	−0.422890	−0.189122	−0.0945610	−	0.995519i	$-0.530145\pi$
$5$	−0.422890	−0.189122	−0.0945610	+	0.995519i	$0.530145\pi$
$6$	1.78235	0.727643
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	0.176787	0.0589289
$10$	−0.422890	−0.133729
$11$	−4.03659	−1.21708	−0.608538	−	0.793524i	$-0.708244\pi$
$11$	−4.03659	−1.21708	−0.608538	+	0.793524i	$0.708244\pi$
$12$	1.78235	0.514521
$13$	3.52451	0.977522	0.488761	−	0.872418i	$-0.337449\pi$
$13$	3.52451	0.977522	0.488761	+	0.872418i	$0.337449\pi$
$14$	−1.00000	−0.267261
$15$	−0.753739	−0.194615
$16$	1.00000	0.250000
$17$	−4.14306	−1.00484	−0.502420	−	0.864624i	$-0.667557\pi$
$17$	−4.14306	−1.00484	−0.502420	+	0.864624i	$0.667557\pi$
$18$	0.176787	0.0416690
$19$	0.963265	0.220988	0.110494	−	0.993877i	$-0.464757\pi$
$19$	0.963265	0.220988	0.110494	+	0.993877i	$0.464757\pi$
$20$	−0.422890	−0.0945610
$21$	−1.78235	−0.388942
$22$	−4.03659	−0.860603
$23$	−5.41079	−1.12823	−0.564113	−	0.825697i	$-0.690782\pi$
$23$	−5.41079	−1.12823	−0.564113	+	0.825697i	$0.690782\pi$
$24$	1.78235	0.363822
$25$	−4.82116	−0.964233
$26$	3.52451	0.691212
$27$	−5.03197	−0.968402
$28$	−1.00000	−0.188982
$29$	−2.60435	−0.483615	−0.241808	−	0.970324i	$-0.577740\pi$
$29$	−2.60435	−0.483615	−0.241808	+	0.970324i	$0.577740\pi$
$30$	−0.753739	−0.137613
$31$	9.81130	1.76216	0.881081	−	0.472965i	$-0.156816\pi$
$31$	9.81130	1.76216	0.881081	+	0.472965i	$0.156816\pi$
$32$	1.00000	0.176777
$33$	−7.19463	−1.25242
$34$	−4.14306	−0.710529
$35$	0.422890	0.0714814
$36$	0.176787	0.0294645
$37$	−10.7725	−1.77099	−0.885493	−	0.464653i	$-0.846179\pi$
$37$	−10.7725	−1.77099	−0.885493	+	0.464653i	$0.846179\pi$
$38$	0.963265	0.156262
$39$	6.28192	1.00591
$40$	−0.422890	−0.0668647
$41$	3.77025	0.588814	0.294407	−	0.955680i	$-0.404878\pi$
$41$	3.77025	0.588814	0.294407	+	0.955680i	$0.404878\pi$
$42$	−1.78235	−0.275023
$43$	−8.90254	−1.35762	−0.678812	−	0.734312i	$-0.737505\pi$
$43$	−8.90254	−1.35762	−0.678812	+	0.734312i	$0.737505\pi$
$44$	−4.03659	−0.608538
$45$	−0.0747613	−0.0111448
$46$	−5.41079	−0.797777
$47$	−3.03453	−0.442631	−0.221316	−	0.975202i	$-0.571035\pi$
$47$	−3.03453	−0.442631	−0.221316	+	0.975202i	$0.571035\pi$
$48$	1.78235	0.257261
$49$	1.00000	0.142857
$50$	−4.82116	−0.681816
$51$	−7.38441	−1.03402
$52$	3.52451	0.488761
$53$	−0.619030	−0.0850302	−0.0425151	−	0.999096i	$-0.513537\pi$
$53$	−0.619030	−0.0850302	−0.0425151	+	0.999096i	$0.513537\pi$
$54$	−5.03197	−0.684764
$55$	1.70703	0.230176
$56$	−1.00000	−0.133631
$57$	1.71688	0.227406
$58$	−2.60435	−0.341968
$59$	5.81038	0.756447	0.378224	−	0.925714i	$-0.376535\pi$
$59$	5.81038	0.756447	0.378224	+	0.925714i	$0.376535\pi$
$60$	−0.753739	−0.0973073
$61$	−7.09467	−0.908380	−0.454190	−	0.890905i	$-0.650071\pi$
$61$	−7.09467	−0.908380	−0.454190	+	0.890905i	$0.650071\pi$
$62$	9.81130	1.24604
$63$	−0.176787	−0.0222730
$64$	1.00000	0.125000
$65$	−1.49048	−0.184871
$66$	−7.19463	−0.885598
$67$	−5.95361	−0.727350	−0.363675	−	0.931526i	$-0.618478\pi$
$67$	−5.95361	−0.727350	−0.363675	+	0.931526i	$0.618478\pi$
$68$	−4.14306	−0.502420
$69$	−9.64394	−1.16099
$70$	0.422890	0.0505450
$71$	1.45430	0.172594	0.0862969	−	0.996269i	$-0.472497\pi$
$71$	1.45430	0.172594	0.0862969	+	0.996269i	$0.472497\pi$
$72$	0.176787	0.0208345
$73$	11.0953	1.29861	0.649304	−	0.760529i	$-0.275060\pi$
$73$	11.0953	1.29861	0.649304	+	0.760529i	$0.275060\pi$
$74$	−10.7725	−1.25228
$75$	−8.59302	−0.992237
$76$	0.963265	0.110494
$77$	4.03659	0.460012
$78$	6.28192	0.711287
$79$	−7.96550	−0.896189	−0.448094	−	0.893986i	$-0.647897\pi$
$79$	−7.96550	−0.896189	−0.448094	+	0.893986i	$0.647897\pi$
$80$	−0.422890	−0.0472805
$81$	−9.49911	−1.05546
$82$	3.77025	0.416355
$83$	−6.25940	−0.687059	−0.343529	−	0.939142i	$-0.611623\pi$
$83$	−6.25940	−0.687059	−0.343529	+	0.939142i	$0.611623\pi$
$84$	−1.78235	−0.194471
$85$	1.75206	0.190037
$86$	−8.90254	−0.959985
$87$	−4.64187	−0.497661
$88$	−4.03659	−0.430302
$89$	6.63706	0.703527	0.351764	−	0.936089i	$-0.385582\pi$
$89$	6.63706	0.703527	0.351764	+	0.936089i	$0.385582\pi$
$90$	−0.0747613	−0.00788053
$91$	−3.52451	−0.369469
$92$	−5.41079	−0.564113
$93$	17.4872	1.81334
$94$	−3.03453	−0.312988
$95$	−0.407355	−0.0417937
$96$	1.78235	0.181911
$97$	13.5480	1.37559	0.687797	−	0.725903i	$-0.258578\pi$
$97$	13.5480	1.37559	0.687797	+	0.725903i	$0.258578\pi$
$98$	1.00000	0.101015
$99$	−0.713615	−0.0717210
$100$	−4.82116	−0.482116
$101$	−6.99828	−0.696355	−0.348177	−	0.937429i	$-0.613199\pi$
$101$	−6.99828	−0.696355	−0.348177	+	0.937429i	$0.613199\pi$
$102$	−7.38441	−0.731165
$103$	−7.08403	−0.698010	−0.349005	−	0.937121i	$-0.613480\pi$
$103$	−7.08403	−0.698010	−0.349005	+	0.937121i	$0.613480\pi$
$104$	3.52451	0.345606
$105$	0.753739	0.0735574
$106$	−0.619030	−0.0601255
$107$	−4.59451	−0.444168	−0.222084	−	0.975028i	$-0.571286\pi$
$107$	−4.59451	−0.444168	−0.222084	+	0.975028i	$0.571286\pi$
$108$	−5.03197	−0.484201
$109$	−0.160480	−0.0153712	−0.00768562	−	0.999970i	$-0.502446\pi$
$109$	−0.160480	−0.0153712	−0.00768562	+	0.999970i	$0.502446\pi$
$110$	1.70703	0.162759
$111$	−19.2004	−1.82242
$112$	−1.00000	−0.0944911
$113$	−5.91832	−0.556749	−0.278374	−	0.960473i	$-0.589796\pi$
$113$	−5.91832	−0.556749	−0.278374	+	0.960473i	$0.589796\pi$
$114$	1.71688	0.160801
$115$	2.28817	0.213373
$116$	−2.60435	−0.241808
$117$	0.623086	0.0576043
$118$	5.81038	0.534889
$119$	4.14306	0.379794
$120$	−0.753739	−0.0688067
$121$	5.29404	0.481276
$122$	−7.09467	−0.642322
$123$	6.71992	0.605915
$124$	9.81130	0.881081
$125$	4.15327	0.371480
$126$	−0.176787	−0.0157494
$127$	14.5306	1.28938	0.644691	−	0.764444i	$-0.276986\pi$
$127$	14.5306	1.28938	0.644691	+	0.764444i	$0.276986\pi$
$128$	1.00000	0.0883883
$129$	−15.8675	−1.39705
$130$	−1.49048	−0.130723
$131$	20.8317	1.82007	0.910037	−	0.414527i	$-0.136053\pi$
$131$	20.8317	1.82007	0.910037	+	0.414527i	$0.136053\pi$
$132$	−7.19463	−0.626212
$133$	−0.963265	−0.0835257
$134$	−5.95361	−0.514314
$135$	2.12797	0.183146
$136$	−4.14306	−0.355265
$137$	2.84342	0.242930	0.121465	−	0.992596i	$-0.461241\pi$
$137$	2.84342	0.242930	0.121465	+	0.992596i	$0.461241\pi$
$138$	−9.64394	−0.820946
$139$	−16.1632	−1.37095	−0.685474	−	0.728097i	$-0.740405\pi$
$139$	−16.1632	−1.37095	−0.685474	+	0.728097i	$0.740405\pi$
$140$	0.422890	0.0357407
$141$	−5.40860	−0.455487
$142$	1.45430	0.122042
$143$	−14.2270	−1.18972
$144$	0.176787	0.0147322
$145$	1.10135	0.0914623
$146$	11.0953	0.918255
$147$	1.78235	0.147006
$148$	−10.7725	−0.885493
$149$	−15.4071	−1.26219	−0.631097	−	0.775704i	$-0.717395\pi$
$149$	−15.4071	−1.26219	−0.631097	+	0.775704i	$0.717395\pi$
$150$	−8.59302	−0.701617
$151$	15.5105	1.26223	0.631113	−	0.775691i	$-0.282598\pi$
$151$	15.5105	1.26223	0.631113	+	0.775691i	$0.282598\pi$
$152$	0.963265	0.0781311
$153$	−0.732439	−0.0592142
$154$	4.03659	0.325277
$155$	−4.14910	−0.333264
$156$	6.28192	0.502956
$157$	3.70964	0.296062	0.148031	−	0.988983i	$-0.452707\pi$
$157$	3.70964	0.296062	0.148031	+	0.988983i	$0.452707\pi$
$158$	−7.96550	−0.633701
$159$	−1.10333	−0.0874998
$160$	−0.422890	−0.0334324
$161$	5.41079	0.426430
$162$	−9.49911	−0.746320
$163$	−1.09350	−0.0856493	−0.0428247	−	0.999083i	$-0.513636\pi$
$163$	−1.09350	−0.0856493	−0.0428247	+	0.999083i	$0.513636\pi$
$164$	3.77025	0.294407
$165$	3.04253	0.236861
$166$	−6.25940	−0.485824
$167$	−14.4215	−1.11597	−0.557984	−	0.829852i	$-0.688425\pi$
$167$	−14.4215	−1.11597	−0.557984	+	0.829852i	$0.688425\pi$
$168$	−1.78235	−0.137512
$169$	−0.577862	−0.0444509
$170$	1.75206	0.134377
$171$	0.170293	0.0130226
$172$	−8.90254	−0.678812
$173$	0.815988	0.0620385	0.0310192	−	0.999519i	$-0.490125\pi$
$173$	0.815988	0.0620385	0.0310192	+	0.999519i	$0.490125\pi$
$174$	−4.64187	−0.351899
$175$	4.82116	0.364446
$176$	−4.03659	−0.304269
$177$	10.3562	0.778417
$178$	6.63706	0.497469
$179$	−6.25599	−0.467595	−0.233797	−	0.972285i	$-0.575115\pi$
$179$	−6.25599	−0.467595	−0.233797	+	0.972285i	$0.575115\pi$
$180$	−0.0747613	−0.00557238
$181$	−12.5566	−0.933321	−0.466661	−	0.884436i	$-0.654543\pi$
$181$	−12.5566	−0.933321	−0.466661	+	0.884436i	$0.654543\pi$
$182$	−3.52451	−0.261254
$183$	−12.6452	−0.934762
$184$	−5.41079	−0.398888
$185$	4.55557	0.334932
$186$	17.4872	1.28223
$187$	16.7238	1.22297
$188$	−3.03453	−0.221316
$189$	5.03197	0.366022
$190$	−0.407355	−0.0295526
$191$	10.9486	0.792210	0.396105	−	0.918205i	$-0.370362\pi$
$191$	10.9486	0.792210	0.396105	+	0.918205i	$0.370362\pi$
$192$	1.78235	0.128630
$193$	24.3149	1.75022	0.875112	−	0.483920i	$-0.160787\pi$
$193$	24.3149	1.75022	0.875112	+	0.483920i	$0.160787\pi$
$194$	13.5480	0.972692
$195$	−2.65656	−0.190240
$196$	1.00000	0.0714286
$197$	−16.8963	−1.20381	−0.601905	−	0.798568i	$-0.705591\pi$
$197$	−16.8963	−1.20381	−0.601905	+	0.798568i	$0.705591\pi$
$198$	−0.713615	−0.0507144
$199$	5.12555	0.363341	0.181670	−	0.983360i	$-0.441850\pi$
$199$	5.12555	0.363341	0.181670	+	0.983360i	$0.441850\pi$
$200$	−4.82116	−0.340908
$201$	−10.6114	−0.748474
$202$	−6.99828	−0.492397
$203$	2.60435	0.182789
$204$	−7.38441	−0.517012
$205$	−1.59440	−0.111358
$206$	−7.08403	−0.493568
$207$	−0.956555	−0.0664852
$208$	3.52451	0.244380
$209$	−3.88830	−0.268960
$210$	0.753739	0.0520130
$211$	4.28659	0.295101	0.147550	−	0.989055i	$-0.452861\pi$
$211$	4.28659	0.295101	0.147550	+	0.989055i	$0.452861\pi$
$212$	−0.619030	−0.0425151
$213$	2.59208	0.177606
$214$	−4.59451	−0.314074
$215$	3.76479	0.256757
$216$	−5.03197	−0.342382
$217$	−9.81130	−0.666035
$218$	−0.160480	−0.0108691
$219$	19.7758	1.33632
$220$	1.70703	0.115088
$221$	−14.6022	−0.982253
$222$	−19.2004	−1.28865
$223$	0.883182	0.0591422	0.0295711	−	0.999563i	$-0.490586\pi$
$223$	0.883182	0.0591422	0.0295711	+	0.999563i	$0.490586\pi$
$224$	−1.00000	−0.0668153
$225$	−0.852318	−0.0568212
$226$	−5.91832	−0.393681
$227$	4.94150	0.327979	0.163989	−	0.986462i	$-0.447564\pi$
$227$	4.94150	0.327979	0.163989	+	0.986462i	$0.447564\pi$
$228$	1.71688	0.113703
$229$	−14.7914	−0.977441	−0.488720	−	0.872440i	$-0.662536\pi$
$229$	−14.7914	−0.977441	−0.488720	+	0.872440i	$0.662536\pi$
$230$	2.28817	0.150877
$231$	7.19463	0.473372
$232$	−2.60435	−0.170984
$233$	2.30554	0.151041	0.0755205	−	0.997144i	$-0.475938\pi$
$233$	2.30554	0.151041	0.0755205	+	0.997144i	$0.475938\pi$
$234$	0.623086	0.0407324
$235$	1.28327	0.0837114
$236$	5.81038	0.378224
$237$	−14.1973	−0.922216
$238$	4.14306	0.268555
$239$	−19.7310	−1.27629	−0.638146	−	0.769916i	$-0.720298\pi$
$239$	−19.7310	−1.27629	−0.638146	+	0.769916i	$0.720298\pi$
$240$	−0.753739	−0.0486537
$241$	5.28809	0.340636	0.170318	−	0.985389i	$-0.445521\pi$
$241$	5.28809	0.340636	0.170318	+	0.985389i	$0.445521\pi$
$242$	5.29404	0.340313
$243$	−1.83487	−0.117707
$244$	−7.09467	−0.454190
$245$	−0.422890	−0.0270174
$246$	6.71992	0.428447
$247$	3.39503	0.216021
$248$	9.81130	0.623018
$249$	−11.1565	−0.707013
$250$	4.15327	0.262676
$251$	−26.6991	−1.68523	−0.842615	−	0.538517i	$-0.818985\pi$
$251$	−26.6991	−1.68523	−0.842615	+	0.538517i	$0.818985\pi$
$252$	−0.176787	−0.0111365
$253$	21.8411	1.37314
$254$	14.5306	0.911730
$255$	3.12279	0.195557
$256$	1.00000	0.0625000
$257$	−17.9544	−1.11996	−0.559982	−	0.828505i	$-0.689192\pi$
$257$	−17.9544	−1.11996	−0.559982	+	0.828505i	$0.689192\pi$
$258$	−15.8675	−0.987866
$259$	10.7725	0.669370
$260$	−1.49048	−0.0924355
$261$	−0.460414	−0.0284989
$262$	20.8317	1.28699
$263$	−3.74420	−0.230877	−0.115439	−	0.993315i	$-0.536827\pi$
$263$	−3.74420	−0.230877	−0.115439	+	0.993315i	$0.536827\pi$
$264$	−7.19463	−0.442799
$265$	0.261781	0.0160811
$266$	−0.963265	−0.0590616
$267$	11.8296	0.723960
$268$	−5.95361	−0.363675
$269$	−18.0650	−1.10144	−0.550722	−	0.834689i	$-0.685648\pi$
$269$	−18.0650	−1.10144	−0.550722	+	0.834689i	$0.685648\pi$
$270$	2.12797	0.129504
$271$	18.7307	1.13781	0.568905	−	0.822403i	$-0.307367\pi$
$271$	18.7307	1.13781	0.568905	+	0.822403i	$0.307367\pi$
$272$	−4.14306	−0.251210
$273$	−6.28192	−0.380199
$274$	2.84342	0.171777
$275$	19.4610	1.17355
$276$	−9.64394	−0.580497
$277$	−26.1665	−1.57219	−0.786096	−	0.618105i	$-0.787901\pi$
$277$	−26.1665	−1.57219	−0.786096	+	0.618105i	$0.787901\pi$
$278$	−16.1632	−0.969407
$279$	1.73451	0.103842
$280$	0.422890	0.0252725
$281$	−16.7993	−1.00216	−0.501081	−	0.865400i	$-0.667064\pi$
$281$	−16.7993	−1.00216	−0.501081	+	0.865400i	$0.667064\pi$
$282$	−5.40860	−0.322078
$283$	18.5346	1.10177	0.550884	−	0.834582i	$-0.314291\pi$
$283$	18.5346	1.10177	0.550884	+	0.834582i	$0.314291\pi$
$284$	1.45430	0.0862969
$285$	−0.726051	−0.0430075
$286$	−14.2270	−0.841259
$287$	−3.77025	−0.222551
$288$	0.176787	0.0104173
$289$	0.164967	0.00970393
$290$	1.10135	0.0646736
$291$	24.1474	1.41555
$292$	11.0953	0.649304
$293$	2.11491	0.123554	0.0617771	−	0.998090i	$-0.480323\pi$
$293$	2.11491	0.123554	0.0617771	+	0.998090i	$0.480323\pi$
$294$	1.78235	0.103949
$295$	−2.45715	−0.143061
$296$	−10.7725	−0.626138
$297$	20.3120	1.17862
$298$	−15.4071	−0.892506
$299$	−19.0703	−1.10287
$300$	−8.59302	−0.496118
$301$	8.90254	0.513134
$302$	15.5105	0.892529
$303$	−12.4734	−0.716579
$304$	0.963265	0.0552471
$305$	3.00026	0.171795
$306$	−0.732439	−0.0418707
$307$	2.82768	0.161384	0.0806920	−	0.996739i	$-0.474287\pi$
$307$	2.82768	0.161384	0.0806920	+	0.996739i	$0.474287\pi$
$308$	4.03659	0.230006
$309$	−12.6263	−0.718283
$310$	−4.14910	−0.235653
$311$	24.1452	1.36915	0.684574	−	0.728944i	$-0.259988\pi$
$311$	24.1452	1.36915	0.684574	+	0.728944i	$0.259988\pi$
$312$	6.28192	0.355644
$313$	24.2623	1.37138	0.685692	−	0.727892i	$-0.259500\pi$
$313$	24.2623	1.37138	0.685692	+	0.727892i	$0.259500\pi$
$314$	3.70964	0.209347
$315$	0.0747613	0.00421232
$316$	−7.96550	−0.448094
$317$	14.0657	0.790009	0.395004	−	0.918679i	$-0.370743\pi$
$317$	14.0657	0.790009	0.395004	+	0.918679i	$0.370743\pi$
$318$	−1.10333	−0.0618717
$319$	10.5127	0.588597
$320$	−0.422890	−0.0236403
$321$	−8.18904	−0.457067
$322$	5.41079	0.301531
$323$	−3.99087	−0.222058
$324$	−9.49911	−0.527728
$325$	−16.9922	−0.942559
$326$	−1.09350	−0.0605632
$327$	−0.286033	−0.0158177
$328$	3.77025	0.208177
$329$	3.03453	0.167299
$330$	3.04253	0.167486
$331$	−5.58314	−0.306877	−0.153439	−	0.988158i	$-0.549035\pi$
$331$	−5.58314	−0.306877	−0.153439	+	0.988158i	$0.549035\pi$
$332$	−6.25940	−0.343529
$333$	−1.90443	−0.104362
$334$	−14.4215	−0.789108
$335$	2.51772	0.137558
$336$	−1.78235	−0.0972354
$337$	26.4450	1.44055	0.720276	−	0.693687i	$-0.244015\pi$
$337$	26.4450	1.44055	0.720276	+	0.693687i	$0.244015\pi$
$338$	−0.577862	−0.0314316
$339$	−10.5485	−0.572918
$340$	1.75206	0.0950187
$341$	−39.6042	−2.14469
$342$	0.170293	0.00920837
$343$	−1.00000	−0.0539949
$344$	−8.90254	−0.479993
$345$	4.07832	0.219569
$346$	0.815988	0.0438678
$347$	−13.4639	−0.722780	−0.361390	−	0.932415i	$-0.617698\pi$
$347$	−13.4639	−0.722780	−0.361390	+	0.932415i	$0.617698\pi$
$348$	−4.64187	−0.248830
$349$	−0.241703	−0.0129381	−0.00646904	−	0.999979i	$-0.502059\pi$
$349$	−0.241703	−0.0129381	−0.00646904	+	0.999979i	$0.502059\pi$
$350$	4.82116	0.257702
$351$	−17.7352	−0.946634
$352$	−4.03659	−0.215151
$353$	18.2330	0.970446	0.485223	−	0.874390i	$-0.338738\pi$
$353$	18.2330	0.970446	0.485223	+	0.874390i	$0.338738\pi$
$354$	10.3562	0.550424
$355$	−0.615009	−0.0326413
$356$	6.63706	0.351764
$357$	7.38441	0.390824
$358$	−6.25599	−0.330639
$359$	1.48220	0.0782274	0.0391137	−	0.999235i	$-0.487547\pi$
$359$	1.48220	0.0782274	0.0391137	+	0.999235i	$0.487547\pi$
$360$	−0.0747613	−0.00394027
$361$	−18.0721	−0.951164
$362$	−12.5566	−0.659958
$363$	9.43585	0.495253
$364$	−3.52451	−0.184734
$365$	−4.69209	−0.245595
$366$	−12.6452	−0.660976
$367$	16.8628	0.880228	0.440114	−	0.897942i	$-0.354938\pi$
$367$	16.8628	0.880228	0.440114	+	0.897942i	$0.354938\pi$
$368$	−5.41079	−0.282057
$369$	0.666530	0.0346982
$370$	4.55557	0.236833
$371$	0.619030	0.0321384
$372$	17.4872	0.906670
$373$	6.10736	0.316227	0.158113	−	0.987421i	$-0.449459\pi$
$373$	6.10736	0.316227	0.158113	+	0.987421i	$0.449459\pi$
$374$	16.7238	0.864769
$375$	7.40260	0.382269
$376$	−3.03453	−0.156494
$377$	−9.17904	−0.472745
$378$	5.03197	0.258816
$379$	10.0052	0.513932	0.256966	−	0.966420i	$-0.417277\pi$
$379$	10.0052	0.513932	0.256966	+	0.966420i	$0.417277\pi$
$380$	−0.407355	−0.0208969
$381$	25.8987	1.32683
$382$	10.9486	0.560177
$383$	29.3683	1.50065	0.750324	−	0.661070i	$-0.229898\pi$
$383$	29.3683	1.50065	0.750324	+	0.661070i	$0.229898\pi$
$384$	1.78235	0.0909554
$385$	−1.70703	−0.0869984
$386$	24.3149	1.23760
$387$	−1.57385	−0.0800033
$388$	13.5480	0.687797
$389$	3.90984	0.198237	0.0991184	−	0.995076i	$-0.468398\pi$
$389$	3.90984	0.198237	0.0991184	+	0.995076i	$0.468398\pi$
$390$	−2.65656	−0.134520
$391$	22.4172	1.13369
$392$	1.00000	0.0505076
$393$	37.1295	1.87293
$394$	−16.8963	−0.851222
$395$	3.36853	0.169489
$396$	−0.713615	−0.0358605
$397$	4.42048	0.221858	0.110929	−	0.993828i	$-0.464617\pi$
$397$	4.42048	0.221858	0.110929	+	0.993828i	$0.464617\pi$
$398$	5.12555	0.256921
$399$	−1.71688	−0.0859515
$400$	−4.82116	−0.241058
$401$	−21.1271	−1.05504	−0.527519	−	0.849543i	$-0.676878\pi$
$401$	−21.1271	−1.05504	−0.527519	+	0.849543i	$0.676878\pi$
$402$	−10.6114	−0.529251
$403$	34.5800	1.72255
$404$	−6.99828	−0.348177
$405$	4.01707	0.199610
$406$	2.60435	0.129252
$407$	43.4841	2.15543
$408$	−7.38441	−0.365583
$409$	−16.0468	−0.793463	−0.396731	−	0.917935i	$-0.629856\pi$
$409$	−16.0468	−0.793463	−0.396731	+	0.917935i	$0.629856\pi$
$410$	−1.59440	−0.0787418
$411$	5.06799	0.249985
$412$	−7.08403	−0.349005
$413$	−5.81038	−0.285910
$414$	−0.956555	−0.0470121
$415$	2.64704	0.129938
$416$	3.52451	0.172803
$417$	−28.8086	−1.41076
$418$	−3.88830	−0.190183
$419$	−18.6243	−0.909858	−0.454929	−	0.890528i	$-0.650335\pi$
$419$	−18.6243	−0.909858	−0.454929	+	0.890528i	$0.650335\pi$
$420$	0.753739	0.0367787
$421$	18.3598	0.894800	0.447400	−	0.894334i	$-0.352350\pi$
$421$	18.3598	0.894800	0.447400	+	0.894334i	$0.352350\pi$
$422$	4.28659	0.208668
$423$	−0.536464	−0.0260838
$424$	−0.619030	−0.0300627
$425$	19.9744	0.968900
$426$	2.59208	0.125587
$427$	7.09467	0.343335
$428$	−4.59451	−0.222084
$429$	−25.3575	−1.22427
$430$	3.76479	0.181554
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.03197	−0.242101
$433$	9.24114	0.444101	0.222051	−	0.975035i	$-0.428725\pi$
$433$	9.24114	0.444101	0.222051	+	0.975035i	$0.428725\pi$
$434$	−9.81130	−0.470958
$435$	1.96300	0.0941186
$436$	−0.160480	−0.00768562
$437$	−5.21202	−0.249325
$438$	19.7758	0.944923
$439$	−6.47302	−0.308940	−0.154470	−	0.987997i	$-0.549367\pi$
$439$	−6.47302	−0.308940	−0.154470	+	0.987997i	$0.549367\pi$
$440$	1.70703	0.0813795
$441$	0.176787	0.00841842
$442$	−14.6022	−0.694558
$443$	28.2967	1.34442	0.672209	−	0.740362i	$-0.265346\pi$
$443$	28.2967	1.34442	0.672209	+	0.740362i	$0.265346\pi$
$444$	−19.2004	−0.911210
$445$	−2.80675	−0.133053
$446$	0.883182	0.0418199
$447$	−27.4608	−1.29885
$448$	−1.00000	−0.0472456
$449$	−14.9250	−0.704355	−0.352177	−	0.935933i	$-0.614559\pi$
$449$	−14.9250	−0.704355	−0.352177	+	0.935933i	$0.614559\pi$
$450$	−0.852318	−0.0401787
$451$	−15.2189	−0.716632
$452$	−5.91832	−0.278374
$453$	27.6452	1.29888
$454$	4.94150	0.231916
$455$	1.49048	0.0698746
$456$	1.71688	0.0804003
$457$	18.3268	0.857293	0.428647	−	0.903472i	$-0.358991\pi$
$457$	18.3268	0.857293	0.428647	+	0.903472i	$0.358991\pi$
$458$	−14.7914	−0.691155
$459$	20.8478	0.973090
$460$	2.28817	0.106686
$461$	34.7634	1.61909	0.809546	−	0.587056i	$-0.199713\pi$
$461$	34.7634	1.61909	0.809546	+	0.587056i	$0.199713\pi$
$462$	7.19463	0.334724
$463$	25.4711	1.18374	0.591870	−	0.806033i	$-0.298390\pi$
$463$	25.4711	1.18374	0.591870	+	0.806033i	$0.298390\pi$
$464$	−2.60435	−0.120904
$465$	−7.39517	−0.342943
$466$	2.30554	0.106802
$467$	−14.8374	−0.686593	−0.343296	−	0.939227i	$-0.611544\pi$
$467$	−14.8374	−0.686593	−0.343296	+	0.939227i	$0.611544\pi$
$468$	0.623086	0.0288022
$469$	5.95361	0.274912
$470$	1.28327	0.0591929
$471$	6.61189	0.304660
$472$	5.81038	0.267444
$473$	35.9359	1.65233
$474$	−14.1973	−0.652105
$475$	−4.64406	−0.213084
$476$	4.14306	0.189897
$477$	−0.109436	−0.00501074
$478$	−19.7310	−0.902474
$479$	8.81699	0.402859	0.201429	−	0.979503i	$-0.435441\pi$
$479$	8.81699	0.402859	0.201429	+	0.979503i	$0.435441\pi$
$480$	−0.753739	−0.0344033
$481$	−37.9677	−1.73118
$482$	5.28809	0.240866
$483$	9.64394	0.438814
$484$	5.29404	0.240638
$485$	−5.72932	−0.260155
$486$	−1.83487	−0.0832316
$487$	−31.8614	−1.44378	−0.721889	−	0.692009i	$-0.756726\pi$
$487$	−31.8614	−1.44378	−0.721889	+	0.692009i	$0.756726\pi$
$488$	−7.09467	−0.321161
$489$	−1.94900	−0.0881368
$490$	−0.422890	−0.0191042
$491$	−30.1444	−1.36040	−0.680199	−	0.733028i	$-0.738107\pi$
$491$	−30.1444	−1.36040	−0.680199	+	0.733028i	$0.738107\pi$
$492$	6.71992	0.302958
$493$	10.7900	0.485956
$494$	3.39503	0.152750
$495$	0.301781	0.0135640
$496$	9.81130	0.440541
$497$	−1.45430	−0.0652343
$498$	−11.1565	−0.499934
$499$	12.8188	0.573846	0.286923	−	0.957954i	$-0.407368\pi$
$499$	12.8188	0.573846	0.286923	+	0.957954i	$0.407368\pi$
$500$	4.15327	0.185740
$501$	−25.7042	−1.14838
$502$	−26.6991	−1.19164
$503$	−27.8214	−1.24049	−0.620246	−	0.784407i	$-0.712967\pi$
$503$	−27.8214	−1.24049	−0.620246	+	0.784407i	$0.712967\pi$
$504$	−0.176787	−0.00787471
$505$	2.95950	0.131696
$506$	21.8411	0.970956
$507$	−1.02996	−0.0457419
$508$	14.5306	0.644691
$509$	21.1171	0.935999	0.468000	−	0.883729i	$-0.344975\pi$
$509$	21.1171	0.935999	0.468000	+	0.883729i	$0.344975\pi$
$510$	3.12279	0.138279
$511$	−11.0953	−0.490828
$512$	1.00000	0.0441942
$513$	−4.84712	−0.214006
$514$	−17.9544	−0.791935
$515$	2.99576	0.132009
$516$	−15.8675	−0.698527
$517$	12.2491	0.538716
$518$	10.7725	0.473316
$519$	1.45438	0.0638402
$520$	−1.49048	−0.0653617
$521$	−4.93956	−0.216406	−0.108203	−	0.994129i	$-0.534510\pi$
$521$	−4.93956	−0.216406	−0.108203	+	0.994129i	$0.534510\pi$
$522$	−0.460414	−0.0201518
$523$	−44.0837	−1.92765	−0.963824	−	0.266541i	$-0.914119\pi$
$523$	−44.0837	−1.92765	−0.963824	+	0.266541i	$0.914119\pi$
$524$	20.8317	0.910037
$525$	8.59302	0.375030
$526$	−3.74420	−0.163255
$527$	−40.6488	−1.77069
$528$	−7.19463	−0.313106
$529$	6.27660	0.272895
$530$	0.261781	0.0113711
$531$	1.02720	0.0445766
$532$	−0.963265	−0.0417628
$533$	13.2883	0.575579
$534$	11.8296	0.511917
$535$	1.94297	0.0840019
$536$	−5.95361	−0.257157
$537$	−11.1504	−0.481175
$538$	−18.0650	−0.778838
$539$	−4.03659	−0.173868
$540$	2.12797	0.0915731
$541$	14.7781	0.635362	0.317681	−	0.948198i	$-0.397096\pi$
$541$	14.7781	0.635362	0.317681	+	0.948198i	$0.397096\pi$
$542$	18.7307	0.804553
$543$	−22.3802	−0.960427
$544$	−4.14306	−0.177632
$545$	0.0678655	0.00290704
$546$	−6.28192	−0.268841
$547$	−3.63991	−0.155631	−0.0778157	−	0.996968i	$-0.524795\pi$
$547$	−3.63991	−0.155631	−0.0778157	+	0.996968i	$0.524795\pi$
$548$	2.84342	0.121465
$549$	−1.25424	−0.0535298
$550$	19.4610	0.829822
$551$	−2.50868	−0.106873
$552$	−9.64394	−0.410473
$553$	7.96550	0.338727
$554$	−26.1665	−1.11171
$555$	8.11965	0.344660
$556$	−16.1632	−0.685474
$557$	0.291079	0.0123334	0.00616670	−	0.999981i	$-0.498037\pi$
$557$	0.291079	0.0123334	0.00616670	+	0.999981i	$0.498037\pi$
$558$	1.73451	0.0734276
$559$	−31.3770	−1.32711
$560$	0.422890	0.0178704
$561$	29.8078	1.25849
$562$	−16.7993	−0.708636
$563$	27.2191	1.14715	0.573575	−	0.819153i	$-0.305556\pi$
$563$	27.2191	1.14715	0.573575	+	0.819153i	$0.305556\pi$
$564$	−5.40860	−0.227743
$565$	2.50280	0.105293
$566$	18.5346	0.779068
$567$	9.49911	0.398925
$568$	1.45430	0.0610211
$569$	−47.4203	−1.98796	−0.993982	−	0.109546i	$-0.965060\pi$
$569$	−47.4203	−1.98796	−0.993982	+	0.109546i	$0.965060\pi$
$570$	−0.726051	−0.0304109
$571$	37.5624	1.57194	0.785968	−	0.618267i	$-0.212165\pi$
$571$	37.5624	1.57194	0.785968	+	0.618267i	$0.212165\pi$
$572$	−14.2270	−0.594860
$573$	19.5142	0.815218
$574$	−3.77025	−0.157367
$575$	26.0863	1.08787
$576$	0.176787	0.00736612
$577$	31.3468	1.30498	0.652492	−	0.757796i	$-0.273724\pi$
$577$	31.3468	1.30498	0.652492	+	0.757796i	$0.273724\pi$
$578$	0.164967	0.00686171
$579$	43.3378	1.80106
$580$	1.10135	0.0457312
$581$	6.25940	0.259684
$582$	24.1474	1.00094
$583$	2.49877	0.103488
$584$	11.0953	0.459127
$585$	−0.263497	−0.0108942
$586$	2.11491	0.0873660
$587$	23.0245	0.950322	0.475161	−	0.879899i	$-0.342390\pi$
$587$	23.0245	0.950322	0.475161	+	0.879899i	$0.342390\pi$
$588$	1.78235	0.0735031
$589$	9.45089	0.389417
$590$	−2.45715	−0.101159
$591$	−30.1152	−1.23877
$592$	−10.7725	−0.442746
$593$	6.64228	0.272766	0.136383	−	0.990656i	$-0.456452\pi$
$593$	6.64228	0.272766	0.136383	+	0.990656i	$0.456452\pi$
$594$	20.3120	0.833410
$595$	−1.75206	−0.0718274
$596$	−15.4071	−0.631097
$597$	9.13554	0.373893
$598$	−19.0703	−0.779844
$599$	−32.3128	−1.32026	−0.660132	−	0.751149i	$-0.729500\pi$
$599$	−32.3128	−1.32026	−0.660132	+	0.751149i	$0.729500\pi$
$600$	−8.59302	−0.350809
$601$	−20.9074	−0.852830	−0.426415	−	0.904528i	$-0.640224\pi$
$601$	−20.9074	−0.852830	−0.426415	+	0.904528i	$0.640224\pi$
$602$	8.90254	0.362840
$603$	−1.05252	−0.0428619
$604$	15.5105	0.631113
$605$	−2.23879	−0.0910199
$606$	−12.4734	−0.506698
$607$	−20.0679	−0.814531	−0.407266	−	0.913310i	$-0.633518\pi$
$607$	−20.0679	−0.814531	−0.407266	+	0.913310i	$0.633518\pi$
$608$	0.963265	0.0390656
$609$	4.64187	0.188098
$610$	3.00026	0.121477
$611$	−10.6952	−0.432682
$612$	−0.732439	−0.0296071
$613$	−21.8040	−0.880654	−0.440327	−	0.897838i	$-0.645137\pi$
$613$	−21.8040	−0.880654	−0.440327	+	0.897838i	$0.645137\pi$
$614$	2.82768	0.114116
$615$	−2.84179	−0.114592
$616$	4.03659	0.162639
$617$	15.8764	0.639161	0.319580	−	0.947559i	$-0.396458\pi$
$617$	15.8764	0.639161	0.319580	+	0.947559i	$0.396458\pi$
$618$	−12.6263	−0.507902
$619$	−48.4325	−1.94667	−0.973333	−	0.229395i	$-0.926325\pi$
$619$	−48.4325	−1.94667	−0.973333	+	0.229395i	$0.926325\pi$
$620$	−4.14910	−0.166632
$621$	27.2269	1.09258
$622$	24.1452	0.968134
$623$	−6.63706	−0.265908
$624$	6.28192	0.251478
$625$	22.3494	0.893978
$626$	24.2623	0.969715
$627$	−6.93034	−0.276771
$628$	3.70964	0.148031
$629$	44.6311	1.77956
$630$	0.0747613	0.00297856
$631$	26.1127	1.03953	0.519764	−	0.854310i	$-0.326020\pi$
$631$	26.1127	1.03953	0.519764	+	0.854310i	$0.326020\pi$
$632$	−7.96550	−0.316850
$633$	7.64022	0.303671
$634$	14.0657	0.558621
$635$	−6.14484	−0.243850
$636$	−1.10333	−0.0437499
$637$	3.52451	0.139646
$638$	10.5127	0.416201
$639$	0.257101	0.0101708
$640$	−0.422890	−0.0167162
$641$	−25.3944	−1.00302	−0.501510	−	0.865152i	$-0.667222\pi$
$641$	−25.3944	−1.00302	−0.501510	+	0.865152i	$0.667222\pi$
$642$	−8.18904	−0.323195
$643$	−17.7965	−0.701827	−0.350913	−	0.936408i	$-0.614129\pi$
$643$	−17.7965	−0.701827	−0.350913	+	0.936408i	$0.614129\pi$
$644$	5.41079	0.213215
$645$	6.71019	0.264214
$646$	−3.99087	−0.157019
$647$	−8.96993	−0.352644	−0.176322	−	0.984333i	$-0.556420\pi$
$647$	−8.96993	−0.352644	−0.176322	+	0.984333i	$0.556420\pi$
$648$	−9.49911	−0.373160
$649$	−23.4541	−0.920654
$650$	−16.9922	−0.666490
$651$	−17.4872	−0.685378
$652$	−1.09350	−0.0428247
$653$	−11.2103	−0.438693	−0.219346	−	0.975647i	$-0.570392\pi$
$653$	−11.2103	−0.438693	−0.219346	+	0.975647i	$0.570392\pi$
$654$	−0.286033	−0.0111848
$655$	−8.80951	−0.344216
$656$	3.77025	0.147204
$657$	1.96150	0.0765256
$658$	3.03453	0.118298
$659$	−2.94648	−0.114778	−0.0573892	−	0.998352i	$-0.518278\pi$
$659$	−2.94648	−0.114778	−0.0573892	+	0.998352i	$0.518278\pi$
$660$	3.04253	0.118430
$661$	23.3022	0.906350	0.453175	−	0.891422i	$-0.350291\pi$
$661$	23.3022	0.906350	0.453175	+	0.891422i	$0.350291\pi$
$662$	−5.58314	−0.216995
$663$	−26.0264	−1.01078
$664$	−6.25940	−0.242912
$665$	0.407355	0.0157966
$666$	−1.90443	−0.0737953
$667$	14.0916	0.545628
$668$	−14.4215	−0.557984
$669$	1.57414	0.0608599
$670$	2.51772	0.0972681
$671$	28.6383	1.10557
$672$	−1.78235	−0.0687558
$673$	38.4528	1.48225	0.741123	−	0.671369i	$-0.234293\pi$
$673$	38.4528	1.48225	0.741123	+	0.671369i	$0.234293\pi$
$674$	26.4450	1.01862
$675$	24.2599	0.933765
$676$	−0.577862	−0.0222255
$677$	−5.26404	−0.202314	−0.101157	−	0.994870i	$-0.532254\pi$
$677$	−5.26404	−0.202314	−0.101157	+	0.994870i	$0.532254\pi$
$678$	−10.5485	−0.405114
$679$	−13.5480	−0.519926
$680$	1.75206	0.0671884
$681$	8.80750	0.337504
$682$	−39.6042	−1.51652
$683$	21.8049	0.834342	0.417171	−	0.908828i	$-0.363022\pi$
$683$	21.8049	0.834342	0.417171	+	0.908828i	$0.363022\pi$
$684$	0.170293	0.00651130
$685$	−1.20245	−0.0459434
$686$	−1.00000	−0.0381802
$687$	−26.3635	−1.00583
$688$	−8.90254	−0.339406
$689$	−2.18177	−0.0831189
$690$	4.07832	0.155259
$691$	−39.0484	−1.48547	−0.742735	−	0.669585i	$-0.766472\pi$
$691$	−39.0484	−1.48547	−0.742735	+	0.669585i	$0.766472\pi$
$692$	0.815988	0.0310192
$693$	0.713615	0.0271080
$694$	−13.4639	−0.511083
$695$	6.83527	0.259277
$696$	−4.64187	−0.175950
$697$	−15.6204	−0.591664
$698$	−0.241703	−0.00914860
$699$	4.10929	0.155428
$700$	4.82116	0.182223
$701$	−18.3994	−0.694937	−0.347468	−	0.937692i	$-0.612959\pi$
$701$	−18.3994	−0.694937	−0.347468	+	0.937692i	$0.612959\pi$
$702$	−17.7352	−0.669372
$703$	−10.3768	−0.391367
$704$	−4.03659	−0.152135
$705$	2.28724	0.0861426
$706$	18.2330	0.686209
$707$	6.99828	0.263197
$708$	10.3562	0.389208
$709$	−12.5589	−0.471660	−0.235830	−	0.971794i	$-0.575781\pi$
$709$	−12.5589	−0.471660	−0.235830	+	0.971794i	$0.575781\pi$
$710$	−0.615009	−0.0230809
$711$	−1.40819	−0.0528114
$712$	6.63706	0.248734
$713$	−53.0869	−1.98812
$714$	7.38441	0.276354
$715$	6.01644	0.225002
$716$	−6.25599	−0.233797
$717$	−35.1676	−1.31336
$718$	1.48220	0.0553152
$719$	26.8645	1.00188	0.500939	−	0.865483i	$-0.332988\pi$
$719$	26.8645	1.00188	0.500939	+	0.865483i	$0.332988\pi$
$720$	−0.0747613	−0.00278619
$721$	7.08403	0.263823
$722$	−18.0721	−0.672575
$723$	9.42526	0.350529
$724$	−12.5566	−0.466661
$725$	12.5560	0.466318
$726$	9.43585	0.350197
$727$	18.5262	0.687097	0.343549	−	0.939135i	$-0.388371\pi$
$727$	18.5262	0.687097	0.343549	+	0.939135i	$0.388371\pi$
$728$	−3.52451	−0.130627
$729$	25.2269	0.934330
$730$	−4.69209	−0.173662
$731$	36.8838	1.36420
$732$	−12.6452	−0.467381
$733$	−0.648071	−0.0239371	−0.0119685	−	0.999928i	$-0.503810\pi$
$733$	−0.648071	−0.0239371	−0.0119685	+	0.999928i	$0.503810\pi$
$734$	16.8628	0.622416
$735$	−0.753739	−0.0278021
$736$	−5.41079	−0.199444
$737$	24.0323	0.885240
$738$	0.666530	0.0245353
$739$	−5.44937	−0.200458	−0.100229	−	0.994964i	$-0.531958\pi$
$739$	−5.44937	−0.200458	−0.100229	+	0.994964i	$0.531958\pi$
$740$	4.55557	0.167466
$741$	6.05115	0.222295
$742$	0.619030	0.0227253
$743$	23.1793	0.850366	0.425183	−	0.905107i	$-0.360210\pi$
$743$	23.1793	0.850366	0.425183	+	0.905107i	$0.360210\pi$
$744$	17.4872	0.641113
$745$	6.51548	0.238709
$746$	6.10736	0.223606
$747$	−1.10658	−0.0404876
$748$	16.7238	0.611484
$749$	4.59451	0.167880
$750$	7.40260	0.270305
$751$	30.6142	1.11713	0.558565	−	0.829461i	$-0.311352\pi$
$751$	30.6142	1.11713	0.558565	+	0.829461i	$0.311352\pi$
$752$	−3.03453	−0.110658
$753$	−47.5872	−1.73417
$754$	−9.17904	−0.334281
$755$	−6.55923	−0.238715
$756$	5.03197	0.183011
$757$	−51.3196	−1.86524	−0.932621	−	0.360858i	$-0.882484\pi$
$757$	−51.3196	−1.86524	−0.932621	+	0.360858i	$0.882484\pi$
$758$	10.0052	0.363405
$759$	38.9286	1.41302
$760$	−0.407355	−0.0147763
$761$	−35.6294	−1.29157	−0.645783	−	0.763521i	$-0.723469\pi$
$761$	−35.6294	−1.29157	−0.645783	+	0.763521i	$0.723469\pi$
$762$	25.8987	0.938209
$763$	0.160480	0.00580978
$764$	10.9486	0.396105
$765$	0.309741	0.0111987
$766$	29.3683	1.06112
$767$	20.4787	0.739444
$768$	1.78235	0.0643152
$769$	42.0799	1.51744	0.758720	−	0.651417i	$-0.225825\pi$
$769$	42.0799	1.51744	0.758720	+	0.651417i	$0.225825\pi$
$770$	−1.70703	−0.0615171
$771$	−32.0011	−1.15249
$772$	24.3149	0.875112
$773$	−14.0504	−0.505357	−0.252678	−	0.967550i	$-0.581311\pi$
$773$	−14.0504	−0.505357	−0.252678	+	0.967550i	$0.581311\pi$
$774$	−1.57385	−0.0565709
$775$	−47.3019	−1.69913
$776$	13.5480	0.486346
$777$	19.2004	0.688810
$778$	3.90984	0.140175
$779$	3.63175	0.130121
$780$	−2.65656	−0.0951200
$781$	−5.87041	−0.210060
$782$	22.4172	0.801638
$783$	13.1050	0.468334
$784$	1.00000	0.0357143
$785$	−1.56877	−0.0559918
$786$	37.1295	1.32436
$787$	17.4884	0.623394	0.311697	−	0.950182i	$-0.399103\pi$
$787$	17.4884	0.623394	0.311697	+	0.950182i	$0.399103\pi$
$788$	−16.8963	−0.601905
$789$	−6.67350	−0.237583
$790$	3.36853	0.119847
$791$	5.91832	0.210431
$792$	−0.713615	−0.0253572
$793$	−25.0052	−0.887961
$794$	4.42048	0.156877
$795$	0.466587	0.0165481
$796$	5.12555	0.181670
$797$	40.1193	1.42110	0.710549	−	0.703648i	$-0.248447\pi$
$797$	40.1193	1.42110	0.710549	+	0.703648i	$0.248447\pi$
$798$	−1.71688	−0.0607769
$799$	12.5722	0.444774
$800$	−4.82116	−0.170454
$801$	1.17334	0.0414581
$802$	−21.1271	−0.746025
$803$	−44.7872	−1.58051
$804$	−10.6114	−0.374237
$805$	−2.28817	−0.0806472
$806$	34.5800	1.21803
$807$	−32.1983	−1.13343
$808$	−6.99828	−0.246199
$809$	−16.7445	−0.588707	−0.294353	−	0.955697i	$-0.595104\pi$
$809$	−16.7445	−0.588707	−0.294353	+	0.955697i	$0.595104\pi$
$810$	4.01707	0.141146
$811$	−5.62720	−0.197598	−0.0987988	−	0.995107i	$-0.531500\pi$
$811$	−5.62720	−0.197598	−0.0987988	+	0.995107i	$0.531500\pi$
$812$	2.60435	0.0913947
$813$	33.3848	1.17085
$814$	43.4841	1.52412
$815$	0.462429	0.0161982
$816$	−7.38441	−0.258506
$817$	−8.57550	−0.300019
$818$	−16.0468	−0.561063
$819$	−0.623086	−0.0217724
$820$	−1.59440	−0.0556789
$821$	34.4505	1.20233	0.601165	−	0.799125i	$-0.294703\pi$
$821$	34.4505	1.20233	0.601165	+	0.799125i	$0.294703\pi$
$822$	5.06799	0.176766
$823$	45.0864	1.57161	0.785806	−	0.618473i	$-0.212248\pi$
$823$	45.0864	1.57161	0.785806	+	0.618473i	$0.212248\pi$
$824$	−7.08403	−0.246784
$825$	34.6865	1.20763
$826$	−5.81038	−0.202169
$827$	20.5786	0.715588	0.357794	−	0.933801i	$-0.383529\pi$
$827$	20.5786	0.715588	0.357794	+	0.933801i	$0.383529\pi$
$828$	−0.956555	−0.0332426
$829$	15.5978	0.541733	0.270866	−	0.962617i	$-0.412690\pi$
$829$	15.5978	0.541733	0.270866	+	0.962617i	$0.412690\pi$
$830$	2.64704	0.0918800
$831$	−46.6379	−1.61785
$832$	3.52451	0.122190
$833$	−4.14306	−0.143549
$834$	−28.8086	−0.997561
$835$	6.09870	0.211054
$836$	−3.88830	−0.134480
$837$	−49.3701	−1.70648
$838$	−18.6243	−0.643367
$839$	−27.5790	−0.952133	−0.476066	−	0.879409i	$-0.657938\pi$
$839$	−27.5790	−0.952133	−0.476066	+	0.879409i	$0.657938\pi$
$840$	0.753739	0.0260065
$841$	−22.2174	−0.766116
$842$	18.3598	0.632719
$843$	−29.9423	−1.03127
$844$	4.28659	0.147550
$845$	0.244372	0.00840665
$846$	−0.536464	−0.0184440
$847$	−5.29404	−0.181905
$848$	−0.619030	−0.0212576
$849$	33.0353	1.13377
$850$	19.9744	0.685116
$851$	58.2876	1.99807
$852$	2.59208	0.0888032
$853$	−51.7947	−1.77342	−0.886708	−	0.462330i	$-0.847014\pi$
$853$	−51.7947	−1.77342	−0.886708	+	0.462330i	$0.847014\pi$
$854$	7.09467	0.242775
$855$	−0.0720150	−0.00246286
$856$	−4.59451	−0.157037
$857$	37.4500	1.27927	0.639633	−	0.768680i	$-0.279086\pi$
$857$	37.4500	1.27927	0.639633	+	0.768680i	$0.279086\pi$
$858$	−25.3575	−0.865691
$859$	−17.6808	−0.603260	−0.301630	−	0.953425i	$-0.597531\pi$
$859$	−17.6808	−0.603260	−0.301630	+	0.953425i	$0.597531\pi$
$860$	3.76479	0.128378
$861$	−6.71992	−0.229014
$862$	1.00000	0.0340601
$863$	−41.4491	−1.41094	−0.705472	−	0.708738i	$-0.749265\pi$
$863$	−41.4491	−1.41094	−0.705472	+	0.708738i	$0.749265\pi$
$864$	−5.03197	−0.171191
$865$	−0.345073	−0.0117328
$866$	9.24114	0.314027
$867$	0.294029	0.00998576
$868$	−9.81130	−0.333017
$869$	32.1534	1.09073
$870$	1.96300	0.0665519
$871$	−20.9835	−0.711000
$872$	−0.160480	−0.00543455
$873$	2.39511	0.0810623
$874$	−5.21202	−0.176299
$875$	−4.15327	−0.140406
$876$	19.7758	0.668162
$877$	0.790851	0.0267051	0.0133526	−	0.999911i	$-0.495750\pi$
$877$	0.790851	0.0267051	0.0133526	+	0.999911i	$0.495750\pi$
$878$	−6.47302	−0.218454
$879$	3.76951	0.127142
$880$	1.70703	0.0575440
$881$	−29.2996	−0.987128	−0.493564	−	0.869709i	$-0.664306\pi$
$881$	−29.2996	−0.987128	−0.493564	+	0.869709i	$0.664306\pi$
$882$	0.176787	0.00595272
$883$	7.71758	0.259717	0.129859	−	0.991533i	$-0.458548\pi$
$883$	7.71758	0.259717	0.129859	+	0.991533i	$0.458548\pi$
$884$	−14.6022	−0.491127
$885$	−4.37951	−0.147216
$886$	28.2967	0.950647
$887$	−10.2535	−0.344278	−0.172139	−	0.985073i	$-0.555068\pi$
$887$	−10.2535	−0.344278	−0.172139	+	0.985073i	$0.555068\pi$
$888$	−19.2004	−0.644323
$889$	−14.5306	−0.487340
$890$	−2.80675	−0.0940823
$891$	38.3440	1.28457
$892$	0.883182	0.0295711
$893$	−2.92306	−0.0978163
$894$	−27.4608	−0.918427
$895$	2.64559	0.0884324
$896$	−1.00000	−0.0334077
$897$	−33.9901	−1.13490
$898$	−14.9250	−0.498054
$899$	−25.5521	−0.852209
$900$	−0.852318	−0.0284106
$901$	2.56468	0.0854418
$902$	−15.2189	−0.506736
$903$	15.8675	0.528036
$904$	−5.91832	−0.196840
$905$	5.31004	0.176512
$906$	27.6452	0.918450
$907$	−51.3375	−1.70463	−0.852317	−	0.523025i	$-0.824803\pi$
$907$	−51.3375	−1.70463	−0.852317	+	0.523025i	$0.824803\pi$
$908$	4.94150	0.163989
$909$	−1.23720	−0.0410354
$910$	1.49048	0.0494088
$911$	−8.91927	−0.295509	−0.147754	−	0.989024i	$-0.547204\pi$
$911$	−8.91927	−0.295509	−0.147754	+	0.989024i	$0.547204\pi$
$912$	1.71688	0.0568516
$913$	25.2666	0.836203
$914$	18.3268	0.606198
$915$	5.34754	0.176784
$916$	−14.7914	−0.488720
$917$	−20.8317	−0.687923
$918$	20.8478	0.688078
$919$	−36.8135	−1.21437	−0.607183	−	0.794562i	$-0.707701\pi$
$919$	−36.8135	−1.21437	−0.607183	+	0.794562i	$0.707701\pi$
$920$	2.28817	0.0754386
$921$	5.03992	0.166071
$922$	34.7634	1.14487
$923$	5.12569	0.168714
$924$	7.19463	0.236686
$925$	51.9359	1.70764
$926$	25.4711	0.837031
$927$	−1.25236	−0.0411330
$928$	−2.60435	−0.0854919
$929$	−16.7965	−0.551074	−0.275537	−	0.961290i	$-0.588856\pi$
$929$	−16.7965	−0.551074	−0.275537	+	0.961290i	$0.588856\pi$
$930$	−7.39517	−0.242497
$931$	0.963265	0.0315697
$932$	2.30554	0.0755205
$933$	43.0353	1.40891
$934$	−14.8374	−0.485494
$935$	−7.07234	−0.231290
$936$	0.623086	0.0203662
$937$	35.1899	1.14960	0.574801	−	0.818293i	$-0.305079\pi$
$937$	35.1899	1.14960	0.574801	+	0.818293i	$0.305079\pi$
$938$	5.95361	0.194392
$939$	43.2439	1.41121
$940$	1.28327	0.0418557
$941$	51.2147	1.66955	0.834776	−	0.550590i	$-0.185597\pi$
$941$	51.2147	1.66955	0.834776	+	0.550590i	$0.185597\pi$
$942$	6.61189	0.215427
$943$	−20.4000	−0.664316
$944$	5.81038	0.189112
$945$	−2.12797	−0.0692228
$946$	35.9359	1.16838
$947$	12.3910	0.402654	0.201327	−	0.979524i	$-0.435475\pi$
$947$	12.3910	0.402654	0.201327	+	0.979524i	$0.435475\pi$
$948$	−14.1973	−0.461108
$949$	39.1055	1.26942
$950$	−4.64406	−0.150673
$951$	25.0701	0.812953
$952$	4.14306	0.134277
$953$	−52.3911	−1.69711	−0.848557	−	0.529103i	$-0.822528\pi$
$953$	−52.3911	−1.69711	−0.848557	+	0.529103i	$0.822528\pi$
$954$	−0.109436	−0.00354313
$955$	−4.63003	−0.149824
$956$	−19.7310	−0.638146
$957$	18.7373	0.605692
$958$	8.81699	0.284864
$959$	−2.84342	−0.0918189
$960$	−0.753739	−0.0243268
$961$	65.2617	2.10522
$962$	−37.9677	−1.22413
$963$	−0.812248	−0.0261743
$964$	5.28809	0.170318
$965$	−10.2825	−0.331006
$966$	9.64394	0.310289
$967$	20.4632	0.658052	0.329026	−	0.944321i	$-0.393280\pi$
$967$	20.4632	0.658052	0.329026	+	0.944321i	$0.393280\pi$
$968$	5.29404	0.170157
$969$	−7.11314	−0.228507
$970$	−5.72932	−0.183957
$971$	24.5998	0.789444	0.394722	−	0.918801i	$-0.370841\pi$
$971$	24.5998	0.789444	0.394722	+	0.918801i	$0.370841\pi$
$972$	−1.83487	−0.0588536
$973$	16.1632	0.518170
$974$	−31.8614	−1.02090
$975$	−30.2862	−0.969933
$976$	−7.09467	−0.227095
$977$	−7.44749	−0.238266	−0.119133	−	0.992878i	$-0.538012\pi$
$977$	−7.44749	−0.238266	−0.119133	+	0.992878i	$0.538012\pi$
$978$	−1.94900	−0.0623221
$979$	−26.7911	−0.856247
$980$	−0.422890	−0.0135087
$981$	−0.0283708	−0.000905810 0
$982$	−30.1444	−0.961946
$983$	31.9662	1.01956	0.509781	−	0.860304i	$-0.329726\pi$
$983$	31.9662	1.01956	0.509781	+	0.860304i	$0.329726\pi$
$984$	6.71992	0.214223
$985$	7.14526	0.227667
$986$	10.7900	0.343623
$987$	5.40860	0.172158
$988$	3.39503	0.108010
$989$	48.1697	1.53171
$990$	0.301781	0.00959122
$991$	46.8612	1.48860	0.744298	−	0.667848i	$-0.232784\pi$
$991$	46.8612	1.48860	0.744298	+	0.667848i	$0.232784\pi$
$992$	9.81130	0.311509
$993$	−9.95114	−0.315790
$994$	−1.45430	−0.0461276
$995$	−2.16754	−0.0687157
$996$	−11.1565	−0.353506
$997$	6.12071	0.193845	0.0969224	−	0.995292i	$-0.469100\pi$
$997$	6.12071	0.193845	0.0969224	+	0.995292i	$0.469100\pi$
$998$	12.8188	0.405771
$999$	54.2068	1.71503

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.17	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.17	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.78235 q^{3} +1.00000 q^{4} -0.422890 q^{5} +1.78235 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.176787 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.78235 q^{3} +1.00000 q^{4} -0.422890 q^{5} +1.78235 q^{6} -1.00000 q^{7} +1.00000 q^{8} +0.176787 q^{9} -0.422890 q^{10} -4.03659 q^{11} +1.78235 q^{12} +3.52451 q^{13} -1.00000 q^{14} -0.753739 q^{15} +1.00000 q^{16} -4.14306 q^{17} +0.176787 q^{18} +0.963265 q^{19} -0.422890 q^{20} -1.78235 q^{21} -4.03659 q^{22} -5.41079 q^{23} +1.78235 q^{24} -4.82116 q^{25} +3.52451 q^{26} -5.03197 q^{27} -1.00000 q^{28} -2.60435 q^{29} -0.753739 q^{30} +9.81130 q^{31} +1.00000 q^{32} -7.19463 q^{33} -4.14306 q^{34} +0.422890 q^{35} +0.176787 q^{36} -10.7725 q^{37} +0.963265 q^{38} +6.28192 q^{39} -0.422890 q^{40} +3.77025 q^{41} -1.78235 q^{42} -8.90254 q^{43} -4.03659 q^{44} -0.0747613 q^{45} -5.41079 q^{46} -3.03453 q^{47} +1.78235 q^{48} +1.00000 q^{49} -4.82116 q^{50} -7.38441 q^{51} +3.52451 q^{52} -0.619030 q^{53} -5.03197 q^{54} +1.70703 q^{55} -1.00000 q^{56} +1.71688 q^{57} -2.60435 q^{58} +5.81038 q^{59} -0.753739 q^{60} -7.09467 q^{61} +9.81130 q^{62} -0.176787 q^{63} +1.00000 q^{64} -1.49048 q^{65} -7.19463 q^{66} -5.95361 q^{67} -4.14306 q^{68} -9.64394 q^{69} +0.422890 q^{70} +1.45430 q^{71} +0.176787 q^{72} +11.0953 q^{73} -10.7725 q^{74} -8.59302 q^{75} +0.963265 q^{76} +4.03659 q^{77} +6.28192 q^{78} -7.96550 q^{79} -0.422890 q^{80} -9.49911 q^{81} +3.77025 q^{82} -6.25940 q^{83} -1.78235 q^{84} +1.75206 q^{85} -8.90254 q^{86} -4.64187 q^{87} -4.03659 q^{88} +6.63706 q^{89} -0.0747613 q^{90} -3.52451 q^{91} -5.41079 q^{92} +17.4872 q^{93} -3.03453 q^{94} -0.407355 q^{95} +1.78235 q^{96} +13.5480 q^{97} +1.00000 q^{98} -0.713615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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