LMFDB - Embedded newform 4026.2.a.n.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.652704 q^{5} -1.00000 q^{6} -1.53209 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.652704 q^{5} -1.00000 q^{6} -1.53209 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.652704 q^{10} +1.00000 q^{11} +1.00000 q^{12} +0.879385 q^{13} +1.53209 q^{14} -0.652704 q^{15} +1.00000 q^{16} +0.305407 q^{17} -1.00000 q^{18} +2.94356 q^{19} -0.652704 q^{20} -1.53209 q^{21} -1.00000 q^{22} -0.120615 q^{23} -1.00000 q^{24} -4.57398 q^{25} -0.879385 q^{26} +1.00000 q^{27} -1.53209 q^{28} -3.98545 q^{29} +0.652704 q^{30} -7.92127 q^{31} -1.00000 q^{32} +1.00000 q^{33} -0.305407 q^{34} +1.00000 q^{35} +1.00000 q^{36} -10.7023 q^{37} -2.94356 q^{38} +0.879385 q^{39} +0.652704 q^{40} -5.69459 q^{41} +1.53209 q^{42} +5.86484 q^{43} +1.00000 q^{44} -0.652704 q^{45} +0.120615 q^{46} +4.32770 q^{47} +1.00000 q^{48} -4.65270 q^{49} +4.57398 q^{50} +0.305407 q^{51} +0.879385 q^{52} +11.5398 q^{53} -1.00000 q^{54} -0.652704 q^{55} +1.53209 q^{56} +2.94356 q^{57} +3.98545 q^{58} -3.14290 q^{59} -0.652704 q^{60} -1.00000 q^{61} +7.92127 q^{62} -1.53209 q^{63} +1.00000 q^{64} -0.573978 q^{65} -1.00000 q^{66} +3.11381 q^{67} +0.305407 q^{68} -0.120615 q^{69} -1.00000 q^{70} +14.0496 q^{71} -1.00000 q^{72} -10.8084 q^{73} +10.7023 q^{74} -4.57398 q^{75} +2.94356 q^{76} -1.53209 q^{77} -0.879385 q^{78} -2.87939 q^{79} -0.652704 q^{80} +1.00000 q^{81} +5.69459 q^{82} +2.55169 q^{83} -1.53209 q^{84} -0.199340 q^{85} -5.86484 q^{86} -3.98545 q^{87} -1.00000 q^{88} -7.55943 q^{89} +0.652704 q^{90} -1.34730 q^{91} -0.120615 q^{92} -7.92127 q^{93} -4.32770 q^{94} -1.92127 q^{95} -1.00000 q^{96} +6.90167 q^{97} +4.65270 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{26} + 3 q^{27} + 6 q^{29} + 3 q^{30} - 15 q^{31} - 3 q^{32} + 3 q^{33} - 3 q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 15 q^{41} - 6 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{46} + 9 q^{47} + 3 q^{48} - 15 q^{49} + 6 q^{50} + 3 q^{51} - 3 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 6 q^{57} - 6 q^{58} - 9 q^{59} - 3 q^{60} - 3 q^{61} + 15 q^{62} + 3 q^{64} + 6 q^{65} - 3 q^{66} - 27 q^{67} + 3 q^{68} - 6 q^{69} - 3 q^{70} + 15 q^{71} - 3 q^{72} + 6 q^{73} + 6 q^{74} - 6 q^{75} - 6 q^{76} + 3 q^{78} - 3 q^{79} - 3 q^{80} + 3 q^{81} + 15 q^{82} + 6 q^{83} - 15 q^{85} + 6 q^{86} + 6 q^{87} - 3 q^{88} + 3 q^{89} + 3 q^{90} - 3 q^{91} - 6 q^{92} - 15 q^{93} - 9 q^{94} + 3 q^{95} - 3 q^{96} + 9 q^{97} + 15 q^{98} + 3 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^26 + 3 * q^27 + 6 * q^29 + 3 * q^30 - 15 * q^31 - 3 * q^32 + 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 15 * q^41 - 6 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^46 + 9 * q^47 + 3 * q^48 - 15 * q^49 + 6 * q^50 + 3 * q^51 - 3 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 6 * q^57 - 6 * q^58 - 9 * q^59 - 3 * q^60 - 3 * q^61 + 15 * q^62 + 3 * q^64 + 6 * q^65 - 3 * q^66 - 27 * q^67 + 3 * q^68 - 6 * q^69 - 3 * q^70 + 15 * q^71 - 3 * q^72 + 6 * q^73 + 6 * q^74 - 6 * q^75 - 6 * q^76 + 3 * q^78 - 3 * q^79 - 3 * q^80 + 3 * q^81 + 15 * q^82 + 6 * q^83 - 15 * q^85 + 6 * q^86 + 6 * q^87 - 3 * q^88 + 3 * q^89 + 3 * q^90 - 3 * q^91 - 6 * q^92 - 15 * q^93 - 9 * q^94 + 3 * q^95 - 3 * q^96 + 9 * q^97 + 15 * q^98 + 3 * 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
$5$	−0.652704	−0.291898	−0.145949	−	0.989292i	$-0.546624\pi$
$5$	−0.652704	−0.291898	−0.145949	+	0.989292i	$0.546624\pi$
$6$	−1.00000	−0.408248
$7$	−1.53209	−0.579075	−0.289538	−	0.957167i	$-0.593502\pi$
$7$	−1.53209	−0.579075	−0.289538	+	0.957167i	$0.593502\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.652704	0.206403
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.00000	0.288675
$13$	0.879385	0.243898	0.121949	−	0.992536i	$-0.461086\pi$
$13$	0.879385	0.243898	0.121949	+	0.992536i	$0.461086\pi$
$14$	1.53209	0.409468
$15$	−0.652704	−0.168527
$16$	1.00000	0.250000
$17$	0.305407	0.0740721	0.0370361	−	0.999314i	$-0.488208\pi$
$17$	0.305407	0.0740721	0.0370361	+	0.999314i	$0.488208\pi$
$18$	−1.00000	−0.235702
$19$	2.94356	0.675300	0.337650	−	0.941272i	$-0.390368\pi$
$19$	2.94356	0.675300	0.337650	+	0.941272i	$0.390368\pi$
$20$	−0.652704	−0.145949
$21$	−1.53209	−0.334329
$22$	−1.00000	−0.213201
$23$	−0.120615	−0.0251499	−0.0125750	−	0.999921i	$-0.504003\pi$
$23$	−0.120615	−0.0251499	−0.0125750	+	0.999921i	$0.504003\pi$
$24$	−1.00000	−0.204124
$25$	−4.57398	−0.914796
$26$	−0.879385	−0.172462
$27$	1.00000	0.192450
$28$	−1.53209	−0.289538
$29$	−3.98545	−0.740080	−0.370040	−	0.929016i	$-0.620656\pi$
$29$	−3.98545	−0.740080	−0.370040	+	0.929016i	$0.620656\pi$
$30$	0.652704	0.119167
$31$	−7.92127	−1.42270	−0.711351	−	0.702836i	$-0.751917\pi$
$31$	−7.92127	−1.42270	−0.711351	+	0.702836i	$0.751917\pi$
$32$	−1.00000	−0.176777
$33$	1.00000	0.174078
$34$	−0.305407	−0.0523769
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−10.7023	−1.75945	−0.879726	−	0.475480i	$-0.842274\pi$
$37$	−10.7023	−1.75945	−0.879726	+	0.475480i	$0.842274\pi$
$38$	−2.94356	−0.477509
$39$	0.879385	0.140814
$40$	0.652704	0.103202
$41$	−5.69459	−0.889346	−0.444673	−	0.895693i	$-0.646680\pi$
$41$	−5.69459	−0.889346	−0.444673	+	0.895693i	$0.646680\pi$
$42$	1.53209	0.236406
$43$	5.86484	0.894379	0.447190	−	0.894439i	$-0.352425\pi$
$43$	5.86484	0.894379	0.447190	+	0.894439i	$0.352425\pi$
$44$	1.00000	0.150756
$45$	−0.652704	−0.0972993
$46$	0.120615	0.0177837
$47$	4.32770	0.631259	0.315630	−	0.948882i	$-0.397784\pi$
$47$	4.32770	0.631259	0.315630	+	0.948882i	$0.397784\pi$
$48$	1.00000	0.144338
$49$	−4.65270	−0.664672
$50$	4.57398	0.646858
$51$	0.305407	0.0427656
$52$	0.879385	0.121949
$53$	11.5398	1.58512	0.792559	−	0.609796i	$-0.208748\pi$
$53$	11.5398	1.58512	0.792559	+	0.609796i	$0.208748\pi$
$54$	−1.00000	−0.136083
$55$	−0.652704	−0.0880105
$56$	1.53209	0.204734
$57$	2.94356	0.389884
$58$	3.98545	0.523315
$59$	−3.14290	−0.409171	−0.204586	−	0.978849i	$-0.565585\pi$
$59$	−3.14290	−0.409171	−0.204586	+	0.978849i	$0.565585\pi$
$60$	−0.652704	−0.0842637
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	7.92127	1.00600
$63$	−1.53209	−0.193025
$64$	1.00000	0.125000
$65$	−0.573978	−0.0711932
$66$	−1.00000	−0.123091
$67$	3.11381	0.380412	0.190206	−	0.981744i	$-0.439084\pi$
$67$	3.11381	0.380412	0.190206	+	0.981744i	$0.439084\pi$
$68$	0.305407	0.0370361
$69$	−0.120615	−0.0145203
$70$	−1.00000	−0.119523
$71$	14.0496	1.66738	0.833692	−	0.552229i	$-0.186223\pi$
$71$	14.0496	1.66738	0.833692	+	0.552229i	$0.186223\pi$
$72$	−1.00000	−0.117851
$73$	−10.8084	−1.26503	−0.632514	−	0.774549i	$-0.717977\pi$
$73$	−10.8084	−1.26503	−0.632514	+	0.774549i	$0.717977\pi$
$74$	10.7023	1.24412
$75$	−4.57398	−0.528157
$76$	2.94356	0.337650
$77$	−1.53209	−0.174598
$78$	−0.879385	−0.0995708
$79$	−2.87939	−0.323956	−0.161978	−	0.986794i	$-0.551787\pi$
$79$	−2.87939	−0.323956	−0.161978	+	0.986794i	$0.551787\pi$
$80$	−0.652704	−0.0729745
$81$	1.00000	0.111111
$82$	5.69459	0.628863
$83$	2.55169	0.280084	0.140042	−	0.990146i	$-0.455276\pi$
$83$	2.55169	0.280084	0.140042	+	0.990146i	$0.455276\pi$
$84$	−1.53209	−0.167165
$85$	−0.199340	−0.0216215
$86$	−5.86484	−0.632422
$87$	−3.98545	−0.427285
$88$	−1.00000	−0.106600
$89$	−7.55943	−0.801298	−0.400649	−	0.916232i	$-0.631215\pi$
$89$	−7.55943	−0.801298	−0.400649	+	0.916232i	$0.631215\pi$
$90$	0.652704	0.0688010
$91$	−1.34730	−0.141235
$92$	−0.120615	−0.0125750
$93$	−7.92127	−0.821398
$94$	−4.32770	−0.446368
$95$	−1.92127	−0.197119
$96$	−1.00000	−0.102062
$97$	6.90167	0.700759	0.350379	−	0.936608i	$-0.386053\pi$
$97$	6.90167	0.700759	0.350379	+	0.936608i	$0.386053\pi$
$98$	4.65270	0.469994
$99$	1.00000	0.100504
$100$	−4.57398	−0.457398
$101$	8.49525	0.845309	0.422655	−	0.906291i	$-0.361098\pi$
$101$	8.49525	0.845309	0.422655	+	0.906291i	$0.361098\pi$
$102$	−0.305407	−0.0302398
$103$	−2.52435	−0.248731	−0.124366	−	0.992236i	$-0.539690\pi$
$103$	−2.52435	−0.248731	−0.124366	+	0.992236i	$0.539690\pi$
$104$	−0.879385	−0.0862308
$105$	1.00000	0.0975900
$106$	−11.5398	−1.12085
$107$	−11.8307	−1.14372	−0.571858	−	0.820353i	$-0.693777\pi$
$107$	−11.8307	−1.14372	−0.571858	+	0.820353i	$0.693777\pi$
$108$	1.00000	0.0962250
$109$	15.5449	1.48893	0.744465	−	0.667662i	$-0.232705\pi$
$109$	15.5449	1.48893	0.744465	+	0.667662i	$0.232705\pi$
$110$	0.652704	0.0622329
$111$	−10.7023	−1.01582
$112$	−1.53209	−0.144769
$113$	−20.6040	−1.93826	−0.969131	−	0.246546i	$-0.920704\pi$
$113$	−20.6040	−1.93826	−0.969131	+	0.246546i	$0.920704\pi$
$114$	−2.94356	−0.275690
$115$	0.0787257	0.00734121
$116$	−3.98545	−0.370040
$117$	0.879385	0.0812992
$118$	3.14290	0.289328
$119$	−0.467911	−0.0428933
$120$	0.652704	0.0595834
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−5.69459	−0.513464
$124$	−7.92127	−0.711351
$125$	6.24897	0.558925
$126$	1.53209	0.136489
$127$	−19.3405	−1.71619	−0.858095	−	0.513490i	$-0.828352\pi$
$127$	−19.3405	−1.71619	−0.858095	+	0.513490i	$0.828352\pi$
$128$	−1.00000	−0.0883883
$129$	5.86484	0.516370
$130$	0.573978	0.0503412
$131$	−14.8452	−1.29703	−0.648517	−	0.761200i	$-0.724611\pi$
$131$	−14.8452	−1.29703	−0.648517	+	0.761200i	$0.724611\pi$
$132$	1.00000	0.0870388
$133$	−4.50980	−0.391049
$134$	−3.11381	−0.268992
$135$	−0.652704	−0.0561758
$136$	−0.305407	−0.0261885
$137$	−8.43376	−0.720545	−0.360272	−	0.932847i	$-0.617316\pi$
$137$	−8.43376	−0.720545	−0.360272	+	0.932847i	$0.617316\pi$
$138$	0.120615	0.0102674
$139$	0.396926	0.0336668	0.0168334	−	0.999858i	$-0.494642\pi$
$139$	0.396926	0.0336668	0.0168334	+	0.999858i	$0.494642\pi$
$140$	1.00000	0.0845154
$141$	4.32770	0.364458
$142$	−14.0496	−1.17902
$143$	0.879385	0.0735379
$144$	1.00000	0.0833333
$145$	2.60132	0.216028
$146$	10.8084	0.894510
$147$	−4.65270	−0.383749
$148$	−10.7023	−0.879726
$149$	20.2763	1.66110	0.830550	−	0.556944i	$-0.188026\pi$
$149$	20.2763	1.66110	0.830550	+	0.556944i	$0.188026\pi$
$150$	4.57398	0.373464
$151$	−4.12836	−0.335961	−0.167980	−	0.985790i	$-0.553725\pi$
$151$	−4.12836	−0.335961	−0.167980	+	0.985790i	$0.553725\pi$
$152$	−2.94356	−0.238754
$153$	0.305407	0.0246907
$154$	1.53209	0.123459
$155$	5.17024	0.415284
$156$	0.879385	0.0704072
$157$	−12.2713	−0.979353	−0.489677	−	0.871904i	$-0.662885\pi$
$157$	−12.2713	−0.979353	−0.489677	+	0.871904i	$0.662885\pi$
$158$	2.87939	0.229072
$159$	11.5398	0.915168
$160$	0.652704	0.0516008
$161$	0.184793	0.0145637
$162$	−1.00000	−0.0785674
$163$	−13.6604	−1.06997	−0.534984	−	0.844862i	$-0.679682\pi$
$163$	−13.6604	−1.06997	−0.534984	+	0.844862i	$0.679682\pi$
$164$	−5.69459	−0.444673
$165$	−0.652704	−0.0508129
$166$	−2.55169	−0.198049
$167$	−2.88444	−0.223204	−0.111602	−	0.993753i	$-0.535598\pi$
$167$	−2.88444	−0.223204	−0.111602	+	0.993753i	$0.535598\pi$
$168$	1.53209	0.118203
$169$	−12.2267	−0.940514
$170$	0.199340	0.0152887
$171$	2.94356	0.225100
$172$	5.86484	0.447190
$173$	9.04963	0.688031	0.344015	−	0.938964i	$-0.388213\pi$
$173$	9.04963	0.688031	0.344015	+	0.938964i	$0.388213\pi$
$174$	3.98545	0.302136
$175$	7.00774	0.529735
$176$	1.00000	0.0753778
$177$	−3.14290	−0.236235
$178$	7.55943	0.566603
$179$	−8.45605	−0.632035	−0.316017	−	0.948753i	$-0.602346\pi$
$179$	−8.45605	−0.632035	−0.316017	+	0.948753i	$0.602346\pi$
$180$	−0.652704	−0.0486497
$181$	−17.9067	−1.33100	−0.665498	−	0.746399i	$-0.731781\pi$
$181$	−17.9067	−1.33100	−0.665498	+	0.746399i	$0.731781\pi$
$182$	1.34730	0.0998683
$183$	−1.00000	−0.0739221
$184$	0.120615	0.00889184
$185$	6.98545	0.513581
$186$	7.92127	0.580816
$187$	0.305407	0.0223336
$188$	4.32770	0.315630
$189$	−1.53209	−0.111443
$190$	1.92127	0.139384
$191$	0.0273411	0.00197834	0.000989168	−	1.00000i	$-0.499685\pi$
$191$	0.0273411	0.00197834	0.000989168		1.00000i	$0.499685\pi$
$192$	1.00000	0.0721688
$193$	−0.985452	−0.0709344	−0.0354672	−	0.999371i	$-0.511292\pi$
$193$	−0.985452	−0.0709344	−0.0354672	+	0.999371i	$0.511292\pi$
$194$	−6.90167	−0.495511
$195$	−0.573978	−0.0411034
$196$	−4.65270	−0.332336
$197$	−16.3550	−1.16525	−0.582624	−	0.812742i	$-0.697974\pi$
$197$	−16.3550	−1.16525	−0.582624	+	0.812742i	$0.697974\pi$
$198$	−1.00000	−0.0710669
$199$	−14.4142	−1.02179	−0.510896	−	0.859642i	$-0.670686\pi$
$199$	−14.4142	−1.02179	−0.510896	+	0.859642i	$0.670686\pi$
$200$	4.57398	0.323429
$201$	3.11381	0.219631
$202$	−8.49525	−0.597724
$203$	6.10607	0.428562
$204$	0.305407	0.0213828
$205$	3.71688	0.259598
$206$	2.52435	0.175880
$207$	−0.120615	−0.00838331
$208$	0.879385	0.0609744
$209$	2.94356	0.203611
$210$	−1.00000	−0.0690066
$211$	−4.45336	−0.306582	−0.153291	−	0.988181i	$-0.548987\pi$
$211$	−4.45336	−0.306582	−0.153291	+	0.988181i	$0.548987\pi$
$212$	11.5398	0.792559
$213$	14.0496	0.962665
$214$	11.8307	0.808729
$215$	−3.82800	−0.261067
$216$	−1.00000	−0.0680414
$217$	12.1361	0.823852
$218$	−15.5449	−1.05283
$219$	−10.8084	−0.730364
$220$	−0.652704	−0.0440053
$221$	0.268571	0.0180660
$222$	10.7023	0.718294
$223$	−16.9736	−1.13664	−0.568318	−	0.822809i	$-0.692406\pi$
$223$	−16.9736	−1.13664	−0.568318	+	0.822809i	$0.692406\pi$
$224$	1.53209	0.102367
$225$	−4.57398	−0.304932
$226$	20.6040	1.37056
$227$	−0.226682	−0.0150454	−0.00752269	−	0.999972i	$-0.502395\pi$
$227$	−0.226682	−0.0150454	−0.00752269	+	0.999972i	$0.502395\pi$
$228$	2.94356	0.194942
$229$	−10.0523	−0.664276	−0.332138	−	0.943231i	$-0.607770\pi$
$229$	−10.0523	−0.664276	−0.332138	+	0.943231i	$0.607770\pi$
$230$	−0.0787257	−0.00519102
$231$	−1.53209	−0.100804
$232$	3.98545	0.261658
$233$	6.95130	0.455395	0.227698	−	0.973732i	$-0.426880\pi$
$233$	6.95130	0.455395	0.227698	+	0.973732i	$0.426880\pi$
$234$	−0.879385	−0.0574872
$235$	−2.82470	−0.184263
$236$	−3.14290	−0.204586
$237$	−2.87939	−0.187036
$238$	0.467911	0.0303302
$239$	15.6040	1.00934	0.504670	−	0.863313i	$-0.331614\pi$
$239$	15.6040	1.00934	0.504670	+	0.863313i	$0.331614\pi$
$240$	−0.652704	−0.0421318
$241$	−16.0077	−1.03115	−0.515575	−	0.856845i	$-0.672422\pi$
$241$	−16.0077	−1.03115	−0.515575	+	0.856845i	$0.672422\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	3.03684	0.194016
$246$	5.69459	0.363074
$247$	2.58853	0.164704
$248$	7.92127	0.503001
$249$	2.55169	0.161707
$250$	−6.24897	−0.395220
$251$	−23.3901	−1.47637	−0.738186	−	0.674598i	$-0.764317\pi$
$251$	−23.3901	−1.47637	−0.738186	+	0.674598i	$0.764317\pi$
$252$	−1.53209	−0.0965125
$253$	−0.120615	−0.00758298
$254$	19.3405	1.21353
$255$	−0.199340	−0.0124832
$256$	1.00000	0.0625000
$257$	−11.8821	−0.741183	−0.370592	−	0.928796i	$-0.620845\pi$
$257$	−11.8821	−0.741183	−0.370592	+	0.928796i	$0.620845\pi$
$258$	−5.86484	−0.365129
$259$	16.3969	1.01886
$260$	−0.573978	−0.0355966
$261$	−3.98545	−0.246693
$262$	14.8452	0.917142
$263$	12.5672	0.774925	0.387462	−	0.921885i	$-0.373352\pi$
$263$	12.5672	0.774925	0.387462	+	0.921885i	$0.373352\pi$
$264$	−1.00000	−0.0615457
$265$	−7.53209	−0.462693
$266$	4.50980	0.276514
$267$	−7.55943	−0.462630
$268$	3.11381	0.190206
$269$	−13.0000	−0.792624	−0.396312	−	0.918116i	$-0.629710\pi$
$269$	−13.0000	−0.792624	−0.396312	+	0.918116i	$0.629710\pi$
$270$	0.652704	0.0397223
$271$	−3.18479	−0.193462	−0.0967312	−	0.995311i	$-0.530839\pi$
$271$	−3.18479	−0.193462	−0.0967312	+	0.995311i	$0.530839\pi$
$272$	0.305407	0.0185180
$273$	−1.34730	−0.0815421
$274$	8.43376	0.509502
$275$	−4.57398	−0.275821
$276$	−0.120615	−0.00726016
$277$	27.3482	1.64320	0.821598	−	0.570067i	$-0.193083\pi$
$277$	27.3482	1.64320	0.821598	+	0.570067i	$0.193083\pi$
$278$	−0.396926	−0.0238061
$279$	−7.92127	−0.474234
$280$	−1.00000	−0.0597614
$281$	−24.0009	−1.43178	−0.715888	−	0.698215i	$-0.753978\pi$
$281$	−24.0009	−1.43178	−0.715888	+	0.698215i	$0.753978\pi$
$282$	−4.32770	−0.257711
$283$	−14.6878	−0.873098	−0.436549	−	0.899680i	$-0.643799\pi$
$283$	−14.6878	−0.873098	−0.436549	+	0.899680i	$0.643799\pi$
$284$	14.0496	0.833692
$285$	−1.92127	−0.113806
$286$	−0.879385	−0.0519991
$287$	8.72462	0.514998
$288$	−1.00000	−0.0589256
$289$	−16.9067	−0.994513
$290$	−2.60132	−0.152755
$291$	6.90167	0.404583
$292$	−10.8084	−0.632514
$293$	25.4561	1.48716	0.743579	−	0.668648i	$-0.233127\pi$
$293$	25.4561	1.48716	0.743579	+	0.668648i	$0.233127\pi$
$294$	4.65270	0.271351
$295$	2.05138	0.119436
$296$	10.7023	0.622060
$297$	1.00000	0.0580259
$298$	−20.2763	−1.17458
$299$	−0.106067	−0.00613400
$300$	−4.57398	−0.264079
$301$	−8.98545	−0.517913
$302$	4.12836	0.237560
$303$	8.49525	0.488039
$304$	2.94356	0.168825
$305$	0.652704	0.0373737
$306$	−0.305407	−0.0174590
$307$	9.67736	0.552316	0.276158	−	0.961112i	$-0.410939\pi$
$307$	9.67736	0.552316	0.276158	+	0.961112i	$0.410939\pi$
$308$	−1.53209	−0.0872989
$309$	−2.52435	−0.143605
$310$	−5.17024	−0.293650
$311$	13.8949	0.787906	0.393953	−	0.919131i	$-0.371107\pi$
$311$	13.8949	0.787906	0.393953	+	0.919131i	$0.371107\pi$
$312$	−0.879385	−0.0497854
$313$	10.2490	0.579306	0.289653	−	0.957132i	$-0.406460\pi$
$313$	10.2490	0.579306	0.289653	+	0.957132i	$0.406460\pi$
$314$	12.2713	0.692507
$315$	1.00000	0.0563436
$316$	−2.87939	−0.161978
$317$	29.9932	1.68459	0.842293	−	0.539020i	$-0.181205\pi$
$317$	29.9932	1.68459	0.842293	+	0.539020i	$0.181205\pi$
$318$	−11.5398	−0.647122
$319$	−3.98545	−0.223142
$320$	−0.652704	−0.0364872
$321$	−11.8307	−0.660325
$322$	−0.184793	−0.0102981
$323$	0.898986	0.0500209
$324$	1.00000	0.0555556
$325$	−4.02229	−0.223116
$326$	13.6604	0.756582
$327$	15.5449	0.859634
$328$	5.69459	0.314431
$329$	−6.63041	−0.365547
$330$	0.652704	0.0359302
$331$	−21.9760	−1.20791	−0.603954	−	0.797019i	$-0.706409\pi$
$331$	−21.9760	−1.20791	−0.603954	+	0.797019i	$0.706409\pi$
$332$	2.55169	0.140042
$333$	−10.7023	−0.586484
$334$	2.88444	0.157829
$335$	−2.03239	−0.111042
$336$	−1.53209	−0.0835823
$337$	11.8135	0.643520	0.321760	−	0.946821i	$-0.395726\pi$
$337$	11.8135	0.643520	0.321760	+	0.946821i	$0.395726\pi$
$338$	12.2267	0.665044
$339$	−20.6040	−1.11906
$340$	−0.199340	−0.0108108
$341$	−7.92127	−0.428961
$342$	−2.94356	−0.159170
$343$	17.8530	0.963970
$344$	−5.86484	−0.316211
$345$	0.0787257	0.00423845
$346$	−9.04963	−0.486511
$347$	9.02229	0.484342	0.242171	−	0.970234i	$-0.422141\pi$
$347$	9.02229	0.484342	0.242171	+	0.970234i	$0.422141\pi$
$348$	−3.98545	−0.213643
$349$	31.5776	1.69031	0.845155	−	0.534521i	$-0.179508\pi$
$349$	31.5776	1.69031	0.845155	+	0.534521i	$0.179508\pi$
$350$	−7.00774	−0.374580
$351$	0.879385	0.0469381
$352$	−1.00000	−0.0533002
$353$	18.3678	0.977621	0.488810	−	0.872390i	$-0.337431\pi$
$353$	18.3678	0.977621	0.488810	+	0.872390i	$0.337431\pi$
$354$	3.14290	0.167043
$355$	−9.17024	−0.486706
$356$	−7.55943	−0.400649
$357$	−0.467911	−0.0247645
$358$	8.45605	0.446916
$359$	3.40879	0.179909	0.0899544	−	0.995946i	$-0.471328\pi$
$359$	3.40879	0.179909	0.0899544	+	0.995946i	$0.471328\pi$
$360$	0.652704	0.0344005
$361$	−10.3354	−0.543970
$362$	17.9067	0.941157
$363$	1.00000	0.0524864
$364$	−1.34730	−0.0706175
$365$	7.05468	0.369259
$366$	1.00000	0.0522708
$367$	−34.8972	−1.82162	−0.910810	−	0.412825i	$-0.864542\pi$
$367$	−34.8972	−1.82162	−0.910810	+	0.412825i	$0.864542\pi$
$368$	−0.120615	−0.00628748
$369$	−5.69459	−0.296449
$370$	−6.98545	−0.363156
$371$	−17.6800	−0.917902
$372$	−7.92127	−0.410699
$373$	19.3996	1.00447	0.502237	−	0.864730i	$-0.332511\pi$
$373$	19.3996	1.00447	0.502237	+	0.864730i	$0.332511\pi$
$374$	−0.305407	−0.0157922
$375$	6.24897	0.322695
$376$	−4.32770	−0.223184
$377$	−3.50475	−0.180504
$378$	1.53209	0.0788021
$379$	−8.18716	−0.420546	−0.210273	−	0.977643i	$-0.567435\pi$
$379$	−8.18716	−0.420546	−0.210273	+	0.977643i	$0.567435\pi$
$380$	−1.92127	−0.0985593
$381$	−19.3405	−0.990843
$382$	−0.0273411	−0.00139889
$383$	28.2472	1.44337	0.721683	−	0.692224i	$-0.243369\pi$
$383$	28.2472	1.44337	0.721683	+	0.692224i	$0.243369\pi$
$384$	−1.00000	−0.0510310
$385$	1.00000	0.0509647
$386$	0.985452	0.0501582
$387$	5.86484	0.298126
$388$	6.90167	0.350379
$389$	1.24628	0.0631890	0.0315945	−	0.999501i	$-0.489941\pi$
$389$	1.24628	0.0631890	0.0315945	+	0.999501i	$0.489941\pi$
$390$	0.573978	0.0290645
$391$	−0.0368366	−0.00186291
$392$	4.65270	0.234997
$393$	−14.8452	−0.748843
$394$	16.3550	0.823955
$395$	1.87939	0.0945621
$396$	1.00000	0.0502519
$397$	−30.1043	−1.51089	−0.755446	−	0.655211i	$-0.772580\pi$
$397$	−30.1043	−1.51089	−0.755446	+	0.655211i	$0.772580\pi$
$398$	14.4142	0.722517
$399$	−4.50980	−0.225772
$400$	−4.57398	−0.228699
$401$	−0.285807	−0.0142725	−0.00713626	−	0.999975i	$-0.502272\pi$
$401$	−0.285807	−0.0142725	−0.00713626	+	0.999975i	$0.502272\pi$
$402$	−3.11381	−0.155303
$403$	−6.96585	−0.346994
$404$	8.49525	0.422655
$405$	−0.652704	−0.0324331
$406$	−6.10607	−0.303039
$407$	−10.7023	−0.530495
$408$	−0.305407	−0.0151199
$409$	−21.6509	−1.07057	−0.535285	−	0.844671i	$-0.679796\pi$
$409$	−21.6509	−1.07057	−0.535285	+	0.844671i	$0.679796\pi$
$410$	−3.71688	−0.183564
$411$	−8.43376	−0.416007
$412$	−2.52435	−0.124366
$413$	4.81521	0.236941
$414$	0.120615	0.00592789
$415$	−1.66550	−0.0817560
$416$	−0.879385	−0.0431154
$417$	0.396926	0.0194376
$418$	−2.94356	−0.143974
$419$	−20.5990	−1.00632	−0.503162	−	0.864192i	$-0.667830\pi$
$419$	−20.5990	−1.00632	−0.503162	+	0.864192i	$0.667830\pi$
$420$	1.00000	0.0487950
$421$	33.2104	1.61857	0.809287	−	0.587413i	$-0.199854\pi$
$421$	33.2104	1.61857	0.809287	+	0.587413i	$0.199854\pi$
$422$	4.45336	0.216786
$423$	4.32770	0.210420
$424$	−11.5398	−0.560424
$425$	−1.39693	−0.0677609
$426$	−14.0496	−0.680707
$427$	1.53209	0.0741430
$428$	−11.8307	−0.571858
$429$	0.879385	0.0424571
$430$	3.82800	0.184603
$431$	−34.7897	−1.67576	−0.837881	−	0.545853i	$-0.816206\pi$
$431$	−34.7897	−1.67576	−0.837881	+	0.545853i	$0.816206\pi$
$432$	1.00000	0.0481125
$433$	5.99050	0.287885	0.143943	−	0.989586i	$-0.454022\pi$
$433$	5.99050	0.287885	0.143943	+	0.989586i	$0.454022\pi$
$434$	−12.1361	−0.582551
$435$	2.60132	0.124724
$436$	15.5449	0.744465
$437$	−0.355037	−0.0169837
$438$	10.8084	0.516445
$439$	0.766511	0.0365836	0.0182918	−	0.999833i	$-0.494177\pi$
$439$	0.766511	0.0365836	0.0182918	+	0.999833i	$0.494177\pi$
$440$	0.652704	0.0311164
$441$	−4.65270	−0.221557
$442$	−0.268571	−0.0127746
$443$	−0.487511	−0.0231624	−0.0115812	−	0.999933i	$-0.503686\pi$
$443$	−0.487511	−0.0231624	−0.0115812	+	0.999933i	$0.503686\pi$
$444$	−10.7023	−0.507910
$445$	4.93407	0.233897
$446$	16.9736	0.803723
$447$	20.2763	0.959037
$448$	−1.53209	−0.0723844
$449$	27.6709	1.30587	0.652935	−	0.757414i	$-0.273538\pi$
$449$	27.6709	1.30587	0.652935	+	0.757414i	$0.273538\pi$
$450$	4.57398	0.215619
$451$	−5.69459	−0.268148
$452$	−20.6040	−0.969131
$453$	−4.12836	−0.193967
$454$	0.226682	0.0106387
$455$	0.879385	0.0412262
$456$	−2.94356	−0.137845
$457$	14.5868	0.682340	0.341170	−	0.940002i	$-0.389177\pi$
$457$	14.5868	0.682340	0.341170	+	0.940002i	$0.389177\pi$
$458$	10.0523	0.469714
$459$	0.305407	0.0142552
$460$	0.0787257	0.00367060
$461$	−16.1729	−0.753249	−0.376624	−	0.926366i	$-0.622915\pi$
$461$	−16.1729	−0.753249	−0.376624	+	0.926366i	$0.622915\pi$
$462$	1.53209	0.0712792
$463$	−20.3678	−0.946573	−0.473287	−	0.880908i	$-0.656933\pi$
$463$	−20.3678	−0.946573	−0.473287	+	0.880908i	$0.656933\pi$
$464$	−3.98545	−0.185020
$465$	5.17024	0.239764
$466$	−6.95130	−0.322013
$467$	14.5895	0.675120	0.337560	−	0.941304i	$-0.390398\pi$
$467$	14.5895	0.675120	0.337560	+	0.941304i	$0.390398\pi$
$468$	0.879385	0.0406496
$469$	−4.77063	−0.220287
$470$	2.82470	0.130294
$471$	−12.2713	−0.565430
$472$	3.14290	0.144664
$473$	5.86484	0.269666
$474$	2.87939	0.132255
$475$	−13.4638	−0.617761
$476$	−0.467911	−0.0214467
$477$	11.5398	0.528373
$478$	−15.6040	−0.713711
$479$	14.2344	0.650387	0.325194	−	0.945647i	$-0.394571\pi$
$479$	14.2344	0.650387	0.325194	+	0.945647i	$0.394571\pi$
$480$	0.652704	0.0297917
$481$	−9.41147	−0.429126
$482$	16.0077	0.729133
$483$	0.184793	0.00840835
$484$	1.00000	0.0454545
$485$	−4.50475	−0.204550
$486$	−1.00000	−0.0453609
$487$	−30.9469	−1.40234	−0.701168	−	0.712996i	$-0.747338\pi$
$487$	−30.9469	−1.40234	−0.701168	+	0.712996i	$0.747338\pi$
$488$	1.00000	0.0452679
$489$	−13.6604	−0.617747
$490$	−3.03684	−0.137190
$491$	36.8607	1.66350	0.831750	−	0.555150i	$-0.187339\pi$
$491$	36.8607	1.66350	0.831750	+	0.555150i	$0.187339\pi$
$492$	−5.69459	−0.256732
$493$	−1.21719	−0.0548193
$494$	−2.58853	−0.116463
$495$	−0.652704	−0.0293368
$496$	−7.92127	−0.355676
$497$	−21.5253	−0.965541
$498$	−2.55169	−0.114344
$499$	−20.7219	−0.927641	−0.463821	−	0.885929i	$-0.653522\pi$
$499$	−20.7219	−0.927641	−0.463821	+	0.885929i	$0.653522\pi$
$500$	6.24897	0.279462
$501$	−2.88444	−0.128867
$502$	23.3901	1.04395
$503$	41.9813	1.87186	0.935928	−	0.352193i	$-0.114564\pi$
$503$	41.9813	1.87186	0.935928	+	0.352193i	$0.114564\pi$
$504$	1.53209	0.0682447
$505$	−5.54488	−0.246744
$506$	0.120615	0.00536198
$507$	−12.2267	−0.543006
$508$	−19.3405	−0.858095
$509$	−7.16931	−0.317774	−0.158887	−	0.987297i	$-0.550791\pi$
$509$	−7.16931	−0.317774	−0.158887	+	0.987297i	$0.550791\pi$
$510$	0.199340	0.00882694
$511$	16.5594	0.732546
$512$	−1.00000	−0.0441942
$513$	2.94356	0.129961
$514$	11.8821	0.524096
$515$	1.64765	0.0726042
$516$	5.86484	0.258185
$517$	4.32770	0.190332
$518$	−16.3969	−0.720440
$519$	9.04963	0.397235
$520$	0.573978	0.0251706
$521$	−27.4638	−1.20321	−0.601605	−	0.798794i	$-0.705472\pi$
$521$	−27.4638	−1.20321	−0.601605	+	0.798794i	$0.705472\pi$
$522$	3.98545	0.174438
$523$	−2.61762	−0.114461	−0.0572303	−	0.998361i	$-0.518227\pi$
$523$	−2.61762	−0.114461	−0.0572303	+	0.998361i	$0.518227\pi$
$524$	−14.8452	−0.648517
$525$	7.00774	0.305843
$526$	−12.5672	−0.547955
$527$	−2.41921	−0.105383
$528$	1.00000	0.0435194
$529$	−22.9855	−0.999367
$530$	7.53209	0.327173
$531$	−3.14290	−0.136390
$532$	−4.50980	−0.195525
$533$	−5.00774	−0.216909
$534$	7.55943	0.327129
$535$	7.72193	0.333848
$536$	−3.11381	−0.134496
$537$	−8.45605	−0.364906
$538$	13.0000	0.560470
$539$	−4.65270	−0.200406
$540$	−0.652704	−0.0280879
$541$	21.9094	0.941959	0.470980	−	0.882144i	$-0.343901\pi$
$541$	21.9094	0.941959	0.470980	+	0.882144i	$0.343901\pi$
$542$	3.18479	0.136799
$543$	−17.9067	−0.768451
$544$	−0.305407	−0.0130942
$545$	−10.1462	−0.434616
$546$	1.34730	0.0576590
$547$	26.2104	1.12067	0.560337	−	0.828264i	$-0.310671\pi$
$547$	26.2104	1.12067	0.560337	+	0.828264i	$0.310671\pi$
$548$	−8.43376	−0.360272
$549$	−1.00000	−0.0426790
$550$	4.57398	0.195035
$551$	−11.7314	−0.499776
$552$	0.120615	0.00513371
$553$	4.41147	0.187595
$554$	−27.3482	−1.16191
$555$	6.98545	0.296516
$556$	0.396926	0.0168334
$557$	−34.2481	−1.45114	−0.725570	−	0.688148i	$-0.758424\pi$
$557$	−34.2481	−1.45114	−0.725570	+	0.688148i	$0.758424\pi$
$558$	7.92127	0.335334
$559$	5.15745	0.218137
$560$	1.00000	0.0422577
$561$	0.305407	0.0128943
$562$	24.0009	1.01242
$563$	22.5776	0.951532	0.475766	−	0.879572i	$-0.342171\pi$
$563$	22.5776	0.951532	0.475766	+	0.879572i	$0.342171\pi$
$564$	4.32770	0.182229
$565$	13.4483	0.565775
$566$	14.6878	0.617374
$567$	−1.53209	−0.0643417
$568$	−14.0496	−0.589509
$569$	−34.1043	−1.42973	−0.714864	−	0.699264i	$-0.753511\pi$
$569$	−34.1043	−1.42973	−0.714864	+	0.699264i	$0.753511\pi$
$570$	1.92127	0.0804733
$571$	−24.0128	−1.00490	−0.502452	−	0.864605i	$-0.667569\pi$
$571$	−24.0128	−1.00490	−0.502452	+	0.864605i	$0.667569\pi$
$572$	0.879385	0.0367689
$573$	0.0273411	0.00114219
$574$	−8.72462	−0.364159
$575$	0.551689	0.0230070
$576$	1.00000	0.0416667
$577$	34.9436	1.45472	0.727360	−	0.686256i	$-0.240747\pi$
$577$	34.9436	1.45472	0.727360	+	0.686256i	$0.240747\pi$
$578$	16.9067	0.703227
$579$	−0.985452	−0.0409540
$580$	2.60132	0.108014
$581$	−3.90941	−0.162190
$582$	−6.90167	−0.286084
$583$	11.5398	0.477931
$584$	10.8084	0.447255
$585$	−0.573978	−0.0237311
$586$	−25.4561	−1.05158
$587$	−20.1334	−0.830995	−0.415497	−	0.909594i	$-0.636392\pi$
$587$	−20.1334	−0.830995	−0.415497	+	0.909594i	$0.636392\pi$
$588$	−4.65270	−0.191874
$589$	−23.3168	−0.960751
$590$	−2.05138	−0.0844542
$591$	−16.3550	−0.672756
$592$	−10.7023	−0.439863
$593$	−2.87433	−0.118035	−0.0590174	−	0.998257i	$-0.518797\pi$
$593$	−2.87433	−0.118035	−0.0590174	+	0.998257i	$0.518797\pi$
$594$	−1.00000	−0.0410305
$595$	0.305407	0.0125205
$596$	20.2763	0.830550
$597$	−14.4142	−0.589932
$598$	0.106067	0.00433740
$599$	−10.4706	−0.427817	−0.213909	−	0.976854i	$-0.568619\pi$
$599$	−10.4706	−0.427817	−0.213909	+	0.976854i	$0.568619\pi$
$600$	4.57398	0.186732
$601$	−19.0101	−0.775438	−0.387719	−	0.921778i	$-0.626737\pi$
$601$	−19.0101	−0.775438	−0.387719	+	0.921778i	$0.626737\pi$
$602$	8.98545	0.366220
$603$	3.11381	0.126804
$604$	−4.12836	−0.167980
$605$	−0.652704	−0.0265362
$606$	−8.49525	−0.345096
$607$	−43.5066	−1.76588	−0.882940	−	0.469487i	$-0.844439\pi$
$607$	−43.5066	−1.76588	−0.882940	+	0.469487i	$0.844439\pi$
$608$	−2.94356	−0.119377
$609$	6.10607	0.247430
$610$	−0.652704	−0.0264272
$611$	3.80571	0.153963
$612$	0.305407	0.0123454
$613$	−19.3286	−0.780676	−0.390338	−	0.920672i	$-0.627642\pi$
$613$	−19.3286	−0.780676	−0.390338	+	0.920672i	$0.627642\pi$
$614$	−9.67736	−0.390546
$615$	3.71688	0.149879
$616$	1.53209	0.0617296
$617$	−6.05913	−0.243931	−0.121966	−	0.992534i	$-0.538920\pi$
$617$	−6.05913	−0.243931	−0.121966	+	0.992534i	$0.538920\pi$
$618$	2.52435	0.101544
$619$	15.3337	0.616313	0.308156	−	0.951336i	$-0.400288\pi$
$619$	15.3337	0.616313	0.308156	+	0.951336i	$0.400288\pi$
$620$	5.17024	0.207642
$621$	−0.120615	−0.00484010
$622$	−13.8949	−0.557133
$623$	11.5817	0.464012
$624$	0.879385	0.0352036
$625$	18.7912	0.751647
$626$	−10.2490	−0.409631
$627$	2.94356	0.117555
$628$	−12.2713	−0.489677
$629$	−3.26857	−0.130326
$630$	−1.00000	−0.0398410
$631$	36.5185	1.45378	0.726889	−	0.686755i	$-0.240966\pi$
$631$	36.5185	1.45378	0.726889	+	0.686755i	$0.240966\pi$
$632$	2.87939	0.114536
$633$	−4.45336	−0.177005
$634$	−29.9932	−1.19118
$635$	12.6236	0.500953
$636$	11.5398	0.457584
$637$	−4.09152	−0.162112
$638$	3.98545	0.157786
$639$	14.0496	0.555795
$640$	0.652704	0.0258004
$641$	28.1539	1.11201	0.556007	−	0.831178i	$-0.312333\pi$
$641$	28.1539	1.11201	0.556007	+	0.831178i	$0.312333\pi$
$642$	11.8307	0.466920
$643$	39.8262	1.57059	0.785297	−	0.619119i	$-0.212510\pi$
$643$	39.8262	1.57059	0.785297	+	0.619119i	$0.212510\pi$
$644$	0.184793	0.00728185
$645$	−3.82800	−0.150727
$646$	−0.898986	−0.0353701
$647$	−1.86484	−0.0733143	−0.0366572	−	0.999328i	$-0.511671\pi$
$647$	−1.86484	−0.0733143	−0.0366572	+	0.999328i	$0.511671\pi$
$648$	−1.00000	−0.0392837
$649$	−3.14290	−0.123370
$650$	4.02229	0.157767
$651$	12.1361	0.475651
$652$	−13.6604	−0.534984
$653$	−16.7297	−0.654683	−0.327341	−	0.944906i	$-0.606153\pi$
$653$	−16.7297	−0.654683	−0.327341	+	0.944906i	$0.606153\pi$
$654$	−15.5449	−0.607853
$655$	9.68954	0.378602
$656$	−5.69459	−0.222336
$657$	−10.8084	−0.421676
$658$	6.63041	0.258480
$659$	−19.6168	−0.764162	−0.382081	−	0.924129i	$-0.624792\pi$
$659$	−19.6168	−0.764162	−0.382081	+	0.924129i	$0.624792\pi$
$660$	−0.652704	−0.0254065
$661$	41.5016	1.61422	0.807112	−	0.590399i	$-0.201029\pi$
$661$	41.5016	1.61422	0.807112	+	0.590399i	$0.201029\pi$
$662$	21.9760	0.854120
$663$	0.268571	0.0104304
$664$	−2.55169	−0.0990247
$665$	2.94356	0.114146
$666$	10.7023	0.414707
$667$	0.480704	0.0186129
$668$	−2.88444	−0.111602
$669$	−16.9736	−0.656237
$670$	2.03239	0.0785182
$671$	−1.00000	−0.0386046
$672$	1.53209	0.0591016
$673$	13.4602	0.518851	0.259426	−	0.965763i	$-0.416467\pi$
$673$	13.4602	0.518851	0.259426	+	0.965763i	$0.416467\pi$
$674$	−11.8135	−0.455037
$675$	−4.57398	−0.176052
$676$	−12.2267	−0.470257
$677$	18.5844	0.714257	0.357128	−	0.934055i	$-0.383756\pi$
$677$	18.5844	0.714257	0.357128	+	0.934055i	$0.383756\pi$
$678$	20.6040	0.791292
$679$	−10.5740	−0.405792
$680$	0.199340	0.00764436
$681$	−0.226682	−0.00868646
$682$	7.92127	0.303321
$683$	−8.85204	−0.338714	−0.169357	−	0.985555i	$-0.554169\pi$
$683$	−8.85204	−0.338714	−0.169357	+	0.985555i	$0.554169\pi$
$684$	2.94356	0.112550
$685$	5.50475	0.210326
$686$	−17.8530	−0.681630
$687$	−10.0523	−0.383520
$688$	5.86484	0.223595
$689$	10.1480	0.386606
$690$	−0.0787257	−0.00299704
$691$	47.5690	1.80961	0.904806	−	0.425825i	$-0.140016\pi$
$691$	47.5690	1.80961	0.904806	+	0.425825i	$0.140016\pi$
$692$	9.04963	0.344015
$693$	−1.53209	−0.0581992
$694$	−9.02229	−0.342481
$695$	−0.259075	−0.00982728
$696$	3.98545	0.151068
$697$	−1.73917	−0.0658758
$698$	−31.5776	−1.19523
$699$	6.95130	0.262922
$700$	7.00774	0.264868
$701$	−24.5604	−0.927632	−0.463816	−	0.885932i	$-0.653520\pi$
$701$	−24.5604	−0.927632	−0.463816	+	0.885932i	$0.653520\pi$
$702$	−0.879385	−0.0331903
$703$	−31.5030	−1.18816
$704$	1.00000	0.0376889
$705$	−2.82470	−0.106384
$706$	−18.3678	−0.691282
$707$	−13.0155	−0.489498
$708$	−3.14290	−0.118118
$709$	27.7196	1.04103	0.520515	−	0.853852i	$-0.325740\pi$
$709$	27.7196	1.04103	0.520515	+	0.853852i	$0.325740\pi$
$710$	9.17024	0.344153
$711$	−2.87939	−0.107985
$712$	7.55943	0.283302
$713$	0.955423	0.0357809
$714$	0.467911	0.0175111
$715$	−0.573978	−0.0214656
$716$	−8.45605	−0.316017
$717$	15.6040	0.582742
$718$	−3.40879	−0.127215
$719$	23.1807	0.864493	0.432247	−	0.901755i	$-0.357721\pi$
$719$	23.1807	0.864493	0.432247	+	0.901755i	$0.357721\pi$
$720$	−0.652704	−0.0243248
$721$	3.86753	0.144034
$722$	10.3354	0.384645
$723$	−16.0077	−0.595334
$724$	−17.9067	−0.665498
$725$	18.2294	0.677022
$726$	−1.00000	−0.0371135
$727$	−6.28075	−0.232940	−0.116470	−	0.993194i	$-0.537158\pi$
$727$	−6.28075	−0.232940	−0.116470	+	0.993194i	$0.537158\pi$
$728$	1.34730	0.0499341
$729$	1.00000	0.0370370
$730$	−7.05468	−0.261106
$731$	1.79116	0.0662486
$732$	−1.00000	−0.0369611
$733$	17.9077	0.661435	0.330717	−	0.943730i	$-0.392709\pi$
$733$	17.9077	0.661435	0.330717	+	0.943730i	$0.392709\pi$
$734$	34.8972	1.28808
$735$	3.03684	0.112015
$736$	0.120615	0.00444592
$737$	3.11381	0.114699
$738$	5.69459	0.209621
$739$	−35.1807	−1.29414	−0.647071	−	0.762430i	$-0.724006\pi$
$739$	−35.1807	−1.29414	−0.647071	+	0.762430i	$0.724006\pi$
$740$	6.98545	0.256790
$741$	2.58853	0.0950919
$742$	17.6800	0.649055
$743$	−29.2181	−1.07191	−0.535954	−	0.844247i	$-0.680048\pi$
$743$	−29.2181	−1.07191	−0.535954	+	0.844247i	$0.680048\pi$
$744$	7.92127	0.290408
$745$	−13.2344	−0.484872
$746$	−19.3996	−0.710270
$747$	2.55169	0.0933614
$748$	0.305407	0.0111668
$749$	18.1257	0.662297
$750$	−6.24897	−0.228180
$751$	−28.0574	−1.02383	−0.511914	−	0.859037i	$-0.671063\pi$
$751$	−28.0574	−1.02383	−0.511914	+	0.859037i	$0.671063\pi$
$752$	4.32770	0.157815
$753$	−23.3901	−0.852383
$754$	3.50475	0.127635
$755$	2.69459	0.0980663
$756$	−1.53209	−0.0557215
$757$	24.0247	0.873191	0.436595	−	0.899658i	$-0.356184\pi$
$757$	24.0247	0.873191	0.436595	+	0.899658i	$0.356184\pi$
$758$	8.18716	0.297371
$759$	−0.120615	−0.00437804
$760$	1.92127	0.0696919
$761$	49.6887	1.80121	0.900607	−	0.434634i	$-0.143122\pi$
$761$	49.6887	1.80121	0.900607	+	0.434634i	$0.143122\pi$
$762$	19.3405	0.700632
$763$	−23.8161	−0.862202
$764$	0.0273411	0.000989168 0
$765$	−0.199340	−0.00720717
$766$	−28.2472	−1.02061
$767$	−2.76382	−0.0997959
$768$	1.00000	0.0360844
$769$	26.6578	0.961303	0.480652	−	0.876912i	$-0.340400\pi$
$769$	26.6578	0.961303	0.480652	+	0.876912i	$0.340400\pi$
$770$	−1.00000	−0.0360375
$771$	−11.8821	−0.427922
$772$	−0.985452	−0.0354672
$773$	−22.7611	−0.818661	−0.409331	−	0.912386i	$-0.634238\pi$
$773$	−22.7611	−0.818661	−0.409331	+	0.912386i	$0.634238\pi$
$774$	−5.86484	−0.210807
$775$	36.2317	1.30148
$776$	−6.90167	−0.247756
$777$	16.3969	0.588236
$778$	−1.24628	−0.0446814
$779$	−16.7624	−0.600575
$780$	−0.573978	−0.0205517
$781$	14.0496	0.502735
$782$	0.0368366	0.00131728
$783$	−3.98545	−0.142428
$784$	−4.65270	−0.166168
$785$	8.00950	0.285871
$786$	14.8452	0.529512
$787$	48.8667	1.74191	0.870955	−	0.491363i	$-0.163501\pi$
$787$	48.8667	1.74191	0.870955	+	0.491363i	$0.163501\pi$
$788$	−16.3550	−0.582624
$789$	12.5672	0.447403
$790$	−1.87939	−0.0668655
$791$	31.5672	1.12240
$792$	−1.00000	−0.0355335
$793$	−0.879385	−0.0312279
$794$	30.1043	1.06836
$795$	−7.53209	−0.267136
$796$	−14.4142	−0.510896
$797$	49.6495	1.75868	0.879338	−	0.476198i	$-0.157985\pi$
$797$	49.6495	1.75868	0.879338	+	0.476198i	$0.157985\pi$
$798$	4.50980	0.159645
$799$	1.32171	0.0467587
$800$	4.57398	0.161715
$801$	−7.55943	−0.267099
$802$	0.285807	0.0100922
$803$	−10.8084	−0.381420
$804$	3.11381	0.109816
$805$	−0.120615	−0.00425111
$806$	6.96585	0.245362
$807$	−13.0000	−0.457622
$808$	−8.49525	−0.298862
$809$	37.1771	1.30708	0.653538	−	0.756894i	$-0.273284\pi$
$809$	37.1771	1.30708	0.653538	+	0.756894i	$0.273284\pi$
$810$	0.652704	0.0229337
$811$	4.21307	0.147941	0.0739704	−	0.997260i	$-0.476433\pi$
$811$	4.21307	0.147941	0.0739704	+	0.997260i	$0.476433\pi$
$812$	6.10607	0.214281
$813$	−3.18479	−0.111696
$814$	10.7023	0.375117
$815$	8.91622	0.312322
$816$	0.305407	0.0106914
$817$	17.2635	0.603974
$818$	21.6509	0.757008
$819$	−1.34730	−0.0470783
$820$	3.71688	0.129799
$821$	−26.2918	−0.917590	−0.458795	−	0.888542i	$-0.651719\pi$
$821$	−26.2918	−0.917590	−0.458795	+	0.888542i	$0.651719\pi$
$822$	8.43376	0.294161
$823$	31.1317	1.08518	0.542591	−	0.839997i	$-0.317444\pi$
$823$	31.1317	1.08518	0.542591	+	0.839997i	$0.317444\pi$
$824$	2.52435	0.0879398
$825$	−4.57398	−0.159245
$826$	−4.81521	−0.167542
$827$	45.9299	1.59714	0.798570	−	0.601901i	$-0.205590\pi$
$827$	45.9299	1.59714	0.798570	+	0.601901i	$0.205590\pi$
$828$	−0.120615	−0.00419165
$829$	24.4293	0.848465	0.424233	−	0.905553i	$-0.360544\pi$
$829$	24.4293	0.848465	0.424233	+	0.905553i	$0.360544\pi$
$830$	1.66550	0.0578102
$831$	27.3482	0.948700
$832$	0.879385	0.0304872
$833$	−1.42097	−0.0492337
$834$	−0.396926	−0.0137444
$835$	1.88268	0.0651529
$836$	2.94356	0.101805
$837$	−7.92127	−0.273799
$838$	20.5990	0.711579
$839$	−30.9222	−1.06755	−0.533777	−	0.845626i	$-0.679228\pi$
$839$	−30.9222	−1.06755	−0.533777	+	0.845626i	$0.679228\pi$
$840$	−1.00000	−0.0345033
$841$	−13.1162	−0.452282
$842$	−33.2104	−1.14451
$843$	−24.0009	−0.826636
$844$	−4.45336	−0.153291
$845$	7.98040	0.274534
$846$	−4.32770	−0.148789
$847$	−1.53209	−0.0526432
$848$	11.5398	0.396279
$849$	−14.6878	−0.504083
$850$	1.39693	0.0479142
$851$	1.29086	0.0442501
$852$	14.0496	0.481332
$853$	−7.17118	−0.245536	−0.122768	−	0.992435i	$-0.539177\pi$
$853$	−7.17118	−0.245536	−0.122768	+	0.992435i	$0.539177\pi$
$854$	−1.53209	−0.0524270
$855$	−1.92127	−0.0657062
$856$	11.8307	0.404365
$857$	48.2695	1.64885	0.824427	−	0.565968i	$-0.191497\pi$
$857$	48.2695	1.64885	0.824427	+	0.565968i	$0.191497\pi$
$858$	−0.879385	−0.0300217
$859$	50.1421	1.71083	0.855413	−	0.517947i	$-0.173303\pi$
$859$	50.1421	1.71083	0.855413	+	0.517947i	$0.173303\pi$
$860$	−3.82800	−0.130534
$861$	8.72462	0.297334
$862$	34.7897	1.18494
$863$	−2.23854	−0.0762008	−0.0381004	−	0.999274i	$-0.512131\pi$
$863$	−2.23854	−0.0762008	−0.0381004	+	0.999274i	$0.512131\pi$
$864$	−1.00000	−0.0340207
$865$	−5.90673	−0.200835
$866$	−5.99050	−0.203566
$867$	−16.9067	−0.574183
$868$	12.1361	0.411926
$869$	−2.87939	−0.0976765
$870$	−2.60132	−0.0881930
$871$	2.73824	0.0927816
$872$	−15.5449	−0.526416
$873$	6.90167	0.233586
$874$	0.355037	0.0120093
$875$	−9.57398	−0.323660
$876$	−10.8084	−0.365182
$877$	−48.9059	−1.65144	−0.825718	−	0.564084i	$-0.809229\pi$
$877$	−48.9059	−1.65144	−0.825718	+	0.564084i	$0.809229\pi$
$878$	−0.766511	−0.0258685
$879$	25.4561	0.858611
$880$	−0.652704	−0.0220026
$881$	−57.3884	−1.93346	−0.966732	−	0.255793i	$-0.917663\pi$
$881$	−57.3884	−1.93346	−0.966732	+	0.255793i	$0.917663\pi$
$882$	4.65270	0.156665
$883$	−39.8813	−1.34211	−0.671056	−	0.741407i	$-0.734159\pi$
$883$	−39.8813	−1.34211	−0.671056	+	0.741407i	$0.734159\pi$
$884$	0.268571	0.00903301
$885$	2.05138	0.0689565
$886$	0.487511	0.0163783
$887$	−30.2995	−1.01736	−0.508679	−	0.860956i	$-0.669866\pi$
$887$	−30.2995	−1.01736	−0.508679	+	0.860956i	$0.669866\pi$
$888$	10.7023	0.359147
$889$	29.6313	0.993804
$890$	−4.93407	−0.165390
$891$	1.00000	0.0335013
$892$	−16.9736	−0.568318
$893$	12.7388	0.426289
$894$	−20.2763	−0.678141
$895$	5.51930	0.184490
$896$	1.53209	0.0511835
$897$	−0.106067	−0.00354147
$898$	−27.6709	−0.923389
$899$	31.5699	1.05291
$900$	−4.57398	−0.152466
$901$	3.52435	0.117413
$902$	5.69459	0.189609
$903$	−8.98545	−0.299017
$904$	20.6040	0.685279
$905$	11.6878	0.388515
$906$	4.12836	0.137155
$907$	−1.06242	−0.0352772	−0.0176386	−	0.999844i	$-0.505615\pi$
$907$	−1.06242	−0.0352772	−0.0176386	+	0.999844i	$0.505615\pi$
$908$	−0.226682	−0.00752269
$909$	8.49525	0.281770
$910$	−0.879385	−0.0291513
$911$	55.4715	1.83785	0.918927	−	0.394428i	$-0.129057\pi$
$911$	55.4715	1.83785	0.918927	+	0.394428i	$0.129057\pi$
$912$	2.94356	0.0974711
$913$	2.55169	0.0844486
$914$	−14.5868	−0.482488
$915$	0.652704	0.0215777
$916$	−10.0523	−0.332138
$917$	22.7442	0.751080
$918$	−0.305407	−0.0100799
$919$	20.4679	0.675174	0.337587	−	0.941294i	$-0.390389\pi$
$919$	20.4679	0.675174	0.337587	+	0.941294i	$0.390389\pi$
$920$	−0.0787257	−0.00259551
$921$	9.67736	0.318880
$922$	16.1729	0.532627
$923$	12.3550	0.406671
$924$	−1.53209	−0.0504020
$925$	48.9522	1.60954
$926$	20.3678	0.669328
$927$	−2.52435	−0.0829105
$928$	3.98545	0.130829
$929$	−35.1593	−1.15354	−0.576770	−	0.816907i	$-0.695687\pi$
$929$	−35.1593	−1.15354	−0.576770	+	0.816907i	$0.695687\pi$
$930$	−5.17024	−0.169539
$931$	−13.6955	−0.448853
$932$	6.95130	0.227698
$933$	13.8949	0.454898
$934$	−14.5895	−0.477382
$935$	−0.199340	−0.00651913
$936$	−0.879385	−0.0287436
$937$	−7.89899	−0.258049	−0.129024	−	0.991641i	$-0.541185\pi$
$937$	−7.89899	−0.258049	−0.129024	+	0.991641i	$0.541185\pi$
$938$	4.77063	0.155767
$939$	10.2490	0.334463
$940$	−2.82470	−0.0921317
$941$	15.9513	0.519998	0.259999	−	0.965609i	$-0.416278\pi$
$941$	15.9513	0.519998	0.259999	+	0.965609i	$0.416278\pi$
$942$	12.2713	0.399819
$943$	0.686852	0.0223670
$944$	−3.14290	−0.102293
$945$	1.00000	0.0325300
$946$	−5.86484	−0.190682
$947$	−26.6400	−0.865684	−0.432842	−	0.901470i	$-0.642489\pi$
$947$	−26.6400	−0.865684	−0.432842	+	0.901470i	$0.642489\pi$
$948$	−2.87939	−0.0935181
$949$	−9.50475	−0.308537
$950$	13.4638	0.436823
$951$	29.9932	0.972596
$952$	0.467911	0.0151651
$953$	7.64084	0.247511	0.123756	−	0.992313i	$-0.460506\pi$
$953$	7.64084	0.247511	0.123756	+	0.992313i	$0.460506\pi$
$954$	−11.5398	−0.373616
$955$	−0.0178457	−0.000577472 0
$956$	15.6040	0.504670
$957$	−3.98545	−0.128831
$958$	−14.2344	−0.459893
$959$	12.9213	0.417250
$960$	−0.652704	−0.0210659
$961$	31.7466	1.02408
$962$	9.41147	0.303438
$963$	−11.8307	−0.381239
$964$	−16.0077	−0.515575
$965$	0.643208	0.0207056
$966$	−0.184793	−0.00594560
$967$	28.5571	0.918333	0.459167	−	0.888350i	$-0.348148\pi$
$967$	28.5571	0.918333	0.459167	+	0.888350i	$0.348148\pi$
$968$	−1.00000	−0.0321412
$969$	0.898986	0.0288796
$970$	4.50475	0.144639
$971$	−49.0692	−1.57471	−0.787353	−	0.616502i	$-0.788549\pi$
$971$	−49.0692	−1.57471	−0.787353	+	0.616502i	$0.788549\pi$
$972$	1.00000	0.0320750
$973$	−0.608126	−0.0194956
$974$	30.9469	0.991601
$975$	−4.02229	−0.128816
$976$	−1.00000	−0.0320092
$977$	22.2540	0.711969	0.355985	−	0.934492i	$-0.384146\pi$
$977$	22.2540	0.711969	0.355985	+	0.934492i	$0.384146\pi$
$978$	13.6604	0.436813
$979$	−7.55943	−0.241600
$980$	3.03684	0.0970082
$981$	15.5449	0.496310
$982$	−36.8607	−1.17627
$983$	58.3441	1.86089	0.930444	−	0.366434i	$-0.119421\pi$
$983$	58.3441	1.86089	0.930444	+	0.366434i	$0.119421\pi$
$984$	5.69459	0.181537
$985$	10.6750	0.340134
$986$	1.21719	0.0387631
$987$	−6.63041	−0.211048
$988$	2.58853	0.0823520
$989$	−0.707386	−0.0224936
$990$	0.652704	0.0207443
$991$	−9.73143	−0.309129	−0.154565	−	0.987983i	$-0.549397\pi$
$991$	−9.73143	−0.309129	−0.154565	+	0.987983i	$0.549397\pi$
$992$	7.92127	0.251501
$993$	−21.9760	−0.697386
$994$	21.5253	0.682740
$995$	9.40818	0.298259
$996$	2.55169	0.0808534
$997$	4.54570	0.143964	0.0719819	−	0.997406i	$-0.477068\pi$
$997$	4.54570	0.143964	0.0719819	+	0.997406i	$0.477068\pi$
$998$	20.7219	0.655941
$999$	−10.7023	−0.338607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.n.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.n.1.2	✓	3	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.652704 q^{5} -1.00000 q^{6} -1.53209 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.652704 q^{5} -1.00000 q^{6} -1.53209 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.652704 q^{10} +1.00000 q^{11} +1.00000 q^{12} +0.879385 q^{13} +1.53209 q^{14} -0.652704 q^{15} +1.00000 q^{16} +0.305407 q^{17} -1.00000 q^{18} +2.94356 q^{19} -0.652704 q^{20} -1.53209 q^{21} -1.00000 q^{22} -0.120615 q^{23} -1.00000 q^{24} -4.57398 q^{25} -0.879385 q^{26} +1.00000 q^{27} -1.53209 q^{28} -3.98545 q^{29} +0.652704 q^{30} -7.92127 q^{31} -1.00000 q^{32} +1.00000 q^{33} -0.305407 q^{34} +1.00000 q^{35} +1.00000 q^{36} -10.7023 q^{37} -2.94356 q^{38} +0.879385 q^{39} +0.652704 q^{40} -5.69459 q^{41} +1.53209 q^{42} +5.86484 q^{43} +1.00000 q^{44} -0.652704 q^{45} +0.120615 q^{46} +4.32770 q^{47} +1.00000 q^{48} -4.65270 q^{49} +4.57398 q^{50} +0.305407 q^{51} +0.879385 q^{52} +11.5398 q^{53} -1.00000 q^{54} -0.652704 q^{55} +1.53209 q^{56} +2.94356 q^{57} +3.98545 q^{58} -3.14290 q^{59} -0.652704 q^{60} -1.00000 q^{61} +7.92127 q^{62} -1.53209 q^{63} +1.00000 q^{64} -0.573978 q^{65} -1.00000 q^{66} +3.11381 q^{67} +0.305407 q^{68} -0.120615 q^{69} -1.00000 q^{70} +14.0496 q^{71} -1.00000 q^{72} -10.8084 q^{73} +10.7023 q^{74} -4.57398 q^{75} +2.94356 q^{76} -1.53209 q^{77} -0.879385 q^{78} -2.87939 q^{79} -0.652704 q^{80} +1.00000 q^{81} +5.69459 q^{82} +2.55169 q^{83} -1.53209 q^{84} -0.199340 q^{85} -5.86484 q^{86} -3.98545 q^{87} -1.00000 q^{88} -7.55943 q^{89} +0.652704 q^{90} -1.34730 q^{91} -0.120615 q^{92} -7.92127 q^{93} -4.32770 q^{94} -1.92127 q^{95} -1.00000 q^{96} +6.90167 q^{97} +4.65270 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{22} - 6 q^{23} - 3 q^{24} - 6 q^{25} + 3 q^{26} + 3 q^{27} + 6 q^{29} + 3 q^{30} - 15 q^{31} - 3 q^{32} + 3 q^{33} - 3 q^{34} + 3 q^{35} + 3 q^{36} - 6 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 15 q^{41} - 6 q^{43} + 3 q^{44} - 3 q^{45} + 6 q^{46} + 9 q^{47} + 3 q^{48} - 15 q^{49} + 6 q^{50} + 3 q^{51} - 3 q^{52} + 6 q^{53} - 3 q^{54} - 3 q^{55} - 6 q^{57} - 6 q^{58} - 9 q^{59} - 3 q^{60} - 3 q^{61} + 15 q^{62} + 3 q^{64} + 6 q^{65} - 3 q^{66} - 27 q^{67} + 3 q^{68} - 6 q^{69} - 3 q^{70} + 15 q^{71} - 3 q^{72} + 6 q^{73} + 6 q^{74} - 6 q^{75} - 6 q^{76} + 3 q^{78} - 3 q^{79} - 3 q^{80} + 3 q^{81} + 15 q^{82} + 6 q^{83} - 15 q^{85} + 6 q^{86} + 6 q^{87} - 3 q^{88} + 3 q^{89} + 3 q^{90} - 3 q^{91} - 6 q^{92} - 15 q^{93} - 9 q^{94} + 3 q^{95} - 3 q^{96} + 9 q^{97} + 15 q^{98} + 3 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 - 3 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^22 - 6 * q^23 - 3 * q^24 - 6 * q^25 + 3 * q^26 + 3 * q^27 + 6 * q^29 + 3 * q^30 - 15 * q^31 - 3 * q^32 + 3 * q^33 - 3 * q^34 + 3 * q^35 + 3 * q^36 - 6 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 15 * q^41 - 6 * q^43 + 3 * q^44 - 3 * q^45 + 6 * q^46 + 9 * q^47 + 3 * q^48 - 15 * q^49 + 6 * q^50 + 3 * q^51 - 3 * q^52 + 6 * q^53 - 3 * q^54 - 3 * q^55 - 6 * q^57 - 6 * q^58 - 9 * q^59 - 3 * q^60 - 3 * q^61 + 15 * q^62 + 3 * q^64 + 6 * q^65 - 3 * q^66 - 27 * q^67 + 3 * q^68 - 6 * q^69 - 3 * q^70 + 15 * q^71 - 3 * q^72 + 6 * q^73 + 6 * q^74 - 6 * q^75 - 6 * q^76 + 3 * q^78 - 3 * q^79 - 3 * q^80 + 3 * q^81 + 15 * q^82 + 6 * q^83 - 15 * q^85 + 6 * q^86 + 6 * q^87 - 3 * q^88 + 3 * q^89 + 3 * q^90 - 3 * q^91 - 6 * q^92 - 15 * q^93 - 9 * q^94 + 3 * q^95 - 3 * q^96 + 9 * q^97 + 15 * q^98 + 3 * q^99

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