LMFDB - Embedded newform 4026.2.a.bb.1.1

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:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 22x^{6} + 42x^{5} + 182x^{4} - 111x^{3} - 538x^{2} - 256x - 32 $ x^8 - 3x^7 - 22x^6 + 42x^5 + 182x^4 - 111x^3 - 538x^2 - 256*x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.83085$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.68259 q^{5} +1.00000 q^{6} +3.83085 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.68259 q^{5} +1.00000 q^{6} +3.83085 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.68259 q^{10} -1.00000 q^{11} +1.00000 q^{12} -4.35543 q^{13} +3.83085 q^{14} -3.68259 q^{15} +1.00000 q^{16} +5.53620 q^{17} +1.00000 q^{18} -2.05059 q^{19} -3.68259 q^{20} +3.83085 q^{21} -1.00000 q^{22} -4.26876 q^{23} +1.00000 q^{24} +8.56149 q^{25} -4.35543 q^{26} +1.00000 q^{27} +3.83085 q^{28} +3.03898 q^{29} -3.68259 q^{30} +9.95136 q^{31} +1.00000 q^{32} -1.00000 q^{33} +5.53620 q^{34} -14.1074 q^{35} +1.00000 q^{36} +4.70666 q^{37} -2.05059 q^{38} -4.35543 q^{39} -3.68259 q^{40} +5.90234 q^{41} +3.83085 q^{42} +4.82768 q^{43} -1.00000 q^{44} -3.68259 q^{45} -4.26876 q^{46} -3.94830 q^{47} +1.00000 q^{48} +7.67538 q^{49} +8.56149 q^{50} +5.53620 q^{51} -4.35543 q^{52} +10.7910 q^{53} +1.00000 q^{54} +3.68259 q^{55} +3.83085 q^{56} -2.05059 q^{57} +3.03898 q^{58} -5.12357 q^{59} -3.68259 q^{60} +1.00000 q^{61} +9.95136 q^{62} +3.83085 q^{63} +1.00000 q^{64} +16.0393 q^{65} -1.00000 q^{66} -5.14887 q^{67} +5.53620 q^{68} -4.26876 q^{69} -14.1074 q^{70} -8.28378 q^{71} +1.00000 q^{72} -2.58389 q^{73} +4.70666 q^{74} +8.56149 q^{75} -2.05059 q^{76} -3.83085 q^{77} -4.35543 q^{78} +13.4434 q^{79} -3.68259 q^{80} +1.00000 q^{81} +5.90234 q^{82} -2.80750 q^{83} +3.83085 q^{84} -20.3876 q^{85} +4.82768 q^{86} +3.03898 q^{87} -1.00000 q^{88} +7.97205 q^{89} -3.68259 q^{90} -16.6850 q^{91} -4.26876 q^{92} +9.95136 q^{93} -3.94830 q^{94} +7.55150 q^{95} +1.00000 q^{96} +17.4223 q^{97} +7.67538 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * 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
$5$	−3.68259	−1.64691	−0.823453	−	0.567385i	$-0.807955\pi$
$5$	−3.68259	−1.64691	−0.823453	+	0.567385i	$0.807955\pi$
$6$	1.00000	0.408248
$7$	3.83085	1.44792	0.723962	−	0.689840i	$-0.242319\pi$
$7$	3.83085	1.44792	0.723962	+	0.689840i	$0.242319\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.68259	−1.16454
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	−4.35543	−1.20798	−0.603989	−	0.796992i	$-0.706423\pi$
$13$	−4.35543	−1.20798	−0.603989	+	0.796992i	$0.706423\pi$
$14$	3.83085	1.02384
$15$	−3.68259	−0.950841
$16$	1.00000	0.250000
$17$	5.53620	1.34273	0.671363	−	0.741129i	$-0.265709\pi$
$17$	5.53620	1.34273	0.671363	+	0.741129i	$0.265709\pi$
$18$	1.00000	0.235702
$19$	−2.05059	−0.470438	−0.235219	−	0.971942i	$-0.575581\pi$
$19$	−2.05059	−0.470438	−0.235219	+	0.971942i	$0.575581\pi$
$20$	−3.68259	−0.823453
$21$	3.83085	0.835959
$22$	−1.00000	−0.213201
$23$	−4.26876	−0.890099	−0.445049	−	0.895506i	$-0.646814\pi$
$23$	−4.26876	−0.890099	−0.445049	+	0.895506i	$0.646814\pi$
$24$	1.00000	0.204124
$25$	8.56149	1.71230
$26$	−4.35543	−0.854170
$27$	1.00000	0.192450
$28$	3.83085	0.723962
$29$	3.03898	0.564324	0.282162	−	0.959367i	$-0.408948\pi$
$29$	3.03898	0.564324	0.282162	+	0.959367i	$0.408948\pi$
$30$	−3.68259	−0.672346
$31$	9.95136	1.78732	0.893658	−	0.448748i	$-0.148130\pi$
$31$	9.95136	1.78732	0.893658	+	0.448748i	$0.148130\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	5.53620	0.949450
$35$	−14.1074	−2.38459
$36$	1.00000	0.166667
$37$	4.70666	0.773771	0.386885	−	0.922128i	$-0.373551\pi$
$37$	4.70666	0.773771	0.386885	+	0.922128i	$0.373551\pi$
$38$	−2.05059	−0.332650
$39$	−4.35543	−0.697427
$40$	−3.68259	−0.582269
$41$	5.90234	0.921791	0.460895	−	0.887455i	$-0.347528\pi$
$41$	5.90234	0.921791	0.460895	+	0.887455i	$0.347528\pi$
$42$	3.83085	0.591112
$43$	4.82768	0.736214	0.368107	−	0.929783i	$-0.380006\pi$
$43$	4.82768	0.736214	0.368107	+	0.929783i	$0.380006\pi$
$44$	−1.00000	−0.150756
$45$	−3.68259	−0.548968
$46$	−4.26876	−0.629395
$47$	−3.94830	−0.575919	−0.287959	−	0.957643i	$-0.592977\pi$
$47$	−3.94830	−0.575919	−0.287959	+	0.957643i	$0.592977\pi$
$48$	1.00000	0.144338
$49$	7.67538	1.09648
$50$	8.56149	1.21078
$51$	5.53620	0.775223
$52$	−4.35543	−0.603989
$53$	10.7910	1.48226	0.741128	−	0.671363i	$-0.234291\pi$
$53$	10.7910	1.48226	0.741128	+	0.671363i	$0.234291\pi$
$54$	1.00000	0.136083
$55$	3.68259	0.496561
$56$	3.83085	0.511918
$57$	−2.05059	−0.271608
$58$	3.03898	0.399037
$59$	−5.12357	−0.667032	−0.333516	−	0.942744i	$-0.608235\pi$
$59$	−5.12357	−0.667032	−0.333516	+	0.942744i	$0.608235\pi$
$60$	−3.68259	−0.475421
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	9.95136	1.26382
$63$	3.83085	0.482641
$64$	1.00000	0.125000
$65$	16.0393	1.98943
$66$	−1.00000	−0.123091
$67$	−5.14887	−0.629035	−0.314517	−	0.949252i	$-0.601843\pi$
$67$	−5.14887	−0.629035	−0.314517	+	0.949252i	$0.601843\pi$
$68$	5.53620	0.671363
$69$	−4.26876	−0.513899
$70$	−14.1074	−1.68616
$71$	−8.28378	−0.983104	−0.491552	−	0.870848i	$-0.663570\pi$
$71$	−8.28378	−0.983104	−0.491552	+	0.870848i	$0.663570\pi$
$72$	1.00000	0.117851
$73$	−2.58389	−0.302421	−0.151211	−	0.988502i	$-0.548317\pi$
$73$	−2.58389	−0.302421	−0.151211	+	0.988502i	$0.548317\pi$
$74$	4.70666	0.547139
$75$	8.56149	0.988596
$76$	−2.05059	−0.235219
$77$	−3.83085	−0.436565
$78$	−4.35543	−0.493155
$79$	13.4434	1.51250	0.756252	−	0.654281i	$-0.227029\pi$
$79$	13.4434	1.51250	0.756252	+	0.654281i	$0.227029\pi$
$80$	−3.68259	−0.411726
$81$	1.00000	0.111111
$82$	5.90234	0.651804
$83$	−2.80750	−0.308163	−0.154081	−	0.988058i	$-0.549242\pi$
$83$	−2.80750	−0.308163	−0.154081	+	0.988058i	$0.549242\pi$
$84$	3.83085	0.417980
$85$	−20.3876	−2.21134
$86$	4.82768	0.520582
$87$	3.03898	0.325813
$88$	−1.00000	−0.106600
$89$	7.97205	0.845035	0.422518	−	0.906355i	$-0.361146\pi$
$89$	7.97205	0.845035	0.422518	+	0.906355i	$0.361146\pi$
$90$	−3.68259	−0.388179
$91$	−16.6850	−1.74906
$92$	−4.26876	−0.445049
$93$	9.95136	1.03191
$94$	−3.94830	−0.407236
$95$	7.55150	0.774767
$96$	1.00000	0.102062
$97$	17.4223	1.76897	0.884484	−	0.466571i	$-0.154511\pi$
$97$	17.4223	1.76897	0.884484	+	0.466571i	$0.154511\pi$
$98$	7.67538	0.775330
$99$	−1.00000	−0.100504
$100$	8.56149	0.856149
$101$	18.6597	1.85671	0.928353	−	0.371699i	$-0.121225\pi$
$101$	18.6597	1.85671	0.928353	+	0.371699i	$0.121225\pi$
$102$	5.53620	0.548165
$103$	5.13200	0.505671	0.252835	−	0.967509i	$-0.418637\pi$
$103$	5.13200	0.505671	0.252835	+	0.967509i	$0.418637\pi$
$104$	−4.35543	−0.427085
$105$	−14.1074	−1.37675
$106$	10.7910	1.04811
$107$	4.79171	0.463233	0.231616	−	0.972807i	$-0.425599\pi$
$107$	4.79171	0.463233	0.231616	+	0.972807i	$0.425599\pi$
$108$	1.00000	0.0962250
$109$	−6.98178	−0.668733	−0.334366	−	0.942443i	$-0.608522\pi$
$109$	−6.98178	−0.668733	−0.334366	+	0.942443i	$0.608522\pi$
$110$	3.68259	0.351121
$111$	4.70666	0.446737
$112$	3.83085	0.361981
$113$	−14.8969	−1.40138	−0.700691	−	0.713465i	$-0.747125\pi$
$113$	−14.8969	−1.40138	−0.700691	+	0.713465i	$0.747125\pi$
$114$	−2.05059	−0.192056
$115$	15.7201	1.46591
$116$	3.03898	0.282162
$117$	−4.35543	−0.402659
$118$	−5.12357	−0.471663
$119$	21.2083	1.94416
$120$	−3.68259	−0.336173
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	5.90234	0.532196
$124$	9.95136	0.893658
$125$	−13.1155	−1.17309
$126$	3.83085	0.341279
$127$	0.330139	0.0292951	0.0146475	−	0.999893i	$-0.495337\pi$
$127$	0.330139	0.0292951	0.0146475	+	0.999893i	$0.495337\pi$
$128$	1.00000	0.0883883
$129$	4.82768	0.425053
$130$	16.0393	1.40674
$131$	−18.2262	−1.59243	−0.796213	−	0.605016i	$-0.793167\pi$
$131$	−18.2262	−1.59243	−0.796213	+	0.605016i	$0.793167\pi$
$132$	−1.00000	−0.0870388
$133$	−7.85550	−0.681159
$134$	−5.14887	−0.444795
$135$	−3.68259	−0.316947
$136$	5.53620	0.474725
$137$	−21.4486	−1.83247	−0.916237	−	0.400637i	$-0.868789\pi$
$137$	−21.4486	−1.83247	−0.916237	+	0.400637i	$0.868789\pi$
$138$	−4.26876	−0.363381
$139$	9.51260	0.806848	0.403424	−	0.915013i	$-0.367820\pi$
$139$	9.51260	0.806848	0.403424	+	0.915013i	$0.367820\pi$
$140$	−14.1074	−1.19230
$141$	−3.94830	−0.332507
$142$	−8.28378	−0.695159
$143$	4.35543	0.364219
$144$	1.00000	0.0833333
$145$	−11.1913	−0.929388
$146$	−2.58389	−0.213844
$147$	7.67538	0.633055
$148$	4.70666	0.386885
$149$	−4.15921	−0.340736	−0.170368	−	0.985381i	$-0.554496\pi$
$149$	−4.15921	−0.340736	−0.170368	+	0.985381i	$0.554496\pi$
$150$	8.56149	0.699043
$151$	13.5048	1.09900	0.549502	−	0.835492i	$-0.314817\pi$
$151$	13.5048	1.09900	0.549502	+	0.835492i	$0.314817\pi$
$152$	−2.05059	−0.166325
$153$	5.53620	0.447575
$154$	−3.83085	−0.308698
$155$	−36.6468	−2.94354
$156$	−4.35543	−0.348713
$157$	1.54656	0.123429	0.0617146	−	0.998094i	$-0.480343\pi$
$157$	1.54656	0.123429	0.0617146	+	0.998094i	$0.480343\pi$
$158$	13.4434	1.06950
$159$	10.7910	0.855781
$160$	−3.68259	−0.291135
$161$	−16.3530	−1.28880
$162$	1.00000	0.0785674
$163$	0.980537	0.0768016	0.0384008	−	0.999262i	$-0.487774\pi$
$163$	0.980537	0.0768016	0.0384008	+	0.999262i	$0.487774\pi$
$164$	5.90234	0.460895
$165$	3.68259	0.286689
$166$	−2.80750	−0.217904
$167$	−1.69205	−0.130935	−0.0654674	−	0.997855i	$-0.520854\pi$
$167$	−1.69205	−0.130935	−0.0654674	+	0.997855i	$0.520854\pi$
$168$	3.83085	0.295556
$169$	5.96976	0.459212
$170$	−20.3876	−1.56365
$171$	−2.05059	−0.156813
$172$	4.82768	0.368107
$173$	1.05341	0.0800889	0.0400445	−	0.999198i	$-0.487250\pi$
$173$	1.05341	0.0800889	0.0400445	+	0.999198i	$0.487250\pi$
$174$	3.03898	0.230384
$175$	32.7977	2.47928
$176$	−1.00000	−0.0753778
$177$	−5.12357	−0.385111
$178$	7.97205	0.597530
$179$	−0.860820	−0.0643407	−0.0321704	−	0.999482i	$-0.510242\pi$
$179$	−0.860820	−0.0643407	−0.0321704	+	0.999482i	$0.510242\pi$
$180$	−3.68259	−0.274484
$181$	−1.84125	−0.136859	−0.0684294	−	0.997656i	$-0.521799\pi$
$181$	−1.84125	−0.136859	−0.0684294	+	0.997656i	$0.521799\pi$
$182$	−16.6850	−1.23677
$183$	1.00000	0.0739221
$184$	−4.26876	−0.314697
$185$	−17.3327	−1.27433
$186$	9.95136	0.729669
$187$	−5.53620	−0.404847
$188$	−3.94830	−0.287959
$189$	3.83085	0.278653
$190$	7.55150	0.547843
$191$	1.45436	0.105234	0.0526170	−	0.998615i	$-0.483244\pi$
$191$	1.45436	0.105234	0.0526170	+	0.998615i	$0.483244\pi$
$192$	1.00000	0.0721688
$193$	−3.31127	−0.238351	−0.119175	−	0.992873i	$-0.538025\pi$
$193$	−3.31127	−0.238351	−0.119175	+	0.992873i	$0.538025\pi$
$194$	17.4223	1.25085
$195$	16.0393	1.14860
$196$	7.67538	0.548241
$197$	19.8874	1.41692	0.708458	−	0.705753i	$-0.249391\pi$
$197$	19.8874	1.41692	0.708458	+	0.705753i	$0.249391\pi$
$198$	−1.00000	−0.0710669
$199$	15.4697	1.09662	0.548309	−	0.836276i	$-0.315272\pi$
$199$	15.4697	1.09662	0.548309	+	0.836276i	$0.315272\pi$
$200$	8.56149	0.605389
$201$	−5.14887	−0.363174
$202$	18.6597	1.31289
$203$	11.6419	0.817098
$204$	5.53620	0.387611
$205$	−21.7359	−1.51810
$206$	5.13200	0.357563
$207$	−4.26876	−0.296700
$208$	−4.35543	−0.301995
$209$	2.05059	0.141842
$210$	−14.1074	−0.973506
$211$	−20.6676	−1.42282	−0.711408	−	0.702779i	$-0.751942\pi$
$211$	−20.6676	−1.42282	−0.711408	+	0.702779i	$0.751942\pi$
$212$	10.7910	0.741128
$213$	−8.28378	−0.567595
$214$	4.79171	0.327555
$215$	−17.7784	−1.21247
$216$	1.00000	0.0680414
$217$	38.1221	2.58790
$218$	−6.98178	−0.472866
$219$	−2.58389	−0.174603
$220$	3.68259	0.248280
$221$	−24.1125	−1.62198
$222$	4.70666	0.315891
$223$	28.0993	1.88167	0.940834	−	0.338868i	$-0.110044\pi$
$223$	28.0993	1.88167	0.940834	+	0.338868i	$0.110044\pi$
$224$	3.83085	0.255959
$225$	8.56149	0.570766
$226$	−14.8969	−0.990926
$227$	−19.0464	−1.26415	−0.632076	−	0.774906i	$-0.717797\pi$
$227$	−19.0464	−1.26415	−0.632076	+	0.774906i	$0.717797\pi$
$228$	−2.05059	−0.135804
$229$	16.9109	1.11750	0.558751	−	0.829336i	$-0.311281\pi$
$229$	16.9109	1.11750	0.558751	+	0.829336i	$0.311281\pi$
$230$	15.7201	1.03655
$231$	−3.83085	−0.252051
$232$	3.03898	0.199519
$233$	−26.8797	−1.76095	−0.880473	−	0.474097i	$-0.842775\pi$
$233$	−26.8797	−1.76095	−0.880473	+	0.474097i	$0.842775\pi$
$234$	−4.35543	−0.284723
$235$	14.5400	0.948484
$236$	−5.12357	−0.333516
$237$	13.4434	0.873244
$238$	21.2083	1.37473
$239$	−9.04315	−0.584953	−0.292476	−	0.956273i	$-0.594479\pi$
$239$	−9.04315	−0.584953	−0.292476	+	0.956273i	$0.594479\pi$
$240$	−3.68259	−0.237710
$241$	10.4582	0.673669	0.336834	−	0.941564i	$-0.390644\pi$
$241$	10.4582	0.673669	0.336834	+	0.941564i	$0.390644\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	1.00000	0.0640184
$245$	−28.2653	−1.80580
$246$	5.90234	0.376319
$247$	8.93121	0.568279
$248$	9.95136	0.631912
$249$	−2.80750	−0.177918
$250$	−13.1155	−0.829498
$251$	26.8104	1.69226	0.846130	−	0.532977i	$-0.178927\pi$
$251$	26.8104	1.69226	0.846130	+	0.532977i	$0.178927\pi$
$252$	3.83085	0.241321
$253$	4.26876	0.268375
$254$	0.330139	0.0207147
$255$	−20.3876	−1.27672
$256$	1.00000	0.0625000
$257$	24.0707	1.50149	0.750745	−	0.660592i	$-0.229695\pi$
$257$	24.0707	1.50149	0.750745	+	0.660592i	$0.229695\pi$
$258$	4.82768	0.300558
$259$	18.0305	1.12036
$260$	16.0393	0.994713
$261$	3.03898	0.188108
$262$	−18.2262	−1.12602
$263$	−21.6213	−1.33323	−0.666613	−	0.745404i	$-0.732256\pi$
$263$	−21.6213	−1.33323	−0.666613	+	0.745404i	$0.732256\pi$
$264$	−1.00000	−0.0615457
$265$	−39.7388	−2.44114
$266$	−7.85550	−0.481652
$267$	7.97205	0.487881
$268$	−5.14887	−0.314517
$269$	10.9305	0.666443	0.333221	−	0.942849i	$-0.391864\pi$
$269$	10.9305	0.666443	0.333221	+	0.942849i	$0.391864\pi$
$270$	−3.68259	−0.224115
$271$	−5.45796	−0.331548	−0.165774	−	0.986164i	$-0.553012\pi$
$271$	−5.45796	−0.331548	−0.165774	+	0.986164i	$0.553012\pi$
$272$	5.53620	0.335681
$273$	−16.6850	−1.00982
$274$	−21.4486	−1.29575
$275$	−8.56149	−0.516277
$276$	−4.26876	−0.256949
$277$	20.6513	1.24081	0.620407	−	0.784280i	$-0.286968\pi$
$277$	20.6513	1.24081	0.620407	+	0.784280i	$0.286968\pi$
$278$	9.51260	0.570528
$279$	9.95136	0.595772
$280$	−14.1074	−0.843081
$281$	−21.5082	−1.28307	−0.641536	−	0.767093i	$-0.721702\pi$
$281$	−21.5082	−1.28307	−0.641536	+	0.767093i	$0.721702\pi$
$282$	−3.94830	−0.235118
$283$	−10.5070	−0.624578	−0.312289	−	0.949987i	$-0.601096\pi$
$283$	−10.5070	−0.624578	−0.312289	+	0.949987i	$0.601096\pi$
$284$	−8.28378	−0.491552
$285$	7.55150	0.447312
$286$	4.35543	0.257542
$287$	22.6110	1.33468
$288$	1.00000	0.0589256
$289$	13.6495	0.802911
$290$	−11.1913	−0.657177
$291$	17.4223	1.02131
$292$	−2.58389	−0.151211
$293$	−24.7215	−1.44425	−0.722123	−	0.691765i	$-0.756833\pi$
$293$	−24.7215	−1.44425	−0.722123	+	0.691765i	$0.756833\pi$
$294$	7.67538	0.447637
$295$	18.8680	1.09854
$296$	4.70666	0.273569
$297$	−1.00000	−0.0580259
$298$	−4.15921	−0.240937
$299$	18.5923	1.07522
$300$	8.56149	0.494298
$301$	18.4941	1.06598
$302$	13.5048	0.777114
$303$	18.6597	1.07197
$304$	−2.05059	−0.117610
$305$	−3.68259	−0.210865
$306$	5.53620	0.316483
$307$	−12.3785	−0.706478	−0.353239	−	0.935533i	$-0.614920\pi$
$307$	−12.3785	−0.706478	−0.353239	+	0.935533i	$0.614920\pi$
$308$	−3.83085	−0.218283
$309$	5.13200	0.291949
$310$	−36.6468	−2.08140
$311$	10.0471	0.569716	0.284858	−	0.958570i	$-0.408053\pi$
$311$	10.0471	0.569716	0.284858	+	0.958570i	$0.408053\pi$
$312$	−4.35543	−0.246578
$313$	−12.3629	−0.698793	−0.349397	−	0.936975i	$-0.613613\pi$
$313$	−12.3629	−0.698793	−0.349397	+	0.936975i	$0.613613\pi$
$314$	1.54656	0.0872776
$315$	−14.1074	−0.794864
$316$	13.4434	0.756252
$317$	3.32754	0.186894	0.0934468	−	0.995624i	$-0.470212\pi$
$317$	3.32754	0.186894	0.0934468	+	0.995624i	$0.470212\pi$
$318$	10.7910	0.605129
$319$	−3.03898	−0.170150
$320$	−3.68259	−0.205863
$321$	4.79171	0.267447
$322$	−16.3530	−0.911316
$323$	−11.3525	−0.631669
$324$	1.00000	0.0555556
$325$	−37.2889	−2.06842
$326$	0.980537	0.0543069
$327$	−6.98178	−0.386093
$328$	5.90234	0.325902
$329$	−15.1253	−0.833886
$330$	3.68259	0.202720
$331$	−1.76615	−0.0970763	−0.0485381	−	0.998821i	$-0.515456\pi$
$331$	−1.76615	−0.0970763	−0.0485381	+	0.998821i	$0.515456\pi$
$332$	−2.80750	−0.154081
$333$	4.70666	0.257924
$334$	−1.69205	−0.0925849
$335$	18.9612	1.03596
$336$	3.83085	0.208990
$337$	−25.6299	−1.39615	−0.698074	−	0.716026i	$-0.745959\pi$
$337$	−25.6299	−1.39615	−0.698074	+	0.716026i	$0.745959\pi$
$338$	5.96976	0.324712
$339$	−14.8969	−0.809088
$340$	−20.3876	−1.10567
$341$	−9.95136	−0.538896
$342$	−2.05059	−0.110883
$343$	2.58727	0.139699
$344$	4.82768	0.260291
$345$	15.7201	0.846343
$346$	1.05341	0.0566314
$347$	−1.19231	−0.0640064	−0.0320032	−	0.999488i	$-0.510189\pi$
$347$	−1.19231	−0.0640064	−0.0320032	+	0.999488i	$0.510189\pi$
$348$	3.03898	0.162906
$349$	−12.0692	−0.646052	−0.323026	−	0.946390i	$-0.604700\pi$
$349$	−12.0692	−0.646052	−0.323026	+	0.946390i	$0.604700\pi$
$350$	32.7977	1.75311
$351$	−4.35543	−0.232476
$352$	−1.00000	−0.0533002
$353$	18.1605	0.966588	0.483294	−	0.875458i	$-0.339440\pi$
$353$	18.1605	0.966588	0.483294	+	0.875458i	$0.339440\pi$
$354$	−5.12357	−0.272315
$355$	30.5058	1.61908
$356$	7.97205	0.422518
$357$	21.2083	1.12246
$358$	−0.860820	−0.0454958
$359$	34.7467	1.83386	0.916930	−	0.399047i	$-0.130659\pi$
$359$	34.7467	1.83386	0.916930	+	0.399047i	$0.130659\pi$
$360$	−3.68259	−0.194090
$361$	−14.7951	−0.778688
$362$	−1.84125	−0.0967739
$363$	1.00000	0.0524864
$364$	−16.6850	−0.874530
$365$	9.51540	0.498059
$366$	1.00000	0.0522708
$367$	16.1766	0.844411	0.422205	−	0.906500i	$-0.361256\pi$
$367$	16.1766	0.844411	0.422205	+	0.906500i	$0.361256\pi$
$368$	−4.26876	−0.222525
$369$	5.90234	0.307264
$370$	−17.3327	−0.901085
$371$	41.3386	2.14619
$372$	9.95136	0.515954
$373$	−25.1833	−1.30394	−0.651972	−	0.758243i	$-0.726058\pi$
$373$	−25.1833	−1.30394	−0.651972	+	0.758243i	$0.726058\pi$
$374$	−5.53620	−0.286270
$375$	−13.1155	−0.677282
$376$	−3.94830	−0.203618
$377$	−13.2360	−0.681691
$378$	3.83085	0.197037
$379$	−12.3196	−0.632815	−0.316408	−	0.948623i	$-0.602477\pi$
$379$	−12.3196	−0.632815	−0.316408	+	0.948623i	$0.602477\pi$
$380$	7.55150	0.387384
$381$	0.330139	0.0169135
$382$	1.45436	0.0744116
$383$	9.74981	0.498192	0.249096	−	0.968479i	$-0.419867\pi$
$383$	9.74981	0.498192	0.249096	+	0.968479i	$0.419867\pi$
$384$	1.00000	0.0510310
$385$	14.1074	0.718982
$386$	−3.31127	−0.168539
$387$	4.82768	0.245405
$388$	17.4223	0.884484
$389$	−14.4568	−0.732991	−0.366496	−	0.930420i	$-0.619442\pi$
$389$	−14.4568	−0.732991	−0.366496	+	0.930420i	$0.619442\pi$
$390$	16.0393	0.812180
$391$	−23.6327	−1.19516
$392$	7.67538	0.387665
$393$	−18.2262	−0.919388
$394$	19.8874	1.00191
$395$	−49.5066	−2.49095
$396$	−1.00000	−0.0502519
$397$	−6.61526	−0.332010	−0.166005	−	0.986125i	$-0.553087\pi$
$397$	−6.61526	−0.332010	−0.166005	+	0.986125i	$0.553087\pi$
$398$	15.4697	0.775426
$399$	−7.85550	−0.393267
$400$	8.56149	0.428074
$401$	−12.8003	−0.639216	−0.319608	−	0.947550i	$-0.603551\pi$
$401$	−12.8003	−0.639216	−0.319608	+	0.947550i	$0.603551\pi$
$402$	−5.14887	−0.256802
$403$	−43.3424	−2.15904
$404$	18.6597	0.928353
$405$	−3.68259	−0.182989
$406$	11.6419	0.577775
$407$	−4.70666	−0.233301
$408$	5.53620	0.274083
$409$	23.3126	1.15273	0.576366	−	0.817192i	$-0.304470\pi$
$409$	23.3126	1.15273	0.576366	+	0.817192i	$0.304470\pi$
$410$	−21.7359	−1.07346
$411$	−21.4486	−1.05798
$412$	5.13200	0.252835
$413$	−19.6276	−0.965811
$414$	−4.26876	−0.209798
$415$	10.3389	0.507515
$416$	−4.35543	−0.213542
$417$	9.51260	0.465834
$418$	2.05059	0.100298
$419$	7.12991	0.348319	0.174159	−	0.984717i	$-0.444279\pi$
$419$	7.12991	0.348319	0.174159	+	0.984717i	$0.444279\pi$
$420$	−14.1074	−0.688373
$421$	−16.5516	−0.806675	−0.403338	−	0.915051i	$-0.632150\pi$
$421$	−16.5516	−0.806675	−0.403338	+	0.915051i	$0.632150\pi$
$422$	−20.6676	−1.00608
$423$	−3.94830	−0.191973
$424$	10.7910	0.524057
$425$	47.3981	2.29915
$426$	−8.28378	−0.401350
$427$	3.83085	0.185388
$428$	4.79171	0.231616
$429$	4.35543	0.210282
$430$	−17.7784	−0.857349
$431$	−14.2639	−0.687067	−0.343533	−	0.939140i	$-0.611624\pi$
$431$	−14.2639	−0.687067	−0.343533	+	0.939140i	$0.611624\pi$
$432$	1.00000	0.0481125
$433$	−1.47511	−0.0708891	−0.0354446	−	0.999372i	$-0.511285\pi$
$433$	−1.47511	−0.0708891	−0.0354446	+	0.999372i	$0.511285\pi$
$434$	38.1221	1.82992
$435$	−11.1913	−0.536582
$436$	−6.98178	−0.334366
$437$	8.75350	0.418737
$438$	−2.58389	−0.123463
$439$	11.9457	0.570139	0.285070	−	0.958507i	$-0.407983\pi$
$439$	11.9457	0.570139	0.285070	+	0.958507i	$0.407983\pi$
$440$	3.68259	0.175561
$441$	7.67538	0.365494
$442$	−24.1125	−1.14692
$443$	8.08754	0.384251	0.192125	−	0.981370i	$-0.438462\pi$
$443$	8.08754	0.384251	0.192125	+	0.981370i	$0.438462\pi$
$444$	4.70666	0.223368
$445$	−29.3578	−1.39169
$446$	28.0993	1.33054
$447$	−4.15921	−0.196724
$448$	3.83085	0.180990
$449$	−3.25432	−0.153581	−0.0767904	−	0.997047i	$-0.524467\pi$
$449$	−3.25432	−0.153581	−0.0767904	+	0.997047i	$0.524467\pi$
$450$	8.56149	0.403592
$451$	−5.90234	−0.277930
$452$	−14.8969	−0.700691
$453$	13.5048	0.634511
$454$	−19.0464	−0.893891
$455$	61.4440	2.88054
$456$	−2.05059	−0.0960278
$457$	28.0754	1.31331	0.656655	−	0.754191i	$-0.271971\pi$
$457$	28.0754	1.31331	0.656655	+	0.754191i	$0.271971\pi$
$458$	16.9109	0.790193
$459$	5.53620	0.258408
$460$	15.7201	0.732954
$461$	−33.8367	−1.57593	−0.787967	−	0.615717i	$-0.788866\pi$
$461$	−33.8367	−1.57593	−0.787967	+	0.615717i	$0.788866\pi$
$462$	−3.83085	−0.178227
$463$	−25.0259	−1.16305	−0.581526	−	0.813528i	$-0.697544\pi$
$463$	−25.0259	−1.16305	−0.581526	+	0.813528i	$0.697544\pi$
$464$	3.03898	0.141081
$465$	−36.6468	−1.69945
$466$	−26.8797	−1.24518
$467$	−34.8540	−1.61285	−0.806425	−	0.591336i	$-0.798601\pi$
$467$	−34.8540	−1.61285	−0.806425	+	0.591336i	$0.798601\pi$
$468$	−4.35543	−0.201330
$469$	−19.7245	−0.910795
$470$	14.5400	0.670679
$471$	1.54656	0.0712619
$472$	−5.12357	−0.235831
$473$	−4.82768	−0.221977
$474$	13.4434	0.617477
$475$	−17.5561	−0.805530
$476$	21.2083	0.972082
$477$	10.7910	0.494086
$478$	−9.04315	−0.413624
$479$	−27.5913	−1.26068	−0.630340	−	0.776320i	$-0.717084\pi$
$479$	−27.5913	−1.26068	−0.630340	+	0.776320i	$0.717084\pi$
$480$	−3.68259	−0.168087
$481$	−20.4995	−0.934698
$482$	10.4582	0.476356
$483$	−16.3530	−0.744086
$484$	1.00000	0.0454545
$485$	−64.1593	−2.91332
$486$	1.00000	0.0453609
$487$	−42.8355	−1.94106	−0.970532	−	0.240974i	$-0.922533\pi$
$487$	−42.8355	−1.94106	−0.970532	+	0.240974i	$0.922533\pi$
$488$	1.00000	0.0452679
$489$	0.980537	0.0443414
$490$	−28.2653	−1.27690
$491$	36.3403	1.64002	0.820008	−	0.572353i	$-0.193969\pi$
$491$	36.3403	1.64002	0.820008	+	0.572353i	$0.193969\pi$
$492$	5.90234	0.266098
$493$	16.8244	0.757732
$494$	8.93121	0.401834
$495$	3.68259	0.165520
$496$	9.95136	0.446829
$497$	−31.7339	−1.42346
$498$	−2.80750	−0.125807
$499$	12.9397	0.579260	0.289630	−	0.957139i	$-0.406468\pi$
$499$	12.9397	0.579260	0.289630	+	0.957139i	$0.406468\pi$
$500$	−13.1155	−0.586543
$501$	−1.69205	−0.0755952
$502$	26.8104	1.19661
$503$	−38.3147	−1.70837	−0.854185	−	0.519969i	$-0.825943\pi$
$503$	−38.3147	−1.70837	−0.854185	+	0.519969i	$0.825943\pi$
$504$	3.83085	0.170639
$505$	−68.7160	−3.05782
$506$	4.26876	0.189770
$507$	5.96976	0.265126
$508$	0.330139	0.0146475
$509$	−23.5110	−1.04211	−0.521053	−	0.853524i	$-0.674461\pi$
$509$	−23.5110	−1.04211	−0.521053	+	0.853524i	$0.674461\pi$
$510$	−20.3876	−0.902777
$511$	−9.89847	−0.437882
$512$	1.00000	0.0441942
$513$	−2.05059	−0.0905359
$514$	24.0707	1.06171
$515$	−18.8991	−0.832792
$516$	4.82768	0.212527
$517$	3.94830	0.173646
$518$	18.0305	0.792215
$519$	1.05341	0.0462394
$520$	16.0393	0.703368
$521$	−20.4288	−0.895004	−0.447502	−	0.894283i	$-0.647686\pi$
$521$	−20.4288	−0.895004	−0.447502	+	0.894283i	$0.647686\pi$
$522$	3.03898	0.133012
$523$	−0.884294	−0.0386675	−0.0193337	−	0.999813i	$-0.506155\pi$
$523$	−0.884294	−0.0386675	−0.0193337	+	0.999813i	$0.506155\pi$
$524$	−18.2262	−0.796213
$525$	32.7977	1.43141
$526$	−21.6213	−0.942733
$527$	55.0927	2.39988
$528$	−1.00000	−0.0435194
$529$	−4.77765	−0.207724
$530$	−39.7388	−1.72614
$531$	−5.12357	−0.222344
$532$	−7.85550	−0.340579
$533$	−25.7072	−1.11350
$534$	7.97205	0.344984
$535$	−17.6459	−0.762900
$536$	−5.14887	−0.222397
$537$	−0.860820	−0.0371471
$538$	10.9305	0.471246
$539$	−7.67538	−0.330602
$540$	−3.68259	−0.158474
$541$	0.193316	0.00831132	0.00415566	−	0.999991i	$-0.498677\pi$
$541$	0.193316	0.00831132	0.00415566	+	0.999991i	$0.498677\pi$
$542$	−5.45796	−0.234440
$543$	−1.84125	−0.0790155
$544$	5.53620	0.237363
$545$	25.7110	1.10134
$546$	−16.6850	−0.714051
$547$	19.6767	0.841313	0.420657	−	0.907220i	$-0.361800\pi$
$547$	19.6767	0.841313	0.420657	+	0.907220i	$0.361800\pi$
$548$	−21.4486	−0.916237
$549$	1.00000	0.0426790
$550$	−8.56149	−0.365063
$551$	−6.23170	−0.265480
$552$	−4.26876	−0.181691
$553$	51.4997	2.18999
$554$	20.6513	0.877388
$555$	−17.3327	−0.735733
$556$	9.51260	0.403424
$557$	−7.09407	−0.300585	−0.150293	−	0.988642i	$-0.548022\pi$
$557$	−7.09407	−0.300585	−0.150293	+	0.988642i	$0.548022\pi$
$558$	9.95136	0.421275
$559$	−21.0266	−0.889330
$560$	−14.1074	−0.596148
$561$	−5.53620	−0.233738
$562$	−21.5082	−0.907269
$563$	−34.7711	−1.46543	−0.732713	−	0.680538i	$-0.761746\pi$
$563$	−34.7711	−1.46543	−0.732713	+	0.680538i	$0.761746\pi$
$564$	−3.94830	−0.166253
$565$	54.8592	2.30794
$566$	−10.5070	−0.441643
$567$	3.83085	0.160880
$568$	−8.28378	−0.347580
$569$	27.7138	1.16182	0.580911	−	0.813967i	$-0.302696\pi$
$569$	27.7138	1.16182	0.580911	+	0.813967i	$0.302696\pi$
$570$	7.55150	0.316297
$571$	−31.0663	−1.30008	−0.650042	−	0.759898i	$-0.725249\pi$
$571$	−31.0663	−1.30008	−0.650042	+	0.759898i	$0.725249\pi$
$572$	4.35543	0.182110
$573$	1.45436	0.0607569
$574$	22.6110	0.943763
$575$	−36.5470	−1.52411
$576$	1.00000	0.0416667
$577$	−17.2276	−0.717196	−0.358598	−	0.933492i	$-0.616745\pi$
$577$	−17.2276	−0.717196	−0.358598	+	0.933492i	$0.616745\pi$
$578$	13.6495	0.567744
$579$	−3.31127	−0.137612
$580$	−11.1913	−0.464694
$581$	−10.7551	−0.446196
$582$	17.4223	0.722178
$583$	−10.7910	−0.446917
$584$	−2.58389	−0.106922
$585$	16.0393	0.663142
$586$	−24.7215	−1.02124
$587$	−28.5693	−1.17918	−0.589591	−	0.807702i	$-0.700711\pi$
$587$	−28.5693	−1.17918	−0.589591	+	0.807702i	$0.700711\pi$
$588$	7.67538	0.316527
$589$	−20.4062	−0.840822
$590$	18.8680	0.776784
$591$	19.8874	0.818057
$592$	4.70666	0.193443
$593$	25.0109	1.02708	0.513538	−	0.858067i	$-0.328335\pi$
$593$	25.0109	1.02708	0.513538	+	0.858067i	$0.328335\pi$
$594$	−1.00000	−0.0410305
$595$	−78.1016	−3.20185
$596$	−4.15921	−0.170368
$597$	15.4697	0.633133
$598$	18.5923	0.760295
$599$	1.74142	0.0711523	0.0355762	−	0.999367i	$-0.488673\pi$
$599$	1.74142	0.0711523	0.0355762	+	0.999367i	$0.488673\pi$
$600$	8.56149	0.349521
$601$	−30.8461	−1.25824	−0.629119	−	0.777309i	$-0.716584\pi$
$601$	−30.8461	−1.25824	−0.629119	+	0.777309i	$0.716584\pi$
$602$	18.4941	0.753762
$603$	−5.14887	−0.209678
$604$	13.5048	0.549502
$605$	−3.68259	−0.149719
$606$	18.6597	0.757997
$607$	46.1493	1.87314	0.936571	−	0.350477i	$-0.113980\pi$
$607$	46.1493	1.87314	0.936571	+	0.350477i	$0.113980\pi$
$608$	−2.05059	−0.0831625
$609$	11.6419	0.471752
$610$	−3.68259	−0.149104
$611$	17.1965	0.695697
$612$	5.53620	0.223788
$613$	−2.08484	−0.0842058	−0.0421029	−	0.999113i	$-0.513406\pi$
$613$	−2.08484	−0.0842058	−0.0421029	+	0.999113i	$0.513406\pi$
$614$	−12.3785	−0.499555
$615$	−21.7359	−0.876477
$616$	−3.83085	−0.154349
$617$	21.6517	0.871664	0.435832	−	0.900028i	$-0.356454\pi$
$617$	21.6517	0.871664	0.435832	+	0.900028i	$0.356454\pi$
$618$	5.13200	0.206439
$619$	−32.4397	−1.30386	−0.651930	−	0.758279i	$-0.726040\pi$
$619$	−32.4397	−1.30386	−0.651930	+	0.758279i	$0.726040\pi$
$620$	−36.6468	−1.47177
$621$	−4.26876	−0.171300
$622$	10.0471	0.402850
$623$	30.5397	1.22355
$624$	−4.35543	−0.174357
$625$	5.49164	0.219666
$626$	−12.3629	−0.494121
$627$	2.05059	0.0818928
$628$	1.54656	0.0617146
$629$	26.0570	1.03896
$630$	−14.1074	−0.562054
$631$	−38.8150	−1.54520	−0.772601	−	0.634892i	$-0.781045\pi$
$631$	−38.8150	−1.54520	−0.772601	+	0.634892i	$0.781045\pi$
$632$	13.4434	0.534751
$633$	−20.6676	−0.821463
$634$	3.32754	0.132154
$635$	−1.21577	−0.0482462
$636$	10.7910	0.427891
$637$	−33.4296	−1.32453
$638$	−3.03898	−0.120314
$639$	−8.28378	−0.327701
$640$	−3.68259	−0.145567
$641$	15.3633	0.606813	0.303406	−	0.952861i	$-0.401876\pi$
$641$	15.3633	0.606813	0.303406	+	0.952861i	$0.401876\pi$
$642$	4.79171	0.189114
$643$	0.777934	0.0306787	0.0153394	−	0.999882i	$-0.495117\pi$
$643$	0.777934	0.0306787	0.0153394	+	0.999882i	$0.495117\pi$
$644$	−16.3530	−0.644398
$645$	−17.7784	−0.700022
$646$	−11.3525	−0.446658
$647$	17.3649	0.682683	0.341342	−	0.939939i	$-0.389119\pi$
$647$	17.3649	0.682683	0.341342	+	0.939939i	$0.389119\pi$
$648$	1.00000	0.0392837
$649$	5.12357	0.201118
$650$	−37.2889	−1.46259
$651$	38.1221	1.49412
$652$	0.980537	0.0384008
$653$	−19.2664	−0.753953	−0.376976	−	0.926223i	$-0.623036\pi$
$653$	−19.2664	−0.753953	−0.376976	+	0.926223i	$0.623036\pi$
$654$	−6.98178	−0.273009
$655$	67.1195	2.62258
$656$	5.90234	0.230448
$657$	−2.58389	−0.100807
$658$	−15.1253	−0.589647
$659$	6.56292	0.255655	0.127828	−	0.991796i	$-0.459200\pi$
$659$	6.56292	0.255655	0.127828	+	0.991796i	$0.459200\pi$
$660$	3.68259	0.143345
$661$	−44.6418	−1.73637	−0.868183	−	0.496244i	$-0.834712\pi$
$661$	−44.6418	−1.73637	−0.868183	+	0.496244i	$0.834712\pi$
$662$	−1.76615	−0.0686433
$663$	−24.1125	−0.936453
$664$	−2.80750	−0.108952
$665$	28.9286	1.12180
$666$	4.70666	0.182380
$667$	−12.9727	−0.502304
$668$	−1.69205	−0.0654674
$669$	28.0993	1.08638
$670$	18.9612	0.732535
$671$	−1.00000	−0.0386046
$672$	3.83085	0.147778
$673$	18.9962	0.732249	0.366124	−	0.930566i	$-0.380684\pi$
$673$	18.9962	0.732249	0.366124	+	0.930566i	$0.380684\pi$
$674$	−25.6299	−0.987225
$675$	8.56149	0.329532
$676$	5.96976	0.229606
$677$	15.4039	0.592020	0.296010	−	0.955185i	$-0.404344\pi$
$677$	15.4039	0.592020	0.296010	+	0.955185i	$0.404344\pi$
$678$	−14.8969	−0.572111
$679$	66.7422	2.56133
$680$	−20.3876	−0.781827
$681$	−19.0464	−0.729859
$682$	−9.95136	−0.381057
$683$	30.2433	1.15723	0.578613	−	0.815602i	$-0.303594\pi$
$683$	30.2433	1.15723	0.578613	+	0.815602i	$0.303594\pi$
$684$	−2.05059	−0.0784064
$685$	78.9863	3.01791
$686$	2.58727	0.0987824
$687$	16.9109	0.645190
$688$	4.82768	0.184053
$689$	−46.9994	−1.79053
$690$	15.7201	0.598455
$691$	3.46475	0.131805	0.0659026	−	0.997826i	$-0.479007\pi$
$691$	3.46475	0.131805	0.0659026	+	0.997826i	$0.479007\pi$
$692$	1.05341	0.0400445
$693$	−3.83085	−0.145522
$694$	−1.19231	−0.0452594
$695$	−35.0310	−1.32880
$696$	3.03898	0.115192
$697$	32.6765	1.23771
$698$	−12.0692	−0.456828
$699$	−26.8797	−1.01668
$700$	32.7977	1.23964
$701$	11.8444	0.447357	0.223678	−	0.974663i	$-0.428194\pi$
$701$	11.8444	0.447357	0.223678	+	0.974663i	$0.428194\pi$
$702$	−4.35543	−0.164385
$703$	−9.65145	−0.364011
$704$	−1.00000	−0.0376889
$705$	14.5400	0.547607
$706$	18.1605	0.683481
$707$	71.4823	2.68837
$708$	−5.12357	−0.192556
$709$	18.9760	0.712657	0.356329	−	0.934361i	$-0.384028\pi$
$709$	18.9760	0.712657	0.356329	+	0.934361i	$0.384028\pi$
$710$	30.5058	1.14486
$711$	13.4434	0.504168
$712$	7.97205	0.298765
$713$	−42.4800	−1.59089
$714$	21.2083	0.793702
$715$	−16.0393	−0.599835
$716$	−0.860820	−0.0321704
$717$	−9.04315	−0.337722
$718$	34.7467	1.29674
$719$	−19.7802	−0.737678	−0.368839	−	0.929493i	$-0.620245\pi$
$719$	−19.7802	−0.737678	−0.368839	+	0.929493i	$0.620245\pi$
$720$	−3.68259	−0.137242
$721$	19.6599	0.732173
$722$	−14.7951	−0.550615
$723$	10.4582	0.388943
$724$	−1.84125	−0.0684294
$725$	26.0182	0.966290
$726$	1.00000	0.0371135
$727$	−18.9098	−0.701326	−0.350663	−	0.936502i	$-0.614044\pi$
$727$	−18.9098	−0.701326	−0.350663	+	0.936502i	$0.614044\pi$
$728$	−16.6850	−0.618386
$729$	1.00000	0.0370370
$730$	9.51540	0.352181
$731$	26.7270	0.988533
$732$	1.00000	0.0369611
$733$	20.1342	0.743673	0.371836	−	0.928298i	$-0.378728\pi$
$733$	20.1342	0.743673	0.371836	+	0.928298i	$0.378728\pi$
$734$	16.1766	0.597089
$735$	−28.2653	−1.04258
$736$	−4.26876	−0.157349
$737$	5.14887	0.189661
$738$	5.90234	0.217268
$739$	8.97925	0.330307	0.165153	−	0.986268i	$-0.447188\pi$
$739$	8.97925	0.330307	0.165153	+	0.986268i	$0.447188\pi$
$740$	−17.3327	−0.637164
$741$	8.93121	0.328096
$742$	41.3386	1.51759
$743$	−24.6117	−0.902914	−0.451457	−	0.892293i	$-0.649096\pi$
$743$	−24.6117	−0.902914	−0.451457	+	0.892293i	$0.649096\pi$
$744$	9.95136	0.364834
$745$	15.3167	0.561160
$746$	−25.1833	−0.922027
$747$	−2.80750	−0.102721
$748$	−5.53620	−0.202423
$749$	18.3563	0.670725
$750$	−13.1155	−0.478911
$751$	−0.00373237	−0.000136196 0	−6.80980e−5	−	1.00000i	$-0.500022\pi$
$751$	−0.00373237	−0.000136196 0	−6.80980e−5		1.00000i	$0.500022\pi$
$752$	−3.94830	−0.143980
$753$	26.8104	0.977026
$754$	−13.2360	−0.482028
$755$	−49.7327	−1.80996
$756$	3.83085	0.139327
$757$	16.4259	0.597009	0.298504	−	0.954408i	$-0.403512\pi$
$757$	16.4259	0.597009	0.298504	+	0.954408i	$0.403512\pi$
$758$	−12.3196	−0.447468
$759$	4.26876	0.154946
$760$	7.55150	0.273922
$761$	24.5799	0.891022	0.445511	−	0.895276i	$-0.353022\pi$
$761$	24.5799	0.891022	0.445511	+	0.895276i	$0.353022\pi$
$762$	0.330139	0.0119597
$763$	−26.7461	−0.968274
$764$	1.45436	0.0526170
$765$	−20.3876	−0.737114
$766$	9.74981	0.352275
$767$	22.3153	0.805760
$768$	1.00000	0.0360844
$769$	−26.1757	−0.943921	−0.471960	−	0.881620i	$-0.656453\pi$
$769$	−26.1757	−0.943921	−0.471960	+	0.881620i	$0.656453\pi$
$770$	14.1074	0.508397
$771$	24.0707	0.866886
$772$	−3.31127	−0.119175
$773$	46.8128	1.68374	0.841870	−	0.539680i	$-0.181455\pi$
$773$	46.8128	1.68374	0.841870	+	0.539680i	$0.181455\pi$
$774$	4.82768	0.173527
$775$	85.1984	3.06042
$776$	17.4223	0.625424
$777$	18.0305	0.646841
$778$	−14.4568	−0.518303
$779$	−12.1033	−0.433646
$780$	16.0393	0.574298
$781$	8.28378	0.296417
$782$	−23.6327	−0.845105
$783$	3.03898	0.108604
$784$	7.67538	0.274121
$785$	−5.69536	−0.203276
$786$	−18.2262	−0.650105
$787$	23.4862	0.837193	0.418597	−	0.908172i	$-0.362522\pi$
$787$	23.4862	0.837193	0.418597	+	0.908172i	$0.362522\pi$
$788$	19.8874	0.708458
$789$	−21.6213	−0.769738
$790$	−49.5066	−1.76137
$791$	−57.0677	−2.02909
$792$	−1.00000	−0.0355335
$793$	−4.35543	−0.154666
$794$	−6.61526	−0.234767
$795$	−39.7388	−1.40939
$796$	15.4697	0.548309
$797$	27.0306	0.957472	0.478736	−	0.877959i	$-0.341095\pi$
$797$	27.0306	0.957472	0.478736	+	0.877959i	$0.341095\pi$
$798$	−7.85550	−0.278082
$799$	−21.8586	−0.773301
$800$	8.56149	0.302694
$801$	7.97205	0.281678
$802$	−12.8003	−0.451994
$803$	2.58389	0.0911834
$804$	−5.14887	−0.181587
$805$	60.2213	2.12252
$806$	−43.3424	−1.52667
$807$	10.9305	0.384771
$808$	18.6597	0.656445
$809$	−43.7495	−1.53815	−0.769076	−	0.639158i	$-0.779283\pi$
$809$	−43.7495	−1.53815	−0.769076	+	0.639158i	$0.779283\pi$
$810$	−3.68259	−0.129393
$811$	−39.9100	−1.40143	−0.700715	−	0.713441i	$-0.747136\pi$
$811$	−39.9100	−1.40143	−0.700715	+	0.713441i	$0.747136\pi$
$812$	11.6419	0.408549
$813$	−5.45796	−0.191419
$814$	−4.70666	−0.164968
$815$	−3.61092	−0.126485
$816$	5.53620	0.193806
$817$	−9.89960	−0.346343
$818$	23.3126	0.815104
$819$	−16.6850	−0.583020
$820$	−21.7359	−0.759051
$821$	50.6215	1.76670	0.883352	−	0.468711i	$-0.155281\pi$
$821$	50.6215	1.76670	0.883352	+	0.468711i	$0.155281\pi$
$822$	−21.4486	−0.748104
$823$	45.9591	1.60203	0.801016	−	0.598643i	$-0.204293\pi$
$823$	45.9591	1.60203	0.801016	+	0.598643i	$0.204293\pi$
$824$	5.13200	0.178782
$825$	−8.56149	−0.298073
$826$	−19.6276	−0.682932
$827$	−28.8509	−1.00324	−0.501622	−	0.865087i	$-0.667263\pi$
$827$	−28.8509	−1.00324	−0.501622	+	0.865087i	$0.667263\pi$
$828$	−4.26876	−0.148350
$829$	−20.7025	−0.719029	−0.359514	−	0.933140i	$-0.617058\pi$
$829$	−20.7025	−0.719029	−0.359514	+	0.933140i	$0.617058\pi$
$830$	10.3389	0.358867
$831$	20.6513	0.716384
$832$	−4.35543	−0.150997
$833$	42.4924	1.47228
$834$	9.51260	0.329394
$835$	6.23113	0.215637
$836$	2.05059	0.0709212
$837$	9.95136	0.343969
$838$	7.12991	0.246299
$839$	12.7613	0.440571	0.220285	−	0.975435i	$-0.429301\pi$
$839$	12.7613	0.440571	0.220285	+	0.975435i	$0.429301\pi$
$840$	−14.1074	−0.486753
$841$	−19.7646	−0.681539
$842$	−16.5516	−0.570406
$843$	−21.5082	−0.740782
$844$	−20.6676	−0.711408
$845$	−21.9842	−0.756279
$846$	−3.94830	−0.135745
$847$	3.83085	0.131629
$848$	10.7910	0.370564
$849$	−10.5070	−0.360600
$850$	47.3981	1.62574
$851$	−20.0916	−0.688732
$852$	−8.28378	−0.283798
$853$	−35.1862	−1.20475	−0.602376	−	0.798213i	$-0.705779\pi$
$853$	−35.1862	−1.20475	−0.602376	+	0.798213i	$0.705779\pi$
$854$	3.83085	0.131089
$855$	7.55150	0.258256
$856$	4.79171	0.163777
$857$	25.1664	0.859666	0.429833	−	0.902908i	$-0.358572\pi$
$857$	25.1664	0.859666	0.429833	+	0.902908i	$0.358572\pi$
$858$	4.35543	0.148692
$859$	−12.8777	−0.439383	−0.219692	−	0.975569i	$-0.570505\pi$
$859$	−12.8777	−0.439383	−0.219692	+	0.975569i	$0.570505\pi$
$860$	−17.7784	−0.606237
$861$	22.6110	0.770579
$862$	−14.2639	−0.485830
$863$	30.3505	1.03314	0.516571	−	0.856244i	$-0.327208\pi$
$863$	30.3505	1.03314	0.516571	+	0.856244i	$0.327208\pi$
$864$	1.00000	0.0340207
$865$	−3.87926	−0.131899
$866$	−1.47511	−0.0501262
$867$	13.6495	0.463561
$868$	38.1221	1.29395
$869$	−13.4434	−0.456037
$870$	−11.1913	−0.379421
$871$	22.4255	0.759861
$872$	−6.98178	−0.236433
$873$	17.4223	0.589656
$874$	8.75350	0.296091
$875$	−50.2435	−1.69854
$876$	−2.58389	−0.0873014
$877$	−37.9112	−1.28017	−0.640085	−	0.768304i	$-0.721101\pi$
$877$	−37.9112	−1.28017	−0.640085	+	0.768304i	$0.721101\pi$
$878$	11.9457	0.403149
$879$	−24.7215	−0.833835
$880$	3.68259	0.124140
$881$	15.6859	0.528470	0.264235	−	0.964458i	$-0.414881\pi$
$881$	15.6859	0.528470	0.264235	+	0.964458i	$0.414881\pi$
$882$	7.67538	0.258443
$883$	−38.6854	−1.30187	−0.650934	−	0.759134i	$-0.725623\pi$
$883$	−38.6854	−1.30187	−0.650934	+	0.759134i	$0.725623\pi$
$884$	−24.1125	−0.810992
$885$	18.8680	0.634242
$886$	8.08754	0.271706
$887$	17.5913	0.590660	0.295330	−	0.955395i	$-0.404570\pi$
$887$	17.5913	0.590660	0.295330	+	0.955395i	$0.404570\pi$
$888$	4.70666	0.157945
$889$	1.26471	0.0424170
$890$	−29.3578	−0.984076
$891$	−1.00000	−0.0335013
$892$	28.0993	0.940834
$893$	8.09636	0.270934
$894$	−4.15921	−0.139105
$895$	3.17005	0.105963
$896$	3.83085	0.127980
$897$	18.5923	0.620779
$898$	−3.25432	−0.108598
$899$	30.2419	1.00863
$900$	8.56149	0.285383
$901$	59.7411	1.99026
$902$	−5.90234	−0.196526
$903$	18.4941	0.615444
$904$	−14.8969	−0.495463
$905$	6.78057	0.225394
$906$	13.5048	0.448667
$907$	−20.1573	−0.669311	−0.334656	−	0.942341i	$-0.608620\pi$
$907$	−20.1573	−0.669311	−0.334656	+	0.942341i	$0.608620\pi$
$908$	−19.0464	−0.632076
$909$	18.6597	0.618902
$910$	61.4440	2.03685
$911$	47.7133	1.58081	0.790406	−	0.612583i	$-0.209870\pi$
$911$	47.7133	1.58081	0.790406	+	0.612583i	$0.209870\pi$
$912$	−2.05059	−0.0679019
$913$	2.80750	0.0929146
$914$	28.0754	0.928650
$915$	−3.68259	−0.121743
$916$	16.9109	0.558751
$917$	−69.8216	−2.30571
$918$	5.53620	0.182722
$919$	49.6403	1.63748	0.818742	−	0.574162i	$-0.194672\pi$
$919$	49.6403	1.63748	0.818742	+	0.574162i	$0.194672\pi$
$920$	15.7201	0.518277
$921$	−12.3785	−0.407885
$922$	−33.8367	−1.11435
$923$	36.0794	1.18757
$924$	−3.83085	−0.126026
$925$	40.2960	1.32493
$926$	−25.0259	−0.822402
$927$	5.13200	0.168557
$928$	3.03898	0.0997593
$929$	−2.18115	−0.0715614	−0.0357807	−	0.999360i	$-0.511392\pi$
$929$	−2.18115	−0.0715614	−0.0357807	+	0.999360i	$0.511392\pi$
$930$	−36.6468	−1.20170
$931$	−15.7391	−0.515827
$932$	−26.8797	−0.880473
$933$	10.0471	0.328926
$934$	−34.8540	−1.14046
$935$	20.3876	0.666745
$936$	−4.35543	−0.142362
$937$	48.9662	1.59966	0.799828	−	0.600229i	$-0.204924\pi$
$937$	48.9662	1.59966	0.799828	+	0.600229i	$0.204924\pi$
$938$	−19.7245	−0.644029
$939$	−12.3629	−0.403448
$940$	14.5400	0.474242
$941$	12.8696	0.419537	0.209768	−	0.977751i	$-0.432729\pi$
$941$	12.8696	0.419537	0.209768	+	0.977751i	$0.432729\pi$
$942$	1.54656	0.0503898
$943$	−25.1957	−0.820485
$944$	−5.12357	−0.166758
$945$	−14.1074	−0.458915
$946$	−4.82768	−0.156961
$947$	−57.8738	−1.88065	−0.940323	−	0.340282i	$-0.889477\pi$
$947$	−57.8738	−1.88065	−0.940323	+	0.340282i	$0.889477\pi$
$948$	13.4434	0.436622
$949$	11.2539	0.365318
$950$	−17.5561	−0.569596
$951$	3.32754	0.107903
$952$	21.2083	0.687366
$953$	7.75448	0.251192	0.125596	−	0.992081i	$-0.459916\pi$
$953$	7.75448	0.251192	0.125596	+	0.992081i	$0.459916\pi$
$954$	10.7910	0.349371
$955$	−5.35582	−0.173310
$956$	−9.04315	−0.292476
$957$	−3.03898	−0.0982362
$958$	−27.5913	−0.891435
$959$	−82.1661	−2.65328
$960$	−3.68259	−0.118855
$961$	68.0295	2.19450
$962$	−20.4995	−0.660932
$963$	4.79171	0.154411
$964$	10.4582	0.336834
$965$	12.1941	0.392541
$966$	−16.3530	−0.526148
$967$	48.0620	1.54557	0.772784	−	0.634669i	$-0.218864\pi$
$967$	48.0620	1.54557	0.772784	+	0.634669i	$0.218864\pi$
$968$	1.00000	0.0321412
$969$	−11.3525	−0.364694
$970$	−64.1593	−2.06003
$971$	23.8468	0.765282	0.382641	−	0.923897i	$-0.375015\pi$
$971$	23.8468	0.765282	0.382641	+	0.923897i	$0.375015\pi$
$972$	1.00000	0.0320750
$973$	36.4413	1.16825
$974$	−42.8355	−1.37254
$975$	−37.2889	−1.19420
$976$	1.00000	0.0320092
$977$	−44.9125	−1.43688	−0.718439	−	0.695590i	$-0.755143\pi$
$977$	−44.9125	−1.43688	−0.718439	+	0.695590i	$0.755143\pi$
$978$	0.980537	0.0313541
$979$	−7.97205	−0.254788
$980$	−28.2653	−0.902902
$981$	−6.98178	−0.222911
$982$	36.3403	1.15967
$983$	−13.0154	−0.415125	−0.207563	−	0.978222i	$-0.566553\pi$
$983$	−13.0154	−0.415125	−0.207563	+	0.978222i	$0.566553\pi$
$984$	5.90234	0.188160
$985$	−73.2371	−2.33353
$986$	16.8244	0.535797
$987$	−15.1253	−0.481445
$988$	8.93121	0.284140
$989$	−20.6082	−0.655303
$990$	3.68259	0.117040
$991$	−27.7800	−0.882461	−0.441231	−	0.897394i	$-0.645458\pi$
$991$	−27.7800	−0.882461	−0.441231	+	0.897394i	$0.645458\pi$
$992$	9.95136	0.315956
$993$	−1.76615	−0.0560470
$994$	−31.7339	−1.00654
$995$	−56.9686	−1.80603
$996$	−2.80750	−0.0889590
$997$	1.79195	0.0567517	0.0283759	−	0.999597i	$-0.490966\pi$
$997$	1.79195	0.0567517	0.0283759	+	0.999597i	$0.490966\pi$
$998$	12.9397	0.409598
$999$	4.70666	0.148912

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.bb.1.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.bb.1.1	✓	8	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.68259 q^{5} +1.00000 q^{6} +3.83085 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -3.68259 q^{5} +1.00000 q^{6} +3.83085 q^{7} +1.00000 q^{8} +1.00000 q^{9} -3.68259 q^{10} -1.00000 q^{11} +1.00000 q^{12} -4.35543 q^{13} +3.83085 q^{14} -3.68259 q^{15} +1.00000 q^{16} +5.53620 q^{17} +1.00000 q^{18} -2.05059 q^{19} -3.68259 q^{20} +3.83085 q^{21} -1.00000 q^{22} -4.26876 q^{23} +1.00000 q^{24} +8.56149 q^{25} -4.35543 q^{26} +1.00000 q^{27} +3.83085 q^{28} +3.03898 q^{29} -3.68259 q^{30} +9.95136 q^{31} +1.00000 q^{32} -1.00000 q^{33} +5.53620 q^{34} -14.1074 q^{35} +1.00000 q^{36} +4.70666 q^{37} -2.05059 q^{38} -4.35543 q^{39} -3.68259 q^{40} +5.90234 q^{41} +3.83085 q^{42} +4.82768 q^{43} -1.00000 q^{44} -3.68259 q^{45} -4.26876 q^{46} -3.94830 q^{47} +1.00000 q^{48} +7.67538 q^{49} +8.56149 q^{50} +5.53620 q^{51} -4.35543 q^{52} +10.7910 q^{53} +1.00000 q^{54} +3.68259 q^{55} +3.83085 q^{56} -2.05059 q^{57} +3.03898 q^{58} -5.12357 q^{59} -3.68259 q^{60} +1.00000 q^{61} +9.95136 q^{62} +3.83085 q^{63} +1.00000 q^{64} +16.0393 q^{65} -1.00000 q^{66} -5.14887 q^{67} +5.53620 q^{68} -4.26876 q^{69} -14.1074 q^{70} -8.28378 q^{71} +1.00000 q^{72} -2.58389 q^{73} +4.70666 q^{74} +8.56149 q^{75} -2.05059 q^{76} -3.83085 q^{77} -4.35543 q^{78} +13.4434 q^{79} -3.68259 q^{80} +1.00000 q^{81} +5.90234 q^{82} -2.80750 q^{83} +3.83085 q^{84} -20.3876 q^{85} +4.82768 q^{86} +3.03898 q^{87} -1.00000 q^{88} +7.97205 q^{89} -3.68259 q^{90} -16.6850 q^{91} -4.26876 q^{92} +9.95136 q^{93} -3.94830 q^{94} +7.55150 q^{95} +1.00000 q^{96} +17.4223 q^{97} +7.67538 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 5 q^{5} + 8 q^{6} + 13 q^{7} + 8 q^{8} + 8 q^{9} + 5 q^{10} - 8 q^{11} + 8 q^{12} + 10 q^{13} + 13 q^{14} + 5 q^{15} + 8 q^{16} + 4 q^{17} + 8 q^{18} + 11 q^{19} + 5 q^{20} + 13 q^{21} - 8 q^{22} + 2 q^{23} + 8 q^{24} + 23 q^{25} + 10 q^{26} + 8 q^{27} + 13 q^{28} + 10 q^{29} + 5 q^{30} + 9 q^{31} + 8 q^{32} - 8 q^{33} + 4 q^{34} - 3 q^{35} + 8 q^{36} + 9 q^{37} + 11 q^{38} + 10 q^{39} + 5 q^{40} + 3 q^{41} + 13 q^{42} + 16 q^{43} - 8 q^{44} + 5 q^{45} + 2 q^{46} - 16 q^{47} + 8 q^{48} + 17 q^{49} + 23 q^{50} + 4 q^{51} + 10 q^{52} + 7 q^{53} + 8 q^{54} - 5 q^{55} + 13 q^{56} + 11 q^{57} + 10 q^{58} - 14 q^{59} + 5 q^{60} + 8 q^{61} + 9 q^{62} + 13 q^{63} + 8 q^{64} + 22 q^{65} - 8 q^{66} + 8 q^{67} + 4 q^{68} + 2 q^{69} - 3 q^{70} + 11 q^{71} + 8 q^{72} + 14 q^{73} + 9 q^{74} + 23 q^{75} + 11 q^{76} - 13 q^{77} + 10 q^{78} + 22 q^{79} + 5 q^{80} + 8 q^{81} + 3 q^{82} - 16 q^{83} + 13 q^{84} + 3 q^{85} + 16 q^{86} + 10 q^{87} - 8 q^{88} + q^{89} + 5 q^{90} + 15 q^{91} + 2 q^{92} + 9 q^{93} - 16 q^{94} - 9 q^{95} + 8 q^{96} + 24 q^{97} + 17 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 5 * q^5 + 8 * q^6 + 13 * q^7 + 8 * q^8 + 8 * q^9 + 5 * q^10 - 8 * q^11 + 8 * q^12 + 10 * q^13 + 13 * q^14 + 5 * q^15 + 8 * q^16 + 4 * q^17 + 8 * q^18 + 11 * q^19 + 5 * q^20 + 13 * q^21 - 8 * q^22 + 2 * q^23 + 8 * q^24 + 23 * q^25 + 10 * q^26 + 8 * q^27 + 13 * q^28 + 10 * q^29 + 5 * q^30 + 9 * q^31 + 8 * q^32 - 8 * q^33 + 4 * q^34 - 3 * q^35 + 8 * q^36 + 9 * q^37 + 11 * q^38 + 10 * q^39 + 5 * q^40 + 3 * q^41 + 13 * q^42 + 16 * q^43 - 8 * q^44 + 5 * q^45 + 2 * q^46 - 16 * q^47 + 8 * q^48 + 17 * q^49 + 23 * q^50 + 4 * q^51 + 10 * q^52 + 7 * q^53 + 8 * q^54 - 5 * q^55 + 13 * q^56 + 11 * q^57 + 10 * q^58 - 14 * q^59 + 5 * q^60 + 8 * q^61 + 9 * q^62 + 13 * q^63 + 8 * q^64 + 22 * q^65 - 8 * q^66 + 8 * q^67 + 4 * q^68 + 2 * q^69 - 3 * q^70 + 11 * q^71 + 8 * q^72 + 14 * q^73 + 9 * q^74 + 23 * q^75 + 11 * q^76 - 13 * q^77 + 10 * q^78 + 22 * q^79 + 5 * q^80 + 8 * q^81 + 3 * q^82 - 16 * q^83 + 13 * q^84 + 3 * q^85 + 16 * q^86 + 10 * q^87 - 8 * q^88 + q^89 + 5 * q^90 + 15 * q^91 + 2 * q^92 + 9 * q^93 - 16 * q^94 - 9 * q^95 + 8 * q^96 + 24 * q^97 + 17 * q^98 - 8 * q^99

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