LMFDB - Embedded newform 1334.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1334,2,Mod(1,1334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1334 = 2 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1334.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:	$10.6520436296$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.4352.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 6x^{2} - 4x + 2 $ x^4 - 6x^2 - 4x + 2
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			1.2
Root			$-1.27133$ of defining polynomial
Character	$\chi$	$=$	1334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +4.21215 q^{5} -2.41421 q^{6} -1.11239 q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +4.21215 q^{5} -2.41421 q^{6} -1.11239 q^{7} +1.00000 q^{8} +2.82843 q^{9} +4.21215 q^{10} -5.09976 q^{11} -2.41421 q^{12} -6.06926 q^{13} -1.11239 q^{14} -10.1690 q^{15} +1.00000 q^{16} -4.52660 q^{17} +2.82843 q^{18} -7.95687 q^{19} +4.21215 q^{20} +2.68554 q^{21} -5.09976 q^{22} +1.00000 q^{23} -2.41421 q^{24} +12.7422 q^{25} -6.06926 q^{26} +0.414214 q^{27} -1.11239 q^{28} -1.00000 q^{29} -10.1690 q^{30} -1.50389 q^{31} +1.00000 q^{32} +12.3119 q^{33} -4.52660 q^{34} -4.68554 q^{35} +2.82843 q^{36} +2.16559 q^{37} -7.95687 q^{38} +14.6525 q^{39} +4.21215 q^{40} -2.82662 q^{41} +2.68554 q^{42} -3.61030 q^{43} -5.09976 q^{44} +11.9137 q^{45} +1.00000 q^{46} -8.55710 q^{47} -2.41421 q^{48} -5.76259 q^{49} +12.7422 q^{50} +10.9282 q^{51} -6.06926 q^{52} +11.0406 q^{53} +0.414214 q^{54} -21.4809 q^{55} -1.11239 q^{56} +19.2096 q^{57} -1.00000 q^{58} +8.65848 q^{59} -10.1690 q^{60} +6.80136 q^{61} -1.50389 q^{62} -3.14631 q^{63} +1.00000 q^{64} -25.5646 q^{65} +12.3119 q^{66} +12.4631 q^{67} -4.52660 q^{68} -2.41421 q^{69} -4.68554 q^{70} -5.31010 q^{71} +2.82843 q^{72} -8.23599 q^{73} +2.16559 q^{74} -30.7623 q^{75} -7.95687 q^{76} +5.67291 q^{77} +14.6525 q^{78} +6.44633 q^{79} +4.21215 q^{80} -9.48528 q^{81} -2.82662 q^{82} -5.28739 q^{83} +2.68554 q^{84} -19.0667 q^{85} -3.61030 q^{86} +2.41421 q^{87} -5.09976 q^{88} -13.3846 q^{89} +11.9137 q^{90} +6.75138 q^{91} +1.00000 q^{92} +3.63072 q^{93} -8.55710 q^{94} -33.5155 q^{95} -2.41421 q^{96} +9.67956 q^{97} -5.76259 q^{98} -14.4243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 4 q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 8 q^{15} + 4 q^{16} - 12 q^{17} - 16 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 4 q^{28} - 4 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{32} + 16 q^{33} - 12 q^{34} - 8 q^{35} - 4 q^{37} - 16 q^{38} + 4 q^{39} - 12 q^{41} + 4 q^{43} - 4 q^{44} + 16 q^{45} + 4 q^{46} - 28 q^{47} - 4 q^{48} - 8 q^{49} + 8 q^{50} + 16 q^{51} - 8 q^{52} + 16 q^{53} - 4 q^{54} - 20 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} + 4 q^{59} - 8 q^{60} - 4 q^{61} - 12 q^{62} + 8 q^{63} + 4 q^{64} - 24 q^{65} + 16 q^{66} - 12 q^{68} - 4 q^{69} - 8 q^{70} - 24 q^{73} - 4 q^{74} - 24 q^{75} - 16 q^{76} - 4 q^{77} + 4 q^{78} + 12 q^{79} - 4 q^{81} - 12 q^{82} - 12 q^{83} - 16 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{88} + 16 q^{89} + 16 q^{90} + 20 q^{91} + 4 q^{92} + 24 q^{93} - 28 q^{94} - 16 q^{95} - 4 q^{96} + 4 q^{97} - 8 q^{98} - 24 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 4 * q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 8 * q^15 + 4 * q^16 - 12 * q^17 - 16 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 4 * q^28 - 4 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^32 + 16 * q^33 - 12 * q^34 - 8 * q^35 - 4 * q^37 - 16 * q^38 + 4 * q^39 - 12 * q^41 + 4 * q^43 - 4 * q^44 + 16 * q^45 + 4 * q^46 - 28 * q^47 - 4 * q^48 - 8 * q^49 + 8 * q^50 + 16 * q^51 - 8 * q^52 + 16 * q^53 - 4 * q^54 - 20 * q^55 - 4 * q^56 + 16 * q^57 - 4 * q^58 + 4 * q^59 - 8 * q^60 - 4 * q^61 - 12 * q^62 + 8 * q^63 + 4 * q^64 - 24 * q^65 + 16 * q^66 - 12 * q^68 - 4 * q^69 - 8 * q^70 - 24 * q^73 - 4 * q^74 - 24 * q^75 - 16 * q^76 - 4 * q^77 + 4 * q^78 + 12 * q^79 - 4 * q^81 - 12 * q^82 - 12 * q^83 - 16 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^88 + 16 * q^89 + 16 * q^90 + 20 * q^91 + 4 * q^92 + 24 * q^93 - 28 * q^94 - 16 * q^95 - 4 * q^96 + 4 * q^97 - 8 * q^98 - 24 * 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
$3$	−2.41421	−1.39385	−0.696923	−	0.717146i	$-0.745448\pi$
$3$	−2.41421	−1.39385	−0.696923	+	0.717146i	$0.745448\pi$
$4$	1.00000	0.500000
$5$	4.21215	1.88373	0.941865	−	0.335993i	$-0.109072\pi$
$5$	4.21215	1.88373	0.941865	+	0.335993i	$0.109072\pi$
$6$	−2.41421	−0.985599
$7$	−1.11239	−0.420443	−0.210222	−	0.977654i	$-0.567419\pi$
$7$	−1.11239	−0.420443	−0.210222	+	0.977654i	$0.567419\pi$
$8$	1.00000	0.353553
$9$	2.82843	0.942809
$10$	4.21215	1.33200
$11$	−5.09976	−1.53763	−0.768817	−	0.639468i	$-0.779154\pi$
$11$	−5.09976	−1.53763	−0.768817	+	0.639468i	$0.779154\pi$
$12$	−2.41421	−0.696923
$13$	−6.06926	−1.68331	−0.841655	−	0.540015i	$-0.818419\pi$
$13$	−6.06926	−1.68331	−0.841655	+	0.540015i	$0.818419\pi$
$14$	−1.11239	−0.297298
$15$	−10.1690	−2.62563
$16$	1.00000	0.250000
$17$	−4.52660	−1.09786	−0.548931	−	0.835868i	$-0.684965\pi$
$17$	−4.52660	−1.09786	−0.548931	+	0.835868i	$0.684965\pi$
$18$	2.82843	0.666667
$19$	−7.95687	−1.82543	−0.912716	−	0.408594i	$-0.866019\pi$
$19$	−7.95687	−1.82543	−0.912716	+	0.408594i	$0.866019\pi$
$20$	4.21215	0.941865
$21$	2.68554	0.586034
$22$	−5.09976	−1.08727
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−2.41421	−0.492799
$25$	12.7422	2.54844
$26$	−6.06926	−1.19028
$27$	0.414214	0.0797154
$28$	−1.11239	−0.210222
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−10.1690	−1.85660
$31$	−1.50389	−0.270107	−0.135054	−	0.990838i	$-0.543121\pi$
$31$	−1.50389	−0.270107	−0.135054	+	0.990838i	$0.543121\pi$
$32$	1.00000	0.176777
$33$	12.3119	2.14323
$34$	−4.52660	−0.776306
$35$	−4.68554	−0.792001
$36$	2.82843	0.471405
$37$	2.16559	0.356021	0.178011	−	0.984029i	$-0.443034\pi$
$37$	2.16559	0.356021	0.178011	+	0.984029i	$0.443034\pi$
$38$	−7.95687	−1.29078
$39$	14.6525	2.34628
$40$	4.21215	0.665999
$41$	−2.82662	−0.441444	−0.220722	−	0.975337i	$-0.570841\pi$
$41$	−2.82662	−0.441444	−0.220722	+	0.975337i	$0.570841\pi$
$42$	2.68554	0.414388
$43$	−3.61030	−0.550566	−0.275283	−	0.961363i	$-0.588772\pi$
$43$	−3.61030	−0.550566	−0.275283	+	0.961363i	$0.588772\pi$
$44$	−5.09976	−0.768817
$45$	11.9137	1.77600
$46$	1.00000	0.147442
$47$	−8.55710	−1.24818	−0.624090	−	0.781352i	$-0.714530\pi$
$47$	−8.55710	−1.24818	−0.624090	+	0.781352i	$0.714530\pi$
$48$	−2.41421	−0.348462
$49$	−5.76259	−0.823227
$50$	12.7422	1.80202
$51$	10.9282	1.53025
$52$	−6.06926	−0.841655
$53$	11.0406	1.51654	0.758270	−	0.651941i	$-0.226045\pi$
$53$	11.0406	1.51654	0.758270	+	0.651941i	$0.226045\pi$
$54$	0.414214	0.0563673
$55$	−21.4809	−2.89649
$56$	−1.11239	−0.148649
$57$	19.2096	2.54437
$58$	−1.00000	−0.131306
$59$	8.65848	1.12724	0.563619	−	0.826035i	$-0.309409\pi$
$59$	8.65848	1.12724	0.563619	+	0.826035i	$0.309409\pi$
$60$	−10.1690	−1.31281
$61$	6.80136	0.870825	0.435412	−	0.900231i	$-0.356603\pi$
$61$	6.80136	0.870825	0.435412	+	0.900231i	$0.356603\pi$
$62$	−1.50389	−0.190994
$63$	−3.14631	−0.396398
$64$	1.00000	0.125000
$65$	−25.5646	−3.17090
$66$	12.3119	1.51549
$67$	12.4631	1.52261	0.761303	−	0.648397i	$-0.224560\pi$
$67$	12.4631	1.52261	0.761303	+	0.648397i	$0.224560\pi$
$68$	−4.52660	−0.548931
$69$	−2.41421	−0.290637
$70$	−4.68554	−0.560030
$71$	−5.31010	−0.630193	−0.315096	−	0.949060i	$-0.602037\pi$
$71$	−5.31010	−0.630193	−0.315096	+	0.949060i	$0.602037\pi$
$72$	2.82843	0.333333
$73$	−8.23599	−0.963950	−0.481975	−	0.876185i	$-0.660080\pi$
$73$	−8.23599	−0.963950	−0.481975	+	0.876185i	$0.660080\pi$
$74$	2.16559	0.251745
$75$	−30.7623	−3.55213
$76$	−7.95687	−0.912716
$77$	5.67291	0.646488
$78$	14.6525	1.65907
$79$	6.44633	0.725269	0.362634	−	0.931931i	$-0.381877\pi$
$79$	6.44633	0.725269	0.362634	+	0.931931i	$0.381877\pi$
$80$	4.21215	0.470932
$81$	−9.48528	−1.05392
$82$	−2.82662	−0.312148
$83$	−5.28739	−0.580366	−0.290183	−	0.956971i	$-0.593716\pi$
$83$	−5.28739	−0.580366	−0.290183	+	0.956971i	$0.593716\pi$
$84$	2.68554	0.293017
$85$	−19.0667	−2.06808
$86$	−3.61030	−0.389309
$87$	2.41421	0.258831
$88$	−5.09976	−0.543636
$89$	−13.3846	−1.41876	−0.709382	−	0.704824i	$-0.751026\pi$
$89$	−13.3846	−1.41876	−0.709382	+	0.704824i	$0.751026\pi$
$90$	11.9137	1.25582
$91$	6.75138	0.707737
$92$	1.00000	0.104257
$93$	3.63072	0.376488
$94$	−8.55710	−0.882597
$95$	−33.5155	−3.43862
$96$	−2.41421	−0.246400
$97$	9.67956	0.982811	0.491405	−	0.870931i	$-0.336483\pi$
$97$	9.67956	0.982811	0.491405	+	0.870931i	$0.336483\pi$
$98$	−5.76259	−0.582110
$99$	−14.4243	−1.44970
$100$	12.7422	1.27422
$101$	9.49356	0.944644	0.472322	−	0.881426i	$-0.343416\pi$
$101$	9.49356	0.944644	0.472322	+	0.881426i	$0.343416\pi$
$102$	10.9282	1.08205
$103$	1.00162	0.0986928	0.0493464	−	0.998782i	$-0.484286\pi$
$103$	1.00162	0.0986928	0.0493464	+	0.998782i	$0.484286\pi$
$104$	−6.06926	−0.595140
$105$	11.3119	1.10393
$106$	11.0406	1.07236
$107$	−12.8738	−1.24456	−0.622281	−	0.782794i	$-0.713794\pi$
$107$	−12.8738	−1.24456	−0.622281	+	0.782794i	$0.713794\pi$
$108$	0.414214	0.0398577
$109$	−17.2197	−1.64935	−0.824673	−	0.565610i	$-0.808641\pi$
$109$	−17.2197	−1.64935	−0.824673	+	0.565610i	$0.808641\pi$
$110$	−21.4809	−2.04813
$111$	−5.22820	−0.496239
$112$	−1.11239	−0.105111
$113$	−3.97474	−0.373912	−0.186956	−	0.982368i	$-0.559862\pi$
$113$	−3.97474	−0.373912	−0.186956	+	0.982368i	$0.559862\pi$
$114$	19.2096	1.79914
$115$	4.21215	0.392785
$116$	−1.00000	−0.0928477
$117$	−17.1665	−1.58704
$118$	8.65848	0.797077
$119$	5.03534	0.461589
$120$	−10.1690	−0.928300
$121$	15.0075	1.36432
$122$	6.80136	0.615766
$123$	6.82407	0.615306
$124$	−1.50389	−0.135054
$125$	32.6112	2.91683
$126$	−3.14631	−0.280296
$127$	−2.37887	−0.211091	−0.105545	−	0.994414i	$-0.533659\pi$
$127$	−2.37887	−0.211091	−0.105545	+	0.994414i	$0.533659\pi$
$128$	1.00000	0.0883883
$129$	8.71604	0.767404
$130$	−25.5646	−2.24217
$131$	2.50894	0.219207	0.109604	−	0.993975i	$-0.465042\pi$
$131$	2.50894	0.219207	0.109604	+	0.993975i	$0.465042\pi$
$132$	12.3119	1.07161
$133$	8.85114	0.767491
$134$	12.4631	1.07664
$135$	1.74473	0.150162
$136$	−4.52660	−0.388153
$137$	0.378669	0.0323519	0.0161760	−	0.999869i	$-0.494851\pi$
$137$	0.378669	0.0323519	0.0161760	+	0.999869i	$0.494851\pi$
$138$	−2.41421	−0.205512
$139$	−3.13510	−0.265916	−0.132958	−	0.991122i	$-0.542447\pi$
$139$	−3.13510	−0.265916	−0.132958	+	0.991122i	$0.542447\pi$
$140$	−4.68554	−0.396001
$141$	20.6587	1.73977
$142$	−5.31010	−0.445614
$143$	30.9518	2.58832
$144$	2.82843	0.235702
$145$	−4.21215	−0.349800
$146$	−8.23599	−0.681615
$147$	13.9121	1.14745
$148$	2.16559	0.178011
$149$	−6.86122	−0.562093	−0.281046	−	0.959694i	$-0.590681\pi$
$149$	−6.86122	−0.562093	−0.281046	+	0.959694i	$0.590681\pi$
$150$	−30.7623	−2.51173
$151$	11.9401	0.971669	0.485834	−	0.874051i	$-0.338516\pi$
$151$	11.9401	0.971669	0.485834	+	0.874051i	$0.338516\pi$
$152$	−7.95687	−0.645388
$153$	−12.8032	−1.03507
$154$	5.67291	0.457136
$155$	−6.33461	−0.508808
$156$	14.6525	1.17314
$157$	21.2866	1.69886	0.849429	−	0.527702i	$-0.176946\pi$
$157$	21.2866	1.69886	0.849429	+	0.527702i	$0.176946\pi$
$158$	6.44633	0.512843
$159$	−26.6543	−2.11382
$160$	4.21215	0.332999
$161$	−1.11239	−0.0876685
$162$	−9.48528	−0.745234
$163$	11.2559	0.881634	0.440817	−	0.897597i	$-0.354689\pi$
$163$	11.2559	0.881634	0.440817	+	0.897597i	$0.354689\pi$
$164$	−2.82662	−0.220722
$165$	51.8595	4.03726
$166$	−5.28739	−0.410381
$167$	1.95203	0.151052	0.0755262	−	0.997144i	$-0.475936\pi$
$167$	1.95203	0.151052	0.0755262	+	0.997144i	$0.475936\pi$
$168$	2.68554	0.207194
$169$	23.8360	1.83353
$170$	−19.0667	−1.46235
$171$	−22.5054	−1.72103
$172$	−3.61030	−0.275283
$173$	−14.2031	−1.07984	−0.539922	−	0.841715i	$-0.681546\pi$
$173$	−14.2031	−1.07984	−0.539922	+	0.841715i	$0.681546\pi$
$174$	2.41421	0.183021
$175$	−14.1743	−1.07147
$176$	−5.09976	−0.384409
$177$	−20.9034	−1.57120
$178$	−13.3846	−1.00322
$179$	−3.32776	−0.248728	−0.124364	−	0.992237i	$-0.539689\pi$
$179$	−3.32776	−0.248728	−0.124364	+	0.992237i	$0.539689\pi$
$180$	11.9137	0.887998
$181$	−12.0243	−0.893762	−0.446881	−	0.894594i	$-0.647465\pi$
$181$	−12.0243	−0.893762	−0.446881	+	0.894594i	$0.647465\pi$
$182$	6.75138	0.500446
$183$	−16.4199	−1.21380
$184$	1.00000	0.0737210
$185$	9.12180	0.670648
$186$	3.63072	0.266217
$187$	23.0846	1.68811
$188$	−8.55710	−0.624090
$189$	−0.460766	−0.0335158
$190$	−33.5155	−2.43147
$191$	1.91375	0.138474	0.0692370	−	0.997600i	$-0.477944\pi$
$191$	1.91375	0.138474	0.0692370	+	0.997600i	$0.477944\pi$
$192$	−2.41421	−0.174231
$193$	1.84562	0.132851	0.0664253	−	0.997791i	$-0.478841\pi$
$193$	1.84562	0.132851	0.0664253	+	0.997791i	$0.478841\pi$
$194$	9.67956	0.694952
$195$	61.7185	4.41975
$196$	−5.76259	−0.411614
$197$	−3.59587	−0.256195	−0.128097	−	0.991762i	$-0.540887\pi$
$197$	−3.59587	−0.256195	−0.128097	+	0.991762i	$0.540887\pi$
$198$	−14.4243	−1.02509
$199$	−16.6779	−1.18227	−0.591134	−	0.806573i	$-0.701320\pi$
$199$	−16.6779	−1.18227	−0.591134	+	0.806573i	$0.701320\pi$
$200$	12.7422	0.901008
$201$	−30.0885	−2.12228
$202$	9.49356	0.667964
$203$	1.11239	0.0780744
$204$	10.9282	0.765126
$205$	−11.9061	−0.831561
$206$	1.00162	0.0697863
$207$	2.82843	0.196589
$208$	−6.06926	−0.420828
$209$	40.5781	2.80685
$210$	11.3119	0.780596
$211$	−1.84268	−0.126855	−0.0634277	−	0.997986i	$-0.520203\pi$
$211$	−1.84268	−0.126855	−0.0634277	+	0.997986i	$0.520203\pi$
$212$	11.0406	0.758270
$213$	12.8197	0.878392
$214$	−12.8738	−0.880038
$215$	−15.2071	−1.03712
$216$	0.414214	0.0281837
$217$	1.67291	0.113565
$218$	−17.2197	−1.16626
$219$	19.8834	1.34360
$220$	−21.4809	−1.44824
$221$	27.4731	1.84804
$222$	−5.22820	−0.350894
$223$	−27.5547	−1.84520	−0.922601	−	0.385755i	$-0.873941\pi$
$223$	−27.5547	−1.84520	−0.922601	+	0.385755i	$0.873941\pi$
$224$	−1.11239	−0.0743246
$225$	36.0403	2.40269
$226$	−3.97474	−0.264396
$227$	27.4041	1.81887	0.909436	−	0.415845i	$-0.136514\pi$
$227$	27.4041	1.81887	0.909436	+	0.415845i	$0.136514\pi$
$228$	19.2096	1.27219
$229$	−0.0245149	−0.00161999	−0.000809994	−	1.00000i	$-0.500258\pi$
$229$	−0.0245149	−0.00161999	−0.000809994		1.00000i	$0.500258\pi$
$230$	4.21215	0.277741
$231$	−13.6956	−0.901106
$232$	−1.00000	−0.0656532
$233$	−2.22060	−0.145477	−0.0727383	−	0.997351i	$-0.523174\pi$
$233$	−2.22060	−0.145477	−0.0727383	+	0.997351i	$0.523174\pi$
$234$	−17.1665	−1.12221
$235$	−36.0437	−2.35123
$236$	8.65848	0.563619
$237$	−15.5628	−1.01091
$238$	5.03534	0.326393
$239$	7.62523	0.493235	0.246617	−	0.969113i	$-0.420681\pi$
$239$	7.62523	0.493235	0.246617	+	0.969113i	$0.420681\pi$
$240$	−10.1690	−0.656407
$241$	−16.2555	−1.04711	−0.523554	−	0.851993i	$-0.675394\pi$
$241$	−16.2555	−1.04711	−0.523554	+	0.851993i	$0.675394\pi$
$242$	15.0075	0.964720
$243$	21.6569	1.38929
$244$	6.80136	0.435412
$245$	−24.2729	−1.55074
$246$	6.82407	0.435087
$247$	48.2924	3.07277
$248$	−1.50389	−0.0954972
$249$	12.7649	0.808942
$250$	32.6112	2.06251
$251$	−20.5928	−1.29981	−0.649904	−	0.760017i	$-0.725191\pi$
$251$	−20.5928	−1.29981	−0.649904	+	0.760017i	$0.725191\pi$
$252$	−3.14631	−0.198199
$253$	−5.09976	−0.320619
$254$	−2.37887	−0.149264
$255$	46.0311	2.88258
$256$	1.00000	0.0625000
$257$	−9.37176	−0.584594	−0.292297	−	0.956328i	$-0.594420\pi$
$257$	−9.37176	−0.584594	−0.292297	+	0.956328i	$0.594420\pi$
$258$	8.71604	0.542637
$259$	−2.40898	−0.149687
$260$	−25.5646	−1.58545
$261$	−2.82843	−0.175075
$262$	2.50894	0.155003
$263$	−23.6128	−1.45603	−0.728014	−	0.685563i	$-0.759556\pi$
$263$	−23.6128	−1.45603	−0.728014	+	0.685563i	$0.759556\pi$
$264$	12.3119	0.757745
$265$	46.5045	2.85675
$266$	8.85114	0.542698
$267$	32.3133	1.97754
$268$	12.4631	0.761303
$269$	−6.53601	−0.398508	−0.199254	−	0.979948i	$-0.563852\pi$
$269$	−6.53601	−0.398508	−0.199254	+	0.979948i	$0.563852\pi$
$270$	1.74473	0.106181
$271$	0.602517	0.0366003	0.0183001	−	0.999833i	$-0.494175\pi$
$271$	0.602517	0.0366003	0.0183001	+	0.999833i	$0.494175\pi$
$272$	−4.52660	−0.274466
$273$	−16.2993	−0.986477
$274$	0.378669	0.0228763
$275$	−64.9820	−3.91856
$276$	−2.41421	−0.145319
$277$	14.9780	0.899939	0.449969	−	0.893044i	$-0.351435\pi$
$277$	14.9780	0.899939	0.449969	+	0.893044i	$0.351435\pi$
$278$	−3.13510	−0.188031
$279$	−4.25365	−0.254659
$280$	−4.68554	−0.280015
$281$	−19.1679	−1.14346	−0.571730	−	0.820442i	$-0.693728\pi$
$281$	−19.1679	−1.14346	−0.571730	+	0.820442i	$0.693728\pi$
$282$	20.6587	1.23021
$283$	8.75499	0.520430	0.260215	−	0.965551i	$-0.416207\pi$
$283$	8.75499	0.520430	0.260215	+	0.965551i	$0.416207\pi$
$284$	−5.31010	−0.315096
$285$	80.9136	4.79291
$286$	30.9518	1.83022
$287$	3.14430	0.185602
$288$	2.82843	0.166667
$289$	3.49013	0.205302
$290$	−4.21215	−0.247346
$291$	−23.3685	−1.36989
$292$	−8.23599	−0.481975
$293$	27.3119	1.59558	0.797789	−	0.602936i	$-0.206003\pi$
$293$	27.3119	1.59558	0.797789	+	0.602936i	$0.206003\pi$
$294$	13.9121	0.811372
$295$	36.4708	2.12341
$296$	2.16559	0.125873
$297$	−2.11239	−0.122573
$298$	−6.86122	−0.397460
$299$	−6.06926	−0.350995
$300$	−30.7623	−1.77606
$301$	4.01606	0.231482
$302$	11.9401	0.687074
$303$	−22.9195	−1.31669
$304$	−7.95687	−0.456358
$305$	28.6483	1.64040
$306$	−12.8032	−0.731908
$307$	19.8531	1.13308	0.566539	−	0.824035i	$-0.308282\pi$
$307$	19.8531	1.13308	0.566539	+	0.824035i	$0.308282\pi$
$308$	5.67291	0.323244
$309$	−2.41813	−0.137563
$310$	−6.33461	−0.359782
$311$	−27.0027	−1.53118	−0.765591	−	0.643328i	$-0.777553\pi$
$311$	−27.0027	−1.53118	−0.765591	+	0.643328i	$0.777553\pi$
$312$	14.6525	0.829534
$313$	8.46829	0.478656	0.239328	−	0.970939i	$-0.423073\pi$
$313$	8.46829	0.478656	0.239328	+	0.970939i	$0.423073\pi$
$314$	21.2866	1.20127
$315$	−13.2527	−0.746706
$316$	6.44633	0.362634
$317$	9.78443	0.549548	0.274774	−	0.961509i	$-0.411397\pi$
$317$	9.78443	0.549548	0.274774	+	0.961509i	$0.411397\pi$
$318$	−26.6543	−1.49470
$319$	5.09976	0.285532
$320$	4.21215	0.235466
$321$	31.0802	1.73473
$322$	−1.11239	−0.0619910
$323$	36.0176	2.00407
$324$	−9.48528	−0.526960
$325$	−77.3356	−4.28981
$326$	11.2559	0.623409
$327$	41.5720	2.29894
$328$	−2.82662	−0.156074
$329$	9.51882	0.524789
$330$	51.8595	2.85477
$331$	−24.6997	−1.35762	−0.678810	−	0.734314i	$-0.737504\pi$
$331$	−24.6997	−1.35762	−0.678810	+	0.734314i	$0.737504\pi$
$332$	−5.28739	−0.290183
$333$	6.12522	0.335660
$334$	1.95203	0.106810
$335$	52.4962	2.86818
$336$	2.68554	0.146508
$337$	8.56537	0.466585	0.233293	−	0.972407i	$-0.425050\pi$
$337$	8.56537	0.466585	0.233293	+	0.972407i	$0.425050\pi$
$338$	23.8360	1.29650
$339$	9.59587	0.521176
$340$	−19.0667	−1.03404
$341$	7.66949	0.415326
$342$	−22.5054	−1.21695
$343$	14.1970	0.766564
$344$	−3.61030	−0.194654
$345$	−10.1690	−0.547482
$346$	−14.2031	−0.763565
$347$	−15.5897	−0.836899	−0.418450	−	0.908240i	$-0.637426\pi$
$347$	−15.5897	−0.836899	−0.418450	+	0.908240i	$0.637426\pi$
$348$	2.41421	0.129415
$349$	−10.6229	−0.568633	−0.284316	−	0.958731i	$-0.591767\pi$
$349$	−10.6229	−0.568633	−0.284316	+	0.958731i	$0.591767\pi$
$350$	−14.1743	−0.757646
$351$	−2.51397	−0.134186
$352$	−5.09976	−0.271818
$353$	−16.2654	−0.865717	−0.432859	−	0.901462i	$-0.642495\pi$
$353$	−16.2654	−0.865717	−0.432859	+	0.901462i	$0.642495\pi$
$354$	−20.9034	−1.11100
$355$	−22.3669	−1.18711
$356$	−13.3846	−0.709382
$357$	−12.1564	−0.643384
$358$	−3.32776	−0.175878
$359$	18.1654	0.958734	0.479367	−	0.877615i	$-0.340866\pi$
$359$	18.1654	0.958734	0.479367	+	0.877615i	$0.340866\pi$
$360$	11.9137	0.627910
$361$	44.3118	2.33220
$362$	−12.0243	−0.631985
$363$	−36.2314	−1.90165
$364$	6.75138	0.353868
$365$	−34.6912	−1.81582
$366$	−16.4199	−0.858284
$367$	−4.46487	−0.233064	−0.116532	−	0.993187i	$-0.537178\pi$
$367$	−4.46487	−0.233064	−0.116532	+	0.993187i	$0.537178\pi$
$368$	1.00000	0.0521286
$369$	−7.99490	−0.416198
$370$	9.12180	0.474220
$371$	−12.2814	−0.637619
$372$	3.63072	0.188244
$373$	−32.6754	−1.69187	−0.845934	−	0.533287i	$-0.820957\pi$
$373$	−32.6754	−1.69187	−0.845934	+	0.533287i	$0.820957\pi$
$374$	23.0846	1.19367
$375$	−78.7303	−4.06562
$376$	−8.55710	−0.441299
$377$	6.06926	0.312583
$378$	−0.460766	−0.0236993
$379$	6.17425	0.317150	0.158575	−	0.987347i	$-0.449310\pi$
$379$	6.17425	0.317150	0.158575	+	0.987347i	$0.449310\pi$
$380$	−33.5155	−1.71931
$381$	5.74311	0.294228
$382$	1.91375	0.0979159
$383$	28.3311	1.44765	0.723827	−	0.689982i	$-0.242382\pi$
$383$	28.3311	1.44765	0.723827	+	0.689982i	$0.242382\pi$
$384$	−2.41421	−0.123200
$385$	23.8951	1.21781
$386$	1.84562	0.0939395
$387$	−10.2115	−0.519078
$388$	9.67956	0.491405
$389$	−12.0584	−0.611387	−0.305694	−	0.952130i	$-0.598888\pi$
$389$	−12.0584	−0.611387	−0.305694	+	0.952130i	$0.598888\pi$
$390$	61.7185	3.12524
$391$	−4.52660	−0.228920
$392$	−5.76259	−0.291055
$393$	−6.05712	−0.305541
$394$	−3.59587	−0.181157
$395$	27.1529	1.36621
$396$	−14.4243	−0.724848
$397$	−1.56612	−0.0786012	−0.0393006	−	0.999227i	$-0.512513\pi$
$397$	−1.56612	−0.0786012	−0.0393006	+	0.999227i	$0.512513\pi$
$398$	−16.6779	−0.835990
$399$	−21.3685	−1.06976
$400$	12.7422	0.637109
$401$	−25.0541	−1.25114	−0.625571	−	0.780168i	$-0.715134\pi$
$401$	−25.0541	−1.25114	−0.625571	+	0.780168i	$0.715134\pi$
$402$	−30.0885	−1.50068
$403$	9.12752	0.454674
$404$	9.49356	0.472322
$405$	−39.9534	−1.98530
$406$	1.11239	0.0552069
$407$	−11.0440	−0.547431
$408$	10.9282	0.541026
$409$	−22.5993	−1.11746	−0.558732	−	0.829349i	$-0.688712\pi$
$409$	−22.5993	−1.11746	−0.558732	+	0.829349i	$0.688712\pi$
$410$	−11.9061	−0.588003
$411$	−0.914189	−0.0450936
$412$	1.00162	0.0493464
$413$	−9.63159	−0.473940
$414$	2.82843	0.139010
$415$	−22.2713	−1.09325
$416$	−6.06926	−0.297570
$417$	7.56880	0.370646
$418$	40.5781	1.98474
$419$	17.9013	0.874536	0.437268	−	0.899331i	$-0.355946\pi$
$419$	17.9013	0.874536	0.437268	+	0.899331i	$0.355946\pi$
$420$	11.3119	0.551964
$421$	−36.3896	−1.77352	−0.886761	−	0.462228i	$-0.847050\pi$
$421$	−36.3896	−1.77352	−0.886761	+	0.462228i	$0.847050\pi$
$422$	−1.84268	−0.0897003
$423$	−24.2031	−1.17680
$424$	11.0406	0.536178
$425$	−57.6788	−2.79783
$426$	12.8197	0.621117
$427$	−7.56576	−0.366133
$428$	−12.8738	−0.622281
$429$	−74.7242	−3.60772
$430$	−15.2071	−0.733352
$431$	13.8849	0.668811	0.334405	−	0.942429i	$-0.391465\pi$
$431$	13.8849	0.668811	0.334405	+	0.942429i	$0.391465\pi$
$432$	0.414214	0.0199289
$433$	−10.2156	−0.490929	−0.245465	−	0.969406i	$-0.578940\pi$
$433$	−10.2156	−0.490929	−0.245465	+	0.969406i	$0.578940\pi$
$434$	1.67291	0.0803024
$435$	10.1690	0.487567
$436$	−17.2197	−0.824673
$437$	−7.95687	−0.380629
$438$	19.8834	0.950067
$439$	−22.9674	−1.09618	−0.548088	−	0.836421i	$-0.684644\pi$
$439$	−22.9674	−1.09618	−0.548088	+	0.836421i	$0.684644\pi$
$440$	−21.4809	−1.02406
$441$	−16.2991	−0.776146
$442$	27.4731	1.30676
$443$	15.4318	0.733188	0.366594	−	0.930381i	$-0.380524\pi$
$443$	15.4318	0.733188	0.366594	+	0.930381i	$0.380524\pi$
$444$	−5.22820	−0.248120
$445$	−56.3779	−2.67257
$446$	−27.5547	−1.30476
$447$	16.5644	0.783471
$448$	−1.11239	−0.0525554
$449$	7.53413	0.355558	0.177779	−	0.984070i	$-0.443109\pi$
$449$	7.53413	0.355558	0.177779	+	0.984070i	$0.443109\pi$
$450$	36.0403	1.69896
$451$	14.4151	0.678780
$452$	−3.97474	−0.186956
$453$	−28.8259	−1.35436
$454$	27.4041	1.28614
$455$	28.4378	1.33318
$456$	19.2096	0.899572
$457$	40.3196	1.88607	0.943036	−	0.332689i	$-0.107956\pi$
$457$	40.3196	1.88607	0.943036	+	0.332689i	$0.107956\pi$
$458$	−0.0245149	−0.00114551
$459$	−1.87498	−0.0875166
$460$	4.21215	0.196392
$461$	11.1945	0.521379	0.260690	−	0.965423i	$-0.416050\pi$
$461$	11.1945	0.521379	0.260690	+	0.965423i	$0.416050\pi$
$462$	−13.6956	−0.637178
$463$	11.5132	0.535065	0.267532	−	0.963549i	$-0.413792\pi$
$463$	11.5132	0.535065	0.267532	+	0.963549i	$0.413792\pi$
$464$	−1.00000	−0.0464238
$465$	15.2931	0.709201
$466$	−2.22060	−0.102867
$467$	35.9983	1.66580	0.832902	−	0.553421i	$-0.186678\pi$
$467$	35.9983	1.66580	0.832902	+	0.553421i	$0.186678\pi$
$468$	−17.1665	−0.793520
$469$	−13.8638	−0.640169
$470$	−36.0437	−1.66257
$471$	−51.3905	−2.36795
$472$	8.65848	0.398539
$473$	18.4117	0.846569
$474$	−15.5628	−0.714824
$475$	−101.388	−4.65200
$476$	5.03534	0.230794
$477$	31.2275	1.42981
$478$	7.62523	0.348770
$479$	27.1477	1.24041	0.620204	−	0.784440i	$-0.287050\pi$
$479$	27.1477	1.24041	0.620204	+	0.784440i	$0.287050\pi$
$480$	−10.1690	−0.464150
$481$	−13.1436	−0.599295
$482$	−16.2555	−0.740417
$483$	2.68554	0.122196
$484$	15.0075	0.682160
$485$	40.7717	1.85135
$486$	21.6569	0.982375
$487$	−35.2290	−1.59638	−0.798189	−	0.602407i	$-0.794209\pi$
$487$	−35.2290	−1.59638	−0.798189	+	0.602407i	$0.794209\pi$
$488$	6.80136	0.307883
$489$	−27.1743	−1.22886
$490$	−24.2729	−1.09654
$491$	34.6862	1.56536	0.782682	−	0.622421i	$-0.213851\pi$
$491$	34.6862	1.56536	0.782682	+	0.622421i	$0.213851\pi$
$492$	6.82407	0.307653
$493$	4.52660	0.203868
$494$	48.2924	2.17278
$495$	−60.7572	−2.73083
$496$	−1.50389	−0.0675268
$497$	5.90689	0.264960
$498$	12.7649	0.572008
$499$	3.88163	0.173766	0.0868828	−	0.996219i	$-0.472309\pi$
$499$	3.88163	0.173766	0.0868828	+	0.996219i	$0.472309\pi$
$500$	32.6112	1.45842
$501$	−4.71261	−0.210544
$502$	−20.5928	−0.919103
$503$	−30.5479	−1.36206	−0.681032	−	0.732254i	$-0.738468\pi$
$503$	−30.5479	−1.36206	−0.681032	+	0.732254i	$0.738468\pi$
$504$	−3.14631	−0.140148
$505$	39.9882	1.77945
$506$	−5.09976	−0.226712
$507$	−57.5451	−2.55567
$508$	−2.37887	−0.105545
$509$	−14.7862	−0.655386	−0.327693	−	0.944784i	$-0.606271\pi$
$509$	−14.7862	−0.655386	−0.327693	+	0.944784i	$0.606271\pi$
$510$	46.0311	2.03829
$511$	9.16162	0.405286
$512$	1.00000	0.0441942
$513$	−3.29585	−0.145515
$514$	−9.37176	−0.413371
$515$	4.21898	0.185910
$516$	8.71604	0.383702
$517$	43.6391	1.91925
$518$	−2.40898	−0.105845
$519$	34.2894	1.50514
$520$	−25.5646	−1.12108
$521$	−2.45324	−0.107478	−0.0537392	−	0.998555i	$-0.517114\pi$
$521$	−2.45324	−0.107478	−0.0537392	+	0.998555i	$0.517114\pi$
$522$	−2.82843	−0.123797
$523$	−14.2038	−0.621090	−0.310545	−	0.950559i	$-0.600511\pi$
$523$	−14.2038	−0.621090	−0.310545	+	0.950559i	$0.600511\pi$
$524$	2.50894	0.109604
$525$	34.2197	1.49347
$526$	−23.6128	−1.02957
$527$	6.80752	0.296540
$528$	12.3119	0.535807
$529$	1.00000	0.0434783
$530$	46.5045	2.02003
$531$	24.4899	1.06277
$532$	8.85114	0.383745
$533$	17.1555	0.743088
$534$	32.3133	1.39833
$535$	−54.2265	−2.34442
$536$	12.4631	0.538322
$537$	8.03392	0.346689
$538$	−6.53601	−0.281787
$539$	29.3878	1.26582
$540$	1.74473	0.0750811
$541$	5.78293	0.248628	0.124314	−	0.992243i	$-0.460327\pi$
$541$	5.78293	0.248628	0.124314	+	0.992243i	$0.460327\pi$
$542$	0.602517	0.0258803
$543$	29.0293	1.24577
$544$	−4.52660	−0.194076
$545$	−72.5318	−3.10692
$546$	−16.2993	−0.697544
$547$	10.5837	0.452527	0.226264	−	0.974066i	$-0.427349\pi$
$547$	10.5837	0.452527	0.226264	+	0.974066i	$0.427349\pi$
$548$	0.378669	0.0161760
$549$	19.2372	0.821022
$550$	−64.9820	−2.77084
$551$	7.95687	0.338974
$552$	−2.41421	−0.102756
$553$	−7.17083	−0.304935
$554$	14.9780	0.636353
$555$	−22.0220	−0.934780
$556$	−3.13510	−0.132958
$557$	−15.8190	−0.670274	−0.335137	−	0.942169i	$-0.608783\pi$
$557$	−15.8190	−0.670274	−0.335137	+	0.942169i	$0.608783\pi$
$558$	−4.25365	−0.180071
$559$	21.9119	0.926773
$560$	−4.68554	−0.198000
$561$	−55.7311	−2.35297
$562$	−19.1679	−0.808549
$563$	30.9795	1.30563	0.652816	−	0.757517i	$-0.273588\pi$
$563$	30.9795	1.30563	0.652816	+	0.757517i	$0.273588\pi$
$564$	20.6587	0.869886
$565$	−16.7422	−0.704349
$566$	8.75499	0.368000
$567$	10.5513	0.443114
$568$	−5.31010	−0.222807
$569$	43.8058	1.83644	0.918218	−	0.396075i	$-0.129628\pi$
$569$	43.8058	1.83644	0.918218	+	0.396075i	$0.129628\pi$
$570$	80.9136	3.38910
$571$	0.843996	0.0353201	0.0176601	−	0.999844i	$-0.494378\pi$
$571$	0.843996	0.0353201	0.0176601	+	0.999844i	$0.494378\pi$
$572$	30.9518	1.29416
$573$	−4.62020	−0.193012
$574$	3.14430	0.131241
$575$	12.7422	0.531385
$576$	2.82843	0.117851
$577$	3.16397	0.131718	0.0658589	−	0.997829i	$-0.479021\pi$
$577$	3.16397	0.131718	0.0658589	+	0.997829i	$0.479021\pi$
$578$	3.49013	0.145170
$579$	−4.45572	−0.185173
$580$	−4.21215	−0.174900
$581$	5.88163	0.244011
$582$	−23.3685	−0.968657
$583$	−56.3042	−2.33188
$584$	−8.23599	−0.340808
$585$	−72.3077	−2.98955
$586$	27.3119	1.12824
$587$	12.0533	0.497494	0.248747	−	0.968568i	$-0.419981\pi$
$587$	12.0533	0.497494	0.248747	+	0.968568i	$0.419981\pi$
$588$	13.9121	0.573726
$589$	11.9663	0.493062
$590$	36.4708	1.50148
$591$	8.68119	0.357096
$592$	2.16559	0.0890053
$593$	−9.73372	−0.399716	−0.199858	−	0.979825i	$-0.564048\pi$
$593$	−9.73372	−0.399716	−0.199858	+	0.979825i	$0.564048\pi$
$594$	−2.11239	−0.0866724
$595$	21.2096	0.869509
$596$	−6.86122	−0.281046
$597$	40.2641	1.64790
$598$	−6.06926	−0.248191
$599$	6.56071	0.268063	0.134032	−	0.990977i	$-0.457208\pi$
$599$	6.56071	0.268063	0.134032	+	0.990977i	$0.457208\pi$
$600$	−30.7623	−1.25587
$601$	−15.3841	−0.627531	−0.313765	−	0.949501i	$-0.601591\pi$
$601$	−15.3841	−0.627531	−0.313765	+	0.949501i	$0.601591\pi$
$602$	4.01606	0.163682
$603$	35.2509	1.43553
$604$	11.9401	0.485834
$605$	63.2139	2.57001
$606$	−22.9195	−0.931040
$607$	−41.8391	−1.69820	−0.849099	−	0.528234i	$-0.822854\pi$
$607$	−41.8391	−1.69820	−0.849099	+	0.528234i	$0.822854\pi$
$608$	−7.95687	−0.322694
$609$	−2.68554	−0.108824
$610$	28.6483	1.15994
$611$	51.9353	2.10108
$612$	−12.8032	−0.517537
$613$	−30.4568	−1.23014	−0.615070	−	0.788473i	$-0.710872\pi$
$613$	−30.4568	−1.23014	−0.615070	+	0.788473i	$0.710872\pi$
$614$	19.8531	0.801208
$615$	28.7440	1.15907
$616$	5.67291	0.228568
$617$	44.4260	1.78853	0.894263	−	0.447543i	$-0.147701\pi$
$617$	44.4260	1.78853	0.894263	+	0.447543i	$0.147701\pi$
$618$	−2.41813	−0.0972715
$619$	−16.8617	−0.677729	−0.338865	−	0.940835i	$-0.610043\pi$
$619$	−16.8617	−0.677729	−0.338865	+	0.940835i	$0.610043\pi$
$620$	−6.33461	−0.254404
$621$	0.414214	0.0166218
$622$	−27.0027	−1.08271
$623$	14.8889	0.596510
$624$	14.6525	0.586569
$625$	73.6522	2.94609
$626$	8.46829	0.338461
$627$	−97.9643	−3.91232
$628$	21.2866	0.849429
$629$	−9.80278	−0.390862
$630$	−13.2527	−0.528001
$631$	28.3741	1.12955	0.564777	−	0.825244i	$-0.308962\pi$
$631$	28.3741	1.12955	0.564777	+	0.825244i	$0.308962\pi$
$632$	6.44633	0.256421
$633$	4.44862	0.176817
$634$	9.78443	0.388589
$635$	−10.0202	−0.397638
$636$	−26.6543	−1.05691
$637$	34.9747	1.38575
$638$	5.09976	0.201901
$639$	−15.0192	−0.594151
$640$	4.21215	0.166500
$641$	3.73625	0.147573	0.0737865	−	0.997274i	$-0.476492\pi$
$641$	3.73625	0.147573	0.0737865	+	0.997274i	$0.476492\pi$
$642$	31.0802	1.22664
$643$	18.8621	0.743848	0.371924	−	0.928263i	$-0.378698\pi$
$643$	18.8621	0.743848	0.371924	+	0.928263i	$0.378698\pi$
$644$	−1.11239	−0.0438343
$645$	36.7132	1.44558
$646$	36.0176	1.41709
$647$	6.64858	0.261383	0.130691	−	0.991423i	$-0.458280\pi$
$647$	6.64858	0.261383	0.130691	+	0.991423i	$0.458280\pi$
$648$	−9.48528	−0.372617
$649$	−44.1561	−1.73328
$650$	−77.3356	−3.03335
$651$	−4.03877	−0.158292
$652$	11.2559	0.440817
$653$	9.89493	0.387219	0.193609	−	0.981079i	$-0.437981\pi$
$653$	9.89493	0.387219	0.193609	+	0.981079i	$0.437981\pi$
$654$	41.5720	1.62559
$655$	10.5680	0.412927
$656$	−2.82662	−0.110361
$657$	−23.2949	−0.908820
$658$	9.51882	0.371082
$659$	0.728649	0.0283841	0.0141921	−	0.999899i	$-0.495482\pi$
$659$	0.728649	0.0283841	0.0141921	+	0.999899i	$0.495482\pi$
$660$	51.8595	2.01863
$661$	−8.48528	−0.330039	−0.165020	−	0.986290i	$-0.552769\pi$
$661$	−8.48528	−0.330039	−0.165020	+	0.986290i	$0.552769\pi$
$662$	−24.6997	−0.959982
$663$	−66.3260	−2.57589
$664$	−5.28739	−0.205190
$665$	37.2823	1.44574
$666$	6.12522	0.237348
$667$	−1.00000	−0.0387202
$668$	1.95203	0.0755262
$669$	66.5230	2.57193
$670$	52.4962	2.02811
$671$	−34.6853	−1.33901
$672$	2.68554	0.103597
$673$	20.4724	0.789153	0.394576	−	0.918863i	$-0.370891\pi$
$673$	20.4724	0.789153	0.394576	+	0.918863i	$0.370891\pi$
$674$	8.56537	0.329926
$675$	5.27798	0.203150
$676$	23.8360	0.916767
$677$	−45.4265	−1.74588	−0.872941	−	0.487825i	$-0.837790\pi$
$677$	−45.4265	−1.74588	−0.872941	+	0.487825i	$0.837790\pi$
$678$	9.59587	0.368527
$679$	−10.7674	−0.413216
$680$	−19.0667	−0.731175
$681$	−66.1593	−2.53523
$682$	7.66949	0.293680
$683$	−2.43399	−0.0931339	−0.0465669	−	0.998915i	$-0.514828\pi$
$683$	−2.43399	−0.0931339	−0.0465669	+	0.998915i	$0.514828\pi$
$684$	−22.5054	−0.860517
$685$	1.59501	0.0609422
$686$	14.1970	0.542043
$687$	0.0591842	0.00225802
$688$	−3.61030	−0.137641
$689$	−67.0081	−2.55281
$690$	−10.1690	−0.387128
$691$	−42.8121	−1.62865	−0.814325	−	0.580410i	$-0.802892\pi$
$691$	−42.8121	−1.62865	−0.814325	+	0.580410i	$0.802892\pi$
$692$	−14.2031	−0.539922
$693$	16.0454	0.609515
$694$	−15.5897	−0.591777
$695$	−13.2055	−0.500913
$696$	2.41421	0.0915105
$697$	12.7950	0.484645
$698$	−10.6229	−0.402084
$699$	5.36101	0.202772
$700$	−14.1743	−0.535736
$701$	19.6981	0.743987	0.371993	−	0.928235i	$-0.378674\pi$
$701$	19.6981	0.743987	0.371993	+	0.928235i	$0.378674\pi$
$702$	−2.51397	−0.0948837
$703$	−17.2314	−0.649893
$704$	−5.09976	−0.192204
$705$	87.0173	3.27726
$706$	−16.2654	−0.612155
$707$	−10.5605	−0.397169
$708$	−20.9034	−0.785598
$709$	36.7425	1.37989	0.689946	−	0.723860i	$-0.257634\pi$
$709$	36.7425	1.37989	0.689946	+	0.723860i	$0.257634\pi$
$710$	−22.3669	−0.839415
$711$	18.2330	0.683790
$712$	−13.3846	−0.501609
$713$	−1.50389	−0.0563212
$714$	−12.1564	−0.454941
$715$	130.373	4.87569
$716$	−3.32776	−0.124364
$717$	−18.4089	−0.687494
$718$	18.1654	0.677927
$719$	−12.2151	−0.455546	−0.227773	−	0.973714i	$-0.573144\pi$
$719$	−12.2151	−0.455546	−0.227773	+	0.973714i	$0.573144\pi$
$720$	11.9137	0.443999
$721$	−1.11419	−0.0414947
$722$	44.3118	1.64912
$723$	39.2442	1.45951
$724$	−12.0243	−0.446881
$725$	−12.7422	−0.473233
$726$	−36.2314	−1.34467
$727$	−13.7869	−0.511329	−0.255664	−	0.966766i	$-0.582294\pi$
$727$	−13.7869	−0.511329	−0.255664	+	0.966766i	$0.582294\pi$
$728$	6.75138	0.250223
$729$	−23.8284	−0.882534
$730$	−34.6912	−1.28398
$731$	16.3424	0.604445
$732$	−16.4199	−0.606898
$733$	−42.2600	−1.56091	−0.780455	−	0.625212i	$-0.785013\pi$
$733$	−42.2600	−1.56091	−0.780455	+	0.625212i	$0.785013\pi$
$734$	−4.46487	−0.164801
$735$	58.5999	2.16149
$736$	1.00000	0.0368605
$737$	−63.5586	−2.34121
$738$	−7.99490	−0.294296
$739$	−41.9897	−1.54461	−0.772307	−	0.635249i	$-0.780897\pi$
$739$	−41.9897	−1.54461	−0.772307	+	0.635249i	$0.780897\pi$
$740$	9.12180	0.335324
$741$	−116.588	−4.28297
$742$	−12.2814	−0.450865
$743$	−24.6644	−0.904848	−0.452424	−	0.891803i	$-0.649441\pi$
$743$	−24.6644	−0.904848	−0.452424	+	0.891803i	$0.649441\pi$
$744$	3.63072	0.133109
$745$	−28.9004	−1.05883
$746$	−32.6754	−1.19633
$747$	−14.9550	−0.547175
$748$	23.0846	0.844056
$749$	14.3207	0.523268
$750$	−78.7303	−2.87483
$751$	−39.1210	−1.42755	−0.713774	−	0.700376i	$-0.753015\pi$
$751$	−39.1210	−1.42755	−0.713774	+	0.700376i	$0.753015\pi$
$752$	−8.55710	−0.312045
$753$	49.7155	1.81173
$754$	6.06926	0.221030
$755$	50.2933	1.83036
$756$	−0.460766	−0.0167579
$757$	−7.16031	−0.260246	−0.130123	−	0.991498i	$-0.541537\pi$
$757$	−7.16031	−0.260246	−0.130123	+	0.991498i	$0.541537\pi$
$758$	6.17425	0.224259
$759$	12.3119	0.446894
$760$	−33.5155	−1.21574
$761$	−35.6589	−1.29263	−0.646316	−	0.763070i	$-0.723691\pi$
$761$	−35.6589	−1.29263	−0.646316	+	0.763070i	$0.723691\pi$
$762$	5.74311	0.208051
$763$	19.1550	0.693456
$764$	1.91375	0.0692370
$765$	−53.9288	−1.94980
$766$	28.3311	1.02365
$767$	−52.5506	−1.89749
$768$	−2.41421	−0.0871154
$769$	−48.7189	−1.75685	−0.878425	−	0.477880i	$-0.841405\pi$
$769$	−48.7189	−1.75685	−0.878425	+	0.477880i	$0.841405\pi$
$770$	23.8951	0.861121
$771$	22.6254	0.814835
$772$	1.84562	0.0664253
$773$	−48.2643	−1.73595	−0.867974	−	0.496610i	$-0.834578\pi$
$773$	−48.2643	−1.73595	−0.867974	+	0.496610i	$0.834578\pi$
$774$	−10.2115	−0.367044
$775$	−19.1629	−0.688350
$776$	9.67956	0.347476
$777$	5.81580	0.208641
$778$	−12.0584	−0.432316
$779$	22.4911	0.805827
$780$	61.7185	2.20988
$781$	27.0802	0.969006
$782$	−4.52660	−0.161871
$783$	−0.414214	−0.0148028
$784$	−5.76259	−0.205807
$785$	89.6624	3.20019
$786$	−6.05712	−0.216050
$787$	16.6460	0.593367	0.296683	−	0.954976i	$-0.404119\pi$
$787$	16.6460	0.593367	0.296683	+	0.954976i	$0.404119\pi$
$788$	−3.59587	−0.128097
$789$	57.0063	2.02948
$790$	27.1529	0.966056
$791$	4.42145	0.157209
$792$	−14.4243	−0.512545
$793$	−41.2792	−1.46587
$794$	−1.56612	−0.0555795
$795$	−112.272	−3.98187
$796$	−16.6779	−0.591134
$797$	−12.3947	−0.439044	−0.219522	−	0.975608i	$-0.570450\pi$
$797$	−12.3947	−0.439044	−0.219522	+	0.975608i	$0.570450\pi$
$798$	−21.3685	−0.756438
$799$	38.7346	1.37033
$800$	12.7422	0.450504
$801$	−37.8573	−1.33762
$802$	−25.0541	−0.884690
$803$	42.0015	1.48220
$804$	−30.0885	−1.06114
$805$	−4.68554	−0.165144
$806$	9.12752	0.321503
$807$	15.7793	0.555458
$808$	9.49356	0.333982
$809$	−14.9872	−0.526921	−0.263460	−	0.964670i	$-0.584864\pi$
$809$	−14.9872	−0.526921	−0.263460	+	0.964670i	$0.584864\pi$
$810$	−39.9534	−1.40382
$811$	23.7102	0.832577	0.416289	−	0.909233i	$-0.363331\pi$
$811$	23.7102	0.832577	0.416289	+	0.909233i	$0.363331\pi$
$812$	1.11239	0.0390372
$813$	−1.45460	−0.0510152
$814$	−11.0440	−0.387092
$815$	47.4117	1.66076
$816$	10.9282	0.382563
$817$	28.7267	1.00502
$818$	−22.5993	−0.790166
$819$	19.0958	0.667261
$820$	−11.9061	−0.415781
$821$	−14.3357	−0.500318	−0.250159	−	0.968205i	$-0.580483\pi$
$821$	−14.3357	−0.500318	−0.250159	+	0.968205i	$0.580483\pi$
$822$	−0.914189	−0.0318860
$823$	9.10643	0.317430	0.158715	−	0.987324i	$-0.449265\pi$
$823$	9.10643	0.317430	0.158715	+	0.987324i	$0.449265\pi$
$824$	1.00162	0.0348932
$825$	156.880	5.46188
$826$	−9.63159	−0.335126
$827$	34.4576	1.19821	0.599104	−	0.800672i	$-0.295524\pi$
$827$	34.4576	1.19821	0.599104	+	0.800672i	$0.295524\pi$
$828$	2.82843	0.0982946
$829$	8.13881	0.282673	0.141336	−	0.989962i	$-0.454860\pi$
$829$	8.13881	0.282673	0.141336	+	0.989962i	$0.454860\pi$
$830$	−22.2713	−0.773047
$831$	−36.1600	−1.25438
$832$	−6.06926	−0.210414
$833$	26.0850	0.903790
$834$	7.56880	0.262086
$835$	8.22223	0.284542
$836$	40.5781	1.40342
$837$	−0.622933	−0.0215317
$838$	17.9013	0.618390
$839$	18.9031	0.652608	0.326304	−	0.945265i	$-0.394197\pi$
$839$	18.9031	0.652608	0.326304	+	0.945265i	$0.394197\pi$
$840$	11.3119	0.390298
$841$	1.00000	0.0344828
$842$	−36.3896	−1.25407
$843$	46.2754	1.59381
$844$	−1.84268	−0.0634277
$845$	100.401	3.45388
$846$	−24.2031	−0.832121
$847$	−16.6942	−0.573620
$848$	11.0406	0.379135
$849$	−21.1364	−0.725400
$850$	−57.6788	−1.97837
$851$	2.16559	0.0742356
$852$	12.8197	0.439196
$853$	47.5762	1.62898	0.814490	−	0.580178i	$-0.197017\pi$
$853$	47.5762	1.62898	0.814490	+	0.580178i	$0.197017\pi$
$854$	−7.56576	−0.258895
$855$	−94.7962	−3.24196
$856$	−12.8738	−0.440019
$857$	36.2609	1.23865	0.619325	−	0.785135i	$-0.287406\pi$
$857$	36.2609	1.23865	0.619325	+	0.785135i	$0.287406\pi$
$858$	−74.7242	−2.55104
$859$	−29.3832	−1.00254	−0.501270	−	0.865291i	$-0.667134\pi$
$859$	−29.3832	−1.00254	−0.501270	+	0.865291i	$0.667134\pi$
$860$	−15.2071	−0.518558
$861$	−7.59102	−0.258701
$862$	13.8849	0.472921
$863$	−35.3535	−1.20345	−0.601723	−	0.798705i	$-0.705519\pi$
$863$	−35.3535	−1.20345	−0.601723	+	0.798705i	$0.705519\pi$
$864$	0.414214	0.0140918
$865$	−59.8256	−2.03413
$866$	−10.2156	−0.347139
$867$	−8.42591	−0.286159
$868$	1.67291	0.0567824
$869$	−32.8747	−1.11520
$870$	10.1690	0.344762
$871$	−75.6416	−2.56302
$872$	−17.2197	−0.583132
$873$	27.3779	0.926603
$874$	−7.95687	−0.269145
$875$	−36.2763	−1.22636
$876$	19.8834	0.671799
$877$	−39.8559	−1.34584	−0.672920	−	0.739716i	$-0.734960\pi$
$877$	−39.8559	−1.34584	−0.672920	+	0.739716i	$0.734960\pi$
$878$	−22.9674	−0.775114
$879$	−65.9368	−2.22399
$880$	−21.4809	−0.724122
$881$	−29.7284	−1.00158	−0.500788	−	0.865570i	$-0.666956\pi$
$881$	−29.7284	−1.00158	−0.500788	+	0.865570i	$0.666956\pi$
$882$	−16.2991	−0.548818
$883$	56.8781	1.91410	0.957051	−	0.289919i	$-0.0936285\pi$
$883$	56.8781	1.91410	0.957051	+	0.289919i	$0.0936285\pi$
$884$	27.4731	0.924022
$885$	−88.0482	−2.95971
$886$	15.4318	0.518442
$887$	3.27131	0.109840	0.0549199	−	0.998491i	$-0.482510\pi$
$887$	3.27131	0.109840	0.0549199	+	0.998491i	$0.482510\pi$
$888$	−5.22820	−0.175447
$889$	2.64623	0.0887517
$890$	−56.3779	−1.88979
$891$	48.3726	1.62054
$892$	−27.5547	−0.922601
$893$	68.0877	2.27847
$894$	16.5644	0.553998
$895$	−14.0170	−0.468537
$896$	−1.11239	−0.0371623
$897$	14.6525	0.489233
$898$	7.53413	0.251417
$899$	1.50389	0.0501576
$900$	36.0403	1.20134
$901$	−49.9763	−1.66495
$902$	14.4151	0.479970
$903$	−9.69562	−0.322650
$904$	−3.97474	−0.132198
$905$	−50.6482	−1.68360
$906$	−28.8259	−0.957676
$907$	−34.0487	−1.13057	−0.565284	−	0.824897i	$-0.691233\pi$
$907$	−34.0487	−1.13057	−0.565284	+	0.824897i	$0.691233\pi$
$908$	27.4041	0.909436
$909$	26.8518	0.890619
$910$	28.4378	0.942704
$911$	−37.0245	−1.22668	−0.613338	−	0.789821i	$-0.710173\pi$
$911$	−37.0245	−1.22668	−0.613338	+	0.789821i	$0.710173\pi$
$912$	19.2096	0.636093
$913$	26.9644	0.892391
$914$	40.3196	1.33365
$915$	−69.1632	−2.28646
$916$	−0.0245149	−0.000809994 0
$917$	−2.79092	−0.0921643
$918$	−1.87498	−0.0618836
$919$	27.8186	0.917649	0.458825	−	0.888527i	$-0.348271\pi$
$919$	27.8186	0.917649	0.458825	+	0.888527i	$0.348271\pi$
$920$	4.21215	0.138870
$921$	−47.9297	−1.57934
$922$	11.1945	0.368671
$923$	32.2284	1.06081
$924$	−13.6956	−0.450553
$925$	27.5944	0.907297
$926$	11.5132	0.378348
$927$	2.83302	0.0930485
$928$	−1.00000	−0.0328266
$929$	−4.45291	−0.146095	−0.0730476	−	0.997328i	$-0.523272\pi$
$929$	−4.45291	−0.146095	−0.0730476	+	0.997328i	$0.523272\pi$
$930$	15.2931	0.501481
$931$	45.8522	1.50275
$932$	−2.22060	−0.0727383
$933$	65.1902	2.13423
$934$	35.9983	1.17790
$935$	97.2356	3.17994
$936$	−17.1665	−0.561104
$937$	−27.1509	−0.886981	−0.443491	−	0.896279i	$-0.646260\pi$
$937$	−27.1509	−0.886981	−0.443491	+	0.896279i	$0.646260\pi$
$938$	−13.8638	−0.452668
$939$	−20.4443	−0.667173
$940$	−36.0437	−1.17562
$941$	7.44595	0.242731	0.121365	−	0.992608i	$-0.461273\pi$
$941$	7.44595	0.242731	0.121365	+	0.992608i	$0.461273\pi$
$942$	−51.3905	−1.67439
$943$	−2.82662	−0.0920475
$944$	8.65848	0.281809
$945$	−1.94082	−0.0631347
$946$	18.4117	0.598615
$947$	14.6709	0.476739	0.238369	−	0.971175i	$-0.423387\pi$
$947$	14.6709	0.476739	0.238369	+	0.971175i	$0.423387\pi$
$948$	−15.5628	−0.505457
$949$	49.9864	1.62263
$950$	−101.388	−3.28946
$951$	−23.6217	−0.765986
$952$	5.03534	0.163196
$953$	54.9523	1.78008	0.890039	−	0.455884i	$-0.150677\pi$
$953$	54.9523	1.78008	0.890039	+	0.455884i	$0.150677\pi$
$954$	31.2275	1.01103
$955$	8.06099	0.260847
$956$	7.62523	0.246617
$957$	−12.3119	−0.397987
$958$	27.1477	0.877102
$959$	−0.421228	−0.0136021
$960$	−10.1690	−0.328204
$961$	−28.7383	−0.927042
$962$	−13.1436	−0.423765
$963$	−36.4127	−1.17338
$964$	−16.2555	−0.523554
$965$	7.77401	0.250254
$966$	2.68554	0.0864060
$967$	−15.3034	−0.492125	−0.246063	−	0.969254i	$-0.579137\pi$
$967$	−15.3034	−0.492125	−0.246063	+	0.969254i	$0.579137\pi$
$968$	15.0075	0.482360
$969$	−86.9542	−2.79337
$970$	40.7717	1.30910
$971$	−10.8368	−0.347769	−0.173884	−	0.984766i	$-0.555632\pi$
$971$	−10.8368	−0.347769	−0.173884	+	0.984766i	$0.555632\pi$
$972$	21.6569	0.694644
$973$	3.48745	0.111802
$974$	−35.2290	−1.12881
$975$	186.705	5.97934
$976$	6.80136	0.217706
$977$	−12.9807	−0.415289	−0.207645	−	0.978204i	$-0.566580\pi$
$977$	−12.9807	−0.415289	−0.207645	+	0.978204i	$0.566580\pi$
$978$	−27.1743	−0.868937
$979$	68.2582	2.18154
$980$	−24.2729	−0.775369
$981$	−48.7046	−1.55502
$982$	34.6862	1.10688
$983$	8.42628	0.268757	0.134378	−	0.990930i	$-0.457096\pi$
$983$	8.42628	0.268757	0.134378	+	0.990930i	$0.457096\pi$
$984$	6.82407	0.217543
$985$	−15.1463	−0.482602
$986$	4.52660	0.144156
$987$	−22.9805	−0.731476
$988$	48.2924	1.53638
$989$	−3.61030	−0.114801
$990$	−60.7572	−1.93099
$991$	10.1445	0.322251	0.161126	−	0.986934i	$-0.448488\pi$
$991$	10.1445	0.322251	0.161126	+	0.986934i	$0.448488\pi$
$992$	−1.50389	−0.0477486
$993$	59.6304	1.89231
$994$	5.90689	0.187355
$995$	−70.2499	−2.22707
$996$	12.7649	0.404471
$997$	39.3820	1.24724	0.623621	−	0.781727i	$-0.285661\pi$
$997$	39.3820	1.24724	0.623621	+	0.781727i	$0.285661\pi$
$998$	3.88163	0.122871
$999$	0.897018	0.0283804

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1334.2.a.e.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1334.2.a.e.1.2	✓	4	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:	\( N \)	\(=\)	\( 1334 = 2 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1334.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +4.21215 q^{5} -2.41421 q^{6} -1.11239 q^{7} +1.00000 q^{8} +2.82843 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.41421 q^{3} +1.00000 q^{4} +4.21215 q^{5} -2.41421 q^{6} -1.11239 q^{7} +1.00000 q^{8} +2.82843 q^{9} +4.21215 q^{10} -5.09976 q^{11} -2.41421 q^{12} -6.06926 q^{13} -1.11239 q^{14} -10.1690 q^{15} +1.00000 q^{16} -4.52660 q^{17} +2.82843 q^{18} -7.95687 q^{19} +4.21215 q^{20} +2.68554 q^{21} -5.09976 q^{22} +1.00000 q^{23} -2.41421 q^{24} +12.7422 q^{25} -6.06926 q^{26} +0.414214 q^{27} -1.11239 q^{28} -1.00000 q^{29} -10.1690 q^{30} -1.50389 q^{31} +1.00000 q^{32} +12.3119 q^{33} -4.52660 q^{34} -4.68554 q^{35} +2.82843 q^{36} +2.16559 q^{37} -7.95687 q^{38} +14.6525 q^{39} +4.21215 q^{40} -2.82662 q^{41} +2.68554 q^{42} -3.61030 q^{43} -5.09976 q^{44} +11.9137 q^{45} +1.00000 q^{46} -8.55710 q^{47} -2.41421 q^{48} -5.76259 q^{49} +12.7422 q^{50} +10.9282 q^{51} -6.06926 q^{52} +11.0406 q^{53} +0.414214 q^{54} -21.4809 q^{55} -1.11239 q^{56} +19.2096 q^{57} -1.00000 q^{58} +8.65848 q^{59} -10.1690 q^{60} +6.80136 q^{61} -1.50389 q^{62} -3.14631 q^{63} +1.00000 q^{64} -25.5646 q^{65} +12.3119 q^{66} +12.4631 q^{67} -4.52660 q^{68} -2.41421 q^{69} -4.68554 q^{70} -5.31010 q^{71} +2.82843 q^{72} -8.23599 q^{73} +2.16559 q^{74} -30.7623 q^{75} -7.95687 q^{76} +5.67291 q^{77} +14.6525 q^{78} +6.44633 q^{79} +4.21215 q^{80} -9.48528 q^{81} -2.82662 q^{82} -5.28739 q^{83} +2.68554 q^{84} -19.0667 q^{85} -3.61030 q^{86} +2.41421 q^{87} -5.09976 q^{88} -13.3846 q^{89} +11.9137 q^{90} +6.75138 q^{91} +1.00000 q^{92} +3.63072 q^{93} -8.55710 q^{94} -33.5155 q^{95} -2.41421 q^{96} +9.67956 q^{97} -5.76259 q^{98} -14.4243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 4 q^{11} - 4 q^{12} - 8 q^{13} - 4 q^{14} - 8 q^{15} + 4 q^{16} - 12 q^{17} - 16 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{24} + 8 q^{25} - 8 q^{26} - 4 q^{27} - 4 q^{28} - 4 q^{29} - 8 q^{30} - 12 q^{31} + 4 q^{32} + 16 q^{33} - 12 q^{34} - 8 q^{35} - 4 q^{37} - 16 q^{38} + 4 q^{39} - 12 q^{41} + 4 q^{43} - 4 q^{44} + 16 q^{45} + 4 q^{46} - 28 q^{47} - 4 q^{48} - 8 q^{49} + 8 q^{50} + 16 q^{51} - 8 q^{52} + 16 q^{53} - 4 q^{54} - 20 q^{55} - 4 q^{56} + 16 q^{57} - 4 q^{58} + 4 q^{59} - 8 q^{60} - 4 q^{61} - 12 q^{62} + 8 q^{63} + 4 q^{64} - 24 q^{65} + 16 q^{66} - 12 q^{68} - 4 q^{69} - 8 q^{70} - 24 q^{73} - 4 q^{74} - 24 q^{75} - 16 q^{76} - 4 q^{77} + 4 q^{78} + 12 q^{79} - 4 q^{81} - 12 q^{82} - 12 q^{83} - 16 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{88} + 16 q^{89} + 16 q^{90} + 20 q^{91} + 4 q^{92} + 24 q^{93} - 28 q^{94} - 16 q^{95} - 4 q^{96} + 4 q^{97} - 8 q^{98} - 24 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 4 * q^11 - 4 * q^12 - 8 * q^13 - 4 * q^14 - 8 * q^15 + 4 * q^16 - 12 * q^17 - 16 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^24 + 8 * q^25 - 8 * q^26 - 4 * q^27 - 4 * q^28 - 4 * q^29 - 8 * q^30 - 12 * q^31 + 4 * q^32 + 16 * q^33 - 12 * q^34 - 8 * q^35 - 4 * q^37 - 16 * q^38 + 4 * q^39 - 12 * q^41 + 4 * q^43 - 4 * q^44 + 16 * q^45 + 4 * q^46 - 28 * q^47 - 4 * q^48 - 8 * q^49 + 8 * q^50 + 16 * q^51 - 8 * q^52 + 16 * q^53 - 4 * q^54 - 20 * q^55 - 4 * q^56 + 16 * q^57 - 4 * q^58 + 4 * q^59 - 8 * q^60 - 4 * q^61 - 12 * q^62 + 8 * q^63 + 4 * q^64 - 24 * q^65 + 16 * q^66 - 12 * q^68 - 4 * q^69 - 8 * q^70 - 24 * q^73 - 4 * q^74 - 24 * q^75 - 16 * q^76 - 4 * q^77 + 4 * q^78 + 12 * q^79 - 4 * q^81 - 12 * q^82 - 12 * q^83 - 16 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^88 + 16 * q^89 + 16 * q^90 + 20 * q^91 + 4 * q^92 + 24 * q^93 - 28 * q^94 - 16 * q^95 - 4 * q^96 + 4 * q^97 - 8 * q^98 - 24 * q^99

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