LMFDB - Embedded newform 546.2.a.j.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(1,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, 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("546.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.56155$ of defining polynomial
Character	$\chi$	$=$	546.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.56155 q^{10} -1.56155 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} +3.56155 q^{15} +1.00000 q^{16} -6.68466 q^{17} +1.00000 q^{18} -4.68466 q^{19} +3.56155 q^{20} -1.00000 q^{21} -1.56155 q^{22} -5.56155 q^{23} +1.00000 q^{24} +7.68466 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +6.68466 q^{29} +3.56155 q^{30} +6.24621 q^{31} +1.00000 q^{32} -1.56155 q^{33} -6.68466 q^{34} -3.56155 q^{35} +1.00000 q^{36} -7.56155 q^{37} -4.68466 q^{38} +1.00000 q^{39} +3.56155 q^{40} -1.12311 q^{41} -1.00000 q^{42} -6.43845 q^{43} -1.56155 q^{44} +3.56155 q^{45} -5.56155 q^{46} +1.00000 q^{48} +1.00000 q^{49} +7.68466 q^{50} -6.68466 q^{51} +1.00000 q^{52} +12.2462 q^{53} +1.00000 q^{54} -5.56155 q^{55} -1.00000 q^{56} -4.68466 q^{57} +6.68466 q^{58} +2.24621 q^{59} +3.56155 q^{60} +6.68466 q^{61} +6.24621 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.56155 q^{65} -1.56155 q^{66} -7.12311 q^{67} -6.68466 q^{68} -5.56155 q^{69} -3.56155 q^{70} +8.00000 q^{71} +1.00000 q^{72} -3.56155 q^{73} -7.56155 q^{74} +7.68466 q^{75} -4.68466 q^{76} +1.56155 q^{77} +1.00000 q^{78} -11.1231 q^{79} +3.56155 q^{80} +1.00000 q^{81} -1.12311 q^{82} +8.87689 q^{83} -1.00000 q^{84} -23.8078 q^{85} -6.43845 q^{86} +6.68466 q^{87} -1.56155 q^{88} +10.0000 q^{89} +3.56155 q^{90} -1.00000 q^{91} -5.56155 q^{92} +6.24621 q^{93} -16.6847 q^{95} +1.00000 q^{96} +14.4924 q^{97} +1.00000 q^{98} -1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 3 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} + 3 q^{20} - 2 q^{21} + q^{22} - 7 q^{23} + 2 q^{24} + 3 q^{25} + 2 q^{26} + 2 q^{27} - 2 q^{28} + q^{29} + 3 q^{30} - 4 q^{31} + 2 q^{32} + q^{33} - q^{34} - 3 q^{35} + 2 q^{36} - 11 q^{37} + 3 q^{38} + 2 q^{39} + 3 q^{40} + 6 q^{41} - 2 q^{42} - 17 q^{43} + q^{44} + 3 q^{45} - 7 q^{46} + 2 q^{48} + 2 q^{49} + 3 q^{50} - q^{51} + 2 q^{52} + 8 q^{53} + 2 q^{54} - 7 q^{55} - 2 q^{56} + 3 q^{57} + q^{58} - 12 q^{59} + 3 q^{60} + q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} + 3 q^{65} + q^{66} - 6 q^{67} - q^{68} - 7 q^{69} - 3 q^{70} + 16 q^{71} + 2 q^{72} - 3 q^{73} - 11 q^{74} + 3 q^{75} + 3 q^{76} - q^{77} + 2 q^{78} - 14 q^{79} + 3 q^{80} + 2 q^{81} + 6 q^{82} + 26 q^{83} - 2 q^{84} - 27 q^{85} - 17 q^{86} + q^{87} + q^{88} + 20 q^{89} + 3 q^{90} - 2 q^{91} - 7 q^{92} - 4 q^{93} - 21 q^{95} + 2 q^{96} - 4 q^{97} + 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 + 3 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 3 * q^15 + 2 * q^16 - q^17 + 2 * q^18 + 3 * q^19 + 3 * q^20 - 2 * q^21 + q^22 - 7 * q^23 + 2 * q^24 + 3 * q^25 + 2 * q^26 + 2 * q^27 - 2 * q^28 + q^29 + 3 * q^30 - 4 * q^31 + 2 * q^32 + q^33 - q^34 - 3 * q^35 + 2 * q^36 - 11 * q^37 + 3 * q^38 + 2 * q^39 + 3 * q^40 + 6 * q^41 - 2 * q^42 - 17 * q^43 + q^44 + 3 * q^45 - 7 * q^46 + 2 * q^48 + 2 * q^49 + 3 * q^50 - q^51 + 2 * q^52 + 8 * q^53 + 2 * q^54 - 7 * q^55 - 2 * q^56 + 3 * q^57 + q^58 - 12 * q^59 + 3 * q^60 + q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 + 3 * q^65 + q^66 - 6 * q^67 - q^68 - 7 * q^69 - 3 * q^70 + 16 * q^71 + 2 * q^72 - 3 * q^73 - 11 * q^74 + 3 * q^75 + 3 * q^76 - q^77 + 2 * q^78 - 14 * q^79 + 3 * q^80 + 2 * q^81 + 6 * q^82 + 26 * q^83 - 2 * q^84 - 27 * q^85 - 17 * q^86 + q^87 + q^88 + 20 * q^89 + 3 * q^90 - 2 * q^91 - 7 * q^92 - 4 * q^93 - 21 * q^95 + 2 * q^96 - 4 * q^97 + 2 * q^98 + 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
$5$	3.56155	1.59277	0.796387	−	0.604787i	$-0.206742\pi$
$5$	3.56155	1.59277	0.796387	+	0.604787i	$0.206742\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.56155	1.12626
$11$	−1.56155	−0.470826	−0.235413	−	0.971895i	$-0.575644\pi$
$11$	−1.56155	−0.470826	−0.235413	+	0.971895i	$0.575644\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.00000	−0.267261
$15$	3.56155	0.919589
$16$	1.00000	0.250000
$17$	−6.68466	−1.62127	−0.810634	−	0.585553i	$-0.800877\pi$
$17$	−6.68466	−1.62127	−0.810634	+	0.585553i	$0.800877\pi$
$18$	1.00000	0.235702
$19$	−4.68466	−1.07473	−0.537367	−	0.843348i	$-0.680581\pi$
$19$	−4.68466	−1.07473	−0.537367	+	0.843348i	$0.680581\pi$
$20$	3.56155	0.796387
$21$	−1.00000	−0.218218
$22$	−1.56155	−0.332924
$23$	−5.56155	−1.15966	−0.579832	−	0.814736i	$-0.696882\pi$
$23$	−5.56155	−1.15966	−0.579832	+	0.814736i	$0.696882\pi$
$24$	1.00000	0.204124
$25$	7.68466	1.53693
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	6.68466	1.24131	0.620655	−	0.784084i	$-0.286867\pi$
$29$	6.68466	1.24131	0.620655	+	0.784084i	$0.286867\pi$
$30$	3.56155	0.650248
$31$	6.24621	1.12185	0.560926	−	0.827866i	$-0.310445\pi$
$31$	6.24621	1.12185	0.560926	+	0.827866i	$0.310445\pi$
$32$	1.00000	0.176777
$33$	−1.56155	−0.271831
$34$	−6.68466	−1.14641
$35$	−3.56155	−0.602012
$36$	1.00000	0.166667
$37$	−7.56155	−1.24311	−0.621556	−	0.783370i	$-0.713499\pi$
$37$	−7.56155	−1.24311	−0.621556	+	0.783370i	$0.713499\pi$
$38$	−4.68466	−0.759952
$39$	1.00000	0.160128
$40$	3.56155	0.563131
$41$	−1.12311	−0.175400	−0.0876998	−	0.996147i	$-0.527952\pi$
$41$	−1.12311	−0.175400	−0.0876998	+	0.996147i	$0.527952\pi$
$42$	−1.00000	−0.154303
$43$	−6.43845	−0.981854	−0.490927	−	0.871201i	$-0.663342\pi$
$43$	−6.43845	−0.981854	−0.490927	+	0.871201i	$0.663342\pi$
$44$	−1.56155	−0.235413
$45$	3.56155	0.530925
$46$	−5.56155	−0.820006
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	7.68466	1.08677
$51$	−6.68466	−0.936039
$52$	1.00000	0.138675
$53$	12.2462	1.68215	0.841073	−	0.540921i	$-0.181924\pi$
$53$	12.2462	1.68215	0.841073	+	0.540921i	$0.181924\pi$
$54$	1.00000	0.136083
$55$	−5.56155	−0.749920
$56$	−1.00000	−0.133631
$57$	−4.68466	−0.620498
$58$	6.68466	0.877739
$59$	2.24621	0.292432	0.146216	−	0.989253i	$-0.453291\pi$
$59$	2.24621	0.292432	0.146216	+	0.989253i	$0.453291\pi$
$60$	3.56155	0.459794
$61$	6.68466	0.855883	0.427941	−	0.903806i	$-0.359239\pi$
$61$	6.68466	0.855883	0.427941	+	0.903806i	$0.359239\pi$
$62$	6.24621	0.793270
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	3.56155	0.441756
$66$	−1.56155	−0.192214
$67$	−7.12311	−0.870226	−0.435113	−	0.900376i	$-0.643292\pi$
$67$	−7.12311	−0.870226	−0.435113	+	0.900376i	$0.643292\pi$
$68$	−6.68466	−0.810634
$69$	−5.56155	−0.669532
$70$	−3.56155	−0.425687
$71$	8.00000	0.949425	0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000	0.949425	0.474713	+	0.880141i	$0.342552\pi$
$72$	1.00000	0.117851
$73$	−3.56155	−0.416848	−0.208424	−	0.978039i	$-0.566833\pi$
$73$	−3.56155	−0.416848	−0.208424	+	0.978039i	$0.566833\pi$
$74$	−7.56155	−0.879013
$75$	7.68466	0.887348
$76$	−4.68466	−0.537367
$77$	1.56155	0.177955
$78$	1.00000	0.113228
$79$	−11.1231	−1.25145	−0.625724	−	0.780045i	$-0.715196\pi$
$79$	−11.1231	−1.25145	−0.625724	+	0.780045i	$0.715196\pi$
$80$	3.56155	0.398194
$81$	1.00000	0.111111
$82$	−1.12311	−0.124026
$83$	8.87689	0.974366	0.487183	−	0.873300i	$-0.338025\pi$
$83$	8.87689	0.974366	0.487183	+	0.873300i	$0.338025\pi$
$84$	−1.00000	−0.109109
$85$	−23.8078	−2.58231
$86$	−6.43845	−0.694276
$87$	6.68466	0.716671
$88$	−1.56155	−0.166462
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	3.56155	0.375421
$91$	−1.00000	−0.104828
$92$	−5.56155	−0.579832
$93$	6.24621	0.647702
$94$	0	0
$95$	−16.6847	−1.71181
$96$	1.00000	0.102062
$97$	14.4924	1.47148	0.735741	−	0.677263i	$-0.236834\pi$
$97$	14.4924	1.47148	0.735741	+	0.677263i	$0.236834\pi$
$98$	1.00000	0.101015
$99$	−1.56155	−0.156942
$100$	7.68466	0.768466
$101$	−5.12311	−0.509768	−0.254884	−	0.966972i	$-0.582037\pi$
$101$	−5.12311	−0.509768	−0.254884	+	0.966972i	$0.582037\pi$
$102$	−6.68466	−0.661880
$103$	−0.684658	−0.0674614	−0.0337307	−	0.999431i	$-0.510739\pi$
$103$	−0.684658	−0.0674614	−0.0337307	+	0.999431i	$0.510739\pi$
$104$	1.00000	0.0980581
$105$	−3.56155	−0.347572
$106$	12.2462	1.18946
$107$	−8.87689	−0.858162	−0.429081	−	0.903266i	$-0.641162\pi$
$107$	−8.87689	−0.858162	−0.429081	+	0.903266i	$0.641162\pi$
$108$	1.00000	0.0962250
$109$	−16.9309	−1.62168	−0.810842	−	0.585266i	$-0.800990\pi$
$109$	−16.9309	−1.62168	−0.810842	+	0.585266i	$0.800990\pi$
$110$	−5.56155	−0.530273
$111$	−7.56155	−0.717711
$112$	−1.00000	−0.0944911
$113$	−4.24621	−0.399450	−0.199725	−	0.979852i	$-0.564005\pi$
$113$	−4.24621	−0.399450	−0.199725	+	0.979852i	$0.564005\pi$
$114$	−4.68466	−0.438758
$115$	−19.8078	−1.84708
$116$	6.68466	0.620655
$117$	1.00000	0.0924500
$118$	2.24621	0.206781
$119$	6.68466	0.612782
$120$	3.56155	0.325124
$121$	−8.56155	−0.778323
$122$	6.68466	0.605201
$123$	−1.12311	−0.101267
$124$	6.24621	0.560926
$125$	9.56155	0.855211
$126$	−1.00000	−0.0890871
$127$	−4.87689	−0.432754	−0.216377	−	0.976310i	$-0.569424\pi$
$127$	−4.87689	−0.432754	−0.216377	+	0.976310i	$0.569424\pi$
$128$	1.00000	0.0883883
$129$	−6.43845	−0.566874
$130$	3.56155	0.312369
$131$	−9.56155	−0.835397	−0.417698	−	0.908586i	$-0.637163\pi$
$131$	−9.56155	−0.835397	−0.417698	+	0.908586i	$0.637163\pi$
$132$	−1.56155	−0.135916
$133$	4.68466	0.406211
$134$	−7.12311	−0.615343
$135$	3.56155	0.306530
$136$	−6.68466	−0.573205
$137$	−3.56155	−0.304284	−0.152142	−	0.988359i	$-0.548617\pi$
$137$	−3.56155	−0.304284	−0.152142	+	0.988359i	$0.548617\pi$
$138$	−5.56155	−0.473431
$139$	12.0000	1.01783	0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000	1.01783	0.508913	+	0.860818i	$0.330047\pi$
$140$	−3.56155	−0.301006
$141$	0	0
$142$	8.00000	0.671345
$143$	−1.56155	−0.130584
$144$	1.00000	0.0833333
$145$	23.8078	1.97713
$146$	−3.56155	−0.294756
$147$	1.00000	0.0824786
$148$	−7.56155	−0.621556
$149$	−17.6155	−1.44312	−0.721560	−	0.692352i	$-0.756575\pi$
$149$	−17.6155	−1.44312	−0.721560	+	0.692352i	$0.756575\pi$
$150$	7.68466	0.627450
$151$	11.8078	0.960902	0.480451	−	0.877022i	$-0.340473\pi$
$151$	11.8078	0.960902	0.480451	+	0.877022i	$0.340473\pi$
$152$	−4.68466	−0.379976
$153$	−6.68466	−0.540423
$154$	1.56155	0.125834
$155$	22.2462	1.78686
$156$	1.00000	0.0800641
$157$	−15.5616	−1.24195	−0.620974	−	0.783832i	$-0.713263\pi$
$157$	−15.5616	−1.24195	−0.620974	+	0.783832i	$0.713263\pi$
$158$	−11.1231	−0.884907
$159$	12.2462	0.971188
$160$	3.56155	0.281565
$161$	5.56155	0.438312
$162$	1.00000	0.0785674
$163$	−16.8769	−1.32190	−0.660950	−	0.750430i	$-0.729847\pi$
$163$	−16.8769	−1.32190	−0.660950	+	0.750430i	$0.729847\pi$
$164$	−1.12311	−0.0876998
$165$	−5.56155	−0.432966
$166$	8.87689	0.688981
$167$	22.9309	1.77444	0.887222	−	0.461343i	$-0.152632\pi$
$167$	22.9309	1.77444	0.887222	+	0.461343i	$0.152632\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	−23.8078	−1.82597
$171$	−4.68466	−0.358245
$172$	−6.43845	−0.490927
$173$	20.2462	1.53929	0.769645	−	0.638471i	$-0.220433\pi$
$173$	20.2462	1.53929	0.769645	+	0.638471i	$0.220433\pi$
$174$	6.68466	0.506763
$175$	−7.68466	−0.580906
$176$	−1.56155	−0.117706
$177$	2.24621	0.168836
$178$	10.0000	0.749532
$179$	16.4924	1.23270	0.616351	−	0.787472i	$-0.288610\pi$
$179$	16.4924	1.23270	0.616351	+	0.787472i	$0.288610\pi$
$180$	3.56155	0.265462
$181$	−0.246211	−0.0183007	−0.00915037	−	0.999958i	$-0.502913\pi$
$181$	−0.246211	−0.0183007	−0.00915037	+	0.999958i	$0.502913\pi$
$182$	−1.00000	−0.0741249
$183$	6.68466	0.494144
$184$	−5.56155	−0.410003
$185$	−26.9309	−1.98000
$186$	6.24621	0.457994
$187$	10.4384	0.763335
$188$	0	0
$189$	−1.00000	−0.0727393
$190$	−16.6847	−1.21043
$191$	14.9309	1.08036	0.540180	−	0.841550i	$-0.318356\pi$
$191$	14.9309	1.08036	0.540180	+	0.841550i	$0.318356\pi$
$192$	1.00000	0.0721688
$193$	19.3693	1.39423	0.697117	−	0.716957i	$-0.254466\pi$
$193$	19.3693	1.39423	0.697117	+	0.716957i	$0.254466\pi$
$194$	14.4924	1.04050
$195$	3.56155	0.255048
$196$	1.00000	0.0714286
$197$	10.8769	0.774947	0.387473	−	0.921881i	$-0.373348\pi$
$197$	10.8769	0.774947	0.387473	+	0.921881i	$0.373348\pi$
$198$	−1.56155	−0.110975
$199$	6.93087	0.491316	0.245658	−	0.969357i	$-0.420996\pi$
$199$	6.93087	0.491316	0.245658	+	0.969357i	$0.420996\pi$
$200$	7.68466	0.543387
$201$	−7.12311	−0.502425
$202$	−5.12311	−0.360460
$203$	−6.68466	−0.469171
$204$	−6.68466	−0.468020
$205$	−4.00000	−0.279372
$206$	−0.684658	−0.0477024
$207$	−5.56155	−0.386555
$208$	1.00000	0.0693375
$209$	7.31534	0.506013
$210$	−3.56155	−0.245770
$211$	−15.8078	−1.08825	−0.544126	−	0.839004i	$-0.683139\pi$
$211$	−15.8078	−1.08825	−0.544126	+	0.839004i	$0.683139\pi$
$212$	12.2462	0.841073
$213$	8.00000	0.548151
$214$	−8.87689	−0.606812
$215$	−22.9309	−1.56387
$216$	1.00000	0.0680414
$217$	−6.24621	−0.424020
$218$	−16.9309	−1.14670
$219$	−3.56155	−0.240667
$220$	−5.56155	−0.374960
$221$	−6.68466	−0.449659
$222$	−7.56155	−0.507498
$223$	−23.6155	−1.58141	−0.790706	−	0.612196i	$-0.790287\pi$
$223$	−23.6155	−1.58141	−0.790706	+	0.612196i	$0.790287\pi$
$224$	−1.00000	−0.0668153
$225$	7.68466	0.512311
$226$	−4.24621	−0.282454
$227$	−7.12311	−0.472777	−0.236389	−	0.971659i	$-0.575964\pi$
$227$	−7.12311	−0.472777	−0.236389	+	0.971659i	$0.575964\pi$
$228$	−4.68466	−0.310249
$229$	28.2462	1.86656	0.933281	−	0.359147i	$-0.116932\pi$
$229$	28.2462	1.86656	0.933281	+	0.359147i	$0.116932\pi$
$230$	−19.8078	−1.30609
$231$	1.56155	0.102743
$232$	6.68466	0.438869
$233$	27.3693	1.79302	0.896512	−	0.443020i	$-0.146093\pi$
$233$	27.3693	1.79302	0.896512	+	0.443020i	$0.146093\pi$
$234$	1.00000	0.0653720
$235$	0	0
$236$	2.24621	0.146216
$237$	−11.1231	−0.722523
$238$	6.68466	0.433302
$239$	16.0000	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$240$	3.56155	0.229897
$241$	−14.0000	−0.901819	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−14.0000	−0.901819	−0.450910	+	0.892570i	$0.648900\pi$
$242$	−8.56155	−0.550357
$243$	1.00000	0.0641500
$244$	6.68466	0.427941
$245$	3.56155	0.227539
$246$	−1.12311	−0.0716066
$247$	−4.68466	−0.298078
$248$	6.24621	0.396635
$249$	8.87689	0.562550
$250$	9.56155	0.604726
$251$	−7.80776	−0.492822	−0.246411	−	0.969165i	$-0.579251\pi$
$251$	−7.80776	−0.492822	−0.246411	+	0.969165i	$0.579251\pi$
$252$	−1.00000	−0.0629941
$253$	8.68466	0.546000
$254$	−4.87689	−0.306004
$255$	−23.8078	−1.49090
$256$	1.00000	0.0625000
$257$	−4.24621	−0.264871	−0.132436	−	0.991192i	$-0.542280\pi$
$257$	−4.24621	−0.264871	−0.132436	+	0.991192i	$0.542280\pi$
$258$	−6.43845	−0.400840
$259$	7.56155	0.469852
$260$	3.56155	0.220878
$261$	6.68466	0.413770
$262$	−9.56155	−0.590715
$263$	−30.2462	−1.86506	−0.932531	−	0.361091i	$-0.882404\pi$
$263$	−30.2462	−1.86506	−0.932531	+	0.361091i	$0.882404\pi$
$264$	−1.56155	−0.0961069
$265$	43.6155	2.67928
$266$	4.68466	0.287235
$267$	10.0000	0.611990
$268$	−7.12311	−0.435113
$269$	20.2462	1.23443	0.617217	−	0.786793i	$-0.288260\pi$
$269$	20.2462	1.23443	0.617217	+	0.786793i	$0.288260\pi$
$270$	3.56155	0.216749
$271$	4.87689	0.296250	0.148125	−	0.988969i	$-0.452676\pi$
$271$	4.87689	0.296250	0.148125	+	0.988969i	$0.452676\pi$
$272$	−6.68466	−0.405317
$273$	−1.00000	−0.0605228
$274$	−3.56155	−0.215161
$275$	−12.0000	−0.723627
$276$	−5.56155	−0.334766
$277$	−22.4924	−1.35144	−0.675719	−	0.737159i	$-0.736167\pi$
$277$	−22.4924	−1.35144	−0.675719	+	0.737159i	$0.736167\pi$
$278$	12.0000	0.719712
$279$	6.24621	0.373951
$280$	−3.56155	−0.212843
$281$	16.2462	0.969168	0.484584	−	0.874745i	$-0.338971\pi$
$281$	16.2462	0.969168	0.484584	+	0.874745i	$0.338971\pi$
$282$	0	0
$283$	18.2462	1.08462	0.542312	−	0.840177i	$-0.317549\pi$
$283$	18.2462	1.08462	0.542312	+	0.840177i	$0.317549\pi$
$284$	8.00000	0.474713
$285$	−16.6847	−0.988314
$286$	−1.56155	−0.0923366
$287$	1.12311	0.0662948
$288$	1.00000	0.0589256
$289$	27.6847	1.62851
$290$	23.8078	1.39804
$291$	14.4924	0.849561
$292$	−3.56155	−0.208424
$293$	24.7386	1.44525	0.722623	−	0.691242i	$-0.242936\pi$
$293$	24.7386	1.44525	0.722623	+	0.691242i	$0.242936\pi$
$294$	1.00000	0.0583212
$295$	8.00000	0.465778
$296$	−7.56155	−0.439506
$297$	−1.56155	−0.0906105
$298$	−17.6155	−1.02044
$299$	−5.56155	−0.321633
$300$	7.68466	0.443674
$301$	6.43845	0.371106
$302$	11.8078	0.679460
$303$	−5.12311	−0.294315
$304$	−4.68466	−0.268684
$305$	23.8078	1.36323
$306$	−6.68466	−0.382136
$307$	26.2462	1.49795	0.748975	−	0.662598i	$-0.230546\pi$
$307$	26.2462	1.49795	0.748975	+	0.662598i	$0.230546\pi$
$308$	1.56155	0.0889777
$309$	−0.684658	−0.0389489
$310$	22.2462	1.26350
$311$	−12.8769	−0.730182	−0.365091	−	0.930972i	$-0.618962\pi$
$311$	−12.8769	−0.730182	−0.365091	+	0.930972i	$0.618962\pi$
$312$	1.00000	0.0566139
$313$	−13.6155	−0.769595	−0.384798	−	0.923001i	$-0.625729\pi$
$313$	−13.6155	−0.769595	−0.384798	+	0.923001i	$0.625729\pi$
$314$	−15.5616	−0.878189
$315$	−3.56155	−0.200671
$316$	−11.1231	−0.625724
$317$	2.87689	0.161582	0.0807912	−	0.996731i	$-0.474255\pi$
$317$	2.87689	0.161582	0.0807912	+	0.996731i	$0.474255\pi$
$318$	12.2462	0.686733
$319$	−10.4384	−0.584441
$320$	3.56155	0.199097
$321$	−8.87689	−0.495460
$322$	5.56155	0.309933
$323$	31.3153	1.74243
$324$	1.00000	0.0555556
$325$	7.68466	0.426268
$326$	−16.8769	−0.934725
$327$	−16.9309	−0.936279
$328$	−1.12311	−0.0620131
$329$	0	0
$330$	−5.56155	−0.306153
$331$	13.3693	0.734844	0.367422	−	0.930054i	$-0.380240\pi$
$331$	13.3693	0.734844	0.367422	+	0.930054i	$0.380240\pi$
$332$	8.87689	0.487183
$333$	−7.56155	−0.414371
$334$	22.9309	1.25472
$335$	−25.3693	−1.38607
$336$	−1.00000	−0.0545545
$337$	4.43845	0.241778	0.120889	−	0.992666i	$-0.461426\pi$
$337$	4.43845	0.241778	0.120889	+	0.992666i	$0.461426\pi$
$338$	1.00000	0.0543928
$339$	−4.24621	−0.230623
$340$	−23.8078	−1.29116
$341$	−9.75379	−0.528197
$342$	−4.68466	−0.253317
$343$	−1.00000	−0.0539949
$344$	−6.43845	−0.347138
$345$	−19.8078	−1.06641
$346$	20.2462	1.08844
$347$	−20.0000	−1.07366	−0.536828	−	0.843692i	$-0.680378\pi$
$347$	−20.0000	−1.07366	−0.536828	+	0.843692i	$0.680378\pi$
$348$	6.68466	0.358335
$349$	7.75379	0.415051	0.207525	−	0.978230i	$-0.433459\pi$
$349$	7.75379	0.415051	0.207525	+	0.978230i	$0.433459\pi$
$350$	−7.68466	−0.410762
$351$	1.00000	0.0533761
$352$	−1.56155	−0.0832310
$353$	30.4924	1.62295	0.811474	−	0.584389i	$-0.198666\pi$
$353$	30.4924	1.62295	0.811474	+	0.584389i	$0.198666\pi$
$354$	2.24621	0.119385
$355$	28.4924	1.51222
$356$	10.0000	0.529999
$357$	6.68466	0.353790
$358$	16.4924	0.871652
$359$	−26.7386	−1.41121	−0.705606	−	0.708605i	$-0.749325\pi$
$359$	−26.7386	−1.41121	−0.705606	+	0.708605i	$0.749325\pi$
$360$	3.56155	0.187710
$361$	2.94602	0.155054
$362$	−0.246211	−0.0129406
$363$	−8.56155	−0.449365
$364$	−1.00000	−0.0524142
$365$	−12.6847	−0.663945
$366$	6.68466	0.349413
$367$	−16.0000	−0.835193	−0.417597	−	0.908633i	$-0.637127\pi$
$367$	−16.0000	−0.835193	−0.417597	+	0.908633i	$0.637127\pi$
$368$	−5.56155	−0.289916
$369$	−1.12311	−0.0584665
$370$	−26.9309	−1.40007
$371$	−12.2462	−0.635792
$372$	6.24621	0.323851
$373$	−17.6155	−0.912097	−0.456049	−	0.889955i	$-0.650736\pi$
$373$	−17.6155	−0.912097	−0.456049	+	0.889955i	$0.650736\pi$
$374$	10.4384	0.539759
$375$	9.56155	0.493756
$376$	0	0
$377$	6.68466	0.344277
$378$	−1.00000	−0.0514344
$379$	34.2462	1.75911	0.879555	−	0.475797i	$-0.157840\pi$
$379$	34.2462	1.75911	0.879555	+	0.475797i	$0.157840\pi$
$380$	−16.6847	−0.855905
$381$	−4.87689	−0.249851
$382$	14.9309	0.763930
$383$	27.4233	1.40126	0.700632	−	0.713522i	$-0.252901\pi$
$383$	27.4233	1.40126	0.700632	+	0.713522i	$0.252901\pi$
$384$	1.00000	0.0510310
$385$	5.56155	0.283443
$386$	19.3693	0.985872
$387$	−6.43845	−0.327285
$388$	14.4924	0.735741
$389$	−28.7386	−1.45711	−0.728553	−	0.684989i	$-0.759807\pi$
$389$	−28.7386	−1.45711	−0.728553	+	0.684989i	$0.759807\pi$
$390$	3.56155	0.180346
$391$	37.1771	1.88013
$392$	1.00000	0.0505076
$393$	−9.56155	−0.482317
$394$	10.8769	0.547970
$395$	−39.6155	−1.99327
$396$	−1.56155	−0.0784710
$397$	−18.0000	−0.903394	−0.451697	−	0.892171i	$-0.649181\pi$
$397$	−18.0000	−0.903394	−0.451697	+	0.892171i	$0.649181\pi$
$398$	6.93087	0.347413
$399$	4.68466	0.234526
$400$	7.68466	0.384233
$401$	8.24621	0.411796	0.205898	−	0.978573i	$-0.433988\pi$
$401$	8.24621	0.411796	0.205898	+	0.978573i	$0.433988\pi$
$402$	−7.12311	−0.355268
$403$	6.24621	0.311146
$404$	−5.12311	−0.254884
$405$	3.56155	0.176975
$406$	−6.68466	−0.331754
$407$	11.8078	0.585289
$408$	−6.68466	−0.330940
$409$	−4.93087	−0.243816	−0.121908	−	0.992541i	$-0.538901\pi$
$409$	−4.93087	−0.243816	−0.121908	+	0.992541i	$0.538901\pi$
$410$	−4.00000	−0.197546
$411$	−3.56155	−0.175678
$412$	−0.684658	−0.0337307
$413$	−2.24621	−0.110529
$414$	−5.56155	−0.273335
$415$	31.6155	1.55195
$416$	1.00000	0.0490290
$417$	12.0000	0.587643
$418$	7.31534	0.357805
$419$	−36.6847	−1.79216	−0.896081	−	0.443890i	$-0.853598\pi$
$419$	−36.6847	−1.79216	−0.896081	+	0.443890i	$0.853598\pi$
$420$	−3.56155	−0.173786
$421$	−3.75379	−0.182948	−0.0914742	−	0.995807i	$-0.529158\pi$
$421$	−3.75379	−0.182948	−0.0914742	+	0.995807i	$0.529158\pi$
$422$	−15.8078	−0.769510
$423$	0	0
$424$	12.2462	0.594729
$425$	−51.3693	−2.49178
$426$	8.00000	0.387601
$427$	−6.68466	−0.323493
$428$	−8.87689	−0.429081
$429$	−1.56155	−0.0753925
$430$	−22.9309	−1.10582
$431$	−33.3693	−1.60734	−0.803672	−	0.595073i	$-0.797123\pi$
$431$	−33.3693	−1.60734	−0.803672	+	0.595073i	$0.797123\pi$
$432$	1.00000	0.0481125
$433$	−31.3693	−1.50751	−0.753757	−	0.657154i	$-0.771760\pi$
$433$	−31.3693	−1.50751	−0.753757	+	0.657154i	$0.771760\pi$
$434$	−6.24621	−0.299828
$435$	23.8078	1.14149
$436$	−16.9309	−0.810842
$437$	26.0540	1.24633
$438$	−3.56155	−0.170178
$439$	−6.93087	−0.330792	−0.165396	−	0.986227i	$-0.552890\pi$
$439$	−6.93087	−0.330792	−0.165396	+	0.986227i	$0.552890\pi$
$440$	−5.56155	−0.265137
$441$	1.00000	0.0476190
$442$	−6.68466	−0.317957
$443$	−5.36932	−0.255104	−0.127552	−	0.991832i	$-0.540712\pi$
$443$	−5.36932	−0.255104	−0.127552	+	0.991832i	$0.540712\pi$
$444$	−7.56155	−0.358855
$445$	35.6155	1.68834
$446$	−23.6155	−1.11823
$447$	−17.6155	−0.833186
$448$	−1.00000	−0.0472456
$449$	10.6847	0.504240	0.252120	−	0.967696i	$-0.418872\pi$
$449$	10.6847	0.504240	0.252120	+	0.967696i	$0.418872\pi$
$450$	7.68466	0.362258
$451$	1.75379	0.0825827
$452$	−4.24621	−0.199725
$453$	11.8078	0.554777
$454$	−7.12311	−0.334304
$455$	−3.56155	−0.166968
$456$	−4.68466	−0.219379
$457$	27.3693	1.28028	0.640141	−	0.768257i	$-0.278876\pi$
$457$	27.3693	1.28028	0.640141	+	0.768257i	$0.278876\pi$
$458$	28.2462	1.31986
$459$	−6.68466	−0.312013
$460$	−19.8078	−0.923542
$461$	−28.0540	−1.30660	−0.653302	−	0.757097i	$-0.726617\pi$
$461$	−28.0540	−1.30660	−0.653302	+	0.757097i	$0.726617\pi$
$462$	1.56155	0.0726500
$463$	−8.68466	−0.403610	−0.201805	−	0.979426i	$-0.564681\pi$
$463$	−8.68466	−0.403610	−0.201805	+	0.979426i	$0.564681\pi$
$464$	6.68466	0.310327
$465$	22.2462	1.03164
$466$	27.3693	1.26786
$467$	−3.31534	−0.153416	−0.0767079	−	0.997054i	$-0.524441\pi$
$467$	−3.31534	−0.153416	−0.0767079	+	0.997054i	$0.524441\pi$
$468$	1.00000	0.0462250
$469$	7.12311	0.328914
$470$	0	0
$471$	−15.5616	−0.717039
$472$	2.24621	0.103390
$473$	10.0540	0.462282
$474$	−11.1231	−0.510901
$475$	−36.0000	−1.65179
$476$	6.68466	0.306391
$477$	12.2462	0.560715
$478$	16.0000	0.731823
$479$	32.3002	1.47583	0.737917	−	0.674892i	$-0.235810\pi$
$479$	32.3002	1.47583	0.737917	+	0.674892i	$0.235810\pi$
$480$	3.56155	0.162562
$481$	−7.56155	−0.344777
$482$	−14.0000	−0.637683
$483$	5.56155	0.253059
$484$	−8.56155	−0.389161
$485$	51.6155	2.34374
$486$	1.00000	0.0453609
$487$	−8.00000	−0.362515	−0.181257	−	0.983436i	$-0.558017\pi$
$487$	−8.00000	−0.362515	−0.181257	+	0.983436i	$0.558017\pi$
$488$	6.68466	0.302600
$489$	−16.8769	−0.763200
$490$	3.56155	0.160895
$491$	−8.87689	−0.400609	−0.200304	−	0.979734i	$-0.564193\pi$
$491$	−8.87689	−0.400609	−0.200304	+	0.979734i	$0.564193\pi$
$492$	−1.12311	−0.0506335
$493$	−44.6847	−2.01250
$494$	−4.68466	−0.210773
$495$	−5.56155	−0.249973
$496$	6.24621	0.280463
$497$	−8.00000	−0.358849
$498$	8.87689	0.397783
$499$	36.0000	1.61158	0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000	1.61158	0.805791	+	0.592200i	$0.201741\pi$
$500$	9.56155	0.427606
$501$	22.9309	1.02448
$502$	−7.80776	−0.348478
$503$	−3.12311	−0.139252	−0.0696262	−	0.997573i	$-0.522181\pi$
$503$	−3.12311	−0.139252	−0.0696262	+	0.997573i	$0.522181\pi$
$504$	−1.00000	−0.0445435
$505$	−18.2462	−0.811946
$506$	8.68466	0.386080
$507$	1.00000	0.0444116
$508$	−4.87689	−0.216377
$509$	−12.0540	−0.534283	−0.267142	−	0.963657i	$-0.586079\pi$
$509$	−12.0540	−0.534283	−0.267142	+	0.963657i	$0.586079\pi$
$510$	−23.8078	−1.05423
$511$	3.56155	0.157554
$512$	1.00000	0.0441942
$513$	−4.68466	−0.206833
$514$	−4.24621	−0.187292
$515$	−2.43845	−0.107451
$516$	−6.43845	−0.283437
$517$	0	0
$518$	7.56155	0.332236
$519$	20.2462	0.888710
$520$	3.56155	0.156184
$521$	2.68466	0.117617	0.0588085	−	0.998269i	$-0.481270\pi$
$521$	2.68466	0.117617	0.0588085	+	0.998269i	$0.481270\pi$
$522$	6.68466	0.292580
$523$	21.7538	0.951227	0.475613	−	0.879654i	$-0.342226\pi$
$523$	21.7538	0.951227	0.475613	+	0.879654i	$0.342226\pi$
$524$	−9.56155	−0.417698
$525$	−7.68466	−0.335386
$526$	−30.2462	−1.31880
$527$	−41.7538	−1.81882
$528$	−1.56155	−0.0679579
$529$	7.93087	0.344820
$530$	43.6155	1.89454
$531$	2.24621	0.0974773
$532$	4.68466	0.203106
$533$	−1.12311	−0.0486471
$534$	10.0000	0.432742
$535$	−31.6155	−1.36686
$536$	−7.12311	−0.307671
$537$	16.4924	0.711701
$538$	20.2462	0.872876
$539$	−1.56155	−0.0672608
$540$	3.56155	0.153265
$541$	−32.9309	−1.41581	−0.707904	−	0.706308i	$-0.750359\pi$
$541$	−32.9309	−1.41581	−0.707904	+	0.706308i	$0.750359\pi$
$542$	4.87689	0.209481
$543$	−0.246211	−0.0105659
$544$	−6.68466	−0.286602
$545$	−60.3002	−2.58298
$546$	−1.00000	−0.0427960
$547$	−28.0000	−1.19719	−0.598597	−	0.801050i	$-0.704275\pi$
$547$	−28.0000	−1.19719	−0.598597	+	0.801050i	$0.704275\pi$
$548$	−3.56155	−0.152142
$549$	6.68466	0.285294
$550$	−12.0000	−0.511682
$551$	−31.3153	−1.33408
$552$	−5.56155	−0.236715
$553$	11.1231	0.473003
$554$	−22.4924	−0.955611
$555$	−26.9309	−1.14315
$556$	12.0000	0.508913
$557$	−3.36932	−0.142763	−0.0713813	−	0.997449i	$-0.522741\pi$
$557$	−3.36932	−0.142763	−0.0713813	+	0.997449i	$0.522741\pi$
$558$	6.24621	0.264423
$559$	−6.43845	−0.272317
$560$	−3.56155	−0.150503
$561$	10.4384	0.440712
$562$	16.2462	0.685305
$563$	−6.05398	−0.255145	−0.127572	−	0.991829i	$-0.540718\pi$
$563$	−6.05398	−0.255145	−0.127572	+	0.991829i	$0.540718\pi$
$564$	0	0
$565$	−15.1231	−0.636234
$566$	18.2462	0.766945
$567$	−1.00000	−0.0419961
$568$	8.00000	0.335673
$569$	41.2311	1.72850	0.864248	−	0.503066i	$-0.167795\pi$
$569$	41.2311	1.72850	0.864248	+	0.503066i	$0.167795\pi$
$570$	−16.6847	−0.698843
$571$	18.2462	0.763580	0.381790	−	0.924249i	$-0.375308\pi$
$571$	18.2462	0.763580	0.381790	+	0.924249i	$0.375308\pi$
$572$	−1.56155	−0.0652918
$573$	14.9309	0.623746
$574$	1.12311	0.0468775
$575$	−42.7386	−1.78232
$576$	1.00000	0.0416667
$577$	−30.0000	−1.24892	−0.624458	−	0.781058i	$-0.714680\pi$
$577$	−30.0000	−1.24892	−0.624458	+	0.781058i	$0.714680\pi$
$578$	27.6847	1.15153
$579$	19.3693	0.804961
$580$	23.8078	0.988564
$581$	−8.87689	−0.368276
$582$	14.4924	0.600730
$583$	−19.1231	−0.791998
$584$	−3.56155	−0.147378
$585$	3.56155	0.147252
$586$	24.7386	1.02194
$587$	13.3693	0.551811	0.275905	−	0.961185i	$-0.411022\pi$
$587$	13.3693	0.551811	0.275905	+	0.961185i	$0.411022\pi$
$588$	1.00000	0.0412393
$589$	−29.2614	−1.20569
$590$	8.00000	0.329355
$591$	10.8769	0.447416
$592$	−7.56155	−0.310778
$593$	−20.2462	−0.831412	−0.415706	−	0.909499i	$-0.636466\pi$
$593$	−20.2462	−0.831412	−0.415706	+	0.909499i	$0.636466\pi$
$594$	−1.56155	−0.0640713
$595$	23.8078	0.976023
$596$	−17.6155	−0.721560
$597$	6.93087	0.283662
$598$	−5.56155	−0.227429
$599$	21.5616	0.880981	0.440491	−	0.897757i	$-0.354805\pi$
$599$	21.5616	0.880981	0.440491	+	0.897757i	$0.354805\pi$
$600$	7.68466	0.313725
$601$	−10.8769	−0.443678	−0.221839	−	0.975083i	$-0.571206\pi$
$601$	−10.8769	−0.443678	−0.221839	+	0.975083i	$0.571206\pi$
$602$	6.43845	0.262412
$603$	−7.12311	−0.290075
$604$	11.8078	0.480451
$605$	−30.4924	−1.23969
$606$	−5.12311	−0.208112
$607$	−18.4384	−0.748393	−0.374197	−	0.927349i	$-0.622082\pi$
$607$	−18.4384	−0.748393	−0.374197	+	0.927349i	$0.622082\pi$
$608$	−4.68466	−0.189988
$609$	−6.68466	−0.270876
$610$	23.8078	0.963948
$611$	0	0
$612$	−6.68466	−0.270211
$613$	44.5464	1.79921	0.899606	−	0.436702i	$-0.143854\pi$
$613$	44.5464	1.79921	0.899606	+	0.436702i	$0.143854\pi$
$614$	26.2462	1.05921
$615$	−4.00000	−0.161296
$616$	1.56155	0.0629168
$617$	−33.4233	−1.34557	−0.672786	−	0.739838i	$-0.734902\pi$
$617$	−33.4233	−1.34557	−0.672786	+	0.739838i	$0.734902\pi$
$618$	−0.684658	−0.0275410
$619$	19.3153	0.776349	0.388175	−	0.921586i	$-0.373106\pi$
$619$	19.3153	0.776349	0.388175	+	0.921586i	$0.373106\pi$
$620$	22.2462	0.893429
$621$	−5.56155	−0.223177
$622$	−12.8769	−0.516316
$623$	−10.0000	−0.400642
$624$	1.00000	0.0400320
$625$	−4.36932	−0.174773
$626$	−13.6155	−0.544186
$627$	7.31534	0.292147
$628$	−15.5616	−0.620974
$629$	50.5464	2.01542
$630$	−3.56155	−0.141896
$631$	−22.9309	−0.912864	−0.456432	−	0.889758i	$-0.650873\pi$
$631$	−22.9309	−0.912864	−0.456432	+	0.889758i	$0.650873\pi$
$632$	−11.1231	−0.442453
$633$	−15.8078	−0.628302
$634$	2.87689	0.114256
$635$	−17.3693	−0.689280
$636$	12.2462	0.485594
$637$	1.00000	0.0396214
$638$	−10.4384	−0.413262
$639$	8.00000	0.316475
$640$	3.56155	0.140783
$641$	−20.2462	−0.799677	−0.399839	−	0.916586i	$-0.630934\pi$
$641$	−20.2462	−0.799677	−0.399839	+	0.916586i	$0.630934\pi$
$642$	−8.87689	−0.350343
$643$	16.1922	0.638559	0.319280	−	0.947661i	$-0.396559\pi$
$643$	16.1922	0.638559	0.319280	+	0.947661i	$0.396559\pi$
$644$	5.56155	0.219156
$645$	−22.9309	−0.902902
$646$	31.3153	1.23209
$647$	−14.2462	−0.560076	−0.280038	−	0.959989i	$-0.590347\pi$
$647$	−14.2462	−0.560076	−0.280038	+	0.959989i	$0.590347\pi$
$648$	1.00000	0.0392837
$649$	−3.50758	−0.137684
$650$	7.68466	0.301417
$651$	−6.24621	−0.244808
$652$	−16.8769	−0.660950
$653$	−16.9309	−0.662556	−0.331278	−	0.943533i	$-0.607480\pi$
$653$	−16.9309	−0.662556	−0.331278	+	0.943533i	$0.607480\pi$
$654$	−16.9309	−0.662049
$655$	−34.0540	−1.33060
$656$	−1.12311	−0.0438499
$657$	−3.56155	−0.138949
$658$	0	0
$659$	21.3693	0.832430	0.416215	−	0.909266i	$-0.363356\pi$
$659$	21.3693	0.832430	0.416215	+	0.909266i	$0.363356\pi$
$660$	−5.56155	−0.216483
$661$	−0.246211	−0.00957651	−0.00478825	−	0.999989i	$-0.501524\pi$
$661$	−0.246211	−0.00957651	−0.00478825	+	0.999989i	$0.501524\pi$
$662$	13.3693	0.519613
$663$	−6.68466	−0.259611
$664$	8.87689	0.344490
$665$	16.6847	0.647003
$666$	−7.56155	−0.293004
$667$	−37.1771	−1.43950
$668$	22.9309	0.887222
$669$	−23.6155	−0.913029
$670$	−25.3693	−0.980102
$671$	−10.4384	−0.402972
$672$	−1.00000	−0.0385758
$673$	−33.8078	−1.30319	−0.651597	−	0.758566i	$-0.725901\pi$
$673$	−33.8078	−1.30319	−0.651597	+	0.758566i	$0.725901\pi$
$674$	4.43845	0.170963
$675$	7.68466	0.295783
$676$	1.00000	0.0384615
$677$	2.49242	0.0957916	0.0478958	−	0.998852i	$-0.484748\pi$
$677$	2.49242	0.0957916	0.0478958	+	0.998852i	$0.484748\pi$
$678$	−4.24621	−0.163075
$679$	−14.4924	−0.556168
$680$	−23.8078	−0.912986
$681$	−7.12311	−0.272958
$682$	−9.75379	−0.373492
$683$	35.3153	1.35130	0.675652	−	0.737221i	$-0.263862\pi$
$683$	35.3153	1.35130	0.675652	+	0.737221i	$0.263862\pi$
$684$	−4.68466	−0.179122
$685$	−12.6847	−0.484656
$686$	−1.00000	−0.0381802
$687$	28.2462	1.07766
$688$	−6.43845	−0.245463
$689$	12.2462	0.466543
$690$	−19.8078	−0.754069
$691$	16.4924	0.627401	0.313701	−	0.949522i	$-0.398431\pi$
$691$	16.4924	0.627401	0.313701	+	0.949522i	$0.398431\pi$
$692$	20.2462	0.769645
$693$	1.56155	0.0593185
$694$	−20.0000	−0.759190
$695$	42.7386	1.62117
$696$	6.68466	0.253381
$697$	7.50758	0.284370
$698$	7.75379	0.293485
$699$	27.3693	1.03520
$700$	−7.68466	−0.290453
$701$	−2.00000	−0.0755390	−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000	−0.0755390	−0.0377695	+	0.999286i	$0.512025\pi$
$702$	1.00000	0.0377426
$703$	35.4233	1.33601
$704$	−1.56155	−0.0588532
$705$	0	0
$706$	30.4924	1.14760
$707$	5.12311	0.192674
$708$	2.24621	0.0844178
$709$	−16.2462	−0.610139	−0.305070	−	0.952330i	$-0.598680\pi$
$709$	−16.2462	−0.610139	−0.305070	+	0.952330i	$0.598680\pi$
$710$	28.4924	1.06930
$711$	−11.1231	−0.417149
$712$	10.0000	0.374766
$713$	−34.7386	−1.30097
$714$	6.68466	0.250167
$715$	−5.56155	−0.207990
$716$	16.4924	0.616351
$717$	16.0000	0.597531
$718$	−26.7386	−0.997877
$719$	43.1231	1.60822	0.804110	−	0.594480i	$-0.202642\pi$
$719$	43.1231	1.60822	0.804110	+	0.594480i	$0.202642\pi$
$720$	3.56155	0.132731
$721$	0.684658	0.0254980
$722$	2.94602	0.109640
$723$	−14.0000	−0.520666
$724$	−0.246211	−0.00915037
$725$	51.3693	1.90781
$726$	−8.56155	−0.317749
$727$	−6.93087	−0.257052	−0.128526	−	0.991706i	$-0.541025\pi$
$727$	−6.93087	−0.257052	−0.128526	+	0.991706i	$0.541025\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	−12.6847	−0.469480
$731$	43.0388	1.59185
$732$	6.68466	0.247072
$733$	−41.6155	−1.53710	−0.768552	−	0.639787i	$-0.779023\pi$
$733$	−41.6155	−1.53710	−0.768552	+	0.639787i	$0.779023\pi$
$734$	−16.0000	−0.590571
$735$	3.56155	0.131370
$736$	−5.56155	−0.205002
$737$	11.1231	0.409725
$738$	−1.12311	−0.0413421
$739$	−32.1080	−1.18111	−0.590555	−	0.806997i	$-0.701091\pi$
$739$	−32.1080	−1.18111	−0.590555	+	0.806997i	$0.701091\pi$
$740$	−26.9309	−0.989998
$741$	−4.68466	−0.172095
$742$	−12.2462	−0.449573
$743$	28.1080	1.03118	0.515590	−	0.856835i	$-0.327573\pi$
$743$	28.1080	1.03118	0.515590	+	0.856835i	$0.327573\pi$
$744$	6.24621	0.228997
$745$	−62.7386	−2.29857
$746$	−17.6155	−0.644950
$747$	8.87689	0.324789
$748$	10.4384	0.381667
$749$	8.87689	0.324355
$750$	9.56155	0.349139
$751$	−6.24621	−0.227927	−0.113964	−	0.993485i	$-0.536355\pi$
$751$	−6.24621	−0.227927	−0.113964	+	0.993485i	$0.536355\pi$
$752$	0	0
$753$	−7.80776	−0.284531
$754$	6.68466	0.243441
$755$	42.0540	1.53050
$756$	−1.00000	−0.0363696
$757$	34.4924	1.25365	0.626824	−	0.779161i	$-0.284354\pi$
$757$	34.4924	1.25365	0.626824	+	0.779161i	$0.284354\pi$
$758$	34.2462	1.24388
$759$	8.68466	0.315233
$760$	−16.6847	−0.605216
$761$	5.12311	0.185712	0.0928562	−	0.995680i	$-0.470400\pi$
$761$	5.12311	0.185712	0.0928562	+	0.995680i	$0.470400\pi$
$762$	−4.87689	−0.176671
$763$	16.9309	0.612939
$764$	14.9309	0.540180
$765$	−23.8078	−0.860772
$766$	27.4233	0.990844
$767$	2.24621	0.0811060
$768$	1.00000	0.0360844
$769$	−16.4384	−0.592786	−0.296393	−	0.955066i	$-0.595784\pi$
$769$	−16.4384	−0.592786	−0.296393	+	0.955066i	$0.595784\pi$
$770$	5.56155	0.200424
$771$	−4.24621	−0.152924
$772$	19.3693	0.697117
$773$	52.9309	1.90379	0.951896	−	0.306423i	$-0.0991321\pi$
$773$	52.9309	1.90379	0.951896	+	0.306423i	$0.0991321\pi$
$774$	−6.43845	−0.231425
$775$	48.0000	1.72421
$776$	14.4924	0.520248
$777$	7.56155	0.271269
$778$	−28.7386	−1.03033
$779$	5.26137	0.188508
$780$	3.56155	0.127524
$781$	−12.4924	−0.447014
$782$	37.1771	1.32945
$783$	6.68466	0.238890
$784$	1.00000	0.0357143
$785$	−55.4233	−1.97814
$786$	−9.56155	−0.341049
$787$	20.3002	0.723624	0.361812	−	0.932251i	$-0.382158\pi$
$787$	20.3002	0.723624	0.361812	+	0.932251i	$0.382158\pi$
$788$	10.8769	0.387473
$789$	−30.2462	−1.07679
$790$	−39.6155	−1.40946
$791$	4.24621	0.150978
$792$	−1.56155	−0.0554874
$793$	6.68466	0.237379
$794$	−18.0000	−0.638796
$795$	43.6155	1.54688
$796$	6.93087	0.245658
$797$	31.3693	1.11116	0.555579	−	0.831464i	$-0.312497\pi$
$797$	31.3693	1.11116	0.555579	+	0.831464i	$0.312497\pi$
$798$	4.68466	0.165835
$799$	0	0
$800$	7.68466	0.271694
$801$	10.0000	0.353333
$802$	8.24621	0.291184
$803$	5.56155	0.196263
$804$	−7.12311	−0.251213
$805$	19.8078	0.698132
$806$	6.24621	0.220013
$807$	20.2462	0.712700
$808$	−5.12311	−0.180230
$809$	−2.49242	−0.0876289	−0.0438145	−	0.999040i	$-0.513951\pi$
$809$	−2.49242	−0.0876289	−0.0438145	+	0.999040i	$0.513951\pi$
$810$	3.56155	0.125140
$811$	41.5616	1.45942	0.729712	−	0.683755i	$-0.239654\pi$
$811$	41.5616	1.45942	0.729712	+	0.683755i	$0.239654\pi$
$812$	−6.68466	−0.234586
$813$	4.87689	0.171040
$814$	11.8078	0.413862
$815$	−60.1080	−2.10549
$816$	−6.68466	−0.234010
$817$	30.1619	1.05523
$818$	−4.93087	−0.172404
$819$	−1.00000	−0.0349428
$820$	−4.00000	−0.139686
$821$	14.3845	0.502022	0.251011	−	0.967984i	$-0.419237\pi$
$821$	14.3845	0.502022	0.251011	+	0.967984i	$0.419237\pi$
$822$	−3.56155	−0.124223
$823$	4.49242	0.156596	0.0782980	−	0.996930i	$-0.475051\pi$
$823$	4.49242	0.156596	0.0782980	+	0.996930i	$0.475051\pi$
$824$	−0.684658	−0.0238512
$825$	−12.0000	−0.417786
$826$	−2.24621	−0.0781557
$827$	26.9309	0.936478	0.468239	−	0.883602i	$-0.344889\pi$
$827$	26.9309	0.936478	0.468239	+	0.883602i	$0.344889\pi$
$828$	−5.56155	−0.193277
$829$	38.6847	1.34357	0.671787	−	0.740744i	$-0.265527\pi$
$829$	38.6847	1.34357	0.671787	+	0.740744i	$0.265527\pi$
$830$	31.6155	1.09739
$831$	−22.4924	−0.780253
$832$	1.00000	0.0346688
$833$	−6.68466	−0.231610
$834$	12.0000	0.415526
$835$	81.6695	2.82629
$836$	7.31534	0.253006
$837$	6.24621	0.215901
$838$	−36.6847	−1.26725
$839$	−10.7386	−0.370739	−0.185369	−	0.982669i	$-0.559348\pi$
$839$	−10.7386	−0.370739	−0.185369	+	0.982669i	$0.559348\pi$
$840$	−3.56155	−0.122885
$841$	15.6847	0.540850
$842$	−3.75379	−0.129364
$843$	16.2462	0.559549
$844$	−15.8078	−0.544126
$845$	3.56155	0.122521
$846$	0	0
$847$	8.56155	0.294178
$848$	12.2462	0.420537
$849$	18.2462	0.626208
$850$	−51.3693	−1.76195
$851$	42.0540	1.44159
$852$	8.00000	0.274075
$853$	−27.3693	−0.937108	−0.468554	−	0.883435i	$-0.655225\pi$
$853$	−27.3693	−0.937108	−0.468554	+	0.883435i	$0.655225\pi$
$854$	−6.68466	−0.228744
$855$	−16.6847	−0.570603
$856$	−8.87689	−0.303406
$857$	−34.4924	−1.17824	−0.589119	−	0.808046i	$-0.700525\pi$
$857$	−34.4924	−1.17824	−0.589119	+	0.808046i	$0.700525\pi$
$858$	−1.56155	−0.0533105
$859$	5.75379	0.196317	0.0981584	−	0.995171i	$-0.468705\pi$
$859$	5.75379	0.196317	0.0981584	+	0.995171i	$0.468705\pi$
$860$	−22.9309	−0.781936
$861$	1.12311	0.0382753
$862$	−33.3693	−1.13656
$863$	−17.3693	−0.591258	−0.295629	−	0.955303i	$-0.595529\pi$
$863$	−17.3693	−0.591258	−0.295629	+	0.955303i	$0.595529\pi$
$864$	1.00000	0.0340207
$865$	72.1080	2.45174
$866$	−31.3693	−1.06597
$867$	27.6847	0.940220
$868$	−6.24621	−0.212010
$869$	17.3693	0.589214
$870$	23.8078	0.807159
$871$	−7.12311	−0.241357
$872$	−16.9309	−0.573352
$873$	14.4924	0.490494
$874$	26.0540	0.881289
$875$	−9.56155	−0.323239
$876$	−3.56155	−0.120334
$877$	−40.2462	−1.35902	−0.679509	−	0.733667i	$-0.737807\pi$
$877$	−40.2462	−1.35902	−0.679509	+	0.733667i	$0.737807\pi$
$878$	−6.93087	−0.233906
$879$	24.7386	0.834413
$880$	−5.56155	−0.187480
$881$	−19.1771	−0.646092	−0.323046	−	0.946383i	$-0.604707\pi$
$881$	−19.1771	−0.646092	−0.323046	+	0.946383i	$0.604707\pi$
$882$	1.00000	0.0336718
$883$	1.56155	0.0525504	0.0262752	−	0.999655i	$-0.491635\pi$
$883$	1.56155	0.0525504	0.0262752	+	0.999655i	$0.491635\pi$
$884$	−6.68466	−0.224829
$885$	8.00000	0.268917
$886$	−5.36932	−0.180386
$887$	−52.4924	−1.76252	−0.881262	−	0.472629i	$-0.843305\pi$
$887$	−52.4924	−1.76252	−0.881262	+	0.472629i	$0.843305\pi$
$888$	−7.56155	−0.253749
$889$	4.87689	0.163566
$890$	35.6155	1.19384
$891$	−1.56155	−0.0523140
$892$	−23.6155	−0.790706
$893$	0	0
$894$	−17.6155	−0.589151
$895$	58.7386	1.96342
$896$	−1.00000	−0.0334077
$897$	−5.56155	−0.185695
$898$	10.6847	0.356552
$899$	41.7538	1.39257
$900$	7.68466	0.256155
$901$	−81.8617	−2.72721
$902$	1.75379	0.0583948
$903$	6.43845	0.214258
$904$	−4.24621	−0.141227
$905$	−0.876894	−0.0291490
$906$	11.8078	0.392287
$907$	−7.50758	−0.249285	−0.124643	−	0.992202i	$-0.539778\pi$
$907$	−7.50758	−0.249285	−0.124643	+	0.992202i	$0.539778\pi$
$908$	−7.12311	−0.236389
$909$	−5.12311	−0.169923
$910$	−3.56155	−0.118064
$911$	−11.4233	−0.378471	−0.189235	−	0.981932i	$-0.560601\pi$
$911$	−11.4233	−0.378471	−0.189235	+	0.981932i	$0.560601\pi$
$912$	−4.68466	−0.155125
$913$	−13.8617	−0.458757
$914$	27.3693	0.905297
$915$	23.8078	0.787060
$916$	28.2462	0.933281
$917$	9.56155	0.315750
$918$	−6.68466	−0.220627
$919$	19.1231	0.630813	0.315407	−	0.948957i	$-0.397859\pi$
$919$	19.1231	0.630813	0.315407	+	0.948957i	$0.397859\pi$
$920$	−19.8078	−0.653043
$921$	26.2462	0.864842
$922$	−28.0540	−0.923908
$923$	8.00000	0.263323
$924$	1.56155	0.0513713
$925$	−58.1080	−1.91058
$926$	−8.68466	−0.285396
$927$	−0.684658	−0.0224871
$928$	6.68466	0.219435
$929$	25.6155	0.840418	0.420209	−	0.907427i	$-0.361957\pi$
$929$	25.6155	0.840418	0.420209	+	0.907427i	$0.361957\pi$
$930$	22.2462	0.729482
$931$	−4.68466	−0.153533
$932$	27.3693	0.896512
$933$	−12.8769	−0.421571
$934$	−3.31534	−0.108481
$935$	37.1771	1.21582
$936$	1.00000	0.0326860
$937$	−46.9848	−1.53493	−0.767464	−	0.641092i	$-0.778482\pi$
$937$	−46.9848	−1.53493	−0.767464	+	0.641092i	$0.778482\pi$
$938$	7.12311	0.232578
$939$	−13.6155	−0.444326
$940$	0	0
$941$	−34.0000	−1.10837	−0.554184	−	0.832394i	$-0.686970\pi$
$941$	−34.0000	−1.10837	−0.554184	+	0.832394i	$0.686970\pi$
$942$	−15.5616	−0.507023
$943$	6.24621	0.203405
$944$	2.24621	0.0731079
$945$	−3.56155	−0.115857
$946$	10.0540	0.326883
$947$	−40.7926	−1.32558	−0.662791	−	0.748805i	$-0.730628\pi$
$947$	−40.7926	−1.32558	−0.662791	+	0.748805i	$0.730628\pi$
$948$	−11.1231	−0.361262
$949$	−3.56155	−0.115613
$950$	−36.0000	−1.16799
$951$	2.87689	0.0932897
$952$	6.68466	0.216651
$953$	11.3693	0.368288	0.184144	−	0.982899i	$-0.441049\pi$
$953$	11.3693	0.368288	0.184144	+	0.982899i	$0.441049\pi$
$954$	12.2462	0.396486
$955$	53.1771	1.72077
$956$	16.0000	0.517477
$957$	−10.4384	−0.337427
$958$	32.3002	1.04357
$959$	3.56155	0.115009
$960$	3.56155	0.114949
$961$	8.01515	0.258553
$962$	−7.56155	−0.243794
$963$	−8.87689	−0.286054
$964$	−14.0000	−0.450910
$965$	68.9848	2.22070
$966$	5.56155	0.178940
$967$	−21.5616	−0.693373	−0.346686	−	0.937981i	$-0.612693\pi$
$967$	−21.5616	−0.693373	−0.346686	+	0.937981i	$0.612693\pi$
$968$	−8.56155	−0.275179
$969$	31.3153	1.00599
$970$	51.6155	1.65727
$971$	2.24621	0.0720843	0.0360422	−	0.999350i	$-0.488525\pi$
$971$	2.24621	0.0720843	0.0360422	+	0.999350i	$0.488525\pi$
$972$	1.00000	0.0320750
$973$	−12.0000	−0.384702
$974$	−8.00000	−0.256337
$975$	7.68466	0.246106
$976$	6.68466	0.213971
$977$	−22.6847	−0.725747	−0.362873	−	0.931839i	$-0.618204\pi$
$977$	−22.6847	−0.725747	−0.362873	+	0.931839i	$0.618204\pi$
$978$	−16.8769	−0.539664
$979$	−15.6155	−0.499074
$980$	3.56155	0.113770
$981$	−16.9309	−0.540561
$982$	−8.87689	−0.283273
$983$	−13.1771	−0.420284	−0.210142	−	0.977671i	$-0.567393\pi$
$983$	−13.1771	−0.420284	−0.210142	+	0.977671i	$0.567393\pi$
$984$	−1.12311	−0.0358033
$985$	38.7386	1.23432
$986$	−44.6847	−1.42305
$987$	0	0
$988$	−4.68466	−0.149039
$989$	35.8078	1.13862
$990$	−5.56155	−0.176758
$991$	−7.61553	−0.241915	−0.120958	−	0.992658i	$-0.538597\pi$
$991$	−7.61553	−0.241915	−0.120958	+	0.992658i	$0.538597\pi$
$992$	6.24621	0.198317
$993$	13.3693	0.424262
$994$	−8.00000	−0.253745
$995$	24.6847	0.782556
$996$	8.87689	0.281275
$997$	40.7386	1.29021	0.645103	−	0.764096i	$-0.276815\pi$
$997$	40.7386	1.29021	0.645103	+	0.764096i	$0.276815\pi$
$998$	36.0000	1.13956
$999$	−7.56155	−0.239237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.a.j.1.2	✓	2
3.2	odd	2		1638.2.a.u.1.1		2
4.3	odd	2		4368.2.a.be.1.2		2
7.6	odd	2		3822.2.a.bo.1.1		2
13.12	even	2		7098.2.a.bl.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.a.j.1.2	✓	2	1.1	even	1	trivial
1638.2.a.u.1.1		2	3.2	odd	2
3822.2.a.bo.1.1		2	7.6	odd	2
4368.2.a.be.1.2		2	4.3	odd	2
7098.2.a.bl.1.1		2	13.12	even	2

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.56155 q^{5} +1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.56155 q^{10} -1.56155 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.00000 q^{14} +3.56155 q^{15} +1.00000 q^{16} -6.68466 q^{17} +1.00000 q^{18} -4.68466 q^{19} +3.56155 q^{20} -1.00000 q^{21} -1.56155 q^{22} -5.56155 q^{23} +1.00000 q^{24} +7.68466 q^{25} +1.00000 q^{26} +1.00000 q^{27} -1.00000 q^{28} +6.68466 q^{29} +3.56155 q^{30} +6.24621 q^{31} +1.00000 q^{32} -1.56155 q^{33} -6.68466 q^{34} -3.56155 q^{35} +1.00000 q^{36} -7.56155 q^{37} -4.68466 q^{38} +1.00000 q^{39} +3.56155 q^{40} -1.12311 q^{41} -1.00000 q^{42} -6.43845 q^{43} -1.56155 q^{44} +3.56155 q^{45} -5.56155 q^{46} +1.00000 q^{48} +1.00000 q^{49} +7.68466 q^{50} -6.68466 q^{51} +1.00000 q^{52} +12.2462 q^{53} +1.00000 q^{54} -5.56155 q^{55} -1.00000 q^{56} -4.68466 q^{57} +6.68466 q^{58} +2.24621 q^{59} +3.56155 q^{60} +6.68466 q^{61} +6.24621 q^{62} -1.00000 q^{63} +1.00000 q^{64} +3.56155 q^{65} -1.56155 q^{66} -7.12311 q^{67} -6.68466 q^{68} -5.56155 q^{69} -3.56155 q^{70} +8.00000 q^{71} +1.00000 q^{72} -3.56155 q^{73} -7.56155 q^{74} +7.68466 q^{75} -4.68466 q^{76} +1.56155 q^{77} +1.00000 q^{78} -11.1231 q^{79} +3.56155 q^{80} +1.00000 q^{81} -1.12311 q^{82} +8.87689 q^{83} -1.00000 q^{84} -23.8078 q^{85} -6.43845 q^{86} +6.68466 q^{87} -1.56155 q^{88} +10.0000 q^{89} +3.56155 q^{90} -1.00000 q^{91} -5.56155 q^{92} +6.24621 q^{93} -16.6847 q^{95} +1.00000 q^{96} +14.4924 q^{97} +1.00000 q^{98} -1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} + 2 q^{3} + 2 q^{4} + 3 q^{5} + 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + 3 q^{10} + q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 3 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} + 3 q^{19} + 3 q^{20} - 2 q^{21} + q^{22} - 7 q^{23} + 2 q^{24} + 3 q^{25} + 2 q^{26} + 2 q^{27} - 2 q^{28} + q^{29} + 3 q^{30} - 4 q^{31} + 2 q^{32} + q^{33} - q^{34} - 3 q^{35} + 2 q^{36} - 11 q^{37} + 3 q^{38} + 2 q^{39} + 3 q^{40} + 6 q^{41} - 2 q^{42} - 17 q^{43} + q^{44} + 3 q^{45} - 7 q^{46} + 2 q^{48} + 2 q^{49} + 3 q^{50} - q^{51} + 2 q^{52} + 8 q^{53} + 2 q^{54} - 7 q^{55} - 2 q^{56} + 3 q^{57} + q^{58} - 12 q^{59} + 3 q^{60} + q^{61} - 4 q^{62} - 2 q^{63} + 2 q^{64} + 3 q^{65} + q^{66} - 6 q^{67} - q^{68} - 7 q^{69} - 3 q^{70} + 16 q^{71} + 2 q^{72} - 3 q^{73} - 11 q^{74} + 3 q^{75} + 3 q^{76} - q^{77} + 2 q^{78} - 14 q^{79} + 3 q^{80} + 2 q^{81} + 6 q^{82} + 26 q^{83} - 2 q^{84} - 27 q^{85} - 17 q^{86} + q^{87} + q^{88} + 20 q^{89} + 3 q^{90} - 2 q^{91} - 7 q^{92} - 4 q^{93} - 21 q^{95} + 2 q^{96} - 4 q^{97} + 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^3 + 2 * q^4 + 3 * q^5 + 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 + 3 * q^10 + q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 3 * q^15 + 2 * q^16 - q^17 + 2 * q^18 + 3 * q^19 + 3 * q^20 - 2 * q^21 + q^22 - 7 * q^23 + 2 * q^24 + 3 * q^25 + 2 * q^26 + 2 * q^27 - 2 * q^28 + q^29 + 3 * q^30 - 4 * q^31 + 2 * q^32 + q^33 - q^34 - 3 * q^35 + 2 * q^36 - 11 * q^37 + 3 * q^38 + 2 * q^39 + 3 * q^40 + 6 * q^41 - 2 * q^42 - 17 * q^43 + q^44 + 3 * q^45 - 7 * q^46 + 2 * q^48 + 2 * q^49 + 3 * q^50 - q^51 + 2 * q^52 + 8 * q^53 + 2 * q^54 - 7 * q^55 - 2 * q^56 + 3 * q^57 + q^58 - 12 * q^59 + 3 * q^60 + q^61 - 4 * q^62 - 2 * q^63 + 2 * q^64 + 3 * q^65 + q^66 - 6 * q^67 - q^68 - 7 * q^69 - 3 * q^70 + 16 * q^71 + 2 * q^72 - 3 * q^73 - 11 * q^74 + 3 * q^75 + 3 * q^76 - q^77 + 2 * q^78 - 14 * q^79 + 3 * q^80 + 2 * q^81 + 6 * q^82 + 26 * q^83 - 2 * q^84 - 27 * q^85 - 17 * q^86 + q^87 + q^88 + 20 * q^89 + 3 * q^90 - 2 * q^91 - 7 * q^92 - 4 * q^93 - 21 * q^95 + 2 * q^96 - 4 * q^97 + 2 * q^98 + q^99

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