LMFDB - Embedded newform 8043.2.a.u.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$53$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.26724 q^{2} +1.00000 q^{3} +3.14038 q^{4} +4.07533 q^{5} -2.26724 q^{6} +1.00000 q^{7} -2.58552 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.26724 q^{2} +1.00000 q^{3} +3.14038 q^{4} +4.07533 q^{5} -2.26724 q^{6} +1.00000 q^{7} -2.58552 q^{8} +1.00000 q^{9} -9.23976 q^{10} +1.78858 q^{11} +3.14038 q^{12} -4.22490 q^{13} -2.26724 q^{14} +4.07533 q^{15} -0.418773 q^{16} -2.89422 q^{17} -2.26724 q^{18} +3.55522 q^{19} +12.7981 q^{20} +1.00000 q^{21} -4.05515 q^{22} +2.84495 q^{23} -2.58552 q^{24} +11.6083 q^{25} +9.57887 q^{26} +1.00000 q^{27} +3.14038 q^{28} -2.32382 q^{29} -9.23976 q^{30} +6.54885 q^{31} +6.12049 q^{32} +1.78858 q^{33} +6.56190 q^{34} +4.07533 q^{35} +3.14038 q^{36} +2.54189 q^{37} -8.06055 q^{38} -4.22490 q^{39} -10.5368 q^{40} -4.29454 q^{41} -2.26724 q^{42} +10.2010 q^{43} +5.61684 q^{44} +4.07533 q^{45} -6.45019 q^{46} +3.94166 q^{47} -0.418773 q^{48} +1.00000 q^{49} -26.3189 q^{50} -2.89422 q^{51} -13.2678 q^{52} -2.82153 q^{53} -2.26724 q^{54} +7.28908 q^{55} -2.58552 q^{56} +3.55522 q^{57} +5.26866 q^{58} +1.60070 q^{59} +12.7981 q^{60} -6.87205 q^{61} -14.8478 q^{62} +1.00000 q^{63} -13.0391 q^{64} -17.2179 q^{65} -4.05515 q^{66} +11.5292 q^{67} -9.08896 q^{68} +2.84495 q^{69} -9.23976 q^{70} +3.69074 q^{71} -2.58552 q^{72} -12.4542 q^{73} -5.76308 q^{74} +11.6083 q^{75} +11.1648 q^{76} +1.78858 q^{77} +9.57887 q^{78} -2.74694 q^{79} -1.70664 q^{80} +1.00000 q^{81} +9.73677 q^{82} -6.73429 q^{83} +3.14038 q^{84} -11.7949 q^{85} -23.1281 q^{86} -2.32382 q^{87} -4.62441 q^{88} +13.9819 q^{89} -9.23976 q^{90} -4.22490 q^{91} +8.93423 q^{92} +6.54885 q^{93} -8.93669 q^{94} +14.4887 q^{95} +6.12049 q^{96} -15.8696 q^{97} -2.26724 q^{98} +1.78858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) $ 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * 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 $

$2$	−2.26724	−1.60318	−0.801591	−	0.597873i	$-0.796013\pi$
$2$	−2.26724	−1.60318	−0.801591	+	0.597873i	$0.796013\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.14038	1.57019
$5$	4.07533	1.82254	0.911272	−	0.411804i	$-0.135101\pi$
$5$	4.07533	1.82254	0.911272	+	0.411804i	$0.135101\pi$
$6$	−2.26724	−0.925597
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.58552	−0.914118
$9$	1.00000	0.333333
$10$	−9.23976	−2.92187
$11$	1.78858	0.539279	0.269639	−	0.962961i	$-0.413096\pi$
$11$	1.78858	0.539279	0.269639	+	0.962961i	$0.413096\pi$
$12$	3.14038	0.906550
$13$	−4.22490	−1.17178	−0.585889	−	0.810392i	$-0.699254\pi$
$13$	−4.22490	−1.17178	−0.585889	+	0.810392i	$0.699254\pi$
$14$	−2.26724	−0.605946
$15$	4.07533	1.05225
$16$	−0.418773	−0.104693
$17$	−2.89422	−0.701952	−0.350976	−	0.936384i	$-0.614150\pi$
$17$	−2.89422	−0.701952	−0.350976	+	0.936384i	$0.614150\pi$
$18$	−2.26724	−0.534394
$19$	3.55522	0.815625	0.407812	−	0.913066i	$-0.366292\pi$
$19$	3.55522	0.815625	0.407812	+	0.913066i	$0.366292\pi$
$20$	12.7981	2.86174
$21$	1.00000	0.218218
$22$	−4.05515	−0.864561
$23$	2.84495	0.593214	0.296607	−	0.955000i	$-0.404145\pi$
$23$	2.84495	0.593214	0.296607	+	0.955000i	$0.404145\pi$
$24$	−2.58552	−0.527766
$25$	11.6083	2.32167
$26$	9.57887	1.87857
$27$	1.00000	0.192450
$28$	3.14038	0.593476
$29$	−2.32382	−0.431522	−0.215761	−	0.976446i	$-0.569223\pi$
$29$	−2.32382	−0.431522	−0.215761	+	0.976446i	$0.569223\pi$
$30$	−9.23976	−1.68694
$31$	6.54885	1.17621	0.588104	−	0.808785i	$-0.299874\pi$
$31$	6.54885	1.17621	0.588104	+	0.808785i	$0.299874\pi$
$32$	6.12049	1.08196
$33$	1.78858	0.311353
$34$	6.56190	1.12536
$35$	4.07533	0.688857
$36$	3.14038	0.523397
$37$	2.54189	0.417884	0.208942	−	0.977928i	$-0.432998\pi$
$37$	2.54189	0.417884	0.208942	+	0.977928i	$0.432998\pi$
$38$	−8.06055	−1.30759
$39$	−4.22490	−0.676526
$40$	−10.5368	−1.66602
$41$	−4.29454	−0.670695	−0.335348	−	0.942094i	$-0.608854\pi$
$41$	−4.29454	−0.670695	−0.335348	+	0.942094i	$0.608854\pi$
$42$	−2.26724	−0.349843
$43$	10.2010	1.55564	0.777820	−	0.628487i	$-0.216326\pi$
$43$	10.2010	1.55564	0.777820	+	0.628487i	$0.216326\pi$
$44$	5.61684	0.846770
$45$	4.07533	0.607515
$46$	−6.45019	−0.951029
$47$	3.94166	0.574950	0.287475	−	0.957788i	$-0.407184\pi$
$47$	3.94166	0.574950	0.287475	+	0.957788i	$0.407184\pi$
$48$	−0.418773	−0.0604447
$49$	1.00000	0.142857
$50$	−26.3189	−3.72206
$51$	−2.89422	−0.405272
$52$	−13.2678	−1.83991
$53$	−2.82153	−0.387567	−0.193784	−	0.981044i	$-0.562076\pi$
$53$	−2.82153	−0.387567	−0.193784	+	0.981044i	$0.562076\pi$
$54$	−2.26724	−0.308532
$55$	7.28908	0.982859
$56$	−2.58552	−0.345504
$57$	3.55522	0.470901
$58$	5.26866	0.691809
$59$	1.60070	0.208393	0.104197	−	0.994557i	$-0.466773\pi$
$59$	1.60070	0.208393	0.104197	+	0.994557i	$0.466773\pi$
$60$	12.7981	1.65223
$61$	−6.87205	−0.879876	−0.439938	−	0.898028i	$-0.645000\pi$
$61$	−6.87205	−0.879876	−0.439938	+	0.898028i	$0.645000\pi$
$62$	−14.8478	−1.88568
$63$	1.00000	0.125988
$64$	−13.0391	−1.62989
$65$	−17.2179	−2.13562
$66$	−4.05515	−0.499155
$67$	11.5292	1.40852	0.704259	−	0.709943i	$-0.251279\pi$
$67$	11.5292	1.40852	0.704259	+	0.709943i	$0.251279\pi$
$68$	−9.08896	−1.10220
$69$	2.84495	0.342492
$70$	−9.23976	−1.10436
$71$	3.69074	0.438011	0.219005	−	0.975724i	$-0.429719\pi$
$71$	3.69074	0.438011	0.219005	+	0.975724i	$0.429719\pi$
$72$	−2.58552	−0.304706
$73$	−12.4542	−1.45766	−0.728829	−	0.684696i	$-0.759935\pi$
$73$	−12.4542	−1.45766	−0.728829	+	0.684696i	$0.759935\pi$
$74$	−5.76308	−0.669944
$75$	11.6083	1.34042
$76$	11.1648	1.28069
$77$	1.78858	0.203828
$78$	9.57887	1.08459
$79$	−2.74694	−0.309055	−0.154528	−	0.987988i	$-0.549386\pi$
$79$	−2.74694	−0.309055	−0.154528	+	0.987988i	$0.549386\pi$
$80$	−1.70664	−0.190808
$81$	1.00000	0.111111
$82$	9.73677	1.07525
$83$	−6.73429	−0.739184	−0.369592	−	0.929194i	$-0.620503\pi$
$83$	−6.73429	−0.739184	−0.369592	+	0.929194i	$0.620503\pi$
$84$	3.14038	0.342644
$85$	−11.7949	−1.27934
$86$	−23.1281	−2.49397
$87$	−2.32382	−0.249140
$88$	−4.62441	−0.492964
$89$	13.9819	1.48207	0.741037	−	0.671465i	$-0.234334\pi$
$89$	13.9819	1.48207	0.741037	+	0.671465i	$0.234334\pi$
$90$	−9.23976	−0.973956
$91$	−4.22490	−0.442890
$92$	8.93423	0.931458
$93$	6.54885	0.679085
$94$	−8.93669	−0.921749
$95$	14.4887	1.48651
$96$	6.12049	0.624670
$97$	−15.8696	−1.61131	−0.805655	−	0.592385i	$-0.798187\pi$
$97$	−15.8696	−1.61131	−0.805655	+	0.592385i	$0.798187\pi$
$98$	−2.26724	−0.229026
$99$	1.78858	0.179760
$100$	36.4546	3.64546
$101$	−0.982382	−0.0977506	−0.0488753	−	0.998805i	$-0.515564\pi$
$101$	−0.982382	−0.0977506	−0.0488753	+	0.998805i	$0.515564\pi$
$102$	6.56190	0.649725
$103$	11.0446	1.08826	0.544129	−	0.839001i	$-0.316860\pi$
$103$	11.0446	1.08826	0.544129	+	0.839001i	$0.316860\pi$
$104$	10.9236	1.07114
$105$	4.07533	0.397712
$106$	6.39709	0.621340
$107$	12.9808	1.25490	0.627451	−	0.778656i	$-0.284098\pi$
$107$	12.9808	1.25490	0.627451	+	0.778656i	$0.284098\pi$
$108$	3.14038	0.302183
$109$	−8.02131	−0.768302	−0.384151	−	0.923270i	$-0.625506\pi$
$109$	−8.02131	−0.768302	−0.384151	+	0.923270i	$0.625506\pi$
$110$	−16.5261	−1.57570
$111$	2.54189	0.241266
$112$	−0.418773	−0.0395704
$113$	−7.57431	−0.712531	−0.356266	−	0.934385i	$-0.615950\pi$
$113$	−7.57431	−0.712531	−0.356266	+	0.934385i	$0.615950\pi$
$114$	−8.06055	−0.754940
$115$	11.5941	1.08116
$116$	−7.29767	−0.677572
$117$	−4.22490	−0.390592
$118$	−3.62917	−0.334092
$119$	−2.89422	−0.265313
$120$	−10.5368	−0.961878
$121$	−7.80096	−0.709179
$122$	15.5806	1.41060
$123$	−4.29454	−0.387226
$124$	20.5659	1.84687
$125$	26.9312	2.40880
$126$	−2.26724	−0.201982
$127$	−0.969796	−0.0860555	−0.0430277	−	0.999074i	$-0.513700\pi$
$127$	−0.969796	−0.0860555	−0.0430277	+	0.999074i	$0.513700\pi$
$128$	17.3218	1.53104
$129$	10.2010	0.898149
$130$	39.0371	3.42378
$131$	0.829412	0.0724661	0.0362330	−	0.999343i	$-0.488464\pi$
$131$	0.829412	0.0724661	0.0362330	+	0.999343i	$0.488464\pi$
$132$	5.61684	0.488883
$133$	3.55522	0.308277
$134$	−26.1395	−2.25811
$135$	4.07533	0.350749
$136$	7.48306	0.641667
$137$	4.01673	0.343172	0.171586	−	0.985169i	$-0.445111\pi$
$137$	4.01673	0.343172	0.171586	+	0.985169i	$0.445111\pi$
$138$	−6.45019	−0.549077
$139$	3.89504	0.330373	0.165186	−	0.986262i	$-0.447177\pi$
$139$	3.89504	0.330373	0.165186	+	0.986262i	$0.447177\pi$
$140$	12.7981	1.08164
$141$	3.94166	0.331948
$142$	−8.36781	−0.702211
$143$	−7.55660	−0.631914
$144$	−0.418773	−0.0348978
$145$	−9.47034	−0.786469
$146$	28.2367	2.33689
$147$	1.00000	0.0824786
$148$	7.98250	0.656158
$149$	5.72166	0.468736	0.234368	−	0.972148i	$-0.424698\pi$
$149$	5.72166	0.468736	0.234368	+	0.972148i	$0.424698\pi$
$150$	−26.3189	−2.14893
$151$	7.37231	0.599950	0.299975	−	0.953947i	$-0.403022\pi$
$151$	7.37231	0.599950	0.299975	+	0.953947i	$0.403022\pi$
$152$	−9.19209	−0.745577
$153$	−2.89422	−0.233984
$154$	−4.05515	−0.326773
$155$	26.6888	2.14369
$156$	−13.2678	−1.06227
$157$	−9.53658	−0.761102	−0.380551	−	0.924760i	$-0.624266\pi$
$157$	−9.53658	−0.761102	−0.380551	+	0.924760i	$0.624266\pi$
$158$	6.22798	0.495471
$159$	−2.82153	−0.223762
$160$	24.9430	1.97192
$161$	2.84495	0.224214
$162$	−2.26724	−0.178131
$163$	6.61232	0.517917	0.258958	−	0.965888i	$-0.416621\pi$
$163$	6.61232	0.517917	0.258958	+	0.965888i	$0.416621\pi$
$164$	−13.4865	−1.05312
$165$	7.28908	0.567454
$166$	15.2682	1.18505
$167$	2.14211	0.165762	0.0828808	−	0.996559i	$-0.473588\pi$
$167$	2.14211	0.165762	0.0828808	+	0.996559i	$0.473588\pi$
$168$	−2.58552	−0.199477
$169$	4.84980	0.373062
$170$	26.7419	2.05101
$171$	3.55522	0.271875
$172$	32.0351	2.44265
$173$	11.6232	0.883693	0.441846	−	0.897091i	$-0.354324\pi$
$173$	11.6232	0.883693	0.441846	+	0.897091i	$0.354324\pi$
$174$	5.26866	0.399416
$175$	11.6083	0.877509
$176$	−0.749012	−0.0564589
$177$	1.60070	0.120316
$178$	−31.7002	−2.37603
$179$	−4.40656	−0.329362	−0.164681	−	0.986347i	$-0.552659\pi$
$179$	−4.40656	−0.329362	−0.164681	+	0.986347i	$0.552659\pi$
$180$	12.7981	0.953914
$181$	−8.31678	−0.618181	−0.309091	−	0.951033i	$-0.600025\pi$
$181$	−8.31678	−0.618181	−0.309091	+	0.951033i	$0.600025\pi$
$182$	9.57887	0.710033
$183$	−6.87205	−0.507997
$184$	−7.35567	−0.542267
$185$	10.3591	0.761613
$186$	−14.8478	−1.08870
$187$	−5.17656	−0.378548
$188$	12.3783	0.902781
$189$	1.00000	0.0727393
$190$	−32.8494	−2.38315
$191$	0.661962	0.0478979	0.0239489	−	0.999713i	$-0.492376\pi$
$191$	0.661962	0.0478979	0.0239489	+	0.999713i	$0.492376\pi$
$192$	−13.0391	−0.941015
$193$	25.7541	1.85382	0.926910	−	0.375283i	$-0.122455\pi$
$193$	25.7541	1.85382	0.926910	+	0.375283i	$0.122455\pi$
$194$	35.9801	2.58322
$195$	−17.2179	−1.23300
$196$	3.14038	0.224313
$197$	−11.9169	−0.849045	−0.424523	−	0.905417i	$-0.639558\pi$
$197$	−11.9169	−0.849045	−0.424523	+	0.905417i	$0.639558\pi$
$198$	−4.05515	−0.288187
$199$	9.70838	0.688209	0.344104	−	0.938931i	$-0.388183\pi$
$199$	9.70838	0.688209	0.344104	+	0.938931i	$0.388183\pi$
$200$	−30.0136	−2.12228
$201$	11.5292	0.813208
$202$	2.22730	0.156712
$203$	−2.32382	−0.163100
$204$	−9.08896	−0.636354
$205$	−17.5017	−1.22237
$206$	−25.0408	−1.74468
$207$	2.84495	0.197738
$208$	1.76928	0.122677
$209$	6.35882	0.439849
$210$	−9.23976	−0.637604
$211$	−11.9440	−0.822256	−0.411128	−	0.911578i	$-0.634865\pi$
$211$	−11.9440	−0.822256	−0.411128	+	0.911578i	$0.634865\pi$
$212$	−8.86068	−0.608554
$213$	3.69074	0.252886
$214$	−29.4306	−2.01184
$215$	41.5725	2.83522
$216$	−2.58552	−0.175922
$217$	6.54885	0.444565
$218$	18.1862	1.23173
$219$	−12.4542	−0.841579
$220$	22.8905	1.54328
$221$	12.2278	0.822531
$222$	−5.76308	−0.386793
$223$	−5.10191	−0.341649	−0.170825	−	0.985301i	$-0.554643\pi$
$223$	−5.10191	−0.341649	−0.170825	+	0.985301i	$0.554643\pi$
$224$	6.12049	0.408943
$225$	11.6083	0.773890
$226$	17.1728	1.14232
$227$	19.1043	1.26800	0.633999	−	0.773334i	$-0.281412\pi$
$227$	19.1043	1.26800	0.633999	+	0.773334i	$0.281412\pi$
$228$	11.1648	0.739404
$229$	−5.30316	−0.350443	−0.175221	−	0.984529i	$-0.556064\pi$
$229$	−5.30316	−0.350443	−0.175221	+	0.984529i	$0.556064\pi$
$230$	−26.2867	−1.73329
$231$	1.78858	0.117680
$232$	6.00827	0.394462
$233$	14.2213	0.931668	0.465834	−	0.884872i	$-0.345754\pi$
$233$	14.2213	0.931668	0.465834	+	0.884872i	$0.345754\pi$
$234$	9.57887	0.626190
$235$	16.0636	1.04787
$236$	5.02681	0.327217
$237$	−2.74694	−0.178433
$238$	6.56190	0.425345
$239$	−10.7379	−0.694577	−0.347288	−	0.937758i	$-0.612897\pi$
$239$	−10.7379	−0.694577	−0.347288	+	0.937758i	$0.612897\pi$
$240$	−1.70664	−0.110163
$241$	−26.9153	−1.73376	−0.866882	−	0.498513i	$-0.833880\pi$
$241$	−26.9153	−1.73376	−0.866882	+	0.498513i	$0.833880\pi$
$242$	17.6867	1.13694
$243$	1.00000	0.0641500
$244$	−21.5808	−1.38157
$245$	4.07533	0.260364
$246$	9.73677	0.620794
$247$	−15.0205	−0.955730
$248$	−16.9322	−1.07519
$249$	−6.73429	−0.426768
$250$	−61.0596	−3.86175
$251$	0.0778104	0.00491135	0.00245567	−	0.999997i	$-0.499218\pi$
$251$	0.0778104	0.00491135	0.00245567	+	0.999997i	$0.499218\pi$
$252$	3.14038	0.197825
$253$	5.08844	0.319907
$254$	2.19876	0.137963
$255$	−11.7949	−0.738627
$256$	−13.1944	−0.824651
$257$	18.6103	1.16088	0.580439	−	0.814304i	$-0.302881\pi$
$257$	18.6103	1.16088	0.580439	+	0.814304i	$0.302881\pi$
$258$	−23.1281	−1.43990
$259$	2.54189	0.157945
$260$	−54.0707	−3.35332
$261$	−2.32382	−0.143841
$262$	−1.88048	−0.116176
$263$	24.4991	1.51068	0.755340	−	0.655333i	$-0.227472\pi$
$263$	24.4991	1.51068	0.755340	+	0.655333i	$0.227472\pi$
$264$	−4.62441	−0.284613
$265$	−11.4987	−0.706358
$266$	−8.06055	−0.494224
$267$	13.9819	0.855675
$268$	36.2061	2.21164
$269$	11.8905	0.724978	0.362489	−	0.931988i	$-0.381927\pi$
$269$	11.8905	0.724978	0.362489	+	0.931988i	$0.381927\pi$
$270$	−9.23976	−0.562314
$271$	−11.3817	−0.691390	−0.345695	−	0.938347i	$-0.612357\pi$
$271$	−11.3817	−0.691390	−0.345695	+	0.938347i	$0.612357\pi$
$272$	1.21202	0.0734897
$273$	−4.22490	−0.255703
$274$	−9.10689	−0.550167
$275$	20.7625	1.25203
$276$	8.93423	0.537778
$277$	9.18751	0.552024	0.276012	−	0.961154i	$-0.410987\pi$
$277$	9.18751	0.552024	0.276012	+	0.961154i	$0.410987\pi$
$278$	−8.83099	−0.529648
$279$	6.54885	0.392070
$280$	−10.5368	−0.629697
$281$	17.3016	1.03213	0.516063	−	0.856551i	$-0.327397\pi$
$281$	17.3016	1.03213	0.516063	+	0.856551i	$0.327397\pi$
$282$	−8.93669	−0.532172
$283$	−30.0244	−1.78477	−0.892383	−	0.451279i	$-0.850968\pi$
$283$	−30.0244	−1.78477	−0.892383	+	0.451279i	$0.850968\pi$
$284$	11.5903	0.687760
$285$	14.4887	0.858238
$286$	17.1326	1.01307
$287$	−4.29454	−0.253499
$288$	6.12049	0.360653
$289$	−8.62348	−0.507263
$290$	21.4715	1.26085
$291$	−15.8696	−0.930291
$292$	−39.1110	−2.28880
$293$	−14.2082	−0.830050	−0.415025	−	0.909810i	$-0.636227\pi$
$293$	−14.2082	−0.830050	−0.415025	+	0.909810i	$0.636227\pi$
$294$	−2.26724	−0.132228
$295$	6.52339	0.379806
$296$	−6.57210	−0.381996
$297$	1.78858	0.103784
$298$	−12.9724	−0.751469
$299$	−12.0196	−0.695114
$300$	36.4546	2.10471
$301$	10.2010	0.587977
$302$	−16.7148	−0.961828
$303$	−0.982382	−0.0564364
$304$	−1.48883	−0.0853904
$305$	−28.0059	−1.60361
$306$	6.56190	0.375119
$307$	−1.19783	−0.0683640	−0.0341820	−	0.999416i	$-0.510883\pi$
$307$	−1.19783	−0.0683640	−0.0341820	+	0.999416i	$0.510883\pi$
$308$	5.61684	0.320049
$309$	11.0446	0.628306
$310$	−60.5099	−3.43673
$311$	−19.2187	−1.08979	−0.544896	−	0.838504i	$-0.683431\pi$
$311$	−19.2187	−1.08979	−0.544896	+	0.838504i	$0.683431\pi$
$312$	10.9236	0.618424
$313$	−8.90641	−0.503420	−0.251710	−	0.967803i	$-0.580993\pi$
$313$	−8.90641	−0.503420	−0.251710	+	0.967803i	$0.580993\pi$
$314$	21.6217	1.22018
$315$	4.07533	0.229619
$316$	−8.62644	−0.485275
$317$	27.5448	1.54707	0.773536	−	0.633753i	$-0.218486\pi$
$317$	27.5448	1.54707	0.773536	+	0.633753i	$0.218486\pi$
$318$	6.39709	0.358731
$319$	−4.15635	−0.232711
$320$	−53.1386	−2.97054
$321$	12.9808	0.724518
$322$	−6.45019	−0.359455
$323$	−10.2896	−0.572529
$324$	3.14038	0.174466
$325$	−49.0441	−2.72048
$326$	−14.9917	−0.830315
$327$	−8.02131	−0.443579
$328$	11.1036	0.613095
$329$	3.94166	0.217311
$330$	−16.5261	−0.909732
$331$	14.4026	0.791641	0.395820	−	0.918328i	$-0.370460\pi$
$331$	14.4026	0.791641	0.395820	+	0.918328i	$0.370460\pi$
$332$	−21.1482	−1.16066
$333$	2.54189	0.139295
$334$	−4.85669	−0.265746
$335$	46.9854	2.56709
$336$	−0.418773	−0.0228460
$337$	16.8738	0.919174	0.459587	−	0.888133i	$-0.347997\pi$
$337$	16.8738	0.919174	0.459587	+	0.888133i	$0.347997\pi$
$338$	−10.9957	−0.598086
$339$	−7.57431	−0.411380
$340$	−37.0405	−2.00881
$341$	11.7132	0.634304
$342$	−8.06055	−0.435865
$343$	1.00000	0.0539949
$344$	−26.3749	−1.42204
$345$	11.5941	0.624207
$346$	−26.3525	−1.41672
$347$	−0.385316	−0.0206849	−0.0103424	−	0.999947i	$-0.503292\pi$
$347$	−0.385316	−0.0206849	−0.0103424	+	0.999947i	$0.503292\pi$
$348$	−7.29767	−0.391196
$349$	12.9341	0.692347	0.346173	−	0.938171i	$-0.387481\pi$
$349$	12.9341	0.692347	0.346173	+	0.938171i	$0.387481\pi$
$350$	−26.3189	−1.40681
$351$	−4.22490	−0.225509
$352$	10.9470	0.583478
$353$	22.4200	1.19330	0.596649	−	0.802502i	$-0.296498\pi$
$353$	22.4200	1.19330	0.596649	+	0.802502i	$0.296498\pi$
$354$	−3.62917	−0.192888
$355$	15.0410	0.798294
$356$	43.9083	2.32714
$357$	−2.89422	−0.153178
$358$	9.99073	0.528026
$359$	16.3662	0.863774	0.431887	−	0.901928i	$-0.357848\pi$
$359$	16.3662	0.863774	0.431887	+	0.901928i	$0.357848\pi$
$360$	−10.5368	−0.555340
$361$	−6.36038	−0.334757
$362$	18.8561	0.991056
$363$	−7.80096	−0.409444
$364$	−13.2678	−0.695422
$365$	−50.7552	−2.65665
$366$	15.5806	0.814411
$367$	4.27187	0.222990	0.111495	−	0.993765i	$-0.464436\pi$
$367$	4.27187	0.222990	0.111495	+	0.993765i	$0.464436\pi$
$368$	−1.19139	−0.0621055
$369$	−4.29454	−0.223565
$370$	−23.4865	−1.22100
$371$	−2.82153	−0.146487
$372$	20.5659	1.06629
$373$	16.3582	0.846995	0.423497	−	0.905897i	$-0.360802\pi$
$373$	16.3582	0.846995	0.423497	+	0.905897i	$0.360802\pi$
$374$	11.7365	0.606881
$375$	26.9312	1.39072
$376$	−10.1912	−0.525572
$377$	9.81791	0.505648
$378$	−2.26724	−0.116614
$379$	−21.6719	−1.11321	−0.556605	−	0.830777i	$-0.687896\pi$
$379$	−21.6719	−1.11321	−0.556605	+	0.830777i	$0.687896\pi$
$380$	45.5001	2.33411
$381$	−0.969796	−0.0496842
$382$	−1.50083	−0.0767890
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	17.3218	0.883947
$385$	7.28908	0.371486
$386$	−58.3907	−2.97201
$387$	10.2010	0.518547
$388$	−49.8365	−2.53006
$389$	−13.9310	−0.706328	−0.353164	−	0.935561i	$-0.614894\pi$
$389$	−13.9310	−0.706328	−0.353164	+	0.935561i	$0.614894\pi$
$390$	39.0371	1.97672
$391$	−8.23392	−0.416407
$392$	−2.58552	−0.130588
$393$	0.829412	0.0418383
$394$	27.0185	1.36117
$395$	−11.1947	−0.563267
$396$	5.61684	0.282257
$397$	−30.3666	−1.52405	−0.762027	−	0.647545i	$-0.775796\pi$
$397$	−30.3666	−1.52405	−0.762027	+	0.647545i	$0.775796\pi$
$398$	−22.0112	−1.10332
$399$	3.55522	0.177984
$400$	−4.86127	−0.243063
$401$	6.61193	0.330184	0.165092	−	0.986278i	$-0.447208\pi$
$401$	6.61193	0.330184	0.165092	+	0.986278i	$0.447208\pi$
$402$	−26.1395	−1.30372
$403$	−27.6683	−1.37825
$404$	−3.08505	−0.153487
$405$	4.07533	0.202505
$406$	5.26866	0.261479
$407$	4.54639	0.225356
$408$	7.48306	0.370467
$409$	−4.13592	−0.204508	−0.102254	−	0.994758i	$-0.532605\pi$
$409$	−4.13592	−0.204508	−0.102254	+	0.994758i	$0.532605\pi$
$410$	39.6806	1.95968
$411$	4.01673	0.198131
$412$	34.6843	1.70877
$413$	1.60070	0.0787653
$414$	−6.45019	−0.317010
$415$	−27.4445	−1.34720
$416$	−25.8585	−1.26782
$417$	3.89504	0.190741
$418$	−14.4170	−0.705157
$419$	−34.2201	−1.67176	−0.835881	−	0.548910i	$-0.815043\pi$
$419$	−34.2201	−1.67176	−0.835881	+	0.548910i	$0.815043\pi$
$420$	12.7981	0.624483
$421$	29.1071	1.41859	0.709296	−	0.704911i	$-0.249013\pi$
$421$	29.1071	1.41859	0.709296	+	0.704911i	$0.249013\pi$
$422$	27.0798	1.31822
$423$	3.94166	0.191650
$424$	7.29511	0.354282
$425$	−33.5971	−1.62970
$426$	−8.36781	−0.405422
$427$	−6.87205	−0.332562
$428$	40.7647	1.97044
$429$	−7.55660	−0.364836
$430$	−94.2549	−4.54538
$431$	−10.9881	−0.529280	−0.264640	−	0.964347i	$-0.585253\pi$
$431$	−10.9881	−0.529280	−0.264640	+	0.964347i	$0.585253\pi$
$432$	−0.418773	−0.0201482
$433$	22.7565	1.09361	0.546803	−	0.837261i	$-0.315845\pi$
$433$	22.7565	1.09361	0.546803	+	0.837261i	$0.315845\pi$
$434$	−14.8478	−0.712719
$435$	−9.47034	−0.454068
$436$	−25.1900	−1.20638
$437$	10.1144	0.483840
$438$	28.2367	1.34920
$439$	−10.7300	−0.512116	−0.256058	−	0.966661i	$-0.582424\pi$
$439$	−10.7300	−0.512116	−0.256058	+	0.966661i	$0.582424\pi$
$440$	−18.8460	−0.898449
$441$	1.00000	0.0476190
$442$	−27.7234	−1.31867
$443$	3.30835	0.157184	0.0785922	−	0.996907i	$-0.474957\pi$
$443$	3.30835	0.157184	0.0785922	+	0.996907i	$0.474957\pi$
$444$	7.98250	0.378833
$445$	56.9807	2.70114
$446$	11.5673	0.547726
$447$	5.72166	0.270625
$448$	−13.0391	−0.616039
$449$	17.7935	0.839725	0.419863	−	0.907588i	$-0.362078\pi$
$449$	17.7935	0.839725	0.419863	+	0.907588i	$0.362078\pi$
$450$	−26.3189	−1.24069
$451$	−7.68116	−0.361692
$452$	−23.7862	−1.11881
$453$	7.37231	0.346381
$454$	−43.3141	−2.03283
$455$	−17.2179	−0.807187
$456$	−9.19209	−0.430459
$457$	2.60641	0.121923	0.0609613	−	0.998140i	$-0.480583\pi$
$457$	2.60641	0.121923	0.0609613	+	0.998140i	$0.480583\pi$
$458$	12.0235	0.561823
$459$	−2.89422	−0.135091
$460$	36.4100	1.69762
$461$	24.0849	1.12175	0.560874	−	0.827901i	$-0.310465\pi$
$461$	24.0849	1.12175	0.560874	+	0.827901i	$0.310465\pi$
$462$	−4.05515	−0.188663
$463$	15.7504	0.731981	0.365991	−	0.930619i	$-0.380730\pi$
$463$	15.7504	0.731981	0.365991	+	0.930619i	$0.380730\pi$
$464$	0.973153	0.0451775
$465$	26.6888	1.23766
$466$	−32.2431	−1.49363
$467$	−26.5177	−1.22709	−0.613547	−	0.789658i	$-0.710258\pi$
$467$	−26.5177	−1.22709	−0.613547	+	0.789658i	$0.710258\pi$
$468$	−13.2678	−0.613304
$469$	11.5292	0.532370
$470$	−36.4200	−1.67993
$471$	−9.53658	−0.439423
$472$	−4.13864	−0.190496
$473$	18.2454	0.838923
$474$	6.22798	0.286061
$475$	41.2703	1.89361
$476$	−9.08896	−0.416592
$477$	−2.82153	−0.129189
$478$	24.3454	1.11353
$479$	12.2417	0.559337	0.279668	−	0.960097i	$-0.409775\pi$
$479$	12.2417	0.559337	0.279668	+	0.960097i	$0.409775\pi$
$480$	24.9430	1.13849
$481$	−10.7392	−0.489667
$482$	61.0234	2.77954
$483$	2.84495	0.129450
$484$	−24.4980	−1.11355
$485$	−64.6738	−2.93669
$486$	−2.26724	−0.102844
$487$	−18.2878	−0.828700	−0.414350	−	0.910118i	$-0.635991\pi$
$487$	−18.2878	−0.828700	−0.414350	+	0.910118i	$0.635991\pi$
$488$	17.7678	0.804310
$489$	6.61232	0.299019
$490$	−9.23976	−0.417410
$491$	−5.22999	−0.236026	−0.118013	−	0.993012i	$-0.537652\pi$
$491$	−5.22999	−0.236026	−0.118013	+	0.993012i	$0.537652\pi$
$492$	−13.4865	−0.608018
$493$	6.72565	0.302908
$494$	34.0550	1.53221
$495$	7.28908	0.327620
$496$	−2.74249	−0.123141
$497$	3.69074	0.165553
$498$	15.2682	0.684187
$499$	24.2632	1.08617	0.543085	−	0.839677i	$-0.317256\pi$
$499$	24.2632	1.08617	0.543085	+	0.839677i	$0.317256\pi$
$500$	84.5743	3.78228
$501$	2.14211	0.0957026
$502$	−0.176415	−0.00787378
$503$	−35.2243	−1.57058	−0.785288	−	0.619131i	$-0.787485\pi$
$503$	−35.2243	−1.57058	−0.785288	+	0.619131i	$0.787485\pi$
$504$	−2.58552	−0.115168
$505$	−4.00353	−0.178155
$506$	−11.5367	−0.512870
$507$	4.84980	0.215387
$508$	−3.04553	−0.135123
$509$	13.2457	0.587107	0.293553	−	0.955943i	$-0.405162\pi$
$509$	13.2457	0.587107	0.293553	+	0.955943i	$0.405162\pi$
$510$	26.7419	1.18415
$511$	−12.4542	−0.550943
$512$	−4.72859	−0.208976
$513$	3.55522	0.156967
$514$	−42.1940	−1.86110
$515$	45.0105	1.98340
$516$	32.0351	1.41026
$517$	7.04999	0.310058
$518$	−5.76308	−0.253215
$519$	11.6232	0.510200
$520$	44.5171	1.95221
$521$	−41.9634	−1.83845	−0.919225	−	0.393732i	$-0.871184\pi$
$521$	−41.9634	−1.83845	−0.919225	+	0.393732i	$0.871184\pi$
$522$	5.26866	0.230603
$523$	−35.4253	−1.54904	−0.774521	−	0.632548i	$-0.782009\pi$
$523$	−35.4253	−1.54904	−0.774521	+	0.632548i	$0.782009\pi$
$524$	2.60467	0.113785
$525$	11.6083	0.506630
$526$	−55.5454	−2.42189
$527$	−18.9538	−0.825642
$528$	−0.749012	−0.0325965
$529$	−14.9062	−0.648098
$530$	26.0703	1.13242
$531$	1.60070	0.0694645
$532$	11.1648	0.484054
$533$	18.1440	0.785905
$534$	−31.7002	−1.37180
$535$	52.9011	2.28712
$536$	−29.8090	−1.28755
$537$	−4.40656	−0.190157
$538$	−26.9587	−1.16227
$539$	1.78858	0.0770398
$540$	12.7981	0.550742
$541$	−16.9045	−0.726781	−0.363390	−	0.931637i	$-0.618381\pi$
$541$	−16.9045	−0.726781	−0.363390	+	0.931637i	$0.618381\pi$
$542$	25.8051	1.10842
$543$	−8.31678	−0.356907
$544$	−17.7141	−0.759484
$545$	−32.6895	−1.40027
$546$	9.57887	0.409938
$547$	17.8369	0.762650	0.381325	−	0.924441i	$-0.375468\pi$
$547$	17.8369	0.762650	0.381325	+	0.924441i	$0.375468\pi$
$548$	12.6140	0.538845
$549$	−6.87205	−0.293292
$550$	−47.0736	−2.00723
$551$	−8.26170	−0.351960
$552$	−7.35567	−0.313078
$553$	−2.74694	−0.116812
$554$	−20.8303	−0.884995
$555$	10.3591	0.439717
$556$	12.2319	0.518748
$557$	26.1441	1.10776	0.553881	−	0.832596i	$-0.313146\pi$
$557$	26.1441	1.10776	0.553881	+	0.832596i	$0.313146\pi$
$558$	−14.8478	−0.628559
$559$	−43.0983	−1.82286
$560$	−1.70664	−0.0721187
$561$	−5.17656	−0.218555
$562$	−39.2268	−1.65468
$563$	−11.8126	−0.497840	−0.248920	−	0.968524i	$-0.580076\pi$
$563$	−11.8126	−0.497840	−0.248920	+	0.968524i	$0.580076\pi$
$564$	12.3783	0.521221
$565$	−30.8678	−1.29862
$566$	68.0726	2.86130
$567$	1.00000	0.0419961
$568$	−9.54248	−0.400394
$569$	−34.0797	−1.42869	−0.714347	−	0.699791i	$-0.753276\pi$
$569$	−34.0797	−1.42869	−0.714347	+	0.699791i	$0.753276\pi$
$570$	−32.8494	−1.37591
$571$	−22.6156	−0.946433	−0.473216	−	0.880946i	$-0.656907\pi$
$571$	−22.6156	−0.946433	−0.473216	+	0.880946i	$0.656907\pi$
$572$	−23.7306	−0.992226
$573$	0.661962	0.0276539
$574$	9.73677	0.406405
$575$	33.0252	1.37725
$576$	−13.0391	−0.543295
$577$	−6.53399	−0.272014	−0.136007	−	0.990708i	$-0.543427\pi$
$577$	−6.53399	−0.272014	−0.136007	+	0.990708i	$0.543427\pi$
$578$	19.5515	0.813235
$579$	25.7541	1.07030
$580$	−29.7405	−1.23491
$581$	−6.73429	−0.279385
$582$	35.9801	1.49142
$583$	−5.04655	−0.209007
$584$	32.2006	1.33247
$585$	−17.2179	−0.711872
$586$	32.2133	1.33072
$587$	−4.08609	−0.168651	−0.0843255	−	0.996438i	$-0.526874\pi$
$587$	−4.08609	−0.168651	−0.0843255	+	0.996438i	$0.526874\pi$
$588$	3.14038	0.129507
$589$	23.2827	0.959345
$590$	−14.7901	−0.608898
$591$	−11.9169	−0.490196
$592$	−1.06448	−0.0437497
$593$	3.84282	0.157806	0.0789029	−	0.996882i	$-0.474858\pi$
$593$	3.84282	0.157806	0.0789029	+	0.996882i	$0.474858\pi$
$594$	−4.05515	−0.166385
$595$	−11.7949	−0.483545
$596$	17.9682	0.736005
$597$	9.70838	0.397337
$598$	27.2514	1.11439
$599$	33.4248	1.36570	0.682850	−	0.730559i	$-0.260740\pi$
$599$	33.4248	1.36570	0.682850	+	0.730559i	$0.260740\pi$
$600$	−30.0136	−1.22530
$601$	−12.8577	−0.524478	−0.262239	−	0.965003i	$-0.584461\pi$
$601$	−12.8577	−0.524478	−0.262239	+	0.965003i	$0.584461\pi$
$602$	−23.1281	−0.942633
$603$	11.5292	0.469506
$604$	23.1518	0.942035
$605$	−31.7915	−1.29251
$606$	2.22730	0.0904777
$607$	−33.4957	−1.35955	−0.679774	−	0.733421i	$-0.737922\pi$
$607$	−33.4957	−1.35955	−0.679774	+	0.733421i	$0.737922\pi$
$608$	21.7597	0.882473
$609$	−2.32382	−0.0941659
$610$	63.4961	2.57088
$611$	−16.6531	−0.673713
$612$	−9.08896	−0.367399
$613$	24.8922	1.00539	0.502693	−	0.864465i	$-0.332343\pi$
$613$	24.8922	1.00539	0.502693	+	0.864465i	$0.332343\pi$
$614$	2.71578	0.109600
$615$	−17.5017	−0.705737
$616$	−4.62441	−0.186323
$617$	14.1621	0.570144	0.285072	−	0.958506i	$-0.407982\pi$
$617$	14.1621	0.570144	0.285072	+	0.958506i	$0.407982\pi$
$618$	−25.0408	−1.00729
$619$	30.4004	1.22190	0.610948	−	0.791671i	$-0.290789\pi$
$619$	30.4004	1.22190	0.610948	+	0.791671i	$0.290789\pi$
$620$	83.8129	3.36601
$621$	2.84495	0.114164
$622$	43.5734	1.74713
$623$	13.9819	0.560171
$624$	1.76928	0.0708277
$625$	51.7120	2.06848
$626$	20.1930	0.807074
$627$	6.35882	0.253947
$628$	−29.9485	−1.19508
$629$	−7.35680	−0.293335
$630$	−9.23976	−0.368121
$631$	45.3482	1.80528	0.902641	−	0.430394i	$-0.141625\pi$
$631$	45.3482	1.80528	0.902641	+	0.430394i	$0.141625\pi$
$632$	7.10226	0.282513
$633$	−11.9440	−0.474729
$634$	−62.4508	−2.48024
$635$	−3.95224	−0.156840
$636$	−8.86068	−0.351349
$637$	−4.22490	−0.167397
$638$	9.42344	0.373078
$639$	3.69074	0.146004
$640$	70.5919	2.79039
$641$	29.2773	1.15638	0.578192	−	0.815901i	$-0.303758\pi$
$641$	29.2773	1.15638	0.578192	+	0.815901i	$0.303758\pi$
$642$	−29.4306	−1.16153
$643$	11.8257	0.466358	0.233179	−	0.972434i	$-0.425087\pi$
$643$	11.8257	0.466358	0.233179	+	0.972434i	$0.425087\pi$
$644$	8.93423	0.352058
$645$	41.5725	1.63692
$646$	23.3290	0.917868
$647$	2.00758	0.0789263	0.0394632	−	0.999221i	$-0.487435\pi$
$647$	2.00758	0.0789263	0.0394632	+	0.999221i	$0.487435\pi$
$648$	−2.58552	−0.101569
$649$	2.86299	0.112382
$650$	111.195	4.36142
$651$	6.54885	0.256670
$652$	20.7652	0.813228
$653$	−46.4655	−1.81834	−0.909169	−	0.416428i	$-0.863282\pi$
$653$	−46.4655	−1.81834	−0.909169	+	0.416428i	$0.863282\pi$
$654$	18.1862	0.711138
$655$	3.38013	0.132073
$656$	1.79844	0.0702173
$657$	−12.4542	−0.485886
$658$	−8.93669	−0.348388
$659$	1.65680	0.0645397	0.0322698	−	0.999479i	$-0.489726\pi$
$659$	1.65680	0.0645397	0.0322698	+	0.999479i	$0.489726\pi$
$660$	22.8905	0.891011
$661$	−19.6819	−0.765536	−0.382768	−	0.923845i	$-0.625029\pi$
$661$	−19.6819	−0.765536	−0.382768	+	0.923845i	$0.625029\pi$
$662$	−32.6543	−1.26914
$663$	12.2278	0.474889
$664$	17.4116	0.675701
$665$	14.4887	0.561849
$666$	−5.76308	−0.223315
$667$	−6.61115	−0.255985
$668$	6.72705	0.260277
$669$	−5.10191	−0.197251
$670$	−106.527	−4.11551
$671$	−12.2912	−0.474498
$672$	6.12049	0.236103
$673$	−15.5129	−0.597977	−0.298989	−	0.954257i	$-0.596649\pi$
$673$	−15.5129	−0.597977	−0.298989	+	0.954257i	$0.596649\pi$
$674$	−38.2569	−1.47360
$675$	11.6083	0.446805
$676$	15.2302	0.585778
$677$	−1.78450	−0.0685840	−0.0342920	−	0.999412i	$-0.510918\pi$
$677$	−1.78450	−0.0685840	−0.0342920	+	0.999412i	$0.510918\pi$
$678$	17.1728	0.659517
$679$	−15.8696	−0.609018
$680$	30.4960	1.16947
$681$	19.1043	0.732079
$682$	−26.5566	−1.01690
$683$	−5.21641	−0.199601	−0.0998003	−	0.995007i	$-0.531820\pi$
$683$	−5.21641	−0.199601	−0.0998003	+	0.995007i	$0.531820\pi$
$684$	11.1648	0.426895
$685$	16.3695	0.625447
$686$	−2.26724	−0.0865636
$687$	−5.30316	−0.202328
$688$	−4.27191	−0.162865
$689$	11.9207	0.454142
$690$	−26.2867	−1.00072
$691$	19.2638	0.732830	0.366415	−	0.930451i	$-0.380585\pi$
$691$	19.2638	0.732830	0.366415	+	0.930451i	$0.380585\pi$
$692$	36.5012	1.38757
$693$	1.78858	0.0679427
$694$	0.873604	0.0331616
$695$	15.8736	0.602120
$696$	6.00827	0.227743
$697$	12.4294	0.470796
$698$	−29.3247	−1.10996
$699$	14.2213	0.537899
$700$	36.4546	1.37786
$701$	−29.4229	−1.11129	−0.555645	−	0.831420i	$-0.687528\pi$
$701$	−29.4229	−1.11129	−0.555645	+	0.831420i	$0.687528\pi$
$702$	9.57887	0.361531
$703$	9.03700	0.340837
$704$	−23.3215	−0.878962
$705$	16.0636	0.604989
$706$	−50.8316	−1.91307
$707$	−0.982382	−0.0369463
$708$	5.02681	0.188919
$709$	−26.8077	−1.00678	−0.503392	−	0.864058i	$-0.667915\pi$
$709$	−26.8077	−1.00678	−0.503392	+	0.864058i	$0.667915\pi$
$710$	−34.1016	−1.27981
$711$	−2.74694	−0.103018
$712$	−36.1503	−1.35479
$713$	18.6312	0.697743
$714$	6.56190	0.245573
$715$	−30.7957	−1.15169
$716$	−13.8383	−0.517160
$717$	−10.7379	−0.401014
$718$	−37.1061	−1.38479
$719$	10.1447	0.378333	0.189166	−	0.981945i	$-0.439421\pi$
$719$	10.1447	0.378333	0.189166	+	0.981945i	$0.439421\pi$
$720$	−1.70664	−0.0636028
$721$	11.0446	0.411323
$722$	14.4205	0.536676
$723$	−26.9153	−1.00099
$724$	−26.1178	−0.970662
$725$	−26.9757	−1.00185
$726$	17.6867	0.656414
$727$	−38.3606	−1.42272	−0.711359	−	0.702829i	$-0.751920\pi$
$727$	−38.3606	−1.42272	−0.711359	+	0.702829i	$0.751920\pi$
$728$	10.9236	0.404854
$729$	1.00000	0.0370370
$730$	115.074	4.25909
$731$	−29.5240	−1.09198
$732$	−21.5808	−0.797651
$733$	−5.17676	−0.191208	−0.0956039	−	0.995419i	$-0.530478\pi$
$733$	−5.17676	−0.191208	−0.0956039	+	0.995419i	$0.530478\pi$
$734$	−9.68536	−0.357493
$735$	4.07533	0.150321
$736$	17.4125	0.641834
$737$	20.6210	0.759584
$738$	9.73677	0.358415
$739$	23.1139	0.850259	0.425130	−	0.905132i	$-0.360228\pi$
$739$	23.1139	0.850259	0.425130	+	0.905132i	$0.360228\pi$
$740$	32.5314	1.19588
$741$	−15.0205	−0.551791
$742$	6.39709	0.234845
$743$	32.2010	1.18134	0.590669	−	0.806914i	$-0.298864\pi$
$743$	32.2010	1.18134	0.590669	+	0.806914i	$0.298864\pi$
$744$	−16.9322	−0.620763
$745$	23.3177	0.854293
$746$	−37.0879	−1.35789
$747$	−6.73429	−0.246395
$748$	−16.2564	−0.594392
$749$	12.9808	0.474309
$750$	−61.0596	−2.22958
$751$	−10.4472	−0.381224	−0.190612	−	0.981665i	$-0.561047\pi$
$751$	−10.4472	−0.381224	−0.190612	+	0.981665i	$0.561047\pi$
$752$	−1.65066	−0.0601934
$753$	0.0778104	0.00283557
$754$	−22.2596	−0.810645
$755$	30.0446	1.09344
$756$	3.14038	0.114215
$757$	32.6046	1.18503	0.592517	−	0.805558i	$-0.298134\pi$
$757$	32.6046	1.18503	0.592517	+	0.805558i	$0.298134\pi$
$758$	49.1354	1.78468
$759$	5.08844	0.184699
$760$	−37.4608	−1.35885
$761$	−21.5317	−0.780523	−0.390261	−	0.920704i	$-0.627615\pi$
$761$	−21.5317	−0.780523	−0.390261	+	0.920704i	$0.627615\pi$
$762$	2.19876	0.0796527
$763$	−8.02131	−0.290391
$764$	2.07881	0.0752088
$765$	−11.7949	−0.426446
$766$	−2.26724	−0.0819187
$767$	−6.76280	−0.244191
$768$	−13.1944	−0.476112
$769$	−19.8325	−0.715178	−0.357589	−	0.933879i	$-0.616401\pi$
$769$	−19.8325	−0.715178	−0.357589	+	0.933879i	$0.616401\pi$
$770$	−16.5261	−0.595559
$771$	18.6103	0.670233
$772$	80.8776	2.91085
$773$	22.4361	0.806969	0.403485	−	0.914986i	$-0.367799\pi$
$773$	22.4361	0.806969	0.403485	+	0.914986i	$0.367799\pi$
$774$	−23.1281	−0.831324
$775$	76.0214	2.73077
$776$	41.0310	1.47293
$777$	2.54189	0.0911898
$778$	31.5848	1.13237
$779$	−15.2681	−0.547035
$780$	−54.0707	−1.93604
$781$	6.60121	0.236210
$782$	18.6683	0.667577
$783$	−2.32382	−0.0830465
$784$	−0.418773	−0.0149562
$785$	−38.8648	−1.38714
$786$	−1.88048	−0.0670744
$787$	45.8160	1.63316	0.816581	−	0.577231i	$-0.195867\pi$
$787$	45.8160	1.63316	0.816581	+	0.577231i	$0.195867\pi$
$788$	−37.4236	−1.33316
$789$	24.4991	0.872192
$790$	25.3811	0.903019
$791$	−7.57431	−0.269311
$792$	−4.62441	−0.164321
$793$	29.0337	1.03102
$794$	68.8483	2.44334
$795$	−11.4987	−0.407816
$796$	30.4880	1.08062
$797$	40.9936	1.45207	0.726034	−	0.687659i	$-0.241362\pi$
$797$	40.9936	1.45207	0.726034	+	0.687659i	$0.241362\pi$
$798$	−8.06055	−0.285340
$799$	−11.4080	−0.403587
$800$	71.0488	2.51195
$801$	13.9819	0.494024
$802$	−14.9908	−0.529345
$803$	−22.2754	−0.786084
$804$	36.2061	1.27689
$805$	11.5941	0.408639
$806$	62.7306	2.20959
$807$	11.8905	0.418566
$808$	2.53996	0.0893556
$809$	−31.6128	−1.11145	−0.555723	−	0.831368i	$-0.687558\pi$
$809$	−31.6128	−1.11145	−0.555723	+	0.831368i	$0.687558\pi$
$810$	−9.23976	−0.324652
$811$	34.3656	1.20674	0.603370	−	0.797461i	$-0.293824\pi$
$811$	34.3656	1.20674	0.603370	+	0.797461i	$0.293824\pi$
$812$	−7.29767	−0.256098
$813$	−11.3817	−0.399174
$814$	−10.3078	−0.361287
$815$	26.9474	0.943927
$816$	1.21202	0.0424293
$817$	36.2669	1.26882
$818$	9.37713	0.327864
$819$	−4.22490	−0.147630
$820$	−54.9620	−1.91936
$821$	−25.0597	−0.874590	−0.437295	−	0.899318i	$-0.644063\pi$
$821$	−25.0597	−0.874590	−0.437295	+	0.899318i	$0.644063\pi$
$822$	−9.10689	−0.317639
$823$	−19.0962	−0.665650	−0.332825	−	0.942989i	$-0.608002\pi$
$823$	−19.0962	−0.665650	−0.332825	+	0.942989i	$0.608002\pi$
$824$	−28.5560	−0.994796
$825$	20.7625	0.722858
$826$	−3.62917	−0.126275
$827$	2.00401	0.0696863	0.0348431	−	0.999393i	$-0.488907\pi$
$827$	2.00401	0.0696863	0.0348431	+	0.999393i	$0.488907\pi$
$828$	8.93423	0.310486
$829$	25.5993	0.889099	0.444549	−	0.895754i	$-0.353364\pi$
$829$	25.5993	0.889099	0.444549	+	0.895754i	$0.353364\pi$
$830$	62.2232	2.15980
$831$	9.18751	0.318711
$832$	55.0888	1.90986
$833$	−2.89422	−0.100279
$834$	−8.83099	−0.305792
$835$	8.72983	0.302108
$836$	19.9691	0.690646
$837$	6.54885	0.226362
$838$	77.5853	2.68014
$839$	0.560388	0.0193467	0.00967337	−	0.999953i	$-0.496921\pi$
$839$	0.560388	0.0193467	0.00967337	+	0.999953i	$0.496921\pi$
$840$	−10.5368	−0.363556
$841$	−23.5999	−0.813788
$842$	−65.9927	−2.27426
$843$	17.3016	0.595898
$844$	−37.5085	−1.29110
$845$	19.7646	0.679922
$846$	−8.93669	−0.307250
$847$	−7.80096	−0.268044
$848$	1.18158	0.0405757
$849$	−30.0244	−1.03044
$850$	76.1728	2.61270
$851$	7.23156	0.247895
$852$	11.5903	0.397079
$853$	11.7903	0.403692	0.201846	−	0.979417i	$-0.435306\pi$
$853$	11.7903	0.403692	0.201846	+	0.979417i	$0.435306\pi$
$854$	15.5806	0.533157
$855$	14.4887	0.495504
$856$	−33.5621	−1.14713
$857$	8.64675	0.295368	0.147684	−	0.989035i	$-0.452818\pi$
$857$	8.64675	0.295368	0.147684	+	0.989035i	$0.452818\pi$
$858$	17.1326	0.584898
$859$	−40.3707	−1.37743	−0.688715	−	0.725032i	$-0.741825\pi$
$859$	−40.3707	−1.37743	−0.688715	+	0.725032i	$0.741825\pi$
$860$	130.554	4.45184
$861$	−4.29454	−0.146358
$862$	24.9128	0.848532
$863$	−1.05681	−0.0359742	−0.0179871	−	0.999838i	$-0.505726\pi$
$863$	−1.05681	−0.0359742	−0.0179871	+	0.999838i	$0.505726\pi$
$864$	6.12049	0.208223
$865$	47.3683	1.61057
$866$	−51.5944	−1.75325
$867$	−8.62348	−0.292869
$868$	20.5659	0.698052
$869$	−4.91314	−0.166667
$870$	21.4715	0.727953
$871$	−48.7098	−1.65047
$872$	20.7392	0.702319
$873$	−15.8696	−0.537104
$874$	−22.9319	−0.775682
$875$	26.9312	0.910441
$876$	−39.1110	−1.32144
$877$	−48.9877	−1.65420	−0.827098	−	0.562058i	$-0.810010\pi$
$877$	−48.9877	−1.65420	−0.827098	+	0.562058i	$0.810010\pi$
$878$	24.3276	0.821015
$879$	−14.2082	−0.479230
$880$	−3.05247	−0.102899
$881$	41.7731	1.40737	0.703686	−	0.710511i	$-0.251536\pi$
$881$	41.7731	1.40737	0.703686	+	0.710511i	$0.251536\pi$
$882$	−2.26724	−0.0763420
$883$	−7.92540	−0.266711	−0.133355	−	0.991068i	$-0.542575\pi$
$883$	−7.92540	−0.266711	−0.133355	+	0.991068i	$0.542575\pi$
$884$	38.4000	1.29153
$885$	6.52339	0.219281
$886$	−7.50082	−0.251995
$887$	49.7915	1.67183	0.835917	−	0.548856i	$-0.184936\pi$
$887$	49.7915	1.67183	0.835917	+	0.548856i	$0.184936\pi$
$888$	−6.57210	−0.220545
$889$	−0.969796	−0.0325259
$890$	−129.189	−4.33042
$891$	1.78858	0.0599198
$892$	−16.0219	−0.536454
$893$	14.0135	0.468943
$894$	−12.9724	−0.433861
$895$	−17.9582	−0.600276
$896$	17.3218	0.578679
$897$	−12.0196	−0.401324
$898$	−40.3421	−1.34623
$899$	−15.2184	−0.507560
$900$	36.4546	1.21515
$901$	8.16614	0.272053
$902$	17.4150	0.579857
$903$	10.2010	0.339468
$904$	19.5835	0.651338
$905$	−33.8936	−1.12666
$906$	−16.7148	−0.555312
$907$	53.3780	1.77239	0.886194	−	0.463315i	$-0.153340\pi$
$907$	53.3780	1.77239	0.886194	+	0.463315i	$0.153340\pi$
$908$	59.9948	1.99100
$909$	−0.982382	−0.0325835
$910$	39.0371	1.29407
$911$	−21.9790	−0.728196	−0.364098	−	0.931361i	$-0.618623\pi$
$911$	−21.9790	−0.728196	−0.364098	+	0.931361i	$0.618623\pi$
$912$	−1.48883	−0.0493002
$913$	−12.0448	−0.398626
$914$	−5.90935	−0.195464
$915$	−28.0059	−0.925846
$916$	−16.6539	−0.550262
$917$	0.829412	0.0273896
$918$	6.56190	0.216575
$919$	9.54387	0.314823	0.157412	−	0.987533i	$-0.449685\pi$
$919$	9.54387	0.314823	0.157412	+	0.987533i	$0.449685\pi$
$920$	−29.9768	−0.988306
$921$	−1.19783	−0.0394699
$922$	−54.6064	−1.79837
$923$	−15.5930	−0.513251
$924$	5.61684	0.184780
$925$	29.5072	0.970189
$926$	−35.7098	−1.17350
$927$	11.0446	0.362753
$928$	−14.2229	−0.466890
$929$	−31.1830	−1.02308	−0.511540	−	0.859259i	$-0.670925\pi$
$929$	−31.1830	−1.02308	−0.511540	+	0.859259i	$0.670925\pi$
$930$	−60.5099	−1.98420
$931$	3.55522	0.116518
$932$	44.6602	1.46290
$933$	−19.2187	−0.629191
$934$	60.1220	1.96725
$935$	−21.0962	−0.689920
$936$	10.9236	0.357048
$937$	35.3605	1.15518	0.577589	−	0.816328i	$-0.303994\pi$
$937$	35.3605	1.15518	0.577589	+	0.816328i	$0.303994\pi$
$938$	−26.1395	−0.853485
$939$	−8.90641	−0.290650
$940$	50.4457	1.64536
$941$	3.03879	0.0990616	0.0495308	−	0.998773i	$-0.484227\pi$
$941$	3.03879	0.0990616	0.0495308	+	0.998773i	$0.484227\pi$
$942$	21.6217	0.704474
$943$	−12.2178	−0.397865
$944$	−0.670331	−0.0218174
$945$	4.07533	0.132571
$946$	−41.3667	−1.34495
$947$	−8.82923	−0.286911	−0.143456	−	0.989657i	$-0.545821\pi$
$947$	−8.82923	−0.286911	−0.143456	+	0.989657i	$0.545821\pi$
$948$	−8.62644	−0.280174
$949$	52.6179	1.70805
$950$	−93.5697	−3.03580
$951$	27.5448	0.893202
$952$	7.48306	0.242527
$953$	54.7546	1.77368	0.886838	−	0.462081i	$-0.152897\pi$
$953$	54.7546	1.77368	0.886838	+	0.462081i	$0.152897\pi$
$954$	6.39709	0.207113
$955$	2.69772	0.0872960
$956$	−33.7211	−1.09062
$957$	−4.15635	−0.134356
$958$	−27.7549	−0.896719
$959$	4.01673	0.129707
$960$	−53.1386	−1.71504
$961$	11.8875	0.383468
$962$	24.3484	0.785025
$963$	12.9808	0.418301
$964$	−84.5241	−2.72234
$965$	104.957	3.37867
$966$	−6.45019	−0.207532
$967$	−30.8187	−0.991063	−0.495532	−	0.868590i	$-0.665027\pi$
$967$	−30.8187	−0.991063	−0.495532	+	0.868590i	$0.665027\pi$
$968$	20.1695	0.648273
$969$	−10.2896	−0.330550
$970$	146.631	4.70804
$971$	−4.92683	−0.158109	−0.0790547	−	0.996870i	$-0.525190\pi$
$971$	−4.92683	−0.158109	−0.0790547	+	0.996870i	$0.525190\pi$
$972$	3.14038	0.100728
$973$	3.89504	0.124869
$974$	41.4629	1.32856
$975$	−49.0441	−1.57067
$976$	2.87783	0.0921171
$977$	−28.6181	−0.915573	−0.457787	−	0.889062i	$-0.651358\pi$
$977$	−28.6181	−0.915573	−0.457787	+	0.889062i	$0.651358\pi$
$978$	−14.9917	−0.479382
$979$	25.0077	0.799250
$980$	12.7981	0.408820
$981$	−8.02131	−0.256101
$982$	11.8576	0.378393
$983$	45.3418	1.44618	0.723089	−	0.690755i	$-0.242722\pi$
$983$	45.3418	1.44618	0.723089	+	0.690755i	$0.242722\pi$
$984$	11.1036	0.353970
$985$	−48.5654	−1.54742
$986$	−15.2487	−0.485616
$987$	3.94166	0.125464
$988$	−47.1700	−1.50068
$989$	29.0214	0.922827
$990$	−16.5261	−0.525234
$991$	21.9085	0.695945	0.347972	−	0.937505i	$-0.386870\pi$
$991$	21.9085	0.695945	0.347972	+	0.937505i	$0.386870\pi$
$992$	40.0822	1.27261
$993$	14.4026	0.457054
$994$	−8.36781	−0.265411
$995$	39.5649	1.25429
$996$	−21.1482	−0.670107
$997$	−21.0927	−0.668012	−0.334006	−	0.942571i	$-0.608401\pi$
$997$	−21.0927	−0.668012	−0.334006	+	0.942571i	$0.608401\pi$
$998$	−55.0106	−1.74133
$999$	2.54189	0.0804219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.u.1.6	✓	53

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.u.1.6	✓	53	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-2.26724 q^{2} +1.00000 q^{3} +3.14038 q^{4} +4.07533 q^{5} -2.26724 q^{6} +1.00000 q^{7} -2.58552 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.26724 q^{2} +1.00000 q^{3} +3.14038 q^{4} +4.07533 q^{5} -2.26724 q^{6} +1.00000 q^{7} -2.58552 q^{8} +1.00000 q^{9} -9.23976 q^{10} +1.78858 q^{11} +3.14038 q^{12} -4.22490 q^{13} -2.26724 q^{14} +4.07533 q^{15} -0.418773 q^{16} -2.89422 q^{17} -2.26724 q^{18} +3.55522 q^{19} +12.7981 q^{20} +1.00000 q^{21} -4.05515 q^{22} +2.84495 q^{23} -2.58552 q^{24} +11.6083 q^{25} +9.57887 q^{26} +1.00000 q^{27} +3.14038 q^{28} -2.32382 q^{29} -9.23976 q^{30} +6.54885 q^{31} +6.12049 q^{32} +1.78858 q^{33} +6.56190 q^{34} +4.07533 q^{35} +3.14038 q^{36} +2.54189 q^{37} -8.06055 q^{38} -4.22490 q^{39} -10.5368 q^{40} -4.29454 q^{41} -2.26724 q^{42} +10.2010 q^{43} +5.61684 q^{44} +4.07533 q^{45} -6.45019 q^{46} +3.94166 q^{47} -0.418773 q^{48} +1.00000 q^{49} -26.3189 q^{50} -2.89422 q^{51} -13.2678 q^{52} -2.82153 q^{53} -2.26724 q^{54} +7.28908 q^{55} -2.58552 q^{56} +3.55522 q^{57} +5.26866 q^{58} +1.60070 q^{59} +12.7981 q^{60} -6.87205 q^{61} -14.8478 q^{62} +1.00000 q^{63} -13.0391 q^{64} -17.2179 q^{65} -4.05515 q^{66} +11.5292 q^{67} -9.08896 q^{68} +2.84495 q^{69} -9.23976 q^{70} +3.69074 q^{71} -2.58552 q^{72} -12.4542 q^{73} -5.76308 q^{74} +11.6083 q^{75} +11.1648 q^{76} +1.78858 q^{77} +9.57887 q^{78} -2.74694 q^{79} -1.70664 q^{80} +1.00000 q^{81} +9.73677 q^{82} -6.73429 q^{83} +3.14038 q^{84} -11.7949 q^{85} -23.1281 q^{86} -2.32382 q^{87} -4.62441 q^{88} +13.9819 q^{89} -9.23976 q^{90} -4.22490 q^{91} +8.93423 q^{92} +6.54885 q^{93} -8.93669 q^{94} +14.4887 q^{95} +6.12049 q^{96} -15.8696 q^{97} -2.26724 q^{98} +1.78858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9}+O(q^{10}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9	\( 53 q + 11 q^{2} + 53 q^{3} + 63 q^{4} + 24 q^{5} + 11 q^{6} + 53 q^{7} + 30 q^{8} + 53 q^{9} + 2 q^{10} + 46 q^{11} + 63 q^{12} + 32 q^{13} + 11 q^{14} + 24 q^{15} + 67 q^{16} + 46 q^{17} + 11 q^{18} + 14 q^{19} + 53 q^{20} + 53 q^{21} + 13 q^{22} + 68 q^{23} + 30 q^{24} + 71 q^{25} + 11 q^{26} + 53 q^{27} + 63 q^{28} + 55 q^{29} + 2 q^{30} - 2 q^{31} + 51 q^{32} + 46 q^{33} - 7 q^{34} + 24 q^{35} + 63 q^{36} + 53 q^{37} + 16 q^{38} + 32 q^{39} - 20 q^{40} + 38 q^{41} + 11 q^{42} + 36 q^{43} + 70 q^{44} + 24 q^{45} + 4 q^{46} + 51 q^{47} + 67 q^{48} + 53 q^{49} + 32 q^{50} + 46 q^{51} + 10 q^{52} + 104 q^{53} + 11 q^{54} + 11 q^{55} + 30 q^{56} + 14 q^{57} + 4 q^{58} + 36 q^{59} + 53 q^{60} + 3 q^{61} + 25 q^{62} + 53 q^{63} + 82 q^{64} + 46 q^{65} + 13 q^{66} + 54 q^{67} + 88 q^{68} + 68 q^{69} + 2 q^{70} + 101 q^{71} + 30 q^{72} + q^{73} + 32 q^{74} + 71 q^{75} - 35 q^{76} + 46 q^{77} + 11 q^{78} + 14 q^{79} + 39 q^{80} + 53 q^{81} - 29 q^{82} + 38 q^{83} + 63 q^{84} + 16 q^{85} + 23 q^{86} + 55 q^{87} - 8 q^{88} + 52 q^{89} + 2 q^{90} + 32 q^{91} + 76 q^{92} - 2 q^{93} - 53 q^{94} + 46 q^{95} + 51 q^{96} - 3 q^{97} + 11 q^{98} + 46 q^{99}+O(q^{100}) \) 53 * q + 11 * q^2 + 53 * q^3 + 63 * q^4 + 24 * q^5 + 11 * q^6 + 53 * q^7 + 30 * q^8 + 53 * q^9 + 2 * q^10 + 46 * q^11 + 63 * q^12 + 32 * q^13 + 11 * q^14 + 24 * q^15 + 67 * q^16 + 46 * q^17 + 11 * q^18 + 14 * q^19 + 53 * q^20 + 53 * q^21 + 13 * q^22 + 68 * q^23 + 30 * q^24 + 71 * q^25 + 11 * q^26 + 53 * q^27 + 63 * q^28 + 55 * q^29 + 2 * q^30 - 2 * q^31 + 51 * q^32 + 46 * q^33 - 7 * q^34 + 24 * q^35 + 63 * q^36 + 53 * q^37 + 16 * q^38 + 32 * q^39 - 20 * q^40 + 38 * q^41 + 11 * q^42 + 36 * q^43 + 70 * q^44 + 24 * q^45 + 4 * q^46 + 51 * q^47 + 67 * q^48 + 53 * q^49 + 32 * q^50 + 46 * q^51 + 10 * q^52 + 104 * q^53 + 11 * q^54 + 11 * q^55 + 30 * q^56 + 14 * q^57 + 4 * q^58 + 36 * q^59 + 53 * q^60 + 3 * q^61 + 25 * q^62 + 53 * q^63 + 82 * q^64 + 46 * q^65 + 13 * q^66 + 54 * q^67 + 88 * q^68 + 68 * q^69 + 2 * q^70 + 101 * q^71 + 30 * q^72 + q^73 + 32 * q^74 + 71 * q^75 - 35 * q^76 + 46 * q^77 + 11 * q^78 + 14 * q^79 + 39 * q^80 + 53 * q^81 - 29 * q^82 + 38 * q^83 + 63 * q^84 + 16 * q^85 + 23 * q^86 + 55 * q^87 - 8 * q^88 + 52 * q^89 + 2 * q^90 + 32 * q^91 + 76 * q^92 - 2 * q^93 - 53 * q^94 + 46 * q^95 + 51 * q^96 - 3 * q^97 + 11 * q^98 + 46 * q^99

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