LMFDB - Embedded newform 8043.2.a.s.1.12

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:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.76145 q^{2} -1.00000 q^{3} +1.10269 q^{4} +2.11729 q^{5} +1.76145 q^{6} -1.00000 q^{7} +1.58056 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.76145 q^{2} -1.00000 q^{3} +1.10269 q^{4} +2.11729 q^{5} +1.76145 q^{6} -1.00000 q^{7} +1.58056 q^{8} +1.00000 q^{9} -3.72950 q^{10} -5.59224 q^{11} -1.10269 q^{12} -0.620009 q^{13} +1.76145 q^{14} -2.11729 q^{15} -4.98945 q^{16} +2.84305 q^{17} -1.76145 q^{18} -6.59922 q^{19} +2.33472 q^{20} +1.00000 q^{21} +9.85043 q^{22} +0.172617 q^{23} -1.58056 q^{24} -0.517070 q^{25} +1.09211 q^{26} -1.00000 q^{27} -1.10269 q^{28} +1.86535 q^{29} +3.72950 q^{30} -6.72864 q^{31} +5.62752 q^{32} +5.59224 q^{33} -5.00789 q^{34} -2.11729 q^{35} +1.10269 q^{36} -5.46603 q^{37} +11.6242 q^{38} +0.620009 q^{39} +3.34652 q^{40} -1.89977 q^{41} -1.76145 q^{42} -6.51833 q^{43} -6.16651 q^{44} +2.11729 q^{45} -0.304056 q^{46} -5.66992 q^{47} +4.98945 q^{48} +1.00000 q^{49} +0.910791 q^{50} -2.84305 q^{51} -0.683677 q^{52} -5.13939 q^{53} +1.76145 q^{54} -11.8404 q^{55} -1.58056 q^{56} +6.59922 q^{57} -3.28571 q^{58} -2.81906 q^{59} -2.33472 q^{60} +12.9288 q^{61} +11.8521 q^{62} -1.00000 q^{63} +0.0663335 q^{64} -1.31274 q^{65} -9.85043 q^{66} -9.71293 q^{67} +3.13501 q^{68} -0.172617 q^{69} +3.72950 q^{70} -1.00152 q^{71} +1.58056 q^{72} +2.88630 q^{73} +9.62812 q^{74} +0.517070 q^{75} -7.27689 q^{76} +5.59224 q^{77} -1.09211 q^{78} +5.49077 q^{79} -10.5641 q^{80} +1.00000 q^{81} +3.34635 q^{82} -6.05119 q^{83} +1.10269 q^{84} +6.01958 q^{85} +11.4817 q^{86} -1.86535 q^{87} -8.83890 q^{88} +2.23886 q^{89} -3.72950 q^{90} +0.620009 q^{91} +0.190343 q^{92} +6.72864 q^{93} +9.98725 q^{94} -13.9725 q^{95} -5.62752 q^{96} -2.93217 q^{97} -1.76145 q^{98} -5.59224 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * 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 $

$2$	−1.76145	−1.24553	−0.622765	−	0.782409i	$-0.713991\pi$
$2$	−1.76145	−1.24553	−0.622765	+	0.782409i	$0.713991\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.10269	0.551345
$5$	2.11729	0.946882	0.473441	−	0.880825i	$-0.343012\pi$
$5$	2.11729	0.946882	0.473441	+	0.880825i	$0.343012\pi$
$6$	1.76145	0.719107
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.58056	0.558814
$9$	1.00000	0.333333
$10$	−3.72950	−1.17937
$11$	−5.59224	−1.68613	−0.843063	−	0.537816i	$-0.819250\pi$
$11$	−5.59224	−1.68613	−0.843063	+	0.537816i	$0.819250\pi$
$12$	−1.10269	−0.318319
$13$	−0.620009	−0.171959	−0.0859797	−	0.996297i	$-0.527402\pi$
$13$	−0.620009	−0.171959	−0.0859797	+	0.996297i	$0.527402\pi$
$14$	1.76145	0.470766
$15$	−2.11729	−0.546683
$16$	−4.98945	−1.24736
$17$	2.84305	0.689542	0.344771	−	0.938687i	$-0.387957\pi$
$17$	2.84305	0.689542	0.344771	+	0.938687i	$0.387957\pi$
$18$	−1.76145	−0.415177
$19$	−6.59922	−1.51396	−0.756982	−	0.653435i	$-0.773327\pi$
$19$	−6.59922	−1.51396	−0.756982	+	0.653435i	$0.773327\pi$
$20$	2.33472	0.522058
$21$	1.00000	0.218218
$22$	9.85043	2.10012
$23$	0.172617	0.0359932	0.0179966	−	0.999838i	$-0.494271\pi$
$23$	0.172617	0.0359932	0.0179966	+	0.999838i	$0.494271\pi$
$24$	−1.58056	−0.322631
$25$	−0.517070	−0.103414
$26$	1.09211	0.214181
$27$	−1.00000	−0.192450
$28$	−1.10269	−0.208389
$29$	1.86535	0.346387	0.173193	−	0.984888i	$-0.444591\pi$
$29$	1.86535	0.346387	0.173193	+	0.984888i	$0.444591\pi$
$30$	3.72950	0.680910
$31$	−6.72864	−1.20850	−0.604249	−	0.796795i	$-0.706527\pi$
$31$	−6.72864	−1.20850	−0.604249	+	0.796795i	$0.706527\pi$
$32$	5.62752	0.994815
$33$	5.59224	0.973485
$34$	−5.00789	−0.858845
$35$	−2.11729	−0.357888
$36$	1.10269	0.183782
$37$	−5.46603	−0.898610	−0.449305	−	0.893378i	$-0.648328\pi$
$37$	−5.46603	−0.898610	−0.449305	+	0.893378i	$0.648328\pi$
$38$	11.6242	1.88569
$39$	0.620009	0.0992808
$40$	3.34652	0.529131
$41$	−1.89977	−0.296695	−0.148347	−	0.988935i	$-0.547395\pi$
$41$	−1.89977	−0.296695	−0.148347	+	0.988935i	$0.547395\pi$
$42$	−1.76145	−0.271797
$43$	−6.51833	−0.994036	−0.497018	−	0.867740i	$-0.665572\pi$
$43$	−6.51833	−0.994036	−0.497018	+	0.867740i	$0.665572\pi$
$44$	−6.16651	−0.929636
$45$	2.11729	0.315627
$46$	−0.304056	−0.0448306
$47$	−5.66992	−0.827042	−0.413521	−	0.910495i	$-0.635701\pi$
$47$	−5.66992	−0.827042	−0.413521	+	0.910495i	$0.635701\pi$
$48$	4.98945	0.720166
$49$	1.00000	0.142857
$50$	0.910791	0.128805
$51$	−2.84305	−0.398107
$52$	−0.683677	−0.0948089
$53$	−5.13939	−0.705949	−0.352974	−	0.935633i	$-0.614830\pi$
$53$	−5.13939	−0.705949	−0.352974	+	0.935633i	$0.614830\pi$
$54$	1.76145	0.239702
$55$	−11.8404	−1.59656
$56$	−1.58056	−0.211212
$57$	6.59922	0.874088
$58$	−3.28571	−0.431435
$59$	−2.81906	−0.367010	−0.183505	−	0.983019i	$-0.558744\pi$
$59$	−2.81906	−0.367010	−0.183505	+	0.983019i	$0.558744\pi$
$60$	−2.33472	−0.301411
$61$	12.9288	1.65536	0.827682	−	0.561198i	$-0.189659\pi$
$61$	12.9288	1.65536	0.827682	+	0.561198i	$0.189659\pi$
$62$	11.8521	1.50522
$63$	−1.00000	−0.125988
$64$	0.0663335	0.00829169
$65$	−1.31274	−0.162825
$66$	−9.85043	−1.21250
$67$	−9.71293	−1.18662	−0.593312	−	0.804973i	$-0.702180\pi$
$67$	−9.71293	−1.18662	−0.593312	+	0.804973i	$0.702180\pi$
$68$	3.13501	0.380175
$69$	−0.172617	−0.0207807
$70$	3.72950	0.445760
$71$	−1.00152	−0.118859	−0.0594294	−	0.998233i	$-0.518928\pi$
$71$	−1.00152	−0.118859	−0.0594294	+	0.998233i	$0.518928\pi$
$72$	1.58056	0.186271
$73$	2.88630	0.337816	0.168908	−	0.985632i	$-0.445976\pi$
$73$	2.88630	0.337816	0.168908	+	0.985632i	$0.445976\pi$
$74$	9.62812	1.11925
$75$	0.517070	0.0597061
$76$	−7.27689	−0.834716
$77$	5.59224	0.637295
$78$	−1.09211	−0.123657
$79$	5.49077	0.617760	0.308880	−	0.951101i	$-0.400046\pi$
$79$	5.49077	0.617760	0.308880	+	0.951101i	$0.400046\pi$
$80$	−10.5641	−1.18111
$81$	1.00000	0.111111
$82$	3.34635	0.369542
$83$	−6.05119	−0.664204	−0.332102	−	0.943243i	$-0.607758\pi$
$83$	−6.05119	−0.664204	−0.332102	+	0.943243i	$0.607758\pi$
$84$	1.10269	0.120313
$85$	6.01958	0.652915
$86$	11.4817	1.23810
$87$	−1.86535	−0.199987
$88$	−8.83890	−0.942230
$89$	2.23886	0.237319	0.118659	−	0.992935i	$-0.462140\pi$
$89$	2.23886	0.237319	0.118659	+	0.992935i	$0.462140\pi$
$90$	−3.72950	−0.393123
$91$	0.620009	0.0649946
$92$	0.190343	0.0198447
$93$	6.72864	0.697727
$94$	9.98725	1.03011
$95$	−13.9725	−1.43355
$96$	−5.62752	−0.574357
$97$	−2.93217	−0.297717	−0.148858	−	0.988859i	$-0.547560\pi$
$97$	−2.93217	−0.297717	−0.148858	+	0.988859i	$0.547560\pi$
$98$	−1.76145	−0.177933
$99$	−5.59224	−0.562042
$100$	−0.570168	−0.0570168
$101$	7.01317	0.697837	0.348918	−	0.937153i	$-0.386549\pi$
$101$	7.01317	0.697837	0.348918	+	0.937153i	$0.386549\pi$
$102$	5.00789	0.495855
$103$	−12.2807	−1.21005	−0.605024	−	0.796207i	$-0.706837\pi$
$103$	−12.2807	−1.21005	−0.605024	+	0.796207i	$0.706837\pi$
$104$	−0.979963	−0.0960933
$105$	2.11729	0.206627
$106$	9.05275	0.879280
$107$	−1.04210	−0.100744	−0.0503719	−	0.998731i	$-0.516041\pi$
$107$	−1.04210	−0.100744	−0.0503719	+	0.998731i	$0.516041\pi$
$108$	−1.10269	−0.106106
$109$	12.0193	1.15124	0.575622	−	0.817716i	$-0.304760\pi$
$109$	12.0193	1.15124	0.575622	+	0.817716i	$0.304760\pi$
$110$	20.8563	1.98857
$111$	5.46603	0.518813
$112$	4.98945	0.471459
$113$	5.07138	0.477075	0.238538	−	0.971133i	$-0.423332\pi$
$113$	5.07138	0.477075	0.238538	+	0.971133i	$0.423332\pi$
$114$	−11.6242	−1.08870
$115$	0.365482	0.0340813
$116$	2.05690	0.190979
$117$	−0.620009	−0.0573198
$118$	4.96562	0.457122
$119$	−2.84305	−0.260622
$120$	−3.34652	−0.305494
$121$	20.2732	1.84302
$122$	−22.7734	−2.06180
$123$	1.89977	0.171297
$124$	−7.41960	−0.666299
$125$	−11.6813	−1.04480
$126$	1.76145	0.156922
$127$	20.3460	1.80542	0.902709	−	0.430251i	$-0.141575\pi$
$127$	20.3460	1.80542	0.902709	+	0.430251i	$0.141575\pi$
$128$	−11.3719	−1.00514
$129$	6.51833	0.573907
$130$	2.31232	0.202804
$131$	3.15578	0.275722	0.137861	−	0.990452i	$-0.455977\pi$
$131$	3.15578	0.275722	0.137861	+	0.990452i	$0.455977\pi$
$132$	6.16651	0.536726
$133$	6.59922	0.572225
$134$	17.1088	1.47798
$135$	−2.11729	−0.182228
$136$	4.49363	0.385326
$137$	−1.27927	−0.109295	−0.0546475	−	0.998506i	$-0.517404\pi$
$137$	−1.27927	−0.109295	−0.0546475	+	0.998506i	$0.517404\pi$
$138$	0.304056	0.0258830
$139$	8.86979	0.752325	0.376163	−	0.926554i	$-0.377243\pi$
$139$	8.86979	0.752325	0.376163	+	0.926554i	$0.377243\pi$
$140$	−2.33472	−0.197320
$141$	5.66992	0.477493
$142$	1.76413	0.148042
$143$	3.46724	0.289945
$144$	−4.98945	−0.415788
$145$	3.94949	0.327988
$146$	−5.08406	−0.420760
$147$	−1.00000	−0.0824786
$148$	−6.02734	−0.495444
$149$	12.1649	0.996585	0.498292	−	0.867009i	$-0.333961\pi$
$149$	12.1649	0.996585	0.498292	+	0.867009i	$0.333961\pi$
$150$	−0.910791	−0.0743658
$151$	−9.13505	−0.743400	−0.371700	−	0.928353i	$-0.621225\pi$
$151$	−9.13505	−0.743400	−0.371700	+	0.928353i	$0.621225\pi$
$152$	−10.4305	−0.846024
$153$	2.84305	0.229847
$154$	−9.85043	−0.793770
$155$	−14.2465	−1.14431
$156$	0.683677	0.0547380
$157$	2.62933	0.209844	0.104922	−	0.994480i	$-0.466541\pi$
$157$	2.62933	0.209844	0.104922	+	0.994480i	$0.466541\pi$
$158$	−9.67170	−0.769439
$159$	5.13939	0.407580
$160$	11.9151	0.941973
$161$	−0.172617	−0.0136042
$162$	−1.76145	−0.138392
$163$	20.6208	1.61515	0.807574	−	0.589766i	$-0.200780\pi$
$163$	20.6208	1.61515	0.807574	+	0.589766i	$0.200780\pi$
$164$	−2.09486	−0.163581
$165$	11.8404	0.921775
$166$	10.6588	0.827286
$167$	21.2273	1.64262	0.821310	−	0.570482i	$-0.193244\pi$
$167$	21.2273	1.64262	0.821310	+	0.570482i	$0.193244\pi$
$168$	1.58056	0.121943
$169$	−12.6156	−0.970430
$170$	−10.6032	−0.813225
$171$	−6.59922	−0.504655
$172$	−7.18769	−0.548056
$173$	18.8503	1.43316	0.716582	−	0.697503i	$-0.245705\pi$
$173$	18.8503	1.43316	0.716582	+	0.697503i	$0.245705\pi$
$174$	3.28571	0.249089
$175$	0.517070	0.0390868
$176$	27.9023	2.10321
$177$	2.81906	0.211893
$178$	−3.94363	−0.295588
$179$	−3.73939	−0.279495	−0.139748	−	0.990187i	$-0.544629\pi$
$179$	−3.73939	−0.279495	−0.139748	+	0.990187i	$0.544629\pi$
$180$	2.33472	0.174019
$181$	−6.46169	−0.480293	−0.240147	−	0.970737i	$-0.577196\pi$
$181$	−6.46169	−0.480293	−0.240147	+	0.970737i	$0.577196\pi$
$182$	−1.09211	−0.0809527
$183$	−12.9288	−0.955724
$184$	0.272833	0.0201135
$185$	−11.5732	−0.850878
$186$	−11.8521	−0.869040
$187$	−15.8991	−1.16265
$188$	−6.25216	−0.455985
$189$	1.00000	0.0727393
$190$	24.6118	1.78552
$191$	9.95956	0.720649	0.360324	−	0.932827i	$-0.382666\pi$
$191$	9.95956	0.720649	0.360324	+	0.932827i	$0.382666\pi$
$192$	−0.0663335	−0.00478721
$193$	−9.41311	−0.677570	−0.338785	−	0.940864i	$-0.610016\pi$
$193$	−9.41311	−0.677570	−0.338785	+	0.940864i	$0.610016\pi$
$194$	5.16486	0.370815
$195$	1.31274	0.0940073
$196$	1.10269	0.0787635
$197$	−0.151937	−0.0108251	−0.00541254	−	0.999985i	$-0.501723\pi$
$197$	−0.151937	−0.0108251	−0.00541254	+	0.999985i	$0.501723\pi$
$198$	9.85043	0.700040
$199$	−20.4642	−1.45067	−0.725335	−	0.688396i	$-0.758315\pi$
$199$	−20.4642	−1.45067	−0.725335	+	0.688396i	$0.758315\pi$
$200$	−0.817262	−0.0577892
$201$	9.71293	0.685097
$202$	−12.3533	−0.869176
$203$	−1.86535	−0.130922
$204$	−3.13501	−0.219494
$205$	−4.02238	−0.280935
$206$	21.6317	1.50715
$207$	0.172617	0.0119977
$208$	3.09351	0.214496
$209$	36.9044	2.55273
$210$	−3.72950	−0.257360
$211$	12.1507	0.836490	0.418245	−	0.908334i	$-0.362645\pi$
$211$	12.1507	0.836490	0.418245	+	0.908334i	$0.362645\pi$
$212$	−5.66715	−0.389221
$213$	1.00152	0.0686232
$214$	1.83561	0.125480
$215$	−13.8012	−0.941235
$216$	−1.58056	−0.107544
$217$	6.72864	0.456770
$218$	−21.1714	−1.43391
$219$	−2.88630	−0.195038
$220$	−13.0563	−0.880256
$221$	−1.76272	−0.118573
$222$	−9.62812	−0.646197
$223$	15.1931	1.01741	0.508703	−	0.860942i	$-0.330125\pi$
$223$	15.1931	1.01741	0.508703	+	0.860942i	$0.330125\pi$
$224$	−5.62752	−0.376005
$225$	−0.517070	−0.0344714
$226$	−8.93296	−0.594211
$227$	−9.90965	−0.657727	−0.328863	−	0.944378i	$-0.606666\pi$
$227$	−9.90965	−0.657727	−0.328863	+	0.944378i	$0.606666\pi$
$228$	7.27689	0.481924
$229$	−8.89081	−0.587521	−0.293760	−	0.955879i	$-0.594907\pi$
$229$	−8.89081	−0.587521	−0.293760	+	0.955879i	$0.594907\pi$
$230$	−0.643776	−0.0424493
$231$	−5.59224	−0.367943
$232$	2.94830	0.193566
$233$	−14.9273	−0.977922	−0.488961	−	0.872306i	$-0.662624\pi$
$233$	−14.9273	−0.977922	−0.488961	+	0.872306i	$0.662624\pi$
$234$	1.09211	0.0713936
$235$	−12.0049	−0.783112
$236$	−3.10855	−0.202349
$237$	−5.49077	−0.356664
$238$	5.00789	0.324613
$239$	−12.9184	−0.835619	−0.417809	−	0.908535i	$-0.637202\pi$
$239$	−12.9184	−0.835619	−0.417809	+	0.908535i	$0.637202\pi$
$240$	10.5641	0.681912
$241$	8.36403	0.538775	0.269387	−	0.963032i	$-0.413179\pi$
$241$	8.36403	0.538775	0.269387	+	0.963032i	$0.413179\pi$
$242$	−35.7101	−2.29553
$243$	−1.00000	−0.0641500
$244$	14.2565	0.912676
$245$	2.11729	0.135269
$246$	−3.34635	−0.213355
$247$	4.09157	0.260341
$248$	−10.6350	−0.675326
$249$	6.05119	0.383479
$250$	20.5759	1.30133
$251$	3.51251	0.221707	0.110854	−	0.993837i	$-0.464641\pi$
$251$	3.51251	0.221707	0.110854	+	0.993837i	$0.464641\pi$
$252$	−1.10269	−0.0694629
$253$	−0.965319	−0.0606891
$254$	−35.8384	−2.24870
$255$	−6.01958	−0.376961
$256$	19.8983	1.24364
$257$	7.04945	0.439733	0.219866	−	0.975530i	$-0.429438\pi$
$257$	7.04945	0.439733	0.219866	+	0.975530i	$0.429438\pi$
$258$	−11.4817	−0.714818
$259$	5.46603	0.339643
$260$	−1.44754	−0.0897729
$261$	1.86535	0.115462
$262$	−5.55873	−0.343419
$263$	−15.1315	−0.933050	−0.466525	−	0.884508i	$-0.654494\pi$
$263$	−15.1315	−0.933050	−0.466525	+	0.884508i	$0.654494\pi$
$264$	8.83890	0.543997
$265$	−10.8816	−0.668450
$266$	−11.6242	−0.712723
$267$	−2.23886	−0.137016
$268$	−10.7103	−0.654239
$269$	−12.4002	−0.756052	−0.378026	−	0.925795i	$-0.623397\pi$
$269$	−12.4002	−0.756052	−0.378026	+	0.925795i	$0.623397\pi$
$270$	3.72950	0.226970
$271$	−16.1477	−0.980901	−0.490451	−	0.871469i	$-0.663168\pi$
$271$	−16.1477	−0.980901	−0.490451	+	0.871469i	$0.663168\pi$
$272$	−14.1853	−0.860110
$273$	−0.620009	−0.0375246
$274$	2.25336	0.136130
$275$	2.89158	0.174369
$276$	−0.190343	−0.0114573
$277$	−10.0406	−0.603279	−0.301640	−	0.953422i	$-0.597534\pi$
$277$	−10.0406	−0.603279	−0.301640	+	0.953422i	$0.597534\pi$
$278$	−15.6236	−0.937044
$279$	−6.72864	−0.402833
$280$	−3.34652	−0.199993
$281$	−1.87074	−0.111599	−0.0557996	−	0.998442i	$-0.517771\pi$
$281$	−1.87074	−0.111599	−0.0557996	+	0.998442i	$0.517771\pi$
$282$	−9.98725	−0.594732
$283$	19.7147	1.17192	0.585958	−	0.810341i	$-0.300718\pi$
$283$	19.7147	1.17192	0.585958	+	0.810341i	$0.300718\pi$
$284$	−1.10437	−0.0655322
$285$	13.9725	0.827658
$286$	−6.10735	−0.361135
$287$	1.89977	0.112140
$288$	5.62752	0.331605
$289$	−8.91704	−0.524532
$290$	−6.95682	−0.408518
$291$	2.93217	0.171887
$292$	3.18269	0.186253
$293$	−2.33079	−0.136166	−0.0680831	−	0.997680i	$-0.521688\pi$
$293$	−2.33079	−0.136166	−0.0680831	+	0.997680i	$0.521688\pi$
$294$	1.76145	0.102730
$295$	−5.96877	−0.347515
$296$	−8.63941	−0.502156
$297$	5.59224	0.324495
$298$	−21.4277	−1.24128
$299$	−0.107024	−0.00618937
$300$	0.570168	0.0329187
$301$	6.51833	0.375710
$302$	16.0909	0.925927
$303$	−7.01317	−0.402896
$304$	32.9265	1.88846
$305$	27.3741	1.56743
$306$	−5.00789	−0.286282
$307$	−2.11392	−0.120648	−0.0603238	−	0.998179i	$-0.519213\pi$
$307$	−2.11392	−0.120648	−0.0603238	+	0.998179i	$0.519213\pi$
$308$	6.16651	0.351369
$309$	12.2807	0.698622
$310$	25.0944	1.42527
$311$	3.87408	0.219679	0.109839	−	0.993949i	$-0.464966\pi$
$311$	3.87408	0.219679	0.109839	+	0.993949i	$0.464966\pi$
$312$	0.979963	0.0554795
$313$	−3.82501	−0.216202	−0.108101	−	0.994140i	$-0.534477\pi$
$313$	−3.82501	−0.216202	−0.108101	+	0.994140i	$0.534477\pi$
$314$	−4.63142	−0.261366
$315$	−2.11729	−0.119296
$316$	6.05462	0.340599
$317$	−20.4919	−1.15094	−0.575470	−	0.817823i	$-0.695181\pi$
$317$	−20.4919	−1.15094	−0.575470	+	0.817823i	$0.695181\pi$
$318$	−9.05275	−0.507653
$319$	−10.4315	−0.584052
$320$	0.140447	0.00785125
$321$	1.04210	0.0581645
$322$	0.304056	0.0169444
$323$	−18.7619	−1.04394
$324$	1.10269	0.0612605
$325$	0.320588	0.0177830
$326$	−36.3225	−2.01172
$327$	−12.0193	−0.664671
$328$	−3.00271	−0.165797
$329$	5.66992	0.312593
$330$	−20.8563	−1.14810
$331$	29.5816	1.62595	0.812975	−	0.582298i	$-0.197846\pi$
$331$	29.5816	1.62595	0.812975	+	0.582298i	$0.197846\pi$
$332$	−6.67258	−0.366206
$333$	−5.46603	−0.299537
$334$	−37.3908	−2.04593
$335$	−20.5651	−1.12359
$336$	−4.98945	−0.272197
$337$	14.7729	0.804732	0.402366	−	0.915479i	$-0.368188\pi$
$337$	14.7729	0.804732	0.402366	+	0.915479i	$0.368188\pi$
$338$	22.2217	1.20870
$339$	−5.07138	−0.275439
$340$	6.63773	0.359981
$341$	37.6282	2.03768
$342$	11.6242	0.628563
$343$	−1.00000	−0.0539949
$344$	−10.3026	−0.555481
$345$	−0.365482	−0.0196769
$346$	−33.2038	−1.78505
$347$	3.55807	0.191007	0.0955035	−	0.995429i	$-0.469554\pi$
$347$	3.55807	0.191007	0.0955035	+	0.995429i	$0.469554\pi$
$348$	−2.05690	−0.110262
$349$	10.0092	0.535781	0.267891	−	0.963449i	$-0.413673\pi$
$349$	10.0092	0.535781	0.267891	+	0.963449i	$0.413673\pi$
$350$	−0.910791	−0.0486838
$351$	0.620009	0.0330936
$352$	−31.4705	−1.67738
$353$	−28.9933	−1.54316	−0.771580	−	0.636132i	$-0.780533\pi$
$353$	−28.9933	−1.54316	−0.771580	+	0.636132i	$0.780533\pi$
$354$	−4.96562	−0.263920
$355$	−2.12052	−0.112545
$356$	2.46877	0.130845
$357$	2.84305	0.150470
$358$	6.58674	0.348120
$359$	−19.0910	−1.00758	−0.503792	−	0.863825i	$-0.668062\pi$
$359$	−19.0910	−1.00758	−0.503792	+	0.863825i	$0.668062\pi$
$360$	3.34652	0.176377
$361$	24.5497	1.29209
$362$	11.3819	0.598220
$363$	−20.2732	−1.06407
$364$	0.683677	0.0358344
$365$	6.11114	0.319872
$366$	22.7734	1.19038
$367$	17.0610	0.890575	0.445288	−	0.895388i	$-0.353101\pi$
$367$	17.0610	0.890575	0.445288	+	0.895388i	$0.353101\pi$
$368$	−0.861267	−0.0448966
$369$	−1.89977	−0.0988982
$370$	20.3855	1.05979
$371$	5.13939	0.266824
$372$	7.41960	0.384688
$373$	25.1584	1.30265	0.651327	−	0.758797i	$-0.274212\pi$
$373$	25.1584	1.30265	0.651327	+	0.758797i	$0.274212\pi$
$374$	28.0053	1.44812
$375$	11.6813	0.603217
$376$	−8.96166	−0.462162
$377$	−1.15653	−0.0595645
$378$	−1.76145	−0.0905990
$379$	19.4069	0.996864	0.498432	−	0.866929i	$-0.333909\pi$
$379$	19.4069	0.996864	0.498432	+	0.866929i	$0.333909\pi$
$380$	−15.4073	−0.790378
$381$	−20.3460	−1.04236
$382$	−17.5432	−0.897590
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	11.3719	0.580319
$385$	11.8404	0.603444
$386$	16.5807	0.843934
$387$	−6.51833	−0.331345
$388$	−3.23327	−0.164145
$389$	−28.1080	−1.42513	−0.712566	−	0.701605i	$-0.752467\pi$
$389$	−28.1080	−1.42513	−0.712566	+	0.701605i	$0.752467\pi$
$390$	−2.31232	−0.117089
$391$	0.490761	0.0248188
$392$	1.58056	0.0798305
$393$	−3.15578	−0.159188
$394$	0.267629	0.0134830
$395$	11.6256	0.584946
$396$	−6.16651	−0.309879
$397$	−22.3740	−1.12292	−0.561459	−	0.827504i	$-0.689760\pi$
$397$	−22.3740	−1.12292	−0.561459	+	0.827504i	$0.689760\pi$
$398$	36.0466	1.80685
$399$	−6.59922	−0.330374
$400$	2.57990	0.128995
$401$	−2.80914	−0.140282	−0.0701409	−	0.997537i	$-0.522345\pi$
$401$	−2.80914	−0.140282	−0.0701409	+	0.997537i	$0.522345\pi$
$402$	−17.1088	−0.853309
$403$	4.17181	0.207813
$404$	7.73335	0.384749
$405$	2.11729	0.105209
$406$	3.28571	0.163067
$407$	30.5674	1.51517
$408$	−4.49363	−0.222468
$409$	−4.98539	−0.246512	−0.123256	−	0.992375i	$-0.539334\pi$
$409$	−4.98539	−0.246512	−0.123256	+	0.992375i	$0.539334\pi$
$410$	7.08519	0.349913
$411$	1.27927	0.0631015
$412$	−13.5417	−0.667154
$413$	2.81906	0.138717
$414$	−0.304056	−0.0149435
$415$	−12.8121	−0.628923
$416$	−3.48911	−0.171068
$417$	−8.86979	−0.434355
$418$	−65.0051	−3.17951
$419$	38.3612	1.87406	0.937032	−	0.349242i	$-0.113561\pi$
$419$	38.3612	1.87406	0.937032	+	0.349242i	$0.113561\pi$
$420$	2.33472	0.113922
$421$	−14.5705	−0.710124	−0.355062	−	0.934843i	$-0.615540\pi$
$421$	−14.5705	−0.710124	−0.355062	+	0.934843i	$0.615540\pi$
$422$	−21.4028	−1.04187
$423$	−5.66992	−0.275681
$424$	−8.12313	−0.394494
$425$	−1.47006	−0.0713083
$426$	−1.76413	−0.0854722
$427$	−12.9288	−0.625669
$428$	−1.14912	−0.0555446
$429$	−3.46724	−0.167400
$430$	24.3101	1.17234
$431$	−32.0124	−1.54198	−0.770992	−	0.636845i	$-0.780239\pi$
$431$	−32.0124	−1.54198	−0.770992	+	0.636845i	$0.780239\pi$
$432$	4.98945	0.240055
$433$	−31.6250	−1.51980	−0.759900	−	0.650040i	$-0.774752\pi$
$433$	−31.6250	−1.51980	−0.759900	+	0.650040i	$0.774752\pi$
$434$	−11.8521	−0.568920
$435$	−3.94949	−0.189364
$436$	13.2536	0.634732
$437$	−1.13914	−0.0544924
$438$	5.08406	0.242926
$439$	16.2913	0.777541	0.388770	−	0.921335i	$-0.372900\pi$
$439$	16.2913	0.777541	0.388770	+	0.921335i	$0.372900\pi$
$440$	−18.7145	−0.892180
$441$	1.00000	0.0476190
$442$	3.10493	0.147687
$443$	18.6439	0.885796	0.442898	−	0.896572i	$-0.353950\pi$
$443$	18.6439	0.885796	0.442898	+	0.896572i	$0.353950\pi$
$444$	6.02734	0.286045
$445$	4.74033	0.224713
$446$	−26.7618	−1.26721
$447$	−12.1649	−0.575378
$448$	−0.0663335	−0.00313396
$449$	−7.20424	−0.339989	−0.169994	−	0.985445i	$-0.554375\pi$
$449$	−7.20424	−0.339989	−0.169994	+	0.985445i	$0.554375\pi$
$450$	0.910791	0.0429351
$451$	10.6240	0.500264
$452$	5.59216	0.263033
$453$	9.13505	0.429202
$454$	17.4553	0.819218
$455$	1.31274	0.0615422
$456$	10.4305	0.488452
$457$	20.6615	0.966506	0.483253	−	0.875481i	$-0.339455\pi$
$457$	20.6615	0.966506	0.483253	+	0.875481i	$0.339455\pi$
$458$	15.6607	0.731775
$459$	−2.84305	−0.132702
$460$	0.403013	0.0187906
$461$	−11.2984	−0.526217	−0.263109	−	0.964766i	$-0.584748\pi$
$461$	−11.2984	−0.526217	−0.263109	+	0.964766i	$0.584748\pi$
$462$	9.85043	0.458284
$463$	32.3415	1.50304	0.751518	−	0.659713i	$-0.229322\pi$
$463$	32.3415	1.50304	0.751518	+	0.659713i	$0.229322\pi$
$464$	−9.30708	−0.432070
$465$	14.2465	0.660665
$466$	26.2937	1.21803
$467$	−31.2170	−1.44455	−0.722276	−	0.691605i	$-0.756904\pi$
$467$	−31.2170	−1.44455	−0.722276	+	0.691605i	$0.756904\pi$
$468$	−0.683677	−0.0316030
$469$	9.71293	0.448502
$470$	21.1459	0.975389
$471$	−2.62933	−0.121153
$472$	−4.45570	−0.205090
$473$	36.4521	1.67607
$474$	9.67170	0.444236
$475$	3.41226	0.156565
$476$	−3.13501	−0.143693
$477$	−5.13939	−0.235316
$478$	22.7550	1.04079
$479$	−0.150826	−0.00689144	−0.00344572	−	0.999994i	$-0.501097\pi$
$479$	−0.150826	−0.00689144	−0.00344572	+	0.999994i	$0.501097\pi$
$480$	−11.9151	−0.543848
$481$	3.38899	0.154525
$482$	−14.7328	−0.671060
$483$	0.172617	0.00785436
$484$	22.3550	1.01614
$485$	−6.20826	−0.281903
$486$	1.76145	0.0799008
$487$	21.1869	0.960070	0.480035	−	0.877249i	$-0.340624\pi$
$487$	21.1869	0.960070	0.480035	+	0.877249i	$0.340624\pi$
$488$	20.4348	0.925040
$489$	−20.6208	−0.932506
$490$	−3.72950	−0.168481
$491$	20.7577	0.936784	0.468392	−	0.883521i	$-0.344834\pi$
$491$	20.7577	0.936784	0.468392	+	0.883521i	$0.344834\pi$
$492$	2.09486	0.0944435
$493$	5.30329	0.238848
$494$	−7.20708	−0.324262
$495$	−11.8404	−0.532187
$496$	33.5722	1.50744
$497$	1.00152	0.0449244
$498$	−10.6588	−0.477634
$499$	4.85283	0.217242	0.108621	−	0.994083i	$-0.465356\pi$
$499$	4.85283	0.217242	0.108621	+	0.994083i	$0.465356\pi$
$500$	−12.8808	−0.576047
$501$	−21.2273	−0.948367
$502$	−6.18709	−0.276143
$503$	−21.8853	−0.975817	−0.487909	−	0.872895i	$-0.662240\pi$
$503$	−21.8853	−0.975817	−0.487909	+	0.872895i	$0.662240\pi$
$504$	−1.58056	−0.0704039
$505$	14.8489	0.660769
$506$	1.70036	0.0755900
$507$	12.6156	0.560278
$508$	22.4354	0.995408
$509$	9.03736	0.400574	0.200287	−	0.979737i	$-0.435813\pi$
$509$	9.03736	0.400574	0.200287	+	0.979737i	$0.435813\pi$
$510$	10.6032	0.469516
$511$	−2.88630	−0.127682
$512$	−12.3060	−0.543853
$513$	6.59922	0.291363
$514$	−12.4172	−0.547700
$515$	−26.0017	−1.14577
$516$	7.18769	0.316421
$517$	31.7076	1.39450
$518$	−9.62812	−0.423035
$519$	−18.8503	−0.827438
$520$	−2.07487	−0.0909890
$521$	−14.8474	−0.650479	−0.325239	−	0.945632i	$-0.605445\pi$
$521$	−14.8474	−0.650479	−0.325239	+	0.945632i	$0.605445\pi$
$522$	−3.28571	−0.143812
$523$	−27.4466	−1.20016	−0.600078	−	0.799941i	$-0.704864\pi$
$523$	−27.4466	−1.20016	−0.600078	+	0.799941i	$0.704864\pi$
$524$	3.47984	0.152018
$525$	−0.517070	−0.0225668
$526$	26.6533	1.16214
$527$	−19.1299	−0.833311
$528$	−27.9023	−1.21429
$529$	−22.9702	−0.998704
$530$	19.1673	0.832575
$531$	−2.81906	−0.122337
$532$	7.27689	0.315493
$533$	1.17788	0.0510195
$534$	3.94363	0.170658
$535$	−2.20644	−0.0953926
$536$	−15.3519	−0.663101
$537$	3.73939	0.161367
$538$	21.8422	0.941686
$539$	−5.59224	−0.240875
$540$	−2.33472	−0.100470
$541$	2.55477	0.109838	0.0549190	−	0.998491i	$-0.482510\pi$
$541$	2.55477	0.109838	0.0549190	+	0.998491i	$0.482510\pi$
$542$	28.4432	1.22174
$543$	6.46169	0.277298
$544$	15.9994	0.685967
$545$	25.4485	1.09009
$546$	1.09211	0.0467381
$547$	36.0992	1.54349	0.771744	−	0.635933i	$-0.219384\pi$
$547$	36.0992	1.54349	0.771744	+	0.635933i	$0.219384\pi$
$548$	−1.41063	−0.0602592
$549$	12.9288	0.551788
$550$	−5.09337	−0.217182
$551$	−12.3099	−0.524417
$552$	−0.272833	−0.0116125
$553$	−5.49077	−0.233491
$554$	17.6859	0.751402
$555$	11.5732	0.491255
$556$	9.78062	0.414791
$557$	−12.5502	−0.531769	−0.265885	−	0.964005i	$-0.585664\pi$
$557$	−12.5502	−0.531769	−0.265885	+	0.964005i	$0.585664\pi$
$558$	11.8521	0.501740
$559$	4.04142	0.170934
$560$	10.5641	0.446416
$561$	15.8991	0.671259
$562$	3.29521	0.139000
$563$	40.5116	1.70736	0.853681	−	0.520797i	$-0.174365\pi$
$563$	40.5116	1.70736	0.853681	+	0.520797i	$0.174365\pi$
$564$	6.25216	0.263263
$565$	10.7376	0.451734
$566$	−34.7263	−1.45966
$567$	−1.00000	−0.0419961
$568$	−1.58297	−0.0664199
$569$	18.0129	0.755140	0.377570	−	0.925981i	$-0.376760\pi$
$569$	18.0129	0.755140	0.377570	+	0.925981i	$0.376760\pi$
$570$	−24.6118	−1.03087
$571$	8.66182	0.362486	0.181243	−	0.983438i	$-0.441988\pi$
$571$	8.66182	0.362486	0.181243	+	0.983438i	$0.441988\pi$
$572$	3.82329	0.159860
$573$	−9.95956	−0.416067
$574$	−3.34635	−0.139674
$575$	−0.0892553	−0.00372220
$576$	0.0663335	0.00276390
$577$	26.1717	1.08954	0.544772	−	0.838584i	$-0.316616\pi$
$577$	26.1717	1.08954	0.544772	+	0.838584i	$0.316616\pi$
$578$	15.7069	0.653320
$579$	9.41311	0.391196
$580$	4.35506	0.180834
$581$	6.05119	0.251046
$582$	−5.16486	−0.214090
$583$	28.7407	1.19032
$584$	4.56198	0.188776
$585$	−1.31274	−0.0542751
$586$	4.10556	0.169599
$587$	−16.8830	−0.696835	−0.348418	−	0.937339i	$-0.613281\pi$
$587$	−16.8830	−0.696835	−0.348418	+	0.937339i	$0.613281\pi$
$588$	−1.10269	−0.0454741
$589$	44.4037	1.82962
$590$	10.5137	0.432841
$591$	0.151937	0.00624987
$592$	27.2725	1.12089
$593$	−9.88785	−0.406045	−0.203023	−	0.979174i	$-0.565077\pi$
$593$	−9.88785	−0.406045	−0.203023	+	0.979174i	$0.565077\pi$
$594$	−9.85043	−0.404168
$595$	−6.01958	−0.246779
$596$	13.4141	0.549462
$597$	20.4642	0.837544
$598$	0.188517	0.00770905
$599$	26.1682	1.06920	0.534602	−	0.845104i	$-0.320462\pi$
$599$	26.1682	1.06920	0.534602	+	0.845104i	$0.320462\pi$
$600$	0.817262	0.0333646
$601$	−11.0326	−0.450029	−0.225015	−	0.974355i	$-0.572243\pi$
$601$	−11.0326	−0.450029	−0.225015	+	0.974355i	$0.572243\pi$
$602$	−11.4817	−0.467958
$603$	−9.71293	−0.395541
$604$	−10.0731	−0.409870
$605$	42.9243	1.74512
$606$	12.3533	0.501819
$607$	−40.1650	−1.63025	−0.815123	−	0.579288i	$-0.803331\pi$
$607$	−40.1650	−1.63025	−0.815123	+	0.579288i	$0.803331\pi$
$608$	−37.1373	−1.50611
$609$	1.86535	0.0755878
$610$	−48.2179	−1.95229
$611$	3.51540	0.142218
$612$	3.13501	0.126725
$613$	41.9945	1.69614	0.848071	−	0.529883i	$-0.177764\pi$
$613$	41.9945	1.69614	0.848071	+	0.529883i	$0.177764\pi$
$614$	3.72355	0.150270
$615$	4.02238	0.162198
$616$	8.83890	0.356129
$617$	4.58977	0.184777	0.0923886	−	0.995723i	$-0.470550\pi$
$617$	4.58977	0.184777	0.0923886	+	0.995723i	$0.470550\pi$
$618$	−21.6317	−0.870155
$619$	6.90148	0.277394	0.138697	−	0.990335i	$-0.455709\pi$
$619$	6.90148	0.277394	0.138697	+	0.990335i	$0.455709\pi$
$620$	−15.7095	−0.630907
$621$	−0.172617	−0.00692690
$622$	−6.82398	−0.273617
$623$	−2.23886	−0.0896981
$624$	−3.09351	−0.123839
$625$	−22.1473	−0.885891
$626$	6.73755	0.269287
$627$	−36.9044	−1.47382
$628$	2.89934	0.115696
$629$	−15.5402	−0.619630
$630$	3.72950	0.148587
$631$	35.3485	1.40720	0.703601	−	0.710596i	$-0.251574\pi$
$631$	35.3485	1.40720	0.703601	+	0.710596i	$0.251574\pi$
$632$	8.67852	0.345213
$633$	−12.1507	−0.482948
$634$	36.0954	1.43353
$635$	43.0785	1.70952
$636$	5.66715	0.224717
$637$	−0.620009	−0.0245656
$638$	18.3745	0.727454
$639$	−1.00152	−0.0396196
$640$	−24.0776	−0.951752
$641$	2.23745	0.0883739	0.0441869	−	0.999023i	$-0.485930\pi$
$641$	2.23745	0.0883739	0.0441869	+	0.999023i	$0.485930\pi$
$642$	−1.83561	−0.0724456
$643$	−41.2542	−1.62691	−0.813453	−	0.581630i	$-0.802415\pi$
$643$	−41.2542	−1.62691	−0.813453	+	0.581630i	$0.802415\pi$
$644$	−0.190343	−0.00750058
$645$	13.8012	0.543422
$646$	33.0481	1.30026
$647$	24.4177	0.959961	0.479980	−	0.877279i	$-0.340644\pi$
$647$	24.4177	0.959961	0.479980	+	0.877279i	$0.340644\pi$
$648$	1.58056	0.0620904
$649$	15.7649	0.618825
$650$	−0.564698	−0.0221493
$651$	−6.72864	−0.263716
$652$	22.7384	0.890504
$653$	30.2303	1.18300	0.591501	−	0.806304i	$-0.298536\pi$
$653$	30.2303	1.18300	0.591501	+	0.806304i	$0.298536\pi$
$654$	21.1714	0.827868
$655$	6.68171	0.261076
$656$	9.47883	0.370086
$657$	2.88630	0.112605
$658$	−9.98725	−0.389343
$659$	−5.02919	−0.195909	−0.0979547	−	0.995191i	$-0.531230\pi$
$659$	−5.02919	−0.195909	−0.0979547	+	0.995191i	$0.531230\pi$
$660$	13.0563	0.508216
$661$	25.0005	0.972408	0.486204	−	0.873845i	$-0.338381\pi$
$661$	25.0005	0.972408	0.486204	+	0.873845i	$0.338381\pi$
$662$	−52.1063	−2.02517
$663$	1.76272	0.0684583
$664$	−9.56429	−0.371166
$665$	13.9725	0.541829
$666$	9.62812	0.373082
$667$	0.321992	0.0124676
$668$	23.4072	0.905650
$669$	−15.1931	−0.587400
$670$	36.2243	1.39947
$671$	−72.3010	−2.79115
$672$	5.62752	0.217086
$673$	20.9294	0.806767	0.403384	−	0.915031i	$-0.367834\pi$
$673$	20.9294	0.806767	0.403384	+	0.915031i	$0.367834\pi$
$674$	−26.0217	−1.00232
$675$	0.517070	0.0199020
$676$	−13.9111	−0.535041
$677$	44.0496	1.69296	0.846482	−	0.532417i	$-0.178716\pi$
$677$	44.0496	1.69296	0.846482	+	0.532417i	$0.178716\pi$
$678$	8.93296	0.343068
$679$	2.93217	0.112526
$680$	9.51433	0.364858
$681$	9.90965	0.379739
$682$	−66.2800	−2.53799
$683$	−13.6804	−0.523467	−0.261734	−	0.965140i	$-0.584294\pi$
$683$	−13.6804	−0.523467	−0.261734	+	0.965140i	$0.584294\pi$
$684$	−7.27689	−0.278239
$685$	−2.70858	−0.103489
$686$	1.76145	0.0672523
$687$	8.89081	0.339205
$688$	32.5229	1.23992
$689$	3.18646	0.121395
$690$	0.643776	0.0245081
$691$	24.8638	0.945864	0.472932	−	0.881099i	$-0.343196\pi$
$691$	24.8638	0.945864	0.472932	+	0.881099i	$0.343196\pi$
$692$	20.7861	0.790168
$693$	5.59224	0.212432
$694$	−6.26734	−0.237905
$695$	18.7799	0.712364
$696$	−2.94830	−0.111755
$697$	−5.40116	−0.204583
$698$	−17.6307	−0.667331
$699$	14.9273	0.564604
$700$	0.570168	0.0215503
$701$	−44.1252	−1.66658	−0.833292	−	0.552833i	$-0.813547\pi$
$701$	−44.1252	−1.66658	−0.833292	+	0.552833i	$0.813547\pi$
$702$	−1.09211	−0.0412191
$703$	36.0715	1.36046
$704$	−0.370953	−0.0139808
$705$	12.0049	0.452130
$706$	51.0702	1.92205
$707$	−7.01317	−0.263757
$708$	3.10855	0.116826
$709$	34.1159	1.28125	0.640625	−	0.767854i	$-0.278676\pi$
$709$	34.1159	1.28125	0.640625	+	0.767854i	$0.278676\pi$
$710$	3.73517	0.140179
$711$	5.49077	0.205920
$712$	3.53866	0.132617
$713$	−1.16148	−0.0434978
$714$	−5.00789	−0.187415
$715$	7.34116	0.274544
$716$	−4.12339	−0.154098
$717$	12.9184	0.482445
$718$	33.6277	1.25498
$719$	30.3023	1.13009	0.565043	−	0.825062i	$-0.308860\pi$
$719$	30.3023	1.13009	0.565043	+	0.825062i	$0.308860\pi$
$720$	−10.5641	−0.393702
$721$	12.2807	0.457355
$722$	−43.2429	−1.60933
$723$	−8.36403	−0.311062
$724$	−7.12523	−0.264807
$725$	−0.964517	−0.0358213
$726$	35.7101	1.32533
$727$	15.6335	0.579815	0.289907	−	0.957055i	$-0.406376\pi$
$727$	15.6335	0.579815	0.289907	+	0.957055i	$0.406376\pi$
$728$	0.979963	0.0363199
$729$	1.00000	0.0370370
$730$	−10.7644	−0.398410
$731$	−18.5320	−0.685430
$732$	−14.2565	−0.526934
$733$	22.3005	0.823686	0.411843	−	0.911255i	$-0.364885\pi$
$733$	22.3005	0.823686	0.411843	+	0.911255i	$0.364885\pi$
$734$	−30.0520	−1.10924
$735$	−2.11729	−0.0780975
$736$	0.971409	0.0358066
$737$	54.3171	2.00080
$738$	3.34635	0.123181
$739$	−8.01328	−0.294773	−0.147387	−	0.989079i	$-0.547086\pi$
$739$	−8.01328	−0.294773	−0.147387	+	0.989079i	$0.547086\pi$
$740$	−12.7616	−0.469127
$741$	−4.09157	−0.150308
$742$	−9.05275	−0.332337
$743$	12.0434	0.441828	0.220914	−	0.975293i	$-0.429096\pi$
$743$	12.0434	0.441828	0.220914	+	0.975293i	$0.429096\pi$
$744$	10.6350	0.389899
$745$	25.7566	0.943648
$746$	−44.3152	−1.62250
$747$	−6.05119	−0.221401
$748$	−17.5317	−0.641023
$749$	1.04210	0.0380776
$750$	−20.5759	−0.751325
$751$	31.1198	1.13558	0.567788	−	0.823175i	$-0.307799\pi$
$751$	31.1198	1.13558	0.567788	+	0.823175i	$0.307799\pi$
$752$	28.2898	1.03162
$753$	−3.51251	−0.128003
$754$	2.03717	0.0741894
$755$	−19.3416	−0.703912
$756$	1.10269	0.0401044
$757$	41.8416	1.52076	0.760380	−	0.649479i	$-0.225013\pi$
$757$	41.8416	1.52076	0.760380	+	0.649479i	$0.225013\pi$
$758$	−34.1842	−1.24162
$759$	0.965319	0.0350388
$760$	−22.0844	−0.801085
$761$	−17.2538	−0.625448	−0.312724	−	0.949844i	$-0.601241\pi$
$761$	−17.2538	−0.625448	−0.312724	+	0.949844i	$0.601241\pi$
$762$	35.8384	1.29829
$763$	−12.0193	−0.435129
$764$	10.9823	0.397326
$765$	6.01958	0.217638
$766$	−1.76145	−0.0636436
$767$	1.74784	0.0631109
$768$	−19.8983	−0.718018
$769$	5.73855	0.206937	0.103469	−	0.994633i	$-0.467006\pi$
$769$	5.73855	0.206937	0.103469	+	0.994633i	$0.467006\pi$
$770$	−20.8563	−0.751607
$771$	−7.04945	−0.253880
$772$	−10.3797	−0.373575
$773$	−5.86340	−0.210892	−0.105446	−	0.994425i	$-0.533627\pi$
$773$	−5.86340	−0.210892	−0.105446	+	0.994425i	$0.533627\pi$
$774$	11.4817	0.412700
$775$	3.47918	0.124976
$776$	−4.63448	−0.166368
$777$	−5.46603	−0.196093
$778$	49.5107	1.77504
$779$	12.5370	0.449185
$780$	1.44754	0.0518304
$781$	5.60076	0.200411
$782$	−0.864448	−0.0309126
$783$	−1.86535	−0.0666622
$784$	−4.98945	−0.178195
$785$	5.56707	0.198697
$786$	5.55873	0.198273
$787$	−47.9507	−1.70926	−0.854629	−	0.519239i	$-0.826215\pi$
$787$	−47.9507	−1.70926	−0.854629	+	0.519239i	$0.826215\pi$
$788$	−0.167540	−0.00596835
$789$	15.1315	0.538696
$790$	−20.4778	−0.728568
$791$	−5.07138	−0.180317
$792$	−8.83890	−0.314077
$793$	−8.01597	−0.284655
$794$	39.4106	1.39863
$795$	10.8816	0.385930
$796$	−22.5657	−0.799819
$797$	−10.5285	−0.372938	−0.186469	−	0.982461i	$-0.559704\pi$
$797$	−10.5285	−0.372938	−0.186469	+	0.982461i	$0.559704\pi$
$798$	11.6242	0.411491
$799$	−16.1199	−0.570280
$800$	−2.90983	−0.102878
$801$	2.23886	0.0791063
$802$	4.94815	0.174725
$803$	−16.1409	−0.569600
$804$	10.7103	0.377725
$805$	−0.365482	−0.0128815
$806$	−7.34842	−0.258837
$807$	12.4002	0.436507
$808$	11.0848	0.389961
$809$	−46.0372	−1.61858	−0.809290	−	0.587409i	$-0.800148\pi$
$809$	−46.0372	−1.61858	−0.809290	+	0.587409i	$0.800148\pi$
$810$	−3.72950	−0.131041
$811$	28.9743	1.01742	0.508712	−	0.860937i	$-0.330122\pi$
$811$	28.9743	1.01742	0.508712	+	0.860937i	$0.330122\pi$
$812$	−2.05690	−0.0721831
$813$	16.1477	0.566323
$814$	−53.8428	−1.88719
$815$	43.6604	1.52936
$816$	14.1853	0.496585
$817$	43.0159	1.50494
$818$	8.78150	0.307038
$819$	0.620009	0.0216649
$820$	−4.43543	−0.154892
$821$	−3.16372	−0.110415	−0.0552074	−	0.998475i	$-0.517582\pi$
$821$	−3.16372	−0.110415	−0.0552074	+	0.998475i	$0.517582\pi$
$822$	−2.25336	−0.0785948
$823$	−25.2770	−0.881099	−0.440550	−	0.897728i	$-0.645216\pi$
$823$	−25.2770	−0.881099	−0.440550	+	0.897728i	$0.645216\pi$
$824$	−19.4104	−0.676192
$825$	−2.89158	−0.100672
$826$	−4.96562	−0.172776
$827$	−12.7854	−0.444591	−0.222295	−	0.974979i	$-0.571355\pi$
$827$	−12.7854	−0.444591	−0.222295	+	0.974979i	$0.571355\pi$
$828$	0.190343	0.00661489
$829$	−22.1935	−0.770813	−0.385407	−	0.922747i	$-0.625939\pi$
$829$	−22.1935	−0.770813	−0.385407	+	0.922747i	$0.625939\pi$
$830$	22.5679	0.783343
$831$	10.0406	0.348303
$832$	−0.0411273	−0.00142583
$833$	2.84305	0.0985060
$834$	15.6236	0.541003
$835$	44.9445	1.55537
$836$	40.6941	1.40744
$837$	6.72864	0.232576
$838$	−67.5711	−2.33420
$839$	−48.2691	−1.66643	−0.833217	−	0.552946i	$-0.813504\pi$
$839$	−48.2691	−1.66643	−0.833217	+	0.552946i	$0.813504\pi$
$840$	3.34652	0.115466
$841$	−25.5205	−0.880016
$842$	25.6652	0.884480
$843$	1.87074	0.0644319
$844$	13.3985	0.461194
$845$	−26.7109	−0.918883
$846$	9.98725	0.343369
$847$	−20.2732	−0.696595
$848$	25.6427	0.880575
$849$	−19.7147	−0.676606
$850$	2.58943	0.0888167
$851$	−0.943532	−0.0323439
$852$	1.10437	0.0378350
$853$	47.1217	1.61342	0.806708	−	0.590950i	$-0.201247\pi$
$853$	47.1217	1.61342	0.806708	+	0.590950i	$0.201247\pi$
$854$	22.7734	0.779289
$855$	−13.9725	−0.477849
$856$	−1.64711	−0.0562971
$857$	51.8046	1.76961	0.884805	−	0.465961i	$-0.154291\pi$
$857$	51.8046	1.76961	0.884805	+	0.465961i	$0.154291\pi$
$858$	6.10735	0.208502
$859$	12.3810	0.422434	0.211217	−	0.977439i	$-0.432257\pi$
$859$	12.3810	0.422434	0.211217	+	0.977439i	$0.432257\pi$
$860$	−15.2185	−0.518945
$861$	−1.89977	−0.0647441
$862$	56.3881	1.92059
$863$	−2.06243	−0.0702061	−0.0351030	−	0.999384i	$-0.511176\pi$
$863$	−2.06243	−0.0702061	−0.0351030	+	0.999384i	$0.511176\pi$
$864$	−5.62752	−0.191452
$865$	39.9117	1.35704
$866$	55.7057	1.89296
$867$	8.91704	0.302839
$868$	7.41960	0.251837
$869$	−30.7057	−1.04162
$870$	6.95682	0.235858
$871$	6.02210	0.204051
$872$	18.9973	0.643331
$873$	−2.93217	−0.0992389
$874$	2.00653	0.0678720
$875$	11.6813	0.394898
$876$	−3.18269	−0.107533
$877$	−51.6456	−1.74395	−0.871974	−	0.489551i	$-0.837161\pi$
$877$	−51.6456	−1.74395	−0.871974	+	0.489551i	$0.837161\pi$
$878$	−28.6962	−0.968450
$879$	2.33079	0.0786156
$880$	59.0772	1.99149
$881$	−32.1538	−1.08329	−0.541644	−	0.840608i	$-0.682198\pi$
$881$	−32.1538	−1.08329	−0.541644	+	0.840608i	$0.682198\pi$
$882$	−1.76145	−0.0593109
$883$	8.04647	0.270785	0.135393	−	0.990792i	$-0.456770\pi$
$883$	8.04647	0.270785	0.135393	+	0.990792i	$0.456770\pi$
$884$	−1.94373	−0.0653748
$885$	5.96877	0.200638
$886$	−32.8401	−1.10329
$887$	44.5505	1.49586	0.747930	−	0.663777i	$-0.231048\pi$
$887$	44.5505	1.49586	0.747930	+	0.663777i	$0.231048\pi$
$888$	8.63941	0.289920
$889$	−20.3460	−0.682384
$890$	−8.34983	−0.279887
$891$	−5.59224	−0.187347
$892$	16.7533	0.560942
$893$	37.4170	1.25211
$894$	21.4277	0.716651
$895$	−7.91739	−0.264649
$896$	11.3719	0.379908
$897$	0.107024	0.00357344
$898$	12.6899	0.423466
$899$	−12.5513	−0.418608
$900$	−0.570168	−0.0190056
$901$	−14.6116	−0.486782
$902$	−18.7136	−0.623094
$903$	−6.51833	−0.216916
$904$	8.01564	0.266596
$905$	−13.6813	−0.454781
$906$	−16.0909	−0.534584
$907$	−22.9085	−0.760663	−0.380332	−	0.924850i	$-0.624190\pi$
$907$	−22.9085	−0.760663	−0.380332	+	0.924850i	$0.624190\pi$
$908$	−10.9273	−0.362634
$909$	7.01317	0.232612
$910$	−2.31232	−0.0766527
$911$	−6.28991	−0.208394	−0.104197	−	0.994557i	$-0.533227\pi$
$911$	−6.28991	−0.208394	−0.104197	+	0.994557i	$0.533227\pi$
$912$	−32.9265	−1.09031
$913$	33.8397	1.11993
$914$	−36.3942	−1.20381
$915$	−27.3741	−0.904958
$916$	−9.80380	−0.323927
$917$	−3.15578	−0.104213
$918$	5.00789	0.165285
$919$	−23.8045	−0.785237	−0.392619	−	0.919701i	$-0.628431\pi$
$919$	−23.8045	−0.785237	−0.392619	+	0.919701i	$0.628431\pi$
$920$	0.577667	0.0190451
$921$	2.11392	0.0696559
$922$	19.9014	0.655419
$923$	0.620953	0.0204389
$924$	−6.16651	−0.202863
$925$	2.82632	0.0929289
$926$	−56.9677	−1.87208
$927$	−12.2807	−0.403350
$928$	10.4973	0.344591
$929$	1.23918	0.0406561	0.0203281	−	0.999793i	$-0.493529\pi$
$929$	1.23918	0.0406561	0.0203281	+	0.999793i	$0.493529\pi$
$930$	−25.0944	−0.822878
$931$	−6.59922	−0.216281
$932$	−16.4602	−0.539172
$933$	−3.87408	−0.126832
$934$	54.9871	1.79923
$935$	−33.6630	−1.10090
$936$	−0.979963	−0.0320311
$937$	−2.41985	−0.0790531	−0.0395265	−	0.999219i	$-0.512585\pi$
$937$	−2.41985	−0.0790531	−0.0395265	+	0.999219i	$0.512585\pi$
$938$	−17.1088	−0.558622
$939$	3.82501	0.124825
$940$	−13.2376	−0.431764
$941$	12.7349	0.415147	0.207573	−	0.978219i	$-0.433443\pi$
$941$	12.7349	0.415147	0.207573	+	0.978219i	$0.433443\pi$
$942$	4.63142	0.150900
$943$	−0.327934	−0.0106790
$944$	14.0656	0.457795
$945$	2.11729	0.0688755
$946$	−64.2084	−2.08759
$947$	23.8035	0.773511	0.386755	−	0.922182i	$-0.373596\pi$
$947$	23.8035	0.773511	0.386755	+	0.922182i	$0.373596\pi$
$948$	−6.05462	−0.196645
$949$	−1.78953	−0.0580906
$950$	−6.01051	−0.195007
$951$	20.4919	0.664496
$952$	−4.49363	−0.145639
$953$	−27.1236	−0.878620	−0.439310	−	0.898335i	$-0.644777\pi$
$953$	−27.1236	−0.878620	−0.439310	+	0.898335i	$0.644777\pi$
$954$	9.05275	0.293093
$955$	21.0873	0.682369
$956$	−14.2449	−0.460714
$957$	10.4315	0.337202
$958$	0.265673	0.00858349
$959$	1.27927	0.0413096
$960$	−0.140447	−0.00453292
$961$	14.2745	0.460469
$962$	−5.96952	−0.192465
$963$	−1.04210	−0.0335813
$964$	9.22293	0.297050
$965$	−19.9303	−0.641579
$966$	−0.304056	−0.00978284
$967$	−0.0503401	−0.00161883	−0.000809414	−	1.00000i	$-0.500258\pi$
$967$	−0.0503401	−0.00161883	−0.000809414		1.00000i	$0.500258\pi$
$968$	32.0431	1.02990
$969$	18.7619	0.602720
$970$	10.9355	0.351118
$971$	52.9415	1.69897	0.849487	−	0.527610i	$-0.176912\pi$
$971$	52.9415	1.69897	0.849487	+	0.527610i	$0.176912\pi$
$972$	−1.10269	−0.0353688
$973$	−8.86979	−0.284352
$974$	−37.3196	−1.19580
$975$	−0.320588	−0.0102670
$976$	−64.5077	−2.06484
$977$	29.3821	0.940015	0.470008	−	0.882662i	$-0.344251\pi$
$977$	29.3821	0.940015	0.470008	+	0.882662i	$0.344251\pi$
$978$	36.3225	1.16146
$979$	−12.5203	−0.400149
$980$	2.33472	0.0745798
$981$	12.0193	0.383748
$982$	−36.5636	−1.16679
$983$	−3.49669	−0.111527	−0.0557635	−	0.998444i	$-0.517759\pi$
$983$	−3.49669	−0.111527	−0.0557635	+	0.998444i	$0.517759\pi$
$984$	3.00271	0.0957229
$985$	−0.321696	−0.0102501
$986$	−9.34146	−0.297493
$987$	−5.66992	−0.180475
$988$	4.51173	0.143537
$989$	−1.12518	−0.0357786
$990$	20.8563	0.662855
$991$	−9.33811	−0.296635	−0.148317	−	0.988940i	$-0.547386\pi$
$991$	−9.33811	−0.296635	−0.148317	+	0.988940i	$0.547386\pi$
$992$	−37.8656	−1.20223
$993$	−29.5816	−0.938743
$994$	−1.76413	−0.0559547
$995$	−43.3287	−1.37361
$996$	6.67258	0.211429
$997$	52.2385	1.65441	0.827205	−	0.561900i	$-0.189929\pi$
$997$	52.2385	1.65441	0.827205	+	0.561900i	$0.189929\pi$
$998$	−8.54799	−0.270582
$999$	5.46603	0.172938

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.12	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.12	✓	50	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)

\(f(q)\)	\(=\)	\(q-1.76145 q^{2} -1.00000 q^{3} +1.10269 q^{4} +2.11729 q^{5} +1.76145 q^{6} -1.00000 q^{7} +1.58056 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.76145 q^{2} -1.00000 q^{3} +1.10269 q^{4} +2.11729 q^{5} +1.76145 q^{6} -1.00000 q^{7} +1.58056 q^{8} +1.00000 q^{9} -3.72950 q^{10} -5.59224 q^{11} -1.10269 q^{12} -0.620009 q^{13} +1.76145 q^{14} -2.11729 q^{15} -4.98945 q^{16} +2.84305 q^{17} -1.76145 q^{18} -6.59922 q^{19} +2.33472 q^{20} +1.00000 q^{21} +9.85043 q^{22} +0.172617 q^{23} -1.58056 q^{24} -0.517070 q^{25} +1.09211 q^{26} -1.00000 q^{27} -1.10269 q^{28} +1.86535 q^{29} +3.72950 q^{30} -6.72864 q^{31} +5.62752 q^{32} +5.59224 q^{33} -5.00789 q^{34} -2.11729 q^{35} +1.10269 q^{36} -5.46603 q^{37} +11.6242 q^{38} +0.620009 q^{39} +3.34652 q^{40} -1.89977 q^{41} -1.76145 q^{42} -6.51833 q^{43} -6.16651 q^{44} +2.11729 q^{45} -0.304056 q^{46} -5.66992 q^{47} +4.98945 q^{48} +1.00000 q^{49} +0.910791 q^{50} -2.84305 q^{51} -0.683677 q^{52} -5.13939 q^{53} +1.76145 q^{54} -11.8404 q^{55} -1.58056 q^{56} +6.59922 q^{57} -3.28571 q^{58} -2.81906 q^{59} -2.33472 q^{60} +12.9288 q^{61} +11.8521 q^{62} -1.00000 q^{63} +0.0663335 q^{64} -1.31274 q^{65} -9.85043 q^{66} -9.71293 q^{67} +3.13501 q^{68} -0.172617 q^{69} +3.72950 q^{70} -1.00152 q^{71} +1.58056 q^{72} +2.88630 q^{73} +9.62812 q^{74} +0.517070 q^{75} -7.27689 q^{76} +5.59224 q^{77} -1.09211 q^{78} +5.49077 q^{79} -10.5641 q^{80} +1.00000 q^{81} +3.34635 q^{82} -6.05119 q^{83} +1.10269 q^{84} +6.01958 q^{85} +11.4817 q^{86} -1.86535 q^{87} -8.83890 q^{88} +2.23886 q^{89} -3.72950 q^{90} +0.620009 q^{91} +0.190343 q^{92} +6.72864 q^{93} +9.98725 q^{94} -13.9725 q^{95} -5.62752 q^{96} -2.93217 q^{97} -1.76145 q^{98} -5.59224 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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