LMFDB - Embedded newform 6046.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.39212 q^{3} +1.00000 q^{4} +0.456785 q^{5} -2.39212 q^{6} +2.48835 q^{7} +1.00000 q^{8} +2.72224 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.39212 q^{3} +1.00000 q^{4} +0.456785 q^{5} -2.39212 q^{6} +2.48835 q^{7} +1.00000 q^{8} +2.72224 q^{9} +0.456785 q^{10} +3.87286 q^{11} -2.39212 q^{12} +2.59377 q^{13} +2.48835 q^{14} -1.09268 q^{15} +1.00000 q^{16} -4.33216 q^{17} +2.72224 q^{18} -5.74783 q^{19} +0.456785 q^{20} -5.95243 q^{21} +3.87286 q^{22} -3.13811 q^{23} -2.39212 q^{24} -4.79135 q^{25} +2.59377 q^{26} +0.664434 q^{27} +2.48835 q^{28} +0.113889 q^{29} -1.09268 q^{30} -6.37388 q^{31} +1.00000 q^{32} -9.26436 q^{33} -4.33216 q^{34} +1.13664 q^{35} +2.72224 q^{36} -6.01041 q^{37} -5.74783 q^{38} -6.20460 q^{39} +0.456785 q^{40} -11.0620 q^{41} -5.95243 q^{42} -3.11355 q^{43} +3.87286 q^{44} +1.24348 q^{45} -3.13811 q^{46} +2.76183 q^{47} -2.39212 q^{48} -0.808114 q^{49} -4.79135 q^{50} +10.3630 q^{51} +2.59377 q^{52} +2.15175 q^{53} +0.664434 q^{54} +1.76907 q^{55} +2.48835 q^{56} +13.7495 q^{57} +0.113889 q^{58} +9.32436 q^{59} -1.09268 q^{60} -0.683978 q^{61} -6.37388 q^{62} +6.77389 q^{63} +1.00000 q^{64} +1.18479 q^{65} -9.26436 q^{66} -15.6558 q^{67} -4.33216 q^{68} +7.50673 q^{69} +1.13664 q^{70} -1.93992 q^{71} +2.72224 q^{72} -4.27673 q^{73} -6.01041 q^{74} +11.4615 q^{75} -5.74783 q^{76} +9.63704 q^{77} -6.20460 q^{78} -15.3512 q^{79} +0.456785 q^{80} -9.75613 q^{81} -11.0620 q^{82} +5.53887 q^{83} -5.95243 q^{84} -1.97886 q^{85} -3.11355 q^{86} -0.272436 q^{87} +3.87286 q^{88} +1.67683 q^{89} +1.24348 q^{90} +6.45420 q^{91} -3.13811 q^{92} +15.2471 q^{93} +2.76183 q^{94} -2.62552 q^{95} -2.39212 q^{96} +16.7786 q^{97} -0.808114 q^{98} +10.5429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.39212	−1.38109	−0.690546	−	0.723289i	$-0.742630\pi$
$3$	−2.39212	−1.38109	−0.690546	+	0.723289i	$0.742630\pi$
$4$	1.00000	0.500000
$5$	0.456785	0.204280	0.102140	−	0.994770i	$-0.467431\pi$
$5$	0.456785	0.204280	0.102140	+	0.994770i	$0.467431\pi$
$6$	−2.39212	−0.976579
$7$	2.48835	0.940508	0.470254	−	0.882531i	$-0.344162\pi$
$7$	2.48835	0.940508	0.470254	+	0.882531i	$0.344162\pi$
$8$	1.00000	0.353553
$9$	2.72224	0.907414
$10$	0.456785	0.144448
$11$	3.87286	1.16771	0.583856	−	0.811857i	$-0.301543\pi$
$11$	3.87286	1.16771	0.583856	+	0.811857i	$0.301543\pi$
$12$	−2.39212	−0.690546
$13$	2.59377	0.719381	0.359691	−	0.933072i	$-0.382882\pi$
$13$	2.59377	0.719381	0.359691	+	0.933072i	$0.382882\pi$
$14$	2.48835	0.665040
$15$	−1.09268	−0.282130
$16$	1.00000	0.250000
$17$	−4.33216	−1.05070	−0.525351	−	0.850885i	$-0.676066\pi$
$17$	−4.33216	−1.05070	−0.525351	+	0.850885i	$0.676066\pi$
$18$	2.72224	0.641638
$19$	−5.74783	−1.31864	−0.659321	−	0.751861i	$-0.729156\pi$
$19$	−5.74783	−1.31864	−0.659321	+	0.751861i	$0.729156\pi$
$20$	0.456785	0.102140
$21$	−5.95243	−1.29893
$22$	3.87286	0.825698
$23$	−3.13811	−0.654340	−0.327170	−	0.944965i	$-0.606095\pi$
$23$	−3.13811	−0.654340	−0.327170	+	0.944965i	$0.606095\pi$
$24$	−2.39212	−0.488290
$25$	−4.79135	−0.958270
$26$	2.59377	0.508679
$27$	0.664434	0.127870
$28$	2.48835	0.470254
$29$	0.113889	0.0211486	0.0105743	−	0.999944i	$-0.496634\pi$
$29$	0.113889	0.0211486	0.0105743	+	0.999944i	$0.496634\pi$
$30$	−1.09268	−0.199496
$31$	−6.37388	−1.14478	−0.572391	−	0.819981i	$-0.693984\pi$
$31$	−6.37388	−1.14478	−0.572391	+	0.819981i	$0.693984\pi$
$32$	1.00000	0.176777
$33$	−9.26436	−1.61272
$34$	−4.33216	−0.742959
$35$	1.13664	0.192127
$36$	2.72224	0.453707
$37$	−6.01041	−0.988106	−0.494053	−	0.869432i	$-0.664485\pi$
$37$	−6.01041	−0.988106	−0.494053	+	0.869432i	$0.664485\pi$
$38$	−5.74783	−0.932421
$39$	−6.20460	−0.993532
$40$	0.456785	0.0722240
$41$	−11.0620	−1.72759	−0.863796	−	0.503841i	$-0.831920\pi$
$41$	−11.0620	−1.72759	−0.863796	+	0.503841i	$0.831920\pi$
$42$	−5.95243	−0.918480
$43$	−3.11355	−0.474811	−0.237406	−	0.971411i	$-0.576297\pi$
$43$	−3.11355	−0.474811	−0.237406	+	0.971411i	$0.576297\pi$
$44$	3.87286	0.583856
$45$	1.24348	0.185367
$46$	−3.13811	−0.462688
$47$	2.76183	0.402854	0.201427	−	0.979503i	$-0.435442\pi$
$47$	2.76183	0.402854	0.201427	+	0.979503i	$0.435442\pi$
$48$	−2.39212	−0.345273
$49$	−0.808114	−0.115445
$50$	−4.79135	−0.677599
$51$	10.3630	1.45112
$52$	2.59377	0.359691
$53$	2.15175	0.295566	0.147783	−	0.989020i	$-0.452786\pi$
$53$	2.15175	0.295566	0.147783	+	0.989020i	$0.452786\pi$
$54$	0.664434	0.0904180
$55$	1.76907	0.238541
$56$	2.48835	0.332520
$57$	13.7495	1.82117
$58$	0.113889	0.0149543
$59$	9.32436	1.21393	0.606964	−	0.794729i	$-0.292387\pi$
$59$	9.32436	1.21393	0.606964	+	0.794729i	$0.292387\pi$
$60$	−1.09268	−0.141065
$61$	−0.683978	−0.0875745	−0.0437872	−	0.999041i	$-0.513942\pi$
$61$	−0.683978	−0.0875745	−0.0437872	+	0.999041i	$0.513942\pi$
$62$	−6.37388	−0.809484
$63$	6.77389	0.853430
$64$	1.00000	0.125000
$65$	1.18479	0.146955
$66$	−9.26436	−1.14036
$67$	−15.6558	−1.91266	−0.956329	−	0.292293i	$-0.905582\pi$
$67$	−15.6558	−1.91266	−0.956329	+	0.292293i	$0.905582\pi$
$68$	−4.33216	−0.525351
$69$	7.50673	0.903704
$70$	1.13664	0.135855
$71$	−1.93992	−0.230226	−0.115113	−	0.993352i	$-0.536723\pi$
$71$	−1.93992	−0.230226	−0.115113	+	0.993352i	$0.536723\pi$
$72$	2.72224	0.320819
$73$	−4.27673	−0.500553	−0.250277	−	0.968174i	$-0.580522\pi$
$73$	−4.27673	−0.500553	−0.250277	+	0.968174i	$0.580522\pi$
$74$	−6.01041	−0.698696
$75$	11.4615	1.32346
$76$	−5.74783	−0.659321
$77$	9.63704	1.09824
$78$	−6.20460	−0.702533
$79$	−15.3512	−1.72714	−0.863571	−	0.504227i	$-0.831777\pi$
$79$	−15.3512	−1.72714	−0.863571	+	0.504227i	$0.831777\pi$
$80$	0.456785	0.0510701
$81$	−9.75613	−1.08401
$82$	−11.0620	−1.22159
$83$	5.53887	0.607970	0.303985	−	0.952677i	$-0.401683\pi$
$83$	5.53887	0.607970	0.303985	+	0.952677i	$0.401683\pi$
$84$	−5.95243	−0.649464
$85$	−1.97886	−0.214638
$86$	−3.11355	−0.335742
$87$	−0.272436	−0.0292082
$88$	3.87286	0.412849
$89$	1.67683	0.177744	0.0888718	−	0.996043i	$-0.471674\pi$
$89$	1.67683	0.177744	0.0888718	+	0.996043i	$0.471674\pi$
$90$	1.24348	0.131074
$91$	6.45420	0.676584
$92$	−3.13811	−0.327170
$93$	15.2471	1.58105
$94$	2.76183	0.284861
$95$	−2.62552	−0.269373
$96$	−2.39212	−0.244145
$97$	16.7786	1.70361	0.851806	−	0.523857i	$-0.175508\pi$
$97$	16.7786	1.70361	0.851806	+	0.523857i	$0.175508\pi$
$98$	−0.808114	−0.0816319
$99$	10.5429	1.05960
$100$	−4.79135	−0.479135
$101$	14.2061	1.41356	0.706778	−	0.707436i	$-0.250148\pi$
$101$	14.2061	1.41356	0.706778	+	0.707436i	$0.250148\pi$
$102$	10.3630	1.02609
$103$	−0.656887	−0.0647250	−0.0323625	−	0.999476i	$-0.510303\pi$
$103$	−0.656887	−0.0647250	−0.0323625	+	0.999476i	$0.510303\pi$
$104$	2.59377	0.254340
$105$	−2.71898	−0.265345
$106$	2.15175	0.208996
$107$	0.0629978	0.00609023	0.00304512	−	0.999995i	$-0.499031\pi$
$107$	0.0629978	0.00609023	0.00304512	+	0.999995i	$0.499031\pi$
$108$	0.664434	0.0639352
$109$	6.48599	0.621245	0.310623	−	0.950533i	$-0.399462\pi$
$109$	6.48599	0.621245	0.310623	+	0.950533i	$0.399462\pi$
$110$	1.76907	0.168674
$111$	14.3776	1.36466
$112$	2.48835	0.235127
$113$	−2.01225	−0.189296	−0.0946482	−	0.995511i	$-0.530173\pi$
$113$	−2.01225	−0.189296	−0.0946482	+	0.995511i	$0.530173\pi$
$114$	13.7495	1.28776
$115$	−1.43344	−0.133669
$116$	0.113889	0.0105743
$117$	7.06086	0.652776
$118$	9.32436	0.858377
$119$	−10.7799	−0.988194
$120$	−1.09268	−0.0997480
$121$	3.99908	0.363553
$122$	−0.683978	−0.0619245
$123$	26.4616	2.38596
$124$	−6.37388	−0.572391
$125$	−4.47254	−0.400036
$126$	6.77389	0.603466
$127$	−3.34619	−0.296926	−0.148463	−	0.988918i	$-0.547433\pi$
$127$	−3.34619	−0.296926	−0.148463	+	0.988918i	$0.547433\pi$
$128$	1.00000	0.0883883
$129$	7.44798	0.655758
$130$	1.18479	0.103913
$131$	2.52892	0.220953	0.110476	−	0.993879i	$-0.464762\pi$
$131$	2.52892	0.220953	0.110476	+	0.993879i	$0.464762\pi$
$132$	−9.26436	−0.806359
$133$	−14.3026	−1.24019
$134$	−15.6558	−1.35245
$135$	0.303503	0.0261214
$136$	−4.33216	−0.371479
$137$	−9.15418	−0.782094	−0.391047	−	0.920371i	$-0.627887\pi$
$137$	−9.15418	−0.782094	−0.391047	+	0.920371i	$0.627887\pi$
$138$	7.50673	0.639015
$139$	−5.98320	−0.507488	−0.253744	−	0.967271i	$-0.581662\pi$
$139$	−5.98320	−0.507488	−0.253744	+	0.967271i	$0.581662\pi$
$140$	1.13664	0.0960636
$141$	−6.60663	−0.556379
$142$	−1.93992	−0.162795
$143$	10.0453	0.840031
$144$	2.72224	0.226853
$145$	0.0520227	0.00432025
$146$	−4.27673	−0.353945
$147$	1.93311	0.159440
$148$	−6.01041	−0.494053
$149$	−11.1514	−0.913554	−0.456777	−	0.889581i	$-0.650996\pi$
$149$	−11.1514	−0.913554	−0.456777	+	0.889581i	$0.650996\pi$
$150$	11.4615	0.935826
$151$	15.2655	1.24229	0.621146	−	0.783695i	$-0.286667\pi$
$151$	15.2655	1.24229	0.621146	+	0.783695i	$0.286667\pi$
$152$	−5.74783	−0.466211
$153$	−11.7932	−0.953422
$154$	9.63704	0.776575
$155$	−2.91149	−0.233857
$156$	−6.20460	−0.496766
$157$	6.53510	0.521558	0.260779	−	0.965399i	$-0.416021\pi$
$157$	6.53510	0.521558	0.260779	+	0.965399i	$0.416021\pi$
$158$	−15.3512	−1.22127
$159$	−5.14724	−0.408203
$160$	0.456785	0.0361120
$161$	−7.80870	−0.615412
$162$	−9.75613	−0.766514
$163$	−18.0602	−1.41459	−0.707293	−	0.706920i	$-0.750084\pi$
$163$	−18.0602	−1.41459	−0.707293	+	0.706920i	$0.750084\pi$
$164$	−11.0620	−0.863796
$165$	−4.23182	−0.329447
$166$	5.53887	0.429900
$167$	−6.95796	−0.538423	−0.269211	−	0.963081i	$-0.586763\pi$
$167$	−6.95796	−0.538423	−0.269211	+	0.963081i	$0.586763\pi$
$168$	−5.95243	−0.459240
$169$	−6.27238	−0.482490
$170$	−1.97886	−0.151772
$171$	−15.6470	−1.19655
$172$	−3.11355	−0.237406
$173$	−11.6541	−0.886041	−0.443021	−	0.896511i	$-0.646093\pi$
$173$	−11.6541	−0.886041	−0.443021	+	0.896511i	$0.646093\pi$
$174$	−0.272436	−0.0206533
$175$	−11.9226	−0.901260
$176$	3.87286	0.291928
$177$	−22.3050	−1.67655
$178$	1.67683	0.125684
$179$	17.3498	1.29678	0.648391	−	0.761308i	$-0.275442\pi$
$179$	17.3498	1.29678	0.648391	+	0.761308i	$0.275442\pi$
$180$	1.24348	0.0926834
$181$	22.9468	1.70563	0.852813	−	0.522217i	$-0.174895\pi$
$181$	22.9468	1.70563	0.852813	+	0.522217i	$0.174895\pi$
$182$	6.45420	0.478417
$183$	1.63616	0.120948
$184$	−3.13811	−0.231344
$185$	−2.74547	−0.201851
$186$	15.2471	1.11797
$187$	−16.7779	−1.22692
$188$	2.76183	0.201427
$189$	1.65334	0.120263
$190$	−2.62552	−0.190475
$191$	−9.90372	−0.716608	−0.358304	−	0.933605i	$-0.616645\pi$
$191$	−9.90372	−0.716608	−0.358304	+	0.933605i	$0.616645\pi$
$192$	−2.39212	−0.172636
$193$	6.50897	0.468526	0.234263	−	0.972173i	$-0.424732\pi$
$193$	6.50897	0.468526	0.234263	+	0.972173i	$0.424732\pi$
$194$	16.7786	1.20464
$195$	−2.83417	−0.202959
$196$	−0.808114	−0.0577224
$197$	−19.7925	−1.41016	−0.705078	−	0.709130i	$-0.749088\pi$
$197$	−19.7925	−1.41016	−0.705078	+	0.709130i	$0.749088\pi$
$198$	10.5429	0.749249
$199$	6.44689	0.457008	0.228504	−	0.973543i	$-0.426617\pi$
$199$	6.44689	0.457008	0.228504	+	0.973543i	$0.426617\pi$
$200$	−4.79135	−0.338799
$201$	37.4505	2.64155
$202$	14.2061	0.999535
$203$	0.283395	0.0198904
$204$	10.3630	0.725558
$205$	−5.05295	−0.352913
$206$	−0.656887	−0.0457675
$207$	−8.54268	−0.593757
$208$	2.59377	0.179845
$209$	−22.2606	−1.53980
$210$	−2.71898	−0.187627
$211$	−1.97919	−0.136253	−0.0681264	−	0.997677i	$-0.521702\pi$
$211$	−1.97919	−0.136253	−0.0681264	+	0.997677i	$0.521702\pi$
$212$	2.15175	0.147783
$213$	4.64053	0.317964
$214$	0.0629978	0.00430644
$215$	−1.42222	−0.0969946
$216$	0.664434	0.0452090
$217$	−15.8604	−1.07668
$218$	6.48599	0.439287
$219$	10.2305	0.691310
$220$	1.76907	0.119270
$221$	−11.2366	−0.755856
$222$	14.3776	0.964964
$223$	−2.16105	−0.144714	−0.0723572	−	0.997379i	$-0.523052\pi$
$223$	−2.16105	−0.144714	−0.0723572	+	0.997379i	$0.523052\pi$
$224$	2.48835	0.166260
$225$	−13.0432	−0.869547
$226$	−2.01225	−0.133853
$227$	−24.3323	−1.61499	−0.807496	−	0.589873i	$-0.799178\pi$
$227$	−24.3323	−1.61499	−0.807496	+	0.589873i	$0.799178\pi$
$228$	13.7495	0.910583
$229$	7.34800	0.485569	0.242785	−	0.970080i	$-0.421939\pi$
$229$	7.34800	0.485569	0.242785	+	0.970080i	$0.421939\pi$
$230$	−1.43344	−0.0945181
$231$	−23.0530	−1.51677
$232$	0.113889	0.00747717
$233$	14.1309	0.925743	0.462872	−	0.886425i	$-0.346819\pi$
$233$	14.1309	0.925743	0.462872	+	0.886425i	$0.346819\pi$
$234$	7.06086	0.461583
$235$	1.26156	0.0822952
$236$	9.32436	0.606964
$237$	36.7219	2.38534
$238$	−10.7799	−0.698759
$239$	11.7456	0.759762	0.379881	−	0.925035i	$-0.375965\pi$
$239$	11.7456	0.759762	0.379881	+	0.925035i	$0.375965\pi$
$240$	−1.09268	−0.0705325
$241$	21.9604	1.41459	0.707297	−	0.706917i	$-0.249915\pi$
$241$	21.9604	1.41459	0.707297	+	0.706917i	$0.249915\pi$
$242$	3.99908	0.257071
$243$	21.3445	1.36925
$244$	−0.683978	−0.0437872
$245$	−0.369134	−0.0235831
$246$	26.4616	1.68713
$247$	−14.9085	−0.948607
$248$	−6.37388	−0.404742
$249$	−13.2497	−0.839663
$250$	−4.47254	−0.282868
$251$	−28.2480	−1.78300	−0.891498	−	0.453024i	$-0.850345\pi$
$251$	−28.2480	−1.78300	−0.891498	+	0.453024i	$0.850345\pi$
$252$	6.77389	0.426715
$253$	−12.1535	−0.764081
$254$	−3.34619	−0.209959
$255$	4.73368	0.296435
$256$	1.00000	0.0625000
$257$	1.19436	0.0745019	0.0372509	−	0.999306i	$-0.488140\pi$
$257$	1.19436	0.0745019	0.0372509	+	0.999306i	$0.488140\pi$
$258$	7.44798	0.463691
$259$	−14.9560	−0.929321
$260$	1.18479	0.0734777
$261$	0.310033	0.0191905
$262$	2.52892	0.156237
$263$	0.133066	0.00820520	0.00410260	−	0.999992i	$-0.498694\pi$
$263$	0.133066	0.00820520	0.00410260	+	0.999992i	$0.498694\pi$
$264$	−9.26436	−0.570182
$265$	0.982886	0.0603782
$266$	−14.3026	−0.876950
$267$	−4.01118	−0.245480
$268$	−15.6558	−0.956329
$269$	4.64131	0.282985	0.141493	−	0.989939i	$-0.454810\pi$
$269$	4.64131	0.282985	0.141493	+	0.989939i	$0.454810\pi$
$270$	0.303503	0.0184706
$271$	−8.71558	−0.529434	−0.264717	−	0.964326i	$-0.585279\pi$
$271$	−8.71558	−0.529434	−0.264717	+	0.964326i	$0.585279\pi$
$272$	−4.33216	−0.262676
$273$	−15.4392	−0.934424
$274$	−9.15418	−0.553024
$275$	−18.5562	−1.11898
$276$	7.50673	0.451852
$277$	1.80193	0.108268	0.0541338	−	0.998534i	$-0.482760\pi$
$277$	1.80193	0.108268	0.0541338	+	0.998534i	$0.482760\pi$
$278$	−5.98320	−0.358849
$279$	−17.3512	−1.03879
$280$	1.13664	0.0679273
$281$	6.05499	0.361211	0.180605	−	0.983556i	$-0.442194\pi$
$281$	6.05499	0.361211	0.180605	+	0.983556i	$0.442194\pi$
$282$	−6.60663	−0.393419
$283$	9.59314	0.570253	0.285126	−	0.958490i	$-0.407964\pi$
$283$	9.59314	0.570253	0.285126	+	0.958490i	$0.407964\pi$
$284$	−1.93992	−0.115113
$285$	6.28056	0.372028
$286$	10.0453	0.593991
$287$	−27.5261	−1.62481
$288$	2.72224	0.160410
$289$	1.76759	0.103976
$290$	0.0520227	0.00305488
$291$	−40.1365	−2.35284
$292$	−4.27673	−0.250277
$293$	−7.24866	−0.423471	−0.211736	−	0.977327i	$-0.567912\pi$
$293$	−7.24866	−0.423471	−0.211736	+	0.977327i	$0.567912\pi$
$294$	1.93311	0.112741
$295$	4.25923	0.247982
$296$	−6.01041	−0.349348
$297$	2.57326	0.149316
$298$	−11.1514	−0.645980
$299$	−8.13951	−0.470720
$300$	11.4615	0.661729
$301$	−7.74759	−0.446564
$302$	15.2655	0.878433
$303$	−33.9826	−1.95225
$304$	−5.74783	−0.329661
$305$	−0.312431	−0.0178897
$306$	−11.7932	−0.674171
$307$	−3.90912	−0.223105	−0.111553	−	0.993759i	$-0.535582\pi$
$307$	−3.90912	−0.223105	−0.111553	+	0.993759i	$0.535582\pi$
$308$	9.63704	0.549122
$309$	1.57135	0.0893911
$310$	−2.91149	−0.165362
$311$	0.822219	0.0466238	0.0233119	−	0.999728i	$-0.492579\pi$
$311$	0.822219	0.0466238	0.0233119	+	0.999728i	$0.492579\pi$
$312$	−6.20460	−0.351266
$313$	−8.18256	−0.462506	−0.231253	−	0.972894i	$-0.574282\pi$
$313$	−8.18256	−0.462506	−0.231253	+	0.972894i	$0.574282\pi$
$314$	6.53510	0.368797
$315$	3.09421	0.174339
$316$	−15.3512	−0.863571
$317$	−16.8186	−0.944629	−0.472315	−	0.881430i	$-0.656581\pi$
$317$	−16.8186	−0.944629	−0.472315	+	0.881430i	$0.656581\pi$
$318$	−5.14724	−0.288643
$319$	0.441076	0.0246955
$320$	0.456785	0.0255350
$321$	−0.150698	−0.00841117
$322$	−7.80870	−0.435162
$323$	24.9005	1.38550
$324$	−9.75613	−0.542007
$325$	−12.4276	−0.689361
$326$	−18.0602	−1.00026
$327$	−15.5153	−0.857997
$328$	−11.0620	−0.610796
$329$	6.87240	0.378888
$330$	−4.23182	−0.232954
$331$	−27.0209	−1.48520	−0.742600	−	0.669735i	$-0.766408\pi$
$331$	−27.0209	−1.48520	−0.742600	+	0.669735i	$0.766408\pi$
$332$	5.53887	0.303985
$333$	−16.3618	−0.896621
$334$	−6.95796	−0.380722
$335$	−7.15132	−0.390718
$336$	−5.95243	−0.324732
$337$	−6.29558	−0.342942	−0.171471	−	0.985189i	$-0.554852\pi$
$337$	−6.29558	−0.342942	−0.171471	+	0.985189i	$0.554852\pi$
$338$	−6.27238	−0.341172
$339$	4.81354	0.261436
$340$	−1.97886	−0.107319
$341$	−24.6852	−1.33678
$342$	−15.6470	−0.846092
$343$	−19.4293	−1.04908
$344$	−3.11355	−0.167871
$345$	3.42896	0.184609
$346$	−11.6541	−0.626526
$347$	−2.03473	−0.109230	−0.0546151	−	0.998507i	$-0.517393\pi$
$347$	−2.03473	−0.109230	−0.0546151	+	0.998507i	$0.517393\pi$
$348$	−0.272436	−0.0146041
$349$	24.8534	1.33037	0.665187	−	0.746677i	$-0.268352\pi$
$349$	24.8534	1.33037	0.665187	+	0.746677i	$0.268352\pi$
$350$	−11.9226	−0.637287
$351$	1.72339	0.0919875
$352$	3.87286	0.206424
$353$	26.1882	1.39386	0.696928	−	0.717141i	$-0.254550\pi$
$353$	26.1882	1.39386	0.696928	+	0.717141i	$0.254550\pi$
$354$	−22.3050	−1.18550
$355$	−0.886127	−0.0470307
$356$	1.67683	0.0888718
$357$	25.7869	1.36479
$358$	17.3498	0.916963
$359$	−15.4107	−0.813346	−0.406673	−	0.913574i	$-0.633311\pi$
$359$	−15.4107	−0.813346	−0.406673	+	0.913574i	$0.633311\pi$
$360$	1.24348	0.0655370
$361$	14.0376	0.738819
$362$	22.9468	1.20606
$363$	−9.56629	−0.502100
$364$	6.45420	0.338292
$365$	−1.95354	−0.102253
$366$	1.63616	0.0855234
$367$	−13.6191	−0.710911	−0.355456	−	0.934693i	$-0.615674\pi$
$367$	−13.6191	−0.710911	−0.355456	+	0.934693i	$0.615674\pi$
$368$	−3.13811	−0.163585
$369$	−30.1134	−1.56764
$370$	−2.74547	−0.142730
$371$	5.35431	0.277982
$372$	15.2471	0.790525
$373$	17.4857	0.905376	0.452688	−	0.891669i	$-0.350465\pi$
$373$	17.4857	0.905376	0.452688	+	0.891669i	$0.350465\pi$
$374$	−16.7779	−0.867563
$375$	10.6989	0.552486
$376$	2.76183	0.142431
$377$	0.295401	0.0152139
$378$	1.65334	0.0850388
$379$	2.09555	0.107641	0.0538205	−	0.998551i	$-0.482860\pi$
$379$	2.09555	0.107641	0.0538205	+	0.998551i	$0.482860\pi$
$380$	−2.62552	−0.134686
$381$	8.00449	0.410082
$382$	−9.90372	−0.506718
$383$	13.0598	0.667325	0.333662	−	0.942693i	$-0.391715\pi$
$383$	13.0598	0.667325	0.333662	+	0.942693i	$0.391715\pi$
$384$	−2.39212	−0.122072
$385$	4.40205	0.224349
$386$	6.50897	0.331298
$387$	−8.47582	−0.430850
$388$	16.7786	0.851806
$389$	−10.5242	−0.533600	−0.266800	−	0.963752i	$-0.585966\pi$
$389$	−10.5242	−0.533600	−0.266800	+	0.963752i	$0.585966\pi$
$390$	−2.83417	−0.143514
$391$	13.5948	0.687517
$392$	−0.808114	−0.0408159
$393$	−6.04948	−0.305156
$394$	−19.7925	−0.997131
$395$	−7.01218	−0.352821
$396$	10.5429	0.529799
$397$	14.5484	0.730162	0.365081	−	0.930976i	$-0.381041\pi$
$397$	14.5484	0.730162	0.365081	+	0.930976i	$0.381041\pi$
$398$	6.44689	0.323153
$399$	34.2136	1.71282
$400$	−4.79135	−0.239567
$401$	−20.2763	−1.01255	−0.506275	−	0.862372i	$-0.668978\pi$
$401$	−20.2763	−1.01255	−0.506275	+	0.862372i	$0.668978\pi$
$402$	37.4505	1.86786
$403$	−16.5324	−0.823535
$404$	14.2061	0.706778
$405$	−4.45645	−0.221443
$406$	0.283395	0.0140647
$407$	−23.2775	−1.15382
$408$	10.3630	0.513047
$409$	−22.2709	−1.10123	−0.550613	−	0.834761i	$-0.685606\pi$
$409$	−22.2709	−1.10123	−0.550613	+	0.834761i	$0.685606\pi$
$410$	−5.05295	−0.249547
$411$	21.8979	1.08014
$412$	−0.656887	−0.0323625
$413$	23.2023	1.14171
$414$	−8.54268	−0.419850
$415$	2.53007	0.124196
$416$	2.59377	0.127170
$417$	14.3125	0.700888
$418$	−22.2606	−1.08880
$419$	−12.9866	−0.634439	−0.317220	−	0.948352i	$-0.602749\pi$
$419$	−12.9866	−0.634439	−0.317220	+	0.948352i	$0.602749\pi$
$420$	−2.71898	−0.132673
$421$	15.6193	0.761237	0.380619	−	0.924732i	$-0.375711\pi$
$421$	15.6193	0.761237	0.380619	+	0.924732i	$0.375711\pi$
$422$	−1.97919	−0.0963453
$423$	7.51837	0.365555
$424$	2.15175	0.104498
$425$	20.7569	1.00686
$426$	4.64053	0.224834
$427$	−1.70198	−0.0823645
$428$	0.0629978	0.00304512
$429$	−24.0296	−1.16016
$430$	−1.42222	−0.0685856
$431$	−21.5923	−1.04007	−0.520033	−	0.854146i	$-0.674080\pi$
$431$	−21.5923	−1.04007	−0.520033	+	0.854146i	$0.674080\pi$
$432$	0.664434	0.0319676
$433$	30.5174	1.46657	0.733286	−	0.679920i	$-0.237986\pi$
$433$	30.5174	1.46657	0.733286	+	0.679920i	$0.237986\pi$
$434$	−15.8604	−0.761326
$435$	−0.124444	−0.00596666
$436$	6.48599	0.310623
$437$	18.0373	0.862841
$438$	10.2305	0.488830
$439$	1.41164	0.0673741	0.0336870	−	0.999432i	$-0.489275\pi$
$439$	1.41164	0.0673741	0.0336870	+	0.999432i	$0.489275\pi$
$440$	1.76907	0.0843369
$441$	−2.19988	−0.104756
$442$	−11.2366	−0.534471
$443$	2.35077	0.111689	0.0558443	−	0.998439i	$-0.482215\pi$
$443$	2.35077	0.111689	0.0558443	+	0.998439i	$0.482215\pi$
$444$	14.3776	0.682332
$445$	0.765950	0.0363095
$446$	−2.16105	−0.102329
$447$	26.6754	1.26170
$448$	2.48835	0.117563
$449$	−21.2102	−1.00097	−0.500485	−	0.865745i	$-0.666845\pi$
$449$	−21.2102	−1.00097	−0.500485	+	0.865745i	$0.666845\pi$
$450$	−13.0432	−0.614862
$451$	−42.8416	−2.01733
$452$	−2.01225	−0.0946482
$453$	−36.5170	−1.71572
$454$	−24.3323	−1.14197
$455$	2.94818	0.138213
$456$	13.7495	0.643879
$457$	27.8526	1.30289	0.651445	−	0.758696i	$-0.274163\pi$
$457$	27.8526	1.30289	0.651445	+	0.758696i	$0.274163\pi$
$458$	7.34800	0.343349
$459$	−2.87843	−0.134354
$460$	−1.43344	−0.0668344
$461$	−20.8286	−0.970086	−0.485043	−	0.874490i	$-0.661196\pi$
$461$	−20.8286	−0.970086	−0.485043	+	0.874490i	$0.661196\pi$
$462$	−23.0530	−1.07252
$463$	29.3622	1.36458	0.682289	−	0.731083i	$-0.260985\pi$
$463$	29.3622	1.36458	0.682289	+	0.731083i	$0.260985\pi$
$464$	0.113889	0.00528715
$465$	6.96464	0.322977
$466$	14.1309	0.654599
$467$	−12.0222	−0.556321	−0.278161	−	0.960535i	$-0.589725\pi$
$467$	−12.0222	−0.556321	−0.278161	+	0.960535i	$0.589725\pi$
$468$	7.06086	0.326388
$469$	−38.9570	−1.79887
$470$	1.26156	0.0581915
$471$	−15.6328	−0.720319
$472$	9.32436	0.429189
$473$	−12.0583	−0.554443
$474$	36.7219	1.68669
$475$	27.5399	1.26362
$476$	−10.7799	−0.494097
$477$	5.85758	0.268200
$478$	11.7456	0.537233
$479$	23.7038	1.08305	0.541526	−	0.840684i	$-0.317847\pi$
$479$	23.7038	1.08305	0.541526	+	0.840684i	$0.317847\pi$
$480$	−1.09268	−0.0498740
$481$	−15.5896	−0.710825
$482$	21.9604	1.00027
$483$	18.6794	0.849940
$484$	3.99908	0.181777
$485$	7.66422	0.348014
$486$	21.3445	0.968208
$487$	18.5064	0.838603	0.419302	−	0.907847i	$-0.362275\pi$
$487$	18.5064	0.838603	0.419302	+	0.907847i	$0.362275\pi$
$488$	−0.683978	−0.0309622
$489$	43.2023	1.95367
$490$	−0.369134	−0.0166758
$491$	−24.6251	−1.11132	−0.555658	−	0.831411i	$-0.687534\pi$
$491$	−24.6251	−1.11132	−0.555658	+	0.831411i	$0.687534\pi$
$492$	26.4616	1.19298
$493$	−0.493384	−0.0222209
$494$	−14.9085	−0.670766
$495$	4.81582	0.216455
$496$	−6.37388	−0.286196
$497$	−4.82720	−0.216530
$498$	−13.2497	−0.593731
$499$	−0.461367	−0.0206536	−0.0103268	−	0.999947i	$-0.503287\pi$
$499$	−0.461367	−0.0206536	−0.0103268	+	0.999947i	$0.503287\pi$
$500$	−4.47254	−0.200018
$501$	16.6443	0.743611
$502$	−28.2480	−1.26077
$503$	17.1804	0.766035	0.383017	−	0.923741i	$-0.374885\pi$
$503$	17.1804	0.766035	0.383017	+	0.923741i	$0.374885\pi$
$504$	6.77389	0.301733
$505$	6.48911	0.288762
$506$	−12.1535	−0.540287
$507$	15.0043	0.666363
$508$	−3.34619	−0.148463
$509$	33.4649	1.48331	0.741653	−	0.670784i	$-0.234042\pi$
$509$	33.4649	1.48331	0.741653	+	0.670784i	$0.234042\pi$
$510$	4.73368	0.209611
$511$	−10.6420	−0.470774
$512$	1.00000	0.0441942
$513$	−3.81905	−0.168615
$514$	1.19436	0.0526808
$515$	−0.300056	−0.0132220
$516$	7.44798	0.327879
$517$	10.6962	0.470418
$518$	−14.9560	−0.657130
$519$	27.8779	1.22370
$520$	1.18479	0.0519566
$521$	40.8705	1.79057	0.895284	−	0.445497i	$-0.146973\pi$
$521$	40.8705	1.79057	0.895284	+	0.445497i	$0.146973\pi$
$522$	0.310033	0.0135698
$523$	−12.4204	−0.543104	−0.271552	−	0.962424i	$-0.587537\pi$
$523$	−12.4204	−0.543104	−0.271552	+	0.962424i	$0.587537\pi$
$524$	2.52892	0.110476
$525$	28.5202	1.24472
$526$	0.133066	0.00580195
$527$	27.6127	1.20283
$528$	−9.26436	−0.403180
$529$	−13.1523	−0.571839
$530$	0.982886	0.0426939
$531$	25.3832	1.10154
$532$	−14.3026	−0.620097
$533$	−28.6922	−1.24280
$534$	−4.01118	−0.173581
$535$	0.0287765	0.00124411
$536$	−15.6558	−0.676227
$537$	−41.5027	−1.79097
$538$	4.64131	0.200101
$539$	−3.12972	−0.134806
$540$	0.303503	0.0130607
$541$	−30.5955	−1.31540	−0.657701	−	0.753279i	$-0.728471\pi$
$541$	−30.5955	−1.31540	−0.657701	+	0.753279i	$0.728471\pi$
$542$	−8.71558	−0.374366
$543$	−54.8916	−2.35562
$544$	−4.33216	−0.185740
$545$	2.96270	0.126908
$546$	−15.4392	−0.660738
$547$	1.97808	0.0845767	0.0422884	−	0.999105i	$-0.486535\pi$
$547$	1.97808	0.0845767	0.0422884	+	0.999105i	$0.486535\pi$
$548$	−9.15418	−0.391047
$549$	−1.86195	−0.0794663
$550$	−18.5562	−0.791241
$551$	−0.654613	−0.0278875
$552$	7.50673	0.319507
$553$	−38.1991	−1.62439
$554$	1.80193	0.0765568
$555$	6.56748	0.278774
$556$	−5.98320	−0.253744
$557$	−9.87504	−0.418419	−0.209209	−	0.977871i	$-0.567089\pi$
$557$	−9.87504	−0.418419	−0.209209	+	0.977871i	$0.567089\pi$
$558$	−17.3512	−0.734536
$559$	−8.07581	−0.341570
$560$	1.13664	0.0480318
$561$	40.1347	1.69449
$562$	6.05499	0.255414
$563$	−17.0658	−0.719237	−0.359618	−	0.933099i	$-0.617093\pi$
$563$	−17.0658	−0.719237	−0.359618	+	0.933099i	$0.617093\pi$
$564$	−6.60663	−0.278189
$565$	−0.919164	−0.0386695
$566$	9.59314	0.403230
$567$	−24.2767	−1.01952
$568$	−1.93992	−0.0813973
$569$	−20.1160	−0.843307	−0.421654	−	0.906757i	$-0.638550\pi$
$569$	−20.1160	−0.843307	−0.421654	+	0.906757i	$0.638550\pi$
$570$	6.28056	0.263064
$571$	28.7324	1.20241	0.601207	−	0.799093i	$-0.294687\pi$
$571$	28.7324	1.20241	0.601207	+	0.799093i	$0.294687\pi$
$572$	10.0453	0.420015
$573$	23.6909	0.989701
$574$	−27.5261	−1.14892
$575$	15.0358	0.627034
$576$	2.72224	0.113427
$577$	40.1866	1.67299	0.836495	−	0.547975i	$-0.184601\pi$
$577$	40.1866	1.67299	0.836495	+	0.547975i	$0.184601\pi$
$578$	1.76759	0.0735220
$579$	−15.5703	−0.647078
$580$	0.0520227	0.00216012
$581$	13.7827	0.571801
$582$	−40.1365	−1.66371
$583$	8.33344	0.345136
$584$	−4.27673	−0.176972
$585$	3.22529	0.133349
$586$	−7.24866	−0.299439
$587$	−34.3782	−1.41894	−0.709471	−	0.704735i	$-0.751066\pi$
$587$	−34.3782	−1.41894	−0.709471	+	0.704735i	$0.751066\pi$
$588$	1.93311	0.0797200
$589$	36.6360	1.50956
$590$	4.25923	0.175350
$591$	47.3460	1.94755
$592$	−6.01041	−0.247026
$593$	−17.6392	−0.724355	−0.362178	−	0.932109i	$-0.617967\pi$
$593$	−17.6392	−0.724355	−0.362178	+	0.932109i	$0.617967\pi$
$594$	2.57326	0.105582
$595$	−4.92410	−0.201869
$596$	−11.1514	−0.456777
$597$	−15.4217	−0.631170
$598$	−8.13951	−0.332849
$599$	3.45354	0.141108	0.0705539	−	0.997508i	$-0.477523\pi$
$599$	3.45354	0.141108	0.0705539	+	0.997508i	$0.477523\pi$
$600$	11.4615	0.467913
$601$	11.1061	0.453028	0.226514	−	0.974008i	$-0.427267\pi$
$601$	11.1061	0.453028	0.226514	+	0.974008i	$0.427267\pi$
$602$	−7.74759	−0.315768
$603$	−42.6188	−1.73557
$604$	15.2655	0.621146
$605$	1.82672	0.0742667
$606$	−33.9826	−1.38045
$607$	42.9670	1.74398	0.871989	−	0.489526i	$-0.162830\pi$
$607$	42.9670	1.74398	0.871989	+	0.489526i	$0.162830\pi$
$608$	−5.74783	−0.233105
$609$	−0.677915	−0.0274705
$610$	−0.312431	−0.0126500
$611$	7.16354	0.289806
$612$	−11.7932	−0.476711
$613$	30.2058	1.22000	0.610000	−	0.792402i	$-0.291169\pi$
$613$	30.2058	1.22000	0.610000	+	0.792402i	$0.291169\pi$
$614$	−3.90912	−0.157759
$615$	12.0873	0.487405
$616$	9.63704	0.388288
$617$	6.35286	0.255757	0.127878	−	0.991790i	$-0.459183\pi$
$617$	6.35286	0.255757	0.127878	+	0.991790i	$0.459183\pi$
$618$	1.57135	0.0632091
$619$	22.8916	0.920092	0.460046	−	0.887895i	$-0.347833\pi$
$619$	22.8916	0.920092	0.460046	+	0.887895i	$0.347833\pi$
$620$	−2.91149	−0.116928
$621$	−2.08506	−0.0836707
$622$	0.822219	0.0329680
$623$	4.17254	0.167169
$624$	−6.20460	−0.248383
$625$	21.9138	0.876550
$626$	−8.18256	−0.327041
$627$	53.2500	2.12660
$628$	6.53510	0.260779
$629$	26.0381	1.03821
$630$	3.09421	0.123276
$631$	−16.5864	−0.660293	−0.330147	−	0.943930i	$-0.607098\pi$
$631$	−16.5864	−0.660293	−0.330147	+	0.943930i	$0.607098\pi$
$632$	−15.3512	−0.610637
$633$	4.73445	0.188178
$634$	−16.8186	−0.667954
$635$	−1.52849	−0.0606562
$636$	−5.14724	−0.204102
$637$	−2.09606	−0.0830489
$638$	0.441076	0.0174624
$639$	−5.28093	−0.208911
$640$	0.456785	0.0180560
$641$	−16.1943	−0.639636	−0.319818	−	0.947479i	$-0.603622\pi$
$641$	−16.1943	−0.639636	−0.319818	+	0.947479i	$0.603622\pi$
$642$	−0.150698	−0.00594759
$643$	−13.5562	−0.534604	−0.267302	−	0.963613i	$-0.586132\pi$
$643$	−13.5562	−0.534604	−0.267302	+	0.963613i	$0.586132\pi$
$644$	−7.80870	−0.307706
$645$	3.40212	0.133958
$646$	24.9005	0.979697
$647$	11.6285	0.457164	0.228582	−	0.973525i	$-0.426591\pi$
$647$	11.6285	0.457164	0.228582	+	0.973525i	$0.426591\pi$
$648$	−9.75613	−0.383257
$649$	36.1120	1.41752
$650$	−12.4276	−0.487452
$651$	37.9401	1.48699
$652$	−18.0602	−0.707293
$653$	25.8132	1.01015	0.505073	−	0.863076i	$-0.331465\pi$
$653$	25.8132	1.01015	0.505073	+	0.863076i	$0.331465\pi$
$654$	−15.5153	−0.606695
$655$	1.15517	0.0451363
$656$	−11.0620	−0.431898
$657$	−11.6423	−0.454209
$658$	6.87240	0.267914
$659$	−31.7963	−1.23861	−0.619303	−	0.785152i	$-0.712585\pi$
$659$	−31.7963	−1.23861	−0.619303	+	0.785152i	$0.712585\pi$
$660$	−4.23182	−0.164723
$661$	−21.3515	−0.830478	−0.415239	−	0.909712i	$-0.636302\pi$
$661$	−21.3515	−0.830478	−0.415239	+	0.909712i	$0.636302\pi$
$662$	−27.0209	−1.05020
$663$	26.8793	1.04391
$664$	5.53887	0.214950
$665$	−6.53322	−0.253347
$666$	−16.3618	−0.634007
$667$	−0.357395	−0.0138384
$668$	−6.95796	−0.269211
$669$	5.16949	0.199864
$670$	−7.15132	−0.276280
$671$	−2.64896	−0.102262
$672$	−5.95243	−0.229620
$673$	4.58193	0.176620	0.0883102	−	0.996093i	$-0.471853\pi$
$673$	4.58193	0.176620	0.0883102	+	0.996093i	$0.471853\pi$
$674$	−6.29558	−0.242497
$675$	−3.18353	−0.122534
$676$	−6.27238	−0.241245
$677$	−10.2959	−0.395705	−0.197853	−	0.980232i	$-0.563397\pi$
$677$	−10.2959	−0.395705	−0.197853	+	0.980232i	$0.563397\pi$
$678$	4.81354	0.184863
$679$	41.7511	1.60226
$680$	−1.97886	−0.0758859
$681$	58.2058	2.23045
$682$	−24.6852	−0.945244
$683$	23.8578	0.912895	0.456447	−	0.889750i	$-0.349122\pi$
$683$	23.8578	0.912895	0.456447	+	0.889750i	$0.349122\pi$
$684$	−15.6470	−0.598277
$685$	−4.18149	−0.159767
$686$	−19.4293	−0.741815
$687$	−17.5773	−0.670616
$688$	−3.11355	−0.118703
$689$	5.58114	0.212624
$690$	3.42896	0.130538
$691$	−48.2901	−1.83704	−0.918521	−	0.395372i	$-0.870616\pi$
$691$	−48.2901	−1.83704	−0.918521	+	0.395372i	$0.870616\pi$
$692$	−11.6541	−0.443021
$693$	26.2344	0.996561
$694$	−2.03473	−0.0772375
$695$	−2.73303	−0.103670
$696$	−0.272436	−0.0103266
$697$	47.9223	1.81519
$698$	24.8534	0.940716
$699$	−33.8027	−1.27854
$700$	−11.9226	−0.450630
$701$	3.16702	0.119617	0.0598083	−	0.998210i	$-0.480951\pi$
$701$	3.16702	0.119617	0.0598083	+	0.998210i	$0.480951\pi$
$702$	1.72339	0.0650450
$703$	34.5468	1.30296
$704$	3.87286	0.145964
$705$	−3.01781	−0.113657
$706$	26.1882	0.985606
$707$	35.3496	1.32946
$708$	−22.3050	−0.838273
$709$	−32.3817	−1.21612	−0.608060	−	0.793891i	$-0.708052\pi$
$709$	−32.3817	−1.21612	−0.608060	+	0.793891i	$0.708052\pi$
$710$	−0.886127	−0.0332557
$711$	−41.7896	−1.56723
$712$	1.67683	0.0628419
$713$	20.0019	0.749077
$714$	25.7869	0.965050
$715$	4.58854	0.171602
$716$	17.3498	0.648391
$717$	−28.0970	−1.04930
$718$	−15.4107	−0.575122
$719$	3.73550	0.139311	0.0696553	−	0.997571i	$-0.477810\pi$
$719$	3.73550	0.139311	0.0696553	+	0.997571i	$0.477810\pi$
$720$	1.24348	0.0463417
$721$	−1.63456	−0.0608744
$722$	14.0376	0.522424
$723$	−52.5319	−1.95368
$724$	22.9468	0.852813
$725$	−0.545681	−0.0202661
$726$	−9.56629	−0.355038
$727$	27.2025	1.00888	0.504442	−	0.863446i	$-0.331698\pi$
$727$	27.2025	1.00888	0.504442	+	0.863446i	$0.331698\pi$
$728$	6.45420	0.239209
$729$	−21.7903	−0.807049
$730$	−1.95354	−0.0723039
$731$	13.4884	0.498885
$732$	1.63616	0.0604742
$733$	44.5821	1.64668	0.823338	−	0.567551i	$-0.192109\pi$
$733$	44.5821	1.64668	0.823338	+	0.567551i	$0.192109\pi$
$734$	−13.6191	−0.502690
$735$	0.883014	0.0325704
$736$	−3.13811	−0.115672
$737$	−60.6327	−2.23343
$738$	−30.1134	−1.10849
$739$	−11.2586	−0.414152	−0.207076	−	0.978325i	$-0.566395\pi$
$739$	−11.2586	−0.414152	−0.207076	+	0.978325i	$0.566395\pi$
$740$	−2.74547	−0.100925
$741$	35.6630	1.31011
$742$	5.35431	0.196563
$743$	−24.1364	−0.885478	−0.442739	−	0.896650i	$-0.645993\pi$
$743$	−24.1364	−0.885478	−0.442739	+	0.896650i	$0.645993\pi$
$744$	15.2471	0.558985
$745$	−5.09377	−0.186621
$746$	17.4857	0.640197
$747$	15.0781	0.551681
$748$	−16.7779	−0.613459
$749$	0.156761	0.00572791
$750$	10.6989	0.390667
$751$	−42.5993	−1.55447	−0.777235	−	0.629211i	$-0.783378\pi$
$751$	−42.5993	−1.55447	−0.777235	+	0.629211i	$0.783378\pi$
$752$	2.76183	0.100714
$753$	67.5726	2.46248
$754$	0.295401	0.0107579
$755$	6.97307	0.253776
$756$	1.65334	0.0601315
$757$	−25.3312	−0.920680	−0.460340	−	0.887743i	$-0.652272\pi$
$757$	−25.3312	−0.920680	−0.460340	+	0.887743i	$0.652272\pi$
$758$	2.09555	0.0761137
$759$	29.0725	1.05527
$760$	−2.62552	−0.0952377
$761$	27.4470	0.994951	0.497476	−	0.867478i	$-0.334260\pi$
$761$	27.4470	0.994951	0.497476	+	0.867478i	$0.334260\pi$
$762$	8.00449	0.289972
$763$	16.1394	0.584286
$764$	−9.90372	−0.358304
$765$	−5.38694	−0.194765
$766$	13.0598	0.471870
$767$	24.1852	0.873278
$768$	−2.39212	−0.0863182
$769$	5.84050	0.210614	0.105307	−	0.994440i	$-0.466418\pi$
$769$	5.84050	0.210614	0.105307	+	0.994440i	$0.466418\pi$
$770$	4.40205	0.158639
$771$	−2.85704	−0.102894
$772$	6.50897	0.234263
$773$	−10.7795	−0.387713	−0.193857	−	0.981030i	$-0.562100\pi$
$773$	−10.7795	−0.387713	−0.193857	+	0.981030i	$0.562100\pi$
$774$	−8.47582	−0.304657
$775$	30.5395	1.09701
$776$	16.7786	0.602318
$777$	35.7766	1.28348
$778$	−10.5242	−0.377312
$779$	63.5825	2.27808
$780$	−2.83417	−0.101479
$781$	−7.51305	−0.268838
$782$	13.5948	0.486148
$783$	0.0756715	0.00270428
$784$	−0.808114	−0.0288612
$785$	2.98514	0.106544
$786$	−6.04948	−0.215778
$787$	−5.70747	−0.203449	−0.101725	−	0.994813i	$-0.532436\pi$
$787$	−5.70747	−0.203449	−0.101725	+	0.994813i	$0.532436\pi$
$788$	−19.7925	−0.705078
$789$	−0.318310	−0.0113321
$790$	−7.01218	−0.249482
$791$	−5.00718	−0.178035
$792$	10.5429	0.374625
$793$	−1.77408	−0.0629994
$794$	14.5484	0.516302
$795$	−2.35118	−0.0833879
$796$	6.44689	0.228504
$797$	−7.67514	−0.271868	−0.135934	−	0.990718i	$-0.543403\pi$
$797$	−7.67514	−0.271868	−0.135934	+	0.990718i	$0.543403\pi$
$798$	34.2136	1.21115
$799$	−11.9647	−0.423280
$800$	−4.79135	−0.169400
$801$	4.56474	0.161287
$802$	−20.2763	−0.715981
$803$	−16.5632	−0.584503
$804$	37.4505	1.32078
$805$	−3.56690	−0.125717
$806$	−16.5324	−0.582327
$807$	−11.1026	−0.390829
$808$	14.2061	0.499767
$809$	4.86287	0.170969	0.0854847	−	0.996339i	$-0.472756\pi$
$809$	4.86287	0.170969	0.0854847	+	0.996339i	$0.472756\pi$
$810$	−4.45645	−0.156584
$811$	−51.7447	−1.81700	−0.908502	−	0.417881i	$-0.862773\pi$
$811$	−51.7447	−1.81700	−0.908502	+	0.417881i	$0.862773\pi$
$812$	0.283395	0.00994522
$813$	20.8487	0.731197
$814$	−23.2775	−0.815877
$815$	−8.24964	−0.288972
$816$	10.3630	0.362779
$817$	17.8961	0.626106
$818$	−22.2709	−0.778684
$819$	17.5699	0.613941
$820$	−5.05295	−0.176457
$821$	36.7393	1.28221	0.641105	−	0.767453i	$-0.278476\pi$
$821$	36.7393	1.28221	0.641105	+	0.767453i	$0.278476\pi$
$822$	21.8979	0.763777
$823$	8.97800	0.312953	0.156477	−	0.987682i	$-0.449986\pi$
$823$	8.97800	0.312953	0.156477	+	0.987682i	$0.449986\pi$
$824$	−0.656887	−0.0228837
$825$	44.3888	1.54542
$826$	23.2023	0.807311
$827$	−18.0355	−0.627155	−0.313577	−	0.949563i	$-0.601528\pi$
$827$	−18.0355	−0.627155	−0.313577	+	0.949563i	$0.601528\pi$
$828$	−8.54268	−0.296879
$829$	−10.9139	−0.379055	−0.189527	−	0.981875i	$-0.560696\pi$
$829$	−10.9139	−0.379055	−0.189527	+	0.981875i	$0.560696\pi$
$830$	2.53007	0.0878201
$831$	−4.31044	−0.149528
$832$	2.59377	0.0899227
$833$	3.50088	0.121298
$834$	14.3125	0.495603
$835$	−3.17829	−0.109989
$836$	−22.2606	−0.769898
$837$	−4.23502	−0.146384
$838$	−12.9866	−0.448616
$839$	−27.5874	−0.952423	−0.476211	−	0.879331i	$-0.657990\pi$
$839$	−27.5874	−0.952423	−0.476211	+	0.879331i	$0.657990\pi$
$840$	−2.71898	−0.0938137
$841$	−28.9870	−0.999553
$842$	15.6193	0.538276
$843$	−14.4843	−0.498865
$844$	−1.97919	−0.0681264
$845$	−2.86513	−0.0985633
$846$	7.51837	0.258487
$847$	9.95112	0.341924
$848$	2.15175	0.0738914
$849$	−22.9479	−0.787571
$850$	20.7569	0.711955
$851$	18.8613	0.646557
$852$	4.64053	0.158982
$853$	41.2515	1.41242	0.706212	−	0.708001i	$-0.250403\pi$
$853$	41.2515	1.41242	0.706212	+	0.708001i	$0.250403\pi$
$854$	−1.70198	−0.0582405
$855$	−7.14730	−0.244433
$856$	0.0629978	0.00215322
$857$	−18.8421	−0.643634	−0.321817	−	0.946802i	$-0.604294\pi$
$857$	−18.8421	−0.643634	−0.321817	+	0.946802i	$0.604294\pi$
$858$	−24.0296	−0.820357
$859$	−27.8405	−0.949907	−0.474953	−	0.880011i	$-0.657535\pi$
$859$	−27.8405	−0.949907	−0.474953	+	0.880011i	$0.657535\pi$
$860$	−1.42222	−0.0484973
$861$	65.8458	2.24402
$862$	−21.5923	−0.735437
$863$	4.88763	0.166377	0.0831884	−	0.996534i	$-0.473490\pi$
$863$	4.88763	0.166377	0.0831884	+	0.996534i	$0.473490\pi$
$864$	0.664434	0.0226045
$865$	−5.32339	−0.181001
$866$	30.5174	1.03702
$867$	−4.22829	−0.143600
$868$	−15.8604	−0.538339
$869$	−59.4530	−2.01681
$870$	−0.124444	−0.00421906
$871$	−40.6074	−1.37593
$872$	6.48599	0.219643
$873$	45.6755	1.54588
$874$	18.0373	0.610121
$875$	−11.1292	−0.376237
$876$	10.2305	0.345655
$877$	−1.73998	−0.0587550	−0.0293775	−	0.999568i	$-0.509352\pi$
$877$	−1.73998	−0.0587550	−0.0293775	+	0.999568i	$0.509352\pi$
$878$	1.41164	0.0476407
$879$	17.3397	0.584852
$880$	1.76907	0.0596352
$881$	−12.4802	−0.420467	−0.210234	−	0.977651i	$-0.567422\pi$
$881$	−12.4802	−0.420467	−0.210234	+	0.977651i	$0.567422\pi$
$882$	−2.19988	−0.0740739
$883$	12.3944	0.417104	0.208552	−	0.978011i	$-0.433125\pi$
$883$	12.3944	0.417104	0.208552	+	0.978011i	$0.433125\pi$
$884$	−11.2366	−0.377928
$885$	−10.1886	−0.342486
$886$	2.35077	0.0789758
$887$	−38.1987	−1.28259	−0.641293	−	0.767296i	$-0.721602\pi$
$887$	−38.1987	−1.28259	−0.641293	+	0.767296i	$0.721602\pi$
$888$	14.3776	0.482482
$889$	−8.32649	−0.279261
$890$	0.765950	0.0256747
$891$	−37.7842	−1.26582
$892$	−2.16105	−0.0723572
$893$	−15.8745	−0.531221
$894$	26.6754	0.892158
$895$	7.92510	0.264907
$896$	2.48835	0.0831299
$897$	19.4707	0.650108
$898$	−21.2102	−0.707792
$899$	−0.725913	−0.0242106
$900$	−13.0432	−0.434773
$901$	−9.32172	−0.310551
$902$	−42.8416	−1.42647
$903$	18.5332	0.616745
$904$	−2.01225	−0.0669264
$905$	10.4818	0.348426
$906$	−36.5170	−1.21320
$907$	42.0685	1.39686	0.698430	−	0.715678i	$-0.253882\pi$
$907$	42.0685	1.39686	0.698430	+	0.715678i	$0.253882\pi$
$908$	−24.3323	−0.807496
$909$	38.6723	1.28268
$910$	2.94818	0.0977312
$911$	−24.3805	−0.807761	−0.403880	−	0.914812i	$-0.632339\pi$
$911$	−24.3805	−0.807761	−0.403880	+	0.914812i	$0.632339\pi$
$912$	13.7495	0.455292
$913$	21.4513	0.709935
$914$	27.8526	0.921282
$915$	0.747372	0.0247074
$916$	7.34800	0.242785
$917$	6.29284	0.207808
$918$	−2.87843	−0.0950024
$919$	9.53073	0.314390	0.157195	−	0.987568i	$-0.449755\pi$
$919$	9.53073	0.314390	0.157195	+	0.987568i	$0.449755\pi$
$920$	−1.43344	−0.0472591
$921$	9.35109	0.308129
$922$	−20.8286	−0.685954
$923$	−5.03170	−0.165621
$924$	−23.0530	−0.758387
$925$	28.7980	0.946872
$926$	29.3622	0.964902
$927$	−1.78820	−0.0587323
$928$	0.113889	0.00373858
$929$	−18.9243	−0.620886	−0.310443	−	0.950592i	$-0.600477\pi$
$929$	−18.9243	−0.620886	−0.310443	+	0.950592i	$0.600477\pi$
$930$	6.96464	0.228379
$931$	4.64490	0.152231
$932$	14.1309	0.462872
$933$	−1.96685	−0.0643917
$934$	−12.0222	−0.393379
$935$	−7.66387	−0.250635
$936$	7.06086	0.230791
$937$	5.67732	0.185470	0.0927350	−	0.995691i	$-0.470439\pi$
$937$	5.67732	0.185470	0.0927350	+	0.995691i	$0.470439\pi$
$938$	−38.9570	−1.27199
$939$	19.5737	0.638763
$940$	1.26156	0.0411476
$941$	23.2200	0.756949	0.378475	−	0.925612i	$-0.376449\pi$
$941$	23.2200	0.756949	0.378475	+	0.925612i	$0.376449\pi$
$942$	−15.6328	−0.509343
$943$	34.7137	1.13043
$944$	9.32436	0.303482
$945$	0.755222	0.0245674
$946$	−12.0583	−0.392051
$947$	35.8836	1.16606	0.583031	−	0.812450i	$-0.301867\pi$
$947$	35.8836	1.16606	0.583031	+	0.812450i	$0.301867\pi$
$948$	36.7219	1.19267
$949$	−11.0928	−0.360089
$950$	27.5399	0.893511
$951$	40.2322	1.30462
$952$	−10.7799	−0.349379
$953$	23.1922	0.751270	0.375635	−	0.926768i	$-0.377425\pi$
$953$	23.1922	0.751270	0.375635	+	0.926768i	$0.377425\pi$
$954$	5.85758	0.189646
$955$	−4.52387	−0.146389
$956$	11.7456	0.379881
$957$	−1.05511	−0.0341068
$958$	23.7038	0.765834
$959$	−22.7788	−0.735566
$960$	−1.09268	−0.0352662
$961$	9.62634	0.310527
$962$	−15.5896	−0.502629
$963$	0.171495	0.00552636
$964$	21.9604	0.707297
$965$	2.97320	0.0957107
$966$	18.6794	0.600999
$967$	−45.9066	−1.47626	−0.738128	−	0.674661i	$-0.764290\pi$
$967$	−45.9066	−1.47626	−0.738128	+	0.674661i	$0.764290\pi$
$968$	3.99908	0.128535
$969$	−59.5650	−1.91350
$970$	7.66422	0.246083
$971$	37.7840	1.21255	0.606274	−	0.795256i	$-0.292664\pi$
$971$	37.7840	1.21255	0.606274	+	0.795256i	$0.292664\pi$
$972$	21.3445	0.684626
$973$	−14.8883	−0.477297
$974$	18.5064	0.592982
$975$	29.7284	0.952071
$976$	−0.683978	−0.0218936
$977$	−48.4963	−1.55153	−0.775767	−	0.631019i	$-0.782637\pi$
$977$	−48.4963	−1.55153	−0.775767	+	0.631019i	$0.782637\pi$
$978$	43.2023	1.38146
$979$	6.49414	0.207554
$980$	−0.369134	−0.0117916
$981$	17.6564	0.563727
$982$	−24.6251	−0.785819
$983$	−19.3611	−0.617523	−0.308762	−	0.951139i	$-0.599915\pi$
$983$	−19.3611	−0.617523	−0.308762	+	0.951139i	$0.599915\pi$
$984$	26.4616	0.843566
$985$	−9.04090	−0.288067
$986$	−0.493384	−0.0157126
$987$	−16.4396	−0.523278
$988$	−14.9085	−0.474304
$989$	9.77063	0.310688
$990$	4.81582	0.153057
$991$	−14.0532	−0.446416	−0.223208	−	0.974771i	$-0.571653\pi$
$991$	−14.0532	−0.446416	−0.223208	+	0.974771i	$0.571653\pi$
$992$	−6.37388	−0.202371
$993$	64.6371	2.05120
$994$	−4.82720	−0.153110
$995$	2.94484	0.0933578
$996$	−13.2497	−0.419831
$997$	−6.97304	−0.220838	−0.110419	−	0.993885i	$-0.535219\pi$
$997$	−6.97304	−0.220838	−0.110419	+	0.993885i	$0.535219\pi$
$998$	−0.461367	−0.0146043
$999$	−3.99352	−0.126349

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.11	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.11	✓	56	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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.39212 q^{3} +1.00000 q^{4} +0.456785 q^{5} -2.39212 q^{6} +2.48835 q^{7} +1.00000 q^{8} +2.72224 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.39212 q^{3} +1.00000 q^{4} +0.456785 q^{5} -2.39212 q^{6} +2.48835 q^{7} +1.00000 q^{8} +2.72224 q^{9} +0.456785 q^{10} +3.87286 q^{11} -2.39212 q^{12} +2.59377 q^{13} +2.48835 q^{14} -1.09268 q^{15} +1.00000 q^{16} -4.33216 q^{17} +2.72224 q^{18} -5.74783 q^{19} +0.456785 q^{20} -5.95243 q^{21} +3.87286 q^{22} -3.13811 q^{23} -2.39212 q^{24} -4.79135 q^{25} +2.59377 q^{26} +0.664434 q^{27} +2.48835 q^{28} +0.113889 q^{29} -1.09268 q^{30} -6.37388 q^{31} +1.00000 q^{32} -9.26436 q^{33} -4.33216 q^{34} +1.13664 q^{35} +2.72224 q^{36} -6.01041 q^{37} -5.74783 q^{38} -6.20460 q^{39} +0.456785 q^{40} -11.0620 q^{41} -5.95243 q^{42} -3.11355 q^{43} +3.87286 q^{44} +1.24348 q^{45} -3.13811 q^{46} +2.76183 q^{47} -2.39212 q^{48} -0.808114 q^{49} -4.79135 q^{50} +10.3630 q^{51} +2.59377 q^{52} +2.15175 q^{53} +0.664434 q^{54} +1.76907 q^{55} +2.48835 q^{56} +13.7495 q^{57} +0.113889 q^{58} +9.32436 q^{59} -1.09268 q^{60} -0.683978 q^{61} -6.37388 q^{62} +6.77389 q^{63} +1.00000 q^{64} +1.18479 q^{65} -9.26436 q^{66} -15.6558 q^{67} -4.33216 q^{68} +7.50673 q^{69} +1.13664 q^{70} -1.93992 q^{71} +2.72224 q^{72} -4.27673 q^{73} -6.01041 q^{74} +11.4615 q^{75} -5.74783 q^{76} +9.63704 q^{77} -6.20460 q^{78} -15.3512 q^{79} +0.456785 q^{80} -9.75613 q^{81} -11.0620 q^{82} +5.53887 q^{83} -5.95243 q^{84} -1.97886 q^{85} -3.11355 q^{86} -0.272436 q^{87} +3.87286 q^{88} +1.67683 q^{89} +1.24348 q^{90} +6.45420 q^{91} -3.13811 q^{92} +15.2471 q^{93} +2.76183 q^{94} -2.62552 q^{95} -2.39212 q^{96} +16.7786 q^{97} -0.808114 q^{98} +10.5429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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