LMFDB - Embedded newform 6022.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.12241 q^{3} +1.00000 q^{4} -2.62309 q^{5} +2.12241 q^{6} -2.27034 q^{7} -1.00000 q^{8} +1.50461 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.12241 q^{3} +1.00000 q^{4} -2.62309 q^{5} +2.12241 q^{6} -2.27034 q^{7} -1.00000 q^{8} +1.50461 q^{9} +2.62309 q^{10} -2.66961 q^{11} -2.12241 q^{12} +5.34242 q^{13} +2.27034 q^{14} +5.56727 q^{15} +1.00000 q^{16} -5.62324 q^{17} -1.50461 q^{18} -5.30987 q^{19} -2.62309 q^{20} +4.81858 q^{21} +2.66961 q^{22} -1.53134 q^{23} +2.12241 q^{24} +1.88062 q^{25} -5.34242 q^{26} +3.17383 q^{27} -2.27034 q^{28} +2.78102 q^{29} -5.56727 q^{30} +2.11381 q^{31} -1.00000 q^{32} +5.66600 q^{33} +5.62324 q^{34} +5.95532 q^{35} +1.50461 q^{36} +1.12415 q^{37} +5.30987 q^{38} -11.3388 q^{39} +2.62309 q^{40} -0.498752 q^{41} -4.81858 q^{42} +3.05600 q^{43} -2.66961 q^{44} -3.94672 q^{45} +1.53134 q^{46} -3.25281 q^{47} -2.12241 q^{48} -1.84555 q^{49} -1.88062 q^{50} +11.9348 q^{51} +5.34242 q^{52} -5.96857 q^{53} -3.17383 q^{54} +7.00264 q^{55} +2.27034 q^{56} +11.2697 q^{57} -2.78102 q^{58} +2.67800 q^{59} +5.56727 q^{60} -0.0729553 q^{61} -2.11381 q^{62} -3.41597 q^{63} +1.00000 q^{64} -14.0137 q^{65} -5.66600 q^{66} +15.5879 q^{67} -5.62324 q^{68} +3.25011 q^{69} -5.95532 q^{70} +14.8439 q^{71} -1.50461 q^{72} -7.69607 q^{73} -1.12415 q^{74} -3.99145 q^{75} -5.30987 q^{76} +6.06093 q^{77} +11.3388 q^{78} +10.7516 q^{79} -2.62309 q^{80} -11.2500 q^{81} +0.498752 q^{82} -2.40844 q^{83} +4.81858 q^{84} +14.7503 q^{85} -3.05600 q^{86} -5.90245 q^{87} +2.66961 q^{88} +3.68899 q^{89} +3.94672 q^{90} -12.1291 q^{91} -1.53134 q^{92} -4.48637 q^{93} +3.25281 q^{94} +13.9283 q^{95} +2.12241 q^{96} -0.133200 q^{97} +1.84555 q^{98} -4.01671 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) $ 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * 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
$3$	−2.12241	−1.22537	−0.612686	−	0.790327i	$-0.709911\pi$
$3$	−2.12241	−1.22537	−0.612686	+	0.790327i	$0.709911\pi$
$4$	1.00000	0.500000
$5$	−2.62309	−1.17308	−0.586542	−	0.809919i	$-0.699511\pi$
$5$	−2.62309	−1.17308	−0.586542	+	0.809919i	$0.699511\pi$
$6$	2.12241	0.866468
$7$	−2.27034	−0.858108	−0.429054	−	0.903279i	$-0.641153\pi$
$7$	−2.27034	−0.858108	−0.429054	+	0.903279i	$0.641153\pi$
$8$	−1.00000	−0.353553
$9$	1.50461	0.501535
$10$	2.62309	0.829495
$11$	−2.66961	−0.804918	−0.402459	−	0.915438i	$-0.631844\pi$
$11$	−2.66961	−0.804918	−0.402459	+	0.915438i	$0.631844\pi$
$12$	−2.12241	−0.612686
$13$	5.34242	1.48172	0.740860	−	0.671660i	$-0.234418\pi$
$13$	5.34242	1.48172	0.740860	+	0.671660i	$0.234418\pi$
$14$	2.27034	0.606774
$15$	5.56727	1.43746
$16$	1.00000	0.250000
$17$	−5.62324	−1.36384	−0.681918	−	0.731429i	$-0.738854\pi$
$17$	−5.62324	−1.36384	−0.681918	+	0.731429i	$0.738854\pi$
$18$	−1.50461	−0.354639
$19$	−5.30987	−1.21817	−0.609084	−	0.793106i	$-0.708463\pi$
$19$	−5.30987	−1.21817	−0.609084	+	0.793106i	$0.708463\pi$
$20$	−2.62309	−0.586542
$21$	4.81858	1.05150
$22$	2.66961	0.569163
$23$	−1.53134	−0.319305	−0.159653	−	0.987173i	$-0.551037\pi$
$23$	−1.53134	−0.319305	−0.159653	+	0.987173i	$0.551037\pi$
$24$	2.12241	0.433234
$25$	1.88062	0.376125
$26$	−5.34242	−1.04773
$27$	3.17383	0.610805
$28$	−2.27034	−0.429054
$29$	2.78102	0.516422	0.258211	−	0.966089i	$-0.416867\pi$
$29$	2.78102	0.516422	0.258211	+	0.966089i	$0.416867\pi$
$30$	−5.56727	−1.01644
$31$	2.11381	0.379652	0.189826	−	0.981818i	$-0.439208\pi$
$31$	2.11381	0.379652	0.189826	+	0.981818i	$0.439208\pi$
$32$	−1.00000	−0.176777
$33$	5.66600	0.986324
$34$	5.62324	0.964377
$35$	5.95532	1.00663
$36$	1.50461	0.250768
$37$	1.12415	0.184810	0.0924049	−	0.995722i	$-0.470545\pi$
$37$	1.12415	0.184810	0.0924049	+	0.995722i	$0.470545\pi$
$38$	5.30987	0.861375
$39$	−11.3388	−1.81566
$40$	2.62309	0.414748
$41$	−0.498752	−0.0778919	−0.0389460	−	0.999241i	$-0.512400\pi$
$41$	−0.498752	−0.0778919	−0.0389460	+	0.999241i	$0.512400\pi$
$42$	−4.81858	−0.743524
$43$	3.05600	0.466035	0.233018	−	0.972473i	$-0.425140\pi$
$43$	3.05600	0.466035	0.233018	+	0.972473i	$0.425140\pi$
$44$	−2.66961	−0.402459
$45$	−3.94672	−0.588343
$46$	1.53134	0.225783
$47$	−3.25281	−0.474471	−0.237236	−	0.971452i	$-0.576241\pi$
$47$	−3.25281	−0.474471	−0.237236	+	0.971452i	$0.576241\pi$
$48$	−2.12241	−0.306343
$49$	−1.84555	−0.263650
$50$	−1.88062	−0.265960
$51$	11.9348	1.67121
$52$	5.34242	0.740860
$53$	−5.96857	−0.819846	−0.409923	−	0.912120i	$-0.634444\pi$
$53$	−5.96857	−0.819846	−0.409923	+	0.912120i	$0.634444\pi$
$54$	−3.17383	−0.431904
$55$	7.00264	0.944236
$56$	2.27034	0.303387
$57$	11.2697	1.49271
$58$	−2.78102	−0.365165
$59$	2.67800	0.348646	0.174323	−	0.984688i	$-0.444226\pi$
$59$	2.67800	0.348646	0.174323	+	0.984688i	$0.444226\pi$
$60$	5.56727	0.718732
$61$	−0.0729553	−0.00934097	−0.00467049	−	0.999989i	$-0.501487\pi$
$61$	−0.0729553	−0.00934097	−0.00467049	+	0.999989i	$0.501487\pi$
$62$	−2.11381	−0.268454
$63$	−3.41597	−0.430372
$64$	1.00000	0.125000
$65$	−14.0137	−1.73818
$66$	−5.66600	−0.697436
$67$	15.5879	1.90436	0.952180	−	0.305538i	$-0.0988365\pi$
$67$	15.5879	1.90436	0.952180	+	0.305538i	$0.0988365\pi$
$68$	−5.62324	−0.681918
$69$	3.25011	0.391268
$70$	−5.95532	−0.711797
$71$	14.8439	1.76165	0.880823	−	0.473446i	$-0.156990\pi$
$71$	14.8439	1.76165	0.880823	+	0.473446i	$0.156990\pi$
$72$	−1.50461	−0.177319
$73$	−7.69607	−0.900757	−0.450379	−	0.892838i	$-0.648711\pi$
$73$	−7.69607	−0.900757	−0.450379	+	0.892838i	$0.648711\pi$
$74$	−1.12415	−0.130680
$75$	−3.99145	−0.460893
$76$	−5.30987	−0.609084
$77$	6.06093	0.690707
$78$	11.3388	1.28386
$79$	10.7516	1.20965	0.604825	−	0.796358i	$-0.293243\pi$
$79$	10.7516	1.20965	0.604825	+	0.796358i	$0.293243\pi$
$80$	−2.62309	−0.293271
$81$	−11.2500	−1.25000
$82$	0.498752	0.0550779
$83$	−2.40844	−0.264361	−0.132180	−	0.991226i	$-0.542198\pi$
$83$	−2.40844	−0.264361	−0.132180	+	0.991226i	$0.542198\pi$
$84$	4.81858	0.525751
$85$	14.7503	1.59989
$86$	−3.05600	−0.329537
$87$	−5.90245	−0.632809
$88$	2.66961	0.284581
$89$	3.68899	0.391032	0.195516	−	0.980700i	$-0.437362\pi$
$89$	3.68899	0.391032	0.195516	+	0.980700i	$0.437362\pi$
$90$	3.94672	0.416021
$91$	−12.1291	−1.27148
$92$	−1.53134	−0.159653
$93$	−4.48637	−0.465215
$94$	3.25281	0.335502
$95$	13.9283	1.42901
$96$	2.12241	0.216617
$97$	−0.133200	−0.0135244	−0.00676221	−	0.999977i	$-0.502152\pi$
$97$	−0.133200	−0.0135244	−0.00676221	+	0.999977i	$0.502152\pi$
$98$	1.84555	0.186429
$99$	−4.01671	−0.403695
$100$	1.88062	0.188062
$101$	−0.684634	−0.0681236	−0.0340618	−	0.999420i	$-0.510844\pi$
$101$	−0.684634	−0.0681236	−0.0340618	+	0.999420i	$0.510844\pi$
$102$	−11.9348	−1.18172
$103$	15.3284	1.51035	0.755176	−	0.655522i	$-0.227551\pi$
$103$	15.3284	1.51035	0.755176	+	0.655522i	$0.227551\pi$
$104$	−5.34242	−0.523867
$105$	−12.6396	−1.23350
$106$	5.96857	0.579719
$107$	−3.26244	−0.315392	−0.157696	−	0.987488i	$-0.550407\pi$
$107$	−3.26244	−0.315392	−0.157696	+	0.987488i	$0.550407\pi$
$108$	3.17383	0.305402
$109$	5.51316	0.528065	0.264032	−	0.964514i	$-0.414947\pi$
$109$	5.51316	0.528065	0.264032	+	0.964514i	$0.414947\pi$
$110$	−7.00264	−0.667676
$111$	−2.38591	−0.226461
$112$	−2.27034	−0.214527
$113$	4.33898	0.408177	0.204089	−	0.978952i	$-0.434577\pi$
$113$	4.33898	0.408177	0.204089	+	0.978952i	$0.434577\pi$
$114$	−11.2697	−1.05550
$115$	4.01684	0.374572
$116$	2.78102	0.258211
$117$	8.03823	0.743134
$118$	−2.67800	−0.246530
$119$	12.7667	1.17032
$120$	−5.56727	−0.508220
$121$	−3.87318	−0.352107
$122$	0.0729553	0.00660506
$123$	1.05855	0.0954465
$124$	2.11381	0.189826
$125$	8.18242	0.731858
$126$	3.41597	0.304319
$127$	12.8550	1.14070	0.570350	−	0.821402i	$-0.306808\pi$
$127$	12.8550	1.14070	0.570350	+	0.821402i	$0.306808\pi$
$128$	−1.00000	−0.0883883
$129$	−6.48606	−0.571066
$130$	14.0137	1.22908
$131$	−7.51035	−0.656182	−0.328091	−	0.944646i	$-0.606405\pi$
$131$	−7.51035	−0.656182	−0.328091	+	0.944646i	$0.606405\pi$
$132$	5.66600	0.493162
$133$	12.0552	1.04532
$134$	−15.5879	−1.34659
$135$	−8.32526	−0.716525
$136$	5.62324	0.482189
$137$	−7.88492	−0.673654	−0.336827	−	0.941567i	$-0.609354\pi$
$137$	−7.88492	−0.673654	−0.336827	+	0.941567i	$0.609354\pi$
$138$	−3.25011	−0.276668
$139$	2.03745	0.172814	0.0864069	−	0.996260i	$-0.472461\pi$
$139$	2.03745	0.172814	0.0864069	+	0.996260i	$0.472461\pi$
$140$	5.95532	0.503316
$141$	6.90379	0.581404
$142$	−14.8439	−1.24567
$143$	−14.2622	−1.19266
$144$	1.50461	0.125384
$145$	−7.29487	−0.605806
$146$	7.69607	0.636931
$147$	3.91701	0.323069
$148$	1.12415	0.0924049
$149$	3.45785	0.283278	0.141639	−	0.989918i	$-0.454763\pi$
$149$	3.45785	0.283278	0.141639	+	0.989918i	$0.454763\pi$
$150$	3.99145	0.325900
$151$	16.2595	1.32318	0.661592	−	0.749864i	$-0.269881\pi$
$151$	16.2595	1.32318	0.661592	+	0.749864i	$0.269881\pi$
$152$	5.30987	0.430687
$153$	−8.46076	−0.684012
$154$	−6.06093	−0.488403
$155$	−5.54473	−0.445363
$156$	−11.3388	−0.907828
$157$	−20.0173	−1.59755	−0.798776	−	0.601628i	$-0.794519\pi$
$157$	−20.0173	−1.59755	−0.798776	+	0.601628i	$0.794519\pi$
$158$	−10.7516	−0.855352
$159$	12.6677	1.00462
$160$	2.62309	0.207374
$161$	3.47665	0.273999
$162$	11.2500	0.883882
$163$	5.67117	0.444200	0.222100	−	0.975024i	$-0.428709\pi$
$163$	5.67117	0.444200	0.222100	+	0.975024i	$0.428709\pi$
$164$	−0.498752	−0.0389460
$165$	−14.8624	−1.15704
$166$	2.40844	0.186931
$167$	3.53755	0.273744	0.136872	−	0.990589i	$-0.456295\pi$
$167$	3.53755	0.273744	0.136872	+	0.990589i	$0.456295\pi$
$168$	−4.81858	−0.371762
$169$	15.5414	1.19549
$170$	−14.7503	−1.13130
$171$	−7.98926	−0.610954
$172$	3.05600	0.233018
$173$	12.8888	0.979915	0.489957	−	0.871746i	$-0.337012\pi$
$173$	12.8888	0.979915	0.489957	+	0.871746i	$0.337012\pi$
$174$	5.90245	0.447463
$175$	−4.26966	−0.322756
$176$	−2.66961	−0.201229
$177$	−5.68381	−0.427221
$178$	−3.68899	−0.276502
$179$	−8.03697	−0.600712	−0.300356	−	0.953827i	$-0.597105\pi$
$179$	−8.03697	−0.600712	−0.300356	+	0.953827i	$0.597105\pi$
$180$	−3.94672	−0.294171
$181$	14.5363	1.08047	0.540237	−	0.841513i	$-0.318335\pi$
$181$	14.5363	1.08047	0.540237	+	0.841513i	$0.318335\pi$
$182$	12.1291	0.899069
$183$	0.154841	0.0114462
$184$	1.53134	0.112892
$185$	−2.94876	−0.216797
$186$	4.48637	0.328956
$187$	15.0119	1.09778
$188$	−3.25281	−0.237236
$189$	−7.20568	−0.524136
$190$	−13.9283	−1.01046
$191$	14.6226	1.05805	0.529027	−	0.848605i	$-0.322557\pi$
$191$	14.6226	1.05805	0.529027	+	0.848605i	$0.322557\pi$
$192$	−2.12241	−0.153171
$193$	−24.8100	−1.78586	−0.892931	−	0.450194i	$-0.851355\pi$
$193$	−24.8100	−1.78586	−0.892931	+	0.450194i	$0.851355\pi$
$194$	0.133200	0.00956321
$195$	29.7427	2.12992
$196$	−1.84555	−0.131825
$197$	0.476264	0.0339324	0.0169662	−	0.999856i	$-0.494599\pi$
$197$	0.476264	0.0339324	0.0169662	+	0.999856i	$0.494599\pi$
$198$	4.01671	0.285455
$199$	18.7761	1.33100	0.665502	−	0.746396i	$-0.268217\pi$
$199$	18.7761	1.33100	0.665502	+	0.746396i	$0.268217\pi$
$200$	−1.88062	−0.132980
$201$	−33.0837	−2.33355
$202$	0.684634	0.0481707
$203$	−6.31386	−0.443146
$204$	11.9348	0.835603
$205$	1.30827	0.0913737
$206$	−15.3284	−1.06798
$207$	−2.30406	−0.160143
$208$	5.34242	0.370430
$209$	14.1753	0.980525
$210$	12.6396	0.872215
$211$	−14.9338	−1.02808	−0.514041	−	0.857766i	$-0.671852\pi$
$211$	−14.9338	−1.02808	−0.514041	+	0.857766i	$0.671852\pi$
$212$	−5.96857	−0.409923
$213$	−31.5048	−2.15867
$214$	3.26244	0.223016
$215$	−8.01617	−0.546698
$216$	−3.17383	−0.215952
$217$	−4.79908	−0.325782
$218$	−5.51316	−0.373398
$219$	16.3342	1.10376
$220$	7.00264	0.472118
$221$	−30.0417	−2.02082
$222$	2.38591	0.160132
$223$	−5.76147	−0.385816	−0.192908	−	0.981217i	$-0.561792\pi$
$223$	−5.76147	−0.385816	−0.192908	+	0.981217i	$0.561792\pi$
$224$	2.27034	0.151694
$225$	2.82960	0.188640
$226$	−4.33898	−0.288625
$227$	10.8563	0.720559	0.360279	−	0.932844i	$-0.382681\pi$
$227$	10.8563	0.720559	0.360279	+	0.932844i	$0.382681\pi$
$228$	11.2697	0.746354
$229$	9.08360	0.600261	0.300131	−	0.953898i	$-0.402970\pi$
$229$	9.08360	0.600261	0.300131	+	0.953898i	$0.402970\pi$
$230$	−4.01684	−0.264862
$231$	−12.8637	−0.846372
$232$	−2.78102	−0.182583
$233$	12.3542	0.809350	0.404675	−	0.914461i	$-0.367385\pi$
$233$	12.3542	0.809350	0.404675	+	0.914461i	$0.367385\pi$
$234$	−8.03823	−0.525475
$235$	8.53243	0.556595
$236$	2.67800	0.174323
$237$	−22.8193	−1.48227
$238$	−12.7667	−0.827540
$239$	−7.78666	−0.503677	−0.251839	−	0.967769i	$-0.581035\pi$
$239$	−7.78666	−0.503677	−0.251839	+	0.967769i	$0.581035\pi$
$240$	5.56727	0.359366
$241$	−16.8509	−1.08546	−0.542731	−	0.839907i	$-0.682610\pi$
$241$	−16.8509	−1.08546	−0.542731	+	0.839907i	$0.682610\pi$
$242$	3.87318	0.248977
$243$	14.3555	0.920907
$244$	−0.0729553	−0.00467049
$245$	4.84106	0.309284
$246$	−1.05855	−0.0674909
$247$	−28.3675	−1.80498
$248$	−2.11381	−0.134227
$249$	5.11169	0.323940
$250$	−8.18242	−0.517501
$251$	4.28783	0.270645	0.135323	−	0.990802i	$-0.456793\pi$
$251$	4.28783	0.270645	0.135323	+	0.990802i	$0.456793\pi$
$252$	−3.41597	−0.215186
$253$	4.08807	0.257015
$254$	−12.8550	−0.806597
$255$	−31.3061	−1.96046
$256$	1.00000	0.0625000
$257$	−17.2501	−1.07603	−0.538017	−	0.842934i	$-0.680826\pi$
$257$	−17.2501	−1.07603	−0.538017	+	0.842934i	$0.680826\pi$
$258$	6.48606	0.403805
$259$	−2.55221	−0.158587
$260$	−14.0137	−0.869090
$261$	4.18433	0.259004
$262$	7.51035	0.463991
$263$	−14.4053	−0.888270	−0.444135	−	0.895960i	$-0.646489\pi$
$263$	−14.4053	−0.888270	−0.444135	+	0.895960i	$0.646489\pi$
$264$	−5.66600	−0.348718
$265$	15.6561	0.961748
$266$	−12.0552	−0.739153
$267$	−7.82954	−0.479160
$268$	15.5879	0.952180
$269$	−19.9231	−1.21473	−0.607367	−	0.794421i	$-0.707774\pi$
$269$	−19.9231	−1.21473	−0.607367	+	0.794421i	$0.707774\pi$
$270$	8.32526	0.506659
$271$	22.9545	1.39439	0.697194	−	0.716882i	$-0.254432\pi$
$271$	22.9545	1.39439	0.697194	+	0.716882i	$0.254432\pi$
$272$	−5.62324	−0.340959
$273$	25.7429	1.55803
$274$	7.88492	0.476345
$275$	−5.02054	−0.302750
$276$	3.25011	0.195634
$277$	11.6956	0.702721	0.351360	−	0.936240i	$-0.385719\pi$
$277$	11.6956	0.702721	0.351360	+	0.936240i	$0.385719\pi$
$278$	−2.03745	−0.122198
$279$	3.18045	0.190409
$280$	−5.95532	−0.355898
$281$	−12.6265	−0.753231	−0.376615	−	0.926370i	$-0.622912\pi$
$281$	−12.6265	−0.753231	−0.376615	+	0.926370i	$0.622912\pi$
$282$	−6.90379	−0.411115
$283$	−15.0384	−0.893938	−0.446969	−	0.894549i	$-0.647497\pi$
$283$	−15.0384	−0.893938	−0.446969	+	0.894549i	$0.647497\pi$
$284$	14.8439	0.880823
$285$	−29.5615	−1.75107
$286$	14.2622	0.843340
$287$	1.13234	0.0668397
$288$	−1.50461	−0.0886597
$289$	14.6208	0.860047
$290$	7.29487	0.428370
$291$	0.282705	0.0165724
$292$	−7.69607	−0.450379
$293$	−11.7120	−0.684224	−0.342112	−	0.939659i	$-0.611142\pi$
$293$	−11.7120	−0.684224	−0.342112	+	0.939659i	$0.611142\pi$
$294$	−3.91701	−0.228445
$295$	−7.02466	−0.408991
$296$	−1.12415	−0.0653402
$297$	−8.47290	−0.491648
$298$	−3.45785	−0.200308
$299$	−8.18103	−0.473121
$300$	−3.99145	−0.230446
$301$	−6.93815	−0.399908
$302$	−16.2595	−0.935632
$303$	1.45307	0.0834767
$304$	−5.30987	−0.304542
$305$	0.191369	0.0109577
$306$	8.46076	0.483669
$307$	−22.6144	−1.29067	−0.645335	−	0.763900i	$-0.723282\pi$
$307$	−22.6144	−1.29067	−0.645335	+	0.763900i	$0.723282\pi$
$308$	6.06093	0.345353
$309$	−32.5331	−1.85074
$310$	5.54473	0.314920
$311$	−12.8547	−0.728925	−0.364462	−	0.931218i	$-0.618747\pi$
$311$	−12.8547	−0.728925	−0.364462	+	0.931218i	$0.618747\pi$
$312$	11.3388	0.641932
$313$	−0.955387	−0.0540016	−0.0270008	−	0.999635i	$-0.508596\pi$
$313$	−0.955387	−0.0540016	−0.0270008	+	0.999635i	$0.508596\pi$
$314$	20.0173	1.12964
$315$	8.96041	0.504862
$316$	10.7516	0.604825
$317$	−18.6844	−1.04942	−0.524709	−	0.851282i	$-0.675826\pi$
$317$	−18.6844	−1.04942	−0.524709	+	0.851282i	$0.675826\pi$
$318$	−12.6677	−0.710371
$319$	−7.42423	−0.415677
$320$	−2.62309	−0.146635
$321$	6.92421	0.386472
$322$	−3.47665	−0.193746
$323$	29.8587	1.66138
$324$	−11.2500	−0.624999
$325$	10.0471	0.557312
$326$	−5.67117	−0.314097
$327$	−11.7012	−0.647075
$328$	0.498752	0.0275390
$329$	7.38499	0.407148
$330$	14.8624	0.818151
$331$	−12.7968	−0.703373	−0.351687	−	0.936118i	$-0.614392\pi$
$331$	−12.7968	−0.703373	−0.351687	+	0.936118i	$0.614392\pi$
$332$	−2.40844	−0.132180
$333$	1.69141	0.0926887
$334$	−3.53755	−0.193566
$335$	−40.8884	−2.23397
$336$	4.81858	0.262875
$337$	−28.1579	−1.53386	−0.766928	−	0.641733i	$-0.778216\pi$
$337$	−28.1579	−1.53386	−0.766928	+	0.641733i	$0.778216\pi$
$338$	−15.5414	−0.845341
$339$	−9.20909	−0.500169
$340$	14.7503	0.799946
$341$	−5.64306	−0.305589
$342$	7.98926	0.432010
$343$	20.0824	1.08435
$344$	−3.05600	−0.164768
$345$	−8.52536	−0.458990
$346$	−12.8888	−0.692904
$347$	−3.35340	−0.180020	−0.0900100	−	0.995941i	$-0.528690\pi$
$347$	−3.35340	−0.180020	−0.0900100	+	0.995941i	$0.528690\pi$
$348$	−5.90245	−0.316404
$349$	20.1823	1.08033	0.540167	−	0.841558i	$-0.318361\pi$
$349$	20.1823	1.08033	0.540167	+	0.841558i	$0.318361\pi$
$350$	4.26966	0.228223
$351$	16.9559	0.905041
$352$	2.66961	0.142291
$353$	18.0386	0.960100	0.480050	−	0.877241i	$-0.340619\pi$
$353$	18.0386	0.960100	0.480050	+	0.877241i	$0.340619\pi$
$354$	5.68381	0.302091
$355$	−38.9369	−2.06656
$356$	3.68899	0.195516
$357$	−27.0960	−1.43407
$358$	8.03697	0.424767
$359$	−11.1192	−0.586847	−0.293423	−	0.955983i	$-0.594795\pi$
$359$	−11.1192	−0.586847	−0.293423	+	0.955983i	$0.594795\pi$
$360$	3.94672	0.208011
$361$	9.19473	0.483933
$362$	−14.5363	−0.764011
$363$	8.22045	0.431462
$364$	−12.1291	−0.635738
$365$	20.1875	1.05666
$366$	−0.154841	−0.00809366
$367$	9.77189	0.510089	0.255044	−	0.966929i	$-0.417910\pi$
$367$	9.77189	0.510089	0.255044	+	0.966929i	$0.417910\pi$
$368$	−1.53134	−0.0798264
$369$	−0.750425	−0.0390655
$370$	2.94876	0.153299
$371$	13.5507	0.703516
$372$	−4.48637	−0.232607
$373$	19.3566	1.00225	0.501123	−	0.865376i	$-0.332921\pi$
$373$	19.3566	1.00225	0.501123	+	0.865376i	$0.332921\pi$
$374$	−15.0119	−0.776245
$375$	−17.3664	−0.896797
$376$	3.25281	0.167751
$377$	14.8573	0.765192
$378$	7.20568	0.370620
$379$	20.9237	1.07478	0.537388	−	0.843335i	$-0.319411\pi$
$379$	20.9237	1.07478	0.537388	+	0.843335i	$0.319411\pi$
$380$	13.9283	0.714506
$381$	−27.2836	−1.39778
$382$	−14.6226	−0.748158
$383$	−17.9898	−0.919237	−0.459618	−	0.888117i	$-0.652014\pi$
$383$	−17.9898	−0.919237	−0.459618	+	0.888117i	$0.652014\pi$
$384$	2.12241	0.108309
$385$	−15.8984	−0.810257
$386$	24.8100	1.26280
$387$	4.59807	0.233733
$388$	−0.133200	−0.00676221
$389$	4.29769	0.217902	0.108951	−	0.994047i	$-0.465251\pi$
$389$	4.29769	0.217902	0.108951	+	0.994047i	$0.465251\pi$
$390$	−29.7427	−1.50608
$391$	8.61106	0.435480
$392$	1.84555	0.0932144
$393$	15.9400	0.804067
$394$	−0.476264	−0.0239939
$395$	−28.2025	−1.41902
$396$	−4.01671	−0.201847
$397$	−11.7741	−0.590923	−0.295461	−	0.955355i	$-0.595473\pi$
$397$	−11.7741	−0.590923	−0.295461	+	0.955355i	$0.595473\pi$
$398$	−18.7761	−0.941162
$399$	−25.5861	−1.28091
$400$	1.88062	0.0940312
$401$	27.0934	1.35298	0.676490	−	0.736452i	$-0.263500\pi$
$401$	27.0934	1.35298	0.676490	+	0.736452i	$0.263500\pi$
$402$	33.0837	1.65007
$403$	11.2929	0.562538
$404$	−0.684634	−0.0340618
$405$	29.5098	1.46635
$406$	6.31386	0.313352
$407$	−3.00106	−0.148757
$408$	−11.9348	−0.590860
$409$	6.98048	0.345163	0.172581	−	0.984995i	$-0.444789\pi$
$409$	6.98048	0.345163	0.172581	+	0.984995i	$0.444789\pi$
$410$	−1.30827	−0.0646110
$411$	16.7350	0.825476
$412$	15.3284	0.755176
$413$	−6.07998	−0.299176
$414$	2.30406	0.113238
$415$	6.31757	0.310117
$416$	−5.34242	−0.261933
$417$	−4.32429	−0.211761
$418$	−14.1753	−0.693336
$419$	33.0283	1.61354	0.806770	−	0.590865i	$-0.201214\pi$
$419$	33.0283	1.61354	0.806770	+	0.590865i	$0.201214\pi$
$420$	−12.6396	−0.616749
$421$	19.1723	0.934399	0.467199	−	0.884152i	$-0.345263\pi$
$421$	19.1723	0.934399	0.467199	+	0.884152i	$0.345263\pi$
$422$	14.9338	0.726964
$423$	−4.89420	−0.237964
$424$	5.96857	0.289859
$425$	−10.5752	−0.512972
$426$	31.5048	1.52641
$427$	0.165633	0.00801556
$428$	−3.26244	−0.157696
$429$	30.2701	1.46145
$430$	8.01617	0.386574
$431$	−4.83406	−0.232849	−0.116424	−	0.993200i	$-0.537143\pi$
$431$	−4.83406	−0.232849	−0.116424	+	0.993200i	$0.537143\pi$
$432$	3.17383	0.152701
$433$	9.62526	0.462560	0.231280	−	0.972887i	$-0.425709\pi$
$433$	9.62526	0.462560	0.231280	+	0.972887i	$0.425709\pi$
$434$	4.79908	0.230363
$435$	15.4827	0.742337
$436$	5.51316	0.264032
$437$	8.13119	0.388968
$438$	−16.3342	−0.780478
$439$	−20.5113	−0.978952	−0.489476	−	0.872017i	$-0.662812\pi$
$439$	−20.5113	−0.978952	−0.489476	+	0.872017i	$0.662812\pi$
$440$	−7.00264	−0.333838
$441$	−2.77683	−0.132230
$442$	30.0417	1.42894
$443$	−3.87506	−0.184110	−0.0920549	−	0.995754i	$-0.529344\pi$
$443$	−3.87506	−0.184110	−0.0920549	+	0.995754i	$0.529344\pi$
$444$	−2.38591	−0.113230
$445$	−9.67657	−0.458714
$446$	5.76147	0.272813
$447$	−7.33895	−0.347121
$448$	−2.27034	−0.107264
$449$	21.4077	1.01029	0.505146	−	0.863034i	$-0.331439\pi$
$449$	21.4077	1.01029	0.505146	+	0.863034i	$0.331439\pi$
$450$	−2.82960	−0.133389
$451$	1.33147	0.0626966
$452$	4.33898	0.204089
$453$	−34.5094	−1.62139
$454$	−10.8563	−0.509512
$455$	31.8158	1.49155
$456$	−11.2697	−0.527752
$457$	−14.1274	−0.660854	−0.330427	−	0.943832i	$-0.607193\pi$
$457$	−14.1274	−0.660854	−0.330427	+	0.943832i	$0.607193\pi$
$458$	−9.08360	−0.424449
$459$	−17.8472	−0.833037
$460$	4.01684	0.187286
$461$	−6.48635	−0.302099	−0.151050	−	0.988526i	$-0.548265\pi$
$461$	−6.48635	−0.302099	−0.151050	+	0.988526i	$0.548265\pi$
$462$	12.8637	0.598476
$463$	−25.7931	−1.19871	−0.599354	−	0.800484i	$-0.704576\pi$
$463$	−25.7931	−1.19871	−0.599354	+	0.800484i	$0.704576\pi$
$464$	2.78102	0.129105
$465$	11.7682	0.545736
$466$	−12.3542	−0.572297
$467$	−31.8267	−1.47276	−0.736382	−	0.676566i	$-0.763467\pi$
$467$	−31.8267	−1.47276	−0.736382	+	0.676566i	$0.763467\pi$
$468$	8.03823	0.371567
$469$	−35.3897	−1.63415
$470$	−8.53243	−0.393572
$471$	42.4848	1.95759
$472$	−2.67800	−0.123265
$473$	−8.15832	−0.375120
$474$	22.8193	1.04812
$475$	−9.98587	−0.458183
$476$	12.7667	0.585159
$477$	−8.98034	−0.411182
$478$	7.78666	0.356154
$479$	6.57135	0.300252	0.150126	−	0.988667i	$-0.452032\pi$
$479$	6.57135	0.300252	0.150126	+	0.988667i	$0.452032\pi$
$480$	−5.56727	−0.254110
$481$	6.00570	0.273836
$482$	16.8509	0.767537
$483$	−7.37887	−0.335750
$484$	−3.87318	−0.176054
$485$	0.349396	0.0158653
$486$	−14.3555	−0.651180
$487$	−9.33311	−0.422924	−0.211462	−	0.977386i	$-0.567822\pi$
$487$	−9.33311	−0.422924	−0.211462	+	0.977386i	$0.567822\pi$
$488$	0.0729553	0.00330253
$489$	−12.0365	−0.544310
$490$	−4.84106	−0.218697
$491$	−27.0410	−1.22034	−0.610172	−	0.792269i	$-0.708900\pi$
$491$	−27.0410	−1.22034	−0.610172	+	0.792269i	$0.708900\pi$
$492$	1.05855	0.0477233
$493$	−15.6383	−0.704315
$494$	28.3675	1.27632
$495$	10.5362	0.473568
$496$	2.11381	0.0949130
$497$	−33.7007	−1.51168
$498$	−5.11169	−0.229060
$499$	21.7038	0.971597	0.485798	−	0.874071i	$-0.338529\pi$
$499$	21.7038	0.971597	0.485798	+	0.874071i	$0.338529\pi$
$500$	8.18242	0.365929
$501$	−7.50812	−0.335438
$502$	−4.28783	−0.191375
$503$	−17.8496	−0.795873	−0.397937	−	0.917413i	$-0.630274\pi$
$503$	−17.8496	−0.795873	−0.397937	+	0.917413i	$0.630274\pi$
$504$	3.41597	0.152159
$505$	1.79586	0.0799147
$506$	−4.08807	−0.181737
$507$	−32.9852	−1.46492
$508$	12.8550	0.570350
$509$	−27.3575	−1.21260	−0.606301	−	0.795235i	$-0.707347\pi$
$509$	−27.3575	−1.21260	−0.606301	+	0.795235i	$0.707347\pi$
$510$	31.3061	1.38626
$511$	17.4727	0.772947
$512$	−1.00000	−0.0441942
$513$	−16.8526	−0.744062
$514$	17.2501	0.760870
$515$	−40.2078	−1.77177
$516$	−6.48606	−0.285533
$517$	8.68374	0.381911
$518$	2.55221	0.112138
$519$	−27.3552	−1.20076
$520$	14.0137	0.614540
$521$	−17.4198	−0.763177	−0.381588	−	0.924332i	$-0.624623\pi$
$521$	−17.4198	−0.763177	−0.381588	+	0.924332i	$0.624623\pi$
$522$	−4.18433	−0.183143
$523$	36.5406	1.59781	0.798904	−	0.601459i	$-0.205414\pi$
$523$	36.5406	1.59781	0.798904	+	0.601459i	$0.205414\pi$
$524$	−7.51035	−0.328091
$525$	9.06195	0.395496
$526$	14.4053	0.628102
$527$	−11.8865	−0.517783
$528$	5.66600	0.246581
$529$	−20.6550	−0.898044
$530$	−15.6561	−0.680058
$531$	4.02934	0.174858
$532$	12.0552	0.522660
$533$	−2.66454	−0.115414
$534$	7.82954	0.338817
$535$	8.55768	0.369981
$536$	−15.5879	−0.673293
$537$	17.0577	0.736095
$538$	19.9231	0.858947
$539$	4.92690	0.212217
$540$	−8.32526	−0.358262
$541$	−7.36609	−0.316693	−0.158346	−	0.987384i	$-0.550616\pi$
$541$	−7.36609	−0.316693	−0.158346	+	0.987384i	$0.550616\pi$
$542$	−22.9545	−0.985981
$543$	−30.8519	−1.32398
$544$	5.62324	0.241094
$545$	−14.4615	−0.619464
$546$	−25.7429	−1.10169
$547$	17.1950	0.735204	0.367602	−	0.929983i	$-0.380179\pi$
$547$	17.1950	0.735204	0.367602	+	0.929983i	$0.380179\pi$
$548$	−7.88492	−0.336827
$549$	−0.109769	−0.00468483
$550$	5.02054	0.214076
$551$	−14.7668	−0.629089
$552$	−3.25011	−0.138334
$553$	−24.4098	−1.03801
$554$	−11.6956	−0.496898
$555$	6.25847	0.265657
$556$	2.03745	0.0864069
$557$	14.8218	0.628018	0.314009	−	0.949420i	$-0.398328\pi$
$557$	14.8218	0.628018	0.314009	+	0.949420i	$0.398328\pi$
$558$	−3.18045	−0.134639
$559$	16.3264	0.690533
$560$	5.95532	0.251658
$561$	−31.8613	−1.34518
$562$	12.6265	0.532615
$563$	−36.8498	−1.55303	−0.776517	−	0.630096i	$-0.783016\pi$
$563$	−36.8498	−1.55303	−0.776517	+	0.630096i	$0.783016\pi$
$564$	6.90379	0.290702
$565$	−11.3816	−0.478826
$566$	15.0384	0.632110
$567$	25.5413	1.07263
$568$	−14.8439	−0.622836
$569$	5.75241	0.241154	0.120577	−	0.992704i	$-0.461526\pi$
$569$	5.75241	0.241154	0.120577	+	0.992704i	$0.461526\pi$
$570$	29.5615	1.23819
$571$	−15.0210	−0.628611	−0.314305	−	0.949322i	$-0.601772\pi$
$571$	−15.0210	−0.628611	−0.314305	+	0.949322i	$0.601772\pi$
$572$	−14.2622	−0.596331
$573$	−31.0351	−1.29651
$574$	−1.13234	−0.0472628
$575$	−2.87987	−0.120099
$576$	1.50461	0.0626919
$577$	−28.8759	−1.20212	−0.601059	−	0.799204i	$-0.705254\pi$
$577$	−28.8759	−1.20212	−0.601059	+	0.799204i	$0.705254\pi$
$578$	−14.6208	−0.608145
$579$	52.6569	2.18834
$580$	−7.29487	−0.302903
$581$	5.46798	0.226850
$582$	−0.282705	−0.0117185
$583$	15.9338	0.659909
$584$	7.69607	0.318466
$585$	−21.0850	−0.871759
$586$	11.7120	0.483819
$587$	−24.5531	−1.01341	−0.506707	−	0.862119i	$-0.669137\pi$
$587$	−24.5531	−1.01341	−0.506707	+	0.862119i	$0.669137\pi$
$588$	3.91701	0.161535
$589$	−11.2241	−0.462480
$590$	7.02466	0.289201
$591$	−1.01083	−0.0415798
$592$	1.12415	0.0462025
$593$	29.1105	1.19543	0.597713	−	0.801710i	$-0.296076\pi$
$593$	29.1105	1.19543	0.597713	+	0.801710i	$0.296076\pi$
$594$	8.47290	0.347647
$595$	−33.4882	−1.37288
$596$	3.45785	0.141639
$597$	−39.8506	−1.63098
$598$	8.18103	0.334547
$599$	28.7755	1.17573	0.587867	−	0.808957i	$-0.299968\pi$
$599$	28.7755	1.17573	0.587867	+	0.808957i	$0.299968\pi$
$600$	3.99145	0.162950
$601$	1.81989	0.0742347	0.0371174	−	0.999311i	$-0.488182\pi$
$601$	1.81989	0.0742347	0.0371174	+	0.999311i	$0.488182\pi$
$602$	6.93815	0.282778
$603$	23.4536	0.955103
$604$	16.2595	0.661592
$605$	10.1597	0.413051
$606$	−1.45307	−0.0590270
$607$	−29.1179	−1.18186	−0.590929	−	0.806723i	$-0.701239\pi$
$607$	−29.1179	−1.18186	−0.590929	+	0.806723i	$0.701239\pi$
$608$	5.30987	0.215344
$609$	13.4006	0.543018
$610$	−0.191369	−0.00774829
$611$	−17.3779	−0.703034
$612$	−8.46076	−0.342006
$613$	−11.4819	−0.463750	−0.231875	−	0.972746i	$-0.574486\pi$
$613$	−11.4819	−0.463750	−0.231875	+	0.972746i	$0.574486\pi$
$614$	22.6144	0.912642
$615$	−2.77669	−0.111967
$616$	−6.06093	−0.244202
$617$	−5.67320	−0.228394	−0.114197	−	0.993458i	$-0.536430\pi$
$617$	−5.67320	−0.228394	−0.114197	+	0.993458i	$0.536430\pi$
$618$	32.5331	1.30867
$619$	−16.5428	−0.664910	−0.332455	−	0.943119i	$-0.607877\pi$
$619$	−16.5428	−0.664910	−0.332455	+	0.943119i	$0.607877\pi$
$620$	−5.54473	−0.222682
$621$	−4.86020	−0.195033
$622$	12.8547	0.515428
$623$	−8.37527	−0.335548
$624$	−11.3388	−0.453914
$625$	−30.8664	−1.23465
$626$	0.955387	0.0381849
$627$	−30.0857	−1.20151
$628$	−20.0173	−0.798776
$629$	−6.32139	−0.252050
$630$	−8.96041	−0.356991
$631$	14.5842	0.580587	0.290293	−	0.956938i	$-0.406247\pi$
$631$	14.5842	0.580587	0.290293	+	0.956938i	$0.406247\pi$
$632$	−10.7516	−0.427676
$633$	31.6955	1.25978
$634$	18.6844	0.742051
$635$	−33.7200	−1.33814
$636$	12.6677	0.502308
$637$	−9.85970	−0.390656
$638$	7.42423	0.293928
$639$	22.3342	0.883527
$640$	2.62309	0.103687
$641$	27.5826	1.08945	0.544724	−	0.838616i	$-0.316635\pi$
$641$	27.5826	1.08945	0.544724	+	0.838616i	$0.316635\pi$
$642$	−6.92421	−0.273277
$643$	−2.10472	−0.0830022	−0.0415011	−	0.999138i	$-0.513214\pi$
$643$	−2.10472	−0.0830022	−0.0415011	+	0.999138i	$0.513214\pi$
$644$	3.47665	0.136999
$645$	17.0136	0.669908
$646$	−29.8587	−1.17477
$647$	27.0554	1.06366	0.531830	−	0.846851i	$-0.321505\pi$
$647$	27.0554	1.06366	0.531830	+	0.846851i	$0.321505\pi$
$648$	11.2500	0.441941
$649$	−7.14923	−0.280632
$650$	−10.0471	−0.394079
$651$	10.1856	0.399205
$652$	5.67117	0.222100
$653$	10.6273	0.415877	0.207938	−	0.978142i	$-0.433325\pi$
$653$	10.6273	0.415877	0.207938	+	0.978142i	$0.433325\pi$
$654$	11.7012	0.457551
$655$	19.7004	0.769757
$656$	−0.498752	−0.0194730
$657$	−11.5796	−0.451761
$658$	−7.38499	−0.287897
$659$	−5.55551	−0.216412	−0.108206	−	0.994128i	$-0.534511\pi$
$659$	−5.55551	−0.216412	−0.108206	+	0.994128i	$0.534511\pi$
$660$	−14.8624	−0.578520
$661$	−4.46823	−0.173794	−0.0868970	−	0.996217i	$-0.527695\pi$
$661$	−4.46823	−0.173794	−0.0868970	+	0.996217i	$0.527695\pi$
$662$	12.7968	0.497360
$663$	63.7606	2.47626
$664$	2.40844	0.0934656
$665$	−31.6220	−1.22625
$666$	−1.69141	−0.0655408
$667$	−4.25867	−0.164896
$668$	3.53755	0.136872
$669$	12.2282	0.472768
$670$	40.8884	1.57966
$671$	0.194762	0.00751872
$672$	−4.81858	−0.185881
$673$	17.4352	0.672079	0.336039	−	0.941848i	$-0.390913\pi$
$673$	17.4352	0.672079	0.336039	+	0.941848i	$0.390913\pi$
$674$	28.1579	1.08460
$675$	5.96879	0.229739
$676$	15.5414	0.597746
$677$	−45.9596	−1.76637	−0.883185	−	0.469025i	$-0.844605\pi$
$677$	−45.9596	−1.76637	−0.883185	+	0.469025i	$0.844605\pi$
$678$	9.20909	0.353673
$679$	0.302410	0.0116054
$680$	−14.7503	−0.565648
$681$	−23.0415	−0.882952
$682$	5.64306	0.216084
$683$	−5.78680	−0.221426	−0.110713	−	0.993852i	$-0.535313\pi$
$683$	−5.78680	−0.221426	−0.110713	+	0.993852i	$0.535313\pi$
$684$	−7.98926	−0.305477
$685$	20.6829	0.790252
$686$	−20.0824	−0.766750
$687$	−19.2791	−0.735543
$688$	3.05600	0.116509
$689$	−31.8866	−1.21478
$690$	8.52536	0.324555
$691$	−25.2484	−0.960494	−0.480247	−	0.877133i	$-0.659453\pi$
$691$	−25.2484	−0.960494	−0.480247	+	0.877133i	$0.659453\pi$
$692$	12.8888	0.489957
$693$	9.11931	0.346414
$694$	3.35340	0.127293
$695$	−5.34441	−0.202725
$696$	5.90245	0.223732
$697$	2.80460	0.106232
$698$	−20.1823	−0.763912
$699$	−26.2206	−0.991754
$700$	−4.26966	−0.161378
$701$	5.33596	0.201537	0.100768	−	0.994910i	$-0.467870\pi$
$701$	5.33596	0.201537	0.100768	+	0.994910i	$0.467870\pi$
$702$	−16.9559	−0.639961
$703$	−5.96912	−0.225129
$704$	−2.66961	−0.100615
$705$	−18.1093	−0.682035
$706$	−18.0386	−0.678893
$707$	1.55435	0.0584574
$708$	−5.68381	−0.213611
$709$	0.991705	0.0372443	0.0186221	−	0.999827i	$-0.494072\pi$
$709$	0.991705	0.0372443	0.0186221	+	0.999827i	$0.494072\pi$
$710$	38.9369	1.46128
$711$	16.1769	0.606683
$712$	−3.68899	−0.138251
$713$	−3.23696	−0.121225
$714$	27.0960	1.01404
$715$	37.4110	1.39909
$716$	−8.03697	−0.300356
$717$	16.5265	0.617192
$718$	11.1192	0.414963
$719$	−10.4712	−0.390508	−0.195254	−	0.980753i	$-0.562553\pi$
$719$	−10.4712	−0.390508	−0.195254	+	0.980753i	$0.562553\pi$
$720$	−3.94672	−0.147086
$721$	−34.8007	−1.29605
$722$	−9.19473	−0.342192
$723$	35.7644	1.33009
$724$	14.5363	0.540237
$725$	5.23005	0.194239
$726$	−8.22045	−0.305090
$727$	0.766939	0.0284442	0.0142221	−	0.999899i	$-0.495473\pi$
$727$	0.766939	0.0284442	0.0142221	+	0.999899i	$0.495473\pi$
$728$	12.1291	0.449535
$729$	3.28170	0.121545
$730$	−20.1875	−0.747174
$731$	−17.1846	−0.635595
$732$	0.154841	0.00572308
$733$	−2.37910	−0.0878740	−0.0439370	−	0.999034i	$-0.513990\pi$
$733$	−2.37910	−0.0878740	−0.0439370	+	0.999034i	$0.513990\pi$
$734$	−9.77189	−0.360687
$735$	−10.2747	−0.378987
$736$	1.53134	0.0564458
$737$	−41.6135	−1.53285
$738$	0.750425	0.0276235
$739$	−38.3199	−1.40962	−0.704810	−	0.709396i	$-0.748968\pi$
$739$	−38.3199	−1.40962	−0.704810	+	0.709396i	$0.748968\pi$
$740$	−2.94876	−0.108399
$741$	60.2074	2.21177
$742$	−13.5507	−0.497461
$743$	−13.4007	−0.491622	−0.245811	−	0.969318i	$-0.579054\pi$
$743$	−13.4007	−0.491622	−0.245811	+	0.969318i	$0.579054\pi$
$744$	4.48637	0.164478
$745$	−9.07026	−0.332309
$746$	−19.3566	−0.708695
$747$	−3.62375	−0.132586
$748$	15.0119	0.548888
$749$	7.40684	0.270640
$750$	17.3664	0.634132
$751$	16.4465	0.600142	0.300071	−	0.953917i	$-0.402990\pi$
$751$	16.4465	0.600142	0.300071	+	0.953917i	$0.402990\pi$
$752$	−3.25281	−0.118618
$753$	−9.10051	−0.331641
$754$	−14.8573	−0.541073
$755$	−42.6503	−1.55220
$756$	−7.20568	−0.262068
$757$	−16.7519	−0.608860	−0.304430	−	0.952535i	$-0.598466\pi$
$757$	−16.7519	−0.608860	−0.304430	+	0.952535i	$0.598466\pi$
$758$	−20.9237	−0.759981
$759$	−8.67654	−0.314939
$760$	−13.9283	−0.505232
$761$	−18.0251	−0.653409	−0.326704	−	0.945127i	$-0.605938\pi$
$761$	−18.0251	−0.653409	−0.326704	+	0.945127i	$0.605938\pi$
$762$	27.2836	0.988381
$763$	−12.5167	−0.453137
$764$	14.6226	0.529027
$765$	22.1934	0.802403
$766$	17.9898	0.649998
$767$	14.3070	0.516596
$768$	−2.12241	−0.0765857
$769$	−12.4159	−0.447730	−0.223865	−	0.974620i	$-0.571868\pi$
$769$	−12.4159	−0.447730	−0.223865	+	0.974620i	$0.571868\pi$
$770$	15.8984	0.572938
$771$	36.6118	1.31854
$772$	−24.8100	−0.892931
$773$	47.2551	1.69965	0.849824	−	0.527066i	$-0.176708\pi$
$773$	47.2551	1.69965	0.849824	+	0.527066i	$0.176708\pi$
$774$	−4.59807	−0.165274
$775$	3.97529	0.142797
$776$	0.133200	0.00478160
$777$	5.41683	0.194328
$778$	−4.29769	−0.154080
$779$	2.64831	0.0948854
$780$	29.7427	1.06496
$781$	−39.6274	−1.41798
$782$	−8.61106	−0.307931
$783$	8.82649	0.315433
$784$	−1.84555	−0.0659125
$785$	52.5072	1.87406
$786$	−15.9400	−0.568561
$787$	−15.0820	−0.537617	−0.268808	−	0.963194i	$-0.586630\pi$
$787$	−15.0820	−0.537617	−0.268808	+	0.963194i	$0.586630\pi$
$788$	0.476264	0.0169662
$789$	30.5739	1.08846
$790$	28.2025	1.00340
$791$	−9.85098	−0.350260
$792$	4.01671	0.142728
$793$	−0.389758	−0.0138407
$794$	11.7741	0.417845
$795$	−33.2286	−1.17850
$796$	18.7761	0.665502
$797$	−13.9874	−0.495460	−0.247730	−	0.968829i	$-0.579685\pi$
$797$	−13.9874	−0.495460	−0.247730	+	0.968829i	$0.579685\pi$
$798$	25.5861	0.905737
$799$	18.2913	0.647101
$800$	−1.88062	−0.0664901
$801$	5.55048	0.196117
$802$	−27.0934	−0.956701
$803$	20.5455	0.725036
$804$	−33.0837	−1.16677
$805$	−9.11959	−0.321423
$806$	−11.2929	−0.397774
$807$	42.2850	1.48850
$808$	0.684634	0.0240853
$809$	16.4108	0.576974	0.288487	−	0.957484i	$-0.406848\pi$
$809$	16.4108	0.576974	0.288487	+	0.957484i	$0.406848\pi$
$810$	−29.5098	−1.03687
$811$	15.2175	0.534360	0.267180	−	0.963647i	$-0.413908\pi$
$811$	15.2175	0.534360	0.267180	+	0.963647i	$0.413908\pi$
$812$	−6.31386	−0.221573
$813$	−48.7188	−1.70864
$814$	3.00106	0.105187
$815$	−14.8760	−0.521084
$816$	11.9348	0.417801
$817$	−16.2269	−0.567709
$818$	−6.98048	−0.244067
$819$	−18.2495	−0.637690
$820$	1.30827	0.0456869
$821$	5.11694	0.178582	0.0892912	−	0.996006i	$-0.471540\pi$
$821$	5.11694	0.178582	0.0892912	+	0.996006i	$0.471540\pi$
$822$	−16.7350	−0.583700
$823$	0.783298	0.0273040	0.0136520	−	0.999907i	$-0.495654\pi$
$823$	0.783298	0.0273040	0.0136520	+	0.999907i	$0.495654\pi$
$824$	−15.3284	−0.533990
$825$	10.6556	0.370981
$826$	6.07998	0.211550
$827$	−45.2586	−1.57379	−0.786897	−	0.617084i	$-0.788314\pi$
$827$	−45.2586	−1.57379	−0.786897	+	0.617084i	$0.788314\pi$
$828$	−2.30406	−0.0800715
$829$	15.4552	0.536780	0.268390	−	0.963310i	$-0.413508\pi$
$829$	15.4552	0.536780	0.268390	+	0.963310i	$0.413508\pi$
$830$	−6.31757	−0.219286
$831$	−24.8228	−0.861094
$832$	5.34242	0.185215
$833$	10.3780	0.359576
$834$	4.32429	0.149738
$835$	−9.27933	−0.321124
$836$	14.1753	0.490263
$837$	6.70889	0.231893
$838$	−33.0283	−1.14095
$839$	45.7916	1.58090	0.790451	−	0.612526i	$-0.209846\pi$
$839$	45.7916	1.58090	0.790451	+	0.612526i	$0.209846\pi$
$840$	12.6396	0.436108
$841$	−21.2659	−0.733308
$842$	−19.1723	−0.660720
$843$	26.7985	0.922988
$844$	−14.9338	−0.514041
$845$	−40.7666	−1.40241
$846$	4.89420	0.168266
$847$	8.79343	0.302146
$848$	−5.96857	−0.204961
$849$	31.9175	1.09541
$850$	10.5752	0.362726
$851$	−1.72146	−0.0590108
$852$	−31.5048	−1.07934
$853$	−29.4075	−1.00689	−0.503447	−	0.864026i	$-0.667935\pi$
$853$	−29.4075	−1.00689	−0.503447	+	0.864026i	$0.667935\pi$
$854$	−0.165633	−0.00566786
$855$	20.9566	0.716700
$856$	3.26244	0.111508
$857$	0.969909	0.0331315	0.0165657	−	0.999863i	$-0.494727\pi$
$857$	0.969909	0.0331315	0.0165657	+	0.999863i	$0.494727\pi$
$858$	−30.2701	−1.03340
$859$	8.00454	0.273111	0.136556	−	0.990632i	$-0.456397\pi$
$859$	8.00454	0.273111	0.136556	+	0.990632i	$0.456397\pi$
$860$	−8.01617	−0.273349
$861$	−2.40328	−0.0819035
$862$	4.83406	0.164649
$863$	7.62653	0.259610	0.129805	−	0.991540i	$-0.458565\pi$
$863$	7.62653	0.259610	0.129805	+	0.991540i	$0.458565\pi$
$864$	−3.17383	−0.107976
$865$	−33.8084	−1.14952
$866$	−9.62526	−0.327080
$867$	−31.0313	−1.05388
$868$	−4.79908	−0.162891
$869$	−28.7026	−0.973670
$870$	−15.4827	−0.524912
$871$	83.2768	2.82173
$872$	−5.51316	−0.186699
$873$	−0.200414	−0.00678297
$874$	−8.13119	−0.275042
$875$	−18.5769	−0.628013
$876$	16.3342	0.551881
$877$	−57.4907	−1.94132	−0.970661	−	0.240451i	$-0.922705\pi$
$877$	−57.4907	−1.94132	−0.970661	+	0.240451i	$0.922705\pi$
$878$	20.5113	0.692224
$879$	24.8577	0.838429
$880$	7.00264	0.236059
$881$	−27.7938	−0.936397	−0.468199	−	0.883623i	$-0.655097\pi$
$881$	−27.7938	−0.936397	−0.468199	+	0.883623i	$0.655097\pi$
$882$	2.77683	0.0935006
$883$	−41.2267	−1.38739	−0.693695	−	0.720269i	$-0.744018\pi$
$883$	−41.2267	−1.38739	−0.693695	+	0.720269i	$0.744018\pi$
$884$	−30.0417	−1.01041
$885$	14.9092	0.501166
$886$	3.87506	0.130185
$887$	36.5807	1.22826	0.614130	−	0.789205i	$-0.289507\pi$
$887$	36.5807	1.22826	0.614130	+	0.789205i	$0.289507\pi$
$888$	2.38591	0.0800660
$889$	−29.1853	−0.978844
$890$	9.67657	0.324360
$891$	30.0331	1.00615
$892$	−5.76147	−0.192908
$893$	17.2720	0.577986
$894$	7.33895	0.245451
$895$	21.0817	0.704685
$896$	2.27034	0.0758468
$897$	17.3635	0.579749
$898$	−21.4077	−0.714385
$899$	5.87855	0.196061
$900$	2.82960	0.0943199
$901$	33.5627	1.11813
$902$	−1.33147	−0.0443332
$903$	14.7256	0.490036
$904$	−4.33898	−0.144312
$905$	−38.1301	−1.26749
$906$	34.5094	1.14650
$907$	38.7528	1.28677	0.643383	−	0.765544i	$-0.277530\pi$
$907$	38.7528	1.28677	0.643383	+	0.765544i	$0.277530\pi$
$908$	10.8563	0.360279
$909$	−1.03010	−0.0341664
$910$	−31.8158	−1.05468
$911$	4.62364	0.153188	0.0765941	−	0.997062i	$-0.475595\pi$
$911$	4.62364	0.153188	0.0765941	+	0.997062i	$0.475595\pi$
$912$	11.2697	0.373177
$913$	6.42960	0.212789
$914$	14.1274	0.467294
$915$	−0.406162	−0.0134273
$916$	9.08360	0.300131
$917$	17.0511	0.563075
$918$	17.8472	0.589046
$919$	46.5292	1.53486	0.767428	−	0.641136i	$-0.221536\pi$
$919$	46.5292	1.53486	0.767428	+	0.641136i	$0.221536\pi$
$920$	−4.01684	−0.132431
$921$	47.9969	1.58155
$922$	6.48635	0.213616
$923$	79.3022	2.61026
$924$	−12.8637	−0.423186
$925$	2.11411	0.0695116
$926$	25.7931	0.847615
$927$	23.0632	0.757495
$928$	−2.78102	−0.0912914
$929$	6.89466	0.226206	0.113103	−	0.993583i	$-0.463921\pi$
$929$	6.89466	0.226206	0.113103	+	0.993583i	$0.463921\pi$
$930$	−11.7682	−0.385893
$931$	9.79964	0.321170
$932$	12.3542	0.404675
$933$	27.2829	0.893204
$934$	31.8267	1.04140
$935$	−39.3775	−1.28778
$936$	−8.03823	−0.262738
$937$	28.3140	0.924977	0.462488	−	0.886625i	$-0.346957\pi$
$937$	28.3140	0.924977	0.462488	+	0.886625i	$0.346957\pi$
$938$	35.3897	1.15552
$939$	2.02772	0.0661721
$940$	8.53243	0.278297
$941$	58.9233	1.92084	0.960422	−	0.278549i	$-0.0898534\pi$
$941$	58.9233	1.92084	0.960422	+	0.278549i	$0.0898534\pi$
$942$	−42.4848	−1.38423
$943$	0.763756	0.0248713
$944$	2.67800	0.0871616
$945$	18.9012	0.614856
$946$	8.15832	0.265250
$947$	24.0475	0.781440	0.390720	−	0.920510i	$-0.372226\pi$
$947$	24.0475	0.781440	0.390720	+	0.920510i	$0.372226\pi$
$948$	−22.8193	−0.741136
$949$	−41.1156	−1.33467
$950$	9.98587	0.323985
$951$	39.6558	1.28593
$952$	−12.7667	−0.413770
$953$	−21.0716	−0.682576	−0.341288	−	0.939959i	$-0.610863\pi$
$953$	−21.0716	−0.682576	−0.341288	+	0.939959i	$0.610863\pi$
$954$	8.98034	0.290749
$955$	−38.3565	−1.24119
$956$	−7.78666	−0.251839
$957$	15.7572	0.509359
$958$	−6.57135	−0.212311
$959$	17.9014	0.578068
$960$	5.56727	0.179683
$961$	−26.5318	−0.855864
$962$	−6.00570	−0.193632
$963$	−4.90868	−0.158180
$964$	−16.8509	−0.542731
$965$	65.0789	2.09497
$966$	7.37887	0.237411
$967$	13.6229	0.438083	0.219042	−	0.975716i	$-0.429707\pi$
$967$	13.6229	0.438083	0.219042	+	0.975716i	$0.429707\pi$
$968$	3.87318	0.124489
$969$	−63.3722	−2.03581
$970$	−0.349396	−0.0112184
$971$	−45.6905	−1.46628	−0.733138	−	0.680080i	$-0.761945\pi$
$971$	−45.6905	−1.46628	−0.733138	+	0.680080i	$0.761945\pi$
$972$	14.3555	0.460453
$973$	−4.62570	−0.148293
$974$	9.33311	0.299052
$975$	−21.3240	−0.682914
$976$	−0.0729553	−0.00233524
$977$	39.0021	1.24779	0.623894	−	0.781509i	$-0.285550\pi$
$977$	39.0021	1.24779	0.623894	+	0.781509i	$0.285550\pi$
$978$	12.0365	0.384885
$979$	−9.84817	−0.314749
$980$	4.84106	0.154642
$981$	8.29512	0.264843
$982$	27.0410	0.862914
$983$	−21.5014	−0.685788	−0.342894	−	0.939374i	$-0.611407\pi$
$983$	−21.5014	−0.685788	−0.342894	+	0.939374i	$0.611407\pi$
$984$	−1.05855	−0.0337454
$985$	−1.24929	−0.0398056
$986$	15.6383	0.498026
$987$	−15.6740	−0.498907
$988$	−28.3675	−0.902492
$989$	−4.67975	−0.148808
$990$	−10.5362	−0.334863
$991$	48.1482	1.52948	0.764740	−	0.644340i	$-0.222868\pi$
$991$	48.1482	1.52948	0.764740	+	0.644340i	$0.222868\pi$
$992$	−2.11381	−0.0671136
$993$	27.1599	0.861893
$994$	33.7007	1.06892
$995$	−49.2516	−1.56138
$996$	5.11169	0.161970
$997$	−2.76531	−0.0875782	−0.0437891	−	0.999041i	$-0.513943\pi$
$997$	−2.76531	−0.0875782	−0.0437891	+	0.999041i	$0.513943\pi$
$998$	−21.7038	−0.687023
$999$	3.56788	0.112883

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.d.1.16	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.d.1.16	✓	64	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.12241 q^{3} +1.00000 q^{4} -2.62309 q^{5} +2.12241 q^{6} -2.27034 q^{7} -1.00000 q^{8} +1.50461 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.12241 q^{3} +1.00000 q^{4} -2.62309 q^{5} +2.12241 q^{6} -2.27034 q^{7} -1.00000 q^{8} +1.50461 q^{9} +2.62309 q^{10} -2.66961 q^{11} -2.12241 q^{12} +5.34242 q^{13} +2.27034 q^{14} +5.56727 q^{15} +1.00000 q^{16} -5.62324 q^{17} -1.50461 q^{18} -5.30987 q^{19} -2.62309 q^{20} +4.81858 q^{21} +2.66961 q^{22} -1.53134 q^{23} +2.12241 q^{24} +1.88062 q^{25} -5.34242 q^{26} +3.17383 q^{27} -2.27034 q^{28} +2.78102 q^{29} -5.56727 q^{30} +2.11381 q^{31} -1.00000 q^{32} +5.66600 q^{33} +5.62324 q^{34} +5.95532 q^{35} +1.50461 q^{36} +1.12415 q^{37} +5.30987 q^{38} -11.3388 q^{39} +2.62309 q^{40} -0.498752 q^{41} -4.81858 q^{42} +3.05600 q^{43} -2.66961 q^{44} -3.94672 q^{45} +1.53134 q^{46} -3.25281 q^{47} -2.12241 q^{48} -1.84555 q^{49} -1.88062 q^{50} +11.9348 q^{51} +5.34242 q^{52} -5.96857 q^{53} -3.17383 q^{54} +7.00264 q^{55} +2.27034 q^{56} +11.2697 q^{57} -2.78102 q^{58} +2.67800 q^{59} +5.56727 q^{60} -0.0729553 q^{61} -2.11381 q^{62} -3.41597 q^{63} +1.00000 q^{64} -14.0137 q^{65} -5.66600 q^{66} +15.5879 q^{67} -5.62324 q^{68} +3.25011 q^{69} -5.95532 q^{70} +14.8439 q^{71} -1.50461 q^{72} -7.69607 q^{73} -1.12415 q^{74} -3.99145 q^{75} -5.30987 q^{76} +6.06093 q^{77} +11.3388 q^{78} +10.7516 q^{79} -2.62309 q^{80} -11.2500 q^{81} +0.498752 q^{82} -2.40844 q^{83} +4.81858 q^{84} +14.7503 q^{85} -3.05600 q^{86} -5.90245 q^{87} +2.66961 q^{88} +3.68899 q^{89} +3.94672 q^{90} -12.1291 q^{91} -1.53134 q^{92} -4.48637 q^{93} +3.25281 q^{94} +13.9283 q^{95} +2.12241 q^{96} -0.133200 q^{97} +1.84555 q^{98} -4.01671 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9}+O(q^{10}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9	\( 64 q - 64 q^{2} - 9 q^{3} + 64 q^{4} - 17 q^{5} + 9 q^{6} - 2 q^{7} - 64 q^{8} + 61 q^{9} + 17 q^{10} - 15 q^{11} - 9 q^{12} - 28 q^{13} + 2 q^{14} + 64 q^{16} - 62 q^{17} - 61 q^{18} + 24 q^{19} - 17 q^{20} - 20 q^{21} + 15 q^{22} - 41 q^{23} + 9 q^{24} + 61 q^{25} + 28 q^{26} - 36 q^{27} - 2 q^{28} - 45 q^{29} + 40 q^{31} - 64 q^{32} - 36 q^{33} + 62 q^{34} - 59 q^{35} + 61 q^{36} - 27 q^{37} - 24 q^{38} + 5 q^{39} + 17 q^{40} - 42 q^{41} + 20 q^{42} - 25 q^{43} - 15 q^{44} - 47 q^{45} + 41 q^{46} - 64 q^{47} - 9 q^{48} + 76 q^{49} - 61 q^{50} + 5 q^{51} - 28 q^{52} - 70 q^{53} + 36 q^{54} + 9 q^{55} + 2 q^{56} - 47 q^{57} + 45 q^{58} - 17 q^{59} - 52 q^{61} - 40 q^{62} - 36 q^{63} + 64 q^{64} - 49 q^{65} + 36 q^{66} + 5 q^{67} - 62 q^{68} - 69 q^{69} + 59 q^{70} - 9 q^{71} - 61 q^{72} - 39 q^{73} + 27 q^{74} - 28 q^{75} + 24 q^{76} - 149 q^{77} - 5 q^{78} + 31 q^{79} - 17 q^{80} + 52 q^{81} + 42 q^{82} - 121 q^{83} - 20 q^{84} - 54 q^{85} + 25 q^{86} - 78 q^{87} + 15 q^{88} - 24 q^{89} + 47 q^{90} + 74 q^{91} - 41 q^{92} - 74 q^{93} + 64 q^{94} - 74 q^{95} + 9 q^{96} - 5 q^{97} - 76 q^{98} - 34 q^{99}+O(q^{100}) \) 64 * q - 64 * q^2 - 9 * q^3 + 64 * q^4 - 17 * q^5 + 9 * q^6 - 2 * q^7 - 64 * q^8 + 61 * q^9 + 17 * q^10 - 15 * q^11 - 9 * q^12 - 28 * q^13 + 2 * q^14 + 64 * q^16 - 62 * q^17 - 61 * q^18 + 24 * q^19 - 17 * q^20 - 20 * q^21 + 15 * q^22 - 41 * q^23 + 9 * q^24 + 61 * q^25 + 28 * q^26 - 36 * q^27 - 2 * q^28 - 45 * q^29 + 40 * q^31 - 64 * q^32 - 36 * q^33 + 62 * q^34 - 59 * q^35 + 61 * q^36 - 27 * q^37 - 24 * q^38 + 5 * q^39 + 17 * q^40 - 42 * q^41 + 20 * q^42 - 25 * q^43 - 15 * q^44 - 47 * q^45 + 41 * q^46 - 64 * q^47 - 9 * q^48 + 76 * q^49 - 61 * q^50 + 5 * q^51 - 28 * q^52 - 70 * q^53 + 36 * q^54 + 9 * q^55 + 2 * q^56 - 47 * q^57 + 45 * q^58 - 17 * q^59 - 52 * q^61 - 40 * q^62 - 36 * q^63 + 64 * q^64 - 49 * q^65 + 36 * q^66 + 5 * q^67 - 62 * q^68 - 69 * q^69 + 59 * q^70 - 9 * q^71 - 61 * q^72 - 39 * q^73 + 27 * q^74 - 28 * q^75 + 24 * q^76 - 149 * q^77 - 5 * q^78 + 31 * q^79 - 17 * q^80 + 52 * q^81 + 42 * q^82 - 121 * q^83 - 20 * q^84 - 54 * q^85 + 25 * q^86 - 78 * q^87 + 15 * q^88 - 24 * q^89 + 47 * q^90 + 74 * q^91 - 41 * q^92 - 74 * q^93 + 64 * q^94 - 74 * q^95 + 9 * q^96 - 5 * q^97 - 76 * q^98 - 34 * q^99

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