LMFDB - Embedded newform 6014.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.09484 q^{3} +1.00000 q^{4} -2.95477 q^{5} -1.09484 q^{6} +4.52432 q^{7} +1.00000 q^{8} -1.80131 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.09484 q^{3} +1.00000 q^{4} -2.95477 q^{5} -1.09484 q^{6} +4.52432 q^{7} +1.00000 q^{8} -1.80131 q^{9} -2.95477 q^{10} +0.973544 q^{11} -1.09484 q^{12} -0.321880 q^{13} +4.52432 q^{14} +3.23502 q^{15} +1.00000 q^{16} +5.47544 q^{17} -1.80131 q^{18} -8.33609 q^{19} -2.95477 q^{20} -4.95342 q^{21} +0.973544 q^{22} -7.79502 q^{23} -1.09484 q^{24} +3.73068 q^{25} -0.321880 q^{26} +5.25669 q^{27} +4.52432 q^{28} +4.73990 q^{29} +3.23502 q^{30} +1.00000 q^{31} +1.00000 q^{32} -1.06588 q^{33} +5.47544 q^{34} -13.3683 q^{35} -1.80131 q^{36} -5.69857 q^{37} -8.33609 q^{38} +0.352409 q^{39} -2.95477 q^{40} -4.64658 q^{41} -4.95342 q^{42} -1.75519 q^{43} +0.973544 q^{44} +5.32247 q^{45} -7.79502 q^{46} +7.45409 q^{47} -1.09484 q^{48} +13.4694 q^{49} +3.73068 q^{50} -5.99476 q^{51} -0.321880 q^{52} +2.49322 q^{53} +5.25669 q^{54} -2.87660 q^{55} +4.52432 q^{56} +9.12672 q^{57} +4.73990 q^{58} -12.3364 q^{59} +3.23502 q^{60} +0.214635 q^{61} +1.00000 q^{62} -8.14972 q^{63} +1.00000 q^{64} +0.951083 q^{65} -1.06588 q^{66} -3.04948 q^{67} +5.47544 q^{68} +8.53433 q^{69} -13.3683 q^{70} +11.4947 q^{71} -1.80131 q^{72} +0.856447 q^{73} -5.69857 q^{74} -4.08451 q^{75} -8.33609 q^{76} +4.40462 q^{77} +0.352409 q^{78} -7.12470 q^{79} -2.95477 q^{80} -0.351320 q^{81} -4.64658 q^{82} -17.1731 q^{83} -4.95342 q^{84} -16.1787 q^{85} -1.75519 q^{86} -5.18945 q^{87} +0.973544 q^{88} -15.0012 q^{89} +5.32247 q^{90} -1.45629 q^{91} -7.79502 q^{92} -1.09484 q^{93} +7.45409 q^{94} +24.6312 q^{95} -1.09484 q^{96} -1.00000 q^{97} +13.4694 q^{98} -1.75366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.09484	−0.632109	−0.316054	−	0.948741i	$-0.602358\pi$
$3$	−1.09484	−0.632109	−0.316054	+	0.948741i	$0.602358\pi$
$4$	1.00000	0.500000
$5$	−2.95477	−1.32141	−0.660707	−	0.750644i	$-0.729743\pi$
$5$	−2.95477	−1.32141	−0.660707	+	0.750644i	$0.729743\pi$
$6$	−1.09484	−0.446969
$7$	4.52432	1.71003	0.855015	−	0.518603i	$-0.173548\pi$
$7$	4.52432	1.71003	0.855015	+	0.518603i	$0.173548\pi$
$8$	1.00000	0.353553
$9$	−1.80131	−0.600438
$10$	−2.95477	−0.934381
$11$	0.973544	0.293535	0.146767	−	0.989171i	$-0.453113\pi$
$11$	0.973544	0.293535	0.146767	+	0.989171i	$0.453113\pi$
$12$	−1.09484	−0.316054
$13$	−0.321880	−0.0892735	−0.0446368	−	0.999003i	$-0.514213\pi$
$13$	−0.321880	−0.0892735	−0.0446368	+	0.999003i	$0.514213\pi$
$14$	4.52432	1.20917
$15$	3.23502	0.835278
$16$	1.00000	0.250000
$17$	5.47544	1.32799	0.663995	−	0.747737i	$-0.268860\pi$
$17$	5.47544	1.32799	0.663995	+	0.747737i	$0.268860\pi$
$18$	−1.80131	−0.424574
$19$	−8.33609	−1.91243	−0.956215	−	0.292666i	$-0.905458\pi$
$19$	−8.33609	−1.91243	−0.956215	+	0.292666i	$0.905458\pi$
$20$	−2.95477	−0.660707
$21$	−4.95342	−1.08093
$22$	0.973544	0.207560
$23$	−7.79502	−1.62537	−0.812687	−	0.582701i	$-0.801996\pi$
$23$	−7.79502	−1.62537	−0.812687	+	0.582701i	$0.801996\pi$
$24$	−1.09484	−0.223484
$25$	3.73068	0.746135
$26$	−0.321880	−0.0631259
$27$	5.25669	1.01165
$28$	4.52432	0.855015
$29$	4.73990	0.880176	0.440088	−	0.897955i	$-0.354947\pi$
$29$	4.73990	0.880176	0.440088	+	0.897955i	$0.354947\pi$
$30$	3.23502	0.590630
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−1.06588	−0.185546
$34$	5.47544	0.939031
$35$	−13.3683	−2.25966
$36$	−1.80131	−0.300219
$37$	−5.69857	−0.936839	−0.468419	−	0.883506i	$-0.655176\pi$
$37$	−5.69857	−0.936839	−0.468419	+	0.883506i	$0.655176\pi$
$38$	−8.33609	−1.35229
$39$	0.352409	0.0564306
$40$	−2.95477	−0.467190
$41$	−4.64658	−0.725675	−0.362837	−	0.931853i	$-0.618192\pi$
$41$	−4.64658	−0.725675	−0.362837	+	0.931853i	$0.618192\pi$
$42$	−4.95342	−0.764330
$43$	−1.75519	−0.267664	−0.133832	−	0.991004i	$-0.542728\pi$
$43$	−1.75519	−0.267664	−0.133832	+	0.991004i	$0.542728\pi$
$44$	0.973544	0.146767
$45$	5.32247	0.793428
$46$	−7.79502	−1.14931
$47$	7.45409	1.08729	0.543646	−	0.839315i	$-0.317044\pi$
$47$	7.45409	1.08729	0.543646	+	0.839315i	$0.317044\pi$
$48$	−1.09484	−0.158027
$49$	13.4694	1.92421
$50$	3.73068	0.527597
$51$	−5.99476	−0.839434
$52$	−0.321880	−0.0446368
$53$	2.49322	0.342470	0.171235	−	0.985230i	$-0.445224\pi$
$53$	2.49322	0.342470	0.171235	+	0.985230i	$0.445224\pi$
$54$	5.25669	0.715346
$55$	−2.87660	−0.387881
$56$	4.52432	0.604587
$57$	9.12672	1.20886
$58$	4.73990	0.622379
$59$	−12.3364	−1.60606	−0.803031	−	0.595937i	$-0.796781\pi$
$59$	−12.3364	−1.60606	−0.803031	+	0.595937i	$0.796781\pi$
$60$	3.23502	0.417639
$61$	0.214635	0.0274812	0.0137406	−	0.999906i	$-0.495626\pi$
$61$	0.214635	0.0274812	0.0137406	+	0.999906i	$0.495626\pi$
$62$	1.00000	0.127000
$63$	−8.14972	−1.02677
$64$	1.00000	0.125000
$65$	0.951083	0.117967
$66$	−1.06588	−0.131201
$67$	−3.04948	−0.372553	−0.186276	−	0.982497i	$-0.559642\pi$
$67$	−3.04948	−0.372553	−0.186276	+	0.982497i	$0.559642\pi$
$68$	5.47544	0.663995
$69$	8.53433	1.02741
$70$	−13.3683	−1.59782
$71$	11.4947	1.36417	0.682083	−	0.731275i	$-0.261074\pi$
$71$	11.4947	1.36417	0.682083	+	0.731275i	$0.261074\pi$
$72$	−1.80131	−0.212287
$73$	0.856447	0.100240	0.0501198	−	0.998743i	$-0.484040\pi$
$73$	0.856447	0.100240	0.0501198	+	0.998743i	$0.484040\pi$
$74$	−5.69857	−0.662445
$75$	−4.08451	−0.471639
$76$	−8.33609	−0.956215
$77$	4.40462	0.501953
$78$	0.352409	0.0399025
$79$	−7.12470	−0.801591	−0.400796	−	0.916167i	$-0.631266\pi$
$79$	−7.12470	−0.801591	−0.400796	+	0.916167i	$0.631266\pi$
$80$	−2.95477	−0.330354
$81$	−0.351320	−0.0390355
$82$	−4.64658	−0.513129
$83$	−17.1731	−1.88499	−0.942496	−	0.334219i	$-0.891528\pi$
$83$	−17.1731	−1.88499	−0.942496	+	0.334219i	$0.891528\pi$
$84$	−4.95342	−0.540463
$85$	−16.1787	−1.75482
$86$	−1.75519	−0.189267
$87$	−5.18945	−0.556367
$88$	0.973544	0.103780
$89$	−15.0012	−1.59012	−0.795062	−	0.606528i	$-0.792562\pi$
$89$	−15.0012	−1.59012	−0.795062	+	0.606528i	$0.792562\pi$
$90$	5.32247	0.561038
$91$	−1.45629	−0.152660
$92$	−7.79502	−0.812687
$93$	−1.09484	−0.113530
$94$	7.45409	0.768831
$95$	24.6312	2.52711
$96$	−1.09484	−0.111742
$97$	−1.00000	−0.101535
$97$	−1.00000	−0.101535
$98$	13.4694	1.36062
$99$	−1.75366	−0.176249
$100$	3.73068	0.373068
$101$	8.74087	0.869749	0.434874	−	0.900491i	$-0.356793\pi$
$101$	8.74087	0.869749	0.434874	+	0.900491i	$0.356793\pi$
$102$	−5.99476	−0.593570
$103$	−4.81002	−0.473945	−0.236973	−	0.971516i	$-0.576155\pi$
$103$	−4.81002	−0.473945	−0.236973	+	0.971516i	$0.576155\pi$
$104$	−0.321880	−0.0315630
$105$	14.6362	1.42835
$106$	2.49322	0.242163
$107$	3.82459	0.369737	0.184868	−	0.982763i	$-0.440814\pi$
$107$	3.82459	0.369737	0.184868	+	0.982763i	$0.440814\pi$
$108$	5.25669	0.505826
$109$	3.87495	0.371153	0.185576	−	0.982630i	$-0.440585\pi$
$109$	3.87495	0.371153	0.185576	+	0.982630i	$0.440585\pi$
$110$	−2.87660	−0.274273
$111$	6.23905	0.592184
$112$	4.52432	0.427508
$113$	3.63515	0.341967	0.170983	−	0.985274i	$-0.445306\pi$
$113$	3.63515	0.341967	0.170983	+	0.985274i	$0.445306\pi$
$114$	9.12672	0.854796
$115$	23.0325	2.14779
$116$	4.73990	0.440088
$117$	0.579808	0.0536032
$118$	−12.3364	−1.13566
$119$	24.7726	2.27090
$120$	3.23502	0.295315
$121$	−10.0522	−0.913837
$122$	0.214635	0.0194321
$123$	5.08729	0.458705
$124$	1.00000	0.0898027
$125$	3.75056	0.335461
$126$	−8.14972	−0.726035
$127$	1.24037	0.110065	0.0550327	−	0.998485i	$-0.482474\pi$
$127$	1.24037	0.110065	0.0550327	+	0.998485i	$0.482474\pi$
$128$	1.00000	0.0883883
$129$	1.92166	0.169193
$130$	0.951083	0.0834155
$131$	−8.36827	−0.731139	−0.365569	−	0.930784i	$-0.619126\pi$
$131$	−8.36827	−0.731139	−0.365569	+	0.930784i	$0.619126\pi$
$132$	−1.06588	−0.0927729
$133$	−37.7151	−3.27031
$134$	−3.04948	−0.263435
$135$	−15.5323	−1.33681
$136$	5.47544	0.469515
$137$	8.12493	0.694160	0.347080	−	0.937836i	$-0.387173\pi$
$137$	8.12493	0.694160	0.347080	+	0.937836i	$0.387173\pi$
$138$	8.53433	0.726491
$139$	6.07479	0.515257	0.257628	−	0.966244i	$-0.417059\pi$
$139$	6.07479	0.515257	0.257628	+	0.966244i	$0.417059\pi$
$140$	−13.3683	−1.12983
$141$	−8.16107	−0.687286
$142$	11.4947	0.964611
$143$	−0.313365	−0.0262049
$144$	−1.80131	−0.150110
$145$	−14.0053	−1.16308
$146$	0.856447	0.0708801
$147$	−14.7469	−1.21631
$148$	−5.69857	−0.468419
$149$	−10.6195	−0.869981	−0.434990	−	0.900435i	$-0.643248\pi$
$149$	−10.6195	−0.869981	−0.434990	+	0.900435i	$0.643248\pi$
$150$	−4.08451	−0.333499
$151$	−7.06892	−0.575260	−0.287630	−	0.957742i	$-0.592867\pi$
$151$	−7.06892	−0.575260	−0.287630	+	0.957742i	$0.592867\pi$
$152$	−8.33609	−0.676146
$153$	−9.86300	−0.797376
$154$	4.40462	0.354935
$155$	−2.95477	−0.237333
$156$	0.352409	0.0282153
$157$	9.59822	0.766021	0.383011	−	0.923744i	$-0.374887\pi$
$157$	9.59822	0.766021	0.383011	+	0.923744i	$0.374887\pi$
$158$	−7.12470	−0.566811
$159$	−2.72969	−0.216478
$160$	−2.95477	−0.233595
$161$	−35.2671	−2.77944
$162$	−0.351320	−0.0276023
$163$	−10.7137	−0.839163	−0.419581	−	0.907718i	$-0.637823\pi$
$163$	−10.7137	−0.839163	−0.419581	+	0.907718i	$0.637823\pi$
$164$	−4.64658	−0.362837
$165$	3.14943	0.245183
$166$	−17.1731	−1.33289
$167$	1.78720	0.138297	0.0691487	−	0.997606i	$-0.477972\pi$
$167$	1.78720	0.138297	0.0691487	+	0.997606i	$0.477972\pi$
$168$	−4.95342	−0.382165
$169$	−12.8964	−0.992030
$170$	−16.1787	−1.24085
$171$	15.0159	1.14830
$172$	−1.75519	−0.133832
$173$	−7.25847	−0.551851	−0.275925	−	0.961179i	$-0.588984\pi$
$173$	−7.25847	−0.551851	−0.275925	+	0.961179i	$0.588984\pi$
$174$	−5.18945	−0.393411
$175$	16.8788	1.27591
$176$	0.973544	0.0733837
$177$	13.5064	1.01521
$178$	−15.0012	−1.12439
$179$	3.82957	0.286235	0.143118	−	0.989706i	$-0.454287\pi$
$179$	3.82957	0.286235	0.143118	+	0.989706i	$0.454287\pi$
$180$	5.32247	0.396714
$181$	−4.38140	−0.325667	−0.162833	−	0.986654i	$-0.552063\pi$
$181$	−4.38140	−0.325667	−0.162833	+	0.986654i	$0.552063\pi$
$182$	−1.45629	−0.107947
$183$	−0.234992	−0.0173711
$184$	−7.79502	−0.574656
$185$	16.8380	1.23795
$186$	−1.09484	−0.0802779
$187$	5.33059	0.389811
$188$	7.45409	0.543646
$189$	23.7829	1.72996
$190$	24.6312	1.78694
$191$	12.5377	0.907193	0.453597	−	0.891207i	$-0.350141\pi$
$191$	12.5377	0.907193	0.453597	+	0.891207i	$0.350141\pi$
$192$	−1.09484	−0.0790136
$193$	−20.3895	−1.46767	−0.733834	−	0.679329i	$-0.762271\pi$
$193$	−20.3895	−1.46767	−0.733834	+	0.679329i	$0.762271\pi$
$194$	−1.00000	−0.0717958
$195$	−1.04129	−0.0745682
$196$	13.4694	0.962103
$197$	−18.4294	−1.31304	−0.656521	−	0.754307i	$-0.727973\pi$
$197$	−18.4294	−1.31304	−0.656521	+	0.754307i	$0.727973\pi$
$198$	−1.75366	−0.124627
$199$	−26.3483	−1.86778	−0.933892	−	0.357555i	$-0.883610\pi$
$199$	−26.3483	−1.86778	−0.933892	+	0.357555i	$0.883610\pi$
$200$	3.73068	0.263799
$201$	3.33870	0.235494
$202$	8.74087	0.615005
$203$	21.4448	1.50513
$204$	−5.99476	−0.419717
$205$	13.7296	0.958917
$206$	−4.81002	−0.335130
$207$	14.0413	0.975936
$208$	−0.321880	−0.0223184
$209$	−8.11555	−0.561364
$210$	14.6362	1.01000
$211$	−0.935098	−0.0643748	−0.0321874	−	0.999482i	$-0.510247\pi$
$211$	−0.935098	−0.0643748	−0.0321874	+	0.999482i	$0.510247\pi$
$212$	2.49322	0.171235
$213$	−12.5849	−0.862302
$214$	3.82459	0.261443
$215$	5.18618	0.353695
$216$	5.25669	0.357673
$217$	4.52432	0.307131
$218$	3.87495	0.262445
$219$	−0.937677	−0.0633623
$220$	−2.87660	−0.193940
$221$	−1.76244	−0.118554
$222$	6.23905	0.418737
$223$	13.3220	0.892107	0.446053	−	0.895006i	$-0.352829\pi$
$223$	13.3220	0.892107	0.446053	+	0.895006i	$0.352829\pi$
$224$	4.52432	0.302294
$225$	−6.72012	−0.448008
$226$	3.63515	0.241807
$227$	−5.63582	−0.374063	−0.187031	−	0.982354i	$-0.559887\pi$
$227$	−5.63582	−0.374063	−0.187031	+	0.982354i	$0.559887\pi$
$228$	9.12672	0.604432
$229$	−22.0969	−1.46020	−0.730102	−	0.683339i	$-0.760527\pi$
$229$	−22.0969	−1.46020	−0.730102	+	0.683339i	$0.760527\pi$
$230$	23.0325	1.51872
$231$	−4.82238	−0.317289
$232$	4.73990	0.311189
$233$	5.44442	0.356676	0.178338	−	0.983969i	$-0.442928\pi$
$233$	5.44442	0.356676	0.178338	+	0.983969i	$0.442928\pi$
$234$	0.579808	0.0379032
$235$	−22.0251	−1.43676
$236$	−12.3364	−0.803031
$237$	7.80044	0.506693
$238$	24.7726	1.60577
$239$	2.20955	0.142924	0.0714621	−	0.997443i	$-0.477234\pi$
$239$	2.20955	0.142924	0.0714621	+	0.997443i	$0.477234\pi$
$240$	3.23502	0.208819
$241$	−17.2397	−1.11050	−0.555252	−	0.831682i	$-0.687378\pi$
$241$	−17.2397	−1.11050	−0.555252	+	0.831682i	$0.687378\pi$
$242$	−10.0522	−0.646181
$243$	−15.3854	−0.986977
$244$	0.214635	0.0137406
$245$	−39.7991	−2.54267
$246$	5.08729	0.324354
$247$	2.68322	0.170729
$248$	1.00000	0.0635001
$249$	18.8019	1.19152
$250$	3.75056	0.237206
$251$	0.472163	0.0298026	0.0149013	−	0.999889i	$-0.495257\pi$
$251$	0.472163	0.0298026	0.0149013	+	0.999889i	$0.495257\pi$
$252$	−8.14972	−0.513384
$253$	−7.58879	−0.477103
$254$	1.24037	0.0778280
$255$	17.7131	1.10924
$256$	1.00000	0.0625000
$257$	−5.85911	−0.365481	−0.182741	−	0.983161i	$-0.558497\pi$
$257$	−5.85911	−0.365481	−0.182741	+	0.983161i	$0.558497\pi$
$258$	1.92166	0.119637
$259$	−25.7821	−1.60202
$260$	0.951083	0.0589837
$261$	−8.53804	−0.528492
$262$	−8.36827	−0.516993
$263$	−3.79897	−0.234255	−0.117127	−	0.993117i	$-0.537369\pi$
$263$	−3.79897	−0.234255	−0.117127	+	0.993117i	$0.537369\pi$
$264$	−1.06588	−0.0656004
$265$	−7.36690	−0.452545
$266$	−37.7151	−2.31246
$267$	16.4240	1.00513
$268$	−3.04948	−0.186276
$269$	−17.0370	−1.03877	−0.519384	−	0.854541i	$-0.673838\pi$
$269$	−17.0370	−1.03877	−0.519384	+	0.854541i	$0.673838\pi$
$270$	−15.5323	−0.945268
$271$	11.9858	0.728083	0.364041	−	0.931383i	$-0.381397\pi$
$271$	11.9858	0.728083	0.364041	+	0.931383i	$0.381397\pi$
$272$	5.47544	0.331998
$273$	1.59441	0.0964981
$274$	8.12493	0.490845
$275$	3.63198	0.219017
$276$	8.53433	0.513706
$277$	−15.6720	−0.941637	−0.470819	−	0.882230i	$-0.656041\pi$
$277$	−15.6720	−0.941637	−0.470819	+	0.882230i	$0.656041\pi$
$278$	6.07479	0.364342
$279$	−1.80131	−0.107842
$280$	−13.3683	−0.798910
$281$	−9.22090	−0.550073	−0.275036	−	0.961434i	$-0.588690\pi$
$281$	−9.22090	−0.550073	−0.275036	+	0.961434i	$0.588690\pi$
$282$	−8.16107	−0.485985
$283$	−25.2947	−1.50361	−0.751807	−	0.659383i	$-0.770818\pi$
$283$	−25.2947	−1.50361	−0.751807	+	0.659383i	$0.770818\pi$
$284$	11.4947	0.682083
$285$	−26.9674	−1.59741
$286$	−0.313365	−0.0185296
$287$	−21.0226	−1.24093
$288$	−1.80131	−0.106143
$289$	12.9805	0.763558
$290$	−14.0053	−0.822420
$291$	1.09484	0.0641809
$292$	0.856447	0.0501198
$293$	−22.5005	−1.31449	−0.657247	−	0.753675i	$-0.728279\pi$
$293$	−22.5005	−1.31449	−0.657247	+	0.753675i	$0.728279\pi$
$294$	−14.7469	−0.860059
$295$	36.4512	2.12227
$296$	−5.69857	−0.331223
$297$	5.11763	0.296955
$298$	−10.6195	−0.615169
$299$	2.50906	0.145103
$300$	−4.08451	−0.235819
$301$	−7.94103	−0.457713
$302$	−7.06892	−0.406770
$303$	−9.56989	−0.549776
$304$	−8.33609	−0.478107
$305$	−0.634196	−0.0363140
$306$	−9.86300	−0.563830
$307$	1.67506	0.0956007	0.0478003	−	0.998857i	$-0.484779\pi$
$307$	1.67506	0.0956007	0.0478003	+	0.998857i	$0.484779\pi$
$308$	4.40462	0.250977
$309$	5.26622	0.299585
$310$	−2.95477	−0.167820
$311$	23.0818	1.30885	0.654423	−	0.756129i	$-0.272912\pi$
$311$	23.0818	1.30885	0.654423	+	0.756129i	$0.272912\pi$
$312$	0.352409	0.0199512
$313$	−17.1048	−0.966820	−0.483410	−	0.875394i	$-0.660602\pi$
$313$	−17.1048	−0.966820	−0.483410	+	0.875394i	$0.660602\pi$
$314$	9.59822	0.541659
$315$	24.0806	1.35679
$316$	−7.12470	−0.400796
$317$	−9.58722	−0.538472	−0.269236	−	0.963074i	$-0.586771\pi$
$317$	−9.58722	−0.538472	−0.269236	+	0.963074i	$0.586771\pi$
$318$	−2.72969	−0.153073
$319$	4.61450	0.258362
$320$	−2.95477	−0.165177
$321$	−4.18733	−0.233714
$322$	−35.2671	−1.96536
$323$	−45.6438	−2.53969
$324$	−0.351320	−0.0195178
$325$	−1.20083	−0.0666101
$326$	−10.7137	−0.593377
$327$	−4.24247	−0.234609
$328$	−4.64658	−0.256565
$329$	33.7247	1.85930
$330$	3.14943	0.173371
$331$	0.463063	0.0254522	0.0127261	−	0.999919i	$-0.495949\pi$
$331$	0.463063	0.0254522	0.0127261	+	0.999919i	$0.495949\pi$
$332$	−17.1731	−0.942496
$333$	10.2649	0.562514
$334$	1.78720	0.0977910
$335$	9.01051	0.492297
$336$	−4.95342	−0.270231
$337$	26.3912	1.43762	0.718811	−	0.695206i	$-0.244687\pi$
$337$	26.3912	1.43762	0.718811	+	0.695206i	$0.244687\pi$
$338$	−12.8964	−0.701471
$339$	−3.97993	−0.216160
$340$	−16.1787	−0.877412
$341$	0.973544	0.0527204
$342$	15.0159	0.811968
$343$	29.2698	1.58042
$344$	−1.75519	−0.0946334
$345$	−25.2170	−1.35764
$346$	−7.25847	−0.390217
$347$	−19.7687	−1.06124	−0.530621	−	0.847610i	$-0.678041\pi$
$347$	−19.7687	−1.06124	−0.530621	+	0.847610i	$0.678041\pi$
$348$	−5.18945	−0.278184
$349$	33.2675	1.78077	0.890384	−	0.455210i	$-0.150436\pi$
$349$	33.2675	1.78077	0.890384	+	0.455210i	$0.150436\pi$
$350$	16.8788	0.902208
$351$	−1.69203	−0.0903137
$352$	0.973544	0.0518901
$353$	−13.9149	−0.740615	−0.370308	−	0.928909i	$-0.620748\pi$
$353$	−13.9149	−0.740615	−0.370308	+	0.928909i	$0.620748\pi$
$354$	13.5064	0.717859
$355$	−33.9641	−1.80263
$356$	−15.0012	−0.795062
$357$	−27.1222	−1.43546
$358$	3.82957	0.202399
$359$	−13.7394	−0.725136	−0.362568	−	0.931957i	$-0.618100\pi$
$359$	−13.7394	−0.725136	−0.362568	+	0.931957i	$0.618100\pi$
$360$	5.32247	0.280519
$361$	50.4904	2.65739
$362$	−4.38140	−0.230281
$363$	11.0056	0.577645
$364$	−1.45629	−0.0763302
$365$	−2.53061	−0.132458
$366$	−0.234992	−0.0122832
$367$	−14.5556	−0.759794	−0.379897	−	0.925029i	$-0.624041\pi$
$367$	−14.5556	−0.759794	−0.379897	+	0.925029i	$0.624041\pi$
$368$	−7.79502	−0.406343
$369$	8.36996	0.435723
$370$	16.8380	0.875364
$371$	11.2801	0.585634
$372$	−1.09484	−0.0567651
$373$	12.6271	0.653809	0.326905	−	0.945057i	$-0.393994\pi$
$373$	12.6271	0.653809	0.326905	+	0.945057i	$0.393994\pi$
$374$	5.33059	0.275638
$375$	−4.10628	−0.212048
$376$	7.45409	0.384415
$377$	−1.52568	−0.0785765
$378$	23.7829	1.22326
$379$	−17.9111	−0.920031	−0.460015	−	0.887911i	$-0.652156\pi$
$379$	−17.9111	−0.920031	−0.460015	+	0.887911i	$0.652156\pi$
$380$	24.6312	1.26356
$381$	−1.35802	−0.0695733
$382$	12.5377	0.641482
$383$	−6.21157	−0.317396	−0.158698	−	0.987327i	$-0.550730\pi$
$383$	−6.21157	−0.317396	−0.158698	+	0.987327i	$0.550730\pi$
$384$	−1.09484	−0.0558711
$385$	−13.0147	−0.663288
$386$	−20.3895	−1.03780
$387$	3.16165	0.160716
$388$	−1.00000	−0.0507673
$389$	30.7819	1.56070	0.780351	−	0.625342i	$-0.215040\pi$
$389$	30.7819	1.56070	0.780351	+	0.625342i	$0.215040\pi$
$390$	−1.04129	−0.0527277
$391$	−42.6812	−2.15848
$392$	13.4694	0.680309
$393$	9.16195	0.462159
$394$	−18.4294	−0.928462
$395$	21.0519	1.05923
$396$	−1.75366	−0.0881247
$397$	−35.1180	−1.76252	−0.881261	−	0.472629i	$-0.843305\pi$
$397$	−35.1180	−1.76252	−0.881261	+	0.472629i	$0.843305\pi$
$398$	−26.3483	−1.32072
$399$	41.2922	2.06719
$400$	3.73068	0.186534
$401$	35.6197	1.77876	0.889380	−	0.457168i	$-0.151136\pi$
$401$	35.6197	1.77876	0.889380	+	0.457168i	$0.151136\pi$
$402$	3.33870	0.166519
$403$	−0.321880	−0.0160340
$404$	8.74087	0.434874
$405$	1.03807	0.0515821
$406$	21.4448	1.06429
$407$	−5.54781	−0.274995
$408$	−5.99476	−0.296785
$409$	23.9055	1.18205	0.591025	−	0.806653i	$-0.298723\pi$
$409$	23.9055	1.18205	0.591025	+	0.806653i	$0.298723\pi$
$410$	13.7296	0.678056
$411$	−8.89554	−0.438785
$412$	−4.81002	−0.236973
$413$	−55.8138	−2.74642
$414$	14.0413	0.690091
$415$	50.7426	2.49085
$416$	−0.321880	−0.0157815
$417$	−6.65095	−0.325698
$418$	−8.11555	−0.396945
$419$	−25.8400	−1.26237	−0.631184	−	0.775633i	$-0.717431\pi$
$419$	−25.8400	−1.26237	−0.631184	+	0.775633i	$0.717431\pi$
$420$	14.6362	0.714175
$421$	−28.4304	−1.38561	−0.692807	−	0.721123i	$-0.743626\pi$
$421$	−28.4304	−1.38561	−0.692807	+	0.721123i	$0.743626\pi$
$422$	−0.935098	−0.0455199
$423$	−13.4272	−0.652851
$424$	2.49322	0.121081
$425$	20.4271	0.990860
$426$	−12.5849	−0.609739
$427$	0.971075	0.0469936
$428$	3.82459	0.184868
$429$	0.343086	0.0165643
$430$	5.18618	0.250100
$431$	−16.0385	−0.772549	−0.386274	−	0.922384i	$-0.626238\pi$
$431$	−16.0385	−0.772549	−0.386274	+	0.922384i	$0.626238\pi$
$432$	5.25669	0.252913
$433$	19.7978	0.951422	0.475711	−	0.879602i	$-0.342191\pi$
$433$	19.7978	0.951422	0.475711	+	0.879602i	$0.342191\pi$
$434$	4.52432	0.217174
$435$	15.3336	0.735192
$436$	3.87495	0.185576
$437$	64.9799	3.10841
$438$	−0.937677	−0.0448039
$439$	−24.8079	−1.18402	−0.592009	−	0.805931i	$-0.701665\pi$
$439$	−24.8079	−1.18402	−0.592009	+	0.805931i	$0.701665\pi$
$440$	−2.87660	−0.137137
$441$	−24.2627	−1.15537
$442$	−1.76244	−0.0838306
$443$	−1.79482	−0.0852746	−0.0426373	−	0.999091i	$-0.513576\pi$
$443$	−1.79482	−0.0852746	−0.0426373	+	0.999091i	$0.513576\pi$
$444$	6.23905	0.296092
$445$	44.3251	2.10121
$446$	13.3220	0.630815
$447$	11.6267	0.549923
$448$	4.52432	0.213754
$449$	−4.33898	−0.204769	−0.102384	−	0.994745i	$-0.532647\pi$
$449$	−4.33898	−0.204769	−0.102384	+	0.994745i	$0.532647\pi$
$450$	−6.72012	−0.316790
$451$	−4.52366	−0.213011
$452$	3.63515	0.170983
$453$	7.73937	0.363627
$454$	−5.63582	−0.264502
$455$	4.30300	0.201728
$456$	9.12672	0.427398
$457$	−18.4851	−0.864698	−0.432349	−	0.901706i	$-0.642315\pi$
$457$	−18.4851	−0.864698	−0.432349	+	0.901706i	$0.642315\pi$
$458$	−22.0969	−1.03252
$459$	28.7827	1.34346
$460$	23.0325	1.07390
$461$	−28.8341	−1.34294	−0.671468	−	0.741033i	$-0.734336\pi$
$461$	−28.8341	−1.34294	−0.671468	+	0.741033i	$0.734336\pi$
$462$	−4.82238	−0.224357
$463$	−9.06046	−0.421075	−0.210538	−	0.977586i	$-0.567521\pi$
$463$	−9.06046	−0.421075	−0.210538	+	0.977586i	$0.567521\pi$
$464$	4.73990	0.220044
$465$	3.23502	0.150020
$466$	5.44442	0.252208
$467$	31.5791	1.46131	0.730654	−	0.682748i	$-0.239215\pi$
$467$	31.5791	1.46131	0.730654	+	0.682748i	$0.239215\pi$
$468$	0.579808	0.0268016
$469$	−13.7968	−0.637077
$470$	−22.0251	−1.01594
$471$	−10.5086	−0.484209
$472$	−12.3364	−0.567829
$473$	−1.70875	−0.0785686
$474$	7.80044	0.358286
$475$	−31.0992	−1.42693
$476$	24.7726	1.13545
$477$	−4.49107	−0.205632
$478$	2.20955	0.101063
$479$	34.7785	1.58907	0.794534	−	0.607219i	$-0.207715\pi$
$479$	34.7785	1.58907	0.794534	+	0.607219i	$0.207715\pi$
$480$	3.23502	0.147658
$481$	1.83426	0.0836349
$482$	−17.2397	−0.785245
$483$	38.6120	1.75691
$484$	−10.0522	−0.456919
$485$	2.95477	0.134169
$486$	−15.3854	−0.697898
$487$	36.2084	1.64076	0.820380	−	0.571819i	$-0.193762\pi$
$487$	36.2084	1.64076	0.820380	+	0.571819i	$0.193762\pi$
$488$	0.214635	0.00971606
$489$	11.7298	0.530442
$490$	−39.7991	−1.79794
$491$	36.9209	1.66622	0.833109	−	0.553108i	$-0.186558\pi$
$491$	36.9209	1.66622	0.833109	+	0.553108i	$0.186558\pi$
$492$	5.08729	0.229353
$493$	25.9530	1.16887
$494$	2.68322	0.120724
$495$	5.18166	0.232899
$496$	1.00000	0.0449013
$497$	52.0055	2.33277
$498$	18.8019	0.842532
$499$	13.5547	0.606790	0.303395	−	0.952865i	$-0.401880\pi$
$499$	13.5547	0.606790	0.303395	+	0.952865i	$0.401880\pi$
$500$	3.75056	0.167730
$501$	−1.95670	−0.0874190
$502$	0.472163	0.0210736
$503$	12.9941	0.579378	0.289689	−	0.957121i	$-0.406448\pi$
$503$	12.9941	0.579378	0.289689	+	0.957121i	$0.406448\pi$
$504$	−8.14972	−0.363017
$505$	−25.8273	−1.14930
$506$	−7.58879	−0.337363
$507$	14.1195	0.627071
$508$	1.24037	0.0550327
$509$	25.3912	1.12544	0.562722	−	0.826646i	$-0.309754\pi$
$509$	25.3912	1.12544	0.562722	+	0.826646i	$0.309754\pi$
$510$	17.7131	0.784351
$511$	3.87484	0.171413
$512$	1.00000	0.0441942
$513$	−43.8203	−1.93471
$514$	−5.85911	−0.258434
$515$	14.2125	0.626278
$516$	1.92166	0.0845963
$517$	7.25689	0.319158
$518$	−25.7821	−1.13280
$519$	7.94689	0.348830
$520$	0.951083	0.0417077
$521$	−15.8278	−0.693427	−0.346714	−	0.937971i	$-0.612702\pi$
$521$	−15.8278	−0.693427	−0.346714	+	0.937971i	$0.612702\pi$
$522$	−8.53804	−0.373700
$523$	−30.8366	−1.34839	−0.674194	−	0.738554i	$-0.735509\pi$
$523$	−30.8366	−1.34839	−0.674194	+	0.738554i	$0.735509\pi$
$524$	−8.36827	−0.365569
$525$	−18.4796	−0.806517
$526$	−3.79897	−0.165643
$527$	5.47544	0.238514
$528$	−1.06588	−0.0463865
$529$	37.7623	1.64184
$530$	−7.36690	−0.319998
$531$	22.2217	0.964341
$532$	−37.7151	−1.63516
$533$	1.49564	0.0647835
$534$	16.4240	0.710735
$535$	−11.3008	−0.488576
$536$	−3.04948	−0.131717
$537$	−4.19278	−0.180932
$538$	−17.0370	−0.734519
$539$	13.1131	0.564821
$540$	−15.5323	−0.668405
$541$	28.0620	1.20648	0.603241	−	0.797559i	$-0.293876\pi$
$541$	28.0620	1.20648	0.603241	+	0.797559i	$0.293876\pi$
$542$	11.9858	0.514832
$543$	4.79695	0.205857
$544$	5.47544	0.234758
$545$	−11.4496	−0.490447
$546$	1.59441	0.0682344
$547$	−33.1952	−1.41933	−0.709663	−	0.704541i	$-0.751153\pi$
$547$	−33.1952	−1.41933	−0.709663	+	0.704541i	$0.751153\pi$
$548$	8.12493	0.347080
$549$	−0.386625	−0.0165007
$550$	3.63198	0.154868
$551$	−39.5122	−1.68328
$552$	8.53433	0.363245
$553$	−32.2344	−1.37075
$554$	−15.6720	−0.665838
$555$	−18.4350	−0.782520
$556$	6.07479	0.257628
$557$	40.6278	1.72145	0.860727	−	0.509067i	$-0.170009\pi$
$557$	40.6278	1.72145	0.860727	+	0.509067i	$0.170009\pi$
$558$	−1.80131	−0.0762557
$559$	0.564960	0.0238953
$560$	−13.3683	−0.564915
$561$	−5.83617	−0.246403
$562$	−9.22090	−0.388960
$563$	45.2740	1.90807	0.954036	−	0.299691i	$-0.0968836\pi$
$563$	45.2740	1.90807	0.954036	+	0.299691i	$0.0968836\pi$
$564$	−8.16107	−0.343643
$565$	−10.7411	−0.451879
$566$	−25.2947	−1.06322
$567$	−1.58948	−0.0667520
$568$	11.4947	0.482306
$569$	−2.27364	−0.0953158	−0.0476579	−	0.998864i	$-0.515176\pi$
$569$	−2.27364	−0.0953158	−0.0476579	+	0.998864i	$0.515176\pi$
$570$	−26.9674	−1.12954
$571$	1.92274	0.0804642	0.0402321	−	0.999190i	$-0.487190\pi$
$571$	1.92274	0.0804642	0.0402321	+	0.999190i	$0.487190\pi$
$572$	−0.313365	−0.0131024
$573$	−13.7268	−0.573445
$574$	−21.0226	−0.877467
$575$	−29.0807	−1.21275
$576$	−1.80131	−0.0750548
$577$	−18.0924	−0.753197	−0.376599	−	0.926376i	$-0.622906\pi$
$577$	−18.0924	−0.753197	−0.376599	+	0.926376i	$0.622906\pi$
$578$	12.9805	0.539917
$579$	22.3233	0.927726
$580$	−14.0053	−0.581539
$581$	−77.6965	−3.22339
$582$	1.09484	0.0453828
$583$	2.42726	0.100527
$584$	0.856447	0.0354400
$585$	−1.71320	−0.0708321
$586$	−22.5005	−0.929488
$587$	−20.8361	−0.859997	−0.429998	−	0.902830i	$-0.641486\pi$
$587$	−20.8361	−0.859997	−0.429998	+	0.902830i	$0.641486\pi$
$588$	−14.7469	−0.608154
$589$	−8.33609	−0.343482
$590$	36.4512	1.50067
$591$	20.1774	0.829986
$592$	−5.69857	−0.234210
$593$	−4.15390	−0.170580	−0.0852902	−	0.996356i	$-0.527182\pi$
$593$	−4.15390	−0.170580	−0.0852902	+	0.996356i	$0.527182\pi$
$594$	5.11763	0.209979
$595$	−73.1975	−3.00080
$596$	−10.6195	−0.434990
$597$	28.8473	1.18064
$598$	2.50906	0.102603
$599$	−8.32003	−0.339947	−0.169974	−	0.985449i	$-0.554368\pi$
$599$	−8.32003	−0.339947	−0.169974	+	0.985449i	$0.554368\pi$
$600$	−4.08451	−0.166749
$601$	13.2010	0.538478	0.269239	−	0.963073i	$-0.413228\pi$
$601$	13.2010	0.538478	0.269239	+	0.963073i	$0.413228\pi$
$602$	−7.94103	−0.323652
$603$	5.49307	0.223695
$604$	−7.06892	−0.287630
$605$	29.7020	1.20756
$606$	−9.56989	−0.388750
$607$	−0.0902719	−0.00366402	−0.00183201	−	0.999998i	$-0.500583\pi$
$607$	−0.0902719	−0.00366402	−0.00183201	+	0.999998i	$0.500583\pi$
$608$	−8.33609	−0.338073
$609$	−23.4787	−0.951405
$610$	−0.634196	−0.0256779
$611$	−2.39933	−0.0970663
$612$	−9.86300	−0.398688
$613$	−10.6833	−0.431493	−0.215746	−	0.976449i	$-0.569218\pi$
$613$	−10.6833	−0.431493	−0.215746	+	0.976449i	$0.569218\pi$
$614$	1.67506	0.0675999
$615$	−15.0318	−0.606140
$616$	4.40462	0.177467
$617$	−22.7216	−0.914736	−0.457368	−	0.889277i	$-0.651208\pi$
$617$	−22.7216	−0.914736	−0.457368	+	0.889277i	$0.651208\pi$
$618$	5.26622	0.211839
$619$	19.8692	0.798610	0.399305	−	0.916818i	$-0.369251\pi$
$619$	19.8692	0.798610	0.399305	+	0.916818i	$0.369251\pi$
$620$	−2.95477	−0.118666
$621$	−40.9760	−1.64431
$622$	23.0818	0.925494
$623$	−67.8702	−2.71916
$624$	0.352409	0.0141076
$625$	−29.7354	−1.18942
$626$	−17.1048	−0.683645
$627$	8.88527	0.354843
$628$	9.59822	0.383011
$629$	−31.2022	−1.24411
$630$	24.0806	0.959392
$631$	6.66645	0.265387	0.132694	−	0.991157i	$-0.457637\pi$
$631$	6.66645	0.265387	0.132694	+	0.991157i	$0.457637\pi$
$632$	−7.12470	−0.283405
$633$	1.02379	0.0406919
$634$	−9.58722	−0.380757
$635$	−3.66502	−0.145442
$636$	−2.72969	−0.108239
$637$	−4.33555	−0.171781
$638$	4.61450	0.182690
$639$	−20.7055	−0.819098
$640$	−2.95477	−0.116798
$641$	46.9477	1.85432	0.927161	−	0.374662i	$-0.122241\pi$
$641$	46.9477	1.85432	0.927161	+	0.374662i	$0.122241\pi$
$642$	−4.18733	−0.165261
$643$	−6.38136	−0.251656	−0.125828	−	0.992052i	$-0.540159\pi$
$643$	−6.38136	−0.251656	−0.125828	+	0.992052i	$0.540159\pi$
$644$	−35.2671	−1.38972
$645$	−5.67806	−0.223573
$646$	−45.6438	−1.79583
$647$	−15.3568	−0.603738	−0.301869	−	0.953349i	$-0.597611\pi$
$647$	−15.3568	−0.603738	−0.301869	+	0.953349i	$0.597611\pi$
$648$	−0.351320	−0.0138011
$649$	−12.0100	−0.471435
$650$	−1.20083	−0.0471005
$651$	−4.95342	−0.194140
$652$	−10.7137	−0.419581
$653$	20.7272	0.811116	0.405558	−	0.914069i	$-0.367077\pi$
$653$	20.7272	0.811116	0.405558	+	0.914069i	$0.367077\pi$
$654$	−4.24247	−0.165894
$655$	24.7263	0.966137
$656$	−4.64658	−0.181419
$657$	−1.54273	−0.0601877
$658$	33.7247	1.31472
$659$	39.6568	1.54481	0.772405	−	0.635130i	$-0.219053\pi$
$659$	39.6568	1.54481	0.772405	+	0.635130i	$0.219053\pi$
$660$	3.14943	0.122591
$661$	11.7714	0.457854	0.228927	−	0.973444i	$-0.426478\pi$
$661$	11.7714	0.457854	0.228927	+	0.973444i	$0.426478\pi$
$662$	0.463063	0.0179975
$663$	1.92960	0.0749393
$664$	−17.1731	−0.666445
$665$	111.440	4.32144
$666$	10.2649	0.397757
$667$	−36.9476	−1.43062
$668$	1.78720	0.0691487
$669$	−14.5855	−0.563909
$670$	9.01051	0.348106
$671$	0.208956	0.00806667
$672$	−4.95342	−0.191082
$673$	−20.8767	−0.804737	−0.402368	−	0.915478i	$-0.631813\pi$
$673$	−20.8767	−0.804737	−0.402368	+	0.915478i	$0.631813\pi$
$674$	26.3912	1.01655
$675$	19.6110	0.754829
$676$	−12.8964	−0.496015
$677$	5.62401	0.216148	0.108074	−	0.994143i	$-0.465532\pi$
$677$	5.62401	0.216148	0.108074	+	0.994143i	$0.465532\pi$
$678$	−3.97993	−0.152848
$679$	−4.52432	−0.173627
$680$	−16.1787	−0.620424
$681$	6.17035	0.236448
$682$	0.973544	0.0372789
$683$	6.79192	0.259886	0.129943	−	0.991521i	$-0.458521\pi$
$683$	6.79192	0.259886	0.129943	+	0.991521i	$0.458521\pi$
$684$	15.0159	0.574148
$685$	−24.0073	−0.917272
$686$	29.2698	1.11753
$687$	24.1927	0.923007
$688$	−1.75519	−0.0669159
$689$	−0.802518	−0.0305735
$690$	−25.2170	−0.959995
$691$	−23.5532	−0.896006	−0.448003	−	0.894032i	$-0.647865\pi$
$691$	−23.5532	−0.896006	−0.448003	+	0.894032i	$0.647865\pi$
$692$	−7.25847	−0.275925
$693$	−7.93411	−0.301392
$694$	−19.7687	−0.750411
$695$	−17.9496	−0.680867
$696$	−5.18945	−0.196706
$697$	−25.4421	−0.963689
$698$	33.2675	1.25919
$699$	−5.96080	−0.225458
$700$	16.8788	0.637957
$701$	40.2143	1.51888	0.759438	−	0.650580i	$-0.225474\pi$
$701$	40.2143	1.51888	0.759438	+	0.650580i	$0.225474\pi$
$702$	−1.69203	−0.0638614
$703$	47.5038	1.79164
$704$	0.973544	0.0366918
$705$	24.1141	0.908190
$706$	−13.9149	−0.523694
$707$	39.5464	1.48730
$708$	13.5064	0.507603
$709$	19.5196	0.733074	0.366537	−	0.930403i	$-0.380543\pi$
$709$	19.5196	0.733074	0.366537	+	0.930403i	$0.380543\pi$
$710$	−33.9641	−1.27465
$711$	12.8338	0.481306
$712$	−15.0012	−0.562194
$713$	−7.79502	−0.291926
$714$	−27.1222	−1.01502
$715$	0.925921	0.0346275
$716$	3.82957	0.143118
$717$	−2.41912	−0.0903436
$718$	−13.7394	−0.512748
$719$	−21.8794	−0.815962	−0.407981	−	0.912990i	$-0.633767\pi$
$719$	−21.8794	−0.815962	−0.407981	+	0.912990i	$0.633767\pi$
$720$	5.32247	0.198357
$721$	−21.7620	−0.810461
$722$	50.4904	1.87906
$723$	18.8747	0.701959
$724$	−4.38140	−0.162833
$725$	17.6830	0.656731
$726$	11.0056	0.408457
$727$	6.95076	0.257790	0.128895	−	0.991658i	$-0.458857\pi$
$727$	6.95076	0.257790	0.128895	+	0.991658i	$0.458857\pi$
$728$	−1.45629	−0.0539736
$729$	17.8986	0.662912
$730$	−2.53061	−0.0936619
$731$	−9.61043	−0.355455
$732$	−0.234992	−0.00868554
$733$	−12.0658	−0.445659	−0.222830	−	0.974857i	$-0.571529\pi$
$733$	−12.0658	−0.445659	−0.222830	+	0.974857i	$0.571529\pi$
$734$	−14.5556	−0.537255
$735$	43.5739	1.60725
$736$	−7.79502	−0.287328
$737$	−2.96880	−0.109357
$738$	8.36996	0.308103
$739$	−0.783738	−0.0288303	−0.0144151	−	0.999896i	$-0.504589\pi$
$739$	−0.783738	−0.0288303	−0.0144151	+	0.999896i	$0.504589\pi$
$740$	16.8380	0.618976
$741$	−2.93771	−0.107920
$742$	11.2801	0.414106
$743$	26.4701	0.971093	0.485547	−	0.874211i	$-0.338621\pi$
$743$	26.4701	0.971093	0.485547	+	0.874211i	$0.338621\pi$
$744$	−1.09484	−0.0401390
$745$	31.3781	1.14961
$746$	12.6271	0.462313
$747$	30.9341	1.13182
$748$	5.33059	0.194906
$749$	17.3036	0.632262
$750$	−4.10628	−0.149940
$751$	10.2328	0.373400	0.186700	−	0.982417i	$-0.440221\pi$
$751$	10.2328	0.373400	0.186700	+	0.982417i	$0.440221\pi$
$752$	7.45409	0.271823
$753$	−0.516945	−0.0188385
$754$	−1.52568	−0.0555619
$755$	20.8870	0.760157
$756$	23.7829	0.864978
$757$	−13.0883	−0.475702	−0.237851	−	0.971302i	$-0.576443\pi$
$757$	−13.0883	−0.475702	−0.237851	+	0.971302i	$0.576443\pi$
$758$	−17.9111	−0.650560
$759$	8.30855	0.301581
$760$	24.6312	0.893469
$761$	22.9846	0.833191	0.416596	−	0.909092i	$-0.363223\pi$
$761$	22.9846	0.833191	0.416596	+	0.909092i	$0.363223\pi$
$762$	−1.35802	−0.0491958
$763$	17.5315	0.634683
$764$	12.5377	0.453597
$765$	29.1429	1.05366
$766$	−6.21157	−0.224433
$767$	3.97084	0.143379
$768$	−1.09484	−0.0395068
$769$	21.2936	0.767867	0.383933	−	0.923361i	$-0.374569\pi$
$769$	21.2936	0.767867	0.383933	+	0.923361i	$0.374569\pi$
$770$	−13.0147	−0.469016
$771$	6.41482	0.231024
$772$	−20.3895	−0.733834
$773$	4.34232	0.156182	0.0780912	−	0.996946i	$-0.475117\pi$
$773$	4.34232	0.156182	0.0780912	+	0.996946i	$0.475117\pi$
$774$	3.16165	0.113643
$775$	3.73068	0.134010
$776$	−1.00000	−0.0358979
$777$	28.2274	1.01265
$778$	30.7819	1.10358
$779$	38.7343	1.38780
$780$	−1.04129	−0.0372841
$781$	11.1906	0.400430
$782$	−42.6812	−1.52628
$783$	24.9162	0.890432
$784$	13.4694	0.481051
$785$	−28.3606	−1.01223
$786$	9.16195	0.326796
$787$	9.60448	0.342363	0.171181	−	0.985240i	$-0.445242\pi$
$787$	9.60448	0.342363	0.171181	+	0.985240i	$0.445242\pi$
$788$	−18.4294	−0.656521
$789$	4.15928	0.148074
$790$	21.0519	0.748992
$791$	16.4466	0.584773
$792$	−1.75366	−0.0623136
$793$	−0.0690867	−0.00245334
$794$	−35.1180	−1.24629
$795$	8.06561	0.286058
$796$	−26.3483	−0.933892
$797$	20.9341	0.741524	0.370762	−	0.928728i	$-0.379097\pi$
$797$	20.9341	0.741524	0.370762	+	0.928728i	$0.379097\pi$
$798$	41.2922	1.46173
$799$	40.8145	1.44391
$800$	3.73068	0.131899
$801$	27.0219	0.954771
$802$	35.6197	1.25777
$803$	0.833789	0.0294238
$804$	3.33870	0.117747
$805$	104.206	3.67279
$806$	−0.321880	−0.0113377
$807$	18.6529	0.656614
$808$	8.74087	0.307503
$809$	42.5090	1.49454	0.747268	−	0.664523i	$-0.231365\pi$
$809$	42.5090	1.49454	0.747268	+	0.664523i	$0.231365\pi$
$810$	1.03807	0.0364741
$811$	1.66329	0.0584059	0.0292030	−	0.999574i	$-0.490703\pi$
$811$	1.66329	0.0584059	0.0292030	+	0.999574i	$0.490703\pi$
$812$	21.4448	0.752564
$813$	−13.1225	−0.460228
$814$	−5.54781	−0.194451
$815$	31.6566	1.10888
$816$	−5.99476	−0.209859
$817$	14.6314	0.511888
$818$	23.9055	0.835836
$819$	2.62323	0.0916632
$820$	13.7296	0.479458
$821$	−5.90611	−0.206125	−0.103062	−	0.994675i	$-0.532864\pi$
$821$	−5.90611	−0.206125	−0.103062	+	0.994675i	$0.532864\pi$
$822$	−8.89554	−0.310268
$823$	6.39440	0.222895	0.111447	−	0.993770i	$-0.464451\pi$
$823$	6.39440	0.222895	0.111447	+	0.993770i	$0.464451\pi$
$824$	−4.81002	−0.167565
$825$	−3.97645	−0.138442
$826$	−55.8138	−1.94201
$827$	−19.4242	−0.675445	−0.337723	−	0.941246i	$-0.609657\pi$
$827$	−19.4242	−0.675445	−0.337723	+	0.941246i	$0.609657\pi$
$828$	14.0413	0.487968
$829$	−11.2876	−0.392034	−0.196017	−	0.980600i	$-0.562801\pi$
$829$	−11.2876	−0.392034	−0.196017	+	0.980600i	$0.562801\pi$
$830$	50.7426	1.76130
$831$	17.1584	0.595217
$832$	−0.321880	−0.0111592
$833$	73.7512	2.55533
$834$	−6.65095	−0.230304
$835$	−5.28076	−0.182748
$836$	−8.11555	−0.280682
$837$	5.25669	0.181698
$838$	−25.8400	−0.892629
$839$	−0.417906	−0.0144277	−0.00721386	−	0.999974i	$-0.502296\pi$
$839$	−0.417906	−0.0144277	−0.00721386	+	0.999974i	$0.502296\pi$
$840$	14.6362	0.504998
$841$	−6.53339	−0.225289
$842$	−28.4304	−0.979776
$843$	10.0955	0.347706
$844$	−0.935098	−0.0321874
$845$	38.1059	1.31088
$846$	−13.4272	−0.461636
$847$	−45.4794	−1.56269
$848$	2.49322	0.0856175
$849$	27.6938	0.950448
$850$	20.4271	0.700644
$851$	44.4204	1.52271
$852$	−12.5849	−0.431151
$853$	−42.9658	−1.47112	−0.735560	−	0.677460i	$-0.763081\pi$
$853$	−42.9658	−1.47112	−0.735560	+	0.677460i	$0.763081\pi$
$854$	0.971075	0.0332295
$855$	−44.3686	−1.51737
$856$	3.82459	0.130722
$857$	10.0983	0.344951	0.172475	−	0.985014i	$-0.444823\pi$
$857$	10.0983	0.344951	0.172475	+	0.985014i	$0.444823\pi$
$858$	0.343086	0.0117128
$859$	−25.4726	−0.869112	−0.434556	−	0.900645i	$-0.643095\pi$
$859$	−25.4726	−0.869112	−0.434556	+	0.900645i	$0.643095\pi$
$860$	5.18618	0.176847
$861$	23.0165	0.784400
$862$	−16.0385	−0.546275
$863$	−40.4777	−1.37788	−0.688938	−	0.724821i	$-0.741923\pi$
$863$	−40.4777	−1.37788	−0.688938	+	0.724821i	$0.741923\pi$
$864$	5.25669	0.178836
$865$	21.4471	0.729224
$866$	19.7978	0.672757
$867$	−14.2116	−0.482652
$868$	4.52432	0.153565
$869$	−6.93621	−0.235295
$870$	15.3336	0.519859
$871$	0.981567	0.0332591
$872$	3.87495	0.131222
$873$	1.80131	0.0609653
$874$	64.9799	2.19798
$875$	16.9687	0.573648
$876$	−0.937677	−0.0316812
$877$	16.0653	0.542487	0.271243	−	0.962511i	$-0.412565\pi$
$877$	16.0653	0.542487	0.271243	+	0.962511i	$0.412565\pi$
$878$	−24.8079	−0.837227
$879$	24.6346	0.830904
$880$	−2.87660	−0.0969702
$881$	32.4087	1.09188	0.545938	−	0.837825i	$-0.316173\pi$
$881$	32.4087	1.09188	0.545938	+	0.837825i	$0.316173\pi$
$882$	−24.2627	−0.816968
$883$	16.9479	0.570341	0.285171	−	0.958477i	$-0.407950\pi$
$883$	16.9479	0.570341	0.285171	+	0.958477i	$0.407950\pi$
$884$	−1.76244	−0.0592772
$885$	−39.9085	−1.34151
$886$	−1.79482	−0.0602983
$887$	2.12395	0.0713154	0.0356577	−	0.999364i	$-0.488647\pi$
$887$	2.12395	0.0713154	0.0356577	+	0.999364i	$0.488647\pi$
$888$	6.23905	0.209369
$889$	5.61185	0.188215
$890$	44.3251	1.48578
$891$	−0.342025	−0.0114583
$892$	13.3220	0.446053
$893$	−62.1380	−2.07937
$894$	11.6267	0.388854
$895$	−11.3155	−0.378235
$896$	4.52432	0.151147
$897$	−2.74703	−0.0917208
$898$	−4.33898	−0.144793
$899$	4.73990	0.158084
$900$	−6.72012	−0.224004
$901$	13.6515	0.454797
$902$	−4.52366	−0.150621
$903$	8.69419	0.289325
$904$	3.63515	0.120903
$905$	12.9460	0.430341
$906$	7.73937	0.257123
$907$	−51.8026	−1.72008	−0.860038	−	0.510230i	$-0.829560\pi$
$907$	−51.8026	−1.72008	−0.860038	+	0.510230i	$0.829560\pi$
$908$	−5.63582	−0.187031
$909$	−15.7451	−0.522230
$910$	4.30300	0.142643
$911$	54.2230	1.79649	0.898244	−	0.439497i	$-0.144843\pi$
$911$	54.2230	1.79649	0.898244	+	0.439497i	$0.144843\pi$
$912$	9.12672	0.302216
$913$	−16.7188	−0.553310
$914$	−18.4851	−0.611434
$915$	0.694347	0.0229544
$916$	−22.0969	−0.730102
$917$	−37.8607	−1.25027
$918$	28.7827	0.949972
$919$	−24.4093	−0.805188	−0.402594	−	0.915379i	$-0.631891\pi$
$919$	−24.4093	−0.805188	−0.402594	+	0.915379i	$0.631891\pi$
$920$	23.0325	0.759359
$921$	−1.83393	−0.0604300
$922$	−28.8341	−0.949600
$923$	−3.69991	−0.121784
$924$	−4.82238	−0.158645
$925$	−21.2595	−0.699008
$926$	−9.06046	−0.297745
$927$	8.66436	0.284575
$928$	4.73990	0.155595
$929$	−13.5092	−0.443221	−0.221611	−	0.975135i	$-0.571131\pi$
$929$	−13.5092	−0.443221	−0.221611	+	0.975135i	$0.571131\pi$
$930$	3.23502	0.106080
$931$	−112.282	−3.67991
$932$	5.44442	0.178338
$933$	−25.2709	−0.827333
$934$	31.5791	1.03330
$935$	−15.7507	−0.515102
$936$	0.579808	0.0189516
$937$	−0.256322	−0.00837368	−0.00418684	−	0.999991i	$-0.501333\pi$
$937$	−0.256322	−0.00837368	−0.00418684	+	0.999991i	$0.501333\pi$
$938$	−13.7968	−0.450482
$939$	18.7271	0.611136
$940$	−22.0251	−0.718381
$941$	55.1903	1.79915	0.899577	−	0.436763i	$-0.143875\pi$
$941$	55.1903	1.79915	0.899577	+	0.436763i	$0.143875\pi$
$942$	−10.5086	−0.342387
$943$	36.2202	1.17949
$944$	−12.3364	−0.401516
$945$	−70.2732	−2.28599
$946$	−1.70875	−0.0555564
$947$	58.8696	1.91300	0.956502	−	0.291726i	$-0.0942295\pi$
$947$	58.8696	1.91300	0.956502	+	0.291726i	$0.0942295\pi$
$948$	7.80044	0.253347
$949$	−0.275673	−0.00894874
$950$	−31.0992	−1.00899
$951$	10.4965	0.340373
$952$	24.7726	0.802886
$953$	43.0214	1.39360	0.696800	−	0.717265i	$-0.254606\pi$
$953$	43.0214	1.39360	0.696800	+	0.717265i	$0.254606\pi$
$954$	−4.49107	−0.145404
$955$	−37.0459	−1.19878
$956$	2.20955	0.0714621
$957$	−5.05216	−0.163313
$958$	34.7785	1.12364
$959$	36.7598	1.18703
$960$	3.23502	0.104410
$961$	1.00000	0.0322581
$962$	1.83426	0.0591388
$963$	−6.88929	−0.222004
$964$	−17.2397	−0.555252
$965$	60.2463	1.93940
$966$	38.6120	1.24232
$967$	−42.9756	−1.38200	−0.691002	−	0.722853i	$-0.742830\pi$
$967$	−42.9756	−1.38200	−0.691002	+	0.722853i	$0.742830\pi$
$968$	−10.0522	−0.323090
$969$	49.9728	1.60536
$970$	2.95477	0.0948720
$971$	−45.1319	−1.44835	−0.724176	−	0.689615i	$-0.757780\pi$
$971$	−45.1319	−1.44835	−0.724176	+	0.689615i	$0.757780\pi$
$972$	−15.3854	−0.493488
$973$	27.4843	0.881105
$974$	36.2084	1.16019
$975$	1.31472	0.0421049
$976$	0.214635	0.00687029
$977$	5.92728	0.189630	0.0948152	−	0.995495i	$-0.469774\pi$
$977$	5.92728	0.189630	0.0948152	+	0.995495i	$0.469774\pi$
$978$	11.7298	0.375079
$979$	−14.6043	−0.466756
$980$	−39.7991	−1.27134
$981$	−6.98001	−0.222854
$982$	36.9209	1.17819
$983$	35.3411	1.12721	0.563604	−	0.826045i	$-0.309415\pi$
$983$	35.3411	1.12721	0.563604	+	0.826045i	$0.309415\pi$
$984$	5.08729	0.162177
$985$	54.4548	1.73507
$986$	25.9530	0.826513
$987$	−36.9233	−1.17528
$988$	2.68322	0.0853647
$989$	13.6817	0.435053
$990$	5.18166	0.164684
$991$	7.60167	0.241475	0.120737	−	0.992684i	$-0.461474\pi$
$991$	7.60167	0.241475	0.120737	+	0.992684i	$0.461474\pi$
$992$	1.00000	0.0317500
$993$	−0.506982	−0.0160886
$994$	52.0055	1.64952
$995$	77.8533	2.46812
$996$	18.8019	0.595760
$997$	−28.9417	−0.916594	−0.458297	−	0.888799i	$-0.651540\pi$
$997$	−28.9417	−0.916594	−0.458297	+	0.888799i	$0.651540\pi$
$998$	13.5547	0.429065
$999$	−29.9556	−0.947754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.e.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.e.1.10	✓	21	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.09484 q^{3} +1.00000 q^{4} -2.95477 q^{5} -1.09484 q^{6} +4.52432 q^{7} +1.00000 q^{8} -1.80131 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.09484 q^{3} +1.00000 q^{4} -2.95477 q^{5} -1.09484 q^{6} +4.52432 q^{7} +1.00000 q^{8} -1.80131 q^{9} -2.95477 q^{10} +0.973544 q^{11} -1.09484 q^{12} -0.321880 q^{13} +4.52432 q^{14} +3.23502 q^{15} +1.00000 q^{16} +5.47544 q^{17} -1.80131 q^{18} -8.33609 q^{19} -2.95477 q^{20} -4.95342 q^{21} +0.973544 q^{22} -7.79502 q^{23} -1.09484 q^{24} +3.73068 q^{25} -0.321880 q^{26} +5.25669 q^{27} +4.52432 q^{28} +4.73990 q^{29} +3.23502 q^{30} +1.00000 q^{31} +1.00000 q^{32} -1.06588 q^{33} +5.47544 q^{34} -13.3683 q^{35} -1.80131 q^{36} -5.69857 q^{37} -8.33609 q^{38} +0.352409 q^{39} -2.95477 q^{40} -4.64658 q^{41} -4.95342 q^{42} -1.75519 q^{43} +0.973544 q^{44} +5.32247 q^{45} -7.79502 q^{46} +7.45409 q^{47} -1.09484 q^{48} +13.4694 q^{49} +3.73068 q^{50} -5.99476 q^{51} -0.321880 q^{52} +2.49322 q^{53} +5.25669 q^{54} -2.87660 q^{55} +4.52432 q^{56} +9.12672 q^{57} +4.73990 q^{58} -12.3364 q^{59} +3.23502 q^{60} +0.214635 q^{61} +1.00000 q^{62} -8.14972 q^{63} +1.00000 q^{64} +0.951083 q^{65} -1.06588 q^{66} -3.04948 q^{67} +5.47544 q^{68} +8.53433 q^{69} -13.3683 q^{70} +11.4947 q^{71} -1.80131 q^{72} +0.856447 q^{73} -5.69857 q^{74} -4.08451 q^{75} -8.33609 q^{76} +4.40462 q^{77} +0.352409 q^{78} -7.12470 q^{79} -2.95477 q^{80} -0.351320 q^{81} -4.64658 q^{82} -17.1731 q^{83} -4.95342 q^{84} -16.1787 q^{85} -1.75519 q^{86} -5.18945 q^{87} +0.973544 q^{88} -15.0012 q^{89} +5.32247 q^{90} -1.45629 q^{91} -7.79502 q^{92} -1.09484 q^{93} +7.45409 q^{94} +24.6312 q^{95} -1.09484 q^{96} -1.00000 q^{97} +13.4694 q^{98} -1.75366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9	\( 21 q + 21 q^{2} - 10 q^{3} + 21 q^{4} - 10 q^{5} - 10 q^{6} - 11 q^{7} + 21 q^{8} + 7 q^{9} - 10 q^{10} - 12 q^{11} - 10 q^{12} - 14 q^{13} - 11 q^{14} + q^{15} + 21 q^{16} + 7 q^{18} - 27 q^{19} - 10 q^{20} - 6 q^{21} - 12 q^{22} - 4 q^{23} - 10 q^{24} + q^{25} - 14 q^{26} - 19 q^{27} - 11 q^{28} - 13 q^{29} + q^{30} + 21 q^{31} + 21 q^{32} - 20 q^{33} - 20 q^{35} + 7 q^{36} - 13 q^{37} - 27 q^{38} - 4 q^{39} - 10 q^{40} - 19 q^{41} - 6 q^{42} - 19 q^{43} - 12 q^{44} + 13 q^{45} - 4 q^{46} - 18 q^{47} - 10 q^{48} - 20 q^{49} + q^{50} - 33 q^{51} - 14 q^{52} - 15 q^{53} - 19 q^{54} - 26 q^{55} - 11 q^{56} + 9 q^{57} - 13 q^{58} - 32 q^{59} + q^{60} - 36 q^{61} + 21 q^{62} - 27 q^{63} + 21 q^{64} - 20 q^{65} - 20 q^{66} - 43 q^{67} - 11 q^{69} - 20 q^{70} - 31 q^{71} + 7 q^{72} - 11 q^{73} - 13 q^{74} - 22 q^{75} - 27 q^{76} + 12 q^{77} - 4 q^{78} - 31 q^{79} - 10 q^{80} - 39 q^{81} - 19 q^{82} - 26 q^{83} - 6 q^{84} - 12 q^{85} - 19 q^{86} + 19 q^{87} - 12 q^{88} - 14 q^{89} + 13 q^{90} - 30 q^{91} - 4 q^{92} - 10 q^{93} - 18 q^{94} - 40 q^{95} - 10 q^{96} - 21 q^{97} - 20 q^{98} - 17 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 10 * q^3 + 21 * q^4 - 10 * q^5 - 10 * q^6 - 11 * q^7 + 21 * q^8 + 7 * q^9 - 10 * q^10 - 12 * q^11 - 10 * q^12 - 14 * q^13 - 11 * q^14 + q^15 + 21 * q^16 + 7 * q^18 - 27 * q^19 - 10 * q^20 - 6 * q^21 - 12 * q^22 - 4 * q^23 - 10 * q^24 + q^25 - 14 * q^26 - 19 * q^27 - 11 * q^28 - 13 * q^29 + q^30 + 21 * q^31 + 21 * q^32 - 20 * q^33 - 20 * q^35 + 7 * q^36 - 13 * q^37 - 27 * q^38 - 4 * q^39 - 10 * q^40 - 19 * q^41 - 6 * q^42 - 19 * q^43 - 12 * q^44 + 13 * q^45 - 4 * q^46 - 18 * q^47 - 10 * q^48 - 20 * q^49 + q^50 - 33 * q^51 - 14 * q^52 - 15 * q^53 - 19 * q^54 - 26 * q^55 - 11 * q^56 + 9 * q^57 - 13 * q^58 - 32 * q^59 + q^60 - 36 * q^61 + 21 * q^62 - 27 * q^63 + 21 * q^64 - 20 * q^65 - 20 * q^66 - 43 * q^67 - 11 * q^69 - 20 * q^70 - 31 * q^71 + 7 * q^72 - 11 * q^73 - 13 * q^74 - 22 * q^75 - 27 * q^76 + 12 * q^77 - 4 * q^78 - 31 * q^79 - 10 * q^80 - 39 * q^81 - 19 * q^82 - 26 * q^83 - 6 * q^84 - 12 * q^85 - 19 * q^86 + 19 * q^87 - 12 * q^88 - 14 * q^89 + 13 * q^90 - 30 * q^91 - 4 * q^92 - 10 * q^93 - 18 * q^94 - 40 * q^95 - 10 * q^96 - 21 * q^97 - 20 * q^98 - 17 * q^99

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