LMFDB - Embedded newform 6034.2.a.m.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.27918 q^{3} +1.00000 q^{4} -0.808180 q^{5} -1.27918 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.36370 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.27918 q^{3} +1.00000 q^{4} -0.808180 q^{5} -1.27918 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.36370 q^{9} -0.808180 q^{10} -1.04999 q^{11} -1.27918 q^{12} +4.47218 q^{13} +1.00000 q^{14} +1.03381 q^{15} +1.00000 q^{16} -2.56170 q^{17} -1.36370 q^{18} +0.0511977 q^{19} -0.808180 q^{20} -1.27918 q^{21} -1.04999 q^{22} -0.498288 q^{23} -1.27918 q^{24} -4.34685 q^{25} +4.47218 q^{26} +5.58195 q^{27} +1.00000 q^{28} +0.297679 q^{29} +1.03381 q^{30} -1.84361 q^{31} +1.00000 q^{32} +1.34312 q^{33} -2.56170 q^{34} -0.808180 q^{35} -1.36370 q^{36} -3.42429 q^{37} +0.0511977 q^{38} -5.72072 q^{39} -0.808180 q^{40} -7.76395 q^{41} -1.27918 q^{42} +7.95661 q^{43} -1.04999 q^{44} +1.10212 q^{45} -0.498288 q^{46} -11.6852 q^{47} -1.27918 q^{48} +1.00000 q^{49} -4.34685 q^{50} +3.27687 q^{51} +4.47218 q^{52} +11.2879 q^{53} +5.58195 q^{54} +0.848578 q^{55} +1.00000 q^{56} -0.0654910 q^{57} +0.297679 q^{58} +7.04519 q^{59} +1.03381 q^{60} +4.41174 q^{61} -1.84361 q^{62} -1.36370 q^{63} +1.00000 q^{64} -3.61433 q^{65} +1.34312 q^{66} -8.94831 q^{67} -2.56170 q^{68} +0.637400 q^{69} -0.808180 q^{70} -2.64602 q^{71} -1.36370 q^{72} -6.92915 q^{73} -3.42429 q^{74} +5.56039 q^{75} +0.0511977 q^{76} -1.04999 q^{77} -5.72072 q^{78} -12.5652 q^{79} -0.808180 q^{80} -3.04921 q^{81} -7.76395 q^{82} -5.79766 q^{83} -1.27918 q^{84} +2.07031 q^{85} +7.95661 q^{86} -0.380785 q^{87} -1.04999 q^{88} +6.66649 q^{89} +1.10212 q^{90} +4.47218 q^{91} -0.498288 q^{92} +2.35831 q^{93} -11.6852 q^{94} -0.0413769 q^{95} -1.27918 q^{96} +14.5355 q^{97} +1.00000 q^{98} +1.43187 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) $ 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * 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
$3$	−1.27918	−0.738534	−0.369267	−	0.929323i	$-0.620391\pi$
$3$	−1.27918	−0.738534	−0.369267	+	0.929323i	$0.620391\pi$
$4$	1.00000	0.500000
$5$	−0.808180	−0.361429	−0.180714	−	0.983536i	$-0.557841\pi$
$5$	−0.808180	−0.361429	−0.180714	+	0.983536i	$0.557841\pi$
$6$	−1.27918	−0.522222
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.36370	−0.454568
$10$	−0.808180	−0.255569
$11$	−1.04999	−0.316583	−0.158291	−	0.987392i	$-0.550599\pi$
$11$	−1.04999	−0.316583	−0.158291	+	0.987392i	$0.550599\pi$
$12$	−1.27918	−0.369267
$13$	4.47218	1.24036	0.620180	−	0.784459i	$-0.287059\pi$
$13$	4.47218	1.24036	0.620180	+	0.784459i	$0.287059\pi$
$14$	1.00000	0.267261
$15$	1.03381	0.266928
$16$	1.00000	0.250000
$17$	−2.56170	−0.621302	−0.310651	−	0.950524i	$-0.600547\pi$
$17$	−2.56170	−0.621302	−0.310651	+	0.950524i	$0.600547\pi$
$18$	−1.36370	−0.321428
$19$	0.0511977	0.0117456	0.00587278	−	0.999983i	$-0.498131\pi$
$19$	0.0511977	0.0117456	0.00587278	+	0.999983i	$0.498131\pi$
$20$	−0.808180	−0.180714
$21$	−1.27918	−0.279140
$22$	−1.04999	−0.223858
$23$	−0.498288	−0.103900	−0.0519501	−	0.998650i	$-0.516544\pi$
$23$	−0.498288	−0.103900	−0.0519501	+	0.998650i	$0.516544\pi$
$24$	−1.27918	−0.261111
$25$	−4.34685	−0.869369
$26$	4.47218	0.877068
$27$	5.58195	1.07425
$28$	1.00000	0.188982
$29$	0.297679	0.0552776	0.0276388	−	0.999618i	$-0.491201\pi$
$29$	0.297679	0.0552776	0.0276388	+	0.999618i	$0.491201\pi$
$30$	1.03381	0.188746
$31$	−1.84361	−0.331123	−0.165561	−	0.986199i	$-0.552944\pi$
$31$	−1.84361	−0.331123	−0.165561	+	0.986199i	$0.552944\pi$
$32$	1.00000	0.176777
$33$	1.34312	0.233807
$34$	−2.56170	−0.439327
$35$	−0.808180	−0.136607
$36$	−1.36370	−0.227284
$37$	−3.42429	−0.562950	−0.281475	−	0.959569i	$-0.590824\pi$
$37$	−3.42429	−0.562950	−0.281475	+	0.959569i	$0.590824\pi$
$38$	0.0511977	0.00830536
$39$	−5.72072	−0.916049
$40$	−0.808180	−0.127784
$41$	−7.76395	−1.21253	−0.606263	−	0.795265i	$-0.707332\pi$
$41$	−7.76395	−1.21253	−0.606263	+	0.795265i	$0.707332\pi$
$42$	−1.27918	−0.197382
$43$	7.95661	1.21337	0.606686	−	0.794941i	$-0.292498\pi$
$43$	7.95661	1.21337	0.606686	+	0.794941i	$0.292498\pi$
$44$	−1.04999	−0.158291
$45$	1.10212	0.164294
$46$	−0.498288	−0.0734686
$47$	−11.6852	−1.70446	−0.852231	−	0.523166i	$-0.824751\pi$
$47$	−11.6852	−1.70446	−0.852231	+	0.523166i	$0.824751\pi$
$48$	−1.27918	−0.184634
$49$	1.00000	0.142857
$50$	−4.34685	−0.614737
$51$	3.27687	0.458853
$52$	4.47218	0.620180
$53$	11.2879	1.55052	0.775259	−	0.631643i	$-0.217619\pi$
$53$	11.2879	1.55052	0.775259	+	0.631643i	$0.217619\pi$
$54$	5.58195	0.759608
$55$	0.848578	0.114422
$56$	1.00000	0.133631
$57$	−0.0654910	−0.00867449
$58$	0.297679	0.0390872
$59$	7.04519	0.917206	0.458603	−	0.888641i	$-0.348350\pi$
$59$	7.04519	0.917206	0.458603	+	0.888641i	$0.348350\pi$
$60$	1.03381	0.133464
$61$	4.41174	0.564866	0.282433	−	0.959287i	$-0.408859\pi$
$61$	4.41174	0.564866	0.282433	+	0.959287i	$0.408859\pi$
$62$	−1.84361	−0.234139
$63$	−1.36370	−0.171810
$64$	1.00000	0.125000
$65$	−3.61433	−0.448302
$66$	1.34312	0.165327
$67$	−8.94831	−1.09321	−0.546605	−	0.837390i	$-0.684080\pi$
$67$	−8.94831	−1.09321	−0.546605	+	0.837390i	$0.684080\pi$
$68$	−2.56170	−0.310651
$69$	0.637400	0.0767339
$70$	−0.808180	−0.0965959
$71$	−2.64602	−0.314025	−0.157013	−	0.987597i	$-0.550186\pi$
$71$	−2.64602	−0.314025	−0.157013	+	0.987597i	$0.550186\pi$
$72$	−1.36370	−0.160714
$73$	−6.92915	−0.810996	−0.405498	−	0.914096i	$-0.632902\pi$
$73$	−6.92915	−0.810996	−0.405498	+	0.914096i	$0.632902\pi$
$74$	−3.42429	−0.398066
$75$	5.56039	0.642059
$76$	0.0511977	0.00587278
$77$	−1.04999	−0.119657
$78$	−5.72072	−0.647744
$79$	−12.5652	−1.41369	−0.706847	−	0.707367i	$-0.749883\pi$
$79$	−12.5652	−1.41369	−0.706847	+	0.707367i	$0.749883\pi$
$80$	−0.808180	−0.0903572
$81$	−3.04921	−0.338801
$82$	−7.76395	−0.857385
$83$	−5.79766	−0.636376	−0.318188	−	0.948028i	$-0.603074\pi$
$83$	−5.79766	−0.636376	−0.318188	+	0.948028i	$0.603074\pi$
$84$	−1.27918	−0.139570
$85$	2.07031	0.224557
$86$	7.95661	0.857984
$87$	−0.380785	−0.0408244
$88$	−1.04999	−0.111929
$89$	6.66649	0.706646	0.353323	−	0.935501i	$-0.385052\pi$
$89$	6.66649	0.706646	0.353323	+	0.935501i	$0.385052\pi$
$90$	1.10212	0.116173
$91$	4.47218	0.468812
$92$	−0.498288	−0.0519501
$93$	2.35831	0.244545
$94$	−11.6852	−1.20524
$95$	−0.0413769	−0.00424518
$96$	−1.27918	−0.130556
$97$	14.5355	1.47586	0.737928	−	0.674879i	$-0.235804\pi$
$97$	14.5355	1.47586	0.737928	+	0.674879i	$0.235804\pi$
$98$	1.00000	0.101015
$99$	1.43187	0.143908
$100$	−4.34685	−0.434685
$101$	−2.05751	−0.204730	−0.102365	−	0.994747i	$-0.532641\pi$
$101$	−2.05751	−0.204730	−0.102365	+	0.994747i	$0.532641\pi$
$102$	3.27687	0.324458
$103$	−3.08673	−0.304144	−0.152072	−	0.988369i	$-0.548595\pi$
$103$	−3.08673	−0.304144	−0.152072	+	0.988369i	$0.548595\pi$
$104$	4.47218	0.438534
$105$	1.03381	0.100889
$106$	11.2879	1.09638
$107$	−3.28701	−0.317767	−0.158884	−	0.987297i	$-0.550789\pi$
$107$	−3.28701	−0.317767	−0.158884	+	0.987297i	$0.550789\pi$
$108$	5.58195	0.537124
$109$	3.25647	0.311913	0.155956	−	0.987764i	$-0.450154\pi$
$109$	3.25647	0.311913	0.155956	+	0.987764i	$0.450154\pi$
$110$	0.848578	0.0809087
$111$	4.38028	0.415757
$112$	1.00000	0.0944911
$113$	−18.0646	−1.69938	−0.849689	−	0.527284i	$-0.823210\pi$
$113$	−18.0646	−1.69938	−0.849689	+	0.527284i	$0.823210\pi$
$114$	−0.0654910	−0.00613379
$115$	0.402706	0.0375526
$116$	0.297679	0.0276388
$117$	−6.09873	−0.563828
$118$	7.04519	0.648563
$119$	−2.56170	−0.234830
$120$	1.03381	0.0943731
$121$	−9.89753	−0.899775
$122$	4.41174	0.399420
$123$	9.93148	0.895491
$124$	−1.84361	−0.165561
$125$	7.55393	0.675644
$126$	−1.36370	−0.121488
$127$	17.1913	1.52548	0.762740	−	0.646705i	$-0.223853\pi$
$127$	17.1913	1.52548	0.762740	+	0.646705i	$0.223853\pi$
$128$	1.00000	0.0883883
$129$	−10.1779	−0.896117
$130$	−3.61433	−0.316998
$131$	−7.70427	−0.673125	−0.336562	−	0.941661i	$-0.609264\pi$
$131$	−7.70427	−0.673125	−0.336562	+	0.941661i	$0.609264\pi$
$132$	1.34312	0.116904
$133$	0.0511977	0.00443940
$134$	−8.94831	−0.773016
$135$	−4.51122	−0.388264
$136$	−2.56170	−0.219664
$137$	−14.7566	−1.26074	−0.630369	−	0.776296i	$-0.717096\pi$
$137$	−14.7566	−1.26074	−0.630369	+	0.776296i	$0.717096\pi$
$138$	0.637400	0.0542591
$139$	3.35452	0.284526	0.142263	−	0.989829i	$-0.454562\pi$
$139$	3.35452	0.284526	0.142263	+	0.989829i	$0.454562\pi$
$140$	−0.808180	−0.0683036
$141$	14.9475	1.25880
$142$	−2.64602	−0.222049
$143$	−4.69573	−0.392677
$144$	−1.36370	−0.113642
$145$	−0.240578	−0.0199789
$146$	−6.92915	−0.573461
$147$	−1.27918	−0.105505
$148$	−3.42429	−0.281475
$149$	5.02417	0.411596	0.205798	−	0.978594i	$-0.434021\pi$
$149$	5.02417	0.411596	0.205798	+	0.978594i	$0.434021\pi$
$150$	5.56039	0.454004
$151$	−22.7740	−1.85332	−0.926662	−	0.375895i	$-0.877335\pi$
$151$	−22.7740	−1.85332	−0.926662	+	0.375895i	$0.877335\pi$
$152$	0.0511977	0.00415268
$153$	3.49339	0.282424
$154$	−1.04999	−0.0846103
$155$	1.48997	0.119677
$156$	−5.72072	−0.458024
$157$	−20.9317	−1.67053	−0.835265	−	0.549848i	$-0.814686\pi$
$157$	−20.9317	−1.67053	−0.835265	+	0.549848i	$0.814686\pi$
$158$	−12.5652	−0.999632
$159$	−14.4393	−1.14511
$160$	−0.808180	−0.0638922
$161$	−0.498288	−0.0392706
$162$	−3.04921	−0.239568
$163$	1.97417	0.154629	0.0773145	−	0.997007i	$-0.475365\pi$
$163$	1.97417	0.154629	0.0773145	+	0.997007i	$0.475365\pi$
$164$	−7.76395	−0.606263
$165$	−1.08548	−0.0845047
$166$	−5.79766	−0.449986
$167$	−13.3556	−1.03349	−0.516744	−	0.856140i	$-0.672856\pi$
$167$	−13.3556	−1.03349	−0.516744	+	0.856140i	$0.672856\pi$
$168$	−1.27918	−0.0986908
$169$	7.00043	0.538495
$170$	2.07031	0.158786
$171$	−0.0698184	−0.00533915
$172$	7.95661	0.606686
$173$	6.01340	0.457190	0.228595	−	0.973522i	$-0.426587\pi$
$173$	6.01340	0.457190	0.228595	+	0.973522i	$0.426587\pi$
$174$	−0.380785	−0.0288672
$175$	−4.34685	−0.328591
$176$	−1.04999	−0.0791457
$177$	−9.01206	−0.677388
$178$	6.66649	0.499674
$179$	−23.4276	−1.75106	−0.875531	−	0.483161i	$-0.839489\pi$
$179$	−23.4276	−1.75106	−0.875531	+	0.483161i	$0.839489\pi$
$180$	1.10212	0.0821469
$181$	14.7939	1.09963	0.549813	−	0.835288i	$-0.314699\pi$
$181$	14.7939	1.09963	0.549813	+	0.835288i	$0.314699\pi$
$182$	4.47218	0.331500
$183$	−5.64341	−0.417173
$184$	−0.498288	−0.0367343
$185$	2.76744	0.203466
$186$	2.35831	0.172920
$187$	2.68975	0.196694
$188$	−11.6852	−0.852231
$189$	5.58195	0.406027
$190$	−0.0413769	−0.00300180
$191$	15.3840	1.11315	0.556575	−	0.830798i	$-0.312115\pi$
$191$	15.3840	1.11315	0.556575	+	0.830798i	$0.312115\pi$
$192$	−1.27918	−0.0923168
$193$	−24.3027	−1.74935	−0.874675	−	0.484711i	$-0.838925\pi$
$193$	−24.3027	−1.74935	−0.874675	+	0.484711i	$0.838925\pi$
$194$	14.5355	1.04359
$195$	4.62337	0.331086
$196$	1.00000	0.0714286
$197$	−21.9170	−1.56152	−0.780760	−	0.624831i	$-0.785168\pi$
$197$	−21.9170	−1.56152	−0.780760	+	0.624831i	$0.785168\pi$
$198$	1.43187	0.101759
$199$	−1.53147	−0.108563	−0.0542816	−	0.998526i	$-0.517287\pi$
$199$	−1.53147	−0.108563	−0.0542816	+	0.998526i	$0.517287\pi$
$200$	−4.34685	−0.307368
$201$	11.4465	0.807373
$202$	−2.05751	−0.144766
$203$	0.297679	0.0208930
$204$	3.27687	0.229426
$205$	6.27467	0.438242
$206$	−3.08673	−0.215063
$207$	0.679517	0.0472297
$208$	4.47218	0.310090
$209$	−0.0537569	−0.00371844
$210$	1.03381	0.0713394
$211$	1.66251	0.114452	0.0572259	−	0.998361i	$-0.481774\pi$
$211$	1.66251	0.114452	0.0572259	+	0.998361i	$0.481774\pi$
$212$	11.2879	0.775259
$213$	3.38474	0.231918
$214$	−3.28701	−0.224695
$215$	−6.43037	−0.438548
$216$	5.58195	0.379804
$217$	−1.84361	−0.125153
$218$	3.25647	0.220556
$219$	8.86362	0.598948
$220$	0.848578	0.0572111
$221$	−11.4564	−0.770639
$222$	4.38028	0.293985
$223$	10.2558	0.686777	0.343389	−	0.939193i	$-0.388425\pi$
$223$	10.2558	0.686777	0.343389	+	0.939193i	$0.388425\pi$
$224$	1.00000	0.0668153
$225$	5.92780	0.395187
$226$	−18.0646	−1.20164
$227$	16.9948	1.12799	0.563993	−	0.825780i	$-0.309264\pi$
$227$	16.9948	1.12799	0.563993	+	0.825780i	$0.309264\pi$
$228$	−0.0654910	−0.00433725
$229$	−21.6619	−1.43146	−0.715729	−	0.698378i	$-0.753906\pi$
$229$	−21.6619	−1.43146	−0.715729	+	0.698378i	$0.753906\pi$
$230$	0.402706	0.0265537
$231$	1.34312	0.0883708
$232$	0.297679	0.0195436
$233$	−16.3523	−1.07128	−0.535638	−	0.844448i	$-0.679929\pi$
$233$	−16.3523	−1.07128	−0.535638	+	0.844448i	$0.679929\pi$
$234$	−6.09873	−0.398686
$235$	9.44374	0.616042
$236$	7.04519	0.458603
$237$	16.0731	1.04406
$238$	−2.56170	−0.166050
$239$	−17.7186	−1.14612	−0.573059	−	0.819514i	$-0.694243\pi$
$239$	−17.7186	−1.14612	−0.573059	+	0.819514i	$0.694243\pi$
$240$	1.03381	0.0667319
$241$	23.3115	1.50163	0.750813	−	0.660515i	$-0.229662\pi$
$241$	23.3115	1.50163	0.750813	+	0.660515i	$0.229662\pi$
$242$	−9.89753	−0.636237
$243$	−12.8454	−0.824032
$244$	4.41174	0.282433
$245$	−0.808180	−0.0516327
$246$	9.93148	0.633208
$247$	0.228965	0.0145687
$248$	−1.84361	−0.117070
$249$	7.41624	0.469985
$250$	7.55393	0.477752
$251$	5.68217	0.358655	0.179328	−	0.983789i	$-0.442608\pi$
$251$	5.68217	0.358655	0.179328	+	0.983789i	$0.442608\pi$
$252$	−1.36370	−0.0859052
$253$	0.523196	0.0328931
$254$	17.1913	1.07868
$255$	−2.64830	−0.165843
$256$	1.00000	0.0625000
$257$	−22.3016	−1.39114	−0.695568	−	0.718460i	$-0.744847\pi$
$257$	−22.3016	−1.39114	−0.695568	+	0.718460i	$0.744847\pi$
$258$	−10.1779	−0.633650
$259$	−3.42429	−0.212775
$260$	−3.61433	−0.224151
$261$	−0.405946	−0.0251274
$262$	−7.70427	−0.475971
$263$	11.1260	0.686058	0.343029	−	0.939325i	$-0.388547\pi$
$263$	11.1260	0.686058	0.343029	+	0.939325i	$0.388547\pi$
$264$	1.34312	0.0826633
$265$	−9.12268	−0.560402
$266$	0.0511977	0.00313913
$267$	−8.52762	−0.521882
$268$	−8.94831	−0.546605
$269$	2.22943	0.135931	0.0679653	−	0.997688i	$-0.478349\pi$
$269$	2.22943	0.135931	0.0679653	+	0.997688i	$0.478349\pi$
$270$	−4.51122	−0.274544
$271$	2.63839	0.160271	0.0801354	−	0.996784i	$-0.474465\pi$
$271$	2.63839	0.160271	0.0801354	+	0.996784i	$0.474465\pi$
$272$	−2.56170	−0.155326
$273$	−5.72072	−0.346234
$274$	−14.7566	−0.891477
$275$	4.56413	0.275227
$276$	0.637400	0.0383669
$277$	−0.513688	−0.0308645	−0.0154323	−	0.999881i	$-0.504912\pi$
$277$	−0.513688	−0.0308645	−0.0154323	+	0.999881i	$0.504912\pi$
$278$	3.35452	0.201191
$279$	2.51414	0.150518
$280$	−0.808180	−0.0482980
$281$	6.79792	0.405530	0.202765	−	0.979227i	$-0.435007\pi$
$281$	6.79792	0.405530	0.202765	+	0.979227i	$0.435007\pi$
$282$	14.9475	0.890108
$283$	1.83224	0.108915	0.0544576	−	0.998516i	$-0.482657\pi$
$283$	1.83224	0.108915	0.0544576	+	0.998516i	$0.482657\pi$
$284$	−2.64602	−0.157013
$285$	0.0529285	0.00313521
$286$	−4.69573	−0.277665
$287$	−7.76395	−0.458291
$288$	−1.36370	−0.0803569
$289$	−10.4377	−0.613983
$290$	−0.240578	−0.0141272
$291$	−18.5935	−1.08997
$292$	−6.92915	−0.405498
$293$	−16.2472	−0.949174	−0.474587	−	0.880209i	$-0.657403\pi$
$293$	−16.2472	−0.949174	−0.474587	+	0.880209i	$0.657403\pi$
$294$	−1.27918	−0.0746032
$295$	−5.69378	−0.331505
$296$	−3.42429	−0.199033
$297$	−5.86098	−0.340088
$298$	5.02417	0.291042
$299$	−2.22844	−0.128874
$300$	5.56039	0.321029
$301$	7.95661	0.458612
$302$	−22.7740	−1.31050
$303$	2.63193	0.151200
$304$	0.0511977	0.00293639
$305$	−3.56548	−0.204159
$306$	3.49339	0.199704
$307$	−7.68156	−0.438410	−0.219205	−	0.975679i	$-0.570346\pi$
$307$	−7.68156	−0.438410	−0.219205	+	0.975679i	$0.570346\pi$
$308$	−1.04999	−0.0598285
$309$	3.94848	0.224621
$310$	1.48997	0.0846246
$311$	−8.75502	−0.496451	−0.248226	−	0.968702i	$-0.579847\pi$
$311$	−8.75502	−0.496451	−0.248226	+	0.968702i	$0.579847\pi$
$312$	−5.72072	−0.323872
$313$	21.5538	1.21829	0.609147	−	0.793058i	$-0.291512\pi$
$313$	21.5538	1.21829	0.609147	+	0.793058i	$0.291512\pi$
$314$	−20.9317	−1.18124
$315$	1.10212	0.0620972
$316$	−12.5652	−0.706847
$317$	−27.2201	−1.52884	−0.764418	−	0.644721i	$-0.776973\pi$
$317$	−27.2201	−1.52884	−0.764418	+	0.644721i	$0.776973\pi$
$318$	−14.4393	−0.809715
$319$	−0.312559	−0.0175000
$320$	−0.808180	−0.0451786
$321$	4.20467	0.234682
$322$	−0.498288	−0.0277685
$323$	−0.131153	−0.00729754
$324$	−3.04921	−0.169400
$325$	−19.4399	−1.07833
$326$	1.97417	0.109339
$327$	−4.16560	−0.230358
$328$	−7.76395	−0.428692
$329$	−11.6852	−0.644226
$330$	−1.08548	−0.0597538
$331$	−34.9962	−1.92357	−0.961783	−	0.273814i	$-0.911715\pi$
$331$	−34.9962	−1.92357	−0.961783	+	0.273814i	$0.911715\pi$
$332$	−5.79766	−0.318188
$333$	4.66971	0.255899
$334$	−13.3556	−0.730786
$335$	7.23184	0.395118
$336$	−1.27918	−0.0697849
$337$	−0.810108	−0.0441294	−0.0220647	−	0.999757i	$-0.507024\pi$
$337$	−0.810108	−0.0441294	−0.0220647	+	0.999757i	$0.507024\pi$
$338$	7.00043	0.380773
$339$	23.1079	1.25505
$340$	2.07031	0.112278
$341$	1.93577	0.104828
$342$	−0.0698184	−0.00377535
$343$	1.00000	0.0539949
$344$	7.95661	0.428992
$345$	−0.515133	−0.0277338
$346$	6.01340	0.323282
$347$	22.0501	1.18371	0.591855	−	0.806045i	$-0.298396\pi$
$347$	22.0501	1.18371	0.591855	+	0.806045i	$0.298396\pi$
$348$	−0.380785	−0.0204122
$349$	−15.8330	−0.847522	−0.423761	−	0.905774i	$-0.639290\pi$
$349$	−15.8330	−0.847522	−0.423761	+	0.905774i	$0.639290\pi$
$350$	−4.34685	−0.232349
$351$	24.9635	1.33245
$352$	−1.04999	−0.0559645
$353$	−30.5174	−1.62428	−0.812138	−	0.583465i	$-0.801697\pi$
$353$	−30.5174	−1.62428	−0.812138	+	0.583465i	$0.801697\pi$
$354$	−9.01206	−0.478986
$355$	2.13846	0.113498
$356$	6.66649	0.353323
$357$	3.27687	0.173430
$358$	−23.4276	−1.23819
$359$	−27.2857	−1.44008	−0.720042	−	0.693930i	$-0.755878\pi$
$359$	−27.2857	−1.44008	−0.720042	+	0.693930i	$0.755878\pi$
$360$	1.10212	0.0580866
$361$	−18.9974	−0.999862
$362$	14.7939	0.777553
$363$	12.6607	0.664515
$364$	4.47218	0.234406
$365$	5.60000	0.293117
$366$	−5.64341	−0.294986
$367$	38.0399	1.98566	0.992832	−	0.119517i	$-0.0381345\pi$
$367$	38.0399	1.98566	0.992832	+	0.119517i	$0.0381345\pi$
$368$	−0.498288	−0.0259751
$369$	10.5877	0.551175
$370$	2.76744	0.143872
$371$	11.2879	0.586041
$372$	2.35831	0.122273
$373$	15.1745	0.785708	0.392854	−	0.919601i	$-0.371488\pi$
$373$	15.1745	0.785708	0.392854	+	0.919601i	$0.371488\pi$
$374$	2.68975	0.139083
$375$	−9.66282	−0.498986
$376$	−11.6852	−0.602618
$377$	1.33128	0.0685642
$378$	5.58195	0.287105
$379$	11.8124	0.606762	0.303381	−	0.952869i	$-0.401885\pi$
$379$	11.8124	0.606762	0.303381	+	0.952869i	$0.401885\pi$
$380$	−0.0413769	−0.00212259
$381$	−21.9907	−1.12662
$382$	15.3840	0.787116
$383$	21.9132	1.11971	0.559856	−	0.828590i	$-0.310856\pi$
$383$	21.9132	1.11971	0.559856	+	0.828590i	$0.310856\pi$
$384$	−1.27918	−0.0652778
$385$	0.848578	0.0432475
$386$	−24.3027	−1.23698
$387$	−10.8505	−0.551560
$388$	14.5355	0.737928
$389$	9.01109	0.456880	0.228440	−	0.973558i	$-0.426637\pi$
$389$	9.01109	0.456880	0.228440	+	0.973558i	$0.426637\pi$
$390$	4.62337	0.234113
$391$	1.27646	0.0645535
$392$	1.00000	0.0505076
$393$	9.85513	0.497126
$394$	−21.9170	−1.10416
$395$	10.1549	0.510950
$396$	1.43187	0.0719541
$397$	−11.7796	−0.591201	−0.295600	−	0.955312i	$-0.595520\pi$
$397$	−11.7796	−0.591201	−0.295600	+	0.955312i	$0.595520\pi$
$398$	−1.53147	−0.0767657
$399$	−0.0654910	−0.00327865
$400$	−4.34685	−0.217342
$401$	0.697875	0.0348502	0.0174251	−	0.999848i	$-0.494453\pi$
$401$	0.697875	0.0348502	0.0174251	+	0.999848i	$0.494453\pi$
$402$	11.4465	0.570899
$403$	−8.24498	−0.410712
$404$	−2.05751	−0.102365
$405$	2.46431	0.122452
$406$	0.297679	0.0147736
$407$	3.59546	0.178220
$408$	3.27687	0.162229
$409$	39.6166	1.95892	0.979458	−	0.201646i	$-0.0646290\pi$
$409$	39.6166	1.95892	0.979458	+	0.201646i	$0.0646290\pi$
$410$	6.27467	0.309884
$411$	18.8763	0.931098
$412$	−3.08673	−0.152072
$413$	7.04519	0.346671
$414$	0.679517	0.0333964
$415$	4.68555	0.230005
$416$	4.47218	0.219267
$417$	−4.29103	−0.210132
$418$	−0.0537569	−0.00262934
$419$	12.5145	0.611375	0.305687	−	0.952132i	$-0.401114\pi$
$419$	12.5145	0.611375	0.305687	+	0.952132i	$0.401114\pi$
$420$	1.03381	0.0504446
$421$	−4.02528	−0.196180	−0.0980900	−	0.995178i	$-0.531273\pi$
$421$	−4.02528	−0.196180	−0.0980900	+	0.995178i	$0.531273\pi$
$422$	1.66251	0.0809296
$423$	15.9351	0.774793
$424$	11.2879	0.548191
$425$	11.1353	0.540141
$426$	3.38474	0.163991
$427$	4.41174	0.213499
$428$	−3.28701	−0.158884
$429$	6.00668	0.290005
$430$	−6.43037	−0.310100
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	5.58195	0.268562
$433$	21.8987	1.05238	0.526192	−	0.850366i	$-0.323619\pi$
$433$	21.8987	1.05238	0.526192	+	0.850366i	$0.323619\pi$
$434$	−1.84361	−0.0884963
$435$	0.307743	0.0147551
$436$	3.25647	0.155956
$437$	−0.0255112	−0.00122037
$438$	8.86362	0.423520
$439$	40.7132	1.94314	0.971569	−	0.236758i	$-0.0760848\pi$
$439$	40.7132	1.94314	0.971569	+	0.236758i	$0.0760848\pi$
$440$	0.848578	0.0404544
$441$	−1.36370	−0.0649382
$442$	−11.4564	−0.544924
$443$	−17.5785	−0.835179	−0.417589	−	0.908636i	$-0.637125\pi$
$443$	−17.5785	−0.835179	−0.417589	+	0.908636i	$0.637125\pi$
$444$	4.38028	0.207879
$445$	−5.38772	−0.255402
$446$	10.2558	0.485625
$447$	−6.42681	−0.303978
$448$	1.00000	0.0472456
$449$	−17.5325	−0.827411	−0.413705	−	0.910411i	$-0.635766\pi$
$449$	−17.5325	−0.827411	−0.413705	+	0.910411i	$0.635766\pi$
$450$	5.92780	0.279439
$451$	8.15204	0.383865
$452$	−18.0646	−0.849689
$453$	29.1321	1.36874
$454$	16.9948	0.797607
$455$	−3.61433	−0.169442
$456$	−0.0654910	−0.00306690
$457$	−35.2240	−1.64771	−0.823854	−	0.566802i	$-0.808180\pi$
$457$	−35.2240	−1.64771	−0.823854	+	0.566802i	$0.808180\pi$
$458$	−21.6619	−1.01219
$459$	−14.2993	−0.667433
$460$	0.402706	0.0187763
$461$	−8.71487	−0.405892	−0.202946	−	0.979190i	$-0.565052\pi$
$461$	−8.71487	−0.405892	−0.202946	+	0.979190i	$0.565052\pi$
$462$	1.34312	0.0624876
$463$	−28.7759	−1.33733	−0.668665	−	0.743564i	$-0.733134\pi$
$463$	−28.7759	−1.33733	−0.668665	+	0.743564i	$0.733134\pi$
$464$	0.297679	0.0138194
$465$	−1.90594	−0.0883858
$466$	−16.3523	−0.757507
$467$	0.989498	0.0457885	0.0228942	−	0.999738i	$-0.492712\pi$
$467$	0.989498	0.0457885	0.0228942	+	0.999738i	$0.492712\pi$
$468$	−6.09873	−0.281914
$469$	−8.94831	−0.413195
$470$	9.44374	0.435607
$471$	26.7753	1.23374
$472$	7.04519	0.324281
$473$	−8.35434	−0.384133
$474$	16.0731	0.738263
$475$	−0.222548	−0.0102112
$476$	−2.56170	−0.117415
$477$	−15.3934	−0.704815
$478$	−17.7186	−0.810428
$479$	0.448707	0.0205020	0.0102510	−	0.999947i	$-0.496737\pi$
$479$	0.448707	0.0205020	0.0102510	+	0.999947i	$0.496737\pi$
$480$	1.03381	0.0471866
$481$	−15.3141	−0.698261
$482$	23.3115	1.06181
$483$	0.637400	0.0290027
$484$	−9.89753	−0.449888
$485$	−11.7473	−0.533417
$486$	−12.8454	−0.582678
$487$	21.6354	0.980392	0.490196	−	0.871612i	$-0.336925\pi$
$487$	21.6354	0.980392	0.490196	+	0.871612i	$0.336925\pi$
$488$	4.41174	0.199710
$489$	−2.52532	−0.114199
$490$	−0.808180	−0.0365098
$491$	31.8179	1.43592	0.717962	−	0.696082i	$-0.245075\pi$
$491$	31.8179	1.43592	0.717962	+	0.696082i	$0.245075\pi$
$492$	9.93148	0.447746
$493$	−0.762563	−0.0343441
$494$	0.228965	0.0103016
$495$	−1.15721	−0.0520126
$496$	−1.84361	−0.0827807
$497$	−2.64602	−0.118690
$498$	7.41624	0.332330
$499$	36.5256	1.63511	0.817556	−	0.575849i	$-0.195328\pi$
$499$	36.5256	1.63511	0.817556	+	0.575849i	$0.195328\pi$
$500$	7.55393	0.337822
$501$	17.0842	0.763266
$502$	5.68217	0.253607
$503$	−43.1769	−1.92516	−0.962582	−	0.270992i	$-0.912648\pi$
$503$	−43.1769	−1.92516	−0.962582	+	0.270992i	$0.912648\pi$
$504$	−1.36370	−0.0607441
$505$	1.66284	0.0739955
$506$	0.523196	0.0232589
$507$	−8.95480	−0.397697
$508$	17.1913	0.762740
$509$	−9.93474	−0.440350	−0.220175	−	0.975460i	$-0.570663\pi$
$509$	−9.93474	−0.440350	−0.220175	+	0.975460i	$0.570663\pi$
$510$	−2.64830	−0.117268
$511$	−6.92915	−0.306528
$512$	1.00000	0.0441942
$513$	0.285783	0.0126176
$514$	−22.3016	−0.983682
$515$	2.49463	0.109927
$516$	−10.1779	−0.448058
$517$	12.2693	0.539603
$518$	−3.42429	−0.150455
$519$	−7.69221	−0.337650
$520$	−3.61433	−0.158499
$521$	16.2003	0.709747	0.354873	−	0.934914i	$-0.384524\pi$
$521$	16.2003	0.709747	0.354873	+	0.934914i	$0.384524\pi$
$522$	−0.405946	−0.0177678
$523$	21.3535	0.933722	0.466861	−	0.884331i	$-0.345385\pi$
$523$	21.3535	0.933722	0.466861	+	0.884331i	$0.345385\pi$
$524$	−7.70427	−0.336562
$525$	5.56039	0.242675
$526$	11.1260	0.485116
$527$	4.72277	0.205727
$528$	1.34312	0.0584518
$529$	−22.7517	−0.989205
$530$	−9.12268	−0.396264
$531$	−9.60755	−0.416932
$532$	0.0511977	0.00221970
$533$	−34.7218	−1.50397
$534$	−8.52762	−0.369026
$535$	2.65649	0.114850
$536$	−8.94831	−0.386508
$537$	29.9681	1.29322
$538$	2.22943	0.0961175
$539$	−1.04999	−0.0452261
$540$	−4.51122	−0.194132
$541$	23.4070	1.00635	0.503173	−	0.864186i	$-0.332166\pi$
$541$	23.4070	1.00635	0.503173	+	0.864186i	$0.332166\pi$
$542$	2.63839	0.113329
$543$	−18.9241	−0.812111
$544$	−2.56170	−0.109832
$545$	−2.63181	−0.112734
$546$	−5.72072	−0.244824
$547$	−34.9548	−1.49456	−0.747280	−	0.664509i	$-0.768641\pi$
$547$	−34.9548	−1.49456	−0.747280	+	0.664509i	$0.768641\pi$
$548$	−14.7566	−0.630369
$549$	−6.01631	−0.256770
$550$	4.56413	0.194615
$551$	0.0152405	0.000649266 0
$552$	0.637400	0.0271295
$553$	−12.5652	−0.534326
$554$	−0.513688	−0.0218245
$555$	−3.54005	−0.150267
$556$	3.35452	0.142263
$557$	−19.1294	−0.810538	−0.405269	−	0.914197i	$-0.632822\pi$
$557$	−19.1294	−0.810538	−0.405269	+	0.914197i	$0.632822\pi$
$558$	2.51414	0.106432
$559$	35.5834	1.50502
$560$	−0.808180	−0.0341518
$561$	−3.44066	−0.145265
$562$	6.79792	0.286753
$563$	3.05134	0.128599	0.0642994	−	0.997931i	$-0.479519\pi$
$563$	3.05134	0.128599	0.0642994	+	0.997931i	$0.479519\pi$
$564$	14.9475	0.629401
$565$	14.5995	0.614204
$566$	1.83224	0.0770146
$567$	−3.04921	−0.128055
$568$	−2.64602	−0.111025
$569$	26.1836	1.09767	0.548837	−	0.835929i	$-0.315071\pi$
$569$	26.1836	1.09767	0.548837	+	0.835929i	$0.315071\pi$
$570$	0.0529285	0.00221693
$571$	−6.26238	−0.262073	−0.131036	−	0.991378i	$-0.541830\pi$
$571$	−6.26238	−0.262073	−0.131036	+	0.991378i	$0.541830\pi$
$572$	−4.69573	−0.196339
$573$	−19.6789	−0.822099
$574$	−7.76395	−0.324061
$575$	2.16598	0.0903277
$576$	−1.36370	−0.0568209
$577$	−21.4583	−0.893322	−0.446661	−	0.894703i	$-0.647387\pi$
$577$	−21.4583	−0.893322	−0.446661	+	0.894703i	$0.647387\pi$
$578$	−10.4377	−0.434152
$579$	31.0875	1.29195
$580$	−0.240578	−0.00998947
$581$	−5.79766	−0.240527
$582$	−18.5935	−0.770725
$583$	−11.8522	−0.490868
$584$	−6.92915	−0.286730
$585$	4.92887	0.203784
$586$	−16.2472	−0.671168
$587$	−1.96235	−0.0809950	−0.0404975	−	0.999180i	$-0.512894\pi$
$587$	−1.96235	−0.0809950	−0.0404975	+	0.999180i	$0.512894\pi$
$588$	−1.27918	−0.0527524
$589$	−0.0943887	−0.00388922
$590$	−5.69378	−0.234409
$591$	28.0357	1.15324
$592$	−3.42429	−0.140737
$593$	−15.4938	−0.636254	−0.318127	−	0.948048i	$-0.603054\pi$
$593$	−15.4938	−0.636254	−0.318127	+	0.948048i	$0.603054\pi$
$594$	−5.86098	−0.240479
$595$	2.07031	0.0848744
$596$	5.02417	0.205798
$597$	1.95902	0.0801776
$598$	−2.22844	−0.0911276
$599$	−34.4398	−1.40717	−0.703587	−	0.710609i	$-0.748419\pi$
$599$	−34.4398	−1.40717	−0.703587	+	0.710609i	$0.748419\pi$
$600$	5.56039	0.227002
$601$	45.0223	1.83650	0.918249	−	0.396003i	$-0.129603\pi$
$601$	45.0223	1.83650	0.918249	+	0.396003i	$0.129603\pi$
$602$	7.95661	0.324287
$603$	12.2028	0.496938
$604$	−22.7740	−0.926662
$605$	7.99898	0.325205
$606$	2.63193	0.106915
$607$	11.6819	0.474154	0.237077	−	0.971491i	$-0.423811\pi$
$607$	11.6819	0.474154	0.237077	+	0.971491i	$0.423811\pi$
$608$	0.0511977	0.00207634
$609$	−0.380785	−0.0154302
$610$	−3.56548	−0.144362
$611$	−52.2584	−2.11415
$612$	3.49339	0.141212
$613$	14.0860	0.568927	0.284464	−	0.958687i	$-0.408185\pi$
$613$	14.0860	0.568927	0.284464	+	0.958687i	$0.408185\pi$
$614$	−7.68156	−0.310003
$615$	−8.02642	−0.323656
$616$	−1.04999	−0.0423052
$617$	39.3811	1.58542	0.792712	−	0.609596i	$-0.208668\pi$
$617$	39.3811	1.58542	0.792712	+	0.609596i	$0.208668\pi$
$618$	3.94848	0.158831
$619$	24.2834	0.976031	0.488016	−	0.872835i	$-0.337721\pi$
$619$	24.2834	0.976031	0.488016	+	0.872835i	$0.337721\pi$
$620$	1.48997	0.0598387
$621$	−2.78142	−0.111615
$622$	−8.75502	−0.351044
$623$	6.66649	0.267087
$624$	−5.72072	−0.229012
$625$	15.6293	0.625172
$626$	21.5538	0.861464
$627$	0.0687646	0.00274620
$628$	−20.9317	−0.835265
$629$	8.77198	0.349762
$630$	1.10212	0.0439094
$631$	−20.5355	−0.817506	−0.408753	−	0.912645i	$-0.634036\pi$
$631$	−20.5355	−0.817506	−0.408753	+	0.912645i	$0.634036\pi$
$632$	−12.5652	−0.499816
$633$	−2.12664	−0.0845265
$634$	−27.2201	−1.08105
$635$	−13.8937	−0.551353
$636$	−14.4393	−0.572555
$637$	4.47218	0.177194
$638$	−0.312559	−0.0123743
$639$	3.60839	0.142746
$640$	−0.808180	−0.0319461
$641$	10.8309	0.427794	0.213897	−	0.976856i	$-0.431384\pi$
$641$	10.8309	0.427794	0.213897	+	0.976856i	$0.431384\pi$
$642$	4.20467	0.165945
$643$	11.3337	0.446957	0.223478	−	0.974709i	$-0.428259\pi$
$643$	11.3337	0.446957	0.223478	+	0.974709i	$0.428259\pi$
$644$	−0.498288	−0.0196353
$645$	8.22559	0.323882
$646$	−0.131153	−0.00516014
$647$	−27.7533	−1.09110	−0.545548	−	0.838080i	$-0.683678\pi$
$647$	−27.7533	−1.09110	−0.545548	+	0.838080i	$0.683678\pi$
$648$	−3.04921	−0.119784
$649$	−7.39736	−0.290372
$650$	−19.4399	−0.762495
$651$	2.35831	0.0924295
$652$	1.97417	0.0773145
$653$	−22.6879	−0.887846	−0.443923	−	0.896065i	$-0.646414\pi$
$653$	−22.6879	−0.887846	−0.443923	+	0.896065i	$0.646414\pi$
$654$	−4.16560	−0.162888
$655$	6.22643	0.243287
$656$	−7.76395	−0.303131
$657$	9.44930	0.368652
$658$	−11.6852	−0.455537
$659$	14.4798	0.564051	0.282026	−	0.959407i	$-0.408994\pi$
$659$	14.4798	0.564051	0.282026	+	0.959407i	$0.408994\pi$
$660$	−1.08548	−0.0422523
$661$	32.7830	1.27511	0.637555	−	0.770405i	$-0.279946\pi$
$661$	32.7830	1.27511	0.637555	+	0.770405i	$0.279946\pi$
$662$	−34.9962	−1.36017
$663$	14.6547	0.569143
$664$	−5.79766	−0.224993
$665$	−0.0413769	−0.00160453
$666$	4.66971	0.180948
$667$	−0.148330	−0.00574336
$668$	−13.3556	−0.516744
$669$	−13.1190	−0.507208
$670$	7.23184	0.279390
$671$	−4.63227	−0.178827
$672$	−1.27918	−0.0493454
$673$	14.7237	0.567559	0.283779	−	0.958890i	$-0.408412\pi$
$673$	14.7237	0.567559	0.283779	+	0.958890i	$0.408412\pi$
$674$	−0.810108	−0.0312042
$675$	−24.2639	−0.933918
$676$	7.00043	0.269247
$677$	−19.6241	−0.754217	−0.377108	−	0.926169i	$-0.623082\pi$
$677$	−19.6241	−0.754217	−0.377108	+	0.926169i	$0.623082\pi$
$678$	23.1079	0.887453
$679$	14.5355	0.557821
$680$	2.07031	0.0793928
$681$	−21.7394	−0.833056
$682$	1.93577	0.0741244
$683$	41.0295	1.56995	0.784975	−	0.619527i	$-0.212676\pi$
$683$	41.0295	1.56995	0.784975	+	0.619527i	$0.212676\pi$
$684$	−0.0698184	−0.00266957
$685$	11.9260	0.455667
$686$	1.00000	0.0381802
$687$	27.7094	1.05718
$688$	7.95661	0.303343
$689$	50.4818	1.92320
$690$	−0.515133	−0.0196108
$691$	−14.2987	−0.543948	−0.271974	−	0.962305i	$-0.587676\pi$
$691$	−14.2987	−0.543948	−0.271974	+	0.962305i	$0.587676\pi$
$692$	6.01340	0.228595
$693$	1.43187	0.0543922
$694$	22.0501	0.837009
$695$	−2.71105	−0.102836
$696$	−0.380785	−0.0144336
$697$	19.8889	0.753345
$698$	−15.8330	−0.599288
$699$	20.9175	0.791174
$700$	−4.34685	−0.164295
$701$	9.59662	0.362459	0.181230	−	0.983441i	$-0.441992\pi$
$701$	9.59662	0.362459	0.181230	+	0.983441i	$0.441992\pi$
$702$	24.9635	0.942188
$703$	−0.175316	−0.00661216
$704$	−1.04999	−0.0395729
$705$	−12.0802	−0.454968
$706$	−30.5174	−1.14854
$707$	−2.05751	−0.0773808
$708$	−9.01206	−0.338694
$709$	−34.1622	−1.28299	−0.641493	−	0.767128i	$-0.721685\pi$
$709$	−34.1622	−1.28299	−0.641493	+	0.767128i	$0.721685\pi$
$710$	2.13846	0.0802551
$711$	17.1352	0.642619
$712$	6.66649	0.249837
$713$	0.918651	0.0344037
$714$	3.27687	0.122634
$715$	3.79500	0.141925
$716$	−23.4276	−0.875531
$717$	22.6652	0.846447
$718$	−27.2857	−1.01829
$719$	−4.89548	−0.182570	−0.0912852	−	0.995825i	$-0.529098\pi$
$719$	−4.89548	−0.182570	−0.0912852	+	0.995825i	$0.529098\pi$
$720$	1.10212	0.0410735
$721$	−3.08673	−0.114956
$722$	−18.9974	−0.707009
$723$	−29.8196	−1.10900
$724$	14.7939	0.549813
$725$	−1.29397	−0.0480567
$726$	12.6607	0.469883
$727$	−13.0868	−0.485361	−0.242680	−	0.970106i	$-0.578027\pi$
$727$	−13.0868	−0.485361	−0.242680	+	0.970106i	$0.578027\pi$
$728$	4.47218	0.165750
$729$	25.5792	0.947376
$730$	5.60000	0.207265
$731$	−20.3824	−0.753871
$732$	−5.64341	−0.208586
$733$	0.769906	0.0284371	0.0142186	−	0.999899i	$-0.495474\pi$
$733$	0.769906	0.0284371	0.0142186	+	0.999899i	$0.495474\pi$
$734$	38.0399	1.40408
$735$	1.03381	0.0381325
$736$	−0.498288	−0.0183671
$737$	9.39561	0.346092
$738$	10.5877	0.389739
$739$	2.71412	0.0998404	0.0499202	−	0.998753i	$-0.484103\pi$
$739$	2.71412	0.0998404	0.0499202	+	0.998753i	$0.484103\pi$
$740$	2.76744	0.101733
$741$	−0.292888	−0.0107595
$742$	11.2879	0.414393
$743$	−10.2093	−0.374543	−0.187271	−	0.982308i	$-0.559964\pi$
$743$	−10.2093	−0.374543	−0.187271	+	0.982308i	$0.559964\pi$
$744$	2.35831	0.0864598
$745$	−4.06043	−0.148763
$746$	15.1745	0.555579
$747$	7.90628	0.289276
$748$	2.68975	0.0983468
$749$	−3.28701	−0.120105
$750$	−9.66282	−0.352836
$751$	−30.2125	−1.10247	−0.551234	−	0.834351i	$-0.685843\pi$
$751$	−30.2125	−1.10247	−0.551234	+	0.834351i	$0.685843\pi$
$752$	−11.6852	−0.426115
$753$	−7.26850	−0.264879
$754$	1.33128	0.0484822
$755$	18.4055	0.669845
$756$	5.58195	0.203014
$757$	−26.4365	−0.960850	−0.480425	−	0.877036i	$-0.659518\pi$
$757$	−26.4365	−0.960850	−0.480425	+	0.877036i	$0.659518\pi$
$758$	11.8124	0.429045
$759$	−0.669261	−0.0242926
$760$	−0.0413769	−0.00150090
$761$	−33.2874	−1.20667	−0.603334	−	0.797489i	$-0.706161\pi$
$761$	−33.2874	−1.20667	−0.603334	+	0.797489i	$0.706161\pi$
$762$	−21.9907	−0.796640
$763$	3.25647	0.117892
$764$	15.3840	0.556575
$765$	−2.82329	−0.102076
$766$	21.9132	0.791756
$767$	31.5074	1.13767
$768$	−1.27918	−0.0461584
$769$	24.3354	0.877558	0.438779	−	0.898595i	$-0.355411\pi$
$769$	24.3354	0.877558	0.438779	+	0.898595i	$0.355411\pi$
$770$	0.848578	0.0305806
$771$	28.5277	1.02740
$772$	−24.3027	−0.874675
$773$	−12.5800	−0.452469	−0.226235	−	0.974073i	$-0.572642\pi$
$773$	−12.5800	−0.452469	−0.226235	+	0.974073i	$0.572642\pi$
$774$	−10.8505	−0.390012
$775$	8.01390	0.287868
$776$	14.5355	0.521794
$777$	4.38028	0.157142
$778$	9.01109	0.323063
$779$	−0.397496	−0.0142418
$780$	4.62337	0.165543
$781$	2.77829	0.0994150
$782$	1.27646	0.0456462
$783$	1.66163	0.0593819
$784$	1.00000	0.0357143
$785$	16.9166	0.603778
$786$	9.85513	0.351521
$787$	15.2314	0.542939	0.271470	−	0.962447i	$-0.412490\pi$
$787$	15.2314	0.542939	0.271470	+	0.962447i	$0.412490\pi$
$788$	−21.9170	−0.780760
$789$	−14.2321	−0.506677
$790$	10.1549	0.361296
$791$	−18.0646	−0.642305
$792$	1.43187	0.0508793
$793$	19.7301	0.700637
$794$	−11.7796	−0.418042
$795$	11.6695	0.413876
$796$	−1.53147	−0.0542816
$797$	5.92235	0.209780	0.104890	−	0.994484i	$-0.466551\pi$
$797$	5.92235	0.209780	0.104890	+	0.994484i	$0.466551\pi$
$798$	−0.0654910	−0.00231836
$799$	29.9339	1.05899
$800$	−4.34685	−0.153684
$801$	−9.09110	−0.321218
$802$	0.697875	0.0246428
$803$	7.27552	0.256747
$804$	11.4465	0.403686
$805$	0.402706	0.0141935
$806$	−8.24498	−0.290417
$807$	−2.85184	−0.100389
$808$	−2.05751	−0.0723831
$809$	0.985383	0.0346442	0.0173221	−	0.999850i	$-0.494486\pi$
$809$	0.985383	0.0346442	0.0173221	+	0.999850i	$0.494486\pi$
$810$	2.46431	0.0865869
$811$	−12.2919	−0.431628	−0.215814	−	0.976435i	$-0.569240\pi$
$811$	−12.2919	−0.431628	−0.215814	+	0.976435i	$0.569240\pi$
$812$	0.297679	0.0104465
$813$	−3.37497	−0.118365
$814$	3.59546	0.126021
$815$	−1.59548	−0.0558874
$816$	3.27687	0.114713
$817$	0.407360	0.0142517
$818$	39.6166	1.38516
$819$	−6.09873	−0.213107
$820$	6.27467	0.219121
$821$	−19.0946	−0.666405	−0.333203	−	0.942855i	$-0.608129\pi$
$821$	−19.0946	−0.666405	−0.333203	+	0.942855i	$0.608129\pi$
$822$	18.8763	0.658386
$823$	28.2501	0.984736	0.492368	−	0.870387i	$-0.336132\pi$
$823$	28.2501	0.984736	0.492368	+	0.870387i	$0.336132\pi$
$824$	−3.08673	−0.107531
$825$	−5.83834	−0.203265
$826$	7.04519	0.245134
$827$	19.1572	0.666163	0.333081	−	0.942898i	$-0.391912\pi$
$827$	19.1572	0.666163	0.333081	+	0.942898i	$0.391912\pi$
$828$	0.679517	0.0236148
$829$	−23.5368	−0.817467	−0.408734	−	0.912654i	$-0.634029\pi$
$829$	−23.5368	−0.817467	−0.408734	+	0.912654i	$0.634029\pi$
$830$	4.68555	0.162638
$831$	0.657099	0.0227945
$832$	4.47218	0.155045
$833$	−2.56170	−0.0887575
$834$	−4.29103	−0.148586
$835$	10.7937	0.373532
$836$	−0.0537569	−0.00185922
$837$	−10.2910	−0.355708
$838$	12.5145	0.432307
$839$	−3.57157	−0.123304	−0.0616522	−	0.998098i	$-0.519637\pi$
$839$	−3.57157	−0.123304	−0.0616522	+	0.998098i	$0.519637\pi$
$840$	1.03381	0.0356697
$841$	−28.9114	−0.996944
$842$	−4.02528	−0.138720
$843$	−8.69576	−0.299498
$844$	1.66251	0.0572259
$845$	−5.65761	−0.194628
$846$	15.9351	0.547861
$847$	−9.89753	−0.340083
$848$	11.2879	0.387630
$849$	−2.34376	−0.0804375
$850$	11.1353	0.381937
$851$	1.70628	0.0584906
$852$	3.38474	0.115959
$853$	−17.4209	−0.596481	−0.298240	−	0.954491i	$-0.596400\pi$
$853$	−17.4209	−0.596481	−0.298240	+	0.954491i	$0.596400\pi$
$854$	4.41174	0.150967
$855$	0.0564258	0.00192972
$856$	−3.28701	−0.112348
$857$	9.19924	0.314240	0.157120	−	0.987580i	$-0.449779\pi$
$857$	9.19924	0.314240	0.157120	+	0.987580i	$0.449779\pi$
$858$	6.00668	0.205065
$859$	45.2404	1.54358	0.771791	−	0.635877i	$-0.219361\pi$
$859$	45.2404	1.54358	0.771791	+	0.635877i	$0.219361\pi$
$860$	−6.43037	−0.219274
$861$	9.93148	0.338464
$862$	−1.00000	−0.0340601
$863$	40.8703	1.39124	0.695620	−	0.718410i	$-0.255130\pi$
$863$	40.8703	1.39124	0.695620	+	0.718410i	$0.255130\pi$
$864$	5.58195	0.189902
$865$	−4.85990	−0.165242
$866$	21.8987	0.744148
$867$	13.3517	0.453448
$868$	−1.84361	−0.0625763
$869$	13.1933	0.447551
$870$	0.307743	0.0104334
$871$	−40.0185	−1.35598
$872$	3.25647	0.110278
$873$	−19.8221	−0.670876
$874$	−0.0255112	−0.000862929 0
$875$	7.55393	0.255369
$876$	8.86362	0.299474
$877$	−10.9083	−0.368349	−0.184174	−	0.982894i	$-0.558961\pi$
$877$	−10.9083	−0.368349	−0.184174	+	0.982894i	$0.558961\pi$
$878$	40.7132	1.37401
$879$	20.7831	0.700997
$880$	0.848578	0.0286056
$881$	25.6661	0.864713	0.432357	−	0.901703i	$-0.357682\pi$
$881$	25.6661	0.864713	0.432357	+	0.901703i	$0.357682\pi$
$882$	−1.36370	−0.0459183
$883$	56.4909	1.90107	0.950536	−	0.310615i	$-0.100535\pi$
$883$	56.4909	1.90107	0.950536	+	0.310615i	$0.100535\pi$
$884$	−11.4564	−0.385320
$885$	7.28336	0.244828
$886$	−17.5785	−0.590561
$887$	43.5705	1.46295	0.731477	−	0.681866i	$-0.238831\pi$
$887$	43.5705	1.46295	0.731477	+	0.681866i	$0.238831\pi$
$888$	4.38028	0.146992
$889$	17.1913	0.576578
$890$	−5.38772	−0.180597
$891$	3.20163	0.107259
$892$	10.2558	0.343389
$893$	−0.598255	−0.0200198
$894$	−6.42681	−0.214945
$895$	18.9337	0.632885
$896$	1.00000	0.0334077
$897$	2.85057	0.0951777
$898$	−17.5325	−0.585068
$899$	−0.548805	−0.0183037
$900$	5.92780	0.197593
$901$	−28.9163	−0.963340
$902$	8.15204	0.271433
$903$	−10.1779	−0.338700
$904$	−18.0646	−0.600821
$905$	−11.9562	−0.397436
$906$	29.1321	0.967848
$907$	−50.7758	−1.68598	−0.842992	−	0.537927i	$-0.819208\pi$
$907$	−50.7758	−1.68598	−0.842992	+	0.537927i	$0.819208\pi$
$908$	16.9948	0.563993
$909$	2.80584	0.0930637
$910$	−3.61433	−0.119814
$911$	27.4290	0.908764	0.454382	−	0.890807i	$-0.349860\pi$
$911$	27.4290	0.908764	0.454382	+	0.890807i	$0.349860\pi$
$912$	−0.0654910	−0.00216862
$913$	6.08747	0.201466
$914$	−35.2240	−1.16511
$915$	4.56089	0.150778
$916$	−21.6619	−0.715729
$917$	−7.70427	−0.254417
$918$	−14.2993	−0.471946
$919$	19.9754	0.658928	0.329464	−	0.944168i	$-0.393132\pi$
$919$	19.9754	0.658928	0.329464	+	0.944168i	$0.393132\pi$
$920$	0.402706	0.0132768
$921$	9.82609	0.323781
$922$	−8.71487	−0.287009
$923$	−11.8335	−0.389505
$924$	1.34312	0.0441854
$925$	14.8849	0.489411
$926$	−28.7759	−0.945635
$927$	4.20938	0.138254
$928$	0.297679	0.00977180
$929$	40.8639	1.34070	0.670350	−	0.742045i	$-0.266144\pi$
$929$	40.8639	1.34070	0.670350	+	0.742045i	$0.266144\pi$
$930$	−1.90594	−0.0624982
$931$	0.0511977	0.00167794
$932$	−16.3523	−0.535638
$933$	11.1992	0.366646
$934$	0.989498	0.0323773
$935$	−2.17380	−0.0710908
$936$	−6.09873	−0.199343
$937$	9.62974	0.314590	0.157295	−	0.987552i	$-0.449723\pi$
$937$	9.62974	0.314590	0.157295	+	0.987552i	$0.449723\pi$
$938$	−8.94831	−0.292173
$939$	−27.5712	−0.899751
$940$	9.44374	0.308021
$941$	−55.4623	−1.80802	−0.904010	−	0.427512i	$-0.859390\pi$
$941$	−55.4623	−1.80802	−0.904010	+	0.427512i	$0.859390\pi$
$942$	26.7753	0.872388
$943$	3.86868	0.125982
$944$	7.04519	0.229302
$945$	−4.51122	−0.146750
$946$	−8.35434	−0.271623
$947$	59.4711	1.93255	0.966276	−	0.257509i	$-0.0829018\pi$
$947$	59.4711	1.93255	0.966276	+	0.257509i	$0.0829018\pi$
$948$	16.0731	0.522030
$949$	−30.9885	−1.00593
$950$	−0.222548	−0.00722042
$951$	34.8194	1.12910
$952$	−2.56170	−0.0830250
$953$	43.0227	1.39364	0.696822	−	0.717244i	$-0.254597\pi$
$953$	43.0227	1.39364	0.696822	+	0.717244i	$0.254597\pi$
$954$	−15.3934	−0.498380
$955$	−12.4331	−0.402324
$956$	−17.7186	−0.573059
$957$	0.399819	0.0129243
$958$	0.448707	0.0144971
$959$	−14.7566	−0.476514
$960$	1.03381	0.0333659
$961$	−27.6011	−0.890358
$962$	−15.3141	−0.493745
$963$	4.48250	0.144447
$964$	23.3115	0.750813
$965$	19.6410	0.632265
$966$	0.637400	0.0205080
$967$	38.4048	1.23502	0.617508	−	0.786564i	$-0.288142\pi$
$967$	38.4048	1.23502	0.617508	+	0.786564i	$0.288142\pi$
$968$	−9.89753	−0.318119
$969$	0.167768	0.00538948
$970$	−11.7473	−0.377183
$971$	−51.2764	−1.64554	−0.822769	−	0.568376i	$-0.807572\pi$
$971$	−51.2764	−1.64554	−0.822769	+	0.568376i	$0.807572\pi$
$972$	−12.8454	−0.412016
$973$	3.35452	0.107541
$974$	21.6354	0.693242
$975$	24.8671	0.796384
$976$	4.41174	0.141216
$977$	52.1448	1.66826	0.834130	−	0.551568i	$-0.185970\pi$
$977$	52.1448	1.66826	0.834130	+	0.551568i	$0.185970\pi$
$978$	−2.52532	−0.0807507
$979$	−6.99972	−0.223712
$980$	−0.808180	−0.0258164
$981$	−4.44085	−0.141785
$982$	31.8179	1.01535
$983$	−21.5642	−0.687791	−0.343895	−	0.939008i	$-0.611747\pi$
$983$	−21.5642	−0.687791	−0.343895	+	0.939008i	$0.611747\pi$
$984$	9.93148	0.316604
$985$	17.7129	0.564378
$986$	−0.762563	−0.0242850
$987$	14.9475	0.475783
$988$	0.228965	0.00728436
$989$	−3.96469	−0.126070
$990$	−1.15721	−0.0367785
$991$	−2.09016	−0.0663960	−0.0331980	−	0.999449i	$-0.510569\pi$
$991$	−2.09016	−0.0663960	−0.0331980	+	0.999449i	$0.510569\pi$
$992$	−1.84361	−0.0585348
$993$	44.7664	1.42062
$994$	−2.64602	−0.0839268
$995$	1.23770	0.0392378
$996$	7.41624	0.234993
$997$	42.6350	1.35026	0.675132	−	0.737697i	$-0.264087\pi$
$997$	42.6350	1.35026	0.675132	+	0.737697i	$0.264087\pi$
$998$	36.5256	1.15620
$999$	−19.1142	−0.604747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.8	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.8	✓	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.27918 q^{3} +1.00000 q^{4} -0.808180 q^{5} -1.27918 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.36370 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.27918 q^{3} +1.00000 q^{4} -0.808180 q^{5} -1.27918 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.36370 q^{9} -0.808180 q^{10} -1.04999 q^{11} -1.27918 q^{12} +4.47218 q^{13} +1.00000 q^{14} +1.03381 q^{15} +1.00000 q^{16} -2.56170 q^{17} -1.36370 q^{18} +0.0511977 q^{19} -0.808180 q^{20} -1.27918 q^{21} -1.04999 q^{22} -0.498288 q^{23} -1.27918 q^{24} -4.34685 q^{25} +4.47218 q^{26} +5.58195 q^{27} +1.00000 q^{28} +0.297679 q^{29} +1.03381 q^{30} -1.84361 q^{31} +1.00000 q^{32} +1.34312 q^{33} -2.56170 q^{34} -0.808180 q^{35} -1.36370 q^{36} -3.42429 q^{37} +0.0511977 q^{38} -5.72072 q^{39} -0.808180 q^{40} -7.76395 q^{41} -1.27918 q^{42} +7.95661 q^{43} -1.04999 q^{44} +1.10212 q^{45} -0.498288 q^{46} -11.6852 q^{47} -1.27918 q^{48} +1.00000 q^{49} -4.34685 q^{50} +3.27687 q^{51} +4.47218 q^{52} +11.2879 q^{53} +5.58195 q^{54} +0.848578 q^{55} +1.00000 q^{56} -0.0654910 q^{57} +0.297679 q^{58} +7.04519 q^{59} +1.03381 q^{60} +4.41174 q^{61} -1.84361 q^{62} -1.36370 q^{63} +1.00000 q^{64} -3.61433 q^{65} +1.34312 q^{66} -8.94831 q^{67} -2.56170 q^{68} +0.637400 q^{69} -0.808180 q^{70} -2.64602 q^{71} -1.36370 q^{72} -6.92915 q^{73} -3.42429 q^{74} +5.56039 q^{75} +0.0511977 q^{76} -1.04999 q^{77} -5.72072 q^{78} -12.5652 q^{79} -0.808180 q^{80} -3.04921 q^{81} -7.76395 q^{82} -5.79766 q^{83} -1.27918 q^{84} +2.07031 q^{85} +7.95661 q^{86} -0.380785 q^{87} -1.04999 q^{88} +6.66649 q^{89} +1.10212 q^{90} +4.47218 q^{91} -0.498288 q^{92} +2.35831 q^{93} -11.6852 q^{94} -0.0413769 q^{95} -1.27918 q^{96} +14.5355 q^{97} +1.00000 q^{98} +1.43187 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9} - 11 q^{10} - 34 q^{11} - 6 q^{12} - 19 q^{13} + 21 q^{14} - 24 q^{15} + 21 q^{16} - 17 q^{17} + 5 q^{18} - 15 q^{19} - 11 q^{20} - 6 q^{21} - 34 q^{22} - 32 q^{23} - 6 q^{24} + 6 q^{25} - 19 q^{26} - 3 q^{27} + 21 q^{28} - 46 q^{29} - 24 q^{30} + 7 q^{31} + 21 q^{32} - 13 q^{33} - 17 q^{34} - 11 q^{35} + 5 q^{36} - 34 q^{37} - 15 q^{38} - 25 q^{39} - 11 q^{40} - 27 q^{41} - 6 q^{42} - 47 q^{43} - 34 q^{44} - 13 q^{45} - 32 q^{46} - 7 q^{47} - 6 q^{48} + 21 q^{49} + 6 q^{50} - 29 q^{51} - 19 q^{52} - 57 q^{53} - 3 q^{54} + 17 q^{55} + 21 q^{56} - 28 q^{57} - 46 q^{58} - 30 q^{59} - 24 q^{60} - 17 q^{61} + 7 q^{62} + 5 q^{63} + 21 q^{64} - 40 q^{65} - 13 q^{66} - 38 q^{67} - 17 q^{68} - 13 q^{69} - 11 q^{70} - 66 q^{71} + 5 q^{72} - 15 q^{73} - 34 q^{74} + 15 q^{75} - 15 q^{76} - 34 q^{77} - 25 q^{78} - 17 q^{79} - 11 q^{80} - 11 q^{81} - 27 q^{82} - 19 q^{83} - 6 q^{84} - 28 q^{85} - 47 q^{86} + 45 q^{87} - 34 q^{88} - 39 q^{89} - 13 q^{90} - 19 q^{91} - 32 q^{92} - 25 q^{93} - 7 q^{94} - 35 q^{95} - 6 q^{96} + 21 q^{98} - 52 q^{99}+O(q^{100}) \) 21 * q + 21 * q^2 - 6 * q^3 + 21 * q^4 - 11 * q^5 - 6 * q^6 + 21 * q^7 + 21 * q^8 + 5 * q^9 - 11 * q^10 - 34 * q^11 - 6 * q^12 - 19 * q^13 + 21 * q^14 - 24 * q^15 + 21 * q^16 - 17 * q^17 + 5 * q^18 - 15 * q^19 - 11 * q^20 - 6 * q^21 - 34 * q^22 - 32 * q^23 - 6 * q^24 + 6 * q^25 - 19 * q^26 - 3 * q^27 + 21 * q^28 - 46 * q^29 - 24 * q^30 + 7 * q^31 + 21 * q^32 - 13 * q^33 - 17 * q^34 - 11 * q^35 + 5 * q^36 - 34 * q^37 - 15 * q^38 - 25 * q^39 - 11 * q^40 - 27 * q^41 - 6 * q^42 - 47 * q^43 - 34 * q^44 - 13 * q^45 - 32 * q^46 - 7 * q^47 - 6 * q^48 + 21 * q^49 + 6 * q^50 - 29 * q^51 - 19 * q^52 - 57 * q^53 - 3 * q^54 + 17 * q^55 + 21 * q^56 - 28 * q^57 - 46 * q^58 - 30 * q^59 - 24 * q^60 - 17 * q^61 + 7 * q^62 + 5 * q^63 + 21 * q^64 - 40 * q^65 - 13 * q^66 - 38 * q^67 - 17 * q^68 - 13 * q^69 - 11 * q^70 - 66 * q^71 + 5 * q^72 - 15 * q^73 - 34 * q^74 + 15 * q^75 - 15 * q^76 - 34 * q^77 - 25 * q^78 - 17 * q^79 - 11 * q^80 - 11 * q^81 - 27 * q^82 - 19 * q^83 - 6 * q^84 - 28 * q^85 - 47 * q^86 + 45 * q^87 - 34 * q^88 - 39 * q^89 - 13 * q^90 - 19 * q^91 - 32 * q^92 - 25 * q^93 - 7 * q^94 - 35 * q^95 - 6 * q^96 + 21 * q^98 - 52 * q^99

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