LMFDB - Embedded newform 6034.2.a.m.1.19

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			1.19
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.14514 q^{3} +1.00000 q^{4} -0.309854 q^{5} +2.14514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60160 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.14514 q^{3} +1.00000 q^{4} -0.309854 q^{5} +2.14514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60160 q^{9} -0.309854 q^{10} -5.74002 q^{11} +2.14514 q^{12} +0.589649 q^{13} +1.00000 q^{14} -0.664680 q^{15} +1.00000 q^{16} -6.54768 q^{17} +1.60160 q^{18} -4.09235 q^{19} -0.309854 q^{20} +2.14514 q^{21} -5.74002 q^{22} -4.05105 q^{23} +2.14514 q^{24} -4.90399 q^{25} +0.589649 q^{26} -2.99975 q^{27} +1.00000 q^{28} -0.169640 q^{29} -0.664680 q^{30} -7.45527 q^{31} +1.00000 q^{32} -12.3131 q^{33} -6.54768 q^{34} -0.309854 q^{35} +1.60160 q^{36} +7.59857 q^{37} -4.09235 q^{38} +1.26488 q^{39} -0.309854 q^{40} +2.61990 q^{41} +2.14514 q^{42} +1.38737 q^{43} -5.74002 q^{44} -0.496264 q^{45} -4.05105 q^{46} +6.71410 q^{47} +2.14514 q^{48} +1.00000 q^{49} -4.90399 q^{50} -14.0457 q^{51} +0.589649 q^{52} -9.35604 q^{53} -2.99975 q^{54} +1.77857 q^{55} +1.00000 q^{56} -8.77864 q^{57} -0.169640 q^{58} +3.72798 q^{59} -0.664680 q^{60} -2.62937 q^{61} -7.45527 q^{62} +1.60160 q^{63} +1.00000 q^{64} -0.182705 q^{65} -12.3131 q^{66} +8.30238 q^{67} -6.54768 q^{68} -8.69005 q^{69} -0.309854 q^{70} -5.51293 q^{71} +1.60160 q^{72} -5.88087 q^{73} +7.59857 q^{74} -10.5197 q^{75} -4.09235 q^{76} -5.74002 q^{77} +1.26488 q^{78} -13.0490 q^{79} -0.309854 q^{80} -11.2397 q^{81} +2.61990 q^{82} +8.50213 q^{83} +2.14514 q^{84} +2.02883 q^{85} +1.38737 q^{86} -0.363900 q^{87} -5.74002 q^{88} +8.52008 q^{89} -0.496264 q^{90} +0.589649 q^{91} -4.05105 q^{92} -15.9926 q^{93} +6.71410 q^{94} +1.26803 q^{95} +2.14514 q^{96} +8.77861 q^{97} +1.00000 q^{98} -9.19323 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.14514	1.23849	0.619247	−	0.785196i	$-0.287438\pi$
$3$	2.14514	1.23849	0.619247	+	0.785196i	$0.287438\pi$
$4$	1.00000	0.500000
$5$	−0.309854	−0.138571	−0.0692856	−	0.997597i	$-0.522072\pi$
$5$	−0.309854	−0.138571	−0.0692856	+	0.997597i	$0.522072\pi$
$6$	2.14514	0.875748
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.60160	0.533868
$10$	−0.309854	−0.0979846
$11$	−5.74002	−1.73068	−0.865340	−	0.501186i	$-0.832897\pi$
$11$	−5.74002	−1.73068	−0.865340	+	0.501186i	$0.832897\pi$
$12$	2.14514	0.619247
$13$	0.589649	0.163539	0.0817695	−	0.996651i	$-0.473943\pi$
$13$	0.589649	0.163539	0.0817695	+	0.996651i	$0.473943\pi$
$14$	1.00000	0.267261
$15$	−0.664680	−0.171620
$16$	1.00000	0.250000
$17$	−6.54768	−1.58805	−0.794023	−	0.607887i	$-0.792017\pi$
$17$	−6.54768	−1.58805	−0.794023	+	0.607887i	$0.792017\pi$
$18$	1.60160	0.377502
$19$	−4.09235	−0.938849	−0.469424	−	0.882973i	$-0.655539\pi$
$19$	−4.09235	−0.938849	−0.469424	+	0.882973i	$0.655539\pi$
$20$	−0.309854	−0.0692856
$21$	2.14514	0.468107
$22$	−5.74002	−1.22378
$23$	−4.05105	−0.844703	−0.422351	−	0.906432i	$-0.638795\pi$
$23$	−4.05105	−0.844703	−0.422351	+	0.906432i	$0.638795\pi$
$24$	2.14514	0.437874
$25$	−4.90399	−0.980798
$26$	0.589649	0.115640
$27$	−2.99975	−0.577302
$28$	1.00000	0.188982
$29$	−0.169640	−0.0315013	−0.0157507	−	0.999876i	$-0.505014\pi$
$29$	−0.169640	−0.0315013	−0.0157507	+	0.999876i	$0.505014\pi$
$30$	−0.664680	−0.121353
$31$	−7.45527	−1.33901	−0.669503	−	0.742810i	$-0.733493\pi$
$31$	−7.45527	−1.33901	−0.669503	+	0.742810i	$0.733493\pi$
$32$	1.00000	0.176777
$33$	−12.3131	−2.14344
$34$	−6.54768	−1.12292
$35$	−0.309854	−0.0523750
$36$	1.60160	0.266934
$37$	7.59857	1.24920	0.624599	−	0.780946i	$-0.285262\pi$
$37$	7.59857	1.24920	0.624599	+	0.780946i	$0.285262\pi$
$38$	−4.09235	−0.663866
$39$	1.26488	0.202542
$40$	−0.309854	−0.0489923
$41$	2.61990	0.409159	0.204580	−	0.978850i	$-0.434417\pi$
$41$	2.61990	0.409159	0.204580	+	0.978850i	$0.434417\pi$
$42$	2.14514	0.331002
$43$	1.38737	0.211571	0.105786	−	0.994389i	$-0.466264\pi$
$43$	1.38737	0.211571	0.105786	+	0.994389i	$0.466264\pi$
$44$	−5.74002	−0.865340
$45$	−0.496264	−0.0739787
$46$	−4.05105	−0.597295
$47$	6.71410	0.979353	0.489676	−	0.871904i	$-0.337115\pi$
$47$	6.71410	0.979353	0.489676	+	0.871904i	$0.337115\pi$
$48$	2.14514	0.309624
$49$	1.00000	0.142857
$50$	−4.90399	−0.693529
$51$	−14.0457	−1.96679
$52$	0.589649	0.0817695
$53$	−9.35604	−1.28515	−0.642576	−	0.766222i	$-0.722134\pi$
$53$	−9.35604	−1.28515	−0.642576	+	0.766222i	$0.722134\pi$
$54$	−2.99975	−0.408214
$55$	1.77857	0.239822
$56$	1.00000	0.133631
$57$	−8.77864	−1.16276
$58$	−0.169640	−0.0222748
$59$	3.72798	0.485342	0.242671	−	0.970109i	$-0.421976\pi$
$59$	3.72798	0.485342	0.242671	+	0.970109i	$0.421976\pi$
$60$	−0.664680	−0.0858098
$61$	−2.62937	−0.336657	−0.168328	−	0.985731i	$-0.553837\pi$
$61$	−2.62937	−0.336657	−0.168328	+	0.985731i	$0.553837\pi$
$62$	−7.45527	−0.946820
$63$	1.60160	0.201783
$64$	1.00000	0.125000
$65$	−0.182705	−0.0226618
$66$	−12.3131	−1.51564
$67$	8.30238	1.01430	0.507149	−	0.861859i	$-0.330699\pi$
$67$	8.30238	1.01430	0.507149	+	0.861859i	$0.330699\pi$
$68$	−6.54768	−0.794023
$69$	−8.69005	−1.04616
$70$	−0.309854	−0.0370347
$71$	−5.51293	−0.654264	−0.327132	−	0.944979i	$-0.606082\pi$
$71$	−5.51293	−0.654264	−0.327132	+	0.944979i	$0.606082\pi$
$72$	1.60160	0.188751
$73$	−5.88087	−0.688304	−0.344152	−	0.938914i	$-0.611834\pi$
$73$	−5.88087	−0.688304	−0.344152	+	0.938914i	$0.611834\pi$
$74$	7.59857	0.883316
$75$	−10.5197	−1.21471
$76$	−4.09235	−0.469424
$77$	−5.74002	−0.654135
$78$	1.26488	0.143219
$79$	−13.0490	−1.46812	−0.734061	−	0.679083i	$-0.762377\pi$
$79$	−13.0490	−1.46812	−0.734061	+	0.679083i	$0.762377\pi$
$80$	−0.309854	−0.0346428
$81$	−11.2397	−1.24885
$82$	2.61990	0.289319
$83$	8.50213	0.933230	0.466615	−	0.884461i	$-0.345473\pi$
$83$	8.50213	0.933230	0.466615	+	0.884461i	$0.345473\pi$
$84$	2.14514	0.234053
$85$	2.02883	0.220057
$86$	1.38737	0.149604
$87$	−0.363900	−0.0390142
$88$	−5.74002	−0.611888
$89$	8.52008	0.903126	0.451563	−	0.892239i	$-0.350867\pi$
$89$	8.52008	0.903126	0.451563	+	0.892239i	$0.350867\pi$
$90$	−0.496264	−0.0523109
$91$	0.589649	0.0618120
$92$	−4.05105	−0.422351
$93$	−15.9926	−1.65835
$94$	6.71410	0.692507
$95$	1.26803	0.130097
$96$	2.14514	0.218937
$97$	8.77861	0.891332	0.445666	−	0.895199i	$-0.352967\pi$
$97$	8.77861	0.891332	0.445666	+	0.895199i	$0.352967\pi$
$98$	1.00000	0.101015
$99$	−9.19323	−0.923955
$100$	−4.90399	−0.490399
$101$	3.14797	0.313234	0.156617	−	0.987659i	$-0.449941\pi$
$101$	3.14797	0.313234	0.156617	+	0.987659i	$0.449941\pi$
$102$	−14.0457	−1.39073
$103$	−3.27955	−0.323144	−0.161572	−	0.986861i	$-0.551656\pi$
$103$	−3.27955	−0.323144	−0.161572	+	0.986861i	$0.551656\pi$
$104$	0.589649	0.0578198
$105$	−0.664680	−0.0648661
$106$	−9.35604	−0.908739
$107$	−2.10577	−0.203572	−0.101786	−	0.994806i	$-0.532456\pi$
$107$	−2.10577	−0.203572	−0.101786	+	0.994806i	$0.532456\pi$
$108$	−2.99975	−0.288651
$109$	0.967565	0.0926759	0.0463379	−	0.998926i	$-0.485245\pi$
$109$	0.967565	0.0926759	0.0463379	+	0.998926i	$0.485245\pi$
$110$	1.77857	0.169580
$111$	16.3000	1.54712
$112$	1.00000	0.0944911
$113$	3.23610	0.304426	0.152213	−	0.988348i	$-0.451360\pi$
$113$	3.23610	0.304426	0.152213	+	0.988348i	$0.451360\pi$
$114$	−8.77864	−0.822195
$115$	1.25524	0.117051
$116$	−0.169640	−0.0157507
$117$	0.944384	0.0873083
$118$	3.72798	0.343189
$119$	−6.54768	−0.600225
$120$	−0.664680	−0.0606767
$121$	21.9478	1.99525
$122$	−2.62937	−0.238052
$123$	5.62003	0.506741
$124$	−7.45527	−0.669503
$125$	3.06880	0.274481
$126$	1.60160	0.142682
$127$	8.30253	0.736730	0.368365	−	0.929681i	$-0.379918\pi$
$127$	8.30253	0.736730	0.368365	+	0.929681i	$0.379918\pi$
$128$	1.00000	0.0883883
$129$	2.97609	0.262030
$130$	−0.182705	−0.0160243
$131$	−6.63553	−0.579749	−0.289875	−	0.957065i	$-0.593614\pi$
$131$	−6.63553	−0.579749	−0.289875	+	0.957065i	$0.593614\pi$
$132$	−12.3131	−1.07172
$133$	−4.09235	−0.354851
$134$	8.30238	0.717217
$135$	0.929485	0.0799973
$136$	−6.54768	−0.561459
$137$	1.40077	0.119676	0.0598378	−	0.998208i	$-0.480942\pi$
$137$	1.40077	0.119676	0.0598378	+	0.998208i	$0.480942\pi$
$138$	−8.69005	−0.739747
$139$	20.8765	1.77072	0.885359	−	0.464909i	$-0.153913\pi$
$139$	20.8765	1.77072	0.885359	+	0.464909i	$0.153913\pi$
$140$	−0.309854	−0.0261875
$141$	14.4027	1.21292
$142$	−5.51293	−0.462635
$143$	−3.38459	−0.283034
$144$	1.60160	0.133467
$145$	0.0525636	0.00436517
$146$	−5.88087	−0.486704
$147$	2.14514	0.176928
$148$	7.59857	0.624599
$149$	3.13466	0.256801	0.128401	−	0.991722i	$-0.459016\pi$
$149$	3.13466	0.256801	0.128401	+	0.991722i	$0.459016\pi$
$150$	−10.5197	−0.858932
$151$	14.4260	1.17397	0.586987	−	0.809596i	$-0.300314\pi$
$151$	14.4260	1.17397	0.586987	+	0.809596i	$0.300314\pi$
$152$	−4.09235	−0.331933
$153$	−10.4868	−0.847807
$154$	−5.74002	−0.462544
$155$	2.31005	0.185548
$156$	1.26488	0.101271
$157$	−8.47733	−0.676565	−0.338282	−	0.941045i	$-0.609846\pi$
$157$	−8.47733	−0.676565	−0.338282	+	0.941045i	$0.609846\pi$
$158$	−13.0490	−1.03812
$159$	−20.0700	−1.59165
$160$	−0.309854	−0.0244961
$161$	−4.05105	−0.319268
$162$	−11.2397	−0.883072
$163$	6.95282	0.544587	0.272293	−	0.962214i	$-0.412218\pi$
$163$	6.95282	0.544587	0.272293	+	0.962214i	$0.412218\pi$
$164$	2.61990	0.204580
$165$	3.81527	0.297019
$166$	8.50213	0.659893
$167$	11.1708	0.864420	0.432210	−	0.901773i	$-0.357734\pi$
$167$	11.1708	0.864420	0.432210	+	0.901773i	$0.357734\pi$
$168$	2.14514	0.165501
$169$	−12.6523	−0.973255
$170$	2.02883	0.155604
$171$	−6.55432	−0.501221
$172$	1.38737	0.105786
$173$	−15.1213	−1.14965	−0.574827	−	0.818275i	$-0.694931\pi$
$173$	−15.1213	−1.14965	−0.574827	+	0.818275i	$0.694931\pi$
$174$	−0.363900	−0.0275872
$175$	−4.90399	−0.370707
$176$	−5.74002	−0.432670
$177$	7.99703	0.601093
$178$	8.52008	0.638607
$179$	19.9345	1.48997	0.744986	−	0.667080i	$-0.232456\pi$
$179$	19.9345	1.48997	0.744986	+	0.667080i	$0.232456\pi$
$180$	−0.496264	−0.0369894
$181$	−11.5038	−0.855074	−0.427537	−	0.903998i	$-0.640619\pi$
$181$	−11.5038	−0.855074	−0.427537	+	0.903998i	$0.640619\pi$
$182$	0.589649	0.0437077
$183$	−5.64036	−0.416947
$184$	−4.05105	−0.298648
$185$	−2.35445	−0.173103
$186$	−15.9926	−1.17263
$187$	37.5838	2.74840
$188$	6.71410	0.489676
$189$	−2.99975	−0.218200
$190$	1.26803	0.0919927
$191$	−2.09484	−0.151577	−0.0757887	−	0.997124i	$-0.524147\pi$
$191$	−2.09484	−0.151577	−0.0757887	+	0.997124i	$0.524147\pi$
$192$	2.14514	0.154812
$193$	6.97172	0.501835	0.250918	−	0.968008i	$-0.419268\pi$
$193$	6.97172	0.501835	0.250918	+	0.968008i	$0.419268\pi$
$194$	8.77861	0.630267
$195$	−0.391927	−0.0280665
$196$	1.00000	0.0714286
$197$	−1.61812	−0.115287	−0.0576433	−	0.998337i	$-0.518359\pi$
$197$	−1.61812	−0.115287	−0.0576433	+	0.998337i	$0.518359\pi$
$198$	−9.19323	−0.653335
$199$	−12.5197	−0.887501	−0.443750	−	0.896150i	$-0.646352\pi$
$199$	−12.5197	−0.887501	−0.443750	+	0.896150i	$0.646352\pi$
$200$	−4.90399	−0.346764
$201$	17.8097	1.25620
$202$	3.14797	0.221490
$203$	−0.169640	−0.0119064
$204$	−14.0457	−0.983393
$205$	−0.811787	−0.0566977
$206$	−3.27955	−0.228497
$207$	−6.48818	−0.450960
$208$	0.589649	0.0408848
$209$	23.4901	1.62485
$210$	−0.664680	−0.0458673
$211$	6.63878	0.457032	0.228516	−	0.973540i	$-0.426613\pi$
$211$	6.63878	0.457032	0.228516	+	0.973540i	$0.426613\pi$
$212$	−9.35604	−0.642576
$213$	−11.8260	−0.810302
$214$	−2.10577	−0.143947
$215$	−0.429882	−0.0293177
$216$	−2.99975	−0.204107
$217$	−7.45527	−0.506097
$218$	0.967565	0.0655317
$219$	−12.6153	−0.852460
$220$	1.77857	0.119911
$221$	−3.86083	−0.259708
$222$	16.3000	1.09398
$223$	18.9429	1.26851	0.634257	−	0.773123i	$-0.281306\pi$
$223$	18.9429	1.26851	0.634257	+	0.773123i	$0.281306\pi$
$224$	1.00000	0.0668153
$225$	−7.85425	−0.523617
$226$	3.23610	0.215262
$227$	−25.5257	−1.69420	−0.847101	−	0.531432i	$-0.821654\pi$
$227$	−25.5257	−1.69420	−0.847101	+	0.531432i	$0.821654\pi$
$228$	−8.77864	−0.581379
$229$	−19.5404	−1.29127	−0.645635	−	0.763647i	$-0.723407\pi$
$229$	−19.5404	−1.29127	−0.645635	+	0.763647i	$0.723407\pi$
$230$	1.25524	0.0827679
$231$	−12.3131	−0.810143
$232$	−0.169640	−0.0111374
$233$	−22.0629	−1.44539	−0.722696	−	0.691166i	$-0.757097\pi$
$233$	−22.0629	−1.44539	−0.722696	+	0.691166i	$0.757097\pi$
$234$	0.944384	0.0617363
$235$	−2.08040	−0.135710
$236$	3.72798	0.242671
$237$	−27.9918	−1.81826
$238$	−6.54768	−0.424423
$239$	−5.49315	−0.355323	−0.177661	−	0.984092i	$-0.556853\pi$
$239$	−5.49315	−0.355323	−0.177661	+	0.984092i	$0.556853\pi$
$240$	−0.664680	−0.0429049
$241$	3.55357	0.228906	0.114453	−	0.993429i	$-0.463489\pi$
$241$	3.55357	0.228906	0.114453	+	0.993429i	$0.463489\pi$
$242$	21.9478	1.41086
$243$	−15.1114	−0.969396
$244$	−2.62937	−0.168328
$245$	−0.309854	−0.0197959
$246$	5.62003	0.358320
$247$	−2.41305	−0.153538
$248$	−7.45527	−0.473410
$249$	18.2382	1.15580
$250$	3.06880	0.194088
$251$	13.9222	0.878762	0.439381	−	0.898301i	$-0.355198\pi$
$251$	13.9222	0.878762	0.439381	+	0.898301i	$0.355198\pi$
$252$	1.60160	0.100892
$253$	23.2531	1.46191
$254$	8.30253	0.520947
$255$	4.35211	0.272540
$256$	1.00000	0.0625000
$257$	−9.67788	−0.603689	−0.301845	−	0.953357i	$-0.597602\pi$
$257$	−9.67788	−0.603689	−0.301845	+	0.953357i	$0.597602\pi$
$258$	2.97609	0.185283
$259$	7.59857	0.472152
$260$	−0.182705	−0.0113309
$261$	−0.271696	−0.0168175
$262$	−6.63553	−0.409945
$263$	−12.2325	−0.754287	−0.377143	−	0.926155i	$-0.623094\pi$
$263$	−12.2325	−0.754287	−0.377143	+	0.926155i	$0.623094\pi$
$264$	−12.3131	−0.757819
$265$	2.89901	0.178085
$266$	−4.09235	−0.250918
$267$	18.2767	1.11852
$268$	8.30238	0.507149
$269$	10.6432	0.648925	0.324462	−	0.945899i	$-0.394817\pi$
$269$	10.6432	0.648925	0.324462	+	0.945899i	$0.394817\pi$
$270$	0.929485	0.0565667
$271$	−14.3200	−0.869877	−0.434938	−	0.900460i	$-0.643230\pi$
$271$	−14.3200	−0.869877	−0.434938	+	0.900460i	$0.643230\pi$
$272$	−6.54768	−0.397012
$273$	1.26488	0.0765538
$274$	1.40077	0.0846234
$275$	28.1490	1.69745
$276$	−8.69005	−0.523080
$277$	9.76247	0.586570	0.293285	−	0.956025i	$-0.405252\pi$
$277$	9.76247	0.586570	0.293285	+	0.956025i	$0.405252\pi$
$278$	20.8765	1.25209
$279$	−11.9404	−0.714852
$280$	−0.309854	−0.0185173
$281$	2.53207	0.151051	0.0755254	−	0.997144i	$-0.475937\pi$
$281$	2.53207	0.151051	0.0755254	+	0.997144i	$0.475937\pi$
$282$	14.4027	0.857666
$283$	21.5443	1.28067	0.640337	−	0.768094i	$-0.278795\pi$
$283$	21.5443	1.28067	0.640337	+	0.768094i	$0.278795\pi$
$284$	−5.51293	−0.327132
$285$	2.72010	0.161125
$286$	−3.38459	−0.200135
$287$	2.61990	0.154648
$288$	1.60160	0.0943754
$289$	25.8722	1.52189
$290$	0.0525636	0.00308664
$291$	18.8313	1.10391
$292$	−5.88087	−0.344152
$293$	−29.5424	−1.72589	−0.862943	−	0.505302i	$-0.831381\pi$
$293$	−29.5424	−1.72589	−0.862943	+	0.505302i	$0.831381\pi$
$294$	2.14514	0.125107
$295$	−1.15513	−0.0672544
$296$	7.59857	0.441658
$297$	17.2186	0.999124
$298$	3.13466	0.181586
$299$	−2.38870	−0.138142
$300$	−10.5197	−0.607356
$301$	1.38737	0.0799665
$302$	14.4260	0.830125
$303$	6.75281	0.387939
$304$	−4.09235	−0.234712
$305$	0.814723	0.0466509
$306$	−10.4868	−0.599490
$307$	−22.7425	−1.29798	−0.648992	−	0.760796i	$-0.724809\pi$
$307$	−22.7425	−1.29798	−0.648992	+	0.760796i	$0.724809\pi$
$308$	−5.74002	−0.327068
$309$	−7.03508	−0.400212
$310$	2.31005	0.131202
$311$	−6.46779	−0.366755	−0.183377	−	0.983043i	$-0.558703\pi$
$311$	−6.46779	−0.366755	−0.183377	+	0.983043i	$0.558703\pi$
$312$	1.26488	0.0716095
$313$	−25.3185	−1.43109	−0.715544	−	0.698568i	$-0.753821\pi$
$313$	−25.3185	−1.43109	−0.715544	+	0.698568i	$0.753821\pi$
$314$	−8.47733	−0.478404
$315$	−0.496264	−0.0279613
$316$	−13.0490	−0.734061
$317$	3.32312	0.186645	0.0933226	−	0.995636i	$-0.470251\pi$
$317$	3.32312	0.186645	0.0933226	+	0.995636i	$0.470251\pi$
$318$	−20.0700	−1.12547
$319$	0.973735	0.0545187
$320$	−0.309854	−0.0173214
$321$	−4.51716	−0.252123
$322$	−4.05105	−0.225756
$323$	26.7954	1.49094
$324$	−11.2397	−0.624426
$325$	−2.89163	−0.160399
$326$	6.95282	0.385081
$327$	2.07556	0.114779
$328$	2.61990	0.144660
$329$	6.71410	0.370161
$330$	3.81527	0.210024
$331$	−4.41023	−0.242408	−0.121204	−	0.992628i	$-0.538676\pi$
$331$	−4.41023	−0.242408	−0.121204	+	0.992628i	$0.538676\pi$
$332$	8.50213	0.466615
$333$	12.1699	0.666907
$334$	11.1708	0.611237
$335$	−2.57253	−0.140552
$336$	2.14514	0.117027
$337$	8.59883	0.468408	0.234204	−	0.972187i	$-0.424752\pi$
$337$	8.59883	0.468408	0.234204	+	0.972187i	$0.424752\pi$
$338$	−12.6523	−0.688195
$339$	6.94186	0.377030
$340$	2.02883	0.110029
$341$	42.7933	2.31739
$342$	−6.55432	−0.354417
$343$	1.00000	0.0539949
$344$	1.38737	0.0748018
$345$	2.69265	0.144968
$346$	−15.1213	−0.812928
$347$	−15.9323	−0.855291	−0.427645	−	0.903947i	$-0.640657\pi$
$347$	−15.9323	−0.855291	−0.427645	+	0.903947i	$0.640657\pi$
$348$	−0.363900	−0.0195071
$349$	12.3250	0.659743	0.329871	−	0.944026i	$-0.392995\pi$
$349$	12.3250	0.659743	0.329871	+	0.944026i	$0.392995\pi$
$350$	−4.90399	−0.262129
$351$	−1.76880	−0.0944114
$352$	−5.74002	−0.305944
$353$	−35.5320	−1.89118	−0.945588	−	0.325367i	$-0.894512\pi$
$353$	−35.5320	−1.89118	−0.945588	+	0.325367i	$0.894512\pi$
$354$	7.99703	0.425037
$355$	1.70820	0.0906621
$356$	8.52008	0.451563
$357$	−14.0457	−0.743375
$358$	19.9345	1.05357
$359$	−35.6520	−1.88164	−0.940820	−	0.338906i	$-0.889943\pi$
$359$	−35.6520	−1.88164	−0.940820	+	0.338906i	$0.889943\pi$
$360$	−0.496264	−0.0261554
$361$	−2.25270	−0.118563
$362$	−11.5038	−0.604629
$363$	47.0809	2.47111
$364$	0.589649	0.0309060
$365$	1.82221	0.0953790
$366$	−5.64036	−0.294826
$367$	−17.2347	−0.899645	−0.449823	−	0.893118i	$-0.648513\pi$
$367$	−17.2347	−0.899645	−0.449823	+	0.893118i	$0.648513\pi$
$368$	−4.05105	−0.211176
$369$	4.19604	0.218437
$370$	−2.35445	−0.122402
$371$	−9.35604	−0.485742
$372$	−15.9926	−0.829175
$373$	35.1320	1.81907	0.909533	−	0.415632i	$-0.136440\pi$
$373$	35.1320	1.81907	0.909533	+	0.415632i	$0.136440\pi$
$374$	37.5838	1.94341
$375$	6.58298	0.339944
$376$	6.71410	0.346254
$377$	−0.100028	−0.00515169
$378$	−2.99975	−0.154290
$379$	−14.5156	−0.745618	−0.372809	−	0.927908i	$-0.621605\pi$
$379$	−14.5156	−0.745618	−0.372809	+	0.927908i	$0.621605\pi$
$380$	1.26803	0.0650487
$381$	17.8100	0.912436
$382$	−2.09484	−0.107181
$383$	−24.1182	−1.23238	−0.616192	−	0.787596i	$-0.711325\pi$
$383$	−24.1182	−1.23238	−0.616192	+	0.787596i	$0.711325\pi$
$384$	2.14514	0.109468
$385$	1.77857	0.0906443
$386$	6.97172	0.354851
$387$	2.22201	0.112951
$388$	8.77861	0.445666
$389$	−17.2610	−0.875169	−0.437585	−	0.899177i	$-0.644166\pi$
$389$	−17.2610	−0.875169	−0.437585	+	0.899177i	$0.644166\pi$
$390$	−0.391927	−0.0198460
$391$	26.5250	1.34143
$392$	1.00000	0.0505076
$393$	−14.2341	−0.718016
$394$	−1.61812	−0.0815199
$395$	4.04328	0.203439
$396$	−9.19323	−0.461977
$397$	4.24508	0.213055	0.106527	−	0.994310i	$-0.466027\pi$
$397$	4.24508	0.213055	0.106527	+	0.994310i	$0.466027\pi$
$398$	−12.5197	−0.627558
$399$	−8.77864	−0.439482
$400$	−4.90399	−0.245200
$401$	−11.0408	−0.551351	−0.275675	−	0.961251i	$-0.588901\pi$
$401$	−11.0408	−0.551351	−0.275675	+	0.961251i	$0.588901\pi$
$402$	17.8097	0.888269
$403$	−4.39599	−0.218980
$404$	3.14797	0.156617
$405$	3.48266	0.173055
$406$	−0.169640	−0.00841908
$407$	−43.6159	−2.16196
$408$	−14.0457	−0.695364
$409$	−20.8897	−1.03293	−0.516464	−	0.856309i	$-0.672752\pi$
$409$	−20.8897	−1.03293	−0.516464	+	0.856309i	$0.672752\pi$
$410$	−0.811787	−0.0400913
$411$	3.00483	0.148218
$412$	−3.27955	−0.161572
$413$	3.72798	0.183442
$414$	−6.48818	−0.318877
$415$	−2.63442	−0.129319
$416$	0.589649	0.0289099
$417$	44.7828	2.19302
$418$	23.4901	1.14894
$419$	−14.0406	−0.685928	−0.342964	−	0.939349i	$-0.611431\pi$
$419$	−14.0406	−0.685928	−0.342964	+	0.939349i	$0.611431\pi$
$420$	−0.664680	−0.0324330
$421$	−8.96580	−0.436966	−0.218483	−	0.975841i	$-0.570111\pi$
$421$	−8.96580	−0.436966	−0.218483	+	0.975841i	$0.570111\pi$
$422$	6.63878	0.323171
$423$	10.7533	0.522845
$424$	−9.35604	−0.454370
$425$	32.1098	1.55755
$426$	−11.8260	−0.572970
$427$	−2.62937	−0.127244
$428$	−2.10577	−0.101786
$429$	−7.26041	−0.350536
$430$	−0.429882	−0.0207307
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−2.99975	−0.144325
$433$	20.5019	0.985259	0.492630	−	0.870239i	$-0.336036\pi$
$433$	20.5019	0.985259	0.492630	+	0.870239i	$0.336036\pi$
$434$	−7.45527	−0.357864
$435$	0.112756	0.00540624
$436$	0.967565	0.0463379
$437$	16.5783	0.793048
$438$	−12.6153	−0.602781
$439$	27.5901	1.31680	0.658402	−	0.752667i	$-0.271233\pi$
$439$	27.5901	1.31680	0.658402	+	0.752667i	$0.271233\pi$
$440$	1.77857	0.0847900
$441$	1.60160	0.0762669
$442$	−3.86083	−0.183641
$443$	−39.9693	−1.89900	−0.949499	−	0.313769i	$-0.898408\pi$
$443$	−39.9693	−1.89900	−0.949499	+	0.313769i	$0.898408\pi$
$444$	16.3000	0.773562
$445$	−2.63998	−0.125147
$446$	18.9429	0.896974
$447$	6.72427	0.318047
$448$	1.00000	0.0472456
$449$	−14.1664	−0.668555	−0.334277	−	0.942475i	$-0.608492\pi$
$449$	−14.1664	−0.668555	−0.334277	+	0.942475i	$0.608492\pi$
$450$	−7.85425	−0.370253
$451$	−15.0383	−0.708124
$452$	3.23610	0.152213
$453$	30.9458	1.45396
$454$	−25.5257	−1.19798
$455$	−0.182705	−0.00856535
$456$	−8.77864	−0.411097
$457$	−10.8746	−0.508691	−0.254346	−	0.967113i	$-0.581860\pi$
$457$	−10.8746	−0.508691	−0.254346	+	0.967113i	$0.581860\pi$
$458$	−19.5404	−0.913065
$459$	19.6414	0.916782
$460$	1.25524	0.0585257
$461$	6.57269	0.306121	0.153060	−	0.988217i	$-0.451087\pi$
$461$	6.57269	0.306121	0.153060	+	0.988217i	$0.451087\pi$
$462$	−12.3131	−0.572858
$463$	11.6662	0.542174	0.271087	−	0.962555i	$-0.412617\pi$
$463$	11.6662	0.542174	0.271087	+	0.962555i	$0.412617\pi$
$464$	−0.169640	−0.00787533
$465$	4.95536	0.229800
$466$	−22.0629	−1.02205
$467$	−3.67835	−0.170214	−0.0851069	−	0.996372i	$-0.527123\pi$
$467$	−3.67835	−0.170214	−0.0851069	+	0.996372i	$0.527123\pi$
$468$	0.944384	0.0436542
$469$	8.30238	0.383368
$470$	−2.08040	−0.0959615
$471$	−18.1850	−0.837922
$472$	3.72798	0.171594
$473$	−7.96350	−0.366162
$474$	−27.9918	−1.28570
$475$	20.0688	0.920821
$476$	−6.54768	−0.300113
$477$	−14.9847	−0.686101
$478$	−5.49315	−0.251251
$479$	−15.0181	−0.686193	−0.343097	−	0.939300i	$-0.611476\pi$
$479$	−15.0181	−0.686193	−0.343097	+	0.939300i	$0.611476\pi$
$480$	−0.664680	−0.0303383
$481$	4.48049	0.204293
$482$	3.55357	0.161861
$483$	−8.69005	−0.395411
$484$	21.9478	0.997626
$485$	−2.72009	−0.123513
$486$	−15.1114	−0.685466
$487$	19.6287	0.889461	0.444730	−	0.895664i	$-0.353299\pi$
$487$	19.6287	0.889461	0.444730	+	0.895664i	$0.353299\pi$
$488$	−2.62937	−0.119026
$489$	14.9147	0.674468
$490$	−0.309854	−0.0139978
$491$	−30.6734	−1.38427	−0.692137	−	0.721767i	$-0.743330\pi$
$491$	−30.6734	−1.38427	−0.692137	+	0.721767i	$0.743330\pi$
$492$	5.62003	0.253371
$493$	1.11075	0.0500255
$494$	−2.41305	−0.108568
$495$	2.84856	0.128033
$496$	−7.45527	−0.334751
$497$	−5.51293	−0.247289
$498$	18.2382	0.817274
$499$	18.3049	0.819442	0.409721	−	0.912211i	$-0.365626\pi$
$499$	18.3049	0.819442	0.409721	+	0.912211i	$0.365626\pi$
$500$	3.06880	0.137241
$501$	23.9628	1.07058
$502$	13.9222	0.621379
$503$	26.9816	1.20305	0.601526	−	0.798853i	$-0.294560\pi$
$503$	26.9816	1.20305	0.601526	+	0.798853i	$0.294560\pi$
$504$	1.60160	0.0713411
$505$	−0.975412	−0.0434053
$506$	23.2531	1.03373
$507$	−27.1409	−1.20537
$508$	8.30253	0.368365
$509$	7.24498	0.321128	0.160564	−	0.987025i	$-0.448669\pi$
$509$	7.24498	0.321128	0.160564	+	0.987025i	$0.448669\pi$
$510$	4.35211	0.192715
$511$	−5.88087	−0.260154
$512$	1.00000	0.0441942
$513$	12.2760	0.541999
$514$	−9.67788	−0.426873
$515$	1.01618	0.0447784
$516$	2.97609	0.131015
$517$	−38.5391	−1.69495
$518$	7.59857	0.333862
$519$	−32.4373	−1.42384
$520$	−0.182705	−0.00801215
$521$	−25.0279	−1.09649	−0.548246	−	0.836317i	$-0.684704\pi$
$521$	−25.0279	−1.09649	−0.548246	+	0.836317i	$0.684704\pi$
$522$	−0.271696	−0.0118918
$523$	3.29491	0.144077	0.0720383	−	0.997402i	$-0.477050\pi$
$523$	3.29491	0.144077	0.0720383	+	0.997402i	$0.477050\pi$
$524$	−6.63553	−0.289875
$525$	−10.5197	−0.459118
$526$	−12.2325	−0.533361
$527$	48.8147	2.12640
$528$	−12.3131	−0.535859
$529$	−6.58897	−0.286477
$530$	2.89901	0.125925
$531$	5.97075	0.259109
$532$	−4.09235	−0.177426
$533$	1.54482	0.0669135
$534$	18.2767	0.790911
$535$	0.652482	0.0282092
$536$	8.30238	0.358608
$537$	42.7621	1.84532
$538$	10.6432	0.458859
$539$	−5.74002	−0.247240
$540$	0.929485	0.0399987
$541$	5.82625	0.250490	0.125245	−	0.992126i	$-0.460028\pi$
$541$	5.82625	0.250490	0.125245	+	0.992126i	$0.460028\pi$
$542$	−14.3200	−0.615096
$543$	−24.6773	−1.05900
$544$	−6.54768	−0.280730
$545$	−0.299804	−0.0128422
$546$	1.26488	0.0541317
$547$	−15.3333	−0.655606	−0.327803	−	0.944746i	$-0.606308\pi$
$547$	−15.3333	−0.655606	−0.327803	+	0.944746i	$0.606308\pi$
$548$	1.40077	0.0598378
$549$	−4.21121	−0.179730
$550$	28.1490	1.20028
$551$	0.694225	0.0295750
$552$	−8.69005	−0.369873
$553$	−13.0490	−0.554898
$554$	9.76247	0.414767
$555$	−5.05062	−0.214387
$556$	20.8765	0.885359
$557$	−42.9885	−1.82148	−0.910740	−	0.412980i	$-0.864488\pi$
$557$	−42.9885	−1.82148	−0.910740	+	0.412980i	$0.864488\pi$
$558$	−11.9404	−0.505477
$559$	0.818059	0.0346002
$560$	−0.309854	−0.0130937
$561$	80.6223	3.40388
$562$	2.53207	0.106809
$563$	16.2343	0.684194	0.342097	−	0.939665i	$-0.388863\pi$
$563$	16.2343	0.684194	0.342097	+	0.939665i	$0.388863\pi$
$564$	14.4027	0.606461
$565$	−1.00272	−0.0421847
$566$	21.5443	0.905573
$567$	−11.2397	−0.472022
$568$	−5.51293	−0.231317
$569$	−35.7527	−1.49883	−0.749415	−	0.662100i	$-0.769665\pi$
$569$	−35.7527	−1.49883	−0.749415	+	0.662100i	$0.769665\pi$
$570$	2.72010	0.113932
$571$	−31.9561	−1.33732	−0.668661	−	0.743568i	$-0.733132\pi$
$571$	−31.9561	−1.33732	−0.668661	+	0.743568i	$0.733132\pi$
$572$	−3.38459	−0.141517
$573$	−4.49372	−0.187728
$574$	2.61990	0.109352
$575$	19.8663	0.828483
$576$	1.60160	0.0667335
$577$	−11.1323	−0.463444	−0.231722	−	0.972782i	$-0.574436\pi$
$577$	−11.1323	−0.463444	−0.231722	+	0.972782i	$0.574436\pi$
$578$	25.8722	1.07614
$579$	14.9553	0.621520
$580$	0.0525636	0.00218259
$581$	8.50213	0.352728
$582$	18.8313	0.780582
$583$	53.7038	2.22419
$584$	−5.88087	−0.243352
$585$	−0.292622	−0.0120984
$586$	−29.5424	−1.22039
$587$	9.86452	0.407152	0.203576	−	0.979059i	$-0.434744\pi$
$587$	9.86452	0.407152	0.203576	+	0.979059i	$0.434744\pi$
$588$	2.14514	0.0884639
$589$	30.5095	1.25712
$590$	−1.15513	−0.0475560
$591$	−3.47109	−0.142782
$592$	7.59857	0.312299
$593$	27.4620	1.12773	0.563864	−	0.825867i	$-0.309314\pi$
$593$	27.4620	1.12773	0.563864	+	0.825867i	$0.309314\pi$
$594$	17.2186	0.706488
$595$	2.02883	0.0831739
$596$	3.13466	0.128401
$597$	−26.8565	−1.09916
$598$	−2.38870	−0.0976811
$599$	−43.8183	−1.79037	−0.895184	−	0.445697i	$-0.852956\pi$
$599$	−43.8183	−1.79037	−0.895184	+	0.445697i	$0.852956\pi$
$600$	−10.5197	−0.429466
$601$	−9.85077	−0.401821	−0.200911	−	0.979610i	$-0.564390\pi$
$601$	−9.85077	−0.401821	−0.200911	+	0.979610i	$0.564390\pi$
$602$	1.38737	0.0565448
$603$	13.2971	0.541501
$604$	14.4260	0.586987
$605$	−6.80062	−0.276484
$606$	6.75281	0.274314
$607$	10.1605	0.412402	0.206201	−	0.978510i	$-0.433890\pi$
$607$	10.1605	0.412402	0.206201	+	0.978510i	$0.433890\pi$
$608$	−4.09235	−0.165967
$609$	−0.363900	−0.0147460
$610$	0.814723	0.0329872
$611$	3.95896	0.160162
$612$	−10.4868	−0.423904
$613$	13.9660	0.564080	0.282040	−	0.959403i	$-0.408989\pi$
$613$	13.9660	0.564080	0.282040	+	0.959403i	$0.408989\pi$
$614$	−22.7425	−0.917813
$615$	−1.74139	−0.0702197
$616$	−5.74002	−0.231272
$617$	−4.75664	−0.191495	−0.0957476	−	0.995406i	$-0.530524\pi$
$617$	−4.75664	−0.191495	−0.0957476	+	0.995406i	$0.530524\pi$
$618$	−7.03508	−0.282992
$619$	25.6917	1.03264	0.516319	−	0.856397i	$-0.327302\pi$
$619$	25.6917	1.03264	0.516319	+	0.856397i	$0.327302\pi$
$620$	2.31005	0.0927738
$621$	12.1521	0.487648
$622$	−6.46779	−0.259335
$623$	8.52008	0.341350
$624$	1.26488	0.0506356
$625$	23.5691	0.942763
$626$	−25.3185	−1.01193
$627$	50.3895	2.01236
$628$	−8.47733	−0.338282
$629$	−49.7531	−1.98378
$630$	−0.496264	−0.0197716
$631$	7.24650	0.288479	0.144239	−	0.989543i	$-0.453926\pi$
$631$	7.24650	0.288479	0.144239	+	0.989543i	$0.453926\pi$
$632$	−13.0490	−0.519060
$633$	14.2411	0.566032
$634$	3.32312	0.131978
$635$	−2.57258	−0.102090
$636$	−20.0700	−0.795826
$637$	0.589649	0.0233627
$638$	0.973735	0.0385505
$639$	−8.82953	−0.349291
$640$	−0.309854	−0.0122481
$641$	33.0816	1.30665	0.653323	−	0.757080i	$-0.273375\pi$
$641$	33.0816	1.30665	0.653323	+	0.757080i	$0.273375\pi$
$642$	−4.51716	−0.178278
$643$	43.6069	1.71969	0.859844	−	0.510557i	$-0.170561\pi$
$643$	43.6069	1.71969	0.859844	+	0.510557i	$0.170561\pi$
$644$	−4.05105	−0.159634
$645$	−0.922154	−0.0363098
$646$	26.7954	1.05425
$647$	4.70996	0.185168	0.0925839	−	0.995705i	$-0.470487\pi$
$647$	4.70996	0.185168	0.0925839	+	0.995705i	$0.470487\pi$
$648$	−11.2397	−0.441536
$649$	−21.3987	−0.839972
$650$	−2.89163	−0.113419
$651$	−15.9926	−0.626798
$652$	6.95282	0.272293
$653$	−17.8428	−0.698243	−0.349122	−	0.937077i	$-0.613520\pi$
$653$	−17.8428	−0.698243	−0.349122	+	0.937077i	$0.613520\pi$
$654$	2.07556	0.0811607
$655$	2.05605	0.0803365
$656$	2.61990	0.102290
$657$	−9.41883	−0.367464
$658$	6.71410	0.261743
$659$	−33.8937	−1.32031	−0.660155	−	0.751130i	$-0.729509\pi$
$659$	−33.8937	−1.32031	−0.660155	+	0.751130i	$0.729509\pi$
$660$	3.81527	0.148509
$661$	−1.57274	−0.0611726	−0.0305863	−	0.999532i	$-0.509737\pi$
$661$	−1.57274	−0.0611726	−0.0305863	+	0.999532i	$0.509737\pi$
$662$	−4.41023	−0.171408
$663$	−8.28201	−0.321646
$664$	8.50213	0.329947
$665$	1.26803	0.0491722
$666$	12.1699	0.471574
$667$	0.687219	0.0266092
$668$	11.1708	0.432210
$669$	40.6352	1.57105
$670$	−2.57253	−0.0993855
$671$	15.0926	0.582645
$672$	2.14514	0.0827504
$673$	−31.9905	−1.23314	−0.616572	−	0.787298i	$-0.711479\pi$
$673$	−31.9905	−1.23314	−0.616572	+	0.787298i	$0.711479\pi$
$674$	8.59883	0.331215
$675$	14.7107	0.566216
$676$	−12.6523	−0.486627
$677$	−8.80600	−0.338442	−0.169221	−	0.985578i	$-0.554125\pi$
$677$	−8.80600	−0.338442	−0.169221	+	0.985578i	$0.554125\pi$
$678$	6.94186	0.266601
$679$	8.77861	0.336892
$680$	2.02883	0.0778020
$681$	−54.7561	−2.09826
$682$	42.7933	1.63864
$683$	12.1106	0.463401	0.231700	−	0.972787i	$-0.425571\pi$
$683$	12.1106	0.463401	0.231700	+	0.972787i	$0.425571\pi$
$684$	−6.55432	−0.250611
$685$	−0.434034	−0.0165836
$686$	1.00000	0.0381802
$687$	−41.9169	−1.59923
$688$	1.38737	0.0528928
$689$	−5.51678	−0.210172
$690$	2.69265	0.102508
$691$	27.9542	1.06343	0.531714	−	0.846924i	$-0.321548\pi$
$691$	27.9542	1.06343	0.531714	+	0.846924i	$0.321548\pi$
$692$	−15.1213	−0.574827
$693$	−9.19323	−0.349222
$694$	−15.9323	−0.604782
$695$	−6.46866	−0.245370
$696$	−0.363900	−0.0137936
$697$	−17.1543	−0.649764
$698$	12.3250	0.466509
$699$	−47.3280	−1.79011
$700$	−4.90399	−0.185353
$701$	−5.87148	−0.221763	−0.110881	−	0.993834i	$-0.535367\pi$
$701$	−5.87148	−0.221763	−0.110881	+	0.993834i	$0.535367\pi$
$702$	−1.76880	−0.0667589
$703$	−31.0960	−1.17281
$704$	−5.74002	−0.216335
$705$	−4.46273	−0.168076
$706$	−35.5320	−1.33726
$707$	3.14797	0.118391
$708$	7.99703	0.300547
$709$	16.9583	0.636882	0.318441	−	0.947943i	$-0.396841\pi$
$709$	16.9583	0.636882	0.318441	+	0.947943i	$0.396841\pi$
$710$	1.70820	0.0641078
$711$	−20.8993	−0.783784
$712$	8.52008	0.319303
$713$	30.2017	1.13106
$714$	−14.0457	−0.525646
$715$	1.04873	0.0392203
$716$	19.9345	0.744986
$717$	−11.7836	−0.440065
$718$	−35.6520	−1.33052
$719$	2.38128	0.0888066	0.0444033	−	0.999014i	$-0.485861\pi$
$719$	2.38128	0.0888066	0.0444033	+	0.999014i	$0.485861\pi$
$720$	−0.496264	−0.0184947
$721$	−3.27955	−0.122137
$722$	−2.25270	−0.0838368
$723$	7.62289	0.283498
$724$	−11.5038	−0.427537
$725$	0.831912	0.0308964
$726$	47.0809	1.74734
$727$	−27.7146	−1.02788	−0.513938	−	0.857827i	$-0.671814\pi$
$727$	−27.7146	−1.02788	−0.513938	+	0.857827i	$0.671814\pi$
$728$	0.589649	0.0218538
$729$	1.30307	0.0482620
$730$	1.82221	0.0674432
$731$	−9.08404	−0.335985
$732$	−5.64036	−0.208474
$733$	13.0408	0.481674	0.240837	−	0.970566i	$-0.422578\pi$
$733$	13.0408	0.481674	0.240837	+	0.970566i	$0.422578\pi$
$734$	−17.2347	−0.636145
$735$	−0.664680	−0.0245171
$736$	−4.05105	−0.149324
$737$	−47.6558	−1.75542
$738$	4.19604	0.154458
$739$	−20.0127	−0.736179	−0.368090	−	0.929790i	$-0.619988\pi$
$739$	−20.0127	−0.736179	−0.368090	+	0.929790i	$0.619988\pi$
$740$	−2.35445	−0.0865514
$741$	−5.17631	−0.190157
$742$	−9.35604	−0.343471
$743$	−21.8136	−0.800264	−0.400132	−	0.916457i	$-0.631036\pi$
$743$	−21.8136	−0.800264	−0.400132	+	0.916457i	$0.631036\pi$
$744$	−15.9926	−0.586316
$745$	−0.971289	−0.0355853
$746$	35.1320	1.28627
$747$	13.6170	0.498222
$748$	37.5838	1.37420
$749$	−2.10577	−0.0769431
$750$	6.58298	0.240376
$751$	−5.04290	−0.184018	−0.0920091	−	0.995758i	$-0.529329\pi$
$751$	−5.04290	−0.184018	−0.0920091	+	0.995758i	$0.529329\pi$
$752$	6.71410	0.244838
$753$	29.8650	1.08834
$754$	−0.100028	−0.00364280
$755$	−4.46997	−0.162679
$756$	−2.99975	−0.109100
$757$	−44.9076	−1.63219	−0.816097	−	0.577916i	$-0.803866\pi$
$757$	−44.9076	−1.63219	−0.816097	+	0.577916i	$0.803866\pi$
$758$	−14.5156	−0.527232
$759$	49.8810	1.81057
$760$	1.26803	0.0459964
$761$	38.1135	1.38161	0.690807	−	0.723039i	$-0.257256\pi$
$761$	38.1135	1.38161	0.690807	+	0.723039i	$0.257256\pi$
$762$	17.8100	0.645190
$763$	0.967565	0.0350282
$764$	−2.09484	−0.0757887
$765$	3.24938	0.117482
$766$	−24.1182	−0.871427
$767$	2.19820	0.0793724
$768$	2.14514	0.0774059
$769$	−35.6210	−1.28453	−0.642264	−	0.766484i	$-0.722005\pi$
$769$	−35.6210	−1.28453	−0.642264	+	0.766484i	$0.722005\pi$
$770$	1.77857	0.0640952
$771$	−20.7604	−0.747666
$772$	6.97172	0.250918
$773$	24.8331	0.893185	0.446592	−	0.894738i	$-0.352637\pi$
$773$	24.8331	0.893185	0.446592	+	0.894738i	$0.352637\pi$
$774$	2.22201	0.0798686
$775$	36.5606	1.31329
$776$	8.77861	0.315134
$777$	16.3000	0.584758
$778$	−17.2610	−0.618838
$779$	−10.7215	−0.384139
$780$	−0.391927	−0.0140333
$781$	31.6443	1.13232
$782$	26.5250	0.948532
$783$	0.508876	0.0181858
$784$	1.00000	0.0357143
$785$	2.62674	0.0937524
$786$	−14.2341	−0.507714
$787$	9.84957	0.351099	0.175550	−	0.984471i	$-0.443830\pi$
$787$	9.84957	0.351099	0.175550	+	0.984471i	$0.443830\pi$
$788$	−1.61812	−0.0576433
$789$	−26.2403	−0.934180
$790$	4.04328	0.143853
$791$	3.23610	0.115062
$792$	−9.19323	−0.326667
$793$	−1.55041	−0.0550565
$794$	4.24508	0.150652
$795$	6.21877	0.220557
$796$	−12.5197	−0.443750
$797$	44.0164	1.55914	0.779571	−	0.626314i	$-0.215437\pi$
$797$	44.0164	1.55914	0.779571	+	0.626314i	$0.215437\pi$
$798$	−8.77864	−0.310760
$799$	−43.9618	−1.55526
$800$	−4.90399	−0.173382
$801$	13.6458	0.482150
$802$	−11.0408	−0.389864
$803$	33.7563	1.19123
$804$	17.8097	0.628101
$805$	1.25524	0.0442413
$806$	−4.39599	−0.154842
$807$	22.8310	0.803689
$808$	3.14797	0.110745
$809$	25.3144	0.890007	0.445003	−	0.895529i	$-0.353203\pi$
$809$	25.3144	0.890007	0.445003	+	0.895529i	$0.353203\pi$
$810$	3.48266	0.122368
$811$	−11.7624	−0.413033	−0.206517	−	0.978443i	$-0.566213\pi$
$811$	−11.7624	−0.413033	−0.206517	+	0.978443i	$0.566213\pi$
$812$	−0.169640	−0.00595319
$813$	−30.7183	−1.07734
$814$	−43.6159	−1.52874
$815$	−2.15436	−0.0754640
$816$	−14.0457	−0.491697
$817$	−5.67758	−0.198634
$818$	−20.8897	−0.730390
$819$	0.944384	0.0329994
$820$	−0.811787	−0.0283488
$821$	28.1973	0.984091	0.492046	−	0.870569i	$-0.336249\pi$
$821$	28.1973	0.984091	0.492046	+	0.870569i	$0.336249\pi$
$822$	3.00483	0.104806
$823$	34.2459	1.19374	0.596869	−	0.802339i	$-0.296411\pi$
$823$	34.2459	1.19374	0.596869	+	0.802339i	$0.296411\pi$
$824$	−3.27955	−0.114249
$825$	60.3834	2.10228
$826$	3.72798	0.129713
$827$	−8.94726	−0.311127	−0.155563	−	0.987826i	$-0.549719\pi$
$827$	−8.94726	−0.311127	−0.155563	+	0.987826i	$0.549719\pi$
$828$	−6.48818	−0.225480
$829$	−39.3593	−1.36700	−0.683502	−	0.729949i	$-0.739544\pi$
$829$	−39.3593	−1.36700	−0.683502	+	0.729949i	$0.739544\pi$
$830$	−2.63442	−0.0914421
$831$	20.9418	0.726463
$832$	0.589649	0.0204424
$833$	−6.54768	−0.226864
$834$	44.7828	1.55070
$835$	−3.46131	−0.119784
$836$	23.4901	0.812423
$837$	22.3639	0.773010
$838$	−14.0406	−0.485024
$839$	−3.12617	−0.107927	−0.0539637	−	0.998543i	$-0.517186\pi$
$839$	−3.12617	−0.107927	−0.0539637	+	0.998543i	$0.517186\pi$
$840$	−0.664680	−0.0229336
$841$	−28.9712	−0.999008
$842$	−8.96580	−0.308982
$843$	5.43164	0.187076
$844$	6.63878	0.228516
$845$	3.92038	0.134865
$846$	10.7533	0.369707
$847$	21.9478	0.754135
$848$	−9.35604	−0.321288
$849$	46.2153	1.58611
$850$	32.1098	1.10136
$851$	−30.7822	−1.05520
$852$	−11.8260	−0.405151
$853$	54.2825	1.85860	0.929298	−	0.369330i	$-0.120413\pi$
$853$	54.2825	1.85860	0.929298	+	0.369330i	$0.120413\pi$
$854$	−2.62937	−0.0899752
$855$	2.03089	0.0694548
$856$	−2.10577	−0.0719737
$857$	10.0080	0.341868	0.170934	−	0.985283i	$-0.445322\pi$
$857$	10.0080	0.341868	0.170934	+	0.985283i	$0.445322\pi$
$858$	−7.26041	−0.247866
$859$	35.9218	1.22564	0.612819	−	0.790224i	$-0.290036\pi$
$859$	35.9218	1.22564	0.612819	+	0.790224i	$0.290036\pi$
$860$	−0.429882	−0.0146588
$861$	5.62003	0.191530
$862$	−1.00000	−0.0340601
$863$	−0.668369	−0.0227516	−0.0113758	−	0.999935i	$-0.503621\pi$
$863$	−0.668369	−0.0227516	−0.0113758	+	0.999935i	$0.503621\pi$
$864$	−2.99975	−0.102053
$865$	4.68542	0.159309
$866$	20.5019	0.696683
$867$	55.4993	1.88485
$868$	−7.45527	−0.253048
$869$	74.9012	2.54085
$870$	0.112756	0.00382279
$871$	4.89549	0.165877
$872$	0.967565	0.0327659
$873$	14.0599	0.475854
$874$	16.5783	0.560770
$875$	3.06880	0.103744
$876$	−12.6153	−0.426230
$877$	15.8048	0.533691	0.266845	−	0.963739i	$-0.414019\pi$
$877$	15.8048	0.533691	0.266845	+	0.963739i	$0.414019\pi$
$878$	27.5901	0.931120
$879$	−63.3724	−2.13750
$880$	1.77857	0.0599556
$881$	−13.9813	−0.471041	−0.235520	−	0.971869i	$-0.575679\pi$
$881$	−13.9813	−0.471041	−0.235520	+	0.971869i	$0.575679\pi$
$882$	1.60160	0.0539288
$883$	−20.8125	−0.700397	−0.350198	−	0.936676i	$-0.613886\pi$
$883$	−20.8125	−0.700397	−0.350198	+	0.936676i	$0.613886\pi$
$884$	−3.86083	−0.129854
$885$	−2.47791	−0.0832942
$886$	−39.9693	−1.34279
$887$	44.3849	1.49030	0.745150	−	0.666897i	$-0.232378\pi$
$887$	44.3849	1.49030	0.745150	+	0.666897i	$0.232378\pi$
$888$	16.3000	0.546991
$889$	8.30253	0.278458
$890$	−2.63998	−0.0884925
$891$	64.5159	2.16136
$892$	18.9429	0.634257
$893$	−27.4764	−0.919464
$894$	6.72427	0.224893
$895$	−6.17678	−0.206467
$896$	1.00000	0.0334077
$897$	−5.12408	−0.171088
$898$	−14.1664	−0.472740
$899$	1.26471	0.0421804
$900$	−7.85425	−0.261808
$901$	61.2604	2.04088
$902$	−15.0383	−0.500719
$903$	2.97609	0.0990380
$904$	3.23610	0.107631
$905$	3.56452	0.118489
$906$	30.9458	1.02811
$907$	−9.55193	−0.317167	−0.158583	−	0.987346i	$-0.550693\pi$
$907$	−9.55193	−0.317167	−0.158583	+	0.987346i	$0.550693\pi$
$908$	−25.5257	−0.847101
$909$	5.04180	0.167226
$910$	−0.182705	−0.00605662
$911$	34.0759	1.12898	0.564492	−	0.825438i	$-0.309072\pi$
$911$	34.0759	1.12898	0.564492	+	0.825438i	$0.309072\pi$
$912$	−8.77864	−0.290690
$913$	−48.8023	−1.61512
$914$	−10.8746	−0.359699
$915$	1.74769	0.0577768
$916$	−19.5404	−0.645635
$917$	−6.63553	−0.219125
$918$	19.6414	0.648263
$919$	13.4268	0.442909	0.221454	−	0.975171i	$-0.428920\pi$
$919$	13.4268	0.442909	0.221454	+	0.975171i	$0.428920\pi$
$920$	1.25524	0.0413839
$921$	−48.7857	−1.60754
$922$	6.57269	0.216460
$923$	−3.25069	−0.106998
$924$	−12.3131	−0.405072
$925$	−37.2633	−1.22521
$926$	11.6662	0.383375
$927$	−5.25254	−0.172516
$928$	−0.169640	−0.00556870
$929$	47.8187	1.56888	0.784441	−	0.620203i	$-0.212950\pi$
$929$	47.8187	1.56888	0.784441	+	0.620203i	$0.212950\pi$
$930$	4.95536	0.162493
$931$	−4.09235	−0.134121
$932$	−22.0629	−0.722696
$933$	−13.8743	−0.454223
$934$	−3.67835	−0.120359
$935$	−11.6455	−0.380849
$936$	0.944384	0.0308681
$937$	−39.7968	−1.30011	−0.650053	−	0.759889i	$-0.725253\pi$
$937$	−39.7968	−1.30011	−0.650053	+	0.759889i	$0.725253\pi$
$938$	8.30238	0.271082
$939$	−54.3117	−1.77239
$940$	−2.08040	−0.0678550
$941$	30.8091	1.00435	0.502174	−	0.864766i	$-0.332534\pi$
$941$	30.8091	1.00435	0.502174	+	0.864766i	$0.332534\pi$
$942$	−18.1850	−0.592500
$943$	−10.6133	−0.345618
$944$	3.72798	0.121335
$945$	0.929485	0.0302362
$946$	−7.96350	−0.258916
$947$	−27.9436	−0.908043	−0.454022	−	0.890991i	$-0.650011\pi$
$947$	−27.9436	−0.908043	−0.454022	+	0.890991i	$0.650011\pi$
$948$	−27.9918	−0.909131
$949$	−3.46765	−0.112565
$950$	20.0688	0.651119
$951$	7.12855	0.231159
$952$	−6.54768	−0.212212
$953$	−37.0966	−1.20168	−0.600838	−	0.799371i	$-0.705166\pi$
$953$	−37.0966	−1.20168	−0.600838	+	0.799371i	$0.705166\pi$
$954$	−14.9847	−0.485147
$955$	0.649096	0.0210042
$956$	−5.49315	−0.177661
$957$	2.08879	0.0675211
$958$	−15.0181	−0.485212
$959$	1.40077	0.0452331
$960$	−0.664680	−0.0214524
$961$	24.5810	0.792936
$962$	4.48049	0.144457
$963$	−3.37261	−0.108681
$964$	3.55357	0.114453
$965$	−2.16022	−0.0695399
$966$	−8.69005	−0.279598
$967$	−20.8437	−0.670287	−0.335144	−	0.942167i	$-0.608785\pi$
$967$	−20.8437	−0.670287	−0.335144	+	0.942167i	$0.608785\pi$
$968$	21.9478	0.705428
$969$	57.4797	1.84652
$970$	−2.72009	−0.0873368
$971$	21.9991	0.705986	0.352993	−	0.935626i	$-0.385164\pi$
$971$	21.9991	0.705986	0.352993	+	0.935626i	$0.385164\pi$
$972$	−15.1114	−0.484698
$973$	20.8765	0.669268
$974$	19.6287	0.628944
$975$	−6.20294	−0.198653
$976$	−2.62937	−0.0841641
$977$	25.0111	0.800176	0.400088	−	0.916477i	$-0.368979\pi$
$977$	25.0111	0.800176	0.400088	+	0.916477i	$0.368979\pi$
$978$	14.9147	0.476921
$979$	−48.9054	−1.56302
$980$	−0.309854	−0.00989794
$981$	1.54966	0.0494767
$982$	−30.6734	−0.978829
$983$	8.75462	0.279229	0.139614	−	0.990206i	$-0.455414\pi$
$983$	8.75462	0.279229	0.139614	+	0.990206i	$0.455414\pi$
$984$	5.62003	0.179160
$985$	0.501383	0.0159754
$986$	1.11075	0.0353734
$987$	14.4027	0.458442
$988$	−2.41305	−0.0767692
$989$	−5.62029	−0.178715
$990$	2.84856	0.0905333
$991$	0.899205	0.0285642	0.0142821	−	0.999898i	$-0.495454\pi$
$991$	0.899205	0.0285642	0.0142821	+	0.999898i	$0.495454\pi$
$992$	−7.45527	−0.236705
$993$	−9.46054	−0.300221
$994$	−5.51293	−0.174859
$995$	3.87930	0.122982
$996$	18.2382	0.577900
$997$	8.75472	0.277265	0.138632	−	0.990344i	$-0.455729\pi$
$997$	8.75472	0.277265	0.138632	+	0.990344i	$0.455729\pi$
$998$	18.3049	0.579433
$999$	−22.7938	−0.721164

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.m.1.19	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.m.1.19	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.14514 q^{3} +1.00000 q^{4} -0.309854 q^{5} +2.14514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60160 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.14514 q^{3} +1.00000 q^{4} -0.309854 q^{5} +2.14514 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.60160 q^{9} -0.309854 q^{10} -5.74002 q^{11} +2.14514 q^{12} +0.589649 q^{13} +1.00000 q^{14} -0.664680 q^{15} +1.00000 q^{16} -6.54768 q^{17} +1.60160 q^{18} -4.09235 q^{19} -0.309854 q^{20} +2.14514 q^{21} -5.74002 q^{22} -4.05105 q^{23} +2.14514 q^{24} -4.90399 q^{25} +0.589649 q^{26} -2.99975 q^{27} +1.00000 q^{28} -0.169640 q^{29} -0.664680 q^{30} -7.45527 q^{31} +1.00000 q^{32} -12.3131 q^{33} -6.54768 q^{34} -0.309854 q^{35} +1.60160 q^{36} +7.59857 q^{37} -4.09235 q^{38} +1.26488 q^{39} -0.309854 q^{40} +2.61990 q^{41} +2.14514 q^{42} +1.38737 q^{43} -5.74002 q^{44} -0.496264 q^{45} -4.05105 q^{46} +6.71410 q^{47} +2.14514 q^{48} +1.00000 q^{49} -4.90399 q^{50} -14.0457 q^{51} +0.589649 q^{52} -9.35604 q^{53} -2.99975 q^{54} +1.77857 q^{55} +1.00000 q^{56} -8.77864 q^{57} -0.169640 q^{58} +3.72798 q^{59} -0.664680 q^{60} -2.62937 q^{61} -7.45527 q^{62} +1.60160 q^{63} +1.00000 q^{64} -0.182705 q^{65} -12.3131 q^{66} +8.30238 q^{67} -6.54768 q^{68} -8.69005 q^{69} -0.309854 q^{70} -5.51293 q^{71} +1.60160 q^{72} -5.88087 q^{73} +7.59857 q^{74} -10.5197 q^{75} -4.09235 q^{76} -5.74002 q^{77} +1.26488 q^{78} -13.0490 q^{79} -0.309854 q^{80} -11.2397 q^{81} +2.61990 q^{82} +8.50213 q^{83} +2.14514 q^{84} +2.02883 q^{85} +1.38737 q^{86} -0.363900 q^{87} -5.74002 q^{88} +8.52008 q^{89} -0.496264 q^{90} +0.589649 q^{91} -4.05105 q^{92} -15.9926 q^{93} +6.71410 q^{94} +1.26803 q^{95} +2.14514 q^{96} +8.77861 q^{97} +1.00000 q^{98} -9.19323 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 21 q^{2} - 6 q^{3} + 21 q^{4} - 11 q^{5} - 6 q^{6} + 21 q^{7} + 21 q^{8} + 5 q^{9}+O(q^{10}) \) 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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