LMFDB - Embedded newform 6034.2.a.n.1.15

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:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.20386 q^{3} +1.00000 q^{4} -2.97794 q^{5} -1.20386 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.55072 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.20386 q^{3} +1.00000 q^{4} -2.97794 q^{5} -1.20386 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.55072 q^{9} +2.97794 q^{10} +4.89942 q^{11} +1.20386 q^{12} +0.849112 q^{13} +1.00000 q^{14} -3.58501 q^{15} +1.00000 q^{16} +0.911913 q^{17} +1.55072 q^{18} -0.375237 q^{19} -2.97794 q^{20} -1.20386 q^{21} -4.89942 q^{22} -0.153613 q^{23} -1.20386 q^{24} +3.86810 q^{25} -0.849112 q^{26} -5.47843 q^{27} -1.00000 q^{28} +6.12429 q^{29} +3.58501 q^{30} +5.66260 q^{31} -1.00000 q^{32} +5.89821 q^{33} -0.911913 q^{34} +2.97794 q^{35} -1.55072 q^{36} -11.1147 q^{37} +0.375237 q^{38} +1.02221 q^{39} +2.97794 q^{40} -3.62198 q^{41} +1.20386 q^{42} -0.855256 q^{43} +4.89942 q^{44} +4.61796 q^{45} +0.153613 q^{46} -8.00473 q^{47} +1.20386 q^{48} +1.00000 q^{49} -3.86810 q^{50} +1.09781 q^{51} +0.849112 q^{52} -3.06278 q^{53} +5.47843 q^{54} -14.5902 q^{55} +1.00000 q^{56} -0.451732 q^{57} -6.12429 q^{58} +9.27497 q^{59} -3.58501 q^{60} +6.50346 q^{61} -5.66260 q^{62} +1.55072 q^{63} +1.00000 q^{64} -2.52860 q^{65} -5.89821 q^{66} -4.31228 q^{67} +0.911913 q^{68} -0.184928 q^{69} -2.97794 q^{70} -0.739152 q^{71} +1.55072 q^{72} -8.19489 q^{73} +11.1147 q^{74} +4.65665 q^{75} -0.375237 q^{76} -4.89942 q^{77} -1.02221 q^{78} +17.0294 q^{79} -2.97794 q^{80} -1.94308 q^{81} +3.62198 q^{82} +6.32734 q^{83} -1.20386 q^{84} -2.71562 q^{85} +0.855256 q^{86} +7.37278 q^{87} -4.89942 q^{88} +0.101939 q^{89} -4.61796 q^{90} -0.849112 q^{91} -0.153613 q^{92} +6.81696 q^{93} +8.00473 q^{94} +1.11743 q^{95} -1.20386 q^{96} +4.01210 q^{97} -1.00000 q^{98} -7.59766 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	1.20386	0.695048	0.347524	−	0.937671i	$-0.387023\pi$
$3$	1.20386	0.695048	0.347524	+	0.937671i	$0.387023\pi$
$4$	1.00000	0.500000
$5$	−2.97794	−1.33177	−0.665887	−	0.746053i	$-0.731947\pi$
$5$	−2.97794	−1.33177	−0.665887	+	0.746053i	$0.731947\pi$
$6$	−1.20386	−0.491473
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−1.55072	−0.516908
$10$	2.97794	0.941706
$11$	4.89942	1.47723	0.738616	−	0.674127i	$-0.235480\pi$
$11$	4.89942	1.47723	0.738616	+	0.674127i	$0.235480\pi$
$12$	1.20386	0.347524
$13$	0.849112	0.235501	0.117751	−	0.993043i	$-0.462432\pi$
$13$	0.849112	0.235501	0.117751	+	0.993043i	$0.462432\pi$
$14$	1.00000	0.267261
$15$	−3.58501	−0.925647
$16$	1.00000	0.250000
$17$	0.911913	0.221171	0.110586	−	0.993867i	$-0.464727\pi$
$17$	0.911913	0.221171	0.110586	+	0.993867i	$0.464727\pi$
$18$	1.55072	0.365509
$19$	−0.375237	−0.0860852	−0.0430426	−	0.999073i	$-0.513705\pi$
$19$	−0.375237	−0.0860852	−0.0430426	+	0.999073i	$0.513705\pi$
$20$	−2.97794	−0.665887
$21$	−1.20386	−0.262703
$22$	−4.89942	−1.04456
$23$	−0.153613	−0.0320304	−0.0160152	−	0.999872i	$-0.505098\pi$
$23$	−0.153613	−0.0320304	−0.0160152	+	0.999872i	$0.505098\pi$
$24$	−1.20386	−0.245737
$25$	3.86810	0.773621
$26$	−0.849112	−0.166525
$27$	−5.47843	−1.05432
$28$	−1.00000	−0.188982
$29$	6.12429	1.13725	0.568626	−	0.822596i	$-0.307475\pi$
$29$	6.12429	1.13725	0.568626	+	0.822596i	$0.307475\pi$
$30$	3.58501	0.654531
$31$	5.66260	1.01703	0.508516	−	0.861052i	$-0.330194\pi$
$31$	5.66260	1.01703	0.508516	+	0.861052i	$0.330194\pi$
$32$	−1.00000	−0.176777
$33$	5.89821	1.02675
$34$	−0.911913	−0.156392
$35$	2.97794	0.503363
$36$	−1.55072	−0.258454
$37$	−11.1147	−1.82725	−0.913626	−	0.406557i	$-0.866729\pi$
$37$	−11.1147	−1.82725	−0.913626	+	0.406557i	$0.866729\pi$
$38$	0.375237	0.0608715
$39$	1.02221	0.163685
$40$	2.97794	0.470853
$41$	−3.62198	−0.565658	−0.282829	−	0.959170i	$-0.591273\pi$
$41$	−3.62198	−0.565658	−0.282829	+	0.959170i	$0.591273\pi$
$42$	1.20386	0.185759
$43$	−0.855256	−0.130425	−0.0652127	−	0.997871i	$-0.520773\pi$
$43$	−0.855256	−0.130425	−0.0652127	+	0.997871i	$0.520773\pi$
$44$	4.89942	0.738616
$45$	4.61796	0.688405
$46$	0.153613	0.0226489
$47$	−8.00473	−1.16761	−0.583805	−	0.811894i	$-0.698437\pi$
$47$	−8.00473	−1.16761	−0.583805	+	0.811894i	$0.698437\pi$
$48$	1.20386	0.173762
$49$	1.00000	0.142857
$50$	−3.86810	−0.547033
$51$	1.09781	0.153725
$52$	0.849112	0.117751
$53$	−3.06278	−0.420705	−0.210353	−	0.977626i	$-0.567461\pi$
$53$	−3.06278	−0.420705	−0.210353	+	0.977626i	$0.567461\pi$
$54$	5.47843	0.745520
$55$	−14.5902	−1.96734
$56$	1.00000	0.133631
$57$	−0.451732	−0.0598334
$58$	−6.12429	−0.804159
$59$	9.27497	1.20750	0.603749	−	0.797174i	$-0.293673\pi$
$59$	9.27497	1.20750	0.603749	+	0.797174i	$0.293673\pi$
$60$	−3.58501	−0.462823
$61$	6.50346	0.832683	0.416341	−	0.909208i	$-0.363312\pi$
$61$	6.50346	0.832683	0.416341	+	0.909208i	$0.363312\pi$
$62$	−5.66260	−0.719150
$63$	1.55072	0.195373
$64$	1.00000	0.125000
$65$	−2.52860	−0.313635
$66$	−5.89821	−0.726020
$67$	−4.31228	−0.526829	−0.263415	−	0.964683i	$-0.584849\pi$
$67$	−4.31228	−0.526829	−0.263415	+	0.964683i	$0.584849\pi$
$68$	0.911913	0.110586
$69$	−0.184928	−0.0222627
$70$	−2.97794	−0.355931
$71$	−0.739152	−0.0877212	−0.0438606	−	0.999038i	$-0.513966\pi$
$71$	−0.739152	−0.0877212	−0.0438606	+	0.999038i	$0.513966\pi$
$72$	1.55072	0.182755
$73$	−8.19489	−0.959139	−0.479570	−	0.877504i	$-0.659207\pi$
$73$	−8.19489	−0.959139	−0.479570	+	0.877504i	$0.659207\pi$
$74$	11.1147	1.29206
$75$	4.65665	0.537704
$76$	−0.375237	−0.0430426
$77$	−4.89942	−0.558341
$78$	−1.02221	−0.115743
$79$	17.0294	1.91596	0.957980	−	0.286836i	$-0.0926035\pi$
$79$	17.0294	1.91596	0.957980	+	0.286836i	$0.0926035\pi$
$80$	−2.97794	−0.332943
$81$	−1.94308	−0.215898
$82$	3.62198	0.399980
$83$	6.32734	0.694516	0.347258	−	0.937770i	$-0.387113\pi$
$83$	6.32734	0.694516	0.347258	+	0.937770i	$0.387113\pi$
$84$	−1.20386	−0.131352
$85$	−2.71562	−0.294550
$86$	0.855256	0.0922246
$87$	7.37278	0.790445
$88$	−4.89942	−0.522280
$89$	0.101939	0.0108055	0.00540276	−	0.999985i	$-0.498280\pi$
$89$	0.101939	0.0108055	0.00540276	+	0.999985i	$0.498280\pi$
$90$	−4.61796	−0.486776
$91$	−0.849112	−0.0890112
$92$	−0.153613	−0.0160152
$93$	6.81696	0.706886
$94$	8.00473	0.825625
$95$	1.11743	0.114646
$96$	−1.20386	−0.122868
$97$	4.01210	0.407367	0.203683	−	0.979037i	$-0.434709\pi$
$97$	4.01210	0.407367	0.203683	+	0.979037i	$0.434709\pi$
$98$	−1.00000	−0.101015
$99$	−7.59766	−0.763593
$100$	3.86810	0.386810
$101$	−3.91128	−0.389187	−0.194594	−	0.980884i	$-0.562339\pi$
$101$	−3.91128	−0.389187	−0.194594	+	0.980884i	$0.562339\pi$
$102$	−1.09781	−0.108700
$103$	6.58489	0.648829	0.324414	−	0.945915i	$-0.394833\pi$
$103$	6.58489	0.648829	0.324414	+	0.945915i	$0.394833\pi$
$104$	−0.849112	−0.0832623
$105$	3.58501	0.349862
$106$	3.06278	0.297484
$107$	−19.3066	−1.86644	−0.933219	−	0.359307i	$-0.883013\pi$
$107$	−19.3066	−1.86644	−0.933219	+	0.359307i	$0.883013\pi$
$108$	−5.47843	−0.527162
$109$	17.7165	1.69693	0.848464	−	0.529252i	$-0.177528\pi$
$109$	17.7165	1.69693	0.848464	+	0.529252i	$0.177528\pi$
$110$	14.5902	1.39112
$111$	−13.3806	−1.27003
$112$	−1.00000	−0.0944911
$113$	−8.03226	−0.755611	−0.377806	−	0.925885i	$-0.623321\pi$
$113$	−8.03226	−0.755611	−0.377806	+	0.925885i	$0.623321\pi$
$114$	0.451732	0.0423086
$115$	0.457448	0.0426573
$116$	6.12429	0.568626
$117$	−1.31674	−0.121733
$118$	−9.27497	−0.853830
$119$	−0.911913	−0.0835949
$120$	3.58501	0.327266
$121$	13.0043	1.18221
$122$	−6.50346	−0.588796
$123$	−4.36035	−0.393159
$124$	5.66260	0.508516
$125$	3.37071	0.301486
$126$	−1.55072	−0.138150
$127$	−17.3063	−1.53569	−0.767843	−	0.640638i	$-0.778670\pi$
$127$	−17.3063	−1.53569	−0.767843	+	0.640638i	$0.778670\pi$
$128$	−1.00000	−0.0883883
$129$	−1.02961	−0.0906519
$130$	2.52860	0.221773
$131$	5.19930	0.454265	0.227132	−	0.973864i	$-0.427065\pi$
$131$	5.19930	0.454265	0.227132	+	0.973864i	$0.427065\pi$
$132$	5.89821	0.513373
$133$	0.375237	0.0325372
$134$	4.31228	0.372524
$135$	16.3144	1.40412
$136$	−0.911913	−0.0781959
$137$	1.31183	0.112077	0.0560384	−	0.998429i	$-0.482153\pi$
$137$	1.31183	0.112077	0.0560384	+	0.998429i	$0.482153\pi$
$138$	0.184928	0.0157421
$139$	−6.40785	−0.543507	−0.271753	−	0.962367i	$-0.587603\pi$
$139$	−6.40785	−0.543507	−0.271753	+	0.962367i	$0.587603\pi$
$140$	2.97794	0.251682
$141$	−9.63656	−0.811545
$142$	0.739152	0.0620282
$143$	4.16016	0.347890
$144$	−1.55072	−0.129227
$145$	−18.2378	−1.51456
$146$	8.19489	0.678214
$147$	1.20386	0.0992926
$148$	−11.1147	−0.913626
$149$	14.5607	1.19286	0.596431	−	0.802665i	$-0.296585\pi$
$149$	14.5607	1.19286	0.596431	+	0.802665i	$0.296585\pi$
$150$	−4.65665	−0.380214
$151$	1.41094	0.114821	0.0574104	−	0.998351i	$-0.481716\pi$
$151$	1.41094	0.114821	0.0574104	+	0.998351i	$0.481716\pi$
$152$	0.375237	0.0304357
$153$	−1.41413	−0.114325
$154$	4.89942	0.394807
$155$	−16.8629	−1.35446
$156$	1.02221	0.0818424
$157$	11.7978	0.941565	0.470782	−	0.882249i	$-0.343972\pi$
$157$	11.7978	0.941565	0.470782	+	0.882249i	$0.343972\pi$
$158$	−17.0294	−1.35479
$159$	−3.68716	−0.292410
$160$	2.97794	0.235427
$161$	0.153613	0.0121064
$162$	1.94308	0.152663
$163$	−4.07480	−0.319163	−0.159581	−	0.987185i	$-0.551014\pi$
$163$	−4.07480	−0.319163	−0.159581	+	0.987185i	$0.551014\pi$
$164$	−3.62198	−0.282829
$165$	−17.5645	−1.36739
$166$	−6.32734	−0.491097
$167$	21.6489	1.67525	0.837623	−	0.546249i	$-0.183945\pi$
$167$	21.6489	1.67525	0.837623	+	0.546249i	$0.183945\pi$
$168$	1.20386	0.0928797
$169$	−12.2790	−0.944539
$170$	2.71562	0.208278
$171$	0.581889	0.0444982
$172$	−0.855256	−0.0652127
$173$	−0.175422	−0.0133371	−0.00666856	−	0.999978i	$-0.502123\pi$
$173$	−0.175422	−0.0133371	−0.00666856	+	0.999978i	$0.502123\pi$
$174$	−7.37278	−0.558929
$175$	−3.86810	−0.292401
$176$	4.89942	0.369308
$177$	11.1657	0.839269
$178$	−0.101939	−0.00764066
$179$	25.9266	1.93785	0.968923	−	0.247362i	$-0.0795637\pi$
$179$	25.9266	1.93785	0.968923	+	0.247362i	$0.0795637\pi$
$180$	4.61796	0.344202
$181$	−13.8892	−1.03238	−0.516188	−	0.856475i	$-0.672649\pi$
$181$	−13.8892	−1.03238	−0.516188	+	0.856475i	$0.672649\pi$
$182$	0.849112	0.0629404
$183$	7.82925	0.578755
$184$	0.153613	0.0113245
$185$	33.0990	2.43348
$186$	−6.81696	−0.499844
$187$	4.46785	0.326721
$188$	−8.00473	−0.583805
$189$	5.47843	0.398497
$190$	−1.11743	−0.0810670
$191$	−2.88488	−0.208742	−0.104371	−	0.994538i	$-0.533283\pi$
$191$	−2.88488	−0.208742	−0.104371	+	0.994538i	$0.533283\pi$
$192$	1.20386	0.0868810
$193$	−17.1765	−1.23639	−0.618195	−	0.786025i	$-0.712136\pi$
$193$	−17.1765	−1.23639	−0.618195	+	0.786025i	$0.712136\pi$
$194$	−4.01210	−0.288052
$195$	−3.04408	−0.217991
$196$	1.00000	0.0714286
$197$	23.8850	1.70174	0.850869	−	0.525377i	$-0.176076\pi$
$197$	23.8850	1.70174	0.850869	+	0.525377i	$0.176076\pi$
$198$	7.59766	0.539942
$199$	21.2542	1.50667	0.753336	−	0.657636i	$-0.228444\pi$
$199$	21.2542	1.50667	0.753336	+	0.657636i	$0.228444\pi$
$200$	−3.86810	−0.273516
$201$	−5.19138	−0.366171
$202$	3.91128	0.275197
$203$	−6.12429	−0.429841
$204$	1.09781	0.0768624
$205$	10.7860	0.753328
$206$	−6.58489	−0.458791
$207$	0.238211	0.0165568
$208$	0.849112	0.0588754
$209$	−1.83844	−0.127168
$210$	−3.58501	−0.247389
$211$	3.44404	0.237097	0.118549	−	0.992948i	$-0.462176\pi$
$211$	3.44404	0.237097	0.118549	+	0.992948i	$0.462176\pi$
$212$	−3.06278	−0.210353
$213$	−0.889834	−0.0609704
$214$	19.3066	1.31977
$215$	2.54690	0.173697
$216$	5.47843	0.372760
$217$	−5.66260	−0.384402
$218$	−17.7165	−1.19991
$219$	−9.86549	−0.666648
$220$	−14.5902	−0.983669
$221$	0.774317	0.0520862
$222$	13.3806	0.898045
$223$	9.70779	0.650081	0.325041	−	0.945700i	$-0.394622\pi$
$223$	9.70779	0.650081	0.325041	+	0.945700i	$0.394622\pi$
$224$	1.00000	0.0668153
$225$	−5.99837	−0.399891
$226$	8.03226	0.534298
$227$	−0.123312	−0.00818453	−0.00409226	−	0.999992i	$-0.501303\pi$
$227$	−0.123312	−0.00818453	−0.00409226	+	0.999992i	$0.501303\pi$
$228$	−0.451732	−0.0299167
$229$	23.6533	1.56306	0.781528	−	0.623870i	$-0.214440\pi$
$229$	23.6533	1.56306	0.781528	+	0.623870i	$0.214440\pi$
$230$	−0.457448	−0.0301632
$231$	−5.89821	−0.388074
$232$	−6.12429	−0.402080
$233$	17.7608	1.16355	0.581773	−	0.813351i	$-0.302359\pi$
$233$	17.7608	1.16355	0.581773	+	0.813351i	$0.302359\pi$
$234$	1.31674	0.0860780
$235$	23.8376	1.55499
$236$	9.27497	0.603749
$237$	20.5010	1.33168
$238$	0.911913	0.0591105
$239$	18.0820	1.16963	0.584813	−	0.811168i	$-0.301168\pi$
$239$	18.0820	1.16963	0.584813	+	0.811168i	$0.301168\pi$
$240$	−3.58501	−0.231412
$241$	24.4403	1.57434	0.787170	−	0.616736i	$-0.211545\pi$
$241$	24.4403	1.57434	0.787170	+	0.616736i	$0.211545\pi$
$242$	−13.0043	−0.835951
$243$	14.0961	0.904265
$244$	6.50346	0.416341
$245$	−2.97794	−0.190253
$246$	4.36035	0.278006
$247$	−0.318618	−0.0202732
$248$	−5.66260	−0.359575
$249$	7.61722	0.482722
$250$	−3.37071	−0.213183
$251$	−13.5545	−0.855554	−0.427777	−	0.903884i	$-0.640703\pi$
$251$	−13.5545	−0.855554	−0.427777	+	0.903884i	$0.640703\pi$
$252$	1.55072	0.0976865
$253$	−0.752613	−0.0473164
$254$	17.3063	1.08589
$255$	−3.26922	−0.204727
$256$	1.00000	0.0625000
$257$	17.4714	1.08984	0.544919	−	0.838489i	$-0.316560\pi$
$257$	17.4714	1.08984	0.544919	+	0.838489i	$0.316560\pi$
$258$	1.02961	0.0641006
$259$	11.1147	0.690636
$260$	−2.52860	−0.156817
$261$	−9.49709	−0.587855
$262$	−5.19930	−0.321214
$263$	5.31907	0.327988	0.163994	−	0.986461i	$-0.447562\pi$
$263$	5.31907	0.327988	0.163994	+	0.986461i	$0.447562\pi$
$264$	−5.89821	−0.363010
$265$	9.12077	0.560284
$266$	−0.375237	−0.0230072
$267$	0.122720	0.00751036
$268$	−4.31228	−0.263415
$269$	22.4922	1.37137	0.685687	−	0.727896i	$-0.259502\pi$
$269$	22.4922	1.37137	0.685687	+	0.727896i	$0.259502\pi$
$270$	−16.3144	−0.992863
$271$	−9.76482	−0.593170	−0.296585	−	0.955006i	$-0.595848\pi$
$271$	−9.76482	−0.593170	−0.296585	+	0.955006i	$0.595848\pi$
$272$	0.911913	0.0552928
$273$	−1.02221	−0.0618670
$274$	−1.31183	−0.0792503
$275$	18.9515	1.14282
$276$	−0.184928	−0.0111313
$277$	−5.29525	−0.318161	−0.159080	−	0.987266i	$-0.550853\pi$
$277$	−5.29525	−0.318161	−0.159080	+	0.987266i	$0.550853\pi$
$278$	6.40785	0.384317
$279$	−8.78113	−0.525712
$280$	−2.97794	−0.177966
$281$	24.7062	1.47385	0.736924	−	0.675976i	$-0.236278\pi$
$281$	24.7062	1.47385	0.736924	+	0.675976i	$0.236278\pi$
$282$	9.63656	0.573849
$283$	−6.29861	−0.374413	−0.187207	−	0.982321i	$-0.559943\pi$
$283$	−6.29861	−0.374413	−0.187207	+	0.982321i	$0.559943\pi$
$284$	−0.739152	−0.0438606
$285$	1.34523	0.0796845
$286$	−4.16016	−0.245995
$287$	3.62198	0.213799
$288$	1.55072	0.0913773
$289$	−16.1684	−0.951083
$290$	18.2378	1.07096
$291$	4.83000	0.283140
$292$	−8.19489	−0.479570
$293$	17.8681	1.04387	0.521933	−	0.852987i	$-0.325211\pi$
$293$	17.8681	1.04387	0.521933	+	0.852987i	$0.325211\pi$
$294$	−1.20386	−0.0702105
$295$	−27.6203	−1.60811
$296$	11.1147	0.646031
$297$	−26.8411	−1.55748
$298$	−14.5607	−0.843480
$299$	−0.130434	−0.00754321
$300$	4.65665	0.268852
$301$	0.855256	0.0492961
$302$	−1.41094	−0.0811905
$303$	−4.70863	−0.270504
$304$	−0.375237	−0.0215213
$305$	−19.3669	−1.10895
$306$	1.41413	0.0808402
$307$	7.20156	0.411015	0.205507	−	0.978656i	$-0.434116\pi$
$307$	7.20156	0.411015	0.205507	+	0.978656i	$0.434116\pi$
$308$	−4.89942	−0.279171
$309$	7.92728	0.450967
$310$	16.8629	0.957746
$311$	−10.2189	−0.579459	−0.289729	−	0.957109i	$-0.593565\pi$
$311$	−10.2189	−0.579459	−0.289729	+	0.957109i	$0.593565\pi$
$312$	−1.02221	−0.0578713
$313$	18.4553	1.04316	0.521579	−	0.853203i	$-0.325343\pi$
$313$	18.4553	1.04316	0.521579	+	0.853203i	$0.325343\pi$
$314$	−11.7978	−0.665787
$315$	−4.61796	−0.260193
$316$	17.0294	0.957980
$317$	35.1777	1.97577	0.987887	−	0.155173i	$-0.0495935\pi$
$317$	35.1777	1.97577	0.987887	+	0.155173i	$0.0495935\pi$
$318$	3.68716	0.206765
$319$	30.0055	1.67999
$320$	−2.97794	−0.166472
$321$	−23.2424	−1.29726
$322$	−0.153613	−0.00856049
$323$	−0.342183	−0.0190396
$324$	−1.94308	−0.107949
$325$	3.28446	0.182189
$326$	4.07480	0.225682
$327$	21.3281	1.17945
$328$	3.62198	0.199990
$329$	8.00473	0.441315
$330$	17.5645	0.966894
$331$	−33.0006	−1.81388	−0.906939	−	0.421261i	$-0.861588\pi$
$331$	−33.0006	−1.81388	−0.906939	+	0.421261i	$0.861588\pi$
$332$	6.32734	0.347258
$333$	17.2359	0.944521
$334$	−21.6489	−1.18458
$335$	12.8417	0.701617
$336$	−1.20386	−0.0656759
$337$	−4.26202	−0.232167	−0.116083	−	0.993239i	$-0.537034\pi$
$337$	−4.26202	−0.232167	−0.116083	+	0.993239i	$0.537034\pi$
$338$	12.2790	0.667890
$339$	−9.66970	−0.525186
$340$	−2.71562	−0.147275
$341$	27.7435	1.50239
$342$	−0.581889	−0.0314650
$343$	−1.00000	−0.0539949
$344$	0.855256	0.0461123
$345$	0.550703	0.0296489
$346$	0.175422	0.00943077
$347$	21.0191	1.12836	0.564181	−	0.825651i	$-0.309192\pi$
$347$	21.0191	1.12836	0.564181	+	0.825651i	$0.309192\pi$
$348$	7.37278	0.395223
$349$	−6.89685	−0.369180	−0.184590	−	0.982816i	$-0.559096\pi$
$349$	−6.89685	−0.369180	−0.184590	+	0.982816i	$0.559096\pi$
$350$	3.86810	0.206759
$351$	−4.65180	−0.248295
$352$	−4.89942	−0.261140
$353$	1.22121	0.0649982	0.0324991	−	0.999472i	$-0.489653\pi$
$353$	1.22121	0.0649982	0.0324991	+	0.999472i	$0.489653\pi$
$354$	−11.1657	−0.593453
$355$	2.20115	0.116825
$356$	0.101939	0.00540276
$357$	−1.09781	−0.0581025
$358$	−25.9266	−1.37026
$359$	10.3281	0.545099	0.272549	−	0.962142i	$-0.412133\pi$
$359$	10.3281	0.545099	0.272549	+	0.962142i	$0.412133\pi$
$360$	−4.61796	−0.243388
$361$	−18.8592	−0.992589
$362$	13.8892	0.730000
$363$	15.6554	0.821695
$364$	−0.849112	−0.0445056
$365$	24.4039	1.27736
$366$	−7.82925	−0.409241
$367$	−16.0744	−0.839078	−0.419539	−	0.907737i	$-0.637808\pi$
$367$	−16.0744	−0.839078	−0.419539	+	0.907737i	$0.637808\pi$
$368$	−0.153613	−0.00800761
$369$	5.61669	0.292393
$370$	−33.0990	−1.72073
$371$	3.06278	0.159012
$372$	6.81696	0.353443
$373$	−21.6027	−1.11854	−0.559272	−	0.828984i	$-0.688919\pi$
$373$	−21.6027	−1.11854	−0.559272	+	0.828984i	$0.688919\pi$
$374$	−4.46785	−0.231027
$375$	4.05786	0.209547
$376$	8.00473	0.412812
$377$	5.20021	0.267825
$378$	−5.47843	−0.281780
$379$	−33.3433	−1.71273	−0.856365	−	0.516370i	$-0.827283\pi$
$379$	−33.3433	−1.71273	−0.856365	+	0.516370i	$0.827283\pi$
$380$	1.11743	0.0573230
$381$	−20.8343	−1.06738
$382$	2.88488	0.147603
$383$	2.61129	0.133431	0.0667153	−	0.997772i	$-0.478748\pi$
$383$	2.61129	0.133431	0.0667153	+	0.997772i	$0.478748\pi$
$384$	−1.20386	−0.0614341
$385$	14.5902	0.743584
$386$	17.1765	0.874259
$387$	1.32627	0.0674179
$388$	4.01210	0.203683
$389$	7.59768	0.385218	0.192609	−	0.981276i	$-0.438305\pi$
$389$	7.59768	0.385218	0.192609	+	0.981276i	$0.438305\pi$
$390$	3.04408	0.154143
$391$	−0.140081	−0.00708421
$392$	−1.00000	−0.0505076
$393$	6.25922	0.315736
$394$	−23.8850	−1.20331
$395$	−50.7125	−2.55162
$396$	−7.59766	−0.381797
$397$	29.3810	1.47459	0.737295	−	0.675571i	$-0.236103\pi$
$397$	29.3810	1.47459	0.737295	+	0.675571i	$0.236103\pi$
$398$	−21.2542	−1.06538
$399$	0.451732	0.0226149
$400$	3.86810	0.193405
$401$	0.873498	0.0436204	0.0218102	−	0.999762i	$-0.493057\pi$
$401$	0.873498	0.0436204	0.0218102	+	0.999762i	$0.493057\pi$
$402$	5.19138	0.258922
$403$	4.80818	0.239513
$404$	−3.91128	−0.194594
$405$	5.78637	0.287527
$406$	6.12429	0.303944
$407$	−54.4558	−2.69927
$408$	−1.09781	−0.0543499
$409$	−14.1825	−0.701277	−0.350639	−	0.936511i	$-0.614035\pi$
$409$	−14.1825	−0.701277	−0.350639	+	0.936511i	$0.614035\pi$
$410$	−10.7860	−0.532683
$411$	1.57925	0.0778988
$412$	6.58489	0.324414
$413$	−9.27497	−0.456391
$414$	−0.238211	−0.0117074
$415$	−18.8424	−0.924938
$416$	−0.849112	−0.0416312
$417$	−7.71414	−0.377763
$418$	1.83844	0.0899212
$419$	−15.3410	−0.749458	−0.374729	−	0.927134i	$-0.622264\pi$
$419$	−15.3410	−0.749458	−0.374729	+	0.927134i	$0.622264\pi$
$420$	3.58501	0.174931
$421$	10.6330	0.518223	0.259112	−	0.965847i	$-0.416570\pi$
$421$	10.6330	0.518223	0.259112	+	0.965847i	$0.416570\pi$
$422$	−3.44404	−0.167653
$423$	12.4131	0.603547
$424$	3.06278	0.148742
$425$	3.52737	0.171103
$426$	0.889834	0.0431126
$427$	−6.50346	−0.314725
$428$	−19.3066	−0.933219
$429$	5.00825	0.241800
$430$	−2.54690	−0.122822
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.47843	−0.263581
$433$	−12.7433	−0.612406	−0.306203	−	0.951966i	$-0.599059\pi$
$433$	−12.7433	−0.612406	−0.306203	+	0.951966i	$0.599059\pi$
$434$	5.66260	0.271813
$435$	−21.9557	−1.05269
$436$	17.7165	0.848464
$437$	0.0576411	0.00275735
$438$	9.86549	0.471391
$439$	5.97985	0.285403	0.142701	−	0.989766i	$-0.454421\pi$
$439$	5.97985	0.285403	0.142701	+	0.989766i	$0.454421\pi$
$440$	14.5902	0.695559
$441$	−1.55072	−0.0738440
$442$	−0.774317	−0.0368305
$443$	−20.8026	−0.988360	−0.494180	−	0.869360i	$-0.664532\pi$
$443$	−20.8026	−0.988360	−0.494180	+	0.869360i	$0.664532\pi$
$444$	−13.3806	−0.635014
$445$	−0.303568	−0.0143905
$446$	−9.70779	−0.459677
$447$	17.5291	0.829096
$448$	−1.00000	−0.0472456
$449$	13.1429	0.620249	0.310125	−	0.950696i	$-0.399629\pi$
$449$	13.1429	0.620249	0.310125	+	0.950696i	$0.399629\pi$
$450$	5.99837	0.282766
$451$	−17.7456	−0.835607
$452$	−8.03226	−0.377806
$453$	1.69857	0.0798059
$454$	0.123312	0.00578733
$455$	2.52860	0.118543
$456$	0.451732	0.0211543
$457$	33.8831	1.58499	0.792493	−	0.609881i	$-0.208783\pi$
$457$	33.8831	1.58499	0.792493	+	0.609881i	$0.208783\pi$
$458$	−23.6533	−1.10525
$459$	−4.99585	−0.233186
$460$	0.457448	0.0213286
$461$	41.3424	1.92551	0.962755	−	0.270376i	$-0.0871482\pi$
$461$	41.3424	1.92551	0.962755	+	0.270376i	$0.0871482\pi$
$462$	5.89821	0.274410
$463$	−8.35730	−0.388397	−0.194198	−	0.980962i	$-0.562211\pi$
$463$	−8.35730	−0.388397	−0.194198	+	0.980962i	$0.562211\pi$
$464$	6.12429	0.284313
$465$	−20.3005	−0.941413
$466$	−17.7608	−0.822751
$467$	−27.6848	−1.28110	−0.640550	−	0.767916i	$-0.721294\pi$
$467$	−27.6848	−1.28110	−0.640550	+	0.767916i	$0.721294\pi$
$468$	−1.31674	−0.0608663
$469$	4.31228	0.199123
$470$	−23.8376	−1.09954
$471$	14.2028	0.654433
$472$	−9.27497	−0.426915
$473$	−4.19026	−0.192668
$474$	−20.5010	−0.941643
$475$	−1.45146	−0.0665973
$476$	−0.911913	−0.0417975
$477$	4.74953	0.217466
$478$	−18.0820	−0.827050
$479$	29.1826	1.33339	0.666694	−	0.745331i	$-0.267709\pi$
$479$	29.1826	1.33339	0.666694	+	0.745331i	$0.267709\pi$
$480$	3.58501	0.163633
$481$	−9.43766	−0.430320
$482$	−24.4403	−1.11323
$483$	0.184928	0.00841450
$484$	13.0043	0.591107
$485$	−11.9478	−0.542521
$486$	−14.0961	−0.639412
$487$	−17.3831	−0.787703	−0.393851	−	0.919174i	$-0.628858\pi$
$487$	−17.3831	−0.787703	−0.393851	+	0.919174i	$0.628858\pi$
$488$	−6.50346	−0.294398
$489$	−4.90548	−0.221834
$490$	2.97794	0.134529
$491$	12.4935	0.563825	0.281912	−	0.959440i	$-0.409031\pi$
$491$	12.4935	0.563825	0.281912	+	0.959440i	$0.409031\pi$
$492$	−4.36035	−0.196580
$493$	5.58482	0.251528
$494$	0.318618	0.0143353
$495$	22.6253	1.01693
$496$	5.66260	0.254258
$497$	0.739152	0.0331555
$498$	−7.61722	−0.341336
$499$	−7.84699	−0.351280	−0.175640	−	0.984454i	$-0.556199\pi$
$499$	−7.84699	−0.351280	−0.175640	+	0.984454i	$0.556199\pi$
$500$	3.37071	0.150743
$501$	26.0623	1.16438
$502$	13.5545	0.604968
$503$	−31.5109	−1.40500	−0.702501	−	0.711682i	$-0.747934\pi$
$503$	−31.5109	−1.40500	−0.702501	+	0.711682i	$0.747934\pi$
$504$	−1.55072	−0.0690748
$505$	11.6475	0.518309
$506$	0.752613	0.0334577
$507$	−14.7822	−0.656500
$508$	−17.3063	−0.767843
$509$	−10.8749	−0.482020	−0.241010	−	0.970523i	$-0.577479\pi$
$509$	−10.8749	−0.482020	−0.241010	+	0.970523i	$0.577479\pi$
$510$	3.26922	0.144764
$511$	8.19489	0.362521
$512$	−1.00000	−0.0441942
$513$	2.05571	0.0907617
$514$	−17.4714	−0.770632
$515$	−19.6094	−0.864093
$516$	−1.02961	−0.0453259
$517$	−39.2185	−1.72483
$518$	−11.1147	−0.488353
$519$	−0.211184	−0.00926994
$520$	2.52860	0.110887
$521$	−9.84742	−0.431423	−0.215712	−	0.976457i	$-0.569207\pi$
$521$	−9.84742	−0.431423	−0.215712	+	0.976457i	$0.569207\pi$
$522$	9.49709	0.415676
$523$	38.6803	1.69137	0.845685	−	0.533682i	$-0.179192\pi$
$523$	38.6803	1.69137	0.845685	+	0.533682i	$0.179192\pi$
$524$	5.19930	0.227132
$525$	−4.65665	−0.203233
$526$	−5.31907	−0.231923
$527$	5.16379	0.224938
$528$	5.89821	0.256687
$529$	−22.9764	−0.998974
$530$	−9.12077	−0.396181
$531$	−14.3829	−0.624166
$532$	0.375237	0.0162686
$533$	−3.07547	−0.133213
$534$	−0.122720	−0.00531062
$535$	57.4938	2.48567
$536$	4.31228	0.186262
$537$	31.2120	1.34690
$538$	−22.4922	−0.969709
$539$	4.89942	0.211033
$540$	16.3144	0.702060
$541$	−14.1263	−0.607339	−0.303669	−	0.952778i	$-0.598212\pi$
$541$	−14.1263	−0.607339	−0.303669	+	0.952778i	$0.598212\pi$
$542$	9.76482	0.419435
$543$	−16.7206	−0.717551
$544$	−0.911913	−0.0390979
$545$	−52.7585	−2.25993
$546$	1.02221	0.0437466
$547$	35.5049	1.51808	0.759040	−	0.651044i	$-0.225669\pi$
$547$	35.5049	1.51808	0.759040	+	0.651044i	$0.225669\pi$
$548$	1.31183	0.0560384
$549$	−10.0851	−0.430421
$550$	−18.9515	−0.808094
$551$	−2.29806	−0.0979007
$552$	0.184928	0.00787105
$553$	−17.0294	−0.724165
$554$	5.29525	0.224974
$555$	39.8465	1.69139
$556$	−6.40785	−0.271753
$557$	−5.55212	−0.235251	−0.117625	−	0.993058i	$-0.537528\pi$
$557$	−5.55212	−0.235251	−0.117625	+	0.993058i	$0.537528\pi$
$558$	8.78113	0.371735
$559$	−0.726209	−0.0307154
$560$	2.97794	0.125841
$561$	5.37866	0.227087
$562$	−24.7062	−1.04217
$563$	23.6788	0.997944	0.498972	−	0.866618i	$-0.333711\pi$
$563$	23.6788	0.997944	0.498972	+	0.866618i	$0.333711\pi$
$564$	−9.63656	−0.405772
$565$	23.9196	1.00630
$566$	6.29861	0.264750
$567$	1.94308	0.0816017
$568$	0.739152	0.0310141
$569$	−35.8502	−1.50292	−0.751459	−	0.659779i	$-0.770650\pi$
$569$	−35.8502	−1.50292	−0.751459	+	0.659779i	$0.770650\pi$
$570$	−1.34523	−0.0563455
$571$	31.0243	1.29833	0.649163	−	0.760650i	$-0.275119\pi$
$571$	31.0243	1.29833	0.649163	+	0.760650i	$0.275119\pi$
$572$	4.16016	0.173945
$573$	−3.47298	−0.145086
$574$	−3.62198	−0.151178
$575$	−0.594189	−0.0247794
$576$	−1.55072	−0.0646135
$577$	−0.533387	−0.0222052	−0.0111026	−	0.999938i	$-0.503534\pi$
$577$	−0.533387	−0.0222052	−0.0111026	+	0.999938i	$0.503534\pi$
$578$	16.1684	0.672517
$579$	−20.6780	−0.859350
$580$	−18.2378	−0.757282
$581$	−6.32734	−0.262502
$582$	−4.83000	−0.200210
$583$	−15.0059	−0.621479
$584$	8.19489	0.339107
$585$	3.92117	0.162120
$586$	−17.8681	−0.738124
$587$	1.56328	0.0645234	0.0322617	−	0.999479i	$-0.489729\pi$
$587$	1.56328	0.0645234	0.0322617	+	0.999479i	$0.489729\pi$
$588$	1.20386	0.0496463
$589$	−2.12481	−0.0875515
$590$	27.6203	1.13711
$591$	28.7542	1.18279
$592$	−11.1147	−0.456813
$593$	39.4369	1.61948	0.809740	−	0.586789i	$-0.199608\pi$
$593$	39.4369	1.61948	0.809740	+	0.586789i	$0.199608\pi$
$594$	26.8411	1.10131
$595$	2.71562	0.111329
$596$	14.5607	0.596431
$597$	25.5871	1.04721
$598$	0.130434	0.00533386
$599$	18.3831	0.751112	0.375556	−	0.926800i	$-0.377452\pi$
$599$	18.3831	0.751112	0.375556	+	0.926800i	$0.377452\pi$
$600$	−4.65665	−0.190107
$601$	17.3942	0.709524	0.354762	−	0.934957i	$-0.384562\pi$
$601$	17.3942	0.709524	0.354762	+	0.934957i	$0.384562\pi$
$602$	−0.855256	−0.0348576
$603$	6.68716	0.272322
$604$	1.41094	0.0574104
$605$	−38.7261	−1.57444
$606$	4.70863	0.191275
$607$	41.3720	1.67924	0.839618	−	0.543177i	$-0.182779\pi$
$607$	41.3720	1.67924	0.839618	+	0.543177i	$0.182779\pi$
$608$	0.375237	0.0152179
$609$	−7.37278	−0.298760
$610$	19.3669	0.784143
$611$	−6.79691	−0.274974
$612$	−1.41413	−0.0571626
$613$	−13.7858	−0.556805	−0.278402	−	0.960465i	$-0.589805\pi$
$613$	−13.7858	−0.556805	−0.278402	+	0.960465i	$0.589805\pi$
$614$	−7.20156	−0.290631
$615$	12.9848	0.523599
$616$	4.89942	0.197403
$617$	41.0153	1.65122	0.825608	−	0.564245i	$-0.190833\pi$
$617$	41.0153	1.65122	0.825608	+	0.564245i	$0.190833\pi$
$618$	−7.92728	−0.318882
$619$	−8.28944	−0.333181	−0.166590	−	0.986026i	$-0.553276\pi$
$619$	−8.28944	−0.333181	−0.166590	+	0.986026i	$0.553276\pi$
$620$	−16.8629	−0.677228
$621$	0.841555	0.0337704
$622$	10.2189	0.409739
$623$	−0.101939	−0.00408410
$624$	1.02221	0.0409212
$625$	−29.3783	−1.17513
$626$	−18.4553	−0.737624
$627$	−2.21323	−0.0883878
$628$	11.7978	0.470782
$629$	−10.1357	−0.404136
$630$	4.61796	0.183984
$631$	−37.2337	−1.48225	−0.741124	−	0.671368i	$-0.765707\pi$
$631$	−37.2337	−1.48225	−0.741124	+	0.671368i	$0.765707\pi$
$632$	−17.0294	−0.677394
$633$	4.14613	0.164794
$634$	−35.1777	−1.39708
$635$	51.5371	2.04519
$636$	−3.68716	−0.146205
$637$	0.849112	0.0336431
$638$	−30.0055	−1.18793
$639$	1.14622	0.0453438
$640$	2.97794	0.117713
$641$	11.2760	0.445374	0.222687	−	0.974890i	$-0.428517\pi$
$641$	11.2760	0.445374	0.222687	+	0.974890i	$0.428517\pi$
$642$	23.2424	0.917305
$643$	−39.7003	−1.56563	−0.782814	−	0.622256i	$-0.786216\pi$
$643$	−39.7003	−1.56563	−0.782814	+	0.622256i	$0.786216\pi$
$644$	0.153613	0.00605318
$645$	3.06611	0.120728
$646$	0.342183	0.0134630
$647$	−6.06715	−0.238524	−0.119262	−	0.992863i	$-0.538053\pi$
$647$	−6.06715	−0.238524	−0.119262	+	0.992863i	$0.538053\pi$
$648$	1.94308	0.0763314
$649$	45.4420	1.78375
$650$	−3.28446	−0.128827
$651$	−6.81696	−0.267178
$652$	−4.07480	−0.159581
$653$	23.3853	0.915138	0.457569	−	0.889174i	$-0.348720\pi$
$653$	23.3853	0.915138	0.457569	+	0.889174i	$0.348720\pi$
$654$	−21.3281	−0.833995
$655$	−15.4832	−0.604978
$656$	−3.62198	−0.141414
$657$	12.7080	0.495787
$658$	−8.00473	−0.312057
$659$	−0.288809	−0.0112504	−0.00562520	−	0.999984i	$-0.501791\pi$
$659$	−0.288809	−0.0112504	−0.00562520	+	0.999984i	$0.501791\pi$
$660$	−17.5645	−0.683697
$661$	1.54303	0.0600168	0.0300084	−	0.999550i	$-0.490447\pi$
$661$	1.54303	0.0600168	0.0300084	+	0.999550i	$0.490447\pi$
$662$	33.0006	1.28261
$663$	0.932168	0.0362024
$664$	−6.32734	−0.245548
$665$	−1.11743	−0.0433321
$666$	−17.2359	−0.667877
$667$	−0.940768	−0.0364267
$668$	21.6489	0.837623
$669$	11.6868	0.451838
$670$	−12.8417	−0.496118
$671$	31.8632	1.23007
$672$	1.20386	0.0464399
$673$	9.80088	0.377796	0.188898	−	0.981997i	$-0.439508\pi$
$673$	9.80088	0.377796	0.188898	+	0.981997i	$0.439508\pi$
$674$	4.26202	0.164167
$675$	−21.1911	−0.815647
$676$	−12.2790	−0.472270
$677$	−14.4180	−0.554131	−0.277065	−	0.960851i	$-0.589362\pi$
$677$	−14.4180	−0.554131	−0.277065	+	0.960851i	$0.589362\pi$
$678$	9.66970	0.371363
$679$	−4.01210	−0.153970
$680$	2.71562	0.104139
$681$	−0.148451	−0.00568864
$682$	−27.7435	−1.06235
$683$	11.9966	0.459037	0.229518	−	0.973304i	$-0.426285\pi$
$683$	11.9966	0.459037	0.229518	+	0.973304i	$0.426285\pi$
$684$	0.581889	0.0222491
$685$	−3.90653	−0.149261
$686$	1.00000	0.0381802
$687$	28.4753	1.08640
$688$	−0.855256	−0.0326063
$689$	−2.60065	−0.0990767
$690$	−0.550703	−0.0209649
$691$	−14.4858	−0.551068	−0.275534	−	0.961291i	$-0.588855\pi$
$691$	−14.4858	−0.551068	−0.275534	+	0.961291i	$0.588855\pi$
$692$	−0.175422	−0.00666856
$693$	7.59766	0.288611
$694$	−21.0191	−0.797872
$695$	19.0822	0.723828
$696$	−7.37278	−0.279465
$697$	−3.30293	−0.125107
$698$	6.89685	0.261049
$699$	21.3814	0.808720
$700$	−3.86810	−0.146201
$701$	1.19892	0.0452825	0.0226413	−	0.999744i	$-0.492792\pi$
$701$	1.19892	0.0452825	0.0226413	+	0.999744i	$0.492792\pi$
$702$	4.65180	0.175571
$703$	4.17066	0.157299
$704$	4.89942	0.184654
$705$	28.6971	1.08079
$706$	−1.22121	−0.0459607
$707$	3.91128	0.147099
$708$	11.1657	0.419635
$709$	−14.2392	−0.534764	−0.267382	−	0.963591i	$-0.586159\pi$
$709$	−14.2392	−0.534764	−0.267382	+	0.963591i	$0.586159\pi$
$710$	−2.20115	−0.0826076
$711$	−26.4079	−0.990375
$712$	−0.101939	−0.00382033
$713$	−0.869846	−0.0325760
$714$	1.09781	0.0410847
$715$	−12.3887	−0.463311
$716$	25.9266	0.968923
$717$	21.7681	0.812946
$718$	−10.3281	−0.385443
$719$	19.0688	0.711146	0.355573	−	0.934648i	$-0.384286\pi$
$719$	19.0688	0.711146	0.355573	+	0.934648i	$0.384286\pi$
$720$	4.61796	0.172101
$721$	−6.58489	−0.245234
$722$	18.8592	0.701867
$723$	29.4227	1.09424
$724$	−13.8892	−0.516188
$725$	23.6894	0.879803
$726$	−15.6554	−0.581026
$727$	38.7830	1.43838	0.719192	−	0.694812i	$-0.244512\pi$
$727$	38.7830	1.43838	0.719192	+	0.694812i	$0.244512\pi$
$728$	0.849112	0.0314702
$729$	22.7989	0.844405
$730$	−24.4039	−0.903227
$731$	−0.779919	−0.0288463
$732$	7.82925	0.289377
$733$	−17.5495	−0.648205	−0.324103	−	0.946022i	$-0.605062\pi$
$733$	−17.5495	−0.648205	−0.324103	+	0.946022i	$0.605062\pi$
$734$	16.0744	0.593318
$735$	−3.58501	−0.132235
$736$	0.153613	0.00566223
$737$	−21.1277	−0.778248
$738$	−5.61669	−0.206753
$739$	−40.7463	−1.49888	−0.749438	−	0.662075i	$-0.769676\pi$
$739$	−40.7463	−1.49888	−0.749438	+	0.662075i	$0.769676\pi$
$740$	33.0990	1.21674
$741$	−0.383571	−0.0140908
$742$	−3.06278	−0.112438
$743$	−7.78704	−0.285679	−0.142839	−	0.989746i	$-0.545623\pi$
$743$	−7.78704	−0.285679	−0.142839	+	0.989746i	$0.545623\pi$
$744$	−6.81696	−0.249922
$745$	−43.3609	−1.58862
$746$	21.6027	0.790930
$747$	−9.81196	−0.359001
$748$	4.46785	0.163361
$749$	19.3066	0.705448
$750$	−4.05786	−0.148172
$751$	−30.4526	−1.11123	−0.555615	−	0.831440i	$-0.687517\pi$
$751$	−30.4526	−1.11123	−0.555615	+	0.831440i	$0.687517\pi$
$752$	−8.00473	−0.291902
$753$	−16.3177	−0.594651
$754$	−5.20021	−0.189381
$755$	−4.20169	−0.152915
$756$	5.47843	0.199249
$757$	15.8007	0.574287	0.287144	−	0.957888i	$-0.407294\pi$
$757$	15.8007	0.574287	0.287144	+	0.957888i	$0.407294\pi$
$758$	33.3433	1.21108
$759$	−0.906039	−0.0328871
$760$	−1.11743	−0.0405335
$761$	−11.7935	−0.427514	−0.213757	−	0.976887i	$-0.568570\pi$
$761$	−11.7935	−0.427514	−0.213757	+	0.976887i	$0.568570\pi$
$762$	20.8343	0.754749
$763$	−17.7165	−0.641379
$764$	−2.88488	−0.104371
$765$	4.21118	0.152255
$766$	−2.61129	−0.0943497
$767$	7.87549	0.284368
$768$	1.20386	0.0434405
$769$	−19.9145	−0.718135	−0.359067	−	0.933312i	$-0.616905\pi$
$769$	−19.9145	−0.718135	−0.359067	+	0.933312i	$0.616905\pi$
$770$	−14.5902	−0.525793
$771$	21.0331	0.757489
$772$	−17.1765	−0.618195
$773$	−15.9098	−0.572237	−0.286118	−	0.958194i	$-0.592365\pi$
$773$	−15.9098	−0.572237	−0.286118	+	0.958194i	$0.592365\pi$
$774$	−1.32627	−0.0476717
$775$	21.9035	0.786797
$776$	−4.01210	−0.144026
$777$	13.3806	0.480025
$778$	−7.59768	−0.272390
$779$	1.35910	0.0486948
$780$	−3.04408	−0.108996
$781$	−3.62142	−0.129584
$782$	0.140081	0.00500929
$783$	−33.5515	−1.19903
$784$	1.00000	0.0357143
$785$	−35.1330	−1.25395
$786$	−6.25922	−0.223259
$787$	16.1022	0.573980	0.286990	−	0.957934i	$-0.407345\pi$
$787$	16.1022	0.573980	0.286990	+	0.957934i	$0.407345\pi$
$788$	23.8850	0.850869
$789$	6.40341	0.227968
$790$	50.7125	1.80427
$791$	8.03226	0.285594
$792$	7.59766	0.269971
$793$	5.52217	0.196098
$794$	−29.3810	−1.04269
$795$	10.9801	0.389425
$796$	21.2542	0.753336
$797$	−17.7679	−0.629373	−0.314686	−	0.949196i	$-0.601899\pi$
$797$	−17.7679	−0.629373	−0.314686	+	0.949196i	$0.601899\pi$
$798$	−0.451732	−0.0159911
$799$	−7.29961	−0.258242
$800$	−3.86810	−0.136758
$801$	−0.158079	−0.00558546
$802$	−0.873498	−0.0308443
$803$	−40.1502	−1.41687
$804$	−5.19138	−0.183086
$805$	−0.457448	−0.0161229
$806$	−4.80818	−0.169361
$807$	27.0775	0.953171
$808$	3.91128	0.137598
$809$	27.3112	0.960212	0.480106	−	0.877210i	$-0.340598\pi$
$809$	27.3112	0.960212	0.480106	+	0.877210i	$0.340598\pi$
$810$	−5.78637	−0.203312
$811$	40.1021	1.40818	0.704088	−	0.710112i	$-0.251356\pi$
$811$	40.1021	1.40818	0.704088	+	0.710112i	$0.251356\pi$
$812$	−6.12429	−0.214921
$813$	−11.7555	−0.412282
$814$	54.4558	1.90867
$815$	12.1345	0.425053
$816$	1.09781	0.0384312
$817$	0.320924	0.0112277
$818$	14.1825	0.495878
$819$	1.31674	0.0460106
$820$	10.7860	0.376664
$821$	−26.4707	−0.923835	−0.461918	−	0.886923i	$-0.652838\pi$
$821$	−26.4707	−0.923835	−0.461918	+	0.886923i	$0.652838\pi$
$822$	−1.57925	−0.0550828
$823$	−28.8445	−1.00546	−0.502728	−	0.864444i	$-0.667670\pi$
$823$	−28.8445	−1.00546	−0.502728	+	0.864444i	$0.667670\pi$
$824$	−6.58489	−0.229396
$825$	22.8149	0.794313
$826$	9.27497	0.322717
$827$	9.00424	0.313108	0.156554	−	0.987669i	$-0.449961\pi$
$827$	9.00424	0.313108	0.156554	+	0.987669i	$0.449961\pi$
$828$	0.238211	0.00827839
$829$	−8.45567	−0.293678	−0.146839	−	0.989160i	$-0.546910\pi$
$829$	−8.45567	−0.293678	−0.146839	+	0.989160i	$0.546910\pi$
$830$	18.8424	0.654030
$831$	−6.37473	−0.221137
$832$	0.849112	0.0294377
$833$	0.911913	0.0315959
$834$	7.71414	0.267119
$835$	−64.4692	−2.23105
$836$	−1.83844	−0.0635839
$837$	−31.0221	−1.07228
$838$	15.3410	0.529947
$839$	5.67357	0.195874	0.0979368	−	0.995193i	$-0.468776\pi$
$839$	5.67357	0.195874	0.0979368	+	0.995193i	$0.468776\pi$
$840$	−3.58501	−0.123695
$841$	8.50697	0.293344
$842$	−10.6330	−0.366439
$843$	29.7428	1.02439
$844$	3.44404	0.118549
$845$	36.5661	1.25791
$846$	−12.4131	−0.426772
$847$	−13.0043	−0.446835
$848$	−3.06278	−0.105176
$849$	−7.58263	−0.260235
$850$	−3.52737	−0.120988
$851$	1.70736	0.0585276
$852$	−0.889834	−0.0304852
$853$	4.22755	0.144749	0.0723743	−	0.997378i	$-0.476942\pi$
$853$	4.22755	0.144749	0.0723743	+	0.997378i	$0.476942\pi$
$854$	6.50346	0.222544
$855$	−1.73283	−0.0592615
$856$	19.3066	0.659886
$857$	10.4515	0.357017	0.178508	−	0.983938i	$-0.442873\pi$
$857$	10.4515	0.357017	0.178508	+	0.983938i	$0.442873\pi$
$858$	−5.00825	−0.170979
$859$	51.3007	1.75036	0.875178	−	0.483801i	$-0.160744\pi$
$859$	51.3007	1.75036	0.875178	+	0.483801i	$0.160744\pi$
$860$	2.54690	0.0868485
$861$	4.36035	0.148600
$862$	−1.00000	−0.0340601
$863$	−30.5520	−1.04000	−0.520000	−	0.854166i	$-0.674068\pi$
$863$	−30.5520	−1.04000	−0.520000	+	0.854166i	$0.674068\pi$
$864$	5.47843	0.186380
$865$	0.522397	0.0177620
$866$	12.7433	0.433036
$867$	−19.4645	−0.661049
$868$	−5.66260	−0.192201
$869$	83.4343	2.83032
$870$	21.9557	0.744367
$871$	−3.66161	−0.124069
$872$	−17.7165	−0.599955
$873$	−6.22166	−0.210571
$874$	−0.0576411	−0.00194974
$875$	−3.37071	−0.113951
$876$	−9.86549	−0.333324
$877$	−26.7214	−0.902319	−0.451160	−	0.892443i	$-0.648989\pi$
$877$	−26.7214	−0.902319	−0.451160	+	0.892443i	$0.648989\pi$
$878$	−5.97985	−0.201810
$879$	21.5107	0.725537
$880$	−14.5902	−0.491835
$881$	18.2124	0.613591	0.306795	−	0.951775i	$-0.400743\pi$
$881$	18.2124	0.613591	0.306795	+	0.951775i	$0.400743\pi$
$882$	1.55072	0.0522156
$883$	17.3310	0.583233	0.291617	−	0.956535i	$-0.405807\pi$
$883$	17.3310	0.583233	0.291617	+	0.956535i	$0.405807\pi$
$884$	0.774317	0.0260431
$885$	−33.2509	−1.11772
$886$	20.8026	0.698876
$887$	−33.0353	−1.10922	−0.554608	−	0.832112i	$-0.687132\pi$
$887$	−33.0353	−1.10922	−0.554608	+	0.832112i	$0.687132\pi$
$888$	13.3806	0.449022
$889$	17.3063	0.580435
$890$	0.303568	0.0101756
$891$	−9.51997	−0.318931
$892$	9.70779	0.325041
$893$	3.00367	0.100514
$894$	−17.5291	−0.586259
$895$	−77.2078	−2.58077
$896$	1.00000	0.0334077
$897$	−0.157024	−0.00524289
$898$	−13.1429	−0.438583
$899$	34.6794	1.15662
$900$	−5.99837	−0.199946
$901$	−2.79299	−0.0930480
$902$	17.7456	0.590864
$903$	1.02961	0.0342632
$904$	8.03226	0.267149
$905$	41.3612	1.37489
$906$	−1.69857	−0.0564313
$907$	−55.8510	−1.85450	−0.927252	−	0.374439i	$-0.877835\pi$
$907$	−55.8510	−1.85450	−0.927252	+	0.374439i	$0.877835\pi$
$908$	−0.123312	−0.00409226
$909$	6.06532	0.201174
$910$	−2.52860	−0.0838224
$911$	−5.59433	−0.185348	−0.0926741	−	0.995696i	$-0.529541\pi$
$911$	−5.59433	−0.185348	−0.0926741	+	0.995696i	$0.529541\pi$
$912$	−0.451732	−0.0149583
$913$	31.0003	1.02596
$914$	−33.8831	−1.12075
$915$	−23.3150	−0.770770
$916$	23.6533	0.781528
$917$	−5.19930	−0.171696
$918$	4.99585	0.164888
$919$	−5.94745	−0.196188	−0.0980942	−	0.995177i	$-0.531275\pi$
$919$	−5.94745	−0.196188	−0.0980942	+	0.995177i	$0.531275\pi$
$920$	−0.457448	−0.0150816
$921$	8.66966	0.285675
$922$	−41.3424	−1.36154
$923$	−0.627623	−0.0206585
$924$	−5.89821	−0.194037
$925$	−42.9930	−1.41360
$926$	8.35730	0.274638
$927$	−10.2114	−0.335385
$928$	−6.12429	−0.201040
$929$	−2.45834	−0.0806554	−0.0403277	−	0.999187i	$-0.512840\pi$
$929$	−2.45834	−0.0806554	−0.0403277	+	0.999187i	$0.512840\pi$
$930$	20.3005	0.665679
$931$	−0.375237	−0.0122979
$932$	17.7608	0.581773
$933$	−12.3021	−0.402752
$934$	27.6848	0.905875
$935$	−13.3050	−0.435119
$936$	1.31674	0.0430390
$937$	18.2375	0.595794	0.297897	−	0.954598i	$-0.403715\pi$
$937$	18.2375	0.595794	0.297897	+	0.954598i	$0.403715\pi$
$938$	−4.31228	−0.140801
$939$	22.2176	0.725045
$940$	23.8376	0.777496
$941$	36.2405	1.18141	0.590703	−	0.806889i	$-0.298851\pi$
$941$	36.2405	1.18141	0.590703	+	0.806889i	$0.298851\pi$
$942$	−14.2028	−0.462754
$943$	0.556381	0.0181183
$944$	9.27497	0.301875
$945$	−16.3144	−0.530708
$946$	4.19026	0.136237
$947$	13.6050	0.442104	0.221052	−	0.975262i	$-0.429051\pi$
$947$	13.6050	0.442104	0.221052	+	0.975262i	$0.429051\pi$
$948$	20.5010	0.665842
$949$	−6.95838	−0.225879
$950$	1.45146	0.0470914
$951$	42.3489	1.37326
$952$	0.911913	0.0295553
$953$	26.9883	0.874235	0.437118	−	0.899404i	$-0.355999\pi$
$953$	26.9883	0.874235	0.437118	+	0.899404i	$0.355999\pi$
$954$	−4.74953	−0.153772
$955$	8.59098	0.277997
$956$	18.0820	0.584813
$957$	36.1224	1.16767
$958$	−29.1826	−0.942848
$959$	−1.31183	−0.0423611
$960$	−3.58501	−0.115706
$961$	1.06499	0.0343546
$962$	9.43766	0.304282
$963$	29.9392	0.964777
$964$	24.4403	0.787170
$965$	51.1504	1.64659
$966$	−0.184928	−0.00594995
$967$	42.8974	1.37949	0.689744	−	0.724054i	$-0.257723\pi$
$967$	42.8974	1.37949	0.689744	+	0.724054i	$0.257723\pi$
$968$	−13.0043	−0.417976
$969$	−0.411940	−0.0132334
$970$	11.9478	0.383620
$971$	−5.99974	−0.192541	−0.0962705	−	0.995355i	$-0.530691\pi$
$971$	−5.99974	−0.192541	−0.0962705	+	0.995355i	$0.530691\pi$
$972$	14.0961	0.452132
$973$	6.40785	0.205426
$974$	17.3831	0.556990
$975$	3.95402	0.126630
$976$	6.50346	0.208171
$977$	−33.4513	−1.07020	−0.535102	−	0.844788i	$-0.679727\pi$
$977$	−33.4513	−1.07020	−0.535102	+	0.844788i	$0.679727\pi$
$978$	4.90548	0.156860
$979$	0.499443	0.0159623
$980$	−2.97794	−0.0951267
$981$	−27.4733	−0.877157
$982$	−12.4935	−0.398684
$983$	16.5376	0.527467	0.263734	−	0.964596i	$-0.415046\pi$
$983$	16.5376	0.527467	0.263734	+	0.964596i	$0.415046\pi$
$984$	4.36035	0.139003
$985$	−71.1281	−2.26633
$986$	−5.58482	−0.177857
$987$	9.63656	0.306735
$988$	−0.318618	−0.0101366
$989$	0.131378	0.00417758
$990$	−22.6253	−0.719080
$991$	−13.8339	−0.439448	−0.219724	−	0.975562i	$-0.570516\pi$
$991$	−13.8339	−0.439448	−0.219724	+	0.975562i	$0.570516\pi$
$992$	−5.66260	−0.179788
$993$	−39.7281	−1.26073
$994$	−0.739152	−0.0234445
$995$	−63.2937	−2.00655
$996$	7.61722	0.241361
$997$	22.4176	0.709974	0.354987	−	0.934871i	$-0.384485\pi$
$997$	22.4176	0.709974	0.354987	+	0.934871i	$0.384485\pi$
$998$	7.84699	0.248392
$999$	60.8913	1.92651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.15	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.15	✓	24	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.20386 q^{3} +1.00000 q^{4} -2.97794 q^{5} -1.20386 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.55072 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.20386 q^{3} +1.00000 q^{4} -2.97794 q^{5} -1.20386 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.55072 q^{9} +2.97794 q^{10} +4.89942 q^{11} +1.20386 q^{12} +0.849112 q^{13} +1.00000 q^{14} -3.58501 q^{15} +1.00000 q^{16} +0.911913 q^{17} +1.55072 q^{18} -0.375237 q^{19} -2.97794 q^{20} -1.20386 q^{21} -4.89942 q^{22} -0.153613 q^{23} -1.20386 q^{24} +3.86810 q^{25} -0.849112 q^{26} -5.47843 q^{27} -1.00000 q^{28} +6.12429 q^{29} +3.58501 q^{30} +5.66260 q^{31} -1.00000 q^{32} +5.89821 q^{33} -0.911913 q^{34} +2.97794 q^{35} -1.55072 q^{36} -11.1147 q^{37} +0.375237 q^{38} +1.02221 q^{39} +2.97794 q^{40} -3.62198 q^{41} +1.20386 q^{42} -0.855256 q^{43} +4.89942 q^{44} +4.61796 q^{45} +0.153613 q^{46} -8.00473 q^{47} +1.20386 q^{48} +1.00000 q^{49} -3.86810 q^{50} +1.09781 q^{51} +0.849112 q^{52} -3.06278 q^{53} +5.47843 q^{54} -14.5902 q^{55} +1.00000 q^{56} -0.451732 q^{57} -6.12429 q^{58} +9.27497 q^{59} -3.58501 q^{60} +6.50346 q^{61} -5.66260 q^{62} +1.55072 q^{63} +1.00000 q^{64} -2.52860 q^{65} -5.89821 q^{66} -4.31228 q^{67} +0.911913 q^{68} -0.184928 q^{69} -2.97794 q^{70} -0.739152 q^{71} +1.55072 q^{72} -8.19489 q^{73} +11.1147 q^{74} +4.65665 q^{75} -0.375237 q^{76} -4.89942 q^{77} -1.02221 q^{78} +17.0294 q^{79} -2.97794 q^{80} -1.94308 q^{81} +3.62198 q^{82} +6.32734 q^{83} -1.20386 q^{84} -2.71562 q^{85} +0.855256 q^{86} +7.37278 q^{87} -4.89942 q^{88} +0.101939 q^{89} -4.61796 q^{90} -0.849112 q^{91} -0.153613 q^{92} +6.81696 q^{93} +8.00473 q^{94} +1.11743 q^{95} -1.20386 q^{96} +4.01210 q^{97} -1.00000 q^{98} -7.59766 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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