LMFDB - Embedded newform 6034.2.a.n.1.5

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			1.5
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.91791 q^{3} +1.00000 q^{4} +0.374562 q^{5} +1.91791 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.678384 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.91791 q^{3} +1.00000 q^{4} +0.374562 q^{5} +1.91791 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.678384 q^{9} -0.374562 q^{10} -1.13103 q^{11} -1.91791 q^{12} +0.0849041 q^{13} +1.00000 q^{14} -0.718376 q^{15} +1.00000 q^{16} -4.64310 q^{17} -0.678384 q^{18} +4.04521 q^{19} +0.374562 q^{20} +1.91791 q^{21} +1.13103 q^{22} +0.619341 q^{23} +1.91791 q^{24} -4.85970 q^{25} -0.0849041 q^{26} +4.45265 q^{27} -1.00000 q^{28} +8.48928 q^{29} +0.718376 q^{30} -2.63740 q^{31} -1.00000 q^{32} +2.16922 q^{33} +4.64310 q^{34} -0.374562 q^{35} +0.678384 q^{36} -5.53403 q^{37} -4.04521 q^{38} -0.162839 q^{39} -0.374562 q^{40} +0.897076 q^{41} -1.91791 q^{42} -3.73812 q^{43} -1.13103 q^{44} +0.254097 q^{45} -0.619341 q^{46} -12.8473 q^{47} -1.91791 q^{48} +1.00000 q^{49} +4.85970 q^{50} +8.90506 q^{51} +0.0849041 q^{52} -9.09566 q^{53} -4.45265 q^{54} -0.423641 q^{55} +1.00000 q^{56} -7.75835 q^{57} -8.48928 q^{58} +1.43086 q^{59} -0.718376 q^{60} +7.69562 q^{61} +2.63740 q^{62} -0.678384 q^{63} +1.00000 q^{64} +0.0318018 q^{65} -2.16922 q^{66} -4.04819 q^{67} -4.64310 q^{68} -1.18784 q^{69} +0.374562 q^{70} +10.9888 q^{71} -0.678384 q^{72} +0.0269734 q^{73} +5.53403 q^{74} +9.32048 q^{75} +4.04521 q^{76} +1.13103 q^{77} +0.162839 q^{78} -3.39249 q^{79} +0.374562 q^{80} -10.5749 q^{81} -0.897076 q^{82} +0.337072 q^{83} +1.91791 q^{84} -1.73913 q^{85} +3.73812 q^{86} -16.2817 q^{87} +1.13103 q^{88} -3.97680 q^{89} -0.254097 q^{90} -0.0849041 q^{91} +0.619341 q^{92} +5.05829 q^{93} +12.8473 q^{94} +1.51518 q^{95} +1.91791 q^{96} -5.17035 q^{97} -1.00000 q^{98} -0.767274 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.91791	−1.10731	−0.553653	−	0.832747i	$-0.686767\pi$
$3$	−1.91791	−1.10731	−0.553653	+	0.832747i	$0.686767\pi$
$4$	1.00000	0.500000
$5$	0.374562	0.167509	0.0837545	−	0.996486i	$-0.473309\pi$
$5$	0.374562	0.167509	0.0837545	+	0.996486i	$0.473309\pi$
$6$	1.91791	0.782984
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0.678384	0.226128
$10$	−0.374562	−0.118447
$11$	−1.13103	−0.341019	−0.170509	−	0.985356i	$-0.554541\pi$
$11$	−1.13103	−0.341019	−0.170509	+	0.985356i	$0.554541\pi$
$12$	−1.91791	−0.553653
$13$	0.0849041	0.0235482	0.0117741	−	0.999931i	$-0.496252\pi$
$13$	0.0849041	0.0235482	0.0117741	+	0.999931i	$0.496252\pi$
$14$	1.00000	0.267261
$15$	−0.718376	−0.185484
$16$	1.00000	0.250000
$17$	−4.64310	−1.12612	−0.563059	−	0.826417i	$-0.690376\pi$
$17$	−4.64310	−1.12612	−0.563059	+	0.826417i	$0.690376\pi$
$18$	−0.678384	−0.159897
$19$	4.04521	0.928034	0.464017	−	0.885826i	$-0.346408\pi$
$19$	4.04521	0.928034	0.464017	+	0.885826i	$0.346408\pi$
$20$	0.374562	0.0837545
$21$	1.91791	0.418523
$22$	1.13103	0.241137
$23$	0.619341	0.129141	0.0645707	−	0.997913i	$-0.479432\pi$
$23$	0.619341	0.129141	0.0645707	+	0.997913i	$0.479432\pi$
$24$	1.91791	0.391492
$25$	−4.85970	−0.971941
$26$	−0.0849041	−0.0166511
$27$	4.45265	0.856914
$28$	−1.00000	−0.188982
$29$	8.48928	1.57642	0.788210	−	0.615406i	$-0.211008\pi$
$29$	8.48928	1.57642	0.788210	+	0.615406i	$0.211008\pi$
$30$	0.718376	0.131157
$31$	−2.63740	−0.473690	−0.236845	−	0.971547i	$-0.576113\pi$
$31$	−2.63740	−0.473690	−0.236845	+	0.971547i	$0.576113\pi$
$32$	−1.00000	−0.176777
$33$	2.16922	0.377612
$34$	4.64310	0.796286
$35$	−0.374562	−0.0633125
$36$	0.678384	0.113064
$37$	−5.53403	−0.909790	−0.454895	−	0.890545i	$-0.650323\pi$
$37$	−5.53403	−0.909790	−0.454895	+	0.890545i	$0.650323\pi$
$38$	−4.04521	−0.656219
$39$	−0.162839	−0.0260750
$40$	−0.374562	−0.0592234
$41$	0.897076	0.140100	0.0700499	−	0.997543i	$-0.477684\pi$
$41$	0.897076	0.140100	0.0700499	+	0.997543i	$0.477684\pi$
$42$	−1.91791	−0.295940
$43$	−3.73812	−0.570058	−0.285029	−	0.958519i	$-0.592003\pi$
$43$	−3.73812	−0.570058	−0.285029	+	0.958519i	$0.592003\pi$
$44$	−1.13103	−0.170509
$45$	0.254097	0.0378785
$46$	−0.619341	−0.0913168
$47$	−12.8473	−1.87396	−0.936982	−	0.349377i	$-0.886393\pi$
$47$	−12.8473	−1.87396	−0.936982	+	0.349377i	$0.886393\pi$
$48$	−1.91791	−0.276827
$49$	1.00000	0.142857
$50$	4.85970	0.687266
$51$	8.90506	1.24696
$52$	0.0849041	0.0117741
$53$	−9.09566	−1.24939	−0.624693	−	0.780871i	$-0.714776\pi$
$53$	−9.09566	−1.24939	−0.624693	+	0.780871i	$0.714776\pi$
$54$	−4.45265	−0.605929
$55$	−0.423641	−0.0571237
$56$	1.00000	0.133631
$57$	−7.75835	−1.02762
$58$	−8.48928	−1.11470
$59$	1.43086	0.186282	0.0931409	−	0.995653i	$-0.470309\pi$
$59$	1.43086	0.186282	0.0931409	+	0.995653i	$0.470309\pi$
$60$	−0.718376	−0.0927419
$61$	7.69562	0.985323	0.492662	−	0.870221i	$-0.336024\pi$
$61$	7.69562	0.985323	0.492662	+	0.870221i	$0.336024\pi$
$62$	2.63740	0.334950
$63$	−0.678384	−0.0854684
$64$	1.00000	0.125000
$65$	0.0318018	0.00394453
$66$	−2.16922	−0.267012
$67$	−4.04819	−0.494565	−0.247282	−	0.968943i	$-0.579538\pi$
$67$	−4.04819	−0.494565	−0.247282	+	0.968943i	$0.579538\pi$
$68$	−4.64310	−0.563059
$69$	−1.18784	−0.142999
$70$	0.374562	0.0447687
$71$	10.9888	1.30413	0.652064	−	0.758164i	$-0.273903\pi$
$71$	10.9888	1.30413	0.652064	+	0.758164i	$0.273903\pi$
$72$	−0.678384	−0.0799484
$73$	0.0269734	0.00315700	0.00157850	−	0.999999i	$-0.499498\pi$
$73$	0.0269734	0.00315700	0.00157850	+	0.999999i	$0.499498\pi$
$74$	5.53403	0.643318
$75$	9.32048	1.07624
$76$	4.04521	0.464017
$77$	1.13103	0.128893
$78$	0.162839	0.0184378
$79$	−3.39249	−0.381685	−0.190842	−	0.981621i	$-0.561122\pi$
$79$	−3.39249	−0.381685	−0.190842	+	0.981621i	$0.561122\pi$
$80$	0.374562	0.0418773
$81$	−10.5749	−1.17499
$82$	−0.897076	−0.0990655
$83$	0.337072	0.0369985	0.0184992	−	0.999829i	$-0.494111\pi$
$83$	0.337072	0.0369985	0.0184992	+	0.999829i	$0.494111\pi$
$84$	1.91791	0.209261
$85$	−1.73913	−0.188635
$86$	3.73812	0.403092
$87$	−16.2817	−1.74558
$88$	1.13103	0.120568
$89$	−3.97680	−0.421540	−0.210770	−	0.977536i	$-0.567597\pi$
$89$	−3.97680	−0.421540	−0.210770	+	0.977536i	$0.567597\pi$
$90$	−0.254097	−0.0267841
$91$	−0.0849041	−0.00890037
$92$	0.619341	0.0645707
$93$	5.05829	0.524520
$94$	12.8473	1.32509
$95$	1.51518	0.155454
$96$	1.91791	0.195746
$97$	−5.17035	−0.524970	−0.262485	−	0.964936i	$-0.584542\pi$
$97$	−5.17035	−0.524970	−0.262485	+	0.964936i	$0.584542\pi$
$98$	−1.00000	−0.101015
$99$	−0.767274	−0.0771139
$100$	−4.85970	−0.485970
$101$	8.50211	0.845992	0.422996	−	0.906132i	$-0.360978\pi$
$101$	8.50211	0.845992	0.422996	+	0.906132i	$0.360978\pi$
$102$	−8.90506	−0.881733
$103$	−12.1665	−1.19880	−0.599399	−	0.800450i	$-0.704594\pi$
$103$	−12.1665	−1.19880	−0.599399	+	0.800450i	$0.704594\pi$
$104$	−0.0849041	−0.00832553
$105$	0.718376	0.0701063
$106$	9.09566	0.883449
$107$	18.5559	1.79386	0.896932	−	0.442168i	$-0.145791\pi$
$107$	18.5559	1.79386	0.896932	+	0.442168i	$0.145791\pi$
$108$	4.45265	0.428457
$109$	12.8769	1.23338	0.616692	−	0.787205i	$-0.288473\pi$
$109$	12.8769	1.23338	0.616692	+	0.787205i	$0.288473\pi$
$110$	0.423641	0.0403926
$111$	10.6138	1.00742
$112$	−1.00000	−0.0944911
$113$	5.48435	0.515924	0.257962	−	0.966155i	$-0.416949\pi$
$113$	5.48435	0.515924	0.257962	+	0.966155i	$0.416949\pi$
$114$	7.75835	0.726636
$115$	0.231981	0.0216324
$116$	8.48928	0.788210
$117$	0.0575976	0.00532490
$118$	−1.43086	−0.131721
$119$	4.64310	0.425633
$120$	0.718376	0.0655784
$121$	−9.72077	−0.883706
$122$	−7.69562	−0.696729
$123$	−1.72051	−0.155133
$124$	−2.63740	−0.236845
$125$	−3.69307	−0.330318
$126$	0.678384	0.0604353
$127$	−1.16750	−0.103599	−0.0517993	−	0.998658i	$-0.516496\pi$
$127$	−1.16750	−0.103599	−0.0517993	+	0.998658i	$0.516496\pi$
$128$	−1.00000	−0.0883883
$129$	7.16938	0.631229
$130$	−0.0318018	−0.00278920
$131$	−17.0004	−1.48533	−0.742664	−	0.669664i	$-0.766438\pi$
$131$	−17.0004	−1.48533	−0.742664	+	0.669664i	$0.766438\pi$
$132$	2.16922	0.188806
$133$	−4.04521	−0.350764
$134$	4.04819	0.349710
$135$	1.66779	0.143541
$136$	4.64310	0.398143
$137$	−0.338549	−0.0289242	−0.0144621	−	0.999895i	$-0.504604\pi$
$137$	−0.338549	−0.0289242	−0.0144621	+	0.999895i	$0.504604\pi$
$138$	1.18784	0.101116
$139$	8.76034	0.743043	0.371521	−	0.928424i	$-0.378836\pi$
$139$	8.76034	0.743043	0.371521	+	0.928424i	$0.378836\pi$
$140$	−0.374562	−0.0316562
$141$	24.6399	2.07505
$142$	−10.9888	−0.922158
$143$	−0.0960292	−0.00803036
$144$	0.678384	0.0565320
$145$	3.17976	0.264065
$146$	−0.0269734	−0.00223234
$147$	−1.91791	−0.158187
$148$	−5.53403	−0.454895
$149$	−1.29509	−0.106098	−0.0530489	−	0.998592i	$-0.516894\pi$
$149$	−1.29509	−0.106098	−0.0530489	+	0.998592i	$0.516894\pi$
$150$	−9.32048	−0.761014
$151$	−20.9656	−1.70616	−0.853078	−	0.521783i	$-0.825267\pi$
$151$	−20.9656	−1.70616	−0.853078	+	0.521783i	$0.825267\pi$
$152$	−4.04521	−0.328110
$153$	−3.14981	−0.254647
$154$	−1.13103	−0.0911411
$155$	−0.987867	−0.0793474
$156$	−0.162839	−0.0130375
$157$	2.38855	0.190627	0.0953135	−	0.995447i	$-0.469615\pi$
$157$	2.38855	0.190627	0.0953135	+	0.995447i	$0.469615\pi$
$158$	3.39249	0.269892
$159$	17.4447	1.38345
$160$	−0.374562	−0.0296117
$161$	−0.619341	−0.0488109
$162$	10.5749	0.830846
$163$	10.2810	0.805274	0.402637	−	0.915360i	$-0.368094\pi$
$163$	10.2810	0.805274	0.402637	+	0.915360i	$0.368094\pi$
$164$	0.897076	0.0700499
$165$	0.812505	0.0632535
$166$	−0.337072	−0.0261619
$167$	21.2172	1.64183	0.820917	−	0.571048i	$-0.193463\pi$
$167$	21.2172	1.64183	0.820917	+	0.571048i	$0.193463\pi$
$168$	−1.91791	−0.147970
$169$	−12.9928	−0.999445
$170$	1.73913	0.133385
$171$	2.74421	0.209855
$172$	−3.73812	−0.285029
$173$	−3.47327	−0.264068	−0.132034	−	0.991245i	$-0.542151\pi$
$173$	−3.47327	−0.264068	−0.132034	+	0.991245i	$0.542151\pi$
$174$	16.2817	1.23431
$175$	4.85970	0.367359
$176$	−1.13103	−0.0852547
$177$	−2.74426	−0.206271
$178$	3.97680	0.298074
$179$	−8.61150	−0.643654	−0.321827	−	0.946799i	$-0.604297\pi$
$179$	−8.61150	−0.643654	−0.321827	+	0.946799i	$0.604297\pi$
$180$	0.254097	0.0189392
$181$	−18.3747	−1.36578	−0.682891	−	0.730521i	$-0.739277\pi$
$181$	−18.3747	−1.36578	−0.682891	+	0.730521i	$0.739277\pi$
$182$	0.0849041	0.00629351
$183$	−14.7595	−1.09106
$184$	−0.619341	−0.0456584
$185$	−2.07284	−0.152398
$186$	−5.05829	−0.370892
$187$	5.25149	0.384027
$188$	−12.8473	−0.936982
$189$	−4.45265	−0.323883
$190$	−1.51518	−0.109923
$191$	−5.44412	−0.393922	−0.196961	−	0.980411i	$-0.563107\pi$
$191$	−5.44412	−0.393922	−0.196961	+	0.980411i	$0.563107\pi$
$192$	−1.91791	−0.138413
$193$	−9.57267	−0.689056	−0.344528	−	0.938776i	$-0.611961\pi$
$193$	−9.57267	−0.689056	−0.344528	+	0.938776i	$0.611961\pi$
$194$	5.17035	0.371210
$195$	−0.0609930	−0.00436780
$196$	1.00000	0.0714286
$197$	−18.7361	−1.33489	−0.667445	−	0.744659i	$-0.732612\pi$
$197$	−18.7361	−1.33489	−0.667445	+	0.744659i	$0.732612\pi$
$198$	0.767274	0.0545278
$199$	11.0058	0.780178	0.390089	−	0.920777i	$-0.372444\pi$
$199$	11.0058	0.780178	0.390089	+	0.920777i	$0.372444\pi$
$200$	4.85970	0.343633
$201$	7.76407	0.547635
$202$	−8.50211	−0.598207
$203$	−8.48928	−0.595831
$204$	8.90506	0.623479
$205$	0.336010	0.0234680
$206$	12.1665	0.847679
$207$	0.420151	0.0292025
$208$	0.0849041	0.00588704
$209$	−4.57526	−0.316477
$210$	−0.718376	−0.0495726
$211$	6.31098	0.434466	0.217233	−	0.976120i	$-0.430297\pi$
$211$	6.31098	0.434466	0.217233	+	0.976120i	$0.430297\pi$
$212$	−9.09566	−0.624693
$213$	−21.0755	−1.44407
$214$	−18.5559	−1.26845
$215$	−1.40016	−0.0954898
$216$	−4.45265	−0.302965
$217$	2.63740	0.179038
$218$	−12.8769	−0.872133
$219$	−0.0517326	−0.00349577
$220$	−0.423641	−0.0285619
$221$	−0.394218	−0.0265180
$222$	−10.6138	−0.712351
$223$	5.62649	0.376778	0.188389	−	0.982094i	$-0.439673\pi$
$223$	5.62649	0.376778	0.188389	+	0.982094i	$0.439673\pi$
$224$	1.00000	0.0668153
$225$	−3.29675	−0.219783
$226$	−5.48435	−0.364814
$227$	18.9786	1.25966	0.629828	−	0.776735i	$-0.283126\pi$
$227$	18.9786	1.25966	0.629828	+	0.776735i	$0.283126\pi$
$228$	−7.75835	−0.513809
$229$	11.8209	0.781147	0.390574	−	0.920572i	$-0.372277\pi$
$229$	11.8209	0.781147	0.390574	+	0.920572i	$0.372277\pi$
$230$	−0.231981	−0.0152964
$231$	−2.16922	−0.142724
$232$	−8.48928	−0.557349
$233$	27.5762	1.80657	0.903287	−	0.429037i	$-0.141147\pi$
$233$	27.5762	1.80657	0.903287	+	0.429037i	$0.141147\pi$
$234$	−0.0575976	−0.00376527
$235$	−4.81209	−0.313906
$236$	1.43086	0.0931409
$237$	6.50649	0.422642
$238$	−4.64310	−0.300968
$239$	−6.76335	−0.437485	−0.218742	−	0.975783i	$-0.570195\pi$
$239$	−6.76335	−0.437485	−0.218742	+	0.975783i	$0.570195\pi$
$240$	−0.718376	−0.0463710
$241$	−19.1051	−1.23067	−0.615334	−	0.788266i	$-0.710979\pi$
$241$	−19.1051	−1.23067	−0.615334	+	0.788266i	$0.710979\pi$
$242$	9.72077	0.624875
$243$	6.92385	0.444165
$244$	7.69562	0.492662
$245$	0.374562	0.0239299
$246$	1.72051	0.109696
$247$	0.343455	0.0218535
$248$	2.63740	0.167475
$249$	−0.646474	−0.0409686
$250$	3.69307	0.233570
$251$	14.2456	0.899177	0.449589	−	0.893236i	$-0.351571\pi$
$251$	14.2456	0.899177	0.449589	+	0.893236i	$0.351571\pi$
$252$	−0.678384	−0.0427342
$253$	−0.700493	−0.0440396
$254$	1.16750	0.0732553
$255$	3.33549	0.208877
$256$	1.00000	0.0625000
$257$	−29.8277	−1.86060	−0.930300	−	0.366799i	$-0.880454\pi$
$257$	−29.8277	−1.86060	−0.930300	+	0.366799i	$0.880454\pi$
$258$	−7.16938	−0.446346
$259$	5.53403	0.343868
$260$	0.0318018	0.00197226
$261$	5.75900	0.356473
$262$	17.0004	1.05029
$263$	1.39805	0.0862072	0.0431036	−	0.999071i	$-0.486275\pi$
$263$	1.39805	0.0862072	0.0431036	+	0.999071i	$0.486275\pi$
$264$	−2.16922	−0.133506
$265$	−3.40689	−0.209283
$266$	4.04521	0.248028
$267$	7.62716	0.466775
$268$	−4.04819	−0.247282
$269$	3.95250	0.240988	0.120494	−	0.992714i	$-0.461552\pi$
$269$	3.95250	0.240988	0.120494	+	0.992714i	$0.461552\pi$
$270$	−1.66779	−0.101499
$271$	13.4976	0.819923	0.409961	−	0.912103i	$-0.365542\pi$
$271$	13.4976	0.819923	0.409961	+	0.912103i	$0.365542\pi$
$272$	−4.64310	−0.281530
$273$	0.162839	0.00985544
$274$	0.338549	0.0204525
$275$	5.49648	0.331450
$276$	−1.18784	−0.0714996
$277$	9.78792	0.588099	0.294050	−	0.955790i	$-0.404997\pi$
$277$	9.78792	0.588099	0.294050	+	0.955790i	$0.404997\pi$
$278$	−8.76034	−0.525410
$279$	−1.78917	−0.107115
$280$	0.374562	0.0223843
$281$	27.7828	1.65738	0.828691	−	0.559707i	$-0.189086\pi$
$281$	27.7828	1.65738	0.828691	+	0.559707i	$0.189086\pi$
$282$	−24.6399	−1.46728
$283$	29.3970	1.74747	0.873736	−	0.486401i	$-0.161691\pi$
$283$	29.3970	1.74747	0.873736	+	0.486401i	$0.161691\pi$
$284$	10.9888	0.652064
$285$	−2.90598	−0.172135
$286$	0.0960292	0.00567832
$287$	−0.897076	−0.0529527
$288$	−0.678384	−0.0399742
$289$	4.55841	0.268142
$290$	−3.17976	−0.186722
$291$	9.91628	0.581303
$292$	0.0269734	0.00157850
$293$	13.0696	0.763532	0.381766	−	0.924259i	$-0.375316\pi$
$293$	13.0696	0.763532	0.381766	+	0.924259i	$0.375316\pi$
$294$	1.91791	0.111855
$295$	0.535944	0.0312039
$296$	5.53403	0.321659
$297$	−5.03609	−0.292224
$298$	1.29509	0.0750224
$299$	0.0525845	0.00304104
$300$	9.32048	0.538118
$301$	3.73812	0.215462
$302$	20.9656	1.20643
$303$	−16.3063	−0.936773
$304$	4.04521	0.232009
$305$	2.88248	0.165051
$306$	3.14981	0.180063
$307$	−9.13612	−0.521426	−0.260713	−	0.965416i	$-0.583958\pi$
$307$	−9.13612	−0.521426	−0.260713	+	0.965416i	$0.583958\pi$
$308$	1.13103	0.0644465
$309$	23.3342	1.32744
$310$	0.987867	0.0561071
$311$	11.1115	0.630077	0.315038	−	0.949079i	$-0.397983\pi$
$311$	11.1115	0.630077	0.315038	+	0.949079i	$0.397983\pi$
$312$	0.162839	0.00921892
$313$	5.66679	0.320306	0.160153	−	0.987092i	$-0.448801\pi$
$313$	5.66679	0.320306	0.160153	+	0.987092i	$0.448801\pi$
$314$	−2.38855	−0.134794
$315$	−0.254097	−0.0143167
$316$	−3.39249	−0.190842
$317$	0.787739	0.0442438	0.0221219	−	0.999755i	$-0.492958\pi$
$317$	0.787739	0.0442438	0.0221219	+	0.999755i	$0.492958\pi$
$318$	−17.4447	−0.978249
$319$	−9.60164	−0.537589
$320$	0.374562	0.0209386
$321$	−35.5885	−1.98636
$322$	0.619341	0.0345145
$323$	−18.7823	−1.04508
$324$	−10.5749	−0.587497
$325$	−0.412609	−0.0228874
$326$	−10.2810	−0.569415
$327$	−24.6967	−1.36573
$328$	−0.897076	−0.0495327
$329$	12.8473	0.708292
$330$	−0.812505	−0.0447270
$331$	15.6030	0.857616	0.428808	−	0.903396i	$-0.358934\pi$
$331$	15.6030	0.857616	0.428808	+	0.903396i	$0.358934\pi$
$332$	0.337072	0.0184992
$333$	−3.75420	−0.205729
$334$	−21.2172	−1.16095
$335$	−1.51630	−0.0828441
$336$	1.91791	0.104631
$337$	−24.5838	−1.33917	−0.669583	−	0.742737i	$-0.733527\pi$
$337$	−24.5838	−1.33917	−0.669583	+	0.742737i	$0.733527\pi$
$338$	12.9928	0.706715
$339$	−10.5185	−0.571286
$340$	−1.73913	−0.0943175
$341$	2.98298	0.161537
$342$	−2.74421	−0.148390
$343$	−1.00000	−0.0539949
$344$	3.73812	0.201546
$345$	−0.444919	−0.0239537
$346$	3.47327	0.186724
$347$	−1.09594	−0.0588331	−0.0294165	−	0.999567i	$-0.509365\pi$
$347$	−1.09594	−0.0588331	−0.0294165	+	0.999567i	$0.509365\pi$
$348$	−16.2817	−0.872790
$349$	18.6415	0.997855	0.498928	−	0.866644i	$-0.333727\pi$
$349$	18.6415	0.997855	0.498928	+	0.866644i	$0.333727\pi$
$350$	−4.85970	−0.259762
$351$	0.378048	0.0201787
$352$	1.13103	0.0602842
$353$	17.6943	0.941771	0.470886	−	0.882194i	$-0.343934\pi$
$353$	17.6943	0.941771	0.470886	+	0.882194i	$0.343934\pi$
$354$	2.74426	0.145856
$355$	4.11598	0.218453
$356$	−3.97680	−0.210770
$357$	−8.90506	−0.471306
$358$	8.61150	0.455132
$359$	27.5567	1.45439	0.727194	−	0.686432i	$-0.240824\pi$
$359$	27.5567	1.45439	0.727194	+	0.686432i	$0.240824\pi$
$360$	−0.254097	−0.0133921
$361$	−2.63629	−0.138752
$362$	18.3747	0.965753
$363$	18.6436	0.978534
$364$	−0.0849041	−0.00445018
$365$	0.0101032	0.000528826 0
$366$	14.7595	0.771492
$367$	24.6436	1.28638	0.643192	−	0.765705i	$-0.277610\pi$
$367$	24.6436	1.28638	0.643192	+	0.765705i	$0.277610\pi$
$368$	0.619341	0.0322854
$369$	0.608562	0.0316805
$370$	2.07284	0.107762
$371$	9.09566	0.472223
$372$	5.05829	0.262260
$373$	2.78023	0.143955	0.0719774	−	0.997406i	$-0.477069\pi$
$373$	2.78023	0.143955	0.0719774	+	0.997406i	$0.477069\pi$
$374$	−5.25149	−0.271548
$375$	7.08297	0.365763
$376$	12.8473	0.662547
$377$	0.720775	0.0371218
$378$	4.45265	0.229020
$379$	−18.3802	−0.944128	−0.472064	−	0.881564i	$-0.656491\pi$
$379$	−18.3802	−0.944128	−0.472064	+	0.881564i	$0.656491\pi$
$380$	1.51518	0.0777271
$381$	2.23916	0.114715
$382$	5.44412	0.278545
$383$	12.9687	0.662671	0.331336	−	0.943513i	$-0.392501\pi$
$383$	12.9687	0.662671	0.331336	+	0.943513i	$0.392501\pi$
$384$	1.91791	0.0978730
$385$	0.423641	0.0215907
$386$	9.57267	0.487236
$387$	−2.53588	−0.128906
$388$	−5.17035	−0.262485
$389$	−9.22742	−0.467849	−0.233924	−	0.972255i	$-0.575157\pi$
$389$	−9.22742	−0.467849	−0.233924	+	0.972255i	$0.575157\pi$
$390$	0.0609930	0.00308850
$391$	−2.87566	−0.145429
$392$	−1.00000	−0.0505076
$393$	32.6052	1.64471
$394$	18.7361	0.943910
$395$	−1.27070	−0.0639356
$396$	−0.767274	−0.0385570
$397$	−5.31928	−0.266967	−0.133484	−	0.991051i	$-0.542616\pi$
$397$	−5.31928	−0.266967	−0.133484	+	0.991051i	$0.542616\pi$
$398$	−11.0058	−0.551669
$399$	7.75835	0.388403
$400$	−4.85970	−0.242985
$401$	−20.4634	−1.02189	−0.510947	−	0.859612i	$-0.670705\pi$
$401$	−20.4634	−1.02189	−0.510947	+	0.859612i	$0.670705\pi$
$402$	−7.76407	−0.387236
$403$	−0.223926	−0.0111545
$404$	8.50211	0.422996
$405$	−3.96097	−0.196822
$406$	8.48928	0.421316
$407$	6.25916	0.310255
$408$	−8.90506	−0.440866
$409$	0.0314586	0.00155553	0.000777764	−	1.00000i	$-0.499752\pi$
$409$	0.0314586	0.00155553	0.000777764		1.00000i	$0.499752\pi$
$410$	−0.336010	−0.0165944
$411$	0.649306	0.0320279
$412$	−12.1665	−0.599399
$413$	−1.43086	−0.0704079
$414$	−0.420151	−0.0206493
$415$	0.126254	0.00619757
$416$	−0.0849041	−0.00416277
$417$	−16.8016	−0.822776
$418$	4.57526	0.223783
$419$	13.8327	0.675770	0.337885	−	0.941187i	$-0.390289\pi$
$419$	13.8327	0.675770	0.337885	+	0.941187i	$0.390289\pi$
$420$	0.718376	0.0350532
$421$	−11.1791	−0.544838	−0.272419	−	0.962179i	$-0.587824\pi$
$421$	−11.1791	−0.544838	−0.272419	+	0.962179i	$0.587824\pi$
$422$	−6.31098	−0.307214
$423$	−8.71538	−0.423756
$424$	9.09566	0.441724
$425$	22.5641	1.09452
$426$	21.0755	1.02111
$427$	−7.69562	−0.372417
$428$	18.5559	0.896932
$429$	0.184175	0.00889207
$430$	1.40016	0.0675215
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	4.45265	0.214228
$433$	12.5297	0.602137	0.301068	−	0.953603i	$-0.402657\pi$
$433$	12.5297	0.602137	0.301068	+	0.953603i	$0.402657\pi$
$434$	−2.63740	−0.126599
$435$	−6.09850	−0.292401
$436$	12.8769	0.616692
$437$	2.50536	0.119848
$438$	0.0517326	0.00247188
$439$	16.1550	0.771034	0.385517	−	0.922701i	$-0.374023\pi$
$439$	16.1550	0.771034	0.385517	+	0.922701i	$0.374023\pi$
$440$	0.423641	0.0201963
$441$	0.678384	0.0323040
$442$	0.394218	0.0187511
$443$	20.8897	0.992499	0.496250	−	0.868180i	$-0.334710\pi$
$443$	20.8897	0.992499	0.496250	+	0.868180i	$0.334710\pi$
$444$	10.6138	0.503708
$445$	−1.48956	−0.0706118
$446$	−5.62649	−0.266422
$447$	2.48386	0.117483
$448$	−1.00000	−0.0472456
$449$	−11.4910	−0.542292	−0.271146	−	0.962538i	$-0.587403\pi$
$449$	−11.4910	−0.542292	−0.271146	+	0.962538i	$0.587403\pi$
$450$	3.29675	0.155410
$451$	−1.01462	−0.0477766
$452$	5.48435	0.257962
$453$	40.2102	1.88924
$454$	−18.9786	−0.890711
$455$	−0.0318018	−0.00149089
$456$	7.75835	0.363318
$457$	−3.51310	−0.164336	−0.0821678	−	0.996619i	$-0.526184\pi$
$457$	−3.51310	−0.164336	−0.0821678	+	0.996619i	$0.526184\pi$
$458$	−11.8209	−0.552355
$459$	−20.6741	−0.964986
$460$	0.231981	0.0108162
$461$	14.4346	0.672286	0.336143	−	0.941811i	$-0.390877\pi$
$461$	14.4346	0.672286	0.336143	+	0.941811i	$0.390877\pi$
$462$	2.16922	0.100921
$463$	23.4921	1.09177	0.545884	−	0.837860i	$-0.316194\pi$
$463$	23.4921	1.09177	0.545884	+	0.837860i	$0.316194\pi$
$464$	8.48928	0.394105
$465$	1.89464	0.0878619
$466$	−27.5762	−1.27744
$467$	23.6821	1.09588	0.547940	−	0.836518i	$-0.315412\pi$
$467$	23.6821	1.09588	0.547940	+	0.836518i	$0.315412\pi$
$468$	0.0575976	0.00266245
$469$	4.04819	0.186928
$470$	4.81209	0.221965
$471$	−4.58102	−0.211082
$472$	−1.43086	−0.0658606
$473$	4.22793	0.194400
$474$	−6.50649	−0.298853
$475$	−19.6585	−0.901994
$476$	4.64310	0.212816
$477$	−6.17036	−0.282521
$478$	6.76335	0.309348
$479$	14.7311	0.673081	0.336540	−	0.941669i	$-0.390743\pi$
$479$	14.7311	0.673081	0.336540	+	0.941669i	$0.390743\pi$
$480$	0.718376	0.0327892
$481$	−0.469862	−0.0214239
$482$	19.1051	0.870214
$483$	1.18784	0.0540486
$484$	−9.72077	−0.441853
$485$	−1.93662	−0.0879372
$486$	−6.92385	−0.314072
$487$	−26.0270	−1.17940	−0.589698	−	0.807624i	$-0.700753\pi$
$487$	−26.0270	−1.17940	−0.589698	+	0.807624i	$0.700753\pi$
$488$	−7.69562	−0.348364
$489$	−19.7181	−0.891685
$490$	−0.374562	−0.0169210
$491$	−12.4349	−0.561180	−0.280590	−	0.959828i	$-0.590530\pi$
$491$	−12.4349	−0.561180	−0.280590	+	0.959828i	$0.590530\pi$
$492$	−1.72051	−0.0775667
$493$	−39.4166	−1.77524
$494$	−0.343455	−0.0154528
$495$	−0.287391	−0.0129173
$496$	−2.63740	−0.118423
$497$	−10.9888	−0.492914
$498$	0.646474	0.0289692
$499$	35.7961	1.60245	0.801227	−	0.598360i	$-0.204181\pi$
$499$	35.7961	1.60245	0.801227	+	0.598360i	$0.204181\pi$
$500$	−3.69307	−0.165159
$501$	−40.6926	−1.81801
$502$	−14.2456	−0.635814
$503$	39.5513	1.76350	0.881752	−	0.471713i	$-0.156364\pi$
$503$	39.5513	1.76350	0.881752	+	0.471713i	$0.156364\pi$
$504$	0.678384	0.0302176
$505$	3.18457	0.141711
$506$	0.700493	0.0311407
$507$	24.9190	1.10669
$508$	−1.16750	−0.0517993
$509$	−7.82845	−0.346990	−0.173495	−	0.984835i	$-0.555506\pi$
$509$	−7.82845	−0.346990	−0.173495	+	0.984835i	$0.555506\pi$
$510$	−3.33549	−0.147698
$511$	−0.0269734	−0.00119323
$512$	−1.00000	−0.0441942
$513$	18.0119	0.795245
$514$	29.8277	1.31564
$515$	−4.55709	−0.200810
$516$	7.16938	0.315614
$517$	14.5306	0.639057
$518$	−5.53403	−0.243152
$519$	6.66142	0.292404
$520$	−0.0318018	−0.00139460
$521$	3.29042	0.144156	0.0720781	−	0.997399i	$-0.477037\pi$
$521$	3.29042	0.144156	0.0720781	+	0.997399i	$0.477037\pi$
$522$	−5.75900	−0.252064
$523$	22.9420	1.00318	0.501591	−	0.865105i	$-0.332748\pi$
$523$	22.9420	1.00318	0.501591	+	0.865105i	$0.332748\pi$
$524$	−17.0004	−0.742664
$525$	−9.32048	−0.406779
$526$	−1.39805	−0.0609577
$527$	12.2457	0.533431
$528$	2.16922	0.0944031
$529$	−22.6164	−0.983322
$530$	3.40689	0.147986
$531$	0.970672	0.0421236
$532$	−4.04521	−0.175382
$533$	0.0761654	0.00329909
$534$	−7.62716	−0.330059
$535$	6.95032	0.300488
$536$	4.04819	0.174855
$537$	16.5161	0.712722
$538$	−3.95250	−0.170405
$539$	−1.13103	−0.0487170
$540$	1.66779	0.0717704
$541$	19.9708	0.858610	0.429305	−	0.903160i	$-0.358759\pi$
$541$	19.9708	0.858610	0.429305	+	0.903160i	$0.358759\pi$
$542$	−13.4976	−0.579773
$543$	35.2411	1.51234
$544$	4.64310	0.199071
$545$	4.82319	0.206603
$546$	−0.162839	−0.00696885
$547$	18.2878	0.781931	0.390966	−	0.920405i	$-0.372141\pi$
$547$	18.2878	0.781931	0.390966	+	0.920405i	$0.372141\pi$
$548$	−0.338549	−0.0144621
$549$	5.22059	0.222809
$550$	−5.49648	−0.234371
$551$	34.3409	1.46297
$552$	1.18784	0.0505578
$553$	3.39249	0.144263
$554$	−9.78792	−0.415849
$555$	3.97552	0.168751
$556$	8.76034	0.371521
$557$	8.92322	0.378089	0.189045	−	0.981969i	$-0.439461\pi$
$557$	8.92322	0.378089	0.189045	+	0.981969i	$0.439461\pi$
$558$	1.78917	0.0757415
$559$	−0.317382	−0.0134238
$560$	−0.374562	−0.0158281
$561$	−10.0719	−0.425236
$562$	−27.7828	−1.17195
$563$	−3.42778	−0.144464	−0.0722318	−	0.997388i	$-0.523012\pi$
$563$	−3.42778	−0.144464	−0.0722318	+	0.997388i	$0.523012\pi$
$564$	24.6399	1.03753
$565$	2.05423	0.0864220
$566$	−29.3970	−1.23565
$567$	10.5749	0.444106
$568$	−10.9888	−0.461079
$569$	35.6879	1.49611	0.748057	−	0.663635i	$-0.230987\pi$
$569$	35.6879	1.49611	0.748057	+	0.663635i	$0.230987\pi$
$570$	2.90598	0.121718
$571$	9.37967	0.392527	0.196263	−	0.980551i	$-0.437119\pi$
$571$	9.37967	0.392527	0.196263	+	0.980551i	$0.437119\pi$
$572$	−0.0960292	−0.00401518
$573$	10.4413	0.436193
$574$	0.897076	0.0374432
$575$	−3.00981	−0.125518
$576$	0.678384	0.0282660
$577$	−5.20382	−0.216638	−0.108319	−	0.994116i	$-0.534547\pi$
$577$	−5.20382	−0.216638	−0.108319	+	0.994116i	$0.534547\pi$
$578$	−4.55841	−0.189605
$579$	18.3595	0.762996
$580$	3.17976	0.132032
$581$	−0.337072	−0.0139841
$582$	−9.91628	−0.411043
$583$	10.2875	0.426064
$584$	−0.0269734	−0.00111617
$585$	0.0215738	0.000891969 0
$586$	−13.0696	−0.539899
$587$	39.5427	1.63210	0.816052	−	0.577979i	$-0.196158\pi$
$587$	39.5427	1.63210	0.816052	+	0.577979i	$0.196158\pi$
$588$	−1.91791	−0.0790933
$589$	−10.6688	−0.439601
$590$	−0.535944	−0.0220645
$591$	35.9341	1.47813
$592$	−5.53403	−0.227447
$593$	−23.0366	−0.945999	−0.472999	−	0.881063i	$-0.656829\pi$
$593$	−23.0366	−0.945999	−0.472999	+	0.881063i	$0.656829\pi$
$594$	5.03609	0.206633
$595$	1.73913	0.0712973
$596$	−1.29509	−0.0530489
$597$	−21.1081	−0.863897
$598$	−0.0525845	−0.00215034
$599$	12.6645	0.517458	0.258729	−	0.965950i	$-0.416696\pi$
$599$	12.6645	0.517458	0.258729	+	0.965950i	$0.416696\pi$
$600$	−9.32048	−0.380507
$601$	19.3119	0.787748	0.393874	−	0.919164i	$-0.371135\pi$
$601$	19.3119	0.787748	0.393874	+	0.919164i	$0.371135\pi$
$602$	−3.73812	−0.152354
$603$	−2.74623	−0.111835
$604$	−20.9656	−0.853078
$605$	−3.64103	−0.148029
$606$	16.3063	0.662398
$607$	−1.42969	−0.0580294	−0.0290147	−	0.999579i	$-0.509237\pi$
$607$	−1.42969	−0.0580294	−0.0290147	+	0.999579i	$0.509237\pi$
$608$	−4.04521	−0.164055
$609$	16.2817	0.659767
$610$	−2.88248	−0.116708
$611$	−1.09078	−0.0441284
$612$	−3.14981	−0.127323
$613$	−19.1170	−0.772128	−0.386064	−	0.922472i	$-0.626166\pi$
$613$	−19.1170	−0.772128	−0.386064	+	0.922472i	$0.626166\pi$
$614$	9.13612	0.368704
$615$	−0.644438	−0.0259862
$616$	−1.13103	−0.0455705
$617$	30.4341	1.22523	0.612615	−	0.790381i	$-0.290117\pi$
$617$	30.4341	1.22523	0.612615	+	0.790381i	$0.290117\pi$
$618$	−23.3342	−0.938640
$619$	30.4860	1.22534	0.612668	−	0.790340i	$-0.290096\pi$
$619$	30.4860	1.22534	0.612668	+	0.790340i	$0.290096\pi$
$620$	−0.987867	−0.0396737
$621$	2.75771	0.110663
$622$	−11.1115	−0.445532
$623$	3.97680	0.159327
$624$	−0.162839	−0.00651876
$625$	22.9152	0.916610
$626$	−5.66679	−0.226491
$627$	8.77494	0.350437
$628$	2.38855	0.0953135
$629$	25.6951	1.02453
$630$	0.254097	0.0101235
$631$	2.84517	0.113265	0.0566323	−	0.998395i	$-0.481964\pi$
$631$	2.84517	0.113265	0.0566323	+	0.998395i	$0.481964\pi$
$632$	3.39249	0.134946
$633$	−12.1039	−0.481087
$634$	−0.787739	−0.0312851
$635$	−0.437300	−0.0173537
$636$	17.4447	0.691726
$637$	0.0849041	0.00336402
$638$	9.60164	0.380133
$639$	7.45462	0.294900
$640$	−0.374562	−0.0148058
$641$	−16.0222	−0.632840	−0.316420	−	0.948619i	$-0.602481\pi$
$641$	−16.0222	−0.632840	−0.316420	+	0.948619i	$0.602481\pi$
$642$	35.5885	1.40457
$643$	−14.6429	−0.577460	−0.288730	−	0.957411i	$-0.593233\pi$
$643$	−14.6429	−0.577460	−0.288730	+	0.957411i	$0.593233\pi$
$644$	−0.619341	−0.0244054
$645$	2.68537	0.105737
$646$	18.7823	0.738981
$647$	−20.1457	−0.792010	−0.396005	−	0.918248i	$-0.629604\pi$
$647$	−20.1457	−0.792010	−0.396005	+	0.918248i	$0.629604\pi$
$648$	10.5749	0.415423
$649$	−1.61834	−0.0635256
$650$	0.412609	0.0161838
$651$	−5.05829	−0.198250
$652$	10.2810	0.402637
$653$	−35.7939	−1.40072	−0.700361	−	0.713788i	$-0.746978\pi$
$653$	−35.7939	−1.40072	−0.700361	+	0.713788i	$0.746978\pi$
$654$	24.6967	0.965719
$655$	−6.36768	−0.248806
$656$	0.897076	0.0350249
$657$	0.0182983	0.000713887 0
$658$	−12.8473	−0.500838
$659$	28.9817	1.12897	0.564483	−	0.825445i	$-0.309076\pi$
$659$	28.9817	1.12897	0.564483	+	0.825445i	$0.309076\pi$
$660$	0.812505	0.0316267
$661$	−21.7990	−0.847881	−0.423941	−	0.905690i	$-0.639353\pi$
$661$	−21.7990	−0.847881	−0.423941	+	0.905690i	$0.639353\pi$
$662$	−15.6030	−0.606426
$663$	0.756076	0.0293636
$664$	−0.337072	−0.0130809
$665$	−1.51518	−0.0587561
$666$	3.75420	0.145472
$667$	5.25776	0.203581
$668$	21.2172	0.820917
$669$	−10.7911	−0.417209
$670$	1.51630	0.0585796
$671$	−8.70399	−0.336014
$672$	−1.91791	−0.0739850
$673$	30.3942	1.17161	0.585806	−	0.810452i	$-0.300778\pi$
$673$	30.3942	1.17161	0.585806	+	0.810452i	$0.300778\pi$
$674$	24.5838	0.946933
$675$	−21.6386	−0.832869
$676$	−12.9928	−0.499723
$677$	−6.78209	−0.260657	−0.130328	−	0.991471i	$-0.541603\pi$
$677$	−6.78209	−0.260657	−0.130328	+	0.991471i	$0.541603\pi$
$678$	10.5185	0.403961
$679$	5.17035	0.198420
$680$	1.73913	0.0666925
$681$	−36.3993	−1.39482
$682$	−2.98298	−0.114224
$683$	5.71109	0.218529	0.109264	−	0.994013i	$-0.465150\pi$
$683$	5.71109	0.218529	0.109264	+	0.994013i	$0.465150\pi$
$684$	2.74421	0.104927
$685$	−0.126807	−0.00484506
$686$	1.00000	0.0381802
$687$	−22.6714	−0.864970
$688$	−3.73812	−0.142514
$689$	−0.772259	−0.0294207
$690$	0.444919	0.0169378
$691$	17.0937	0.650273	0.325137	−	0.945667i	$-0.394590\pi$
$691$	17.0937	0.650273	0.325137	+	0.945667i	$0.394590\pi$
$692$	−3.47327	−0.132034
$693$	0.767274	0.0291463
$694$	1.09594	0.0416013
$695$	3.28129	0.124466
$696$	16.2817	0.617156
$697$	−4.16522	−0.157769
$698$	−18.6415	−0.705590
$699$	−52.8886	−2.00043
$700$	4.85970	0.183680
$701$	26.0168	0.982642	0.491321	−	0.870979i	$-0.336514\pi$
$701$	26.0168	0.982642	0.491321	+	0.870979i	$0.336514\pi$
$702$	−0.378048	−0.0142685
$703$	−22.3863	−0.844316
$704$	−1.13103	−0.0426273
$705$	9.22916	0.347590
$706$	−17.6943	−0.665933
$707$	−8.50211	−0.319755
$708$	−2.74426	−0.103136
$709$	−30.7062	−1.15319	−0.576597	−	0.817028i	$-0.695620\pi$
$709$	−30.7062	−1.15319	−0.576597	+	0.817028i	$0.695620\pi$
$710$	−4.11598	−0.154470
$711$	−2.30141	−0.0863097
$712$	3.97680	0.149037
$713$	−1.63345	−0.0611730
$714$	8.90506	0.333264
$715$	−0.0359688	−0.00134516
$716$	−8.61150	−0.321827
$717$	12.9715	0.484430
$718$	−27.5567	−1.02841
$719$	7.41077	0.276375	0.138188	−	0.990406i	$-0.455872\pi$
$719$	7.41077	0.276375	0.138188	+	0.990406i	$0.455872\pi$
$720$	0.254097	0.00946962
$721$	12.1665	0.453103
$722$	2.63629	0.0981126
$723$	36.6419	1.36273
$724$	−18.3747	−0.682891
$725$	−41.2554	−1.53219
$726$	−18.6436	−0.691928
$727$	−12.7969	−0.474610	−0.237305	−	0.971435i	$-0.576264\pi$
$727$	−12.7969	−0.474610	−0.237305	+	0.971435i	$0.576264\pi$
$728$	0.0849041	0.00314675
$729$	18.4455	0.683167
$730$	−0.0101032	−0.000373937 0
$731$	17.3565	0.641953
$732$	−14.7595	−0.545528
$733$	−3.99740	−0.147647	−0.0738237	−	0.997271i	$-0.523520\pi$
$733$	−3.99740	−0.147647	−0.0738237	+	0.997271i	$0.523520\pi$
$734$	−24.6436	−0.909611
$735$	−0.718376	−0.0264977
$736$	−0.619341	−0.0228292
$737$	4.57863	0.168656
$738$	−0.608562	−0.0224015
$739$	4.57525	0.168303	0.0841516	−	0.996453i	$-0.473182\pi$
$739$	4.57525	0.168303	0.0841516	+	0.996453i	$0.473182\pi$
$740$	−2.07284	−0.0761990
$741$	−0.658716	−0.0241985
$742$	−9.09566	−0.333912
$743$	31.6605	1.16151	0.580755	−	0.814078i	$-0.302757\pi$
$743$	31.6605	1.16151	0.580755	+	0.814078i	$0.302757\pi$
$744$	−5.05829	−0.185446
$745$	−0.485090	−0.0177723
$746$	−2.78023	−0.101791
$747$	0.228664	0.00836639
$748$	5.25149	0.192014
$749$	−18.5559	−0.678017
$750$	−7.08297	−0.258634
$751$	8.16944	0.298107	0.149054	−	0.988829i	$-0.452377\pi$
$751$	8.16944	0.298107	0.149054	+	0.988829i	$0.452377\pi$
$752$	−12.8473	−0.468491
$753$	−27.3219	−0.995665
$754$	−0.720775	−0.0262491
$755$	−7.85291	−0.285797
$756$	−4.45265	−0.161941
$757$	−19.2913	−0.701153	−0.350576	−	0.936534i	$-0.614014\pi$
$757$	−19.2913	−0.701153	−0.350576	+	0.936534i	$0.614014\pi$
$758$	18.3802	0.667599
$759$	1.34348	0.0487654
$760$	−1.51518	−0.0549613
$761$	41.6094	1.50834	0.754170	−	0.656679i	$-0.228039\pi$
$761$	41.6094	1.50834	0.754170	+	0.656679i	$0.228039\pi$
$762$	−2.23916	−0.0811161
$763$	−12.8769	−0.466175
$764$	−5.44412	−0.196961
$765$	−1.17980	−0.0426557
$766$	−12.9687	−0.468579
$767$	0.121486	0.00438659
$768$	−1.91791	−0.0692067
$769$	14.7376	0.531451	0.265725	−	0.964049i	$-0.414389\pi$
$769$	14.7376	0.531451	0.265725	+	0.964049i	$0.414389\pi$
$770$	−0.423641	−0.0152670
$771$	57.2069	2.06026
$772$	−9.57267	−0.344528
$773$	−24.4036	−0.877735	−0.438868	−	0.898552i	$-0.644620\pi$
$773$	−24.4036	−0.877735	−0.438868	+	0.898552i	$0.644620\pi$
$774$	2.53588	0.0911504
$775$	12.8170	0.460399
$776$	5.17035	0.185605
$777$	−10.6138	−0.380768
$778$	9.22742	0.330819
$779$	3.62886	0.130017
$780$	−0.0609930	−0.00218390
$781$	−12.4287	−0.444732
$782$	2.87566	0.102833
$783$	37.7998	1.35086
$784$	1.00000	0.0357143
$785$	0.894658	0.0319317
$786$	−32.6052	−1.16299
$787$	42.7338	1.52330	0.761648	−	0.647991i	$-0.224391\pi$
$787$	42.7338	1.52330	0.761648	+	0.647991i	$0.224391\pi$
$788$	−18.7361	−0.667445
$789$	−2.68133	−0.0954578
$790$	1.27070	0.0452093
$791$	−5.48435	−0.195001
$792$	0.767274	0.0272639
$793$	0.653390	0.0232025
$794$	5.31928	0.188774
$795$	6.53411	0.231741
$796$	11.0058	0.390089
$797$	−15.7509	−0.557927	−0.278964	−	0.960302i	$-0.589991\pi$
$797$	−15.7509	−0.557927	−0.278964	+	0.960302i	$0.589991\pi$
$798$	−7.75835	−0.274643
$799$	59.6511	2.11031
$800$	4.85970	0.171816
$801$	−2.69780	−0.0953221
$802$	20.4634	0.722589
$803$	−0.0305078	−0.00107660
$804$	7.76407	0.273818
$805$	−0.231981	−0.00817626
$806$	0.223926	0.00788745
$807$	−7.58055	−0.266848
$808$	−8.50211	−0.299103
$809$	−22.1383	−0.778342	−0.389171	−	0.921165i	$-0.627239\pi$
$809$	−22.1383	−0.778342	−0.389171	+	0.921165i	$0.627239\pi$
$810$	3.96097	0.139174
$811$	−37.8564	−1.32932	−0.664659	−	0.747147i	$-0.731423\pi$
$811$	−37.8564	−1.32932	−0.664659	+	0.747147i	$0.731423\pi$
$812$	−8.48928	−0.297915
$813$	−25.8873	−0.907906
$814$	−6.25916	−0.219384
$815$	3.85089	0.134891
$816$	8.90506	0.311740
$817$	−15.1215	−0.529033
$818$	−0.0314586	−0.00109992
$819$	−0.0575976	−0.00201262
$820$	0.336010	0.0117340
$821$	30.5930	1.06770	0.533851	−	0.845578i	$-0.320744\pi$
$821$	30.5930	1.06770	0.533851	+	0.845578i	$0.320744\pi$
$822$	−0.649306	−0.0226472
$823$	−19.1524	−0.667610	−0.333805	−	0.942642i	$-0.608333\pi$
$823$	−19.1524	−0.667610	−0.333805	+	0.942642i	$0.608333\pi$
$824$	12.1665	0.423839
$825$	−10.5418	−0.367017
$826$	1.43086	0.0497859
$827$	46.0121	1.60000	0.800000	−	0.600001i	$-0.204833\pi$
$827$	46.0121	1.60000	0.800000	+	0.600001i	$0.204833\pi$
$828$	0.420151	0.0146013
$829$	45.6645	1.58599	0.792996	−	0.609226i	$-0.208520\pi$
$829$	45.6645	1.58599	0.792996	+	0.609226i	$0.208520\pi$
$830$	−0.126254	−0.00438235
$831$	−18.7724	−0.651206
$832$	0.0849041	0.00294352
$833$	−4.64310	−0.160874
$834$	16.8016	0.581790
$835$	7.94713	0.275022
$836$	−4.57526	−0.158239
$837$	−11.7434	−0.405912
$838$	−13.8327	−0.477841
$839$	−14.7372	−0.508784	−0.254392	−	0.967101i	$-0.581875\pi$
$839$	−14.7372	−0.508784	−0.254392	+	0.967101i	$0.581875\pi$
$840$	−0.718376	−0.0247863
$841$	43.0679	1.48510
$842$	11.1791	0.385259
$843$	−53.2849	−1.83523
$844$	6.31098	0.217233
$845$	−4.86660	−0.167416
$846$	8.71538	0.299641
$847$	9.72077	0.334010
$848$	−9.09566	−0.312346
$849$	−56.3809	−1.93499
$850$	−22.5641	−0.773943
$851$	−3.42745	−0.117492
$852$	−21.0755	−0.722035
$853$	34.4596	1.17987	0.589937	−	0.807449i	$-0.299152\pi$
$853$	34.4596	1.17987	0.589937	+	0.807449i	$0.299152\pi$
$854$	7.69562	0.263339
$855$	1.02787	0.0351525
$856$	−18.5559	−0.634227
$857$	33.7112	1.15155	0.575776	−	0.817608i	$-0.304700\pi$
$857$	33.7112	1.15155	0.575776	+	0.817608i	$0.304700\pi$
$858$	−0.184175	−0.00628764
$859$	1.43061	0.0488118	0.0244059	−	0.999702i	$-0.492231\pi$
$859$	1.43061	0.0488118	0.0244059	+	0.999702i	$0.492231\pi$
$860$	−1.40016	−0.0477449
$861$	1.72051	0.0586349
$862$	−1.00000	−0.0340601
$863$	−26.1745	−0.890990	−0.445495	−	0.895284i	$-0.646972\pi$
$863$	−26.1745	−0.890990	−0.445495	+	0.895284i	$0.646972\pi$
$864$	−4.45265	−0.151482
$865$	−1.30095	−0.0442337
$866$	−12.5297	−0.425775
$867$	−8.74263	−0.296915
$868$	2.63740	0.0895191
$869$	3.83701	0.130162
$870$	6.09850	0.206758
$871$	−0.343708	−0.0116461
$872$	−12.8769	−0.436067
$873$	−3.50749	−0.118710
$874$	−2.50536	−0.0847451
$875$	3.69307	0.124848
$876$	−0.0517326	−0.00174788
$877$	7.68450	0.259487	0.129744	−	0.991548i	$-0.458585\pi$
$877$	7.68450	0.259487	0.129744	+	0.991548i	$0.458585\pi$
$878$	−16.1550	−0.545204
$879$	−25.0663	−0.845464
$880$	−0.423641	−0.0142809
$881$	33.8698	1.14110	0.570551	−	0.821262i	$-0.306730\pi$
$881$	33.8698	1.14110	0.570551	+	0.821262i	$0.306730\pi$
$882$	−0.678384	−0.0228424
$883$	−31.0495	−1.04490	−0.522450	−	0.852670i	$-0.674982\pi$
$883$	−31.0495	−1.04490	−0.522450	+	0.852670i	$0.674982\pi$
$884$	−0.394218	−0.0132590
$885$	−1.02789	−0.0345523
$886$	−20.8897	−0.701803
$887$	−13.6669	−0.458891	−0.229445	−	0.973322i	$-0.573691\pi$
$887$	−13.6669	−0.458891	−0.229445	+	0.973322i	$0.573691\pi$
$888$	−10.6138	−0.356175
$889$	1.16750	0.0391566
$890$	1.48956	0.0499301
$891$	11.9606	0.400695
$892$	5.62649	0.188389
$893$	−51.9698	−1.73910
$894$	−2.48386	−0.0830729
$895$	−3.22554	−0.107818
$896$	1.00000	0.0334077
$897$	−0.100853	−0.00336737
$898$	11.4910	0.383459
$899$	−22.3896	−0.746735
$900$	−3.29675	−0.109892
$901$	42.2321	1.40696
$902$	1.01462	0.0337832
$903$	−7.16938	−0.238582
$904$	−5.48435	−0.182407
$905$	−6.88246	−0.228781
$906$	−40.2102	−1.33589
$907$	15.5681	0.516931	0.258466	−	0.966020i	$-0.416783\pi$
$907$	15.5681	0.516931	0.258466	+	0.966020i	$0.416783\pi$
$908$	18.9786	0.629828
$909$	5.76770	0.191303
$910$	0.0318018	0.00105422
$911$	19.8186	0.656618	0.328309	−	0.944570i	$-0.393521\pi$
$911$	19.8186	0.656618	0.328309	+	0.944570i	$0.393521\pi$
$912$	−7.75835	−0.256905
$913$	−0.381239	−0.0126172
$914$	3.51310	0.116203
$915$	−5.52835	−0.182762
$916$	11.8209	0.390574
$917$	17.0004	0.561402
$918$	20.6741	0.682348
$919$	−41.9862	−1.38500	−0.692498	−	0.721419i	$-0.743490\pi$
$919$	−41.9862	−1.38500	−0.692498	+	0.721419i	$0.743490\pi$
$920$	−0.231981	−0.00764819
$921$	17.5223	0.577378
$922$	−14.4346	−0.475378
$923$	0.932993	0.0307098
$924$	−2.16922	−0.0713620
$925$	26.8938	0.884262
$926$	−23.4921	−0.771997
$927$	−8.25355	−0.271082
$928$	−8.48928	−0.278674
$929$	24.4665	0.802721	0.401361	−	0.915920i	$-0.368537\pi$
$929$	24.4665	0.802721	0.401361	+	0.915920i	$0.368537\pi$
$930$	−1.89464	−0.0621278
$931$	4.04521	0.132576
$932$	27.5762	0.903287
$933$	−21.3109	−0.697688
$934$	−23.6821	−0.774904
$935$	1.96701	0.0643280
$936$	−0.0575976	−0.00188264
$937$	−24.4087	−0.797396	−0.398698	−	0.917082i	$-0.630538\pi$
$937$	−24.4087	−0.797396	−0.398698	+	0.917082i	$0.630538\pi$
$938$	−4.04819	−0.132178
$939$	−10.8684	−0.354677
$940$	−4.81209	−0.156953
$941$	−45.8036	−1.49315	−0.746577	−	0.665299i	$-0.768304\pi$
$941$	−45.8036	−1.49315	−0.746577	+	0.665299i	$0.768304\pi$
$942$	4.58102	0.149258
$943$	0.555596	0.0180927
$944$	1.43086	0.0465705
$945$	−1.66779	−0.0542533
$946$	−4.22793	−0.137462
$947$	41.6781	1.35436	0.677178	−	0.735819i	$-0.263203\pi$
$947$	41.6781	1.35436	0.677178	+	0.735819i	$0.263203\pi$
$948$	6.50649	0.211321
$949$	0.00229015	7.43415e−5 0
$950$	19.6585	0.637806
$951$	−1.51081	−0.0489915
$952$	−4.64310	−0.150484
$953$	−57.2421	−1.85425	−0.927127	−	0.374746i	$-0.877730\pi$
$953$	−57.2421	−1.85425	−0.927127	+	0.374746i	$0.877730\pi$
$954$	6.17036	0.199773
$955$	−2.03916	−0.0659856
$956$	−6.76335	−0.218742
$957$	18.4151	0.595276
$958$	−14.7311	−0.475940
$959$	0.338549	0.0109323
$960$	−0.718376	−0.0231855
$961$	−24.0441	−0.775617
$962$	0.469862	0.0151490
$963$	12.5880	0.405643
$964$	−19.1051	−0.615334
$965$	−3.58555	−0.115423
$966$	−1.18784	−0.0382181
$967$	15.4385	0.496468	0.248234	−	0.968700i	$-0.420150\pi$
$967$	15.4385	0.496468	0.248234	+	0.968700i	$0.420150\pi$
$968$	9.72077	0.312437
$969$	36.0228	1.15722
$970$	1.93662	0.0621810
$971$	35.5013	1.13929	0.569646	−	0.821890i	$-0.307080\pi$
$971$	35.5013	1.13929	0.569646	+	0.821890i	$0.307080\pi$
$972$	6.92385	0.222083
$973$	−8.76034	−0.280844
$974$	26.0270	0.833959
$975$	0.791347	0.0253434
$976$	7.69562	0.246331
$977$	−34.5771	−1.10622	−0.553110	−	0.833108i	$-0.686559\pi$
$977$	−34.5771	−1.10622	−0.553110	+	0.833108i	$0.686559\pi$
$978$	19.7181	0.630517
$979$	4.49789	0.143753
$980$	0.374562	0.0119649
$981$	8.73548	0.278903
$982$	12.4349	0.396814
$983$	33.1448	1.05716	0.528578	−	0.848885i	$-0.322726\pi$
$983$	33.1448	1.05716	0.528578	+	0.848885i	$0.322726\pi$
$984$	1.72051	0.0548479
$985$	−7.01781	−0.223606
$986$	39.4166	1.25528
$987$	−24.6399	−0.784297
$988$	0.343455	0.0109267
$989$	−2.31517	−0.0736181
$990$	0.287391	0.00913389
$991$	15.6202	0.496191	0.248096	−	0.968736i	$-0.420195\pi$
$991$	15.6202	0.496191	0.248096	+	0.968736i	$0.420195\pi$
$992$	2.63740	0.0837374
$993$	−29.9251	−0.949644
$994$	10.9888	0.348543
$995$	4.12234	0.130687
$996$	−0.646474	−0.0204843
$997$	17.2903	0.547589	0.273795	−	0.961788i	$-0.411721\pi$
$997$	17.2903	0.547589	0.273795	+	0.961788i	$0.411721\pi$
$998$	−35.7961	−1.13311
$999$	−24.6411	−0.779611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.91791 q^{3} +1.00000 q^{4} +0.374562 q^{5} +1.91791 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.678384 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.91791 q^{3} +1.00000 q^{4} +0.374562 q^{5} +1.91791 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.678384 q^{9} -0.374562 q^{10} -1.13103 q^{11} -1.91791 q^{12} +0.0849041 q^{13} +1.00000 q^{14} -0.718376 q^{15} +1.00000 q^{16} -4.64310 q^{17} -0.678384 q^{18} +4.04521 q^{19} +0.374562 q^{20} +1.91791 q^{21} +1.13103 q^{22} +0.619341 q^{23} +1.91791 q^{24} -4.85970 q^{25} -0.0849041 q^{26} +4.45265 q^{27} -1.00000 q^{28} +8.48928 q^{29} +0.718376 q^{30} -2.63740 q^{31} -1.00000 q^{32} +2.16922 q^{33} +4.64310 q^{34} -0.374562 q^{35} +0.678384 q^{36} -5.53403 q^{37} -4.04521 q^{38} -0.162839 q^{39} -0.374562 q^{40} +0.897076 q^{41} -1.91791 q^{42} -3.73812 q^{43} -1.13103 q^{44} +0.254097 q^{45} -0.619341 q^{46} -12.8473 q^{47} -1.91791 q^{48} +1.00000 q^{49} +4.85970 q^{50} +8.90506 q^{51} +0.0849041 q^{52} -9.09566 q^{53} -4.45265 q^{54} -0.423641 q^{55} +1.00000 q^{56} -7.75835 q^{57} -8.48928 q^{58} +1.43086 q^{59} -0.718376 q^{60} +7.69562 q^{61} +2.63740 q^{62} -0.678384 q^{63} +1.00000 q^{64} +0.0318018 q^{65} -2.16922 q^{66} -4.04819 q^{67} -4.64310 q^{68} -1.18784 q^{69} +0.374562 q^{70} +10.9888 q^{71} -0.678384 q^{72} +0.0269734 q^{73} +5.53403 q^{74} +9.32048 q^{75} +4.04521 q^{76} +1.13103 q^{77} +0.162839 q^{78} -3.39249 q^{79} +0.374562 q^{80} -10.5749 q^{81} -0.897076 q^{82} +0.337072 q^{83} +1.91791 q^{84} -1.73913 q^{85} +3.73812 q^{86} -16.2817 q^{87} +1.13103 q^{88} -3.97680 q^{89} -0.254097 q^{90} -0.0849041 q^{91} +0.619341 q^{92} +5.05829 q^{93} +12.8473 q^{94} +1.51518 q^{95} +1.91791 q^{96} -5.17035 q^{97} -1.00000 q^{98} -0.767274 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 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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