LMFDB - Embedded newform 6034.2.a.r.1.13

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:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.307546 q^{3} +1.00000 q^{4} -1.88818 q^{5} -0.307546 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.90542 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.307546 q^{3} +1.00000 q^{4} -1.88818 q^{5} -0.307546 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.90542 q^{9} -1.88818 q^{10} -3.09211 q^{11} -0.307546 q^{12} +1.77759 q^{13} -1.00000 q^{14} +0.580703 q^{15} +1.00000 q^{16} -4.64669 q^{17} -2.90542 q^{18} -2.38627 q^{19} -1.88818 q^{20} +0.307546 q^{21} -3.09211 q^{22} +4.30702 q^{23} -0.307546 q^{24} -1.43477 q^{25} +1.77759 q^{26} +1.81619 q^{27} -1.00000 q^{28} -0.399130 q^{29} +0.580703 q^{30} +0.946224 q^{31} +1.00000 q^{32} +0.950967 q^{33} -4.64669 q^{34} +1.88818 q^{35} -2.90542 q^{36} +4.06466 q^{37} -2.38627 q^{38} -0.546691 q^{39} -1.88818 q^{40} +12.5147 q^{41} +0.307546 q^{42} -4.51678 q^{43} -3.09211 q^{44} +5.48595 q^{45} +4.30702 q^{46} -5.52917 q^{47} -0.307546 q^{48} +1.00000 q^{49} -1.43477 q^{50} +1.42907 q^{51} +1.77759 q^{52} -6.03409 q^{53} +1.81619 q^{54} +5.83847 q^{55} -1.00000 q^{56} +0.733888 q^{57} -0.399130 q^{58} +0.838958 q^{59} +0.580703 q^{60} -0.512615 q^{61} +0.946224 q^{62} +2.90542 q^{63} +1.00000 q^{64} -3.35641 q^{65} +0.950967 q^{66} +0.881863 q^{67} -4.64669 q^{68} -1.32461 q^{69} +1.88818 q^{70} -1.08345 q^{71} -2.90542 q^{72} -2.99282 q^{73} +4.06466 q^{74} +0.441259 q^{75} -2.38627 q^{76} +3.09211 q^{77} -0.546691 q^{78} +5.73733 q^{79} -1.88818 q^{80} +8.15769 q^{81} +12.5147 q^{82} +15.5118 q^{83} +0.307546 q^{84} +8.77379 q^{85} -4.51678 q^{86} +0.122751 q^{87} -3.09211 q^{88} +0.547194 q^{89} +5.48595 q^{90} -1.77759 q^{91} +4.30702 q^{92} -0.291007 q^{93} -5.52917 q^{94} +4.50571 q^{95} -0.307546 q^{96} +0.186503 q^{97} +1.00000 q^{98} +8.98387 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) $ 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * 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
$3$	−0.307546	−0.177562	−0.0887809	−	0.996051i	$-0.528297\pi$
$3$	−0.307546	−0.177562	−0.0887809	+	0.996051i	$0.528297\pi$
$4$	1.00000	0.500000
$5$	−1.88818	−0.844420	−0.422210	−	0.906498i	$-0.638746\pi$
$5$	−1.88818	−0.844420	−0.422210	+	0.906498i	$0.638746\pi$
$6$	−0.307546	−0.125555
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.90542	−0.968472
$10$	−1.88818	−0.597095
$11$	−3.09211	−0.932307	−0.466153	−	0.884704i	$-0.654360\pi$
$11$	−3.09211	−0.932307	−0.466153	+	0.884704i	$0.654360\pi$
$12$	−0.307546	−0.0887809
$13$	1.77759	0.493015	0.246508	−	0.969141i	$-0.420717\pi$
$13$	1.77759	0.493015	0.246508	+	0.969141i	$0.420717\pi$
$14$	−1.00000	−0.267261
$15$	0.580703	0.149937
$16$	1.00000	0.250000
$17$	−4.64669	−1.12699	−0.563494	−	0.826120i	$-0.690543\pi$
$17$	−4.64669	−1.12699	−0.563494	+	0.826120i	$0.690543\pi$
$18$	−2.90542	−0.684813
$19$	−2.38627	−0.547448	−0.273724	−	0.961808i	$-0.588255\pi$
$19$	−2.38627	−0.547448	−0.273724	+	0.961808i	$0.588255\pi$
$20$	−1.88818	−0.422210
$21$	0.307546	0.0671120
$22$	−3.09211	−0.659240
$23$	4.30702	0.898076	0.449038	−	0.893513i	$-0.351767\pi$
$23$	4.30702	0.898076	0.449038	+	0.893513i	$0.351767\pi$
$24$	−0.307546	−0.0627776
$25$	−1.43477	−0.286955
$26$	1.77759	0.348614
$27$	1.81619	0.349525
$28$	−1.00000	−0.188982
$29$	−0.399130	−0.0741166	−0.0370583	−	0.999313i	$-0.511799\pi$
$29$	−0.399130	−0.0741166	−0.0370583	+	0.999313i	$0.511799\pi$
$30$	0.580703	0.106021
$31$	0.946224	0.169947	0.0849734	−	0.996383i	$-0.472919\pi$
$31$	0.946224	0.169947	0.0849734	+	0.996383i	$0.472919\pi$
$32$	1.00000	0.176777
$33$	0.950967	0.165542
$34$	−4.64669	−0.796901
$35$	1.88818	0.319161
$36$	−2.90542	−0.484236
$37$	4.06466	0.668226	0.334113	−	0.942533i	$-0.391563\pi$
$37$	4.06466	0.668226	0.334113	+	0.942533i	$0.391563\pi$
$38$	−2.38627	−0.387104
$39$	−0.546691	−0.0875407
$40$	−1.88818	−0.298548
$41$	12.5147	1.95446	0.977231	−	0.212178i	$-0.0680556\pi$
$41$	12.5147	1.95446	0.977231	+	0.212178i	$0.0680556\pi$
$42$	0.307546	0.0474554
$43$	−4.51678	−0.688802	−0.344401	−	0.938823i	$-0.611918\pi$
$43$	−4.51678	−0.688802	−0.344401	+	0.938823i	$0.611918\pi$
$44$	−3.09211	−0.466153
$45$	5.48595	0.817797
$46$	4.30702	0.635036
$47$	−5.52917	−0.806513	−0.403256	−	0.915087i	$-0.632122\pi$
$47$	−5.52917	−0.806513	−0.403256	+	0.915087i	$0.632122\pi$
$48$	−0.307546	−0.0443904
$49$	1.00000	0.142857
$50$	−1.43477	−0.202908
$51$	1.42907	0.200110
$52$	1.77759	0.246508
$53$	−6.03409	−0.828846	−0.414423	−	0.910084i	$-0.636017\pi$
$53$	−6.03409	−0.828846	−0.414423	+	0.910084i	$0.636017\pi$
$54$	1.81619	0.247152
$55$	5.83847	0.787259
$56$	−1.00000	−0.133631
$57$	0.733888	0.0972058
$58$	−0.399130	−0.0524083
$59$	0.838958	0.109223	0.0546115	−	0.998508i	$-0.482608\pi$
$59$	0.838958	0.109223	0.0546115	+	0.998508i	$0.482608\pi$
$60$	0.580703	0.0749684
$61$	−0.512615	−0.0656336	−0.0328168	−	0.999461i	$-0.510448\pi$
$61$	−0.512615	−0.0656336	−0.0328168	+	0.999461i	$0.510448\pi$
$62$	0.946224	0.120171
$63$	2.90542	0.366048
$64$	1.00000	0.125000
$65$	−3.35641	−0.416312
$66$	0.950967	0.117056
$67$	0.881863	0.107737	0.0538684	−	0.998548i	$-0.482845\pi$
$67$	0.881863	0.107737	0.0538684	+	0.998548i	$0.482845\pi$
$68$	−4.64669	−0.563494
$69$	−1.32461	−0.159464
$70$	1.88818	0.225681
$71$	−1.08345	−0.128582	−0.0642910	−	0.997931i	$-0.520479\pi$
$71$	−1.08345	−0.128582	−0.0642910	+	0.997931i	$0.520479\pi$
$72$	−2.90542	−0.342406
$73$	−2.99282	−0.350283	−0.175141	−	0.984543i	$-0.556038\pi$
$73$	−2.99282	−0.350283	−0.175141	+	0.984543i	$0.556038\pi$
$74$	4.06466	0.472507
$75$	0.441259	0.0509522
$76$	−2.38627	−0.273724
$77$	3.09211	0.352379
$78$	−0.546691	−0.0619006
$79$	5.73733	0.645500	0.322750	−	0.946484i	$-0.395393\pi$
$79$	5.73733	0.645500	0.322750	+	0.946484i	$0.395393\pi$
$80$	−1.88818	−0.211105
$81$	8.15769	0.906409
$82$	12.5147	1.38201
$83$	15.5118	1.70264	0.851319	−	0.524648i	$-0.175803\pi$
$83$	15.5118	1.70264	0.851319	+	0.524648i	$0.175803\pi$
$84$	0.307546	0.0335560
$85$	8.77379	0.951651
$86$	−4.51678	−0.487057
$87$	0.122751	0.0131603
$88$	−3.09211	−0.329620
$89$	0.547194	0.0580024	0.0290012	−	0.999579i	$-0.490767\pi$
$89$	0.547194	0.0580024	0.0290012	+	0.999579i	$0.490767\pi$
$90$	5.48595	0.578270
$91$	−1.77759	−0.186342
$92$	4.30702	0.449038
$93$	−0.291007	−0.0301761
$94$	−5.52917	−0.570291
$95$	4.50571	0.462276
$96$	−0.307546	−0.0313888
$97$	0.186503	0.0189365	0.00946824	−	0.999955i	$-0.496986\pi$
$97$	0.186503	0.0189365	0.00946824	+	0.999955i	$0.496986\pi$
$98$	1.00000	0.101015
$99$	8.98387	0.902913
$100$	−1.43477	−0.143477
$101$	19.6953	1.95975	0.979877	−	0.199603i	$-0.0639653\pi$
$101$	19.6953	1.95975	0.979877	+	0.199603i	$0.0639653\pi$
$102$	1.42907	0.141499
$103$	0.490497	0.0483302	0.0241651	−	0.999708i	$-0.492307\pi$
$103$	0.490497	0.0483302	0.0241651	+	0.999708i	$0.492307\pi$
$104$	1.77759	0.174307
$105$	−0.580703	−0.0566708
$106$	−6.03409	−0.586082
$107$	15.9484	1.54179	0.770894	−	0.636964i	$-0.219810\pi$
$107$	15.9484	1.54179	0.770894	+	0.636964i	$0.219810\pi$
$108$	1.81619	0.174763
$109$	7.36597	0.705532	0.352766	−	0.935712i	$-0.385241\pi$
$109$	7.36597	0.705532	0.352766	+	0.935712i	$0.385241\pi$
$110$	5.83847	0.556676
$111$	−1.25007	−0.118651
$112$	−1.00000	−0.0944911
$113$	−2.57757	−0.242478	−0.121239	−	0.992623i	$-0.538687\pi$
$113$	−2.57757	−0.242478	−0.121239	+	0.992623i	$0.538687\pi$
$114$	0.733888	0.0687349
$115$	−8.13244	−0.758354
$116$	−0.399130	−0.0370583
$117$	−5.16464	−0.477471
$118$	0.838958	0.0772323
$119$	4.64669	0.425961
$120$	0.580703	0.0530106
$121$	−1.43885	−0.130804
$122$	−0.512615	−0.0464100
$123$	−3.84884	−0.347038
$124$	0.946224	0.0849734
$125$	12.1500	1.08673
$126$	2.90542	0.258835
$127$	20.6583	1.83313	0.916563	−	0.399891i	$-0.130952\pi$
$127$	20.6583	1.83313	0.916563	+	0.399891i	$0.130952\pi$
$128$	1.00000	0.0883883
$129$	1.38912	0.122305
$130$	−3.35641	−0.294377
$131$	−9.75823	−0.852581	−0.426290	−	0.904586i	$-0.640180\pi$
$131$	−9.75823	−0.852581	−0.426290	+	0.904586i	$0.640180\pi$
$132$	0.950967	0.0827710
$133$	2.38627	0.206916
$134$	0.881863	0.0761814
$135$	−3.42929	−0.295146
$136$	−4.64669	−0.398450
$137$	−5.64193	−0.482022	−0.241011	−	0.970522i	$-0.577479\pi$
$137$	−5.64193	−0.482022	−0.241011	+	0.970522i	$0.577479\pi$
$138$	−1.32461	−0.112758
$139$	−16.1984	−1.37393	−0.686966	−	0.726690i	$-0.741058\pi$
$139$	−16.1984	−1.37393	−0.686966	+	0.726690i	$0.741058\pi$
$140$	1.88818	0.159580
$141$	1.70047	0.143206
$142$	−1.08345	−0.0909212
$143$	−5.49651	−0.459641
$144$	−2.90542	−0.242118
$145$	0.753629	0.0625855
$146$	−2.99282	−0.247687
$147$	−0.307546	−0.0253660
$148$	4.06466	0.334113
$149$	−13.6479	−1.11808	−0.559040	−	0.829141i	$-0.688830\pi$
$149$	−13.6479	−1.11808	−0.559040	+	0.829141i	$0.688830\pi$
$150$	0.441259	0.0360286
$151$	5.17650	0.421257	0.210629	−	0.977566i	$-0.432449\pi$
$151$	5.17650	0.421257	0.210629	+	0.977566i	$0.432449\pi$
$152$	−2.38627	−0.193552
$153$	13.5006	1.09146
$154$	3.09211	0.249169
$155$	−1.78664	−0.143507
$156$	−0.546691	−0.0437703
$157$	−4.83990	−0.386266	−0.193133	−	0.981173i	$-0.561865\pi$
$157$	−4.83990	−0.386266	−0.193133	+	0.981173i	$0.561865\pi$
$158$	5.73733	0.456437
$159$	1.85576	0.147171
$160$	−1.88818	−0.149274
$161$	−4.30702	−0.339441
$162$	8.15769	0.640928
$163$	−4.25710	−0.333442	−0.166721	−	0.986004i	$-0.553318\pi$
$163$	−4.25710	−0.333442	−0.166721	+	0.986004i	$0.553318\pi$
$164$	12.5147	0.977231
$165$	−1.79560	−0.139787
$166$	15.5118	1.20395
$167$	17.8121	1.37834	0.689171	−	0.724599i	$-0.257975\pi$
$167$	17.8121	1.37834	0.689171	+	0.724599i	$0.257975\pi$
$168$	0.307546	0.0237277
$169$	−9.84017	−0.756936
$170$	8.77379	0.672919
$171$	6.93311	0.530188
$172$	−4.51678	−0.344401
$173$	24.8683	1.89070	0.945349	−	0.326059i	$-0.105721\pi$
$173$	24.8683	1.89070	0.945349	+	0.326059i	$0.105721\pi$
$174$	0.122751	0.00930571
$175$	1.43477	0.108459
$176$	−3.09211	−0.233077
$177$	−0.258018	−0.0193938
$178$	0.547194	0.0410139
$179$	−9.26945	−0.692831	−0.346416	−	0.938081i	$-0.612601\pi$
$179$	−9.26945	−0.692831	−0.346416	+	0.938081i	$0.612601\pi$
$180$	5.48595	0.408899
$181$	20.7394	1.54154	0.770772	−	0.637111i	$-0.219871\pi$
$181$	20.7394	1.54154	0.770772	+	0.637111i	$0.219871\pi$
$182$	−1.77759	−0.131764
$183$	0.157653	0.0116540
$184$	4.30702	0.317518
$185$	−7.67481	−0.564263
$186$	−0.291007	−0.0213377
$187$	14.3681	1.05070
$188$	−5.52917	−0.403256
$189$	−1.81619	−0.132108
$190$	4.50571	0.326879
$191$	−9.46407	−0.684796	−0.342398	−	0.939555i	$-0.611239\pi$
$191$	−9.46407	−0.684796	−0.342398	+	0.939555i	$0.611239\pi$
$192$	−0.307546	−0.0221952
$193$	−15.9484	−1.14799	−0.573995	−	0.818859i	$-0.694607\pi$
$193$	−15.9484	−1.14799	−0.573995	+	0.818859i	$0.694607\pi$
$194$	0.186503	0.0133901
$195$	1.03225	0.0739211
$196$	1.00000	0.0714286
$197$	−9.49025	−0.676152	−0.338076	−	0.941119i	$-0.609776\pi$
$197$	−9.49025	−0.676152	−0.338076	+	0.941119i	$0.609776\pi$
$198$	8.98387	0.638456
$199$	14.4728	1.02595	0.512974	−	0.858404i	$-0.328544\pi$
$199$	14.4728	1.02595	0.512974	+	0.858404i	$0.328544\pi$
$200$	−1.43477	−0.101454
$201$	−0.271214	−0.0191299
$202$	19.6953	1.38576
$203$	0.399130	0.0280134
$204$	1.42907	0.100055
$205$	−23.6299	−1.65039
$206$	0.490497	0.0341746
$207$	−12.5137	−0.869762
$208$	1.77759	0.123254
$209$	7.37861	0.510389
$210$	−0.580703	−0.0400723
$211$	−1.32701	−0.0913549	−0.0456774	−	0.998956i	$-0.514545\pi$
$211$	−1.32701	−0.0913549	−0.0456774	+	0.998956i	$0.514545\pi$
$212$	−6.03409	−0.414423
$213$	0.333211	0.0228312
$214$	15.9484	1.09021
$215$	8.52850	0.581639
$216$	1.81619	0.123576
$217$	−0.946224	−0.0642339
$218$	7.36597	0.498887
$219$	0.920429	0.0621968
$220$	5.83847	0.393629
$221$	−8.25992	−0.555622
$222$	−1.25007	−0.0838992
$223$	−21.6241	−1.44806	−0.724028	−	0.689771i	$-0.757711\pi$
$223$	−21.6241	−1.44806	−0.724028	+	0.689771i	$0.757711\pi$
$224$	−1.00000	−0.0668153
$225$	4.16861	0.277907
$226$	−2.57757	−0.171458
$227$	−1.22482	−0.0812944	−0.0406472	−	0.999174i	$-0.512942\pi$
$227$	−1.22482	−0.0812944	−0.0406472	+	0.999174i	$0.512942\pi$
$228$	0.733888	0.0486029
$229$	−13.7904	−0.911295	−0.455648	−	0.890160i	$-0.650592\pi$
$229$	−13.7904	−0.911295	−0.455648	+	0.890160i	$0.650592\pi$
$230$	−8.13244	−0.536237
$231$	−0.950967	−0.0625690
$232$	−0.399130	−0.0262042
$233$	5.86379	0.384150	0.192075	−	0.981380i	$-0.438478\pi$
$233$	5.86379	0.384150	0.192075	+	0.981380i	$0.438478\pi$
$234$	−5.16464	−0.337623
$235$	10.4401	0.681036
$236$	0.838958	0.0546115
$237$	−1.76449	−0.114616
$238$	4.64669	0.301200
$239$	29.0511	1.87916	0.939580	−	0.342330i	$-0.111216\pi$
$239$	29.0511	1.87916	0.939580	+	0.342330i	$0.111216\pi$
$240$	0.580703	0.0374842
$241$	15.6626	1.00891	0.504457	−	0.863437i	$-0.331693\pi$
$241$	15.6626	1.00891	0.504457	+	0.863437i	$0.331693\pi$
$242$	−1.43885	−0.0924926
$243$	−7.95742	−0.510469
$244$	−0.512615	−0.0328168
$245$	−1.88818	−0.120631
$246$	−3.84884	−0.245393
$247$	−4.24181	−0.269900
$248$	0.946224	0.0600853
$249$	−4.77059	−0.302324
$250$	12.1500	0.768434
$251$	9.31877	0.588196	0.294098	−	0.955775i	$-0.404981\pi$
$251$	9.31877	0.588196	0.294098	+	0.955775i	$0.404981\pi$
$252$	2.90542	0.183024
$253$	−13.3178	−0.837283
$254$	20.6583	1.29622
$255$	−2.69834	−0.168977
$256$	1.00000	0.0625000
$257$	29.8289	1.86067	0.930337	−	0.366706i	$-0.119515\pi$
$257$	29.8289	1.86067	0.930337	+	0.366706i	$0.119515\pi$
$258$	1.38912	0.0864827
$259$	−4.06466	−0.252566
$260$	−3.35641	−0.208156
$261$	1.15964	0.0717798
$262$	−9.75823	−0.602866
$263$	−26.0902	−1.60879	−0.804397	−	0.594093i	$-0.797511\pi$
$263$	−26.0902	−1.60879	−0.804397	+	0.594093i	$0.797511\pi$
$264$	0.950967	0.0585279
$265$	11.3934	0.699894
$266$	2.38627	0.146312
$267$	−0.168287	−0.0102990
$268$	0.881863	0.0538684
$269$	−1.20507	−0.0734744	−0.0367372	−	0.999325i	$-0.511696\pi$
$269$	−1.20507	−0.0734744	−0.0367372	+	0.999325i	$0.511696\pi$
$270$	−3.42929	−0.208700
$271$	30.5220	1.85408	0.927040	−	0.374964i	$-0.122345\pi$
$271$	30.5220	1.85408	0.927040	+	0.374964i	$0.122345\pi$
$272$	−4.64669	−0.281747
$273$	0.546691	0.0330873
$274$	−5.64193	−0.340841
$275$	4.43648	0.267530
$276$	−1.32461	−0.0797320
$277$	19.0691	1.14575	0.572877	−	0.819642i	$-0.305827\pi$
$277$	19.0691	1.14575	0.572877	+	0.819642i	$0.305827\pi$
$278$	−16.1984	−0.971517
$279$	−2.74917	−0.164589
$280$	1.88818	0.112840
$281$	1.70890	0.101944	0.0509722	−	0.998700i	$-0.483768\pi$
$281$	1.70890	0.101944	0.0509722	+	0.998700i	$0.483768\pi$
$282$	1.70047	0.101262
$283$	−1.31932	−0.0784252	−0.0392126	−	0.999231i	$-0.512485\pi$
$283$	−1.31932	−0.0784252	−0.0392126	+	0.999231i	$0.512485\pi$
$284$	−1.08345	−0.0642910
$285$	−1.38571	−0.0820826
$286$	−5.49651	−0.325016
$287$	−12.5147	−0.738717
$288$	−2.90542	−0.171203
$289$	4.59172	0.270101
$290$	0.753629	0.0442546
$291$	−0.0573582	−0.00336240
$292$	−2.99282	−0.175141
$293$	7.52435	0.439577	0.219789	−	0.975548i	$-0.429463\pi$
$293$	7.52435	0.439577	0.219789	+	0.975548i	$0.429463\pi$
$294$	−0.307546	−0.0179364
$295$	−1.58410	−0.0922301
$296$	4.06466	0.236254
$297$	−5.61585	−0.325865
$298$	−13.6479	−0.790601
$299$	7.65613	0.442765
$300$	0.441259	0.0254761
$301$	4.51678	0.260343
$302$	5.17650	0.297874
$303$	−6.05721	−0.347977
$304$	−2.38627	−0.136862
$305$	0.967909	0.0554223
$306$	13.5006	0.771776
$307$	−4.39835	−0.251027	−0.125513	−	0.992092i	$-0.540058\pi$
$307$	−4.39835	−0.251027	−0.125513	+	0.992092i	$0.540058\pi$
$308$	3.09211	0.176189
$309$	−0.150851	−0.00858159
$310$	−1.78664	−0.101474
$311$	−0.0387819	−0.00219912	−0.00109956	−	0.999999i	$-0.500350\pi$
$311$	−0.0387819	−0.00219912	−0.00109956	+	0.999999i	$0.500350\pi$
$312$	−0.546691	−0.0309503
$313$	−25.6215	−1.44821	−0.724107	−	0.689687i	$-0.757748\pi$
$313$	−25.6215	−1.44821	−0.724107	+	0.689687i	$0.757748\pi$
$314$	−4.83990	−0.273131
$315$	−5.48595	−0.309098
$316$	5.73733	0.322750
$317$	−3.70625	−0.208164	−0.104082	−	0.994569i	$-0.533190\pi$
$317$	−3.70625	−0.208164	−0.104082	+	0.994569i	$0.533190\pi$
$318$	1.85576	0.104066
$319$	1.23415	0.0690994
$320$	−1.88818	−0.105553
$321$	−4.90486	−0.273762
$322$	−4.30702	−0.240021
$323$	11.0883	0.616967
$324$	8.15769	0.453205
$325$	−2.55044	−0.141473
$326$	−4.25710	−0.235779
$327$	−2.26538	−0.125276
$328$	12.5147	0.691007
$329$	5.52917	0.304833
$330$	−1.79560	−0.0988444
$331$	−6.64123	−0.365035	−0.182517	−	0.983203i	$-0.558425\pi$
$331$	−6.64123	−0.365035	−0.182517	+	0.983203i	$0.558425\pi$
$332$	15.5118	0.851319
$333$	−11.8095	−0.647158
$334$	17.8121	0.974634
$335$	−1.66512	−0.0909751
$336$	0.307546	0.0167780
$337$	24.3154	1.32454	0.662271	−	0.749264i	$-0.269593\pi$
$337$	24.3154	1.32454	0.662271	+	0.749264i	$0.269593\pi$
$338$	−9.84017	−0.535235
$339$	0.792723	0.0430548
$340$	8.77379	0.475826
$341$	−2.92583	−0.158443
$342$	6.93311	0.374899
$343$	−1.00000	−0.0539949
$344$	−4.51678	−0.243528
$345$	2.50110	0.134655
$346$	24.8683	1.33693
$347$	9.41672	0.505516	0.252758	−	0.967530i	$-0.418662\pi$
$347$	9.41672	0.505516	0.252758	+	0.967530i	$0.418662\pi$
$348$	0.122751	0.00658013
$349$	−13.0204	−0.696966	−0.348483	−	0.937315i	$-0.613303\pi$
$349$	−13.0204	−0.696966	−0.348483	+	0.937315i	$0.613303\pi$
$350$	1.43477	0.0766918
$351$	3.22844	0.172321
$352$	−3.09211	−0.164810
$353$	−31.6043	−1.68213	−0.841063	−	0.540938i	$-0.818069\pi$
$353$	−31.6043	−1.68213	−0.841063	+	0.540938i	$0.818069\pi$
$354$	−0.258018	−0.0137135
$355$	2.04575	0.108577
$356$	0.547194	0.0290012
$357$	−1.42907	−0.0756345
$358$	−9.26945	−0.489906
$359$	26.9058	1.42004	0.710018	−	0.704184i	$-0.248687\pi$
$359$	26.9058	1.42004	0.710018	+	0.704184i	$0.248687\pi$
$360$	5.48595	0.289135
$361$	−13.3057	−0.700301
$362$	20.7394	1.09004
$363$	0.442512	0.0232258
$364$	−1.77759	−0.0931711
$365$	5.65098	0.295786
$366$	0.157653	0.00824063
$367$	−19.2909	−1.00698	−0.503488	−	0.864002i	$-0.667950\pi$
$367$	−19.2909	−1.00698	−0.503488	+	0.864002i	$0.667950\pi$
$368$	4.30702	0.224519
$369$	−36.3603	−1.89284
$370$	−7.67481	−0.398994
$371$	6.03409	0.313274
$372$	−0.291007	−0.0150880
$373$	36.4314	1.88635	0.943174	−	0.332298i	$-0.107824\pi$
$373$	36.4314	1.88635	0.943174	+	0.332298i	$0.107824\pi$
$374$	14.3681	0.742956
$375$	−3.73669	−0.192962
$376$	−5.52917	−0.285145
$377$	−0.709490	−0.0365406
$378$	−1.81619	−0.0934146
$379$	11.1643	0.573474	0.286737	−	0.958009i	$-0.407429\pi$
$379$	11.1643	0.573474	0.286737	+	0.958009i	$0.407429\pi$
$380$	4.50571	0.231138
$381$	−6.35337	−0.325493
$382$	−9.46407	−0.484224
$383$	29.6867	1.51692	0.758460	−	0.651720i	$-0.225952\pi$
$383$	29.6867	1.51692	0.758460	+	0.651720i	$0.225952\pi$
$384$	−0.307546	−0.0156944
$385$	−5.83847	−0.297556
$386$	−15.9484	−0.811751
$387$	13.1231	0.667086
$388$	0.186503	0.00946824
$389$	9.20038	0.466478	0.233239	−	0.972419i	$-0.425068\pi$
$389$	9.20038	0.466478	0.233239	+	0.972419i	$0.425068\pi$
$390$	1.03225	0.0522701
$391$	−20.0134	−1.01212
$392$	1.00000	0.0505076
$393$	3.00111	0.151386
$394$	−9.49025	−0.478112
$395$	−10.8331	−0.545073
$396$	8.98387	0.451456
$397$	20.0789	1.00773	0.503865	−	0.863782i	$-0.331911\pi$
$397$	20.0789	1.00773	0.503865	+	0.863782i	$0.331911\pi$
$398$	14.4728	0.725455
$399$	−0.733888	−0.0367404
$400$	−1.43477	−0.0717386
$401$	−4.50474	−0.224956	−0.112478	−	0.993654i	$-0.535879\pi$
$401$	−4.50474	−0.224956	−0.112478	+	0.993654i	$0.535879\pi$
$402$	−0.271214	−0.0135269
$403$	1.68200	0.0837864
$404$	19.6953	0.979877
$405$	−15.4032	−0.765390
$406$	0.399130	0.0198085
$407$	−12.5684	−0.622991
$408$	1.42907	0.0707496
$409$	−17.0794	−0.844521	−0.422261	−	0.906474i	$-0.638763\pi$
$409$	−17.0794	−0.844521	−0.422261	+	0.906474i	$0.638763\pi$
$410$	−23.6299	−1.16700
$411$	1.73515	0.0855888
$412$	0.490497	0.0241651
$413$	−0.838958	−0.0412824
$414$	−12.5137	−0.615014
$415$	−29.2890	−1.43774
$416$	1.77759	0.0871536
$417$	4.98176	0.243958
$418$	7.37861	0.360900
$419$	27.7579	1.35606	0.678030	−	0.735034i	$-0.262834\pi$
$419$	27.7579	1.35606	0.678030	+	0.735034i	$0.262834\pi$
$420$	−0.580703	−0.0283354
$421$	−18.6848	−0.910639	−0.455320	−	0.890328i	$-0.650475\pi$
$421$	−18.6848	−0.910639	−0.455320	+	0.890328i	$0.650475\pi$
$422$	−1.32701	−0.0645977
$423$	16.0645	0.781085
$424$	−6.03409	−0.293041
$425$	6.66694	0.323394
$426$	0.333211	0.0161441
$427$	0.512615	0.0248072
$428$	15.9484	0.770894
$429$	1.69043	0.0816147
$430$	8.52850	0.411281
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.81619	0.0873813
$433$	−17.2534	−0.829143	−0.414572	−	0.910017i	$-0.636069\pi$
$433$	−17.2534	−0.829143	−0.414572	+	0.910017i	$0.636069\pi$
$434$	−0.946224	−0.0454202
$435$	−0.231776	−0.0111128
$436$	7.36597	0.352766
$437$	−10.2777	−0.491650
$438$	0.920429	0.0439798
$439$	−25.0805	−1.19703	−0.598515	−	0.801112i	$-0.704242\pi$
$439$	−25.0805	−1.19703	−0.598515	+	0.801112i	$0.704242\pi$
$440$	5.83847	0.278338
$441$	−2.90542	−0.138353
$442$	−8.25992	−0.392884
$443$	−40.9140	−1.94388	−0.971942	−	0.235220i	$-0.924419\pi$
$443$	−40.9140	−1.94388	−0.971942	+	0.235220i	$0.924419\pi$
$444$	−1.25007	−0.0593257
$445$	−1.03320	−0.0489784
$446$	−21.6241	−1.02393
$447$	4.19736	0.198528
$448$	−1.00000	−0.0472456
$449$	0.546646	0.0257978	0.0128989	−	0.999917i	$-0.495894\pi$
$449$	0.546646	0.0257978	0.0128989	+	0.999917i	$0.495894\pi$
$450$	4.16861	0.196510
$451$	−38.6967	−1.82216
$452$	−2.57757	−0.121239
$453$	−1.59201	−0.0747992
$454$	−1.22482	−0.0574838
$455$	3.35641	0.157351
$456$	0.733888	0.0343675
$457$	30.2903	1.41692	0.708461	−	0.705750i	$-0.249390\pi$
$457$	30.2903	1.41692	0.708461	+	0.705750i	$0.249390\pi$
$458$	−13.7904	−0.644383
$459$	−8.43926	−0.393911
$460$	−8.13244	−0.379177
$461$	−2.22466	−0.103613	−0.0518064	−	0.998657i	$-0.516498\pi$
$461$	−2.22466	−0.103613	−0.0518064	+	0.998657i	$0.516498\pi$
$462$	−0.950967	−0.0442430
$463$	−39.9034	−1.85447	−0.927235	−	0.374481i	$-0.877821\pi$
$463$	−39.9034	−1.85447	−0.927235	+	0.374481i	$0.877821\pi$
$464$	−0.399130	−0.0185291
$465$	0.549475	0.0254813
$466$	5.86379	0.271635
$467$	17.2350	0.797539	0.398770	−	0.917051i	$-0.369437\pi$
$467$	17.2350	0.797539	0.398770	+	0.917051i	$0.369437\pi$
$468$	−5.16464	−0.238736
$469$	−0.881863	−0.0407207
$470$	10.4401	0.481565
$471$	1.48849	0.0685861
$472$	0.838958	0.0386162
$473$	13.9664	0.642175
$474$	−1.76449	−0.0810458
$475$	3.42376	0.157093
$476$	4.64669	0.212981
$477$	17.5315	0.802714
$478$	29.0511	1.32877
$479$	26.8274	1.22577	0.612887	−	0.790171i	$-0.290008\pi$
$479$	26.8274	1.22577	0.612887	+	0.790171i	$0.290008\pi$
$480$	0.580703	0.0265053
$481$	7.22530	0.329445
$482$	15.6626	0.713410
$483$	1.32461	0.0602717
$484$	−1.43885	−0.0654021
$485$	−0.352151	−0.0159904
$486$	−7.95742	−0.360956
$487$	−35.5943	−1.61293	−0.806467	−	0.591279i	$-0.798623\pi$
$487$	−35.5943	−1.61293	−0.806467	+	0.591279i	$0.798623\pi$
$488$	−0.512615	−0.0232050
$489$	1.30926	0.0592066
$490$	−1.88818	−0.0852993
$491$	−17.8443	−0.805303	−0.402652	−	0.915353i	$-0.631911\pi$
$491$	−17.8443	−0.805303	−0.402652	+	0.915353i	$0.631911\pi$
$492$	−3.84884	−0.173519
$493$	1.85463	0.0835284
$494$	−4.24181	−0.190848
$495$	−16.9632	−0.762438
$496$	0.946224	0.0424867
$497$	1.08345	0.0485994
$498$	−4.77059	−0.213775
$499$	−25.1745	−1.12696	−0.563482	−	0.826129i	$-0.690538\pi$
$499$	−25.1745	−1.12696	−0.563482	+	0.826129i	$0.690538\pi$
$500$	12.1500	0.543365
$501$	−5.47804	−0.244741
$502$	9.31877	0.415917
$503$	11.8342	0.527661	0.263830	−	0.964569i	$-0.415014\pi$
$503$	11.8342	0.527661	0.263830	+	0.964569i	$0.415014\pi$
$504$	2.90542	0.129417
$505$	−37.1883	−1.65486
$506$	−13.3178	−0.592048
$507$	3.02630	0.134403
$508$	20.6583	0.916563
$509$	12.7179	0.563712	0.281856	−	0.959457i	$-0.409050\pi$
$509$	12.7179	0.563712	0.281856	+	0.959457i	$0.409050\pi$
$510$	−2.69834	−0.119485
$511$	2.99282	0.132394
$512$	1.00000	0.0441942
$513$	−4.33391	−0.191347
$514$	29.8289	1.31569
$515$	−0.926148	−0.0408110
$516$	1.38912	0.0611525
$517$	17.0968	0.751917
$518$	−4.06466	−0.178591
$519$	−7.64814	−0.335716
$520$	−3.35641	−0.147189
$521$	22.1863	0.972000	0.486000	−	0.873959i	$-0.338456\pi$
$521$	22.1863	0.972000	0.486000	+	0.873959i	$0.338456\pi$
$522$	1.15964	0.0507560
$523$	39.7618	1.73866	0.869330	−	0.494232i	$-0.164551\pi$
$523$	39.7618	1.73866	0.869330	+	0.494232i	$0.164551\pi$
$524$	−9.75823	−0.426290
$525$	−0.441259	−0.0192581
$526$	−26.0902	−1.13759
$527$	−4.39681	−0.191528
$528$	0.950967	0.0413855
$529$	−4.44956	−0.193459
$530$	11.3934	0.494900
$531$	−2.43752	−0.105779
$532$	2.38627	0.103458
$533$	22.2460	0.963580
$534$	−0.168287	−0.00728250
$535$	−30.1134	−1.30192
$536$	0.881863	0.0380907
$537$	2.85078	0.123020
$538$	−1.20507	−0.0519543
$539$	−3.09211	−0.133187
$540$	−3.42929	−0.147573
$541$	−2.27576	−0.0978427	−0.0489214	−	0.998803i	$-0.515578\pi$
$541$	−2.27576	−0.0978427	−0.0489214	+	0.998803i	$0.515578\pi$
$542$	30.5220	1.31103
$543$	−6.37831	−0.273719
$544$	−4.64669	−0.199225
$545$	−13.9083	−0.595766
$546$	0.546691	0.0233962
$547$	−14.7679	−0.631429	−0.315714	−	0.948854i	$-0.602244\pi$
$547$	−14.7679	−0.631429	−0.315714	+	0.948854i	$0.602244\pi$
$548$	−5.64193	−0.241011
$549$	1.48936	0.0635643
$550$	4.43648	0.189172
$551$	0.952432	0.0405750
$552$	−1.32461	−0.0563790
$553$	−5.73733	−0.243976
$554$	19.0691	0.810170
$555$	2.36036	0.100192
$556$	−16.1984	−0.686966
$557$	40.4269	1.71294	0.856471	−	0.516195i	$-0.172652\pi$
$557$	40.4269	1.71294	0.856471	+	0.516195i	$0.172652\pi$
$558$	−2.74917	−0.116382
$559$	−8.02899	−0.339590
$560$	1.88818	0.0797902
$561$	−4.41885	−0.186564
$562$	1.70890	0.0720856
$563$	−36.1347	−1.52290	−0.761448	−	0.648226i	$-0.775511\pi$
$563$	−36.1347	−1.52290	−0.761448	+	0.648226i	$0.775511\pi$
$564$	1.70047	0.0716029
$565$	4.86693	0.204753
$566$	−1.31932	−0.0554550
$567$	−8.15769	−0.342591
$568$	−1.08345	−0.0454606
$569$	−1.71406	−0.0718571	−0.0359286	−	0.999354i	$-0.511439\pi$
$569$	−1.71406	−0.0718571	−0.0359286	+	0.999354i	$0.511439\pi$
$570$	−1.38571	−0.0580411
$571$	−44.6292	−1.86767	−0.933837	−	0.357700i	$-0.883561\pi$
$571$	−44.6292	−1.86767	−0.933837	+	0.357700i	$0.883561\pi$
$572$	−5.49651	−0.229821
$573$	2.91064	0.121594
$574$	−12.5147	−0.522352
$575$	−6.17960	−0.257707
$576$	−2.90542	−0.121059
$577$	−6.61939	−0.275569	−0.137784	−	0.990462i	$-0.543998\pi$
$577$	−6.61939	−0.275569	−0.137784	+	0.990462i	$0.543998\pi$
$578$	4.59172	0.190991
$579$	4.90486	0.203839
$580$	0.753629	0.0312928
$581$	−15.5118	−0.643537
$582$	−0.0573582	−0.00237757
$583$	18.6581	0.772738
$584$	−2.99282	−0.123844
$585$	9.75178	0.403186
$586$	7.52435	0.310828
$587$	26.2025	1.08149	0.540746	−	0.841186i	$-0.318142\pi$
$587$	26.2025	1.08149	0.540746	+	0.841186i	$0.318142\pi$
$588$	−0.307546	−0.0126830
$589$	−2.25795	−0.0930370
$590$	−1.58410	−0.0652165
$591$	2.91869	0.120059
$592$	4.06466	0.167056
$593$	9.17157	0.376631	0.188316	−	0.982109i	$-0.439697\pi$
$593$	9.17157	0.376631	0.188316	+	0.982109i	$0.439697\pi$
$594$	−5.61585	−0.230421
$595$	−8.77379	−0.359690
$596$	−13.6479	−0.559040
$597$	−4.45105	−0.182169
$598$	7.65613	0.313082
$599$	−3.38216	−0.138191	−0.0690956	−	0.997610i	$-0.522011\pi$
$599$	−3.38216	−0.138191	−0.0690956	+	0.997610i	$0.522011\pi$
$600$	0.441259	0.0180143
$601$	27.6078	1.12614	0.563072	−	0.826408i	$-0.309619\pi$
$601$	27.6078	1.12614	0.563072	+	0.826408i	$0.309619\pi$
$602$	4.51678	0.184090
$603$	−2.56218	−0.104340
$604$	5.17650	0.210629
$605$	2.71680	0.110454
$606$	−6.05721	−0.246057
$607$	17.0990	0.694026	0.347013	−	0.937860i	$-0.387196\pi$
$607$	17.0990	0.694026	0.347013	+	0.937860i	$0.387196\pi$
$608$	−2.38627	−0.0967760
$609$	−0.122751	−0.00497411
$610$	0.967909	0.0391895
$611$	−9.82861	−0.397623
$612$	13.5006	0.545728
$613$	31.3304	1.26542	0.632710	−	0.774388i	$-0.281942\pi$
$613$	31.3304	1.26542	0.632710	+	0.774388i	$0.281942\pi$
$614$	−4.39835	−0.177503
$615$	7.26730	0.293046
$616$	3.09211	0.124585
$617$	−32.9533	−1.32665	−0.663325	−	0.748331i	$-0.730855\pi$
$617$	−32.9533	−1.32665	−0.663325	+	0.748331i	$0.730855\pi$
$618$	−0.150851	−0.00606810
$619$	21.7880	0.875732	0.437866	−	0.899040i	$-0.355734\pi$
$619$	21.7880	0.875732	0.437866	+	0.899040i	$0.355734\pi$
$620$	−1.78664	−0.0717533
$621$	7.82236	0.313900
$622$	−0.0387819	−0.00155501
$623$	−0.547194	−0.0219229
$624$	−0.546691	−0.0218852
$625$	−15.7676	−0.630702
$626$	−25.6215	−1.02404
$627$	−2.26926	−0.0906257
$628$	−4.83990	−0.193133
$629$	−18.8872	−0.753082
$630$	−5.48595	−0.218565
$631$	5.92584	0.235904	0.117952	−	0.993019i	$-0.462367\pi$
$631$	5.92584	0.235904	0.117952	+	0.993019i	$0.462367\pi$
$632$	5.73733	0.228219
$633$	0.408116	0.0162211
$634$	−3.70625	−0.147194
$635$	−39.0066	−1.54793
$636$	1.85576	0.0735856
$637$	1.77759	0.0704307
$638$	1.23415	0.0488606
$639$	3.14787	0.124528
$640$	−1.88818	−0.0746369
$641$	27.4915	1.08585	0.542924	−	0.839782i	$-0.317317\pi$
$641$	27.4915	1.08585	0.542924	+	0.839782i	$0.317317\pi$
$642$	−4.90486	−0.193579
$643$	−29.2339	−1.15287	−0.576435	−	0.817143i	$-0.695557\pi$
$643$	−29.2339	−1.15287	−0.576435	+	0.817143i	$0.695557\pi$
$644$	−4.30702	−0.169720
$645$	−2.62291	−0.103277
$646$	11.0883	0.436262
$647$	2.18332	0.0858350	0.0429175	−	0.999079i	$-0.486335\pi$
$647$	2.18332	0.0858350	0.0429175	+	0.999079i	$0.486335\pi$
$648$	8.15769	0.320464
$649$	−2.59415	−0.101829
$650$	−2.55044	−0.100036
$651$	0.291007	0.0114055
$652$	−4.25710	−0.166721
$653$	−26.1235	−1.02229	−0.511146	−	0.859494i	$-0.670779\pi$
$653$	−26.1235	−1.02229	−0.511146	+	0.859494i	$0.670779\pi$
$654$	−2.26538	−0.0885832
$655$	18.4253	0.719936
$656$	12.5147	0.488616
$657$	8.69538	0.339239
$658$	5.52917	0.215550
$659$	17.6616	0.688000	0.344000	−	0.938970i	$-0.388218\pi$
$659$	17.6616	0.688000	0.344000	+	0.938970i	$0.388218\pi$
$660$	−1.79560	−0.0698935
$661$	28.5098	1.10890	0.554451	−	0.832216i	$-0.312928\pi$
$661$	28.5098	1.10890	0.554451	+	0.832216i	$0.312928\pi$
$662$	−6.64123	−0.258119
$663$	2.54030	0.0986572
$664$	15.5118	0.601974
$665$	−4.50571	−0.174724
$666$	−11.8095	−0.457610
$667$	−1.71906	−0.0665623
$668$	17.8121	0.689171
$669$	6.65040	0.257119
$670$	−1.66512	−0.0643291
$671$	1.58506	0.0611906
$672$	0.307546	0.0118638
$673$	15.1411	0.583646	0.291823	−	0.956472i	$-0.405738\pi$
$673$	15.1411	0.583646	0.291823	+	0.956472i	$0.405738\pi$
$674$	24.3154	0.936593
$675$	−2.60582	−0.100298
$676$	−9.84017	−0.378468
$677$	24.9854	0.960269	0.480134	−	0.877195i	$-0.340588\pi$
$677$	24.9854	0.960269	0.480134	+	0.877195i	$0.340588\pi$
$678$	0.792723	0.0304443
$679$	−0.186503	−0.00715732
$680$	8.77379	0.336460
$681$	0.376690	0.0144348
$682$	−2.92583	−0.112036
$683$	8.12204	0.310781	0.155391	−	0.987853i	$-0.450336\pi$
$683$	8.12204	0.310781	0.155391	+	0.987853i	$0.450336\pi$
$684$	6.93311	0.265094
$685$	10.6530	0.407029
$686$	−1.00000	−0.0381802
$687$	4.24118	0.161811
$688$	−4.51678	−0.172201
$689$	−10.7261	−0.408633
$690$	2.50110	0.0952152
$691$	−11.2368	−0.427468	−0.213734	−	0.976892i	$-0.568563\pi$
$691$	−11.2368	−0.427468	−0.213734	+	0.976892i	$0.568563\pi$
$692$	24.8683	0.945349
$693$	−8.98387	−0.341269
$694$	9.41672	0.357454
$695$	30.5855	1.16018
$696$	0.122751	0.00465286
$697$	−58.1518	−2.20265
$698$	−13.0204	−0.492829
$699$	−1.80339	−0.0682103
$700$	1.43477	0.0542293
$701$	−19.6929	−0.743789	−0.371895	−	0.928275i	$-0.621292\pi$
$701$	−19.6929	−0.743789	−0.371895	+	0.928275i	$0.621292\pi$
$702$	3.22844	0.121850
$703$	−9.69938	−0.365819
$704$	−3.09211	−0.116538
$705$	−3.21080	−0.120926
$706$	−31.6043	−1.18944
$707$	−19.6953	−0.740717
$708$	−0.258018	−0.00969691
$709$	−4.87725	−0.183169	−0.0915846	−	0.995797i	$-0.529193\pi$
$709$	−4.87725	−0.183169	−0.0915846	+	0.995797i	$0.529193\pi$
$710$	2.04575	0.0767757
$711$	−16.6693	−0.625148
$712$	0.547194	0.0205070
$713$	4.07541	0.152625
$714$	−1.42907	−0.0534816
$715$	10.3784	0.388130
$716$	−9.26945	−0.346416
$717$	−8.93455	−0.333667
$718$	26.9058	1.00412
$719$	−17.2141	−0.641978	−0.320989	−	0.947083i	$-0.604015\pi$
$719$	−17.2141	−0.641978	−0.320989	+	0.947083i	$0.604015\pi$
$720$	5.48595	0.204449
$721$	−0.490497	−0.0182671
$722$	−13.3057	−0.495187
$723$	−4.81696	−0.179145
$724$	20.7394	0.770772
$725$	0.572661	0.0212681
$726$	0.442512	0.0164231
$727$	16.5326	0.613160	0.306580	−	0.951845i	$-0.400815\pi$
$727$	16.5326	0.613160	0.306580	+	0.951845i	$0.400815\pi$
$728$	−1.77759	−0.0658819
$729$	−22.0258	−0.815770
$730$	5.65098	0.209152
$731$	20.9881	0.776272
$732$	0.157653	0.00582701
$733$	20.5484	0.758972	0.379486	−	0.925198i	$-0.376101\pi$
$733$	20.5484	0.758972	0.379486	+	0.925198i	$0.376101\pi$
$734$	−19.2909	−0.712039
$735$	0.580703	0.0214195
$736$	4.30702	0.158759
$737$	−2.72682	−0.100444
$738$	−36.3603	−1.33844
$739$	−20.3393	−0.748195	−0.374097	−	0.927389i	$-0.622047\pi$
$739$	−20.3393	−0.748195	−0.374097	+	0.927389i	$0.622047\pi$
$740$	−7.67481	−0.282132
$741$	1.30455	0.0479240
$742$	6.03409	0.221518
$743$	16.2076	0.594597	0.297299	−	0.954785i	$-0.403914\pi$
$743$	16.2076	0.594597	0.297299	+	0.954785i	$0.403914\pi$
$744$	−0.291007	−0.0106688
$745$	25.7697	0.944129
$746$	36.4314	1.33385
$747$	−45.0682	−1.64896
$748$	14.3681	0.525349
$749$	−15.9484	−0.582741
$750$	−3.73669	−0.136445
$751$	19.3313	0.705411	0.352705	−	0.935734i	$-0.385262\pi$
$751$	19.3313	0.705411	0.352705	+	0.935734i	$0.385262\pi$
$752$	−5.52917	−0.201628
$753$	−2.86595	−0.104441
$754$	−0.709490	−0.0258381
$755$	−9.77416	−0.355718
$756$	−1.81619	−0.0660541
$757$	50.7037	1.84286	0.921430	−	0.388545i	$-0.127022\pi$
$757$	50.7037	1.84286	0.921430	+	0.388545i	$0.127022\pi$
$758$	11.1643	0.405507
$759$	4.09583	0.148669
$760$	4.50571	0.163439
$761$	−20.5583	−0.745239	−0.372620	−	0.927984i	$-0.621540\pi$
$761$	−20.5583	−0.745239	−0.372620	+	0.927984i	$0.621540\pi$
$762$	−6.35337	−0.230158
$763$	−7.36597	−0.266666
$764$	−9.46407	−0.342398
$765$	−25.4915	−0.921647
$766$	29.6867	1.07262
$767$	1.49132	0.0538486
$768$	−0.307546	−0.0110976
$769$	22.2272	0.801535	0.400767	−	0.916180i	$-0.368744\pi$
$769$	22.2272	0.801535	0.400767	+	0.916180i	$0.368744\pi$
$770$	−5.83847	−0.210404
$771$	−9.17375	−0.330385
$772$	−15.9484	−0.573995
$773$	45.9239	1.65177	0.825883	−	0.563841i	$-0.190677\pi$
$773$	45.9239	1.65177	0.825883	+	0.563841i	$0.190677\pi$
$774$	13.1231	0.471701
$775$	−1.35762	−0.0487670
$776$	0.186503	0.00669506
$777$	1.25007	0.0448460
$778$	9.20038	0.329850
$779$	−29.8634	−1.06997
$780$	1.03225	0.0369605
$781$	3.35015	0.119878
$782$	−20.0134	−0.715678
$783$	−0.724894	−0.0259056
$784$	1.00000	0.0357143
$785$	9.13861	0.326171
$786$	3.00111	0.107046
$787$	−0.801943	−0.0285862	−0.0142931	−	0.999898i	$-0.504550\pi$
$787$	−0.801943	−0.0285862	−0.0142931	+	0.999898i	$0.504550\pi$
$788$	−9.49025	−0.338076
$789$	8.02395	0.285660
$790$	−10.8331	−0.385425
$791$	2.57757	0.0916480
$792$	8.98387	0.319228
$793$	−0.911219	−0.0323584
$794$	20.0789	0.712573
$795$	−3.50401	−0.124274
$796$	14.4728	0.512974
$797$	−19.0027	−0.673110	−0.336555	−	0.941664i	$-0.609262\pi$
$797$	−19.0027	−0.673110	−0.336555	+	0.941664i	$0.609262\pi$
$798$	−0.733888	−0.0259794
$799$	25.6923	0.908930
$800$	−1.43477	−0.0507269
$801$	−1.58982	−0.0561737
$802$	−4.50474	−0.159068
$803$	9.25412	0.326571
$804$	−0.271214	−0.00956497
$805$	8.13244	0.286631
$806$	1.68200	0.0592459
$807$	0.370615	0.0130463
$808$	19.6953	0.692878
$809$	15.4070	0.541682	0.270841	−	0.962624i	$-0.412698\pi$
$809$	15.4070	0.541682	0.270841	+	0.962624i	$0.412698\pi$
$810$	−15.4032	−0.541213
$811$	28.2496	0.991979	0.495989	−	0.868329i	$-0.334805\pi$
$811$	28.2496	0.991979	0.495989	+	0.868329i	$0.334805\pi$
$812$	0.399130	0.0140067
$813$	−9.38692	−0.329214
$814$	−12.5684	−0.440521
$815$	8.03818	0.281565
$816$	1.42907	0.0500275
$817$	10.7783	0.377083
$818$	−17.0794	−0.597167
$819$	5.16464	0.180467
$820$	−23.6299	−0.825194
$821$	−49.2604	−1.71920	−0.859599	−	0.510969i	$-0.829287\pi$
$821$	−49.2604	−1.71920	−0.859599	+	0.510969i	$0.829287\pi$
$822$	1.73515	0.0605204
$823$	−6.73656	−0.234822	−0.117411	−	0.993083i	$-0.537459\pi$
$823$	−6.73656	−0.234822	−0.117411	+	0.993083i	$0.537459\pi$
$824$	0.490497	0.0170873
$825$	−1.36442	−0.0475030
$826$	−0.838958	−0.0291911
$827$	9.40055	0.326889	0.163445	−	0.986553i	$-0.447740\pi$
$827$	9.40055	0.326889	0.163445	+	0.986553i	$0.447740\pi$
$828$	−12.5137	−0.434881
$829$	−17.5153	−0.608330	−0.304165	−	0.952619i	$-0.598377\pi$
$829$	−17.5153	−0.608330	−0.304165	+	0.952619i	$0.598377\pi$
$830$	−29.2890	−1.01664
$831$	−5.86464	−0.203442
$832$	1.77759	0.0616269
$833$	−4.64669	−0.160998
$834$	4.98176	0.172504
$835$	−33.6325	−1.16390
$836$	7.37861	0.255195
$837$	1.71852	0.0594007
$838$	27.7579	0.958880
$839$	−17.1676	−0.592693	−0.296346	−	0.955081i	$-0.595768\pi$
$839$	−17.1676	−0.592693	−0.296346	+	0.955081i	$0.595768\pi$
$840$	−0.580703	−0.0200361
$841$	−28.8407	−0.994507
$842$	−18.6848	−0.643919
$843$	−0.525566	−0.0181014
$844$	−1.32701	−0.0456774
$845$	18.5800	0.639172
$846$	16.0645	0.552310
$847$	1.43885	0.0494394
$848$	−6.03409	−0.207211
$849$	0.405750	0.0139253
$850$	6.66694	0.228674
$851$	17.5066	0.600118
$852$	0.333211	0.0114156
$853$	46.2392	1.58320	0.791600	−	0.611039i	$-0.209248\pi$
$853$	46.2392	1.58320	0.791600	+	0.611039i	$0.209248\pi$
$854$	0.512615	0.0175413
$855$	−13.0910	−0.447701
$856$	15.9484	0.545104
$857$	18.2350	0.622896	0.311448	−	0.950263i	$-0.399186\pi$
$857$	18.2350	0.622896	0.311448	+	0.950263i	$0.399186\pi$
$858$	1.69043	0.0577103
$859$	7.98616	0.272484	0.136242	−	0.990676i	$-0.456498\pi$
$859$	7.98616	0.272484	0.136242	+	0.990676i	$0.456498\pi$
$860$	8.52850	0.290819
$861$	3.84884	0.131168
$862$	−1.00000	−0.0340601
$863$	−12.1939	−0.415085	−0.207543	−	0.978226i	$-0.566547\pi$
$863$	−12.1939	−0.415085	−0.207543	+	0.978226i	$0.566547\pi$
$864$	1.81619	0.0617879
$865$	−46.9558	−1.59654
$866$	−17.2534	−0.586293
$867$	−1.41217	−0.0479597
$868$	−0.946224	−0.0321169
$869$	−17.7405	−0.601804
$870$	−0.231776	−0.00785793
$871$	1.56759	0.0531159
$872$	7.36597	0.249443
$873$	−0.541868	−0.0183395
$874$	−10.2777	−0.347649
$875$	−12.1500	−0.410745
$876$	0.920429	0.0310984
$877$	−21.9595	−0.741520	−0.370760	−	0.928729i	$-0.620903\pi$
$877$	−21.9595	−0.741520	−0.370760	+	0.928729i	$0.620903\pi$
$878$	−25.0805	−0.846427
$879$	−2.31408	−0.0780521
$880$	5.83847	0.196815
$881$	37.4318	1.26111	0.630554	−	0.776145i	$-0.282828\pi$
$881$	37.4318	1.26111	0.630554	+	0.776145i	$0.282828\pi$
$882$	−2.90542	−0.0978304
$883$	−57.7661	−1.94398	−0.971992	−	0.235012i	$-0.924487\pi$
$883$	−57.7661	−1.94398	−0.971992	+	0.235012i	$0.924487\pi$
$884$	−8.25992	−0.277811
$885$	0.487185	0.0163765
$886$	−40.9140	−1.37453
$887$	−41.6058	−1.39699	−0.698493	−	0.715617i	$-0.746146\pi$
$887$	−41.6058	−1.39699	−0.698493	+	0.715617i	$0.746146\pi$
$888$	−1.25007	−0.0419496
$889$	−20.6583	−0.692856
$890$	−1.03320	−0.0346330
$891$	−25.2245	−0.845052
$892$	−21.6241	−0.724028
$893$	13.1941	0.441524
$894$	4.19736	0.140381
$895$	17.5024	0.585041
$896$	−1.00000	−0.0334077
$897$	−2.35461	−0.0786182
$898$	0.546646	0.0182418
$899$	−0.377666	−0.0125959
$900$	4.16861	0.138954
$901$	28.0385	0.934099
$902$	−38.6967	−1.28846
$903$	−1.38912	−0.0462269
$904$	−2.57757	−0.0857288
$905$	−39.1597	−1.30171
$906$	−1.59201	−0.0528910
$907$	−50.0197	−1.66088	−0.830438	−	0.557111i	$-0.811910\pi$
$907$	−50.0197	−1.66088	−0.830438	+	0.557111i	$0.811910\pi$
$908$	−1.22482	−0.0406472
$909$	−57.2230	−1.89797
$910$	3.35641	0.111264
$911$	−12.0331	−0.398673	−0.199336	−	0.979931i	$-0.563879\pi$
$911$	−12.0331	−0.398673	−0.199336	+	0.979931i	$0.563879\pi$
$912$	0.733888	0.0243015
$913$	−47.9641	−1.58738
$914$	30.2903	1.00191
$915$	−0.297677	−0.00984089
$916$	−13.7904	−0.455648
$917$	9.75823	0.322245
$918$	−8.43926	−0.278537
$919$	17.2026	0.567460	0.283730	−	0.958904i	$-0.408428\pi$
$919$	17.2026	0.567460	0.283730	+	0.958904i	$0.408428\pi$
$920$	−8.13244	−0.268119
$921$	1.35269	0.0445728
$922$	−2.22466	−0.0732654
$923$	−1.92593	−0.0633929
$924$	−0.950967	−0.0312845
$925$	−5.83186	−0.191750
$926$	−39.9034	−1.31131
$927$	−1.42510	−0.0468064
$928$	−0.399130	−0.0131021
$929$	−4.45003	−0.146001	−0.0730003	−	0.997332i	$-0.523257\pi$
$929$	−4.45003	−0.146001	−0.0730003	+	0.997332i	$0.523257\pi$
$930$	0.549475	0.0180180
$931$	−2.38627	−0.0782069
$932$	5.86379	0.192075
$933$	0.0119272	0.000390480 0
$934$	17.2350	0.563945
$935$	−27.1295	−0.887231
$936$	−5.16464	−0.168812
$937$	−30.6345	−1.00079	−0.500393	−	0.865798i	$-0.666811\pi$
$937$	−30.6345	−1.00079	−0.500393	+	0.865798i	$0.666811\pi$
$938$	−0.881863	−0.0287939
$939$	7.87980	0.257148
$940$	10.4401	0.340518
$941$	−40.7464	−1.32829	−0.664147	−	0.747602i	$-0.731205\pi$
$941$	−40.7464	−1.32829	−0.664147	+	0.747602i	$0.731205\pi$
$942$	1.48849	0.0484977
$943$	53.9009	1.75526
$944$	0.838958	0.0273057
$945$	3.42929	0.111555
$946$	13.9664	0.454086
$947$	22.7244	0.738444	0.369222	−	0.929341i	$-0.379624\pi$
$947$	22.7244	0.738444	0.369222	+	0.929341i	$0.379624\pi$
$948$	−1.76449	−0.0573081
$949$	−5.32001	−0.172695
$950$	3.42376	0.111081
$951$	1.13984	0.0369619
$952$	4.64669	0.150600
$953$	14.8219	0.480129	0.240064	−	0.970757i	$-0.422831\pi$
$953$	14.8219	0.480129	0.240064	+	0.970757i	$0.422831\pi$
$954$	17.5315	0.567604
$955$	17.8699	0.578255
$956$	29.0511	0.939580
$957$	−0.379559	−0.0122694
$958$	26.8274	0.866753
$959$	5.64193	0.182187
$960$	0.580703	0.0187421
$961$	−30.1047	−0.971118
$962$	7.22530	0.232953
$963$	−46.3366	−1.49318
$964$	15.6626	0.504457
$965$	30.1134	0.969385
$966$	1.32461	0.0426186
$967$	−26.7449	−0.860057	−0.430029	−	0.902815i	$-0.641497\pi$
$967$	−26.7449	−0.860057	−0.430029	+	0.902815i	$0.641497\pi$
$968$	−1.43885	−0.0462463
$969$	−3.41015	−0.109550
$970$	−0.352151	−0.0113069
$971$	36.5123	1.17174	0.585868	−	0.810406i	$-0.300754\pi$
$971$	36.5123	1.17174	0.585868	+	0.810406i	$0.300754\pi$
$972$	−7.95742	−0.255235
$973$	16.1984	0.519297
$974$	−35.5943	−1.14052
$975$	0.784378	0.0251202
$976$	−0.512615	−0.0164084
$977$	10.4356	0.333864	0.166932	−	0.985968i	$-0.446614\pi$
$977$	10.4356	0.333864	0.166932	+	0.985968i	$0.446614\pi$
$978$	1.30926	0.0418654
$979$	−1.69198	−0.0540760
$980$	−1.88818	−0.0603157
$981$	−21.4012	−0.683288
$982$	−17.8443	−0.569435
$983$	−21.3755	−0.681772	−0.340886	−	0.940105i	$-0.610727\pi$
$983$	−21.3755	−0.681772	−0.340886	+	0.940105i	$0.610727\pi$
$984$	−3.84884	−0.122696
$985$	17.9193	0.570957
$986$	1.85463	0.0590635
$987$	−1.70047	−0.0541267
$988$	−4.24181	−0.134950
$989$	−19.4539	−0.618597
$990$	−16.9632	−0.539125
$991$	5.15255	0.163676	0.0818381	−	0.996646i	$-0.473921\pi$
$991$	5.15255	0.163676	0.0818381	+	0.996646i	$0.473921\pi$
$992$	0.946224	0.0300426
$993$	2.04248	0.0648162
$994$	1.08345	0.0343650
$995$	−27.3272	−0.866331
$996$	−4.77059	−0.151162
$997$	−4.11267	−0.130250	−0.0651248	−	0.997877i	$-0.520745\pi$
$997$	−4.11267	−0.130250	−0.0651248	+	0.997877i	$0.520745\pi$
$998$	−25.1745	−0.796883
$999$	7.38218	0.233562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.r.1.13	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.r.1.13	✓	31	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.307546 q^{3} +1.00000 q^{4} -1.88818 q^{5} -0.307546 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.90542 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.307546 q^{3} +1.00000 q^{4} -1.88818 q^{5} -0.307546 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.90542 q^{9} -1.88818 q^{10} -3.09211 q^{11} -0.307546 q^{12} +1.77759 q^{13} -1.00000 q^{14} +0.580703 q^{15} +1.00000 q^{16} -4.64669 q^{17} -2.90542 q^{18} -2.38627 q^{19} -1.88818 q^{20} +0.307546 q^{21} -3.09211 q^{22} +4.30702 q^{23} -0.307546 q^{24} -1.43477 q^{25} +1.77759 q^{26} +1.81619 q^{27} -1.00000 q^{28} -0.399130 q^{29} +0.580703 q^{30} +0.946224 q^{31} +1.00000 q^{32} +0.950967 q^{33} -4.64669 q^{34} +1.88818 q^{35} -2.90542 q^{36} +4.06466 q^{37} -2.38627 q^{38} -0.546691 q^{39} -1.88818 q^{40} +12.5147 q^{41} +0.307546 q^{42} -4.51678 q^{43} -3.09211 q^{44} +5.48595 q^{45} +4.30702 q^{46} -5.52917 q^{47} -0.307546 q^{48} +1.00000 q^{49} -1.43477 q^{50} +1.42907 q^{51} +1.77759 q^{52} -6.03409 q^{53} +1.81619 q^{54} +5.83847 q^{55} -1.00000 q^{56} +0.733888 q^{57} -0.399130 q^{58} +0.838958 q^{59} +0.580703 q^{60} -0.512615 q^{61} +0.946224 q^{62} +2.90542 q^{63} +1.00000 q^{64} -3.35641 q^{65} +0.950967 q^{66} +0.881863 q^{67} -4.64669 q^{68} -1.32461 q^{69} +1.88818 q^{70} -1.08345 q^{71} -2.90542 q^{72} -2.99282 q^{73} +4.06466 q^{74} +0.441259 q^{75} -2.38627 q^{76} +3.09211 q^{77} -0.546691 q^{78} +5.73733 q^{79} -1.88818 q^{80} +8.15769 q^{81} +12.5147 q^{82} +15.5118 q^{83} +0.307546 q^{84} +8.77379 q^{85} -4.51678 q^{86} +0.122751 q^{87} -3.09211 q^{88} +0.547194 q^{89} +5.48595 q^{90} -1.77759 q^{91} +4.30702 q^{92} -0.291007 q^{93} -5.52917 q^{94} +4.50571 q^{95} -0.307546 q^{96} +0.186503 q^{97} +1.00000 q^{98} +8.98387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9}+O(q^{10}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9	\( 31 q + 31 q^{2} + 7 q^{3} + 31 q^{4} + 15 q^{5} + 7 q^{6} - 31 q^{7} + 31 q^{8} + 42 q^{9} + 15 q^{10} + 12 q^{11} + 7 q^{12} + 26 q^{13} - 31 q^{14} + 6 q^{15} + 31 q^{16} + 33 q^{17} + 42 q^{18} + 34 q^{19} + 15 q^{20} - 7 q^{21} + 12 q^{22} - 14 q^{23} + 7 q^{24} + 58 q^{25} + 26 q^{26} + 28 q^{27} - 31 q^{28} + 11 q^{29} + 6 q^{30} + 19 q^{31} + 31 q^{32} + 43 q^{33} + 33 q^{34} - 15 q^{35} + 42 q^{36} + 2 q^{37} + 34 q^{38} - 16 q^{39} + 15 q^{40} + 53 q^{41} - 7 q^{42} + 22 q^{43} + 12 q^{44} + 43 q^{45} - 14 q^{46} + 27 q^{47} + 7 q^{48} + 31 q^{49} + 58 q^{50} + 17 q^{51} + 26 q^{52} + 11 q^{53} + 28 q^{54} + 19 q^{55} - 31 q^{56} + 45 q^{57} + 11 q^{58} + 54 q^{59} + 6 q^{60} + 41 q^{61} + 19 q^{62} - 42 q^{63} + 31 q^{64} + 30 q^{65} + 43 q^{66} + 13 q^{67} + 33 q^{68} + 17 q^{69} - 15 q^{70} + 43 q^{71} + 42 q^{72} + 42 q^{73} + 2 q^{74} + 62 q^{75} + 34 q^{76} - 12 q^{77} - 16 q^{78} - 12 q^{79} + 15 q^{80} + 63 q^{81} + 53 q^{82} + 35 q^{83} - 7 q^{84} + 16 q^{85} + 22 q^{86} - 4 q^{87} + 12 q^{88} + 115 q^{89} + 43 q^{90} - 26 q^{91} - 14 q^{92} + q^{93} + 27 q^{94} - 13 q^{95} + 7 q^{96} + 32 q^{97} + 31 q^{98} + 34 q^{99}+O(q^{100}) \) 31 * q + 31 * q^2 + 7 * q^3 + 31 * q^4 + 15 * q^5 + 7 * q^6 - 31 * q^7 + 31 * q^8 + 42 * q^9 + 15 * q^10 + 12 * q^11 + 7 * q^12 + 26 * q^13 - 31 * q^14 + 6 * q^15 + 31 * q^16 + 33 * q^17 + 42 * q^18 + 34 * q^19 + 15 * q^20 - 7 * q^21 + 12 * q^22 - 14 * q^23 + 7 * q^24 + 58 * q^25 + 26 * q^26 + 28 * q^27 - 31 * q^28 + 11 * q^29 + 6 * q^30 + 19 * q^31 + 31 * q^32 + 43 * q^33 + 33 * q^34 - 15 * q^35 + 42 * q^36 + 2 * q^37 + 34 * q^38 - 16 * q^39 + 15 * q^40 + 53 * q^41 - 7 * q^42 + 22 * q^43 + 12 * q^44 + 43 * q^45 - 14 * q^46 + 27 * q^47 + 7 * q^48 + 31 * q^49 + 58 * q^50 + 17 * q^51 + 26 * q^52 + 11 * q^53 + 28 * q^54 + 19 * q^55 - 31 * q^56 + 45 * q^57 + 11 * q^58 + 54 * q^59 + 6 * q^60 + 41 * q^61 + 19 * q^62 - 42 * q^63 + 31 * q^64 + 30 * q^65 + 43 * q^66 + 13 * q^67 + 33 * q^68 + 17 * q^69 - 15 * q^70 + 43 * q^71 + 42 * q^72 + 42 * q^73 + 2 * q^74 + 62 * q^75 + 34 * q^76 - 12 * q^77 - 16 * q^78 - 12 * q^79 + 15 * q^80 + 63 * q^81 + 53 * q^82 + 35 * q^83 - 7 * q^84 + 16 * q^85 + 22 * q^86 - 4 * q^87 + 12 * q^88 + 115 * q^89 + 43 * q^90 - 26 * q^91 - 14 * q^92 + q^93 + 27 * q^94 - 13 * q^95 + 7 * q^96 + 32 * q^97 + 31 * q^98 + 34 * q^99

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