LMFDB - Embedded newform 6034.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 36 x^{18} + 97 x^{17} + 573 x^{16} - 1292 x^{15} - 5329 x^{14} + 9121 x^{13} + \cdots - 21776 $ x^20 - 3x^19 - 36x^18 + 97x^17 + 573x^16 - 1292x^15 - 5329x^14 + 9121x^13 + 31784x^12 - 36075x^11 - 124276x^10 + 74594x^9 + 312410x^8 - 47208x^7 - 477646x^6 - 101137x^5 + 391391x^4 + 205294x^3 - 112848x^2 - 109144*x - 21776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-0.860159$ of defining polynomial
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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.860159 q^{3} +1.00000 q^{4} -0.340662 q^{5} +0.860159 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.26013 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.860159 q^{3} +1.00000 q^{4} -0.340662 q^{5} +0.860159 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.26013 q^{9} -0.340662 q^{10} +5.68270 q^{11} +0.860159 q^{12} +0.227482 q^{13} -1.00000 q^{14} -0.293024 q^{15} +1.00000 q^{16} -8.10736 q^{17} -2.26013 q^{18} -4.24928 q^{19} -0.340662 q^{20} -0.860159 q^{21} +5.68270 q^{22} +2.64862 q^{23} +0.860159 q^{24} -4.88395 q^{25} +0.227482 q^{26} -4.52455 q^{27} -1.00000 q^{28} -3.69994 q^{29} -0.293024 q^{30} -3.23746 q^{31} +1.00000 q^{32} +4.88803 q^{33} -8.10736 q^{34} +0.340662 q^{35} -2.26013 q^{36} -6.09832 q^{37} -4.24928 q^{38} +0.195671 q^{39} -0.340662 q^{40} +3.58541 q^{41} -0.860159 q^{42} +4.72035 q^{43} +5.68270 q^{44} +0.769939 q^{45} +2.64862 q^{46} -0.338317 q^{47} +0.860159 q^{48} +1.00000 q^{49} -4.88395 q^{50} -6.97362 q^{51} +0.227482 q^{52} +8.13973 q^{53} -4.52455 q^{54} -1.93588 q^{55} -1.00000 q^{56} -3.65506 q^{57} -3.69994 q^{58} -13.6930 q^{59} -0.293024 q^{60} -8.33524 q^{61} -3.23746 q^{62} +2.26013 q^{63} +1.00000 q^{64} -0.0774946 q^{65} +4.88803 q^{66} -0.319047 q^{67} -8.10736 q^{68} +2.27824 q^{69} +0.340662 q^{70} -16.3054 q^{71} -2.26013 q^{72} +4.74322 q^{73} -6.09832 q^{74} -4.20097 q^{75} -4.24928 q^{76} -5.68270 q^{77} +0.195671 q^{78} +9.18061 q^{79} -0.340662 q^{80} +2.88855 q^{81} +3.58541 q^{82} -5.46591 q^{83} -0.860159 q^{84} +2.76187 q^{85} +4.72035 q^{86} -3.18254 q^{87} +5.68270 q^{88} -4.64881 q^{89} +0.769939 q^{90} -0.227482 q^{91} +2.64862 q^{92} -2.78473 q^{93} -0.338317 q^{94} +1.44757 q^{95} +0.860159 q^{96} +4.79958 q^{97} +1.00000 q^{98} -12.8436 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * 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
$3$	0.860159	0.496613	0.248307	−	0.968681i	$-0.420126\pi$
$3$	0.860159	0.496613	0.248307	+	0.968681i	$0.420126\pi$
$4$	1.00000	0.500000
$5$	−0.340662	−0.152349	−0.0761743	−	0.997095i	$-0.524271\pi$
$5$	−0.340662	−0.152349	−0.0761743	+	0.997095i	$0.524271\pi$
$6$	0.860159	0.351159
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	−2.26013	−0.753375
$10$	−0.340662	−0.107727
$11$	5.68270	1.71340	0.856699	−	0.515816i	$-0.172511\pi$
$11$	5.68270	1.71340	0.856699	+	0.515816i	$0.172511\pi$
$12$	0.860159	0.248307
$13$	0.227482	0.0630923	0.0315461	−	0.999502i	$-0.489957\pi$
$13$	0.227482	0.0630923	0.0315461	+	0.999502i	$0.489957\pi$
$14$	−1.00000	−0.267261
$15$	−0.293024	−0.0756583
$16$	1.00000	0.250000
$17$	−8.10736	−1.96632	−0.983162	−	0.182737i	$-0.941504\pi$
$17$	−8.10736	−1.96632	−0.983162	+	0.182737i	$0.941504\pi$
$18$	−2.26013	−0.532717
$19$	−4.24928	−0.974852	−0.487426	−	0.873164i	$-0.662064\pi$
$19$	−4.24928	−0.974852	−0.487426	+	0.873164i	$0.662064\pi$
$20$	−0.340662	−0.0761743
$21$	−0.860159	−0.187702
$22$	5.68270	1.21156
$23$	2.64862	0.552276	0.276138	−	0.961118i	$-0.410945\pi$
$23$	2.64862	0.552276	0.276138	+	0.961118i	$0.410945\pi$
$24$	0.860159	0.175579
$25$	−4.88395	−0.976790
$26$	0.227482	0.0446130
$27$	−4.52455	−0.870749
$28$	−1.00000	−0.188982
$29$	−3.69994	−0.687062	−0.343531	−	0.939141i	$-0.611623\pi$
$29$	−3.69994	−0.687062	−0.343531	+	0.939141i	$0.611623\pi$
$30$	−0.293024	−0.0534985
$31$	−3.23746	−0.581465	−0.290733	−	0.956804i	$-0.593899\pi$
$31$	−3.23746	−0.581465	−0.290733	+	0.956804i	$0.593899\pi$
$32$	1.00000	0.176777
$33$	4.88803	0.850896
$34$	−8.10736	−1.39040
$35$	0.340662	0.0575824
$36$	−2.26013	−0.376688
$37$	−6.09832	−1.00256	−0.501279	−	0.865286i	$-0.667137\pi$
$37$	−6.09832	−1.00256	−0.501279	+	0.865286i	$0.667137\pi$
$38$	−4.24928	−0.689324
$39$	0.195671	0.0313325
$40$	−0.340662	−0.0538634
$41$	3.58541	0.559947	0.279974	−	0.960008i	$-0.409674\pi$
$41$	3.58541	0.559947	0.279974	+	0.960008i	$0.409674\pi$
$42$	−0.860159	−0.132725
$43$	4.72035	0.719846	0.359923	−	0.932982i	$-0.382803\pi$
$43$	4.72035	0.719846	0.359923	+	0.932982i	$0.382803\pi$
$44$	5.68270	0.856699
$45$	0.769939	0.114776
$46$	2.64862	0.390518
$47$	−0.338317	−0.0493486	−0.0246743	−	0.999696i	$-0.507855\pi$
$47$	−0.338317	−0.0493486	−0.0246743	+	0.999696i	$0.507855\pi$
$48$	0.860159	0.124153
$49$	1.00000	0.142857
$50$	−4.88395	−0.690695
$51$	−6.97362	−0.976502
$52$	0.227482	0.0315461
$53$	8.13973	1.11808	0.559039	−	0.829141i	$-0.311170\pi$
$53$	8.13973	1.11808	0.559039	+	0.829141i	$0.311170\pi$
$54$	−4.52455	−0.615713
$55$	−1.93588	−0.261034
$56$	−1.00000	−0.133631
$57$	−3.65506	−0.484124
$58$	−3.69994	−0.485826
$59$	−13.6930	−1.78267	−0.891336	−	0.453343i	$-0.850231\pi$
$59$	−13.6930	−1.78267	−0.891336	+	0.453343i	$0.850231\pi$
$60$	−0.293024	−0.0378292
$61$	−8.33524	−1.06722	−0.533609	−	0.845731i	$-0.679165\pi$
$61$	−8.33524	−1.06722	−0.533609	+	0.845731i	$0.679165\pi$
$62$	−3.23746	−0.411158
$63$	2.26013	0.284749
$64$	1.00000	0.125000
$65$	−0.0774946	−0.00961202
$66$	4.88803	0.601675
$67$	−0.319047	−0.0389778	−0.0194889	−	0.999810i	$-0.506204\pi$
$67$	−0.319047	−0.0389778	−0.0194889	+	0.999810i	$0.506204\pi$
$68$	−8.10736	−0.983162
$69$	2.27824	0.274267
$70$	0.340662	0.0407169
$71$	−16.3054	−1.93510	−0.967548	−	0.252689i	$-0.918685\pi$
$71$	−16.3054	−1.93510	−0.967548	+	0.252689i	$0.918685\pi$
$72$	−2.26013	−0.266358
$73$	4.74322	0.555151	0.277576	−	0.960704i	$-0.410469\pi$
$73$	4.74322	0.555151	0.277576	+	0.960704i	$0.410469\pi$
$74$	−6.09832	−0.708916
$75$	−4.20097	−0.485087
$76$	−4.24928	−0.487426
$77$	−5.68270	−0.647604
$78$	0.195671	0.0221554
$79$	9.18061	1.03290	0.516449	−	0.856318i	$-0.327253\pi$
$79$	9.18061	1.03290	0.516449	+	0.856318i	$0.327253\pi$
$80$	−0.340662	−0.0380872
$81$	2.88855	0.320950
$82$	3.58541	0.395943
$83$	−5.46591	−0.599961	−0.299981	−	0.953945i	$-0.596980\pi$
$83$	−5.46591	−0.599961	−0.299981	+	0.953945i	$0.596980\pi$
$84$	−0.860159	−0.0938511
$85$	2.76187	0.299567
$86$	4.72035	0.509008
$87$	−3.18254	−0.341204
$88$	5.68270	0.605778
$89$	−4.64881	−0.492772	−0.246386	−	0.969172i	$-0.579243\pi$
$89$	−4.64881	−0.492772	−0.246386	+	0.969172i	$0.579243\pi$
$90$	0.769939	0.0811587
$91$	−0.227482	−0.0238466
$92$	2.64862	0.276138
$93$	−2.78473	−0.288763
$94$	−0.338317	−0.0348947
$95$	1.44757	0.148517
$96$	0.860159	0.0877896
$97$	4.79958	0.487323	0.243662	−	0.969860i	$-0.421651\pi$
$97$	4.79958	0.487323	0.243662	+	0.969860i	$0.421651\pi$
$98$	1.00000	0.101015
$99$	−12.8436	−1.29083
$100$	−4.88395	−0.488395
$101$	−3.11910	−0.310363	−0.155181	−	0.987886i	$-0.549596\pi$
$101$	−3.11910	−0.310363	−0.155181	+	0.987886i	$0.549596\pi$
$102$	−6.97362	−0.690491
$103$	−5.14608	−0.507059	−0.253529	−	0.967328i	$-0.581591\pi$
$103$	−5.14608	−0.507059	−0.253529	+	0.967328i	$0.581591\pi$
$104$	0.227482	0.0223065
$105$	0.293024	0.0285962
$106$	8.13973	0.790600
$107$	−4.06017	−0.392511	−0.196256	−	0.980553i	$-0.562878\pi$
$107$	−4.06017	−0.392511	−0.196256	+	0.980553i	$0.562878\pi$
$108$	−4.52455	−0.435375
$109$	−1.56945	−0.150326	−0.0751628	−	0.997171i	$-0.523948\pi$
$109$	−1.56945	−0.150326	−0.0751628	+	0.997171i	$0.523948\pi$
$110$	−1.93588	−0.184579
$111$	−5.24553	−0.497884
$112$	−1.00000	−0.0944911
$113$	14.7966	1.39195	0.695975	−	0.718066i	$-0.254972\pi$
$113$	14.7966	1.39195	0.695975	+	0.718066i	$0.254972\pi$
$114$	−3.65506	−0.342328
$115$	−0.902284	−0.0841384
$116$	−3.69994	−0.343531
$117$	−0.514139	−0.0475322
$118$	−13.6930	−1.26054
$119$	8.10736	0.743200
$120$	−0.293024	−0.0267493
$121$	21.2931	1.93573
$122$	−8.33524	−0.754637
$123$	3.08403	0.278077
$124$	−3.23746	−0.290733
$125$	3.36709	0.301161
$126$	2.26013	0.201348
$127$	−19.2865	−1.71140	−0.855702	−	0.517469i	$-0.826874\pi$
$127$	−19.2865	−1.71140	−0.855702	+	0.517469i	$0.826874\pi$
$128$	1.00000	0.0883883
$129$	4.06025	0.357485
$130$	−0.0774946	−0.00679673
$131$	4.12248	0.360183	0.180092	−	0.983650i	$-0.442361\pi$
$131$	4.12248	0.360183	0.180092	+	0.983650i	$0.442361\pi$
$132$	4.88803	0.425448
$133$	4.24928	0.368459
$134$	−0.319047	−0.0275615
$135$	1.54134	0.132657
$136$	−8.10736	−0.695200
$137$	14.2058	1.21369	0.606843	−	0.794821i	$-0.292436\pi$
$137$	14.2058	1.21369	0.606843	+	0.794821i	$0.292436\pi$
$138$	2.27824	0.193936
$139$	0.0336061	0.00285044	0.00142522	−	0.999999i	$-0.499546\pi$
$139$	0.0336061	0.00285044	0.00142522	+	0.999999i	$0.499546\pi$
$140$	0.340662	0.0287912
$141$	−0.291007	−0.0245072
$142$	−16.3054	−1.36832
$143$	1.29271	0.108102
$144$	−2.26013	−0.188344
$145$	1.26043	0.104673
$146$	4.74322	0.392551
$147$	0.860159	0.0709447
$148$	−6.09832	−0.501279
$149$	14.9473	1.22453	0.612264	−	0.790654i	$-0.290259\pi$
$149$	14.9473	1.22453	0.612264	+	0.790654i	$0.290259\pi$
$150$	−4.20097	−0.343008
$151$	7.62294	0.620346	0.310173	−	0.950680i	$-0.399613\pi$
$151$	7.62294	0.620346	0.310173	+	0.950680i	$0.399613\pi$
$152$	−4.24928	−0.344662
$153$	18.3237	1.48138
$154$	−5.68270	−0.457925
$155$	1.10288	0.0885855
$156$	0.195671	0.0156662
$157$	−15.9038	−1.26926	−0.634632	−	0.772815i	$-0.718848\pi$
$157$	−15.9038	−1.26926	−0.634632	+	0.772815i	$0.718848\pi$
$158$	9.18061	0.730370
$159$	7.00146	0.555252
$160$	−0.340662	−0.0269317
$161$	−2.64862	−0.208741
$162$	2.88855	0.226946
$163$	−21.7578	−1.70420	−0.852101	−	0.523377i	$-0.824672\pi$
$163$	−21.7578	−1.70420	−0.852101	+	0.523377i	$0.824672\pi$
$164$	3.58541	0.279974
$165$	−1.66516	−0.129633
$166$	−5.46591	−0.424237
$167$	−7.53265	−0.582894	−0.291447	−	0.956587i	$-0.594137\pi$
$167$	−7.53265	−0.582894	−0.291447	+	0.956587i	$0.594137\pi$
$168$	−0.860159	−0.0663627
$169$	−12.9483	−0.996019
$170$	2.76187	0.211826
$171$	9.60391	0.734429
$172$	4.72035	0.359923
$173$	18.6287	1.41632	0.708158	−	0.706054i	$-0.249526\pi$
$173$	18.6287	1.41632	0.708158	+	0.706054i	$0.249526\pi$
$174$	−3.18254	−0.241268
$175$	4.88395	0.369192
$176$	5.68270	0.428350
$177$	−11.7781	−0.885298
$178$	−4.64881	−0.348443
$179$	6.88746	0.514793	0.257397	−	0.966306i	$-0.417135\pi$
$179$	6.88746	0.514793	0.257397	+	0.966306i	$0.417135\pi$
$180$	0.769939	0.0573879
$181$	−21.8393	−1.62330	−0.811649	−	0.584145i	$-0.801430\pi$
$181$	−21.8393	−1.62330	−0.811649	+	0.584145i	$0.801430\pi$
$182$	−0.227482	−0.0168621
$183$	−7.16964	−0.529995
$184$	2.64862	0.195259
$185$	2.07747	0.152738
$186$	−2.78473	−0.204187
$187$	−46.0717	−3.36910
$188$	−0.338317	−0.0246743
$189$	4.52455	0.329112
$190$	1.44757	0.105018
$191$	9.02783	0.653231	0.326615	−	0.945157i	$-0.394092\pi$
$191$	9.02783	0.653231	0.326615	+	0.945157i	$0.394092\pi$
$192$	0.860159	0.0620766
$193$	−8.43384	−0.607081	−0.303541	−	0.952819i	$-0.598169\pi$
$193$	−8.43384	−0.607081	−0.303541	+	0.952819i	$0.598169\pi$
$194$	4.79958	0.344590
$195$	−0.0666577	−0.00477346
$196$	1.00000	0.0714286
$197$	10.9384	0.779328	0.389664	−	0.920957i	$-0.372591\pi$
$197$	10.9384	0.779328	0.389664	+	0.920957i	$0.372591\pi$
$198$	−12.8436	−0.912756
$199$	27.9189	1.97912	0.989561	−	0.144116i	$-0.0460338\pi$
$199$	27.9189	1.97912	0.989561	+	0.144116i	$0.0460338\pi$
$200$	−4.88395	−0.345347
$201$	−0.274431	−0.0193569
$202$	−3.11910	−0.219459
$203$	3.69994	0.259685
$204$	−6.97362	−0.488251
$205$	−1.22141	−0.0853072
$206$	−5.14608	−0.358545
$207$	−5.98622	−0.416071
$208$	0.227482	0.0157731
$209$	−24.1474	−1.67031
$210$	0.293024	0.0202205
$211$	−3.02438	−0.208207	−0.104103	−	0.994566i	$-0.533197\pi$
$211$	−3.02438	−0.208207	−0.104103	+	0.994566i	$0.533197\pi$
$212$	8.13973	0.559039
$213$	−14.0252	−0.960994
$214$	−4.06017	−0.277547
$215$	−1.60804	−0.109668
$216$	−4.52455	−0.307856
$217$	3.23746	0.219773
$218$	−1.56945	−0.106296
$219$	4.07992	0.275696
$220$	−1.93588	−0.130517
$221$	−1.84428	−0.124060
$222$	−5.24553	−0.352057
$223$	−20.5951	−1.37915	−0.689576	−	0.724213i	$-0.742203\pi$
$223$	−20.5951	−1.37915	−0.689576	+	0.724213i	$0.742203\pi$
$224$	−1.00000	−0.0668153
$225$	11.0383	0.735889
$226$	14.7966	0.984258
$227$	−15.1081	−1.00276	−0.501379	−	0.865228i	$-0.667174\pi$
$227$	−15.1081	−1.00276	−0.501379	+	0.865228i	$0.667174\pi$
$228$	−3.65506	−0.242062
$229$	−0.232037	−0.0153335	−0.00766673	−	0.999971i	$-0.502440\pi$
$229$	−0.232037	−0.0153335	−0.00766673	+	0.999971i	$0.502440\pi$
$230$	−0.902284	−0.0594949
$231$	−4.88803	−0.321609
$232$	−3.69994	−0.242913
$233$	−27.6729	−1.81291	−0.906457	−	0.422299i	$-0.861223\pi$
$233$	−27.6729	−1.81291	−0.906457	+	0.422299i	$0.861223\pi$
$234$	−0.514139	−0.0336103
$235$	0.115252	0.00751820
$236$	−13.6930	−0.891336
$237$	7.89678	0.512951
$238$	8.10736	0.525522
$239$	−10.5379	−0.681639	−0.340819	−	0.940129i	$-0.610704\pi$
$239$	−10.5379	−0.681639	−0.340819	+	0.940129i	$0.610704\pi$
$240$	−0.293024	−0.0189146
$241$	2.42398	0.156143	0.0780713	−	0.996948i	$-0.475124\pi$
$241$	2.42398	0.156143	0.0780713	+	0.996948i	$0.475124\pi$
$242$	21.2931	1.36877
$243$	16.0582	1.03014
$244$	−8.33524	−0.533609
$245$	−0.340662	−0.0217641
$246$	3.08403	0.196630
$247$	−0.966637	−0.0615056
$248$	−3.23746	−0.205579
$249$	−4.70155	−0.297949
$250$	3.36709	0.212953
$251$	31.2355	1.97157	0.985785	−	0.168011i	$-0.0537344\pi$
$251$	31.2355	1.97157	0.985785	+	0.168011i	$0.0537344\pi$
$252$	2.26013	0.142375
$253$	15.0513	0.946268
$254$	−19.2865	−1.21015
$255$	2.37565	0.148769
$256$	1.00000	0.0625000
$257$	−23.2686	−1.45146	−0.725728	−	0.687982i	$-0.758497\pi$
$257$	−23.2686	−1.45146	−0.725728	+	0.687982i	$0.758497\pi$
$258$	4.06025	0.252780
$259$	6.09832	0.378931
$260$	−0.0774946	−0.00480601
$261$	8.36233	0.517615
$262$	4.12248	0.254688
$263$	−10.1933	−0.628548	−0.314274	−	0.949332i	$-0.601761\pi$
$263$	−10.1933	−0.628548	−0.314274	+	0.949332i	$0.601761\pi$
$264$	4.88803	0.300837
$265$	−2.77290	−0.170338
$266$	4.24928	0.260540
$267$	−3.99871	−0.244717
$268$	−0.319047	−0.0194889
$269$	16.5828	1.01107	0.505535	−	0.862806i	$-0.331295\pi$
$269$	16.5828	1.01107	0.505535	+	0.862806i	$0.331295\pi$
$270$	1.54134	0.0938030
$271$	−8.34115	−0.506689	−0.253344	−	0.967376i	$-0.581531\pi$
$271$	−8.34115	−0.506689	−0.253344	+	0.967376i	$0.581531\pi$
$272$	−8.10736	−0.491581
$273$	−0.195671	−0.0118426
$274$	14.2058	0.858206
$275$	−27.7540	−1.67363
$276$	2.27824	0.137134
$277$	6.86628	0.412555	0.206277	−	0.978494i	$-0.433865\pi$
$277$	6.86628	0.412555	0.206277	+	0.978494i	$0.433865\pi$
$278$	0.0336061	0.00201556
$279$	7.31707	0.438062
$280$	0.340662	0.0203584
$281$	−7.69434	−0.459006	−0.229503	−	0.973308i	$-0.573710\pi$
$281$	−7.69434	−0.459006	−0.229503	+	0.973308i	$0.573710\pi$
$282$	−0.291007	−0.0173292
$283$	13.7588	0.817875	0.408937	−	0.912562i	$-0.365899\pi$
$283$	13.7588	0.817875	0.408937	+	0.912562i	$0.365899\pi$
$284$	−16.3054	−0.967548
$285$	1.24514	0.0737557
$286$	1.29271	0.0764398
$287$	−3.58541	−0.211640
$288$	−2.26013	−0.133179
$289$	48.7293	2.86643
$290$	1.26043	0.0740149
$291$	4.12840	0.242011
$292$	4.74322	0.277576
$293$	22.7322	1.32803	0.664014	−	0.747721i	$-0.268852\pi$
$293$	22.7322	1.32803	0.664014	+	0.747721i	$0.268852\pi$
$294$	0.860159	0.0501655
$295$	4.66467	0.271588
$296$	−6.09832	−0.354458
$297$	−25.7116	−1.49194
$298$	14.9473	0.865872
$299$	0.602515	0.0348443
$300$	−4.20097	−0.242543
$301$	−4.72035	−0.272076
$302$	7.62294	0.438651
$303$	−2.68293	−0.154130
$304$	−4.24928	−0.243713
$305$	2.83950	0.162589
$306$	18.3237	1.04749
$307$	−1.58502	−0.0904619	−0.0452309	−	0.998977i	$-0.514402\pi$
$307$	−1.58502	−0.0904619	−0.0452309	+	0.998977i	$0.514402\pi$
$308$	−5.68270	−0.323802
$309$	−4.42645	−0.251812
$310$	1.10288	0.0626394
$311$	−16.8599	−0.956039	−0.478019	−	0.878349i	$-0.658645\pi$
$311$	−16.8599	−0.956039	−0.478019	+	0.878349i	$0.658645\pi$
$312$	0.195671	0.0110777
$313$	−29.0807	−1.64374	−0.821869	−	0.569676i	$-0.807069\pi$
$313$	−29.0807	−1.64374	−0.821869	+	0.569676i	$0.807069\pi$
$314$	−15.9038	−0.897505
$315$	−0.769939	−0.0433811
$316$	9.18061	0.516449
$317$	−15.7924	−0.886991	−0.443496	−	0.896277i	$-0.646262\pi$
$317$	−15.7924	−0.886991	−0.443496	+	0.896277i	$0.646262\pi$
$318$	7.00146	0.392623
$319$	−21.0257	−1.17721
$320$	−0.340662	−0.0190436
$321$	−3.49239	−0.194926
$322$	−2.64862	−0.147602
$323$	34.4504	1.91687
$324$	2.88855	0.160475
$325$	−1.11101	−0.0616279
$326$	−21.7578	−1.20505
$327$	−1.34997	−0.0746537
$328$	3.58541	0.197971
$329$	0.338317	0.0186520
$330$	−1.66516	−0.0916643
$331$	−30.7419	−1.68973	−0.844864	−	0.534980i	$-0.820319\pi$
$331$	−30.7419	−1.68973	−0.844864	+	0.534980i	$0.820319\pi$
$332$	−5.46591	−0.299981
$333$	13.7830	0.755303
$334$	−7.53265	−0.412168
$335$	0.108687	0.00593821
$336$	−0.860159	−0.0469255
$337$	17.4687	0.951583	0.475791	−	0.879558i	$-0.342162\pi$
$337$	17.4687	0.951583	0.475791	+	0.879558i	$0.342162\pi$
$338$	−12.9483	−0.704292
$339$	12.7275	0.691261
$340$	2.76187	0.149783
$341$	−18.3975	−0.996282
$342$	9.60391	0.519320
$343$	−1.00000	−0.0539949
$344$	4.72035	0.254504
$345$	−0.776108	−0.0417843
$346$	18.6287	1.00149
$347$	−5.86571	−0.314888	−0.157444	−	0.987528i	$-0.550325\pi$
$347$	−5.86571	−0.314888	−0.157444	+	0.987528i	$0.550325\pi$
$348$	−3.18254	−0.170602
$349$	−13.3261	−0.713331	−0.356666	−	0.934232i	$-0.616086\pi$
$349$	−13.3261	−0.713331	−0.356666	+	0.934232i	$0.616086\pi$
$350$	4.88395	0.261058
$351$	−1.02925	−0.0549376
$352$	5.68270	0.302889
$353$	−5.72861	−0.304903	−0.152452	−	0.988311i	$-0.548717\pi$
$353$	−5.72861	−0.304903	−0.152452	+	0.988311i	$0.548717\pi$
$354$	−11.7781	−0.626001
$355$	5.55463	0.294809
$356$	−4.64881	−0.246386
$357$	6.97362	0.369083
$358$	6.88746	0.364014
$359$	−25.5109	−1.34641	−0.673207	−	0.739454i	$-0.735084\pi$
$359$	−25.5109	−1.34641	−0.673207	+	0.739454i	$0.735084\pi$
$360$	0.769939	0.0405793
$361$	−0.943613	−0.0496639
$362$	−21.8393	−1.14785
$363$	18.3154	0.961311
$364$	−0.227482	−0.0119233
$365$	−1.61583	−0.0845766
$366$	−7.16964	−0.374763
$367$	22.4977	1.17437	0.587185	−	0.809453i	$-0.300236\pi$
$367$	22.4977	1.17437	0.587185	+	0.809453i	$0.300236\pi$
$368$	2.64862	0.138069
$369$	−8.10349	−0.421851
$370$	2.07747	0.108002
$371$	−8.13973	−0.422594
$372$	−2.78473	−0.144382
$373$	−2.20751	−0.114300	−0.0571502	−	0.998366i	$-0.518201\pi$
$373$	−2.20751	−0.114300	−0.0571502	+	0.998366i	$0.518201\pi$
$374$	−46.0717	−2.38231
$375$	2.89623	0.149561
$376$	−0.338317	−0.0174474
$377$	−0.841671	−0.0433483
$378$	4.52455	0.232718
$379$	−8.06907	−0.414480	−0.207240	−	0.978290i	$-0.566448\pi$
$379$	−8.06907	−0.414480	−0.207240	+	0.978290i	$0.566448\pi$
$380$	1.44757	0.0742587
$381$	−16.5895	−0.849906
$382$	9.02783	0.461904
$383$	11.5148	0.588378	0.294189	−	0.955747i	$-0.404950\pi$
$383$	11.5148	0.588378	0.294189	+	0.955747i	$0.404950\pi$
$384$	0.860159	0.0438948
$385$	1.93588	0.0986616
$386$	−8.43384	−0.429271
$387$	−10.6686	−0.542314
$388$	4.79958	0.243662
$389$	6.54596	0.331893	0.165947	−	0.986135i	$-0.446932\pi$
$389$	6.54596	0.331893	0.165947	+	0.986135i	$0.446932\pi$
$390$	−0.0666577	−0.00337534
$391$	−21.4733	−1.08595
$392$	1.00000	0.0505076
$393$	3.54599	0.178872
$394$	10.9384	0.551068
$395$	−3.12748	−0.157361
$396$	−12.8436	−0.645416
$397$	8.23725	0.413416	0.206708	−	0.978403i	$-0.433725\pi$
$397$	8.23725	0.413416	0.206708	+	0.978403i	$0.433725\pi$
$398$	27.9189	1.39945
$399$	3.65506	0.182982
$400$	−4.88395	−0.244197
$401$	−16.3456	−0.816260	−0.408130	−	0.912924i	$-0.633819\pi$
$401$	−16.3456	−0.816260	−0.408130	+	0.912924i	$0.633819\pi$
$402$	−0.274431	−0.0136874
$403$	−0.736466	−0.0366860
$404$	−3.11910	−0.155181
$405$	−0.984019	−0.0488963
$406$	3.69994	0.183625
$407$	−34.6549	−1.71778
$408$	−6.97362	−0.345246
$409$	15.8718	0.784808	0.392404	−	0.919793i	$-0.371643\pi$
$409$	15.8718	0.784808	0.392404	+	0.919793i	$0.371643\pi$
$410$	−1.22141	−0.0603213
$411$	12.2193	0.602733
$412$	−5.14608	−0.253529
$413$	13.6930	0.673787
$414$	−5.98622	−0.294206
$415$	1.86203	0.0914033
$416$	0.227482	0.0111532
$417$	0.0289066	0.00141556
$418$	−24.1474	−1.18109
$419$	29.6647	1.44921	0.724607	−	0.689163i	$-0.242022\pi$
$419$	29.6647	1.44921	0.724607	+	0.689163i	$0.242022\pi$
$420$	0.293024	0.0142981
$421$	9.91409	0.483183	0.241592	−	0.970378i	$-0.422331\pi$
$421$	9.91409	0.483183	0.241592	+	0.970378i	$0.422331\pi$
$422$	−3.02438	−0.147224
$423$	0.764639	0.0371780
$424$	8.13973	0.395300
$425$	39.5959	1.92069
$426$	−14.0252	−0.679525
$427$	8.33524	0.403371
$428$	−4.06017	−0.196256
$429$	1.11194	0.0536850
$430$	−1.60804	−0.0775467
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−4.52455	−0.217687
$433$	16.1471	0.775982	0.387991	−	0.921663i	$-0.373169\pi$
$433$	16.1471	0.775982	0.387991	+	0.921663i	$0.373169\pi$
$434$	3.23746	0.155403
$435$	1.08417	0.0519819
$436$	−1.56945	−0.0751628
$437$	−11.2547	−0.538387
$438$	4.07992	0.194946
$439$	−16.1610	−0.771321	−0.385660	−	0.922641i	$-0.626026\pi$
$439$	−16.1610	−0.771321	−0.385660	+	0.922641i	$0.626026\pi$
$440$	−1.93588	−0.0922894
$441$	−2.26013	−0.107625
$442$	−1.84428	−0.0877235
$443$	17.1146	0.813139	0.406570	−	0.913620i	$-0.366725\pi$
$443$	17.1146	0.813139	0.406570	+	0.913620i	$0.366725\pi$
$444$	−5.24553	−0.248942
$445$	1.58367	0.0750732
$446$	−20.5951	−0.975208
$447$	12.8570	0.608116
$448$	−1.00000	−0.0472456
$449$	11.4568	0.540681	0.270341	−	0.962765i	$-0.412864\pi$
$449$	11.4568	0.540681	0.270341	+	0.962765i	$0.412864\pi$
$450$	11.0383	0.520352
$451$	20.3748	0.959413
$452$	14.7966	0.695975
$453$	6.55695	0.308072
$454$	−15.1081	−0.709057
$455$	0.0774946	0.00363300
$456$	−3.65506	−0.171164
$457$	−29.6565	−1.38727	−0.693635	−	0.720326i	$-0.743992\pi$
$457$	−29.6565	−1.38727	−0.693635	+	0.720326i	$0.743992\pi$
$458$	−0.232037	−0.0108424
$459$	36.6821	1.71217
$460$	−0.902284	−0.0420692
$461$	−1.72676	−0.0804234	−0.0402117	−	0.999191i	$-0.512803\pi$
$461$	−1.72676	−0.0804234	−0.0402117	+	0.999191i	$0.512803\pi$
$462$	−4.88803	−0.227412
$463$	25.0622	1.16474	0.582368	−	0.812925i	$-0.302126\pi$
$463$	25.0622	1.16474	0.582368	+	0.812925i	$0.302126\pi$
$464$	−3.69994	−0.171765
$465$	0.948653	0.0439927
$466$	−27.6729	−1.28192
$467$	27.9205	1.29201	0.646003	−	0.763335i	$-0.276440\pi$
$467$	27.9205	1.29201	0.646003	+	0.763335i	$0.276440\pi$
$468$	−0.514139	−0.0237661
$469$	0.319047	0.0147322
$470$	0.115252	0.00531617
$471$	−13.6798	−0.630333
$472$	−13.6930	−0.630270
$473$	26.8243	1.23338
$474$	7.89678	0.362711
$475$	20.7533	0.952225
$476$	8.10736	0.371600
$477$	−18.3968	−0.842332
$478$	−10.5379	−0.481991
$479$	−21.5393	−0.984154	−0.492077	−	0.870552i	$-0.663762\pi$
$479$	−21.5393	−0.984154	−0.492077	+	0.870552i	$0.663762\pi$
$480$	−0.293024	−0.0133746
$481$	−1.38726	−0.0632537
$482$	2.42398	0.110409
$483$	−2.27824	−0.103663
$484$	21.2931	0.967867
$485$	−1.63503	−0.0742430
$486$	16.0582	0.728417
$487$	28.8526	1.30743	0.653717	−	0.756739i	$-0.273209\pi$
$487$	28.8526	1.30743	0.653717	+	0.756739i	$0.273209\pi$
$488$	−8.33524	−0.377319
$489$	−18.7152	−0.846329
$490$	−0.340662	−0.0153895
$491$	40.4661	1.82621	0.913105	−	0.407724i	$-0.133678\pi$
$491$	40.4661	1.82621	0.913105	+	0.407724i	$0.133678\pi$
$492$	3.08403	0.139039
$493$	29.9967	1.35099
$494$	−0.966637	−0.0434910
$495$	4.37533	0.196657
$496$	−3.23746	−0.145366
$497$	16.3054	0.731397
$498$	−4.70155	−0.210682
$499$	6.42644	0.287687	0.143843	−	0.989600i	$-0.454054\pi$
$499$	6.42644	0.287687	0.143843	+	0.989600i	$0.454054\pi$
$500$	3.36709	0.150581
$501$	−6.47928	−0.289473
$502$	31.2355	1.39411
$503$	−1.68563	−0.0751587	−0.0375793	−	0.999294i	$-0.511965\pi$
$503$	−1.68563	−0.0751587	−0.0375793	+	0.999294i	$0.511965\pi$
$504$	2.26013	0.100674
$505$	1.06256	0.0472833
$506$	15.0513	0.669113
$507$	−11.1376	−0.494636
$508$	−19.2865	−0.855702
$509$	−7.34639	−0.325623	−0.162811	−	0.986657i	$-0.552056\pi$
$509$	−7.34639	−0.325623	−0.162811	+	0.986657i	$0.552056\pi$
$510$	2.37565	0.105195
$511$	−4.74322	−0.209828
$512$	1.00000	0.0441942
$513$	19.2261	0.848852
$514$	−23.2686	−1.02633
$515$	1.75308	0.0772497
$516$	4.06025	0.178742
$517$	−1.92255	−0.0845539
$518$	6.09832	0.267945
$519$	16.0237	0.703361
$520$	−0.0774946	−0.00339836
$521$	17.8657	0.782711	0.391355	−	0.920240i	$-0.372006\pi$
$521$	17.8657	0.782711	0.391355	+	0.920240i	$0.372006\pi$
$522$	8.36233	0.366009
$523$	0.878940	0.0384334	0.0192167	−	0.999815i	$-0.493883\pi$
$523$	0.878940	0.0384334	0.0192167	+	0.999815i	$0.493883\pi$
$524$	4.12248	0.180092
$525$	4.20097	0.183346
$526$	−10.1933	−0.444450
$527$	26.2473	1.14335
$528$	4.88803	0.212724
$529$	−15.9848	−0.694992
$530$	−2.77290	−0.120447
$531$	30.9478	1.34302
$532$	4.24928	0.184230
$533$	0.815619	0.0353284
$534$	−3.99871	−0.173041
$535$	1.38314	0.0597985
$536$	−0.319047	−0.0137807
$537$	5.92431	0.255653
$538$	16.5828	0.714935
$539$	5.68270	0.244771
$540$	1.54134	0.0663287
$541$	−0.567780	−0.0244108	−0.0122054	−	0.999926i	$-0.503885\pi$
$541$	−0.567780	−0.0244108	−0.0122054	+	0.999926i	$0.503885\pi$
$542$	−8.34115	−0.358283
$543$	−18.7852	−0.806152
$544$	−8.10736	−0.347600
$545$	0.534650	0.0229019
$546$	−0.195671	−0.00837395
$547$	−18.5953	−0.795078	−0.397539	−	0.917585i	$-0.630136\pi$
$547$	−18.5953	−0.795078	−0.397539	+	0.917585i	$0.630136\pi$
$548$	14.2058	0.606843
$549$	18.8387	0.804016
$550$	−27.7540	−1.18344
$551$	15.7221	0.669783
$552$	2.27824	0.0969681
$553$	−9.18061	−0.390399
$554$	6.86628	0.291720
$555$	1.78695	0.0758519
$556$	0.0336061	0.00142522
$557$	−12.7293	−0.539357	−0.269679	−	0.962950i	$-0.586917\pi$
$557$	−12.7293	−0.539357	−0.269679	+	0.962950i	$0.586917\pi$
$558$	7.31707	0.309756
$559$	1.07380	0.0454167
$560$	0.340662	0.0143956
$561$	−39.6290	−1.67314
$562$	−7.69434	−0.324566
$563$	16.9358	0.713758	0.356879	−	0.934151i	$-0.383841\pi$
$563$	16.9358	0.713758	0.356879	+	0.934151i	$0.383841\pi$
$564$	−0.291007	−0.0122536
$565$	−5.04065	−0.212062
$566$	13.7588	0.578325
$567$	−2.88855	−0.121308
$568$	−16.3054	−0.684159
$569$	6.32536	0.265173	0.132586	−	0.991171i	$-0.457672\pi$
$569$	6.32536	0.265173	0.132586	+	0.991171i	$0.457672\pi$
$570$	1.24514	0.0521531
$571$	20.7736	0.869347	0.434673	−	0.900588i	$-0.356864\pi$
$571$	20.7736	0.869347	0.434673	+	0.900588i	$0.356864\pi$
$572$	1.29271	0.0540511
$573$	7.76537	0.324403
$574$	−3.58541	−0.149652
$575$	−12.9357	−0.539457
$576$	−2.26013	−0.0941719
$577$	−3.59598	−0.149703	−0.0748514	−	0.997195i	$-0.523848\pi$
$577$	−3.59598	−0.149703	−0.0748514	+	0.997195i	$0.523848\pi$
$578$	48.7293	2.02687
$579$	−7.25445	−0.301485
$580$	1.26043	0.0523365
$581$	5.46591	0.226764
$582$	4.12840	0.171128
$583$	46.2556	1.91571
$584$	4.74322	0.196276
$585$	0.175148	0.00724146
$586$	22.7322	0.939057
$587$	5.77122	0.238204	0.119102	−	0.992882i	$-0.461998\pi$
$587$	5.77122	0.238204	0.119102	+	0.992882i	$0.461998\pi$
$588$	0.860159	0.0354724
$589$	13.7569	0.566843
$590$	4.66467	0.192042
$591$	9.40876	0.387024
$592$	−6.09832	−0.250640
$593$	−28.4753	−1.16934	−0.584671	−	0.811271i	$-0.698776\pi$
$593$	−28.4753	−1.16934	−0.584671	+	0.811271i	$0.698776\pi$
$594$	−25.7116	−1.05496
$595$	−2.76187	−0.113226
$596$	14.9473	0.612264
$597$	24.0147	0.982858
$598$	0.602515	0.0246387
$599$	−4.91286	−0.200734	−0.100367	−	0.994950i	$-0.532002\pi$
$599$	−4.91286	−0.200734	−0.100367	+	0.994950i	$0.532002\pi$
$600$	−4.20097	−0.171504
$601$	−15.1966	−0.619883	−0.309941	−	0.950756i	$-0.600309\pi$
$601$	−15.1966	−0.619883	−0.309941	+	0.950756i	$0.600309\pi$
$602$	−4.72035	−0.192387
$603$	0.721086	0.0293649
$604$	7.62294	0.310173
$605$	−7.25374	−0.294907
$606$	−2.68293	−0.108986
$607$	−1.66949	−0.0677627	−0.0338813	−	0.999426i	$-0.510787\pi$
$607$	−1.66949	−0.0677627	−0.0338813	+	0.999426i	$0.510787\pi$
$608$	−4.24928	−0.172331
$609$	3.18254	0.128963
$610$	2.83950	0.114968
$611$	−0.0769612	−0.00311352
$612$	18.3237	0.740690
$613$	8.54297	0.345047	0.172524	−	0.985005i	$-0.444808\pi$
$613$	8.54297	0.345047	0.172524	+	0.985005i	$0.444808\pi$
$614$	−1.58502	−0.0639662
$615$	−1.05061	−0.0423647
$616$	−5.68270	−0.228963
$617$	7.64517	0.307783	0.153892	−	0.988088i	$-0.450819\pi$
$617$	7.64517	0.307783	0.153892	+	0.988088i	$0.450819\pi$
$618$	−4.42645	−0.178058
$619$	48.3828	1.94467	0.972334	−	0.233597i	$-0.0750496\pi$
$619$	48.3828	1.94467	0.972334	+	0.233597i	$0.0750496\pi$
$620$	1.10288	0.0442927
$621$	−11.9838	−0.480893
$622$	−16.8599	−0.676022
$623$	4.64881	0.186250
$624$	0.195671	0.00783311
$625$	23.2727	0.930908
$626$	−29.0807	−1.16230
$627$	−20.7706	−0.829498
$628$	−15.9038	−0.634632
$629$	49.4413	1.97135
$630$	−0.769939	−0.0306751
$631$	19.5819	0.779544	0.389772	−	0.920911i	$-0.372554\pi$
$631$	19.5819	0.779544	0.389772	+	0.920911i	$0.372554\pi$
$632$	9.18061	0.365185
$633$	−2.60145	−0.103398
$634$	−15.7924	−0.627197
$635$	6.57019	0.260730
$636$	7.00146	0.277626
$637$	0.227482	0.00901318
$638$	−21.0257	−0.832413
$639$	36.8523	1.45785
$640$	−0.340662	−0.0134658
$641$	−4.16999	−0.164705	−0.0823523	−	0.996603i	$-0.526243\pi$
$641$	−4.16999	−0.164705	−0.0823523	+	0.996603i	$0.526243\pi$
$642$	−3.49239	−0.137834
$643$	−13.1639	−0.519132	−0.259566	−	0.965725i	$-0.583579\pi$
$643$	−13.1639	−0.519132	−0.259566	+	0.965725i	$0.583579\pi$
$644$	−2.64862	−0.104370
$645$	−1.38317	−0.0544624
$646$	34.4504	1.35543
$647$	10.4341	0.410206	0.205103	−	0.978740i	$-0.434247\pi$
$647$	10.4341	0.410206	0.205103	+	0.978740i	$0.434247\pi$
$648$	2.88855	0.113473
$649$	−77.8130	−3.05443
$650$	−1.11101	−0.0435775
$651$	2.78473	0.109142
$652$	−21.7578	−0.852101
$653$	−2.23442	−0.0874396	−0.0437198	−	0.999044i	$-0.513921\pi$
$653$	−2.23442	−0.0874396	−0.0437198	+	0.999044i	$0.513921\pi$
$654$	−1.34997	−0.0527881
$655$	−1.40437	−0.0548734
$656$	3.58541	0.139987
$657$	−10.7203	−0.418237
$658$	0.338317	0.0131890
$659$	−45.7517	−1.78223	−0.891116	−	0.453775i	$-0.850077\pi$
$659$	−45.7517	−1.78223	−0.891116	+	0.453775i	$0.850077\pi$
$660$	−1.66516	−0.0648165
$661$	6.64124	0.258314	0.129157	−	0.991624i	$-0.458773\pi$
$661$	6.64124	0.258314	0.129157	+	0.991624i	$0.458773\pi$
$662$	−30.7419	−1.19482
$663$	−1.58638	−0.0616097
$664$	−5.46591	−0.212118
$665$	−1.44757	−0.0561343
$666$	13.7830	0.534080
$667$	−9.79974	−0.379447
$668$	−7.53265	−0.291447
$669$	−17.7151	−0.684905
$670$	0.108687	0.00419895
$671$	−47.3667	−1.82857
$672$	−0.860159	−0.0331814
$673$	26.1181	1.00678	0.503389	−	0.864060i	$-0.332086\pi$
$673$	26.1181	1.00678	0.503389	+	0.864060i	$0.332086\pi$
$674$	17.4687	0.672871
$675$	22.0977	0.850539
$676$	−12.9483	−0.498010
$677$	−39.7340	−1.52710	−0.763551	−	0.645747i	$-0.776546\pi$
$677$	−39.7340	−1.52710	−0.763551	+	0.645747i	$0.776546\pi$
$678$	12.7275	0.488795
$679$	−4.79958	−0.184191
$680$	2.76187	0.105913
$681$	−12.9953	−0.497983
$682$	−18.3975	−0.704478
$683$	−0.508219	−0.0194465	−0.00972323	−	0.999953i	$-0.503095\pi$
$683$	−0.508219	−0.0194465	−0.00972323	+	0.999953i	$0.503095\pi$
$684$	9.60391	0.367215
$685$	−4.83939	−0.184904
$686$	−1.00000	−0.0381802
$687$	−0.199589	−0.00761479
$688$	4.72035	0.179962
$689$	1.85165	0.0705421
$690$	−0.776108	−0.0295459
$691$	−36.6522	−1.39431	−0.697157	−	0.716918i	$-0.745552\pi$
$691$	−36.6522	−1.39431	−0.697157	+	0.716918i	$0.745552\pi$
$692$	18.6287	0.708158
$693$	12.8436	0.487889
$694$	−5.86571	−0.222659
$695$	−0.0114483	−0.000434260 0
$696$	−3.18254	−0.120634
$697$	−29.0682	−1.10104
$698$	−13.3261	−0.504401
$699$	−23.8031	−0.900317
$700$	4.88395	0.184596
$701$	−13.3621	−0.504680	−0.252340	−	0.967639i	$-0.581200\pi$
$701$	−13.3621	−0.504680	−0.252340	+	0.967639i	$0.581200\pi$
$702$	−1.02925	−0.0388467
$703$	25.9135	0.977346
$704$	5.68270	0.214175
$705$	0.0991349	0.00373364
$706$	−5.72861	−0.215599
$707$	3.11910	0.117306
$708$	−11.7781	−0.442649
$709$	−7.91421	−0.297225	−0.148612	−	0.988896i	$-0.547481\pi$
$709$	−7.91421	−0.297225	−0.148612	+	0.988896i	$0.547481\pi$
$710$	5.55463	0.208462
$711$	−20.7493	−0.778161
$712$	−4.64881	−0.174221
$713$	−8.57481	−0.321129
$714$	6.97362	0.260981
$715$	−0.440379	−0.0164692
$716$	6.88746	0.257397
$717$	−9.06425	−0.338511
$718$	−25.5109	−0.952059
$719$	−3.50906	−0.130866	−0.0654329	−	0.997857i	$-0.520843\pi$
$719$	−3.50906	−0.130866	−0.0654329	+	0.997857i	$0.520843\pi$
$720$	0.769939	0.0286939
$721$	5.14608	0.191650
$722$	−0.943613	−0.0351177
$723$	2.08501	0.0775425
$724$	−21.8393	−0.811649
$725$	18.0703	0.671115
$726$	18.3154	0.679750
$727$	22.0629	0.818269	0.409134	−	0.912474i	$-0.365831\pi$
$727$	22.0629	0.818269	0.409134	+	0.912474i	$0.365831\pi$
$728$	−0.227482	−0.00843106
$729$	5.14701	0.190630
$730$	−1.61583	−0.0598047
$731$	−38.2695	−1.41545
$732$	−7.16964	−0.264997
$733$	44.4019	1.64002	0.820010	−	0.572348i	$-0.193968\pi$
$733$	44.4019	1.64002	0.820010	+	0.572348i	$0.193968\pi$
$734$	22.4977	0.830405
$735$	−0.293024	−0.0108083
$736$	2.64862	0.0976294
$737$	−1.81305	−0.0667845
$738$	−8.10349	−0.298293
$739$	−6.46423	−0.237791	−0.118895	−	0.992907i	$-0.537935\pi$
$739$	−6.46423	−0.237791	−0.118895	+	0.992907i	$0.537935\pi$
$740$	2.07747	0.0763692
$741$	−0.831461	−0.0305445
$742$	−8.13973	−0.298819
$743$	−20.4203	−0.749148	−0.374574	−	0.927197i	$-0.622211\pi$
$743$	−20.4203	−0.749148	−0.374574	+	0.927197i	$0.622211\pi$
$744$	−2.78473	−0.102093
$745$	−5.09196	−0.186555
$746$	−2.20751	−0.0808226
$747$	12.3536	0.451996
$748$	−46.0717	−1.68455
$749$	4.06017	0.148355
$750$	2.89623	0.105755
$751$	11.9313	0.435381	0.217691	−	0.976018i	$-0.430148\pi$
$751$	11.9313	0.435381	0.217691	+	0.976018i	$0.430148\pi$
$752$	−0.338317	−0.0123372
$753$	26.8675	0.979108
$754$	−0.841671	−0.0306519
$755$	−2.59685	−0.0945089
$756$	4.52455	0.164556
$757$	8.99935	0.327087	0.163543	−	0.986536i	$-0.447708\pi$
$757$	8.99935	0.327087	0.163543	+	0.986536i	$0.447708\pi$
$758$	−8.06907	−0.293082
$759$	12.9465	0.469929
$760$	1.44757	0.0525088
$761$	3.46100	0.125461	0.0627305	−	0.998031i	$-0.480019\pi$
$761$	3.46100	0.125461	0.0627305	+	0.998031i	$0.480019\pi$
$762$	−16.5895	−0.600974
$763$	1.56945	0.0568177
$764$	9.02783	0.326615
$765$	−6.24217	−0.225686
$766$	11.5148	0.416046
$767$	−3.11491	−0.112473
$768$	0.860159	0.0310383
$769$	21.6285	0.779944	0.389972	−	0.920827i	$-0.372485\pi$
$769$	21.6285	0.779944	0.389972	+	0.920827i	$0.372485\pi$
$770$	1.93588	0.0697643
$771$	−20.0147	−0.720812
$772$	−8.43384	−0.303541
$773$	8.26546	0.297288	0.148644	−	0.988891i	$-0.452509\pi$
$773$	8.26546	0.297288	0.148644	+	0.988891i	$0.452509\pi$
$774$	−10.6686	−0.383474
$775$	15.8116	0.567970
$776$	4.79958	0.172295
$777$	5.24553	0.188182
$778$	6.54596	0.234684
$779$	−15.2354	−0.545866
$780$	−0.0666577	−0.00238673
$781$	−92.6587	−3.31559
$782$	−21.4733	−0.767884
$783$	16.7405	0.598258
$784$	1.00000	0.0357143
$785$	5.41783	0.193371
$786$	3.54599	0.126481
$787$	−2.50621	−0.0893369	−0.0446684	−	0.999002i	$-0.514223\pi$
$787$	−2.50621	−0.0893369	−0.0446684	+	0.999002i	$0.514223\pi$
$788$	10.9384	0.389664
$789$	−8.76789	−0.312145
$790$	−3.12748	−0.111271
$791$	−14.7966	−0.526108
$792$	−12.8436	−0.456378
$793$	−1.89612	−0.0673332
$794$	8.23725	0.292329
$795$	−2.38513	−0.0845919
$796$	27.9189	0.989561
$797$	−17.3964	−0.616211	−0.308105	−	0.951352i	$-0.599695\pi$
$797$	−17.3964	−0.616211	−0.308105	+	0.951352i	$0.599695\pi$
$798$	3.65506	0.129388
$799$	2.74286	0.0970354
$800$	−4.88395	−0.172674
$801$	10.5069	0.371243
$802$	−16.3456	−0.577183
$803$	26.9543	0.951196
$804$	−0.274431	−0.00967844
$805$	0.902284	0.0318013
$806$	−0.736466	−0.0259409
$807$	14.2638	0.502111
$808$	−3.11910	−0.109730
$809$	−11.7782	−0.414101	−0.207050	−	0.978330i	$-0.566386\pi$
$809$	−11.7782	−0.414101	−0.207050	+	0.978330i	$0.566386\pi$
$810$	−0.984019	−0.0345749
$811$	−25.4005	−0.891930	−0.445965	−	0.895050i	$-0.647140\pi$
$811$	−25.4005	−0.891930	−0.445965	+	0.895050i	$0.647140\pi$
$812$	3.69994	0.129842
$813$	−7.17472	−0.251628
$814$	−34.6549	−1.21466
$815$	7.41206	0.259633
$816$	−6.97362	−0.244126
$817$	−20.0581	−0.701743
$818$	15.8718	0.554943
$819$	0.514139	0.0179655
$820$	−1.22141	−0.0426536
$821$	22.3791	0.781037	0.390519	−	0.920595i	$-0.372296\pi$
$821$	22.3791	0.781037	0.390519	+	0.920595i	$0.372296\pi$
$822$	12.2193	0.426196
$823$	47.1993	1.64526	0.822632	−	0.568574i	$-0.192505\pi$
$823$	47.1993	1.64526	0.822632	+	0.568574i	$0.192505\pi$
$824$	−5.14608	−0.179272
$825$	−23.8729	−0.831147
$826$	13.6930	0.476439
$827$	0.797354	0.0277267	0.0138634	−	0.999904i	$-0.495587\pi$
$827$	0.797354	0.0277267	0.0138634	+	0.999904i	$0.495587\pi$
$828$	−5.98622	−0.208035
$829$	14.1057	0.489911	0.244955	−	0.969534i	$-0.421227\pi$
$829$	14.1057	0.489911	0.244955	+	0.969534i	$0.421227\pi$
$830$	1.86203	0.0646319
$831$	5.90609	0.204880
$832$	0.227482	0.00788653
$833$	−8.10736	−0.280903
$834$	0.0289066	0.00100095
$835$	2.56609	0.0888031
$836$	−24.1474	−0.835155
$837$	14.6480	0.506311
$838$	29.6647	1.02475
$839$	−11.8342	−0.408561	−0.204281	−	0.978912i	$-0.565486\pi$
$839$	−11.8342	−0.408561	−0.204281	+	0.978912i	$0.565486\pi$
$840$	0.293024	0.0101103
$841$	−15.3104	−0.527946
$842$	9.91409	0.341662
$843$	−6.61836	−0.227948
$844$	−3.02438	−0.104103
$845$	4.41098	0.151742
$846$	0.764639	0.0262888
$847$	−21.2931	−0.731639
$848$	8.13973	0.279519
$849$	11.8347	0.406167
$850$	39.5959	1.35813
$851$	−16.1521	−0.553688
$852$	−14.0252	−0.480497
$853$	−28.1132	−0.962579	−0.481290	−	0.876562i	$-0.659831\pi$
$853$	−28.1132	−0.962579	−0.481290	+	0.876562i	$0.659831\pi$
$854$	8.33524	0.285226
$855$	−3.27169	−0.111889
$856$	−4.06017	−0.138774
$857$	49.8339	1.70229	0.851146	−	0.524929i	$-0.175908\pi$
$857$	49.8339	1.70229	0.851146	+	0.524929i	$0.175908\pi$
$858$	1.11194	0.0379610
$859$	38.4470	1.31179	0.655897	−	0.754851i	$-0.272291\pi$
$859$	38.4470	1.31179	0.655897	+	0.754851i	$0.272291\pi$
$860$	−1.60804	−0.0548338
$861$	−3.08403	−0.105103
$862$	1.00000	0.0340601
$863$	−1.65649	−0.0563875	−0.0281937	−	0.999602i	$-0.508976\pi$
$863$	−1.65649	−0.0563875	−0.0281937	+	0.999602i	$0.508976\pi$
$864$	−4.52455	−0.153928
$865$	−6.34610	−0.215774
$866$	16.1471	0.548702
$867$	41.9149	1.42351
$868$	3.23746	0.109887
$869$	52.1706	1.76977
$870$	1.08417	0.0367568
$871$	−0.0725776	−0.00245920
$872$	−1.56945	−0.0531481
$873$	−10.8476	−0.367137
$874$	−11.2547	−0.380697
$875$	−3.36709	−0.113828
$876$	4.07992	0.137848
$877$	44.7240	1.51022	0.755111	−	0.655597i	$-0.227583\pi$
$877$	44.7240	1.51022	0.755111	+	0.655597i	$0.227583\pi$
$878$	−16.1610	−0.545406
$879$	19.5533	0.659516
$880$	−1.93588	−0.0652585
$881$	−41.7095	−1.40523	−0.702615	−	0.711570i	$-0.747984\pi$
$881$	−41.7095	−1.40523	−0.702615	+	0.711570i	$0.747984\pi$
$882$	−2.26013	−0.0761024
$883$	−48.8021	−1.64232	−0.821160	−	0.570697i	$-0.806673\pi$
$883$	−48.8021	−1.64232	−0.821160	+	0.570697i	$0.806673\pi$
$884$	−1.84428	−0.0620299
$885$	4.01236	0.134874
$886$	17.1146	0.574976
$887$	−20.2111	−0.678622	−0.339311	−	0.940674i	$-0.610194\pi$
$887$	−20.2111	−0.678622	−0.339311	+	0.940674i	$0.610194\pi$
$888$	−5.24553	−0.176028
$889$	19.2865	0.646850
$890$	1.58367	0.0530848
$891$	16.4148	0.549915
$892$	−20.5951	−0.689576
$893$	1.43760	0.0481076
$894$	12.8570	0.430003
$895$	−2.34630	−0.0784280
$896$	−1.00000	−0.0334077
$897$	0.518258	0.0173041
$898$	11.4568	0.382319
$899$	11.9784	0.399503
$900$	11.0383	0.367945
$901$	−65.9917	−2.19850
$902$	20.3748	0.678408
$903$	−4.06025	−0.135117
$904$	14.7966	0.492129
$905$	7.43980	0.247307
$906$	6.55695	0.217840
$907$	7.75971	0.257657	0.128828	−	0.991667i	$-0.458878\pi$
$907$	7.75971	0.257657	0.128828	+	0.991667i	$0.458878\pi$
$908$	−15.1081	−0.501379
$909$	7.04957	0.233819
$910$	0.0774946	0.00256892
$911$	−11.7410	−0.388995	−0.194498	−	0.980903i	$-0.562308\pi$
$911$	−11.7410	−0.388995	−0.194498	+	0.980903i	$0.562308\pi$
$912$	−3.65506	−0.121031
$913$	−31.0611	−1.02797
$914$	−29.6565	−0.980948
$915$	2.44242	0.0807440
$916$	−0.232037	−0.00766673
$917$	−4.12248	−0.136136
$918$	36.6821	1.21069
$919$	−10.4459	−0.344580	−0.172290	−	0.985046i	$-0.555117\pi$
$919$	−10.4459	−0.344580	−0.172290	+	0.985046i	$0.555117\pi$
$920$	−0.902284	−0.0297474
$921$	−1.36337	−0.0449245
$922$	−1.72676	−0.0568679
$923$	−3.70919	−0.122090
$924$	−4.88803	−0.160804
$925$	29.7839	0.979289
$926$	25.0622	0.823593
$927$	11.6308	0.382006
$928$	−3.69994	−0.121456
$929$	−30.3015	−0.994160	−0.497080	−	0.867705i	$-0.665594\pi$
$929$	−30.3015	−0.994160	−0.497080	+	0.867705i	$0.665594\pi$
$930$	0.948653	0.0311075
$931$	−4.24928	−0.139265
$932$	−27.6729	−0.906457
$933$	−14.5022	−0.474781
$934$	27.9205	0.913586
$935$	15.6949	0.513277
$936$	−0.514139	−0.0168052
$937$	−47.7715	−1.56063	−0.780313	−	0.625389i	$-0.784940\pi$
$937$	−47.7715	−1.56063	−0.780313	+	0.625389i	$0.784940\pi$
$938$	0.319047	0.0104173
$939$	−25.0140	−0.816302
$940$	0.115252	0.00375910
$941$	−25.3334	−0.825846	−0.412923	−	0.910766i	$-0.635492\pi$
$941$	−25.3334	−0.825846	−0.412923	+	0.910766i	$0.635492\pi$
$942$	−13.6798	−0.445713
$943$	9.49640	0.309245
$944$	−13.6930	−0.445668
$945$	−1.54134	−0.0501398
$946$	26.8243	0.872134
$947$	54.4867	1.77058	0.885289	−	0.465040i	$-0.153960\pi$
$947$	54.4867	1.77058	0.885289	+	0.465040i	$0.153960\pi$
$948$	7.89678	0.256476
$949$	1.07900	0.0350258
$950$	20.7533	0.673325
$951$	−13.5840	−0.440491
$952$	8.10736	0.262761
$953$	19.8641	0.643463	0.321731	−	0.946831i	$-0.395735\pi$
$953$	19.8641	0.643463	0.321731	+	0.946831i	$0.395735\pi$
$954$	−18.3968	−0.595619
$955$	−3.07544	−0.0995188
$956$	−10.5379	−0.340819
$957$	−18.0854	−0.584618
$958$	−21.5393	−0.695902
$959$	−14.2058	−0.458730
$960$	−0.293024	−0.00945729
$961$	−20.5188	−0.661898
$962$	−1.38726	−0.0447271
$963$	9.17649	0.295708
$964$	2.42398	0.0780713
$965$	2.87309	0.0924880
$966$	−2.27824	−0.0733010
$967$	0.918010	0.0295212	0.0147606	−	0.999891i	$-0.495301\pi$
$967$	0.918010	0.0295212	0.0147606	+	0.999891i	$0.495301\pi$
$968$	21.2931	0.684386
$969$	29.6329	0.951945
$970$	−1.63503	−0.0524978
$971$	−21.8398	−0.700874	−0.350437	−	0.936586i	$-0.613967\pi$
$971$	−21.8398	−0.700874	−0.350437	+	0.936586i	$0.613967\pi$
$972$	16.0582	0.515069
$973$	−0.0336061	−0.00107736
$974$	28.8526	0.924496
$975$	−0.955648	−0.0306052
$976$	−8.33524	−0.266805
$977$	−41.0986	−1.31486	−0.657431	−	0.753515i	$-0.728357\pi$
$977$	−41.0986	−1.31486	−0.657431	+	0.753515i	$0.728357\pi$
$978$	−18.7152	−0.598445
$979$	−26.4178	−0.844316
$980$	−0.340662	−0.0108820
$981$	3.54714	0.113252
$982$	40.4661	1.29133
$983$	−11.4013	−0.363646	−0.181823	−	0.983331i	$-0.558200\pi$
$983$	−11.4013	−0.363646	−0.181823	+	0.983331i	$0.558200\pi$
$984$	3.08403	0.0983152
$985$	−3.72629	−0.118730
$986$	29.9967	0.955291
$987$	0.291007	0.00926284
$988$	−0.966637	−0.0307528
$989$	12.5024	0.397553
$990$	4.37533	0.139057
$991$	−28.0126	−0.889850	−0.444925	−	0.895568i	$-0.646770\pi$
$991$	−28.0126	−0.889850	−0.444925	+	0.895568i	$0.646770\pi$
$992$	−3.23746	−0.102790
$993$	−26.4429	−0.839142
$994$	16.3054	0.517176
$995$	−9.51092	−0.301517
$996$	−4.70155	−0.148974
$997$	39.3405	1.24592	0.622962	−	0.782252i	$-0.285929\pi$
$997$	39.3405	1.24592	0.622962	+	0.782252i	$0.285929\pi$
$998$	6.42644	0.203425
$999$	27.5921	0.872977

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.11	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.l.1.11	✓	20	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.860159 q^{3} +1.00000 q^{4} -0.340662 q^{5} +0.860159 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.26013 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.860159 q^{3} +1.00000 q^{4} -0.340662 q^{5} +0.860159 q^{6} -1.00000 q^{7} +1.00000 q^{8} -2.26013 q^{9} -0.340662 q^{10} +5.68270 q^{11} +0.860159 q^{12} +0.227482 q^{13} -1.00000 q^{14} -0.293024 q^{15} +1.00000 q^{16} -8.10736 q^{17} -2.26013 q^{18} -4.24928 q^{19} -0.340662 q^{20} -0.860159 q^{21} +5.68270 q^{22} +2.64862 q^{23} +0.860159 q^{24} -4.88395 q^{25} +0.227482 q^{26} -4.52455 q^{27} -1.00000 q^{28} -3.69994 q^{29} -0.293024 q^{30} -3.23746 q^{31} +1.00000 q^{32} +4.88803 q^{33} -8.10736 q^{34} +0.340662 q^{35} -2.26013 q^{36} -6.09832 q^{37} -4.24928 q^{38} +0.195671 q^{39} -0.340662 q^{40} +3.58541 q^{41} -0.860159 q^{42} +4.72035 q^{43} +5.68270 q^{44} +0.769939 q^{45} +2.64862 q^{46} -0.338317 q^{47} +0.860159 q^{48} +1.00000 q^{49} -4.88395 q^{50} -6.97362 q^{51} +0.227482 q^{52} +8.13973 q^{53} -4.52455 q^{54} -1.93588 q^{55} -1.00000 q^{56} -3.65506 q^{57} -3.69994 q^{58} -13.6930 q^{59} -0.293024 q^{60} -8.33524 q^{61} -3.23746 q^{62} +2.26013 q^{63} +1.00000 q^{64} -0.0774946 q^{65} +4.88803 q^{66} -0.319047 q^{67} -8.10736 q^{68} +2.27824 q^{69} +0.340662 q^{70} -16.3054 q^{71} -2.26013 q^{72} +4.74322 q^{73} -6.09832 q^{74} -4.20097 q^{75} -4.24928 q^{76} -5.68270 q^{77} +0.195671 q^{78} +9.18061 q^{79} -0.340662 q^{80} +2.88855 q^{81} +3.58541 q^{82} -5.46591 q^{83} -0.860159 q^{84} +2.76187 q^{85} +4.72035 q^{86} -3.18254 q^{87} +5.68270 q^{88} -4.64881 q^{89} +0.769939 q^{90} -0.227482 q^{91} +2.64862 q^{92} -2.78473 q^{93} -0.338317 q^{94} +1.44757 q^{95} +0.860159 q^{96} +4.79958 q^{97} +1.00000 q^{98} -12.8436 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9} - 10 q^{10} - 17 q^{11} - 3 q^{12} - 23 q^{13} - 20 q^{14} - 3 q^{15} + 20 q^{16} - 21 q^{17} + 21 q^{18} - 22 q^{19} - 10 q^{20} + 3 q^{21} - 17 q^{22} + 15 q^{23} - 3 q^{24} - 23 q^{26} - 42 q^{27} - 20 q^{28} - 3 q^{29} - 3 q^{30} - 3 q^{31} + 20 q^{32} - 12 q^{33} - 21 q^{34} + 10 q^{35} + 21 q^{36} - 14 q^{37} - 22 q^{38} + q^{39} - 10 q^{40} - 37 q^{41} + 3 q^{42} - 5 q^{43} - 17 q^{44} - 55 q^{45} + 15 q^{46} - 29 q^{47} - 3 q^{48} + 20 q^{49} - 7 q^{51} - 23 q^{52} - 28 q^{53} - 42 q^{54} + 4 q^{55} - 20 q^{56} - 23 q^{57} - 3 q^{58} - 47 q^{59} - 3 q^{60} - 13 q^{61} - 3 q^{62} - 21 q^{63} + 20 q^{64} - 26 q^{65} - 12 q^{66} - 24 q^{67} - 21 q^{68} - 76 q^{69} + 10 q^{70} - 22 q^{71} + 21 q^{72} - 37 q^{73} - 14 q^{74} - 39 q^{75} - 22 q^{76} + 17 q^{77} + q^{78} + 25 q^{79} - 10 q^{80} - 36 q^{81} - 37 q^{82} - 33 q^{83} + 3 q^{84} - 2 q^{85} - 5 q^{86} - 26 q^{87} - 17 q^{88} - 71 q^{89} - 55 q^{90} + 23 q^{91} + 15 q^{92} - 49 q^{93} - 29 q^{94} - 14 q^{95} - 3 q^{96} - 51 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 3 * q^3 + 20 * q^4 - 10 * q^5 - 3 * q^6 - 20 * q^7 + 20 * q^8 + 21 * q^9 - 10 * q^10 - 17 * q^11 - 3 * q^12 - 23 * q^13 - 20 * q^14 - 3 * q^15 + 20 * q^16 - 21 * q^17 + 21 * q^18 - 22 * q^19 - 10 * q^20 + 3 * q^21 - 17 * q^22 + 15 * q^23 - 3 * q^24 - 23 * q^26 - 42 * q^27 - 20 * q^28 - 3 * q^29 - 3 * q^30 - 3 * q^31 + 20 * q^32 - 12 * q^33 - 21 * q^34 + 10 * q^35 + 21 * q^36 - 14 * q^37 - 22 * q^38 + q^39 - 10 * q^40 - 37 * q^41 + 3 * q^42 - 5 * q^43 - 17 * q^44 - 55 * q^45 + 15 * q^46 - 29 * q^47 - 3 * q^48 + 20 * q^49 - 7 * q^51 - 23 * q^52 - 28 * q^53 - 42 * q^54 + 4 * q^55 - 20 * q^56 - 23 * q^57 - 3 * q^58 - 47 * q^59 - 3 * q^60 - 13 * q^61 - 3 * q^62 - 21 * q^63 + 20 * q^64 - 26 * q^65 - 12 * q^66 - 24 * q^67 - 21 * q^68 - 76 * q^69 + 10 * q^70 - 22 * q^71 + 21 * q^72 - 37 * q^73 - 14 * q^74 - 39 * q^75 - 22 * q^76 + 17 * q^77 + q^78 + 25 * q^79 - 10 * q^80 - 36 * q^81 - 37 * q^82 - 33 * q^83 + 3 * q^84 - 2 * q^85 - 5 * q^86 - 26 * q^87 - 17 * q^88 - 71 * q^89 - 55 * q^90 + 23 * q^91 + 15 * q^92 - 49 * q^93 - 29 * q^94 - 14 * q^95 - 3 * q^96 - 51 * q^97 + 20 * q^98 - 10 * q^99

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