LMFDB - Embedded newform 6034.2.a.l.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
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			1.19
Root			$-2.34324$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.34324 q^{3} +1.00000 q^{4} -0.555415 q^{5} +2.34324 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.49080 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.34324 q^{3} +1.00000 q^{4} -0.555415 q^{5} +2.34324 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.49080 q^{9} -0.555415 q^{10} -0.0472117 q^{11} +2.34324 q^{12} -6.27732 q^{13} -1.00000 q^{14} -1.30147 q^{15} +1.00000 q^{16} -0.624629 q^{17} +2.49080 q^{18} -3.30418 q^{19} -0.555415 q^{20} -2.34324 q^{21} -0.0472117 q^{22} -4.45001 q^{23} +2.34324 q^{24} -4.69151 q^{25} -6.27732 q^{26} -1.19319 q^{27} -1.00000 q^{28} -7.08772 q^{29} -1.30147 q^{30} +0.805231 q^{31} +1.00000 q^{32} -0.110629 q^{33} -0.624629 q^{34} +0.555415 q^{35} +2.49080 q^{36} +5.91966 q^{37} -3.30418 q^{38} -14.7093 q^{39} -0.555415 q^{40} -7.21735 q^{41} -2.34324 q^{42} +3.84229 q^{43} -0.0472117 q^{44} -1.38343 q^{45} -4.45001 q^{46} +7.45525 q^{47} +2.34324 q^{48} +1.00000 q^{49} -4.69151 q^{50} -1.46366 q^{51} -6.27732 q^{52} -0.468704 q^{53} -1.19319 q^{54} +0.0262221 q^{55} -1.00000 q^{56} -7.74250 q^{57} -7.08772 q^{58} -9.94400 q^{59} -1.30147 q^{60} -1.47594 q^{61} +0.805231 q^{62} -2.49080 q^{63} +1.00000 q^{64} +3.48652 q^{65} -0.110629 q^{66} -16.0720 q^{67} -0.624629 q^{68} -10.4275 q^{69} +0.555415 q^{70} +11.0324 q^{71} +2.49080 q^{72} +12.5793 q^{73} +5.91966 q^{74} -10.9934 q^{75} -3.30418 q^{76} +0.0472117 q^{77} -14.7093 q^{78} +2.91682 q^{79} -0.555415 q^{80} -10.2683 q^{81} -7.21735 q^{82} +0.229852 q^{83} -2.34324 q^{84} +0.346928 q^{85} +3.84229 q^{86} -16.6083 q^{87} -0.0472117 q^{88} +11.6121 q^{89} -1.38343 q^{90} +6.27732 q^{91} -4.45001 q^{92} +1.88685 q^{93} +7.45525 q^{94} +1.83519 q^{95} +2.34324 q^{96} -7.84746 q^{97} +1.00000 q^{98} -0.117595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.34324	1.35287	0.676436	−	0.736501i	$-0.263523\pi$
$3$	2.34324	1.35287	0.676436	+	0.736501i	$0.263523\pi$
$4$	1.00000	0.500000
$5$	−0.555415	−0.248389	−0.124195	−	0.992258i	$-0.539635\pi$
$5$	−0.555415	−0.248389	−0.124195	+	0.992258i	$0.539635\pi$
$6$	2.34324	0.956626
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	2.49080	0.830265
$10$	−0.555415	−0.175638
$11$	−0.0472117	−0.0142349	−0.00711743	−	0.999975i	$-0.502266\pi$
$11$	−0.0472117	−0.0142349	−0.00711743	+	0.999975i	$0.502266\pi$
$12$	2.34324	0.676436
$13$	−6.27732	−1.74102	−0.870508	−	0.492154i	$-0.836210\pi$
$13$	−6.27732	−1.74102	−0.870508	+	0.492154i	$0.836210\pi$
$14$	−1.00000	−0.267261
$15$	−1.30147	−0.336039
$16$	1.00000	0.250000
$17$	−0.624629	−0.151495	−0.0757474	−	0.997127i	$-0.524134\pi$
$17$	−0.624629	−0.151495	−0.0757474	+	0.997127i	$0.524134\pi$
$18$	2.49080	0.587086
$19$	−3.30418	−0.758031	−0.379016	−	0.925390i	$-0.623737\pi$
$19$	−3.30418	−0.758031	−0.379016	+	0.925390i	$0.623737\pi$
$20$	−0.555415	−0.124195
$21$	−2.34324	−0.511338
$22$	−0.0472117	−0.0100656
$23$	−4.45001	−0.927892	−0.463946	−	0.885863i	$-0.653567\pi$
$23$	−4.45001	−0.927892	−0.463946	+	0.885863i	$0.653567\pi$
$24$	2.34324	0.478313
$25$	−4.69151	−0.938303
$26$	−6.27732	−1.23108
$27$	−1.19319	−0.229630
$28$	−1.00000	−0.188982
$29$	−7.08772	−1.31616	−0.658078	−	0.752950i	$-0.728630\pi$
$29$	−7.08772	−1.31616	−0.658078	+	0.752950i	$0.728630\pi$
$30$	−1.30147	−0.237616
$31$	0.805231	0.144624	0.0723119	−	0.997382i	$-0.476962\pi$
$31$	0.805231	0.144624	0.0723119	+	0.997382i	$0.476962\pi$
$32$	1.00000	0.176777
$33$	−0.110629	−0.0192580
$34$	−0.624629	−0.107123
$35$	0.555415	0.0938823
$36$	2.49080	0.415133
$37$	5.91966	0.973186	0.486593	−	0.873629i	$-0.338239\pi$
$37$	5.91966	0.973186	0.486593	+	0.873629i	$0.338239\pi$
$38$	−3.30418	−0.536009
$39$	−14.7093	−2.35537
$40$	−0.555415	−0.0878189
$41$	−7.21735	−1.12716	−0.563580	−	0.826061i	$-0.690577\pi$
$41$	−7.21735	−1.12716	−0.563580	+	0.826061i	$0.690577\pi$
$42$	−2.34324	−0.361570
$43$	3.84229	0.585944	0.292972	−	0.956121i	$-0.405356\pi$
$43$	3.84229	0.585944	0.292972	+	0.956121i	$0.405356\pi$
$44$	−0.0472117	−0.00711743
$45$	−1.38343	−0.206229
$46$	−4.45001	−0.656119
$47$	7.45525	1.08746	0.543730	−	0.839260i	$-0.317012\pi$
$47$	7.45525	1.08746	0.543730	+	0.839260i	$0.317012\pi$
$48$	2.34324	0.338218
$49$	1.00000	0.142857
$50$	−4.69151	−0.663480
$51$	−1.46366	−0.204953
$52$	−6.27732	−0.870508
$53$	−0.468704	−0.0643814	−0.0321907	−	0.999482i	$-0.510248\pi$
$53$	−0.468704	−0.0643814	−0.0321907	+	0.999482i	$0.510248\pi$
$54$	−1.19319	−0.162373
$55$	0.0262221	0.00353579
$56$	−1.00000	−0.133631
$57$	−7.74250	−1.02552
$58$	−7.08772	−0.930663
$59$	−9.94400	−1.29460	−0.647299	−	0.762236i	$-0.724102\pi$
$59$	−9.94400	−1.29460	−0.647299	+	0.762236i	$0.724102\pi$
$60$	−1.30147	−0.168020
$61$	−1.47594	−0.188974	−0.0944871	−	0.995526i	$-0.530121\pi$
$61$	−1.47594	−0.188974	−0.0944871	+	0.995526i	$0.530121\pi$
$62$	0.805231	0.102264
$63$	−2.49080	−0.313811
$64$	1.00000	0.125000
$65$	3.48652	0.432450
$66$	−0.110629	−0.0136174
$67$	−16.0720	−1.96350	−0.981752	−	0.190164i	$-0.939098\pi$
$67$	−16.0720	−1.96350	−0.981752	+	0.190164i	$0.939098\pi$
$68$	−0.624629	−0.0757474
$69$	−10.4275	−1.25532
$70$	0.555415	0.0663848
$71$	11.0324	1.30931	0.654653	−	0.755930i	$-0.272815\pi$
$71$	11.0324	1.30931	0.654653	+	0.755930i	$0.272815\pi$
$72$	2.49080	0.293543
$73$	12.5793	1.47230	0.736148	−	0.676821i	$-0.236643\pi$
$73$	12.5793	1.47230	0.736148	+	0.676821i	$0.236643\pi$
$74$	5.91966	0.688146
$75$	−10.9934	−1.26940
$76$	−3.30418	−0.379016
$77$	0.0472117	0.00538027
$78$	−14.7093	−1.66550
$79$	2.91682	0.328168	0.164084	−	0.986446i	$-0.447533\pi$
$79$	2.91682	0.328168	0.164084	+	0.986446i	$0.447533\pi$
$80$	−0.555415	−0.0620973
$81$	−10.2683	−1.14092
$82$	−7.21735	−0.797023
$83$	0.229852	0.0252296	0.0126148	−	0.999920i	$-0.495984\pi$
$83$	0.229852	0.0252296	0.0126148	+	0.999920i	$0.495984\pi$
$84$	−2.34324	−0.255669
$85$	0.346928	0.0376297
$86$	3.84229	0.414325
$87$	−16.6083	−1.78059
$88$	−0.0472117	−0.00503279
$89$	11.6121	1.23088	0.615440	−	0.788184i	$-0.288978\pi$
$89$	11.6121	1.23088	0.615440	+	0.788184i	$0.288978\pi$
$90$	−1.38343	−0.145826
$91$	6.27732	0.658042
$92$	−4.45001	−0.463946
$93$	1.88685	0.195658
$94$	7.45525	0.768950
$95$	1.83519	0.188287
$96$	2.34324	0.239156
$97$	−7.84746	−0.796789	−0.398395	−	0.917214i	$-0.630433\pi$
$97$	−7.84746	−0.796789	−0.398395	+	0.917214i	$0.630433\pi$
$98$	1.00000	0.101015
$99$	−0.117595	−0.0118187
$100$	−4.69151	−0.469151
$101$	−8.98896	−0.894435	−0.447217	−	0.894425i	$-0.647585\pi$
$101$	−8.98896	−0.894435	−0.447217	+	0.894425i	$0.647585\pi$
$102$	−1.46366	−0.144924
$103$	−5.68316	−0.559979	−0.279989	−	0.960003i	$-0.590331\pi$
$103$	−5.68316	−0.559979	−0.279989	+	0.960003i	$0.590331\pi$
$104$	−6.27732	−0.615542
$105$	1.30147	0.127011
$106$	−0.468704	−0.0455245
$107$	0.981344	0.0948701	0.0474351	−	0.998874i	$-0.484895\pi$
$107$	0.981344	0.0948701	0.0474351	+	0.998874i	$0.484895\pi$
$108$	−1.19319	−0.114815
$109$	6.85788	0.656866	0.328433	−	0.944527i	$-0.393479\pi$
$109$	6.85788	0.656866	0.328433	+	0.944527i	$0.393479\pi$
$110$	0.0262221	0.00250018
$111$	13.8712	1.31660
$112$	−1.00000	−0.0944911
$113$	11.1464	1.04856	0.524281	−	0.851545i	$-0.324334\pi$
$113$	11.1464	1.04856	0.524281	+	0.851545i	$0.324334\pi$
$114$	−7.74250	−0.725152
$115$	2.47161	0.230478
$116$	−7.08772	−0.658078
$117$	−15.6355	−1.44550
$118$	−9.94400	−0.915420
$119$	0.624629	0.0572596
$120$	−1.30147	−0.118808
$121$	−10.9978	−0.999797
$122$	−1.47594	−0.133625
$123$	−16.9120	−1.52491
$124$	0.805231	0.0723119
$125$	5.38281	0.481454
$126$	−2.49080	−0.221898
$127$	13.6045	1.20720	0.603600	−	0.797287i	$-0.293732\pi$
$127$	13.6045	1.20720	0.603600	+	0.797287i	$0.293732\pi$
$128$	1.00000	0.0883883
$129$	9.00342	0.792707
$130$	3.48652	0.305788
$131$	−18.8124	−1.64365	−0.821824	−	0.569742i	$-0.807043\pi$
$131$	−18.8124	−1.64365	−0.821824	+	0.569742i	$0.807043\pi$
$132$	−0.110629	−0.00962898
$133$	3.30418	0.286509
$134$	−16.0720	−1.38841
$135$	0.662716	0.0570375
$136$	−0.624629	−0.0535615
$137$	13.3766	1.14284	0.571419	−	0.820659i	$-0.306393\pi$
$137$	13.3766	1.14284	0.571419	+	0.820659i	$0.306393\pi$
$138$	−10.4275	−0.887645
$139$	12.0918	1.02561	0.512805	−	0.858505i	$-0.328606\pi$
$139$	12.0918	1.02561	0.512805	+	0.858505i	$0.328606\pi$
$140$	0.555415	0.0469412
$141$	17.4695	1.47120
$142$	11.0324	0.925819
$143$	0.296363	0.0247831
$144$	2.49080	0.207566
$145$	3.93663	0.326919
$146$	12.5793	1.04107
$147$	2.34324	0.193268
$148$	5.91966	0.486593
$149$	−11.5340	−0.944906	−0.472453	−	0.881356i	$-0.656631\pi$
$149$	−11.5340	−0.944906	−0.472453	+	0.881356i	$0.656631\pi$
$150$	−10.9934	−0.897604
$151$	11.2839	0.918271	0.459135	−	0.888366i	$-0.348159\pi$
$151$	11.2839	0.918271	0.459135	+	0.888366i	$0.348159\pi$
$152$	−3.30418	−0.268004
$153$	−1.55582	−0.125781
$154$	0.0472117	0.00380443
$155$	−0.447238	−0.0359230
$156$	−14.7093	−1.17769
$157$	−4.99981	−0.399028	−0.199514	−	0.979895i	$-0.563936\pi$
$157$	−4.99981	−0.399028	−0.199514	+	0.979895i	$0.563936\pi$
$158$	2.91682	0.232050
$159$	−1.09829	−0.0870998
$160$	−0.555415	−0.0439094
$161$	4.45001	0.350710
$162$	−10.2683	−0.806756
$163$	−3.42502	−0.268268	−0.134134	−	0.990963i	$-0.542825\pi$
$163$	−3.42502	−0.268268	−0.134134	+	0.990963i	$0.542825\pi$
$164$	−7.21735	−0.563580
$165$	0.0614448	0.00478347
$166$	0.229852	0.0178400
$167$	4.37170	0.338292	0.169146	−	0.985591i	$-0.445899\pi$
$167$	4.37170	0.338292	0.169146	+	0.985591i	$0.445899\pi$
$168$	−2.34324	−0.180785
$169$	26.4048	2.03114
$170$	0.346928	0.0266082
$171$	−8.23004	−0.629367
$172$	3.84229	0.292972
$173$	20.4103	1.55177	0.775884	−	0.630876i	$-0.217304\pi$
$173$	20.4103	1.55177	0.775884	+	0.630876i	$0.217304\pi$
$174$	−16.6083	−1.25907
$175$	4.69151	0.354645
$176$	−0.0472117	−0.00355872
$177$	−23.3012	−1.75143
$178$	11.6121	0.870364
$179$	−1.36165	−0.101775	−0.0508874	−	0.998704i	$-0.516205\pi$
$179$	−1.36165	−0.101775	−0.0508874	+	0.998704i	$0.516205\pi$
$180$	−1.38343	−0.103114
$181$	−9.41264	−0.699636	−0.349818	−	0.936818i	$-0.613757\pi$
$181$	−9.41264	−0.699636	−0.349818	+	0.936818i	$0.613757\pi$
$182$	6.27732	0.465306
$183$	−3.45848	−0.255658
$184$	−4.45001	−0.328059
$185$	−3.28787	−0.241729
$186$	1.88685	0.138351
$187$	0.0294898	0.00215651
$188$	7.45525	0.543730
$189$	1.19319	0.0867919
$190$	1.83519	0.133139
$191$	−3.89930	−0.282144	−0.141072	−	0.989999i	$-0.545055\pi$
$191$	−3.89930	−0.282144	−0.141072	+	0.989999i	$0.545055\pi$
$192$	2.34324	0.169109
$193$	−6.65733	−0.479205	−0.239602	−	0.970871i	$-0.577017\pi$
$193$	−6.65733	−0.479205	−0.239602	+	0.970871i	$0.577017\pi$
$194$	−7.84746	−0.563415
$195$	8.16977	0.585049
$196$	1.00000	0.0714286
$197$	−6.14220	−0.437613	−0.218807	−	0.975768i	$-0.570216\pi$
$197$	−6.14220	−0.437613	−0.218807	+	0.975768i	$0.570216\pi$
$198$	−0.117595	−0.00835709
$199$	0.0317040	0.00224744	0.00112372	−	0.999999i	$-0.499642\pi$
$199$	0.0317040	0.00224744	0.00112372	+	0.999999i	$0.499642\pi$
$200$	−4.69151	−0.331740
$201$	−37.6606	−2.65637
$202$	−8.98896	−0.632461
$203$	7.08772	0.497460
$204$	−1.46366	−0.102477
$205$	4.00863	0.279975
$206$	−5.68316	−0.395965
$207$	−11.0841	−0.770397
$208$	−6.27732	−0.435254
$209$	0.155996	0.0107905
$210$	1.30147	0.0898102
$211$	−6.26781	−0.431494	−0.215747	−	0.976449i	$-0.569219\pi$
$211$	−6.26781	−0.431494	−0.215747	+	0.976449i	$0.569219\pi$
$212$	−0.468704	−0.0321907
$213$	25.8516	1.77132
$214$	0.981344	0.0670833
$215$	−2.13407	−0.145542
$216$	−1.19319	−0.0811863
$217$	−0.805231	−0.0546627
$218$	6.85788	0.464474
$219$	29.4764	1.99183
$220$	0.0262221	0.00176789
$221$	3.92100	0.263755
$222$	13.8712	0.930975
$223$	−26.8017	−1.79477	−0.897386	−	0.441246i	$-0.854537\pi$
$223$	−26.8017	−1.79477	−0.897386	+	0.441246i	$0.854537\pi$
$224$	−1.00000	−0.0668153
$225$	−11.6856	−0.779040
$226$	11.1464	0.741445
$227$	−13.9117	−0.923355	−0.461677	−	0.887048i	$-0.652752\pi$
$227$	−13.9117	−0.923355	−0.461677	+	0.887048i	$0.652752\pi$
$228$	−7.74250	−0.512760
$229$	10.1337	0.669655	0.334827	−	0.942280i	$-0.391322\pi$
$229$	10.1337	0.669655	0.334827	+	0.942280i	$0.391322\pi$
$230$	2.47161	0.162973
$231$	0.110629	0.00727883
$232$	−7.08772	−0.465332
$233$	7.16302	0.469265	0.234633	−	0.972084i	$-0.424611\pi$
$233$	7.16302	0.469265	0.234633	+	0.972084i	$0.424611\pi$
$234$	−15.6355	−1.02213
$235$	−4.14076	−0.270113
$236$	−9.94400	−0.647299
$237$	6.83483	0.443970
$238$	0.624629	0.0404887
$239$	9.12669	0.590357	0.295178	−	0.955442i	$-0.404621\pi$
$239$	9.12669	0.590357	0.295178	+	0.955442i	$0.404621\pi$
$240$	−1.30147	−0.0840098
$241$	17.3532	1.11782	0.558909	−	0.829229i	$-0.311220\pi$
$241$	17.3532	1.11782	0.558909	+	0.829229i	$0.311220\pi$
$242$	−10.9978	−0.706963
$243$	−20.4816	−1.31390
$244$	−1.47594	−0.0944871
$245$	−0.555415	−0.0354842
$246$	−16.9120	−1.07827
$247$	20.7414	1.31974
$248$	0.805231	0.0511322
$249$	0.538600	0.0341324
$250$	5.38281	0.340439
$251$	−0.240020	−0.0151499	−0.00757496	−	0.999971i	$-0.502411\pi$
$251$	−0.240020	−0.0151499	−0.00757496	+	0.999971i	$0.502411\pi$
$252$	−2.49080	−0.156905
$253$	0.210093	0.0132084
$254$	13.6045	0.853619
$255$	0.812938	0.0509082
$256$	1.00000	0.0625000
$257$	−12.7962	−0.798202	−0.399101	−	0.916907i	$-0.630678\pi$
$257$	−12.7962	−0.798202	−0.399101	+	0.916907i	$0.630678\pi$
$258$	9.00342	0.560529
$259$	−5.91966	−0.367830
$260$	3.48652	0.216225
$261$	−17.6541	−1.09276
$262$	−18.8124	−1.16223
$263$	8.26056	0.509368	0.254684	−	0.967024i	$-0.418029\pi$
$263$	8.26056	0.509368	0.254684	+	0.967024i	$0.418029\pi$
$264$	−0.110629	−0.00680872
$265$	0.260325	0.0159916
$266$	3.30418	0.202592
$267$	27.2100	1.66522
$268$	−16.0720	−0.981752
$269$	3.81798	0.232787	0.116393	−	0.993203i	$-0.462867\pi$
$269$	3.81798	0.232787	0.116393	+	0.993203i	$0.462867\pi$
$270$	0.662716	0.0403316
$271$	2.61340	0.158753	0.0793763	−	0.996845i	$-0.474707\pi$
$271$	2.61340	0.158753	0.0793763	+	0.996845i	$0.474707\pi$
$272$	−0.624629	−0.0378737
$273$	14.7093	0.890247
$274$	13.3766	0.808108
$275$	0.221494	0.0133566
$276$	−10.4275	−0.627660
$277$	−4.05734	−0.243782	−0.121891	−	0.992543i	$-0.538896\pi$
$277$	−4.05734	−0.243782	−0.121891	+	0.992543i	$0.538896\pi$
$278$	12.0918	0.725216
$279$	2.00567	0.120076
$280$	0.555415	0.0331924
$281$	13.6682	0.815378	0.407689	−	0.913121i	$-0.366335\pi$
$281$	13.6682	0.815378	0.407689	+	0.913121i	$0.366335\pi$
$282$	17.4695	1.04029
$283$	−27.5451	−1.63739	−0.818694	−	0.574230i	$-0.805301\pi$
$283$	−27.5451	−1.63739	−0.818694	+	0.574230i	$0.805301\pi$
$284$	11.0324	0.654653
$285$	4.30030	0.254728
$286$	0.296363	0.0175243
$287$	7.21735	0.426027
$288$	2.49080	0.146772
$289$	−16.6098	−0.977049
$290$	3.93663	0.231167
$291$	−18.3885	−1.07795
$292$	12.5793	0.736148
$293$	−14.5867	−0.852163	−0.426082	−	0.904685i	$-0.640106\pi$
$293$	−14.5867	−0.852163	−0.426082	+	0.904685i	$0.640106\pi$
$294$	2.34324	0.136661
$295$	5.52305	0.321564
$296$	5.91966	0.344073
$297$	0.0563326	0.00326875
$298$	−11.5340	−0.668149
$299$	27.9342	1.61547
$300$	−10.9934	−0.634702
$301$	−3.84229	−0.221466
$302$	11.2839	0.649316
$303$	−21.0633	−1.21006
$304$	−3.30418	−0.189508
$305$	0.819757	0.0469392
$306$	−1.55582	−0.0889405
$307$	−13.6024	−0.776331	−0.388165	−	0.921590i	$-0.626891\pi$
$307$	−13.6024	−0.776331	−0.388165	+	0.921590i	$0.626891\pi$
$308$	0.0472117	0.00269014
$309$	−13.3170	−0.757580
$310$	−0.447238	−0.0254014
$311$	−13.1889	−0.747876	−0.373938	−	0.927454i	$-0.621993\pi$
$311$	−13.1889	−0.747876	−0.373938	+	0.927454i	$0.621993\pi$
$312$	−14.7093	−0.832750
$313$	−4.14707	−0.234406	−0.117203	−	0.993108i	$-0.537393\pi$
$313$	−4.14707	−0.234406	−0.117203	+	0.993108i	$0.537393\pi$
$314$	−4.99981	−0.282155
$315$	1.38343	0.0779472
$316$	2.91682	0.164084
$317$	−6.08452	−0.341741	−0.170870	−	0.985294i	$-0.554658\pi$
$317$	−6.08452	−0.341741	−0.170870	+	0.985294i	$0.554658\pi$
$318$	−1.09829	−0.0615889
$319$	0.334623	0.0187353
$320$	−0.555415	−0.0310487
$321$	2.29953	0.128347
$322$	4.45001	0.247990
$323$	2.06389	0.114838
$324$	−10.2683	−0.570462
$325$	29.4501	1.63360
$326$	−3.42502	−0.189694
$327$	16.0697	0.888656
$328$	−7.21735	−0.398512
$329$	−7.45525	−0.411021
$330$	0.0614448	0.00338243
$331$	6.22576	0.342199	0.171099	−	0.985254i	$-0.445268\pi$
$331$	6.22576	0.342199	0.171099	+	0.985254i	$0.445268\pi$
$332$	0.229852	0.0126148
$333$	14.7447	0.808003
$334$	4.37170	0.239209
$335$	8.92662	0.487713
$336$	−2.34324	−0.127834
$337$	−25.0475	−1.36442	−0.682212	−	0.731154i	$-0.738982\pi$
$337$	−25.0475	−1.36442	−0.682212	+	0.731154i	$0.738982\pi$
$338$	26.4048	1.43623
$339$	26.1187	1.41857
$340$	0.346928	0.0188148
$341$	−0.0380163	−0.00205870
$342$	−8.23004	−0.445030
$343$	−1.00000	−0.0539949
$344$	3.84229	0.207162
$345$	5.79158	0.311808
$346$	20.4103	1.09727
$347$	5.69473	0.305709	0.152855	−	0.988249i	$-0.451153\pi$
$347$	5.69473	0.305709	0.152855	+	0.988249i	$0.451153\pi$
$348$	−16.6083	−0.890296
$349$	23.1363	1.23846	0.619230	−	0.785210i	$-0.287445\pi$
$349$	23.1363	1.23846	0.619230	+	0.785210i	$0.287445\pi$
$350$	4.69151	0.250772
$351$	7.49004	0.399789
$352$	−0.0472117	−0.00251639
$353$	7.11301	0.378588	0.189294	−	0.981921i	$-0.439380\pi$
$353$	7.11301	0.378588	0.189294	+	0.981921i	$0.439380\pi$
$354$	−23.3012	−1.23845
$355$	−6.12756	−0.325217
$356$	11.6121	0.615440
$357$	1.46366	0.0774650
$358$	−1.36165	−0.0719657
$359$	26.4168	1.39422	0.697112	−	0.716963i	$-0.254468\pi$
$359$	26.4168	1.39422	0.697112	+	0.716963i	$0.254468\pi$
$360$	−1.38343	−0.0729129
$361$	−8.08239	−0.425389
$362$	−9.41264	−0.494717
$363$	−25.7705	−1.35260
$364$	6.27732	0.329021
$365$	−6.98674	−0.365703
$366$	−3.45848	−0.180778
$367$	−20.7652	−1.08393	−0.541967	−	0.840400i	$-0.682320\pi$
$367$	−20.7652	−1.08393	−0.541967	+	0.840400i	$0.682320\pi$
$368$	−4.45001	−0.231973
$369$	−17.9769	−0.935842
$370$	−3.28787	−0.170928
$371$	0.468704	0.0243339
$372$	1.88685	0.0978288
$373$	−13.1745	−0.682147	−0.341074	−	0.940037i	$-0.610791\pi$
$373$	−13.1745	−0.682147	−0.341074	+	0.940037i	$0.610791\pi$
$374$	0.0294898	0.00152488
$375$	12.6133	0.651345
$376$	7.45525	0.384475
$377$	44.4919	2.29145
$378$	1.19319	0.0613711
$379$	12.1811	0.625700	0.312850	−	0.949803i	$-0.398716\pi$
$379$	12.1811	0.625700	0.312850	+	0.949803i	$0.398716\pi$
$380$	1.83519	0.0941434
$381$	31.8786	1.63319
$382$	−3.89930	−0.199506
$383$	−10.8795	−0.555917	−0.277958	−	0.960593i	$-0.589658\pi$
$383$	−10.8795	−0.555917	−0.277958	+	0.960593i	$0.589658\pi$
$384$	2.34324	0.119578
$385$	−0.0262221	−0.00133640
$386$	−6.65733	−0.338849
$387$	9.57035	0.486488
$388$	−7.84746	−0.398395
$389$	14.8202	0.751416	0.375708	−	0.926738i	$-0.377400\pi$
$389$	14.8202	0.751416	0.375708	+	0.926738i	$0.377400\pi$
$390$	8.16977	0.413692
$391$	2.77961	0.140571
$392$	1.00000	0.0505076
$393$	−44.0821	−2.22365
$394$	−6.14220	−0.309439
$395$	−1.62005	−0.0815135
$396$	−0.117595	−0.00590936
$397$	−30.2995	−1.52069	−0.760345	−	0.649519i	$-0.774970\pi$
$397$	−30.2995	−1.52069	−0.760345	+	0.649519i	$0.774970\pi$
$398$	0.0317040	0.00158918
$399$	7.74250	0.387610
$400$	−4.69151	−0.234576
$401$	7.75541	0.387287	0.193643	−	0.981072i	$-0.437970\pi$
$401$	7.75541	0.387287	0.193643	+	0.981072i	$0.437970\pi$
$402$	−37.6606	−1.87834
$403$	−5.05470	−0.251792
$404$	−8.98896	−0.447217
$405$	5.70318	0.283393
$406$	7.08772	0.351758
$407$	−0.279477	−0.0138532
$408$	−1.46366	−0.0724619
$409$	−6.37148	−0.315049	−0.157525	−	0.987515i	$-0.550351\pi$
$409$	−6.37148	−0.315049	−0.157525	+	0.987515i	$0.550351\pi$
$410$	4.00863	0.197972
$411$	31.3446	1.54611
$412$	−5.68316	−0.279989
$413$	9.94400	0.489312
$414$	−11.0841	−0.544753
$415$	−0.127663	−0.00626675
$416$	−6.27732	−0.307771
$417$	28.3340	1.38752
$418$	0.155996	0.00763002
$419$	−32.1996	−1.57306	−0.786528	−	0.617555i	$-0.788123\pi$
$419$	−32.1996	−1.57306	−0.786528	+	0.617555i	$0.788123\pi$
$420$	1.30147	0.0635054
$421$	−2.92058	−0.142340	−0.0711701	−	0.997464i	$-0.522673\pi$
$421$	−2.92058	−0.142340	−0.0711701	+	0.997464i	$0.522673\pi$
$422$	−6.26781	−0.305112
$423$	18.5695	0.902880
$424$	−0.468704	−0.0227623
$425$	2.93045	0.142148
$426$	25.8516	1.25252
$427$	1.47594	0.0714256
$428$	0.981344	0.0474351
$429$	0.694451	0.0335284
$430$	−2.13407	−0.102914
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−1.19319	−0.0574074
$433$	−29.4125	−1.41348	−0.706738	−	0.707475i	$-0.749834\pi$
$433$	−29.4125	−1.41348	−0.706738	+	0.707475i	$0.749834\pi$
$434$	−0.805231	−0.0386523
$435$	9.22448	0.442280
$436$	6.85788	0.328433
$437$	14.7037	0.703371
$438$	29.4764	1.40844
$439$	26.8471	1.28134	0.640672	−	0.767815i	$-0.278656\pi$
$439$	26.8471	1.28134	0.640672	+	0.767815i	$0.278656\pi$
$440$	0.0262221	0.00125009
$441$	2.49080	0.118609
$442$	3.92100	0.186503
$443$	−35.2006	−1.67243	−0.836215	−	0.548401i	$-0.815237\pi$
$443$	−35.2006	−1.67243	−0.836215	+	0.548401i	$0.815237\pi$
$444$	13.8712	0.658299
$445$	−6.44954	−0.305737
$446$	−26.8017	−1.26910
$447$	−27.0271	−1.27834
$448$	−1.00000	−0.0472456
$449$	−33.0672	−1.56054	−0.780269	−	0.625445i	$-0.784918\pi$
$449$	−33.0672	−1.56054	−0.780269	+	0.625445i	$0.784918\pi$
$450$	−11.6856	−0.550865
$451$	0.340744	0.0160450
$452$	11.1464	0.524281
$453$	26.4409	1.24230
$454$	−13.9117	−0.652910
$455$	−3.48652	−0.163451
$456$	−7.74250	−0.362576
$457$	21.6691	1.01364	0.506820	−	0.862052i	$-0.330821\pi$
$457$	21.6691	1.01364	0.506820	+	0.862052i	$0.330821\pi$
$458$	10.1337	0.473517
$459$	0.745301	0.0347877
$460$	2.47161	0.115239
$461$	15.3033	0.712747	0.356373	−	0.934344i	$-0.384013\pi$
$461$	15.3033	0.712747	0.356373	+	0.934344i	$0.384013\pi$
$462$	0.110629	0.00514691
$463$	−28.3336	−1.31677	−0.658386	−	0.752680i	$-0.728761\pi$
$463$	−28.3336	−1.31677	−0.658386	+	0.752680i	$0.728761\pi$
$464$	−7.08772	−0.329039
$465$	−1.04799	−0.0485992
$466$	7.16302	0.331821
$467$	−28.7849	−1.33201	−0.666004	−	0.745948i	$-0.731997\pi$
$467$	−28.7849	−1.33201	−0.666004	+	0.745948i	$0.731997\pi$
$468$	−15.6355	−0.722752
$469$	16.0720	0.742135
$470$	−4.14076	−0.190999
$471$	−11.7158	−0.539834
$472$	−9.94400	−0.457710
$473$	−0.181401	−0.00834083
$474$	6.83483	0.313934
$475$	15.5016	0.711263
$476$	0.624629	0.0286298
$477$	−1.16744	−0.0534536
$478$	9.12669	0.417445
$479$	16.7313	0.764471	0.382236	−	0.924065i	$-0.375154\pi$
$479$	16.7313	0.764471	0.382236	+	0.924065i	$0.375154\pi$
$480$	−1.30147	−0.0594039
$481$	−37.1596	−1.69433
$482$	17.3532	0.790416
$483$	10.4275	0.474466
$484$	−10.9978	−0.499899
$485$	4.35860	0.197914
$486$	−20.4816	−0.929065
$487$	−14.5361	−0.658692	−0.329346	−	0.944209i	$-0.606828\pi$
$487$	−14.5361	−0.658692	−0.329346	+	0.944209i	$0.606828\pi$
$488$	−1.47594	−0.0668125
$489$	−8.02565	−0.362933
$490$	−0.555415	−0.0250911
$491$	−9.89203	−0.446421	−0.223211	−	0.974770i	$-0.571654\pi$
$491$	−9.89203	−0.446421	−0.223211	+	0.974770i	$0.571654\pi$
$492$	−16.9120	−0.762453
$493$	4.42719	0.199391
$494$	20.7414	0.933200
$495$	0.0653139	0.00293564
$496$	0.805231	0.0361559
$497$	−11.0324	−0.494871
$498$	0.538600	0.0241353
$499$	−15.5668	−0.696868	−0.348434	−	0.937333i	$-0.613286\pi$
$499$	−15.5668	−0.696868	−0.348434	+	0.937333i	$0.613286\pi$
$500$	5.38281	0.240727
$501$	10.2440	0.457666
$502$	−0.240020	−0.0107126
$503$	22.5576	1.00579	0.502896	−	0.864347i	$-0.332268\pi$
$503$	22.5576	1.00579	0.502896	+	0.864347i	$0.332268\pi$
$504$	−2.49080	−0.110949
$505$	4.99260	0.222168
$506$	0.210093	0.00933976
$507$	61.8728	2.74787
$508$	13.6045	0.603600
$509$	2.11298	0.0936562	0.0468281	−	0.998903i	$-0.485089\pi$
$509$	2.11298	0.0936562	0.0468281	+	0.998903i	$0.485089\pi$
$510$	0.812938	0.0359975
$511$	−12.5793	−0.556476
$512$	1.00000	0.0441942
$513$	3.94252	0.174066
$514$	−12.7962	−0.564414
$515$	3.15652	0.139093
$516$	9.00342	0.396354
$517$	−0.351975	−0.0154799
$518$	−5.91966	−0.260095
$519$	47.8264	2.09934
$520$	3.48652	0.152894
$521$	−9.64363	−0.422495	−0.211247	−	0.977433i	$-0.567753\pi$
$521$	−9.64363	−0.422495	−0.211247	+	0.977433i	$0.567753\pi$
$522$	−17.6541	−0.772697
$523$	28.4598	1.24446	0.622230	−	0.782835i	$-0.286227\pi$
$523$	28.4598	1.24446	0.622230	+	0.782835i	$0.286227\pi$
$524$	−18.8124	−0.821824
$525$	10.9934	0.479790
$526$	8.26056	0.360177
$527$	−0.502971	−0.0219097
$528$	−0.110629	−0.00481449
$529$	−3.19737	−0.139016
$530$	0.260325	0.0113078
$531$	−24.7685	−1.07486
$532$	3.30418	0.143254
$533$	45.3056	1.96241
$534$	27.2100	1.17749
$535$	−0.545053	−0.0235647
$536$	−16.0720	−0.694204
$537$	−3.19069	−0.137688
$538$	3.81798	0.164605
$539$	−0.0472117	−0.00203355
$540$	0.662716	0.0285188
$541$	−2.39043	−0.102772	−0.0513862	−	0.998679i	$-0.516364\pi$
$541$	−2.39043	−0.102772	−0.0513862	+	0.998679i	$0.516364\pi$
$542$	2.61340	0.112255
$543$	−22.0561	−0.946519
$544$	−0.624629	−0.0267807
$545$	−3.80897	−0.163158
$546$	14.7093	0.629500
$547$	40.7031	1.74034	0.870170	−	0.492751i	$-0.164009\pi$
$547$	40.7031	1.74034	0.870170	+	0.492751i	$0.164009\pi$
$548$	13.3766	0.571419
$549$	−3.67626	−0.156899
$550$	0.221494	0.00944455
$551$	23.4191	0.997687
$552$	−10.4275	−0.443823
$553$	−2.91682	−0.124036
$554$	−4.05734	−0.172380
$555$	−7.70428	−0.327029
$556$	12.0918	0.512805
$557$	−40.2964	−1.70741	−0.853707	−	0.520753i	$-0.825651\pi$
$557$	−40.2964	−1.70741	−0.853707	+	0.520753i	$0.825651\pi$
$558$	2.00567	0.0849066
$559$	−24.1193	−1.02014
$560$	0.555415	0.0234706
$561$	0.0691018	0.00291748
$562$	13.6682	0.576560
$563$	24.8732	1.04828	0.524141	−	0.851631i	$-0.324386\pi$
$563$	24.8732	1.04828	0.524141	+	0.851631i	$0.324386\pi$
$564$	17.4695	0.735598
$565$	−6.19086	−0.260451
$566$	−27.5451	−1.15781
$567$	10.2683	0.431229
$568$	11.0324	0.462909
$569$	−1.84965	−0.0775415	−0.0387708	−	0.999248i	$-0.512344\pi$
$569$	−1.84965	−0.0775415	−0.0387708	+	0.999248i	$0.512344\pi$
$570$	4.30030	0.180120
$571$	−25.2568	−1.05696	−0.528481	−	0.848945i	$-0.677238\pi$
$571$	−25.2568	−1.05696	−0.528481	+	0.848945i	$0.677238\pi$
$572$	0.296363	0.0123916
$573$	−9.13702	−0.381705
$574$	7.21735	0.301246
$575$	20.8773	0.870644
$576$	2.49080	0.103783
$577$	16.7810	0.698603	0.349301	−	0.937010i	$-0.386419\pi$
$577$	16.7810	0.698603	0.349301	+	0.937010i	$0.386419\pi$
$578$	−16.6098	−0.690878
$579$	−15.5997	−0.648303
$580$	3.93663	0.163460
$581$	−0.229852	−0.00953588
$582$	−18.3885	−0.762229
$583$	0.0221283	0.000916461 0
$584$	12.5793	0.520535
$585$	8.68421	0.359048
$586$	−14.5867	−0.602570
$587$	−21.0496	−0.868811	−0.434405	−	0.900717i	$-0.643041\pi$
$587$	−21.0496	−0.868811	−0.434405	+	0.900717i	$0.643041\pi$
$588$	2.34324	0.0966338
$589$	−2.66063	−0.109629
$590$	5.52305	0.227380
$591$	−14.3927	−0.592035
$592$	5.91966	0.243297
$593$	0.0550561	0.00226088	0.00113044	−	0.999999i	$-0.499640\pi$
$593$	0.0550561	0.00226088	0.00113044	+	0.999999i	$0.499640\pi$
$594$	0.0563326	0.00231135
$595$	−0.346928	−0.0142227
$596$	−11.5340	−0.472453
$597$	0.0742902	0.00304050
$598$	27.9342	1.14231
$599$	−4.30593	−0.175936	−0.0879678	−	0.996123i	$-0.528037\pi$
$599$	−4.30593	−0.175936	−0.0879678	+	0.996123i	$0.528037\pi$
$600$	−10.9934	−0.448802
$601$	−1.14430	−0.0466771	−0.0233386	−	0.999728i	$-0.507430\pi$
$601$	−1.14430	−0.0466771	−0.0233386	+	0.999728i	$0.507430\pi$
$602$	−3.84229	−0.156600
$603$	−40.0320	−1.63023
$604$	11.2839	0.459135
$605$	6.10833	0.248339
$606$	−21.0633	−0.855639
$607$	5.38069	0.218395	0.109198	−	0.994020i	$-0.465172\pi$
$607$	5.38069	0.218395	0.109198	+	0.994020i	$0.465172\pi$
$608$	−3.30418	−0.134002
$609$	16.6083	0.673001
$610$	0.819757	0.0331910
$611$	−46.7990	−1.89329
$612$	−1.55582	−0.0628904
$613$	8.96183	0.361965	0.180982	−	0.983486i	$-0.442072\pi$
$613$	8.96183	0.361965	0.180982	+	0.983486i	$0.442072\pi$
$614$	−13.6024	−0.548949
$615$	9.39319	0.378770
$616$	0.0472117	0.00190221
$617$	−17.4951	−0.704326	−0.352163	−	0.935939i	$-0.614554\pi$
$617$	−17.4951	−0.704326	−0.352163	+	0.935939i	$0.614554\pi$
$618$	−13.3170	−0.535690
$619$	15.5766	0.626077	0.313039	−	0.949740i	$-0.398653\pi$
$619$	15.5766	0.626077	0.313039	+	0.949740i	$0.398653\pi$
$620$	−0.447238	−0.0179615
$621$	5.30972	0.213072
$622$	−13.1889	−0.528828
$623$	−11.6121	−0.465229
$624$	−14.7093	−0.588843
$625$	20.4679	0.818715
$626$	−4.14707	−0.165750
$627$	0.365537	0.0145981
$628$	−4.99981	−0.199514
$629$	−3.69759	−0.147433
$630$	1.38343	0.0551170
$631$	−1.83109	−0.0728947	−0.0364474	−	0.999336i	$-0.511604\pi$
$631$	−1.83109	−0.0728947	−0.0364474	+	0.999336i	$0.511604\pi$
$632$	2.91682	0.116025
$633$	−14.6870	−0.583756
$634$	−6.08452	−0.241647
$635$	−7.55612	−0.299856
$636$	−1.09829	−0.0435499
$637$	−6.27732	−0.248717
$638$	0.334623	0.0132479
$639$	27.4795	1.08707
$640$	−0.555415	−0.0219547
$641$	22.2587	0.879166	0.439583	−	0.898202i	$-0.355126\pi$
$641$	22.2587	0.879166	0.439583	+	0.898202i	$0.355126\pi$
$642$	2.29953	0.0907552
$643$	37.9844	1.49796	0.748979	−	0.662594i	$-0.230544\pi$
$643$	37.9844	1.49796	0.748979	+	0.662594i	$0.230544\pi$
$644$	4.45001	0.175355
$645$	−5.00064	−0.196900
$646$	2.06389	0.0812025
$647$	10.8140	0.425140	0.212570	−	0.977146i	$-0.431817\pi$
$647$	10.8140	0.425140	0.212570	+	0.977146i	$0.431817\pi$
$648$	−10.2683	−0.403378
$649$	0.469473	0.0184284
$650$	29.4501	1.15513
$651$	−1.88685	−0.0739516
$652$	−3.42502	−0.134134
$653$	−1.92160	−0.0751982	−0.0375991	−	0.999293i	$-0.511971\pi$
$653$	−1.92160	−0.0751982	−0.0375991	+	0.999293i	$0.511971\pi$
$654$	16.0697	0.628375
$655$	10.4487	0.408264
$656$	−7.21735	−0.281790
$657$	31.3325	1.22240
$658$	−7.45525	−0.290636
$659$	17.8156	0.693997	0.346999	−	0.937866i	$-0.387201\pi$
$659$	17.8156	0.693997	0.346999	+	0.937866i	$0.387201\pi$
$660$	0.0614448	0.00239174
$661$	48.3969	1.88242	0.941210	−	0.337822i	$-0.109690\pi$
$661$	48.3969	1.88242	0.941210	+	0.337822i	$0.109690\pi$
$662$	6.22576	0.241971
$663$	9.18785	0.356827
$664$	0.229852	0.00892000
$665$	−1.83519	−0.0711657
$666$	14.7447	0.571344
$667$	31.5405	1.22125
$668$	4.37170	0.169146
$669$	−62.8029	−2.42810
$670$	8.92662	0.344865
$671$	0.0696815	0.00269002
$672$	−2.34324	−0.0903926
$673$	42.8181	1.65052	0.825258	−	0.564756i	$-0.191030\pi$
$673$	42.8181	1.65052	0.825258	+	0.564756i	$0.191030\pi$
$674$	−25.0475	−0.964793
$675$	5.59787	0.215462
$676$	26.4048	1.01557
$677$	31.1779	1.19826	0.599131	−	0.800651i	$-0.295513\pi$
$677$	31.1779	1.19826	0.599131	+	0.800651i	$0.295513\pi$
$678$	26.1187	1.00308
$679$	7.84746	0.301158
$680$	0.346928	0.0133041
$681$	−32.5986	−1.24918
$682$	−0.0380163	−0.00145572
$683$	−29.5021	−1.12887	−0.564434	−	0.825478i	$-0.690906\pi$
$683$	−29.5021	−1.12887	−0.564434	+	0.825478i	$0.690906\pi$
$684$	−8.23004	−0.314683
$685$	−7.42955	−0.283868
$686$	−1.00000	−0.0381802
$687$	23.7458	0.905958
$688$	3.84229	0.146486
$689$	2.94220	0.112089
$690$	5.79158	0.220482
$691$	−38.9159	−1.48043	−0.740216	−	0.672369i	$-0.765277\pi$
$691$	−38.9159	−1.48043	−0.740216	+	0.672369i	$0.765277\pi$
$692$	20.4103	0.775884
$693$	0.117595	0.00446705
$694$	5.69473	0.216169
$695$	−6.71595	−0.254751
$696$	−16.6083	−0.629534
$697$	4.50817	0.170759
$698$	23.1363	0.875723
$699$	16.7847	0.634856
$700$	4.69151	0.177323
$701$	30.7454	1.16124	0.580618	−	0.814176i	$-0.302811\pi$
$701$	30.7454	1.16124	0.580618	+	0.814176i	$0.302811\pi$
$702$	7.49004	0.282693
$703$	−19.5596	−0.737705
$704$	−0.0472117	−0.00177936
$705$	−9.70281	−0.365429
$706$	7.11301	0.267702
$707$	8.98896	0.338065
$708$	−23.3012	−0.875714
$709$	3.23576	0.121522	0.0607608	−	0.998152i	$-0.480647\pi$
$709$	3.23576	0.121522	0.0607608	+	0.998152i	$0.480647\pi$
$710$	−6.12756	−0.229963
$711$	7.26521	0.272467
$712$	11.6121	0.435182
$713$	−3.58329	−0.134195
$714$	1.46366	0.0547760
$715$	−0.164605	−0.00615586
$716$	−1.36165	−0.0508874
$717$	21.3861	0.798678
$718$	26.4168	0.985865
$719$	−30.4568	−1.13585	−0.567923	−	0.823081i	$-0.692253\pi$
$719$	−30.4568	−1.13585	−0.567923	+	0.823081i	$0.692253\pi$
$720$	−1.38343	−0.0515572
$721$	5.68316	0.211652
$722$	−8.08239	−0.300795
$723$	40.6628	1.51226
$724$	−9.41264	−0.349818
$725$	33.2521	1.23495
$726$	−25.7705	−0.956432
$727$	20.2523	0.751118	0.375559	−	0.926799i	$-0.377451\pi$
$727$	20.2523	0.751118	0.375559	+	0.926799i	$0.377451\pi$
$728$	6.27732	0.232653
$729$	−17.1885	−0.636610
$730$	−6.98674	−0.258591
$731$	−2.40000	−0.0887674
$732$	−3.45848	−0.127829
$733$	18.8118	0.694831	0.347415	−	0.937711i	$-0.387059\pi$
$733$	18.8118	0.694831	0.347415	+	0.937711i	$0.387059\pi$
$734$	−20.7652	−0.766458
$735$	−1.30147	−0.0480056
$736$	−4.45001	−0.164030
$737$	0.758786	0.0279502
$738$	−17.9769	−0.661741
$739$	−22.0767	−0.812104	−0.406052	−	0.913850i	$-0.633095\pi$
$739$	−22.0767	−0.812104	−0.406052	+	0.913850i	$0.633095\pi$
$740$	−3.28787	−0.120864
$741$	48.6022	1.78545
$742$	0.468704	0.0172067
$743$	−7.97441	−0.292553	−0.146276	−	0.989244i	$-0.546729\pi$
$743$	−7.97441	−0.292553	−0.146276	+	0.989244i	$0.546729\pi$
$744$	1.88685	0.0691754
$745$	6.40618	0.234704
$746$	−13.1745	−0.482351
$747$	0.572515	0.0209472
$748$	0.0294898	0.00107825
$749$	−0.981344	−0.0358575
$750$	12.6133	0.460571
$751$	16.7081	0.609688	0.304844	−	0.952402i	$-0.401396\pi$
$751$	16.7081	0.609688	0.304844	+	0.952402i	$0.401396\pi$
$752$	7.45525	0.271865
$753$	−0.562425	−0.0204959
$754$	44.4919	1.62030
$755$	−6.26725	−0.228089
$756$	1.19319	0.0433959
$757$	7.86380	0.285815	0.142907	−	0.989736i	$-0.454355\pi$
$757$	7.86380	0.285815	0.142907	+	0.989736i	$0.454355\pi$
$758$	12.1811	0.442437
$759$	0.492299	0.0178693
$760$	1.83519	0.0665694
$761$	−32.6344	−1.18300	−0.591498	−	0.806306i	$-0.701463\pi$
$761$	−32.6344	−1.18300	−0.591498	+	0.806306i	$0.701463\pi$
$762$	31.8786	1.15484
$763$	−6.85788	−0.248272
$764$	−3.89930	−0.141072
$765$	0.864128	0.0312426
$766$	−10.8795	−0.393092
$767$	62.4217	2.25392
$768$	2.34324	0.0845546
$769$	12.4257	0.448081	0.224041	−	0.974580i	$-0.428075\pi$
$769$	12.4257	0.448081	0.224041	+	0.974580i	$0.428075\pi$
$770$	−0.0262221	−0.000944979 0
$771$	−29.9845	−1.07987
$772$	−6.65733	−0.239602
$773$	10.0596	0.361820	0.180910	−	0.983500i	$-0.442096\pi$
$773$	10.0596	0.361820	0.180910	+	0.983500i	$0.442096\pi$
$774$	9.57035	0.343999
$775$	−3.77775	−0.135701
$776$	−7.84746	−0.281707
$777$	−13.8712	−0.497627
$778$	14.8202	0.531331
$779$	23.8474	0.854423
$780$	8.16977	0.292525
$781$	−0.520859	−0.0186378
$782$	2.77961	0.0993986
$783$	8.45700	0.302229
$784$	1.00000	0.0357143
$785$	2.77697	0.0991142
$786$	−44.0821	−1.57235
$787$	−31.5852	−1.12589	−0.562945	−	0.826495i	$-0.690332\pi$
$787$	−31.5852	−1.12589	−0.562945	+	0.826495i	$0.690332\pi$
$788$	−6.14220	−0.218807
$789$	19.3565	0.689110
$790$	−1.62005	−0.0576387
$791$	−11.1464	−0.396319
$792$	−0.117595	−0.00417855
$793$	9.26493	0.329007
$794$	−30.2995	−1.07529
$795$	0.610005	0.0216347
$796$	0.0317040	0.00112372
$797$	−40.7657	−1.44400	−0.721998	−	0.691895i	$-0.756776\pi$
$797$	−40.7657	−1.44400	−0.721998	+	0.691895i	$0.756776\pi$
$798$	7.74250	0.274082
$799$	−4.65676	−0.164744
$800$	−4.69151	−0.165870
$801$	28.9234	1.02196
$802$	7.75541	0.273853
$803$	−0.593891	−0.0209579
$804$	−37.6606	−1.32819
$805$	−2.47161	−0.0871127
$806$	−5.05470	−0.178044
$807$	8.94647	0.314931
$808$	−8.98896	−0.316230
$809$	16.9838	0.597119	0.298559	−	0.954391i	$-0.403494\pi$
$809$	16.9838	0.597119	0.298559	+	0.954391i	$0.403494\pi$
$810$	5.70318	0.200389
$811$	0.567200	0.0199171	0.00995855	−	0.999950i	$-0.496830\pi$
$811$	0.567200	0.0199171	0.00995855	+	0.999950i	$0.496830\pi$
$812$	7.08772	0.248730
$813$	6.12383	0.214772
$814$	−0.279477	−0.00979567
$815$	1.90231	0.0666349
$816$	−1.46366	−0.0512383
$817$	−12.6956	−0.444163
$818$	−6.37148	−0.222774
$819$	15.6355	0.546349
$820$	4.00863	0.139987
$821$	13.4005	0.467679	0.233839	−	0.972275i	$-0.424871\pi$
$821$	13.4005	0.467679	0.233839	+	0.972275i	$0.424871\pi$
$822$	31.3446	1.09327
$823$	44.9865	1.56813	0.784066	−	0.620678i	$-0.213142\pi$
$823$	44.9865	1.56813	0.784066	+	0.620678i	$0.213142\pi$
$824$	−5.68316	−0.197982
$825$	0.519016	0.0180698
$826$	9.94400	0.345996
$827$	10.3810	0.360982	0.180491	−	0.983577i	$-0.442231\pi$
$827$	10.3810	0.360982	0.180491	+	0.983577i	$0.442231\pi$
$828$	−11.0841	−0.385198
$829$	13.9469	0.484394	0.242197	−	0.970227i	$-0.422132\pi$
$829$	13.9469	0.484394	0.242197	+	0.970227i	$0.422132\pi$
$830$	−0.127663	−0.00443126
$831$	−9.50735	−0.329806
$832$	−6.27732	−0.217627
$833$	−0.624629	−0.0216421
$834$	28.3340	0.981125
$835$	−2.42811	−0.0840282
$836$	0.155996	0.00539524
$837$	−0.960794	−0.0332099
$838$	−32.1996	−1.11232
$839$	−35.5016	−1.22565	−0.612826	−	0.790218i	$-0.709967\pi$
$839$	−35.5016	−1.22565	−0.612826	+	0.790218i	$0.709967\pi$
$840$	1.30147	0.0449051
$841$	21.2358	0.732268
$842$	−2.92058	−0.100650
$843$	32.0280	1.10310
$844$	−6.26781	−0.215747
$845$	−14.6656	−0.504512
$846$	18.5695	0.638433
$847$	10.9978	0.377888
$848$	−0.468704	−0.0160953
$849$	−64.5450	−2.21518
$850$	2.93045	0.100514
$851$	−26.3426	−0.903012
$852$	25.8516	0.885662
$853$	−54.3499	−1.86091	−0.930453	−	0.366412i	$-0.880586\pi$
$853$	−54.3499	−1.86091	−0.930453	+	0.366412i	$0.880586\pi$
$854$	1.47594	0.0505055
$855$	4.57109	0.156328
$856$	0.981344	0.0335416
$857$	−22.8582	−0.780823	−0.390411	−	0.920641i	$-0.627667\pi$
$857$	−22.8582	−0.780823	−0.390411	+	0.920641i	$0.627667\pi$
$858$	0.694451	0.0237082
$859$	−40.4327	−1.37955	−0.689773	−	0.724026i	$-0.742290\pi$
$859$	−40.4327	−1.37955	−0.689773	+	0.724026i	$0.742290\pi$
$860$	−2.13407	−0.0727710
$861$	16.9120	0.576360
$862$	1.00000	0.0340601
$863$	−4.35363	−0.148199	−0.0740996	−	0.997251i	$-0.523608\pi$
$863$	−4.35363	−0.148199	−0.0740996	+	0.997251i	$0.523608\pi$
$864$	−1.19319	−0.0405932
$865$	−11.3362	−0.385442
$866$	−29.4125	−0.999479
$867$	−38.9209	−1.32182
$868$	−0.805231	−0.0273313
$869$	−0.137708	−0.00467143
$870$	9.22448	0.312739
$871$	100.889	3.41849
$872$	6.85788	0.232237
$873$	−19.5464	−0.661546
$874$	14.7037	0.497358
$875$	−5.38281	−0.181972
$876$	29.4764	0.995915
$877$	−27.8173	−0.939323	−0.469661	−	0.882847i	$-0.655624\pi$
$877$	−27.8173	−0.939323	−0.469661	+	0.882847i	$0.655624\pi$
$878$	26.8471	0.906047
$879$	−34.1802	−1.15287
$880$	0.0262221	0.000883947 0
$881$	27.6926	0.932987	0.466494	−	0.884525i	$-0.345517\pi$
$881$	27.6926	0.932987	0.466494	+	0.884525i	$0.345517\pi$
$882$	2.49080	0.0838694
$883$	26.8298	0.902894	0.451447	−	0.892298i	$-0.350908\pi$
$883$	26.8298	0.902894	0.451447	+	0.892298i	$0.350908\pi$
$884$	3.92100	0.131877
$885$	12.9419	0.435036
$886$	−35.2006	−1.18259
$887$	−16.5441	−0.555496	−0.277748	−	0.960654i	$-0.589588\pi$
$887$	−16.5441	−0.555496	−0.277748	+	0.960654i	$0.589588\pi$
$888$	13.8712	0.465487
$889$	−13.6045	−0.456279
$890$	−6.44954	−0.216189
$891$	0.484785	0.0162409
$892$	−26.8017	−0.897386
$893$	−24.6335	−0.824329
$894$	−27.0271	−0.903921
$895$	0.756284	0.0252798
$896$	−1.00000	−0.0334077
$897$	65.4566	2.18553
$898$	−33.0672	−1.10347
$899$	−5.70725	−0.190348
$900$	−11.6856	−0.389520
$901$	0.292766	0.00975344
$902$	0.340744	0.0113455
$903$	−9.00342	−0.299615
$904$	11.1464	0.370723
$905$	5.22792	0.173782
$906$	26.4409	0.878441
$907$	−27.6062	−0.916649	−0.458325	−	0.888785i	$-0.651550\pi$
$907$	−27.6062	−0.916649	−0.458325	+	0.888785i	$0.651550\pi$
$908$	−13.9117	−0.461677
$909$	−22.3897	−0.742618
$910$	−3.48652	−0.115577
$911$	−22.4557	−0.743991	−0.371995	−	0.928235i	$-0.621326\pi$
$911$	−22.4557	−0.743991	−0.371995	+	0.928235i	$0.621326\pi$
$912$	−7.74250	−0.256380
$913$	−0.0108517	−0.000359140 0
$914$	21.6691	0.716751
$915$	1.92089	0.0635027
$916$	10.1337	0.334827
$917$	18.8124	0.621240
$918$	0.745301	0.0245986
$919$	−37.5124	−1.23742	−0.618710	−	0.785619i	$-0.712345\pi$
$919$	−37.5124	−1.23742	−0.618710	+	0.785619i	$0.712345\pi$
$920$	2.47161	0.0814864
$921$	−31.8738	−1.05028
$922$	15.3033	0.503988
$923$	−69.2539	−2.27952
$924$	0.110629	0.00363941
$925$	−27.7722	−0.913143
$926$	−28.3336	−0.931099
$927$	−14.1556	−0.464931
$928$	−7.08772	−0.232666
$929$	−42.3655	−1.38997	−0.694983	−	0.719026i	$-0.744588\pi$
$929$	−42.3655	−1.38997	−0.694983	+	0.719026i	$0.744588\pi$
$930$	−1.04799	−0.0343649
$931$	−3.30418	−0.108290
$932$	7.16302	0.234633
$933$	−30.9049	−1.01178
$934$	−28.7849	−0.941872
$935$	−0.0163791	−0.000535653 0
$936$	−15.6355	−0.511063
$937$	15.8031	0.516266	0.258133	−	0.966109i	$-0.416893\pi$
$937$	15.8031	0.516266	0.258133	+	0.966109i	$0.416893\pi$
$938$	16.0720	0.524769
$939$	−9.71759	−0.317122
$940$	−4.14076	−0.135057
$941$	−43.9964	−1.43424	−0.717121	−	0.696949i	$-0.754540\pi$
$941$	−43.9964	−1.43424	−0.717121	+	0.696949i	$0.754540\pi$
$942$	−11.7158	−0.381720
$943$	32.1173	1.04588
$944$	−9.94400	−0.323650
$945$	−0.662716	−0.0215582
$946$	−0.181401	−0.00589786
$947$	−42.7900	−1.39049	−0.695244	−	0.718774i	$-0.744704\pi$
$947$	−42.7900	−1.39049	−0.695244	+	0.718774i	$0.744704\pi$
$948$	6.83483	0.221985
$949$	−78.9643	−2.56329
$950$	15.5016	0.502939
$951$	−14.2575	−0.462332
$952$	0.624629	0.0202443
$953$	44.7387	1.44923	0.724614	−	0.689155i	$-0.242018\pi$
$953$	44.7387	1.44923	0.724614	+	0.689155i	$0.242018\pi$
$954$	−1.16744	−0.0377974
$955$	2.16573	0.0700814
$956$	9.12669	0.295178
$957$	0.784104	0.0253465
$958$	16.7313	0.540563
$959$	−13.3766	−0.431952
$960$	−1.30147	−0.0420049
$961$	−30.3516	−0.979084
$962$	−37.1596	−1.19807
$963$	2.44433	0.0787673
$964$	17.3532	0.558909
$965$	3.69758	0.119029
$966$	10.4275	0.335498
$967$	49.0970	1.57885	0.789426	−	0.613846i	$-0.210378\pi$
$967$	49.0970	1.57885	0.789426	+	0.613846i	$0.210378\pi$
$968$	−10.9978	−0.353482
$969$	4.83619	0.155361
$970$	4.35860	0.139946
$971$	−49.2249	−1.57970	−0.789851	−	0.613299i	$-0.789842\pi$
$971$	−49.2249	−1.57970	−0.789851	+	0.613299i	$0.789842\pi$
$972$	−20.4816	−0.656948
$973$	−12.0918	−0.387644
$974$	−14.5361	−0.465765
$975$	69.0089	2.21005
$976$	−1.47594	−0.0472436
$977$	−10.0958	−0.322994	−0.161497	−	0.986873i	$-0.551632\pi$
$977$	−10.0958	−0.322994	−0.161497	+	0.986873i	$0.551632\pi$
$978$	−8.02565	−0.256632
$979$	−0.548227	−0.0175214
$980$	−0.555415	−0.0177421
$981$	17.0816	0.545373
$982$	−9.89203	−0.315668
$983$	26.9190	0.858584	0.429292	−	0.903166i	$-0.358763\pi$
$983$	26.9190	0.858584	0.429292	+	0.903166i	$0.358763\pi$
$984$	−16.9120	−0.539135
$985$	3.41147	0.108698
$986$	4.42719	0.140991
$987$	−17.4695	−0.556060
$988$	20.7414	0.659872
$989$	−17.0982	−0.543692
$990$	0.0653139	0.00207581
$991$	36.6990	1.16578	0.582890	−	0.812551i	$-0.301922\pi$
$991$	36.6990	1.16578	0.582890	+	0.812551i	$0.301922\pi$
$992$	0.805231	0.0255661
$993$	14.5885	0.462952
$994$	−11.0324	−0.349927
$995$	−0.0176089	−0.000558239 0
$996$	0.538600	0.0170662
$997$	−7.32651	−0.232033	−0.116016	−	0.993247i	$-0.537013\pi$
$997$	−7.32651	−0.232033	−0.116016	+	0.993247i	$0.537013\pi$
$998$	−15.5668	−0.492760
$999$	−7.06328	−0.223472

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.l.1.19	✓	20

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.34324 q^{3} +1.00000 q^{4} -0.555415 q^{5} +2.34324 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.49080 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.34324 q^{3} +1.00000 q^{4} -0.555415 q^{5} +2.34324 q^{6} -1.00000 q^{7} +1.00000 q^{8} +2.49080 q^{9} -0.555415 q^{10} -0.0472117 q^{11} +2.34324 q^{12} -6.27732 q^{13} -1.00000 q^{14} -1.30147 q^{15} +1.00000 q^{16} -0.624629 q^{17} +2.49080 q^{18} -3.30418 q^{19} -0.555415 q^{20} -2.34324 q^{21} -0.0472117 q^{22} -4.45001 q^{23} +2.34324 q^{24} -4.69151 q^{25} -6.27732 q^{26} -1.19319 q^{27} -1.00000 q^{28} -7.08772 q^{29} -1.30147 q^{30} +0.805231 q^{31} +1.00000 q^{32} -0.110629 q^{33} -0.624629 q^{34} +0.555415 q^{35} +2.49080 q^{36} +5.91966 q^{37} -3.30418 q^{38} -14.7093 q^{39} -0.555415 q^{40} -7.21735 q^{41} -2.34324 q^{42} +3.84229 q^{43} -0.0472117 q^{44} -1.38343 q^{45} -4.45001 q^{46} +7.45525 q^{47} +2.34324 q^{48} +1.00000 q^{49} -4.69151 q^{50} -1.46366 q^{51} -6.27732 q^{52} -0.468704 q^{53} -1.19319 q^{54} +0.0262221 q^{55} -1.00000 q^{56} -7.74250 q^{57} -7.08772 q^{58} -9.94400 q^{59} -1.30147 q^{60} -1.47594 q^{61} +0.805231 q^{62} -2.49080 q^{63} +1.00000 q^{64} +3.48652 q^{65} -0.110629 q^{66} -16.0720 q^{67} -0.624629 q^{68} -10.4275 q^{69} +0.555415 q^{70} +11.0324 q^{71} +2.49080 q^{72} +12.5793 q^{73} +5.91966 q^{74} -10.9934 q^{75} -3.30418 q^{76} +0.0472117 q^{77} -14.7093 q^{78} +2.91682 q^{79} -0.555415 q^{80} -10.2683 q^{81} -7.21735 q^{82} +0.229852 q^{83} -2.34324 q^{84} +0.346928 q^{85} +3.84229 q^{86} -16.6083 q^{87} -0.0472117 q^{88} +11.6121 q^{89} -1.38343 q^{90} +6.27732 q^{91} -4.45001 q^{92} +1.88685 q^{93} +7.45525 q^{94} +1.83519 q^{95} +2.34324 q^{96} -7.84746 q^{97} +1.00000 q^{98} -0.117595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 3 q^{3} + 20 q^{4} - 10 q^{5} - 3 q^{6} - 20 q^{7} + 20 q^{8} + 21 q^{9}+O(q^{10}) \) 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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