LMFDB - Embedded newform 671.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, 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("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2661761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 3x^{3} + 9x^{2} - x - 1 $ x^6 - x^5 - 6x^4 + 3x^3 + 9*x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.34697$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.782747 q^{2} +1.34697 q^{3} -1.38731 q^{4} -0.742408 q^{5} +1.05434 q^{6} -2.34697 q^{7} -2.65140 q^{8} -1.18568 q^{9} +O(q^{10})$	\(q+0.782747 q^{2} +1.34697 q^{3} -1.38731 q^{4} -0.742408 q^{5} +1.05434 q^{6} -2.34697 q^{7} -2.65140 q^{8} -1.18568 q^{9} -0.581118 q^{10} -1.00000 q^{11} -1.86866 q^{12} -2.09467 q^{13} -1.83708 q^{14} -1.00000 q^{15} +0.699234 q^{16} -4.14567 q^{17} -0.928086 q^{18} +3.60293 q^{19} +1.02995 q^{20} -3.16129 q^{21} -0.782747 q^{22} -0.776241 q^{23} -3.57136 q^{24} -4.44883 q^{25} -1.63960 q^{26} -5.63797 q^{27} +3.25596 q^{28} +2.99837 q^{29} -0.782747 q^{30} -5.41725 q^{31} +5.85013 q^{32} -1.34697 q^{33} -3.24501 q^{34} +1.74241 q^{35} +1.64490 q^{36} +8.69435 q^{37} +2.82019 q^{38} -2.82146 q^{39} +1.96842 q^{40} +7.27899 q^{41} -2.47449 q^{42} -10.4140 q^{43} +1.38731 q^{44} +0.880257 q^{45} -0.607600 q^{46} +9.01495 q^{47} +0.941846 q^{48} -1.49174 q^{49} -3.48231 q^{50} -5.58408 q^{51} +2.90596 q^{52} -8.90673 q^{53} -4.41311 q^{54} +0.742408 q^{55} +6.22276 q^{56} +4.85303 q^{57} +2.34697 q^{58} -7.30217 q^{59} +1.38731 q^{60} -1.00000 q^{61} -4.24034 q^{62} +2.78275 q^{63} +3.18071 q^{64} +1.55510 q^{65} -1.05434 q^{66} +12.2026 q^{67} +5.75131 q^{68} -1.04557 q^{69} +1.36387 q^{70} -14.2107 q^{71} +3.14371 q^{72} +11.6807 q^{73} +6.80548 q^{74} -5.99243 q^{75} -4.99837 q^{76} +2.34697 q^{77} -2.20849 q^{78} +8.08687 q^{79} -0.519117 q^{80} -4.03714 q^{81} +5.69761 q^{82} -0.786515 q^{83} +4.38568 q^{84} +3.07778 q^{85} -8.15153 q^{86} +4.03871 q^{87} +2.65140 q^{88} -4.13148 q^{89} +0.689019 q^{90} +4.91613 q^{91} +1.07688 q^{92} -7.29687 q^{93} +7.05643 q^{94} -2.67485 q^{95} +7.87994 q^{96} -10.2966 q^{97} -1.16766 q^{98} +1.18568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * 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 $

$2$	0.782747	0.553486	0.276743	−	0.960944i	$-0.410745\pi$
$2$	0.782747	0.553486	0.276743	+	0.960944i	$0.410745\pi$
$3$	1.34697	0.777672	0.388836	−	0.921307i	$-0.372877\pi$
$3$	1.34697	0.777672	0.388836	+	0.921307i	$0.372877\pi$
$4$	−1.38731	−0.693653
$5$	−0.742408	−0.332015	−0.166008	−	0.986124i	$-0.553088\pi$
$5$	−0.742408	−0.332015	−0.166008	+	0.986124i	$0.553088\pi$
$6$	1.05434	0.430431
$7$	−2.34697	−0.887070	−0.443535	−	0.896257i	$-0.646276\pi$
$7$	−2.34697	−0.887070	−0.443535	+	0.896257i	$0.646276\pi$
$8$	−2.65140	−0.937413
$9$	−1.18568	−0.395226
$10$	−0.581118	−0.183766
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.86866	−0.539435
$13$	−2.09467	−0.580958	−0.290479	−	0.956881i	$-0.593815\pi$
$13$	−2.09467	−0.580958	−0.290479	+	0.956881i	$0.593815\pi$
$14$	−1.83708	−0.490981
$15$	−1.00000	−0.258199
$16$	0.699234	0.174808
$17$	−4.14567	−1.00547	−0.502736	−	0.864440i	$-0.667673\pi$
$17$	−4.14567	−1.00547	−0.502736	+	0.864440i	$0.667673\pi$
$18$	−0.928086	−0.218752
$19$	3.60293	0.826569	0.413285	−	0.910602i	$-0.364381\pi$
$19$	3.60293	0.826569	0.413285	+	0.910602i	$0.364381\pi$
$20$	1.02995	0.230303
$21$	−3.16129	−0.689850
$22$	−0.782747	−0.166882
$23$	−0.776241	−0.161857	−0.0809287	−	0.996720i	$-0.525789\pi$
$23$	−0.776241	−0.161857	−0.0809287	+	0.996720i	$0.525789\pi$
$24$	−3.57136	−0.729000
$25$	−4.44883	−0.889766
$26$	−1.63960	−0.321552
$27$	−5.63797	−1.08503
$28$	3.25596	0.615319
$29$	2.99837	0.556784	0.278392	−	0.960468i	$-0.410199\pi$
$29$	2.99837	0.556784	0.278392	+	0.960468i	$0.410199\pi$
$30$	−0.782747	−0.142909
$31$	−5.41725	−0.972968	−0.486484	−	0.873690i	$-0.661721\pi$
$31$	−5.41725	−0.972968	−0.486484	+	0.873690i	$0.661721\pi$
$32$	5.85013	1.03417
$33$	−1.34697	−0.234477
$34$	−3.24501	−0.556514
$35$	1.74241	0.294521
$36$	1.64490	0.274150
$37$	8.69435	1.42934	0.714671	−	0.699460i	$-0.246576\pi$
$37$	8.69435	1.42934	0.714671	+	0.699460i	$0.246576\pi$
$38$	2.82019	0.457494
$39$	−2.82146	−0.451795
$40$	1.96842	0.311235
$41$	7.27899	1.13679	0.568393	−	0.822757i	$-0.307565\pi$
$41$	7.27899	1.13679	0.568393	+	0.822757i	$0.307565\pi$
$42$	−2.47449	−0.381822
$43$	−10.4140	−1.58812	−0.794060	−	0.607839i	$-0.792036\pi$
$43$	−10.4140	−1.58812	−0.794060	+	0.607839i	$0.792036\pi$
$44$	1.38731	0.209144
$45$	0.880257	0.131221
$46$	−0.607600	−0.0895858
$47$	9.01495	1.31497	0.657483	−	0.753469i	$-0.271621\pi$
$47$	9.01495	1.31497	0.657483	+	0.753469i	$0.271621\pi$
$48$	0.941846	0.135944
$49$	−1.49174	−0.213106
$50$	−3.48231	−0.492473
$51$	−5.58408	−0.781928
$52$	2.90596	0.402984
$53$	−8.90673	−1.22343	−0.611716	−	0.791077i	$-0.709521\pi$
$53$	−8.90673	−1.22343	−0.611716	+	0.791077i	$0.709521\pi$
$54$	−4.41311	−0.600548
$55$	0.742408	0.100106
$56$	6.22276	0.831552
$57$	4.85303	0.642800
$58$	2.34697	0.308172
$59$	−7.30217	−0.950661	−0.475331	−	0.879807i	$-0.657672\pi$
$59$	−7.30217	−0.950661	−0.475331	+	0.879807i	$0.657672\pi$
$60$	1.38731	0.179101
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−4.24034	−0.538524
$63$	2.78275	0.350593
$64$	3.18071	0.397588
$65$	1.55510	0.192887
$66$	−1.05434	−0.129780
$67$	12.2026	1.49079	0.745393	−	0.666625i	$-0.232262\pi$
$67$	12.2026	1.49079	0.745393	+	0.666625i	$0.232262\pi$
$68$	5.75131	0.697449
$69$	−1.04557	−0.125872
$70$	1.36387	0.163013
$71$	−14.2107	−1.68651	−0.843253	−	0.537518i	$-0.819362\pi$
$71$	−14.2107	−1.68651	−0.843253	+	0.537518i	$0.819362\pi$
$72$	3.14371	0.370490
$73$	11.6807	1.36712	0.683560	−	0.729894i	$-0.260431\pi$
$73$	11.6807	1.36712	0.683560	+	0.729894i	$0.260431\pi$
$74$	6.80548	0.791121
$75$	−5.99243	−0.691946
$76$	−4.99837	−0.573353
$77$	2.34697	0.267462
$78$	−2.20849	−0.250062
$79$	8.08687	0.909844	0.454922	−	0.890531i	$-0.349667\pi$
$79$	8.08687	0.909844	0.454922	+	0.890531i	$0.349667\pi$
$80$	−0.519117	−0.0580390
$81$	−4.03714	−0.448571
$82$	5.69761	0.629195
$83$	−0.786515	−0.0863312	−0.0431656	−	0.999068i	$-0.513744\pi$
$83$	−0.786515	−0.0863312	−0.0431656	+	0.999068i	$0.513744\pi$
$84$	4.38568	0.478517
$85$	3.07778	0.333832
$86$	−8.15153	−0.879002
$87$	4.03871	0.432995
$88$	2.65140	0.282641
$89$	−4.13148	−0.437936	−0.218968	−	0.975732i	$-0.570269\pi$
$89$	−4.13148	−0.437936	−0.218968	+	0.975732i	$0.570269\pi$
$90$	0.689019	0.0726289
$91$	4.91613	0.515351
$92$	1.07688	0.112273
$93$	−7.29687	−0.756650
$94$	7.05643	0.727815
$95$	−2.67485	−0.274433
$96$	7.87994	0.804243
$97$	−10.2966	−1.04546	−0.522729	−	0.852499i	$-0.675086\pi$
$97$	−10.2966	−1.04546	−0.522729	+	0.852499i	$0.675086\pi$
$98$	−1.16766	−0.117951
$99$	1.18568	0.119165
$100$	6.17189	0.617189
$101$	−4.05895	−0.403881	−0.201940	−	0.979398i	$-0.564725\pi$
$101$	−4.05895	−0.403881	−0.201940	+	0.979398i	$0.564725\pi$
$102$	−4.37092	−0.432786
$103$	−5.66377	−0.558068	−0.279034	−	0.960281i	$-0.590014\pi$
$103$	−5.66377	−0.558068	−0.279034	+	0.960281i	$0.590014\pi$
$104$	5.55383	0.544598
$105$	2.34697	0.229041
$106$	−6.97171	−0.677153
$107$	2.69077	0.260127	0.130063	−	0.991506i	$-0.458482\pi$
$107$	2.69077	0.260127	0.130063	+	0.991506i	$0.458482\pi$
$108$	7.82160	0.752634
$109$	−15.6641	−1.50035	−0.750174	−	0.661240i	$-0.770031\pi$
$109$	−15.6641	−1.50035	−0.750174	+	0.661240i	$0.770031\pi$
$110$	0.581118	0.0554074
$111$	11.7110	1.11156
$112$	−1.64108	−0.155067
$113$	−1.78319	−0.167748	−0.0838742	−	0.996476i	$-0.526729\pi$
$113$	−1.78319	−0.167748	−0.0838742	+	0.996476i	$0.526729\pi$
$114$	3.79870	0.355781
$115$	0.576288	0.0537391
$116$	−4.15966	−0.386215
$117$	2.48361	0.229610
$118$	−5.71575	−0.526177
$119$	9.72975	0.891924
$120$	2.65140	0.242039
$121$	1.00000	0.0909091
$122$	−0.782747	−0.0708666
$123$	9.80456	0.884048
$124$	7.51539	0.674902
$125$	7.01489	0.627431
$126$	2.17819	0.194048
$127$	−2.31761	−0.205655	−0.102827	−	0.994699i	$-0.532789\pi$
$127$	−2.31761	−0.205655	−0.102827	+	0.994699i	$0.532789\pi$
$128$	−9.21058	−0.814108
$129$	−14.0273	−1.23504
$130$	1.21725	0.106760
$131$	−0.614737	−0.0537098	−0.0268549	−	0.999639i	$-0.508549\pi$
$131$	−0.614737	−0.0537098	−0.0268549	+	0.999639i	$0.508549\pi$
$132$	1.86866	0.162646
$133$	−8.45597	−0.733225
$134$	9.55156	0.825129
$135$	4.18568	0.360246
$136$	10.9918	0.942543
$137$	16.8439	1.43907	0.719535	−	0.694456i	$-0.244355\pi$
$137$	16.8439	1.43907	0.719535	+	0.694456i	$0.244355\pi$
$138$	−0.818418	−0.0696684
$139$	−10.1653	−0.862211	−0.431106	−	0.902301i	$-0.641876\pi$
$139$	−10.1653	−0.862211	−0.431106	+	0.902301i	$0.641876\pi$
$140$	−2.41725	−0.204295
$141$	12.1429	1.02261
$142$	−11.1234	−0.933457
$143$	2.09467	0.175165
$144$	−0.829066	−0.0690888
$145$	−2.22602	−0.184861
$146$	9.14302	0.756682
$147$	−2.00933	−0.165727
$148$	−12.0617	−0.991468
$149$	−9.13134	−0.748068	−0.374034	−	0.927415i	$-0.622026\pi$
$149$	−9.13134	−0.748068	−0.374034	+	0.927415i	$0.622026\pi$
$150$	−4.69056	−0.382983
$151$	19.9281	1.62172	0.810862	−	0.585238i	$-0.198999\pi$
$151$	19.9281	1.62172	0.810862	+	0.585238i	$0.198999\pi$
$152$	−9.55283	−0.774837
$153$	4.91542	0.397388
$154$	1.83708	0.148036
$155$	4.02181	0.323040
$156$	3.91423	0.313389
$157$	4.89609	0.390750	0.195375	−	0.980729i	$-0.437408\pi$
$157$	4.89609	0.390750	0.195375	+	0.980729i	$0.437408\pi$
$158$	6.32997	0.503586
$159$	−11.9971	−0.951430
$160$	−4.34319	−0.343359
$161$	1.82181	0.143579
$162$	−3.16006	−0.248278
$163$	−15.2596	−1.19522	−0.597610	−	0.801787i	$-0.703883\pi$
$163$	−15.2596	−1.19522	−0.597610	+	0.801787i	$0.703883\pi$
$164$	−10.0982	−0.788536
$165$	1.00000	0.0778499
$166$	−0.615642	−0.0477831
$167$	8.81814	0.682368	0.341184	−	0.939996i	$-0.389172\pi$
$167$	8.81814	0.682368	0.341184	+	0.939996i	$0.389172\pi$
$168$	8.38186	0.646675
$169$	−8.61234	−0.662488
$170$	2.40912	0.184771
$171$	−4.27192	−0.326682
$172$	14.4474	1.10160
$173$	−7.21491	−0.548540	−0.274270	−	0.961653i	$-0.588436\pi$
$173$	−7.21491	−0.548540	−0.274270	+	0.961653i	$0.588436\pi$
$174$	3.16129	0.239657
$175$	10.4413	0.789285
$176$	−0.699234	−0.0527067
$177$	−9.83578	−0.739303
$178$	−3.23391	−0.242392
$179$	−1.51078	−0.112921	−0.0564604	−	0.998405i	$-0.517981\pi$
$179$	−1.51078	−0.112921	−0.0564604	+	0.998405i	$0.517981\pi$
$180$	−1.22119	−0.0910218
$181$	−22.7664	−1.69221	−0.846106	−	0.533014i	$-0.821059\pi$
$181$	−22.7664	−1.69221	−0.846106	+	0.533014i	$0.821059\pi$
$182$	3.84809	0.285239
$183$	−1.34697	−0.0995707
$184$	2.05813	0.151727
$185$	−6.45476	−0.474563
$186$	−5.71160	−0.418795
$187$	4.14567	0.303161
$188$	−12.5065	−0.912131
$189$	13.2321	0.962497
$190$	−2.09373	−0.151895
$191$	18.2867	1.32318	0.661591	−	0.749865i	$-0.269882\pi$
$191$	18.2867	1.32318	0.661591	+	0.749865i	$0.269882\pi$
$192$	4.28431	0.309193
$193$	−15.9280	−1.14652	−0.573262	−	0.819372i	$-0.694322\pi$
$193$	−15.9280	−1.14652	−0.573262	+	0.819372i	$0.694322\pi$
$194$	−8.05961	−0.578646
$195$	2.09467	0.150003
$196$	2.06950	0.147822
$197$	25.0595	1.78542	0.892708	−	0.450635i	$-0.148802\pi$
$197$	25.0595	1.78542	0.892708	+	0.450635i	$0.148802\pi$
$198$	0.928086	0.0659562
$199$	−14.1429	−1.00257	−0.501283	−	0.865283i	$-0.667139\pi$
$199$	−14.1429	−1.00257	−0.501283	+	0.865283i	$0.667139\pi$
$200$	11.7956	0.834078
$201$	16.4365	1.15934
$202$	−3.17713	−0.223542
$203$	−7.03708	−0.493907
$204$	7.74683	0.542387
$205$	−5.40398	−0.377430
$206$	−4.43330	−0.308883
$207$	0.920371	0.0639702
$208$	−1.46467	−0.101556
$209$	−3.60293	−0.249220
$210$	1.83708	0.126771
$211$	1.14274	0.0786697	0.0393348	−	0.999226i	$-0.487476\pi$
$211$	1.14274	0.0786697	0.0393348	+	0.999226i	$0.487476\pi$
$212$	12.3564	0.848638
$213$	−19.1414	−1.31155
$214$	2.10619	0.143976
$215$	7.73144	0.527280
$216$	14.9485	1.01712
$217$	12.7141	0.863091
$218$	−12.2610	−0.830422
$219$	15.7335	1.06317
$220$	−1.02995	−0.0694391
$221$	8.68382	0.584137
$222$	9.16676	0.615233
$223$	21.1618	1.41710	0.708549	−	0.705661i	$-0.249350\pi$
$223$	21.1618	1.41710	0.708549	+	0.705661i	$0.249350\pi$
$224$	−13.7301	−0.917379
$225$	5.27488	0.351659
$226$	−1.39579	−0.0928463
$227$	−16.4976	−1.09499	−0.547493	−	0.836810i	$-0.684418\pi$
$227$	−16.4976	−1.09499	−0.547493	+	0.836810i	$0.684418\pi$
$228$	−6.73265	−0.445880
$229$	−8.65820	−0.572150	−0.286075	−	0.958207i	$-0.592351\pi$
$229$	−8.65820	−0.572150	−0.286075	+	0.958207i	$0.592351\pi$
$230$	0.451088	0.0297438
$231$	3.16129	0.207998
$232$	−7.94990	−0.521937
$233$	6.62984	0.434335	0.217168	−	0.976134i	$-0.430318\pi$
$233$	6.62984	0.434335	0.217168	+	0.976134i	$0.430318\pi$
$234$	1.94404	0.127086
$235$	−6.69278	−0.436589
$236$	10.1303	0.659429
$237$	10.8928	0.707560
$238$	7.61593	0.493668
$239$	−19.6278	−1.26962	−0.634810	−	0.772669i	$-0.718921\pi$
$239$	−19.6278	−1.26962	−0.634810	+	0.772669i	$0.718921\pi$
$240$	−0.699234	−0.0451354
$241$	−2.16872	−0.139699	−0.0698497	−	0.997558i	$-0.522252\pi$
$241$	−2.16872	−0.139699	−0.0698497	+	0.997558i	$0.522252\pi$
$242$	0.782747	0.0503169
$243$	11.4760	0.736187
$244$	1.38731	0.0888132
$245$	1.10748	0.0707544
$246$	7.67449	0.489308
$247$	−7.54697	−0.480202
$248$	14.3633	0.912073
$249$	−1.05941	−0.0671374
$250$	5.49088	0.347274
$251$	4.59988	0.290342	0.145171	−	0.989407i	$-0.453627\pi$
$251$	4.59988	0.290342	0.145171	+	0.989407i	$0.453627\pi$
$252$	−3.86052	−0.243190
$253$	0.776241	0.0488018
$254$	−1.81410	−0.113827
$255$	4.14567	0.259612
$256$	−13.5710	−0.848185
$257$	−28.6344	−1.78617	−0.893084	−	0.449891i	$-0.851463\pi$
$257$	−28.6344	−1.78617	−0.893084	+	0.449891i	$0.851463\pi$
$258$	−10.9798	−0.683575
$259$	−20.4054	−1.26793
$260$	−2.15741	−0.133797
$261$	−3.55510	−0.220055
$262$	−0.481184	−0.0297276
$263$	25.2920	1.55957	0.779785	−	0.626047i	$-0.215328\pi$
$263$	25.2920	1.55957	0.779785	+	0.626047i	$0.215328\pi$
$264$	3.57136	0.219802
$265$	6.61243	0.406198
$266$	−6.61888	−0.405830
$267$	−5.56497	−0.340571
$268$	−16.9288	−1.03409
$269$	27.0396	1.64864	0.824318	−	0.566127i	$-0.191559\pi$
$269$	27.0396	1.64864	0.824318	+	0.566127i	$0.191559\pi$
$270$	3.27633	0.199391
$271$	14.8280	0.900735	0.450367	−	0.892843i	$-0.351293\pi$
$271$	14.8280	0.900735	0.450367	+	0.892843i	$0.351293\pi$
$272$	−2.89879	−0.175765
$273$	6.62187	0.400774
$274$	13.1845	0.796505
$275$	4.44883	0.268275
$276$	1.45053	0.0873116
$277$	16.3212	0.980648	0.490324	−	0.871540i	$-0.336878\pi$
$277$	16.3212	0.980648	0.490324	+	0.871540i	$0.336878\pi$
$278$	−7.95688	−0.477222
$279$	6.42312	0.384542
$280$	−4.61983	−0.276088
$281$	5.15314	0.307411	0.153705	−	0.988117i	$-0.450879\pi$
$281$	5.15314	0.307411	0.153705	+	0.988117i	$0.450879\pi$
$282$	9.50478	0.566002
$283$	−13.8984	−0.826173	−0.413087	−	0.910692i	$-0.635549\pi$
$283$	−13.8984	−0.826173	−0.413087	+	0.910692i	$0.635549\pi$
$284$	19.7147	1.16985
$285$	−3.60293	−0.213419
$286$	1.63960	0.0969516
$287$	−17.0835	−1.00841
$288$	−6.93637	−0.408730
$289$	0.186552	0.0109737
$290$	−1.74241	−0.102318
$291$	−13.8691	−0.813024
$292$	−16.2047	−0.948308
$293$	20.8020	1.21527	0.607633	−	0.794218i	$-0.292119\pi$
$293$	20.8020	1.21527	0.607633	+	0.794218i	$0.292119\pi$
$294$	−1.57280	−0.0917273
$295$	5.42119	0.315634
$296$	−23.0522	−1.33988
$297$	5.63797	0.327148
$298$	−7.14753	−0.414045
$299$	1.62597	0.0940324
$300$	8.31334	0.479971
$301$	24.4413	1.40877
$302$	15.5986	0.897601
$303$	−5.46728	−0.314087
$304$	2.51929	0.144491
$305$	0.742408	0.0425102
$306$	3.84753	0.219949
$307$	−24.7144	−1.41053	−0.705263	−	0.708945i	$-0.749171\pi$
$307$	−24.7144	−1.41053	−0.705263	+	0.708945i	$0.749171\pi$
$308$	−3.25596	−0.185526
$309$	−7.62892	−0.433994
$310$	3.14806	0.178798
$311$	−32.5170	−1.84387	−0.921935	−	0.387344i	$-0.873393\pi$
$311$	−32.5170	−1.84387	−0.921935	+	0.387344i	$0.873393\pi$
$312$	7.48083	0.423519
$313$	−24.8070	−1.40217	−0.701086	−	0.713077i	$-0.747301\pi$
$313$	−24.8070	−1.40217	−0.701086	+	0.713077i	$0.747301\pi$
$314$	3.83240	0.216275
$315$	−2.06593	−0.116402
$316$	−11.2190	−0.631116
$317$	−11.9411	−0.670680	−0.335340	−	0.942097i	$-0.608851\pi$
$317$	−11.9411	−0.670680	−0.335340	+	0.942097i	$0.608851\pi$
$318$	−9.39068	−0.526603
$319$	−2.99837	−0.167877
$320$	−2.36138	−0.132005
$321$	3.62438	0.202293
$322$	1.42602	0.0794689
$323$	−14.9366	−0.831092
$324$	5.60075	0.311153
$325$	9.31885	0.516917
$326$	−11.9444	−0.661538
$327$	−21.0990	−1.16678
$328$	−19.2995	−1.06564
$329$	−21.1578	−1.16647
$330$	0.782747	0.0430888
$331$	−27.7681	−1.52627	−0.763137	−	0.646236i	$-0.776342\pi$
$331$	−27.7681	−1.52627	−0.763137	+	0.646236i	$0.776342\pi$
$332$	1.09114	0.0598839
$333$	−10.3087	−0.564913
$334$	6.90238	0.377681
$335$	−9.05932	−0.494963
$336$	−2.21048	−0.120592
$337$	−21.9254	−1.19435	−0.597177	−	0.802109i	$-0.703711\pi$
$337$	−21.9254	−1.19435	−0.597177	+	0.802109i	$0.703711\pi$
$338$	−6.74128	−0.366678
$339$	−2.40190	−0.130453
$340$	−4.26982	−0.231564
$341$	5.41725	0.293361
$342$	−3.34383	−0.180814
$343$	19.9298	1.07611
$344$	27.6117	1.48872
$345$	0.776241	0.0417914
$346$	−5.64745	−0.303609
$347$	15.0235	0.806503	0.403251	−	0.915089i	$-0.367880\pi$
$347$	15.0235	0.806503	0.403251	+	0.915089i	$0.367880\pi$
$348$	−5.60293	−0.300349
$349$	8.84347	0.473380	0.236690	−	0.971585i	$-0.423937\pi$
$349$	8.84347	0.473380	0.236690	+	0.971585i	$0.423937\pi$
$350$	8.17287	0.436858
$351$	11.8097	0.630356
$352$	−5.85013	−0.311813
$353$	−15.4240	−0.820939	−0.410469	−	0.911874i	$-0.634635\pi$
$353$	−15.4240	−0.820939	−0.410469	+	0.911874i	$0.634635\pi$
$354$	−7.69893	−0.409194
$355$	10.5502	0.559945
$356$	5.73163	0.303776
$357$	13.1057	0.693625
$358$	−1.18256	−0.0625001
$359$	15.0616	0.794921	0.397461	−	0.917619i	$-0.369892\pi$
$359$	15.0616	0.794921	0.397461	+	0.917619i	$0.369892\pi$
$360$	−2.33392	−0.123008
$361$	−6.01888	−0.316783
$362$	−17.8203	−0.936616
$363$	1.34697	0.0706975
$364$	−6.82019	−0.357475
$365$	−8.67184	−0.453905
$366$	−1.05434	−0.0551110
$367$	−10.4821	−0.547160	−0.273580	−	0.961849i	$-0.588208\pi$
$367$	−10.4821	−0.547160	−0.273580	+	0.961849i	$0.588208\pi$
$368$	−0.542774	−0.0282940
$369$	−8.63053	−0.449288
$370$	−5.05244	−0.262664
$371$	20.9038	1.08527
$372$	10.1230	0.524853
$373$	−34.6725	−1.79527	−0.897637	−	0.440735i	$-0.854718\pi$
$373$	−34.6725	−1.79527	−0.897637	+	0.440735i	$0.854718\pi$
$374$	3.24501	0.167795
$375$	9.44883	0.487935
$376$	−23.9023	−1.23267
$377$	−6.28061	−0.323468
$378$	10.3574	0.532728
$379$	−8.67507	−0.445609	−0.222804	−	0.974863i	$-0.571521\pi$
$379$	−8.67507	−0.445609	−0.222804	+	0.974863i	$0.571521\pi$
$380$	3.71083	0.190362
$381$	−3.12175	−0.159932
$382$	14.3139	0.732362
$383$	−22.9990	−1.17519	−0.587596	−	0.809154i	$-0.699926\pi$
$383$	−22.9990	−1.17519	−0.587596	+	0.809154i	$0.699926\pi$
$384$	−12.4064	−0.633109
$385$	−1.74241	−0.0888013
$386$	−12.4676	−0.634584
$387$	12.3476	0.627666
$388$	14.2845	0.725185
$389$	−4.71837	−0.239231	−0.119615	−	0.992820i	$-0.538166\pi$
$389$	−4.71837	−0.239231	−0.119615	+	0.992820i	$0.538166\pi$
$390$	1.63960	0.0830244
$391$	3.21804	0.162743
$392$	3.95521	0.199768
$393$	−0.828031	−0.0417686
$394$	19.6153	0.988203
$395$	−6.00376	−0.302082
$396$	−1.64490	−0.0826593
$397$	−15.8309	−0.794532	−0.397266	−	0.917704i	$-0.630041\pi$
$397$	−15.8309	−0.794532	−0.397266	+	0.917704i	$0.630041\pi$
$398$	−11.0704	−0.554907
$399$	−11.3899	−0.570209
$400$	−3.11077	−0.155539
$401$	−4.05194	−0.202344	−0.101172	−	0.994869i	$-0.532259\pi$
$401$	−4.05194	−0.202344	−0.101172	+	0.994869i	$0.532259\pi$
$402$	12.8656	0.641680
$403$	11.3474	0.565253
$404$	5.63101	0.280153
$405$	2.99720	0.148932
$406$	−5.50826	−0.273370
$407$	−8.69435	−0.430963
$408$	14.8057	0.732989
$409$	−23.6231	−1.16809	−0.584044	−	0.811722i	$-0.698530\pi$
$409$	−23.6231	−1.16809	−0.584044	+	0.811722i	$0.698530\pi$
$410$	−4.22995	−0.208902
$411$	22.6882	1.11912
$412$	7.85739	0.387106
$413$	17.1379	0.843303
$414$	0.720418	0.0354066
$415$	0.583915	0.0286633
$416$	−12.2541	−0.600808
$417$	−13.6924	−0.670518
$418$	−2.82019	−0.137940
$419$	11.2846	0.551289	0.275644	−	0.961260i	$-0.411109\pi$
$419$	11.2846	0.551289	0.275644	+	0.961260i	$0.411109\pi$
$420$	−3.25596	−0.158875
$421$	−6.66693	−0.324926	−0.162463	−	0.986715i	$-0.551944\pi$
$421$	−6.66693	−0.324926	−0.162463	+	0.986715i	$0.551944\pi$
$422$	0.894479	0.0435425
$423$	−10.6888	−0.519709
$424$	23.6153	1.14686
$425$	18.4434	0.894635
$426$	−14.9829	−0.725923
$427$	2.34697	0.113578
$428$	−3.73293	−0.180438
$429$	2.82146	0.136221
$430$	6.05176	0.291842
$431$	36.0050	1.73430	0.867149	−	0.498049i	$-0.165950\pi$
$431$	36.0050	1.73430	0.867149	+	0.498049i	$0.165950\pi$
$432$	−3.94226	−0.189672
$433$	28.1159	1.35116	0.675581	−	0.737286i	$-0.263893\pi$
$433$	28.1159	1.35116	0.675581	+	0.737286i	$0.263893\pi$
$434$	9.95194	0.477709
$435$	−2.99837	−0.143761
$436$	21.7309	1.04072
$437$	−2.79674	−0.133786
$438$	12.3154	0.588451
$439$	15.1618	0.723631	0.361816	−	0.932250i	$-0.382157\pi$
$439$	15.1618	0.723631	0.361816	+	0.932250i	$0.382157\pi$
$440$	−1.96842	−0.0938410
$441$	1.76872	0.0842250
$442$	6.79724	0.323312
$443$	5.44752	0.258820	0.129410	−	0.991591i	$-0.458692\pi$
$443$	5.44752	0.258820	0.129410	+	0.991591i	$0.458692\pi$
$444$	−16.2468	−0.771038
$445$	3.06725	0.145401
$446$	16.5643	0.784344
$447$	−12.2996	−0.581752
$448$	−7.46502	−0.352689
$449$	−38.0951	−1.79782	−0.898910	−	0.438133i	$-0.855640\pi$
$449$	−38.0951	−1.79782	−0.898910	+	0.438133i	$0.855640\pi$
$450$	4.12890	0.194638
$451$	−7.27899	−0.342754
$452$	2.47383	0.116359
$453$	26.8425	1.26117
$454$	−12.9135	−0.606059
$455$	−3.64978	−0.171104
$456$	−12.8674	−0.602569
$457$	−27.3024	−1.27715	−0.638576	−	0.769559i	$-0.720476\pi$
$457$	−27.3024	−1.27715	−0.638576	+	0.769559i	$0.720476\pi$
$458$	−6.77718	−0.316677
$459$	23.3732	1.09097
$460$	−0.799488	−0.0372763
$461$	−20.5148	−0.955470	−0.477735	−	0.878504i	$-0.658542\pi$
$461$	−20.5148	−0.955470	−0.477735	+	0.878504i	$0.658542\pi$
$462$	2.47449	0.115124
$463$	−27.1915	−1.26370	−0.631848	−	0.775092i	$-0.717703\pi$
$463$	−27.1915	−1.26370	−0.631848	+	0.775092i	$0.717703\pi$
$464$	2.09656	0.0973305
$465$	5.41725	0.251219
$466$	5.18949	0.240398
$467$	27.6045	1.27739	0.638693	−	0.769462i	$-0.279476\pi$
$467$	27.6045	1.27739	0.638693	+	0.769462i	$0.279476\pi$
$468$	−3.44553	−0.159270
$469$	−28.6391	−1.32243
$470$	−5.23875	−0.241646
$471$	6.59487	0.303876
$472$	19.3610	0.891162
$473$	10.4140	0.478836
$474$	8.52627	0.391625
$475$	−16.0288	−0.735453
$476$	−13.4981	−0.618686
$477$	10.5605	0.483532
$478$	−15.3636	−0.702716
$479$	30.7998	1.40728	0.703638	−	0.710558i	$-0.251557\pi$
$479$	30.7998	1.40728	0.703638	+	0.710558i	$0.251557\pi$
$480$	−5.85013	−0.267021
$481$	−18.2118	−0.830388
$482$	−1.69756	−0.0773217
$483$	2.45392	0.111657
$484$	−1.38731	−0.0630594
$485$	7.64426	0.347108
$486$	8.98283	0.407469
$487$	33.2214	1.50541	0.752703	−	0.658360i	$-0.228750\pi$
$487$	33.2214	1.50541	0.752703	+	0.658360i	$0.228750\pi$
$488$	2.65140	0.120023
$489$	−20.5541	−0.929490
$490$	0.866878	0.0391616
$491$	21.6482	0.976969	0.488485	−	0.872572i	$-0.337550\pi$
$491$	21.6482	0.976969	0.488485	+	0.872572i	$0.337550\pi$
$492$	−13.6019	−0.613223
$493$	−12.4303	−0.559830
$494$	−5.90737	−0.265785
$495$	−0.880257	−0.0395646
$496$	−3.78793	−0.170083
$497$	33.3522	1.49605
$498$	−0.829250	−0.0371596
$499$	8.29598	0.371379	0.185690	−	0.982608i	$-0.440548\pi$
$499$	8.29598	0.371379	0.185690	+	0.982608i	$0.440548\pi$
$500$	−9.73180	−0.435219
$501$	11.8778	0.530659
$502$	3.60055	0.160700
$503$	22.0223	0.981926	0.490963	−	0.871180i	$-0.336645\pi$
$503$	22.0223	0.981926	0.490963	+	0.871180i	$0.336645\pi$
$504$	−7.37819	−0.328651
$505$	3.01340	0.134094
$506$	0.607600	0.0270111
$507$	−11.6005	−0.515198
$508$	3.21524	0.142653
$509$	29.7192	1.31728	0.658640	−	0.752458i	$-0.271132\pi$
$509$	29.7192	1.31728	0.658640	+	0.752458i	$0.271132\pi$
$510$	3.24501	0.143691
$511$	−27.4142	−1.21273
$512$	7.79852	0.344649
$513$	−20.3132	−0.896851
$514$	−22.4135	−0.988618
$515$	4.20483	0.185287
$516$	19.4602	0.856688
$517$	−9.01495	−0.396477
$518$	−15.9722	−0.701780
$519$	−9.71826	−0.426584
$520$	−4.12321	−0.180815
$521$	−5.09711	−0.223308	−0.111654	−	0.993747i	$-0.535615\pi$
$521$	−5.09711	−0.223308	−0.111654	+	0.993747i	$0.535615\pi$
$522$	−2.78275	−0.121798
$523$	29.5947	1.29408	0.647042	−	0.762454i	$-0.276006\pi$
$523$	29.5947	1.29408	0.647042	+	0.762454i	$0.276006\pi$
$524$	0.852829	0.0372560
$525$	14.0640	0.613805
$526$	19.7972	0.863200
$527$	22.4581	0.978292
$528$	−0.941846	−0.0409886
$529$	−22.3975	−0.973802
$530$	5.17586	0.224825
$531$	8.65801	0.375726
$532$	11.7310	0.508604
$533$	−15.2471	−0.660426
$534$	−4.35597	−0.188501
$535$	−1.99765	−0.0863660
$536$	−32.3541	−1.39748
$537$	−2.03497	−0.0878154
$538$	21.1652	0.912497
$539$	1.49174	0.0642539
$540$	−5.80682	−0.249886
$541$	−14.3729	−0.617939	−0.308969	−	0.951072i	$-0.599984\pi$
$541$	−14.3729	−0.617939	−0.308969	+	0.951072i	$0.599984\pi$
$542$	11.6065	0.498544
$543$	−30.6656	−1.31599
$544$	−24.2527	−1.03983
$545$	11.6292	0.498138
$546$	5.18325	0.221823
$547$	8.45243	0.361400	0.180700	−	0.983538i	$-0.442164\pi$
$547$	8.45243	0.361400	0.180700	+	0.983538i	$0.442164\pi$
$548$	−23.3676	−0.998215
$549$	1.18568	0.0506035
$550$	3.48231	0.148486
$551$	10.8029	0.460220
$552$	2.77223	0.117994
$553$	−18.9796	−0.807096
$554$	12.7754	0.542775
$555$	−8.69435	−0.369055
$556$	14.1024	0.598076
$557$	21.8207	0.924572	0.462286	−	0.886731i	$-0.347029\pi$
$557$	21.8207	0.924572	0.462286	+	0.886731i	$0.347029\pi$
$558$	5.02768	0.212839
$559$	21.8139	0.922631
$560$	1.21835	0.0514847
$561$	5.58408	0.235760
$562$	4.03361	0.170148
$563$	6.93536	0.292291	0.146145	−	0.989263i	$-0.453313\pi$
$563$	6.93536	0.292291	0.146145	+	0.989263i	$0.453313\pi$
$564$	−16.8459	−0.709339
$565$	1.32385	0.0556950
$566$	−10.8789	−0.457275
$567$	9.47503	0.397914
$568$	37.6784	1.58095
$569$	−13.8735	−0.581608	−0.290804	−	0.956783i	$-0.593923\pi$
$569$	−13.8735	−0.581608	−0.290804	+	0.956783i	$0.593923\pi$
$570$	−2.82019	−0.118125
$571$	0.346433	0.0144978	0.00724888	−	0.999974i	$-0.497693\pi$
$571$	0.346433	0.0144978	0.00724888	+	0.999974i	$0.497693\pi$
$572$	−2.90596	−0.121504
$573$	24.6316	1.02900
$574$	−13.3721	−0.558141
$575$	3.45336	0.144015
$576$	−3.77129	−0.157137
$577$	16.0839	0.669583	0.334791	−	0.942292i	$-0.391334\pi$
$577$	16.0839	0.669583	0.334791	+	0.942292i	$0.391334\pi$
$578$	0.146023	0.00607377
$579$	−21.4545	−0.891619
$580$	3.08817	0.128229
$581$	1.84593	0.0765819
$582$	−10.8560	−0.449997
$583$	8.90673	0.368879
$584$	−30.9702	−1.28156
$585$	−1.84385	−0.0762339
$586$	16.2827	0.672633
$587$	5.60753	0.231448	0.115724	−	0.993281i	$-0.463081\pi$
$587$	5.60753	0.231448	0.115724	+	0.993281i	$0.463081\pi$
$588$	2.78755	0.114957
$589$	−19.5180	−0.804225
$590$	4.24342	0.174699
$591$	33.7544	1.38847
$592$	6.07939	0.249861
$593$	1.21408	0.0498565	0.0249282	−	0.999689i	$-0.492064\pi$
$593$	1.21408	0.0498565	0.0249282	+	0.999689i	$0.492064\pi$
$594$	4.41311	0.181072
$595$	−7.22344	−0.296132
$596$	12.6680	0.518900
$597$	−19.0501	−0.779668
$598$	1.27272	0.0520456
$599$	26.6122	1.08735	0.543673	−	0.839297i	$-0.317033\pi$
$599$	26.6122	1.08735	0.543673	+	0.839297i	$0.317033\pi$
$600$	15.8884	0.648640
$601$	30.0085	1.22407	0.612036	−	0.790830i	$-0.290351\pi$
$601$	30.0085	1.22407	0.612036	+	0.790830i	$0.290351\pi$
$602$	19.1314	0.779737
$603$	−14.4684	−0.589197
$604$	−27.6463	−1.12491
$605$	−0.742408	−0.0301832
$606$	−4.27949	−0.173843
$607$	−13.2646	−0.538395	−0.269197	−	0.963085i	$-0.586758\pi$
$607$	−13.2646	−0.538395	−0.269197	+	0.963085i	$0.586758\pi$
$608$	21.0776	0.854811
$609$	−9.47873	−0.384097
$610$	0.581118	0.0235288
$611$	−18.8834	−0.763940
$612$	−6.81920	−0.275650
$613$	18.3360	0.740585	0.370292	−	0.928915i	$-0.379257\pi$
$613$	18.3360	0.740585	0.370292	+	0.928915i	$0.379257\pi$
$614$	−19.3452	−0.780707
$615$	−7.27899	−0.293517
$616$	−6.22276	−0.250722
$617$	−18.8802	−0.760089	−0.380045	−	0.924968i	$-0.624091\pi$
$617$	−18.8802	−0.760089	−0.380045	+	0.924968i	$0.624091\pi$
$618$	−5.97152	−0.240210
$619$	12.8874	0.517987	0.258993	−	0.965879i	$-0.416609\pi$
$619$	12.8874	0.517987	0.258993	+	0.965879i	$0.416609\pi$
$620$	−5.57949	−0.224078
$621$	4.37643	0.175620
$622$	−25.4526	−1.02056
$623$	9.69646	0.388480
$624$	−1.97286	−0.0789776
$625$	17.0362	0.681450
$626$	−19.4176	−0.776082
$627$	−4.85303	−0.193812
$628$	−6.79237	−0.271045
$629$	−36.0439	−1.43716
$630$	−1.61710	−0.0644270
$631$	−27.7977	−1.10661	−0.553304	−	0.832980i	$-0.686633\pi$
$631$	−27.7977	−1.10661	−0.553304	+	0.832980i	$0.686633\pi$
$632$	−21.4416	−0.852900
$633$	1.53924	0.0611792
$634$	−9.34688	−0.371212
$635$	1.72061	0.0682805
$636$	16.6436	0.659963
$637$	3.12471	0.123806
$638$	−2.34697	−0.0929173
$639$	16.8494	0.666550
$640$	6.83801	0.270296
$641$	17.3218	0.684172	0.342086	−	0.939669i	$-0.388867\pi$
$641$	17.3218	0.684172	0.342086	+	0.939669i	$0.388867\pi$
$642$	2.83698	0.111967
$643$	31.5859	1.24563	0.622813	−	0.782371i	$-0.285990\pi$
$643$	31.5859	1.24563	0.622813	+	0.782371i	$0.285990\pi$
$644$	−2.52741	−0.0995940
$645$	10.4140	0.410051
$646$	−11.6915	−0.459998
$647$	24.2187	0.952137	0.476069	−	0.879408i	$-0.342061\pi$
$647$	24.2187	0.952137	0.476069	+	0.879408i	$0.342061\pi$
$648$	10.7041	0.420496
$649$	7.30217	0.286635
$650$	7.29430	0.286106
$651$	17.1255	0.671202
$652$	21.1697	0.829069
$653$	−18.8038	−0.735849	−0.367924	−	0.929856i	$-0.619931\pi$
$653$	−18.8038	−0.735849	−0.367924	+	0.929856i	$0.619931\pi$
$654$	−16.5152	−0.645796
$655$	0.456386	0.0178325
$656$	5.08971	0.198720
$657$	−13.8495	−0.540321
$658$	−16.5612	−0.645623
$659$	11.7243	0.456715	0.228358	−	0.973577i	$-0.426664\pi$
$659$	11.7243	0.456715	0.228358	+	0.973577i	$0.426664\pi$
$660$	−1.38731	−0.0540008
$661$	16.5459	0.643560	0.321780	−	0.946815i	$-0.395719\pi$
$661$	16.5459	0.643560	0.321780	+	0.946815i	$0.395719\pi$
$662$	−21.7354	−0.844771
$663$	11.6968	0.454267
$664$	2.08537	0.0809280
$665$	6.27778	0.243442
$666$	−8.06910	−0.312671
$667$	−2.32746	−0.0901196
$668$	−12.2335	−0.473327
$669$	28.5043	1.10204
$670$	−7.09116	−0.273955
$671$	1.00000	0.0386046
$672$	−18.4940	−0.713420
$673$	49.7277	1.91686	0.958431	−	0.285326i	$-0.0921019\pi$
$673$	49.7277	1.91686	0.958431	+	0.285326i	$0.0921019\pi$
$674$	−17.1621	−0.661058
$675$	25.0824	0.965421
$676$	11.9480	0.459537
$677$	27.4558	1.05521	0.527606	−	0.849489i	$-0.323090\pi$
$677$	27.4558	1.05521	0.527606	+	0.849489i	$0.323090\pi$
$678$	−1.88008	−0.0722040
$679$	24.1657	0.927395
$680$	−8.16043	−0.312938
$681$	−22.2218	−0.851540
$682$	4.24034	0.162371
$683$	−23.2171	−0.888379	−0.444189	−	0.895933i	$-0.646508\pi$
$683$	−23.2171	−0.888379	−0.444189	+	0.895933i	$0.646508\pi$
$684$	5.92646	0.226604
$685$	−12.5050	−0.477793
$686$	15.6000	0.595612
$687$	−11.6623	−0.444945
$688$	−7.28182	−0.277617
$689$	18.6567	0.710763
$690$	0.607600	0.0231310
$691$	−1.30752	−0.0497405	−0.0248702	−	0.999691i	$-0.507917\pi$
$691$	−1.30752	−0.0497405	−0.0248702	+	0.999691i	$0.507917\pi$
$692$	10.0093	0.380496
$693$	−2.78275	−0.105708
$694$	11.7596	0.446388
$695$	7.54682	0.286267
$696$	−10.7083	−0.405896
$697$	−30.1763	−1.14301
$698$	6.92220	0.262009
$699$	8.93018	0.337771
$700$	−14.4852	−0.547490
$701$	24.2219	0.914848	0.457424	−	0.889249i	$-0.348772\pi$
$701$	24.2219	0.914848	0.457424	+	0.889249i	$0.348772\pi$
$702$	9.24402	0.348893
$703$	31.3252	1.18145
$704$	−3.18071	−0.119877
$705$	−9.01495	−0.339523
$706$	−12.0731	−0.454378
$707$	9.52623	0.358271
$708$	13.6452	0.512820
$709$	−6.36928	−0.239203	−0.119602	−	0.992822i	$-0.538162\pi$
$709$	−6.36928	−0.239203	−0.119602	+	0.992822i	$0.538162\pi$
$710$	8.25812	0.309922
$711$	−9.58842	−0.359594
$712$	10.9542	0.410527
$713$	4.20509	0.157482
$714$	10.2584	0.383912
$715$	−1.55510	−0.0581576
$716$	2.09591	0.0783279
$717$	−26.4381	−0.987347
$718$	11.7894	0.439978
$719$	40.1944	1.49900	0.749499	−	0.662006i	$-0.230295\pi$
$719$	40.1944	1.49900	0.749499	+	0.662006i	$0.230295\pi$
$720$	0.615505	0.0229385
$721$	13.2927	0.495046
$722$	−4.71126	−0.175335
$723$	−2.92120	−0.108640
$724$	31.5840	1.17381
$725$	−13.3393	−0.495407
$726$	1.05434	0.0391301
$727$	28.5809	1.06001	0.530003	−	0.847996i	$-0.322191\pi$
$727$	28.5809	1.06001	0.530003	+	0.847996i	$0.322191\pi$
$728$	−13.0347	−0.483097
$729$	27.5692	1.02108
$730$	−6.78786	−0.251230
$731$	43.1730	1.59681
$732$	1.86866	0.0690676
$733$	−23.6903	−0.875023	−0.437511	−	0.899213i	$-0.644140\pi$
$733$	−23.6903	−0.875023	−0.437511	+	0.899213i	$0.644140\pi$
$734$	−8.20481	−0.302845
$735$	1.49174	0.0550237
$736$	−4.54111	−0.167388
$737$	−12.2026	−0.449489
$738$	−6.75552	−0.248674
$739$	−26.2807	−0.966751	−0.483375	−	0.875413i	$-0.660589\pi$
$739$	−26.2807	−0.966751	−0.483375	+	0.875413i	$0.660589\pi$
$740$	8.95473	0.329182
$741$	−10.1655	−0.373440
$742$	16.3624	0.600682
$743$	−44.7849	−1.64300	−0.821500	−	0.570209i	$-0.806862\pi$
$743$	−44.7849	−1.64300	−0.821500	+	0.570209i	$0.806862\pi$
$744$	19.3470	0.709294
$745$	6.77918	0.248370
$746$	−27.1398	−0.993659
$747$	0.932553	0.0341203
$748$	−5.75131	−0.210289
$749$	−6.31516	−0.230751
$750$	7.39605	0.270065
$751$	8.52302	0.311009	0.155505	−	0.987835i	$-0.450300\pi$
$751$	8.52302	0.311009	0.155505	+	0.987835i	$0.450300\pi$
$752$	6.30356	0.229867
$753$	6.19590	0.225791
$754$	−4.91613	−0.179035
$755$	−14.7948	−0.538437
$756$	−18.3570	−0.667639
$757$	−21.1129	−0.767362	−0.383681	−	0.923466i	$-0.625344\pi$
$757$	−21.1129	−0.767362	−0.383681	+	0.923466i	$0.625344\pi$
$758$	−6.79039	−0.246638
$759$	1.04557	0.0379518
$760$	7.09210	0.257258
$761$	45.7062	1.65685	0.828424	−	0.560101i	$-0.189238\pi$
$761$	45.7062	1.65685	0.828424	+	0.560101i	$0.189238\pi$
$762$	−2.44354	−0.0885201
$763$	36.7631	1.33092
$764$	−25.3693	−0.917829
$765$	−3.64925	−0.131939
$766$	−18.0024	−0.650453
$767$	15.2957	0.552294
$768$	−18.2797	−0.659610
$769$	−25.3430	−0.913892	−0.456946	−	0.889494i	$-0.651057\pi$
$769$	−25.3430	−0.913892	−0.456946	+	0.889494i	$0.651057\pi$
$770$	−1.36387	−0.0491503
$771$	−38.5697	−1.38905
$772$	22.0970	0.795290
$773$	−22.8642	−0.822367	−0.411183	−	0.911553i	$-0.634884\pi$
$773$	−22.8642	−0.822367	−0.411183	+	0.911553i	$0.634884\pi$
$774$	9.66509	0.347404
$775$	24.1004	0.865714
$776$	27.3004	0.980026
$777$	−27.4854	−0.986032
$778$	−3.69329	−0.132411
$779$	26.2257	0.939633
$780$	−2.90596	−0.104050
$781$	14.2107	0.508500
$782$	2.51891	0.0900760
$783$	−16.9047	−0.604126
$784$	−1.04308	−0.0372527
$785$	−3.63489	−0.129735
$786$	−0.648139	−0.0231183
$787$	15.6127	0.556531	0.278266	−	0.960504i	$-0.410240\pi$
$787$	15.6127	0.556531	0.278266	+	0.960504i	$0.410240\pi$
$788$	−34.7652	−1.23846
$789$	34.0675	1.21283
$790$	−4.69942	−0.167198
$791$	4.18509	0.148805
$792$	−3.14371	−0.111707
$793$	2.09467	0.0743841
$794$	−12.3916	−0.439762
$795$	8.90673	0.315889
$796$	19.6206	0.695434
$797$	−4.30125	−0.152358	−0.0761790	−	0.997094i	$-0.524272\pi$
$797$	−4.30125	−0.152358	−0.0761790	+	0.997094i	$0.524272\pi$
$798$	−8.91542	−0.315603
$799$	−37.3730	−1.32216
$800$	−26.0262	−0.920167
$801$	4.89861	0.173084
$802$	−3.17164	−0.111995
$803$	−11.6807	−0.412202
$804$	−22.8025	−0.804182
$805$	−1.35253	−0.0476704
$806$	8.88213	0.312860
$807$	36.4215	1.28210
$808$	10.7619	0.378603
$809$	−23.8068	−0.837003	−0.418502	−	0.908216i	$-0.637445\pi$
$809$	−23.8068	−0.837003	−0.418502	+	0.908216i	$0.637445\pi$
$810$	2.34605	0.0824319
$811$	−21.2381	−0.745769	−0.372885	−	0.927878i	$-0.621631\pi$
$811$	−21.2381	−0.745769	−0.372885	+	0.927878i	$0.621631\pi$
$812$	9.76260	0.342600
$813$	19.9728	0.700476
$814$	−6.80548	−0.238532
$815$	11.3288	0.396831
$816$	−3.90458	−0.136688
$817$	−37.5209	−1.31269
$818$	−18.4909	−0.646520
$819$	−5.82895	−0.203680
$820$	7.49698	0.261806
$821$	−12.0309	−0.419882	−0.209941	−	0.977714i	$-0.567327\pi$
$821$	−12.0309	−0.419882	−0.209941	+	0.977714i	$0.567327\pi$
$822$	17.7591	0.619420
$823$	45.3529	1.58090	0.790452	−	0.612525i	$-0.209846\pi$
$823$	45.3529	1.58090	0.790452	+	0.612525i	$0.209846\pi$
$824$	15.0170	0.523141
$825$	5.99243	0.208630
$826$	13.4147	0.466756
$827$	12.2112	0.424627	0.212313	−	0.977202i	$-0.431900\pi$
$827$	12.2112	0.424627	0.212313	+	0.977202i	$0.431900\pi$
$828$	−1.27684	−0.0443732
$829$	−2.05546	−0.0713892	−0.0356946	−	0.999363i	$-0.511364\pi$
$829$	−2.05546	−0.0713892	−0.0356946	+	0.999363i	$0.511364\pi$
$830$	0.457058	0.0158647
$831$	21.9842	0.762623
$832$	−6.66255	−0.230982
$833$	6.18426	0.214272
$834$	−10.7177	−0.371122
$835$	−6.54666	−0.226557
$836$	4.99837	0.172872
$837$	30.5423	1.05570
$838$	8.83299	0.305130
$839$	−21.5294	−0.743278	−0.371639	−	0.928377i	$-0.621204\pi$
$839$	−21.5294	−0.743278	−0.371639	+	0.928377i	$0.621204\pi$
$840$	−6.22276	−0.214706
$841$	−20.0098	−0.689992
$842$	−5.21852	−0.179842
$843$	6.94112	0.239065
$844$	−1.58534	−0.0545695
$845$	6.39387	0.219956
$846$	−8.36665	−0.287651
$847$	−2.34697	−0.0806428
$848$	−6.22789	−0.213866
$849$	−18.7207	−0.642492
$850$	14.4365	0.495168
$851$	−6.74891	−0.231350
$852$	26.5550	0.909760
$853$	14.9370	0.511432	0.255716	−	0.966752i	$-0.417689\pi$
$853$	14.9370	0.511432	0.255716	+	0.966752i	$0.417689\pi$
$854$	1.83708	0.0628637
$855$	3.17151	0.108463
$856$	−7.13433	−0.243846
$857$	38.4497	1.31342	0.656708	−	0.754145i	$-0.271948\pi$
$857$	38.4497	1.31342	0.656708	+	0.754145i	$0.271948\pi$
$858$	2.20849	0.0753966
$859$	−8.13613	−0.277601	−0.138801	−	0.990320i	$-0.544325\pi$
$859$	−8.13613	−0.277601	−0.138801	+	0.990320i	$0.544325\pi$
$860$	−10.7259	−0.365749
$861$	−23.0110	−0.784212
$862$	28.1828	0.959910
$863$	−15.3403	−0.522191	−0.261096	−	0.965313i	$-0.584084\pi$
$863$	−15.3403	−0.522191	−0.261096	+	0.965313i	$0.584084\pi$
$864$	−32.9829	−1.12210
$865$	5.35641	0.182123
$866$	22.0076	0.747849
$867$	0.251280	0.00853392
$868$	−17.6384	−0.598686
$869$	−8.08687	−0.274328
$870$	−2.34697	−0.0795697
$871$	−25.5605	−0.866084
$872$	41.5319	1.40645
$873$	12.2084	0.413192
$874$	−2.18914	−0.0740489
$875$	−16.4637	−0.556575
$876$	−21.8272	−0.737473
$877$	13.3372	0.450366	0.225183	−	0.974316i	$-0.427702\pi$
$877$	13.3372	0.450366	0.225183	+	0.974316i	$0.427702\pi$
$878$	11.8678	0.400520
$879$	28.0196	0.945079
$880$	0.519117	0.0174994
$881$	−16.8053	−0.566186	−0.283093	−	0.959092i	$-0.591361\pi$
$881$	−16.8053	−0.566186	−0.283093	+	0.959092i	$0.591361\pi$
$882$	1.38446	0.0466173
$883$	−9.84775	−0.331403	−0.165702	−	0.986176i	$-0.552989\pi$
$883$	−9.84775	−0.331403	−0.165702	+	0.986176i	$0.552989\pi$
$884$	−12.0471	−0.405189
$885$	7.30217	0.245460
$886$	4.26403	0.143253
$887$	−1.36447	−0.0458145	−0.0229072	−	0.999738i	$-0.507292\pi$
$887$	−1.36447	−0.0458145	−0.0229072	+	0.999738i	$0.507292\pi$
$888$	−31.0506	−1.04199
$889$	5.43936	0.182430
$890$	2.40088	0.0804776
$891$	4.03714	0.135249
$892$	−29.3579	−0.982976
$893$	32.4803	1.08691
$894$	−9.62749	−0.321992
$895$	1.12161	0.0374914
$896$	21.6169	0.722171
$897$	2.19013	0.0731264
$898$	−29.8189	−0.995068
$899$	−16.2429	−0.541733
$900$	−7.31787	−0.243929
$901$	36.9243	1.23013
$902$	−5.69761	−0.189710
$903$	32.9217	1.09556
$904$	4.72796	0.157249
$905$	16.9020	0.561840
$906$	21.0109	0.698039
$907$	−8.95204	−0.297248	−0.148624	−	0.988894i	$-0.547484\pi$
$907$	−8.95204	−0.297248	−0.148624	+	0.988894i	$0.547484\pi$
$908$	22.8873	0.759541
$909$	4.81261	0.159624
$910$	−2.85685	−0.0947038
$911$	−15.5635	−0.515641	−0.257820	−	0.966193i	$-0.583004\pi$
$911$	−15.5635	−0.515641	−0.257820	+	0.966193i	$0.583004\pi$
$912$	3.39341	0.112367
$913$	0.786515	0.0260298
$914$	−21.3709	−0.706885
$915$	1.00000	0.0330590
$916$	12.0116	0.396874
$917$	1.44277	0.0476444
$918$	18.2953	0.603834
$919$	−8.14172	−0.268571	−0.134285	−	0.990943i	$-0.542874\pi$
$919$	−8.14172	−0.268571	−0.134285	+	0.990943i	$0.542874\pi$
$920$	−1.52797	−0.0503757
$921$	−33.2895	−1.09693
$922$	−16.0579	−0.528839
$923$	29.7669	0.979789
$924$	−4.38568	−0.144278
$925$	−38.6797	−1.27178
$926$	−21.2841	−0.699438
$927$	6.71541	0.220563
$928$	17.5409	0.575808
$929$	32.0097	1.05020	0.525102	−	0.851039i	$-0.324027\pi$
$929$	32.0097	1.05020	0.525102	+	0.851039i	$0.324027\pi$
$930$	4.24034	0.139046
$931$	−5.37465	−0.176147
$932$	−9.19762	−0.301278
$933$	−43.7994	−1.43393
$934$	21.6074	0.707015
$935$	−3.07778	−0.100654
$936$	−6.58505	−0.215239
$937$	−24.4613	−0.799114	−0.399557	−	0.916708i	$-0.630836\pi$
$937$	−24.4613	−0.799114	−0.399557	+	0.916708i	$0.630836\pi$
$938$	−22.4172	−0.731948
$939$	−33.4142	−1.09043
$940$	9.28493	0.302841
$941$	−34.8804	−1.13707	−0.568534	−	0.822660i	$-0.692489\pi$
$941$	−34.8804	−1.13707	−0.568534	+	0.822660i	$0.692489\pi$
$942$	5.16212	0.168191
$943$	−5.65025	−0.183997
$944$	−5.10592	−0.166184
$945$	−9.82365	−0.319563
$946$	8.15153	0.265029
$947$	−11.9348	−0.387830	−0.193915	−	0.981018i	$-0.562119\pi$
$947$	−11.9348	−0.387830	−0.193915	+	0.981018i	$0.562119\pi$
$948$	−15.1116	−0.490802
$949$	−24.4672	−0.794240
$950$	−12.5465	−0.407063
$951$	−16.0843	−0.521569
$952$	−25.7975	−0.836102
$953$	−16.3997	−0.531238	−0.265619	−	0.964078i	$-0.585576\pi$
$953$	−16.3997	−0.531238	−0.265619	+	0.964078i	$0.585576\pi$
$954$	8.26621	0.267628
$955$	−13.5762	−0.439316
$956$	27.2298	0.880676
$957$	−4.03871	−0.130553
$958$	24.1084	0.778908
$959$	−39.5320	−1.27656
$960$	−3.18071	−0.102657
$961$	−1.65335	−0.0533339
$962$	−14.2553	−0.459608
$963$	−3.19039	−0.102809
$964$	3.00868	0.0969030
$965$	11.8251	0.380663
$966$	1.92080	0.0618008
$967$	52.4183	1.68566	0.842830	−	0.538180i	$-0.180888\pi$
$967$	52.4183	1.68566	0.842830	+	0.538180i	$0.180888\pi$
$968$	−2.65140	−0.0852194
$969$	−20.1191	−0.646317
$970$	5.98352	0.192119
$971$	−39.7148	−1.27451	−0.637254	−	0.770654i	$-0.719930\pi$
$971$	−39.7148	−1.27451	−0.637254	+	0.770654i	$0.719930\pi$
$972$	−15.9208	−0.510659
$973$	23.8577	0.764842
$974$	26.0040	0.833221
$975$	12.5522	0.401992
$976$	−0.699234	−0.0223819
$977$	−1.51718	−0.0485390	−0.0242695	−	0.999705i	$-0.507726\pi$
$977$	−1.51718	−0.0485390	−0.0242695	+	0.999705i	$0.507726\pi$
$978$	−16.0887	−0.514460
$979$	4.13148	0.132043
$980$	−1.53642	−0.0490790
$981$	18.5726	0.592977
$982$	16.9451	0.540739
$983$	−22.4709	−0.716709	−0.358355	−	0.933586i	$-0.616662\pi$
$983$	−22.4709	−0.716709	−0.358355	+	0.933586i	$0.616662\pi$
$984$	−25.9959	−0.828718
$985$	−18.6044	−0.592785
$986$	−9.72975	−0.309858
$987$	−28.4989	−0.907130
$988$	10.4700	0.333094
$989$	8.08377	0.257049
$990$	−0.689019	−0.0218984
$991$	45.2946	1.43883	0.719415	−	0.694581i	$-0.244410\pi$
$991$	45.2946	1.43883	0.719415	+	0.694581i	$0.244410\pi$
$992$	−31.6917	−1.00621
$993$	−37.4028	−1.18694
$994$	26.1063	0.828042
$995$	10.4998	0.332867
$996$	1.46973	0.0465701
$997$	−1.80367	−0.0571228	−0.0285614	−	0.999592i	$-0.509093\pi$
$997$	−1.80367	−0.0571228	−0.0285614	+	0.999592i	$0.509093\pi$
$998$	6.49366	0.205553
$999$	−49.0185	−1.55088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.b.1.4	✓	6
3.2	odd	2		6039.2.a.b.1.3		6
11.10	odd	2		7381.2.a.h.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.b.1.4	✓	6	1.1	even	1	trivial
6039.2.a.b.1.3		6	3.2	odd	2
7381.2.a.h.1.3		6	11.10	odd	2

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q+0.782747 q^{2} +1.34697 q^{3} -1.38731 q^{4} -0.742408 q^{5} +1.05434 q^{6} -2.34697 q^{7} -2.65140 q^{8} -1.18568 q^{9} +O(q^{10})\)	\(q+0.782747 q^{2} +1.34697 q^{3} -1.38731 q^{4} -0.742408 q^{5} +1.05434 q^{6} -2.34697 q^{7} -2.65140 q^{8} -1.18568 q^{9} -0.581118 q^{10} -1.00000 q^{11} -1.86866 q^{12} -2.09467 q^{13} -1.83708 q^{14} -1.00000 q^{15} +0.699234 q^{16} -4.14567 q^{17} -0.928086 q^{18} +3.60293 q^{19} +1.02995 q^{20} -3.16129 q^{21} -0.782747 q^{22} -0.776241 q^{23} -3.57136 q^{24} -4.44883 q^{25} -1.63960 q^{26} -5.63797 q^{27} +3.25596 q^{28} +2.99837 q^{29} -0.782747 q^{30} -5.41725 q^{31} +5.85013 q^{32} -1.34697 q^{33} -3.24501 q^{34} +1.74241 q^{35} +1.64490 q^{36} +8.69435 q^{37} +2.82019 q^{38} -2.82146 q^{39} +1.96842 q^{40} +7.27899 q^{41} -2.47449 q^{42} -10.4140 q^{43} +1.38731 q^{44} +0.880257 q^{45} -0.607600 q^{46} +9.01495 q^{47} +0.941846 q^{48} -1.49174 q^{49} -3.48231 q^{50} -5.58408 q^{51} +2.90596 q^{52} -8.90673 q^{53} -4.41311 q^{54} +0.742408 q^{55} +6.22276 q^{56} +4.85303 q^{57} +2.34697 q^{58} -7.30217 q^{59} +1.38731 q^{60} -1.00000 q^{61} -4.24034 q^{62} +2.78275 q^{63} +3.18071 q^{64} +1.55510 q^{65} -1.05434 q^{66} +12.2026 q^{67} +5.75131 q^{68} -1.04557 q^{69} +1.36387 q^{70} -14.2107 q^{71} +3.14371 q^{72} +11.6807 q^{73} +6.80548 q^{74} -5.99243 q^{75} -4.99837 q^{76} +2.34697 q^{77} -2.20849 q^{78} +8.08687 q^{79} -0.519117 q^{80} -4.03714 q^{81} +5.69761 q^{82} -0.786515 q^{83} +4.38568 q^{84} +3.07778 q^{85} -8.15153 q^{86} +4.03871 q^{87} +2.65140 q^{88} -4.13148 q^{89} +0.689019 q^{90} +4.91613 q^{91} +1.07688 q^{92} -7.29687 q^{93} +7.05643 q^{94} -2.67485 q^{95} +7.87994 q^{96} -10.2966 q^{97} -1.16766 q^{98} +1.18568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

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