LMFDB - Embedded newform 4334.2.a.a.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, 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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-1.70683$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.70683 q^{3} +1.00000 q^{4} +1.14577 q^{5} -1.70683 q^{6} -1.19968 q^{7} -1.00000 q^{8} -0.0867259 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.70683 q^{3} +1.00000 q^{4} +1.14577 q^{5} -1.70683 q^{6} -1.19968 q^{7} -1.00000 q^{8} -0.0867259 q^{9} -1.14577 q^{10} +1.00000 q^{11} +1.70683 q^{12} +1.87419 q^{13} +1.19968 q^{14} +1.95564 q^{15} +1.00000 q^{16} -5.53362 q^{17} +0.0867259 q^{18} +1.61590 q^{19} +1.14577 q^{20} -2.04765 q^{21} -1.00000 q^{22} -5.50920 q^{23} -1.70683 q^{24} -3.68720 q^{25} -1.87419 q^{26} -5.26852 q^{27} -1.19968 q^{28} +8.88499 q^{29} -1.95564 q^{30} -7.44726 q^{31} -1.00000 q^{32} +1.70683 q^{33} +5.53362 q^{34} -1.37456 q^{35} -0.0867259 q^{36} +3.02478 q^{37} -1.61590 q^{38} +3.19893 q^{39} -1.14577 q^{40} -5.93132 q^{41} +2.04765 q^{42} -4.16246 q^{43} +1.00000 q^{44} -0.0993682 q^{45} +5.50920 q^{46} -6.81072 q^{47} +1.70683 q^{48} -5.56078 q^{49} +3.68720 q^{50} -9.44495 q^{51} +1.87419 q^{52} -6.71218 q^{53} +5.26852 q^{54} +1.14577 q^{55} +1.19968 q^{56} +2.75806 q^{57} -8.88499 q^{58} +8.03264 q^{59} +1.95564 q^{60} -8.11062 q^{61} +7.44726 q^{62} +0.104043 q^{63} +1.00000 q^{64} +2.14740 q^{65} -1.70683 q^{66} +8.40718 q^{67} -5.53362 q^{68} -9.40328 q^{69} +1.37456 q^{70} +1.08059 q^{71} +0.0867259 q^{72} -6.81363 q^{73} -3.02478 q^{74} -6.29344 q^{75} +1.61590 q^{76} -1.19968 q^{77} -3.19893 q^{78} -5.42875 q^{79} +1.14577 q^{80} -8.73230 q^{81} +5.93132 q^{82} +17.4686 q^{83} -2.04765 q^{84} -6.34027 q^{85} +4.16246 q^{86} +15.1652 q^{87} -1.00000 q^{88} -1.98437 q^{89} +0.0993682 q^{90} -2.24842 q^{91} -5.50920 q^{92} -12.7112 q^{93} +6.81072 q^{94} +1.85145 q^{95} -1.70683 q^{96} +16.3133 q^{97} +5.56078 q^{98} -0.0867259 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.70683	0.985440	0.492720	−	0.870188i	$-0.336003\pi$
$3$	1.70683	0.985440	0.492720	+	0.870188i	$0.336003\pi$
$4$	1.00000	0.500000
$5$	1.14577	0.512405	0.256203	−	0.966623i	$-0.417529\pi$
$5$	1.14577	0.512405	0.256203	+	0.966623i	$0.417529\pi$
$6$	−1.70683	−0.696811
$7$	−1.19968	−0.453435	−0.226718	−	0.973961i	$-0.572799\pi$
$7$	−1.19968	−0.453435	−0.226718	+	0.973961i	$0.572799\pi$
$8$	−1.00000	−0.353553
$9$	−0.0867259	−0.0289086
$10$	−1.14577	−0.362325
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.70683	0.492720
$13$	1.87419	0.519807	0.259903	−	0.965635i	$-0.416309\pi$
$13$	1.87419	0.519807	0.259903	+	0.965635i	$0.416309\pi$
$14$	1.19968	0.320627
$15$	1.95564	0.504944
$16$	1.00000	0.250000
$17$	−5.53362	−1.34210	−0.671049	−	0.741413i	$-0.734156\pi$
$17$	−5.53362	−1.34210	−0.671049	+	0.741413i	$0.734156\pi$
$18$	0.0867259	0.0204415
$19$	1.61590	0.370712	0.185356	−	0.982671i	$-0.440656\pi$
$19$	1.61590	0.370712	0.185356	+	0.982671i	$0.440656\pi$
$20$	1.14577	0.256203
$21$	−2.04765	−0.446833
$22$	−1.00000	−0.213201
$23$	−5.50920	−1.14875	−0.574374	−	0.818593i	$-0.694755\pi$
$23$	−5.50920	−1.14875	−0.574374	+	0.818593i	$0.694755\pi$
$24$	−1.70683	−0.348406
$25$	−3.68720	−0.737441
$26$	−1.87419	−0.367559
$27$	−5.26852	−1.01393
$28$	−1.19968	−0.226718
$29$	8.88499	1.64990	0.824951	−	0.565205i	$-0.191203\pi$
$29$	8.88499	1.64990	0.824951	+	0.565205i	$0.191203\pi$
$30$	−1.95564	−0.357050
$31$	−7.44726	−1.33757	−0.668783	−	0.743457i	$-0.733185\pi$
$31$	−7.44726	−1.33757	−0.668783	+	0.743457i	$0.733185\pi$
$32$	−1.00000	−0.176777
$33$	1.70683	0.297121
$34$	5.53362	0.949007
$35$	−1.37456	−0.232343
$36$	−0.0867259	−0.0144543
$37$	3.02478	0.497271	0.248635	−	0.968597i	$-0.420018\pi$
$37$	3.02478	0.497271	0.248635	+	0.968597i	$0.420018\pi$
$38$	−1.61590	−0.262133
$39$	3.19893	0.512238
$40$	−1.14577	−0.181163
$41$	−5.93132	−0.926317	−0.463158	−	0.886276i	$-0.653284\pi$
$41$	−5.93132	−0.926317	−0.463158	+	0.886276i	$0.653284\pi$
$42$	2.04765	0.315959
$43$	−4.16246	−0.634769	−0.317385	−	0.948297i	$-0.602805\pi$
$43$	−4.16246	−0.634769	−0.317385	+	0.948297i	$0.602805\pi$
$44$	1.00000	0.150756
$45$	−0.0993682	−0.0148129
$46$	5.50920	0.812288
$47$	−6.81072	−0.993446	−0.496723	−	0.867909i	$-0.665463\pi$
$47$	−6.81072	−0.993446	−0.496723	+	0.867909i	$0.665463\pi$
$48$	1.70683	0.246360
$49$	−5.56078	−0.794396
$50$	3.68720	0.521449
$51$	−9.44495	−1.32256
$52$	1.87419	0.259903
$53$	−6.71218	−0.921989	−0.460994	−	0.887403i	$-0.652507\pi$
$53$	−6.71218	−0.921989	−0.460994	+	0.887403i	$0.652507\pi$
$54$	5.26852	0.716955
$55$	1.14577	0.154496
$56$	1.19968	0.160314
$57$	2.75806	0.365314
$58$	−8.88499	−1.16666
$59$	8.03264	1.04576	0.522881	−	0.852406i	$-0.324857\pi$
$59$	8.03264	1.04576	0.522881	+	0.852406i	$0.324857\pi$
$60$	1.95564	0.252472
$61$	−8.11062	−1.03846	−0.519229	−	0.854635i	$-0.673781\pi$
$61$	−8.11062	−1.03846	−0.519229	+	0.854635i	$0.673781\pi$
$62$	7.44726	0.945802
$63$	0.104043	0.0131082
$64$	1.00000	0.125000
$65$	2.14740	0.266352
$66$	−1.70683	−0.210096
$67$	8.40718	1.02710	0.513550	−	0.858059i	$-0.328330\pi$
$67$	8.40718	1.02710	0.513550	+	0.858059i	$0.328330\pi$
$68$	−5.53362	−0.671049
$69$	−9.40328	−1.13202
$70$	1.37456	0.164291
$71$	1.08059	0.128242	0.0641210	−	0.997942i	$-0.479576\pi$
$71$	1.08059	0.128242	0.0641210	+	0.997942i	$0.479576\pi$
$72$	0.0867259	0.0102207
$73$	−6.81363	−0.797475	−0.398738	−	0.917065i	$-0.630552\pi$
$73$	−6.81363	−0.797475	−0.398738	+	0.917065i	$0.630552\pi$
$74$	−3.02478	−0.351623
$75$	−6.29344	−0.726703
$76$	1.61590	0.185356
$77$	−1.19968	−0.136716
$78$	−3.19893	−0.362207
$79$	−5.42875	−0.610782	−0.305391	−	0.952227i	$-0.598787\pi$
$79$	−5.42875	−0.610782	−0.305391	+	0.952227i	$0.598787\pi$
$80$	1.14577	0.128101
$81$	−8.73230	−0.970256
$82$	5.93132	0.655005
$83$	17.4686	1.91743	0.958715	−	0.284369i	$-0.0917840\pi$
$83$	17.4686	1.91743	0.958715	+	0.284369i	$0.0917840\pi$
$84$	−2.04765	−0.223417
$85$	−6.34027	−0.687699
$86$	4.16246	0.448850
$87$	15.1652	1.62588
$88$	−1.00000	−0.106600
$89$	−1.98437	−0.210343	−0.105171	−	0.994454i	$-0.533539\pi$
$89$	−1.98437	−0.210343	−0.105171	+	0.994454i	$0.533539\pi$
$90$	0.0993682	0.0104743
$91$	−2.24842	−0.235699
$92$	−5.50920	−0.574374
$93$	−12.7112	−1.31809
$94$	6.81072	0.702472
$95$	1.85145	0.189955
$96$	−1.70683	−0.174203
$97$	16.3133	1.65636	0.828181	−	0.560461i	$-0.189376\pi$
$97$	16.3133	1.65636	0.828181	+	0.560461i	$0.189376\pi$
$98$	5.56078	0.561723
$99$	−0.0867259	−0.00871628
$100$	−3.68720	−0.368720
$101$	10.2901	1.02391	0.511954	−	0.859013i	$-0.328922\pi$
$101$	10.2901	1.02391	0.511954	+	0.859013i	$0.328922\pi$
$102$	9.44495	0.935189
$103$	−8.16069	−0.804097	−0.402048	−	0.915618i	$-0.631702\pi$
$103$	−8.16069	−0.804097	−0.402048	+	0.915618i	$0.631702\pi$
$104$	−1.87419	−0.183779
$105$	−2.34614	−0.228960
$106$	6.71218	0.651945
$107$	6.49869	0.628252	0.314126	−	0.949381i	$-0.398288\pi$
$107$	6.49869	0.628252	0.314126	+	0.949381i	$0.398288\pi$
$108$	−5.26852	−0.506964
$109$	−10.7274	−1.02750	−0.513748	−	0.857941i	$-0.671743\pi$
$109$	−10.7274	−1.02750	−0.513748	+	0.857941i	$0.671743\pi$
$110$	−1.14577	−0.109245
$111$	5.16279	0.490030
$112$	−1.19968	−0.113359
$113$	−13.9026	−1.30785	−0.653924	−	0.756561i	$-0.726878\pi$
$113$	−13.9026	−1.30785	−0.653924	+	0.756561i	$0.726878\pi$
$114$	−2.75806	−0.258316
$115$	−6.31230	−0.588625
$116$	8.88499	0.824951
$117$	−0.162541	−0.0150269
$118$	−8.03264	−0.739465
$119$	6.63855	0.608555
$120$	−1.95564	−0.178525
$121$	1.00000	0.0909091
$122$	8.11062	0.734301
$123$	−10.1238	−0.912829
$124$	−7.44726	−0.668783
$125$	−9.95356	−0.890274
$126$	−0.104043	−0.00926889
$127$	13.7068	1.21628	0.608141	−	0.793829i	$-0.291915\pi$
$127$	13.7068	1.21628	0.608141	+	0.793829i	$0.291915\pi$
$128$	−1.00000	−0.0883883
$129$	−7.10462	−0.625527
$130$	−2.14740	−0.188339
$131$	−18.6812	−1.63218	−0.816091	−	0.577923i	$-0.803863\pi$
$131$	−18.6812	−1.63218	−0.816091	+	0.577923i	$0.803863\pi$
$132$	1.70683	0.148561
$133$	−1.93855	−0.168094
$134$	−8.40718	−0.726270
$135$	−6.03653	−0.519542
$136$	5.53362	0.474504
$137$	7.98434	0.682148	0.341074	−	0.940036i	$-0.389209\pi$
$137$	7.98434	0.682148	0.341074	+	0.940036i	$0.389209\pi$
$138$	9.40328	0.800461
$139$	−18.3920	−1.55999	−0.779993	−	0.625789i	$-0.784777\pi$
$139$	−18.3920	−1.55999	−0.779993	+	0.625789i	$0.784777\pi$
$140$	−1.37456	−0.116171
$141$	−11.6248	−0.978981
$142$	−1.08059	−0.0906808
$143$	1.87419	0.156728
$144$	−0.0867259	−0.00722716
$145$	10.1802	0.845418
$146$	6.81363	0.563900
$147$	−9.49131	−0.782830
$148$	3.02478	0.248635
$149$	−8.92237	−0.730949	−0.365474	−	0.930821i	$-0.619093\pi$
$149$	−8.92237	−0.730949	−0.365474	+	0.930821i	$0.619093\pi$
$150$	6.29344	0.513857
$151$	1.46432	0.119165	0.0595825	−	0.998223i	$-0.481023\pi$
$151$	1.46432	0.119165	0.0595825	+	0.998223i	$0.481023\pi$
$152$	−1.61590	−0.131066
$153$	0.479908	0.0387982
$154$	1.19968	0.0966727
$155$	−8.53286	−0.685376
$156$	3.19893	0.256119
$157$	−13.7949	−1.10095	−0.550477	−	0.834850i	$-0.685554\pi$
$157$	−13.7949	−1.10095	−0.550477	+	0.834850i	$0.685554\pi$
$158$	5.42875	0.431888
$159$	−11.4566	−0.908564
$160$	−1.14577	−0.0905813
$161$	6.60926	0.520883
$162$	8.73230	0.686074
$163$	2.63145	0.206111	0.103056	−	0.994676i	$-0.467138\pi$
$163$	2.63145	0.206111	0.103056	+	0.994676i	$0.467138\pi$
$164$	−5.93132	−0.463158
$165$	1.95564	0.152246
$166$	−17.4686	−1.35583
$167$	−1.78283	−0.137959	−0.0689797	−	0.997618i	$-0.521974\pi$
$167$	−1.78283	−0.137959	−0.0689797	+	0.997618i	$0.521974\pi$
$168$	2.04765	0.157979
$169$	−9.48741	−0.729801
$170$	6.34027	0.486276
$171$	−0.140140	−0.0107168
$172$	−4.16246	−0.317385
$173$	12.1139	0.921003	0.460502	−	0.887659i	$-0.347670\pi$
$173$	12.1139	0.921003	0.460502	+	0.887659i	$0.347670\pi$
$174$	−15.1652	−1.14967
$175$	4.42345	0.334382
$176$	1.00000	0.0753778
$177$	13.7104	1.03053
$178$	1.98437	0.148735
$179$	−11.9199	−0.890933	−0.445467	−	0.895299i	$-0.646962\pi$
$179$	−11.9199	−0.890933	−0.445467	+	0.895299i	$0.646962\pi$
$180$	−0.0993682	−0.00740647
$181$	1.58015	0.117452	0.0587258	−	0.998274i	$-0.481296\pi$
$181$	1.58015	0.117452	0.0587258	+	0.998274i	$0.481296\pi$
$182$	2.24842	0.166664
$183$	−13.8435	−1.02334
$184$	5.50920	0.406144
$185$	3.46571	0.254804
$186$	12.7112	0.932031
$187$	−5.53362	−0.404658
$188$	−6.81072	−0.496723
$189$	6.32052	0.459750
$190$	−1.85145	−0.134318
$191$	−18.8839	−1.36639	−0.683196	−	0.730235i	$-0.739411\pi$
$191$	−18.8839	−1.36639	−0.683196	+	0.730235i	$0.739411\pi$
$192$	1.70683	0.123180
$193$	10.5416	0.758800	0.379400	−	0.925233i	$-0.376130\pi$
$193$	10.5416	0.758800	0.379400	+	0.925233i	$0.376130\pi$
$194$	−16.3133	−1.17122
$195$	3.66524	0.262473
$196$	−5.56078	−0.397198
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	0.0867259	0.00616334
$199$	−6.29150	−0.445992	−0.222996	−	0.974819i	$-0.571584\pi$
$199$	−6.29150	−0.445992	−0.222996	+	0.974819i	$0.571584\pi$
$200$	3.68720	0.260725
$201$	14.3496	1.01215
$202$	−10.2901	−0.724012
$203$	−10.6591	−0.748124
$204$	−9.44495	−0.661279
$205$	−6.79595	−0.474650
$206$	8.16069	0.568582
$207$	0.477791	0.0332087
$208$	1.87419	0.129952
$209$	1.61590	0.111774
$210$	2.34614	0.161899
$211$	1.80977	0.124589	0.0622947	−	0.998058i	$-0.480158\pi$
$211$	1.80977	0.124589	0.0622947	+	0.998058i	$0.480158\pi$
$212$	−6.71218	−0.460994
$213$	1.84438	0.126375
$214$	−6.49869	−0.444242
$215$	−4.76924	−0.325259
$216$	5.26852	0.358477
$217$	8.93430	0.606500
$218$	10.7274	0.726549
$219$	−11.6297	−0.785864
$220$	1.14577	0.0772480
$221$	−10.3710	−0.697632
$222$	−5.16279	−0.346504
$223$	−7.58628	−0.508015	−0.254007	−	0.967202i	$-0.581749\pi$
$223$	−7.58628	−0.508015	−0.254007	+	0.967202i	$0.581749\pi$
$224$	1.19968	0.0801568
$225$	0.319776	0.0213184
$226$	13.9026	0.924788
$227$	12.3775	0.821521	0.410761	−	0.911743i	$-0.365263\pi$
$227$	12.3775	0.821521	0.410761	+	0.911743i	$0.365263\pi$
$228$	2.75806	0.182657
$229$	−4.25397	−0.281110	−0.140555	−	0.990073i	$-0.544889\pi$
$229$	−4.25397	−0.281110	−0.140555	+	0.990073i	$0.544889\pi$
$230$	6.31230	0.416221
$231$	−2.04765	−0.134725
$232$	−8.88499	−0.583328
$233$	−7.59700	−0.497696	−0.248848	−	0.968543i	$-0.580052\pi$
$233$	−7.59700	−0.497696	−0.248848	+	0.968543i	$0.580052\pi$
$234$	0.162541	0.0106256
$235$	−7.80354	−0.509047
$236$	8.03264	0.522881
$237$	−9.26595	−0.601888
$238$	−6.63855	−0.430313
$239$	8.61541	0.557285	0.278642	−	0.960395i	$-0.410116\pi$
$239$	8.61541	0.557285	0.278642	+	0.960395i	$0.410116\pi$
$240$	1.95564	0.126236
$241$	21.9775	1.41569	0.707847	−	0.706366i	$-0.249667\pi$
$241$	21.9775	1.41569	0.707847	+	0.706366i	$0.249667\pi$
$242$	−1.00000	−0.0642824
$243$	0.900997	0.0577990
$244$	−8.11062	−0.519229
$245$	−6.37139	−0.407053
$246$	10.1238	0.645468
$247$	3.02849	0.192698
$248$	7.44726	0.472901
$249$	29.8160	1.88951
$250$	9.95356	0.629519
$251$	8.67911	0.547821	0.273910	−	0.961755i	$-0.411683\pi$
$251$	8.67911	0.547821	0.273910	+	0.961755i	$0.411683\pi$
$252$	0.104043	0.00655410
$253$	−5.50920	−0.346361
$254$	−13.7068	−0.860042
$255$	−10.8218	−0.677685
$256$	1.00000	0.0625000
$257$	15.4743	0.965259	0.482629	−	0.875825i	$-0.339682\pi$
$257$	15.4743	0.965259	0.482629	+	0.875825i	$0.339682\pi$
$258$	7.10462	0.442314
$259$	−3.62876	−0.225480
$260$	2.14740	0.133176
$261$	−0.770559	−0.0476964
$262$	18.6812	1.15413
$263$	30.1966	1.86200	0.931001	−	0.365016i	$-0.118936\pi$
$263$	30.1966	1.86200	0.931001	+	0.365016i	$0.118936\pi$
$264$	−1.70683	−0.105048
$265$	−7.69063	−0.472432
$266$	1.93855	0.118860
$267$	−3.38698	−0.207280
$268$	8.40718	0.513550
$269$	−22.5400	−1.37429	−0.687145	−	0.726520i	$-0.741136\pi$
$269$	−22.5400	−1.37429	−0.687145	+	0.726520i	$0.741136\pi$
$270$	6.03653	0.367371
$271$	23.0806	1.40205	0.701024	−	0.713138i	$-0.252727\pi$
$271$	23.0806	1.40205	0.701024	+	0.713138i	$0.252727\pi$
$272$	−5.53362	−0.335525
$273$	−3.83768	−0.232267
$274$	−7.98434	−0.482352
$275$	−3.68720	−0.222347
$276$	−9.40328	−0.566011
$277$	26.9413	1.61875	0.809373	−	0.587294i	$-0.199807\pi$
$277$	26.9413	1.61875	0.809373	+	0.587294i	$0.199807\pi$
$278$	18.3920	1.10308
$279$	0.645870	0.0386672
$280$	1.37456	0.0821455
$281$	5.19557	0.309942	0.154971	−	0.987919i	$-0.450472\pi$
$281$	5.19557	0.309942	0.154971	+	0.987919i	$0.450472\pi$
$282$	11.6248	0.692244
$283$	−7.02171	−0.417397	−0.208699	−	0.977980i	$-0.566923\pi$
$283$	−7.02171	−0.417397	−0.208699	+	0.977980i	$0.566923\pi$
$284$	1.08059	0.0641210
$285$	3.16011	0.187189
$286$	−1.87419	−0.110823
$287$	7.11567	0.420025
$288$	0.0867259	0.00511037
$289$	13.6209	0.801230
$290$	−10.1802	−0.597801
$291$	27.8440	1.63224
$292$	−6.81363	−0.398738
$293$	20.7718	1.21350	0.606752	−	0.794891i	$-0.292472\pi$
$293$	20.7718	1.21350	0.606752	+	0.794891i	$0.292472\pi$
$294$	9.49131	0.553544
$295$	9.20359	0.535854
$296$	−3.02478	−0.175812
$297$	−5.26852	−0.305711
$298$	8.92237	0.516859
$299$	−10.3253	−0.597127
$300$	−6.29344	−0.363352
$301$	4.99361	0.287827
$302$	−1.46432	−0.0842623
$303$	17.5636	1.00900
$304$	1.61590	0.0926779
$305$	−9.29292	−0.532111
$306$	−0.479908	−0.0274345
$307$	−27.0682	−1.54487	−0.772433	−	0.635097i	$-0.780960\pi$
$307$	−27.0682	−1.54487	−0.772433	+	0.635097i	$0.780960\pi$
$308$	−1.19968	−0.0683579
$309$	−13.9289	−0.792389
$310$	8.53286	0.484634
$311$	−9.87629	−0.560033	−0.280016	−	0.959995i	$-0.590340\pi$
$311$	−9.87629	−0.560033	−0.280016	+	0.959995i	$0.590340\pi$
$312$	−3.19893	−0.181103
$313$	2.58209	0.145949	0.0729743	−	0.997334i	$-0.476751\pi$
$313$	2.58209	0.145949	0.0729743	+	0.997334i	$0.476751\pi$
$314$	13.7949	0.778492
$315$	0.119210	0.00671671
$316$	−5.42875	−0.305391
$317$	−2.07068	−0.116301	−0.0581505	−	0.998308i	$-0.518520\pi$
$317$	−2.07068	−0.116301	−0.0581505	+	0.998308i	$0.518520\pi$
$318$	11.4566	0.642452
$319$	8.88499	0.497464
$320$	1.14577	0.0640507
$321$	11.0922	0.619105
$322$	−6.60926	−0.368320
$323$	−8.94174	−0.497532
$324$	−8.73230	−0.485128
$325$	−6.91052	−0.383327
$326$	−2.63145	−0.145743
$327$	−18.3098	−1.01253
$328$	5.93132	0.327502
$329$	8.17066	0.450463
$330$	−1.95564	−0.107655
$331$	7.21290	0.396457	0.198228	−	0.980156i	$-0.436481\pi$
$331$	7.21290	0.396457	0.198228	+	0.980156i	$0.436481\pi$
$332$	17.4686	0.958715
$333$	−0.262327	−0.0143754
$334$	1.78283	0.0975520
$335$	9.63272	0.526292
$336$	−2.04765	−0.111708
$337$	−24.1101	−1.31336	−0.656682	−	0.754168i	$-0.728040\pi$
$337$	−24.1101	−1.31336	−0.656682	+	0.754168i	$0.728040\pi$
$338$	9.48741	0.516047
$339$	−23.7294	−1.28880
$340$	−6.34027	−0.343849
$341$	−7.44726	−0.403291
$342$	0.140140	0.00757790
$343$	15.0689	0.813643
$344$	4.16246	0.224425
$345$	−10.7740	−0.580054
$346$	−12.1139	−0.651247
$347$	33.6719	1.80760	0.903802	−	0.427951i	$-0.140764\pi$
$347$	33.6719	1.80760	0.903802	+	0.427951i	$0.140764\pi$
$348$	15.1652	0.812939
$349$	−10.9087	−0.583932	−0.291966	−	0.956429i	$-0.594309\pi$
$349$	−10.9087	−0.583932	−0.291966	+	0.956429i	$0.594309\pi$
$350$	−4.42345	−0.236444
$351$	−9.87421	−0.527046
$352$	−1.00000	−0.0533002
$353$	−34.0928	−1.81458	−0.907288	−	0.420510i	$-0.861851\pi$
$353$	−34.0928	−1.81458	−0.907288	+	0.420510i	$0.861851\pi$
$354$	−13.7104	−0.728698
$355$	1.23811	0.0657119
$356$	−1.98437	−0.105171
$357$	11.3309	0.599694
$358$	11.9199	0.629985
$359$	−12.5651	−0.663162	−0.331581	−	0.943427i	$-0.607582\pi$
$359$	−12.5651	−0.663162	−0.331581	+	0.943427i	$0.607582\pi$
$360$	0.0993682	0.00523716
$361$	−16.3889	−0.862573
$362$	−1.58015	−0.0830509
$363$	1.70683	0.0895854
$364$	−2.24842	−0.117849
$365$	−7.80688	−0.408631
$366$	13.8435	0.723609
$367$	−2.14332	−0.111880	−0.0559401	−	0.998434i	$-0.517816\pi$
$367$	−2.14332	−0.111880	−0.0559401	+	0.998434i	$0.517816\pi$
$368$	−5.50920	−0.287187
$369$	0.514399	0.0267785
$370$	−3.46571	−0.180174
$371$	8.05245	0.418062
$372$	−12.7112	−0.659046
$373$	−2.85050	−0.147593	−0.0737965	−	0.997273i	$-0.523512\pi$
$373$	−2.85050	−0.147593	−0.0737965	+	0.997273i	$0.523512\pi$
$374$	5.53362	0.286136
$375$	−16.9891	−0.877311
$376$	6.81072	0.351236
$377$	16.6522	0.857630
$378$	−6.32052	−0.325093
$379$	−29.9256	−1.53717	−0.768586	−	0.639746i	$-0.779039\pi$
$379$	−29.9256	−1.53717	−0.768586	+	0.639746i	$0.779039\pi$
$380$	1.85145	0.0949773
$381$	23.3952	1.19857
$382$	18.8839	0.966185
$383$	−13.3893	−0.684161	−0.342080	−	0.939671i	$-0.611131\pi$
$383$	−13.3893	−0.684161	−0.342080	+	0.939671i	$0.611131\pi$
$384$	−1.70683	−0.0871014
$385$	−1.37456	−0.0700539
$386$	−10.5416	−0.536553
$387$	0.360993	0.0183503
$388$	16.3133	0.828181
$389$	14.9613	0.758570	0.379285	−	0.925280i	$-0.376170\pi$
$389$	14.9613	0.758570	0.379285	+	0.925280i	$0.376170\pi$
$390$	−3.66524	−0.185597
$391$	30.4858	1.54173
$392$	5.56078	0.280862
$393$	−31.8856	−1.60842
$394$	−1.00000	−0.0503793
$395$	−6.22011	−0.312968
$396$	−0.0867259	−0.00435814
$397$	−28.0241	−1.40649	−0.703244	−	0.710949i	$-0.748266\pi$
$397$	−28.0241	−1.40649	−0.703244	+	0.710949i	$0.748266\pi$
$398$	6.29150	0.315364
$399$	−3.30878	−0.165646
$400$	−3.68720	−0.184360
$401$	−0.888495	−0.0443693	−0.0221847	−	0.999754i	$-0.507062\pi$
$401$	−0.888495	−0.0443693	−0.0221847	+	0.999754i	$0.507062\pi$
$402$	−14.3496	−0.715695
$403$	−13.9576	−0.695276
$404$	10.2901	0.511954
$405$	−10.0052	−0.497164
$406$	10.6591	0.529003
$407$	3.02478	0.149933
$408$	9.44495	0.467595
$409$	−8.93554	−0.441834	−0.220917	−	0.975293i	$-0.570905\pi$
$409$	−8.93554	−0.441834	−0.220917	+	0.975293i	$0.570905\pi$
$410$	6.79595	0.335628
$411$	13.6279	0.672216
$412$	−8.16069	−0.402048
$413$	−9.63658	−0.474185
$414$	−0.477791	−0.0234821
$415$	20.0151	0.982501
$416$	−1.87419	−0.0918897
$417$	−31.3920	−1.53727
$418$	−1.61590	−0.0790360
$419$	8.77232	0.428556	0.214278	−	0.976773i	$-0.431260\pi$
$419$	8.77232	0.428556	0.214278	+	0.976773i	$0.431260\pi$
$420$	−2.34614	−0.114480
$421$	−34.4629	−1.67962	−0.839809	−	0.542882i	$-0.817333\pi$
$421$	−34.4629	−1.67962	−0.839809	+	0.542882i	$0.817333\pi$
$422$	−1.80977	−0.0880981
$423$	0.590666	0.0287192
$424$	6.71218	0.325972
$425$	20.4036	0.989719
$426$	−1.84438	−0.0893604
$427$	9.73012	0.470873
$428$	6.49869	0.314126
$429$	3.19893	0.154446
$430$	4.76924	0.229993
$431$	−22.8149	−1.09896	−0.549479	−	0.835508i	$-0.685174\pi$
$431$	−22.8149	−1.09896	−0.549479	+	0.835508i	$0.685174\pi$
$432$	−5.26852	−0.253482
$433$	32.0875	1.54203	0.771014	−	0.636818i	$-0.219750\pi$
$433$	32.0875	1.54203	0.771014	+	0.636818i	$0.219750\pi$
$434$	−8.93430	−0.428860
$435$	17.3759	0.833109
$436$	−10.7274	−0.513748
$437$	−8.90230	−0.425855
$438$	11.6297	0.555690
$439$	−32.1294	−1.53345	−0.766725	−	0.641975i	$-0.778115\pi$
$439$	−32.1294	−1.53345	−0.766725	+	0.641975i	$0.778115\pi$
$440$	−1.14577	−0.0546226
$441$	0.482263	0.0229649
$442$	10.3710	0.493300
$443$	10.6860	0.507705	0.253853	−	0.967243i	$-0.418302\pi$
$443$	10.6860	0.507705	0.253853	+	0.967243i	$0.418302\pi$
$444$	5.16279	0.245015
$445$	−2.27364	−0.107781
$446$	7.58628	0.359221
$447$	−15.2290	−0.720306
$448$	−1.19968	−0.0566794
$449$	18.0967	0.854037	0.427018	−	0.904243i	$-0.359564\pi$
$449$	18.0967	0.854037	0.427018	+	0.904243i	$0.359564\pi$
$450$	−0.319776	−0.0150744
$451$	−5.93132	−0.279295
$452$	−13.9026	−0.653924
$453$	2.49935	0.117430
$454$	−12.3775	−0.580903
$455$	−2.57618	−0.120773
$456$	−2.75806	−0.129158
$457$	−10.3791	−0.485512	−0.242756	−	0.970087i	$-0.578051\pi$
$457$	−10.3791	−0.485512	−0.242756	+	0.970087i	$0.578051\pi$
$458$	4.25397	0.198775
$459$	29.1540	1.36079
$460$	−6.31230	−0.294312
$461$	−13.4670	−0.627222	−0.313611	−	0.949552i	$-0.601539\pi$
$461$	−13.4670	−0.627222	−0.313611	+	0.949552i	$0.601539\pi$
$462$	2.04765	0.0952651
$463$	24.1611	1.12286	0.561430	−	0.827524i	$-0.310251\pi$
$463$	24.1611	1.12286	0.561430	+	0.827524i	$0.310251\pi$
$464$	8.88499	0.412475
$465$	−14.5642	−0.675397
$466$	7.59700	0.351924
$467$	−30.2544	−1.40000	−0.700002	−	0.714141i	$-0.746818\pi$
$467$	−30.2544	−1.40000	−0.700002	+	0.714141i	$0.746818\pi$
$468$	−0.162541	−0.00751345
$469$	−10.0859	−0.465724
$470$	7.80354	0.359950
$471$	−23.5456	−1.08492
$472$	−8.03264	−0.369732
$473$	−4.16246	−0.191390
$474$	9.26595	0.425599
$475$	−5.95814	−0.273378
$476$	6.63855	0.304277
$477$	0.582120	0.0266534
$478$	−8.61541	−0.394060
$479$	15.8719	0.725204	0.362602	−	0.931944i	$-0.381888\pi$
$479$	15.8719	0.725204	0.362602	+	0.931944i	$0.381888\pi$
$480$	−1.95564	−0.0892624
$481$	5.66901	0.258485
$482$	−21.9775	−1.00105
$483$	11.2809	0.513299
$484$	1.00000	0.0454545
$485$	18.6913	0.848728
$486$	−0.900997	−0.0408700
$487$	5.36705	0.243204	0.121602	−	0.992579i	$-0.461197\pi$
$487$	5.36705	0.243204	0.121602	+	0.992579i	$0.461197\pi$
$488$	8.11062	0.367150
$489$	4.49144	0.203110
$490$	6.37139	0.287830
$491$	38.8560	1.75355	0.876774	−	0.480902i	$-0.159691\pi$
$491$	38.8560	1.75355	0.876774	+	0.480902i	$0.159691\pi$
$492$	−10.1238	−0.456415
$493$	−49.1661	−2.21433
$494$	−3.02849	−0.136258
$495$	−0.0993682	−0.00446627
$496$	−7.44726	−0.334392
$497$	−1.29635	−0.0581494
$498$	−29.8160	−1.33609
$499$	3.60886	0.161555	0.0807773	−	0.996732i	$-0.474260\pi$
$499$	3.60886	0.161555	0.0807773	+	0.996732i	$0.474260\pi$
$500$	−9.95356	−0.445137
$501$	−3.04299	−0.135951
$502$	−8.67911	−0.387368
$503$	5.81700	0.259367	0.129684	−	0.991555i	$-0.458604\pi$
$503$	5.81700	0.259367	0.129684	+	0.991555i	$0.458604\pi$
$504$	−0.104043	−0.00463445
$505$	11.7902	0.524656
$506$	5.50920	0.244914
$507$	−16.1934	−0.719175
$508$	13.7068	0.608141
$509$	−27.6151	−1.22402	−0.612009	−	0.790851i	$-0.709638\pi$
$509$	−27.6151	−1.22402	−0.612009	+	0.790851i	$0.709638\pi$
$510$	10.8218	0.479196
$511$	8.17416	0.361603
$512$	−1.00000	−0.0441942
$513$	−8.51338	−0.375875
$514$	−15.4743	−0.682541
$515$	−9.35030	−0.412023
$516$	−7.10462	−0.312763
$517$	−6.81072	−0.299535
$518$	3.62876	0.159438
$519$	20.6764	0.907593
$520$	−2.14740	−0.0941695
$521$	−36.4205	−1.59561	−0.797806	−	0.602914i	$-0.794006\pi$
$521$	−36.4205	−1.59561	−0.797806	+	0.602914i	$0.794006\pi$
$522$	0.770559	0.0337264
$523$	−15.1819	−0.663857	−0.331928	−	0.943305i	$-0.607699\pi$
$523$	−15.1819	−0.663857	−0.331928	+	0.943305i	$0.607699\pi$
$524$	−18.6812	−0.816091
$525$	7.55009	0.329513
$526$	−30.1966	−1.31663
$527$	41.2102	1.79515
$528$	1.70683	0.0742803
$529$	7.35133	0.319623
$530$	7.69063	0.334060
$531$	−0.696638	−0.0302315
$532$	−1.93855	−0.0840469
$533$	−11.1164	−0.481506
$534$	3.38698	0.146569
$535$	7.44603	0.321920
$536$	−8.40718	−0.363135
$537$	−20.3452	−0.877961
$538$	22.5400	0.971770
$539$	−5.56078	−0.239520
$540$	−6.03653	−0.259771
$541$	22.5318	0.968719	0.484359	−	0.874869i	$-0.339053\pi$
$541$	22.5318	0.968719	0.484359	+	0.874869i	$0.339053\pi$
$542$	−23.0806	−0.991397
$543$	2.69705	0.115742
$544$	5.53362	0.237252
$545$	−12.2911	−0.526494
$546$	3.83768	0.164237
$547$	−26.8040	−1.14605	−0.573027	−	0.819536i	$-0.694231\pi$
$547$	−26.8040	−1.14605	−0.573027	+	0.819536i	$0.694231\pi$
$548$	7.98434	0.341074
$549$	0.703400	0.0300204
$550$	3.68720	0.157223
$551$	14.3572	0.611638
$552$	9.40328	0.400230
$553$	6.51274	0.276950
$554$	−26.9413	−1.14463
$555$	5.91538	0.251094
$556$	−18.3920	−0.779993
$557$	39.3675	1.66806	0.834028	−	0.551722i	$-0.186029\pi$
$557$	39.3675	1.66806	0.834028	+	0.551722i	$0.186029\pi$
$558$	−0.645870	−0.0273418
$559$	−7.80124	−0.329957
$560$	−1.37456	−0.0580856
$561$	−9.44495	−0.398766
$562$	−5.19557	−0.219162
$563$	−39.1964	−1.65193	−0.825966	−	0.563720i	$-0.809370\pi$
$563$	−39.1964	−1.65193	−0.825966	+	0.563720i	$0.809370\pi$
$564$	−11.6248	−0.489490
$565$	−15.9292	−0.670148
$566$	7.02171	0.295144
$567$	10.4759	0.439948
$568$	−1.08059	−0.0453404
$569$	27.6319	1.15839	0.579195	−	0.815189i	$-0.303367\pi$
$569$	27.6319	1.15839	0.579195	+	0.815189i	$0.303367\pi$
$570$	−3.16011	−0.132363
$571$	19.1761	0.802493	0.401246	−	0.915970i	$-0.368577\pi$
$571$	19.1761	0.802493	0.401246	+	0.915970i	$0.368577\pi$
$572$	1.87419	0.0783638
$573$	−32.2317	−1.34650
$574$	−7.11567	−0.297002
$575$	20.3136	0.847134
$576$	−0.0867259	−0.00361358
$577$	6.82894	0.284292	0.142146	−	0.989846i	$-0.454600\pi$
$577$	6.82894	0.284292	0.142146	+	0.989846i	$0.454600\pi$
$578$	−13.6209	−0.566555
$579$	17.9927	0.747752
$580$	10.1802	0.422709
$581$	−20.9567	−0.869430
$582$	−27.8440	−1.15417
$583$	−6.71218	−0.277990
$584$	6.81363	0.281950
$585$	−0.186235	−0.00769986
$586$	−20.7718	−0.858077
$587$	27.1012	1.11859	0.559293	−	0.828970i	$-0.311073\pi$
$587$	27.1012	1.11859	0.559293	+	0.828970i	$0.311073\pi$
$588$	−9.49131	−0.391415
$589$	−12.0340	−0.495852
$590$	−9.20359	−0.378906
$591$	1.70683	0.0702097
$592$	3.02478	0.124318
$593$	24.8088	1.01878	0.509388	−	0.860537i	$-0.329872\pi$
$593$	24.8088	1.01878	0.509388	+	0.860537i	$0.329872\pi$
$594$	5.26852	0.216170
$595$	7.60627	0.311827
$596$	−8.92237	−0.365474
$597$	−10.7385	−0.439499
$598$	10.3253	0.422233
$599$	21.2393	0.867816	0.433908	−	0.900957i	$-0.357134\pi$
$599$	21.2393	0.867816	0.433908	+	0.900957i	$0.357134\pi$
$600$	6.29344	0.256928
$601$	−14.7481	−0.601586	−0.300793	−	0.953690i	$-0.597251\pi$
$601$	−14.7481	−0.601586	−0.300793	+	0.953690i	$0.597251\pi$
$602$	−4.99361	−0.203524
$603$	−0.729120	−0.0296921
$604$	1.46432	0.0595825
$605$	1.14577	0.0465823
$606$	−17.5636	−0.713470
$607$	−16.6528	−0.675915	−0.337958	−	0.941161i	$-0.609736\pi$
$607$	−16.6528	−0.675915	−0.337958	+	0.941161i	$0.609736\pi$
$608$	−1.61590	−0.0655332
$609$	−18.1933	−0.737231
$610$	9.29292	0.376259
$611$	−12.7646	−0.516400
$612$	0.479908	0.0193991
$613$	13.8192	0.558150	0.279075	−	0.960269i	$-0.409972\pi$
$613$	13.8192	0.558150	0.279075	+	0.960269i	$0.409972\pi$
$614$	27.0682	1.09238
$615$	−11.5995	−0.467739
$616$	1.19968	0.0483364
$617$	−6.89996	−0.277782	−0.138891	−	0.990308i	$-0.544354\pi$
$617$	−6.89996	−0.277782	−0.138891	+	0.990308i	$0.544354\pi$
$618$	13.9289	0.560303
$619$	15.9224	0.639974	0.319987	−	0.947422i	$-0.396321\pi$
$619$	15.9224	0.639974	0.319987	+	0.947422i	$0.396321\pi$
$620$	−8.53286	−0.342688
$621$	29.0254	1.16475
$622$	9.87629	0.396003
$623$	2.38060	0.0953767
$624$	3.19893	0.128060
$625$	7.03150	0.281260
$626$	−2.58209	−0.103201
$627$	2.75806	0.110146
$628$	−13.7949	−0.550477
$629$	−16.7380	−0.667386
$630$	−0.119210	−0.00474943
$631$	6.07520	0.241850	0.120925	−	0.992662i	$-0.461414\pi$
$631$	6.07520	0.241850	0.120925	+	0.992662i	$0.461414\pi$
$632$	5.42875	0.215944
$633$	3.08897	0.122775
$634$	2.07068	0.0822372
$635$	15.7049	0.623230
$636$	−11.4566	−0.454282
$637$	−10.4219	−0.412933
$638$	−8.88499	−0.351760
$639$	−0.0937148	−0.00370730
$640$	−1.14577	−0.0452907
$641$	−34.2875	−1.35427	−0.677137	−	0.735857i	$-0.736779\pi$
$641$	−34.2875	−1.35427	−0.677137	+	0.735857i	$0.736779\pi$
$642$	−11.0922	−0.437773
$643$	29.4437	1.16115	0.580574	−	0.814208i	$-0.302828\pi$
$643$	29.4437	1.16115	0.580574	+	0.814208i	$0.302828\pi$
$644$	6.60926	0.260442
$645$	−8.14028	−0.320523
$646$	8.94174	0.351808
$647$	−1.67685	−0.0659237	−0.0329619	−	0.999457i	$-0.510494\pi$
$647$	−1.67685	−0.0659237	−0.0329619	+	0.999457i	$0.510494\pi$
$648$	8.73230	0.343037
$649$	8.03264	0.315309
$650$	6.91052	0.271053
$651$	15.2493	0.597669
$652$	2.63145	0.103056
$653$	36.8803	1.44324	0.721619	−	0.692291i	$-0.243398\pi$
$653$	36.8803	1.44324	0.721619	+	0.692291i	$0.243398\pi$
$654$	18.3098	0.715970
$655$	−21.4044	−0.836339
$656$	−5.93132	−0.231579
$657$	0.590918	0.0230539
$658$	−8.17066	−0.318526
$659$	−17.0850	−0.665537	−0.332769	−	0.943009i	$-0.607983\pi$
$659$	−17.0850	−0.665537	−0.332769	+	0.943009i	$0.607983\pi$
$660$	1.95564	0.0761232
$661$	2.09579	0.0815169	0.0407584	−	0.999169i	$-0.487023\pi$
$661$	2.09579	0.0815169	0.0407584	+	0.999169i	$0.487023\pi$
$662$	−7.21290	−0.280337
$663$	−17.7016	−0.687474
$664$	−17.4686	−0.677914
$665$	−2.22114	−0.0861321
$666$	0.262327	0.0101650
$667$	−48.9492	−1.89532
$668$	−1.78283	−0.0689797
$669$	−12.9485	−0.500618
$670$	−9.63272	−0.372145
$671$	−8.11062	−0.313107
$672$	2.04765	0.0789897
$673$	−17.6802	−0.681521	−0.340761	−	0.940150i	$-0.610685\pi$
$673$	−17.6802	−0.681521	−0.340761	+	0.940150i	$0.610685\pi$
$674$	24.1101	0.928688
$675$	19.4261	0.747711
$676$	−9.48741	−0.364901
$677$	10.3928	0.399427	0.199713	−	0.979854i	$-0.435999\pi$
$677$	10.3928	0.399427	0.199713	+	0.979854i	$0.435999\pi$
$678$	23.7294	0.911323
$679$	−19.5706	−0.751053
$680$	6.34027	0.243138
$681$	21.1262	0.809559
$682$	7.44726	0.285170
$683$	−6.20800	−0.237542	−0.118771	−	0.992922i	$-0.537896\pi$
$683$	−6.20800	−0.237542	−0.118771	+	0.992922i	$0.537896\pi$
$684$	−0.140140	−0.00535838
$685$	9.14824	0.349536
$686$	−15.0689	−0.575332
$687$	−7.26081	−0.277017
$688$	−4.16246	−0.158692
$689$	−12.5799	−0.479256
$690$	10.7740	0.410160
$691$	−21.1760	−0.805572	−0.402786	−	0.915294i	$-0.631958\pi$
$691$	−21.1760	−0.805572	−0.402786	+	0.915294i	$0.631958\pi$
$692$	12.1139	0.460502
$693$	0.104043	0.00395227
$694$	−33.6719	−1.27817
$695$	−21.0730	−0.799345
$696$	−15.1652	−0.574835
$697$	32.8217	1.24321
$698$	10.9087	0.412902
$699$	−12.9668	−0.490449
$700$	4.42345	0.167191
$701$	−12.9472	−0.489007	−0.244504	−	0.969648i	$-0.578625\pi$
$701$	−12.9472	−0.489007	−0.244504	+	0.969648i	$0.578625\pi$
$702$	9.87421	0.372678
$703$	4.88773	0.184344
$704$	1.00000	0.0376889
$705$	−13.3193	−0.501635
$706$	34.0928	1.28310
$707$	−12.3449	−0.464276
$708$	13.7104	0.515267
$709$	−0.413937	−0.0155457	−0.00777287	−	0.999970i	$-0.502474\pi$
$709$	−0.413937	−0.0155457	−0.00777287	+	0.999970i	$0.502474\pi$
$710$	−1.23811	−0.0464653
$711$	0.470813	0.0176569
$712$	1.98437	0.0743673
$713$	41.0284	1.53653
$714$	−11.3309	−0.424048
$715$	2.14740	0.0803080
$716$	−11.9199	−0.445467
$717$	14.7051	0.549171
$718$	12.5651	0.468927
$719$	28.6745	1.06938	0.534690	−	0.845049i	$-0.320429\pi$
$719$	28.6745	1.06938	0.534690	+	0.845049i	$0.320429\pi$
$720$	−0.0993682	−0.00370323
$721$	9.79019	0.364606
$722$	16.3889	0.609931
$723$	37.5119	1.39508
$724$	1.58015	0.0587258
$725$	−32.7608	−1.21670
$726$	−1.70683	−0.0633465
$727$	−22.1091	−0.819980	−0.409990	−	0.912090i	$-0.634468\pi$
$727$	−22.1091	−0.819980	−0.409990	+	0.912090i	$0.634468\pi$
$728$	2.24842	0.0833321
$729$	27.7348	1.02721
$730$	7.80688	0.288945
$731$	23.0335	0.851923
$732$	−13.8435	−0.511669
$733$	−35.2251	−1.30107	−0.650535	−	0.759476i	$-0.725455\pi$
$733$	−35.2251	−1.30107	−0.650535	+	0.759476i	$0.725455\pi$
$734$	2.14332	0.0791113
$735$	−10.8749	−0.401126
$736$	5.50920	0.203072
$737$	8.40718	0.309683
$738$	−0.514399	−0.0189353
$739$	28.4707	1.04731	0.523655	−	0.851930i	$-0.324568\pi$
$739$	28.4707	1.04731	0.523655	+	0.851930i	$0.324568\pi$
$740$	3.46571	0.127402
$741$	5.16913	0.189893
$742$	−8.05245	−0.295615
$743$	−12.5455	−0.460249	−0.230125	−	0.973161i	$-0.573913\pi$
$743$	−12.5455	−0.460249	−0.230125	+	0.973161i	$0.573913\pi$
$744$	12.7112	0.466016
$745$	−10.2230	−0.374542
$746$	2.85050	0.104364
$747$	−1.51498	−0.0554303
$748$	−5.53362	−0.202329
$749$	−7.79633	−0.284872
$750$	16.9891	0.620353
$751$	−8.96471	−0.327127	−0.163563	−	0.986533i	$-0.552299\pi$
$751$	−8.96471	−0.327127	−0.163563	+	0.986533i	$0.552299\pi$
$752$	−6.81072	−0.248361
$753$	14.8138	0.539844
$754$	−16.6522	−0.606436
$755$	1.67778	0.0610607
$756$	6.32052	0.229875
$757$	19.2191	0.698530	0.349265	−	0.937024i	$-0.386431\pi$
$757$	19.2191	0.698530	0.349265	+	0.937024i	$0.386431\pi$
$758$	29.9256	1.08694
$759$	−9.40328	−0.341318
$760$	−1.85145	−0.0671591
$761$	−35.4948	−1.28669	−0.643343	−	0.765578i	$-0.722453\pi$
$761$	−35.4948	−1.28669	−0.643343	+	0.765578i	$0.722453\pi$
$762$	−23.3952	−0.847519
$763$	12.8694	0.465903
$764$	−18.8839	−0.683196
$765$	0.549865	0.0198804
$766$	13.3893	0.483775
$767$	15.0547	0.543594
$768$	1.70683	0.0615900
$769$	−47.2942	−1.70547	−0.852736	−	0.522343i	$-0.825058\pi$
$769$	−47.2942	−1.70547	−0.852736	+	0.522343i	$0.825058\pi$
$770$	1.37456	0.0495356
$771$	26.4120	0.951204
$772$	10.5416	0.379400
$773$	−0.0165424	−0.000594989 0	−0.000297495	−	1.00000i	$-0.500095\pi$
$773$	−0.0165424	−0.000594989 0	−0.000297495		1.00000i	$0.500095\pi$
$774$	−0.360993	−0.0129756
$775$	27.4596	0.986376
$776$	−16.3133	−0.585612
$777$	−6.19368	−0.222197
$778$	−14.9613	−0.536390
$779$	−9.58439	−0.343397
$780$	3.66524	0.131237
$781$	1.08059	0.0386664
$782$	−30.4858	−1.09017
$783$	−46.8108	−1.67288
$784$	−5.56078	−0.198599
$785$	−15.8058	−0.564134
$786$	31.8856	1.13732
$787$	−6.27120	−0.223544	−0.111772	−	0.993734i	$-0.535653\pi$
$787$	−6.27120	−0.223544	−0.111772	+	0.993734i	$0.535653\pi$
$788$	1.00000	0.0356235
$789$	51.5405	1.83489
$790$	6.22011	0.221302
$791$	16.6786	0.593024
$792$	0.0867259	0.00308167
$793$	−15.2008	−0.539797
$794$	28.0241	0.994537
$795$	−13.1266	−0.465553
$796$	−6.29150	−0.222996
$797$	35.5928	1.26076	0.630381	−	0.776286i	$-0.282899\pi$
$797$	35.5928	1.26076	0.630381	+	0.776286i	$0.282899\pi$
$798$	3.30878	0.117130
$799$	37.6879	1.33330
$800$	3.68720	0.130362
$801$	0.172096	0.00608072
$802$	0.888495	0.0313738
$803$	−6.81363	−0.240448
$804$	14.3496	0.506073
$805$	7.57272	0.266903
$806$	13.9576	0.491634
$807$	−38.4720	−1.35428
$808$	−10.2901	−0.362006
$809$	13.4244	0.471978	0.235989	−	0.971756i	$-0.424167\pi$
$809$	13.4244	0.471978	0.235989	+	0.971756i	$0.424167\pi$
$810$	10.0052	0.351548
$811$	22.7799	0.799911	0.399955	−	0.916535i	$-0.369026\pi$
$811$	22.7799	0.799911	0.399955	+	0.916535i	$0.369026\pi$
$812$	−10.6591	−0.374062
$813$	39.3947	1.38163
$814$	−3.02478	−0.106018
$815$	3.01504	0.105612
$816$	−9.44495	−0.330639
$817$	−6.72610	−0.235316
$818$	8.93554	0.312424
$819$	0.194996	0.00681372
$820$	−6.79595	−0.237325
$821$	21.6675	0.756200	0.378100	−	0.925765i	$-0.376578\pi$
$821$	21.6675	0.756200	0.378100	+	0.925765i	$0.376578\pi$
$822$	−13.6279	−0.475329
$823$	−14.4015	−0.502003	−0.251002	−	0.967987i	$-0.580760\pi$
$823$	−14.4015	−0.502003	−0.251002	+	0.967987i	$0.580760\pi$
$824$	8.16069	0.284291
$825$	−6.29344	−0.219109
$826$	9.63658	0.335299
$827$	−36.1731	−1.25786	−0.628931	−	0.777461i	$-0.716507\pi$
$827$	−36.1731	−1.25786	−0.628931	+	0.777461i	$0.716507\pi$
$828$	0.477791	0.0166044
$829$	8.16328	0.283523	0.141761	−	0.989901i	$-0.454723\pi$
$829$	8.16328	0.283523	0.141761	+	0.989901i	$0.454723\pi$
$830$	−20.0151	−0.694733
$831$	45.9843	1.59518
$832$	1.87419	0.0649758
$833$	30.7712	1.06616
$834$	31.3920	1.08702
$835$	−2.04272	−0.0706911
$836$	1.61590	0.0558869
$837$	39.2360	1.35620
$838$	−8.77232	−0.303035
$839$	20.6387	0.712527	0.356264	−	0.934386i	$-0.384051\pi$
$839$	20.6387	0.712527	0.356264	+	0.934386i	$0.384051\pi$
$840$	2.34614	0.0809494
$841$	49.9431	1.72218
$842$	34.4629	1.18767
$843$	8.86797	0.305429
$844$	1.80977	0.0622947
$845$	−10.8704	−0.373954
$846$	−0.590666	−0.0203075
$847$	−1.19968	−0.0412214
$848$	−6.71218	−0.230497
$849$	−11.9849	−0.411320
$850$	−20.4036	−0.699837
$851$	−16.6641	−0.571239
$852$	1.84438	0.0631874
$853$	3.24788	0.111205	0.0556026	−	0.998453i	$-0.482292\pi$
$853$	3.24788	0.111205	0.0556026	+	0.998453i	$0.482292\pi$
$854$	−9.73012	−0.332958
$855$	−0.160569	−0.00549133
$856$	−6.49869	−0.222121
$857$	−3.52734	−0.120492	−0.0602458	−	0.998184i	$-0.519188\pi$
$857$	−3.52734	−0.120492	−0.0602458	+	0.998184i	$0.519188\pi$
$858$	−3.19893	−0.109210
$859$	5.52256	0.188427	0.0942136	−	0.995552i	$-0.469966\pi$
$859$	5.52256	0.188427	0.0942136	+	0.995552i	$0.469966\pi$
$860$	−4.76924	−0.162630
$861$	12.1452	0.413909
$862$	22.8149	0.777080
$863$	44.6795	1.52091	0.760454	−	0.649392i	$-0.224977\pi$
$863$	44.6795	1.52091	0.760454	+	0.649392i	$0.224977\pi$
$864$	5.26852	0.179239
$865$	13.8798	0.471927
$866$	−32.0875	−1.09038
$867$	23.2486	0.789564
$868$	8.93430	0.303250
$869$	−5.42875	−0.184158
$870$	−17.3759	−0.589097
$871$	15.7567	0.533894
$872$	10.7274	0.363275
$873$	−1.41478	−0.0478831
$874$	8.90230	0.301125
$875$	11.9411	0.403682
$876$	−11.6297	−0.392932
$877$	−11.8032	−0.398566	−0.199283	−	0.979942i	$-0.563861\pi$
$877$	−11.8032	−0.398566	−0.199283	+	0.979942i	$0.563861\pi$
$878$	32.1294	1.08431
$879$	35.4540	1.19584
$880$	1.14577	0.0386240
$881$	−2.57876	−0.0868807	−0.0434403	−	0.999056i	$-0.513832\pi$
$881$	−2.57876	−0.0868807	−0.0434403	+	0.999056i	$0.513832\pi$
$882$	−0.482263	−0.0162386
$883$	−19.5155	−0.656748	−0.328374	−	0.944548i	$-0.606501\pi$
$883$	−19.5155	−0.656748	−0.328374	+	0.944548i	$0.606501\pi$
$884$	−10.3710	−0.348816
$885$	15.7090	0.528051
$886$	−10.6860	−0.359002
$887$	54.2383	1.82114	0.910572	−	0.413350i	$-0.135642\pi$
$887$	54.2383	1.82114	0.910572	+	0.413350i	$0.135642\pi$
$888$	−5.16279	−0.173252
$889$	−16.4437	−0.551505
$890$	2.27364	0.0762124
$891$	−8.73230	−0.292543
$892$	−7.58628	−0.254007
$893$	−11.0054	−0.368282
$894$	15.2290	0.509333
$895$	−13.6575	−0.456519
$896$	1.19968	0.0400784
$897$	−17.6235	−0.588433
$898$	−18.0967	−0.603895
$899$	−66.1688	−2.20685
$900$	0.319776	0.0106592
$901$	37.1426	1.23740
$902$	5.93132	0.197491
$903$	8.52325	0.283636
$904$	13.9026	0.462394
$905$	1.81049	0.0601829
$906$	−2.49935	−0.0830355
$907$	11.8694	0.394118	0.197059	−	0.980392i	$-0.436861\pi$
$907$	11.8694	0.394118	0.197059	+	0.980392i	$0.436861\pi$
$908$	12.3775	0.410761
$909$	−0.892422	−0.0295998
$910$	2.57618	0.0853996
$911$	43.6223	1.44527	0.722636	−	0.691229i	$-0.242930\pi$
$911$	43.6223	1.44527	0.722636	+	0.691229i	$0.242930\pi$
$912$	2.75806	0.0913285
$913$	17.4686	0.578127
$914$	10.3791	0.343309
$915$	−15.8615	−0.524364
$916$	−4.25397	−0.140555
$917$	22.4114	0.740089
$918$	−29.1540	−0.962224
$919$	−13.0653	−0.430985	−0.215492	−	0.976506i	$-0.569136\pi$
$919$	−13.0653	−0.430985	−0.215492	+	0.976506i	$0.569136\pi$
$920$	6.31230	0.208110
$921$	−46.2009	−1.52237
$922$	13.4670	0.443513
$923$	2.02522	0.0666610
$924$	−2.04765	−0.0673626
$925$	−11.1530	−0.366708
$926$	−24.1611	−0.793982
$927$	0.707743	0.0232453
$928$	−8.88499	−0.291664
$929$	14.3779	0.471724	0.235862	−	0.971787i	$-0.424209\pi$
$929$	14.3779	0.471724	0.235862	+	0.971787i	$0.424209\pi$
$930$	14.5642	0.477578
$931$	−8.98563	−0.294492
$932$	−7.59700	−0.248848
$933$	−16.8572	−0.551879
$934$	30.2544	0.989953
$935$	−6.34027	−0.207349
$936$	0.162541	0.00531281
$937$	−56.7189	−1.85292	−0.926462	−	0.376388i	$-0.877166\pi$
$937$	−56.7189	−1.85292	−0.926462	+	0.376388i	$0.877166\pi$
$938$	10.0859	0.329316
$939$	4.40720	0.143824
$940$	−7.80354	−0.254523
$941$	36.4087	1.18689	0.593444	−	0.804875i	$-0.297768\pi$
$941$	36.4087	1.18689	0.593444	+	0.804875i	$0.297768\pi$
$942$	23.5456	0.767157
$943$	32.6769	1.06410
$944$	8.03264	0.261440
$945$	7.24188	0.235579
$946$	4.16246	0.135333
$947$	−10.8371	−0.352159	−0.176079	−	0.984376i	$-0.556342\pi$
$947$	−10.8371	−0.352159	−0.176079	+	0.984376i	$0.556342\pi$
$948$	−9.26595	−0.300944
$949$	−12.7700	−0.414533
$950$	5.95814	0.193307
$951$	−3.53430	−0.114608
$952$	−6.63855	−0.215157
$953$	−25.8897	−0.838651	−0.419325	−	0.907836i	$-0.637733\pi$
$953$	−25.8897	−0.838651	−0.419325	+	0.907836i	$0.637733\pi$
$954$	−0.582120	−0.0188468
$955$	−21.6367	−0.700146
$956$	8.61541	0.278642
$957$	15.1652	0.490221
$958$	−15.8719	−0.512797
$959$	−9.57863	−0.309310
$960$	1.95564	0.0631181
$961$	24.4616	0.789084
$962$	−5.66901	−0.182776
$963$	−0.563605	−0.0181619
$964$	21.9775	0.707847
$965$	12.0783	0.388813
$966$	−11.2809	−0.362957
$967$	−3.72928	−0.119926	−0.0599628	−	0.998201i	$-0.519098\pi$
$967$	−3.72928	−0.119926	−0.0599628	+	0.998201i	$0.519098\pi$
$968$	−1.00000	−0.0321412
$969$	−15.2620	−0.490288
$970$	−18.6913	−0.600141
$971$	2.01530	0.0646740	0.0323370	−	0.999477i	$-0.489705\pi$
$971$	2.01530	0.0646740	0.0323370	+	0.999477i	$0.489705\pi$
$972$	0.900997	0.0288995
$973$	22.0644	0.707352
$974$	−5.36705	−0.171971
$975$	−11.7951	−0.377745
$976$	−8.11062	−0.259614
$977$	−28.2612	−0.904156	−0.452078	−	0.891978i	$-0.649317\pi$
$977$	−28.2612	−0.904156	−0.452078	+	0.891978i	$0.649317\pi$
$978$	−4.49144	−0.143620
$979$	−1.98437	−0.0634207
$980$	−6.37139	−0.203526
$981$	0.930341	0.0297035
$982$	−38.8560	−1.23995
$983$	40.5240	1.29252	0.646258	−	0.763119i	$-0.276333\pi$
$983$	40.5240	1.29252	0.646258	+	0.763119i	$0.276333\pi$
$984$	10.1238	0.322734
$985$	1.14577	0.0365074
$986$	49.1661	1.56577
$987$	13.9459	0.443904
$988$	3.02849	0.0963492
$989$	22.9318	0.729190
$990$	0.0993682	0.00315813
$991$	30.4052	0.965852	0.482926	−	0.875661i	$-0.339574\pi$
$991$	30.4052	0.965852	0.482926	+	0.875661i	$0.339574\pi$
$992$	7.44726	0.236451
$993$	12.3112	0.390684
$994$	1.29635	0.0411179
$995$	−7.20863	−0.228529
$996$	29.8160	0.944756
$997$	−20.2150	−0.640216	−0.320108	−	0.947381i	$-0.603719\pi$
$997$	−20.2150	−0.640216	−0.320108	+	0.947381i	$0.603719\pi$
$998$	−3.60886	−0.114236
$999$	−15.9361	−0.504196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.12	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.12	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.70683 q^{3} +1.00000 q^{4} +1.14577 q^{5} -1.70683 q^{6} -1.19968 q^{7} -1.00000 q^{8} -0.0867259 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.70683 q^{3} +1.00000 q^{4} +1.14577 q^{5} -1.70683 q^{6} -1.19968 q^{7} -1.00000 q^{8} -0.0867259 q^{9} -1.14577 q^{10} +1.00000 q^{11} +1.70683 q^{12} +1.87419 q^{13} +1.19968 q^{14} +1.95564 q^{15} +1.00000 q^{16} -5.53362 q^{17} +0.0867259 q^{18} +1.61590 q^{19} +1.14577 q^{20} -2.04765 q^{21} -1.00000 q^{22} -5.50920 q^{23} -1.70683 q^{24} -3.68720 q^{25} -1.87419 q^{26} -5.26852 q^{27} -1.19968 q^{28} +8.88499 q^{29} -1.95564 q^{30} -7.44726 q^{31} -1.00000 q^{32} +1.70683 q^{33} +5.53362 q^{34} -1.37456 q^{35} -0.0867259 q^{36} +3.02478 q^{37} -1.61590 q^{38} +3.19893 q^{39} -1.14577 q^{40} -5.93132 q^{41} +2.04765 q^{42} -4.16246 q^{43} +1.00000 q^{44} -0.0993682 q^{45} +5.50920 q^{46} -6.81072 q^{47} +1.70683 q^{48} -5.56078 q^{49} +3.68720 q^{50} -9.44495 q^{51} +1.87419 q^{52} -6.71218 q^{53} +5.26852 q^{54} +1.14577 q^{55} +1.19968 q^{56} +2.75806 q^{57} -8.88499 q^{58} +8.03264 q^{59} +1.95564 q^{60} -8.11062 q^{61} +7.44726 q^{62} +0.104043 q^{63} +1.00000 q^{64} +2.14740 q^{65} -1.70683 q^{66} +8.40718 q^{67} -5.53362 q^{68} -9.40328 q^{69} +1.37456 q^{70} +1.08059 q^{71} +0.0867259 q^{72} -6.81363 q^{73} -3.02478 q^{74} -6.29344 q^{75} +1.61590 q^{76} -1.19968 q^{77} -3.19893 q^{78} -5.42875 q^{79} +1.14577 q^{80} -8.73230 q^{81} +5.93132 q^{82} +17.4686 q^{83} -2.04765 q^{84} -6.34027 q^{85} +4.16246 q^{86} +15.1652 q^{87} -1.00000 q^{88} -1.98437 q^{89} +0.0993682 q^{90} -2.24842 q^{91} -5.50920 q^{92} -12.7112 q^{93} +6.81072 q^{94} +1.85145 q^{95} -1.70683 q^{96} +16.3133 q^{97} +5.56078 q^{98} -0.0867259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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