LMFDB - Embedded newform 538.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.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:	$4.29595162874$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 10x^{5} + 7x^{4} + 27x^{3} - 15x^{2} - 20x + 12 $ x^7 - x^6 - 10x^5 + 7x^4 + 27x^3 - 15x^2 - 20*x + 12
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			1.3
Root			$-2.30699$ of defining polynomial
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.20937 q^{3} +1.00000 q^{4} -2.40321 q^{5} +1.20937 q^{6} +1.52017 q^{7} -1.00000 q^{8} -1.53742 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.20937 q^{3} +1.00000 q^{4} -2.40321 q^{5} +1.20937 q^{6} +1.52017 q^{7} -1.00000 q^{8} -1.53742 q^{9} +2.40321 q^{10} +5.07638 q^{11} -1.20937 q^{12} +5.11021 q^{13} -1.52017 q^{14} +2.90637 q^{15} +1.00000 q^{16} -6.65764 q^{17} +1.53742 q^{18} -5.71222 q^{19} -2.40321 q^{20} -1.83846 q^{21} -5.07638 q^{22} -6.36685 q^{23} +1.20937 q^{24} +0.775401 q^{25} -5.11021 q^{26} +5.48743 q^{27} +1.52017 q^{28} -6.00511 q^{29} -2.90637 q^{30} +2.77822 q^{31} -1.00000 q^{32} -6.13924 q^{33} +6.65764 q^{34} -3.65329 q^{35} -1.53742 q^{36} -1.59410 q^{37} +5.71222 q^{38} -6.18015 q^{39} +2.40321 q^{40} +9.69619 q^{41} +1.83846 q^{42} -9.26120 q^{43} +5.07638 q^{44} +3.69473 q^{45} +6.36685 q^{46} -7.55235 q^{47} -1.20937 q^{48} -4.68907 q^{49} -0.775401 q^{50} +8.05157 q^{51} +5.11021 q^{52} -9.42058 q^{53} -5.48743 q^{54} -12.1996 q^{55} -1.52017 q^{56} +6.90820 q^{57} +6.00511 q^{58} -6.31332 q^{59} +2.90637 q^{60} -7.97918 q^{61} -2.77822 q^{62} -2.33714 q^{63} +1.00000 q^{64} -12.2809 q^{65} +6.13924 q^{66} -2.54885 q^{67} -6.65764 q^{68} +7.69990 q^{69} +3.65329 q^{70} +1.98957 q^{71} +1.53742 q^{72} +12.7523 q^{73} +1.59410 q^{74} -0.937750 q^{75} -5.71222 q^{76} +7.71699 q^{77} +6.18015 q^{78} +3.64283 q^{79} -2.40321 q^{80} -2.02411 q^{81} -9.69619 q^{82} -0.689504 q^{83} -1.83846 q^{84} +15.9997 q^{85} +9.26120 q^{86} +7.26242 q^{87} -5.07638 q^{88} +2.78972 q^{89} -3.69473 q^{90} +7.76841 q^{91} -6.36685 q^{92} -3.35991 q^{93} +7.55235 q^{94} +13.7276 q^{95} +1.20937 q^{96} +11.9363 q^{97} +4.68907 q^{98} -7.80451 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 4 q^{3} + 7 q^{4} - 6 q^{5} + 4 q^{6} - 3 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 4 * q^3 + 7 * q^4 - 6 * q^5 + 4 * q^6 - 3 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 4 q^{3} + 7 q^{4} - 6 q^{5} + 4 q^{6} - 3 q^{7} - 7 q^{8} + 7 q^{9} + 6 q^{10} - 12 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} - 6 q^{15} + 7 q^{16} - 8 q^{17} - 7 q^{18} - 7 q^{19} - 6 q^{20} - 5 q^{21} + 12 q^{22} - 22 q^{23} + 4 q^{24} + 9 q^{25} - 3 q^{26} - 22 q^{27} - 3 q^{28} - 7 q^{29} + 6 q^{30} - 3 q^{31} - 7 q^{32} - 19 q^{33} + 8 q^{34} - 25 q^{35} + 7 q^{36} - 13 q^{37} + 7 q^{38} + q^{39} + 6 q^{40} - 11 q^{41} + 5 q^{42} - 14 q^{43} - 12 q^{44} - 17 q^{45} + 22 q^{46} - 23 q^{47} - 4 q^{48} + 6 q^{49} - 9 q^{50} - 21 q^{51} + 3 q^{52} - 21 q^{53} + 22 q^{54} + 15 q^{55} + 3 q^{56} - 14 q^{57} + 7 q^{58} - 20 q^{59} - 6 q^{60} + 13 q^{61} + 3 q^{62} - 12 q^{63} + 7 q^{64} - 29 q^{65} + 19 q^{66} - 30 q^{67} - 8 q^{68} + 13 q^{69} + 25 q^{70} - 23 q^{71} - 7 q^{72} + 9 q^{73} + 13 q^{74} + 3 q^{75} - 7 q^{76} + 8 q^{77} - q^{78} + 11 q^{79} - 6 q^{80} + 43 q^{81} + 11 q^{82} - 3 q^{83} - 5 q^{84} + 21 q^{85} + 14 q^{86} + 28 q^{87} + 12 q^{88} + 16 q^{89} + 17 q^{90} - 10 q^{91} - 22 q^{92} - 13 q^{93} + 23 q^{94} + 4 q^{96} + 21 q^{97} - 6 q^{98} - 9 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 4 * q^3 + 7 * q^4 - 6 * q^5 + 4 * q^6 - 3 * q^7 - 7 * q^8 + 7 * q^9 + 6 * q^10 - 12 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 - 6 * q^15 + 7 * q^16 - 8 * q^17 - 7 * q^18 - 7 * q^19 - 6 * q^20 - 5 * q^21 + 12 * q^22 - 22 * q^23 + 4 * q^24 + 9 * q^25 - 3 * q^26 - 22 * q^27 - 3 * q^28 - 7 * q^29 + 6 * q^30 - 3 * q^31 - 7 * q^32 - 19 * q^33 + 8 * q^34 - 25 * q^35 + 7 * q^36 - 13 * q^37 + 7 * q^38 + q^39 + 6 * q^40 - 11 * q^41 + 5 * q^42 - 14 * q^43 - 12 * q^44 - 17 * q^45 + 22 * q^46 - 23 * q^47 - 4 * q^48 + 6 * q^49 - 9 * q^50 - 21 * q^51 + 3 * q^52 - 21 * q^53 + 22 * q^54 + 15 * q^55 + 3 * q^56 - 14 * q^57 + 7 * q^58 - 20 * q^59 - 6 * q^60 + 13 * q^61 + 3 * q^62 - 12 * q^63 + 7 * q^64 - 29 * q^65 + 19 * q^66 - 30 * q^67 - 8 * q^68 + 13 * q^69 + 25 * q^70 - 23 * q^71 - 7 * q^72 + 9 * q^73 + 13 * q^74 + 3 * q^75 - 7 * q^76 + 8 * q^77 - q^78 + 11 * q^79 - 6 * q^80 + 43 * q^81 + 11 * q^82 - 3 * q^83 - 5 * q^84 + 21 * q^85 + 14 * q^86 + 28 * q^87 + 12 * q^88 + 16 * q^89 + 17 * q^90 - 10 * q^91 - 22 * q^92 - 13 * q^93 + 23 * q^94 + 4 * q^96 + 21 * q^97 - 6 * q^98 - 9 * 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
$3$	−1.20937	−0.698232	−0.349116	−	0.937079i	$-0.613518\pi$
$3$	−1.20937	−0.698232	−0.349116	+	0.937079i	$0.613518\pi$
$4$	1.00000	0.500000
$5$	−2.40321	−1.07475	−0.537373	−	0.843344i	$-0.680583\pi$
$5$	−2.40321	−1.07475	−0.537373	+	0.843344i	$0.680583\pi$
$6$	1.20937	0.493725
$7$	1.52017	0.574572	0.287286	−	0.957845i	$-0.407247\pi$
$7$	1.52017	0.574572	0.287286	+	0.957845i	$0.407247\pi$
$8$	−1.00000	−0.353553
$9$	−1.53742	−0.512472
$10$	2.40321	0.759961
$11$	5.07638	1.53059	0.765294	−	0.643681i	$-0.222594\pi$
$11$	5.07638	1.53059	0.765294	+	0.643681i	$0.222594\pi$
$12$	−1.20937	−0.349116
$13$	5.11021	1.41732	0.708659	−	0.705552i	$-0.249301\pi$
$13$	5.11021	1.41732	0.708659	+	0.705552i	$0.249301\pi$
$14$	−1.52017	−0.406284
$15$	2.90637	0.750423
$16$	1.00000	0.250000
$17$	−6.65764	−1.61471	−0.807357	−	0.590063i	$-0.799103\pi$
$17$	−6.65764	−1.61471	−0.807357	+	0.590063i	$0.799103\pi$
$18$	1.53742	0.362372
$19$	−5.71222	−1.31047	−0.655236	−	0.755424i	$-0.727431\pi$
$19$	−5.71222	−1.31047	−0.655236	+	0.755424i	$0.727431\pi$
$20$	−2.40321	−0.537373
$21$	−1.83846	−0.401184
$22$	−5.07638	−1.08229
$23$	−6.36685	−1.32758	−0.663790	−	0.747919i	$-0.731053\pi$
$23$	−6.36685	−1.32758	−0.663790	+	0.747919i	$0.731053\pi$
$24$	1.20937	0.246862
$25$	0.775401	0.155080
$26$	−5.11021	−1.00219
$27$	5.48743	1.05606
$28$	1.52017	0.287286
$29$	−6.00511	−1.11512	−0.557560	−	0.830137i	$-0.688262\pi$
$29$	−6.00511	−1.11512	−0.557560	+	0.830137i	$0.688262\pi$
$30$	−2.90637	−0.530629
$31$	2.77822	0.498984	0.249492	−	0.968377i	$-0.419736\pi$
$31$	2.77822	0.498984	0.249492	+	0.968377i	$0.419736\pi$
$32$	−1.00000	−0.176777
$33$	−6.13924	−1.06871
$34$	6.65764	1.14178
$35$	−3.65329	−0.617519
$36$	−1.53742	−0.256236
$37$	−1.59410	−0.262069	−0.131034	−	0.991378i	$-0.541830\pi$
$37$	−1.59410	−0.262069	−0.131034	+	0.991378i	$0.541830\pi$
$38$	5.71222	0.926644
$39$	−6.18015	−0.989616
$40$	2.40321	0.379980
$41$	9.69619	1.51429	0.757146	−	0.653246i	$-0.226593\pi$
$41$	9.69619	1.51429	0.757146	+	0.653246i	$0.226593\pi$
$42$	1.83846	0.283680
$43$	−9.26120	−1.41232	−0.706160	−	0.708053i	$-0.749574\pi$
$43$	−9.26120	−1.41232	−0.706160	+	0.708053i	$0.749574\pi$
$44$	5.07638	0.765294
$45$	3.69473	0.550777
$46$	6.36685	0.938741
$47$	−7.55235	−1.10162	−0.550811	−	0.834630i	$-0.685682\pi$
$47$	−7.55235	−1.10162	−0.550811	+	0.834630i	$0.685682\pi$
$48$	−1.20937	−0.174558
$49$	−4.68907	−0.669867
$50$	−0.775401	−0.109658
$51$	8.05157	1.12745
$52$	5.11021	0.708659
$53$	−9.42058	−1.29402	−0.647008	−	0.762483i	$-0.723980\pi$
$53$	−9.42058	−1.29402	−0.647008	+	0.762483i	$0.723980\pi$
$54$	−5.48743	−0.746745
$55$	−12.1996	−1.64499
$56$	−1.52017	−0.203142
$57$	6.90820	0.915014
$58$	6.00511	0.788509
$59$	−6.31332	−0.821924	−0.410962	−	0.911652i	$-0.634807\pi$
$59$	−6.31332	−0.821924	−0.410962	+	0.911652i	$0.634807\pi$
$60$	2.90637	0.375211
$61$	−7.97918	−1.02163	−0.510815	−	0.859691i	$-0.670656\pi$
$61$	−7.97918	−1.02163	−0.510815	+	0.859691i	$0.670656\pi$
$62$	−2.77822	−0.352835
$63$	−2.33714	−0.294452
$64$	1.00000	0.125000
$65$	−12.2809	−1.52326
$66$	6.13924	0.755689
$67$	−2.54885	−0.311392	−0.155696	−	0.987805i	$-0.549762\pi$
$67$	−2.54885	−0.311392	−0.155696	+	0.987805i	$0.549762\pi$
$68$	−6.65764	−0.807357
$69$	7.69990	0.926959
$70$	3.65329	0.436652
$71$	1.98957	0.236118	0.118059	−	0.993007i	$-0.462333\pi$
$71$	1.98957	0.236118	0.118059	+	0.993007i	$0.462333\pi$
$72$	1.53742	0.181186
$73$	12.7523	1.49254	0.746269	−	0.665644i	$-0.231843\pi$
$73$	12.7523	1.49254	0.746269	+	0.665644i	$0.231843\pi$
$74$	1.59410	0.185311
$75$	−0.937750	−0.108282
$76$	−5.71222	−0.655236
$77$	7.71699	0.879432
$78$	6.18015	0.699764
$79$	3.64283	0.409851	0.204925	−	0.978778i	$-0.434305\pi$
$79$	3.64283	0.409851	0.204925	+	0.978778i	$0.434305\pi$
$80$	−2.40321	−0.268687
$81$	−2.02411	−0.224901
$82$	−9.69619	−1.07077
$83$	−0.689504	−0.0756829	−0.0378415	−	0.999284i	$-0.512048\pi$
$83$	−0.689504	−0.0756829	−0.0378415	+	0.999284i	$0.512048\pi$
$84$	−1.83846	−0.200592
$85$	15.9997	1.73541
$86$	9.26120	0.998660
$87$	7.26242	0.778613
$88$	−5.07638	−0.541144
$89$	2.78972	0.295709	0.147855	−	0.989009i	$-0.452763\pi$
$89$	2.78972	0.295709	0.147855	+	0.989009i	$0.452763\pi$
$90$	−3.69473	−0.389458
$91$	7.76841	0.814350
$92$	−6.36685	−0.663790
$93$	−3.35991	−0.348407
$94$	7.55235	0.778965
$95$	13.7276	1.40843
$96$	1.20937	0.123431
$97$	11.9363	1.21194	0.605972	−	0.795486i	$-0.292784\pi$
$97$	11.9363	1.21194	0.605972	+	0.795486i	$0.292784\pi$
$98$	4.68907	0.473668
$99$	−7.80451	−0.784383
$100$	0.775401	0.0775401
$101$	−14.5273	−1.44552	−0.722759	−	0.691100i	$-0.757127\pi$
$101$	−14.5273	−1.44552	−0.722759	+	0.691100i	$0.757127\pi$
$102$	−8.05157	−0.797224
$103$	−10.1048	−0.995656	−0.497828	−	0.867276i	$-0.665869\pi$
$103$	−10.1048	−0.995656	−0.497828	+	0.867276i	$0.665869\pi$
$104$	−5.11021	−0.501097
$105$	4.41819	0.431172
$106$	9.42058	0.915007
$107$	−12.2725	−1.18643	−0.593214	−	0.805045i	$-0.702141\pi$
$107$	−12.2725	−1.18643	−0.593214	+	0.805045i	$0.702141\pi$
$108$	5.48743	0.528028
$109$	14.2163	1.36168	0.680838	−	0.732434i	$-0.261616\pi$
$109$	14.2163	1.36168	0.680838	+	0.732434i	$0.261616\pi$
$110$	12.1996	1.16319
$111$	1.92786	0.182985
$112$	1.52017	0.143643
$113$	12.7024	1.19494	0.597471	−	0.801891i	$-0.296172\pi$
$113$	12.7024	1.19494	0.597471	+	0.801891i	$0.296172\pi$
$114$	−6.90820	−0.647013
$115$	15.3009	1.42681
$116$	−6.00511	−0.557560
$117$	−7.85652	−0.726335
$118$	6.31332	0.581188
$119$	−10.1208	−0.927769
$120$	−2.90637	−0.265314
$121$	14.7697	1.34270
$122$	7.97918	0.722401
$123$	−11.7263	−1.05733
$124$	2.77822	0.249492
$125$	10.1526	0.908075
$126$	2.33714	0.208209
$127$	−17.1800	−1.52448	−0.762238	−	0.647297i	$-0.775899\pi$
$127$	−17.1800	−1.52448	−0.762238	+	0.647297i	$0.775899\pi$
$128$	−1.00000	−0.0883883
$129$	11.2002	0.986127
$130$	12.2809	1.07711
$131$	5.22919	0.456877	0.228438	−	0.973558i	$-0.426638\pi$
$131$	5.22919	0.456877	0.228438	+	0.973558i	$0.426638\pi$
$132$	−6.13924	−0.534353
$133$	−8.68356	−0.752960
$134$	2.54885	0.220187
$135$	−13.1874	−1.13499
$136$	6.65764	0.570888
$137$	−12.9664	−1.10779	−0.553895	−	0.832586i	$-0.686859\pi$
$137$	−12.9664	−1.10779	−0.553895	+	0.832586i	$0.686859\pi$
$138$	−7.69990	−0.655459
$139$	−0.692646	−0.0587495	−0.0293747	−	0.999568i	$-0.509352\pi$
$139$	−0.692646	−0.0587495	−0.0293747	+	0.999568i	$0.509352\pi$
$140$	−3.65329	−0.308759
$141$	9.13361	0.769189
$142$	−1.98957	−0.166961
$143$	25.9414	2.16933
$144$	−1.53742	−0.128118
$145$	14.4315	1.19847
$146$	−12.7523	−1.05538
$147$	5.67084	0.467723
$148$	−1.59410	−0.131034
$149$	11.5986	0.950197	0.475099	−	0.879933i	$-0.342412\pi$
$149$	11.5986	0.950197	0.475099	+	0.879933i	$0.342412\pi$
$150$	0.937750	0.0765669
$151$	1.14291	0.0930089	0.0465045	−	0.998918i	$-0.485192\pi$
$151$	1.14291	0.0930089	0.0465045	+	0.998918i	$0.485192\pi$
$152$	5.71222	0.463322
$153$	10.2356	0.827496
$154$	−7.71699	−0.621852
$155$	−6.67665	−0.536281
$156$	−6.18015	−0.494808
$157$	−12.2350	−0.976460	−0.488230	−	0.872715i	$-0.662357\pi$
$157$	−12.2350	−0.976460	−0.488230	+	0.872715i	$0.662357\pi$
$158$	−3.64283	−0.289808
$159$	11.3930	0.903523
$160$	2.40321	0.189990
$161$	−9.67872	−0.762790
$162$	2.02411	0.159029
$163$	−23.6815	−1.85488	−0.927438	−	0.373978i	$-0.877994\pi$
$163$	−23.6815	−1.85488	−0.927438	+	0.373978i	$0.877994\pi$
$164$	9.69619	0.757146
$165$	14.7539	1.14859
$166$	0.689504	0.0535159
$167$	−3.54694	−0.274470	−0.137235	−	0.990538i	$-0.543822\pi$
$167$	−3.54694	−0.274470	−0.137235	+	0.990538i	$0.543822\pi$
$168$	1.83846	0.141840
$169$	13.1142	1.00879
$170$	−15.9997	−1.22712
$171$	8.78205	0.671580
$172$	−9.26120	−0.706160
$173$	20.8927	1.58844	0.794220	−	0.607630i	$-0.207880\pi$
$173$	20.8927	1.58844	0.794220	+	0.607630i	$0.207880\pi$
$174$	−7.26242	−0.550562
$175$	1.17874	0.0891047
$176$	5.07638	0.382647
$177$	7.63516	0.573894
$178$	−2.78972	−0.209098
$179$	2.13073	0.159258	0.0796290	−	0.996825i	$-0.474626\pi$
$179$	2.13073	0.159258	0.0796290	+	0.996825i	$0.474626\pi$
$180$	3.69473	0.275389
$181$	18.5589	1.37948	0.689738	−	0.724059i	$-0.257726\pi$
$181$	18.5589	1.37948	0.689738	+	0.724059i	$0.257726\pi$
$182$	−7.76841	−0.575833
$183$	9.64981	0.713334
$184$	6.36685	0.469371
$185$	3.83095	0.281657
$186$	3.35991	0.246361
$187$	−33.7967	−2.47146
$188$	−7.55235	−0.550811
$189$	8.34185	0.606780
$190$	−13.7276	−0.995907
$191$	15.6213	1.13032	0.565160	−	0.824982i	$-0.308815\pi$
$191$	15.6213	1.13032	0.565160	+	0.824982i	$0.308815\pi$
$192$	−1.20937	−0.0872790
$193$	−18.5417	−1.33466	−0.667330	−	0.744762i	$-0.732563\pi$
$193$	−18.5417	−1.33466	−0.667330	+	0.744762i	$0.732563\pi$
$194$	−11.9363	−0.856974
$195$	14.8522	1.06359
$196$	−4.68907	−0.334934
$197$	−9.98285	−0.711249	−0.355624	−	0.934629i	$-0.615732\pi$
$197$	−9.98285	−0.711249	−0.355624	+	0.934629i	$0.615732\pi$
$198$	7.80451	0.554643
$199$	5.33431	0.378139	0.189070	−	0.981964i	$-0.439453\pi$
$199$	5.33431	0.378139	0.189070	+	0.981964i	$0.439453\pi$
$200$	−0.775401	−0.0548292
$201$	3.08251	0.217424
$202$	14.5273	1.02214
$203$	−9.12880	−0.640716
$204$	8.05157	0.563723
$205$	−23.3020	−1.62748
$206$	10.1048	0.704035
$207$	9.78850	0.680348
$208$	5.11021	0.354329
$209$	−28.9974	−2.00579
$210$	−4.41819	−0.304884
$211$	−19.7945	−1.36271	−0.681355	−	0.731953i	$-0.738609\pi$
$211$	−19.7945	−1.36271	−0.681355	+	0.731953i	$0.738609\pi$
$212$	−9.42058	−0.647008
$213$	−2.40613	−0.164865
$214$	12.2725	0.838931
$215$	22.2566	1.51789
$216$	−5.48743	−0.373372
$217$	4.22338	0.286702
$218$	−14.2163	−0.962850
$219$	−15.4222	−1.04214
$220$	−12.1996	−0.822497
$221$	−34.0219	−2.28856
$222$	−1.92786	−0.129390
$223$	29.2824	1.96089	0.980447	−	0.196783i	$-0.0630495\pi$
$223$	29.2824	1.96089	0.980447	+	0.196783i	$0.0630495\pi$
$224$	−1.52017	−0.101571
$225$	−1.19211	−0.0794743
$226$	−12.7024	−0.844951
$227$	−5.90479	−0.391915	−0.195957	−	0.980612i	$-0.562781\pi$
$227$	−5.90479	−0.391915	−0.195957	+	0.980612i	$0.562781\pi$
$228$	6.90820	0.457507
$229$	14.2761	0.943391	0.471695	−	0.881762i	$-0.343642\pi$
$229$	14.2761	0.943391	0.471695	+	0.881762i	$0.343642\pi$
$230$	−15.3009	−1.00891
$231$	−9.33272	−0.614048
$232$	6.00511	0.394254
$233$	−27.0850	−1.77440	−0.887198	−	0.461389i	$-0.847351\pi$
$233$	−27.0850	−1.77440	−0.887198	+	0.461389i	$0.847351\pi$
$234$	7.85652	0.513597
$235$	18.1498	1.18397
$236$	−6.31332	−0.410962
$237$	−4.40555	−0.286171
$238$	10.1208	0.656032
$239$	7.97200	0.515666	0.257833	−	0.966190i	$-0.416992\pi$
$239$	7.97200	0.515666	0.257833	+	0.966190i	$0.416992\pi$
$240$	2.90637	0.187606
$241$	−2.36516	−0.152353	−0.0761767	−	0.997094i	$-0.524271\pi$
$241$	−2.36516	−0.152353	−0.0761767	+	0.997094i	$0.524271\pi$
$242$	−14.7697	−0.949430
$243$	−14.0144	−0.899024
$244$	−7.97918	−0.510815
$245$	11.2688	0.719938
$246$	11.7263	0.747643
$247$	−29.1906	−1.85735
$248$	−2.77822	−0.176417
$249$	0.833868	0.0528443
$250$	−10.1526	−0.642106
$251$	−23.0435	−1.45449	−0.727246	−	0.686376i	$-0.759200\pi$
$251$	−23.0435	−1.45449	−0.727246	+	0.686376i	$0.759200\pi$
$252$	−2.33714	−0.147226
$253$	−32.3206	−2.03198
$254$	17.1800	1.07797
$255$	−19.3496	−1.21172
$256$	1.00000	0.0625000
$257$	23.2436	1.44990	0.724948	−	0.688803i	$-0.241864\pi$
$257$	23.2436	1.44990	0.724948	+	0.688803i	$0.241864\pi$
$258$	−11.2002	−0.697297
$259$	−2.42331	−0.150577
$260$	−12.2809	−0.761628
$261$	9.23234	0.571468
$262$	−5.22919	−0.323061
$263$	4.62308	0.285072	0.142536	−	0.989790i	$-0.454474\pi$
$263$	4.62308	0.285072	0.142536	+	0.989790i	$0.454474\pi$
$264$	6.13924	0.377844
$265$	22.6396	1.39074
$266$	8.68356	0.532423
$267$	−3.37381	−0.206474
$268$	−2.54885	−0.155696
$269$	−1.00000	−0.0609711
$269$	−1.00000	−0.0609711
$270$	13.1874	0.802561
$271$	12.4311	0.755135	0.377568	−	0.925982i	$-0.376761\pi$
$271$	12.4311	0.755135	0.377568	+	0.925982i	$0.376761\pi$
$272$	−6.65764	−0.403679
$273$	−9.39490	−0.568605
$274$	12.9664	0.783326
$275$	3.93623	0.237364
$276$	7.69990	0.463480
$277$	−4.92762	−0.296072	−0.148036	−	0.988982i	$-0.547295\pi$
$277$	−4.92762	−0.296072	−0.148036	+	0.988982i	$0.547295\pi$
$278$	0.692646	0.0415422
$279$	−4.27129	−0.255715
$280$	3.65329	0.218326
$281$	−21.3194	−1.27181	−0.635905	−	0.771767i	$-0.719373\pi$
$281$	−21.3194	−1.27181	−0.635905	+	0.771767i	$0.719373\pi$
$282$	−9.13361	−0.543898
$283$	−29.9997	−1.78330	−0.891649	−	0.452728i	$-0.850451\pi$
$283$	−29.9997	−1.78330	−0.891649	+	0.452728i	$0.850451\pi$
$284$	1.98957	0.118059
$285$	−16.6018	−0.983408
$286$	−25.9414	−1.53395
$287$	14.7399	0.870069
$288$	1.53742	0.0905931
$289$	27.3241	1.60730
$290$	−14.4315	−0.847447
$291$	−14.4354	−0.846218
$292$	12.7523	0.746269
$293$	16.9481	0.990120	0.495060	−	0.868859i	$-0.335146\pi$
$293$	16.9481	0.990120	0.495060	+	0.868859i	$0.335146\pi$
$294$	−5.67084	−0.330730
$295$	15.1722	0.883360
$296$	1.59410	0.0926553
$297$	27.8563	1.61639
$298$	−11.5986	−0.671891
$299$	−32.5360	−1.88160
$300$	−0.937750	−0.0541410
$301$	−14.0786	−0.811479
$302$	−1.14291	−0.0657672
$303$	17.5689	1.00931
$304$	−5.71222	−0.327618
$305$	19.1756	1.09799
$306$	−10.2356	−0.585128
$307$	18.4715	1.05422	0.527112	−	0.849796i	$-0.323275\pi$
$307$	18.4715	1.05422	0.527112	+	0.849796i	$0.323275\pi$
$308$	7.71699	0.439716
$309$	12.2205	0.695199
$310$	6.67665	0.379208
$311$	13.9141	0.788995	0.394497	−	0.918897i	$-0.370919\pi$
$311$	13.9141	0.788995	0.394497	+	0.918897i	$0.370919\pi$
$312$	6.18015	0.349882
$313$	21.9666	1.24162	0.620812	−	0.783959i	$-0.286803\pi$
$313$	21.9666	1.24162	0.620812	+	0.783959i	$0.286803\pi$
$314$	12.2350	0.690462
$315$	5.61663	0.316461
$316$	3.64283	0.204925
$317$	−3.38070	−0.189879	−0.0949395	−	0.995483i	$-0.530266\pi$
$317$	−3.38070	−0.189879	−0.0949395	+	0.995483i	$0.530266\pi$
$318$	−11.3930	−0.638887
$319$	−30.4842	−1.70679
$320$	−2.40321	−0.134343
$321$	14.8420	0.828402
$322$	9.67872	0.539374
$323$	38.0299	2.11604
$324$	−2.02411	−0.112450
$325$	3.96246	0.219798
$326$	23.6815	1.31159
$327$	−17.1928	−0.950765
$328$	−9.69619	−0.535383
$329$	−11.4809	−0.632961
$330$	−14.7539	−0.812174
$331$	21.9585	1.20695	0.603476	−	0.797382i	$-0.293782\pi$
$331$	21.9585	1.20695	0.603476	+	0.797382i	$0.293782\pi$
$332$	−0.689504	−0.0378415
$333$	2.45080	0.134303
$334$	3.54694	0.194080
$335$	6.12542	0.334667
$336$	−1.83846	−0.100296
$337$	3.21883	0.175341	0.0876705	−	0.996150i	$-0.472058\pi$
$337$	3.21883	0.175341	0.0876705	+	0.996150i	$0.472058\pi$
$338$	−13.1142	−0.713321
$339$	−15.3619	−0.834346
$340$	15.9997	0.867704
$341$	14.1033	0.763738
$342$	−8.78205	−0.474879
$343$	−17.7694	−0.959459
$344$	9.26120	0.499330
$345$	−18.5045	−0.996246
$346$	−20.8927	−1.12320
$347$	15.8474	0.850734	0.425367	−	0.905021i	$-0.360145\pi$
$347$	15.8474	0.850734	0.425367	+	0.905021i	$0.360145\pi$
$348$	7.26242	0.389306
$349$	−17.0834	−0.914451	−0.457226	−	0.889351i	$-0.651157\pi$
$349$	−17.0834	−0.914451	−0.457226	+	0.889351i	$0.651157\pi$
$350$	−1.17874	−0.0630066
$351$	28.0419	1.49677
$352$	−5.07638	−0.270572
$353$	−4.73633	−0.252090	−0.126045	−	0.992025i	$-0.540228\pi$
$353$	−4.73633	−0.252090	−0.126045	+	0.992025i	$0.540228\pi$
$354$	−7.63516	−0.405804
$355$	−4.78134	−0.253767
$356$	2.78972	0.147855
$357$	12.2398	0.647798
$358$	−2.13073	−0.112612
$359$	18.2662	0.964051	0.482025	−	0.876157i	$-0.339901\pi$
$359$	18.2662	0.964051	0.482025	+	0.876157i	$0.339901\pi$
$360$	−3.69473	−0.194729
$361$	13.6294	0.717338
$362$	−18.5589	−0.975437
$363$	−17.8620	−0.937514
$364$	7.76841	0.407175
$365$	−30.6463	−1.60410
$366$	−9.64981	−0.504404
$367$	5.99172	0.312765	0.156383	−	0.987697i	$-0.450017\pi$
$367$	5.99172	0.312765	0.156383	+	0.987697i	$0.450017\pi$
$368$	−6.36685	−0.331895
$369$	−14.9071	−0.776032
$370$	−3.83095	−0.199162
$371$	−14.3209	−0.743505
$372$	−3.35991	−0.174203
$373$	−16.9416	−0.877203	−0.438601	−	0.898682i	$-0.644526\pi$
$373$	−16.9416	−0.877203	−0.438601	+	0.898682i	$0.644526\pi$
$374$	33.7967	1.74759
$375$	−12.2783	−0.634047
$376$	7.55235	0.389483
$377$	−30.6873	−1.58048
$378$	−8.34185	−0.429058
$379$	−16.7293	−0.859325	−0.429663	−	0.902989i	$-0.641368\pi$
$379$	−16.7293	−0.859325	−0.429663	+	0.902989i	$0.641368\pi$
$380$	13.7276	0.704213
$381$	20.7770	1.06444
$382$	−15.6213	−0.799257
$383$	−26.8421	−1.37157	−0.685785	−	0.727804i	$-0.740541\pi$
$383$	−26.8421	−1.37157	−0.685785	+	0.727804i	$0.740541\pi$
$384$	1.20937	0.0617156
$385$	−18.5455	−0.945167
$386$	18.5417	0.943747
$387$	14.2383	0.723774
$388$	11.9363	0.605972
$389$	8.89100	0.450792	0.225396	−	0.974267i	$-0.427632\pi$
$389$	8.89100	0.450792	0.225396	+	0.974267i	$0.427632\pi$
$390$	−14.8522	−0.752069
$391$	42.3882	2.14366
$392$	4.68907	0.236834
$393$	−6.32405	−0.319006
$394$	9.98285	0.502929
$395$	−8.75448	−0.440486
$396$	−7.80451	−0.392191
$397$	−15.3011	−0.767939	−0.383970	−	0.923346i	$-0.625443\pi$
$397$	−15.3011	−0.767939	−0.383970	+	0.923346i	$0.625443\pi$
$398$	−5.33431	−0.267385
$399$	10.5017	0.525741
$400$	0.775401	0.0387701
$401$	−9.91869	−0.495316	−0.247658	−	0.968848i	$-0.579661\pi$
$401$	−9.91869	−0.495316	−0.247658	+	0.968848i	$0.579661\pi$
$402$	−3.08251	−0.153742
$403$	14.1973	0.707218
$404$	−14.5273	−0.722759
$405$	4.86434	0.241711
$406$	9.12880	0.453055
$407$	−8.09227	−0.401119
$408$	−8.05157	−0.398612
$409$	−13.4737	−0.666233	−0.333117	−	0.942886i	$-0.608100\pi$
$409$	−13.4737	−0.666233	−0.333117	+	0.942886i	$0.608100\pi$
$410$	23.3020	1.15080
$411$	15.6812	0.773495
$412$	−10.1048	−0.497828
$413$	−9.59734	−0.472254
$414$	−9.78850	−0.481079
$415$	1.65702	0.0813400
$416$	−5.11021	−0.250549
$417$	0.837668	0.0410208
$418$	28.9974	1.41831
$419$	−24.5320	−1.19847	−0.599233	−	0.800574i	$-0.704528\pi$
$419$	−24.5320	−1.19847	−0.599233	+	0.800574i	$0.704528\pi$
$420$	4.41819	0.215586
$421$	−27.8189	−1.35581	−0.677906	−	0.735149i	$-0.737112\pi$
$421$	−27.8189	−1.35581	−0.677906	+	0.735149i	$0.737112\pi$
$422$	19.7945	0.963581
$423$	11.6111	0.564551
$424$	9.42058	0.457504
$425$	−5.16234	−0.250410
$426$	2.40613	0.116577
$427$	−12.1297	−0.586999
$428$	−12.2725	−0.593214
$429$	−31.3728	−1.51469
$430$	−22.2566	−1.07331
$431$	32.5743	1.56905	0.784525	−	0.620097i	$-0.212907\pi$
$431$	32.5743	1.56905	0.784525	+	0.620097i	$0.212907\pi$
$432$	5.48743	0.264014
$433$	−5.11693	−0.245904	−0.122952	−	0.992413i	$-0.539236\pi$
$433$	−5.11693	−0.245904	−0.122952	+	0.992413i	$0.539236\pi$
$434$	−4.22338	−0.202729
$435$	−17.4531	−0.836811
$436$	14.2163	0.680838
$437$	36.3688	1.73976
$438$	15.4222	0.736903
$439$	18.8040	0.897466	0.448733	−	0.893666i	$-0.351875\pi$
$439$	18.8040	0.897466	0.448733	+	0.893666i	$0.351875\pi$
$440$	12.1996	0.581593
$441$	7.20905	0.343288
$442$	34.0219	1.61826
$443$	16.7817	0.797325	0.398662	−	0.917098i	$-0.369475\pi$
$443$	16.7817	0.797325	0.398662	+	0.917098i	$0.369475\pi$
$444$	1.92786	0.0914924
$445$	−6.70426	−0.317812
$446$	−29.2824	−1.38656
$447$	−14.0271	−0.663458
$448$	1.52017	0.0718215
$449$	29.1983	1.37795	0.688977	−	0.724784i	$-0.258060\pi$
$449$	29.1983	1.37795	0.688977	+	0.724784i	$0.258060\pi$
$450$	1.19211	0.0561968
$451$	49.2216	2.31775
$452$	12.7024	0.597471
$453$	−1.38221	−0.0649418
$454$	5.90479	0.277126
$455$	−18.6691	−0.875220
$456$	−6.90820	−0.323506
$457$	6.74219	0.315387	0.157693	−	0.987488i	$-0.449594\pi$
$457$	6.74219	0.315387	0.157693	+	0.987488i	$0.449594\pi$
$458$	−14.2761	−0.667078
$459$	−36.5333	−1.70523
$460$	15.3009	0.713406
$461$	17.8901	0.833226	0.416613	−	0.909084i	$-0.363217\pi$
$461$	17.8901	0.833226	0.416613	+	0.909084i	$0.363217\pi$
$462$	9.33272	0.434197
$463$	17.2936	0.803703	0.401851	−	0.915705i	$-0.368367\pi$
$463$	17.2936	0.803703	0.401851	+	0.915705i	$0.368367\pi$
$464$	−6.00511	−0.278780
$465$	8.07456	0.374449
$466$	27.0850	1.25469
$467$	−3.00187	−0.138910	−0.0694550	−	0.997585i	$-0.522126\pi$
$467$	−3.00187	−0.138910	−0.0694550	+	0.997585i	$0.522126\pi$
$468$	−7.85652	−0.363168
$469$	−3.87470	−0.178917
$470$	−18.1498	−0.837190
$471$	14.7967	0.681796
$472$	6.31332	0.290594
$473$	−47.0134	−2.16168
$474$	4.40555	0.202354
$475$	−4.42926	−0.203228
$476$	−10.1208	−0.463884
$477$	14.4833	0.663147
$478$	−7.97200	−0.364631
$479$	−25.7701	−1.17747	−0.588734	−	0.808327i	$-0.700373\pi$
$479$	−25.7701	−1.17747	−0.588734	+	0.808327i	$0.700373\pi$
$480$	−2.90637	−0.132657
$481$	−8.14619	−0.371434
$482$	2.36516	0.107730
$483$	11.7052	0.532605
$484$	14.7697	0.671349
$485$	−28.6853	−1.30253
$486$	14.0144	0.635706
$487$	9.85904	0.446756	0.223378	−	0.974732i	$-0.428292\pi$
$487$	9.85904	0.446756	0.223378	+	0.974732i	$0.428292\pi$
$488$	7.97918	0.361200
$489$	28.6397	1.29513
$490$	−11.2688	−0.509073
$491$	9.75565	0.440266	0.220133	−	0.975470i	$-0.429351\pi$
$491$	9.75565	0.440266	0.220133	+	0.975470i	$0.429351\pi$
$492$	−11.7263	−0.528663
$493$	39.9798	1.80060
$494$	29.1906	1.31335
$495$	18.7559	0.843013
$496$	2.77822	0.124746
$497$	3.02448	0.135667
$498$	−0.833868	−0.0373665
$499$	−3.06163	−0.137058	−0.0685288	−	0.997649i	$-0.521830\pi$
$499$	−3.06163	−0.137058	−0.0685288	+	0.997649i	$0.521830\pi$
$500$	10.1526	0.454037
$501$	4.28957	0.191644
$502$	23.0435	1.02848
$503$	−15.0940	−0.673010	−0.336505	−	0.941682i	$-0.609245\pi$
$503$	−15.0940	−0.673010	−0.336505	+	0.941682i	$0.609245\pi$
$504$	2.33714	0.104104
$505$	34.9121	1.55357
$506$	32.3206	1.43683
$507$	−15.8600	−0.704368
$508$	−17.1800	−0.762238
$509$	13.2575	0.587629	0.293814	−	0.955863i	$-0.405075\pi$
$509$	13.2575	0.587629	0.293814	+	0.955863i	$0.405075\pi$
$510$	19.3496	0.856814
$511$	19.3856	0.857570
$512$	−1.00000	−0.0441942
$513$	−31.3454	−1.38393
$514$	−23.2436	−1.02523
$515$	24.2839	1.07008
$516$	11.2002	0.493063
$517$	−38.3386	−1.68613
$518$	2.42331	0.106474
$519$	−25.2670	−1.10910
$520$	12.2809	0.538553
$521$	20.2639	0.887776	0.443888	−	0.896082i	$-0.353599\pi$
$521$	20.2639	0.887776	0.443888	+	0.896082i	$0.353599\pi$
$522$	−9.23234	−0.404089
$523$	−2.18471	−0.0955307	−0.0477654	−	0.998859i	$-0.515210\pi$
$523$	−2.18471	−0.0955307	−0.0477654	+	0.998859i	$0.515210\pi$
$524$	5.22919	0.228438
$525$	−1.42554	−0.0622158
$526$	−4.62308	−0.201576
$527$	−18.4964	−0.805716
$528$	−6.13924	−0.267176
$529$	17.5368	0.762470
$530$	−22.6396	−0.983401
$531$	9.70620	0.421213
$532$	−8.68356	−0.376480
$533$	49.5496	2.14623
$534$	3.37381	0.145999
$535$	29.4933	1.27511
$536$	2.54885	0.110094
$537$	−2.57685	−0.111199
$538$	1.00000	0.0431131
$539$	−23.8035	−1.02529
$540$	−13.1874	−0.567497
$541$	21.9779	0.944903	0.472452	−	0.881357i	$-0.343369\pi$
$541$	21.9779	0.944903	0.472452	+	0.881357i	$0.343369\pi$
$542$	−12.4311	−0.533961
$543$	−22.4447	−0.963194
$544$	6.65764	0.285444
$545$	−34.1647	−1.46346
$546$	9.39490	0.402065
$547$	−2.59714	−0.111046	−0.0555229	−	0.998457i	$-0.517683\pi$
$547$	−2.59714	−0.111046	−0.0555229	+	0.998457i	$0.517683\pi$
$548$	−12.9664	−0.553895
$549$	12.2673	0.523556
$550$	−3.93623	−0.167842
$551$	34.3025	1.46133
$552$	−7.69990	−0.327730
$553$	5.53774	0.235489
$554$	4.92762	0.209354
$555$	−4.63305	−0.196662
$556$	−0.692646	−0.0293747
$557$	32.9165	1.39471	0.697357	−	0.716724i	$-0.254359\pi$
$557$	32.9165	1.39471	0.697357	+	0.716724i	$0.254359\pi$
$558$	4.27129	0.180818
$559$	−47.3266	−2.00170
$560$	−3.65329	−0.154380
$561$	40.8729	1.72565
$562$	21.3194	0.899306
$563$	−16.1700	−0.681485	−0.340742	−	0.940157i	$-0.610678\pi$
$563$	−16.1700	−0.681485	−0.340742	+	0.940157i	$0.610678\pi$
$564$	9.13361	0.384594
$565$	−30.5265	−1.28426
$566$	29.9997	1.26098
$567$	−3.07699	−0.129222
$568$	−1.98957	−0.0834803
$569$	−11.9495	−0.500951	−0.250476	−	0.968123i	$-0.580587\pi$
$569$	−11.9495	−0.500951	−0.250476	+	0.968123i	$0.580587\pi$
$570$	16.6018	0.695375
$571$	−18.1326	−0.758824	−0.379412	−	0.925228i	$-0.623874\pi$
$571$	−18.1326	−0.758824	−0.379412	+	0.925228i	$0.623874\pi$
$572$	25.9414	1.08466
$573$	−18.8920	−0.789225
$574$	−14.7399	−0.615232
$575$	−4.93687	−0.205882
$576$	−1.53742	−0.0640590
$577$	22.5512	0.938817	0.469408	−	0.882981i	$-0.344467\pi$
$577$	22.5512	0.938817	0.469408	+	0.882981i	$0.344467\pi$
$578$	−27.3241	−1.13653
$579$	22.4238	0.931903
$580$	14.4315	0.599236
$581$	−1.04817	−0.0434853
$582$	14.4354	0.598367
$583$	−47.8225	−1.98060
$584$	−12.7523	−0.527692
$585$	18.8808	0.780626
$586$	−16.9481	−0.700121
$587$	22.1880	0.915796	0.457898	−	0.889005i	$-0.348603\pi$
$587$	22.1880	0.915796	0.457898	+	0.889005i	$0.348603\pi$
$588$	5.67084	0.233861
$589$	−15.8698	−0.653905
$590$	−15.1722	−0.624630
$591$	12.0730	0.496617
$592$	−1.59410	−0.0655172
$593$	30.4282	1.24954	0.624768	−	0.780811i	$-0.285194\pi$
$593$	30.4282	1.24954	0.624768	+	0.780811i	$0.285194\pi$
$594$	−27.8563	−1.14296
$595$	24.3223	0.997117
$596$	11.5986	0.475099
$597$	−6.45118	−0.264029
$598$	32.5360	1.33049
$599$	15.6413	0.639086	0.319543	−	0.947572i	$-0.396471\pi$
$599$	15.6413	0.639086	0.319543	+	0.947572i	$0.396471\pi$
$600$	0.937750	0.0382835
$601$	−19.9435	−0.813512	−0.406756	−	0.913537i	$-0.633340\pi$
$601$	−19.9435	−0.813512	−0.406756	+	0.913537i	$0.633340\pi$
$602$	14.0786	0.573802
$603$	3.91864	0.159580
$604$	1.14291	0.0465045
$605$	−35.4946	−1.44306
$606$	−17.5689	−0.713688
$607$	−11.4793	−0.465932	−0.232966	−	0.972485i	$-0.574843\pi$
$607$	−11.4793	−0.465932	−0.232966	+	0.972485i	$0.574843\pi$
$608$	5.71222	0.231661
$609$	11.0401	0.447369
$610$	−19.1756	−0.776398
$611$	−38.5941	−1.56135
$612$	10.2356	0.413748
$613$	11.2663	0.455044	0.227522	−	0.973773i	$-0.426938\pi$
$613$	11.2663	0.455044	0.227522	+	0.973773i	$0.426938\pi$
$614$	−18.4715	−0.745449
$615$	28.1808	1.13636
$616$	−7.71699	−0.310926
$617$	10.0317	0.403861	0.201930	−	0.979400i	$-0.435279\pi$
$617$	10.0317	0.403861	0.201930	+	0.979400i	$0.435279\pi$
$618$	−12.2205	−0.491580
$619$	10.0658	0.404579	0.202289	−	0.979326i	$-0.435162\pi$
$619$	10.0658	0.404579	0.202289	+	0.979326i	$0.435162\pi$
$620$	−6.67665	−0.268141
$621$	−34.9377	−1.40200
$622$	−13.9141	−0.557904
$623$	4.24085	0.169906
$624$	−6.18015	−0.247404
$625$	−28.2758	−1.13103
$626$	−21.9666	−0.877961
$627$	35.0687	1.40051
$628$	−12.2350	−0.488230
$629$	10.6129	0.423166
$630$	−5.61663	−0.223772
$631$	−35.3530	−1.40738	−0.703691	−	0.710506i	$-0.748466\pi$
$631$	−35.3530	−1.40738	−0.703691	+	0.710506i	$0.748466\pi$
$632$	−3.64283	−0.144904
$633$	23.9389	0.951488
$634$	3.38070	0.134265
$635$	41.2870	1.63842
$636$	11.3930	0.451762
$637$	−23.9621	−0.949414
$638$	30.4842	1.20688
$639$	−3.05879	−0.121004
$640$	2.40321	0.0949951
$641$	0.166926	0.00659316	0.00329658	−	0.999995i	$-0.498951\pi$
$641$	0.166926	0.00659316	0.00329658	+	0.999995i	$0.498951\pi$
$642$	−14.8420	−0.585768
$643$	−30.9571	−1.22083	−0.610415	−	0.792082i	$-0.708997\pi$
$643$	−30.9571	−1.22083	−0.610415	+	0.792082i	$0.708997\pi$
$644$	−9.67872	−0.381395
$645$	−26.9165	−1.05984
$646$	−38.0299	−1.49626
$647$	−0.959927	−0.0377386	−0.0188693	−	0.999822i	$-0.506007\pi$
$647$	−0.959927	−0.0377386	−0.0188693	+	0.999822i	$0.506007\pi$
$648$	2.02411	0.0795144
$649$	−32.0488	−1.25803
$650$	−3.96246	−0.155421
$651$	−5.10765	−0.200185
$652$	−23.6815	−0.927438
$653$	27.5173	1.07684	0.538418	−	0.842678i	$-0.319022\pi$
$653$	27.5173	1.07684	0.538418	+	0.842678i	$0.319022\pi$
$654$	17.1928	0.672293
$655$	−12.5668	−0.491027
$656$	9.69619	0.378573
$657$	−19.6055	−0.764884
$658$	11.4809	0.447571
$659$	3.87281	0.150863	0.0754316	−	0.997151i	$-0.475967\pi$
$659$	3.87281	0.150863	0.0754316	+	0.997151i	$0.475967\pi$
$660$	14.7539	0.574294
$661$	2.60845	0.101457	0.0507285	−	0.998712i	$-0.483846\pi$
$661$	2.60845	0.101457	0.0507285	+	0.998712i	$0.483846\pi$
$662$	−21.9585	−0.853443
$663$	41.1452	1.59795
$664$	0.689504	0.0267580
$665$	20.8684	0.809242
$666$	−2.45080	−0.0949664
$667$	38.2336	1.48041
$668$	−3.54694	−0.137235
$669$	−35.4134	−1.36916
$670$	−6.12542	−0.236645
$671$	−40.5054	−1.56369
$672$	1.83846	0.0709201
$673$	−12.9907	−0.500753	−0.250376	−	0.968149i	$-0.580554\pi$
$673$	−12.9907	−0.500753	−0.250376	+	0.968149i	$0.580554\pi$
$674$	−3.21883	−0.123985
$675$	4.25496	0.163774
$676$	13.1142	0.504394
$677$	30.7406	1.18146	0.590728	−	0.806871i	$-0.298841\pi$
$677$	30.7406	1.18146	0.590728	+	0.806871i	$0.298841\pi$
$678$	15.3619	0.589972
$679$	18.1452	0.696349
$680$	−15.9997	−0.613560
$681$	7.14110	0.273648
$682$	−14.1033	−0.540045
$683$	−6.20328	−0.237362	−0.118681	−	0.992932i	$-0.537867\pi$
$683$	−6.20328	−0.237362	−0.118681	+	0.992932i	$0.537867\pi$
$684$	8.78205	0.335790
$685$	31.1608	1.19059
$686$	17.7694	0.678440
$687$	−17.2651	−0.658706
$688$	−9.26120	−0.353080
$689$	−48.1411	−1.83403
$690$	18.5045	0.704453
$691$	18.1544	0.690626	0.345313	−	0.938488i	$-0.387773\pi$
$691$	18.1544	0.690626	0.345313	+	0.938488i	$0.387773\pi$
$692$	20.8927	0.794220
$693$	−11.8642	−0.450684
$694$	−15.8474	−0.601560
$695$	1.66457	0.0631408
$696$	−7.26242	−0.275281
$697$	−64.5537	−2.44515
$698$	17.0834	0.646615
$699$	32.7559	1.23894
$700$	1.17874	0.0445524
$701$	−46.2492	−1.74681	−0.873404	−	0.486996i	$-0.838093\pi$
$701$	−46.2492	−1.74681	−0.873404	+	0.486996i	$0.838093\pi$
$702$	−28.0419	−1.05837
$703$	9.10585	0.343434
$704$	5.07638	0.191323
$705$	−21.9499	−0.826683
$706$	4.73633	0.178254
$707$	−22.0840	−0.830554
$708$	7.63516	0.286947
$709$	−35.6219	−1.33781	−0.668904	−	0.743349i	$-0.733236\pi$
$709$	−35.6219	−1.33781	−0.668904	+	0.743349i	$0.733236\pi$
$710$	4.78134	0.179440
$711$	−5.60055	−0.210037
$712$	−2.78972	−0.104549
$713$	−17.6885	−0.662441
$714$	−12.2398	−0.458062
$715$	−62.3425	−2.33148
$716$	2.13073	0.0796290
$717$	−9.64112	−0.360054
$718$	−18.2662	−0.681687
$719$	−37.4220	−1.39561	−0.697803	−	0.716290i	$-0.745839\pi$
$719$	−37.4220	−1.39561	−0.697803	+	0.716290i	$0.745839\pi$
$720$	3.69473	0.137694
$721$	−15.3611	−0.572076
$722$	−13.6294	−0.507234
$723$	2.86036	0.106378
$724$	18.5589	0.689738
$725$	−4.65637	−0.172933
$726$	17.8620	0.662923
$727$	−24.4331	−0.906172	−0.453086	−	0.891467i	$-0.649677\pi$
$727$	−24.4331	−0.906172	−0.453086	+	0.891467i	$0.649677\pi$
$728$	−7.76841	−0.287916
$729$	23.0209	0.852628
$730$	30.6463	1.13427
$731$	61.6577	2.28049
$732$	9.64981	0.356667
$733$	37.4726	1.38408	0.692042	−	0.721857i	$-0.256711\pi$
$733$	37.4726	1.38408	0.692042	+	0.721857i	$0.256711\pi$
$734$	−5.99172	−0.221159
$735$	−13.6282	−0.502684
$736$	6.36685	0.234685
$737$	−12.9389	−0.476612
$738$	14.9071	0.548737
$739$	−18.6134	−0.684707	−0.342353	−	0.939571i	$-0.611224\pi$
$739$	−18.6134	−0.684707	−0.342353	+	0.939571i	$0.611224\pi$
$740$	3.83095	0.140829
$741$	35.3024	1.29686
$742$	14.3209	0.525737
$743$	0.773612	0.0283811	0.0141905	−	0.999899i	$-0.495483\pi$
$743$	0.773612	0.0283811	0.0141905	+	0.999899i	$0.495483\pi$
$744$	3.35991	0.123180
$745$	−27.8739	−1.02122
$746$	16.9416	0.620276
$747$	1.06005	0.0387854
$748$	−33.7967	−1.23573
$749$	−18.6563	−0.681688
$750$	12.2783	0.448339
$751$	−11.0543	−0.403377	−0.201689	−	0.979450i	$-0.564643\pi$
$751$	−11.0543	−0.403377	−0.201689	+	0.979450i	$0.564643\pi$
$752$	−7.55235	−0.275406
$753$	27.8682	1.01557
$754$	30.6873	1.11757
$755$	−2.74666	−0.0999610
$756$	8.34185	0.303390
$757$	31.9235	1.16028	0.580140	−	0.814517i	$-0.302998\pi$
$757$	31.9235	1.16028	0.580140	+	0.814517i	$0.302998\pi$
$758$	16.7293	0.607635
$759$	39.0877	1.41879
$760$	−13.7276	−0.497954
$761$	14.7166	0.533477	0.266739	−	0.963769i	$-0.414054\pi$
$761$	14.7166	0.533477	0.266739	+	0.963769i	$0.414054\pi$
$762$	−20.7770	−0.752671
$763$	21.6113	0.782380
$764$	15.6213	0.565160
$765$	−24.5982	−0.889348
$766$	26.8421	0.969846
$767$	−32.2624	−1.16493
$768$	−1.20937	−0.0436395
$769$	−18.0186	−0.649768	−0.324884	−	0.945754i	$-0.605325\pi$
$769$	−18.0186	−0.649768	−0.324884	+	0.945754i	$0.605325\pi$
$770$	18.5455	0.668334
$771$	−28.1102	−1.01236
$772$	−18.5417	−0.667330
$773$	48.8663	1.75760	0.878799	−	0.477193i	$-0.158346\pi$
$773$	48.8663	1.75760	0.878799	+	0.477193i	$0.158346\pi$
$774$	−14.2383	−0.511785
$775$	2.15424	0.0773825
$776$	−11.9363	−0.428487
$777$	2.93069	0.105138
$778$	−8.89100	−0.318758
$779$	−55.3868	−1.98444
$780$	14.8522	0.531793
$781$	10.0998	0.361399
$782$	−42.3882	−1.51580
$783$	−32.9526	−1.17763
$784$	−4.68907	−0.167467
$785$	29.4033	1.04945
$786$	6.32405	0.225571
$787$	−31.8942	−1.13691	−0.568453	−	0.822715i	$-0.692458\pi$
$787$	−31.8942	−1.13691	−0.568453	+	0.822715i	$0.692458\pi$
$788$	−9.98285	−0.355624
$789$	−5.59103	−0.199046
$790$	8.75448	0.311471
$791$	19.3099	0.686579
$792$	7.80451	0.277321
$793$	−40.7753	−1.44797
$794$	15.3011	0.543015
$795$	−27.3797	−0.971059
$796$	5.33431	0.189070
$797$	−26.0846	−0.923964	−0.461982	−	0.886889i	$-0.652861\pi$
$797$	−26.0846	−0.923964	−0.461982	+	0.886889i	$0.652861\pi$
$798$	−10.5017	−0.371755
$799$	50.2808	1.77881
$800$	−0.775401	−0.0274146
$801$	−4.28895	−0.151543
$802$	9.91869	0.350241
$803$	64.7353	2.28446
$804$	3.08251	0.108712
$805$	23.2600	0.819806
$806$	−14.1973	−0.500079
$807$	1.20937	0.0425720
$808$	14.5273	0.511068
$809$	−2.45878	−0.0864461	−0.0432231	−	0.999065i	$-0.513763\pi$
$809$	−2.45878	−0.0864461	−0.0432231	+	0.999065i	$0.513763\pi$
$810$	−4.86434	−0.170916
$811$	−20.3841	−0.715783	−0.357891	−	0.933763i	$-0.616504\pi$
$811$	−20.3841	−0.715783	−0.357891	+	0.933763i	$0.616504\pi$
$812$	−9.12880	−0.320358
$813$	−15.0338	−0.527260
$814$	8.09227	0.283634
$815$	56.9114	1.99352
$816$	8.05157	0.281861
$817$	52.9020	1.85081
$818$	13.4737	0.471098
$819$	−11.9433	−0.417332
$820$	−23.3020	−0.813740
$821$	−8.31824	−0.290309	−0.145154	−	0.989409i	$-0.546368\pi$
$821$	−8.31824	−0.290309	−0.145154	+	0.989409i	$0.546368\pi$
$822$	−15.6812	−0.546943
$823$	−25.5967	−0.892244	−0.446122	−	0.894972i	$-0.647195\pi$
$823$	−25.5967	−0.892244	−0.446122	+	0.894972i	$0.647195\pi$
$824$	10.1048	0.352017
$825$	−4.76038	−0.165735
$826$	9.59734	0.333934
$827$	28.4900	0.990693	0.495347	−	0.868695i	$-0.335041\pi$
$827$	28.4900	0.990693	0.495347	+	0.868695i	$0.335041\pi$
$828$	9.78850	0.340174
$829$	−15.2875	−0.530956	−0.265478	−	0.964117i	$-0.585530\pi$
$829$	−15.2875	−0.530956	−0.265478	+	0.964117i	$0.585530\pi$
$830$	−1.65702	−0.0575161
$831$	5.95933	0.206727
$832$	5.11021	0.177165
$833$	31.2181	1.08164
$834$	−0.837668	−0.0290061
$835$	8.52403	0.294986
$836$	−28.9974	−1.00290
$837$	15.2453	0.526955
$838$	24.5320	0.847444
$839$	33.9640	1.17257	0.586283	−	0.810106i	$-0.300591\pi$
$839$	33.9640	1.17257	0.586283	+	0.810106i	$0.300591\pi$
$840$	−4.41819	−0.152442
$841$	7.06129	0.243493
$842$	27.8189	0.958704
$843$	25.7832	0.888019
$844$	−19.7945	−0.681355
$845$	−31.5162	−1.08419
$846$	−11.6111	−0.399198
$847$	22.4525	0.771476
$848$	−9.42058	−0.323504
$849$	36.2808	1.24516
$850$	5.16234	0.177067
$851$	10.1494	0.347917
$852$	−2.40613	−0.0824326
$853$	−18.6395	−0.638203	−0.319102	−	0.947720i	$-0.603381\pi$
$853$	−18.6395	−0.638203	−0.319102	+	0.947720i	$0.603381\pi$
$854$	12.1297	0.415071
$855$	−21.1051	−0.721779
$856$	12.2725	0.419465
$857$	38.5929	1.31831	0.659154	−	0.752008i	$-0.270915\pi$
$857$	38.5929	1.31831	0.659154	+	0.752008i	$0.270915\pi$
$858$	31.3728	1.07105
$859$	36.7533	1.25400	0.627002	−	0.779017i	$-0.284282\pi$
$859$	36.7533	1.25400	0.627002	+	0.779017i	$0.284282\pi$
$860$	22.2566	0.758943
$861$	−17.8260	−0.607510
$862$	−32.5743	−1.10949
$863$	39.5677	1.34690	0.673450	−	0.739233i	$-0.264812\pi$
$863$	39.5677	1.34690	0.673450	+	0.739233i	$0.264812\pi$
$864$	−5.48743	−0.186686
$865$	−50.2094	−1.70717
$866$	5.11693	0.173880
$867$	−33.0451	−1.12227
$868$	4.22338	0.143351
$869$	18.4924	0.627313
$870$	17.4531	0.591715
$871$	−13.0252	−0.441341
$872$	−14.2163	−0.481425
$873$	−18.3510	−0.621087
$874$	−36.3688	−1.23019
$875$	15.4337	0.521754
$876$	−15.4222	−0.521069
$877$	4.55367	0.153766	0.0768832	−	0.997040i	$-0.475503\pi$
$877$	4.55367	0.153766	0.0768832	+	0.997040i	$0.475503\pi$
$878$	−18.8040	−0.634604
$879$	−20.4966	−0.691334
$880$	−12.1996	−0.411248
$881$	−16.4979	−0.555828	−0.277914	−	0.960606i	$-0.589643\pi$
$881$	−16.4979	−0.555828	−0.277914	+	0.960606i	$0.589643\pi$
$882$	−7.20905	−0.242741
$883$	−43.4286	−1.46149	−0.730744	−	0.682652i	$-0.760827\pi$
$883$	−43.4286	−1.46149	−0.730744	+	0.682652i	$0.760827\pi$
$884$	−34.0219	−1.14428
$885$	−18.3489	−0.616790
$886$	−16.7817	−0.563794
$887$	−9.36355	−0.314397	−0.157199	−	0.987567i	$-0.550246\pi$
$887$	−9.36355	−0.314397	−0.157199	+	0.987567i	$0.550246\pi$
$888$	−1.92786	−0.0646949
$889$	−26.1165	−0.875920
$890$	6.70426	0.224727
$891$	−10.2751	−0.344230
$892$	29.2824	0.980447
$893$	43.1406	1.44365
$894$	14.0271	0.469136
$895$	−5.12058	−0.171162
$896$	−1.52017	−0.0507854
$897$	39.3481	1.31380
$898$	−29.1983	−0.974360
$899$	−16.6835	−0.556427
$900$	−1.19211	−0.0397371
$901$	62.7188	2.08947
$902$	−49.2216	−1.63890
$903$	17.0263	0.566600
$904$	−12.7024	−0.422476
$905$	−44.6010	−1.48259
$906$	1.38221	0.0459208
$907$	−43.0813	−1.43049	−0.715246	−	0.698873i	$-0.753685\pi$
$907$	−43.0813	−1.43049	−0.715246	+	0.698873i	$0.753685\pi$
$908$	−5.90479	−0.195957
$909$	22.3345	0.740788
$910$	18.6691	0.618874
$911$	−3.70489	−0.122749	−0.0613743	−	0.998115i	$-0.519548\pi$
$911$	−3.70489	−0.122749	−0.0613743	+	0.998115i	$0.519548\pi$
$912$	6.90820	0.228753
$913$	−3.50019	−0.115839
$914$	−6.74219	−0.223012
$915$	−23.1905	−0.766654
$916$	14.2761	0.471695
$917$	7.94928	0.262508
$918$	36.5333	1.20578
$919$	42.2046	1.39220	0.696101	−	0.717944i	$-0.254917\pi$
$919$	42.2046	1.39220	0.696101	+	0.717944i	$0.254917\pi$
$920$	−15.3009	−0.504454
$921$	−22.3390	−0.736093
$922$	−17.8901	−0.589180
$923$	10.1671	0.334654
$924$	−9.33272	−0.307024
$925$	−1.23607	−0.0406417
$926$	−17.2936	−0.568304
$927$	15.5353	0.510246
$928$	6.00511	0.197127
$929$	−40.9616	−1.34391	−0.671954	−	0.740593i	$-0.734545\pi$
$929$	−40.9616	−1.34391	−0.671954	+	0.740593i	$0.734545\pi$
$930$	−8.07456	−0.264775
$931$	26.7850	0.877843
$932$	−27.0850	−0.887198
$933$	−16.8273	−0.550901
$934$	3.00187	0.0982243
$935$	81.2205	2.65619
$936$	7.85652	0.256798
$937$	−11.2419	−0.367258	−0.183629	−	0.982996i	$-0.558785\pi$
$937$	−11.2419	−0.367258	−0.183629	+	0.982996i	$0.558785\pi$
$938$	3.87470	0.126513
$939$	−26.5658	−0.866942
$940$	18.1498	0.591983
$941$	1.14007	0.0371652	0.0185826	−	0.999827i	$-0.494085\pi$
$941$	1.14007	0.0371652	0.0185826	+	0.999827i	$0.494085\pi$
$942$	−14.7967	−0.482102
$943$	−61.7342	−2.01034
$944$	−6.31332	−0.205481
$945$	−20.0472	−0.652135
$946$	47.0134	1.52854
$947$	−20.5389	−0.667424	−0.333712	−	0.942675i	$-0.608301\pi$
$947$	−20.5389	−0.667424	−0.333712	+	0.942675i	$0.608301\pi$
$948$	−4.40555	−0.143086
$949$	65.1667	2.11540
$950$	4.42926	0.143704
$951$	4.08853	0.132580
$952$	10.1208	0.328016
$953$	−18.6016	−0.602567	−0.301283	−	0.953535i	$-0.597415\pi$
$953$	−18.6016	−0.602567	−0.301283	+	0.953535i	$0.597415\pi$
$954$	−14.4833	−0.468916
$955$	−37.5413	−1.21481
$956$	7.97200	0.257833
$957$	36.8668	1.19173
$958$	25.7701	0.832595
$959$	−19.7111	−0.636505
$960$	2.90637	0.0938028
$961$	−23.2815	−0.751015
$962$	8.14619	0.262644
$963$	18.8679	0.608011
$964$	−2.36516	−0.0761767
$965$	44.5595	1.43442
$966$	−11.7052	−0.376608
$967$	−21.3331	−0.686026	−0.343013	−	0.939331i	$-0.611447\pi$
$967$	−21.3331	−0.686026	−0.343013	+	0.939331i	$0.611447\pi$
$968$	−14.7697	−0.474715
$969$	−45.9923	−1.47749
$970$	28.6853	0.921030
$971$	13.0827	0.419844	0.209922	−	0.977718i	$-0.432679\pi$
$971$	13.0827	0.419844	0.209922	+	0.977718i	$0.432679\pi$
$972$	−14.0144	−0.449512
$973$	−1.05294	−0.0337558
$974$	−9.85904	−0.315904
$975$	−4.79210	−0.153470
$976$	−7.97918	−0.255407
$977$	−22.6902	−0.725924	−0.362962	−	0.931804i	$-0.618234\pi$
$977$	−22.6902	−0.725924	−0.362962	+	0.931804i	$0.618234\pi$
$978$	−28.6397	−0.915798
$979$	14.1617	0.452609
$980$	11.2688	0.359969
$981$	−21.8564	−0.697820
$982$	−9.75565	−0.311315
$983$	−51.3612	−1.63817	−0.819084	−	0.573674i	$-0.805518\pi$
$983$	−51.3612	−1.63817	−0.819084	+	0.573674i	$0.805518\pi$
$984$	11.7263	0.373821
$985$	23.9909	0.764412
$986$	−39.9798	−1.27322
$987$	13.8847	0.441954
$988$	−29.1906	−0.928677
$989$	58.9647	1.87497
$990$	−18.7559	−0.596100
$991$	−11.0015	−0.349475	−0.174737	−	0.984615i	$-0.555908\pi$
$991$	−11.0015	−0.349475	−0.174737	+	0.984615i	$0.555908\pi$
$992$	−2.77822	−0.0882087
$993$	−26.5561	−0.842732
$994$	−3.02448	−0.0959308
$995$	−12.8195	−0.406404
$996$	0.833868	0.0264221
$997$	12.2415	0.387693	0.193846	−	0.981032i	$-0.437904\pi$
$997$	12.2415	0.387693	0.193846	+	0.981032i	$0.437904\pi$
$998$	3.06163	0.0969143
$999$	−8.74752	−0.276759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.a.d.1.3	✓	7
3.2	odd	2		4842.2.a.o.1.5		7
4.3	odd	2		4304.2.a.i.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.a.d.1.3	✓	7	1.1	even	1	trivial
4304.2.a.i.1.5		7	4.3	odd	2
4842.2.a.o.1.5		7	3.2	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:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.20937 q^{3} +1.00000 q^{4} -2.40321 q^{5} +1.20937 q^{6} +1.52017 q^{7} -1.00000 q^{8} -1.53742 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.20937 q^{3} +1.00000 q^{4} -2.40321 q^{5} +1.20937 q^{6} +1.52017 q^{7} -1.00000 q^{8} -1.53742 q^{9} +2.40321 q^{10} +5.07638 q^{11} -1.20937 q^{12} +5.11021 q^{13} -1.52017 q^{14} +2.90637 q^{15} +1.00000 q^{16} -6.65764 q^{17} +1.53742 q^{18} -5.71222 q^{19} -2.40321 q^{20} -1.83846 q^{21} -5.07638 q^{22} -6.36685 q^{23} +1.20937 q^{24} +0.775401 q^{25} -5.11021 q^{26} +5.48743 q^{27} +1.52017 q^{28} -6.00511 q^{29} -2.90637 q^{30} +2.77822 q^{31} -1.00000 q^{32} -6.13924 q^{33} +6.65764 q^{34} -3.65329 q^{35} -1.53742 q^{36} -1.59410 q^{37} +5.71222 q^{38} -6.18015 q^{39} +2.40321 q^{40} +9.69619 q^{41} +1.83846 q^{42} -9.26120 q^{43} +5.07638 q^{44} +3.69473 q^{45} +6.36685 q^{46} -7.55235 q^{47} -1.20937 q^{48} -4.68907 q^{49} -0.775401 q^{50} +8.05157 q^{51} +5.11021 q^{52} -9.42058 q^{53} -5.48743 q^{54} -12.1996 q^{55} -1.52017 q^{56} +6.90820 q^{57} +6.00511 q^{58} -6.31332 q^{59} +2.90637 q^{60} -7.97918 q^{61} -2.77822 q^{62} -2.33714 q^{63} +1.00000 q^{64} -12.2809 q^{65} +6.13924 q^{66} -2.54885 q^{67} -6.65764 q^{68} +7.69990 q^{69} +3.65329 q^{70} +1.98957 q^{71} +1.53742 q^{72} +12.7523 q^{73} +1.59410 q^{74} -0.937750 q^{75} -5.71222 q^{76} +7.71699 q^{77} +6.18015 q^{78} +3.64283 q^{79} -2.40321 q^{80} -2.02411 q^{81} -9.69619 q^{82} -0.689504 q^{83} -1.83846 q^{84} +15.9997 q^{85} +9.26120 q^{86} +7.26242 q^{87} -5.07638 q^{88} +2.78972 q^{89} -3.69473 q^{90} +7.76841 q^{91} -6.36685 q^{92} -3.35991 q^{93} +7.55235 q^{94} +13.7276 q^{95} +1.20937 q^{96} +11.9363 q^{97} +4.68907 q^{98} -7.80451 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 4 q^{3} + 7 q^{4} - 6 q^{5} + 4 q^{6} - 3 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 4 * q^3 + 7 * q^4 - 6 * q^5 + 4 * q^6 - 3 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 4 q^{3} + 7 q^{4} - 6 q^{5} + 4 q^{6} - 3 q^{7} - 7 q^{8} + 7 q^{9} + 6 q^{10} - 12 q^{11} - 4 q^{12} + 3 q^{13} + 3 q^{14} - 6 q^{15} + 7 q^{16} - 8 q^{17} - 7 q^{18} - 7 q^{19} - 6 q^{20} - 5 q^{21} + 12 q^{22} - 22 q^{23} + 4 q^{24} + 9 q^{25} - 3 q^{26} - 22 q^{27} - 3 q^{28} - 7 q^{29} + 6 q^{30} - 3 q^{31} - 7 q^{32} - 19 q^{33} + 8 q^{34} - 25 q^{35} + 7 q^{36} - 13 q^{37} + 7 q^{38} + q^{39} + 6 q^{40} - 11 q^{41} + 5 q^{42} - 14 q^{43} - 12 q^{44} - 17 q^{45} + 22 q^{46} - 23 q^{47} - 4 q^{48} + 6 q^{49} - 9 q^{50} - 21 q^{51} + 3 q^{52} - 21 q^{53} + 22 q^{54} + 15 q^{55} + 3 q^{56} - 14 q^{57} + 7 q^{58} - 20 q^{59} - 6 q^{60} + 13 q^{61} + 3 q^{62} - 12 q^{63} + 7 q^{64} - 29 q^{65} + 19 q^{66} - 30 q^{67} - 8 q^{68} + 13 q^{69} + 25 q^{70} - 23 q^{71} - 7 q^{72} + 9 q^{73} + 13 q^{74} + 3 q^{75} - 7 q^{76} + 8 q^{77} - q^{78} + 11 q^{79} - 6 q^{80} + 43 q^{81} + 11 q^{82} - 3 q^{83} - 5 q^{84} + 21 q^{85} + 14 q^{86} + 28 q^{87} + 12 q^{88} + 16 q^{89} + 17 q^{90} - 10 q^{91} - 22 q^{92} - 13 q^{93} + 23 q^{94} + 4 q^{96} + 21 q^{97} - 6 q^{98} - 9 q^{99}+O(q^{100}) \) 7 * q - 7 * q^2 - 4 * q^3 + 7 * q^4 - 6 * q^5 + 4 * q^6 - 3 * q^7 - 7 * q^8 + 7 * q^9 + 6 * q^10 - 12 * q^11 - 4 * q^12 + 3 * q^13 + 3 * q^14 - 6 * q^15 + 7 * q^16 - 8 * q^17 - 7 * q^18 - 7 * q^19 - 6 * q^20 - 5 * q^21 + 12 * q^22 - 22 * q^23 + 4 * q^24 + 9 * q^25 - 3 * q^26 - 22 * q^27 - 3 * q^28 - 7 * q^29 + 6 * q^30 - 3 * q^31 - 7 * q^32 - 19 * q^33 + 8 * q^34 - 25 * q^35 + 7 * q^36 - 13 * q^37 + 7 * q^38 + q^39 + 6 * q^40 - 11 * q^41 + 5 * q^42 - 14 * q^43 - 12 * q^44 - 17 * q^45 + 22 * q^46 - 23 * q^47 - 4 * q^48 + 6 * q^49 - 9 * q^50 - 21 * q^51 + 3 * q^52 - 21 * q^53 + 22 * q^54 + 15 * q^55 + 3 * q^56 - 14 * q^57 + 7 * q^58 - 20 * q^59 - 6 * q^60 + 13 * q^61 + 3 * q^62 - 12 * q^63 + 7 * q^64 - 29 * q^65 + 19 * q^66 - 30 * q^67 - 8 * q^68 + 13 * q^69 + 25 * q^70 - 23 * q^71 - 7 * q^72 + 9 * q^73 + 13 * q^74 + 3 * q^75 - 7 * q^76 + 8 * q^77 - q^78 + 11 * q^79 - 6 * q^80 + 43 * q^81 + 11 * q^82 - 3 * q^83 - 5 * q^84 + 21 * q^85 + 14 * q^86 + 28 * q^87 + 12 * q^88 + 16 * q^89 + 17 * q^90 - 10 * q^91 - 22 * q^92 - 13 * q^93 + 23 * q^94 + 4 * q^96 + 21 * q^97 - 6 * q^98 - 9 * q^99

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