LMFDB - Embedded newform 4026.2.a.x.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4026,2,Mod(1,4026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.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:	$32.1477718538$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.46101901.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 5x^{4} + 12x^{3} + 6x^{2} - 5x - 2 $ x^6 - 3x^5 - 5x^4 + 12x^3 + 6x^2 - 5*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.702675$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40842 q^{5} -1.00000 q^{6} -3.03430 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40842 q^{5} -1.00000 q^{6} -3.03430 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.40842 q^{10} -1.00000 q^{11} -1.00000 q^{12} +3.73698 q^{13} -3.03430 q^{14} -1.40842 q^{15} +1.00000 q^{16} -7.21005 q^{17} +1.00000 q^{18} +6.74572 q^{19} +1.40842 q^{20} +3.03430 q^{21} -1.00000 q^{22} -5.31695 q^{23} -1.00000 q^{24} -3.01635 q^{25} +3.73698 q^{26} -1.00000 q^{27} -3.03430 q^{28} -10.4311 q^{29} -1.40842 q^{30} -0.0646549 q^{31} +1.00000 q^{32} +1.00000 q^{33} -7.21005 q^{34} -4.27358 q^{35} +1.00000 q^{36} +1.89946 q^{37} +6.74572 q^{38} -3.73698 q^{39} +1.40842 q^{40} -7.30675 q^{41} +3.03430 q^{42} +9.52587 q^{43} -1.00000 q^{44} +1.40842 q^{45} -5.31695 q^{46} +4.75913 q^{47} -1.00000 q^{48} +2.20698 q^{49} -3.01635 q^{50} +7.21005 q^{51} +3.73698 q^{52} -7.05339 q^{53} -1.00000 q^{54} -1.40842 q^{55} -3.03430 q^{56} -6.74572 q^{57} -10.4311 q^{58} +2.27606 q^{59} -1.40842 q^{60} +1.00000 q^{61} -0.0646549 q^{62} -3.03430 q^{63} +1.00000 q^{64} +5.26324 q^{65} +1.00000 q^{66} -8.39590 q^{67} -7.21005 q^{68} +5.31695 q^{69} -4.27358 q^{70} -2.31627 q^{71} +1.00000 q^{72} +6.68527 q^{73} +1.89946 q^{74} +3.01635 q^{75} +6.74572 q^{76} +3.03430 q^{77} -3.73698 q^{78} -16.0892 q^{79} +1.40842 q^{80} +1.00000 q^{81} -7.30675 q^{82} +2.10515 q^{83} +3.03430 q^{84} -10.1548 q^{85} +9.52587 q^{86} +10.4311 q^{87} -1.00000 q^{88} +6.76628 q^{89} +1.40842 q^{90} -11.3391 q^{91} -5.31695 q^{92} +0.0646549 q^{93} +4.75913 q^{94} +9.50083 q^{95} -1.00000 q^{96} +14.0271 q^{97} +2.20698 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + q^14 + 6 * q^15 + 6 * q^16 - 13 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - q^21 - 6 * q^22 - 11 * q^23 - 6 * q^24 + 8 * q^25 + 2 * q^26 - 6 * q^27 + q^28 - 14 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + 6 * q^33 - 13 * q^34 - 13 * q^35 + 6 * q^36 - 6 * q^37 + q^38 - 2 * q^39 - 6 * q^40 - 25 * q^41 - q^42 + 19 * q^43 - 6 * q^44 - 6 * q^45 - 11 * q^46 - 10 * q^47 - 6 * q^48 - 5 * q^49 + 8 * q^50 + 13 * q^51 + 2 * q^52 - 17 * q^53 - 6 * q^54 + 6 * q^55 + q^56 - q^57 - 14 * q^58 - 14 * q^59 + 6 * q^60 + 6 * q^61 - 5 * q^62 + q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 12 * q^67 - 13 * q^68 + 11 * q^69 - 13 * q^70 + 6 * q^71 + 6 * q^72 - 29 * q^73 - 6 * q^74 - 8 * q^75 + q^76 - q^77 - 2 * q^78 - 24 * q^79 - 6 * q^80 + 6 * q^81 - 25 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 19 * q^86 + 14 * q^87 - 6 * q^88 - 4 * q^89 - 6 * q^90 - 29 * q^91 - 11 * q^92 + 5 * q^93 - 10 * q^94 - 27 * q^95 - 6 * q^96 - 5 * q^97 - 5 * q^98 - 6 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.40842	0.629866	0.314933	−	0.949114i	$-0.398018\pi$
$5$	1.40842	0.629866	0.314933	+	0.949114i	$0.398018\pi$
$6$	−1.00000	−0.408248
$7$	−3.03430	−1.14686	−0.573429	−	0.819255i	$-0.694387\pi$
$7$	−3.03430	−1.14686	−0.573429	+	0.819255i	$0.694387\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.40842	0.445382
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.00000	−0.288675
$13$	3.73698	1.03645	0.518225	−	0.855244i	$-0.326593\pi$
$13$	3.73698	1.03645	0.518225	+	0.855244i	$0.326593\pi$
$14$	−3.03430	−0.810951
$15$	−1.40842	−0.363653
$16$	1.00000	0.250000
$17$	−7.21005	−1.74869	−0.874347	−	0.485301i	$-0.838710\pi$
$17$	−7.21005	−1.74869	−0.874347	+	0.485301i	$0.838710\pi$
$18$	1.00000	0.235702
$19$	6.74572	1.54757	0.773787	−	0.633445i	$-0.218360\pi$
$19$	6.74572	1.54757	0.773787	+	0.633445i	$0.218360\pi$
$20$	1.40842	0.314933
$21$	3.03430	0.662139
$22$	−1.00000	−0.213201
$23$	−5.31695	−1.10866	−0.554330	−	0.832297i	$-0.687025\pi$
$23$	−5.31695	−1.10866	−0.554330	+	0.832297i	$0.687025\pi$
$24$	−1.00000	−0.204124
$25$	−3.01635	−0.603269
$26$	3.73698	0.732881
$27$	−1.00000	−0.192450
$28$	−3.03430	−0.573429
$29$	−10.4311	−1.93701	−0.968505	−	0.248994i	$-0.919900\pi$
$29$	−10.4311	−1.93701	−0.968505	+	0.248994i	$0.919900\pi$
$30$	−1.40842	−0.257142
$31$	−0.0646549	−0.0116124	−0.00580618	−	0.999983i	$-0.501848\pi$
$31$	−0.0646549	−0.0116124	−0.00580618	+	0.999983i	$0.501848\pi$
$32$	1.00000	0.176777
$33$	1.00000	0.174078
$34$	−7.21005	−1.23651
$35$	−4.27358	−0.722367
$36$	1.00000	0.166667
$37$	1.89946	0.312269	0.156134	−	0.987736i	$-0.450097\pi$
$37$	1.89946	0.312269	0.156134	+	0.987736i	$0.450097\pi$
$38$	6.74572	1.09430
$39$	−3.73698	−0.598395
$40$	1.40842	0.222691
$41$	−7.30675	−1.14112	−0.570561	−	0.821255i	$-0.693274\pi$
$41$	−7.30675	−1.14112	−0.570561	+	0.821255i	$0.693274\pi$
$42$	3.03430	0.468203
$43$	9.52587	1.45268	0.726341	−	0.687335i	$-0.241219\pi$
$43$	9.52587	1.45268	0.726341	+	0.687335i	$0.241219\pi$
$44$	−1.00000	−0.150756
$45$	1.40842	0.209955
$46$	−5.31695	−0.783941
$47$	4.75913	0.694191	0.347095	−	0.937830i	$-0.387168\pi$
$47$	4.75913	0.694191	0.347095	+	0.937830i	$0.387168\pi$
$48$	−1.00000	−0.144338
$49$	2.20698	0.315283
$50$	−3.01635	−0.426576
$51$	7.21005	1.00961
$52$	3.73698	0.518225
$53$	−7.05339	−0.968857	−0.484428	−	0.874831i	$-0.660972\pi$
$53$	−7.05339	−0.968857	−0.484428	+	0.874831i	$0.660972\pi$
$54$	−1.00000	−0.136083
$55$	−1.40842	−0.189912
$56$	−3.03430	−0.405475
$57$	−6.74572	−0.893493
$58$	−10.4311	−1.36967
$59$	2.27606	0.296318	0.148159	−	0.988964i	$-0.452665\pi$
$59$	2.27606	0.296318	0.148159	+	0.988964i	$0.452665\pi$
$60$	−1.40842	−0.181827
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−0.0646549	−0.00821118
$63$	−3.03430	−0.382286
$64$	1.00000	0.125000
$65$	5.26324	0.652825
$66$	1.00000	0.123091
$67$	−8.39590	−1.02572	−0.512861	−	0.858471i	$-0.671415\pi$
$67$	−8.39590	−1.02572	−0.512861	+	0.858471i	$0.671415\pi$
$68$	−7.21005	−0.874347
$69$	5.31695	0.640085
$70$	−4.27358	−0.510790
$71$	−2.31627	−0.274891	−0.137445	−	0.990509i	$-0.543889\pi$
$71$	−2.31627	−0.274891	−0.137445	+	0.990509i	$0.543889\pi$
$72$	1.00000	0.117851
$73$	6.68527	0.782452	0.391226	−	0.920295i	$-0.372051\pi$
$73$	6.68527	0.782452	0.391226	+	0.920295i	$0.372051\pi$
$74$	1.89946	0.220807
$75$	3.01635	0.348298
$76$	6.74572	0.773787
$77$	3.03430	0.345791
$78$	−3.73698	−0.423129
$79$	−16.0892	−1.81017	−0.905085	−	0.425230i	$-0.860193\pi$
$79$	−16.0892	−1.81017	−0.905085	+	0.425230i	$0.860193\pi$
$80$	1.40842	0.157466
$81$	1.00000	0.111111
$82$	−7.30675	−0.806895
$83$	2.10515	0.231070	0.115535	−	0.993303i	$-0.463142\pi$
$83$	2.10515	0.231070	0.115535	+	0.993303i	$0.463142\pi$
$84$	3.03430	0.331069
$85$	−10.1548	−1.10144
$86$	9.52587	1.02720
$87$	10.4311	1.11833
$88$	−1.00000	−0.106600
$89$	6.76628	0.717224	0.358612	−	0.933487i	$-0.383250\pi$
$89$	6.76628	0.717224	0.358612	+	0.933487i	$0.383250\pi$
$90$	1.40842	0.148461
$91$	−11.3391	−1.18866
$92$	−5.31695	−0.554330
$93$	0.0646549	0.00670440
$94$	4.75913	0.490867
$95$	9.50083	0.974765
$96$	−1.00000	−0.102062
$97$	14.0271	1.42424	0.712118	−	0.702060i	$-0.247736\pi$
$97$	14.0271	1.42424	0.712118	+	0.702060i	$0.247736\pi$
$98$	2.20698	0.222939
$99$	−1.00000	−0.100504
$100$	−3.01635	−0.301635
$101$	−13.6600	−1.35922	−0.679612	−	0.733571i	$-0.737852\pi$
$101$	−13.6600	−1.35922	−0.679612	+	0.733571i	$0.737852\pi$
$102$	7.21005	0.713902
$103$	−3.41695	−0.336683	−0.168341	−	0.985729i	$-0.553841\pi$
$103$	−3.41695	−0.336683	−0.168341	+	0.985729i	$0.553841\pi$
$104$	3.73698	0.366441
$105$	4.27358	0.417058
$106$	−7.05339	−0.685085
$107$	−11.7043	−1.13150	−0.565751	−	0.824576i	$-0.691413\pi$
$107$	−11.7043	−1.13150	−0.565751	+	0.824576i	$0.691413\pi$
$108$	−1.00000	−0.0962250
$109$	−9.74822	−0.933710	−0.466855	−	0.884334i	$-0.654613\pi$
$109$	−9.74822	−0.933710	−0.466855	+	0.884334i	$0.654613\pi$
$110$	−1.40842	−0.134288
$111$	−1.89946	−0.180288
$112$	−3.03430	−0.286714
$113$	−16.3317	−1.53636	−0.768178	−	0.640237i	$-0.778836\pi$
$113$	−16.3317	−1.53636	−0.768178	+	0.640237i	$0.778836\pi$
$114$	−6.74572	−0.631795
$115$	−7.48851	−0.698307
$116$	−10.4311	−0.968505
$117$	3.73698	0.345483
$118$	2.27606	0.209528
$119$	21.8775	2.00550
$120$	−1.40842	−0.128571
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	7.30675	0.658827
$124$	−0.0646549	−0.00580618
$125$	−11.2904	−1.00984
$126$	−3.03430	−0.270317
$127$	5.54313	0.491873	0.245937	−	0.969286i	$-0.420905\pi$
$127$	5.54313	0.491873	0.245937	+	0.969286i	$0.420905\pi$
$128$	1.00000	0.0883883
$129$	−9.52587	−0.838706
$130$	5.26324	0.461617
$131$	−10.9765	−0.959019	−0.479509	−	0.877537i	$-0.659185\pi$
$131$	−10.9765	−0.959019	−0.479509	+	0.877537i	$0.659185\pi$
$132$	1.00000	0.0870388
$133$	−20.4686	−1.77485
$134$	−8.39590	−0.725296
$135$	−1.40842	−0.121218
$136$	−7.21005	−0.618257
$137$	12.7683	1.09087	0.545434	−	0.838154i	$-0.316365\pi$
$137$	12.7683	1.09087	0.545434	+	0.838154i	$0.316365\pi$
$138$	5.31695	0.452609
$139$	2.78236	0.235997	0.117998	−	0.993014i	$-0.462352\pi$
$139$	2.78236	0.235997	0.117998	+	0.993014i	$0.462352\pi$
$140$	−4.27358	−0.361183
$141$	−4.75913	−0.400791
$142$	−2.31627	−0.194377
$143$	−3.73698	−0.312502
$144$	1.00000	0.0833333
$145$	−14.6914	−1.22006
$146$	6.68527	0.553277
$147$	−2.20698	−0.182029
$148$	1.89946	0.156134
$149$	−6.32694	−0.518323	−0.259162	−	0.965834i	$-0.583446\pi$
$149$	−6.32694	−0.518323	−0.259162	+	0.965834i	$0.583446\pi$
$150$	3.01635	0.246284
$151$	−10.4838	−0.853157	−0.426579	−	0.904451i	$-0.640281\pi$
$151$	−10.4838	−0.853157	−0.426579	+	0.904451i	$0.640281\pi$
$152$	6.74572	0.547150
$153$	−7.21005	−0.582898
$154$	3.03430	0.244511
$155$	−0.0910614	−0.00731423
$156$	−3.73698	−0.299197
$157$	−20.6648	−1.64923	−0.824614	−	0.565695i	$-0.808608\pi$
$157$	−20.6648	−1.64923	−0.824614	+	0.565695i	$0.808608\pi$
$158$	−16.0892	−1.27998
$159$	7.05339	0.559370
$160$	1.40842	0.111346
$161$	16.1332	1.27148
$162$	1.00000	0.0785674
$163$	−7.65605	−0.599668	−0.299834	−	0.953991i	$-0.596931\pi$
$163$	−7.65605	−0.599668	−0.299834	+	0.953991i	$0.596931\pi$
$164$	−7.30675	−0.570561
$165$	1.40842	0.109646
$166$	2.10515	0.163391
$167$	23.3019	1.80316	0.901578	−	0.432617i	$-0.142410\pi$
$167$	23.3019	1.80316	0.901578	+	0.432617i	$0.142410\pi$
$168$	3.03430	0.234101
$169$	0.964983	0.0742295
$170$	−10.1548	−0.778838
$171$	6.74572	0.515858
$172$	9.52587	0.726341
$173$	−14.4732	−1.10038	−0.550188	−	0.835041i	$-0.685444\pi$
$173$	−14.4732	−1.10038	−0.550188	+	0.835041i	$0.685444\pi$
$174$	10.4311	0.790781
$175$	9.15250	0.691864
$176$	−1.00000	−0.0753778
$177$	−2.27606	−0.171079
$178$	6.76628	0.507154
$179$	−13.1880	−0.985718	−0.492859	−	0.870109i	$-0.664048\pi$
$179$	−13.1880	−0.985718	−0.492859	+	0.870109i	$0.664048\pi$
$180$	1.40842	0.104978
$181$	−5.51177	−0.409686	−0.204843	−	0.978795i	$-0.565668\pi$
$181$	−5.51177	−0.409686	−0.204843	+	0.978795i	$0.565668\pi$
$182$	−11.3391	−0.840510
$183$	−1.00000	−0.0739221
$184$	−5.31695	−0.391971
$185$	2.67524	0.196687
$186$	0.0646549	0.00474072
$187$	7.21005	0.527251
$188$	4.75913	0.347095
$189$	3.03430	0.220713
$190$	9.50083	0.689263
$191$	23.6388	1.71044	0.855221	−	0.518263i	$-0.173421\pi$
$191$	23.6388	1.71044	0.855221	+	0.518263i	$0.173421\pi$
$192$	−1.00000	−0.0721688
$193$	−20.4144	−1.46946	−0.734732	−	0.678357i	$-0.762692\pi$
$193$	−20.4144	−1.46946	−0.734732	+	0.678357i	$0.762692\pi$
$194$	14.0271	1.00709
$195$	−5.26324	−0.376909
$196$	2.20698	0.157641
$197$	14.3631	1.02333	0.511663	−	0.859186i	$-0.329030\pi$
$197$	14.3631	1.02333	0.511663	+	0.859186i	$0.329030\pi$
$198$	−1.00000	−0.0710669
$199$	20.5789	1.45880	0.729399	−	0.684089i	$-0.239800\pi$
$199$	20.5789	1.45880	0.729399	+	0.684089i	$0.239800\pi$
$200$	−3.01635	−0.213288
$201$	8.39590	0.592201
$202$	−13.6600	−0.961117
$203$	31.6511	2.22147
$204$	7.21005	0.504805
$205$	−10.2910	−0.718754
$206$	−3.41695	−0.238071
$207$	−5.31695	−0.369553
$208$	3.73698	0.259113
$209$	−6.74572	−0.466611
$210$	4.27358	0.294905
$211$	21.4537	1.47693	0.738466	−	0.674291i	$-0.235551\pi$
$211$	21.4537	1.47693	0.738466	+	0.674291i	$0.235551\pi$
$212$	−7.05339	−0.484428
$213$	2.31627	0.158708
$214$	−11.7043	−0.800092
$215$	13.4165	0.914994
$216$	−1.00000	−0.0680414
$217$	0.196182	0.0133177
$218$	−9.74822	−0.660233
$219$	−6.68527	−0.451749
$220$	−1.40842	−0.0949558
$221$	−26.9438	−1.81244
$222$	−1.89946	−0.127483
$223$	−27.5859	−1.84729	−0.923643	−	0.383253i	$-0.874804\pi$
$223$	−27.5859	−1.84729	−0.923643	+	0.383253i	$0.874804\pi$
$224$	−3.03430	−0.202738
$225$	−3.01635	−0.201090
$226$	−16.3317	−1.08637
$227$	−8.24093	−0.546970	−0.273485	−	0.961876i	$-0.588176\pi$
$227$	−8.24093	−0.546970	−0.273485	+	0.961876i	$0.588176\pi$
$228$	−6.74572	−0.446746
$229$	−6.01323	−0.397365	−0.198683	−	0.980064i	$-0.563666\pi$
$229$	−6.01323	−0.397365	−0.198683	+	0.980064i	$0.563666\pi$
$230$	−7.48851	−0.493778
$231$	−3.03430	−0.199642
$232$	−10.4311	−0.684836
$233$	11.4829	0.752271	0.376135	−	0.926565i	$-0.377253\pi$
$233$	11.4829	0.752271	0.376135	+	0.926565i	$0.377253\pi$
$234$	3.73698	0.244294
$235$	6.70287	0.437247
$236$	2.27606	0.148159
$237$	16.0892	1.04510
$238$	21.8775	1.41811
$239$	11.5750	0.748728	0.374364	−	0.927282i	$-0.377861\pi$
$239$	11.5750	0.748728	0.374364	+	0.927282i	$0.377861\pi$
$240$	−1.40842	−0.0909133
$241$	−19.9827	−1.28720	−0.643601	−	0.765362i	$-0.722560\pi$
$241$	−19.9827	−1.28720	−0.643601	+	0.765362i	$0.722560\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	3.10836	0.198586
$246$	7.30675	0.465861
$247$	25.2086	1.60398
$248$	−0.0646549	−0.00410559
$249$	−2.10515	−0.133408
$250$	−11.2904	−0.714068
$251$	5.90735	0.372869	0.186434	−	0.982467i	$-0.440307\pi$
$251$	5.90735	0.372869	0.186434	+	0.982467i	$0.440307\pi$
$252$	−3.03430	−0.191143
$253$	5.31695	0.334274
$254$	5.54313	0.347807
$255$	10.1548	0.635918
$256$	1.00000	0.0625000
$257$	18.9700	1.18332	0.591658	−	0.806189i	$-0.298474\pi$
$257$	18.9700	1.18332	0.591658	+	0.806189i	$0.298474\pi$
$258$	−9.52587	−0.593055
$259$	−5.76352	−0.358128
$260$	5.26324	0.326412
$261$	−10.4311	−0.645670
$262$	−10.9765	−0.678128
$263$	−5.53289	−0.341173	−0.170586	−	0.985343i	$-0.554566\pi$
$263$	−5.53289	−0.341173	−0.170586	+	0.985343i	$0.554566\pi$
$264$	1.00000	0.0615457
$265$	−9.93415	−0.610250
$266$	−20.4686	−1.25501
$267$	−6.76628	−0.414089
$268$	−8.39590	−0.512861
$269$	−27.2840	−1.66353	−0.831766	−	0.555126i	$-0.812670\pi$
$269$	−27.2840	−1.66353	−0.831766	+	0.555126i	$0.812670\pi$
$270$	−1.40842	−0.0857139
$271$	−1.23156	−0.0748119	−0.0374060	−	0.999300i	$-0.511909\pi$
$271$	−1.23156	−0.0748119	−0.0374060	+	0.999300i	$0.511909\pi$
$272$	−7.21005	−0.437174
$273$	11.3391	0.686274
$274$	12.7683	0.771360
$275$	3.01635	0.181892
$276$	5.31695	0.320043
$277$	−9.30982	−0.559373	−0.279686	−	0.960091i	$-0.590230\pi$
$277$	−9.30982	−0.559373	−0.279686	+	0.960091i	$0.590230\pi$
$278$	2.78236	0.166875
$279$	−0.0646549	−0.00387079
$280$	−4.27358	−0.255395
$281$	−27.6316	−1.64836	−0.824182	−	0.566325i	$-0.808365\pi$
$281$	−27.6316	−1.64836	−0.824182	+	0.566325i	$0.808365\pi$
$282$	−4.75913	−0.283402
$283$	4.09935	0.243681	0.121841	−	0.992550i	$-0.461120\pi$
$283$	4.09935	0.243681	0.121841	+	0.992550i	$0.461120\pi$
$284$	−2.31627	−0.137445
$285$	−9.50083	−0.562781
$286$	−3.73698	−0.220972
$287$	22.1709	1.30871
$288$	1.00000	0.0589256
$289$	34.9849	2.05793
$290$	−14.6914	−0.862710
$291$	−14.0271	−0.822283
$292$	6.68527	0.391226
$293$	−1.60737	−0.0939034	−0.0469517	−	0.998897i	$-0.514951\pi$
$293$	−1.60737	−0.0939034	−0.0469517	+	0.998897i	$0.514951\pi$
$294$	−2.20698	−0.128714
$295$	3.20565	0.186640
$296$	1.89946	0.110404
$297$	1.00000	0.0580259
$298$	−6.32694	−0.366510
$299$	−19.8693	−1.14907
$300$	3.01635	0.174149
$301$	−28.9044	−1.66602
$302$	−10.4838	−0.603273
$303$	13.6600	0.784749
$304$	6.74572	0.386894
$305$	1.40842	0.0806461
$306$	−7.21005	−0.412171
$307$	32.7234	1.86762	0.933812	−	0.357765i	$-0.116461\pi$
$307$	32.7234	1.86762	0.933812	+	0.357765i	$0.116461\pi$
$308$	3.03430	0.172895
$309$	3.41695	0.194384
$310$	−0.0910614	−0.00517194
$311$	−8.31320	−0.471398	−0.235699	−	0.971826i	$-0.575738\pi$
$311$	−8.31320	−0.471398	−0.235699	+	0.971826i	$0.575738\pi$
$312$	−3.73698	−0.211565
$313$	19.4825	1.10122	0.550608	−	0.834764i	$-0.314396\pi$
$313$	19.4825	1.10122	0.550608	+	0.834764i	$0.314396\pi$
$314$	−20.6648	−1.16618
$315$	−4.27358	−0.240789
$316$	−16.0892	−0.905085
$317$	3.27526	0.183957	0.0919785	−	0.995761i	$-0.470681\pi$
$317$	3.27526	0.183957	0.0919785	+	0.995761i	$0.470681\pi$
$318$	7.05339	0.395534
$319$	10.4311	0.584030
$320$	1.40842	0.0787332
$321$	11.7043	0.653272
$322$	16.1332	0.899069
$323$	−48.6370	−2.70624
$324$	1.00000	0.0555556
$325$	−11.2720	−0.625258
$326$	−7.65605	−0.424030
$327$	9.74822	0.539078
$328$	−7.30675	−0.403448
$329$	−14.4406	−0.796138
$330$	1.40842	0.0775311
$331$	12.7899	0.702995	0.351497	−	0.936189i	$-0.385673\pi$
$331$	12.7899	0.702995	0.351497	+	0.936189i	$0.385673\pi$
$332$	2.10515	0.115535
$333$	1.89946	0.104090
$334$	23.3019	1.27502
$335$	−11.8250	−0.646068
$336$	3.03430	0.165535
$337$	24.5110	1.33520	0.667599	−	0.744521i	$-0.267322\pi$
$337$	24.5110	1.33520	0.667599	+	0.744521i	$0.267322\pi$
$338$	0.964983	0.0524882
$339$	16.3317	0.887015
$340$	−10.1548	−0.550721
$341$	0.0646549	0.00350126
$342$	6.74572	0.364767
$343$	14.5435	0.785273
$344$	9.52587	0.513600
$345$	7.48851	0.403168
$346$	−14.4732	−0.778083
$347$	11.7048	0.628347	0.314174	−	0.949366i	$-0.398273\pi$
$347$	11.7048	0.628347	0.314174	+	0.949366i	$0.398273\pi$
$348$	10.4311	0.559167
$349$	1.06874	0.0572083	0.0286042	−	0.999591i	$-0.490894\pi$
$349$	1.06874	0.0572083	0.0286042	+	0.999591i	$0.490894\pi$
$350$	9.15250	0.489222
$351$	−3.73698	−0.199465
$352$	−1.00000	−0.0533002
$353$	−13.4233	−0.714448	−0.357224	−	0.934019i	$-0.616277\pi$
$353$	−13.4233	−0.714448	−0.357224	+	0.934019i	$0.616277\pi$
$354$	−2.27606	−0.120971
$355$	−3.26229	−0.173144
$356$	6.76628	0.358612
$357$	−21.8775	−1.15788
$358$	−13.1880	−0.697008
$359$	−1.80284	−0.0951502	−0.0475751	−	0.998868i	$-0.515149\pi$
$359$	−1.80284	−0.0951502	−0.0475751	+	0.998868i	$0.515149\pi$
$360$	1.40842	0.0742304
$361$	26.5048	1.39499
$362$	−5.51177	−0.289692
$363$	−1.00000	−0.0524864
$364$	−11.3391	−0.594331
$365$	9.41569	0.492840
$366$	−1.00000	−0.0522708
$367$	1.20063	0.0626722	0.0313361	−	0.999509i	$-0.490024\pi$
$367$	1.20063	0.0626722	0.0313361	+	0.999509i	$0.490024\pi$
$368$	−5.31695	−0.277165
$369$	−7.30675	−0.380374
$370$	2.67524	0.139079
$371$	21.4021	1.11114
$372$	0.0646549	0.00335220
$373$	29.7593	1.54088	0.770438	−	0.637515i	$-0.220037\pi$
$373$	29.7593	1.54088	0.770438	+	0.637515i	$0.220037\pi$
$374$	7.21005	0.372823
$375$	11.2904	0.583034
$376$	4.75913	0.245434
$377$	−38.9808	−2.00761
$378$	3.03430	0.156068
$379$	−33.8047	−1.73643	−0.868214	−	0.496189i	$-0.834732\pi$
$379$	−33.8047	−1.73643	−0.868214	+	0.496189i	$0.834732\pi$
$380$	9.50083	0.487382
$381$	−5.54313	−0.283983
$382$	23.6388	1.20947
$383$	−29.4868	−1.50671	−0.753353	−	0.657617i	$-0.771565\pi$
$383$	−29.4868	−1.50671	−0.753353	+	0.657617i	$0.771565\pi$
$384$	−1.00000	−0.0510310
$385$	4.27358	0.217802
$386$	−20.4144	−1.03907
$387$	9.52587	0.484227
$388$	14.0271	0.712118
$389$	27.8701	1.41307	0.706536	−	0.707677i	$-0.250257\pi$
$389$	27.8701	1.41307	0.706536	+	0.707677i	$0.250257\pi$
$390$	−5.26324	−0.266515
$391$	38.3355	1.93871
$392$	2.20698	0.111469
$393$	10.9765	0.553690
$394$	14.3631	0.723601
$395$	−22.6603	−1.14016
$396$	−1.00000	−0.0502519
$397$	34.1615	1.71452	0.857259	−	0.514886i	$-0.172166\pi$
$397$	34.1615	1.71452	0.857259	+	0.514886i	$0.172166\pi$
$398$	20.5789	1.03153
$399$	20.4686	1.02471
$400$	−3.01635	−0.150817
$401$	31.0638	1.55125	0.775627	−	0.631192i	$-0.217434\pi$
$401$	31.0638	1.55125	0.775627	+	0.631192i	$0.217434\pi$
$402$	8.39590	0.418750
$403$	−0.241614	−0.0120356
$404$	−13.6600	−0.679612
$405$	1.40842	0.0699851
$406$	31.6511	1.57082
$407$	−1.89946	−0.0941525
$408$	7.21005	0.356951
$409$	−31.2021	−1.54284	−0.771421	−	0.636325i	$-0.780454\pi$
$409$	−31.2021	−1.54284	−0.771421	+	0.636325i	$0.780454\pi$
$410$	−10.2910	−0.508236
$411$	−12.7683	−0.629813
$412$	−3.41695	−0.168341
$413$	−6.90624	−0.339834
$414$	−5.31695	−0.261314
$415$	2.96494	0.145543
$416$	3.73698	0.183220
$417$	−2.78236	−0.136253
$418$	−6.74572	−0.329944
$419$	2.26674	0.110737	0.0553687	−	0.998466i	$-0.482367\pi$
$419$	2.26674	0.110737	0.0553687	+	0.998466i	$0.482367\pi$
$420$	4.27358	0.208529
$421$	−4.03890	−0.196844	−0.0984220	−	0.995145i	$-0.531379\pi$
$421$	−4.03890	−0.196844	−0.0984220	+	0.995145i	$0.531379\pi$
$422$	21.4537	1.04435
$423$	4.75913	0.231397
$424$	−7.05339	−0.342543
$425$	21.7480	1.05493
$426$	2.31627	0.112224
$427$	−3.03430	−0.146840
$428$	−11.7043	−0.565751
$429$	3.73698	0.180423
$430$	13.4165	0.646999
$431$	−0.429194	−0.0206736	−0.0103368	−	0.999947i	$-0.503290\pi$
$431$	−0.429194	−0.0206736	−0.0103368	+	0.999947i	$0.503290\pi$
$432$	−1.00000	−0.0481125
$433$	−1.24263	−0.0597170	−0.0298585	−	0.999554i	$-0.509506\pi$
$433$	−1.24263	−0.0597170	−0.0298585	+	0.999554i	$0.509506\pi$
$434$	0.196182	0.00941705
$435$	14.6914	0.704400
$436$	−9.74822	−0.466855
$437$	−35.8667	−1.71573
$438$	−6.68527	−0.319435
$439$	−36.4916	−1.74165	−0.870825	−	0.491594i	$-0.836414\pi$
$439$	−36.4916	−1.74165	−0.870825	+	0.491594i	$0.836414\pi$
$440$	−1.40842	−0.0671439
$441$	2.20698	0.105094
$442$	−26.9438	−1.28159
$443$	13.6792	0.649917	0.324958	−	0.945728i	$-0.394650\pi$
$443$	13.6792	0.649917	0.324958	+	0.945728i	$0.394650\pi$
$444$	−1.89946	−0.0901442
$445$	9.52978	0.451755
$446$	−27.5859	−1.30623
$447$	6.32694	0.299254
$448$	−3.03430	−0.143357
$449$	−28.5043	−1.34520	−0.672601	−	0.740005i	$-0.734823\pi$
$449$	−28.5043	−1.34520	−0.672601	+	0.740005i	$0.734823\pi$
$450$	−3.01635	−0.142192
$451$	7.30675	0.344061
$452$	−16.3317	−0.768178
$453$	10.4838	0.492570
$454$	−8.24093	−0.386766
$455$	−15.9703	−0.748697
$456$	−6.74572	−0.315897
$457$	−38.3299	−1.79300	−0.896498	−	0.443048i	$-0.853897\pi$
$457$	−38.3299	−1.79300	−0.896498	+	0.443048i	$0.853897\pi$
$458$	−6.01323	−0.280980
$459$	7.21005	0.336536
$460$	−7.48851	−0.349154
$461$	−32.7462	−1.52514	−0.762572	−	0.646904i	$-0.776063\pi$
$461$	−32.7462	−1.52514	−0.762572	+	0.646904i	$0.776063\pi$
$462$	−3.03430	−0.141168
$463$	28.7527	1.33625	0.668127	−	0.744048i	$-0.267096\pi$
$463$	28.7527	1.33625	0.668127	+	0.744048i	$0.267096\pi$
$464$	−10.4311	−0.484252
$465$	0.0910614	0.00422287
$466$	11.4829	0.531936
$467$	21.9657	1.01645	0.508226	−	0.861224i	$-0.330301\pi$
$467$	21.9657	1.01645	0.508226	+	0.861224i	$0.330301\pi$
$468$	3.73698	0.172742
$469$	25.4757	1.17636
$470$	6.70287	0.309180
$471$	20.6648	0.952183
$472$	2.27606	0.104764
$473$	−9.52587	−0.438000
$474$	16.0892	0.738999
$475$	−20.3474	−0.933604
$476$	21.8775	1.00275
$477$	−7.05339	−0.322952
$478$	11.5750	0.529430
$479$	21.0786	0.963107	0.481554	−	0.876417i	$-0.340073\pi$
$479$	21.0786	0.963107	0.481554	+	0.876417i	$0.340073\pi$
$480$	−1.40842	−0.0642854
$481$	7.09822	0.323651
$482$	−19.9827	−0.910189
$483$	−16.1332	−0.734087
$484$	1.00000	0.0454545
$485$	19.7561	0.897077
$486$	−1.00000	−0.0453609
$487$	8.77076	0.397441	0.198720	−	0.980056i	$-0.436321\pi$
$487$	8.77076	0.397441	0.198720	+	0.980056i	$0.436321\pi$
$488$	1.00000	0.0452679
$489$	7.65605	0.346219
$490$	3.10836	0.140421
$491$	−33.8576	−1.52797	−0.763986	−	0.645233i	$-0.776760\pi$
$491$	−33.8576	−1.52797	−0.763986	+	0.645233i	$0.776760\pi$
$492$	7.30675	0.329414
$493$	75.2089	3.38724
$494$	25.2086	1.13419
$495$	−1.40842	−0.0633039
$496$	−0.0646549	−0.00290309
$497$	7.02826	0.315261
$498$	−2.10515	−0.0943339
$499$	14.9697	0.670137	0.335068	−	0.942194i	$-0.391241\pi$
$499$	14.9697	0.670137	0.335068	+	0.942194i	$0.391241\pi$
$500$	−11.2904	−0.504922
$501$	−23.3019	−1.04105
$502$	5.90735	0.263658
$503$	32.4097	1.44507	0.722537	−	0.691332i	$-0.242976\pi$
$503$	32.4097	1.44507	0.722537	+	0.691332i	$0.242976\pi$
$504$	−3.03430	−0.135158
$505$	−19.2391	−0.856129
$506$	5.31695	0.236367
$507$	−0.964983	−0.0428564
$508$	5.54313	0.245937
$509$	33.9646	1.50545	0.752726	−	0.658333i	$-0.228738\pi$
$509$	33.9646	1.50545	0.752726	+	0.658333i	$0.228738\pi$
$510$	10.1548	0.449662
$511$	−20.2851	−0.897361
$512$	1.00000	0.0441942
$513$	−6.74572	−0.297831
$514$	18.9700	0.836731
$515$	−4.81252	−0.212065
$516$	−9.52587	−0.419353
$517$	−4.75913	−0.209306
$518$	−5.76352	−0.253234
$519$	14.4732	0.635302
$520$	5.26324	0.230808
$521$	−5.77628	−0.253064	−0.126532	−	0.991963i	$-0.540385\pi$
$521$	−5.77628	−0.253064	−0.126532	+	0.991963i	$0.540385\pi$
$522$	−10.4311	−0.456558
$523$	11.4889	0.502374	0.251187	−	0.967939i	$-0.419179\pi$
$523$	11.4889	0.502374	0.251187	+	0.967939i	$0.419179\pi$
$524$	−10.9765	−0.479509
$525$	−9.15250	−0.399448
$526$	−5.53289	−0.241245
$527$	0.466165	0.0203065
$528$	1.00000	0.0435194
$529$	5.26992	0.229127
$530$	−9.93415	−0.431512
$531$	2.27606	0.0987725
$532$	−20.4686	−0.887424
$533$	−27.3051	−1.18272
$534$	−6.76628	−0.292805
$535$	−16.4847	−0.712694
$536$	−8.39590	−0.362648
$537$	13.1880	0.569105
$538$	−27.2840	−1.17630
$539$	−2.20698	−0.0950613
$540$	−1.40842	−0.0606089
$541$	0.687754	0.0295689	0.0147844	−	0.999891i	$-0.495294\pi$
$541$	0.687754	0.0295689	0.0147844	+	0.999891i	$0.495294\pi$
$542$	−1.23156	−0.0529000
$543$	5.51177	0.236532
$544$	−7.21005	−0.309128
$545$	−13.7296	−0.588112
$546$	11.3391	0.485269
$547$	−5.93503	−0.253763	−0.126882	−	0.991918i	$-0.540497\pi$
$547$	−5.93503	−0.253763	−0.126882	+	0.991918i	$0.540497\pi$
$548$	12.7683	0.545434
$549$	1.00000	0.0426790
$550$	3.01635	0.128617
$551$	−70.3654	−2.99767
$552$	5.31695	0.226304
$553$	48.8193	2.07601
$554$	−9.30982	−0.395536
$555$	−2.67524	−0.113557
$556$	2.78236	0.117998
$557$	−11.3263	−0.479910	−0.239955	−	0.970784i	$-0.577133\pi$
$557$	−11.3263	−0.479910	−0.239955	+	0.970784i	$0.577133\pi$
$558$	−0.0646549	−0.00273706
$559$	35.5979	1.50563
$560$	−4.27358	−0.180592
$561$	−7.21005	−0.304409
$562$	−27.6316	−1.16557
$563$	10.9215	0.460285	0.230143	−	0.973157i	$-0.426081\pi$
$563$	10.9215	0.460285	0.230143	+	0.973157i	$0.426081\pi$
$564$	−4.75913	−0.200396
$565$	−23.0019	−0.967698
$566$	4.09935	0.172309
$567$	−3.03430	−0.127429
$568$	−2.31627	−0.0971886
$569$	−28.5401	−1.19647	−0.598233	−	0.801322i	$-0.704130\pi$
$569$	−28.5401	−1.19647	−0.598233	+	0.801322i	$0.704130\pi$
$570$	−9.50083	−0.397946
$571$	0.120431	0.00503987	0.00251994	−	0.999997i	$-0.499198\pi$
$571$	0.120431	0.00503987	0.00251994	+	0.999997i	$0.499198\pi$
$572$	−3.73698	−0.156251
$573$	−23.6388	−0.987524
$574$	22.1709	0.925394
$575$	16.0377	0.668820
$576$	1.00000	0.0416667
$577$	−0.358156	−0.0149102	−0.00745512	−	0.999972i	$-0.502373\pi$
$577$	−0.358156	−0.0149102	−0.00745512	+	0.999972i	$0.502373\pi$
$578$	34.9849	1.45518
$579$	20.4144	0.848395
$580$	−14.6914	−0.610028
$581$	−6.38765	−0.265004
$582$	−14.0271	−0.581442
$583$	7.05339	0.292121
$584$	6.68527	0.276638
$585$	5.26324	0.217608
$586$	−1.60737	−0.0663997
$587$	39.4056	1.62644	0.813222	−	0.581953i	$-0.197711\pi$
$587$	39.4056	1.62644	0.813222	+	0.581953i	$0.197711\pi$
$588$	−2.20698	−0.0910143
$589$	−0.436144	−0.0179710
$590$	3.20565	0.131975
$591$	−14.3631	−0.590817
$592$	1.89946	0.0780671
$593$	−12.3710	−0.508016	−0.254008	−	0.967202i	$-0.581749\pi$
$593$	−12.3710	−0.508016	−0.254008	+	0.967202i	$0.581749\pi$
$594$	1.00000	0.0410305
$595$	30.8127	1.26320
$596$	−6.32694	−0.259162
$597$	−20.5789	−0.842237
$598$	−19.8693	−0.812516
$599$	23.8904	0.976135	0.488068	−	0.872806i	$-0.337702\pi$
$599$	23.8904	0.976135	0.488068	+	0.872806i	$0.337702\pi$
$600$	3.01635	0.123142
$601$	1.29880	0.0529790	0.0264895	−	0.999649i	$-0.491567\pi$
$601$	1.29880	0.0529790	0.0264895	+	0.999649i	$0.491567\pi$
$602$	−28.9044	−1.17805
$603$	−8.39590	−0.341908
$604$	−10.4838	−0.426579
$605$	1.40842	0.0572605
$606$	13.6600	0.554901
$607$	−22.0873	−0.896496	−0.448248	−	0.893909i	$-0.647952\pi$
$607$	−22.0873	−0.896496	−0.448248	+	0.893909i	$0.647952\pi$
$608$	6.74572	0.273575
$609$	−31.6511	−1.28257
$610$	1.40842	0.0570254
$611$	17.7848	0.719495
$612$	−7.21005	−0.291449
$613$	−9.98559	−0.403314	−0.201657	−	0.979456i	$-0.564633\pi$
$613$	−9.98559	−0.403314	−0.201657	+	0.979456i	$0.564633\pi$
$614$	32.7234	1.32061
$615$	10.2910	0.414973
$616$	3.03430	0.122255
$617$	30.0394	1.20934	0.604671	−	0.796475i	$-0.293305\pi$
$617$	30.0394	1.20934	0.604671	+	0.796475i	$0.293305\pi$
$618$	3.41695	0.137450
$619$	−37.7101	−1.51570	−0.757849	−	0.652430i	$-0.773749\pi$
$619$	−37.7101	−1.51570	−0.757849	+	0.652430i	$0.773749\pi$
$620$	−0.0910614	−0.00365711
$621$	5.31695	0.213362
$622$	−8.31320	−0.333329
$623$	−20.5309	−0.822554
$624$	−3.73698	−0.149599
$625$	−0.819934	−0.0327974
$626$	19.4825	0.778677
$627$	6.74572	0.269398
$628$	−20.6648	−0.824614
$629$	−13.6952	−0.546062
$630$	−4.27358	−0.170263
$631$	−14.6186	−0.581958	−0.290979	−	0.956729i	$-0.593981\pi$
$631$	−14.6186	−0.581958	−0.290979	+	0.956729i	$0.593981\pi$
$632$	−16.0892	−0.639992
$633$	−21.4537	−0.852707
$634$	3.27526	0.130077
$635$	7.80707	0.309814
$636$	7.05339	0.279685
$637$	8.24743	0.326775
$638$	10.4311	0.412972
$639$	−2.31627	−0.0916303
$640$	1.40842	0.0556728
$641$	−21.7571	−0.859354	−0.429677	−	0.902983i	$-0.641373\pi$
$641$	−21.7571	−0.859354	−0.429677	+	0.902983i	$0.641373\pi$
$642$	11.7043	0.461933
$643$	15.1182	0.596204	0.298102	−	0.954534i	$-0.403647\pi$
$643$	15.1182	0.596204	0.298102	+	0.954534i	$0.403647\pi$
$644$	16.1332	0.635738
$645$	−13.4165	−0.528272
$646$	−48.6370	−1.91360
$647$	−2.47481	−0.0972948	−0.0486474	−	0.998816i	$-0.515491\pi$
$647$	−2.47481	−0.0972948	−0.0486474	+	0.998816i	$0.515491\pi$
$648$	1.00000	0.0392837
$649$	−2.27606	−0.0893431
$650$	−11.2720	−0.442125
$651$	−0.196182	−0.00768899
$652$	−7.65605	−0.299834
$653$	38.2987	1.49874	0.749372	−	0.662149i	$-0.230356\pi$
$653$	38.2987	1.49874	0.749372	+	0.662149i	$0.230356\pi$
$654$	9.74822	0.381186
$655$	−15.4595	−0.604053
$656$	−7.30675	−0.285281
$657$	6.68527	0.260817
$658$	−14.4406	−0.562955
$659$	26.4076	1.02870	0.514348	−	0.857582i	$-0.328034\pi$
$659$	26.4076	1.02870	0.514348	+	0.857582i	$0.328034\pi$
$660$	1.40842	0.0548228
$661$	25.7497	1.00155	0.500773	−	0.865579i	$-0.333049\pi$
$661$	25.7497	1.00155	0.500773	+	0.865579i	$0.333049\pi$
$662$	12.7899	0.497092
$663$	26.9438	1.04641
$664$	2.10515	0.0816956
$665$	−28.8284	−1.11792
$666$	1.89946	0.0736024
$667$	55.4617	2.14749
$668$	23.3019	0.901578
$669$	27.5859	1.06653
$670$	−11.8250	−0.456839
$671$	−1.00000	−0.0386046
$672$	3.03430	0.117051
$673$	5.45991	0.210464	0.105232	−	0.994448i	$-0.466441\pi$
$673$	5.45991	0.210464	0.105232	+	0.994448i	$0.466441\pi$
$674$	24.5110	0.944128
$675$	3.01635	0.116099
$676$	0.964983	0.0371147
$677$	−28.4301	−1.09266	−0.546329	−	0.837571i	$-0.683975\pi$
$677$	−28.4301	−1.09266	−0.546329	+	0.837571i	$0.683975\pi$
$678$	16.3317	0.627215
$679$	−42.5624	−1.63340
$680$	−10.1548	−0.389419
$681$	8.24093	0.315793
$682$	0.0646549	0.00247576
$683$	20.6744	0.791085	0.395542	−	0.918448i	$-0.370557\pi$
$683$	20.6744	0.791085	0.395542	+	0.918448i	$0.370557\pi$
$684$	6.74572	0.257929
$685$	17.9831	0.687100
$686$	14.5435	0.555272
$687$	6.01323	0.229419
$688$	9.52587	0.363170
$689$	−26.3583	−1.00417
$690$	7.48851	0.285083
$691$	32.4843	1.23576	0.617880	−	0.786272i	$-0.287992\pi$
$691$	32.4843	1.23576	0.617880	+	0.786272i	$0.287992\pi$
$692$	−14.4732	−0.550188
$693$	3.03430	0.115264
$694$	11.7048	0.444309
$695$	3.91874	0.148646
$696$	10.4311	0.395391
$697$	52.6820	1.99547
$698$	1.06874	0.0404524
$699$	−11.4829	−0.434324
$700$	9.15250	0.345932
$701$	19.5722	0.739231	0.369615	−	0.929185i	$-0.379489\pi$
$701$	19.5722	0.739231	0.369615	+	0.929185i	$0.379489\pi$
$702$	−3.73698	−0.141043
$703$	12.8132	0.483259
$704$	−1.00000	−0.0376889
$705$	−6.70287	−0.252445
$706$	−13.4233	−0.505191
$707$	41.4487	1.55884
$708$	−2.27606	−0.0855395
$709$	−33.6848	−1.26506	−0.632529	−	0.774537i	$-0.717983\pi$
$709$	−33.6848	−1.26506	−0.632529	+	0.774537i	$0.717983\pi$
$710$	−3.26229	−0.122432
$711$	−16.0892	−0.603390
$712$	6.76628	0.253577
$713$	0.343766	0.0128742
$714$	−21.8775	−0.818744
$715$	−5.26324	−0.196834
$716$	−13.1880	−0.492859
$717$	−11.5750	−0.432278
$718$	−1.80284	−0.0672813
$719$	48.5164	1.80936	0.904678	−	0.426096i	$-0.140111\pi$
$719$	48.5164	1.80936	0.904678	+	0.426096i	$0.140111\pi$
$720$	1.40842	0.0524888
$721$	10.3681	0.386127
$722$	26.5048	0.986406
$723$	19.9827	0.743166
$724$	−5.51177	−0.204843
$725$	31.4639	1.16854
$726$	−1.00000	−0.0371135
$727$	38.4534	1.42616	0.713078	−	0.701084i	$-0.247300\pi$
$727$	38.4534	1.42616	0.713078	+	0.701084i	$0.247300\pi$
$728$	−11.3391	−0.420255
$729$	1.00000	0.0370370
$730$	9.41569	0.348490
$731$	−68.6820	−2.54030
$732$	−1.00000	−0.0369611
$733$	31.4643	1.16216	0.581081	−	0.813846i	$-0.302630\pi$
$733$	31.4643	1.16216	0.581081	+	0.813846i	$0.302630\pi$
$734$	1.20063	0.0443159
$735$	−3.10836	−0.114654
$736$	−5.31695	−0.195985
$737$	8.39590	0.309267
$738$	−7.30675	−0.268965
$739$	−3.21482	−0.118259	−0.0591295	−	0.998250i	$-0.518832\pi$
$739$	−3.21482	−0.118259	−0.0591295	+	0.998250i	$0.518832\pi$
$740$	2.67524	0.0983436
$741$	−25.2086	−0.926061
$742$	21.4021	0.785695
$743$	−39.7280	−1.45748	−0.728740	−	0.684791i	$-0.759894\pi$
$743$	−39.7280	−1.45748	−0.728740	+	0.684791i	$0.759894\pi$
$744$	0.0646549	0.00237036
$745$	−8.91101	−0.326474
$746$	29.7593	1.08956
$747$	2.10515	0.0770233
$748$	7.21005	0.263626
$749$	35.5145	1.29767
$750$	11.2904	0.412267
$751$	−27.4919	−1.00319	−0.501596	−	0.865102i	$-0.667254\pi$
$751$	−27.4919	−1.00319	−0.501596	+	0.865102i	$0.667254\pi$
$752$	4.75913	0.173548
$753$	−5.90735	−0.215276
$754$	−38.9808	−1.41960
$755$	−14.7656	−0.537374
$756$	3.03430	0.110356
$757$	45.6745	1.66007	0.830034	−	0.557713i	$-0.188321\pi$
$757$	45.6745	1.66007	0.830034	+	0.557713i	$0.188321\pi$
$758$	−33.8047	−1.22784
$759$	−5.31695	−0.192993
$760$	9.50083	0.344631
$761$	47.7541	1.73108	0.865542	−	0.500836i	$-0.166974\pi$
$761$	47.7541	1.73108	0.865542	+	0.500836i	$0.166974\pi$
$762$	−5.54313	−0.200806
$763$	29.5790	1.07083
$764$	23.6388	0.855221
$765$	−10.1548	−0.367148
$766$	−29.4868	−1.06540
$767$	8.50557	0.307118
$768$	−1.00000	−0.0360844
$769$	−39.1548	−1.41196	−0.705978	−	0.708233i	$-0.749492\pi$
$769$	−39.1548	−1.41196	−0.705978	+	0.708233i	$0.749492\pi$
$770$	4.27358	0.154009
$771$	−18.9700	−0.683188
$772$	−20.4144	−0.734732
$773$	−13.0579	−0.469661	−0.234830	−	0.972036i	$-0.575454\pi$
$773$	−13.0579	−0.469661	−0.234830	+	0.972036i	$0.575454\pi$
$774$	9.52587	0.342400
$775$	0.195021	0.00700538
$776$	14.0271	0.503543
$777$	5.76352	0.206765
$778$	27.8701	0.999193
$779$	−49.2893	−1.76597
$780$	−5.26324	−0.188454
$781$	2.31627	0.0828827
$782$	38.3355	1.37087
$783$	10.4311	0.372778
$784$	2.20698	0.0788207
$785$	−29.1047	−1.03879
$786$	10.9765	0.391518
$787$	−14.1806	−0.505484	−0.252742	−	0.967534i	$-0.581332\pi$
$787$	−14.1806	−0.505484	−0.252742	+	0.967534i	$0.581332\pi$
$788$	14.3631	0.511663
$789$	5.53289	0.196976
$790$	−22.6603	−0.806218
$791$	49.5552	1.76198
$792$	−1.00000	−0.0355335
$793$	3.73698	0.132704
$794$	34.1615	1.21235
$795$	9.93415	0.352328
$796$	20.5789	0.729399
$797$	−8.54901	−0.302822	−0.151411	−	0.988471i	$-0.548382\pi$
$797$	−8.54901	−0.302822	−0.151411	+	0.988471i	$0.548382\pi$
$798$	20.4686	0.724579
$799$	−34.3136	−1.21393
$800$	−3.01635	−0.106644
$801$	6.76628	0.239075
$802$	31.0638	1.09690
$803$	−6.68527	−0.235918
$804$	8.39590	0.296101
$805$	22.7224	0.800859
$806$	−0.241614	−0.00851048
$807$	27.2840	0.960441
$808$	−13.6600	−0.480559
$809$	35.7169	1.25574	0.627870	−	0.778319i	$-0.283927\pi$
$809$	35.7169	1.25574	0.627870	+	0.778319i	$0.283927\pi$
$810$	1.40842	0.0494869
$811$	−27.5359	−0.966916	−0.483458	−	0.875368i	$-0.660619\pi$
$811$	−27.5359	−0.966916	−0.483458	+	0.875368i	$0.660619\pi$
$812$	31.6511	1.11074
$813$	1.23156	0.0431927
$814$	−1.89946	−0.0665759
$815$	−10.7830	−0.377711
$816$	7.21005	0.252402
$817$	64.2589	2.24813
$818$	−31.2021	−1.09095
$819$	−11.3391	−0.396220
$820$	−10.2910	−0.359377
$821$	36.5950	1.27718	0.638588	−	0.769549i	$-0.279519\pi$
$821$	36.5950	1.27718	0.638588	+	0.769549i	$0.279519\pi$
$822$	−12.7683	−0.445345
$823$	35.5673	1.23980	0.619899	−	0.784681i	$-0.287173\pi$
$823$	35.5673	1.23980	0.619899	+	0.784681i	$0.287173\pi$
$824$	−3.41695	−0.119035
$825$	−3.01635	−0.105016
$826$	−6.90624	−0.240299
$827$	−13.7128	−0.476839	−0.238420	−	0.971162i	$-0.576629\pi$
$827$	−13.7128	−0.476839	−0.238420	+	0.971162i	$0.576629\pi$
$828$	−5.31695	−0.184777
$829$	−42.5715	−1.47857	−0.739284	−	0.673394i	$-0.764836\pi$
$829$	−42.5715	−1.47857	−0.739284	+	0.673394i	$0.764836\pi$
$830$	2.96494	0.102915
$831$	9.30982	0.322954
$832$	3.73698	0.129556
$833$	−15.9124	−0.551333
$834$	−2.78236	−0.0963453
$835$	32.8189	1.13575
$836$	−6.74572	−0.233306
$837$	0.0646549	0.00223480
$838$	2.26674	0.0783031
$839$	30.9493	1.06849	0.534244	−	0.845330i	$-0.320596\pi$
$839$	30.9493	1.06849	0.534244	+	0.845330i	$0.320596\pi$
$840$	4.27358	0.147452
$841$	79.8082	2.75201
$842$	−4.03890	−0.139190
$843$	27.6316	0.951683
$844$	21.4537	0.738466
$845$	1.35910	0.0467546
$846$	4.75913	0.163622
$847$	−3.03430	−0.104260
$848$	−7.05339	−0.242214
$849$	−4.09935	−0.140689
$850$	21.7480	0.745951
$851$	−10.0993	−0.346200
$852$	2.31627	0.0793542
$853$	47.4800	1.62569	0.812843	−	0.582483i	$-0.197919\pi$
$853$	47.4800	1.62569	0.812843	+	0.582483i	$0.197919\pi$
$854$	−3.03430	−0.103832
$855$	9.50083	0.324922
$856$	−11.7043	−0.400046
$857$	16.3308	0.557848	0.278924	−	0.960313i	$-0.410022\pi$
$857$	16.3308	0.557848	0.278924	+	0.960313i	$0.410022\pi$
$858$	3.73698	0.127578
$859$	12.1919	0.415982	0.207991	−	0.978131i	$-0.433307\pi$
$859$	12.1919	0.415982	0.207991	+	0.978131i	$0.433307\pi$
$860$	13.4165	0.457497
$861$	−22.1709	−0.755581
$862$	−0.429194	−0.0146184
$863$	−3.31211	−0.112745	−0.0563727	−	0.998410i	$-0.517954\pi$
$863$	−3.31211	−0.112745	−0.0563727	+	0.998410i	$0.517954\pi$
$864$	−1.00000	−0.0340207
$865$	−20.3843	−0.693089
$866$	−1.24263	−0.0422263
$867$	−34.9849	−1.18815
$868$	0.196182	0.00665886
$869$	16.0892	0.545787
$870$	14.6914	0.498086
$871$	−31.3753	−1.06311
$872$	−9.74822	−0.330116
$873$	14.0271	0.474745
$874$	−35.8667	−1.21321
$875$	34.2585	1.15815
$876$	−6.68527	−0.225874
$877$	−22.0439	−0.744370	−0.372185	−	0.928159i	$-0.621391\pi$
$877$	−22.0439	−0.744370	−0.372185	+	0.928159i	$0.621391\pi$
$878$	−36.4916	−1.23153
$879$	1.60737	0.0542151
$880$	−1.40842	−0.0474779
$881$	−21.9650	−0.740018	−0.370009	−	0.929028i	$-0.620645\pi$
$881$	−21.9650	−0.740018	−0.370009	+	0.929028i	$0.620645\pi$
$882$	2.20698	0.0743129
$883$	35.0209	1.17855	0.589274	−	0.807933i	$-0.299414\pi$
$883$	35.0209	1.17855	0.589274	+	0.807933i	$0.299414\pi$
$884$	−26.9438	−0.906218
$885$	−3.20565	−0.107757
$886$	13.6792	0.459560
$887$	−16.0773	−0.539821	−0.269911	−	0.962885i	$-0.586994\pi$
$887$	−16.0773	−0.539821	−0.269911	+	0.962885i	$0.586994\pi$
$888$	−1.89946	−0.0637416
$889$	−16.8195	−0.564109
$890$	9.52978	0.319439
$891$	−1.00000	−0.0335013
$892$	−27.5859	−0.923643
$893$	32.1038	1.07431
$894$	6.32694	0.211605
$895$	−18.5743	−0.620870
$896$	−3.03430	−0.101369
$897$	19.8693	0.663417
$898$	−28.5043	−0.951201
$899$	0.674422	0.0224932
$900$	−3.01635	−0.100545
$901$	50.8553	1.69424
$902$	7.30675	0.243288
$903$	28.9044	0.961877
$904$	−16.3317	−0.543184
$905$	−7.76290	−0.258047
$906$	10.4838	0.348300
$907$	0.973735	0.0323323	0.0161662	−	0.999869i	$-0.494854\pi$
$907$	0.973735	0.0323323	0.0161662	+	0.999869i	$0.494854\pi$
$908$	−8.24093	−0.273485
$909$	−13.6600	−0.453075
$910$	−15.9703	−0.529409
$911$	16.4751	0.545846	0.272923	−	0.962036i	$-0.412010\pi$
$911$	16.4751	0.545846	0.272923	+	0.962036i	$0.412010\pi$
$912$	−6.74572	−0.223373
$913$	−2.10515	−0.0696702
$914$	−38.3299	−1.26784
$915$	−1.40842	−0.0465610
$916$	−6.01323	−0.198683
$917$	33.3059	1.09986
$918$	7.21005	0.237967
$919$	−3.18084	−0.104926	−0.0524631	−	0.998623i	$-0.516707\pi$
$919$	−3.18084	−0.104926	−0.0524631	+	0.998623i	$0.516707\pi$
$920$	−7.48851	−0.246889
$921$	−32.7234	−1.07827
$922$	−32.7462	−1.07844
$923$	−8.65585	−0.284911
$924$	−3.03430	−0.0998212
$925$	−5.72941	−0.188382
$926$	28.7527	0.944874
$927$	−3.41695	−0.112228
$928$	−10.4311	−0.342418
$929$	18.8655	0.618956	0.309478	−	0.950907i	$-0.399846\pi$
$929$	18.8655	0.618956	0.309478	+	0.950907i	$0.399846\pi$
$930$	0.0910614	0.00298602
$931$	14.8877	0.487924
$932$	11.4829	0.376135
$933$	8.31320	0.272162
$934$	21.9657	0.718740
$935$	10.1548	0.332098
$936$	3.73698	0.122147
$937$	−14.2539	−0.465656	−0.232828	−	0.972518i	$-0.574798\pi$
$937$	−14.2539	−0.465656	−0.232828	+	0.972518i	$0.574798\pi$
$938$	25.4757	0.831811
$939$	−19.4825	−0.635787
$940$	6.70287	0.218624
$941$	−27.2827	−0.889389	−0.444695	−	0.895682i	$-0.646688\pi$
$941$	−27.2827	−0.889389	−0.444695	+	0.895682i	$0.646688\pi$
$942$	20.6648	0.673295
$943$	38.8496	1.26512
$944$	2.27606	0.0740794
$945$	4.27358	0.139019
$946$	−9.52587	−0.309713
$947$	−59.7925	−1.94299	−0.971497	−	0.237051i	$-0.923819\pi$
$947$	−59.7925	−1.94299	−0.971497	+	0.237051i	$0.923819\pi$
$948$	16.0892	0.522551
$949$	24.9827	0.810973
$950$	−20.3474	−0.660158
$951$	−3.27526	−0.106208
$952$	21.8775	0.709053
$953$	42.9656	1.39179	0.695897	−	0.718142i	$-0.255007\pi$
$953$	42.9656	1.39179	0.695897	+	0.718142i	$0.255007\pi$
$954$	−7.05339	−0.228362
$955$	33.2934	1.07735
$956$	11.5750	0.374364
$957$	−10.4311	−0.337190
$958$	21.0786	0.681020
$959$	−38.7428	−1.25107
$960$	−1.40842	−0.0454566
$961$	−30.9958	−0.999865
$962$	7.09822	0.228856
$963$	−11.7043	−0.377167
$964$	−19.9827	−0.643601
$965$	−28.7522	−0.925565
$966$	−16.1332	−0.519078
$967$	−32.9814	−1.06061	−0.530306	−	0.847807i	$-0.677923\pi$
$967$	−32.9814	−1.06061	−0.530306	+	0.847807i	$0.677923\pi$
$968$	1.00000	0.0321412
$969$	48.6370	1.56245
$970$	19.7561	0.634330
$971$	−43.3916	−1.39250	−0.696252	−	0.717797i	$-0.745150\pi$
$971$	−43.3916	−1.39250	−0.696252	+	0.717797i	$0.745150\pi$
$972$	−1.00000	−0.0320750
$973$	−8.44253	−0.270655
$974$	8.77076	0.281033
$975$	11.2720	0.360993
$976$	1.00000	0.0320092
$977$	16.9592	0.542572	0.271286	−	0.962499i	$-0.412551\pi$
$977$	16.9592	0.542572	0.271286	+	0.962499i	$0.412551\pi$
$978$	7.65605	0.244814
$979$	−6.76628	−0.216251
$980$	3.10836	0.0992929
$981$	−9.74822	−0.311237
$982$	−33.8576	−1.08044
$983$	−60.8240	−1.93998	−0.969991	−	0.243139i	$-0.921823\pi$
$983$	−60.8240	−1.93998	−0.969991	+	0.243139i	$0.921823\pi$
$984$	7.30675	0.232931
$985$	20.2293	0.644558
$986$	75.2089	2.39514
$987$	14.4406	0.459651
$988$	25.2086	0.801992
$989$	−50.6485	−1.61053
$990$	−1.40842	−0.0447626
$991$	32.4152	1.02970	0.514851	−	0.857280i	$-0.327847\pi$
$991$	32.4152	1.02970	0.514851	+	0.857280i	$0.327847\pi$
$992$	−0.0646549	−0.00205279
$993$	−12.7899	−0.405874
$994$	7.02826	0.222923
$995$	28.9838	0.918847
$996$	−2.10515	−0.0667042
$997$	12.8669	0.407499	0.203750	−	0.979023i	$-0.434687\pi$
$997$	12.8669	0.407499	0.203750	+	0.979023i	$0.434687\pi$
$998$	14.9697	0.473858
$999$	−1.89946	−0.0600961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.x.1.6	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.x.1.6	✓	6	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:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40842 q^{5} -1.00000 q^{6} -3.03430 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40842 q^{5} -1.00000 q^{6} -3.03430 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.40842 q^{10} -1.00000 q^{11} -1.00000 q^{12} +3.73698 q^{13} -3.03430 q^{14} -1.40842 q^{15} +1.00000 q^{16} -7.21005 q^{17} +1.00000 q^{18} +6.74572 q^{19} +1.40842 q^{20} +3.03430 q^{21} -1.00000 q^{22} -5.31695 q^{23} -1.00000 q^{24} -3.01635 q^{25} +3.73698 q^{26} -1.00000 q^{27} -3.03430 q^{28} -10.4311 q^{29} -1.40842 q^{30} -0.0646549 q^{31} +1.00000 q^{32} +1.00000 q^{33} -7.21005 q^{34} -4.27358 q^{35} +1.00000 q^{36} +1.89946 q^{37} +6.74572 q^{38} -3.73698 q^{39} +1.40842 q^{40} -7.30675 q^{41} +3.03430 q^{42} +9.52587 q^{43} -1.00000 q^{44} +1.40842 q^{45} -5.31695 q^{46} +4.75913 q^{47} -1.00000 q^{48} +2.20698 q^{49} -3.01635 q^{50} +7.21005 q^{51} +3.73698 q^{52} -7.05339 q^{53} -1.00000 q^{54} -1.40842 q^{55} -3.03430 q^{56} -6.74572 q^{57} -10.4311 q^{58} +2.27606 q^{59} -1.40842 q^{60} +1.00000 q^{61} -0.0646549 q^{62} -3.03430 q^{63} +1.00000 q^{64} +5.26324 q^{65} +1.00000 q^{66} -8.39590 q^{67} -7.21005 q^{68} +5.31695 q^{69} -4.27358 q^{70} -2.31627 q^{71} +1.00000 q^{72} +6.68527 q^{73} +1.89946 q^{74} +3.01635 q^{75} +6.74572 q^{76} +3.03430 q^{77} -3.73698 q^{78} -16.0892 q^{79} +1.40842 q^{80} +1.00000 q^{81} -7.30675 q^{82} +2.10515 q^{83} +3.03430 q^{84} -10.1548 q^{85} +9.52587 q^{86} +10.4311 q^{87} -1.00000 q^{88} +6.76628 q^{89} +1.40842 q^{90} -11.3391 q^{91} -5.31695 q^{92} +0.0646549 q^{93} +4.75913 q^{94} +9.50083 q^{95} -1.00000 q^{96} +14.0271 q^{97} +2.20698 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{5} - 6 q^{6} + q^{7} + 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} - 6 q^{12} + 2 q^{13} + q^{14} + 6 q^{15} + 6 q^{16} - 13 q^{17} + 6 q^{18} + q^{19} - 6 q^{20} - q^{21} - 6 q^{22} - 11 q^{23} - 6 q^{24} + 8 q^{25} + 2 q^{26} - 6 q^{27} + q^{28} - 14 q^{29} + 6 q^{30} - 5 q^{31} + 6 q^{32} + 6 q^{33} - 13 q^{34} - 13 q^{35} + 6 q^{36} - 6 q^{37} + q^{38} - 2 q^{39} - 6 q^{40} - 25 q^{41} - q^{42} + 19 q^{43} - 6 q^{44} - 6 q^{45} - 11 q^{46} - 10 q^{47} - 6 q^{48} - 5 q^{49} + 8 q^{50} + 13 q^{51} + 2 q^{52} - 17 q^{53} - 6 q^{54} + 6 q^{55} + q^{56} - q^{57} - 14 q^{58} - 14 q^{59} + 6 q^{60} + 6 q^{61} - 5 q^{62} + q^{63} + 6 q^{64} + 6 q^{65} + 6 q^{66} + 12 q^{67} - 13 q^{68} + 11 q^{69} - 13 q^{70} + 6 q^{71} + 6 q^{72} - 29 q^{73} - 6 q^{74} - 8 q^{75} + q^{76} - q^{77} - 2 q^{78} - 24 q^{79} - 6 q^{80} + 6 q^{81} - 25 q^{82} - 9 q^{83} - q^{84} - 22 q^{85} + 19 q^{86} + 14 q^{87} - 6 q^{88} - 4 q^{89} - 6 q^{90} - 29 q^{91} - 11 q^{92} + 5 q^{93} - 10 q^{94} - 27 q^{95} - 6 q^{96} - 5 q^{97} - 5 q^{98} - 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^5 - 6 * q^6 + q^7 + 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 - 6 * q^12 + 2 * q^13 + q^14 + 6 * q^15 + 6 * q^16 - 13 * q^17 + 6 * q^18 + q^19 - 6 * q^20 - q^21 - 6 * q^22 - 11 * q^23 - 6 * q^24 + 8 * q^25 + 2 * q^26 - 6 * q^27 + q^28 - 14 * q^29 + 6 * q^30 - 5 * q^31 + 6 * q^32 + 6 * q^33 - 13 * q^34 - 13 * q^35 + 6 * q^36 - 6 * q^37 + q^38 - 2 * q^39 - 6 * q^40 - 25 * q^41 - q^42 + 19 * q^43 - 6 * q^44 - 6 * q^45 - 11 * q^46 - 10 * q^47 - 6 * q^48 - 5 * q^49 + 8 * q^50 + 13 * q^51 + 2 * q^52 - 17 * q^53 - 6 * q^54 + 6 * q^55 + q^56 - q^57 - 14 * q^58 - 14 * q^59 + 6 * q^60 + 6 * q^61 - 5 * q^62 + q^63 + 6 * q^64 + 6 * q^65 + 6 * q^66 + 12 * q^67 - 13 * q^68 + 11 * q^69 - 13 * q^70 + 6 * q^71 + 6 * q^72 - 29 * q^73 - 6 * q^74 - 8 * q^75 + q^76 - q^77 - 2 * q^78 - 24 * q^79 - 6 * q^80 + 6 * q^81 - 25 * q^82 - 9 * q^83 - q^84 - 22 * q^85 + 19 * q^86 + 14 * q^87 - 6 * q^88 - 4 * q^89 - 6 * q^90 - 29 * q^91 - 11 * q^92 + 5 * q^93 - 10 * q^94 - 27 * q^95 - 6 * q^96 - 5 * q^97 - 5 * q^98 - 6 * q^99

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