LMFDB - Embedded newform 4026.2.a.u.1.3

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:	$0$
Dimension:	$5$
Coefficient field:	5.5.9176805.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 12x^{3} + 7x^{2} + 30x - 20 $ x^5 - x^4 - 12x^3 + 7x^2 + 30*x - 20
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			1.3
Root			$0.689091$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.689091 q^{5} -1.00000 q^{6} +4.91945 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.689091 q^{5} -1.00000 q^{6} +4.91945 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.689091 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.15959 q^{13} -4.91945 q^{14} -0.689091 q^{15} +1.00000 q^{16} +1.70520 q^{17} -1.00000 q^{18} -3.32636 q^{19} -0.689091 q^{20} +4.91945 q^{21} +1.00000 q^{22} -0.135207 q^{23} -1.00000 q^{24} -4.52515 q^{25} -2.15959 q^{26} +1.00000 q^{27} +4.91945 q^{28} +4.83606 q^{29} +0.689091 q^{30} +2.55388 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.70520 q^{34} -3.38995 q^{35} +1.00000 q^{36} +7.89072 q^{37} +3.32636 q^{38} +2.15959 q^{39} +0.689091 q^{40} -7.38995 q^{41} -4.91945 q^{42} +3.02873 q^{43} -1.00000 q^{44} -0.689091 q^{45} +0.135207 q^{46} +10.3738 q^{47} +1.00000 q^{48} +17.2010 q^{49} +4.52515 q^{50} +1.70520 q^{51} +2.15959 q^{52} -1.60571 q^{53} -1.00000 q^{54} +0.689091 q^{55} -4.91945 q^{56} -3.32636 q^{57} -4.83606 q^{58} -1.90614 q^{59} -0.689091 q^{60} -1.00000 q^{61} -2.55388 q^{62} +4.91945 q^{63} +1.00000 q^{64} -1.48815 q^{65} +1.00000 q^{66} +12.0862 q^{67} +1.70520 q^{68} -0.135207 q^{69} +3.38995 q^{70} -9.93207 q^{71} -1.00000 q^{72} -1.42566 q^{73} -7.89072 q^{74} -4.52515 q^{75} -3.32636 q^{76} -4.91945 q^{77} -2.15959 q^{78} +0.110825 q^{79} -0.689091 q^{80} +1.00000 q^{81} +7.38995 q^{82} +14.1106 q^{83} +4.91945 q^{84} -1.17504 q^{85} -3.02873 q^{86} +4.83606 q^{87} +1.00000 q^{88} +3.25345 q^{89} +0.689091 q^{90} +10.6240 q^{91} -0.135207 q^{92} +2.55388 q^{93} -10.3738 q^{94} +2.29216 q^{95} -1.00000 q^{96} -6.01545 q^{97} -17.2010 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.689091	−0.308171	−0.154085	−	0.988058i	$-0.549243\pi$
$5$	−0.689091	−0.308171	−0.154085	+	0.988058i	$0.549243\pi$
$6$	−1.00000	−0.408248
$7$	4.91945	1.85938	0.929688	−	0.368347i	$-0.120076\pi$
$7$	4.91945	1.85938	0.929688	+	0.368347i	$0.120076\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.689091	0.217910
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.00000	0.288675
$13$	2.15959	0.598962	0.299481	−	0.954102i	$-0.403186\pi$
$13$	2.15959	0.598962	0.299481	+	0.954102i	$0.403186\pi$
$14$	−4.91945	−1.31478
$15$	−0.689091	−0.177922
$16$	1.00000	0.250000
$17$	1.70520	0.413572	0.206786	−	0.978386i	$-0.433700\pi$
$17$	1.70520	0.413572	0.206786	+	0.978386i	$0.433700\pi$
$18$	−1.00000	−0.235702
$19$	−3.32636	−0.763119	−0.381560	−	0.924344i	$-0.624613\pi$
$19$	−3.32636	−0.763119	−0.381560	+	0.924344i	$0.624613\pi$
$20$	−0.689091	−0.154085
$21$	4.91945	1.07351
$22$	1.00000	0.213201
$23$	−0.135207	−0.0281927	−0.0140963	−	0.999901i	$-0.504487\pi$
$23$	−0.135207	−0.0281927	−0.0140963	+	0.999901i	$0.504487\pi$
$24$	−1.00000	−0.204124
$25$	−4.52515	−0.905031
$26$	−2.15959	−0.423530
$27$	1.00000	0.192450
$28$	4.91945	0.929688
$29$	4.83606	0.898034	0.449017	−	0.893523i	$-0.351774\pi$
$29$	4.83606	0.898034	0.449017	+	0.893523i	$0.351774\pi$
$30$	0.689091	0.125810
$31$	2.55388	0.458691	0.229346	−	0.973345i	$-0.426341\pi$
$31$	2.55388	0.458691	0.229346	+	0.973345i	$0.426341\pi$
$32$	−1.00000	−0.176777
$33$	−1.00000	−0.174078
$34$	−1.70520	−0.292440
$35$	−3.38995	−0.573006
$36$	1.00000	0.166667
$37$	7.89072	1.29723	0.648613	−	0.761118i	$-0.275349\pi$
$37$	7.89072	1.29723	0.648613	+	0.761118i	$0.275349\pi$
$38$	3.32636	0.539607
$39$	2.15959	0.345811
$40$	0.689091	0.108955
$41$	−7.38995	−1.15412	−0.577058	−	0.816703i	$-0.695799\pi$
$41$	−7.38995	−1.15412	−0.577058	+	0.816703i	$0.695799\pi$
$42$	−4.91945	−0.759087
$43$	3.02873	0.461877	0.230938	−	0.972968i	$-0.425820\pi$
$43$	3.02873	0.461877	0.230938	+	0.972968i	$0.425820\pi$
$44$	−1.00000	−0.150756
$45$	−0.689091	−0.102724
$46$	0.135207	0.0199352
$47$	10.3738	1.51318	0.756590	−	0.653890i	$-0.226864\pi$
$47$	10.3738	1.51318	0.756590	+	0.653890i	$0.226864\pi$
$48$	1.00000	0.144338
$49$	17.2010	2.45728
$50$	4.52515	0.639953
$51$	1.70520	0.238776
$52$	2.15959	0.299481
$53$	−1.60571	−0.220561	−0.110280	−	0.993901i	$-0.535175\pi$
$53$	−1.60571	−0.220561	−0.110280	+	0.993901i	$0.535175\pi$
$54$	−1.00000	−0.136083
$55$	0.689091	0.0929170
$56$	−4.91945	−0.657389
$57$	−3.32636	−0.440587
$58$	−4.83606	−0.635006
$59$	−1.90614	−0.248158	−0.124079	−	0.992272i	$-0.539598\pi$
$59$	−1.90614	−0.248158	−0.124079	+	0.992272i	$0.539598\pi$
$60$	−0.689091	−0.0889612
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−2.55388	−0.324344
$63$	4.91945	0.619792
$64$	1.00000	0.125000
$65$	−1.48815	−0.184583
$66$	1.00000	0.123091
$67$	12.0862	1.47657	0.738283	−	0.674491i	$-0.235637\pi$
$67$	12.0862	1.47657	0.738283	+	0.674491i	$0.235637\pi$
$68$	1.70520	0.206786
$69$	−0.135207	−0.0162770
$70$	3.38995	0.405176
$71$	−9.93207	−1.17872	−0.589360	−	0.807871i	$-0.700620\pi$
$71$	−9.93207	−1.17872	−0.589360	+	0.807871i	$0.700620\pi$
$72$	−1.00000	−0.117851
$73$	−1.42566	−0.166861	−0.0834303	−	0.996514i	$-0.526588\pi$
$73$	−1.42566	−0.166861	−0.0834303	+	0.996514i	$0.526588\pi$
$74$	−7.89072	−0.917277
$75$	−4.52515	−0.522520
$76$	−3.32636	−0.381560
$77$	−4.91945	−0.560623
$78$	−2.15959	−0.244525
$79$	0.110825	0.0124688	0.00623438	−	0.999981i	$-0.498016\pi$
$79$	0.110825	0.0124688	0.00623438	+	0.999981i	$0.498016\pi$
$80$	−0.689091	−0.0770427
$81$	1.00000	0.111111
$82$	7.38995	0.816083
$83$	14.1106	1.54884	0.774420	−	0.632672i	$-0.218042\pi$
$83$	14.1106	1.54884	0.774420	+	0.632672i	$0.218042\pi$
$84$	4.91945	0.536756
$85$	−1.17504	−0.127451
$86$	−3.02873	−0.326596
$87$	4.83606	0.518480
$88$	1.00000	0.106600
$89$	3.25345	0.344865	0.172432	−	0.985021i	$-0.444837\pi$
$89$	3.25345	0.344865	0.172432	+	0.985021i	$0.444837\pi$
$90$	0.689091	0.0726366
$91$	10.6240	1.11370
$92$	−0.135207	−0.0140963
$93$	2.55388	0.264825
$94$	−10.3738	−1.06998
$95$	2.29216	0.235171
$96$	−1.00000	−0.102062
$97$	−6.01545	−0.610776	−0.305388	−	0.952228i	$-0.598786\pi$
$97$	−6.01545	−0.610776	−0.305388	+	0.952228i	$0.598786\pi$
$98$	−17.2010	−1.73756
$99$	−1.00000	−0.100504
$100$	−4.52515	−0.452515
$101$	−8.20881	−0.816807	−0.408403	−	0.912802i	$-0.633914\pi$
$101$	−8.20881	−0.816807	−0.408403	+	0.912802i	$0.633914\pi$
$102$	−1.70520	−0.168840
$103$	−0.150657	−0.0148447	−0.00742236	−	0.999972i	$-0.502363\pi$
$103$	−0.150657	−0.0148447	−0.00742236	+	0.999972i	$0.502363\pi$
$104$	−2.15959	−0.211765
$105$	−3.38995	−0.330825
$106$	1.60571	0.155960
$107$	−20.2746	−1.96002	−0.980008	−	0.198958i	$-0.936244\pi$
$107$	−20.2746	−1.96002	−0.980008	+	0.198958i	$0.936244\pi$
$108$	1.00000	0.0962250
$109$	11.4418	1.09592	0.547961	−	0.836504i	$-0.315404\pi$
$109$	11.4418	1.09592	0.547961	+	0.836504i	$0.315404\pi$
$110$	−0.689091	−0.0657022
$111$	7.89072	0.748954
$112$	4.91945	0.464844
$113$	−0.451754	−0.0424974	−0.0212487	−	0.999774i	$-0.506764\pi$
$113$	−0.451754	−0.0424974	−0.0212487	+	0.999774i	$0.506764\pi$
$114$	3.32636	0.311542
$115$	0.0931701	0.00868816
$116$	4.83606	0.449017
$117$	2.15959	0.199654
$118$	1.90614	0.175474
$119$	8.38866	0.768987
$120$	0.689091	0.0629051
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−7.38995	−0.666329
$124$	2.55388	0.229346
$125$	6.56370	0.587075
$126$	−4.91945	−0.438259
$127$	21.0873	1.87120	0.935598	−	0.353067i	$-0.114861\pi$
$127$	21.0873	1.87120	0.935598	+	0.353067i	$0.114861\pi$
$128$	−1.00000	−0.0883883
$129$	3.02873	0.266665
$130$	1.48815	0.130520
$131$	−10.7653	−0.940571	−0.470285	−	0.882514i	$-0.655849\pi$
$131$	−10.7653	−0.940571	−0.470285	+	0.882514i	$0.655849\pi$
$132$	−1.00000	−0.0870388
$133$	−16.3638	−1.41893
$134$	−12.0862	−1.04409
$135$	−0.689091	−0.0593075
$136$	−1.70520	−0.146220
$137$	−16.8515	−1.43972	−0.719861	−	0.694118i	$-0.755794\pi$
$137$	−16.8515	−1.43972	−0.719861	+	0.694118i	$0.755794\pi$
$138$	0.135207	0.0115096
$139$	−10.7997	−0.916018	−0.458009	−	0.888948i	$-0.651437\pi$
$139$	−10.7997	−0.916018	−0.458009	+	0.888948i	$0.651437\pi$
$140$	−3.38995	−0.286503
$141$	10.3738	0.873634
$142$	9.93207	0.833480
$143$	−2.15959	−0.180594
$144$	1.00000	0.0833333
$145$	−3.33249	−0.276748
$146$	1.42566	0.117988
$147$	17.2010	1.41871
$148$	7.89072	0.648613
$149$	5.50795	0.451229	0.225614	−	0.974217i	$-0.427561\pi$
$149$	5.50795	0.451229	0.225614	+	0.974217i	$0.427561\pi$
$150$	4.52515	0.369477
$151$	7.12038	0.579449	0.289724	−	0.957110i	$-0.406436\pi$
$151$	7.12038	0.579449	0.289724	+	0.957110i	$0.406436\pi$
$152$	3.32636	0.269803
$153$	1.70520	0.137857
$154$	4.91945	0.396420
$155$	−1.75986	−0.141355
$156$	2.15959	0.172906
$157$	16.7836	1.33948	0.669738	−	0.742598i	$-0.266407\pi$
$157$	16.7836	1.33948	0.669738	+	0.742598i	$0.266407\pi$
$158$	−0.110825	−0.00881675
$159$	−1.60571	−0.127341
$160$	0.689091	0.0544774
$161$	−0.665145	−0.0524208
$162$	−1.00000	−0.0785674
$163$	3.13171	0.245295	0.122647	−	0.992450i	$-0.460862\pi$
$163$	3.13171	0.245295	0.122647	+	0.992450i	$0.460862\pi$
$164$	−7.38995	−0.577058
$165$	0.689091	0.0536457
$166$	−14.1106	−1.09519
$167$	−10.1883	−0.788398	−0.394199	−	0.919025i	$-0.628978\pi$
$167$	−10.1883	−0.788398	−0.394199	+	0.919025i	$0.628978\pi$
$168$	−4.91945	−0.379544
$169$	−8.33617	−0.641244
$170$	1.17504	0.0901214
$171$	−3.32636	−0.254373
$172$	3.02873	0.230938
$173$	23.8598	1.81403	0.907014	−	0.421101i	$-0.138356\pi$
$173$	23.8598	1.81403	0.907014	+	0.421101i	$0.138356\pi$
$174$	−4.83606	−0.366621
$175$	−22.2613	−1.68279
$176$	−1.00000	−0.0753778
$177$	−1.90614	−0.143274
$178$	−3.25345	−0.243856
$179$	−13.4202	−1.00307	−0.501537	−	0.865136i	$-0.667232\pi$
$179$	−13.4202	−1.00307	−0.501537	+	0.865136i	$0.667232\pi$
$180$	−0.689091	−0.0513618
$181$	2.21639	0.164743	0.0823714	−	0.996602i	$-0.473751\pi$
$181$	2.21639	0.164743	0.0823714	+	0.996602i	$0.473751\pi$
$182$	−10.6240	−0.787502
$183$	−1.00000	−0.0739221
$184$	0.135207	0.00996761
$185$	−5.43742	−0.399767
$186$	−2.55388	−0.187260
$187$	−1.70520	−0.124697
$188$	10.3738	0.756590
$189$	4.91945	0.357837
$190$	−2.29216	−0.166291
$191$	−8.20752	−0.593875	−0.296938	−	0.954897i	$-0.595965\pi$
$191$	−8.20752	−0.593875	−0.296938	+	0.954897i	$0.595965\pi$
$192$	1.00000	0.0721688
$193$	10.2032	0.734440	0.367220	−	0.930134i	$-0.380310\pi$
$193$	10.2032	0.734440	0.367220	+	0.930134i	$0.380310\pi$
$194$	6.01545	0.431884
$195$	−1.48815	−0.106569
$196$	17.2010	1.22864
$197$	0.297629	0.0212052	0.0106026	−	0.999944i	$-0.496625\pi$
$197$	0.297629	0.0212052	0.0106026	+	0.999944i	$0.496625\pi$
$198$	1.00000	0.0710669
$199$	−23.4585	−1.66293	−0.831466	−	0.555576i	$-0.812498\pi$
$199$	−23.4585	−1.66293	−0.831466	+	0.555576i	$0.812498\pi$
$200$	4.52515	0.319977
$201$	12.0862	0.852496
$202$	8.20881	0.577570
$203$	23.7908	1.66978
$204$	1.70520	0.119388
$205$	5.09234	0.355665
$206$	0.150657	0.0104968
$207$	−0.135207	−0.00939756
$208$	2.15959	0.149741
$209$	3.32636	0.230089
$210$	3.38995	0.233929
$211$	−18.8108	−1.29499	−0.647494	−	0.762070i	$-0.724183\pi$
$211$	−18.8108	−1.29499	−0.647494	+	0.762070i	$0.724183\pi$
$212$	−1.60571	−0.110280
$213$	−9.93207	−0.680534
$214$	20.2746	1.38594
$215$	−2.08707	−0.142337
$216$	−1.00000	−0.0680414
$217$	12.5637	0.852879
$218$	−11.4418	−0.774934
$219$	−1.42566	−0.0963370
$220$	0.689091	0.0464585
$221$	3.68254	0.247714
$222$	−7.89072	−0.529590
$223$	27.5578	1.84541	0.922705	−	0.385508i	$-0.125974\pi$
$223$	27.5578	1.84541	0.922705	+	0.385508i	$0.125974\pi$
$224$	−4.91945	−0.328694
$225$	−4.52515	−0.301677
$226$	0.451754	0.0300502
$227$	25.8110	1.71314	0.856570	−	0.516031i	$-0.172591\pi$
$227$	25.8110	1.71314	0.856570	+	0.516031i	$0.172591\pi$
$228$	−3.32636	−0.220294
$229$	6.33420	0.418576	0.209288	−	0.977854i	$-0.432885\pi$
$229$	6.33420	0.418576	0.209288	+	0.977854i	$0.432885\pi$
$230$	−0.0931701	−0.00614345
$231$	−4.91945	−0.323676
$232$	−4.83606	−0.317503
$233$	17.3954	1.13961	0.569806	−	0.821779i	$-0.307018\pi$
$233$	17.3954	1.13961	0.569806	+	0.821779i	$0.307018\pi$
$234$	−2.15959	−0.141177
$235$	−7.14851	−0.466318
$236$	−1.90614	−0.124079
$237$	0.110825	0.00719885
$238$	−8.38866	−0.543756
$239$	8.57417	0.554617	0.277309	−	0.960781i	$-0.410558\pi$
$239$	8.57417	0.554617	0.277309	+	0.960781i	$0.410558\pi$
$240$	−0.689091	−0.0444806
$241$	−21.1128	−1.35999	−0.679997	−	0.733215i	$-0.738019\pi$
$241$	−21.1128	−1.35999	−0.679997	+	0.733215i	$0.738019\pi$
$242$	−1.00000	−0.0642824
$243$	1.00000	0.0641500
$244$	−1.00000	−0.0640184
$245$	−11.8530	−0.757262
$246$	7.38995	0.471166
$247$	−7.18357	−0.457080
$248$	−2.55388	−0.162172
$249$	14.1106	0.894223
$250$	−6.56370	−0.415125
$251$	1.83060	0.115546	0.0577731	−	0.998330i	$-0.481600\pi$
$251$	1.83060	0.115546	0.0577731	+	0.998330i	$0.481600\pi$
$252$	4.91945	0.309896
$253$	0.135207	0.00850041
$254$	−21.0873	−1.32314
$255$	−1.17504	−0.0735838
$256$	1.00000	0.0625000
$257$	14.2530	0.889077	0.444538	−	0.895760i	$-0.353368\pi$
$257$	14.2530	0.889077	0.444538	+	0.895760i	$0.353368\pi$
$258$	−3.02873	−0.188560
$259$	38.8180	2.41203
$260$	−1.48815	−0.0922914
$261$	4.83606	0.299345
$262$	10.7653	0.665084
$263$	30.0013	1.84996	0.924981	−	0.380013i	$-0.124081\pi$
$263$	30.0013	1.84996	0.924981	+	0.380013i	$0.124081\pi$
$264$	1.00000	0.0615457
$265$	1.10648	0.0679704
$266$	16.3638	1.00333
$267$	3.25345	0.199108
$268$	12.0862	0.738283
$269$	22.6897	1.38342	0.691708	−	0.722177i	$-0.256858\pi$
$269$	22.6897	1.38342	0.691708	+	0.722177i	$0.256858\pi$
$270$	0.689091	0.0419367
$271$	5.92225	0.359751	0.179876	−	0.983689i	$-0.442430\pi$
$271$	5.92225	0.359751	0.179876	+	0.983689i	$0.442430\pi$
$272$	1.70520	0.103393
$273$	10.6240	0.642993
$274$	16.8515	1.01804
$275$	4.52515	0.272877
$276$	−0.135207	−0.00813852
$277$	−2.44262	−0.146763	−0.0733815	−	0.997304i	$-0.523379\pi$
$277$	−2.44262	−0.146763	−0.0733815	+	0.997304i	$0.523379\pi$
$278$	10.7997	0.647722
$279$	2.55388	0.152897
$280$	3.38995	0.202588
$281$	1.08055	0.0644604	0.0322302	−	0.999480i	$-0.489739\pi$
$281$	1.08055	0.0644604	0.0322302	+	0.999480i	$0.489739\pi$
$282$	−10.3738	−0.617753
$283$	−21.3543	−1.26938	−0.634690	−	0.772767i	$-0.718872\pi$
$283$	−21.3543	−1.26938	−0.634690	+	0.772767i	$0.718872\pi$
$284$	−9.93207	−0.589360
$285$	2.29216	0.135776
$286$	2.15959	0.127699
$287$	−36.3545	−2.14594
$288$	−1.00000	−0.0589256
$289$	−14.0923	−0.828958
$290$	3.33249	0.195690
$291$	−6.01545	−0.352632
$292$	−1.42566	−0.0834303
$293$	−27.8023	−1.62423	−0.812115	−	0.583498i	$-0.801684\pi$
$293$	−27.8023	−1.62423	−0.812115	+	0.583498i	$0.801684\pi$
$294$	−17.2010	−1.00318
$295$	1.31350	0.0764752
$296$	−7.89072	−0.458639
$297$	−1.00000	−0.0580259
$298$	−5.50795	−0.319067
$299$	−0.291992	−0.0168863
$300$	−4.52515	−0.261260
$301$	14.8997	0.858803
$302$	−7.12038	−0.409732
$303$	−8.20881	−0.471584
$304$	−3.32636	−0.190780
$305$	0.689091	0.0394572
$306$	−1.70520	−0.0974800
$307$	−31.9388	−1.82285	−0.911423	−	0.411470i	$-0.865015\pi$
$307$	−31.9388	−1.82285	−0.911423	+	0.411470i	$0.865015\pi$
$308$	−4.91945	−0.280312
$309$	−0.150657	−0.00857060
$310$	1.75986	0.0999532
$311$	14.0050	0.794151	0.397075	−	0.917786i	$-0.370025\pi$
$311$	14.0050	0.794151	0.397075	+	0.917786i	$0.370025\pi$
$312$	−2.15959	−0.122263
$313$	6.21229	0.351140	0.175570	−	0.984467i	$-0.443823\pi$
$313$	6.21229	0.351140	0.175570	+	0.984467i	$0.443823\pi$
$314$	−16.7836	−0.947152
$315$	−3.38995	−0.191002
$316$	0.110825	0.00623438
$317$	−0.166142	−0.00933145	−0.00466573	−	0.999989i	$-0.501485\pi$
$317$	−0.166142	−0.00933145	−0.00466573	+	0.999989i	$0.501485\pi$
$318$	1.60571	0.0900435
$319$	−4.83606	−0.270768
$320$	−0.689091	−0.0385214
$321$	−20.2746	−1.13162
$322$	0.665145	0.0370671
$323$	−5.67212	−0.315605
$324$	1.00000	0.0555556
$325$	−9.77248	−0.542079
$326$	−3.13171	−0.173450
$327$	11.4418	0.632731
$328$	7.38995	0.408042
$329$	51.0335	2.81357
$330$	−0.689091	−0.0379332
$331$	−29.9118	−1.64410	−0.822051	−	0.569414i	$-0.807170\pi$
$331$	−29.9118	−1.64410	−0.822051	+	0.569414i	$0.807170\pi$
$332$	14.1106	0.774420
$333$	7.89072	0.432409
$334$	10.1883	0.557482
$335$	−8.32850	−0.455035
$336$	4.91945	0.268378
$337$	8.19725	0.446533	0.223266	−	0.974757i	$-0.428328\pi$
$337$	8.19725	0.446533	0.223266	+	0.974757i	$0.428328\pi$
$338$	8.33617	0.453428
$339$	−0.451754	−0.0245359
$340$	−1.17504	−0.0637255
$341$	−2.55388	−0.138301
$342$	3.32636	0.179869
$343$	50.1831	2.70963
$344$	−3.02873	−0.163298
$345$	0.0931701	0.00501611
$346$	−23.8598	−1.28271
$347$	26.4965	1.42240	0.711202	−	0.702988i	$-0.248151\pi$
$347$	26.4965	1.42240	0.711202	+	0.702988i	$0.248151\pi$
$348$	4.83606	0.259240
$349$	14.7589	0.790028	0.395014	−	0.918675i	$-0.370740\pi$
$349$	14.7589	0.790028	0.395014	+	0.918675i	$0.370740\pi$
$350$	22.2613	1.18991
$351$	2.15959	0.115270
$352$	1.00000	0.0533002
$353$	−23.3634	−1.24351	−0.621753	−	0.783213i	$-0.713579\pi$
$353$	−23.3634	−1.24351	−0.621753	+	0.783213i	$0.713579\pi$
$354$	1.90614	0.101310
$355$	6.84410	0.363247
$356$	3.25345	0.172432
$357$	8.38866	0.443975
$358$	13.4202	0.709281
$359$	−16.5426	−0.873083	−0.436541	−	0.899684i	$-0.643797\pi$
$359$	−16.5426	−0.873083	−0.436541	+	0.899684i	$0.643797\pi$
$360$	0.689091	0.0363183
$361$	−7.93533	−0.417649
$362$	−2.21639	−0.116491
$363$	1.00000	0.0524864
$364$	10.6240	0.556848
$365$	0.982407	0.0514215
$366$	1.00000	0.0522708
$367$	−18.8578	−0.984371	−0.492185	−	0.870490i	$-0.663802\pi$
$367$	−18.8578	−0.984371	−0.492185	+	0.870490i	$0.663802\pi$
$368$	−0.135207	−0.00704817
$369$	−7.38995	−0.384705
$370$	5.43742	0.282678
$371$	−7.89919	−0.410105
$372$	2.55388	0.132413
$373$	17.7078	0.916877	0.458439	−	0.888726i	$-0.348409\pi$
$373$	17.7078	0.916877	0.458439	+	0.888726i	$0.348409\pi$
$374$	1.70520	0.0881739
$375$	6.56370	0.338948
$376$	−10.3738	−0.534990
$377$	10.4439	0.537889
$378$	−4.91945	−0.253029
$379$	−18.2613	−0.938019	−0.469010	−	0.883193i	$-0.655389\pi$
$379$	−18.2613	−0.938019	−0.469010	+	0.883193i	$0.655389\pi$
$380$	2.29216	0.117586
$381$	21.0873	1.08034
$382$	8.20752	0.419933
$383$	24.7651	1.26544	0.632719	−	0.774382i	$-0.281939\pi$
$383$	24.7651	1.26544	0.632719	+	0.774382i	$0.281939\pi$
$384$	−1.00000	−0.0510310
$385$	3.38995	0.172768
$386$	−10.2032	−0.519328
$387$	3.02873	0.153959
$388$	−6.01545	−0.305388
$389$	11.5147	0.583819	0.291909	−	0.956446i	$-0.405709\pi$
$389$	11.5147	0.583819	0.291909	+	0.956446i	$0.405709\pi$
$390$	1.48815	0.0753556
$391$	−0.230556	−0.0116597
$392$	−17.2010	−0.868780
$393$	−10.7653	−0.543039
$394$	−0.297629	−0.0149944
$395$	−0.0763684	−0.00384251
$396$	−1.00000	−0.0502519
$397$	0.602648	0.0302461	0.0151230	−	0.999886i	$-0.495186\pi$
$397$	0.602648	0.0302461	0.0151230	+	0.999886i	$0.495186\pi$
$398$	23.4585	1.17587
$399$	−16.3638	−0.819217
$400$	−4.52515	−0.226258
$401$	−19.3012	−0.963854	−0.481927	−	0.876212i	$-0.660063\pi$
$401$	−19.3012	−0.963854	−0.481927	+	0.876212i	$0.660063\pi$
$402$	−12.0862	−0.602806
$403$	5.51534	0.274739
$404$	−8.20881	−0.408403
$405$	−0.689091	−0.0342412
$406$	−23.7908	−1.18072
$407$	−7.89072	−0.391128
$408$	−1.70520	−0.0844201
$409$	19.9815	0.988023	0.494011	−	0.869455i	$-0.335530\pi$
$409$	19.9815	0.988023	0.494011	+	0.869455i	$0.335530\pi$
$410$	−5.09234	−0.251493
$411$	−16.8515	−0.831224
$412$	−0.150657	−0.00742236
$413$	−9.37716	−0.461420
$414$	0.135207	0.00664508
$415$	−9.72349	−0.477307
$416$	−2.15959	−0.105883
$417$	−10.7997	−0.528863
$418$	−3.32636	−0.162698
$419$	7.15349	0.349471	0.174735	−	0.984615i	$-0.444093\pi$
$419$	7.15349	0.349471	0.174735	+	0.984615i	$0.444093\pi$
$420$	−3.38995	−0.165412
$421$	18.9743	0.924751	0.462375	−	0.886684i	$-0.346997\pi$
$421$	18.9743	0.924751	0.462375	+	0.886684i	$0.346997\pi$
$422$	18.8108	0.915695
$423$	10.3738	0.504393
$424$	1.60571	0.0779800
$425$	−7.71631	−0.374296
$426$	9.93207	0.481210
$427$	−4.91945	−0.238069
$428$	−20.2746	−0.980008
$429$	−2.15959	−0.104266
$430$	2.08707	0.100647
$431$	2.07792	0.100090	0.0500449	−	0.998747i	$-0.484064\pi$
$431$	2.07792	0.100090	0.0500449	+	0.998747i	$0.484064\pi$
$432$	1.00000	0.0481125
$433$	−0.261229	−0.0125539	−0.00627694	−	0.999980i	$-0.501998\pi$
$433$	−0.261229	−0.0125539	−0.00627694	+	0.999980i	$0.501998\pi$
$434$	−12.5637	−0.603077
$435$	−3.33249	−0.159781
$436$	11.4418	0.547961
$437$	0.449748	0.0215144
$438$	1.42566	0.0681205
$439$	−3.23121	−0.154217	−0.0771086	−	0.997023i	$-0.524569\pi$
$439$	−3.23121	−0.154217	−0.0771086	+	0.997023i	$0.524569\pi$
$440$	−0.689091	−0.0328511
$441$	17.2010	0.819094
$442$	−3.68254	−0.175161
$443$	−27.5554	−1.30920	−0.654599	−	0.755976i	$-0.727162\pi$
$443$	−27.5554	−1.30920	−0.654599	+	0.755976i	$0.727162\pi$
$444$	7.89072	0.374477
$445$	−2.24192	−0.106277
$446$	−27.5578	−1.30490
$447$	5.50795	0.260517
$448$	4.91945	0.232422
$449$	0.671436	0.0316870	0.0158435	−	0.999874i	$-0.494957\pi$
$449$	0.671436	0.0316870	0.0158435	+	0.999874i	$0.494957\pi$
$450$	4.52515	0.213318
$451$	7.38995	0.347979
$452$	−0.451754	−0.0212487
$453$	7.12038	0.334545
$454$	−25.8110	−1.21137
$455$	−7.32089	−0.343209
$456$	3.32636	0.155771
$457$	11.7230	0.548380	0.274190	−	0.961675i	$-0.411590\pi$
$457$	11.7230	0.548380	0.274190	+	0.961675i	$0.411590\pi$
$458$	−6.33420	−0.295978
$459$	1.70520	0.0795921
$460$	0.0931701	0.00434408
$461$	2.33180	0.108603	0.0543013	−	0.998525i	$-0.482707\pi$
$461$	2.33180	0.108603	0.0543013	+	0.998525i	$0.482707\pi$
$462$	4.91945	0.228873
$463$	−2.70741	−0.125824	−0.0629120	−	0.998019i	$-0.520039\pi$
$463$	−2.70741	−0.125824	−0.0629120	+	0.998019i	$0.520039\pi$
$464$	4.83606	0.224509
$465$	−1.75986	−0.0816115
$466$	−17.3954	−0.805827
$467$	5.81429	0.269053	0.134527	−	0.990910i	$-0.457049\pi$
$467$	5.81429	0.269053	0.134527	+	0.990910i	$0.457049\pi$
$468$	2.15959	0.0998271
$469$	59.4575	2.74549
$470$	7.14851	0.329736
$471$	16.7836	0.773346
$472$	1.90614	0.0877372
$473$	−3.02873	−0.139261
$474$	−0.110825	−0.00509035
$475$	15.0523	0.690646
$476$	8.38866	0.384493
$477$	−1.60571	−0.0735202
$478$	−8.57417	−0.392173
$479$	34.4070	1.57209	0.786047	−	0.618166i	$-0.212124\pi$
$479$	34.4070	1.57209	0.786047	+	0.618166i	$0.212124\pi$
$480$	0.689091	0.0314526
$481$	17.0407	0.776990
$482$	21.1128	0.961660
$483$	−0.665145	−0.0302652
$484$	1.00000	0.0454545
$485$	4.14519	0.188223
$486$	−1.00000	−0.0453609
$487$	−18.4235	−0.834848	−0.417424	−	0.908712i	$-0.637067\pi$
$487$	−18.4235	−0.834848	−0.417424	+	0.908712i	$0.637067\pi$
$488$	1.00000	0.0452679
$489$	3.13171	0.141621
$490$	11.8530	0.535465
$491$	14.3565	0.647898	0.323949	−	0.946075i	$-0.394989\pi$
$491$	14.3565	0.647898	0.323949	+	0.946075i	$0.394989\pi$
$492$	−7.38995	−0.333165
$493$	8.24647	0.371402
$494$	7.18357	0.323204
$495$	0.689091	0.0309723
$496$	2.55388	0.114673
$497$	−48.8603	−2.19168
$498$	−14.1106	−0.632311
$499$	−3.64007	−0.162952	−0.0814760	−	0.996675i	$-0.525963\pi$
$499$	−3.64007	−0.162952	−0.0814760	+	0.996675i	$0.525963\pi$
$500$	6.56370	0.293537
$501$	−10.1883	−0.455182
$502$	−1.83060	−0.0817036
$503$	13.6647	0.609280	0.304640	−	0.952467i	$-0.401464\pi$
$503$	13.6647	0.609280	0.304640	+	0.952467i	$0.401464\pi$
$504$	−4.91945	−0.219130
$505$	5.65661	0.251716
$506$	−0.135207	−0.00601070
$507$	−8.33617	−0.370222
$508$	21.0873	0.935598
$509$	−29.1894	−1.29380	−0.646900	−	0.762575i	$-0.723935\pi$
$509$	−29.1894	−1.29380	−0.646900	+	0.762575i	$0.723935\pi$
$510$	1.17504	0.0520316
$511$	−7.01344	−0.310257
$512$	−1.00000	−0.0441942
$513$	−3.32636	−0.146862
$514$	−14.2530	−0.628672
$515$	0.103817	0.00457471
$516$	3.02873	0.133332
$517$	−10.3738	−0.456241
$518$	−38.8180	−1.70556
$519$	23.8598	1.04733
$520$	1.48815	0.0652599
$521$	−31.1413	−1.36433	−0.682163	−	0.731200i	$-0.738961\pi$
$521$	−31.1413	−1.36433	−0.682163	+	0.731200i	$0.738961\pi$
$522$	−4.83606	−0.211669
$523$	4.32422	0.189085	0.0945424	−	0.995521i	$-0.469861\pi$
$523$	4.32422	0.189085	0.0945424	+	0.995521i	$0.469861\pi$
$524$	−10.7653	−0.470285
$525$	−22.2613	−0.971561
$526$	−30.0013	−1.30812
$527$	4.35489	0.189702
$528$	−1.00000	−0.0435194
$529$	−22.9817	−0.999205
$530$	−1.10648	−0.0480623
$531$	−1.90614	−0.0827194
$532$	−16.3638	−0.709463
$533$	−15.9593	−0.691272
$534$	−3.25345	−0.140791
$535$	13.9710	0.604020
$536$	−12.0862	−0.522045
$537$	−13.4202	−0.579125
$538$	−22.6897	−0.978223
$539$	−17.2010	−0.740898
$540$	−0.689091	−0.0296537
$541$	1.36227	0.0585685	0.0292843	−	0.999571i	$-0.490677\pi$
$541$	1.36227	0.0585685	0.0292843	+	0.999571i	$0.490677\pi$
$542$	−5.92225	−0.254383
$543$	2.21639	0.0951143
$544$	−1.70520	−0.0731100
$545$	−7.88442	−0.337731
$546$	−10.6240	−0.454665
$547$	6.82934	0.292001	0.146001	−	0.989284i	$-0.453360\pi$
$547$	6.82934	0.292001	0.146001	+	0.989284i	$0.453360\pi$
$548$	−16.8515	−0.719861
$549$	−1.00000	−0.0426790
$550$	−4.52515	−0.192953
$551$	−16.0865	−0.685307
$552$	0.135207	0.00575480
$553$	0.545197	0.0231841
$554$	2.44262	0.103777
$555$	−5.43742	−0.230806
$556$	−10.7997	−0.458009
$557$	21.0429	0.891617	0.445809	−	0.895128i	$-0.352916\pi$
$557$	21.0429	0.891617	0.445809	+	0.895128i	$0.352916\pi$
$558$	−2.55388	−0.108115
$559$	6.54081	0.276647
$560$	−3.38995	−0.143251
$561$	−1.70520	−0.0719937
$562$	−1.08055	−0.0455804
$563$	−32.1944	−1.35683	−0.678417	−	0.734677i	$-0.737334\pi$
$563$	−32.1944	−1.35683	−0.678417	+	0.734677i	$0.737334\pi$
$564$	10.3738	0.436817
$565$	0.311299	0.0130965
$566$	21.3543	0.897587
$567$	4.91945	0.206597
$568$	9.93207	0.416740
$569$	−6.11670	−0.256425	−0.128213	−	0.991747i	$-0.540924\pi$
$569$	−6.11670	−0.256425	−0.128213	+	0.991747i	$0.540924\pi$
$570$	−2.29216	−0.0960082
$571$	35.3475	1.47925	0.739623	−	0.673022i	$-0.235004\pi$
$571$	35.3475	1.47925	0.739623	+	0.673022i	$0.235004\pi$
$572$	−2.15959	−0.0902970
$573$	−8.20752	−0.342874
$574$	36.3545	1.51741
$575$	0.611834	0.0255152
$576$	1.00000	0.0416667
$577$	−8.46446	−0.352380	−0.176190	−	0.984356i	$-0.556377\pi$
$577$	−8.46446	−0.352380	−0.176190	+	0.984356i	$0.556377\pi$
$578$	14.0923	0.586162
$579$	10.2032	0.424029
$580$	−3.33249	−0.138374
$581$	69.4164	2.87988
$582$	6.01545	0.249348
$583$	1.60571	0.0665016
$584$	1.42566	0.0589941
$585$	−1.48815	−0.0615276
$586$	27.8023	1.14850
$587$	−17.8062	−0.734941	−0.367471	−	0.930035i	$-0.619776\pi$
$587$	−17.8062	−0.734941	−0.367471	+	0.930035i	$0.619776\pi$
$588$	17.2010	0.709356
$589$	−8.49513	−0.350036
$590$	−1.31350	−0.0540761
$591$	0.297629	0.0122428
$592$	7.89072	0.324307
$593$	−14.8308	−0.609029	−0.304514	−	0.952508i	$-0.598494\pi$
$593$	−14.8308	−0.609029	−0.304514	+	0.952508i	$0.598494\pi$
$594$	1.00000	0.0410305
$595$	−5.78055	−0.236979
$596$	5.50795	0.225614
$597$	−23.4585	−0.960094
$598$	0.291992	0.0119405
$599$	−22.6525	−0.925558	−0.462779	−	0.886474i	$-0.653148\pi$
$599$	−22.6525	−0.925558	−0.462779	+	0.886474i	$0.653148\pi$
$600$	4.52515	0.184739
$601$	41.7118	1.70146	0.850729	−	0.525604i	$-0.176161\pi$
$601$	41.7118	1.70146	0.850729	+	0.525604i	$0.176161\pi$
$602$	−14.8997	−0.607266
$603$	12.0862	0.492189
$604$	7.12038	0.289724
$605$	−0.689091	−0.0280155
$606$	8.20881	0.333460
$607$	16.9020	0.686033	0.343016	−	0.939329i	$-0.388551\pi$
$607$	16.9020	0.686033	0.343016	+	0.939329i	$0.388551\pi$
$608$	3.32636	0.134902
$609$	23.7908	0.964050
$610$	−0.689091	−0.0279005
$611$	22.4032	0.906338
$612$	1.70520	0.0689287
$613$	9.28221	0.374905	0.187452	−	0.982274i	$-0.439977\pi$
$613$	9.28221	0.374905	0.187452	+	0.982274i	$0.439977\pi$
$614$	31.9388	1.28895
$615$	5.09234	0.205343
$616$	4.91945	0.198210
$617$	1.75491	0.0706500	0.0353250	−	0.999376i	$-0.488753\pi$
$617$	1.75491	0.0706500	0.0353250	+	0.999376i	$0.488753\pi$
$618$	0.150657	0.00606033
$619$	18.0534	0.725626	0.362813	−	0.931862i	$-0.381816\pi$
$619$	18.0534	0.725626	0.362813	+	0.931862i	$0.381816\pi$
$620$	−1.75986	−0.0706776
$621$	−0.135207	−0.00542568
$622$	−14.0050	−0.561549
$623$	16.0052	0.641234
$624$	2.15959	0.0864528
$625$	18.1028	0.724111
$626$	−6.21229	−0.248293
$627$	3.32636	0.132842
$628$	16.7836	0.669738
$629$	13.4553	0.536497
$630$	3.38995	0.135059
$631$	−44.0205	−1.75243	−0.876214	−	0.481923i	$-0.839939\pi$
$631$	−44.0205	−1.75243	−0.876214	+	0.481923i	$0.839939\pi$
$632$	−0.110825	−0.00440838
$633$	−18.8108	−0.747662
$634$	0.166142	0.00659833
$635$	−14.5311	−0.576648
$636$	−1.60571	−0.0636704
$637$	37.1470	1.47182
$638$	4.83606	0.191462
$639$	−9.93207	−0.392906
$640$	0.689091	0.0272387
$641$	−35.6691	−1.40884	−0.704422	−	0.709781i	$-0.748794\pi$
$641$	−35.6691	−1.40884	−0.704422	+	0.709781i	$0.748794\pi$
$642$	20.2746	0.800173
$643$	33.6105	1.32547	0.662735	−	0.748854i	$-0.269396\pi$
$643$	33.6105	1.32547	0.662735	+	0.748854i	$0.269396\pi$
$644$	−0.665145	−0.0262104
$645$	−2.08707	−0.0821783
$646$	5.67212	0.223166
$647$	−31.4010	−1.23450	−0.617251	−	0.786767i	$-0.711754\pi$
$647$	−31.4010	−1.23450	−0.617251	+	0.786767i	$0.711754\pi$
$648$	−1.00000	−0.0392837
$649$	1.90614	0.0748226
$650$	9.77248	0.383308
$651$	12.5637	0.492410
$652$	3.13171	0.122647
$653$	50.2918	1.96807	0.984034	−	0.177978i	$-0.0569556\pi$
$653$	50.2918	1.96807	0.984034	+	0.177978i	$0.0569556\pi$
$654$	−11.4418	−0.447409
$655$	7.41829	0.289856
$656$	−7.38995	−0.288529
$657$	−1.42566	−0.0556202
$658$	−51.0335	−1.98949
$659$	−8.34616	−0.325120	−0.162560	−	0.986699i	$-0.551975\pi$
$659$	−8.34616	−0.325120	−0.162560	+	0.986699i	$0.551975\pi$
$660$	0.689091	0.0268228
$661$	−40.5254	−1.57625	−0.788127	−	0.615513i	$-0.788949\pi$
$661$	−40.5254	−1.57625	−0.788127	+	0.615513i	$0.788949\pi$
$662$	29.9118	1.16256
$663$	3.68254	0.143018
$664$	−14.1106	−0.547597
$665$	11.2762	0.437271
$666$	−7.89072	−0.305759
$667$	−0.653871	−0.0253180
$668$	−10.1883	−0.394199
$669$	27.5578	1.06545
$670$	8.32850	0.321758
$671$	1.00000	0.0386046
$672$	−4.91945	−0.189772
$673$	−25.2843	−0.974640	−0.487320	−	0.873223i	$-0.662025\pi$
$673$	−25.2843	−0.974640	−0.487320	+	0.873223i	$0.662025\pi$
$674$	−8.19725	−0.315746
$675$	−4.52515	−0.174173
$676$	−8.33617	−0.320622
$677$	49.1342	1.88838	0.944190	−	0.329402i	$-0.106847\pi$
$677$	49.1342	1.88838	0.944190	+	0.329402i	$0.106847\pi$
$678$	0.451754	0.0173495
$679$	−29.5927	−1.13566
$680$	1.17504	0.0450607
$681$	25.8110	0.989081
$682$	2.55388	0.0977933
$683$	45.0460	1.72364	0.861818	−	0.507218i	$-0.169326\pi$
$683$	45.0460	1.72364	0.861818	+	0.507218i	$0.169326\pi$
$684$	−3.32636	−0.127187
$685$	11.6122	0.443680
$686$	−50.1831	−1.91600
$687$	6.33420	0.241665
$688$	3.02873	0.115469
$689$	−3.46767	−0.132108
$690$	−0.0931701	−0.00354693
$691$	20.0217	0.761663	0.380832	−	0.924644i	$-0.375638\pi$
$691$	20.0217	0.761663	0.380832	+	0.924644i	$0.375638\pi$
$692$	23.8598	0.907014
$693$	−4.91945	−0.186874
$694$	−26.4965	−1.00579
$695$	7.44197	0.282290
$696$	−4.83606	−0.183310
$697$	−12.6014	−0.477310
$698$	−14.7589	−0.558634
$699$	17.3954	0.657955
$700$	−22.2613	−0.841396
$701$	−1.73762	−0.0656289	−0.0328145	−	0.999461i	$-0.510447\pi$
$701$	−1.73762	−0.0656289	−0.0328145	+	0.999461i	$0.510447\pi$
$702$	−2.15959	−0.0815085
$703$	−26.2474	−0.989938
$704$	−1.00000	−0.0376889
$705$	−7.14851	−0.269229
$706$	23.3634	0.879292
$707$	−40.3828	−1.51875
$708$	−1.90614	−0.0716371
$709$	−43.0523	−1.61686	−0.808431	−	0.588591i	$-0.799683\pi$
$709$	−43.0523	−1.61686	−0.808431	+	0.588591i	$0.799683\pi$
$710$	−6.84410	−0.256854
$711$	0.110825	0.00415626
$712$	−3.25345	−0.121928
$713$	−0.345304	−0.0129317
$714$	−8.38866	−0.313938
$715$	1.48815	0.0556538
$716$	−13.4202	−0.501537
$717$	8.57417	0.320208
$718$	16.5426	0.617363
$719$	5.15587	0.192281	0.0961407	−	0.995368i	$-0.469350\pi$
$719$	5.15587	0.192281	0.0961407	+	0.995368i	$0.469350\pi$
$720$	−0.689091	−0.0256809
$721$	−0.741151	−0.0276019
$722$	7.93533	0.295323
$723$	−21.1128	−0.785192
$724$	2.21639	0.0823714
$725$	−21.8839	−0.812749
$726$	−1.00000	−0.0371135
$727$	−8.87678	−0.329222	−0.164611	−	0.986359i	$-0.552637\pi$
$727$	−8.87678	−0.329222	−0.164611	+	0.986359i	$0.552637\pi$
$728$	−10.6240	−0.393751
$729$	1.00000	0.0370370
$730$	−0.982407	−0.0363605
$731$	5.16460	0.191020
$732$	−1.00000	−0.0369611
$733$	−18.6538	−0.688994	−0.344497	−	0.938787i	$-0.611951\pi$
$733$	−18.6538	−0.688994	−0.344497	+	0.938787i	$0.611951\pi$
$734$	18.8578	0.696055
$735$	−11.8530	−0.437206
$736$	0.135207	0.00498381
$737$	−12.0862	−0.445202
$738$	7.38995	0.272028
$739$	−9.78121	−0.359808	−0.179904	−	0.983684i	$-0.557579\pi$
$739$	−9.78121	−0.359808	−0.179904	+	0.983684i	$0.557579\pi$
$740$	−5.43742	−0.199884
$741$	−7.18357	−0.263895
$742$	7.89919	0.289988
$743$	−14.7455	−0.540959	−0.270480	−	0.962726i	$-0.587182\pi$
$743$	−14.7455	−0.540959	−0.270480	+	0.962726i	$0.587182\pi$
$744$	−2.55388	−0.0936299
$745$	−3.79548	−0.139056
$746$	−17.7078	−0.648330
$747$	14.1106	0.516280
$748$	−1.70520	−0.0623484
$749$	−99.7397	−3.64441
$750$	−6.56370	−0.239672
$751$	−28.8023	−1.05101	−0.525506	−	0.850790i	$-0.676124\pi$
$751$	−28.8023	−1.05101	−0.525506	+	0.850790i	$0.676124\pi$
$752$	10.3738	0.378295
$753$	1.83060	0.0667107
$754$	−10.4439	−0.380345
$755$	−4.90659	−0.178569
$756$	4.91945	0.178919
$757$	−11.5289	−0.419023	−0.209512	−	0.977806i	$-0.567187\pi$
$757$	−11.5289	−0.419023	−0.209512	+	0.977806i	$0.567187\pi$
$758$	18.2613	0.663280
$759$	0.135207	0.00490771
$760$	−2.29216	−0.0831455
$761$	−7.56742	−0.274319	−0.137159	−	0.990549i	$-0.543797\pi$
$761$	−7.56742	−0.274319	−0.137159	+	0.990549i	$0.543797\pi$
$762$	−21.0873	−0.763913
$763$	56.2872	2.03773
$764$	−8.20752	−0.296938
$765$	−1.17504	−0.0424837
$766$	−24.7651	−0.894799
$767$	−4.11648	−0.148638
$768$	1.00000	0.0360844
$769$	−45.7037	−1.64812	−0.824060	−	0.566503i	$-0.808296\pi$
$769$	−45.7037	−1.64812	−0.824060	+	0.566503i	$0.808296\pi$
$770$	−3.38995	−0.122165
$771$	14.2530	0.513309
$772$	10.2032	0.367220
$773$	−6.87501	−0.247277	−0.123639	−	0.992327i	$-0.539456\pi$
$773$	−6.87501	−0.247277	−0.123639	+	0.992327i	$0.539456\pi$
$774$	−3.02873	−0.108865
$775$	−11.5567	−0.415129
$776$	6.01545	0.215942
$777$	38.8180	1.39259
$778$	−11.5147	−0.412822
$779$	24.5816	0.880728
$780$	−1.48815	−0.0532844
$781$	9.93207	0.355397
$782$	0.230556	0.00824466
$783$	4.83606	0.172827
$784$	17.2010	0.614320
$785$	−11.5654	−0.412787
$786$	10.7653	0.383986
$787$	25.0305	0.892240	0.446120	−	0.894973i	$-0.352805\pi$
$787$	25.0305	0.892240	0.446120	+	0.894973i	$0.352805\pi$
$788$	0.297629	0.0106026
$789$	30.0013	1.06808
$790$	0.0763684	0.00271707
$791$	−2.22238	−0.0790187
$792$	1.00000	0.0355335
$793$	−2.15959	−0.0766893
$794$	−0.602648	−0.0213872
$795$	1.10648	0.0392427
$796$	−23.4585	−0.831466
$797$	−14.6273	−0.518124	−0.259062	−	0.965861i	$-0.583413\pi$
$797$	−14.6273	−0.518124	−0.259062	+	0.965861i	$0.583413\pi$
$798$	16.3638	0.579274
$799$	17.6895	0.625809
$800$	4.52515	0.159988
$801$	3.25345	0.114955
$802$	19.3012	0.681547
$803$	1.42566	0.0503103
$804$	12.0862	0.426248
$805$	0.458345	0.0161546
$806$	−5.51534	−0.194270
$807$	22.6897	0.798716
$808$	8.20881	0.288785
$809$	−28.0719	−0.986955	−0.493477	−	0.869759i	$-0.664274\pi$
$809$	−28.0719	−0.986955	−0.493477	+	0.869759i	$0.664274\pi$
$810$	0.689091	0.0242122
$811$	38.1920	1.34110	0.670552	−	0.741863i	$-0.266057\pi$
$811$	38.1920	1.34110	0.670552	+	0.741863i	$0.266057\pi$
$812$	23.7908	0.834892
$813$	5.92225	0.207702
$814$	7.89072	0.276570
$815$	−2.15803	−0.0755927
$816$	1.70520	0.0596940
$817$	−10.0746	−0.352467
$818$	−19.9815	−0.698637
$819$	10.6240	0.371232
$820$	5.09234	0.177832
$821$	−17.7797	−0.620517	−0.310259	−	0.950652i	$-0.600416\pi$
$821$	−17.7797	−0.620517	−0.310259	+	0.950652i	$0.600416\pi$
$822$	16.8515	0.587764
$823$	−29.3850	−1.02430	−0.512148	−	0.858897i	$-0.671150\pi$
$823$	−29.3850	−1.02430	−0.512148	+	0.858897i	$0.671150\pi$
$824$	0.150657	0.00524840
$825$	4.52515	0.157546
$826$	9.37716	0.326273
$827$	16.7562	0.582669	0.291335	−	0.956621i	$-0.405901\pi$
$827$	16.7562	0.582669	0.291335	+	0.956621i	$0.405901\pi$
$828$	−0.135207	−0.00469878
$829$	−36.0749	−1.25293	−0.626466	−	0.779449i	$-0.715499\pi$
$829$	−36.0749	−1.25293	−0.626466	+	0.779449i	$0.715499\pi$
$830$	9.72349	0.337507
$831$	−2.44262	−0.0847336
$832$	2.15959	0.0748703
$833$	29.3311	1.01626
$834$	10.7997	0.373963
$835$	7.02070	0.242961
$836$	3.32636	0.115045
$837$	2.55388	0.0882751
$838$	−7.15349	−0.247113
$839$	−37.8008	−1.30503	−0.652514	−	0.757777i	$-0.726286\pi$
$839$	−37.8008	−1.30503	−0.652514	+	0.757777i	$0.726286\pi$
$840$	3.38995	0.116964
$841$	−5.61250	−0.193534
$842$	−18.9743	−0.653898
$843$	1.08055	0.0372162
$844$	−18.8108	−0.647494
$845$	5.74438	0.197613
$846$	−10.3738	−0.356660
$847$	4.91945	0.169034
$848$	−1.60571	−0.0551402
$849$	−21.3543	−0.732876
$850$	7.71631	0.264667
$851$	−1.06688	−0.0365723
$852$	−9.93207	−0.340267
$853$	−25.8469	−0.884982	−0.442491	−	0.896773i	$-0.645905\pi$
$853$	−25.8469	−0.884982	−0.442491	+	0.896773i	$0.645905\pi$
$854$	4.91945	0.168340
$855$	2.29216	0.0783903
$856$	20.2746	0.692970
$857$	−14.6922	−0.501875	−0.250938	−	0.968003i	$-0.580739\pi$
$857$	−14.6922	−0.501875	−0.250938	+	0.968003i	$0.580739\pi$
$858$	2.15959	0.0737272
$859$	−7.58960	−0.258954	−0.129477	−	0.991582i	$-0.541330\pi$
$859$	−7.58960	−0.258954	−0.129477	+	0.991582i	$0.541330\pi$
$860$	−2.08707	−0.0711685
$861$	−36.3545	−1.23896
$862$	−2.07792	−0.0707742
$863$	37.4827	1.27593	0.637963	−	0.770067i	$-0.279777\pi$
$863$	37.4827	1.27593	0.637963	+	0.770067i	$0.279777\pi$
$864$	−1.00000	−0.0340207
$865$	−16.4416	−0.559030
$866$	0.261229	0.00887693
$867$	−14.0923	−0.478599
$868$	12.5637	0.426440
$869$	−0.110825	−0.00375948
$870$	3.33249	0.112982
$871$	26.1013	0.884408
$872$	−11.4418	−0.387467
$873$	−6.01545	−0.203592
$874$	−0.449748	−0.0152130
$875$	32.2898	1.09159
$876$	−1.42566	−0.0481685
$877$	−2.09692	−0.0708079	−0.0354039	−	0.999373i	$-0.511272\pi$
$877$	−2.09692	−0.0708079	−0.0354039	+	0.999373i	$0.511272\pi$
$878$	3.23121	0.109048
$879$	−27.8023	−0.937749
$880$	0.689091	0.0232292
$881$	39.5733	1.33326	0.666629	−	0.745389i	$-0.267736\pi$
$881$	39.5733	1.33326	0.666629	+	0.745389i	$0.267736\pi$
$882$	−17.2010	−0.579187
$883$	49.5629	1.66792	0.833962	−	0.551822i	$-0.186067\pi$
$883$	49.5629	1.66792	0.833962	+	0.551822i	$0.186067\pi$
$884$	3.68254	0.123857
$885$	1.31350	0.0441529
$886$	27.5554	0.925743
$887$	2.72368	0.0914521	0.0457261	−	0.998954i	$-0.485440\pi$
$887$	2.72368	0.0914521	0.0457261	+	0.998954i	$0.485440\pi$
$888$	−7.89072	−0.264795
$889$	103.738	3.47926
$890$	2.24192	0.0751494
$891$	−1.00000	−0.0335013
$892$	27.5578	0.922705
$893$	−34.5071	−1.15474
$894$	−5.50795	−0.184213
$895$	9.24775	0.309118
$896$	−4.91945	−0.164347
$897$	−0.291992	−0.00974934
$898$	−0.671436	−0.0224061
$899$	12.3507	0.411920
$900$	−4.52515	−0.150838
$901$	−2.73805	−0.0912178
$902$	−7.38995	−0.246058
$903$	14.8997	0.495830
$904$	0.451754	0.0150251
$905$	−1.52729	−0.0507689
$906$	−7.12038	−0.236559
$907$	36.4446	1.21012	0.605061	−	0.796179i	$-0.293149\pi$
$907$	36.4446	1.21012	0.605061	+	0.796179i	$0.293149\pi$
$908$	25.8110	0.856570
$909$	−8.20881	−0.272269
$910$	7.32089	0.242685
$911$	−8.92886	−0.295826	−0.147913	−	0.989000i	$-0.547256\pi$
$911$	−8.92886	−0.295826	−0.147913	+	0.989000i	$0.547256\pi$
$912$	−3.32636	−0.110147
$913$	−14.1106	−0.466993
$914$	−11.7230	−0.387763
$915$	0.689091	0.0227806
$916$	6.33420	0.209288
$917$	−52.9594	−1.74887
$918$	−1.70520	−0.0562801
$919$	−36.3192	−1.19806	−0.599030	−	0.800727i	$-0.704447\pi$
$919$	−36.3192	−1.19806	−0.599030	+	0.800727i	$0.704447\pi$
$920$	−0.0931701	−0.00307173
$921$	−31.9388	−1.05242
$922$	−2.33180	−0.0767937
$923$	−21.4492	−0.706009
$924$	−4.91945	−0.161838
$925$	−35.7067	−1.17403
$926$	2.70741	0.0889709
$927$	−0.150657	−0.00494824
$928$	−4.83606	−0.158752
$929$	16.2375	0.532736	0.266368	−	0.963871i	$-0.414176\pi$
$929$	16.2375	0.532736	0.266368	+	0.963871i	$0.414176\pi$
$930$	1.75986	0.0577080
$931$	−57.2166	−1.87520
$932$	17.3954	0.569806
$933$	14.0050	0.458503
$934$	−5.81429	−0.190249
$935$	1.17504	0.0384279
$936$	−2.15959	−0.0705884
$937$	−52.9033	−1.72828	−0.864138	−	0.503254i	$-0.832136\pi$
$937$	−52.9033	−1.72828	−0.864138	+	0.503254i	$0.832136\pi$
$938$	−59.4575	−1.94136
$939$	6.21229	0.202731
$940$	−7.14851	−0.233159
$941$	−12.3309	−0.401977	−0.200989	−	0.979594i	$-0.564415\pi$
$941$	−12.3309	−0.401977	−0.200989	+	0.979594i	$0.564415\pi$
$942$	−16.7836	−0.546839
$943$	0.999175	0.0325376
$944$	−1.90614	−0.0620396
$945$	−3.38995	−0.110275
$946$	3.02873	0.0984725
$947$	15.7603	0.512141	0.256070	−	0.966658i	$-0.417572\pi$
$947$	15.7603	0.512141	0.256070	+	0.966658i	$0.417572\pi$
$948$	0.110825	0.00359942
$949$	−3.07883	−0.0999432
$950$	−15.0523	−0.488361
$951$	−0.166142	−0.00538752
$952$	−8.38866	−0.271878
$953$	−8.16087	−0.264357	−0.132178	−	0.991226i	$-0.542197\pi$
$953$	−8.16087	−0.264357	−0.132178	+	0.991226i	$0.542197\pi$
$954$	1.60571	0.0519867
$955$	5.65573	0.183015
$956$	8.57417	0.277309
$957$	−4.83606	−0.156328
$958$	−34.4070	−1.11164
$959$	−82.9001	−2.67698
$960$	−0.689091	−0.0222403
$961$	−24.4777	−0.789603
$962$	−17.0407	−0.549415
$963$	−20.2746	−0.653339
$964$	−21.1128	−0.679997
$965$	−7.03091	−0.226333
$966$	0.665145	0.0214007
$967$	−20.9588	−0.673990	−0.336995	−	0.941506i	$-0.609411\pi$
$967$	−20.9588	−0.673990	−0.336995	+	0.941506i	$0.609411\pi$
$968$	−1.00000	−0.0321412
$969$	−5.67212	−0.182215
$970$	−4.14519	−0.133094
$971$	17.2349	0.553095	0.276547	−	0.961000i	$-0.410810\pi$
$971$	17.2349	0.553095	0.276547	+	0.961000i	$0.410810\pi$
$972$	1.00000	0.0320750
$973$	−53.1285	−1.70322
$974$	18.4235	0.590326
$975$	−9.77248	−0.312970
$976$	−1.00000	−0.0320092
$977$	25.4526	0.814301	0.407151	−	0.913361i	$-0.366522\pi$
$977$	25.4526	0.814301	0.407151	+	0.913361i	$0.366522\pi$
$978$	−3.13171	−0.100141
$979$	−3.25345	−0.103981
$980$	−11.8530	−0.378631
$981$	11.4418	0.365308
$982$	−14.3565	−0.458133
$983$	−17.1080	−0.545660	−0.272830	−	0.962062i	$-0.587960\pi$
$983$	−17.1080	−0.545660	−0.272830	+	0.962062i	$0.587960\pi$
$984$	7.38995	0.235583
$985$	−0.205094	−0.00653483
$986$	−8.24647	−0.262621
$987$	51.0335	1.62442
$988$	−7.18357	−0.228540
$989$	−0.409506	−0.0130215
$990$	−0.689091	−0.0219007
$991$	18.4409	0.585796	0.292898	−	0.956144i	$-0.405380\pi$
$991$	18.4409	0.585796	0.292898	+	0.956144i	$0.405380\pi$
$992$	−2.55388	−0.0810859
$993$	−29.9118	−0.949222
$994$	48.8603	1.54975
$995$	16.1651	0.512467
$996$	14.1106	0.447111
$997$	−37.2711	−1.18039	−0.590193	−	0.807262i	$-0.700948\pi$
$997$	−37.2711	−1.18039	−0.590193	+	0.807262i	$0.700948\pi$
$998$	3.64007	0.115225
$999$	7.89072	0.249651

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.u.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.u.1.3	✓	5	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.689091 q^{5} -1.00000 q^{6} +4.91945 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.689091 q^{5} -1.00000 q^{6} +4.91945 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.689091 q^{10} -1.00000 q^{11} +1.00000 q^{12} +2.15959 q^{13} -4.91945 q^{14} -0.689091 q^{15} +1.00000 q^{16} +1.70520 q^{17} -1.00000 q^{18} -3.32636 q^{19} -0.689091 q^{20} +4.91945 q^{21} +1.00000 q^{22} -0.135207 q^{23} -1.00000 q^{24} -4.52515 q^{25} -2.15959 q^{26} +1.00000 q^{27} +4.91945 q^{28} +4.83606 q^{29} +0.689091 q^{30} +2.55388 q^{31} -1.00000 q^{32} -1.00000 q^{33} -1.70520 q^{34} -3.38995 q^{35} +1.00000 q^{36} +7.89072 q^{37} +3.32636 q^{38} +2.15959 q^{39} +0.689091 q^{40} -7.38995 q^{41} -4.91945 q^{42} +3.02873 q^{43} -1.00000 q^{44} -0.689091 q^{45} +0.135207 q^{46} +10.3738 q^{47} +1.00000 q^{48} +17.2010 q^{49} +4.52515 q^{50} +1.70520 q^{51} +2.15959 q^{52} -1.60571 q^{53} -1.00000 q^{54} +0.689091 q^{55} -4.91945 q^{56} -3.32636 q^{57} -4.83606 q^{58} -1.90614 q^{59} -0.689091 q^{60} -1.00000 q^{61} -2.55388 q^{62} +4.91945 q^{63} +1.00000 q^{64} -1.48815 q^{65} +1.00000 q^{66} +12.0862 q^{67} +1.70520 q^{68} -0.135207 q^{69} +3.38995 q^{70} -9.93207 q^{71} -1.00000 q^{72} -1.42566 q^{73} -7.89072 q^{74} -4.52515 q^{75} -3.32636 q^{76} -4.91945 q^{77} -2.15959 q^{78} +0.110825 q^{79} -0.689091 q^{80} +1.00000 q^{81} +7.38995 q^{82} +14.1106 q^{83} +4.91945 q^{84} -1.17504 q^{85} -3.02873 q^{86} +4.83606 q^{87} +1.00000 q^{88} +3.25345 q^{89} +0.689091 q^{90} +10.6240 q^{91} -0.135207 q^{92} +2.55388 q^{93} -10.3738 q^{94} +2.29216 q^{95} -1.00000 q^{96} -6.01545 q^{97} -17.2010 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9	\( 5 q - 5 q^{2} + 5 q^{3} + 5 q^{4} - q^{5} - 5 q^{6} - 3 q^{7} - 5 q^{8} + 5 q^{9} + q^{10} - 5 q^{11} + 5 q^{12} + 2 q^{13} + 3 q^{14} - q^{15} + 5 q^{16} + 6 q^{17} - 5 q^{18} + 7 q^{19} - q^{20} - 3 q^{21} + 5 q^{22} - 12 q^{23} - 5 q^{24} - 2 q^{26} + 5 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} - q^{31} - 5 q^{32} - 5 q^{33} - 6 q^{34} + 17 q^{35} + 5 q^{36} + 3 q^{37} - 7 q^{38} + 2 q^{39} + q^{40} - 3 q^{41} + 3 q^{42} + 24 q^{43} - 5 q^{44} - q^{45} + 12 q^{46} + 18 q^{47} + 5 q^{48} + 26 q^{49} + 6 q^{51} + 2 q^{52} - 13 q^{53} - 5 q^{54} + q^{55} + 3 q^{56} + 7 q^{57} - 4 q^{58} - 16 q^{59} - q^{60} - 5 q^{61} + q^{62} - 3 q^{63} + 5 q^{64} + 4 q^{65} + 5 q^{66} + 18 q^{67} + 6 q^{68} - 12 q^{69} - 17 q^{70} - 31 q^{71} - 5 q^{72} + 8 q^{73} - 3 q^{74} + 7 q^{76} + 3 q^{77} - 2 q^{78} + 32 q^{79} - q^{80} + 5 q^{81} + 3 q^{82} + 8 q^{83} - 3 q^{84} + 29 q^{85} - 24 q^{86} + 4 q^{87} + 5 q^{88} + q^{89} + q^{90} - 3 q^{91} - 12 q^{92} - q^{93} - 18 q^{94} + 33 q^{95} - 5 q^{96} - 4 q^{97} - 26 q^{98} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^2 + 5 * q^3 + 5 * q^4 - q^5 - 5 * q^6 - 3 * q^7 - 5 * q^8 + 5 * q^9 + q^10 - 5 * q^11 + 5 * q^12 + 2 * q^13 + 3 * q^14 - q^15 + 5 * q^16 + 6 * q^17 - 5 * q^18 + 7 * q^19 - q^20 - 3 * q^21 + 5 * q^22 - 12 * q^23 - 5 * q^24 - 2 * q^26 + 5 * q^27 - 3 * q^28 + 4 * q^29 + q^30 - q^31 - 5 * q^32 - 5 * q^33 - 6 * q^34 + 17 * q^35 + 5 * q^36 + 3 * q^37 - 7 * q^38 + 2 * q^39 + q^40 - 3 * q^41 + 3 * q^42 + 24 * q^43 - 5 * q^44 - q^45 + 12 * q^46 + 18 * q^47 + 5 * q^48 + 26 * q^49 + 6 * q^51 + 2 * q^52 - 13 * q^53 - 5 * q^54 + q^55 + 3 * q^56 + 7 * q^57 - 4 * q^58 - 16 * q^59 - q^60 - 5 * q^61 + q^62 - 3 * q^63 + 5 * q^64 + 4 * q^65 + 5 * q^66 + 18 * q^67 + 6 * q^68 - 12 * q^69 - 17 * q^70 - 31 * q^71 - 5 * q^72 + 8 * q^73 - 3 * q^74 + 7 * q^76 + 3 * q^77 - 2 * q^78 + 32 * q^79 - q^80 + 5 * q^81 + 3 * q^82 + 8 * q^83 - 3 * q^84 + 29 * q^85 - 24 * q^86 + 4 * q^87 + 5 * q^88 + q^89 + q^90 - 3 * q^91 - 12 * q^92 - q^93 - 18 * q^94 + 33 * q^95 - 5 * q^96 - 4 * q^97 - 26 * q^98 - 5 * q^99

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