LMFDB - Embedded newform 6026.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.27426 q^{3} +1.00000 q^{4} +0.325199 q^{5} +2.27426 q^{6} -2.71769 q^{7} -1.00000 q^{8} +2.17227 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.27426 q^{3} +1.00000 q^{4} +0.325199 q^{5} +2.27426 q^{6} -2.71769 q^{7} -1.00000 q^{8} +2.17227 q^{9} -0.325199 q^{10} -1.74697 q^{11} -2.27426 q^{12} +2.11485 q^{13} +2.71769 q^{14} -0.739587 q^{15} +1.00000 q^{16} -2.19305 q^{17} -2.17227 q^{18} +4.66099 q^{19} +0.325199 q^{20} +6.18074 q^{21} +1.74697 q^{22} -1.00000 q^{23} +2.27426 q^{24} -4.89425 q^{25} -2.11485 q^{26} +1.88249 q^{27} -2.71769 q^{28} +3.76165 q^{29} +0.739587 q^{30} -0.684085 q^{31} -1.00000 q^{32} +3.97308 q^{33} +2.19305 q^{34} -0.883790 q^{35} +2.17227 q^{36} -10.3852 q^{37} -4.66099 q^{38} -4.80973 q^{39} -0.325199 q^{40} +9.10405 q^{41} -6.18074 q^{42} +6.79922 q^{43} -1.74697 q^{44} +0.706418 q^{45} +1.00000 q^{46} -4.83190 q^{47} -2.27426 q^{48} +0.385839 q^{49} +4.89425 q^{50} +4.98757 q^{51} +2.11485 q^{52} -11.1185 q^{53} -1.88249 q^{54} -0.568114 q^{55} +2.71769 q^{56} -10.6003 q^{57} -3.76165 q^{58} +1.21410 q^{59} -0.739587 q^{60} -9.68636 q^{61} +0.684085 q^{62} -5.90354 q^{63} +1.00000 q^{64} +0.687748 q^{65} -3.97308 q^{66} +0.587348 q^{67} -2.19305 q^{68} +2.27426 q^{69} +0.883790 q^{70} +2.20883 q^{71} -2.17227 q^{72} -12.7817 q^{73} +10.3852 q^{74} +11.1308 q^{75} +4.66099 q^{76} +4.74773 q^{77} +4.80973 q^{78} +14.2748 q^{79} +0.325199 q^{80} -10.7981 q^{81} -9.10405 q^{82} -11.8175 q^{83} +6.18074 q^{84} -0.713178 q^{85} -6.79922 q^{86} -8.55498 q^{87} +1.74697 q^{88} -4.61090 q^{89} -0.706418 q^{90} -5.74752 q^{91} -1.00000 q^{92} +1.55579 q^{93} +4.83190 q^{94} +1.51575 q^{95} +2.27426 q^{96} +15.6283 q^{97} -0.385839 q^{98} -3.79489 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * 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
$3$	−2.27426	−1.31305	−0.656523	−	0.754306i	$-0.727973\pi$
$3$	−2.27426	−1.31305	−0.656523	+	0.754306i	$0.727973\pi$
$4$	1.00000	0.500000
$5$	0.325199	0.145433	0.0727167	−	0.997353i	$-0.476833\pi$
$5$	0.325199	0.145433	0.0727167	+	0.997353i	$0.476833\pi$
$6$	2.27426	0.928463
$7$	−2.71769	−1.02719	−0.513595	−	0.858033i	$-0.671687\pi$
$7$	−2.71769	−1.02719	−0.513595	+	0.858033i	$0.671687\pi$
$8$	−1.00000	−0.353553
$9$	2.17227	0.724088
$10$	−0.325199	−0.102837
$11$	−1.74697	−0.526732	−0.263366	−	0.964696i	$-0.584833\pi$
$11$	−1.74697	−0.526732	−0.263366	+	0.964696i	$0.584833\pi$
$12$	−2.27426	−0.656523
$13$	2.11485	0.586555	0.293277	−	0.956027i	$-0.405254\pi$
$13$	2.11485	0.586555	0.293277	+	0.956027i	$0.405254\pi$
$14$	2.71769	0.726333
$15$	−0.739587	−0.190961
$16$	1.00000	0.250000
$17$	−2.19305	−0.531893	−0.265947	−	0.963988i	$-0.585684\pi$
$17$	−2.19305	−0.531893	−0.265947	+	0.963988i	$0.585684\pi$
$18$	−2.17227	−0.512008
$19$	4.66099	1.06930	0.534652	−	0.845073i	$-0.320443\pi$
$19$	4.66099	1.06930	0.534652	+	0.845073i	$0.320443\pi$
$20$	0.325199	0.0727167
$21$	6.18074	1.34875
$22$	1.74697	0.372456
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.27426	0.464232
$25$	−4.89425	−0.978849
$26$	−2.11485	−0.414757
$27$	1.88249	0.362284
$28$	−2.71769	−0.513595
$29$	3.76165	0.698522	0.349261	−	0.937026i	$-0.386433\pi$
$29$	3.76165	0.698522	0.349261	+	0.937026i	$0.386433\pi$
$30$	0.739587	0.135030
$31$	−0.684085	−0.122865	−0.0614327	−	0.998111i	$-0.519567\pi$
$31$	−0.684085	−0.122865	−0.0614327	+	0.998111i	$0.519567\pi$
$32$	−1.00000	−0.176777
$33$	3.97308	0.691624
$34$	2.19305	0.376105
$35$	−0.883790	−0.149388
$36$	2.17227	0.362044
$37$	−10.3852	−1.70732	−0.853659	−	0.520832i	$-0.825622\pi$
$37$	−10.3852	−1.70732	−0.853659	+	0.520832i	$0.825622\pi$
$38$	−4.66099	−0.756112
$39$	−4.80973	−0.770173
$40$	−0.325199	−0.0514185
$41$	9.10405	1.42181	0.710907	−	0.703286i	$-0.248285\pi$
$41$	9.10405	1.42181	0.710907	+	0.703286i	$0.248285\pi$
$42$	−6.18074	−0.953709
$43$	6.79922	1.03687	0.518435	−	0.855117i	$-0.326515\pi$
$43$	6.79922	1.03687	0.518435	+	0.855117i	$0.326515\pi$
$44$	−1.74697	−0.263366
$45$	0.706418	0.105307
$46$	1.00000	0.147442
$47$	−4.83190	−0.704805	−0.352403	−	0.935848i	$-0.614635\pi$
$47$	−4.83190	−0.704805	−0.352403	+	0.935848i	$0.614635\pi$
$48$	−2.27426	−0.328261
$49$	0.385839	0.0551199
$50$	4.89425	0.692151
$51$	4.98757	0.698400
$52$	2.11485	0.293277
$53$	−11.1185	−1.52724	−0.763622	−	0.645664i	$-0.776581\pi$
$53$	−11.1185	−1.52724	−0.763622	+	0.645664i	$0.776581\pi$
$54$	−1.88249	−0.256174
$55$	−0.568114	−0.0766045
$56$	2.71769	0.363167
$57$	−10.6003	−1.40404
$58$	−3.76165	−0.493929
$59$	1.21410	0.158063	0.0790313	−	0.996872i	$-0.474817\pi$
$59$	1.21410	0.158063	0.0790313	+	0.996872i	$0.474817\pi$
$60$	−0.739587	−0.0954803
$61$	−9.68636	−1.24021	−0.620106	−	0.784518i	$-0.712910\pi$
$61$	−9.68636	−1.24021	−0.620106	+	0.784518i	$0.712910\pi$
$62$	0.684085	0.0868789
$63$	−5.90354	−0.743777
$64$	1.00000	0.125000
$65$	0.687748	0.0853047
$66$	−3.97308	−0.489052
$67$	0.587348	0.0717560	0.0358780	−	0.999356i	$-0.488577\pi$
$67$	0.587348	0.0717560	0.0358780	+	0.999356i	$0.488577\pi$
$68$	−2.19305	−0.265947
$69$	2.27426	0.273789
$70$	0.883790	0.105633
$71$	2.20883	0.262140	0.131070	−	0.991373i	$-0.458159\pi$
$71$	2.20883	0.262140	0.131070	+	0.991373i	$0.458159\pi$
$72$	−2.17227	−0.256004
$73$	−12.7817	−1.49599	−0.747994	−	0.663706i	$-0.768983\pi$
$73$	−12.7817	−1.49599	−0.747994	+	0.663706i	$0.768983\pi$
$74$	10.3852	1.20726
$75$	11.1308	1.28527
$76$	4.66099	0.534652
$77$	4.74773	0.541054
$78$	4.80973	0.544595
$79$	14.2748	1.60605	0.803023	−	0.595948i	$-0.203224\pi$
$79$	14.2748	1.60605	0.803023	+	0.595948i	$0.203224\pi$
$80$	0.325199	0.0363583
$81$	−10.7981	−1.19978
$82$	−9.10405	−1.00537
$83$	−11.8175	−1.29714	−0.648572	−	0.761154i	$-0.724633\pi$
$83$	−11.8175	−1.29714	−0.648572	+	0.761154i	$0.724633\pi$
$84$	6.18074	0.674374
$85$	−0.713178	−0.0773550
$86$	−6.79922	−0.733178
$87$	−8.55498	−0.917191
$88$	1.74697	0.186228
$89$	−4.61090	−0.488754	−0.244377	−	0.969680i	$-0.578583\pi$
$89$	−4.61090	−0.488754	−0.244377	+	0.969680i	$0.578583\pi$
$90$	−0.706418	−0.0744630
$91$	−5.74752	−0.602503
$92$	−1.00000	−0.104257
$93$	1.55579	0.161328
$94$	4.83190	0.498373
$95$	1.51575	0.155512
$96$	2.27426	0.232116
$97$	15.6283	1.58682	0.793409	−	0.608689i	$-0.208304\pi$
$97$	15.6283	1.58682	0.793409	+	0.608689i	$0.208304\pi$
$98$	−0.385839	−0.0389757
$99$	−3.79489	−0.381401
$100$	−4.89425	−0.489425
$101$	6.33106	0.629964	0.314982	−	0.949098i	$-0.398001\pi$
$101$	6.33106	0.629964	0.314982	+	0.949098i	$0.398001\pi$
$102$	−4.98757	−0.493843
$103$	17.5533	1.72958	0.864788	−	0.502137i	$-0.167453\pi$
$103$	17.5533	1.72958	0.864788	+	0.502137i	$0.167453\pi$
$104$	−2.11485	−0.207378
$105$	2.00997	0.196153
$106$	11.1185	1.07992
$107$	−12.1043	−1.17016	−0.585081	−	0.810975i	$-0.698937\pi$
$107$	−12.1043	−1.17016	−0.585081	+	0.810975i	$0.698937\pi$
$108$	1.88249	0.181142
$109$	−16.2841	−1.55973	−0.779865	−	0.625948i	$-0.784712\pi$
$109$	−16.2841	−1.55973	−0.779865	+	0.625948i	$0.784712\pi$
$110$	0.568114	0.0541675
$111$	23.6187	2.24179
$112$	−2.71769	−0.256798
$113$	−5.64770	−0.531291	−0.265645	−	0.964071i	$-0.585585\pi$
$113$	−5.64770	−0.531291	−0.265645	+	0.964071i	$0.585585\pi$
$114$	10.6003	0.992809
$115$	−0.325199	−0.0303250
$116$	3.76165	0.349261
$117$	4.59402	0.424718
$118$	−1.21410	−0.111767
$119$	5.96003	0.546355
$120$	0.739587	0.0675148
$121$	−7.94808	−0.722553
$122$	9.68636	0.876962
$123$	−20.7050	−1.86691
$124$	−0.684085	−0.0614327
$125$	−3.21760	−0.287791
$126$	5.90354	0.525929
$127$	−1.11446	−0.0988920	−0.0494460	−	0.998777i	$-0.515746\pi$
$127$	−1.11446	−0.0988920	−0.0494460	+	0.998777i	$0.515746\pi$
$128$	−1.00000	−0.0883883
$129$	−15.4632	−1.36146
$130$	−0.687748	−0.0603195
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	3.97308	0.345812
$133$	−12.6671	−1.09838
$134$	−0.587348	−0.0507392
$135$	0.612182	0.0526882
$136$	2.19305	0.188053
$137$	7.39323	0.631646	0.315823	−	0.948818i	$-0.397719\pi$
$137$	7.39323	0.631646	0.315823	+	0.948818i	$0.397719\pi$
$138$	−2.27426	−0.193598
$139$	13.5941	1.15304	0.576519	−	0.817084i	$-0.304411\pi$
$139$	13.5941	1.15304	0.576519	+	0.817084i	$0.304411\pi$
$140$	−0.883790	−0.0746939
$141$	10.9890	0.925441
$142$	−2.20883	−0.185361
$143$	−3.69459	−0.308957
$144$	2.17227	0.181022
$145$	1.22329	0.101588
$146$	12.7817	1.05782
$147$	−0.877499	−0.0723749
$148$	−10.3852	−0.853659
$149$	−13.1251	−1.07525	−0.537626	−	0.843184i	$-0.680679\pi$
$149$	−13.1251	−1.07525	−0.537626	+	0.843184i	$0.680679\pi$
$150$	−11.1308	−0.908826
$151$	−1.77867	−0.144747	−0.0723733	−	0.997378i	$-0.523057\pi$
$151$	−1.77867	−0.144747	−0.0723733	+	0.997378i	$0.523057\pi$
$152$	−4.66099	−0.378056
$153$	−4.76389	−0.385138
$154$	−4.74773	−0.382583
$155$	−0.222464	−0.0178687
$156$	−4.80973	−0.385087
$157$	10.3809	0.828484	0.414242	−	0.910167i	$-0.364047\pi$
$157$	10.3809	0.828484	0.414242	+	0.910167i	$0.364047\pi$
$158$	−14.2748	−1.13565
$159$	25.2864	2.00534
$160$	−0.325199	−0.0257092
$161$	2.71769	0.214184
$162$	10.7981	0.848376
$163$	−2.76324	−0.216434	−0.108217	−	0.994127i	$-0.534514\pi$
$163$	−2.76324	−0.216434	−0.108217	+	0.994127i	$0.534514\pi$
$164$	9.10405	0.710907
$165$	1.29204	0.100585
$166$	11.8175	0.917219
$167$	−12.7973	−0.990284	−0.495142	−	0.868812i	$-0.664884\pi$
$167$	−12.7973	−0.990284	−0.495142	+	0.868812i	$0.664884\pi$
$168$	−6.18074	−0.476854
$169$	−8.52739	−0.655953
$170$	0.713178	0.0546983
$171$	10.1249	0.774270
$172$	6.79922	0.518435
$173$	−2.20247	−0.167450	−0.0837252	−	0.996489i	$-0.526682\pi$
$173$	−2.20247	−0.167450	−0.0837252	+	0.996489i	$0.526682\pi$
$174$	8.55498	0.648552
$175$	13.3010	1.00546
$176$	−1.74697	−0.131683
$177$	−2.76119	−0.207543
$178$	4.61090	0.345601
$179$	3.03325	0.226716	0.113358	−	0.993554i	$-0.463839\pi$
$179$	3.03325	0.226716	0.113358	+	0.993554i	$0.463839\pi$
$180$	0.706418	0.0526533
$181$	11.8927	0.883980	0.441990	−	0.897020i	$-0.354273\pi$
$181$	11.8927	0.883980	0.441990	+	0.897020i	$0.354273\pi$
$182$	5.74752	0.426034
$183$	22.0293	1.62845
$184$	1.00000	0.0737210
$185$	−3.37726	−0.248301
$186$	−1.55579	−0.114076
$187$	3.83120	0.280165
$188$	−4.83190	−0.352403
$189$	−5.11601	−0.372135
$190$	−1.51575	−0.109964
$191$	5.64186	0.408231	0.204115	−	0.978947i	$-0.434568\pi$
$191$	5.64186	0.408231	0.204115	+	0.978947i	$0.434568\pi$
$192$	−2.27426	−0.164131
$193$	−3.66162	−0.263569	−0.131784	−	0.991278i	$-0.542071\pi$
$193$	−3.66162	−0.263569	−0.131784	+	0.991278i	$0.542071\pi$
$194$	−15.6283	−1.12205
$195$	−1.56412	−0.112009
$196$	0.385839	0.0275600
$197$	−5.40363	−0.384993	−0.192496	−	0.981298i	$-0.561658\pi$
$197$	−5.40363	−0.384993	−0.192496	+	0.981298i	$0.561658\pi$
$198$	3.79489	0.269691
$199$	−7.88470	−0.558931	−0.279466	−	0.960156i	$-0.590157\pi$
$199$	−7.88470	−0.558931	−0.279466	+	0.960156i	$0.590157\pi$
$200$	4.89425	0.346075
$201$	−1.33578	−0.0942189
$202$	−6.33106	−0.445452
$203$	−10.2230	−0.717515
$204$	4.98757	0.349200
$205$	2.96063	0.206779
$206$	−17.5533	−1.22299
$207$	−2.17227	−0.150983
$208$	2.11485	0.146639
$209$	−8.14262	−0.563237
$210$	−2.00997	−0.138701
$211$	−1.54255	−0.106194	−0.0530969	−	0.998589i	$-0.516909\pi$
$211$	−1.54255	−0.106194	−0.0530969	+	0.998589i	$0.516909\pi$
$212$	−11.1185	−0.763622
$213$	−5.02346	−0.344202
$214$	12.1043	0.827430
$215$	2.21110	0.150796
$216$	−1.88249	−0.128087
$217$	1.85913	0.126206
$218$	16.2841	1.10290
$219$	29.0690	1.96430
$220$	−0.568114	−0.0383022
$221$	−4.63798	−0.311985
$222$	−23.6187	−1.58518
$223$	13.2258	0.885668	0.442834	−	0.896604i	$-0.353973\pi$
$223$	13.2258	0.885668	0.442834	+	0.896604i	$0.353973\pi$
$224$	2.71769	0.181583
$225$	−10.6316	−0.708773
$226$	5.64770	0.375679
$227$	17.4516	1.15830	0.579152	−	0.815220i	$-0.303384\pi$
$227$	17.4516	1.15830	0.579152	+	0.815220i	$0.303384\pi$
$228$	−10.6003	−0.702022
$229$	−9.38605	−0.620247	−0.310124	−	0.950696i	$-0.600370\pi$
$229$	−9.38605	−0.620247	−0.310124	+	0.950696i	$0.600370\pi$
$230$	0.325199	0.0214430
$231$	−10.7976	−0.710429
$232$	−3.76165	−0.246965
$233$	6.73917	0.441498	0.220749	−	0.975331i	$-0.429150\pi$
$233$	6.73917	0.441498	0.220749	+	0.975331i	$0.429150\pi$
$234$	−4.59402	−0.300321
$235$	−1.57133	−0.102502
$236$	1.21410	0.0790313
$237$	−32.4647	−2.10881
$238$	−5.96003	−0.386332
$239$	−10.5705	−0.683746	−0.341873	−	0.939746i	$-0.611061\pi$
$239$	−10.5705	−0.683746	−0.341873	+	0.939746i	$0.611061\pi$
$240$	−0.739587	−0.0477402
$241$	2.35469	0.151679	0.0758395	−	0.997120i	$-0.475836\pi$
$241$	2.35469	0.151679	0.0758395	+	0.997120i	$0.475836\pi$
$242$	7.94808	0.510922
$243$	18.9102	1.21309
$244$	−9.68636	−0.620106
$245$	0.125475	0.00801627
$246$	20.7050	1.32010
$247$	9.85730	0.627205
$248$	0.684085	0.0434395
$249$	26.8762	1.70321
$250$	3.21760	0.203499
$251$	18.0235	1.13764	0.568818	−	0.822464i	$-0.307401\pi$
$251$	18.0235	1.13764	0.568818	+	0.822464i	$0.307401\pi$
$252$	−5.90354	−0.371888
$253$	1.74697	0.109831
$254$	1.11446	0.0699272
$255$	1.62195	0.101571
$256$	1.00000	0.0625000
$257$	−6.49560	−0.405185	−0.202592	−	0.979263i	$-0.564937\pi$
$257$	−6.49560	−0.405185	−0.202592	+	0.979263i	$0.564937\pi$
$258$	15.4632	0.962697
$259$	28.2238	1.75374
$260$	0.687748	0.0426523
$261$	8.17131	0.505791
$262$	−1.00000	−0.0617802
$263$	−25.2769	−1.55864	−0.779322	−	0.626624i	$-0.784436\pi$
$263$	−25.2769	−1.55864	−0.779322	+	0.626624i	$0.784436\pi$
$264$	−3.97308	−0.244526
$265$	−3.61572	−0.222112
$266$	12.6671	0.776671
$267$	10.4864	0.641757
$268$	0.587348	0.0358780
$269$	−19.1688	−1.16874	−0.584371	−	0.811487i	$-0.698659\pi$
$269$	−19.1688	−1.16874	−0.584371	+	0.811487i	$0.698659\pi$
$270$	−0.612182	−0.0372562
$271$	11.8979	0.722749	0.361374	−	0.932421i	$-0.382308\pi$
$271$	11.8979	0.722749	0.361374	+	0.932421i	$0.382308\pi$
$272$	−2.19305	−0.132973
$273$	13.0714	0.791114
$274$	−7.39323	−0.446641
$275$	8.55012	0.515592
$276$	2.27426	0.136894
$277$	−25.3065	−1.52052	−0.760260	−	0.649619i	$-0.774929\pi$
$277$	−25.3065	−1.52052	−0.760260	+	0.649619i	$0.774929\pi$
$278$	−13.5941	−0.815321
$279$	−1.48601	−0.0889654
$280$	0.883790	0.0528165
$281$	30.1473	1.79844	0.899218	−	0.437502i	$-0.144137\pi$
$281$	30.1473	1.79844	0.899218	+	0.437502i	$0.144137\pi$
$282$	−10.9890	−0.654386
$283$	−10.0937	−0.600006	−0.300003	−	0.953938i	$-0.596988\pi$
$283$	−10.0937	−0.600006	−0.300003	+	0.953938i	$0.596988\pi$
$284$	2.20883	0.131070
$285$	−3.44721	−0.204195
$286$	3.69459	0.218466
$287$	−24.7420	−1.46047
$288$	−2.17227	−0.128002
$289$	−12.1905	−0.717090
$290$	−1.22329	−0.0718338
$291$	−35.5429	−2.08356
$292$	−12.7817	−0.747994
$293$	23.1157	1.35044	0.675218	−	0.737618i	$-0.264050\pi$
$293$	23.1157	1.35044	0.675218	+	0.737618i	$0.264050\pi$
$294$	0.877499	0.0511768
$295$	0.394825	0.0229876
$296$	10.3852	0.603628
$297$	−3.28865	−0.190827
$298$	13.1251	0.760318
$299$	−2.11485	−0.122305
$300$	11.1308	0.642637
$301$	−18.4782	−1.06506
$302$	1.77867	0.102351
$303$	−14.3985	−0.827172
$304$	4.66099	0.267326
$305$	−3.14999	−0.180368
$306$	4.76389	0.272333
$307$	0.841501	0.0480270	0.0240135	−	0.999712i	$-0.492356\pi$
$307$	0.841501	0.0480270	0.0240135	+	0.999712i	$0.492356\pi$
$308$	4.74773	0.270527
$309$	−39.9207	−2.27101
$310$	0.222464	0.0126351
$311$	1.89892	0.107678	0.0538389	−	0.998550i	$-0.482854\pi$
$311$	1.89892	0.107678	0.0538389	+	0.998550i	$0.482854\pi$
$312$	4.80973	0.272297
$313$	17.8503	1.00896	0.504480	−	0.863424i	$-0.331684\pi$
$313$	17.8503	1.00896	0.504480	+	0.863424i	$0.331684\pi$
$314$	−10.3809	−0.585827
$315$	−1.91983	−0.108170
$316$	14.2748	0.803023
$317$	1.80987	0.101652	0.0508262	−	0.998708i	$-0.483815\pi$
$317$	1.80987	0.101652	0.0508262	+	0.998708i	$0.483815\pi$
$318$	−25.2864	−1.41799
$319$	−6.57151	−0.367934
$320$	0.325199	0.0181792
$321$	27.5282	1.53648
$322$	−2.71769	−0.151451
$323$	−10.2218	−0.568755
$324$	−10.7981	−0.599892
$325$	−10.3506	−0.574149
$326$	2.76324	0.153042
$327$	37.0342	2.04800
$328$	−9.10405	−0.502687
$329$	13.1316	0.723969
$330$	−1.29204	−0.0711244
$331$	26.6348	1.46398	0.731989	−	0.681316i	$-0.238592\pi$
$331$	26.6348	1.46398	0.731989	+	0.681316i	$0.238592\pi$
$332$	−11.8175	−0.648572
$333$	−22.5594	−1.23625
$334$	12.7973	0.700237
$335$	0.191005	0.0104357
$336$	6.18074	0.337187
$337$	24.1099	1.31335	0.656674	−	0.754174i	$-0.271963\pi$
$337$	24.1099	1.31335	0.656674	+	0.754174i	$0.271963\pi$
$338$	8.52739	0.463829
$339$	12.8443	0.697609
$340$	−0.713178	−0.0386775
$341$	1.19508	0.0647172
$342$	−10.1249	−0.547492
$343$	17.9752	0.970572
$344$	−6.79922	−0.366589
$345$	0.739587	0.0398180
$346$	2.20247	0.118405
$347$	8.78096	0.471387	0.235693	−	0.971827i	$-0.424264\pi$
$347$	8.78096	0.471387	0.235693	+	0.971827i	$0.424264\pi$
$348$	−8.55498	−0.458595
$349$	−3.98370	−0.213243	−0.106621	−	0.994300i	$-0.534003\pi$
$349$	−3.98370	−0.213243	−0.106621	+	0.994300i	$0.534003\pi$
$350$	−13.3010	−0.710971
$351$	3.98118	0.212500
$352$	1.74697	0.0931140
$353$	15.7911	0.840478	0.420239	−	0.907414i	$-0.361946\pi$
$353$	15.7911	0.840478	0.420239	+	0.907414i	$0.361946\pi$
$354$	2.76119	0.146755
$355$	0.718310	0.0381239
$356$	−4.61090	−0.244377
$357$	−13.5547	−0.717390
$358$	−3.03325	−0.160312
$359$	−32.6853	−1.72507	−0.862533	−	0.506001i	$-0.831123\pi$
$359$	−32.6853	−1.72507	−0.862533	+	0.506001i	$0.831123\pi$
$360$	−0.706418	−0.0372315
$361$	2.72478	0.143410
$362$	−11.8927	−0.625068
$363$	18.0760	0.948745
$364$	−5.74752	−0.301252
$365$	−4.15660	−0.217566
$366$	−22.0293	−1.15149
$367$	−16.9367	−0.884090	−0.442045	−	0.896993i	$-0.645747\pi$
$367$	−16.9367	−0.884090	−0.442045	+	0.896993i	$0.645747\pi$
$368$	−1.00000	−0.0521286
$369$	19.7764	1.02952
$370$	3.37726	0.175575
$371$	30.2166	1.56877
$372$	1.55579	0.0806639
$373$	5.88217	0.304567	0.152284	−	0.988337i	$-0.451337\pi$
$373$	5.88217	0.304567	0.152284	+	0.988337i	$0.451337\pi$
$374$	−3.83120	−0.198107
$375$	7.31766	0.377882
$376$	4.83190	0.249186
$377$	7.95535	0.409721
$378$	5.11601	0.263139
$379$	17.0314	0.874843	0.437422	−	0.899256i	$-0.355892\pi$
$379$	17.0314	0.874843	0.437422	+	0.899256i	$0.355892\pi$
$380$	1.51575	0.0777562
$381$	2.53457	0.129850
$382$	−5.64186	−0.288663
$383$	0.955076	0.0488021	0.0244011	−	0.999702i	$-0.492232\pi$
$383$	0.955076	0.0488021	0.0244011	+	0.999702i	$0.492232\pi$
$384$	2.27426	0.116058
$385$	1.54396	0.0786874
$386$	3.66162	0.186371
$387$	14.7697	0.750786
$388$	15.6283	0.793409
$389$	10.6821	0.541604	0.270802	−	0.962635i	$-0.412711\pi$
$389$	10.6821	0.541604	0.270802	+	0.962635i	$0.412711\pi$
$390$	1.56412	0.0792022
$391$	2.19305	0.110907
$392$	−0.385839	−0.0194878
$393$	−2.27426	−0.114721
$394$	5.40363	0.272231
$395$	4.64216	0.233573
$396$	−3.79489	−0.190700
$397$	0.237836	0.0119367	0.00596833	−	0.999982i	$-0.498100\pi$
$397$	0.237836	0.0119367	0.00596833	+	0.999982i	$0.498100\pi$
$398$	7.88470	0.395224
$399$	28.8083	1.44222
$400$	−4.89425	−0.244712
$401$	−3.31747	−0.165666	−0.0828332	−	0.996563i	$-0.526397\pi$
$401$	−3.31747	−0.165666	−0.0828332	+	0.996563i	$0.526397\pi$
$402$	1.33578	0.0666228
$403$	−1.44674	−0.0720673
$404$	6.33106	0.314982
$405$	−3.51152	−0.174489
$406$	10.2230	0.507359
$407$	18.1427	0.899300
$408$	−4.98757	−0.246922
$409$	15.4264	0.762787	0.381393	−	0.924413i	$-0.375444\pi$
$409$	15.4264	0.762787	0.381393	+	0.924413i	$0.375444\pi$
$410$	−2.96063	−0.146215
$411$	−16.8141	−0.829381
$412$	17.5533	0.864788
$413$	−3.29955	−0.162360
$414$	2.17227	0.106761
$415$	−3.84305	−0.188648
$416$	−2.11485	−0.103689
$417$	−30.9166	−1.51399
$418$	8.14262	0.398269
$419$	−7.62582	−0.372546	−0.186273	−	0.982498i	$-0.559641\pi$
$419$	−7.62582	−0.372546	−0.186273	+	0.982498i	$0.559641\pi$
$420$	2.00997	0.0980765
$421$	32.2817	1.57331	0.786656	−	0.617392i	$-0.211811\pi$
$421$	32.2817	1.57331	0.786656	+	0.617392i	$0.211811\pi$
$422$	1.54255	0.0750904
$423$	−10.4962	−0.510341
$424$	11.1185	0.539962
$425$	10.7333	0.520643
$426$	5.02346	0.243387
$427$	26.3245	1.27393
$428$	−12.1043	−0.585081
$429$	8.40247	0.405675
$430$	−2.21110	−0.106629
$431$	33.8634	1.63114	0.815572	−	0.578656i	$-0.196423\pi$
$431$	33.8634	1.63114	0.815572	+	0.578656i	$0.196423\pi$
$432$	1.88249	0.0905711
$433$	36.8346	1.77016	0.885080	−	0.465439i	$-0.154103\pi$
$433$	36.8346	1.77016	0.885080	+	0.465439i	$0.154103\pi$
$434$	−1.85913	−0.0892412
$435$	−2.78207	−0.133390
$436$	−16.2841	−0.779865
$437$	−4.66099	−0.222965
$438$	−29.0690	−1.38897
$439$	9.51695	0.454219	0.227110	−	0.973869i	$-0.427072\pi$
$439$	9.51695	0.454219	0.227110	+	0.973869i	$0.427072\pi$
$440$	0.568114	0.0270838
$441$	0.838145	0.0399117
$442$	4.63798	0.220606
$443$	−14.6894	−0.697916	−0.348958	−	0.937138i	$-0.613464\pi$
$443$	−14.6894	−0.697916	−0.348958	+	0.937138i	$0.613464\pi$
$444$	23.6187	1.12089
$445$	−1.49946	−0.0710812
$446$	−13.2258	−0.626262
$447$	29.8499	1.41185
$448$	−2.71769	−0.128399
$449$	0.913551	0.0431132	0.0215566	−	0.999768i	$-0.493138\pi$
$449$	0.913551	0.0431132	0.0215566	+	0.999768i	$0.493138\pi$
$450$	10.6316	0.501178
$451$	−15.9045	−0.748915
$452$	−5.64770	−0.265645
$453$	4.04517	0.190059
$454$	−17.4516	−0.819044
$455$	−1.86909	−0.0876241
$456$	10.6003	0.496404
$457$	15.6796	0.733459	0.366730	−	0.930328i	$-0.380477\pi$
$457$	15.6796	0.733459	0.366730	+	0.930328i	$0.380477\pi$
$458$	9.38605	0.438581
$459$	−4.12839	−0.192697
$460$	−0.325199	−0.0151625
$461$	−1.18864	−0.0553607	−0.0276803	−	0.999617i	$-0.508812\pi$
$461$	−1.18864	−0.0553607	−0.0276803	+	0.999617i	$0.508812\pi$
$462$	10.7976	0.502349
$463$	−12.7126	−0.590804	−0.295402	−	0.955373i	$-0.595454\pi$
$463$	−12.7126	−0.590804	−0.295402	+	0.955373i	$0.595454\pi$
$464$	3.76165	0.174630
$465$	0.505941	0.0234624
$466$	−6.73917	−0.312186
$467$	−12.4325	−0.575309	−0.287654	−	0.957734i	$-0.592875\pi$
$467$	−12.4325	−0.575309	−0.287654	+	0.957734i	$0.592875\pi$
$468$	4.59402	0.212359
$469$	−1.59623	−0.0737071
$470$	1.57133	0.0724800
$471$	−23.6088	−1.08784
$472$	−1.21410	−0.0558836
$473$	−11.8781	−0.546153
$474$	32.4647	1.49115
$475$	−22.8120	−1.04669
$476$	5.96003	0.273178
$477$	−24.1523	−1.10586
$478$	10.5705	0.483481
$479$	30.3813	1.38816	0.694079	−	0.719899i	$-0.255812\pi$
$479$	30.3813	1.38816	0.694079	+	0.719899i	$0.255812\pi$
$480$	0.739587	0.0337574
$481$	−21.9632	−1.00144
$482$	−2.35469	−0.107253
$483$	−6.18074	−0.281233
$484$	−7.94808	−0.361276
$485$	5.08232	0.230776
$486$	−18.9102	−0.857782
$487$	16.9926	0.770009	0.385004	−	0.922915i	$-0.374200\pi$
$487$	16.9926	0.770009	0.385004	+	0.922915i	$0.374200\pi$
$488$	9.68636	0.438481
$489$	6.28433	0.284187
$490$	−0.125475	−0.00566836
$491$	30.3702	1.37059	0.685295	−	0.728266i	$-0.259673\pi$
$491$	30.3702	1.37059	0.685295	+	0.728266i	$0.259673\pi$
$492$	−20.7050	−0.933453
$493$	−8.24950	−0.371539
$494$	−9.85730	−0.443501
$495$	−1.23409	−0.0554684
$496$	−0.684085	−0.0307163
$497$	−6.00292	−0.269268
$498$	−26.8762	−1.20435
$499$	32.7680	1.46690	0.733448	−	0.679746i	$-0.237910\pi$
$499$	32.7680	1.46690	0.733448	+	0.679746i	$0.237910\pi$
$500$	−3.21760	−0.143895
$501$	29.1044	1.30029
$502$	−18.0235	−0.804430
$503$	−11.8452	−0.528151	−0.264076	−	0.964502i	$-0.585067\pi$
$503$	−11.8452	−0.528151	−0.264076	+	0.964502i	$0.585067\pi$
$504$	5.90354	0.262965
$505$	2.05885	0.0916178
$506$	−1.74697	−0.0776625
$507$	19.3935	0.861297
$508$	−1.11446	−0.0494460
$509$	−1.50754	−0.0668206	−0.0334103	−	0.999442i	$-0.510637\pi$
$509$	−1.50754	−0.0668206	−0.0334103	+	0.999442i	$0.510637\pi$
$510$	−1.62195	−0.0718213
$511$	34.7368	1.53666
$512$	−1.00000	−0.0441942
$513$	8.77424	0.387392
$514$	6.49560	0.286509
$515$	5.70831	0.251538
$516$	−15.4632	−0.680729
$517$	8.44121	0.371244
$518$	−28.2238	−1.24008
$519$	5.00898	0.219870
$520$	−0.687748	−0.0301597
$521$	−0.151501	−0.00663739	−0.00331869	−	0.999994i	$-0.501056\pi$
$521$	−0.151501	−0.00663739	−0.00331869	+	0.999994i	$0.501056\pi$
$522$	−8.17131	−0.357649
$523$	1.07900	0.0471812	0.0235906	−	0.999722i	$-0.492490\pi$
$523$	1.07900	0.0471812	0.0235906	+	0.999722i	$0.492490\pi$
$524$	1.00000	0.0436852
$525$	−30.2500	−1.32022
$526$	25.2769	1.10213
$527$	1.50023	0.0653512
$528$	3.97308	0.172906
$529$	1.00000	0.0434783
$530$	3.61572	0.157057
$531$	2.63735	0.114451
$532$	−12.6671	−0.549189
$533$	19.2537	0.833972
$534$	−10.4864	−0.453790
$535$	−3.93629	−0.170181
$536$	−0.587348	−0.0253696
$537$	−6.89841	−0.297689
$538$	19.1688	0.826425
$539$	−0.674051	−0.0290334
$540$	0.612182	0.0263441
$541$	−29.7049	−1.27711	−0.638557	−	0.769574i	$-0.720468\pi$
$541$	−29.7049	−1.27711	−0.638557	+	0.769574i	$0.720468\pi$
$542$	−11.8979	−0.511061
$543$	−27.0472	−1.16071
$544$	2.19305	0.0940263
$545$	−5.29556	−0.226837
$546$	−13.0714	−0.559402
$547$	19.3750	0.828414	0.414207	−	0.910183i	$-0.364059\pi$
$547$	19.3750	0.828414	0.414207	+	0.910183i	$0.364059\pi$
$548$	7.39323	0.315823
$549$	−21.0414	−0.898023
$550$	−8.55012	−0.364578
$551$	17.5330	0.746931
$552$	−2.27426	−0.0967990
$553$	−38.7946	−1.64971
$554$	25.3065	1.07517
$555$	7.68077	0.326031
$556$	13.5941	0.576519
$557$	41.1945	1.74547	0.872734	−	0.488196i	$-0.162345\pi$
$557$	41.1945	1.74547	0.872734	+	0.488196i	$0.162345\pi$
$558$	1.48601	0.0629080
$559$	14.3793	0.608182
$560$	−0.883790	−0.0373469
$561$	−8.71316	−0.367870
$562$	−30.1473	−1.27169
$563$	−7.84309	−0.330547	−0.165273	−	0.986248i	$-0.552851\pi$
$563$	−7.84309	−0.330547	−0.165273	+	0.986248i	$0.552851\pi$
$564$	10.9890	0.462721
$565$	−1.83663	−0.0772674
$566$	10.0937	0.424268
$567$	29.3458	1.23241
$568$	−2.20883	−0.0926805
$569$	−2.96701	−0.124384	−0.0621918	−	0.998064i	$-0.519809\pi$
$569$	−2.96701	−0.124384	−0.0621918	+	0.998064i	$0.519809\pi$
$570$	3.44721	0.144388
$571$	−19.2491	−0.805551	−0.402775	−	0.915299i	$-0.631954\pi$
$571$	−19.2491	−0.805551	−0.402775	+	0.915299i	$0.631954\pi$
$572$	−3.69459	−0.154479
$573$	−12.8311	−0.536026
$574$	24.7420	1.03271
$575$	4.89425	0.204104
$576$	2.17227	0.0905111
$577$	12.8094	0.533260	0.266630	−	0.963799i	$-0.414090\pi$
$577$	12.8094	0.533260	0.266630	+	0.963799i	$0.414090\pi$
$578$	12.1905	0.507059
$579$	8.32747	0.346078
$580$	1.22329	0.0507942
$581$	32.1164	1.33241
$582$	35.5429	1.47330
$583$	19.4237	0.804449
$584$	12.7817	0.528911
$585$	1.49397	0.0617681
$586$	−23.1157	−0.954902
$587$	−13.1126	−0.541214	−0.270607	−	0.962690i	$-0.587224\pi$
$587$	−13.1126	−0.541214	−0.270607	+	0.962690i	$0.587224\pi$
$588$	−0.877499	−0.0361875
$589$	−3.18851	−0.131380
$590$	−0.394825	−0.0162547
$591$	12.2893	0.505513
$592$	−10.3852	−0.426830
$593$	0.148537	0.00609968	0.00304984	−	0.999995i	$-0.499029\pi$
$593$	0.148537	0.00609968	0.00304984	+	0.999995i	$0.499029\pi$
$594$	3.28865	0.134935
$595$	1.93820	0.0794583
$596$	−13.1251	−0.537626
$597$	17.9319	0.733902
$598$	2.11485	0.0864828
$599$	28.8323	1.17806	0.589029	−	0.808112i	$-0.299510\pi$
$599$	28.8323	1.17806	0.589029	+	0.808112i	$0.299510\pi$
$600$	−11.1308	−0.454413
$601$	−4.29180	−0.175066	−0.0875331	−	0.996162i	$-0.527898\pi$
$601$	−4.29180	−0.175066	−0.0875331	+	0.996162i	$0.527898\pi$
$602$	18.4782	0.753114
$603$	1.27588	0.0519577
$604$	−1.77867	−0.0723733
$605$	−2.58471	−0.105083
$606$	14.3985	0.584899
$607$	25.3399	1.02851	0.514257	−	0.857636i	$-0.328068\pi$
$607$	25.3399	1.02851	0.514257	+	0.857636i	$0.328068\pi$
$608$	−4.66099	−0.189028
$609$	23.2498	0.942129
$610$	3.14999	0.127540
$611$	−10.2188	−0.413407
$612$	−4.76389	−0.192569
$613$	23.7299	0.958443	0.479222	−	0.877694i	$-0.340919\pi$
$613$	23.7299	0.958443	0.479222	+	0.877694i	$0.340919\pi$
$614$	−0.841501	−0.0339602
$615$	−6.73324	−0.271510
$616$	−4.74773	−0.191292
$617$	19.4509	0.783063	0.391531	−	0.920165i	$-0.371945\pi$
$617$	19.4509	0.783063	0.391531	+	0.920165i	$0.371945\pi$
$618$	39.9207	1.60585
$619$	14.9990	0.602861	0.301431	−	0.953488i	$-0.402536\pi$
$619$	14.9990	0.602861	0.301431	+	0.953488i	$0.402536\pi$
$620$	−0.222464	−0.00893436
$621$	−1.88249	−0.0755415
$622$	−1.89892	−0.0761397
$623$	12.5310	0.502044
$624$	−4.80973	−0.192543
$625$	23.4249	0.936995
$626$	−17.8503	−0.713442
$627$	18.5184	0.739555
$628$	10.3809	0.414242
$629$	22.7753	0.908111
$630$	1.91983	0.0764877
$631$	33.9984	1.35345	0.676727	−	0.736234i	$-0.263398\pi$
$631$	33.9984	1.35345	0.676727	+	0.736234i	$0.263398\pi$
$632$	−14.2748	−0.567823
$633$	3.50817	0.139437
$634$	−1.80987	−0.0718792
$635$	−0.362420	−0.0143822
$636$	25.2864	1.00267
$637$	0.815994	0.0323308
$638$	6.57151	0.260169
$639$	4.79817	0.189813
$640$	−0.325199	−0.0128546
$641$	11.9505	0.472018	0.236009	−	0.971751i	$-0.424161\pi$
$641$	11.9505	0.472018	0.236009	+	0.971751i	$0.424161\pi$
$642$	−27.5282	−1.08645
$643$	−35.4437	−1.39776	−0.698882	−	0.715237i	$-0.746319\pi$
$643$	−35.4437	−1.39776	−0.698882	+	0.715237i	$0.746319\pi$
$644$	2.71769	0.107092
$645$	−5.02861	−0.198002
$646$	10.2218	0.402171
$647$	1.82684	0.0718204	0.0359102	−	0.999355i	$-0.488567\pi$
$647$	1.82684	0.0718204	0.0359102	+	0.999355i	$0.488567\pi$
$648$	10.7981	0.424188
$649$	−2.12100	−0.0832567
$650$	10.3506	0.405984
$651$	−4.22815	−0.165714
$652$	−2.76324	−0.108217
$653$	29.2705	1.14544	0.572722	−	0.819749i	$-0.305887\pi$
$653$	29.2705	1.14544	0.572722	+	0.819749i	$0.305887\pi$
$654$	−37.0342	−1.44815
$655$	0.325199	0.0127066
$656$	9.10405	0.355453
$657$	−27.7653	−1.08323
$658$	−13.1316	−0.511924
$659$	−10.5587	−0.411309	−0.205655	−	0.978625i	$-0.565932\pi$
$659$	−10.5587	−0.411309	−0.205655	+	0.978625i	$0.565932\pi$
$660$	1.29204	0.0502926
$661$	11.2586	0.437910	0.218955	−	0.975735i	$-0.429735\pi$
$661$	11.2586	0.437910	0.218955	+	0.975735i	$0.429735\pi$
$662$	−26.6348	−1.03519
$663$	10.5480	0.409650
$664$	11.8175	0.458609
$665$	−4.11933	−0.159741
$666$	22.5594	0.874161
$667$	−3.76165	−0.145652
$668$	−12.7973	−0.495142
$669$	−30.0790	−1.16292
$670$	−0.191005	−0.00737917
$671$	16.9218	0.653260
$672$	−6.18074	−0.238427
$673$	19.7637	0.761835	0.380917	−	0.924609i	$-0.375608\pi$
$673$	19.7637	0.761835	0.380917	+	0.924609i	$0.375608\pi$
$674$	−24.1099	−0.928678
$675$	−9.21334	−0.354622
$676$	−8.52739	−0.327977
$677$	−46.2515	−1.77759	−0.888795	−	0.458306i	$-0.848456\pi$
$677$	−46.2515	−1.77759	−0.888795	+	0.458306i	$0.848456\pi$
$678$	−12.8443	−0.493284
$679$	−42.4730	−1.62996
$680$	0.713178	0.0273491
$681$	−39.6895	−1.52090
$682$	−1.19508	−0.0457619
$683$	22.7301	0.869745	0.434872	−	0.900492i	$-0.356793\pi$
$683$	22.7301	0.869745	0.434872	+	0.900492i	$0.356793\pi$
$684$	10.1249	0.387135
$685$	2.40427	0.0918625
$686$	−17.9752	−0.686298
$687$	21.3463	0.814413
$688$	6.79922	0.259218
$689$	−23.5140	−0.895812
$690$	−0.739587	−0.0281556
$691$	−12.2339	−0.465401	−0.232700	−	0.972548i	$-0.574756\pi$
$691$	−12.2339	−0.465401	−0.232700	+	0.972548i	$0.574756\pi$
$692$	−2.20247	−0.0837252
$693$	10.3133	0.391771
$694$	−8.78096	−0.333321
$695$	4.42079	0.167690
$696$	8.55498	0.324276
$697$	−19.9657	−0.756253
$698$	3.98370	0.150785
$699$	−15.3266	−0.579707
$700$	13.3010	0.502732
$701$	−2.65591	−0.100312	−0.0501561	−	0.998741i	$-0.515972\pi$
$701$	−2.65591	−0.100312	−0.0501561	+	0.998741i	$0.515972\pi$
$702$	−3.98118	−0.150260
$703$	−48.4053	−1.82564
$704$	−1.74697	−0.0658415
$705$	3.57361	0.134590
$706$	−15.7911	−0.594308
$707$	−17.2059	−0.647093
$708$	−2.76119	−0.103772
$709$	32.6169	1.22495	0.612476	−	0.790489i	$-0.290173\pi$
$709$	32.6169	1.22495	0.612476	+	0.790489i	$0.290173\pi$
$710$	−0.718310	−0.0269577
$711$	31.0088	1.16292
$712$	4.61090	0.172801
$713$	0.684085	0.0256192
$714$	13.5547	0.507271
$715$	−1.20148	−0.0449327
$716$	3.03325	0.113358
$717$	24.0400	0.897790
$718$	32.6853	1.21981
$719$	−3.17467	−0.118395	−0.0591977	−	0.998246i	$-0.518854\pi$
$719$	−3.17467	−0.118395	−0.0591977	+	0.998246i	$0.518854\pi$
$720$	0.706418	0.0263267
$721$	−47.7044	−1.77660
$722$	−2.72478	−0.101406
$723$	−5.35518	−0.199161
$724$	11.8927	0.441990
$725$	−18.4105	−0.683747
$726$	−18.0760	−0.670864
$727$	−9.91734	−0.367814	−0.183907	−	0.982944i	$-0.558874\pi$
$727$	−9.91734	−0.367814	−0.183907	+	0.982944i	$0.558874\pi$
$728$	5.74752	0.213017
$729$	−10.6125	−0.393054
$730$	4.15660	0.153843
$731$	−14.9110	−0.551504
$732$	22.0293	0.814227
$733$	3.53872	0.130705	0.0653527	−	0.997862i	$-0.479183\pi$
$733$	3.53872	0.130705	0.0653527	+	0.997862i	$0.479183\pi$
$734$	16.9367	0.625146
$735$	−0.285362	−0.0105257
$736$	1.00000	0.0368605
$737$	−1.02608	−0.0377962
$738$	−19.7764	−0.727980
$739$	34.6768	1.27561	0.637803	−	0.770200i	$-0.279843\pi$
$739$	34.6768	1.27561	0.637803	+	0.770200i	$0.279843\pi$
$740$	−3.37726	−0.124151
$741$	−22.4181	−0.823549
$742$	−30.2166	−1.10929
$743$	1.61041	0.0590804	0.0295402	−	0.999564i	$-0.490596\pi$
$743$	1.61041	0.0590804	0.0295402	+	0.999564i	$0.490596\pi$
$744$	−1.55579	−0.0570380
$745$	−4.26827	−0.156377
$746$	−5.88217	−0.215362
$747$	−25.6708	−0.939247
$748$	3.83120	0.140083
$749$	32.8956	1.20198
$750$	−7.31766	−0.267203
$751$	30.7048	1.12043	0.560217	−	0.828346i	$-0.310718\pi$
$751$	30.7048	1.12043	0.560217	+	0.828346i	$0.310718\pi$
$752$	−4.83190	−0.176201
$753$	−40.9902	−1.49377
$754$	−7.95535	−0.289717
$755$	−0.578423	−0.0210510
$756$	−5.11601	−0.186068
$757$	3.75730	0.136561	0.0682807	−	0.997666i	$-0.478249\pi$
$757$	3.75730	0.136561	0.0682807	+	0.997666i	$0.478249\pi$
$758$	−17.0314	−0.618608
$759$	−3.97308	−0.144213
$760$	−1.51575	−0.0549819
$761$	−42.5377	−1.54199	−0.770996	−	0.636840i	$-0.780241\pi$
$761$	−42.5377	−1.54199	−0.770996	+	0.636840i	$0.780241\pi$
$762$	−2.53457	−0.0918176
$763$	44.2550	1.60214
$764$	5.64186	0.204115
$765$	−1.54921	−0.0560119
$766$	−0.955076	−0.0345083
$767$	2.56765	0.0927124
$768$	−2.27426	−0.0820653
$769$	−1.42760	−0.0514807	−0.0257404	−	0.999669i	$-0.508194\pi$
$769$	−1.42760	−0.0514807	−0.0257404	+	0.999669i	$0.508194\pi$
$770$	−1.54396	−0.0556404
$771$	14.7727	0.532026
$772$	−3.66162	−0.131784
$773$	43.4556	1.56299	0.781495	−	0.623911i	$-0.214457\pi$
$773$	43.4556	1.56299	0.781495	+	0.623911i	$0.214457\pi$
$774$	−14.7697	−0.530886
$775$	3.34808	0.120267
$776$	−15.6283	−0.561025
$777$	−64.1883	−2.30274
$778$	−10.6821	−0.382972
$779$	42.4338	1.52035
$780$	−1.56412	−0.0560044
$781$	−3.85877	−0.138078
$782$	−2.19305	−0.0784234
$783$	7.08126	0.253063
$784$	0.385839	0.0137800
$785$	3.37585	0.120489
$786$	2.27426	0.0811202
$787$	39.4655	1.40679	0.703396	−	0.710798i	$-0.251666\pi$
$787$	39.4655	1.40679	0.703396	+	0.710798i	$0.251666\pi$
$788$	−5.40363	−0.192496
$789$	57.4864	2.04657
$790$	−4.64216	−0.165161
$791$	15.3487	0.545737
$792$	3.79489	0.134846
$793$	−20.4852	−0.727452
$794$	−0.237836	−0.00844049
$795$	8.22310	0.291643
$796$	−7.88470	−0.279466
$797$	7.25230	0.256890	0.128445	−	0.991717i	$-0.459001\pi$
$797$	7.25230	0.256890	0.128445	+	0.991717i	$0.459001\pi$
$798$	−28.8083	−1.01980
$799$	10.5966	0.374881
$800$	4.89425	0.173038
$801$	−10.0161	−0.353901
$802$	3.31747	0.117144
$803$	22.3293	0.787985
$804$	−1.33578	−0.0471095
$805$	0.883790	0.0311495
$806$	1.44674	0.0509593
$807$	43.5948	1.53461
$808$	−6.33106	−0.222726
$809$	14.0253	0.493104	0.246552	−	0.969130i	$-0.420702\pi$
$809$	14.0253	0.493104	0.246552	+	0.969130i	$0.420702\pi$
$810$	3.51152	0.123382
$811$	56.3344	1.97817	0.989083	−	0.147357i	$-0.0470765\pi$
$811$	56.3344	1.97817	0.989083	+	0.147357i	$0.0470765\pi$
$812$	−10.2230	−0.358757
$813$	−27.0590	−0.949002
$814$	−18.1427	−0.635901
$815$	−0.898603	−0.0314767
$816$	4.98757	0.174600
$817$	31.6910	1.10873
$818$	−15.4264	−0.539372
$819$	−12.4851	−0.436266
$820$	2.96063	0.103390
$821$	−33.9887	−1.18621	−0.593107	−	0.805123i	$-0.702099\pi$
$821$	−33.9887	−1.18621	−0.593107	+	0.805123i	$0.702099\pi$
$822$	16.8141	0.586461
$823$	−22.5460	−0.785903	−0.392951	−	0.919559i	$-0.628546\pi$
$823$	−22.5460	−0.785903	−0.392951	+	0.919559i	$0.628546\pi$
$824$	−17.5533	−0.611497
$825$	−19.4452	−0.676995
$826$	3.29955	0.114806
$827$	−44.6443	−1.55243	−0.776217	−	0.630466i	$-0.782864\pi$
$827$	−44.6443	−1.55243	−0.776217	+	0.630466i	$0.782864\pi$
$828$	−2.17227	−0.0754914
$829$	10.3210	0.358462	0.179231	−	0.983807i	$-0.442639\pi$
$829$	10.3210	0.358462	0.179231	+	0.983807i	$0.442639\pi$
$830$	3.84305	0.133394
$831$	57.5536	1.99651
$832$	2.11485	0.0733194
$833$	−0.846165	−0.0293179
$834$	30.9166	1.07055
$835$	−4.16166	−0.144020
$836$	−8.14262	−0.281618
$837$	−1.28778	−0.0445122
$838$	7.62582	0.263429
$839$	−19.2904	−0.665979	−0.332990	−	0.942930i	$-0.608057\pi$
$839$	−19.2904	−0.665979	−0.332990	+	0.942930i	$0.608057\pi$
$840$	−2.00997	−0.0693505
$841$	−14.8500	−0.512068
$842$	−32.2817	−1.11250
$843$	−68.5628	−2.36143
$844$	−1.54255	−0.0530969
$845$	−2.77310	−0.0953975
$846$	10.4962	0.360866
$847$	21.6004	0.742199
$848$	−11.1185	−0.381811
$849$	22.9556	0.787835
$850$	−10.7333	−0.368150
$851$	10.3852	0.356001
$852$	−5.02346	−0.172101
$853$	−3.13348	−0.107288	−0.0536441	−	0.998560i	$-0.517084\pi$
$853$	−3.13348	−0.107288	−0.0536441	+	0.998560i	$0.517084\pi$
$854$	−26.3245	−0.900807
$855$	3.29261	0.112605
$856$	12.1043	0.413715
$857$	−30.6480	−1.04692	−0.523458	−	0.852051i	$-0.675358\pi$
$857$	−30.6480	−1.04692	−0.523458	+	0.852051i	$0.675358\pi$
$858$	−8.40247	−0.286856
$859$	−8.89747	−0.303578	−0.151789	−	0.988413i	$-0.548503\pi$
$859$	−8.89747	−0.303578	−0.151789	+	0.988413i	$0.548503\pi$
$860$	2.21110	0.0753978
$861$	56.2697	1.91767
$862$	−33.8634	−1.15339
$863$	−3.34699	−0.113933	−0.0569664	−	0.998376i	$-0.518143\pi$
$863$	−3.34699	−0.113933	−0.0569664	+	0.998376i	$0.518143\pi$
$864$	−1.88249	−0.0640434
$865$	−0.716239	−0.0243529
$866$	−36.8346	−1.25169
$867$	27.7244	0.941571
$868$	1.85913	0.0631031
$869$	−24.9378	−0.845956
$870$	2.78207	0.0943211
$871$	1.24216	0.0420888
$872$	16.2841	0.551448
$873$	33.9489	1.14900
$874$	4.66099	0.157660
$875$	8.74443	0.295616
$876$	29.0690	0.982150
$877$	−38.4765	−1.29926	−0.649630	−	0.760251i	$-0.725076\pi$
$877$	−38.4765	−1.29926	−0.649630	+	0.760251i	$0.725076\pi$
$878$	−9.51695	−0.321182
$879$	−52.5712	−1.77318
$880$	−0.568114	−0.0191511
$881$	32.8031	1.10517	0.552583	−	0.833458i	$-0.313642\pi$
$881$	32.8031	1.10517	0.552583	+	0.833458i	$0.313642\pi$
$882$	−0.838145	−0.0282218
$883$	22.7021	0.763988	0.381994	−	0.924165i	$-0.375237\pi$
$883$	22.7021	0.763988	0.381994	+	0.924165i	$0.375237\pi$
$884$	−4.63798	−0.155992
$885$	−0.897935	−0.0301837
$886$	14.6894	0.493501
$887$	−3.13037	−0.105107	−0.0525537	−	0.998618i	$-0.516736\pi$
$887$	−3.13037	−0.105107	−0.0525537	+	0.998618i	$0.516736\pi$
$888$	−23.6187	−0.792591
$889$	3.02875	0.101581
$890$	1.49946	0.0502620
$891$	18.8639	0.631965
$892$	13.2258	0.442834
$893$	−22.5214	−0.753651
$894$	−29.8499	−0.998332
$895$	0.986411	0.0329721
$896$	2.71769	0.0907917
$897$	4.80973	0.160592
$898$	−0.913551	−0.0304856
$899$	−2.57329	−0.0858241
$900$	−10.6316	−0.354387
$901$	24.3834	0.812330
$902$	15.9045	0.529563
$903$	42.0242	1.39848
$904$	5.64770	0.187840
$905$	3.86751	0.128560
$906$	−4.04517	−0.134392
$907$	3.91931	0.130138	0.0650692	−	0.997881i	$-0.479273\pi$
$907$	3.91931	0.130138	0.0650692	+	0.997881i	$0.479273\pi$
$908$	17.4516	0.579152
$909$	13.7527	0.456150
$910$	1.86909	0.0619596
$911$	−27.4261	−0.908668	−0.454334	−	0.890832i	$-0.650123\pi$
$911$	−27.4261	−0.908668	−0.454334	+	0.890832i	$0.650123\pi$
$912$	−10.6003	−0.351011
$913$	20.6449	0.683248
$914$	−15.6796	−0.518634
$915$	7.16391	0.236832
$916$	−9.38605	−0.310124
$917$	−2.71769	−0.0897460
$918$	4.12839	0.136257
$919$	20.1014	0.663082	0.331541	−	0.943441i	$-0.392431\pi$
$919$	20.1014	0.663082	0.331541	+	0.943441i	$0.392431\pi$
$920$	0.325199	0.0107215
$921$	−1.91379	−0.0630616
$922$	1.18864	0.0391459
$923$	4.67136	0.153760
$924$	−10.7976	−0.355215
$925$	50.8278	1.67121
$926$	12.7126	0.417762
$927$	38.1304	1.25237
$928$	−3.76165	−0.123482
$929$	−29.7943	−0.977519	−0.488760	−	0.872418i	$-0.662551\pi$
$929$	−29.7943	−0.977519	−0.488760	+	0.872418i	$0.662551\pi$
$930$	−0.505941	−0.0165905
$931$	1.79839	0.0589399
$932$	6.73917	0.220749
$933$	−4.31864	−0.141386
$934$	12.4325	0.406805
$935$	1.24590	0.0407454
$936$	−4.59402	−0.150160
$937$	−14.2075	−0.464138	−0.232069	−	0.972699i	$-0.574549\pi$
$937$	−14.2075	−0.464138	−0.232069	+	0.972699i	$0.574549\pi$
$938$	1.59623	0.0521188
$939$	−40.5963	−1.32481
$940$	−1.57133	−0.0512511
$941$	52.5388	1.71272	0.856359	−	0.516382i	$-0.172721\pi$
$941$	52.5388	1.71272	0.856359	+	0.516382i	$0.172721\pi$
$942$	23.6088	0.769217
$943$	−9.10405	−0.296469
$944$	1.21410	0.0395157
$945$	−1.66372	−0.0541209
$946$	11.8781	0.386189
$947$	−27.4735	−0.892770	−0.446385	−	0.894841i	$-0.647289\pi$
$947$	−27.4735	−0.892770	−0.446385	+	0.894841i	$0.647289\pi$
$948$	−32.4647	−1.05441
$949$	−27.0315	−0.877479
$950$	22.8120	0.740119
$951$	−4.11612	−0.133474
$952$	−5.96003	−0.193166
$953$	−32.2078	−1.04331	−0.521656	−	0.853156i	$-0.674686\pi$
$953$	−32.2078	−1.04331	−0.521656	+	0.853156i	$0.674686\pi$
$954$	24.1523	0.781961
$955$	1.83473	0.0593704
$956$	−10.5705	−0.341873
$957$	14.9453	0.483114
$958$	−30.3813	−0.981576
$959$	−20.0925	−0.648821
$960$	−0.739587	−0.0238701
$961$	−30.5320	−0.984904
$962$	21.9632	0.708122
$963$	−26.2937	−0.847301
$964$	2.35469	0.0758395
$965$	−1.19075	−0.0383317
$966$	6.18074	0.198862
$967$	−50.0920	−1.61085	−0.805425	−	0.592697i	$-0.798063\pi$
$967$	−50.0920	−1.61085	−0.805425	+	0.592697i	$0.798063\pi$
$968$	7.94808	0.255461
$969$	23.2470	0.746801
$970$	−5.08232	−0.163183
$971$	41.7880	1.34104	0.670520	−	0.741892i	$-0.266071\pi$
$971$	41.7880	1.34104	0.670520	+	0.741892i	$0.266071\pi$
$972$	18.9102	0.606544
$973$	−36.9446	−1.18439
$974$	−16.9926	−0.544478
$975$	23.5400	0.753883
$976$	−9.68636	−0.310053
$977$	13.5034	0.432011	0.216005	−	0.976392i	$-0.430697\pi$
$977$	13.5034	0.432011	0.216005	+	0.976392i	$0.430697\pi$
$978$	−6.28433	−0.200951
$979$	8.05512	0.257443
$980$	0.125475	0.00400814
$981$	−35.3733	−1.12938
$982$	−30.3702	−0.969153
$983$	−19.0417	−0.607336	−0.303668	−	0.952778i	$-0.598211\pi$
$983$	−19.0417	−0.607336	−0.303668	+	0.952778i	$0.598211\pi$
$984$	20.7050	0.660051
$985$	−1.75726	−0.0559908
$986$	8.24950	0.262718
$987$	−29.8647	−0.950604
$988$	9.85730	0.313603
$989$	−6.79922	−0.216203
$990$	1.23409	0.0392221
$991$	−51.1706	−1.62549	−0.812743	−	0.582622i	$-0.802027\pi$
$991$	−51.1706	−1.62549	−0.812743	+	0.582622i	$0.802027\pi$
$992$	0.684085	0.0217197
$993$	−60.5744	−1.92227
$994$	6.00292	0.190401
$995$	−2.56409	−0.0812873
$996$	26.8762	0.851604
$997$	57.4772	1.82032	0.910161	−	0.414256i	$-0.135958\pi$
$997$	57.4772	1.82032	0.910161	+	0.414256i	$0.135958\pi$
$998$	−32.7680	−1.03725
$999$	−19.5500	−0.618535

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.6	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.6	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.27426 q^{3} +1.00000 q^{4} +0.325199 q^{5} +2.27426 q^{6} -2.71769 q^{7} -1.00000 q^{8} +2.17227 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.27426 q^{3} +1.00000 q^{4} +0.325199 q^{5} +2.27426 q^{6} -2.71769 q^{7} -1.00000 q^{8} +2.17227 q^{9} -0.325199 q^{10} -1.74697 q^{11} -2.27426 q^{12} +2.11485 q^{13} +2.71769 q^{14} -0.739587 q^{15} +1.00000 q^{16} -2.19305 q^{17} -2.17227 q^{18} +4.66099 q^{19} +0.325199 q^{20} +6.18074 q^{21} +1.74697 q^{22} -1.00000 q^{23} +2.27426 q^{24} -4.89425 q^{25} -2.11485 q^{26} +1.88249 q^{27} -2.71769 q^{28} +3.76165 q^{29} +0.739587 q^{30} -0.684085 q^{31} -1.00000 q^{32} +3.97308 q^{33} +2.19305 q^{34} -0.883790 q^{35} +2.17227 q^{36} -10.3852 q^{37} -4.66099 q^{38} -4.80973 q^{39} -0.325199 q^{40} +9.10405 q^{41} -6.18074 q^{42} +6.79922 q^{43} -1.74697 q^{44} +0.706418 q^{45} +1.00000 q^{46} -4.83190 q^{47} -2.27426 q^{48} +0.385839 q^{49} +4.89425 q^{50} +4.98757 q^{51} +2.11485 q^{52} -11.1185 q^{53} -1.88249 q^{54} -0.568114 q^{55} +2.71769 q^{56} -10.6003 q^{57} -3.76165 q^{58} +1.21410 q^{59} -0.739587 q^{60} -9.68636 q^{61} +0.684085 q^{62} -5.90354 q^{63} +1.00000 q^{64} +0.687748 q^{65} -3.97308 q^{66} +0.587348 q^{67} -2.19305 q^{68} +2.27426 q^{69} +0.883790 q^{70} +2.20883 q^{71} -2.17227 q^{72} -12.7817 q^{73} +10.3852 q^{74} +11.1308 q^{75} +4.66099 q^{76} +4.74773 q^{77} +4.80973 q^{78} +14.2748 q^{79} +0.325199 q^{80} -10.7981 q^{81} -9.10405 q^{82} -11.8175 q^{83} +6.18074 q^{84} -0.713178 q^{85} -6.79922 q^{86} -8.55498 q^{87} +1.74697 q^{88} -4.61090 q^{89} -0.706418 q^{90} -5.74752 q^{91} -1.00000 q^{92} +1.55579 q^{93} +4.83190 q^{94} +1.51575 q^{95} +2.27426 q^{96} +15.6283 q^{97} -0.385839 q^{98} -3.79489 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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