LMFDB - Embedded newform 6026.2.a.i.1.19

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:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.50502 q^{3} +1.00000 q^{4} -2.72563 q^{5} -1.50502 q^{6} -2.36491 q^{7} -1.00000 q^{8} -0.734912 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.50502 q^{3} +1.00000 q^{4} -2.72563 q^{5} -1.50502 q^{6} -2.36491 q^{7} -1.00000 q^{8} -0.734912 q^{9} +2.72563 q^{10} +3.29273 q^{11} +1.50502 q^{12} -0.0258940 q^{13} +2.36491 q^{14} -4.10213 q^{15} +1.00000 q^{16} +1.25710 q^{17} +0.734912 q^{18} -1.42633 q^{19} -2.72563 q^{20} -3.55924 q^{21} -3.29273 q^{22} +1.00000 q^{23} -1.50502 q^{24} +2.42906 q^{25} +0.0258940 q^{26} -5.62112 q^{27} -2.36491 q^{28} +1.18615 q^{29} +4.10213 q^{30} +5.97814 q^{31} -1.00000 q^{32} +4.95562 q^{33} -1.25710 q^{34} +6.44587 q^{35} -0.734912 q^{36} +6.53848 q^{37} +1.42633 q^{38} -0.0389711 q^{39} +2.72563 q^{40} +1.11334 q^{41} +3.55924 q^{42} +3.03969 q^{43} +3.29273 q^{44} +2.00310 q^{45} -1.00000 q^{46} +11.9054 q^{47} +1.50502 q^{48} -1.40721 q^{49} -2.42906 q^{50} +1.89196 q^{51} -0.0258940 q^{52} -8.79403 q^{53} +5.62112 q^{54} -8.97475 q^{55} +2.36491 q^{56} -2.14666 q^{57} -1.18615 q^{58} -0.637130 q^{59} -4.10213 q^{60} -10.4294 q^{61} -5.97814 q^{62} +1.73800 q^{63} +1.00000 q^{64} +0.0705775 q^{65} -4.95562 q^{66} +4.76854 q^{67} +1.25710 q^{68} +1.50502 q^{69} -6.44587 q^{70} -7.69944 q^{71} +0.734912 q^{72} -6.63515 q^{73} -6.53848 q^{74} +3.65578 q^{75} -1.42633 q^{76} -7.78700 q^{77} +0.0389711 q^{78} +7.08175 q^{79} -2.72563 q^{80} -6.25517 q^{81} -1.11334 q^{82} -13.3908 q^{83} -3.55924 q^{84} -3.42638 q^{85} -3.03969 q^{86} +1.78519 q^{87} -3.29273 q^{88} +11.0810 q^{89} -2.00310 q^{90} +0.0612370 q^{91} +1.00000 q^{92} +8.99723 q^{93} -11.9054 q^{94} +3.88765 q^{95} -1.50502 q^{96} +2.00602 q^{97} +1.40721 q^{98} -2.41986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.50502	0.868924	0.434462	−	0.900690i	$-0.356938\pi$
$3$	1.50502	0.868924	0.434462	+	0.900690i	$0.356938\pi$
$4$	1.00000	0.500000
$5$	−2.72563	−1.21894	−0.609469	−	0.792810i	$-0.708617\pi$
$5$	−2.72563	−1.21894	−0.609469	+	0.792810i	$0.708617\pi$
$6$	−1.50502	−0.614422
$7$	−2.36491	−0.893851	−0.446926	−	0.894571i	$-0.647481\pi$
$7$	−2.36491	−0.893851	−0.446926	+	0.894571i	$0.647481\pi$
$8$	−1.00000	−0.353553
$9$	−0.734912	−0.244971
$10$	2.72563	0.861920
$11$	3.29273	0.992794	0.496397	−	0.868095i	$-0.334656\pi$
$11$	3.29273	0.992794	0.496397	+	0.868095i	$0.334656\pi$
$12$	1.50502	0.434462
$13$	−0.0258940	−0.00718171	−0.00359086	−	0.999994i	$-0.501143\pi$
$13$	−0.0258940	−0.00718171	−0.00359086	+	0.999994i	$0.501143\pi$
$14$	2.36491	0.632048
$15$	−4.10213	−1.05917
$16$	1.00000	0.250000
$17$	1.25710	0.304891	0.152445	−	0.988312i	$-0.451285\pi$
$17$	1.25710	0.304891	0.152445	+	0.988312i	$0.451285\pi$
$18$	0.734912	0.173220
$19$	−1.42633	−0.327223	−0.163612	−	0.986525i	$-0.552314\pi$
$19$	−1.42633	−0.327223	−0.163612	+	0.986525i	$0.552314\pi$
$20$	−2.72563	−0.609469
$21$	−3.55924	−0.776689
$22$	−3.29273	−0.702012
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.50502	−0.307211
$25$	2.42906	0.485812
$26$	0.0258940	0.00507824
$27$	−5.62112	−1.08179
$28$	−2.36491	−0.446926
$29$	1.18615	0.220263	0.110132	−	0.993917i	$-0.464873\pi$
$29$	1.18615	0.220263	0.110132	+	0.993917i	$0.464873\pi$
$30$	4.10213	0.748943
$31$	5.97814	1.07371	0.536853	−	0.843676i	$-0.319613\pi$
$31$	5.97814	1.07371	0.536853	+	0.843676i	$0.319613\pi$
$32$	−1.00000	−0.176777
$33$	4.95562	0.862663
$34$	−1.25710	−0.215590
$35$	6.44587	1.08955
$36$	−0.734912	−0.122485
$37$	6.53848	1.07492	0.537460	−	0.843289i	$-0.319384\pi$
$37$	6.53848	1.07492	0.537460	+	0.843289i	$0.319384\pi$
$38$	1.42633	0.231382
$39$	−0.0389711	−0.00624036
$40$	2.72563	0.430960
$41$	1.11334	0.173874	0.0869370	−	0.996214i	$-0.472292\pi$
$41$	1.11334	0.173874	0.0869370	+	0.996214i	$0.472292\pi$
$42$	3.55924	0.549202
$43$	3.03969	0.463549	0.231774	−	0.972770i	$-0.425547\pi$
$43$	3.03969	0.463549	0.231774	+	0.972770i	$0.425547\pi$
$44$	3.29273	0.496397
$45$	2.00310	0.298604
$46$	−1.00000	−0.147442
$47$	11.9054	1.73658	0.868288	−	0.496061i	$-0.165221\pi$
$47$	11.9054	1.73658	0.868288	+	0.496061i	$0.165221\pi$
$48$	1.50502	0.217231
$49$	−1.40721	−0.201030
$50$	−2.42906	−0.343521
$51$	1.89196	0.264927
$52$	−0.0258940	−0.00359086
$53$	−8.79403	−1.20795	−0.603977	−	0.797002i	$-0.706418\pi$
$53$	−8.79403	−1.20795	−0.603977	+	0.797002i	$0.706418\pi$
$54$	5.62112	0.764938
$55$	−8.97475	−1.21016
$56$	2.36491	0.316024
$57$	−2.14666	−0.284332
$58$	−1.18615	−0.155750
$59$	−0.637130	−0.0829473	−0.0414737	−	0.999140i	$-0.513205\pi$
$59$	−0.637130	−0.0829473	−0.0414737	+	0.999140i	$0.513205\pi$
$60$	−4.10213	−0.529583
$61$	−10.4294	−1.33534	−0.667672	−	0.744456i	$-0.732709\pi$
$61$	−10.4294	−1.33534	−0.667672	+	0.744456i	$0.732709\pi$
$62$	−5.97814	−0.759225
$63$	1.73800	0.218967
$64$	1.00000	0.125000
$65$	0.0705775	0.00875407
$66$	−4.95562	−0.609995
$67$	4.76854	0.582570	0.291285	−	0.956636i	$-0.405917\pi$
$67$	4.76854	0.582570	0.291285	+	0.956636i	$0.405917\pi$
$68$	1.25710	0.152445
$69$	1.50502	0.181183
$70$	−6.44587	−0.770428
$71$	−7.69944	−0.913756	−0.456878	−	0.889529i	$-0.651032\pi$
$71$	−7.69944	−0.913756	−0.456878	+	0.889529i	$0.651032\pi$
$72$	0.734912	0.0866102
$73$	−6.63515	−0.776586	−0.388293	−	0.921536i	$-0.626935\pi$
$73$	−6.63515	−0.776586	−0.388293	+	0.921536i	$0.626935\pi$
$74$	−6.53848	−0.760083
$75$	3.65578	0.422134
$76$	−1.42633	−0.163612
$77$	−7.78700	−0.887411
$78$	0.0389711	0.00441260
$79$	7.08175	0.796760	0.398380	−	0.917221i	$-0.369573\pi$
$79$	7.08175	0.796760	0.398380	+	0.917221i	$0.369573\pi$
$80$	−2.72563	−0.304735
$81$	−6.25517	−0.695019
$82$	−1.11334	−0.122947
$83$	−13.3908	−1.46983	−0.734913	−	0.678162i	$-0.762777\pi$
$83$	−13.3908	−1.46983	−0.734913	+	0.678162i	$0.762777\pi$
$84$	−3.55924	−0.388345
$85$	−3.42638	−0.371643
$86$	−3.03969	−0.327778
$87$	1.78519	0.191392
$88$	−3.29273	−0.351006
$89$	11.0810	1.17458	0.587292	−	0.809375i	$-0.300194\pi$
$89$	11.0810	1.17458	0.587292	+	0.809375i	$0.300194\pi$
$90$	−2.00310	−0.211145
$91$	0.0612370	0.00641938
$92$	1.00000	0.104257
$93$	8.99723	0.932969
$94$	−11.9054	−1.22794
$95$	3.88765	0.398865
$96$	−1.50502	−0.153606
$97$	2.00602	0.203680	0.101840	−	0.994801i	$-0.467527\pi$
$97$	2.00602	0.203680	0.101840	+	0.994801i	$0.467527\pi$
$98$	1.40721	0.142150
$99$	−2.41986	−0.243206
$100$	2.42906	0.242906
$101$	−12.6988	−1.26358	−0.631790	−	0.775140i	$-0.717679\pi$
$101$	−12.6988	−1.26358	−0.631790	+	0.775140i	$0.717679\pi$
$102$	−1.89196	−0.187332
$103$	2.47387	0.243758	0.121879	−	0.992545i	$-0.461108\pi$
$103$	2.47387	0.243758	0.121879	+	0.992545i	$0.461108\pi$
$104$	0.0258940	0.00253912
$105$	9.70116	0.946736
$106$	8.79403	0.854152
$107$	−19.8351	−1.91753	−0.958763	−	0.284205i	$-0.908270\pi$
$107$	−19.8351	−1.91753	−0.958763	+	0.284205i	$0.908270\pi$
$108$	−5.62112	−0.540893
$109$	1.14841	0.109997	0.0549987	−	0.998486i	$-0.482485\pi$
$109$	1.14841	0.109997	0.0549987	+	0.998486i	$0.482485\pi$
$110$	8.97475	0.855709
$111$	9.84056	0.934024
$112$	−2.36491	−0.223463
$113$	20.1469	1.89526	0.947630	−	0.319369i	$-0.103471\pi$
$113$	20.1469	1.89526	0.947630	+	0.319369i	$0.103471\pi$
$114$	2.14666	0.201053
$115$	−2.72563	−0.254166
$116$	1.18615	0.110132
$117$	0.0190298	0.00175931
$118$	0.637130	0.0586526
$119$	−2.97292	−0.272527
$120$	4.10213	0.374472
$121$	−0.157950	−0.0143591
$122$	10.4294	0.944230
$123$	1.67559	0.151083
$124$	5.97814	0.536853
$125$	7.00744	0.626764
$126$	−1.73800	−0.154833
$127$	7.11064	0.630967	0.315484	−	0.948931i	$-0.397833\pi$
$127$	7.11064	0.630967	0.315484	+	0.948931i	$0.397833\pi$
$128$	−1.00000	−0.0883883
$129$	4.57480	0.402789
$130$	−0.0705775	−0.00619006
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	4.95562	0.431332
$133$	3.37315	0.292489
$134$	−4.76854	−0.411939
$135$	15.3211	1.31863
$136$	−1.25710	−0.107795
$137$	−18.3591	−1.56853	−0.784264	−	0.620427i	$-0.786959\pi$
$137$	−18.3591	−1.56853	−0.784264	+	0.620427i	$0.786959\pi$
$138$	−1.50502	−0.128116
$139$	−16.4313	−1.39368	−0.696841	−	0.717226i	$-0.745412\pi$
$139$	−16.4313	−1.39368	−0.696841	+	0.717226i	$0.745412\pi$
$140$	6.44587	0.544775
$141$	17.9178	1.50895
$142$	7.69944	0.646123
$143$	−0.0852620	−0.00712996
$144$	−0.734912	−0.0612427
$145$	−3.23302	−0.268488
$146$	6.63515	0.549129
$147$	−2.11788	−0.174680
$148$	6.53848	0.537460
$149$	−8.63910	−0.707743	−0.353871	−	0.935294i	$-0.615135\pi$
$149$	−8.63910	−0.707743	−0.353871	+	0.935294i	$0.615135\pi$
$150$	−3.65578	−0.298493
$151$	0.717568	0.0583948	0.0291974	−	0.999574i	$-0.490705\pi$
$151$	0.717568	0.0583948	0.0291974	+	0.999574i	$0.490705\pi$
$152$	1.42633	0.115691
$153$	−0.923856	−0.0746893
$154$	7.78700	0.627494
$155$	−16.2942	−1.30878
$156$	−0.0389711	−0.00312018
$157$	−6.64964	−0.530699	−0.265349	−	0.964152i	$-0.585487\pi$
$157$	−6.64964	−0.530699	−0.265349	+	0.964152i	$0.585487\pi$
$158$	−7.08175	−0.563394
$159$	−13.2352	−1.04962
$160$	2.72563	0.215480
$161$	−2.36491	−0.186381
$162$	6.25517	0.491452
$163$	−10.6956	−0.837741	−0.418871	−	0.908046i	$-0.637574\pi$
$163$	−10.6956	−0.837741	−0.418871	+	0.908046i	$0.637574\pi$
$164$	1.11334	0.0869370
$165$	−13.5072	−1.05153
$166$	13.3908	1.03932
$167$	0.226009	0.0174891	0.00874453	−	0.999962i	$-0.497216\pi$
$167$	0.226009	0.0174891	0.00874453	+	0.999962i	$0.497216\pi$
$168$	3.55924	0.274601
$169$	−12.9993	−0.999948
$170$	3.42638	0.262791
$171$	1.04823	0.0801601
$172$	3.03969	0.231774
$173$	8.60643	0.654335	0.327167	−	0.944966i	$-0.393906\pi$
$173$	8.60643	0.654335	0.327167	+	0.944966i	$0.393906\pi$
$174$	−1.78519	−0.135335
$175$	−5.74450	−0.434243
$176$	3.29273	0.248199
$177$	−0.958895	−0.0720749
$178$	−11.0810	−0.830556
$179$	16.1662	1.20832	0.604159	−	0.796864i	$-0.293509\pi$
$179$	16.1662	1.20832	0.604159	+	0.796864i	$0.293509\pi$
$180$	2.00310	0.149302
$181$	−13.0720	−0.971636	−0.485818	−	0.874060i	$-0.661478\pi$
$181$	−13.0720	−0.971636	−0.485818	+	0.874060i	$0.661478\pi$
$182$	−0.0612370	−0.00453919
$183$	−15.6964	−1.16031
$184$	−1.00000	−0.0737210
$185$	−17.8215	−1.31026
$186$	−8.99723	−0.659709
$187$	4.13928	0.302694
$188$	11.9054	0.868288
$189$	13.2934	0.966955
$190$	−3.88765	−0.282040
$191$	26.9462	1.94976	0.974878	−	0.222737i	$-0.0714993\pi$
$191$	26.9462	1.94976	0.974878	+	0.222737i	$0.0714993\pi$
$192$	1.50502	0.108616
$193$	−14.5321	−1.04604	−0.523021	−	0.852320i	$-0.675195\pi$
$193$	−14.5321	−1.04604	−0.523021	+	0.852320i	$0.675195\pi$
$194$	−2.00602	−0.144024
$195$	0.106221	0.00760662
$196$	−1.40721	−0.100515
$197$	−22.9483	−1.63500	−0.817499	−	0.575930i	$-0.804640\pi$
$197$	−22.9483	−1.63500	−0.817499	+	0.575930i	$0.804640\pi$
$198$	2.41986	0.171972
$199$	12.6803	0.898880	0.449440	−	0.893311i	$-0.351624\pi$
$199$	12.6803	0.898880	0.449440	+	0.893311i	$0.351624\pi$
$200$	−2.42906	−0.171760
$201$	7.17676	0.506209
$202$	12.6988	0.893485
$203$	−2.80515	−0.196883
$204$	1.89196	0.132464
$205$	−3.03454	−0.211942
$206$	−2.47387	−0.172363
$207$	−0.734912	−0.0510799
$208$	−0.0258940	−0.00179543
$209$	−4.69652	−0.324865
$210$	−9.70116	−0.669444
$211$	−28.6231	−1.97050	−0.985249	−	0.171126i	$-0.945259\pi$
$211$	−28.6231	−1.97050	−0.985249	+	0.171126i	$0.945259\pi$
$212$	−8.79403	−0.603977
$213$	−11.5878	−0.793984
$214$	19.8351	1.35590
$215$	−8.28508	−0.565038
$216$	5.62112	0.382469
$217$	−14.1378	−0.959733
$218$	−1.14841	−0.0777799
$219$	−9.98604	−0.674794
$220$	−8.97475	−0.605078
$221$	−0.0325513	−0.00218964
$222$	−9.84056	−0.660455
$223$	−21.6945	−1.45277	−0.726385	−	0.687288i	$-0.758801\pi$
$223$	−21.6945	−1.45277	−0.726385	+	0.687288i	$0.758801\pi$
$224$	2.36491	0.158012
$225$	−1.78514	−0.119010
$226$	−20.1469	−1.34015
$227$	−10.9881	−0.729303	−0.364652	−	0.931144i	$-0.618812\pi$
$227$	−10.9881	−0.729303	−0.364652	+	0.931144i	$0.618812\pi$
$228$	−2.14666	−0.142166
$229$	11.6536	0.770089	0.385045	−	0.922898i	$-0.374186\pi$
$229$	11.6536	0.770089	0.385045	+	0.922898i	$0.374186\pi$
$230$	2.72563	0.179723
$231$	−11.7196	−0.771093
$232$	−1.18615	−0.0778749
$233$	14.5619	0.953980	0.476990	−	0.878909i	$-0.341728\pi$
$233$	14.5619	0.953980	0.476990	+	0.878909i	$0.341728\pi$
$234$	−0.0190298	−0.00124402
$235$	−32.4496	−2.11678
$236$	−0.637130	−0.0414737
$237$	10.6582	0.692324
$238$	2.97292	0.192706
$239$	−23.8632	−1.54358	−0.771791	−	0.635877i	$-0.780639\pi$
$239$	−23.8632	−1.54358	−0.771791	+	0.635877i	$0.780639\pi$
$240$	−4.10213	−0.264791
$241$	−22.7518	−1.46557	−0.732786	−	0.680459i	$-0.761780\pi$
$241$	−22.7518	−1.46557	−0.732786	+	0.680459i	$0.761780\pi$
$242$	0.157950	0.0101534
$243$	7.44920	0.477867
$244$	−10.4294	−0.667672
$245$	3.83553	0.245043
$246$	−1.67559	−0.106832
$247$	0.0369335	0.00235002
$248$	−5.97814	−0.379612
$249$	−20.1534	−1.27717
$250$	−7.00744	−0.443189
$251$	−21.0619	−1.32942	−0.664708	−	0.747103i	$-0.731444\pi$
$251$	−21.0619	−1.32942	−0.664708	+	0.747103i	$0.731444\pi$
$252$	1.73800	0.109484
$253$	3.29273	0.207012
$254$	−7.11064	−0.446161
$255$	−5.15678	−0.322930
$256$	1.00000	0.0625000
$257$	0.995340	0.0620876	0.0310438	−	0.999518i	$-0.490117\pi$
$257$	0.995340	0.0620876	0.0310438	+	0.999518i	$0.490117\pi$
$258$	−4.57480	−0.284815
$259$	−15.4629	−0.960819
$260$	0.0705775	0.00437703
$261$	−0.871719	−0.0539581
$262$	−1.00000	−0.0617802
$263$	19.0437	1.17429	0.587143	−	0.809483i	$-0.300253\pi$
$263$	19.0437	1.17429	0.587143	+	0.809483i	$0.300253\pi$
$264$	−4.95562	−0.304997
$265$	23.9693	1.47242
$266$	−3.37315	−0.206821
$267$	16.6771	1.02062
$268$	4.76854	0.291285
$269$	23.1840	1.41355	0.706777	−	0.707437i	$-0.250149\pi$
$269$	23.1840	1.41355	0.706777	+	0.707437i	$0.250149\pi$
$270$	−15.3211	−0.932412
$271$	−0.0952327	−0.00578497	−0.00289249	−	0.999996i	$-0.500921\pi$
$271$	−0.0952327	−0.00578497	−0.00289249	+	0.999996i	$0.500921\pi$
$272$	1.25710	0.0762227
$273$	0.0921630	0.00557796
$274$	18.3591	1.10912
$275$	7.99823	0.482311
$276$	1.50502	0.0905916
$277$	−10.8520	−0.652033	−0.326016	−	0.945364i	$-0.605706\pi$
$277$	−10.8520	−0.652033	−0.326016	+	0.945364i	$0.605706\pi$
$278$	16.4313	0.985482
$279$	−4.39341	−0.263026
$280$	−6.44587	−0.385214
$281$	−8.69946	−0.518966	−0.259483	−	0.965748i	$-0.583552\pi$
$281$	−8.69946	−0.518966	−0.259483	+	0.965748i	$0.583552\pi$
$282$	−17.9178	−1.06699
$283$	−13.0236	−0.774174	−0.387087	−	0.922043i	$-0.626519\pi$
$283$	−13.0236	−0.774174	−0.387087	+	0.922043i	$0.626519\pi$
$284$	−7.69944	−0.456878
$285$	5.85100	0.346583
$286$	0.0852620	0.00504165
$287$	−2.63294	−0.155417
$288$	0.734912	0.0433051
$289$	−15.4197	−0.907042
$290$	3.23302	0.189849
$291$	3.01910	0.176983
$292$	−6.63515	−0.388293
$293$	13.7640	0.804100	0.402050	−	0.915618i	$-0.368298\pi$
$293$	13.7640	0.804100	0.402050	+	0.915618i	$0.368298\pi$
$294$	2.11788	0.123517
$295$	1.73658	0.101108
$296$	−6.53848	−0.380042
$297$	−18.5088	−1.07399
$298$	8.63910	0.500450
$299$	−0.0258940	−0.00149749
$300$	3.65578	0.211067
$301$	−7.18859	−0.414344
$302$	−0.717568	−0.0412914
$303$	−19.1120	−1.09795
$304$	−1.42633	−0.0818058
$305$	28.4266	1.62770
$306$	0.923856	0.0528133
$307$	32.3442	1.84598	0.922990	−	0.384825i	$-0.125738\pi$
$307$	32.3442	1.84598	0.922990	+	0.384825i	$0.125738\pi$
$308$	−7.78700	−0.443705
$309$	3.72323	0.211807
$310$	16.2942	0.925448
$311$	−4.72919	−0.268168	−0.134084	−	0.990970i	$-0.542809\pi$
$311$	−4.72919	−0.268168	−0.134084	+	0.990970i	$0.542809\pi$
$312$	0.0389711	0.00220630
$313$	−21.3739	−1.20812	−0.604061	−	0.796938i	$-0.706452\pi$
$313$	−21.3739	−1.20812	−0.604061	+	0.796938i	$0.706452\pi$
$314$	6.64964	0.375261
$315$	−4.73714	−0.266908
$316$	7.08175	0.398380
$317$	−16.9856	−0.954006	−0.477003	−	0.878902i	$-0.658277\pi$
$317$	−16.9856	−0.954006	−0.477003	+	0.878902i	$0.658277\pi$
$318$	13.2352	0.742193
$319$	3.90568	0.218676
$320$	−2.72563	−0.152367
$321$	−29.8522	−1.66619
$322$	2.36491	0.131791
$323$	−1.79304	−0.0997673
$324$	−6.25517	−0.347509
$325$	−0.0628981	−0.00348896
$326$	10.6956	0.592373
$327$	1.72838	0.0955794
$328$	−1.11334	−0.0614737
$329$	−28.1551	−1.55224
$330$	13.5072	0.743547
$331$	−29.0657	−1.59760	−0.798799	−	0.601598i	$-0.794531\pi$
$331$	−29.0657	−1.59760	−0.798799	+	0.601598i	$0.794531\pi$
$332$	−13.3908	−0.734913
$333$	−4.80521	−0.263324
$334$	−0.226009	−0.0123666
$335$	−12.9973	−0.710117
$336$	−3.55924	−0.194172
$337$	19.9216	1.08520	0.542599	−	0.839992i	$-0.317440\pi$
$337$	19.9216	1.08520	0.542599	+	0.839992i	$0.317440\pi$
$338$	12.9993	0.707070
$339$	30.3215	1.64684
$340$	−3.42638	−0.185822
$341$	19.6844	1.06597
$342$	−1.04823	−0.0566817
$343$	19.8823	1.07354
$344$	−3.03969	−0.163889
$345$	−4.10213	−0.220851
$346$	−8.60643	−0.462685
$347$	31.5949	1.69610	0.848051	−	0.529914i	$-0.177776\pi$
$347$	31.5949	1.69610	0.848051	+	0.529914i	$0.177776\pi$
$348$	1.78519	0.0956961
$349$	2.88986	0.154691	0.0773454	−	0.997004i	$-0.475356\pi$
$349$	2.88986	0.154691	0.0773454	+	0.997004i	$0.475356\pi$
$350$	5.74450	0.307056
$351$	0.145553	0.00776907
$352$	−3.29273	−0.175503
$353$	−12.6049	−0.670890	−0.335445	−	0.942060i	$-0.608887\pi$
$353$	−12.6049	−0.670890	−0.335445	+	0.942060i	$0.608887\pi$
$354$	0.958895	0.0509647
$355$	20.9858	1.11381
$356$	11.0810	0.587292
$357$	−4.47431	−0.236805
$358$	−16.1662	−0.854410
$359$	11.3247	0.597697	0.298848	−	0.954301i	$-0.403397\pi$
$359$	11.3247	0.597697	0.298848	+	0.954301i	$0.403397\pi$
$360$	−2.00310	−0.105573
$361$	−16.9656	−0.892925
$362$	13.0720	0.687051
$363$	−0.237719	−0.0124770
$364$	0.0612370	0.00320969
$365$	18.0850	0.946611
$366$	15.6964	0.820464
$367$	−12.3212	−0.643162	−0.321581	−	0.946882i	$-0.604214\pi$
$367$	−12.3212	−0.643162	−0.321581	+	0.946882i	$0.604214\pi$
$368$	1.00000	0.0521286
$369$	−0.818204	−0.0425940
$370$	17.8215	0.926495
$371$	20.7971	1.07973
$372$	8.99723	0.466484
$373$	−31.4290	−1.62733	−0.813667	−	0.581331i	$-0.802532\pi$
$373$	−31.4290	−1.62733	−0.813667	+	0.581331i	$0.802532\pi$
$374$	−4.13928	−0.214037
$375$	10.5463	0.544610
$376$	−11.9054	−0.613972
$377$	−0.0307143	−0.00158187
$378$	−13.2934	−0.683741
$379$	4.54449	0.233435	0.116717	−	0.993165i	$-0.462763\pi$
$379$	4.54449	0.233435	0.116717	+	0.993165i	$0.462763\pi$
$380$	3.88765	0.199432
$381$	10.7017	0.548263
$382$	−26.9462	−1.37869
$383$	2.24326	0.114625	0.0573127	−	0.998356i	$-0.481747\pi$
$383$	2.24326	0.114625	0.0573127	+	0.998356i	$0.481747\pi$
$384$	−1.50502	−0.0768028
$385$	21.2245	1.08170
$386$	14.5321	0.739663
$387$	−2.23391	−0.113556
$388$	2.00602	0.101840
$389$	−18.5644	−0.941251	−0.470626	−	0.882333i	$-0.655972\pi$
$389$	−18.5644	−0.941251	−0.470626	+	0.882333i	$0.655972\pi$
$390$	−0.106221	−0.00537869
$391$	1.25710	0.0635741
$392$	1.40721	0.0710748
$393$	1.50502	0.0759183
$394$	22.9483	1.15612
$395$	−19.3022	−0.971201
$396$	−2.41986	−0.121603
$397$	0.594174	0.0298207	0.0149104	−	0.999889i	$-0.495254\pi$
$397$	0.594174	0.0298207	0.0149104	+	0.999889i	$0.495254\pi$
$398$	−12.6803	−0.635604
$399$	5.07666	0.254151
$400$	2.42906	0.121453
$401$	0.754936	0.0376997	0.0188499	−	0.999822i	$-0.494000\pi$
$401$	0.754936	0.0376997	0.0188499	+	0.999822i	$0.494000\pi$
$402$	−7.17676	−0.357944
$403$	−0.154798	−0.00771104
$404$	−12.6988	−0.631790
$405$	17.0493	0.847185
$406$	2.80515	0.139217
$407$	21.5294	1.06717
$408$	−1.89196	−0.0936658
$409$	−25.8626	−1.27882	−0.639411	−	0.768865i	$-0.720822\pi$
$409$	−25.8626	−1.27882	−0.639411	+	0.768865i	$0.720822\pi$
$410$	3.03454	0.149865
$411$	−27.6309	−1.36293
$412$	2.47387	0.121879
$413$	1.50676	0.0741426
$414$	0.734912	0.0361190
$415$	36.4982	1.79163
$416$	0.0258940	0.00126956
$417$	−24.7294	−1.21100
$418$	4.69652	0.229714
$419$	17.2461	0.842525	0.421263	−	0.906939i	$-0.361587\pi$
$419$	17.2461	0.842525	0.421263	+	0.906939i	$0.361587\pi$
$420$	9.70116	0.473368
$421$	36.3621	1.77218	0.886091	−	0.463511i	$-0.153410\pi$
$421$	36.3621	1.77218	0.886091	+	0.463511i	$0.153410\pi$
$422$	28.6231	1.39335
$423$	−8.74939	−0.425410
$424$	8.79403	0.427076
$425$	3.05356	0.148120
$426$	11.5878	0.561432
$427$	24.6645	1.19360
$428$	−19.8351	−0.958763
$429$	−0.128321	−0.00619540
$430$	8.28508	0.399542
$431$	−21.9180	−1.05575	−0.527875	−	0.849322i	$-0.677011\pi$
$431$	−21.9180	−1.05575	−0.527875	+	0.849322i	$0.677011\pi$
$432$	−5.62112	−0.270446
$433$	−32.9831	−1.58507	−0.792533	−	0.609829i	$-0.791238\pi$
$433$	−32.9831	−1.58507	−0.792533	+	0.609829i	$0.791238\pi$
$434$	14.1378	0.678634
$435$	−4.86576	−0.233295
$436$	1.14841	0.0549987
$437$	−1.42633	−0.0682307
$438$	9.98604	0.477152
$439$	35.6717	1.70252	0.851260	−	0.524744i	$-0.175839\pi$
$439$	35.6717	1.70252	0.851260	+	0.524744i	$0.175839\pi$
$440$	8.97475	0.427855
$441$	1.03417	0.0492464
$442$	0.0325513	0.00154831
$443$	19.4406	0.923653	0.461826	−	0.886970i	$-0.347194\pi$
$443$	19.4406	0.923653	0.461826	+	0.886970i	$0.347194\pi$
$444$	9.84056	0.467012
$445$	−30.2027	−1.43175
$446$	21.6945	1.02726
$447$	−13.0020	−0.614975
$448$	−2.36491	−0.111731
$449$	−30.5372	−1.44114	−0.720571	−	0.693382i	$-0.756120\pi$
$449$	−30.5372	−1.44114	−0.720571	+	0.693382i	$0.756120\pi$
$450$	1.78514	0.0841525
$451$	3.66591	0.172621
$452$	20.1469	0.947630
$453$	1.07995	0.0507407
$454$	10.9881	0.515695
$455$	−0.166909	−0.00782483
$456$	2.14666	0.100527
$457$	−19.9037	−0.931055	−0.465527	−	0.885033i	$-0.654135\pi$
$457$	−19.9037	−0.931055	−0.465527	+	0.885033i	$0.654135\pi$
$458$	−11.6536	−0.544535
$459$	−7.06629	−0.329826
$460$	−2.72563	−0.127083
$461$	−4.60202	−0.214337	−0.107169	−	0.994241i	$-0.534178\pi$
$461$	−4.60202	−0.214337	−0.107169	+	0.994241i	$0.534178\pi$
$462$	11.7196	0.545245
$463$	−9.67270	−0.449528	−0.224764	−	0.974413i	$-0.572161\pi$
$463$	−9.67270	−0.449528	−0.224764	+	0.974413i	$0.572161\pi$
$464$	1.18615	0.0550659
$465$	−24.5231	−1.13723
$466$	−14.5619	−0.674566
$467$	38.8060	1.79573	0.897864	−	0.440273i	$-0.145118\pi$
$467$	38.8060	1.79573	0.897864	+	0.440273i	$0.145118\pi$
$468$	0.0190298	0.000879654 0
$469$	−11.2772	−0.520731
$470$	32.4496	1.49679
$471$	−10.0078	−0.461137
$472$	0.637130	0.0293263
$473$	10.0089	0.460209
$474$	−10.6582	−0.489547
$475$	−3.46465	−0.158969
$476$	−2.97292	−0.136264
$477$	6.46284	0.295913
$478$	23.8632	1.09148
$479$	21.0216	0.960501	0.480250	−	0.877131i	$-0.340546\pi$
$479$	21.0216	0.960501	0.480250	+	0.877131i	$0.340546\pi$
$480$	4.10213	0.187236
$481$	−0.169308	−0.00771977
$482$	22.7518	1.03632
$483$	−3.55924	−0.161951
$484$	−0.157950	−0.00717956
$485$	−5.46767	−0.248274
$486$	−7.44920	−0.337903
$487$	−15.4903	−0.701934	−0.350967	−	0.936388i	$-0.614147\pi$
$487$	−15.4903	−0.701934	−0.350967	+	0.936388i	$0.614147\pi$
$488$	10.4294	0.472115
$489$	−16.0970	−0.727934
$490$	−3.83553	−0.173272
$491$	−6.46100	−0.291581	−0.145791	−	0.989315i	$-0.546573\pi$
$491$	−6.46100	−0.291581	−0.145791	+	0.989315i	$0.546573\pi$
$492$	1.67559	0.0755416
$493$	1.49111	0.0671563
$494$	−0.0369335	−0.00166172
$495$	6.59566	0.296453
$496$	5.97814	0.268426
$497$	18.2085	0.816762
$498$	20.1534	0.903094
$499$	−35.8164	−1.60336	−0.801681	−	0.597752i	$-0.796061\pi$
$499$	−35.8164	−1.60336	−0.801681	+	0.597752i	$0.796061\pi$
$500$	7.00744	0.313382
$501$	0.340148	0.0151967
$502$	21.0619	0.940039
$503$	7.48407	0.333698	0.166849	−	0.985982i	$-0.446641\pi$
$503$	7.48407	0.333698	0.166849	+	0.985982i	$0.446641\pi$
$504$	−1.73800	−0.0774167
$505$	34.6123	1.54023
$506$	−3.29273	−0.146380
$507$	−19.5643	−0.868879
$508$	7.11064	0.315484
$509$	−43.0640	−1.90878	−0.954390	−	0.298563i	$-0.903493\pi$
$509$	−43.0640	−1.90878	−0.954390	+	0.298563i	$0.903493\pi$
$510$	5.15678	0.228346
$511$	15.6915	0.694152
$512$	−1.00000	−0.0441942
$513$	8.01759	0.353985
$514$	−0.995340	−0.0439026
$515$	−6.74286	−0.297126
$516$	4.57480	0.201394
$517$	39.2011	1.72406
$518$	15.4629	0.679402
$519$	12.9529	0.568567
$520$	−0.0705775	−0.00309503
$521$	−7.08185	−0.310261	−0.155131	−	0.987894i	$-0.549580\pi$
$521$	−7.08185	−0.310261	−0.155131	+	0.987894i	$0.549580\pi$
$522$	0.871719	0.0381541
$523$	12.8597	0.562315	0.281158	−	0.959662i	$-0.409282\pi$
$523$	12.8597	0.562315	0.281158	+	0.959662i	$0.409282\pi$
$524$	1.00000	0.0436852
$525$	−8.64559	−0.377325
$526$	−19.0437	−0.830345
$527$	7.51510	0.327363
$528$	4.95562	0.215666
$529$	1.00000	0.0434783
$530$	−23.9693	−1.04116
$531$	0.468235	0.0203197
$532$	3.37315	0.146244
$533$	−0.0288288	−0.00124871
$534$	−16.6771	−0.721690
$535$	54.0630	2.33735
$536$	−4.76854	−0.205970
$537$	24.3305	1.04994
$538$	−23.1840	−0.999533
$539$	−4.63355	−0.199581
$540$	15.3211	0.659315
$541$	−8.15798	−0.350739	−0.175369	−	0.984503i	$-0.556112\pi$
$541$	−8.15798	−0.350739	−0.175369	+	0.984503i	$0.556112\pi$
$542$	0.0952327	0.00409059
$543$	−19.6737	−0.844278
$544$	−1.25710	−0.0538976
$545$	−3.13013	−0.134080
$546$	−0.0921630	−0.00394421
$547$	−3.69883	−0.158150	−0.0790752	−	0.996869i	$-0.525197\pi$
$547$	−3.69883	−0.158150	−0.0790752	+	0.996869i	$0.525197\pi$
$548$	−18.3591	−0.784264
$549$	7.66467	0.327120
$550$	−7.99823	−0.341045
$551$	−1.69185	−0.0720753
$552$	−1.50502	−0.0640579
$553$	−16.7477	−0.712185
$554$	10.8520	0.461057
$555$	−26.8217	−1.13852
$556$	−16.4313	−0.696841
$557$	20.0270	0.848569	0.424285	−	0.905529i	$-0.360526\pi$
$557$	20.0270	0.848569	0.424285	+	0.905529i	$0.360526\pi$
$558$	4.39341	0.185988
$559$	−0.0787099	−0.00332907
$560$	6.44587	0.272388
$561$	6.22970	0.263018
$562$	8.69946	0.366965
$563$	−13.1630	−0.554755	−0.277378	−	0.960761i	$-0.589465\pi$
$563$	−13.1630	−0.554755	−0.277378	+	0.960761i	$0.589465\pi$
$564$	17.9178	0.754476
$565$	−54.9130	−2.31021
$566$	13.0236	0.547424
$567$	14.7929	0.621243
$568$	7.69944	0.323061
$569$	20.6842	0.867129	0.433564	−	0.901123i	$-0.357256\pi$
$569$	20.6842	0.867129	0.433564	+	0.901123i	$0.357256\pi$
$570$	−5.85100	−0.245071
$571$	−19.4022	−0.811958	−0.405979	−	0.913882i	$-0.633069\pi$
$571$	−19.4022	−0.811958	−0.405979	+	0.913882i	$0.633069\pi$
$572$	−0.0852620	−0.00356498
$573$	40.5546	1.69419
$574$	2.63294	0.109897
$575$	2.42906	0.101299
$576$	−0.734912	−0.0306213
$577$	17.4130	0.724912	0.362456	−	0.932001i	$-0.381938\pi$
$577$	17.4130	0.724912	0.362456	+	0.932001i	$0.381938\pi$
$578$	15.4197	0.641375
$579$	−21.8711	−0.908930
$580$	−3.23302	−0.134244
$581$	31.6679	1.31381
$582$	−3.01910	−0.125146
$583$	−28.9563	−1.19925
$584$	6.63515	0.274565
$585$	−0.0518683	−0.00214449
$586$	−13.7640	−0.568585
$587$	43.8593	1.81027	0.905133	−	0.425129i	$-0.139771\pi$
$587$	43.8593	1.81027	0.905133	+	0.425129i	$0.139771\pi$
$588$	−2.11788	−0.0873398
$589$	−8.52682	−0.351341
$590$	−1.73658	−0.0714939
$591$	−34.5376	−1.42069
$592$	6.53848	0.268730
$593$	42.1191	1.72962	0.864812	−	0.502097i	$-0.167438\pi$
$593$	42.1191	1.72962	0.864812	+	0.502097i	$0.167438\pi$
$594$	18.5088	0.759426
$595$	8.10308	0.332194
$596$	−8.63910	−0.353871
$597$	19.0841	0.781059
$598$	0.0258940	0.00105889
$599$	−2.44539	−0.0999160	−0.0499580	−	0.998751i	$-0.515909\pi$
$599$	−2.44539	−0.0999160	−0.0499580	+	0.998751i	$0.515909\pi$
$600$	−3.65578	−0.149247
$601$	8.82383	0.359932	0.179966	−	0.983673i	$-0.442401\pi$
$601$	8.82383	0.359932	0.179966	+	0.983673i	$0.442401\pi$
$602$	7.18859	0.292985
$603$	−3.50446	−0.142713
$604$	0.717568	0.0291974
$605$	0.430514	0.0175029
$606$	19.1120	0.776371
$607$	−15.1174	−0.613596	−0.306798	−	0.951775i	$-0.599258\pi$
$607$	−15.1174	−0.613596	−0.306798	+	0.951775i	$0.599258\pi$
$608$	1.42633	0.0578454
$609$	−4.22181	−0.171076
$610$	−28.4266	−1.15096
$611$	−0.308278	−0.0124716
$612$	−0.923856	−0.0373447
$613$	−37.7298	−1.52389	−0.761946	−	0.647640i	$-0.775756\pi$
$613$	−37.7298	−1.52389	−0.761946	+	0.647640i	$0.775756\pi$
$614$	−32.3442	−1.30530
$615$	−4.56705	−0.184161
$616$	7.78700	0.313747
$617$	8.20391	0.330277	0.165138	−	0.986270i	$-0.447193\pi$
$617$	8.20391	0.330277	0.165138	+	0.986270i	$0.447193\pi$
$618$	−3.72323	−0.149770
$619$	23.4058	0.940760	0.470380	−	0.882464i	$-0.344117\pi$
$619$	23.4058	0.940760	0.470380	+	0.882464i	$0.344117\pi$
$620$	−16.2942	−0.654391
$621$	−5.62112	−0.225568
$622$	4.72919	0.189623
$623$	−26.2055	−1.04990
$624$	−0.0389711	−0.00156009
$625$	−31.2450	−1.24980
$626$	21.3739	0.854271
$627$	−7.06837	−0.282283
$628$	−6.64964	−0.265349
$629$	8.21951	0.327733
$630$	4.73714	0.188732
$631$	7.69701	0.306413	0.153206	−	0.988194i	$-0.451040\pi$
$631$	7.69701	0.306413	0.153206	+	0.988194i	$0.451040\pi$
$632$	−7.08175	−0.281697
$633$	−43.0784	−1.71221
$634$	16.9856	0.674584
$635$	−19.3810	−0.769110
$636$	−13.2352	−0.524810
$637$	0.0364383	0.00144374
$638$	−3.90568	−0.154627
$639$	5.65841	0.223843
$640$	2.72563	0.107740
$641$	5.82604	0.230115	0.115057	−	0.993359i	$-0.463295\pi$
$641$	5.82604	0.230115	0.115057	+	0.993359i	$0.463295\pi$
$642$	29.8522	1.17817
$643$	14.2332	0.561304	0.280652	−	0.959810i	$-0.409449\pi$
$643$	14.2332	0.561304	0.280652	+	0.959810i	$0.409449\pi$
$644$	−2.36491	−0.0931904
$645$	−12.4692	−0.490975
$646$	1.79304	0.0705462
$647$	−26.2737	−1.03292	−0.516462	−	0.856310i	$-0.672751\pi$
$647$	−26.2737	−1.03292	−0.516462	+	0.856310i	$0.672751\pi$
$648$	6.25517	0.245726
$649$	−2.09790	−0.0823496
$650$	0.0628981	0.00246707
$651$	−21.2776	−0.833936
$652$	−10.6956	−0.418871
$653$	42.9247	1.67977	0.839887	−	0.542762i	$-0.182621\pi$
$653$	42.9247	1.67977	0.839887	+	0.542762i	$0.182621\pi$
$654$	−1.72838	−0.0675849
$655$	−2.72563	−0.106499
$656$	1.11334	0.0434685
$657$	4.87625	0.190241
$658$	28.1551	1.09760
$659$	−19.0280	−0.741224	−0.370612	−	0.928788i	$-0.620852\pi$
$659$	−19.0280	−0.741224	−0.370612	+	0.928788i	$0.620852\pi$
$660$	−13.5072	−0.525767
$661$	2.91174	0.113253	0.0566267	−	0.998395i	$-0.481966\pi$
$661$	2.91174	0.113253	0.0566267	+	0.998395i	$0.481966\pi$
$662$	29.0657	1.12967
$663$	−0.0489904	−0.00190263
$664$	13.3908	0.519662
$665$	−9.19395	−0.356526
$666$	4.80521	0.186198
$667$	1.18615	0.0459281
$668$	0.226009	0.00874453
$669$	−32.6506	−1.26235
$670$	12.9973	0.502129
$671$	−34.3410	−1.32572
$672$	3.55924	0.137301
$673$	37.1715	1.43285	0.716427	−	0.697662i	$-0.245776\pi$
$673$	37.1715	1.43285	0.716427	+	0.697662i	$0.245776\pi$
$674$	−19.9216	−0.767350
$675$	−13.6540	−0.525544
$676$	−12.9993	−0.499974
$677$	−30.5435	−1.17388	−0.586941	−	0.809630i	$-0.699668\pi$
$677$	−30.5435	−1.17388	−0.586941	+	0.809630i	$0.699668\pi$
$678$	−30.3215	−1.16449
$679$	−4.74405	−0.182060
$680$	3.42638	0.131396
$681$	−16.5373	−0.633709
$682$	−19.6844	−0.753754
$683$	−2.73959	−0.104827	−0.0524137	−	0.998625i	$-0.516691\pi$
$683$	−2.73959	−0.104827	−0.0524137	+	0.998625i	$0.516691\pi$
$684$	1.04823	0.0400800
$685$	50.0402	1.91194
$686$	−19.8823	−0.759109
$687$	17.5389	0.669149
$688$	3.03969	0.115887
$689$	0.227713	0.00867517
$690$	4.10213	0.156165
$691$	−28.5369	−1.08560	−0.542798	−	0.839863i	$-0.682635\pi$
$691$	−28.5369	−1.08560	−0.542798	+	0.839863i	$0.682635\pi$
$692$	8.60643	0.327167
$693$	5.72276	0.217390
$694$	−31.5949	−1.19933
$695$	44.7856	1.69881
$696$	−1.78519	−0.0676674
$697$	1.39957	0.0530126
$698$	−2.88986	−0.109383
$699$	21.9159	0.828937
$700$	−5.74450	−0.217122
$701$	2.55875	0.0966426	0.0483213	−	0.998832i	$-0.484613\pi$
$701$	2.55875	0.0966426	0.0483213	+	0.998832i	$0.484613\pi$
$702$	−0.145553	−0.00549356
$703$	−9.32605	−0.351739
$704$	3.29273	0.124099
$705$	−48.8373	−1.83932
$706$	12.6049	0.474391
$707$	30.0315	1.12945
$708$	−0.958895	−0.0360375
$709$	27.6084	1.03686	0.518428	−	0.855121i	$-0.326517\pi$
$709$	27.6084	1.03686	0.518428	+	0.855121i	$0.326517\pi$
$710$	−20.9858	−0.787584
$711$	−5.20447	−0.195183
$712$	−11.0810	−0.415278
$713$	5.97814	0.223883
$714$	4.47431	0.167447
$715$	0.232393	0.00869099
$716$	16.1662	0.604159
$717$	−35.9146	−1.34126
$718$	−11.3247	−0.422636
$719$	−27.6135	−1.02981	−0.514905	−	0.857247i	$-0.672173\pi$
$719$	−27.6135	−1.02981	−0.514905	+	0.857247i	$0.672173\pi$
$720$	2.00310	0.0746511
$721$	−5.85048	−0.217883
$722$	16.9656	0.631393
$723$	−34.2419	−1.27347
$724$	−13.0720	−0.485818
$725$	2.88124	0.107007
$726$	0.237719	0.00882256
$727$	−1.00716	−0.0373534	−0.0186767	−	0.999826i	$-0.505945\pi$
$727$	−1.00716	−0.0373534	−0.0186767	+	0.999826i	$0.505945\pi$
$728$	−0.0612370	−0.00226959
$729$	29.9767	1.11025
$730$	−18.0850	−0.669355
$731$	3.82119	0.141332
$732$	−15.6964	−0.580156
$733$	−52.7200	−1.94726	−0.973630	−	0.228135i	$-0.926737\pi$
$733$	−52.7200	−1.94726	−0.973630	+	0.228135i	$0.926737\pi$
$734$	12.3212	0.454784
$735$	5.77255	0.212924
$736$	−1.00000	−0.0368605
$737$	15.7015	0.578372
$738$	0.818204	0.0301185
$739$	36.1844	1.33106	0.665532	−	0.746369i	$-0.268205\pi$
$739$	36.1844	1.33106	0.665532	+	0.746369i	$0.268205\pi$
$740$	−17.8215	−0.655131
$741$	0.0555857	0.00204199
$742$	−20.7971	−0.763485
$743$	23.9930	0.880219	0.440109	−	0.897944i	$-0.354940\pi$
$743$	23.9930	0.880219	0.440109	+	0.897944i	$0.354940\pi$
$744$	−8.99723	−0.329854
$745$	23.5470	0.862695
$746$	31.4290	1.15070
$747$	9.84102	0.360064
$748$	4.13928	0.151347
$749$	46.9081	1.71398
$750$	−10.5463	−0.385098
$751$	20.9951	0.766121	0.383061	−	0.923723i	$-0.374870\pi$
$751$	20.9951	0.766121	0.383061	+	0.923723i	$0.374870\pi$
$752$	11.9054	0.434144
$753$	−31.6986	−1.15516
$754$	0.0307143	0.00111855
$755$	−1.95582	−0.0711797
$756$	13.2934	0.483478
$757$	−53.9004	−1.95904	−0.979521	−	0.201341i	$-0.935470\pi$
$757$	−53.9004	−1.95904	−0.979521	+	0.201341i	$0.935470\pi$
$758$	−4.54449	−0.165063
$759$	4.95562	0.179878
$760$	−3.88765	−0.141020
$761$	−52.8201	−1.91473	−0.957364	−	0.288886i	$-0.906715\pi$
$761$	−52.8201	−1.91473	−0.957364	+	0.288886i	$0.906715\pi$
$762$	−10.7017	−0.387680
$763$	−2.71588	−0.0983214
$764$	26.9462	0.974878
$765$	2.51809	0.0910417
$766$	−2.24326	−0.0810524
$767$	0.0164979	0.000595704 0
$768$	1.50502	0.0543078
$769$	11.1251	0.401180	0.200590	−	0.979675i	$-0.435714\pi$
$769$	11.1251	0.401180	0.200590	+	0.979675i	$0.435714\pi$
$770$	−21.2245	−0.764877
$771$	1.49801	0.0539494
$772$	−14.5321	−0.523021
$773$	−15.4461	−0.555557	−0.277779	−	0.960645i	$-0.589598\pi$
$773$	−15.4461	−0.555557	−0.277779	+	0.960645i	$0.589598\pi$
$774$	2.23391	0.0802961
$775$	14.5213	0.521619
$776$	−2.00602	−0.0720119
$777$	−23.2720	−0.834879
$778$	18.5644	0.665565
$779$	−1.58799	−0.0568956
$780$	0.106221	0.00380331
$781$	−25.3522	−0.907172
$782$	−1.25710	−0.0449537
$783$	−6.66752	−0.238278
$784$	−1.40721	−0.0502574
$785$	18.1244	0.646889
$786$	−1.50502	−0.0536823
$787$	−29.2598	−1.04300	−0.521500	−	0.853251i	$-0.674627\pi$
$787$	−29.2598	−1.04300	−0.521500	+	0.853251i	$0.674627\pi$
$788$	−22.9483	−0.817499
$789$	28.6612	1.02036
$790$	19.3022	0.686743
$791$	−47.6456	−1.69408
$792$	2.41986	0.0859862
$793$	0.270058	0.00959005
$794$	−0.594174	−0.0210864
$795$	36.0743	1.27942
$796$	12.6803	0.449440
$797$	36.7528	1.30185	0.650926	−	0.759141i	$-0.274381\pi$
$797$	36.7528	1.30185	0.650926	+	0.759141i	$0.274381\pi$
$798$	−5.07666	−0.179712
$799$	14.9662	0.529466
$800$	−2.42906	−0.0858802
$801$	−8.14356	−0.287739
$802$	−0.754936	−0.0266577
$803$	−21.8477	−0.770990
$804$	7.17676	0.253105
$805$	6.44587	0.227187
$806$	0.154798	0.00545253
$807$	34.8924	1.22827
$808$	12.6988	0.446743
$809$	22.0877	0.776561	0.388280	−	0.921541i	$-0.373069\pi$
$809$	22.0877	0.776561	0.388280	+	0.921541i	$0.373069\pi$
$810$	−17.0493	−0.599050
$811$	−32.2394	−1.13208	−0.566039	−	0.824378i	$-0.691525\pi$
$811$	−32.2394	−1.13208	−0.566039	+	0.824378i	$0.691525\pi$
$812$	−2.80515	−0.0984414
$813$	−0.143327	−0.00502670
$814$	−21.5294	−0.754607
$815$	29.1522	1.02116
$816$	1.89196	0.0662318
$817$	−4.33561	−0.151684
$818$	25.8626	0.904263
$819$	−0.0450038	−0.00157256
$820$	−3.03454	−0.105971
$821$	42.6236	1.48757	0.743786	−	0.668418i	$-0.233028\pi$
$821$	42.6236	1.48757	0.743786	+	0.668418i	$0.233028\pi$
$822$	27.6309	0.963738
$823$	22.7196	0.791955	0.395978	−	0.918260i	$-0.370406\pi$
$823$	22.7196	0.791955	0.395978	+	0.918260i	$0.370406\pi$
$824$	−2.47387	−0.0861815
$825$	12.0375	0.419092
$826$	−1.50676	−0.0524267
$827$	26.8990	0.935368	0.467684	−	0.883896i	$-0.345088\pi$
$827$	26.8990	0.935368	0.467684	+	0.883896i	$0.345088\pi$
$828$	−0.734912	−0.0255400
$829$	−22.5320	−0.782569	−0.391285	−	0.920270i	$-0.627969\pi$
$829$	−22.5320	−0.782569	−0.391285	+	0.920270i	$0.627969\pi$
$830$	−36.4982	−1.26687
$831$	−16.3325	−0.566567
$832$	−0.0258940	−0.000897714 0
$833$	−1.76900	−0.0612921
$834$	24.7294	0.856309
$835$	−0.616016	−0.0213181
$836$	−4.69652	−0.162433
$837$	−33.6039	−1.16152
$838$	−17.2461	−0.595755
$839$	−6.74190	−0.232756	−0.116378	−	0.993205i	$-0.537128\pi$
$839$	−6.74190	−0.232756	−0.116378	+	0.993205i	$0.537128\pi$
$840$	−9.70116	−0.334722
$841$	−27.5930	−0.951484
$842$	−36.3621	−1.25312
$843$	−13.0929	−0.450942
$844$	−28.6231	−0.985249
$845$	35.4314	1.21888
$846$	8.74939	0.300810
$847$	0.373538	0.0128349
$848$	−8.79403	−0.301988
$849$	−19.6008	−0.672698
$850$	−3.05356	−0.104736
$851$	6.53848	0.224136
$852$	−11.5878	−0.396992
$853$	56.3687	1.93003	0.965013	−	0.262200i	$-0.0844482\pi$
$853$	56.3687	1.93003	0.965013	+	0.262200i	$0.0844482\pi$
$854$	−24.6645	−0.844001
$855$	−2.85708	−0.0977102
$856$	19.8351	0.677948
$857$	−16.5555	−0.565524	−0.282762	−	0.959190i	$-0.591251\pi$
$857$	−16.5555	−0.565524	−0.282762	+	0.959190i	$0.591251\pi$
$858$	0.128321	0.00438081
$859$	−7.21115	−0.246041	−0.123021	−	0.992404i	$-0.539258\pi$
$859$	−7.21115	−0.246041	−0.123021	+	0.992404i	$0.539258\pi$
$860$	−8.28508	−0.282519
$861$	−3.96263	−0.135046
$862$	21.9180	0.746528
$863$	−40.5122	−1.37905	−0.689526	−	0.724261i	$-0.742181\pi$
$863$	−40.5122	−1.37905	−0.689526	+	0.724261i	$0.742181\pi$
$864$	5.62112	0.191234
$865$	−23.4579	−0.797594
$866$	32.9831	1.12081
$867$	−23.2070	−0.788150
$868$	−14.1378	−0.479867
$869$	23.3183	0.791018
$870$	4.86576	0.164965
$871$	−0.123477	−0.00418385
$872$	−1.14841	−0.0388900
$873$	−1.47425	−0.0498957
$874$	1.42633	0.0482464
$875$	−16.5719	−0.560234
$876$	−9.98604	−0.337397
$877$	−35.4033	−1.19549	−0.597743	−	0.801688i	$-0.703936\pi$
$877$	−35.4033	−1.19549	−0.597743	+	0.801688i	$0.703936\pi$
$878$	−35.6717	−1.20386
$879$	20.7151	0.698702
$880$	−8.97475	−0.302539
$881$	−38.3142	−1.29084	−0.645418	−	0.763829i	$-0.723317\pi$
$881$	−38.3142	−1.29084	−0.645418	+	0.763829i	$0.723317\pi$
$882$	−1.03417	−0.0348225
$883$	−5.41348	−0.182178	−0.0910891	−	0.995843i	$-0.529035\pi$
$883$	−5.41348	−0.182178	−0.0910891	+	0.995843i	$0.529035\pi$
$884$	−0.0325513	−0.00109482
$885$	2.61359	0.0878549
$886$	−19.4406	−0.653121
$887$	24.3464	0.817471	0.408736	−	0.912653i	$-0.365970\pi$
$887$	24.3464	0.817471	0.408736	+	0.912653i	$0.365970\pi$
$888$	−9.84056	−0.330227
$889$	−16.8160	−0.563991
$890$	30.2027	1.01240
$891$	−20.5966	−0.690011
$892$	−21.6945	−0.726385
$893$	−16.9810	−0.568248
$894$	13.0020	0.434853
$895$	−44.0631	−1.47287
$896$	2.36491	0.0790060
$897$	−0.0389711	−0.00130121
$898$	30.5372	1.01904
$899$	7.09100	0.236498
$900$	−1.78514	−0.0595048
$901$	−11.0550	−0.368294
$902$	−3.66591	−0.122062
$903$	−10.8190	−0.360033
$904$	−20.1469	−0.670076
$905$	35.6295	1.18437
$906$	−1.07995	−0.0358791
$907$	−36.5304	−1.21297	−0.606486	−	0.795094i	$-0.707422\pi$
$907$	−36.5304	−1.21297	−0.606486	+	0.795094i	$0.707422\pi$
$908$	−10.9881	−0.364652
$909$	9.33251	0.309540
$910$	0.166909	0.00553299
$911$	−42.7219	−1.41544	−0.707720	−	0.706493i	$-0.750276\pi$
$911$	−42.7219	−1.41544	−0.707720	+	0.706493i	$0.750276\pi$
$912$	−2.14666	−0.0710830
$913$	−44.0921	−1.45923
$914$	19.9037	0.658355
$915$	42.7826	1.41435
$916$	11.6536	0.385045
$917$	−2.36491	−0.0780962
$918$	7.06629	0.233222
$919$	41.5850	1.37176	0.685881	−	0.727714i	$-0.259417\pi$
$919$	41.5850	1.37176	0.685881	+	0.727714i	$0.259417\pi$
$920$	2.72563	0.0898614
$921$	48.6787	1.60402
$922$	4.60202	0.151559
$923$	0.199370	0.00656233
$924$	−11.7196	−0.385546
$925$	15.8824	0.522209
$926$	9.67270	0.317865
$927$	−1.81808	−0.0597136
$928$	−1.18615	−0.0389374
$929$	−1.27879	−0.0419559	−0.0209780	−	0.999780i	$-0.506678\pi$
$929$	−1.27879	−0.0419559	−0.0209780	+	0.999780i	$0.506678\pi$
$930$	24.5231	0.804144
$931$	2.00715	0.0657816
$932$	14.5619	0.476990
$933$	−7.11753	−0.233018
$934$	−38.8060	−1.26977
$935$	−11.2821	−0.368965
$936$	−0.0190298	−0.000622010 0
$937$	−23.5815	−0.770375	−0.385188	−	0.922838i	$-0.625863\pi$
$937$	−23.5815	−0.770375	−0.385188	+	0.922838i	$0.625863\pi$
$938$	11.2772	0.368213
$939$	−32.1681	−1.04977
$940$	−32.4496	−1.05839
$941$	8.58786	0.279956	0.139978	−	0.990155i	$-0.455297\pi$
$941$	8.58786	0.279956	0.139978	+	0.990155i	$0.455297\pi$
$942$	10.0078	0.326073
$943$	1.11334	0.0362552
$944$	−0.637130	−0.0207368
$945$	−36.2330	−1.17866
$946$	−10.0089	−0.325417
$947$	−19.1246	−0.621465	−0.310733	−	0.950497i	$-0.600574\pi$
$947$	−19.1246	−0.621465	−0.310733	+	0.950497i	$0.600574\pi$
$948$	10.6582	0.346162
$949$	0.171811	0.00557722
$950$	3.46465	0.112408
$951$	−25.5637	−0.828959
$952$	2.97292	0.0963529
$953$	37.7713	1.22353	0.611766	−	0.791038i	$-0.290459\pi$
$953$	37.7713	1.22353	0.611766	+	0.791038i	$0.290459\pi$
$954$	−6.46284	−0.209242
$955$	−73.4453	−2.37663
$956$	−23.8632	−0.771791
$957$	5.87814	0.190013
$958$	−21.0216	−0.679177
$959$	43.4177	1.40203
$960$	−4.10213	−0.132396
$961$	4.73817	0.152844
$962$	0.169308	0.00545870
$963$	14.5770	0.469738
$964$	−22.7518	−0.732786
$965$	39.6090	1.27506
$966$	3.55924	0.114517
$967$	−17.0636	−0.548728	−0.274364	−	0.961626i	$-0.588467\pi$
$967$	−17.0636	−0.548728	−0.274364	+	0.961626i	$0.588467\pi$
$968$	0.157950	0.00507672
$969$	−2.69856	−0.0866903
$970$	5.46767	0.175556
$971$	−36.6032	−1.17465	−0.587326	−	0.809350i	$-0.699819\pi$
$971$	−36.6032	−1.17465	−0.587326	+	0.809350i	$0.699819\pi$
$972$	7.44920	0.238933
$973$	38.8584	1.24574
$974$	15.4903	0.496342
$975$	−0.0946630	−0.00303164
$976$	−10.4294	−0.333836
$977$	−12.6657	−0.405212	−0.202606	−	0.979260i	$-0.564941\pi$
$977$	−12.6657	−0.405212	−0.202606	+	0.979260i	$0.564941\pi$
$978$	16.0970	0.514727
$979$	36.4867	1.16612
$980$	3.83553	0.122521
$981$	−0.843978	−0.0269462
$982$	6.46100	0.206179
$983$	16.9931	0.541995	0.270997	−	0.962580i	$-0.412647\pi$
$983$	16.9931	0.541995	0.270997	+	0.962580i	$0.412647\pi$
$984$	−1.67559	−0.0534160
$985$	62.5485	1.99296
$986$	−1.49111	−0.0474867
$987$	−42.3740	−1.34878
$988$	0.0369335	0.00117501
$989$	3.03969	0.0966566
$990$	−6.59566	−0.209624
$991$	−8.90226	−0.282790	−0.141395	−	0.989953i	$-0.545159\pi$
$991$	−8.90226	−0.282790	−0.141395	+	0.989953i	$0.545159\pi$
$992$	−5.97814	−0.189806
$993$	−43.7446	−1.38819
$994$	−18.2085	−0.577538
$995$	−34.5617	−1.09568
$996$	−20.1534	−0.638584
$997$	0.603734	0.0191204	0.00956022	−	0.999954i	$-0.496957\pi$
$997$	0.603734	0.0191204	0.00956022	+	0.999954i	$0.496957\pi$
$998$	35.8164	1.13375
$999$	−36.7536	−1.16283

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.i.1.19	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.i.1.19	✓	25	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.50502 q^{3} +1.00000 q^{4} -2.72563 q^{5} -1.50502 q^{6} -2.36491 q^{7} -1.00000 q^{8} -0.734912 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.50502 q^{3} +1.00000 q^{4} -2.72563 q^{5} -1.50502 q^{6} -2.36491 q^{7} -1.00000 q^{8} -0.734912 q^{9} +2.72563 q^{10} +3.29273 q^{11} +1.50502 q^{12} -0.0258940 q^{13} +2.36491 q^{14} -4.10213 q^{15} +1.00000 q^{16} +1.25710 q^{17} +0.734912 q^{18} -1.42633 q^{19} -2.72563 q^{20} -3.55924 q^{21} -3.29273 q^{22} +1.00000 q^{23} -1.50502 q^{24} +2.42906 q^{25} +0.0258940 q^{26} -5.62112 q^{27} -2.36491 q^{28} +1.18615 q^{29} +4.10213 q^{30} +5.97814 q^{31} -1.00000 q^{32} +4.95562 q^{33} -1.25710 q^{34} +6.44587 q^{35} -0.734912 q^{36} +6.53848 q^{37} +1.42633 q^{38} -0.0389711 q^{39} +2.72563 q^{40} +1.11334 q^{41} +3.55924 q^{42} +3.03969 q^{43} +3.29273 q^{44} +2.00310 q^{45} -1.00000 q^{46} +11.9054 q^{47} +1.50502 q^{48} -1.40721 q^{49} -2.42906 q^{50} +1.89196 q^{51} -0.0258940 q^{52} -8.79403 q^{53} +5.62112 q^{54} -8.97475 q^{55} +2.36491 q^{56} -2.14666 q^{57} -1.18615 q^{58} -0.637130 q^{59} -4.10213 q^{60} -10.4294 q^{61} -5.97814 q^{62} +1.73800 q^{63} +1.00000 q^{64} +0.0705775 q^{65} -4.95562 q^{66} +4.76854 q^{67} +1.25710 q^{68} +1.50502 q^{69} -6.44587 q^{70} -7.69944 q^{71} +0.734912 q^{72} -6.63515 q^{73} -6.53848 q^{74} +3.65578 q^{75} -1.42633 q^{76} -7.78700 q^{77} +0.0389711 q^{78} +7.08175 q^{79} -2.72563 q^{80} -6.25517 q^{81} -1.11334 q^{82} -13.3908 q^{83} -3.55924 q^{84} -3.42638 q^{85} -3.03969 q^{86} +1.78519 q^{87} -3.29273 q^{88} +11.0810 q^{89} -2.00310 q^{90} +0.0612370 q^{91} +1.00000 q^{92} +8.99723 q^{93} -11.9054 q^{94} +3.88765 q^{95} -1.50502 q^{96} +2.00602 q^{97} +1.40721 q^{98} -2.41986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} - 3 q^{5} + 4 q^{6} - 11 q^{7} - 25 q^{8} + 19 q^{9} + 3 q^{10} - 12 q^{11} - 4 q^{12} - 6 q^{13} + 11 q^{14} + 25 q^{16} + 8 q^{17} - 19 q^{18} - 23 q^{19} - 3 q^{20} - 16 q^{21} + 12 q^{22} + 25 q^{23} + 4 q^{24} + 4 q^{25} + 6 q^{26} - 13 q^{27} - 11 q^{28} - 7 q^{29} - 7 q^{31} - 25 q^{32} + 3 q^{33} - 8 q^{34} - 18 q^{35} + 19 q^{36} - 7 q^{37} + 23 q^{38} - 2 q^{39} + 3 q^{40} - 10 q^{41} + 16 q^{42} - 26 q^{43} - 12 q^{44} + 20 q^{45} - 25 q^{46} - 2 q^{47} - 4 q^{48} + 2 q^{49} - 4 q^{50} - 28 q^{51} - 6 q^{52} + 47 q^{53} + 13 q^{54} - 38 q^{55} + 11 q^{56} - 4 q^{57} + 7 q^{58} - 19 q^{59} - 26 q^{61} + 7 q^{62} - 15 q^{63} + 25 q^{64} + 13 q^{65} - 3 q^{66} - 34 q^{67} + 8 q^{68} - 4 q^{69} + 18 q^{70} - 10 q^{71} - 19 q^{72} - 22 q^{73} + 7 q^{74} - 8 q^{75} - 23 q^{76} + 28 q^{77} + 2 q^{78} - 21 q^{79} - 3 q^{80} - 27 q^{81} + 10 q^{82} - 16 q^{83} - 16 q^{84} - 42 q^{85} + 26 q^{86} - 17 q^{87} + 12 q^{88} + 27 q^{89} - 20 q^{90} - 26 q^{91} + 25 q^{92} - 27 q^{93} + 2 q^{94} + 4 q^{96} + 4 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 - 3 * q^5 + 4 * q^6 - 11 * q^7 - 25 * q^8 + 19 * q^9 + 3 * q^10 - 12 * q^11 - 4 * q^12 - 6 * q^13 + 11 * q^14 + 25 * q^16 + 8 * q^17 - 19 * q^18 - 23 * q^19 - 3 * q^20 - 16 * q^21 + 12 * q^22 + 25 * q^23 + 4 * q^24 + 4 * q^25 + 6 * q^26 - 13 * q^27 - 11 * q^28 - 7 * q^29 - 7 * q^31 - 25 * q^32 + 3 * q^33 - 8 * q^34 - 18 * q^35 + 19 * q^36 - 7 * q^37 + 23 * q^38 - 2 * q^39 + 3 * q^40 - 10 * q^41 + 16 * q^42 - 26 * q^43 - 12 * q^44 + 20 * q^45 - 25 * q^46 - 2 * q^47 - 4 * q^48 + 2 * q^49 - 4 * q^50 - 28 * q^51 - 6 * q^52 + 47 * q^53 + 13 * q^54 - 38 * q^55 + 11 * q^56 - 4 * q^57 + 7 * q^58 - 19 * q^59 - 26 * q^61 + 7 * q^62 - 15 * q^63 + 25 * q^64 + 13 * q^65 - 3 * q^66 - 34 * q^67 + 8 * q^68 - 4 * q^69 + 18 * q^70 - 10 * q^71 - 19 * q^72 - 22 * q^73 + 7 * q^74 - 8 * q^75 - 23 * q^76 + 28 * q^77 + 2 * q^78 - 21 * q^79 - 3 * q^80 - 27 * q^81 + 10 * q^82 - 16 * q^83 - 16 * q^84 - 42 * q^85 + 26 * q^86 - 17 * q^87 + 12 * q^88 + 27 * q^89 - 20 * q^90 - 26 * q^91 + 25 * q^92 - 27 * q^93 + 2 * q^94 + 4 * q^96 + 4 * q^97 - 2 * q^98 - 2 * q^99

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