LMFDB - Embedded newform 4026.2.a.v.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4026 = 2 \cdot 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4026.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.1477718538$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.11492689.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 13x^{2} + 18x - 8 $ x^5 - 2x^4 - 9x^3 + 13x^2 + 18x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.97479$ of defining polynomial
Character	$\chi$	$=$	4026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97479 q^{5} -1.00000 q^{6} -1.87458 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97479 q^{5} -1.00000 q^{6} -1.87458 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.97479 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.755573 q^{13} -1.87458 q^{14} -3.97479 q^{15} +1.00000 q^{16} -2.84613 q^{17} +1.00000 q^{18} -0.849373 q^{19} +3.97479 q^{20} +1.87458 q^{21} +1.00000 q^{22} +7.44783 q^{23} -1.00000 q^{24} +10.7990 q^{25} +0.755573 q^{26} -1.00000 q^{27} -1.87458 q^{28} -3.72071 q^{29} -3.97479 q^{30} -3.73036 q^{31} +1.00000 q^{32} -1.00000 q^{33} -2.84613 q^{34} -7.45108 q^{35} +1.00000 q^{36} +9.94317 q^{37} -0.849373 q^{38} -0.755573 q^{39} +3.97479 q^{40} +6.29421 q^{41} +1.87458 q^{42} -2.11901 q^{43} +1.00000 q^{44} +3.97479 q^{45} +7.44783 q^{46} -0.984439 q^{47} -1.00000 q^{48} -3.48594 q^{49} +10.7990 q^{50} +2.84613 q^{51} +0.755573 q^{52} +11.9778 q^{53} -1.00000 q^{54} +3.97479 q^{55} -1.87458 q^{56} +0.849373 q^{57} -3.72071 q^{58} +8.16880 q^{59} -3.97479 q^{60} +1.00000 q^{61} -3.73036 q^{62} -1.87458 q^{63} +1.00000 q^{64} +3.00324 q^{65} -1.00000 q^{66} -3.62691 q^{67} -2.84613 q^{68} -7.44783 q^{69} -7.45108 q^{70} -8.61987 q^{71} +1.00000 q^{72} +13.7334 q^{73} +9.94317 q^{74} -10.7990 q^{75} -0.849373 q^{76} -1.87458 q^{77} -0.755573 q^{78} +8.83972 q^{79} +3.97479 q^{80} +1.00000 q^{81} +6.29421 q^{82} -13.4068 q^{83} +1.87458 q^{84} -11.3128 q^{85} -2.11901 q^{86} +3.72071 q^{87} +1.00000 q^{88} +7.02820 q^{89} +3.97479 q^{90} -1.41638 q^{91} +7.44783 q^{92} +3.73036 q^{93} -0.984439 q^{94} -3.37608 q^{95} -1.00000 q^{96} +5.62076 q^{97} -3.48594 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9	$ 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 5 * q^12 - 2 * q^13 - 7 * q^15 + 5 * q^16 + 2 * q^17 + 5 * q^18 + 18 * q^19 + 7 * q^20 + 5 * q^22 - q^23 - 5 * q^24 + 6 * q^25 - 2 * q^26 - 5 * q^27 + 7 * q^29 - 7 * q^30 + 5 * q^32 - 5 * q^33 + 2 * q^34 + 7 * q^35 + 5 * q^36 + 11 * q^37 + 18 * q^38 + 2 * q^39 + 7 * q^40 + 8 * q^41 - 7 * q^43 + 5 * q^44 + 7 * q^45 - q^46 + q^47 - 5 * q^48 + 7 * q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 + 10 * q^53 - 5 * q^54 + 7 * q^55 - 18 * q^57 + 7 * q^58 + 8 * q^59 - 7 * q^60 + 5 * q^61 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 + 2 * q^68 + q^69 + 7 * q^70 + 34 * q^71 + 5 * q^72 + 13 * q^73 + 11 * q^74 - 6 * q^75 + 18 * q^76 + 2 * q^78 + 15 * q^79 + 7 * q^80 + 5 * q^81 + 8 * q^82 - 27 * q^83 - 2 * q^85 - 7 * q^86 - 7 * q^87 + 5 * q^88 + 11 * q^89 + 7 * q^90 + q^91 - q^92 + q^94 + 11 * q^95 - 5 * q^96 + 37 * q^97 + 7 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.97479	1.77758	0.888790	−	0.458315i	$-0.151547\pi$
$5$	3.97479	1.77758	0.888790	+	0.458315i	$0.151547\pi$
$6$	−1.00000	−0.408248
$7$	−1.87458	−0.708526	−0.354263	−	0.935146i	$-0.615268\pi$
$7$	−1.87458	−0.708526	−0.354263	+	0.935146i	$0.615268\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.97479	1.25694
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	0.755573	0.209558	0.104779	−	0.994496i	$-0.466586\pi$
$13$	0.755573	0.209558	0.104779	+	0.994496i	$0.466586\pi$
$14$	−1.87458	−0.501004
$15$	−3.97479	−1.02629
$16$	1.00000	0.250000
$17$	−2.84613	−0.690288	−0.345144	−	0.938550i	$-0.612170\pi$
$17$	−2.84613	−0.690288	−0.345144	+	0.938550i	$0.612170\pi$
$18$	1.00000	0.235702
$19$	−0.849373	−0.194860	−0.0974298	−	0.995242i	$-0.531062\pi$
$19$	−0.849373	−0.194860	−0.0974298	+	0.995242i	$0.531062\pi$
$20$	3.97479	0.888790
$21$	1.87458	0.409068
$22$	1.00000	0.213201
$23$	7.44783	1.55298	0.776490	−	0.630129i	$-0.216998\pi$
$23$	7.44783	1.55298	0.776490	+	0.630129i	$0.216998\pi$
$24$	−1.00000	−0.204124
$25$	10.7990	2.15979
$26$	0.755573	0.148180
$27$	−1.00000	−0.192450
$28$	−1.87458	−0.354263
$29$	−3.72071	−0.690919	−0.345460	−	0.938434i	$-0.612277\pi$
$29$	−3.72071	−0.690919	−0.345460	+	0.938434i	$0.612277\pi$
$30$	−3.97479	−0.725694
$31$	−3.73036	−0.669993	−0.334996	−	0.942219i	$-0.608735\pi$
$31$	−3.73036	−0.669993	−0.334996	+	0.942219i	$0.608735\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−2.84613	−0.488107
$35$	−7.45108	−1.25946
$36$	1.00000	0.166667
$37$	9.94317	1.63465	0.817324	−	0.576179i	$-0.195457\pi$
$37$	9.94317	1.63465	0.817324	+	0.576179i	$0.195457\pi$
$38$	−0.849373	−0.137787
$39$	−0.755573	−0.120989
$40$	3.97479	0.628469
$41$	6.29421	0.982991	0.491495	−	0.870880i	$-0.336450\pi$
$41$	6.29421	0.982991	0.491495	+	0.870880i	$0.336450\pi$
$42$	1.87458	0.289255
$43$	−2.11901	−0.323146	−0.161573	−	0.986861i	$-0.551657\pi$
$43$	−2.11901	−0.323146	−0.161573	+	0.986861i	$0.551657\pi$
$44$	1.00000	0.150756
$45$	3.97479	0.592527
$46$	7.44783	1.09812
$47$	−0.984439	−0.143595	−0.0717976	−	0.997419i	$-0.522874\pi$
$47$	−0.984439	−0.143595	−0.0717976	+	0.997419i	$0.522874\pi$
$48$	−1.00000	−0.144338
$49$	−3.48594	−0.497991
$50$	10.7990	1.52720
$51$	2.84613	0.398538
$52$	0.755573	0.104779
$53$	11.9778	1.64528	0.822638	−	0.568566i	$-0.192502\pi$
$53$	11.9778	1.64528	0.822638	+	0.568566i	$0.192502\pi$
$54$	−1.00000	−0.136083
$55$	3.97479	0.535961
$56$	−1.87458	−0.250502
$57$	0.849373	0.112502
$58$	−3.72071	−0.488554
$59$	8.16880	1.06349	0.531743	−	0.846906i	$-0.321537\pi$
$59$	8.16880	1.06349	0.531743	+	0.846906i	$0.321537\pi$
$60$	−3.97479	−0.513143
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−3.73036	−0.473757
$63$	−1.87458	−0.236175
$64$	1.00000	0.125000
$65$	3.00324	0.372507
$66$	−1.00000	−0.123091
$67$	−3.62691	−0.443098	−0.221549	−	0.975149i	$-0.571111\pi$
$67$	−3.62691	−0.443098	−0.221549	+	0.975149i	$0.571111\pi$
$68$	−2.84613	−0.345144
$69$	−7.44783	−0.896614
$70$	−7.45108	−0.890574
$71$	−8.61987	−1.02299	−0.511495	−	0.859286i	$-0.670908\pi$
$71$	−8.61987	−1.02299	−0.511495	+	0.859286i	$0.670908\pi$
$72$	1.00000	0.117851
$73$	13.7334	1.60737	0.803684	−	0.595056i	$-0.202870\pi$
$73$	13.7334	1.60737	0.803684	+	0.595056i	$0.202870\pi$
$74$	9.94317	1.15587
$75$	−10.7990	−1.24696
$76$	−0.849373	−0.0974298
$77$	−1.87458	−0.213629
$78$	−0.755573	−0.0855518
$79$	8.83972	0.994547	0.497273	−	0.867594i	$-0.334335\pi$
$79$	8.83972	0.994547	0.497273	+	0.867594i	$0.334335\pi$
$80$	3.97479	0.444395
$81$	1.00000	0.111111
$82$	6.29421	0.695079
$83$	−13.4068	−1.47159	−0.735795	−	0.677205i	$-0.763191\pi$
$83$	−13.4068	−1.47159	−0.735795	+	0.677205i	$0.763191\pi$
$84$	1.87458	0.204534
$85$	−11.3128	−1.22704
$86$	−2.11901	−0.228499
$87$	3.72071	0.398902
$88$	1.00000	0.106600
$89$	7.02820	0.744988	0.372494	−	0.928035i	$-0.378503\pi$
$89$	7.02820	0.744988	0.372494	+	0.928035i	$0.378503\pi$
$90$	3.97479	0.418980
$91$	−1.41638	−0.148477
$92$	7.44783	0.776490
$93$	3.73036	0.386821
$94$	−0.984439	−0.101537
$95$	−3.37608	−0.346379
$96$	−1.00000	−0.102062
$97$	5.62076	0.570701	0.285351	−	0.958423i	$-0.407890\pi$
$97$	5.62076	0.570701	0.285351	+	0.958423i	$0.407890\pi$
$98$	−3.48594	−0.352133
$99$	1.00000	0.100504
$100$	10.7990	1.07990
$101$	−10.2720	−1.02210	−0.511051	−	0.859550i	$-0.670744\pi$
$101$	−10.2720	−1.02210	−0.511051	+	0.859550i	$0.670744\pi$
$102$	2.84613	0.281809
$103$	9.51967	0.938001	0.469000	−	0.883198i	$-0.344614\pi$
$103$	9.51967	0.938001	0.469000	+	0.883198i	$0.344614\pi$
$104$	0.755573	0.0740900
$105$	7.45108	0.727151
$106$	11.9778	1.16339
$107$	−15.2908	−1.47822	−0.739109	−	0.673586i	$-0.764753\pi$
$107$	−15.2908	−1.47822	−0.739109	+	0.673586i	$0.764753\pi$
$108$	−1.00000	−0.0962250
$109$	0.555161	0.0531748	0.0265874	−	0.999646i	$-0.491536\pi$
$109$	0.555161	0.0531748	0.0265874	+	0.999646i	$0.491536\pi$
$110$	3.97479	0.378981
$111$	−9.94317	−0.943764
$112$	−1.87458	−0.177132
$113$	−10.9813	−1.03303	−0.516516	−	0.856278i	$-0.672771\pi$
$113$	−10.9813	−1.03303	−0.516516	+	0.856278i	$0.672771\pi$
$114$	0.849373	0.0795511
$115$	29.6036	2.76055
$116$	−3.72071	−0.345460
$117$	0.755573	0.0698527
$118$	8.16880	0.751999
$119$	5.33531	0.489087
$120$	−3.97479	−0.362847
$121$	1.00000	0.0909091
$122$	1.00000	0.0905357
$123$	−6.29421	−0.567530
$124$	−3.73036	−0.334996
$125$	23.0496	2.06162
$126$	−1.87458	−0.167001
$127$	−12.5449	−1.11318	−0.556589	−	0.830788i	$-0.687890\pi$
$127$	−12.5449	−1.11318	−0.556589	+	0.830788i	$0.687890\pi$
$128$	1.00000	0.0883883
$129$	2.11901	0.186569
$130$	3.00324	0.263402
$131$	15.2190	1.32969	0.664844	−	0.746983i	$-0.268498\pi$
$131$	15.2190	1.32969	0.664844	+	0.746983i	$0.268498\pi$
$132$	−1.00000	−0.0870388
$133$	1.59222	0.138063
$134$	−3.62691	−0.313318
$135$	−3.97479	−0.342095
$136$	−2.84613	−0.244054
$137$	5.99035	0.511790	0.255895	−	0.966705i	$-0.417630\pi$
$137$	5.99035	0.511790	0.255895	+	0.966705i	$0.417630\pi$
$138$	−7.44783	−0.634002
$139$	9.59205	0.813587	0.406794	−	0.913520i	$-0.366647\pi$
$139$	9.59205	0.813587	0.406794	+	0.913520i	$0.366647\pi$
$140$	−7.45108	−0.629731
$141$	0.984439	0.0829047
$142$	−8.61987	−0.723364
$143$	0.755573	0.0631842
$144$	1.00000	0.0833333
$145$	−14.7891	−1.22816
$146$	13.7334	1.13658
$147$	3.48594	0.287515
$148$	9.94317	0.817324
$149$	0.247671	0.0202900	0.0101450	−	0.999949i	$-0.496771\pi$
$149$	0.247671	0.0202900	0.0101450	+	0.999949i	$0.496771\pi$
$150$	−10.7990	−0.881731
$151$	13.6923	1.11426	0.557130	−	0.830425i	$-0.311902\pi$
$151$	13.6923	1.11426	0.557130	+	0.830425i	$0.311902\pi$
$152$	−0.849373	−0.0688933
$153$	−2.84613	−0.230096
$154$	−1.87458	−0.151058
$155$	−14.8274	−1.19097
$156$	−0.755573	−0.0604943
$157$	0.0284539	0.00227087	0.00113543	−	0.999999i	$-0.499639\pi$
$157$	0.0284539	0.00227087	0.00113543	+	0.999999i	$0.499639\pi$
$158$	8.83972	0.703251
$159$	−11.9778	−0.949900
$160$	3.97479	0.314235
$161$	−13.9616	−1.10033
$162$	1.00000	0.0785674
$163$	15.6768	1.22790	0.613950	−	0.789345i	$-0.289580\pi$
$163$	15.6768	1.22790	0.613950	+	0.789345i	$0.289580\pi$
$164$	6.29421	0.491495
$165$	−3.97479	−0.309437
$166$	−13.4068	−1.04057
$167$	−17.9274	−1.38726	−0.693630	−	0.720331i	$-0.743990\pi$
$167$	−17.9274	−1.38726	−0.693630	+	0.720331i	$0.743990\pi$
$168$	1.87458	0.144627
$169$	−12.4291	−0.956085
$170$	−11.3128	−0.867650
$171$	−0.849373	−0.0649532
$172$	−2.11901	−0.161573
$173$	5.46988	0.415867	0.207934	−	0.978143i	$-0.433326\pi$
$173$	5.46988	0.415867	0.207934	+	0.978143i	$0.433326\pi$
$174$	3.72071	0.282067
$175$	−20.2435	−1.53027
$176$	1.00000	0.0753778
$177$	−8.16880	−0.614004
$178$	7.02820	0.526786
$179$	−20.9739	−1.56766	−0.783832	−	0.620973i	$-0.786737\pi$
$179$	−20.9739	−1.56766	−0.783832	+	0.620973i	$0.786737\pi$
$180$	3.97479	0.296263
$181$	−18.1906	−1.35210	−0.676048	−	0.736857i	$-0.736309\pi$
$181$	−18.1906	−1.35210	−0.676048	+	0.736857i	$0.736309\pi$
$182$	−1.41638	−0.104989
$183$	−1.00000	−0.0739221
$184$	7.44783	0.549062
$185$	39.5220	2.90572
$186$	3.73036	0.273523
$187$	−2.84613	−0.208130
$188$	−0.984439	−0.0717976
$189$	1.87458	0.136356
$190$	−3.37608	−0.244927
$191$	−13.4547	−0.973548	−0.486774	−	0.873528i	$-0.661827\pi$
$191$	−13.4547	−0.973548	−0.486774	+	0.873528i	$0.661827\pi$
$192$	−1.00000	−0.0721688
$193$	−20.3564	−1.46529	−0.732643	−	0.680613i	$-0.761713\pi$
$193$	−20.3564	−1.46529	−0.732643	+	0.680613i	$0.761713\pi$
$194$	5.62076	0.403547
$195$	−3.00324	−0.215067
$196$	−3.48594	−0.248995
$197$	−15.4660	−1.10191	−0.550954	−	0.834536i	$-0.685736\pi$
$197$	−15.4660	−1.10191	−0.550954	+	0.834536i	$0.685736\pi$
$198$	1.00000	0.0710669
$199$	5.09380	0.361090	0.180545	−	0.983567i	$-0.442214\pi$
$199$	5.09380	0.361090	0.180545	+	0.983567i	$0.442214\pi$
$200$	10.7990	0.763601
$201$	3.62691	0.255823
$202$	−10.2720	−0.722735
$203$	6.97479	0.489534
$204$	2.84613	0.199269
$205$	25.0182	1.74734
$206$	9.51967	0.663267
$207$	7.44783	0.517660
$208$	0.755573	0.0523896
$209$	−0.849373	−0.0587524
$210$	7.45108	0.514173
$211$	−12.6487	−0.870773	−0.435387	−	0.900244i	$-0.643388\pi$
$211$	−12.6487	−0.870773	−0.435387	+	0.900244i	$0.643388\pi$
$212$	11.9778	0.822638
$213$	8.61987	0.590624
$214$	−15.2908	−1.04526
$215$	−8.42262	−0.574418
$216$	−1.00000	−0.0680414
$217$	6.99288	0.474707
$218$	0.555161	0.0376003
$219$	−13.7334	−0.928014
$220$	3.97479	0.267980
$221$	−2.15046	−0.144656
$222$	−9.94317	−0.667342
$223$	23.1180	1.54809	0.774046	−	0.633129i	$-0.218230\pi$
$223$	23.1180	1.54809	0.774046	+	0.633129i	$0.218230\pi$
$224$	−1.87458	−0.125251
$225$	10.7990	0.719930
$226$	−10.9813	−0.730464
$227$	14.8776	0.987460	0.493730	−	0.869615i	$-0.335633\pi$
$227$	14.8776	0.987460	0.493730	+	0.869615i	$0.335633\pi$
$228$	0.849373	0.0562511
$229$	24.1097	1.59321	0.796606	−	0.604498i	$-0.206626\pi$
$229$	24.1097	1.59321	0.796606	+	0.604498i	$0.206626\pi$
$230$	29.6036	1.95200
$231$	1.87458	0.123339
$232$	−3.72071	−0.244277
$233$	14.2633	0.934420	0.467210	−	0.884146i	$-0.345259\pi$
$233$	14.2633	0.934420	0.467210	+	0.884146i	$0.345259\pi$
$234$	0.755573	0.0493933
$235$	−3.91294	−0.255252
$236$	8.16880	0.531743
$237$	−8.83972	−0.574202
$238$	5.33531	0.345837
$239$	−9.20316	−0.595303	−0.297652	−	0.954675i	$-0.596203\pi$
$239$	−9.20316	−0.595303	−0.297652	+	0.954675i	$0.596203\pi$
$240$	−3.97479	−0.256572
$241$	9.24093	0.595261	0.297630	−	0.954681i	$-0.403804\pi$
$241$	9.24093	0.595261	0.297630	+	0.954681i	$0.403804\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−13.8559	−0.885218
$246$	−6.29421	−0.401304
$247$	−0.641764	−0.0408344
$248$	−3.73036	−0.236878
$249$	13.4068	0.849623
$250$	23.0496	1.45779
$251$	10.8677	0.685964	0.342982	−	0.939342i	$-0.388563\pi$
$251$	10.8677	0.685964	0.342982	+	0.939342i	$0.388563\pi$
$252$	−1.87458	−0.118088
$253$	7.44783	0.468241
$254$	−12.5449	−0.787136
$255$	11.3128	0.708433
$256$	1.00000	0.0625000
$257$	21.5068	1.34156	0.670778	−	0.741658i	$-0.265960\pi$
$257$	21.5068	1.34156	0.670778	+	0.741658i	$0.265960\pi$
$258$	2.11901	0.131924
$259$	−18.6393	−1.15819
$260$	3.00324	0.186253
$261$	−3.72071	−0.230306
$262$	15.2190	0.940231
$263$	−4.38872	−0.270620	−0.135310	−	0.990803i	$-0.543203\pi$
$263$	−4.38872	−0.270620	−0.135310	+	0.990803i	$0.543203\pi$
$264$	−1.00000	−0.0615457
$265$	47.6092	2.92461
$266$	1.59222	0.0976254
$267$	−7.02820	−0.430119
$268$	−3.62691	−0.221549
$269$	10.2373	0.624179	0.312090	−	0.950053i	$-0.398971\pi$
$269$	10.2373	0.624179	0.312090	+	0.950053i	$0.398971\pi$
$270$	−3.97479	−0.241898
$271$	20.0997	1.22097	0.610483	−	0.792029i	$-0.290975\pi$
$271$	20.0997	1.22097	0.610483	+	0.792029i	$0.290975\pi$
$272$	−2.84613	−0.172572
$273$	1.41638	0.0857235
$274$	5.99035	0.361890
$275$	10.7990	0.651201
$276$	−7.44783	−0.448307
$277$	−19.7923	−1.18920	−0.594602	−	0.804020i	$-0.702690\pi$
$277$	−19.7923	−1.18920	−0.594602	+	0.804020i	$0.702690\pi$
$278$	9.59205	0.575293
$279$	−3.73036	−0.223331
$280$	−7.45108	−0.445287
$281$	14.8776	0.887522	0.443761	−	0.896145i	$-0.353644\pi$
$281$	14.8776	0.887522	0.443761	+	0.896145i	$0.353644\pi$
$282$	0.984439	0.0586225
$283$	9.36280	0.556561	0.278280	−	0.960500i	$-0.410236\pi$
$283$	9.36280	0.556561	0.278280	+	0.960500i	$0.410236\pi$
$284$	−8.61987	−0.511495
$285$	3.37608	0.199982
$286$	0.755573	0.0446780
$287$	−11.7990	−0.696475
$288$	1.00000	0.0589256
$289$	−8.89954	−0.523503
$290$	−14.7891	−0.868443
$291$	−5.62076	−0.329495
$292$	13.7334	0.803684
$293$	−13.9108	−0.812680	−0.406340	−	0.913722i	$-0.633195\pi$
$293$	−13.9108	−0.812680	−0.406340	+	0.913722i	$0.633195\pi$
$294$	3.48594	0.203304
$295$	32.4692	1.89043
$296$	9.94317	0.577935
$297$	−1.00000	−0.0580259
$298$	0.247671	0.0143472
$299$	5.62738	0.325440
$300$	−10.7990	−0.623478
$301$	3.97226	0.228957
$302$	13.6923	0.787901
$303$	10.2720	0.590111
$304$	−0.849373	−0.0487149
$305$	3.97479	0.227596
$306$	−2.84613	−0.162702
$307$	−13.5320	−0.772311	−0.386156	−	0.922434i	$-0.626197\pi$
$307$	−13.5320	−0.772311	−0.386156	+	0.922434i	$0.626197\pi$
$308$	−1.87458	−0.106814
$309$	−9.51967	−0.541555
$310$	−14.8274	−0.842140
$311$	−27.5007	−1.55942	−0.779711	−	0.626140i	$-0.784634\pi$
$311$	−27.5007	−1.55942	−0.779711	+	0.626140i	$0.784634\pi$
$312$	−0.755573	−0.0427759
$313$	−20.2339	−1.14369	−0.571844	−	0.820363i	$-0.693772\pi$
$313$	−20.2339	−1.14369	−0.571844	+	0.820363i	$0.693772\pi$
$314$	0.0284539	0.00160575
$315$	−7.45108	−0.419821
$316$	8.83972	0.497273
$317$	18.8109	1.05652	0.528262	−	0.849081i	$-0.322844\pi$
$317$	18.8109	1.05652	0.528262	+	0.849081i	$0.322844\pi$
$318$	−11.9778	−0.671681
$319$	−3.72071	−0.208320
$320$	3.97479	0.222197
$321$	15.2908	0.853449
$322$	−13.9616	−0.778049
$323$	2.41743	0.134509
$324$	1.00000	0.0555556
$325$	8.15940	0.452602
$326$	15.6768	0.868257
$327$	−0.555161	−0.0307005
$328$	6.29421	0.347540
$329$	1.84541	0.101741
$330$	−3.97479	−0.218805
$331$	3.10873	0.170871	0.0854355	−	0.996344i	$-0.472772\pi$
$331$	3.10873	0.170871	0.0854355	+	0.996344i	$0.472772\pi$
$332$	−13.4068	−0.735795
$333$	9.94317	0.544883
$334$	−17.9274	−0.980942
$335$	−14.4162	−0.787642
$336$	1.87458	0.102267
$337$	−21.7957	−1.18729	−0.593644	−	0.804728i	$-0.702311\pi$
$337$	−21.7957	−1.18729	−0.593644	+	0.804728i	$0.702311\pi$
$338$	−12.4291	−0.676054
$339$	10.9813	0.596421
$340$	−11.3128	−0.613521
$341$	−3.73036	−0.202010
$342$	−0.849373	−0.0459289
$343$	19.6568	1.06137
$344$	−2.11901	−0.114249
$345$	−29.6036	−1.59380
$346$	5.46988	0.294063
$347$	26.1684	1.40479	0.702396	−	0.711786i	$-0.252114\pi$
$347$	26.1684	1.40479	0.702396	+	0.711786i	$0.252114\pi$
$348$	3.72071	0.199451
$349$	5.28773	0.283045	0.141523	−	0.989935i	$-0.454800\pi$
$349$	5.28773	0.283045	0.141523	+	0.989935i	$0.454800\pi$
$350$	−20.2435	−1.08206
$351$	−0.755573	−0.0403295
$352$	1.00000	0.0533002
$353$	−5.19013	−0.276243	−0.138121	−	0.990415i	$-0.544106\pi$
$353$	−5.19013	−0.276243	−0.138121	+	0.990415i	$0.544106\pi$
$354$	−8.16880	−0.434167
$355$	−34.2622	−1.81845
$356$	7.02820	0.372494
$357$	−5.33531	−0.282374
$358$	−20.9739	−1.10851
$359$	18.3910	0.970640	0.485320	−	0.874337i	$-0.338703\pi$
$359$	18.3910	0.970640	0.485320	+	0.874337i	$0.338703\pi$
$360$	3.97479	0.209490
$361$	−18.2786	−0.962030
$362$	−18.1906	−0.956076
$363$	−1.00000	−0.0524864
$364$	−1.41638	−0.0742387
$365$	54.5872	2.85722
$366$	−1.00000	−0.0522708
$367$	−26.8737	−1.40280	−0.701398	−	0.712770i	$-0.747440\pi$
$367$	−26.8737	−1.40280	−0.701398	+	0.712770i	$0.747440\pi$
$368$	7.44783	0.388245
$369$	6.29421	0.327664
$370$	39.5220	2.05465
$371$	−22.4534	−1.16572
$372$	3.73036	0.193410
$373$	21.3591	1.10593	0.552965	−	0.833204i	$-0.313496\pi$
$373$	21.3591	1.10593	0.552965	+	0.833204i	$0.313496\pi$
$374$	−2.84613	−0.147170
$375$	−23.0496	−1.19028
$376$	−0.984439	−0.0507685
$377$	−2.81127	−0.144788
$378$	1.87458	0.0964182
$379$	−30.3241	−1.55764	−0.778821	−	0.627246i	$-0.784182\pi$
$379$	−30.3241	−1.55764	−0.778821	+	0.627246i	$0.784182\pi$
$380$	−3.37608	−0.173189
$381$	12.5449	0.642694
$382$	−13.4547	−0.688403
$383$	−26.5848	−1.35842	−0.679209	−	0.733945i	$-0.737677\pi$
$383$	−26.5848	−1.35842	−0.679209	+	0.733945i	$0.737677\pi$
$384$	−1.00000	−0.0510310
$385$	−7.45108	−0.379742
$386$	−20.3564	−1.03611
$387$	−2.11901	−0.107715
$388$	5.62076	0.285351
$389$	−8.25611	−0.418601	−0.209301	−	0.977851i	$-0.567119\pi$
$389$	−8.25611	−0.418601	−0.209301	+	0.977851i	$0.567119\pi$
$390$	−3.00324	−0.152075
$391$	−21.1975	−1.07200
$392$	−3.48594	−0.176066
$393$	−15.2190	−0.767695
$394$	−15.4660	−0.779166
$395$	35.1360	1.76789
$396$	1.00000	0.0502519
$397$	−30.9866	−1.55517	−0.777587	−	0.628775i	$-0.783557\pi$
$397$	−30.9866	−1.55517	−0.777587	+	0.628775i	$0.783557\pi$
$398$	5.09380	0.255329
$399$	−1.59222	−0.0797108
$400$	10.7990	0.539948
$401$	25.3908	1.26796	0.633979	−	0.773350i	$-0.281421\pi$
$401$	25.3908	1.26796	0.633979	+	0.773350i	$0.281421\pi$
$402$	3.62691	0.180894
$403$	−2.81856	−0.140403
$404$	−10.2720	−0.511051
$405$	3.97479	0.197509
$406$	6.97479	0.346153
$407$	9.94317	0.492865
$408$	2.84613	0.140904
$409$	25.3213	1.25206	0.626028	−	0.779800i	$-0.284679\pi$
$409$	25.3213	1.25206	0.626028	+	0.779800i	$0.284679\pi$
$410$	25.0182	1.23556
$411$	−5.99035	−0.295482
$412$	9.51967	0.469000
$413$	−15.3131	−0.753508
$414$	7.44783	0.366041
$415$	−53.2893	−2.61587
$416$	0.755573	0.0370450
$417$	−9.59205	−0.469725
$418$	−0.849373	−0.0415442
$419$	−11.0466	−0.539663	−0.269831	−	0.962908i	$-0.586968\pi$
$419$	−11.0466	−0.539663	−0.269831	+	0.962908i	$0.586968\pi$
$420$	7.45108	0.363575
$421$	32.4851	1.58322	0.791612	−	0.611024i	$-0.209242\pi$
$421$	32.4851	1.58322	0.791612	+	0.611024i	$0.209242\pi$
$422$	−12.6487	−0.615730
$423$	−0.984439	−0.0478650
$424$	11.9778	0.581693
$425$	−30.7352	−1.49088
$426$	8.61987	0.417634
$427$	−1.87458	−0.0907175
$428$	−15.2908	−0.739109
$429$	−0.755573	−0.0364794
$430$	−8.42262	−0.406175
$431$	−22.8291	−1.09964	−0.549820	−	0.835283i	$-0.685304\pi$
$431$	−22.8291	−1.09964	−0.549820	+	0.835283i	$0.685304\pi$
$432$	−1.00000	−0.0481125
$433$	−39.6328	−1.90463	−0.952316	−	0.305112i	$-0.901306\pi$
$433$	−39.6328	−1.90463	−0.952316	+	0.305112i	$0.901306\pi$
$434$	6.99288	0.335669
$435$	14.7891	0.709081
$436$	0.555161	0.0265874
$437$	−6.32599	−0.302613
$438$	−13.7334	−0.656205
$439$	−18.3616	−0.876351	−0.438175	−	0.898889i	$-0.644375\pi$
$439$	−18.3616	−0.876351	−0.438175	+	0.898889i	$0.644375\pi$
$440$	3.97479	0.189491
$441$	−3.48594	−0.165997
$442$	−2.15046	−0.102287
$443$	12.6071	0.598980	0.299490	−	0.954100i	$-0.403184\pi$
$443$	12.6071	0.598980	0.299490	+	0.954100i	$0.403184\pi$
$444$	−9.94317	−0.471882
$445$	27.9356	1.32428
$446$	23.1180	1.09467
$447$	−0.247671	−0.0117144
$448$	−1.87458	−0.0885658
$449$	26.9183	1.27035	0.635176	−	0.772367i	$-0.280927\pi$
$449$	26.9183	1.27035	0.635176	+	0.772367i	$0.280927\pi$
$450$	10.7990	0.509068
$451$	6.29421	0.296383
$452$	−10.9813	−0.516516
$453$	−13.6923	−0.643318
$454$	14.8776	0.698239
$455$	−5.62983	−0.263931
$456$	0.849373	0.0397756
$457$	−25.3503	−1.18584	−0.592918	−	0.805263i	$-0.702024\pi$
$457$	−25.3503	−1.18584	−0.592918	+	0.805263i	$0.702024\pi$
$458$	24.1097	1.12657
$459$	2.84613	0.132846
$460$	29.6036	1.38027
$461$	19.1063	0.889868	0.444934	−	0.895563i	$-0.353227\pi$
$461$	19.1063	0.889868	0.444934	+	0.895563i	$0.353227\pi$
$462$	1.87458	0.0872135
$463$	−27.2869	−1.26813	−0.634065	−	0.773279i	$-0.718615\pi$
$463$	−27.2869	−1.26813	−0.634065	+	0.773279i	$0.718615\pi$
$464$	−3.72071	−0.172730
$465$	14.8274	0.687605
$466$	14.2633	0.660735
$467$	24.4241	1.13021	0.565106	−	0.825018i	$-0.308835\pi$
$467$	24.4241	1.13021	0.565106	+	0.825018i	$0.308835\pi$
$468$	0.755573	0.0349264
$469$	6.79895	0.313946
$470$	−3.91294	−0.180490
$471$	−0.0284539	−0.00131109
$472$	8.16880	0.375999
$473$	−2.11901	−0.0974322
$474$	−8.83972	−0.406022
$475$	−9.17234	−0.420856
$476$	5.33531	0.244543
$477$	11.9778	0.548425
$478$	−9.20316	−0.420943
$479$	−20.7116	−0.946339	−0.473169	−	0.880971i	$-0.656890\pi$
$479$	−20.7116	−0.946339	−0.473169	+	0.880971i	$0.656890\pi$
$480$	−3.97479	−0.181423
$481$	7.51279	0.342554
$482$	9.24093	0.420913
$483$	13.9616	0.635274
$484$	1.00000	0.0454545
$485$	22.3413	1.01447
$486$	−1.00000	−0.0453609
$487$	−8.80379	−0.398938	−0.199469	−	0.979904i	$-0.563922\pi$
$487$	−8.80379	−0.398938	−0.199469	+	0.979904i	$0.563922\pi$
$488$	1.00000	0.0452679
$489$	−15.6768	−0.708929
$490$	−13.8559	−0.625944
$491$	−19.9650	−0.901007	−0.450503	−	0.892775i	$-0.648755\pi$
$491$	−19.9650	−0.901007	−0.450503	+	0.892775i	$0.648755\pi$
$492$	−6.29421	−0.283765
$493$	10.5896	0.476933
$494$	−0.641764	−0.0288743
$495$	3.97479	0.178654
$496$	−3.73036	−0.167498
$497$	16.1587	0.724816
$498$	13.4068	0.600774
$499$	2.90540	0.130063	0.0650317	−	0.997883i	$-0.479285\pi$
$499$	2.90540	0.130063	0.0650317	+	0.997883i	$0.479285\pi$
$500$	23.0496	1.03081
$501$	17.9274	0.800936
$502$	10.8677	0.485050
$503$	23.9266	1.06683	0.533416	−	0.845853i	$-0.320908\pi$
$503$	23.9266	1.06683	0.533416	+	0.845853i	$0.320908\pi$
$504$	−1.87458	−0.0835006
$505$	−40.8290	−1.81687
$506$	7.44783	0.331097
$507$	12.4291	0.551996
$508$	−12.5449	−0.556589
$509$	15.8589	0.702931	0.351466	−	0.936201i	$-0.385683\pi$
$509$	15.8589	0.702931	0.351466	+	0.936201i	$0.385683\pi$
$510$	11.3128	0.500938
$511$	−25.7443	−1.13886
$512$	1.00000	0.0441942
$513$	0.849373	0.0375008
$514$	21.5068	0.948623
$515$	37.8387	1.66737
$516$	2.11901	0.0932843
$517$	−0.984439	−0.0432956
$518$	−18.6393	−0.818964
$519$	−5.46988	−0.240101
$520$	3.00324	0.131701
$521$	2.67068	0.117005	0.0585023	−	0.998287i	$-0.481368\pi$
$521$	2.67068	0.117005	0.0585023	+	0.998287i	$0.481368\pi$
$522$	−3.72071	−0.162851
$523$	−11.9340	−0.521838	−0.260919	−	0.965361i	$-0.584026\pi$
$523$	−11.9340	−0.521838	−0.260919	+	0.965361i	$0.584026\pi$
$524$	15.2190	0.664844
$525$	20.2435	0.883501
$526$	−4.38872	−0.191357
$527$	10.6171	0.462488
$528$	−1.00000	−0.0435194
$529$	32.4702	1.41175
$530$	47.6092	2.06801
$531$	8.16880	0.354496
$532$	1.59222	0.0690316
$533$	4.75574	0.205994
$534$	−7.02820	−0.304140
$535$	−60.7777	−2.62765
$536$	−3.62691	−0.156659
$537$	20.9739	0.905091
$538$	10.2373	0.441362
$539$	−3.48594	−0.150150
$540$	−3.97479	−0.171048
$541$	−20.8702	−0.897282	−0.448641	−	0.893712i	$-0.648092\pi$
$541$	−20.8702	−0.897282	−0.448641	+	0.893712i	$0.648092\pi$
$542$	20.0997	0.863354
$543$	18.1906	0.780633
$544$	−2.84613	−0.122027
$545$	2.20665	0.0945225
$546$	1.41638	0.0606157
$547$	15.1689	0.648574	0.324287	−	0.945959i	$-0.394876\pi$
$547$	15.1689	0.648574	0.324287	+	0.945959i	$0.394876\pi$
$548$	5.99035	0.255895
$549$	1.00000	0.0426790
$550$	10.7990	0.460469
$551$	3.16028	0.134632
$552$	−7.44783	−0.317001
$553$	−16.5708	−0.704662
$554$	−19.7923	−0.840894
$555$	−39.5220	−1.67762
$556$	9.59205	0.406794
$557$	−0.425616	−0.0180339	−0.00901697	−	0.999959i	$-0.502870\pi$
$557$	−0.425616	−0.0180339	−0.00901697	+	0.999959i	$0.502870\pi$
$558$	−3.73036	−0.157919
$559$	−1.60107	−0.0677179
$560$	−7.45108	−0.314865
$561$	2.84613	0.120164
$562$	14.8776	0.627573
$563$	−36.3968	−1.53394	−0.766972	−	0.641681i	$-0.778237\pi$
$563$	−36.3968	−1.53394	−0.766972	+	0.641681i	$0.778237\pi$
$564$	0.984439	0.0414523
$565$	−43.6483	−1.83630
$566$	9.36280	0.393548
$567$	−1.87458	−0.0787251
$568$	−8.61987	−0.361682
$569$	31.6905	1.32853	0.664267	−	0.747495i	$-0.268744\pi$
$569$	31.6905	1.32853	0.664267	+	0.747495i	$0.268744\pi$
$570$	3.37608	0.141408
$571$	12.4442	0.520773	0.260386	−	0.965505i	$-0.416150\pi$
$571$	12.4442	0.520773	0.260386	+	0.965505i	$0.416150\pi$
$572$	0.755573	0.0315921
$573$	13.4547	0.562078
$574$	−11.7990	−0.492482
$575$	80.4288	3.35411
$576$	1.00000	0.0416667
$577$	22.5845	0.940203	0.470102	−	0.882612i	$-0.344217\pi$
$577$	22.5845	0.940203	0.470102	+	0.882612i	$0.344217\pi$
$578$	−8.89954	−0.370172
$579$	20.3564	0.845983
$580$	−14.7891	−0.614082
$581$	25.1322	1.04266
$582$	−5.62076	−0.232988
$583$	11.9778	0.496069
$584$	13.7334	0.568290
$585$	3.00324	0.124169
$586$	−13.9108	−0.574652
$587$	−6.36921	−0.262885	−0.131443	−	0.991324i	$-0.541961\pi$
$587$	−6.36921	−0.262885	−0.131443	+	0.991324i	$0.541961\pi$
$588$	3.48594	0.143758
$589$	3.16847	0.130555
$590$	32.4692	1.33674
$591$	15.4660	0.636186
$592$	9.94317	0.408662
$593$	−11.5985	−0.476295	−0.238147	−	0.971229i	$-0.576540\pi$
$593$	−11.5985	−0.476295	−0.238147	+	0.971229i	$0.576540\pi$
$594$	−1.00000	−0.0410305
$595$	21.2067	0.869391
$596$	0.247671	0.0101450
$597$	−5.09380	−0.208475
$598$	5.62738	0.230121
$599$	−16.6860	−0.681772	−0.340886	−	0.940105i	$-0.610727\pi$
$599$	−16.6860	−0.681772	−0.340886	+	0.940105i	$0.610727\pi$
$600$	−10.7990	−0.440865
$601$	−40.9251	−1.66937	−0.834685	−	0.550727i	$-0.814351\pi$
$601$	−40.9251	−1.66937	−0.834685	+	0.550727i	$0.814351\pi$
$602$	3.97226	0.161897
$603$	−3.62691	−0.147699
$604$	13.6923	0.557130
$605$	3.97479	0.161598
$606$	10.2720	0.417271
$607$	−23.0838	−0.936944	−0.468472	−	0.883478i	$-0.655195\pi$
$607$	−23.0838	−0.936944	−0.468472	+	0.883478i	$0.655195\pi$
$608$	−0.849373	−0.0344466
$609$	−6.97479	−0.282633
$610$	3.97479	0.160935
$611$	−0.743815	−0.0300915
$612$	−2.84613	−0.115048
$613$	−38.8392	−1.56870	−0.784350	−	0.620319i	$-0.787003\pi$
$613$	−38.8392	−1.56870	−0.784350	+	0.620319i	$0.787003\pi$
$614$	−13.5320	−0.546106
$615$	−25.0182	−1.00883
$616$	−1.87458	−0.0755291
$617$	−2.97825	−0.119900	−0.0599499	−	0.998201i	$-0.519094\pi$
$617$	−2.97825	−0.119900	−0.0599499	+	0.998201i	$0.519094\pi$
$618$	−9.51967	−0.382937
$619$	−16.4408	−0.660811	−0.330406	−	0.943839i	$-0.607186\pi$
$619$	−16.4408	−0.660811	−0.330406	+	0.943839i	$0.607186\pi$
$620$	−14.8274	−0.595483
$621$	−7.44783	−0.298871
$622$	−27.5007	−1.10268
$623$	−13.1750	−0.527844
$624$	−0.755573	−0.0302471
$625$	37.6226	1.50490
$626$	−20.2339	−0.808709
$627$	0.849373	0.0339207
$628$	0.0284539	0.00113543
$629$	−28.2996	−1.12838
$630$	−7.45108	−0.296858
$631$	−31.0372	−1.23557	−0.617786	−	0.786346i	$-0.711970\pi$
$631$	−31.0372	−1.23557	−0.617786	+	0.786346i	$0.711970\pi$
$632$	8.83972	0.351625
$633$	12.6487	0.502741
$634$	18.8109	0.747076
$635$	−49.8632	−1.97876
$636$	−11.9778	−0.474950
$637$	−2.63388	−0.104358
$638$	−3.72071	−0.147304
$639$	−8.61987	−0.340997
$640$	3.97479	0.157117
$641$	−24.6847	−0.974988	−0.487494	−	0.873126i	$-0.662089\pi$
$641$	−24.6847	−0.974988	−0.487494	+	0.873126i	$0.662089\pi$
$642$	15.2908	0.603480
$643$	−47.9077	−1.88929	−0.944647	−	0.328088i	$-0.893596\pi$
$643$	−47.9077	−1.88929	−0.944647	+	0.328088i	$0.893596\pi$
$644$	−13.9616	−0.550164
$645$	8.42262	0.331640
$646$	2.41743	0.0951124
$647$	−12.4691	−0.490210	−0.245105	−	0.969497i	$-0.578822\pi$
$647$	−12.4691	−0.490210	−0.245105	+	0.969497i	$0.578822\pi$
$648$	1.00000	0.0392837
$649$	8.16880	0.320653
$650$	8.15940	0.320038
$651$	−6.99288	−0.274072
$652$	15.6768	0.613950
$653$	−10.9997	−0.430450	−0.215225	−	0.976564i	$-0.569049\pi$
$653$	−10.9997	−0.430450	−0.215225	+	0.976564i	$0.569049\pi$
$654$	−0.555161	−0.0217085
$655$	60.4922	2.36363
$656$	6.29421	0.245748
$657$	13.7334	0.535789
$658$	1.84541	0.0719417
$659$	−24.8832	−0.969311	−0.484656	−	0.874705i	$-0.661055\pi$
$659$	−24.8832	−0.969311	−0.484656	+	0.874705i	$0.661055\pi$
$660$	−3.97479	−0.154718
$661$	18.2700	0.710622	0.355311	−	0.934748i	$-0.384375\pi$
$661$	18.2700	0.710622	0.355311	+	0.934748i	$0.384375\pi$
$662$	3.10873	0.120824
$663$	2.15046	0.0835169
$664$	−13.4068	−0.520285
$665$	6.32875	0.245418
$666$	9.94317	0.385290
$667$	−27.7113	−1.07298
$668$	−17.9274	−0.693630
$669$	−23.1180	−0.893792
$670$	−14.4162	−0.556947
$671$	1.00000	0.0386046
$672$	1.87458	0.0723136
$673$	−11.1320	−0.429106	−0.214553	−	0.976712i	$-0.568830\pi$
$673$	−11.1320	−0.429106	−0.214553	+	0.976712i	$0.568830\pi$
$674$	−21.7957	−0.839539
$675$	−10.7990	−0.415652
$676$	−12.4291	−0.478043
$677$	−42.1931	−1.62161	−0.810806	−	0.585316i	$-0.800971\pi$
$677$	−42.1931	−1.62161	−0.810806	+	0.585316i	$0.800971\pi$
$678$	10.9813	0.421733
$679$	−10.5366	−0.404357
$680$	−11.3128	−0.433825
$681$	−14.8776	−0.570110
$682$	−3.73036	−0.142843
$683$	−31.1425	−1.19163	−0.595816	−	0.803121i	$-0.703171\pi$
$683$	−31.1425	−1.19163	−0.595816	+	0.803121i	$0.703171\pi$
$684$	−0.849373	−0.0324766
$685$	23.8104	0.909748
$686$	19.6568	0.750499
$687$	−24.1097	−0.919842
$688$	−2.11901	−0.0807865
$689$	9.05009	0.344781
$690$	−29.6036	−1.12699
$691$	26.3940	1.00408	0.502038	−	0.864846i	$-0.332584\pi$
$691$	26.3940	1.00408	0.502038	+	0.864846i	$0.332584\pi$
$692$	5.46988	0.207934
$693$	−1.87458	−0.0712096
$694$	26.1684	0.993338
$695$	38.1264	1.44622
$696$	3.72071	0.141033
$697$	−17.9141	−0.678547
$698$	5.28773	0.200143
$699$	−14.2633	−0.539488
$700$	−20.2435	−0.765134
$701$	−8.21897	−0.310426	−0.155213	−	0.987881i	$-0.549606\pi$
$701$	−8.21897	−0.310426	−0.155213	+	0.987881i	$0.549606\pi$
$702$	−0.755573	−0.0285173
$703$	−8.44547	−0.318527
$704$	1.00000	0.0376889
$705$	3.91294	0.147370
$706$	−5.19013	−0.195333
$707$	19.2557	0.724186
$708$	−8.16880	−0.307002
$709$	50.7242	1.90499	0.952493	−	0.304560i	$-0.0985096\pi$
$709$	50.7242	1.90499	0.952493	+	0.304560i	$0.0985096\pi$
$710$	−34.2622	−1.28584
$711$	8.83972	0.331516
$712$	7.02820	0.263393
$713$	−27.7831	−1.04049
$714$	−5.33531	−0.199669
$715$	3.00324	0.112315
$716$	−20.9739	−0.783832
$717$	9.20316	0.343698
$718$	18.3910	0.686346
$719$	−27.5167	−1.02620	−0.513099	−	0.858329i	$-0.671503\pi$
$719$	−27.5167	−1.02620	−0.513099	+	0.858329i	$0.671503\pi$
$720$	3.97479	0.148132
$721$	−17.8454	−0.664598
$722$	−18.2786	−0.680258
$723$	−9.24093	−0.343674
$724$	−18.1906	−0.676048
$725$	−40.1798	−1.49224
$726$	−1.00000	−0.0371135
$727$	20.1657	0.747904	0.373952	−	0.927448i	$-0.378002\pi$
$727$	20.1657	0.747904	0.373952	+	0.927448i	$0.378002\pi$
$728$	−1.41638	−0.0524947
$729$	1.00000	0.0370370
$730$	54.5872	2.02036
$731$	6.03098	0.223064
$732$	−1.00000	−0.0369611
$733$	−42.9803	−1.58751	−0.793757	−	0.608235i	$-0.791878\pi$
$733$	−42.9803	−1.58751	−0.793757	+	0.608235i	$0.791878\pi$
$734$	−26.8737	−0.991927
$735$	13.8559	0.511081
$736$	7.44783	0.274531
$737$	−3.62691	−0.133599
$738$	6.29421	0.231693
$739$	3.03980	0.111821	0.0559105	−	0.998436i	$-0.482194\pi$
$739$	3.03980	0.111821	0.0559105	+	0.998436i	$0.482194\pi$
$740$	39.5220	1.45286
$741$	0.641764	0.0235758
$742$	−22.4534	−0.824289
$743$	38.0490	1.39588	0.697941	−	0.716155i	$-0.254100\pi$
$743$	38.0490	1.39588	0.697941	+	0.716155i	$0.254100\pi$
$744$	3.73036	0.136762
$745$	0.984439	0.0360670
$746$	21.3591	0.782011
$747$	−13.4068	−0.490530
$748$	−2.84613	−0.104065
$749$	28.6639	1.04736
$750$	−23.0496	−0.841653
$751$	21.3569	0.779323	0.389661	−	0.920958i	$-0.372592\pi$
$751$	21.3569	0.779323	0.389661	+	0.920958i	$0.372592\pi$
$752$	−0.984439	−0.0358988
$753$	−10.8677	−0.396041
$754$	−2.81127	−0.102380
$755$	54.4239	1.98069
$756$	1.87458	0.0681780
$757$	−29.2087	−1.06161	−0.530804	−	0.847495i	$-0.678110\pi$
$757$	−29.2087	−1.06161	−0.530804	+	0.847495i	$0.678110\pi$
$758$	−30.3241	−1.10142
$759$	−7.44783	−0.270339
$760$	−3.37608	−0.122463
$761$	21.8051	0.790435	0.395217	−	0.918588i	$-0.370669\pi$
$761$	21.8051	0.790435	0.395217	+	0.918588i	$0.370669\pi$
$762$	12.5449	0.454453
$763$	−1.04070	−0.0376757
$764$	−13.4547	−0.486774
$765$	−11.3128	−0.409014
$766$	−26.5848	−0.960547
$767$	6.17212	0.222862
$768$	−1.00000	−0.0360844
$769$	3.96814	0.143095	0.0715474	−	0.997437i	$-0.477206\pi$
$769$	3.96814	0.143095	0.0715474	+	0.997437i	$0.477206\pi$
$770$	−7.45108	−0.268518
$771$	−21.5068	−0.774548
$772$	−20.3564	−0.732643
$773$	−24.6384	−0.886181	−0.443090	−	0.896477i	$-0.646118\pi$
$773$	−24.6384	−0.886181	−0.443090	+	0.896477i	$0.646118\pi$
$774$	−2.11901	−0.0761663
$775$	−40.2840	−1.44704
$776$	5.62076	0.201773
$777$	18.6393	0.668682
$778$	−8.25611	−0.295996
$779$	−5.34614	−0.191545
$780$	−3.00324	−0.107533
$781$	−8.61987	−0.308443
$782$	−21.1975	−0.758021
$783$	3.72071	0.132967
$784$	−3.48594	−0.124498
$785$	0.113098	0.00403665
$786$	−15.2190	−0.542843
$787$	5.01218	0.178665	0.0893325	−	0.996002i	$-0.471527\pi$
$787$	5.01218	0.178665	0.0893325	+	0.996002i	$0.471527\pi$
$788$	−15.4660	−0.550954
$789$	4.38872	0.156243
$790$	35.1360	1.25008
$791$	20.5853	0.731930
$792$	1.00000	0.0355335
$793$	0.755573	0.0268312
$794$	−30.9866	−1.09967
$795$	−47.6092	−1.68852
$796$	5.09380	0.180545
$797$	41.9347	1.48540	0.742702	−	0.669623i	$-0.233544\pi$
$797$	41.9347	1.48540	0.742702	+	0.669623i	$0.233544\pi$
$798$	−1.59222	−0.0563640
$799$	2.80184	0.0991220
$800$	10.7990	0.381801
$801$	7.02820	0.248329
$802$	25.3908	0.896582
$803$	13.7334	0.484640
$804$	3.62691	0.127911
$805$	−55.4944	−1.95592
$806$	−2.81856	−0.0992796
$807$	−10.2373	−0.360370
$808$	−10.2720	−0.361368
$809$	−54.3274	−1.91005	−0.955025	−	0.296526i	$-0.904172\pi$
$809$	−54.3274	−1.91005	−0.955025	+	0.296526i	$0.904172\pi$
$810$	3.97479	0.139660
$811$	1.32527	0.0465367	0.0232683	−	0.999729i	$-0.492593\pi$
$811$	1.32527	0.0465367	0.0232683	+	0.999729i	$0.492593\pi$
$812$	6.97479	0.244767
$813$	−20.0997	−0.704926
$814$	9.94317	0.348508
$815$	62.3119	2.18269
$816$	2.84613	0.0996345
$817$	1.79983	0.0629681
$818$	25.3213	0.885338
$819$	−1.41638	−0.0494925
$820$	25.0182	0.873672
$821$	4.26647	0.148901	0.0744504	−	0.997225i	$-0.476280\pi$
$821$	4.26647	0.148901	0.0744504	+	0.997225i	$0.476280\pi$
$822$	−5.99035	−0.208937
$823$	−29.2568	−1.01983	−0.509915	−	0.860225i	$-0.670323\pi$
$823$	−29.2568	−1.01983	−0.509915	+	0.860225i	$0.670323\pi$
$824$	9.51967	0.331633
$825$	−10.7990	−0.375971
$826$	−15.3131	−0.532811
$827$	−40.6546	−1.41370	−0.706849	−	0.707365i	$-0.749884\pi$
$827$	−40.6546	−1.41370	−0.706849	+	0.707365i	$0.749884\pi$
$828$	7.44783	0.258830
$829$	4.89179	0.169899	0.0849495	−	0.996385i	$-0.472927\pi$
$829$	4.89179	0.169899	0.0849495	+	0.996385i	$0.472927\pi$
$830$	−53.2893	−1.84970
$831$	19.7923	0.686587
$832$	0.755573	0.0261948
$833$	9.92143	0.343757
$834$	−9.59205	−0.332146
$835$	−71.2575	−2.46597
$836$	−0.849373	−0.0293762
$837$	3.73036	0.128940
$838$	−11.0466	−0.381599
$839$	4.31617	0.149011	0.0745054	−	0.997221i	$-0.476262\pi$
$839$	4.31617	0.149011	0.0745054	+	0.997221i	$0.476262\pi$
$840$	7.45108	0.257087
$841$	−15.1563	−0.522631
$842$	32.4851	1.11951
$843$	−14.8776	−0.512411
$844$	−12.6487	−0.435387
$845$	−49.4031	−1.69952
$846$	−0.984439	−0.0338457
$847$	−1.87458	−0.0644115
$848$	11.9778	0.411319
$849$	−9.36280	−0.321331
$850$	−30.7352	−1.05421
$851$	74.0551	2.53858
$852$	8.61987	0.295312
$853$	31.3832	1.07454	0.537270	−	0.843411i	$-0.319456\pi$
$853$	31.3832	1.07454	0.537270	+	0.843411i	$0.319456\pi$
$854$	−1.87458	−0.0641469
$855$	−3.37608	−0.115460
$856$	−15.2908	−0.522629
$857$	13.7651	0.470207	0.235104	−	0.971970i	$-0.424457\pi$
$857$	13.7651	0.470207	0.235104	+	0.971970i	$0.424457\pi$
$858$	−0.755573	−0.0257948
$859$	20.1210	0.686518	0.343259	−	0.939241i	$-0.388469\pi$
$859$	20.1210	0.686518	0.343259	+	0.939241i	$0.388469\pi$
$860$	−8.42262	−0.287209
$861$	11.7990	0.402110
$862$	−22.8291	−0.777563
$863$	−19.6688	−0.669535	−0.334768	−	0.942301i	$-0.608658\pi$
$863$	−19.6688	−0.669535	−0.334768	+	0.942301i	$0.608658\pi$
$864$	−1.00000	−0.0340207
$865$	21.7416	0.739238
$866$	−39.6328	−1.34678
$867$	8.89954	0.302244
$868$	6.99288	0.237354
$869$	8.83972	0.299867
$870$	14.7891	0.501396
$871$	−2.74040	−0.0928548
$872$	0.555161	0.0188001
$873$	5.62076	0.190234
$874$	−6.32599	−0.213980
$875$	−43.2084	−1.46071
$876$	−13.7334	−0.464007
$877$	−6.76102	−0.228303	−0.114152	−	0.993463i	$-0.536415\pi$
$877$	−6.76102	−0.228303	−0.114152	+	0.993463i	$0.536415\pi$
$878$	−18.3616	−0.619674
$879$	13.9108	0.469201
$880$	3.97479	0.133990
$881$	−21.1773	−0.713480	−0.356740	−	0.934204i	$-0.616112\pi$
$881$	−21.1773	−0.713480	−0.356740	+	0.934204i	$0.616112\pi$
$882$	−3.48594	−0.117378
$883$	−17.2732	−0.581290	−0.290645	−	0.956831i	$-0.593870\pi$
$883$	−17.2732	−0.581290	−0.290645	+	0.956831i	$0.593870\pi$
$884$	−2.15046	−0.0723278
$885$	−32.4692	−1.09144
$886$	12.6071	0.423543
$887$	−7.67037	−0.257546	−0.128773	−	0.991674i	$-0.541104\pi$
$887$	−7.67037	−0.257546	−0.128773	+	0.991674i	$0.541104\pi$
$888$	−9.94317	−0.333671
$889$	23.5164	0.788716
$890$	27.9356	0.936405
$891$	1.00000	0.0335013
$892$	23.1180	0.774046
$893$	0.836156	0.0279809
$894$	−0.247671	−0.00828334
$895$	−83.3669	−2.78665
$896$	−1.87458	−0.0626254
$897$	−5.62738	−0.187893
$898$	26.9183	0.898275
$899$	13.8796	0.462911
$900$	10.7990	0.359965
$901$	−34.0903	−1.13571
$902$	6.29421	0.209574
$903$	−3.97226	−0.132189
$904$	−10.9813	−0.365232
$905$	−72.3038	−2.40346
$906$	−13.6923	−0.454895
$907$	−21.9586	−0.729125	−0.364562	−	0.931179i	$-0.618781\pi$
$907$	−21.9586	−0.729125	−0.364562	+	0.931179i	$0.618781\pi$
$908$	14.8776	0.493730
$909$	−10.2720	−0.340701
$910$	−5.62983	−0.186627
$911$	28.1422	0.932393	0.466196	−	0.884681i	$-0.345624\pi$
$911$	28.1422	0.932393	0.466196	+	0.884681i	$0.345624\pi$
$912$	0.849373	0.0281256
$913$	−13.4068	−0.443701
$914$	−25.3503	−0.838513
$915$	−3.97479	−0.131402
$916$	24.1097	0.796606
$917$	−28.5292	−0.942118
$918$	2.84613	0.0939363
$919$	−17.0589	−0.562720	−0.281360	−	0.959602i	$-0.590785\pi$
$919$	−17.0589	−0.562720	−0.281360	+	0.959602i	$0.590785\pi$
$920$	29.6036	0.976001
$921$	13.5320	0.445894
$922$	19.1063	0.629232
$923$	−6.51294	−0.214376
$924$	1.87458	0.0616693
$925$	107.376	3.53050
$926$	−27.2869	−0.896704
$927$	9.51967	0.312667
$928$	−3.72071	−0.122138
$929$	−8.04599	−0.263980	−0.131990	−	0.991251i	$-0.542137\pi$
$929$	−8.04599	−0.263980	−0.131990	+	0.991251i	$0.542137\pi$
$930$	14.8274	0.486210
$931$	2.96086	0.0970383
$932$	14.2633	0.467210
$933$	27.5007	0.900332
$934$	24.4241	0.799181
$935$	−11.3128	−0.369967
$936$	0.755573	0.0246967
$937$	8.47280	0.276794	0.138397	−	0.990377i	$-0.455805\pi$
$937$	8.47280	0.276794	0.138397	+	0.990377i	$0.455805\pi$
$938$	6.79895	0.221994
$939$	20.2339	0.660308
$940$	−3.91294	−0.127626
$941$	−11.9250	−0.388744	−0.194372	−	0.980928i	$-0.562267\pi$
$941$	−11.9250	−0.388744	−0.194372	+	0.980928i	$0.562267\pi$
$942$	−0.0284539	−0.000927078 0
$943$	46.8782	1.52657
$944$	8.16880	0.265872
$945$	7.45108	0.242384
$946$	−2.11901	−0.0688950
$947$	0.206431	0.00670811	0.00335405	−	0.999994i	$-0.498932\pi$
$947$	0.206431	0.00670811	0.00335405	+	0.999994i	$0.498932\pi$
$948$	−8.83972	−0.287101
$949$	10.3766	0.336837
$950$	−9.17234	−0.297590
$951$	−18.8109	−0.609985
$952$	5.33531	0.172918
$953$	−24.8392	−0.804622	−0.402311	−	0.915503i	$-0.631793\pi$
$953$	−24.8392	−0.804622	−0.402311	+	0.915503i	$0.631793\pi$
$954$	11.9778	0.387795
$955$	−53.4796	−1.73056
$956$	−9.20316	−0.297652
$957$	3.72071	0.120274
$958$	−20.7116	−0.669162
$959$	−11.2294	−0.362617
$960$	−3.97479	−0.128286
$961$	−17.0844	−0.551110
$962$	7.51279	0.242222
$963$	−15.2908	−0.492739
$964$	9.24093	0.297630
$965$	−80.9124	−2.60466
$966$	13.9616	0.449207
$967$	−25.5657	−0.822139	−0.411069	−	0.911604i	$-0.634845\pi$
$967$	−25.5657	−0.822139	−0.411069	+	0.911604i	$0.634845\pi$
$968$	1.00000	0.0321412
$969$	−2.41743	−0.0776589
$970$	22.3413	0.717337
$971$	−3.56189	−0.114307	−0.0571533	−	0.998365i	$-0.518202\pi$
$971$	−3.56189	−0.114307	−0.0571533	+	0.998365i	$0.518202\pi$
$972$	−1.00000	−0.0320750
$973$	−17.9811	−0.576448
$974$	−8.80379	−0.282092
$975$	−8.15940	−0.261310
$976$	1.00000	0.0320092
$977$	−48.6076	−1.55510	−0.777548	−	0.628824i	$-0.783537\pi$
$977$	−48.6076	−1.55510	−0.777548	+	0.628824i	$0.783537\pi$
$978$	−15.6768	−0.501288
$979$	7.02820	0.224622
$980$	−13.8559	−0.442609
$981$	0.555161	0.0177249
$982$	−19.9650	−0.637108
$983$	19.5051	0.622117	0.311058	−	0.950391i	$-0.399317\pi$
$983$	19.5051	0.622117	0.311058	+	0.950391i	$0.399317\pi$
$984$	−6.29421	−0.200652
$985$	−61.4741	−1.95873
$986$	10.5896	0.337243
$987$	−1.84541	−0.0587401
$988$	−0.641764	−0.0204172
$989$	−15.7820	−0.501840
$990$	3.97479	0.126327
$991$	10.5395	0.334797	0.167398	−	0.985889i	$-0.446463\pi$
$991$	10.5395	0.334797	0.167398	+	0.985889i	$0.446463\pi$
$992$	−3.73036	−0.118439
$993$	−3.10873	−0.0986525
$994$	16.1587	0.512522
$995$	20.2468	0.641866
$996$	13.4068	0.424811
$997$	−35.8862	−1.13653	−0.568263	−	0.822847i	$-0.692384\pi$
$997$	−35.8862	−1.13653	−0.568263	+	0.822847i	$0.692384\pi$
$998$	2.90540	0.0919687
$999$	−9.94317	−0.314588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4026.2.a.v.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4026.2.a.v.1.5	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4026 = 2 \cdot 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97479 q^{5} -1.00000 q^{6} -1.87458 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.97479 q^{5} -1.00000 q^{6} -1.87458 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.97479 q^{10} +1.00000 q^{11} -1.00000 q^{12} +0.755573 q^{13} -1.87458 q^{14} -3.97479 q^{15} +1.00000 q^{16} -2.84613 q^{17} +1.00000 q^{18} -0.849373 q^{19} +3.97479 q^{20} +1.87458 q^{21} +1.00000 q^{22} +7.44783 q^{23} -1.00000 q^{24} +10.7990 q^{25} +0.755573 q^{26} -1.00000 q^{27} -1.87458 q^{28} -3.72071 q^{29} -3.97479 q^{30} -3.73036 q^{31} +1.00000 q^{32} -1.00000 q^{33} -2.84613 q^{34} -7.45108 q^{35} +1.00000 q^{36} +9.94317 q^{37} -0.849373 q^{38} -0.755573 q^{39} +3.97479 q^{40} +6.29421 q^{41} +1.87458 q^{42} -2.11901 q^{43} +1.00000 q^{44} +3.97479 q^{45} +7.44783 q^{46} -0.984439 q^{47} -1.00000 q^{48} -3.48594 q^{49} +10.7990 q^{50} +2.84613 q^{51} +0.755573 q^{52} +11.9778 q^{53} -1.00000 q^{54} +3.97479 q^{55} -1.87458 q^{56} +0.849373 q^{57} -3.72071 q^{58} +8.16880 q^{59} -3.97479 q^{60} +1.00000 q^{61} -3.73036 q^{62} -1.87458 q^{63} +1.00000 q^{64} +3.00324 q^{65} -1.00000 q^{66} -3.62691 q^{67} -2.84613 q^{68} -7.44783 q^{69} -7.45108 q^{70} -8.61987 q^{71} +1.00000 q^{72} +13.7334 q^{73} +9.94317 q^{74} -10.7990 q^{75} -0.849373 q^{76} -1.87458 q^{77} -0.755573 q^{78} +8.83972 q^{79} +3.97479 q^{80} +1.00000 q^{81} +6.29421 q^{82} -13.4068 q^{83} +1.87458 q^{84} -11.3128 q^{85} -2.11901 q^{86} +3.72071 q^{87} +1.00000 q^{88} +7.02820 q^{89} +3.97479 q^{90} -1.41638 q^{91} +7.44783 q^{92} +3.73036 q^{93} -0.984439 q^{94} -3.37608 q^{95} -1.00000 q^{96} +5.62076 q^{97} -3.48594 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9	\( 5 q + 5 q^{2} - 5 q^{3} + 5 q^{4} + 7 q^{5} - 5 q^{6} + 5 q^{8} + 5 q^{9} + 7 q^{10} + 5 q^{11} - 5 q^{12} - 2 q^{13} - 7 q^{15} + 5 q^{16} + 2 q^{17} + 5 q^{18} + 18 q^{19} + 7 q^{20} + 5 q^{22} - q^{23} - 5 q^{24} + 6 q^{25} - 2 q^{26} - 5 q^{27} + 7 q^{29} - 7 q^{30} + 5 q^{32} - 5 q^{33} + 2 q^{34} + 7 q^{35} + 5 q^{36} + 11 q^{37} + 18 q^{38} + 2 q^{39} + 7 q^{40} + 8 q^{41} - 7 q^{43} + 5 q^{44} + 7 q^{45} - q^{46} + q^{47} - 5 q^{48} + 7 q^{49} + 6 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} - 5 q^{54} + 7 q^{55} - 18 q^{57} + 7 q^{58} + 8 q^{59} - 7 q^{60} + 5 q^{61} + 5 q^{64} + 9 q^{65} - 5 q^{66} - 9 q^{67} + 2 q^{68} + q^{69} + 7 q^{70} + 34 q^{71} + 5 q^{72} + 13 q^{73} + 11 q^{74} - 6 q^{75} + 18 q^{76} + 2 q^{78} + 15 q^{79} + 7 q^{80} + 5 q^{81} + 8 q^{82} - 27 q^{83} - 2 q^{85} - 7 q^{86} - 7 q^{87} + 5 q^{88} + 11 q^{89} + 7 q^{90} + q^{91} - q^{92} + q^{94} + 11 q^{95} - 5 q^{96} + 37 q^{97} + 7 q^{98} + 5 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 5 * q^3 + 5 * q^4 + 7 * q^5 - 5 * q^6 + 5 * q^8 + 5 * q^9 + 7 * q^10 + 5 * q^11 - 5 * q^12 - 2 * q^13 - 7 * q^15 + 5 * q^16 + 2 * q^17 + 5 * q^18 + 18 * q^19 + 7 * q^20 + 5 * q^22 - q^23 - 5 * q^24 + 6 * q^25 - 2 * q^26 - 5 * q^27 + 7 * q^29 - 7 * q^30 + 5 * q^32 - 5 * q^33 + 2 * q^34 + 7 * q^35 + 5 * q^36 + 11 * q^37 + 18 * q^38 + 2 * q^39 + 7 * q^40 + 8 * q^41 - 7 * q^43 + 5 * q^44 + 7 * q^45 - q^46 + q^47 - 5 * q^48 + 7 * q^49 + 6 * q^50 - 2 * q^51 - 2 * q^52 + 10 * q^53 - 5 * q^54 + 7 * q^55 - 18 * q^57 + 7 * q^58 + 8 * q^59 - 7 * q^60 + 5 * q^61 + 5 * q^64 + 9 * q^65 - 5 * q^66 - 9 * q^67 + 2 * q^68 + q^69 + 7 * q^70 + 34 * q^71 + 5 * q^72 + 13 * q^73 + 11 * q^74 - 6 * q^75 + 18 * q^76 + 2 * q^78 + 15 * q^79 + 7 * q^80 + 5 * q^81 + 8 * q^82 - 27 * q^83 - 2 * q^85 - 7 * q^86 - 7 * q^87 + 5 * q^88 + 11 * q^89 + 7 * q^90 + q^91 - q^92 + q^94 + 11 * q^95 - 5 * q^96 + 37 * q^97 + 7 * q^98 + 5 * q^99

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