LMFDB - Embedded newform 1058.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1058,2,Mod(1,1058)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1058, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1058.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1058 = 2 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1058.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:	$8.44817253385$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\Q(\zeta_{22})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 4x^{3} + 3x^{2} + 3x - 1 $ x^5 - x^4 - 4x^3 + 3x^2 + 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 46)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.68251$ of defining polynomial
Character	$\chi$	$=$	1058.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.39788 q^{3} +1.00000 q^{4} +2.54620 q^{5} +1.39788 q^{6} +2.08816 q^{7} +1.00000 q^{8} -1.04594 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.39788 q^{3} +1.00000 q^{4} +2.54620 q^{5} +1.39788 q^{6} +2.08816 q^{7} +1.00000 q^{8} -1.04594 q^{9} +2.54620 q^{10} +3.81881 q^{11} +1.39788 q^{12} -6.19584 q^{13} +2.08816 q^{14} +3.55928 q^{15} +1.00000 q^{16} +1.30258 q^{17} -1.04594 q^{18} -2.48047 q^{19} +2.54620 q^{20} +2.91899 q^{21} +3.81881 q^{22} +1.39788 q^{24} +1.48314 q^{25} -6.19584 q^{26} -5.65573 q^{27} +2.08816 q^{28} +7.16723 q^{29} +3.55928 q^{30} -4.02157 q^{31} +1.00000 q^{32} +5.33823 q^{33} +1.30258 q^{34} +5.31686 q^{35} -1.04594 q^{36} -11.4282 q^{37} -2.48047 q^{38} -8.66103 q^{39} +2.54620 q^{40} -4.29298 q^{41} +2.91899 q^{42} -2.77780 q^{43} +3.81881 q^{44} -2.66317 q^{45} +9.34150 q^{47} +1.39788 q^{48} -2.63960 q^{49} +1.48314 q^{50} +1.82085 q^{51} -6.19584 q^{52} -2.36584 q^{53} -5.65573 q^{54} +9.72346 q^{55} +2.08816 q^{56} -3.46740 q^{57} +7.16723 q^{58} +0.611476 q^{59} +3.55928 q^{60} +4.03969 q^{61} -4.02157 q^{62} -2.18408 q^{63} +1.00000 q^{64} -15.7759 q^{65} +5.33823 q^{66} +12.8258 q^{67} +1.30258 q^{68} +5.31686 q^{70} -6.61122 q^{71} -1.04594 q^{72} -2.92492 q^{73} -11.4282 q^{74} +2.07324 q^{75} -2.48047 q^{76} +7.97428 q^{77} -8.66103 q^{78} -1.88675 q^{79} +2.54620 q^{80} -4.76820 q^{81} -4.29298 q^{82} +10.4404 q^{83} +2.91899 q^{84} +3.31663 q^{85} -2.77780 q^{86} +10.0189 q^{87} +3.81881 q^{88} +5.01225 q^{89} -2.66317 q^{90} -12.9379 q^{91} -5.62165 q^{93} +9.34150 q^{94} -6.31578 q^{95} +1.39788 q^{96} +12.5459 q^{97} -2.63960 q^{98} -3.99425 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} - 2 q^{3} + 5 q^{4} + 8 q^{5} - 2 q^{6} + 7 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 - 2 * q^3 + 5 * q^4 + 8 * q^5 - 2 * q^6 + 7 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} - 2 q^{3} + 5 q^{4} + 8 q^{5} - 2 q^{6} + 7 q^{7} + 5 q^{8} - q^{9} + 8 q^{10} + 5 q^{11} - 2 q^{12} - 7 q^{13} + 7 q^{14} - q^{15} + 5 q^{16} + 13 q^{17} - q^{18} + 12 q^{19} + 8 q^{20} + 6 q^{21} + 5 q^{22} - 2 q^{24} + q^{25} - 7 q^{26} - 20 q^{27} + 7 q^{28} - 4 q^{29} - q^{30} + 6 q^{31} + 5 q^{32} + 9 q^{33} + 13 q^{34} + 9 q^{35} - q^{36} + 14 q^{37} + 12 q^{38} - 6 q^{39} + 8 q^{40} + q^{41} + 6 q^{42} + 11 q^{43} + 5 q^{44} + 5 q^{45} + 9 q^{47} - 2 q^{48} - 12 q^{49} + q^{50} - 14 q^{51} - 7 q^{52} + 6 q^{53} - 20 q^{54} - 14 q^{55} + 7 q^{56} - 7 q^{57} - 4 q^{58} + 3 q^{59} - q^{60} + 13 q^{61} + 6 q^{62} - 19 q^{63} + 5 q^{64} - 9 q^{65} + 9 q^{66} + 10 q^{67} + 13 q^{68} + 9 q^{70} + 8 q^{71} - q^{72} - 4 q^{73} + 14 q^{74} + 4 q^{75} + 12 q^{76} + 18 q^{77} - 6 q^{78} - 18 q^{79} + 8 q^{80} + 33 q^{81} + q^{82} + 2 q^{83} + 6 q^{84} + 23 q^{85} + 11 q^{86} + 6 q^{87} + 5 q^{88} + 10 q^{89} + 5 q^{90} - 12 q^{91} - 20 q^{93} + 9 q^{94} + 28 q^{95} - 2 q^{96} + 17 q^{97} - 12 q^{98} - 34 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 2 * q^3 + 5 * q^4 + 8 * q^5 - 2 * q^6 + 7 * q^7 + 5 * q^8 - q^9 + 8 * q^10 + 5 * q^11 - 2 * q^12 - 7 * q^13 + 7 * q^14 - q^15 + 5 * q^16 + 13 * q^17 - q^18 + 12 * q^19 + 8 * q^20 + 6 * q^21 + 5 * q^22 - 2 * q^24 + q^25 - 7 * q^26 - 20 * q^27 + 7 * q^28 - 4 * q^29 - q^30 + 6 * q^31 + 5 * q^32 + 9 * q^33 + 13 * q^34 + 9 * q^35 - q^36 + 14 * q^37 + 12 * q^38 - 6 * q^39 + 8 * q^40 + q^41 + 6 * q^42 + 11 * q^43 + 5 * q^44 + 5 * q^45 + 9 * q^47 - 2 * q^48 - 12 * q^49 + q^50 - 14 * q^51 - 7 * q^52 + 6 * q^53 - 20 * q^54 - 14 * q^55 + 7 * q^56 - 7 * q^57 - 4 * q^58 + 3 * q^59 - q^60 + 13 * q^61 + 6 * q^62 - 19 * q^63 + 5 * q^64 - 9 * q^65 + 9 * q^66 + 10 * q^67 + 13 * q^68 + 9 * q^70 + 8 * q^71 - q^72 - 4 * q^73 + 14 * q^74 + 4 * q^75 + 12 * q^76 + 18 * q^77 - 6 * q^78 - 18 * q^79 + 8 * q^80 + 33 * q^81 + q^82 + 2 * q^83 + 6 * q^84 + 23 * q^85 + 11 * q^86 + 6 * q^87 + 5 * q^88 + 10 * q^89 + 5 * q^90 - 12 * q^91 - 20 * q^93 + 9 * q^94 + 28 * q^95 - 2 * q^96 + 17 * q^97 - 12 * q^98 - 34 * 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
$3$	1.39788	0.807065	0.403532	−	0.914965i	$-0.367782\pi$
$3$	1.39788	0.807065	0.403532	+	0.914965i	$0.367782\pi$
$4$	1.00000	0.500000
$5$	2.54620	1.13870	0.569348	−	0.822097i	$-0.307196\pi$
$5$	2.54620	1.13870	0.569348	+	0.822097i	$0.307196\pi$
$6$	1.39788	0.570681
$7$	2.08816	0.789249	0.394624	−	0.918843i	$-0.370875\pi$
$7$	2.08816	0.789249	0.394624	+	0.918843i	$0.370875\pi$
$8$	1.00000	0.353553
$9$	−1.04594	−0.348646
$10$	2.54620	0.805179
$11$	3.81881	1.15142	0.575708	−	0.817655i	$-0.304727\pi$
$11$	3.81881	1.15142	0.575708	+	0.817655i	$0.304727\pi$
$12$	1.39788	0.403532
$13$	−6.19584	−1.71842	−0.859209	−	0.511625i	$-0.829044\pi$
$13$	−6.19584	−1.71842	−0.859209	+	0.511625i	$0.829044\pi$
$14$	2.08816	0.558083
$15$	3.55928	0.919001
$16$	1.00000	0.250000
$17$	1.30258	0.315922	0.157961	−	0.987445i	$-0.449508\pi$
$17$	1.30258	0.315922	0.157961	+	0.987445i	$0.449508\pi$
$18$	−1.04594	−0.246530
$19$	−2.48047	−0.569060	−0.284530	−	0.958667i	$-0.591837\pi$
$19$	−2.48047	−0.569060	−0.284530	+	0.958667i	$0.591837\pi$
$20$	2.54620	0.569348
$21$	2.91899	0.636975
$22$	3.81881	0.814174
$23$	0	0
$23$	0	0
$24$	1.39788	0.285341
$25$	1.48314	0.296627
$26$	−6.19584	−1.21511
$27$	−5.65573	−1.08845
$28$	2.08816	0.394624
$29$	7.16723	1.33092	0.665460	−	0.746433i	$-0.268235\pi$
$29$	7.16723	1.33092	0.665460	+	0.746433i	$0.268235\pi$
$30$	3.55928	0.649832
$31$	−4.02157	−0.722294	−0.361147	−	0.932509i	$-0.617615\pi$
$31$	−4.02157	−0.722294	−0.361147	+	0.932509i	$0.617615\pi$
$32$	1.00000	0.176777
$33$	5.33823	0.929267
$34$	1.30258	0.223391
$35$	5.31686	0.898714
$36$	−1.04594	−0.174323
$37$	−11.4282	−1.87878	−0.939390	−	0.342852i	$-0.888607\pi$
$37$	−11.4282	−1.87878	−0.939390	+	0.342852i	$0.888607\pi$
$38$	−2.48047	−0.402386
$39$	−8.66103	−1.38687
$40$	2.54620	0.402590
$41$	−4.29298	−0.670451	−0.335225	−	0.942138i	$-0.608812\pi$
$41$	−4.29298	−0.670451	−0.335225	+	0.942138i	$0.608812\pi$
$42$	2.91899	0.450409
$43$	−2.77780	−0.423611	−0.211806	−	0.977312i	$-0.567934\pi$
$43$	−2.77780	−0.423611	−0.211806	+	0.977312i	$0.567934\pi$
$44$	3.81881	0.575708
$45$	−2.66317	−0.397002
$46$	0	0
$47$	9.34150	1.36260	0.681299	−	0.732005i	$-0.261415\pi$
$47$	9.34150	1.36260	0.681299	+	0.732005i	$0.261415\pi$
$48$	1.39788	0.201766
$49$	−2.63960	−0.377086
$50$	1.48314	0.209747
$51$	1.82085	0.254970
$52$	−6.19584	−0.859209
$53$	−2.36584	−0.324973	−0.162486	−	0.986711i	$-0.551951\pi$
$53$	−2.36584	−0.324973	−0.162486	+	0.986711i	$0.551951\pi$
$54$	−5.65573	−0.769647
$55$	9.72346	1.31111
$56$	2.08816	0.279042
$57$	−3.46740	−0.459268
$58$	7.16723	0.941103
$59$	0.611476	0.0796075	0.0398037	−	0.999208i	$-0.487327\pi$
$59$	0.611476	0.0796075	0.0398037	+	0.999208i	$0.487327\pi$
$60$	3.55928	0.459501
$61$	4.03969	0.517230	0.258615	−	0.965980i	$-0.416734\pi$
$61$	4.03969	0.517230	0.258615	+	0.965980i	$0.416734\pi$
$62$	−4.02157	−0.510739
$63$	−2.18408	−0.275169
$64$	1.00000	0.125000
$65$	−15.7759	−1.95675
$66$	5.33823	0.657091
$67$	12.8258	1.56693	0.783463	−	0.621438i	$-0.213451\pi$
$67$	12.8258	1.56693	0.783463	+	0.621438i	$0.213451\pi$
$68$	1.30258	0.157961
$69$	0	0
$70$	5.31686	0.635487
$71$	−6.61122	−0.784608	−0.392304	−	0.919836i	$-0.628322\pi$
$71$	−6.61122	−0.784608	−0.392304	+	0.919836i	$0.628322\pi$
$72$	−1.04594	−0.123265
$73$	−2.92492	−0.342336	−0.171168	−	0.985242i	$-0.554754\pi$
$73$	−2.92492	−0.342336	−0.171168	+	0.985242i	$0.554754\pi$
$74$	−11.4282	−1.32850
$75$	2.07324	0.239397
$76$	−2.48047	−0.284530
$77$	7.97428	0.908753
$78$	−8.66103	−0.980669
$79$	−1.88675	−0.212276	−0.106138	−	0.994351i	$-0.533849\pi$
$79$	−1.88675	−0.212276	−0.106138	+	0.994351i	$0.533849\pi$
$80$	2.54620	0.284674
$81$	−4.76820	−0.529800
$82$	−4.29298	−0.474080
$83$	10.4404	1.14598	0.572989	−	0.819563i	$-0.305784\pi$
$83$	10.4404	1.14598	0.572989	+	0.819563i	$0.305784\pi$
$84$	2.91899	0.318487
$85$	3.31663	0.359739
$86$	−2.77780	−0.299538
$87$	10.0189	1.07414
$88$	3.81881	0.407087
$89$	5.01225	0.531298	0.265649	−	0.964070i	$-0.414414\pi$
$89$	5.01225	0.531298	0.265649	+	0.964070i	$0.414414\pi$
$90$	−2.66317	−0.280723
$91$	−12.9379	−1.35626
$92$	0	0
$93$	−5.62165	−0.582938
$94$	9.34150	0.963503
$95$	−6.31578	−0.647986
$96$	1.39788	0.142670
$97$	12.5459	1.27385	0.636924	−	0.770927i	$-0.280207\pi$
$97$	12.5459	1.27385	0.636924	+	0.770927i	$0.280207\pi$
$98$	−2.63960	−0.266640
$99$	−3.99425	−0.401437
$100$	1.48314	0.148314
$101$	3.52251	0.350503	0.175252	−	0.984524i	$-0.443926\pi$
$101$	3.52251	0.350503	0.175252	+	0.984524i	$0.443926\pi$
$102$	1.82085	0.180291
$103$	1.56622	0.154325	0.0771623	−	0.997019i	$-0.475414\pi$
$103$	1.56622	0.154325	0.0771623	+	0.997019i	$0.475414\pi$
$104$	−6.19584	−0.607553
$105$	7.43232	0.725320
$106$	−2.36584	−0.229791
$107$	3.40318	0.328998	0.164499	−	0.986377i	$-0.447399\pi$
$107$	3.40318	0.328998	0.164499	+	0.986377i	$0.447399\pi$
$108$	−5.65573	−0.544223
$109$	−8.62324	−0.825956	−0.412978	−	0.910741i	$-0.635511\pi$
$109$	−8.62324	−0.825956	−0.412978	+	0.910741i	$0.635511\pi$
$110$	9.72346	0.927096
$111$	−15.9752	−1.51630
$112$	2.08816	0.197312
$113$	−3.56622	−0.335482	−0.167741	−	0.985831i	$-0.553647\pi$
$113$	−3.56622	−0.335482	−0.167741	+	0.985831i	$0.553647\pi$
$114$	−3.46740	−0.324752
$115$	0	0
$116$	7.16723	0.665460
$117$	6.48047	0.599120
$118$	0.611476	0.0562910
$119$	2.71999	0.249341
$120$	3.55928	0.324916
$121$	3.58334	0.325758
$122$	4.03969	0.365737
$123$	−6.00106	−0.541097
$124$	−4.02157	−0.361147
$125$	−8.95464	−0.800927
$126$	−2.18408	−0.194574
$127$	−5.62165	−0.498841	−0.249421	−	0.968395i	$-0.580240\pi$
$127$	−5.62165	−0.498841	−0.249421	+	0.968395i	$0.580240\pi$
$128$	1.00000	0.0883883
$129$	−3.88303	−0.341882
$130$	−15.7759	−1.38363
$131$	7.97296	0.696601	0.348301	−	0.937383i	$-0.386759\pi$
$131$	7.97296	0.696601	0.348301	+	0.937383i	$0.386759\pi$
$132$	5.33823	0.464634
$133$	−5.17962	−0.449130
$134$	12.8258	1.10798
$135$	−14.4006	−1.23941
$136$	1.30258	0.111695
$137$	2.06934	0.176796	0.0883979	−	0.996085i	$-0.471825\pi$
$137$	2.06934	0.176796	0.0883979	+	0.996085i	$0.471825\pi$
$138$	0	0
$139$	−13.0620	−1.10790	−0.553950	−	0.832550i	$-0.686880\pi$
$139$	−13.0620	−1.10790	−0.553950	+	0.832550i	$0.686880\pi$
$140$	5.31686	0.449357
$141$	13.0583	1.09971
$142$	−6.61122	−0.554801
$143$	−23.6608	−1.97861
$144$	−1.04594	−0.0871616
$145$	18.2492	1.51551
$146$	−2.92492	−0.242068
$147$	−3.68984	−0.304333
$148$	−11.4282	−0.939390
$149$	14.8452	1.21617	0.608083	−	0.793873i	$-0.291939\pi$
$149$	14.8452	1.21617	0.608083	+	0.793873i	$0.291939\pi$
$150$	2.07324	0.169280
$151$	3.85308	0.313559	0.156780	−	0.987634i	$-0.449889\pi$
$151$	3.85308	0.313559	0.156780	+	0.987634i	$0.449889\pi$
$152$	−2.48047	−0.201193
$153$	−1.36242	−0.110145
$154$	7.97428	0.642586
$155$	−10.2397	−0.822473
$156$	−8.66103	−0.693437
$157$	22.6511	1.80776	0.903878	−	0.427790i	$-0.140708\pi$
$157$	22.6511	1.80776	0.903878	+	0.427790i	$0.140708\pi$
$158$	−1.88675	−0.150102
$159$	−3.30715	−0.262274
$160$	2.54620	0.201295
$161$	0	0
$162$	−4.76820	−0.374625
$163$	−18.9635	−1.48533	−0.742667	−	0.669660i	$-0.766440\pi$
$163$	−18.9635	−1.48533	−0.742667	+	0.669660i	$0.766440\pi$
$164$	−4.29298	−0.335225
$165$	13.5922	1.05815
$166$	10.4404	0.810329
$167$	−0.979634	−0.0758063	−0.0379032	−	0.999281i	$-0.512068\pi$
$167$	−0.979634	−0.0758063	−0.0379032	+	0.999281i	$0.512068\pi$
$168$	2.91899	0.225205
$169$	25.3885	1.95296
$170$	3.31663	0.254374
$171$	2.59442	0.198401
$172$	−2.77780	−0.211806
$173$	−8.92203	−0.678330	−0.339165	−	0.940727i	$-0.610144\pi$
$173$	−8.92203	−0.678330	−0.339165	+	0.940727i	$0.610144\pi$
$174$	10.0189	0.759531
$175$	3.09702	0.234113
$176$	3.81881	0.287854
$177$	0.854769	0.0642484
$178$	5.01225	0.375684
$179$	−8.49152	−0.634686	−0.317343	−	0.948311i	$-0.602791\pi$
$179$	−8.49152	−0.634686	−0.317343	+	0.948311i	$0.602791\pi$
$180$	−2.66317	−0.198501
$181$	−0.537425	−0.0399465	−0.0199732	−	0.999801i	$-0.506358\pi$
$181$	−0.537425	−0.0399465	−0.0199732	+	0.999801i	$0.506358\pi$
$182$	−12.9379	−0.959020
$183$	5.64700	0.417438
$184$	0	0
$185$	−29.0984	−2.13936
$186$	−5.62165	−0.412200
$187$	4.97431	0.363757
$188$	9.34150	0.681299
$189$	−11.8100	−0.859054
$190$	−6.31578	−0.458195
$191$	−26.8320	−1.94149	−0.970747	−	0.240105i	$-0.922818\pi$
$191$	−26.8320	−1.94149	−0.970747	+	0.240105i	$0.922818\pi$
$192$	1.39788	0.100883
$193$	−1.40434	−0.101087	−0.0505434	−	0.998722i	$-0.516095\pi$
$193$	−1.40434	−0.101087	−0.0505434	+	0.998722i	$0.516095\pi$
$194$	12.5459	0.900746
$195$	−22.0527	−1.57923
$196$	−2.63960	−0.188543
$197$	−8.24471	−0.587411	−0.293706	−	0.955896i	$-0.594889\pi$
$197$	−8.24471	−0.587411	−0.293706	+	0.955896i	$0.594889\pi$
$198$	−3.99425	−0.283859
$199$	−3.11512	−0.220825	−0.110412	−	0.993886i	$-0.535217\pi$
$199$	−3.11512	−0.220825	−0.110412	+	0.993886i	$0.535217\pi$
$200$	1.48314	0.104874
$201$	17.9290	1.26461
$202$	3.52251	0.247843
$203$	14.9663	1.05043
$204$	1.82085	0.127485
$205$	−10.9308	−0.763439
$206$	1.56622	0.109124
$207$	0	0
$208$	−6.19584	−0.429604
$209$	−9.47247	−0.655224
$210$	7.43232	0.512879
$211$	−22.0077	−1.51508	−0.757538	−	0.652791i	$-0.773598\pi$
$211$	−22.0077	−1.51508	−0.757538	+	0.652791i	$0.773598\pi$
$212$	−2.36584	−0.162486
$213$	−9.24168	−0.633229
$214$	3.40318	0.232637
$215$	−7.07285	−0.482364
$216$	−5.65573	−0.384823
$217$	−8.39765	−0.570070
$218$	−8.62324	−0.584039
$219$	−4.08868	−0.276287
$220$	9.72346	0.655556
$221$	−8.07058	−0.542886
$222$	−15.9752	−1.07218
$223$	12.3097	0.824321	0.412161	−	0.911111i	$-0.364774\pi$
$223$	12.3097	0.824321	0.412161	+	0.911111i	$0.364774\pi$
$224$	2.08816	0.139521
$225$	−1.55127	−0.103418
$226$	−3.56622	−0.237222
$227$	5.33249	0.353930	0.176965	−	0.984217i	$-0.443372\pi$
$227$	5.33249	0.353930	0.176965	+	0.984217i	$0.443372\pi$
$228$	−3.46740	−0.229634
$229$	14.1070	0.932216	0.466108	−	0.884728i	$-0.345656\pi$
$229$	14.1070	0.932216	0.466108	+	0.884728i	$0.345656\pi$
$230$	0	0
$231$	11.1471	0.733423
$232$	7.16723	0.470551
$233$	17.1828	1.12568	0.562841	−	0.826565i	$-0.309708\pi$
$233$	17.1828	1.12568	0.562841	+	0.826565i	$0.309708\pi$
$234$	6.48047	0.423642
$235$	23.7853	1.55158
$236$	0.611476	0.0398037
$237$	−2.63745	−0.171321
$238$	2.71999	0.176311
$239$	−5.64042	−0.364848	−0.182424	−	0.983220i	$-0.558394\pi$
$239$	−5.64042	−0.364848	−0.182424	+	0.983220i	$0.558394\pi$
$240$	3.55928	0.229750
$241$	−5.03768	−0.324505	−0.162253	−	0.986749i	$-0.551876\pi$
$241$	−5.03768	−0.324505	−0.162253	+	0.986749i	$0.551876\pi$
$242$	3.58334	0.230346
$243$	10.3018	0.660862
$244$	4.03969	0.258615
$245$	−6.72096	−0.429387
$246$	−6.00106	−0.382614
$247$	15.3686	0.977882
$248$	−4.02157	−0.255370
$249$	14.5943	0.924879
$250$	−8.95464	−0.566341
$251$	−17.6811	−1.11602	−0.558012	−	0.829833i	$-0.688436\pi$
$251$	−17.6811	−1.11602	−0.558012	+	0.829833i	$0.688436\pi$
$252$	−2.18408	−0.137584
$253$	0	0
$254$	−5.62165	−0.352734
$255$	4.63624	0.290333
$256$	1.00000	0.0625000
$257$	22.0654	1.37640	0.688202	−	0.725520i	$-0.258400\pi$
$257$	22.0654	1.37640	0.688202	+	0.725520i	$0.258400\pi$
$258$	−3.88303	−0.241747
$259$	−23.8638	−1.48282
$260$	−15.7759	−0.978377
$261$	−7.49648	−0.464020
$262$	7.97296	0.492571
$263$	−7.75842	−0.478405	−0.239202	−	0.970970i	$-0.576886\pi$
$263$	−7.75842	−0.478405	−0.239202	+	0.970970i	$0.576886\pi$
$264$	5.33823	0.328546
$265$	−6.02390	−0.370045
$266$	−5.17962	−0.317583
$267$	7.00651	0.428792
$268$	12.8258	0.783463
$269$	17.0193	1.03768	0.518842	−	0.854870i	$-0.326363\pi$
$269$	17.0193	1.03768	0.518842	+	0.854870i	$0.326363\pi$
$270$	−14.4006	−0.876393
$271$	11.6475	0.707533	0.353767	−	0.935334i	$-0.384901\pi$
$271$	11.6475	0.707533	0.353767	+	0.935334i	$0.384901\pi$
$272$	1.30258	0.0789805
$273$	−18.0856	−1.09459
$274$	2.06934	0.125014
$275$	5.66382	0.341541
$276$	0	0
$277$	16.8299	1.01121	0.505604	−	0.862766i	$-0.331270\pi$
$277$	16.8299	1.01121	0.505604	+	0.862766i	$0.331270\pi$
$278$	−13.0620	−0.783404
$279$	4.20631	0.251825
$280$	5.31686	0.317743
$281$	−5.29050	−0.315605	−0.157802	−	0.987471i	$-0.550441\pi$
$281$	−5.29050	−0.315605	−0.157802	+	0.987471i	$0.550441\pi$
$282$	13.0583	0.777609
$283$	−15.3696	−0.913627	−0.456814	−	0.889562i	$-0.651009\pi$
$283$	−15.3696	−0.913627	−0.456814	+	0.889562i	$0.651009\pi$
$284$	−6.61122	−0.392304
$285$	−8.82869	−0.522967
$286$	−23.6608	−1.39909
$287$	−8.96441	−0.529152
$288$	−1.04594	−0.0616325
$289$	−15.3033	−0.900193
$290$	18.2492	1.07163
$291$	17.5377	1.02808
$292$	−2.92492	−0.171168
$293$	−10.7552	−0.628323	−0.314161	−	0.949370i	$-0.601723\pi$
$293$	−10.7552	−0.628323	−0.314161	+	0.949370i	$0.601723\pi$
$294$	−3.68984	−0.215196
$295$	1.55694	0.0906486
$296$	−11.4282	−0.664249
$297$	−21.5982	−1.25325
$298$	14.8452	0.859959
$299$	0	0
$300$	2.07324	0.119699
$301$	−5.80049	−0.334335
$302$	3.85308	0.221720
$303$	4.92404	0.282879
$304$	−2.48047	−0.142265
$305$	10.2859	0.588967
$306$	−1.36242	−0.0778843
$307$	−25.7849	−1.47162	−0.735810	−	0.677188i	$-0.763199\pi$
$307$	−25.7849	−1.47162	−0.735810	+	0.677188i	$0.763199\pi$
$308$	7.97428	0.454377
$309$	2.18939	0.124550
$310$	−10.2397	−0.581576
$311$	16.3169	0.925244	0.462622	−	0.886556i	$-0.346909\pi$
$311$	16.3169	0.925244	0.462622	+	0.886556i	$0.346909\pi$
$312$	−8.66103	−0.490334
$313$	12.5034	0.706731	0.353366	−	0.935485i	$-0.385037\pi$
$313$	12.5034	0.706731	0.353366	+	0.935485i	$0.385037\pi$
$314$	22.6511	1.27828
$315$	−5.56111	−0.313333
$316$	−1.88675	−0.106138
$317$	−13.5387	−0.760410	−0.380205	−	0.924902i	$-0.624147\pi$
$317$	−13.5387	−0.760410	−0.380205	+	0.924902i	$0.624147\pi$
$318$	−3.30715	−0.185456
$319$	27.3703	1.53244
$320$	2.54620	0.142337
$321$	4.75723	0.265523
$322$	0	0
$323$	−3.23101	−0.179778
$324$	−4.76820	−0.264900
$325$	−9.18928	−0.509730
$326$	−18.9635	−1.05029
$327$	−12.0542	−0.666600
$328$	−4.29298	−0.237040
$329$	19.5065	1.07543
$330$	13.5922	0.748227
$331$	28.3332	1.55734	0.778668	−	0.627437i	$-0.215896\pi$
$331$	28.3332	1.55734	0.778668	+	0.627437i	$0.215896\pi$
$332$	10.4404	0.572989
$333$	11.9532	0.655029
$334$	−0.979634	−0.0536032
$335$	32.6572	1.78425
$336$	2.91899	0.159244
$337$	−14.4856	−0.789082	−0.394541	−	0.918878i	$-0.629096\pi$
$337$	−14.4856	−0.789082	−0.394541	+	0.918878i	$0.629096\pi$
$338$	25.3885	1.38095
$339$	−4.98514	−0.270756
$340$	3.31663	0.179869
$341$	−15.3576	−0.831661
$342$	2.59442	0.140290
$343$	−20.1290	−1.08686
$344$	−2.77780	−0.149769
$345$	0	0
$346$	−8.92203	−0.479651
$347$	32.9050	1.76643	0.883217	−	0.468964i	$-0.155373\pi$
$347$	32.9050	1.76643	0.883217	+	0.468964i	$0.155373\pi$
$348$	10.0189	0.537070
$349$	−11.3601	−0.608090	−0.304045	−	0.952658i	$-0.598337\pi$
$349$	−11.3601	−0.608090	−0.304045	+	0.952658i	$0.598337\pi$
$350$	3.09702	0.165543
$351$	35.0420	1.87040
$352$	3.81881	0.203543
$353$	1.50436	0.0800689	0.0400344	−	0.999198i	$-0.487253\pi$
$353$	1.50436	0.0800689	0.0400344	+	0.999198i	$0.487253\pi$
$354$	0.854769	0.0454305
$355$	−16.8335	−0.893429
$356$	5.01225	0.265649
$357$	3.80221	0.201234
$358$	−8.49152	−0.448791
$359$	20.3544	1.07426	0.537131	−	0.843499i	$-0.319508\pi$
$359$	20.3544	1.07426	0.537131	+	0.843499i	$0.319508\pi$
$360$	−2.66317	−0.140361
$361$	−12.8472	−0.676171
$362$	−0.537425	−0.0282464
$363$	5.00907	0.262908
$364$	−12.9379	−0.678130
$365$	−7.44743	−0.389816
$366$	5.64700	0.295173
$367$	−12.2425	−0.639051	−0.319525	−	0.947578i	$-0.603523\pi$
$367$	−12.2425	−0.639051	−0.319525	+	0.947578i	$0.603523\pi$
$368$	0	0
$369$	4.49019	0.233750
$370$	−29.0984	−1.51275
$371$	−4.94024	−0.256484
$372$	−5.62165	−0.291469
$373$	16.4239	0.850398	0.425199	−	0.905100i	$-0.360204\pi$
$373$	16.4239	0.850398	0.425199	+	0.905100i	$0.360204\pi$
$374$	4.97431	0.257215
$375$	−12.5175	−0.646400
$376$	9.34150	0.481751
$377$	−44.4070	−2.28708
$378$	−11.8100	−0.607443
$379$	−25.7579	−1.32309	−0.661547	−	0.749904i	$-0.730100\pi$
$379$	−25.7579	−1.32309	−0.661547	+	0.749904i	$0.730100\pi$
$380$	−6.31578	−0.323993
$381$	−7.85838	−0.402597
$382$	−26.8320	−1.37284
$383$	−15.0901	−0.771070	−0.385535	−	0.922693i	$-0.625983\pi$
$383$	−15.0901	−0.771070	−0.385535	+	0.922693i	$0.625983\pi$
$384$	1.39788	0.0713351
$385$	20.3041	1.03479
$386$	−1.40434	−0.0714792
$387$	2.90541	0.147690
$388$	12.5459	0.636924
$389$	22.9846	1.16537	0.582684	−	0.812699i	$-0.302003\pi$
$389$	22.9846	1.16537	0.582684	+	0.812699i	$0.302003\pi$
$390$	−22.0527	−1.11668
$391$	0	0
$392$	−2.63960	−0.133320
$393$	11.1452	0.562202
$394$	−8.24471	−0.415363
$395$	−4.80405	−0.241718
$396$	−3.99425	−0.200718
$397$	−29.6670	−1.48895	−0.744473	−	0.667653i	$-0.767299\pi$
$397$	−29.6670	−1.48895	−0.744473	+	0.667653i	$0.767299\pi$
$398$	−3.11512	−0.156147
$399$	−7.24047	−0.362477
$400$	1.48314	0.0741568
$401$	29.2330	1.45983	0.729913	−	0.683540i	$-0.239561\pi$
$401$	29.2330	1.45983	0.729913	+	0.683540i	$0.239561\pi$
$402$	17.9290	0.894215
$403$	24.9170	1.24120
$404$	3.52251	0.175252
$405$	−12.1408	−0.603280
$406$	14.9663	0.742764
$407$	−43.6420	−2.16326
$408$	1.82085	0.0901453
$409$	33.6998	1.66635	0.833175	−	0.553009i	$-0.186521\pi$
$409$	33.6998	1.66635	0.833175	+	0.553009i	$0.186521\pi$
$410$	−10.9308	−0.539833
$411$	2.89269	0.142686
$412$	1.56622	0.0771623
$413$	1.27686	0.0628301
$414$	0	0
$415$	26.5833	1.30492
$416$	−6.19584	−0.303776
$417$	−18.2590	−0.894148
$418$	−9.47247	−0.463314
$419$	8.82612	0.431184	0.215592	−	0.976484i	$-0.430832\pi$
$419$	8.82612	0.431184	0.215592	+	0.976484i	$0.430832\pi$
$420$	7.43232	0.362660
$421$	27.3740	1.33413	0.667063	−	0.745001i	$-0.267551\pi$
$421$	27.3740	1.33413	0.667063	+	0.745001i	$0.267551\pi$
$422$	−22.0077	−1.07132
$423$	−9.77064	−0.475065
$424$	−2.36584	−0.114895
$425$	1.93190	0.0937111
$426$	−9.24168	−0.447761
$427$	8.43551	0.408223
$428$	3.40318	0.164499
$429$	−33.0749	−1.59687
$430$	−7.07285	−0.341083
$431$	−29.8688	−1.43873	−0.719365	−	0.694632i	$-0.755567\pi$
$431$	−29.8688	−1.43873	−0.719365	+	0.694632i	$0.755567\pi$
$432$	−5.65573	−0.272111
$433$	27.3484	1.31428	0.657139	−	0.753769i	$-0.271766\pi$
$433$	27.3484	1.31428	0.657139	+	0.753769i	$0.271766\pi$
$434$	−8.39765	−0.403100
$435$	25.5101	1.22312
$436$	−8.62324	−0.412978
$437$	0	0
$438$	−4.08868	−0.195365
$439$	−13.1196	−0.626164	−0.313082	−	0.949726i	$-0.601361\pi$
$439$	−13.1196	−0.626164	−0.313082	+	0.949726i	$0.601361\pi$
$440$	9.72346	0.463548
$441$	2.76087	0.131470
$442$	−8.07058	−0.383878
$443$	−10.7702	−0.511706	−0.255853	−	0.966716i	$-0.582356\pi$
$443$	−10.7702	−0.511706	−0.255853	+	0.966716i	$0.582356\pi$
$444$	−15.9752	−0.758148
$445$	12.7622	0.604986
$446$	12.3097	0.582883
$447$	20.7518	0.981525
$448$	2.08816	0.0986561
$449$	4.69291	0.221472	0.110736	−	0.993850i	$-0.464679\pi$
$449$	4.69291	0.221472	0.110736	+	0.993850i	$0.464679\pi$
$450$	−1.55127	−0.0731276
$451$	−16.3941	−0.771968
$452$	−3.56622	−0.167741
$453$	5.38613	0.253063
$454$	5.33249	0.250266
$455$	−32.9425	−1.54437
$456$	−3.46740	−0.162376
$457$	6.93568	0.324437	0.162219	−	0.986755i	$-0.448135\pi$
$457$	6.93568	0.324437	0.162219	+	0.986755i	$0.448135\pi$
$458$	14.1070	0.659176
$459$	−7.36703	−0.343864
$460$	0	0
$461$	−21.3273	−0.993312	−0.496656	−	0.867947i	$-0.665439\pi$
$461$	−21.3273	−0.993312	−0.496656	+	0.867947i	$0.665439\pi$
$462$	11.1471	0.518608
$463$	−6.41490	−0.298126	−0.149063	−	0.988828i	$-0.547626\pi$
$463$	−6.41490	−0.298126	−0.149063	+	0.988828i	$0.547626\pi$
$464$	7.16723	0.332730
$465$	−14.3139	−0.663789
$466$	17.1828	0.795977
$467$	14.4723	0.669696	0.334848	−	0.942272i	$-0.391315\pi$
$467$	14.4723	0.669696	0.334848	+	0.942272i	$0.391315\pi$
$468$	6.48047	0.299560
$469$	26.7824	1.23670
$470$	23.7853	1.09714
$471$	31.6635	1.45898
$472$	0.611476	0.0281455
$473$	−10.6079	−0.487753
$474$	−2.63745	−0.121142
$475$	−3.67888	−0.168799
$476$	2.71999	0.124671
$477$	2.47452	0.113301
$478$	−5.64042	−0.257987
$479$	−5.37524	−0.245601	−0.122801	−	0.992431i	$-0.539188\pi$
$479$	−5.37524	−0.245601	−0.122801	+	0.992431i	$0.539188\pi$
$480$	3.55928	0.162458
$481$	70.8071	3.22853
$482$	−5.03768	−0.229460
$483$	0	0
$484$	3.58334	0.162879
$485$	31.9445	1.45052
$486$	10.3018	0.467300
$487$	3.21931	0.145881	0.0729405	−	0.997336i	$-0.476762\pi$
$487$	3.21931	0.145881	0.0729405	+	0.997336i	$0.476762\pi$
$488$	4.03969	0.182868
$489$	−26.5086	−1.19876
$490$	−6.72096	−0.303622
$491$	30.0754	1.35728	0.678642	−	0.734470i	$-0.262569\pi$
$491$	30.0754	1.35728	0.678642	+	0.734470i	$0.262569\pi$
$492$	−6.00106	−0.270549
$493$	9.33588	0.420467
$494$	15.3686	0.691467
$495$	−10.1701	−0.457114
$496$	−4.02157	−0.180574
$497$	−13.8053	−0.619251
$498$	14.5943	0.653988
$499$	17.7485	0.794533	0.397266	−	0.917703i	$-0.369959\pi$
$499$	17.7485	0.794533	0.397266	+	0.917703i	$0.369959\pi$
$500$	−8.95464	−0.400464
$501$	−1.36941	−0.0611806
$502$	−17.6811	−0.789148
$503$	24.7648	1.10421	0.552105	−	0.833775i	$-0.313825\pi$
$503$	24.7648	1.10421	0.552105	+	0.833775i	$0.313825\pi$
$504$	−2.18408	−0.0972868
$505$	8.96902	0.399116
$506$	0	0
$507$	35.4900	1.57617
$508$	−5.62165	−0.249421
$509$	−31.0419	−1.37591	−0.687953	−	0.725755i	$-0.741491\pi$
$509$	−31.0419	−1.37591	−0.687953	+	0.725755i	$0.741491\pi$
$510$	4.63624	0.205296
$511$	−6.10769	−0.270188
$512$	1.00000	0.0441942
$513$	14.0289	0.619390
$514$	22.0654	0.973264
$515$	3.98792	0.175729
$516$	−3.88303	−0.170941
$517$	35.6735	1.56892
$518$	−23.8638	−1.04851
$519$	−12.4719	−0.547456
$520$	−15.7759	−0.691817
$521$	33.3116	1.45941	0.729703	−	0.683764i	$-0.239658\pi$
$521$	33.3116	1.45941	0.729703	+	0.683764i	$0.239658\pi$
$522$	−7.49648	−0.328112
$523$	31.0406	1.35731	0.678655	−	0.734457i	$-0.262563\pi$
$523$	31.0406	1.35731	0.678655	+	0.734457i	$0.262563\pi$
$524$	7.97296	0.348301
$525$	4.32925	0.188944
$526$	−7.75842	−0.338283
$527$	−5.23841	−0.228189
$528$	5.33823	0.232317
$529$	0	0
$530$	−6.02390	−0.261661
$531$	−0.639567	−0.0277548
$532$	−5.17962	−0.224565
$533$	26.5986	1.15211
$534$	7.00651	0.303201
$535$	8.66518	0.374628
$536$	12.8258	0.553992
$537$	−11.8701	−0.512233
$538$	17.0193	0.733754
$539$	−10.0802	−0.434183
$540$	−14.4006	−0.619704
$541$	−5.14103	−0.221030	−0.110515	−	0.993874i	$-0.535250\pi$
$541$	−5.14103	−0.221030	−0.110515	+	0.993874i	$0.535250\pi$
$542$	11.6475	0.500301
$543$	−0.751254	−0.0322394
$544$	1.30258	0.0558476
$545$	−21.9565	−0.940513
$546$	−18.0856	−0.773991
$547$	19.0128	0.812930	0.406465	−	0.913666i	$-0.366761\pi$
$547$	19.0128	0.812930	0.406465	+	0.913666i	$0.366761\pi$
$548$	2.06934	0.0883979
$549$	−4.22527	−0.180330
$550$	5.66382	0.241506
$551$	−17.7781	−0.757373
$552$	0	0
$553$	−3.93983	−0.167539
$554$	16.8299	0.715032
$555$	−40.6760	−1.72660
$556$	−13.0620	−0.553950
$557$	12.0728	0.511541	0.255770	−	0.966738i	$-0.417671\pi$
$557$	12.0728	0.511541	0.255770	+	0.966738i	$0.417671\pi$
$558$	4.20631	0.178067
$559$	17.2108	0.727941
$560$	5.31686	0.224678
$561$	6.95347	0.293576
$562$	−5.29050	−0.223166
$563$	−21.2359	−0.894988	−0.447494	−	0.894287i	$-0.647683\pi$
$563$	−21.2359	−0.894988	−0.447494	+	0.894287i	$0.647683\pi$
$564$	13.0583	0.549853
$565$	−9.08032	−0.382012
$566$	−15.3696	−0.646032
$567$	−9.95674	−0.418144
$568$	−6.61122	−0.277401
$569$	11.7217	0.491401	0.245700	−	0.969346i	$-0.420982\pi$
$569$	11.7217	0.491401	0.245700	+	0.969346i	$0.420982\pi$
$570$	−8.82869	−0.369793
$571$	−44.3277	−1.85506	−0.927529	−	0.373751i	$-0.878071\pi$
$571$	−44.3277	−1.85506	−0.927529	+	0.373751i	$0.878071\pi$
$572$	−23.6608	−0.989307
$573$	−37.5078	−1.56691
$574$	−8.96441	−0.374167
$575$	0	0
$576$	−1.04594	−0.0435808
$577$	29.9213	1.24564	0.622819	−	0.782366i	$-0.285987\pi$
$577$	29.9213	1.24564	0.622819	+	0.782366i	$0.285987\pi$
$578$	−15.3033	−0.636533
$579$	−1.96310	−0.0815837
$580$	18.2492	0.757756
$581$	21.8011	0.904462
$582$	17.5377	0.726961
$583$	−9.03470	−0.374179
$584$	−2.92492	−0.121034
$585$	16.5006	0.682215
$586$	−10.7552	−0.444291
$587$	10.5653	0.436077	0.218038	−	0.975940i	$-0.430034\pi$
$587$	10.5653	0.436077	0.218038	+	0.975940i	$0.430034\pi$
$588$	−3.68984	−0.152167
$589$	9.97539	0.411029
$590$	1.55694	0.0640983
$591$	−11.5251	−0.474079
$592$	−11.4282	−0.469695
$593$	8.64892	0.355169	0.177584	−	0.984106i	$-0.443172\pi$
$593$	8.64892	0.355169	0.177584	+	0.984106i	$0.443172\pi$
$594$	−21.5982	−0.886183
$595$	6.92564	0.283923
$596$	14.8452	0.608083
$597$	−4.35455	−0.178220
$598$	0	0
$599$	20.5800	0.840877	0.420439	−	0.907321i	$-0.361876\pi$
$599$	20.5800	0.840877	0.420439	+	0.907321i	$0.361876\pi$
$600$	2.07324	0.0846398
$601$	17.6734	0.720914	0.360457	−	0.932776i	$-0.382621\pi$
$601$	17.6734	0.720914	0.360457	+	0.932776i	$0.382621\pi$
$602$	−5.80049	−0.236410
$603$	−13.4151	−0.546303
$604$	3.85308	0.156780
$605$	9.12390	0.370939
$606$	4.92404	0.200025
$607$	−41.9751	−1.70372	−0.851859	−	0.523771i	$-0.824525\pi$
$607$	−41.9751	−1.70372	−0.851859	+	0.523771i	$0.824525\pi$
$608$	−2.48047	−0.100596
$609$	20.9210	0.847763
$610$	10.2859	0.416463
$611$	−57.8785	−2.34151
$612$	−1.36242	−0.0550725
$613$	17.9340	0.724348	0.362174	−	0.932110i	$-0.382035\pi$
$613$	17.9340	0.724348	0.362174	+	0.932110i	$0.382035\pi$
$614$	−25.7849	−1.04059
$615$	−15.2799	−0.616145
$616$	7.97428	0.321293
$617$	2.95899	0.119124	0.0595622	−	0.998225i	$-0.481030\pi$
$617$	2.95899	0.119124	0.0595622	+	0.998225i	$0.481030\pi$
$618$	2.18939	0.0880701
$619$	28.0180	1.12614	0.563070	−	0.826409i	$-0.309620\pi$
$619$	28.0180	1.12614	0.563070	+	0.826409i	$0.309620\pi$
$620$	−10.2397	−0.411237
$621$	0	0
$622$	16.3169	0.654247
$623$	10.4664	0.419326
$624$	−8.66103	−0.346719
$625$	−30.2160	−1.20864
$626$	12.5034	0.499735
$627$	−13.2413	−0.528809
$628$	22.6511	0.903878
$629$	−14.8861	−0.593548
$630$	−5.56111	−0.221560
$631$	−2.43747	−0.0970340	−0.0485170	−	0.998822i	$-0.515450\pi$
$631$	−2.43747	−0.0970340	−0.0485170	+	0.998822i	$0.515450\pi$
$632$	−1.88675	−0.0750510
$633$	−30.7641	−1.22276
$634$	−13.5387	−0.537691
$635$	−14.3139	−0.568028
$636$	−3.30715	−0.131137
$637$	16.3546	0.647992
$638$	27.3703	1.08360
$639$	6.91493	0.273551
$640$	2.54620	0.100647
$641$	3.20307	0.126514	0.0632569	−	0.997997i	$-0.479851\pi$
$641$	3.20307	0.126514	0.0632569	+	0.997997i	$0.479851\pi$
$642$	4.75723	0.187753
$643$	35.8609	1.41422	0.707108	−	0.707105i	$-0.249999\pi$
$643$	35.8609	1.41422	0.707108	+	0.707105i	$0.249999\pi$
$644$	0	0
$645$	−9.88697	−0.389299
$646$	−3.23101	−0.127123
$647$	9.86585	0.387866	0.193933	−	0.981015i	$-0.437875\pi$
$647$	9.86585	0.387866	0.193933	+	0.981015i	$0.437875\pi$
$648$	−4.76820	−0.187312
$649$	2.33511	0.0916613
$650$	−9.18928	−0.360433
$651$	−11.7389	−0.460083
$652$	−18.9635	−0.742667
$653$	−12.7863	−0.500367	−0.250183	−	0.968198i	$-0.580491\pi$
$653$	−12.7863	−0.500367	−0.250183	+	0.968198i	$0.580491\pi$
$654$	−12.0542	−0.471358
$655$	20.3008	0.793216
$656$	−4.29298	−0.167613
$657$	3.05929	0.119354
$658$	19.5065	0.760443
$659$	−5.10798	−0.198979	−0.0994893	−	0.995039i	$-0.531721\pi$
$659$	−5.10798	−0.198979	−0.0994893	+	0.995039i	$0.531721\pi$
$660$	13.5922	0.529076
$661$	−26.9524	−1.04833	−0.524163	−	0.851618i	$-0.675622\pi$
$661$	−26.9524	−1.04833	−0.524163	+	0.851618i	$0.675622\pi$
$662$	28.3332	1.10120
$663$	−11.2817	−0.438144
$664$	10.4404	0.405165
$665$	−13.1883	−0.511422
$666$	11.9532	0.463176
$667$	0	0
$668$	−0.979634	−0.0379032
$669$	17.2075	0.665281
$670$	32.6572	1.26166
$671$	15.4268	0.595547
$672$	2.91899	0.112602
$673$	27.1196	1.04538	0.522691	−	0.852522i	$-0.324928\pi$
$673$	27.1196	1.04538	0.522691	+	0.852522i	$0.324928\pi$
$674$	−14.4856	−0.557965
$675$	−8.38821	−0.322862
$676$	25.3885	0.976480
$677$	28.2117	1.08426	0.542132	−	0.840294i	$-0.317617\pi$
$677$	28.2117	1.08426	0.542132	+	0.840294i	$0.317617\pi$
$678$	−4.98514	−0.191453
$679$	26.1979	1.00538
$680$	3.31663	0.127187
$681$	7.45417	0.285645
$682$	−15.3576	−0.588073
$683$	−2.26699	−0.0867439	−0.0433720	−	0.999059i	$-0.513810\pi$
$683$	−2.26699	−0.0867439	−0.0433720	+	0.999059i	$0.513810\pi$
$684$	2.59442	0.0992003
$685$	5.26896	0.201317
$686$	−20.1290	−0.768529
$687$	19.7198	0.752359
$688$	−2.77780	−0.105903
$689$	14.6584	0.558439
$690$	0	0
$691$	2.62969	0.100038	0.0500191	−	0.998748i	$-0.484072\pi$
$691$	2.62969	0.100038	0.0500191	+	0.998748i	$0.484072\pi$
$692$	−8.92203	−0.339165
$693$	−8.34061	−0.316833
$694$	32.9050	1.24906
$695$	−33.2584	−1.26156
$696$	10.0189	0.379766
$697$	−5.59195	−0.211810
$698$	−11.3601	−0.429985
$699$	24.0194	0.908498
$700$	3.09702	0.117056
$701$	−17.2208	−0.650422	−0.325211	−	0.945641i	$-0.605435\pi$
$701$	−17.2208	−0.650422	−0.325211	+	0.945641i	$0.605435\pi$
$702$	35.0420	1.32258
$703$	28.3473	1.06914
$704$	3.81881	0.143927
$705$	33.2490	1.25223
$706$	1.50436	0.0566172
$707$	7.35555	0.276634
$708$	0.854769	0.0321242
$709$	36.1353	1.35709	0.678544	−	0.734559i	$-0.262611\pi$
$709$	36.1353	1.35709	0.678544	+	0.734559i	$0.262611\pi$
$710$	−16.8335	−0.631750
$711$	1.97343	0.0740093
$712$	5.01225	0.187842
$713$	0	0
$714$	3.80221	0.142294
$715$	−60.2451	−2.25304
$716$	−8.49152	−0.317343
$717$	−7.88461	−0.294456
$718$	20.3544	0.759618
$719$	28.0142	1.04476	0.522378	−	0.852714i	$-0.325045\pi$
$719$	28.0142	1.04476	0.522378	+	0.852714i	$0.325045\pi$
$720$	−2.66317	−0.0992505
$721$	3.27052	0.121800
$722$	−12.8472	−0.478125
$723$	−7.04206	−0.261897
$724$	−0.537425	−0.0199732
$725$	10.6300	0.394787
$726$	5.00907	0.185904
$727$	48.6681	1.80500	0.902501	−	0.430688i	$-0.141729\pi$
$727$	48.6681	1.80500	0.902501	+	0.430688i	$0.141729\pi$
$728$	−12.9379	−0.479510
$729$	28.7053	1.06316
$730$	−7.44743	−0.275642
$731$	−3.61831	−0.133828
$732$	5.64700	0.208719
$733$	−3.42952	−0.126672	−0.0633362	−	0.997992i	$-0.520174\pi$
$733$	−3.42952	−0.126672	−0.0633362	+	0.997992i	$0.520174\pi$
$734$	−12.2425	−0.451877
$735$	−9.39508	−0.346543
$736$	0	0
$737$	48.9795	1.80418
$738$	4.49019	0.165286
$739$	−12.1486	−0.446894	−0.223447	−	0.974716i	$-0.571731\pi$
$739$	−12.1486	−0.446894	−0.223447	+	0.974716i	$0.571731\pi$
$740$	−29.0984	−1.06968
$741$	21.4835	0.789215
$742$	−4.94024	−0.181362
$743$	−44.9522	−1.64914	−0.824568	−	0.565763i	$-0.808582\pi$
$743$	−44.9522	−1.64914	−0.824568	+	0.565763i	$0.808582\pi$
$744$	−5.62165	−0.206100
$745$	37.7989	1.38484
$746$	16.4239	0.601322
$747$	−10.9200	−0.399541
$748$	4.97431	0.181879
$749$	7.10637	0.259661
$750$	−12.5175	−0.457074
$751$	6.17883	0.225469	0.112734	−	0.993625i	$-0.464039\pi$
$751$	6.17883	0.225469	0.112734	+	0.993625i	$0.464039\pi$
$752$	9.34150	0.340650
$753$	−24.7161	−0.900703
$754$	−44.4070	−1.61721
$755$	9.81071	0.357048
$756$	−11.8100	−0.429527
$757$	13.7458	0.499599	0.249799	−	0.968298i	$-0.419635\pi$
$757$	13.7458	0.499599	0.249799	+	0.968298i	$0.419635\pi$
$758$	−25.7579	−0.935569
$759$	0	0
$760$	−6.31578	−0.229098
$761$	−51.1112	−1.85278	−0.926390	−	0.376566i	$-0.877105\pi$
$761$	−51.1112	−1.85278	−0.926390	+	0.376566i	$0.877105\pi$
$762$	−7.85838	−0.284679
$763$	−18.0067	−0.651885
$764$	−26.8320	−0.970747
$765$	−3.46899	−0.125422
$766$	−15.0901	−0.545229
$767$	−3.78861	−0.136799
$768$	1.39788	0.0504416
$769$	15.6086	0.562861	0.281430	−	0.959582i	$-0.409191\pi$
$769$	15.6086	0.562861	0.281430	+	0.959582i	$0.409191\pi$
$770$	20.3041	0.731709
$771$	30.8448	1.11085
$772$	−1.40434	−0.0505434
$773$	−2.63936	−0.0949310	−0.0474655	−	0.998873i	$-0.515114\pi$
$773$	−2.63936	−0.0949310	−0.0474655	+	0.998873i	$0.515114\pi$
$774$	2.90541	0.104433
$775$	−5.96453	−0.214252
$776$	12.5459	0.450373
$777$	−33.3587	−1.19674
$778$	22.9846	0.824040
$779$	10.6486	0.381527
$780$	−22.0527	−0.789614
$781$	−25.2470	−0.903409
$782$	0	0
$783$	−40.5359	−1.44863
$784$	−2.63960	−0.0942716
$785$	57.6743	2.05848
$786$	11.1452	0.397537
$787$	36.5824	1.30402	0.652011	−	0.758210i	$-0.273926\pi$
$787$	36.5824	1.30402	0.652011	+	0.758210i	$0.273926\pi$
$788$	−8.24471	−0.293706
$789$	−10.8453	−0.386104
$790$	−4.80405	−0.170920
$791$	−7.44683	−0.264779
$792$	−3.99425	−0.141929
$793$	−25.0293	−0.888817
$794$	−29.6670	−1.05284
$795$	−8.42067	−0.298650
$796$	−3.11512	−0.110412
$797$	−19.6922	−0.697534	−0.348767	−	0.937210i	$-0.613400\pi$
$797$	−19.6922	−0.697534	−0.348767	+	0.937210i	$0.613400\pi$
$798$	−7.24047	−0.256310
$799$	12.1681	0.430475
$800$	1.48314	0.0524368
$801$	−5.24251	−0.185235
$802$	29.2330	1.03225
$803$	−11.1697	−0.394171
$804$	17.9290	0.632306
$805$	0	0
$806$	24.9170	0.877664
$807$	23.7909	0.837478
$808$	3.52251	0.123922
$809$	−13.5968	−0.478038	−0.239019	−	0.971015i	$-0.576826\pi$
$809$	−13.5968	−0.478038	−0.239019	+	0.971015i	$0.576826\pi$
$810$	−12.1408	−0.426584
$811$	−22.6677	−0.795970	−0.397985	−	0.917392i	$-0.630290\pi$
$811$	−22.6677	−0.795970	−0.397985	+	0.917392i	$0.630290\pi$
$812$	14.9663	0.525214
$813$	16.2817	0.571025
$814$	−43.6420	−1.52965
$815$	−48.2848	−1.69134
$816$	1.82085	0.0637424
$817$	6.89027	0.241060
$818$	33.6998	1.17829
$819$	13.5322	0.472855
$820$	−10.9308	−0.381720
$821$	−16.4984	−0.575799	−0.287900	−	0.957661i	$-0.592957\pi$
$821$	−16.4984	−0.575799	−0.287900	+	0.957661i	$0.592957\pi$
$822$	2.89269	0.100894
$823$	−30.5690	−1.06557	−0.532785	−	0.846251i	$-0.678854\pi$
$823$	−30.5690	−1.06557	−0.532785	+	0.846251i	$0.678854\pi$
$824$	1.56622	0.0545620
$825$	7.91733	0.275646
$826$	1.27686	0.0444276
$827$	24.1171	0.838633	0.419316	−	0.907840i	$-0.362270\pi$
$827$	24.1171	0.838633	0.419316	+	0.907840i	$0.362270\pi$
$828$	0	0
$829$	−11.3407	−0.393879	−0.196939	−	0.980416i	$-0.563100\pi$
$829$	−11.3407	−0.393879	−0.196939	+	0.980416i	$0.563100\pi$
$830$	26.5833	0.922718
$831$	23.5261	0.816111
$832$	−6.19584	−0.214802
$833$	−3.43830	−0.119130
$834$	−18.2590	−0.632258
$835$	−2.49434	−0.0863203
$836$	−9.47247	−0.327612
$837$	22.7449	0.786178
$838$	8.82612	0.304893
$839$	−18.8321	−0.650157	−0.325079	−	0.945687i	$-0.605391\pi$
$839$	−18.8321	−0.650157	−0.325079	+	0.945687i	$0.605391\pi$
$840$	7.43232	0.256440
$841$	22.3691	0.771349
$842$	27.3740	0.943370
$843$	−7.39547	−0.254713
$844$	−22.0077	−0.757538
$845$	64.6442	2.22383
$846$	−9.77064	−0.335922
$847$	7.48257	0.257104
$848$	−2.36584	−0.0812432
$849$	−21.4848	−0.737357
$850$	1.93190	0.0662637
$851$	0	0
$852$	−9.24168	−0.316615
$853$	2.46467	0.0843887	0.0421943	−	0.999109i	$-0.486565\pi$
$853$	2.46467	0.0843887	0.0421943	+	0.999109i	$0.486565\pi$
$854$	8.43551	0.288657
$855$	6.60592	0.225918
$856$	3.40318	0.116318
$857$	−15.2700	−0.521614	−0.260807	−	0.965391i	$-0.583989\pi$
$857$	−15.2700	−0.521614	−0.260807	+	0.965391i	$0.583989\pi$
$858$	−33.0749	−1.12916
$859$	−3.96389	−0.135246	−0.0676231	−	0.997711i	$-0.521542\pi$
$859$	−3.96389	−0.135246	−0.0676231	+	0.997711i	$0.521542\pi$
$860$	−7.07285	−0.241182
$861$	−12.5311	−0.427060
$862$	−29.8688	−1.01734
$863$	7.20518	0.245267	0.122634	−	0.992452i	$-0.460866\pi$
$863$	7.20518	0.245267	0.122634	+	0.992452i	$0.460866\pi$
$864$	−5.65573	−0.192412
$865$	−22.7173	−0.772411
$866$	27.3484	0.929335
$867$	−21.3921	−0.726514
$868$	−8.39765	−0.285035
$869$	−7.20516	−0.244418
$870$	25.5101	0.864875
$871$	−79.4670	−2.69264
$872$	−8.62324	−0.292020
$873$	−13.1223	−0.444122
$874$	0	0
$875$	−18.6987	−0.632131
$876$	−4.08868	−0.138144
$877$	−46.6196	−1.57423	−0.787116	−	0.616805i	$-0.788427\pi$
$877$	−46.6196	−1.57423	−0.787116	+	0.616805i	$0.788427\pi$
$878$	−13.1196	−0.442765
$879$	−15.0344	−0.507097
$880$	9.72346	0.327778
$881$	1.12202	0.0378019	0.0189009	−	0.999821i	$-0.493983\pi$
$881$	1.12202	0.0378019	0.0189009	+	0.999821i	$0.493983\pi$
$882$	2.76087	0.0929632
$883$	−2.12015	−0.0713488	−0.0356744	−	0.999363i	$-0.511358\pi$
$883$	−2.12015	−0.0713488	−0.0356744	+	0.999363i	$0.511358\pi$
$884$	−8.07058	−0.271443
$885$	2.17641	0.0731593
$886$	−10.7702	−0.361831
$887$	15.6021	0.523869	0.261934	−	0.965086i	$-0.415640\pi$
$887$	15.6021	0.523869	0.261934	+	0.965086i	$0.415640\pi$
$888$	−15.9752	−0.536092
$889$	−11.7389	−0.393710
$890$	12.7622	0.427790
$891$	−18.2089	−0.610019
$892$	12.3097	0.412161
$893$	−23.1714	−0.775400
$894$	20.7518	0.694043
$895$	−21.6211	−0.722714
$896$	2.08816	0.0697604
$897$	0	0
$898$	4.69291	0.156605
$899$	−28.8235	−0.961316
$900$	−1.55127	−0.0517090
$901$	−3.08169	−0.102666
$902$	−16.3941	−0.545863
$903$	−8.10837	−0.269830
$904$	−3.56622	−0.118611
$905$	−1.36839	−0.0454869
$906$	5.38613	0.178942
$907$	−30.4920	−1.01247	−0.506235	−	0.862395i	$-0.668963\pi$
$907$	−30.4920	−1.01247	−0.506235	+	0.862395i	$0.668963\pi$
$908$	5.33249	0.176965
$909$	−3.68433	−0.122202
$910$	−32.9425	−1.09203
$911$	−35.8245	−1.18692	−0.593460	−	0.804864i	$-0.702238\pi$
$911$	−35.8245	−1.18692	−0.593460	+	0.804864i	$0.702238\pi$
$912$	−3.46740	−0.114817
$913$	39.8698	1.31950
$914$	6.93568	0.229412
$915$	14.3784	0.475335
$916$	14.1070	0.466108
$917$	16.6488	0.549792
$918$	−7.36703	−0.243148
$919$	29.8477	0.984585	0.492292	−	0.870430i	$-0.336159\pi$
$919$	29.8477	0.984585	0.492292	+	0.870430i	$0.336159\pi$
$920$	0	0
$921$	−36.0441	−1.18769
$922$	−21.3273	−0.702378
$923$	40.9621	1.34828
$924$	11.1471	0.366711
$925$	−16.9495	−0.557297
$926$	−6.41490	−0.210807
$927$	−1.63817	−0.0538047
$928$	7.16723	0.235276
$929$	−39.7085	−1.30279	−0.651397	−	0.758737i	$-0.725817\pi$
$929$	−39.7085	−1.30279	−0.651397	+	0.758737i	$0.725817\pi$
$930$	−14.3139	−0.469370
$931$	6.54747	0.214585
$932$	17.1828	0.562841
$933$	22.8090	0.746732
$934$	14.4723	0.473547
$935$	12.6656	0.414209
$936$	6.48047	0.211821
$937$	20.8680	0.681728	0.340864	−	0.940113i	$-0.389280\pi$
$937$	20.8680	0.681728	0.340864	+	0.940113i	$0.389280\pi$
$938$	26.7824	0.874475
$939$	17.4782	0.570378
$940$	23.7853	0.775792
$941$	−35.1554	−1.14603	−0.573017	−	0.819543i	$-0.694227\pi$
$941$	−35.1554	−1.14603	−0.573017	+	0.819543i	$0.694227\pi$
$942$	31.6635	1.03165
$943$	0	0
$944$	0.611476	0.0199019
$945$	−30.0707	−0.978201
$946$	−10.6079	−0.344893
$947$	28.6519	0.931062	0.465531	−	0.885032i	$-0.345863\pi$
$947$	28.6519	0.931062	0.465531	+	0.885032i	$0.345863\pi$
$948$	−2.63745	−0.0856603
$949$	18.1223	0.588276
$950$	−3.67888	−0.119359
$951$	−18.9255	−0.613700
$952$	2.71999	0.0881554
$953$	−19.5950	−0.634745	−0.317373	−	0.948301i	$-0.602801\pi$
$953$	−19.5950	−0.634745	−0.317373	+	0.948301i	$0.602801\pi$
$954$	2.47452	0.0801156
$955$	−68.3196	−2.21077
$956$	−5.64042	−0.182424
$957$	38.2603	1.23678
$958$	−5.37524	−0.173666
$959$	4.32111	0.139536
$960$	3.55928	0.114875
$961$	−14.8270	−0.478291
$962$	70.8071	2.28291
$963$	−3.55952	−0.114704
$964$	−5.03768	−0.162253
$965$	−3.57574	−0.115107
$966$	0	0
$967$	−45.4032	−1.46007	−0.730035	−	0.683410i	$-0.760496\pi$
$967$	−45.4032	−1.46007	−0.730035	+	0.683410i	$0.760496\pi$
$968$	3.58334	0.115173
$969$	−4.51656	−0.145093
$970$	31.9445	1.02568
$971$	38.4219	1.23302	0.616509	−	0.787348i	$-0.288547\pi$
$971$	38.4219	1.23302	0.616509	+	0.787348i	$0.288547\pi$
$972$	10.3018	0.330431
$973$	−27.2754	−0.874409
$974$	3.21931	0.103153
$975$	−12.8455	−0.411385
$976$	4.03969	0.129307
$977$	−1.16775	−0.0373596	−0.0186798	−	0.999826i	$-0.505946\pi$
$977$	−1.16775	−0.0373596	−0.0186798	+	0.999826i	$0.505946\pi$
$978$	−26.5086	−0.847652
$979$	19.1409	0.611744
$980$	−6.72096	−0.214693
$981$	9.01938	0.287967
$982$	30.0754	0.959744
$983$	−55.6335	−1.77443	−0.887216	−	0.461355i	$-0.847364\pi$
$983$	−55.6335	−1.77443	−0.887216	+	0.461355i	$0.847364\pi$
$984$	−6.00106	−0.191307
$985$	−20.9927	−0.668883
$986$	9.33588	0.297315
$987$	27.2677	0.867941
$988$	15.3686	0.488941
$989$	0	0
$990$	−10.1701	−0.323229
$991$	29.3329	0.931792	0.465896	−	0.884840i	$-0.345732\pi$
$991$	29.3329	0.931792	0.465896	+	0.884840i	$0.345732\pi$
$992$	−4.02157	−0.127685
$993$	39.6064	1.25687
$994$	−13.8053	−0.437876
$995$	−7.93171	−0.251452
$996$	14.5943	0.462440
$997$	22.8243	0.722852	0.361426	−	0.932401i	$-0.382290\pi$
$997$	22.8243	0.722852	0.361426	+	0.932401i	$0.382290\pi$
$998$	17.7485	0.561819
$999$	64.6346	2.04495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1058.2.a.m.1.5		5
3.2	odd	2		9522.2.a.bp.1.2		5
4.3	odd	2		8464.2.a.bx.1.1		5
23.13	even	11		46.2.c.a.31.1	yes	10
23.16	even	11		46.2.c.a.3.1	✓	10
23.22	odd	2		1058.2.a.l.1.5		5
69.59	odd	22		414.2.i.f.307.1		10
69.62	odd	22		414.2.i.f.325.1		10
69.68	even	2		9522.2.a.bu.1.4		5
92.39	odd	22		368.2.m.b.49.1		10
92.59	odd	22		368.2.m.b.353.1		10
92.91	even	2		8464.2.a.bw.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.2.c.a.3.1	✓	10	23.16	even	11
46.2.c.a.31.1	yes	10	23.13	even	11
368.2.m.b.49.1		10	92.39	odd	22
368.2.m.b.353.1		10	92.59	odd	22
414.2.i.f.307.1		10	69.59	odd	22
414.2.i.f.325.1		10	69.62	odd	22
1058.2.a.l.1.5		5	23.22	odd	2
1058.2.a.m.1.5		5	1.1	even	1	trivial
8464.2.a.bw.1.1		5	92.91	even	2
8464.2.a.bx.1.1		5	4.3	odd	2
9522.2.a.bp.1.2		5	3.2	odd	2
9522.2.a.bu.1.4		5	69.68	even	2

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:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1058.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.39788 q^{3} +1.00000 q^{4} +2.54620 q^{5} +1.39788 q^{6} +2.08816 q^{7} +1.00000 q^{8} -1.04594 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.39788 q^{3} +1.00000 q^{4} +2.54620 q^{5} +1.39788 q^{6} +2.08816 q^{7} +1.00000 q^{8} -1.04594 q^{9} +2.54620 q^{10} +3.81881 q^{11} +1.39788 q^{12} -6.19584 q^{13} +2.08816 q^{14} +3.55928 q^{15} +1.00000 q^{16} +1.30258 q^{17} -1.04594 q^{18} -2.48047 q^{19} +2.54620 q^{20} +2.91899 q^{21} +3.81881 q^{22} +1.39788 q^{24} +1.48314 q^{25} -6.19584 q^{26} -5.65573 q^{27} +2.08816 q^{28} +7.16723 q^{29} +3.55928 q^{30} -4.02157 q^{31} +1.00000 q^{32} +5.33823 q^{33} +1.30258 q^{34} +5.31686 q^{35} -1.04594 q^{36} -11.4282 q^{37} -2.48047 q^{38} -8.66103 q^{39} +2.54620 q^{40} -4.29298 q^{41} +2.91899 q^{42} -2.77780 q^{43} +3.81881 q^{44} -2.66317 q^{45} +9.34150 q^{47} +1.39788 q^{48} -2.63960 q^{49} +1.48314 q^{50} +1.82085 q^{51} -6.19584 q^{52} -2.36584 q^{53} -5.65573 q^{54} +9.72346 q^{55} +2.08816 q^{56} -3.46740 q^{57} +7.16723 q^{58} +0.611476 q^{59} +3.55928 q^{60} +4.03969 q^{61} -4.02157 q^{62} -2.18408 q^{63} +1.00000 q^{64} -15.7759 q^{65} +5.33823 q^{66} +12.8258 q^{67} +1.30258 q^{68} +5.31686 q^{70} -6.61122 q^{71} -1.04594 q^{72} -2.92492 q^{73} -11.4282 q^{74} +2.07324 q^{75} -2.48047 q^{76} +7.97428 q^{77} -8.66103 q^{78} -1.88675 q^{79} +2.54620 q^{80} -4.76820 q^{81} -4.29298 q^{82} +10.4404 q^{83} +2.91899 q^{84} +3.31663 q^{85} -2.77780 q^{86} +10.0189 q^{87} +3.81881 q^{88} +5.01225 q^{89} -2.66317 q^{90} -12.9379 q^{91} -5.62165 q^{93} +9.34150 q^{94} -6.31578 q^{95} +1.39788 q^{96} +12.5459 q^{97} -2.63960 q^{98} -3.99425 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} - 2 q^{3} + 5 q^{4} + 8 q^{5} - 2 q^{6} + 7 q^{7} + 5 q^{8} - q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 - 2 * q^3 + 5 * q^4 + 8 * q^5 - 2 * q^6 + 7 * q^7 + 5 * q^8 - q^9	\( 5 q + 5 q^{2} - 2 q^{3} + 5 q^{4} + 8 q^{5} - 2 q^{6} + 7 q^{7} + 5 q^{8} - q^{9} + 8 q^{10} + 5 q^{11} - 2 q^{12} - 7 q^{13} + 7 q^{14} - q^{15} + 5 q^{16} + 13 q^{17} - q^{18} + 12 q^{19} + 8 q^{20} + 6 q^{21} + 5 q^{22} - 2 q^{24} + q^{25} - 7 q^{26} - 20 q^{27} + 7 q^{28} - 4 q^{29} - q^{30} + 6 q^{31} + 5 q^{32} + 9 q^{33} + 13 q^{34} + 9 q^{35} - q^{36} + 14 q^{37} + 12 q^{38} - 6 q^{39} + 8 q^{40} + q^{41} + 6 q^{42} + 11 q^{43} + 5 q^{44} + 5 q^{45} + 9 q^{47} - 2 q^{48} - 12 q^{49} + q^{50} - 14 q^{51} - 7 q^{52} + 6 q^{53} - 20 q^{54} - 14 q^{55} + 7 q^{56} - 7 q^{57} - 4 q^{58} + 3 q^{59} - q^{60} + 13 q^{61} + 6 q^{62} - 19 q^{63} + 5 q^{64} - 9 q^{65} + 9 q^{66} + 10 q^{67} + 13 q^{68} + 9 q^{70} + 8 q^{71} - q^{72} - 4 q^{73} + 14 q^{74} + 4 q^{75} + 12 q^{76} + 18 q^{77} - 6 q^{78} - 18 q^{79} + 8 q^{80} + 33 q^{81} + q^{82} + 2 q^{83} + 6 q^{84} + 23 q^{85} + 11 q^{86} + 6 q^{87} + 5 q^{88} + 10 q^{89} + 5 q^{90} - 12 q^{91} - 20 q^{93} + 9 q^{94} + 28 q^{95} - 2 q^{96} + 17 q^{97} - 12 q^{98} - 34 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 - 2 * q^3 + 5 * q^4 + 8 * q^5 - 2 * q^6 + 7 * q^7 + 5 * q^8 - q^9 + 8 * q^10 + 5 * q^11 - 2 * q^12 - 7 * q^13 + 7 * q^14 - q^15 + 5 * q^16 + 13 * q^17 - q^18 + 12 * q^19 + 8 * q^20 + 6 * q^21 + 5 * q^22 - 2 * q^24 + q^25 - 7 * q^26 - 20 * q^27 + 7 * q^28 - 4 * q^29 - q^30 + 6 * q^31 + 5 * q^32 + 9 * q^33 + 13 * q^34 + 9 * q^35 - q^36 + 14 * q^37 + 12 * q^38 - 6 * q^39 + 8 * q^40 + q^41 + 6 * q^42 + 11 * q^43 + 5 * q^44 + 5 * q^45 + 9 * q^47 - 2 * q^48 - 12 * q^49 + q^50 - 14 * q^51 - 7 * q^52 + 6 * q^53 - 20 * q^54 - 14 * q^55 + 7 * q^56 - 7 * q^57 - 4 * q^58 + 3 * q^59 - q^60 + 13 * q^61 + 6 * q^62 - 19 * q^63 + 5 * q^64 - 9 * q^65 + 9 * q^66 + 10 * q^67 + 13 * q^68 + 9 * q^70 + 8 * q^71 - q^72 - 4 * q^73 + 14 * q^74 + 4 * q^75 + 12 * q^76 + 18 * q^77 - 6 * q^78 - 18 * q^79 + 8 * q^80 + 33 * q^81 + q^82 + 2 * q^83 + 6 * q^84 + 23 * q^85 + 11 * q^86 + 6 * q^87 + 5 * q^88 + 10 * q^89 + 5 * q^90 - 12 * q^91 - 20 * q^93 + 9 * q^94 + 28 * q^95 - 2 * q^96 + 17 * q^97 - 12 * q^98 - 34 * q^99

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