LMFDB - Embedded newform 6041.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$132$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22730 q^{2} +1.19588 q^{3} +2.96085 q^{4} +2.18062 q^{5} -2.66358 q^{6} +1.00000 q^{7} -2.14009 q^{8} -1.56986 q^{9} +O(q^{10})$	\(q-2.22730 q^{2} +1.19588 q^{3} +2.96085 q^{4} +2.18062 q^{5} -2.66358 q^{6} +1.00000 q^{7} -2.14009 q^{8} -1.56986 q^{9} -4.85688 q^{10} -5.84643 q^{11} +3.54083 q^{12} -4.49009 q^{13} -2.22730 q^{14} +2.60776 q^{15} -1.15508 q^{16} +4.28348 q^{17} +3.49655 q^{18} +2.48108 q^{19} +6.45647 q^{20} +1.19588 q^{21} +13.0217 q^{22} -2.32428 q^{23} -2.55930 q^{24} -0.244915 q^{25} +10.0008 q^{26} -5.46502 q^{27} +2.96085 q^{28} +5.18312 q^{29} -5.80826 q^{30} -7.27372 q^{31} +6.85288 q^{32} -6.99164 q^{33} -9.54057 q^{34} +2.18062 q^{35} -4.64813 q^{36} +4.26264 q^{37} -5.52609 q^{38} -5.36962 q^{39} -4.66672 q^{40} +1.15584 q^{41} -2.66358 q^{42} +12.7528 q^{43} -17.3104 q^{44} -3.42327 q^{45} +5.17687 q^{46} +1.87446 q^{47} -1.38134 q^{48} +1.00000 q^{49} +0.545499 q^{50} +5.12254 q^{51} -13.2945 q^{52} +8.62506 q^{53} +12.1722 q^{54} -12.7488 q^{55} -2.14009 q^{56} +2.96708 q^{57} -11.5443 q^{58} +3.08648 q^{59} +7.72118 q^{60} -6.77092 q^{61} +16.2007 q^{62} -1.56986 q^{63} -12.9532 q^{64} -9.79116 q^{65} +15.5725 q^{66} -5.38241 q^{67} +12.6827 q^{68} -2.77957 q^{69} -4.85688 q^{70} -3.33010 q^{71} +3.35965 q^{72} -2.43851 q^{73} -9.49416 q^{74} -0.292890 q^{75} +7.34609 q^{76} -5.84643 q^{77} +11.9597 q^{78} +7.22282 q^{79} -2.51878 q^{80} -1.82593 q^{81} -2.57439 q^{82} -9.50584 q^{83} +3.54083 q^{84} +9.34062 q^{85} -28.4042 q^{86} +6.19840 q^{87} +12.5119 q^{88} -5.53939 q^{89} +7.62464 q^{90} -4.49009 q^{91} -6.88185 q^{92} -8.69851 q^{93} -4.17497 q^{94} +5.41027 q^{95} +8.19524 q^{96} -0.269867 q^{97} -2.22730 q^{98} +9.17809 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) $ 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * 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 $

$2$	−2.22730	−1.57494	−0.787468	−	0.616355i	$-0.788608\pi$
$2$	−2.22730	−1.57494	−0.787468	+	0.616355i	$0.788608\pi$
$3$	1.19588	0.690443	0.345222	−	0.938521i	$-0.387804\pi$
$3$	1.19588	0.690443	0.345222	+	0.938521i	$0.387804\pi$
$4$	2.96085	1.48042
$5$	2.18062	0.975201	0.487600	−	0.873067i	$-0.337872\pi$
$5$	2.18062	0.975201	0.487600	+	0.873067i	$0.337872\pi$
$6$	−2.66358	−1.08740
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.14009	−0.756637
$9$	−1.56986	−0.523288
$10$	−4.85688	−1.53588
$11$	−5.84643	−1.76276	−0.881382	−	0.472405i	$-0.843386\pi$
$11$	−5.84643	−1.76276	−0.881382	+	0.472405i	$0.843386\pi$
$12$	3.54083	1.02215
$13$	−4.49009	−1.24533	−0.622663	−	0.782490i	$-0.713949\pi$
$13$	−4.49009	−1.24533	−0.622663	+	0.782490i	$0.713949\pi$
$14$	−2.22730	−0.595270
$15$	2.60776	0.673321
$16$	−1.15508	−0.288769
$17$	4.28348	1.03890	0.519448	−	0.854502i	$-0.326138\pi$
$17$	4.28348	1.03890	0.519448	+	0.854502i	$0.326138\pi$
$18$	3.49655	0.824145
$19$	2.48108	0.569198	0.284599	−	0.958647i	$-0.408140\pi$
$19$	2.48108	0.569198	0.284599	+	0.958647i	$0.408140\pi$
$20$	6.45647	1.44371
$21$	1.19588	0.260963
$22$	13.0217	2.77624
$23$	−2.32428	−0.484646	−0.242323	−	0.970196i	$-0.577909\pi$
$23$	−2.32428	−0.484646	−0.242323	+	0.970196i	$0.577909\pi$
$24$	−2.55930	−0.522415
$25$	−0.244915	−0.0489831
$26$	10.0008	1.96131
$27$	−5.46502	−1.05174
$28$	2.96085	0.559548
$29$	5.18312	0.962481	0.481240	−	0.876589i	$-0.340186\pi$
$29$	5.18312	0.962481	0.481240	+	0.876589i	$0.340186\pi$
$30$	−5.80826	−1.06044
$31$	−7.27372	−1.30640	−0.653199	−	0.757186i	$-0.726573\pi$
$31$	−7.27372	−1.30640	−0.653199	+	0.757186i	$0.726573\pi$
$32$	6.85288	1.21143
$33$	−6.99164	−1.21709
$34$	−9.54057	−1.63619
$35$	2.18062	0.368591
$36$	−4.64813	−0.774688
$37$	4.26264	0.700773	0.350387	−	0.936605i	$-0.386050\pi$
$37$	4.26264	0.700773	0.350387	+	0.936605i	$0.386050\pi$
$38$	−5.52609	−0.896450
$39$	−5.36962	−0.859827
$40$	−4.66672	−0.737873
$41$	1.15584	0.180511	0.0902556	−	0.995919i	$-0.471232\pi$
$41$	1.15584	0.180511	0.0902556	+	0.995919i	$0.471232\pi$
$42$	−2.66358	−0.411000
$43$	12.7528	1.94478	0.972388	−	0.233369i	$-0.0749750\pi$
$43$	12.7528	1.94478	0.972388	+	0.233369i	$0.0749750\pi$
$44$	−17.3104	−2.60964
$45$	−3.42327	−0.510311
$46$	5.17687	0.763287
$47$	1.87446	0.273418	0.136709	−	0.990611i	$-0.456348\pi$
$47$	1.87446	0.273418	0.136709	+	0.990611i	$0.456348\pi$
$48$	−1.38134	−0.199379
$49$	1.00000	0.142857
$50$	0.545499	0.0771452
$51$	5.12254	0.717299
$52$	−13.2945	−1.84361
$53$	8.62506	1.18474	0.592372	−	0.805665i	$-0.298192\pi$
$53$	8.62506	1.18474	0.592372	+	0.805665i	$0.298192\pi$
$54$	12.1722	1.65643
$55$	−12.7488	−1.71905
$56$	−2.14009	−0.285982
$57$	2.96708	0.392999
$58$	−11.5443	−1.51585
$59$	3.08648	0.401825	0.200913	−	0.979609i	$-0.435609\pi$
$59$	3.08648	0.401825	0.200913	+	0.979609i	$0.435609\pi$
$60$	7.72118	0.996800
$61$	−6.77092	−0.866928	−0.433464	−	0.901171i	$-0.642709\pi$
$61$	−6.77092	−0.866928	−0.433464	+	0.901171i	$0.642709\pi$
$62$	16.2007	2.05749
$63$	−1.56986	−0.197784
$64$	−12.9532	−1.61916
$65$	−9.79116	−1.21444
$66$	15.5725	1.91684
$67$	−5.38241	−0.657566	−0.328783	−	0.944406i	$-0.606638\pi$
$67$	−5.38241	−0.657566	−0.328783	+	0.944406i	$0.606638\pi$
$68$	12.6827	1.53801
$69$	−2.77957	−0.334621
$70$	−4.85688	−0.580508
$71$	−3.33010	−0.395210	−0.197605	−	0.980282i	$-0.563316\pi$
$71$	−3.33010	−0.395210	−0.197605	+	0.980282i	$0.563316\pi$
$72$	3.35965	0.395939
$73$	−2.43851	−0.285406	−0.142703	−	0.989766i	$-0.545579\pi$
$73$	−2.43851	−0.285406	−0.142703	+	0.989766i	$0.545579\pi$
$74$	−9.49416	−1.10367
$75$	−0.292890	−0.0338200
$76$	7.34609	0.842654
$77$	−5.84643	−0.666262
$78$	11.9597	1.35417
$79$	7.22282	0.812630	0.406315	−	0.913733i	$-0.366814\pi$
$79$	7.22282	0.812630	0.406315	+	0.913733i	$0.366814\pi$
$80$	−2.51878	−0.281608
$81$	−1.82593	−0.202881
$82$	−2.57439	−0.284294
$83$	−9.50584	−1.04340	−0.521701	−	0.853128i	$-0.674702\pi$
$83$	−9.50584	−1.04340	−0.521701	+	0.853128i	$0.674702\pi$
$84$	3.54083	0.386336
$85$	9.34062	1.01313
$86$	−28.4042	−3.06290
$87$	6.19840	0.664538
$88$	12.5119	1.33377
$89$	−5.53939	−0.587174	−0.293587	−	0.955932i	$-0.594849\pi$
$89$	−5.53939	−0.587174	−0.293587	+	0.955932i	$0.594849\pi$
$90$	7.62464	0.803707
$91$	−4.49009	−0.470689
$92$	−6.88185	−0.717482
$93$	−8.69851	−0.901994
$94$	−4.17497	−0.430615
$95$	5.41027	0.555082
$96$	8.19524	0.836424
$97$	−0.269867	−0.0274008	−0.0137004	−	0.999906i	$-0.504361\pi$
$97$	−0.269867	−0.0274008	−0.0137004	+	0.999906i	$0.504361\pi$
$98$	−2.22730	−0.224991
$99$	9.17809	0.922433
$100$	−0.725157	−0.0725157
$101$	−13.0109	−1.29463	−0.647315	−	0.762222i	$-0.724108\pi$
$101$	−13.0109	−1.29463	−0.647315	+	0.762222i	$0.724108\pi$
$102$	−11.4094	−1.12970
$103$	15.4070	1.51810	0.759050	−	0.651032i	$-0.225664\pi$
$103$	15.4070	1.51810	0.759050	+	0.651032i	$0.225664\pi$
$104$	9.60920	0.942259
$105$	2.60776	0.254491
$106$	−19.2106	−1.86590
$107$	18.6000	1.79813	0.899063	−	0.437820i	$-0.144249\pi$
$107$	18.6000	1.79813	0.899063	+	0.437820i	$0.144249\pi$
$108$	−16.1811	−1.55703
$109$	12.5373	1.20086	0.600428	−	0.799679i	$-0.294997\pi$
$109$	12.5373	1.20086	0.600428	+	0.799679i	$0.294997\pi$
$110$	28.3954	2.70739
$111$	5.09762	0.483844
$112$	−1.15508	−0.109145
$113$	14.6439	1.37759	0.688793	−	0.724958i	$-0.258141\pi$
$113$	14.6439	1.37759	0.688793	+	0.724958i	$0.258141\pi$
$114$	−6.60856	−0.618948
$115$	−5.06837	−0.472628
$116$	15.3464	1.42488
$117$	7.04883	0.651664
$118$	−6.87450	−0.632849
$119$	4.28348	0.392666
$120$	−5.58085	−0.509459
$121$	23.1807	2.10734
$122$	15.0808	1.36536
$123$	1.38224	0.124633
$124$	−21.5364	−1.93402
$125$	−11.4371	−1.02297
$126$	3.49655	0.311498
$127$	16.9043	1.50001	0.750007	−	0.661430i	$-0.230050\pi$
$127$	16.9043	1.50001	0.750007	+	0.661430i	$0.230050\pi$
$128$	15.1449	1.33864
$129$	15.2508	1.34276
$130$	21.8078	1.91267
$131$	−18.4901	−1.61548	−0.807742	−	0.589537i	$-0.799310\pi$
$131$	−18.4901	−1.61548	−0.807742	+	0.589537i	$0.799310\pi$
$132$	−20.7012	−1.80181
$133$	2.48108	0.215137
$134$	11.9882	1.03562
$135$	−11.9171	−1.02566
$136$	−9.16703	−0.786067
$137$	−7.50135	−0.640883	−0.320442	−	0.947268i	$-0.603831\pi$
$137$	−7.50135	−0.640883	−0.320442	+	0.947268i	$0.603831\pi$
$138$	6.19092	0.527006
$139$	18.9659	1.60867	0.804334	−	0.594177i	$-0.202522\pi$
$139$	18.9659	1.60867	0.804334	+	0.594177i	$0.202522\pi$
$140$	6.45647	0.545671
$141$	2.24163	0.188779
$142$	7.41711	0.622430
$143$	26.2510	2.19522
$144$	1.81332	0.151110
$145$	11.3024	0.938612
$146$	5.43128	0.449496
$147$	1.19588	0.0986348
$148$	12.6210	1.03744
$149$	19.8707	1.62787	0.813937	−	0.580954i	$-0.197320\pi$
$149$	19.8707	1.62787	0.813937	+	0.580954i	$0.197320\pi$
$150$	0.652353	0.0532644
$151$	18.2791	1.48754	0.743768	−	0.668438i	$-0.233037\pi$
$151$	18.2791	1.48754	0.743768	+	0.668438i	$0.233037\pi$
$152$	−5.30973	−0.430676
$153$	−6.72448	−0.543642
$154$	13.0217	1.04932
$155$	−15.8612	−1.27400
$156$	−15.8986	−1.27291
$157$	−6.41181	−0.511718	−0.255859	−	0.966714i	$-0.582358\pi$
$157$	−6.41181	−0.511718	−0.255859	+	0.966714i	$0.582358\pi$
$158$	−16.0873	−1.27984
$159$	10.3146	0.817998
$160$	14.9435	1.18139
$161$	−2.32428	−0.183179
$162$	4.06689	0.319525
$163$	17.9690	1.40744	0.703720	−	0.710477i	$-0.251521\pi$
$163$	17.9690	1.40744	0.703720	+	0.710477i	$0.251521\pi$
$164$	3.42225	0.267233
$165$	−15.2461	−1.18691
$166$	21.1723	1.64329
$167$	3.51886	0.272297	0.136149	−	0.990688i	$-0.456527\pi$
$167$	3.51886	0.272297	0.136149	+	0.990688i	$0.456527\pi$
$168$	−2.55930	−0.197454
$169$	7.16089	0.550838
$170$	−20.8043	−1.59562
$171$	−3.89495	−0.297855
$172$	37.7590	2.87909
$173$	18.1529	1.38014	0.690069	−	0.723744i	$-0.257580\pi$
$173$	18.1529	1.38014	0.690069	+	0.723744i	$0.257580\pi$
$174$	−13.8057	−1.04661
$175$	−0.244915	−0.0185139
$176$	6.75308	0.509032
$177$	3.69106	0.277437
$178$	12.3379	0.924761
$179$	20.1362	1.50505	0.752524	−	0.658564i	$-0.228836\pi$
$179$	20.1362	1.50505	0.752524	+	0.658564i	$0.228836\pi$
$180$	−10.1358	−0.755477
$181$	−23.3117	−1.73274	−0.866371	−	0.499401i	$-0.833553\pi$
$181$	−23.3117	−1.73274	−0.866371	+	0.499401i	$0.833553\pi$
$182$	10.0008	0.741305
$183$	−8.09723	−0.598564
$184$	4.97418	0.366701
$185$	9.29518	0.683395
$186$	19.3742	1.42058
$187$	−25.0430	−1.83133
$188$	5.54998	0.404774
$189$	−5.46502	−0.397522
$190$	−12.0503	−0.874219
$191$	−19.5755	−1.41643	−0.708216	−	0.705996i	$-0.750500\pi$
$191$	−19.5755	−1.41643	−0.708216	+	0.705996i	$0.750500\pi$
$192$	−15.4906	−1.11793
$193$	8.22184	0.591821	0.295910	−	0.955216i	$-0.404377\pi$
$193$	8.22184	0.591821	0.295910	+	0.955216i	$0.404377\pi$
$194$	0.601073	0.0431545
$195$	−11.7091	−0.838504
$196$	2.96085	0.211489
$197$	−18.0713	−1.28753	−0.643764	−	0.765224i	$-0.722628\pi$
$197$	−18.0713	−1.28753	−0.643764	+	0.765224i	$0.722628\pi$
$198$	−20.4423	−1.45277
$199$	24.3622	1.72699	0.863495	−	0.504357i	$-0.168270\pi$
$199$	24.3622	1.72699	0.863495	+	0.504357i	$0.168270\pi$
$200$	0.524141	0.0370624
$201$	−6.43673	−0.454012
$202$	28.9791	2.03896
$203$	5.18312	0.363784
$204$	15.1670	1.06191
$205$	2.52043	0.176035
$206$	−34.3160	−2.39091
$207$	3.64881	0.253610
$208$	5.18640	0.359612
$209$	−14.5054	−1.00336
$210$	−5.80826	−0.400808
$211$	−8.10524	−0.557987	−0.278994	−	0.960293i	$-0.590001\pi$
$211$	−8.10524	−0.557987	−0.278994	+	0.960293i	$0.590001\pi$
$212$	25.5375	1.75392
$213$	−3.98240	−0.272870
$214$	−41.4276	−2.83193
$215$	27.8089	1.89655
$216$	11.6956	0.795788
$217$	−7.27372	−0.493772
$218$	−27.9243	−1.89127
$219$	−2.91617	−0.197057
$220$	−37.7473	−2.54492
$221$	−19.2332	−1.29376
$222$	−11.3539	−0.762024
$223$	17.8084	1.19254	0.596269	−	0.802785i	$-0.296649\pi$
$223$	17.8084	1.19254	0.596269	+	0.802785i	$0.296649\pi$
$224$	6.85288	0.457877
$225$	0.384484	0.0256323
$226$	−32.6164	−2.16961
$227$	13.9969	0.929009	0.464504	−	0.885571i	$-0.346232\pi$
$227$	13.9969	0.929009	0.464504	+	0.885571i	$0.346232\pi$
$228$	8.78506	0.581805
$229$	−9.21215	−0.608756	−0.304378	−	0.952551i	$-0.598449\pi$
$229$	−9.21215	−0.608756	−0.304378	+	0.952551i	$0.598449\pi$
$230$	11.2888	0.744358
$231$	−6.99164	−0.460016
$232$	−11.0923	−0.728248
$233$	11.4843	0.752360	0.376180	−	0.926547i	$-0.377237\pi$
$233$	11.4843	0.752360	0.376180	+	0.926547i	$0.377237\pi$
$234$	−15.6998	−1.02633
$235$	4.08747	0.266637
$236$	9.13859	0.594871
$237$	8.63764	0.561075
$238$	−9.54057	−0.618423
$239$	−6.88178	−0.445145	−0.222573	−	0.974916i	$-0.571445\pi$
$239$	−6.88178	−0.445145	−0.222573	+	0.974916i	$0.571445\pi$
$240$	−3.01217	−0.194435
$241$	−2.65568	−0.171067	−0.0855337	−	0.996335i	$-0.527260\pi$
$241$	−2.65568	−0.171067	−0.0855337	+	0.996335i	$0.527260\pi$
$242$	−51.6303	−3.31892
$243$	14.2115	0.911666
$244$	−20.0477	−1.28342
$245$	2.18062	0.139314
$246$	−3.07867	−0.196289
$247$	−11.1403	−0.708837
$248$	15.5664	0.988468
$249$	−11.3679	−0.720410
$250$	25.4739	1.61111
$251$	−9.92008	−0.626150	−0.313075	−	0.949728i	$-0.601359\pi$
$251$	−9.92008	−0.626150	−0.313075	+	0.949728i	$0.601359\pi$
$252$	−4.64813	−0.292805
$253$	13.5887	0.854317
$254$	−37.6509	−2.36242
$255$	11.1703	0.699510
$256$	−7.82578	−0.489111
$257$	−7.54536	−0.470667	−0.235333	−	0.971915i	$-0.575618\pi$
$257$	−7.54536	−0.470667	−0.235333	+	0.971915i	$0.575618\pi$
$258$	−33.9680	−2.11476
$259$	4.26264	0.264867
$260$	−28.9901	−1.79789
$261$	−8.13679	−0.503655
$262$	41.1828	2.54428
$263$	−8.64286	−0.532941	−0.266471	−	0.963843i	$-0.585858\pi$
$263$	−8.64286	−0.532941	−0.266471	+	0.963843i	$0.585858\pi$
$264$	14.9627	0.920893
$265$	18.8079	1.15536
$266$	−5.52609	−0.338826
$267$	−6.62446	−0.405410
$268$	−15.9365	−0.973476
$269$	20.7250	1.26362	0.631811	−	0.775122i	$-0.282312\pi$
$269$	20.7250	1.26362	0.631811	+	0.775122i	$0.282312\pi$
$270$	26.5429	1.61535
$271$	−9.67677	−0.587822	−0.293911	−	0.955833i	$-0.594957\pi$
$271$	−9.67677	−0.587822	−0.293911	+	0.955833i	$0.594957\pi$
$272$	−4.94775	−0.300001
$273$	−5.36962	−0.324984
$274$	16.7077	1.00935
$275$	1.43188	0.0863456
$276$	−8.22988	−0.495381
$277$	14.8937	0.894877	0.447438	−	0.894315i	$-0.352336\pi$
$277$	14.8937	0.894877	0.447438	+	0.894315i	$0.352336\pi$
$278$	−42.2427	−2.53355
$279$	11.4187	0.683622
$280$	−4.66672	−0.278890
$281$	−31.8158	−1.89797	−0.948987	−	0.315316i	$-0.897889\pi$
$281$	−31.8158	−1.89797	−0.948987	+	0.315316i	$0.897889\pi$
$282$	−4.99277	−0.297315
$283$	−5.45037	−0.323991	−0.161995	−	0.986792i	$-0.551793\pi$
$283$	−5.45037	−0.323991	−0.161995	+	0.986792i	$0.551793\pi$
$284$	−9.85990	−0.585078
$285$	6.47005	0.383253
$286$	−58.4687	−3.45732
$287$	1.15584	0.0682268
$288$	−10.7581	−0.633927
$289$	1.34818	0.0793046
$290$	−25.1738	−1.47825
$291$	−0.322729	−0.0189187
$292$	−7.22005	−0.422522
$293$	13.0449	0.762092	0.381046	−	0.924556i	$-0.375564\pi$
$293$	13.0449	0.762092	0.381046	+	0.924556i	$0.375564\pi$
$294$	−2.66358	−0.155343
$295$	6.73042	0.391860
$296$	−9.12244	−0.530231
$297$	31.9508	1.85398
$298$	−44.2580	−2.56380
$299$	10.4362	0.603543
$300$	−0.867203	−0.0500680
$301$	12.7528	0.735056
$302$	−40.7130	−2.34277
$303$	−15.5595	−0.893869
$304$	−2.86584	−0.164367
$305$	−14.7648	−0.845429
$306$	14.9774	0.856201
$307$	−0.164746	−0.00940257	−0.00470128	−	0.999989i	$-0.501496\pi$
$307$	−0.164746	−0.00940257	−0.00470128	+	0.999989i	$0.501496\pi$
$308$	−17.3104	−0.986350
$309$	18.4250	1.04816
$310$	35.3275	2.00647
$311$	−13.4348	−0.761817	−0.380908	−	0.924613i	$-0.624389\pi$
$311$	−13.4348	−0.761817	−0.380908	+	0.924613i	$0.624389\pi$
$312$	11.4915	0.650577
$313$	1.65894	0.0937686	0.0468843	−	0.998900i	$-0.485071\pi$
$313$	1.65894	0.0937686	0.0468843	+	0.998900i	$0.485071\pi$
$314$	14.2810	0.805923
$315$	−3.42327	−0.192879
$316$	21.3857	1.20304
$317$	−15.1120	−0.848774	−0.424387	−	0.905481i	$-0.639510\pi$
$317$	−15.1120	−0.848774	−0.424387	+	0.905481i	$0.639510\pi$
$318$	−22.9736	−1.28829
$319$	−30.3027	−1.69663
$320$	−28.2460	−1.57900
$321$	22.2434	1.24150
$322$	5.17687	0.288495
$323$	10.6276	0.591337
$324$	−5.40631	−0.300350
$325$	1.09969	0.0609999
$326$	−40.0223	−2.21663
$327$	14.9931	0.829122
$328$	−2.47359	−0.136581
$329$	1.87446	0.103342
$330$	33.9575	1.86930
$331$	33.5435	1.84371	0.921857	−	0.387529i	$-0.126671\pi$
$331$	33.5435	1.84371	0.921857	+	0.387529i	$0.126671\pi$
$332$	−28.1454	−1.54468
$333$	−6.69176	−0.366706
$334$	−7.83754	−0.428851
$335$	−11.7370	−0.641259
$336$	−1.38134	−0.0753581
$337$	18.1782	0.990232	0.495116	−	0.868827i	$-0.335126\pi$
$337$	18.1782	0.990232	0.495116	+	0.868827i	$0.335126\pi$
$338$	−15.9494	−0.867534
$339$	17.5124	0.951145
$340$	27.6561	1.49986
$341$	42.5252	2.30287
$342$	8.67521	0.469102
$343$	1.00000	0.0539949
$344$	−27.2921	−1.47149
$345$	−6.06117	−0.326323
$346$	−40.4318	−2.17363
$347$	−25.4729	−1.36746	−0.683730	−	0.729735i	$-0.739643\pi$
$347$	−25.4729	−1.36746	−0.683730	+	0.729735i	$0.739643\pi$
$348$	18.3525	0.983798
$349$	−32.4353	−1.73622	−0.868111	−	0.496371i	$-0.834666\pi$
$349$	−32.4353	−1.73622	−0.868111	+	0.496371i	$0.834666\pi$
$350$	0.545499	0.0291581
$351$	24.5384	1.30976
$352$	−40.0649	−2.13546
$353$	6.94211	0.369491	0.184746	−	0.982786i	$-0.440854\pi$
$353$	6.94211	0.369491	0.184746	+	0.982786i	$0.440854\pi$
$354$	−8.22109	−0.436946
$355$	−7.26166	−0.385409
$356$	−16.4013	−0.869266
$357$	5.12254	0.271113
$358$	−44.8492	−2.37036
$359$	16.4892	0.870269	0.435134	−	0.900366i	$-0.356701\pi$
$359$	16.4892	0.870269	0.435134	+	0.900366i	$0.356701\pi$
$360$	7.32611	0.386120
$361$	−12.8443	−0.676014
$362$	51.9219	2.72896
$363$	27.7214	1.45500
$364$	−13.2945	−0.696819
$365$	−5.31745	−0.278328
$366$	18.0349	0.942701
$367$	−6.28337	−0.327989	−0.163995	−	0.986461i	$-0.552438\pi$
$367$	−6.28337	−0.327989	−0.163995	+	0.986461i	$0.552438\pi$
$368$	2.68473	0.139951
$369$	−1.81451	−0.0944594
$370$	−20.7031	−1.07630
$371$	8.62506	0.447791
$372$	−25.7550	−1.33533
$373$	−4.66801	−0.241700	−0.120850	−	0.992671i	$-0.538562\pi$
$373$	−4.66801	−0.241700	−0.120850	+	0.992671i	$0.538562\pi$
$374$	55.7782	2.88422
$375$	−13.6775	−0.706302
$376$	−4.01151	−0.206878
$377$	−23.2727	−1.19860
$378$	12.1722	0.626072
$379$	15.3002	0.785916	0.392958	−	0.919556i	$-0.371452\pi$
$379$	15.3002	0.785916	0.392958	+	0.919556i	$0.371452\pi$
$380$	16.0190	0.821757
$381$	20.2155	1.03567
$382$	43.6004	2.23079
$383$	25.2108	1.28821	0.644106	−	0.764936i	$-0.277230\pi$
$383$	25.2108	1.28821	0.644106	+	0.764936i	$0.277230\pi$
$384$	18.1116	0.924252
$385$	−12.7488	−0.649739
$386$	−18.3125	−0.932080
$387$	−20.0201	−1.01768
$388$	−0.799035	−0.0405648
$389$	18.5290	0.939455	0.469728	−	0.882811i	$-0.344352\pi$
$389$	18.5290	0.939455	0.469728	+	0.882811i	$0.344352\pi$
$390$	26.0796	1.32059
$391$	−9.95601	−0.503497
$392$	−2.14009	−0.108091
$393$	−22.1119	−1.11540
$394$	40.2502	2.02778
$395$	15.7502	0.792478
$396$	27.1749	1.36559
$397$	6.17885	0.310108	0.155054	−	0.987906i	$-0.450445\pi$
$397$	6.17885	0.310108	0.155054	+	0.987906i	$0.450445\pi$
$398$	−54.2618	−2.71990
$399$	2.96708	0.148540
$400$	0.282896	0.0141448
$401$	25.8361	1.29019	0.645097	−	0.764101i	$-0.276817\pi$
$401$	25.8361	1.29019	0.645097	+	0.764101i	$0.276817\pi$
$402$	14.3365	0.715040
$403$	32.6596	1.62689
$404$	−38.5232	−1.91660
$405$	−3.98166	−0.197850
$406$	−11.5443	−0.572936
$407$	−24.9212	−1.23530
$408$	−10.9627	−0.542734
$409$	−28.8343	−1.42576	−0.712882	−	0.701284i	$-0.752610\pi$
$409$	−28.8343	−1.42576	−0.712882	+	0.701284i	$0.752610\pi$
$410$	−5.61375	−0.277243
$411$	−8.97073	−0.442493
$412$	45.6179	2.24743
$413$	3.08648	0.151876
$414$	−8.12698	−0.399419
$415$	−20.7286	−1.01753
$416$	−30.7700	−1.50863
$417$	22.6810	1.11069
$418$	32.3079	1.58023
$419$	−3.11865	−0.152356	−0.0761780	−	0.997094i	$-0.524272\pi$
$419$	−3.11865	−0.152356	−0.0761780	+	0.997094i	$0.524272\pi$
$420$	7.72118	0.376755
$421$	28.7995	1.40360	0.701800	−	0.712374i	$-0.252380\pi$
$421$	28.7995	1.40360	0.701800	+	0.712374i	$0.252380\pi$
$422$	18.0528	0.878795
$423$	−2.94264	−0.143076
$424$	−18.4584	−0.896420
$425$	−1.04909	−0.0508883
$426$	8.86999	0.429752
$427$	−6.77092	−0.327668
$428$	55.0716	2.66199
$429$	31.3931	1.51567
$430$	−61.9385	−2.98694
$431$	−31.4626	−1.51550	−0.757750	−	0.652545i	$-0.773701\pi$
$431$	−31.4626	−1.51550	−0.757750	+	0.652545i	$0.773701\pi$
$432$	6.31253	0.303712
$433$	14.3822	0.691164	0.345582	−	0.938389i	$-0.387681\pi$
$433$	14.3822	0.691164	0.345582	+	0.938389i	$0.387681\pi$
$434$	16.2007	0.777659
$435$	13.5163	0.648058
$436$	37.1210	1.77777
$437$	−5.76672	−0.275860
$438$	6.49517	0.310351
$439$	30.2141	1.44204	0.721020	−	0.692914i	$-0.243673\pi$
$439$	30.2141	1.44204	0.721020	+	0.692914i	$0.243673\pi$
$440$	27.2836	1.30070
$441$	−1.56986	−0.0747554
$442$	42.8380	2.03760
$443$	25.5218	1.21258	0.606290	−	0.795244i	$-0.292657\pi$
$443$	25.5218	1.21258	0.606290	+	0.795244i	$0.292657\pi$
$444$	15.0933	0.716295
$445$	−12.0793	−0.572612
$446$	−39.6645	−1.87817
$447$	23.7631	1.12395
$448$	−12.9532	−0.611983
$449$	−23.6624	−1.11670	−0.558348	−	0.829607i	$-0.688565\pi$
$449$	−23.6624	−1.11670	−0.558348	+	0.829607i	$0.688565\pi$
$450$	−0.856359	−0.0403692
$451$	−6.75751	−0.318199
$452$	43.3585	2.03941
$453$	21.8597	1.02706
$454$	−31.1753	−1.46313
$455$	−9.79116	−0.459016
$456$	−6.34981	−0.297357
$457$	−7.73181	−0.361679	−0.180839	−	0.983513i	$-0.557881\pi$
$457$	−7.73181	−0.361679	−0.180839	+	0.983513i	$0.557881\pi$
$458$	20.5182	0.958752
$459$	−23.4093	−1.09265
$460$	−15.0067	−0.699689
$461$	−16.3231	−0.760240	−0.380120	−	0.924937i	$-0.624117\pi$
$461$	−16.3231	−0.760240	−0.380120	+	0.924937i	$0.624117\pi$
$462$	15.5725	0.724496
$463$	−1.92773	−0.0895894	−0.0447947	−	0.998996i	$-0.514263\pi$
$463$	−1.92773	−0.0895894	−0.0447947	+	0.998996i	$0.514263\pi$
$464$	−5.98690	−0.277935
$465$	−18.9681	−0.879625
$466$	−25.5789	−1.18492
$467$	18.9733	0.877978	0.438989	−	0.898492i	$-0.355337\pi$
$467$	18.9733	0.877978	0.438989	+	0.898492i	$0.355337\pi$
$468$	20.8705	0.964739
$469$	−5.38241	−0.248536
$470$	−9.10400	−0.419936
$471$	−7.66777	−0.353312
$472$	−6.60534	−0.304035
$473$	−74.5580	−3.42818
$474$	−19.2386	−0.883657
$475$	−0.607654	−0.0278811
$476$	12.6827	0.581312
$477$	−13.5402	−0.619962
$478$	15.3278	0.701075
$479$	−28.4712	−1.30088	−0.650440	−	0.759558i	$-0.725416\pi$
$479$	−28.4712	−1.30088	−0.650440	+	0.759558i	$0.725416\pi$
$480$	17.8707	0.815681
$481$	−19.1396	−0.872692
$482$	5.91499	0.269420
$483$	−2.77957	−0.126475
$484$	68.6345	3.11975
$485$	−0.588476	−0.0267213
$486$	−31.6531	−1.43582
$487$	1.95913	0.0887767	0.0443883	−	0.999014i	$-0.485866\pi$
$487$	1.95913	0.0887767	0.0443883	+	0.999014i	$0.485866\pi$
$488$	14.4904	0.655949
$489$	21.4888	0.971758
$490$	−4.85688	−0.219411
$491$	25.4213	1.14725	0.573624	−	0.819119i	$-0.305537\pi$
$491$	25.4213	1.14725	0.573624	+	0.819119i	$0.305537\pi$
$492$	4.09261	0.184509
$493$	22.2018	0.999917
$494$	24.8126	1.11637
$495$	20.0139	0.899558
$496$	8.40171	0.377248
$497$	−3.33010	−0.149375
$498$	25.3196	1.13460
$499$	16.2976	0.729579	0.364790	−	0.931090i	$-0.381141\pi$
$499$	16.2976	0.729579	0.364790	+	0.931090i	$0.381141\pi$
$500$	−33.8636	−1.51443
$501$	4.20814	0.188006
$502$	22.0949	0.986146
$503$	17.2582	0.769506	0.384753	−	0.923019i	$-0.374287\pi$
$503$	17.2582	0.769506	0.384753	+	0.923019i	$0.374287\pi$
$504$	3.35965	0.149651
$505$	−28.3717	−1.26253
$506$	−30.2662	−1.34549
$507$	8.56358	0.380322
$508$	50.0510	2.22065
$509$	−38.2480	−1.69531	−0.847657	−	0.530544i	$-0.821988\pi$
$509$	−38.2480	−1.69531	−0.847657	+	0.530544i	$0.821988\pi$
$510$	−24.8795	−1.10168
$511$	−2.43851	−0.107873
$512$	−12.8596	−0.568317
$513$	−13.5591	−0.598651
$514$	16.8058	0.741270
$515$	33.5968	1.48045
$516$	45.1553	1.98785
$517$	−10.9589	−0.481971
$518$	−9.49416	−0.417149
$519$	21.7087	0.952906
$520$	20.9540	0.918892
$521$	36.5144	1.59973	0.799863	−	0.600183i	$-0.204905\pi$
$521$	36.5144	1.59973	0.799863	+	0.600183i	$0.204905\pi$
$522$	18.1230	0.793224
$523$	−16.1836	−0.707659	−0.353830	−	0.935310i	$-0.615121\pi$
$523$	−16.1836	−0.707659	−0.353830	+	0.935310i	$0.615121\pi$
$524$	−54.7462	−2.39160
$525$	−0.292890	−0.0127828
$526$	19.2502	0.839349
$527$	−31.1568	−1.35721
$528$	8.07589	0.351458
$529$	−17.5977	−0.765118
$530$	−41.8909	−1.81962
$531$	−4.84535	−0.210270
$532$	7.34609	0.318493
$533$	−5.18980	−0.224795
$534$	14.7546	0.638495
$535$	40.5594	1.75353
$536$	11.5188	0.497538
$537$	24.0805	1.03915
$538$	−46.1606	−1.99013
$539$	−5.84643	−0.251823
$540$	−35.2848	−1.51841
$541$	25.0018	1.07491	0.537455	−	0.843292i	$-0.319386\pi$
$541$	25.0018	1.07491	0.537455	+	0.843292i	$0.319386\pi$
$542$	21.5530	0.925782
$543$	−27.8780	−1.19636
$544$	29.3542	1.25855
$545$	27.3390	1.17108
$546$	11.9597	0.511829
$547$	23.1374	0.989283	0.494642	−	0.869097i	$-0.335299\pi$
$547$	23.1374	0.989283	0.494642	+	0.869097i	$0.335299\pi$
$548$	−22.2103	−0.948779
$549$	10.6294	0.453653
$550$	−3.18922	−0.135989
$551$	12.8597	0.547842
$552$	5.94853	0.253186
$553$	7.22282	0.307145
$554$	−33.1727	−1.40937
$555$	11.1159	0.471845
$556$	56.1552	2.38151
$557$	36.9668	1.56633	0.783167	−	0.621812i	$-0.213603\pi$
$557$	36.9668	1.56633	0.783167	+	0.621812i	$0.213603\pi$
$558$	−25.4329	−1.07666
$559$	−57.2610	−2.42188
$560$	−2.51878	−0.106438
$561$	−29.9485	−1.26443
$562$	70.8633	2.98919
$563$	−46.5101	−1.96017	−0.980084	−	0.198581i	$-0.936367\pi$
$563$	−46.5101	−1.96017	−0.980084	+	0.198581i	$0.936367\pi$
$564$	6.63713	0.279473
$565$	31.9328	1.34342
$566$	12.1396	0.510265
$567$	−1.82593	−0.0766820
$568$	7.12671	0.299030
$569$	26.1957	1.09818	0.549091	−	0.835762i	$-0.314974\pi$
$569$	26.1957	1.09818	0.549091	+	0.835762i	$0.314974\pi$
$570$	−14.4107	−0.603599
$571$	−15.5573	−0.651054	−0.325527	−	0.945533i	$-0.605542\pi$
$571$	−15.5573	−0.651054	−0.325527	+	0.945533i	$0.605542\pi$
$572$	77.7251	3.24985
$573$	−23.4100	−0.977966
$574$	−2.57439	−0.107453
$575$	0.569252	0.0237395
$576$	20.3348	0.847285
$577$	−41.1177	−1.71175	−0.855876	−	0.517181i	$-0.826982\pi$
$577$	−41.1177	−1.71175	−0.855876	+	0.517181i	$0.826982\pi$
$578$	−3.00279	−0.124900
$579$	9.83236	0.408619
$580$	33.4646	1.38954
$581$	−9.50584	−0.394369
$582$	0.718813	0.0297958
$583$	−50.4258	−2.08842
$584$	5.21863	0.215948
$585$	15.3708	0.635504
$586$	−29.0549	−1.20025
$587$	−4.59120	−0.189499	−0.0947496	−	0.995501i	$-0.530205\pi$
$587$	−4.59120	−0.189499	−0.0947496	+	0.995501i	$0.530205\pi$
$588$	3.54083	0.146021
$589$	−18.0466	−0.743599
$590$	−14.9906	−0.617155
$591$	−21.6112	−0.888965
$592$	−4.92368	−0.202362
$593$	9.79557	0.402256	0.201128	−	0.979565i	$-0.435539\pi$
$593$	9.79557	0.402256	0.201128	+	0.979565i	$0.435539\pi$
$594$	−71.1640	−2.91989
$595$	9.34062	0.382928
$596$	58.8342	2.40994
$597$	29.1343	1.19239
$598$	−23.2446	−0.950541
$599$	−10.5584	−0.431404	−0.215702	−	0.976459i	$-0.569204\pi$
$599$	−10.5584	−0.431404	−0.215702	+	0.976459i	$0.569204\pi$
$600$	0.626811	0.0255895
$601$	−7.65674	−0.312325	−0.156162	−	0.987731i	$-0.549912\pi$
$601$	−7.65674	−0.312325	−0.156162	+	0.987731i	$0.549912\pi$
$602$	−28.4042	−1.15767
$603$	8.44965	0.344096
$604$	54.1217	2.20218
$605$	50.5482	2.05508
$606$	34.6556	1.40779
$607$	2.47254	0.100357	0.0501786	−	0.998740i	$-0.484021\pi$
$607$	2.47254	0.100357	0.0501786	+	0.998740i	$0.484021\pi$
$608$	17.0025	0.689543
$609$	6.19840	0.251172
$610$	32.8855	1.33150
$611$	−8.41647	−0.340494
$612$	−19.9102	−0.804820
$613$	16.0514	0.648310	0.324155	−	0.946004i	$-0.394920\pi$
$613$	16.0514	0.648310	0.324155	+	0.946004i	$0.394920\pi$
$614$	0.366939	0.0148084
$615$	3.01414	0.121542
$616$	12.5119	0.504118
$617$	33.2170	1.33727	0.668633	−	0.743592i	$-0.266880\pi$
$617$	33.2170	1.33727	0.668633	+	0.743592i	$0.266880\pi$
$618$	−41.0379	−1.65079
$619$	44.4863	1.78805	0.894027	−	0.448012i	$-0.147868\pi$
$619$	44.4863	1.78805	0.894027	+	0.448012i	$0.147868\pi$
$620$	−46.9625	−1.88606
$621$	12.7023	0.509724
$622$	29.9232	1.19981
$623$	−5.53939	−0.221931
$624$	6.20233	0.248292
$625$	−23.7154	−0.948618
$626$	−3.69494	−0.147680
$627$	−17.3468	−0.692764
$628$	−18.9844	−0.757559
$629$	18.2589	0.728031
$630$	7.62464	0.303773
$631$	47.6570	1.89719	0.948597	−	0.316485i	$-0.102503\pi$
$631$	47.6570	1.89719	0.948597	+	0.316485i	$0.102503\pi$
$632$	−15.4575	−0.614866
$633$	−9.69291	−0.385259
$634$	33.6589	1.33676
$635$	36.8618	1.46281
$636$	30.5398	1.21098
$637$	−4.49009	−0.177904
$638$	67.4931	2.67208
$639$	5.22780	0.206808
$640$	33.0253	1.30544
$641$	22.0375	0.870429	0.435215	−	0.900327i	$-0.356673\pi$
$641$	22.0375	0.870429	0.435215	+	0.900327i	$0.356673\pi$
$642$	−49.5426	−1.95529
$643$	−23.1274	−0.912055	−0.456028	−	0.889966i	$-0.650728\pi$
$643$	−23.1274	−0.912055	−0.456028	+	0.889966i	$0.650728\pi$
$644$	−6.88185	−0.271183
$645$	33.2561	1.30946
$646$	−23.6709	−0.931319
$647$	−29.6723	−1.16654	−0.583270	−	0.812279i	$-0.698227\pi$
$647$	−29.6723	−1.16654	−0.583270	+	0.812279i	$0.698227\pi$
$648$	3.90766	0.153508
$649$	−18.0449	−0.708322
$650$	−2.44934	−0.0960709
$651$	−8.69851	−0.340922
$652$	53.2034	2.08361
$653$	13.4979	0.528212	0.264106	−	0.964494i	$-0.414923\pi$
$653$	13.4979	0.528212	0.264106	+	0.964494i	$0.414923\pi$
$654$	−33.3942	−1.30581
$655$	−40.3197	−1.57542
$656$	−1.33508	−0.0521261
$657$	3.82813	0.149349
$658$	−4.17497	−0.162757
$659$	−18.4992	−0.720628	−0.360314	−	0.932831i	$-0.617330\pi$
$659$	−18.4992	−0.720628	−0.360314	+	0.932831i	$0.617330\pi$
$660$	−45.1413	−1.75712
$661$	28.8748	1.12310	0.561550	−	0.827443i	$-0.310205\pi$
$661$	28.8748	1.12310	0.561550	+	0.827443i	$0.310205\pi$
$662$	−74.7112	−2.90373
$663$	−23.0006	−0.893271
$664$	20.3434	0.789476
$665$	5.41027	0.209801
$666$	14.9045	0.577539
$667$	−12.0470	−0.466463
$668$	10.4188	0.403116
$669$	21.2967	0.823379
$670$	26.1417	1.00994
$671$	39.5857	1.52819
$672$	8.19524	0.316138
$673$	−20.5832	−0.793424	−0.396712	−	0.917943i	$-0.629849\pi$
$673$	−20.5832	−0.793424	−0.396712	+	0.917943i	$0.629849\pi$
$674$	−40.4883	−1.55955
$675$	1.33847	0.0515176
$676$	21.2023	0.815473
$677$	−33.0179	−1.26898	−0.634490	−	0.772931i	$-0.718790\pi$
$677$	−33.0179	−1.26898	−0.634490	+	0.772931i	$0.718790\pi$
$678$	−39.0054	−1.49799
$679$	−0.269867	−0.0103565
$680$	−19.9898	−0.766573
$681$	16.7387	0.641428
$682$	−94.7163	−3.62687
$683$	−37.2165	−1.42405	−0.712025	−	0.702154i	$-0.752222\pi$
$683$	−37.2165	−1.42405	−0.712025	+	0.702154i	$0.752222\pi$
$684$	−11.5324	−0.440951
$685$	−16.3576	−0.624990
$686$	−2.22730	−0.0850386
$687$	−11.0166	−0.420311
$688$	−14.7304	−0.561592
$689$	−38.7273	−1.47539
$690$	13.5000	0.513937
$691$	−38.8762	−1.47892	−0.739460	−	0.673200i	$-0.764919\pi$
$691$	−38.8762	−1.47892	−0.739460	+	0.673200i	$0.764919\pi$
$692$	53.7479	2.04319
$693$	9.17809	0.348647
$694$	56.7358	2.15366
$695$	41.3574	1.56878
$696$	−13.2651	−0.502814
$697$	4.95100	0.187532
$698$	72.2430	2.73444
$699$	13.7339	0.519462
$700$	−0.725157	−0.0274084
$701$	−44.3377	−1.67461	−0.837307	−	0.546734i	$-0.815871\pi$
$701$	−44.3377	−1.67461	−0.837307	+	0.546734i	$0.815871\pi$
$702$	−54.6543	−2.06280
$703$	10.5759	0.398879
$704$	75.7302	2.85419
$705$	4.88813	0.184098
$706$	−15.4621	−0.581925
$707$	−13.0109	−0.489324
$708$	10.9287	0.410725
$709$	25.8576	0.971104	0.485552	−	0.874208i	$-0.338619\pi$
$709$	25.8576	0.971104	0.485552	+	0.874208i	$0.338619\pi$
$710$	16.1739	0.606994
$711$	−11.3388	−0.425240
$712$	11.8548	0.444277
$713$	16.9062	0.633141
$714$	−11.4094	−0.426986
$715$	57.2433	2.14078
$716$	59.6201	2.22811
$717$	−8.22980	−0.307347
$718$	−36.7264	−1.37062
$719$	26.2662	0.979564	0.489782	−	0.871845i	$-0.337076\pi$
$719$	26.2662	0.979564	0.489782	+	0.871845i	$0.337076\pi$
$720$	3.95414	0.147362
$721$	15.4070	0.573788
$722$	28.6080	1.06468
$723$	−3.17588	−0.118112
$724$	−69.0222	−2.56519
$725$	−1.26942	−0.0471453
$726$	−61.7437	−2.29152
$727$	33.0514	1.22581	0.612905	−	0.790157i	$-0.290001\pi$
$727$	33.0514	1.22581	0.612905	+	0.790157i	$0.290001\pi$
$728$	9.60920	0.356141
$729$	22.4730	0.832335
$730$	11.8435	0.438349
$731$	54.6261	2.02042
$732$	−23.9747	−0.886129
$733$	37.5614	1.38736	0.693681	−	0.720282i	$-0.255988\pi$
$733$	37.5614	1.38736	0.693681	+	0.720282i	$0.255988\pi$
$734$	13.9949	0.516562
$735$	2.60776	0.0961887
$736$	−15.9280	−0.587115
$737$	31.4678	1.15913
$738$	4.04144	0.148767
$739$	8.16143	0.300223	0.150112	−	0.988669i	$-0.452037\pi$
$739$	8.16143	0.300223	0.150112	+	0.988669i	$0.452037\pi$
$740$	27.5216	1.01171
$741$	−13.3224	−0.489412
$742$	−19.2106	−0.705242
$743$	−20.0265	−0.734701	−0.367350	−	0.930083i	$-0.619735\pi$
$743$	−20.0265	−0.734701	−0.367350	+	0.930083i	$0.619735\pi$
$744$	18.6156	0.682481
$745$	43.3304	1.58750
$746$	10.3970	0.380662
$747$	14.9229	0.546000
$748$	−74.1486	−2.71114
$749$	18.6000	0.679628
$750$	30.4638	1.11238
$751$	−13.1738	−0.480719	−0.240360	−	0.970684i	$-0.577265\pi$
$751$	−13.1738	−0.480719	−0.240360	+	0.970684i	$0.577265\pi$
$752$	−2.16514	−0.0789546
$753$	−11.8632	−0.432321
$754$	51.8351	1.88772
$755$	39.8598	1.45065
$756$	−16.1811	−0.588501
$757$	40.4649	1.47072	0.735361	−	0.677676i	$-0.237013\pi$
$757$	40.4649	1.47072	0.735361	+	0.677676i	$0.237013\pi$
$758$	−34.0780	−1.23777
$759$	16.2505	0.589857
$760$	−11.5785	−0.419996
$761$	27.5598	0.999044	0.499522	−	0.866301i	$-0.333509\pi$
$761$	27.5598	0.999044	0.499522	+	0.866301i	$0.333509\pi$
$762$	−45.0260	−1.63112
$763$	12.5373	0.453881
$764$	−57.9600	−2.09692
$765$	−14.6635	−0.530160
$766$	−56.1519	−2.02885
$767$	−13.8586	−0.500403
$768$	−9.35871	−0.337703
$769$	15.7974	0.569668	0.284834	−	0.958577i	$-0.408062\pi$
$769$	15.7974	0.569668	0.284834	+	0.958577i	$0.408062\pi$
$770$	28.3954	1.02330
$771$	−9.02337	−0.324969
$772$	24.3436	0.876146
$773$	−39.3312	−1.41465	−0.707323	−	0.706891i	$-0.750097\pi$
$773$	−39.3312	−1.41465	−0.707323	+	0.706891i	$0.750097\pi$
$774$	44.5907	1.60278
$775$	1.78144	0.0639914
$776$	0.577540	0.0207325
$777$	5.09762	0.182876
$778$	−41.2695	−1.47958
$779$	2.86772	0.102747
$780$	−34.6688	−1.24134
$781$	19.4692	0.696661
$782$	22.1750	0.792976
$783$	−28.3259	−1.01228
$784$	−1.15508	−0.0412528
$785$	−13.9817	−0.499028
$786$	49.2498	1.75668
$787$	−45.7031	−1.62914	−0.814569	−	0.580066i	$-0.803027\pi$
$787$	−45.7031	−1.62914	−0.814569	+	0.580066i	$0.803027\pi$
$788$	−53.5064	−1.90609
$789$	−10.3358	−0.367966
$790$	−35.0803	−1.24810
$791$	14.6439	0.520679
$792$	−19.6420	−0.697947
$793$	30.4020	1.07961
$794$	−13.7621	−0.488400
$795$	22.4921	0.797712
$796$	72.1327	2.55668
$797$	29.3448	1.03945	0.519724	−	0.854334i	$-0.326035\pi$
$797$	29.3448	1.03945	0.519724	+	0.854334i	$0.326035\pi$
$798$	−6.60856	−0.233940
$799$	8.02919	0.284052
$800$	−1.67838	−0.0593396
$801$	8.69608	0.307261
$802$	−57.5447	−2.03197
$803$	14.2566	0.503103
$804$	−19.0582	−0.672130
$805$	−5.06837	−0.178636
$806$	−72.7426	−2.56225
$807$	24.7846	0.872460
$808$	27.8445	0.979565
$809$	−36.2137	−1.27321	−0.636603	−	0.771192i	$-0.719661\pi$
$809$	−36.2137	−1.27321	−0.636603	+	0.771192i	$0.719661\pi$
$810$	8.86833	0.311601
$811$	−0.892016	−0.0313229	−0.0156615	−	0.999877i	$-0.504985\pi$
$811$	−0.892016	−0.0313229	−0.0156615	+	0.999877i	$0.504985\pi$
$812$	15.3464	0.538554
$813$	−11.5723	−0.405857
$814$	55.5069	1.94552
$815$	39.1835	1.37254
$816$	−5.91693	−0.207134
$817$	31.6406	1.10696
$818$	64.2225	2.24549
$819$	7.04883	0.246306
$820$	7.46262	0.260606
$821$	−53.3399	−1.86158	−0.930788	−	0.365559i	$-0.880878\pi$
$821$	−53.3399	−1.86158	−0.930788	+	0.365559i	$0.880878\pi$
$822$	19.9805	0.696899
$823$	22.8237	0.795583	0.397792	−	0.917476i	$-0.369777\pi$
$823$	22.8237	0.795583	0.397792	+	0.917476i	$0.369777\pi$
$824$	−32.9725	−1.14865
$825$	1.71236	0.0596167
$826$	−6.87450	−0.239194
$827$	29.4656	1.02462	0.512310	−	0.858800i	$-0.328790\pi$
$827$	29.4656	1.02462	0.512310	+	0.858800i	$0.328790\pi$
$828$	10.8036	0.375450
$829$	−4.99904	−0.173624	−0.0868118	−	0.996225i	$-0.527668\pi$
$829$	−4.99904	−0.173624	−0.0868118	+	0.996225i	$0.527668\pi$
$830$	46.1687	1.60254
$831$	17.8111	0.617862
$832$	58.1612	2.01638
$833$	4.28348	0.148414
$834$	−50.5173	−1.74927
$835$	7.67328	0.265545
$836$	−42.9484	−1.48540
$837$	39.7510	1.37400
$838$	6.94615	0.239951
$839$	−19.4660	−0.672042	−0.336021	−	0.941854i	$-0.609081\pi$
$839$	−19.4660	−0.672042	−0.336021	+	0.941854i	$0.609081\pi$
$840$	−5.58085	−0.192557
$841$	−2.13530	−0.0736309
$842$	−64.1449	−2.21058
$843$	−38.0480	−1.31044
$844$	−23.9984	−0.826058
$845$	15.6151	0.537177
$846$	6.55414	0.225336
$847$	23.1807	0.796498
$848$	−9.96262	−0.342118
$849$	−6.51800	−0.223697
$850$	2.33663	0.0801458
$851$	−9.90758	−0.339627
$852$	−11.7913	−0.403963
$853$	−3.92711	−0.134462	−0.0672309	−	0.997737i	$-0.521416\pi$
$853$	−3.92711	−0.134462	−0.0672309	+	0.997737i	$0.521416\pi$
$854$	15.0808	0.516056
$855$	−8.49340	−0.290468
$856$	−39.8056	−1.36053
$857$	−35.8128	−1.22334	−0.611671	−	0.791112i	$-0.709503\pi$
$857$	−35.8128	−1.22334	−0.611671	+	0.791112i	$0.709503\pi$
$858$	−69.9217	−2.38709
$859$	41.0091	1.39921	0.699606	−	0.714529i	$-0.253359\pi$
$859$	41.0091	1.39921	0.699606	+	0.714529i	$0.253359\pi$
$860$	82.3378	2.80769
$861$	1.38224	0.0471067
$862$	70.0765	2.38682
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−37.4512	−1.27411
$865$	39.5844	1.34591
$866$	−32.0334	−1.08854
$867$	1.61226	0.0547553
$868$	−21.5364	−0.730992
$869$	−42.2277	−1.43247
$870$	−30.1049	−1.02065
$871$	24.1675	0.818884
$872$	−26.8310	−0.908611
$873$	0.423654	0.0143385
$874$	12.8442	0.434461
$875$	−11.4371	−0.386646
$876$	−8.63433	−0.291727
$877$	−10.6040	−0.358073	−0.179036	−	0.983842i	$-0.557298\pi$
$877$	−10.6040	−0.358073	−0.179036	+	0.983842i	$0.557298\pi$
$878$	−67.2958	−2.27112
$879$	15.6002	0.526181
$880$	14.7259	0.496409
$881$	−14.8788	−0.501281	−0.250640	−	0.968080i	$-0.580641\pi$
$881$	−14.8788	−0.501281	−0.250640	+	0.968080i	$0.580641\pi$
$882$	3.49655	0.117735
$883$	−44.2645	−1.48962	−0.744809	−	0.667277i	$-0.767460\pi$
$883$	−44.2645	−1.48962	−0.744809	+	0.667277i	$0.767460\pi$
$884$	−56.9465	−1.91532
$885$	8.04879	0.270557
$886$	−56.8447	−1.90974
$887$	36.5172	1.22613	0.613064	−	0.790033i	$-0.289937\pi$
$887$	36.5172	1.22613	0.613064	+	0.790033i	$0.289937\pi$
$888$	−10.9094	−0.366094
$889$	16.9043	0.566952
$890$	26.9041	0.901828
$891$	10.6752	0.357632
$892$	52.7279	1.76546
$893$	4.65067	0.155629
$894$	−52.9274	−1.77016
$895$	43.9093	1.46772
$896$	15.1449	0.505957
$897$	12.4805	0.416712
$898$	52.7031	1.75872
$899$	−37.7005	−1.25738
$900$	1.13840	0.0379466
$901$	36.9453	1.23082
$902$	15.0510	0.501142
$903$	15.2508	0.507515
$904$	−31.3394	−1.04233
$905$	−50.8338	−1.68977
$906$	−48.6880	−1.61755
$907$	−1.12836	−0.0374667	−0.0187333	−	0.999825i	$-0.505963\pi$
$907$	−1.12836	−0.0374667	−0.0187333	+	0.999825i	$0.505963\pi$
$908$	41.4428	1.37533
$909$	20.4253	0.677465
$910$	21.8078	0.722922
$911$	−11.5145	−0.381491	−0.190746	−	0.981640i	$-0.561091\pi$
$911$	−11.5145	−0.381491	−0.190746	+	0.981640i	$0.561091\pi$
$912$	−3.42720	−0.113486
$913$	55.5752	1.83927
$914$	17.2210	0.569621
$915$	−17.6569	−0.583721
$916$	−27.2758	−0.901217
$917$	−18.4901	−0.610595
$918$	52.1394	1.72086
$919$	1.77145	0.0584348	0.0292174	−	0.999573i	$-0.490698\pi$
$919$	1.77145	0.0584348	0.0292174	+	0.999573i	$0.490698\pi$
$920$	10.8468	0.357607
$921$	−0.197017	−0.00649194
$922$	36.3563	1.19733
$923$	14.9524	0.492165
$924$	−20.7012	−0.681019
$925$	−1.04399	−0.0343260
$926$	4.29363	0.141098
$927$	−24.1870	−0.794404
$928$	35.5193	1.16598
$929$	−22.5707	−0.740522	−0.370261	−	0.928928i	$-0.620732\pi$
$929$	−22.5707	−0.740522	−0.370261	+	0.928928i	$0.620732\pi$
$930$	42.2476	1.38535
$931$	2.48108	0.0813140
$932$	34.0032	1.11381
$933$	−16.0664	−0.525991
$934$	−42.2591	−1.38276
$935$	−54.6092	−1.78591
$936$	−15.0851	−0.493073
$937$	32.6902	1.06794	0.533971	−	0.845503i	$-0.320699\pi$
$937$	32.6902	1.06794	0.533971	+	0.845503i	$0.320699\pi$
$938$	11.9882	0.391429
$939$	1.98389	0.0647419
$940$	12.1024	0.394736
$941$	13.9985	0.456337	0.228168	−	0.973622i	$-0.426726\pi$
$941$	13.9985	0.456337	0.228168	+	0.973622i	$0.426726\pi$
$942$	17.0784	0.556444
$943$	−2.68649	−0.0874841
$944$	−3.56512	−0.116035
$945$	−11.9171	−0.387664
$946$	166.063	5.39917
$947$	17.1140	0.556129	0.278065	−	0.960562i	$-0.410307\pi$
$947$	17.1140	0.556129	0.278065	+	0.960562i	$0.410307\pi$
$948$	25.5747	0.830629
$949$	10.9491	0.355423
$950$	1.35342	0.0439109
$951$	−18.0722	−0.586030
$952$	−9.16703	−0.297105
$953$	−46.4166	−1.50358	−0.751791	−	0.659402i	$-0.770810\pi$
$953$	−46.4166	−1.50358	−0.751791	+	0.659402i	$0.770810\pi$
$954$	30.1580	0.976401
$955$	−42.6866	−1.38131
$956$	−20.3759	−0.659003
$957$	−36.2385	−1.17142
$958$	63.4137	2.04880
$959$	−7.50135	−0.242231
$960$	−33.7790	−1.09021
$961$	21.9069	0.706675
$962$	42.6296	1.37443
$963$	−29.1994	−0.940938
$964$	−7.86307	−0.253252
$965$	17.9287	0.577144
$966$	6.19092	0.199190
$967$	36.6621	1.17897	0.589487	−	0.807778i	$-0.299330\pi$
$967$	36.6621	1.17897	0.589487	+	0.807778i	$0.299330\pi$
$968$	−49.6088	−1.59449
$969$	12.7094	0.408285
$970$	1.31071	0.0420844
$971$	−23.4903	−0.753840	−0.376920	−	0.926246i	$-0.623017\pi$
$971$	−23.4903	−0.753840	−0.376920	+	0.926246i	$0.623017\pi$
$972$	42.0780	1.34965
$973$	18.9659	0.608020
$974$	−4.36356	−0.139818
$975$	1.31510	0.0421170
$976$	7.82094	0.250342
$977$	36.4141	1.16499	0.582496	−	0.812834i	$-0.302076\pi$
$977$	36.4141	1.16499	0.582496	+	0.812834i	$0.302076\pi$
$978$	−47.8619	−1.53046
$979$	32.3856	1.03505
$980$	6.45647	0.206244
$981$	−19.6819	−0.628393
$982$	−56.6208	−1.80684
$983$	−40.0144	−1.27626	−0.638130	−	0.769928i	$-0.720292\pi$
$983$	−40.0144	−1.27626	−0.638130	+	0.769928i	$0.720292\pi$
$984$	−2.95813	−0.0943017
$985$	−39.4066	−1.25560
$986$	−49.4499	−1.57481
$987$	2.24163	0.0713519
$988$	−32.9846	−1.04938
$989$	−29.6410	−0.942529
$990$	−44.5769	−1.41675
$991$	20.6691	0.656575	0.328287	−	0.944578i	$-0.393529\pi$
$991$	20.6691	0.656575	0.328287	+	0.944578i	$0.393529\pi$
$992$	−49.8459	−1.58261
$993$	40.1140	1.27298
$994$	7.41711	0.235256
$995$	53.1246	1.68416
$996$	−33.6585	−1.06651
$997$	1.77657	0.0562645	0.0281322	−	0.999604i	$-0.491044\pi$
$997$	1.77657	0.0562645	0.0281322	+	0.999604i	$0.491044\pi$
$998$	−36.2995	−1.14904
$999$	−23.2954	−0.737034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.f.1.20	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.f.1.20	✓	132	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22730 q^{2} +1.19588 q^{3} +2.96085 q^{4} +2.18062 q^{5} -2.66358 q^{6} +1.00000 q^{7} -2.14009 q^{8} -1.56986 q^{9} +O(q^{10})\)	\(q-2.22730 q^{2} +1.19588 q^{3} +2.96085 q^{4} +2.18062 q^{5} -2.66358 q^{6} +1.00000 q^{7} -2.14009 q^{8} -1.56986 q^{9} -4.85688 q^{10} -5.84643 q^{11} +3.54083 q^{12} -4.49009 q^{13} -2.22730 q^{14} +2.60776 q^{15} -1.15508 q^{16} +4.28348 q^{17} +3.49655 q^{18} +2.48108 q^{19} +6.45647 q^{20} +1.19588 q^{21} +13.0217 q^{22} -2.32428 q^{23} -2.55930 q^{24} -0.244915 q^{25} +10.0008 q^{26} -5.46502 q^{27} +2.96085 q^{28} +5.18312 q^{29} -5.80826 q^{30} -7.27372 q^{31} +6.85288 q^{32} -6.99164 q^{33} -9.54057 q^{34} +2.18062 q^{35} -4.64813 q^{36} +4.26264 q^{37} -5.52609 q^{38} -5.36962 q^{39} -4.66672 q^{40} +1.15584 q^{41} -2.66358 q^{42} +12.7528 q^{43} -17.3104 q^{44} -3.42327 q^{45} +5.17687 q^{46} +1.87446 q^{47} -1.38134 q^{48} +1.00000 q^{49} +0.545499 q^{50} +5.12254 q^{51} -13.2945 q^{52} +8.62506 q^{53} +12.1722 q^{54} -12.7488 q^{55} -2.14009 q^{56} +2.96708 q^{57} -11.5443 q^{58} +3.08648 q^{59} +7.72118 q^{60} -6.77092 q^{61} +16.2007 q^{62} -1.56986 q^{63} -12.9532 q^{64} -9.79116 q^{65} +15.5725 q^{66} -5.38241 q^{67} +12.6827 q^{68} -2.77957 q^{69} -4.85688 q^{70} -3.33010 q^{71} +3.35965 q^{72} -2.43851 q^{73} -9.49416 q^{74} -0.292890 q^{75} +7.34609 q^{76} -5.84643 q^{77} +11.9597 q^{78} +7.22282 q^{79} -2.51878 q^{80} -1.82593 q^{81} -2.57439 q^{82} -9.50584 q^{83} +3.54083 q^{84} +9.34062 q^{85} -28.4042 q^{86} +6.19840 q^{87} +12.5119 q^{88} -5.53939 q^{89} +7.62464 q^{90} -4.49009 q^{91} -6.88185 q^{92} -8.69851 q^{93} -4.17497 q^{94} +5.41027 q^{95} +8.19524 q^{96} -0.269867 q^{97} -2.22730 q^{98} +9.17809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9}+O(q^{10}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9	\( 132 q + 8 q^{2} + 10 q^{3} + 174 q^{4} + 11 q^{5} + 16 q^{6} + 132 q^{7} + 30 q^{8} + 178 q^{9} + 22 q^{10} + 32 q^{11} + 30 q^{12} + 16 q^{13} + 8 q^{14} + 59 q^{15} + 254 q^{16} + 11 q^{17} + 33 q^{18} + 40 q^{19} + 4 q^{20} + 10 q^{21} + 66 q^{22} + 62 q^{23} + 36 q^{24} + 235 q^{25} + 25 q^{26} + 37 q^{27} + 174 q^{28} + 28 q^{29} + 45 q^{30} + 121 q^{31} + 53 q^{32} - 13 q^{33} + 44 q^{34} + 11 q^{35} + 274 q^{36} + 61 q^{37} - 28 q^{38} + 114 q^{39} + 32 q^{40} - q^{41} + 16 q^{42} + 105 q^{43} + 54 q^{44} + 29 q^{45} + 104 q^{46} + 33 q^{47} + 16 q^{48} + 132 q^{49} - 14 q^{50} + 53 q^{51} - 11 q^{52} + 48 q^{53} + 11 q^{54} + 118 q^{55} + 30 q^{56} + 93 q^{57} + 87 q^{58} + 12 q^{59} + 41 q^{60} + 54 q^{61} - 28 q^{62} + 178 q^{63} + 376 q^{64} + 22 q^{65} + 6 q^{66} + 123 q^{67} - 47 q^{68} + 58 q^{69} + 22 q^{70} + 108 q^{71} + 97 q^{72} + q^{73} - 10 q^{74} + 23 q^{75} + 71 q^{76} + 32 q^{77} + 5 q^{78} + 204 q^{79} - 10 q^{80} + 296 q^{81} + 80 q^{82} - 10 q^{83} + 30 q^{84} + 94 q^{85} + 48 q^{86} + 4 q^{87} + 155 q^{88} + q^{89} - 66 q^{90} + 16 q^{91} + 49 q^{92} + 90 q^{93} + 79 q^{94} + 100 q^{95} + q^{96} + 18 q^{97} + 8 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q + 8 * q^2 + 10 * q^3 + 174 * q^4 + 11 * q^5 + 16 * q^6 + 132 * q^7 + 30 * q^8 + 178 * q^9 + 22 * q^10 + 32 * q^11 + 30 * q^12 + 16 * q^13 + 8 * q^14 + 59 * q^15 + 254 * q^16 + 11 * q^17 + 33 * q^18 + 40 * q^19 + 4 * q^20 + 10 * q^21 + 66 * q^22 + 62 * q^23 + 36 * q^24 + 235 * q^25 + 25 * q^26 + 37 * q^27 + 174 * q^28 + 28 * q^29 + 45 * q^30 + 121 * q^31 + 53 * q^32 - 13 * q^33 + 44 * q^34 + 11 * q^35 + 274 * q^36 + 61 * q^37 - 28 * q^38 + 114 * q^39 + 32 * q^40 - q^41 + 16 * q^42 + 105 * q^43 + 54 * q^44 + 29 * q^45 + 104 * q^46 + 33 * q^47 + 16 * q^48 + 132 * q^49 - 14 * q^50 + 53 * q^51 - 11 * q^52 + 48 * q^53 + 11 * q^54 + 118 * q^55 + 30 * q^56 + 93 * q^57 + 87 * q^58 + 12 * q^59 + 41 * q^60 + 54 * q^61 - 28 * q^62 + 178 * q^63 + 376 * q^64 + 22 * q^65 + 6 * q^66 + 123 * q^67 - 47 * q^68 + 58 * q^69 + 22 * q^70 + 108 * q^71 + 97 * q^72 + q^73 - 10 * q^74 + 23 * q^75 + 71 * q^76 + 32 * q^77 + 5 * q^78 + 204 * q^79 - 10 * q^80 + 296 * q^81 + 80 * q^82 - 10 * q^83 + 30 * q^84 + 94 * q^85 + 48 * q^86 + 4 * q^87 + 155 * q^88 + q^89 - 66 * q^90 + 16 * q^91 + 49 * q^92 + 90 * q^93 + 79 * q^94 + 100 * q^95 + q^96 + 18 * q^97 + 8 * q^98 + 96 * q^99

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