LMFDB - Embedded newform 8041.2.a.j.1.40

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.40
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.138157 q^{2} -1.77026 q^{3} -1.98091 q^{4} -2.30104 q^{5} +0.244574 q^{6} +3.07957 q^{7} +0.549992 q^{8} +0.133817 q^{9} +O(q^{10})$	\(q-0.138157 q^{2} -1.77026 q^{3} -1.98091 q^{4} -2.30104 q^{5} +0.244574 q^{6} +3.07957 q^{7} +0.549992 q^{8} +0.133817 q^{9} +0.317905 q^{10} +1.00000 q^{11} +3.50673 q^{12} -4.12800 q^{13} -0.425465 q^{14} +4.07343 q^{15} +3.88584 q^{16} +1.00000 q^{17} -0.0184878 q^{18} +4.62750 q^{19} +4.55816 q^{20} -5.45163 q^{21} -0.138157 q^{22} +1.54030 q^{23} -0.973628 q^{24} +0.294780 q^{25} +0.570313 q^{26} +5.07389 q^{27} -6.10035 q^{28} +2.75925 q^{29} -0.562775 q^{30} +0.899523 q^{31} -1.63684 q^{32} -1.77026 q^{33} -0.138157 q^{34} -7.08620 q^{35} -0.265080 q^{36} -3.77749 q^{37} -0.639322 q^{38} +7.30763 q^{39} -1.26555 q^{40} +6.22956 q^{41} +0.753183 q^{42} +1.00000 q^{43} -1.98091 q^{44} -0.307918 q^{45} -0.212803 q^{46} +4.88646 q^{47} -6.87894 q^{48} +2.48374 q^{49} -0.0407260 q^{50} -1.77026 q^{51} +8.17721 q^{52} -6.19798 q^{53} -0.700994 q^{54} -2.30104 q^{55} +1.69374 q^{56} -8.19187 q^{57} -0.381211 q^{58} -10.5833 q^{59} -8.06912 q^{60} +14.6357 q^{61} -0.124276 q^{62} +0.412099 q^{63} -7.54554 q^{64} +9.49869 q^{65} +0.244574 q^{66} -9.39569 q^{67} -1.98091 q^{68} -2.72673 q^{69} +0.979011 q^{70} +10.8128 q^{71} +0.0735983 q^{72} -7.35850 q^{73} +0.521888 q^{74} -0.521837 q^{75} -9.16667 q^{76} +3.07957 q^{77} -1.00960 q^{78} +16.4825 q^{79} -8.94147 q^{80} -9.38354 q^{81} -0.860659 q^{82} -8.51612 q^{83} +10.7992 q^{84} -2.30104 q^{85} -0.138157 q^{86} -4.88460 q^{87} +0.549992 q^{88} +13.2611 q^{89} +0.0425411 q^{90} -12.7125 q^{91} -3.05120 q^{92} -1.59239 q^{93} -0.675099 q^{94} -10.6480 q^{95} +2.89763 q^{96} +3.98635 q^{97} -0.343146 q^{98} +0.133817 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) $ 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * 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 $

$2$	−0.138157	−0.0976920	−0.0488460	−	0.998806i	$-0.515554\pi$
$2$	−0.138157	−0.0976920	−0.0488460	+	0.998806i	$0.515554\pi$
$3$	−1.77026	−1.02206	−0.511030	−	0.859563i	$-0.670736\pi$
$3$	−1.77026	−1.02206	−0.511030	+	0.859563i	$0.670736\pi$
$4$	−1.98091	−0.990456
$5$	−2.30104	−1.02906	−0.514528	−	0.857474i	$-0.672033\pi$
$5$	−2.30104	−1.02906	−0.514528	+	0.857474i	$0.672033\pi$
$6$	0.244574	0.0998470
$7$	3.07957	1.16397	0.581984	−	0.813201i	$-0.302277\pi$
$7$	3.07957	1.16397	0.581984	+	0.813201i	$0.302277\pi$
$8$	0.549992	0.194452
$9$	0.133817	0.0446057
$10$	0.317905	0.100530
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.50673	1.01231
$13$	−4.12800	−1.14490	−0.572451	−	0.819939i	$-0.694007\pi$
$13$	−4.12800	−1.14490	−0.572451	+	0.819939i	$0.694007\pi$
$14$	−0.425465	−0.113710
$15$	4.07343	1.05176
$16$	3.88584	0.971460
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.0184878	−0.00435762
$19$	4.62750	1.06162	0.530810	−	0.847491i	$-0.321888\pi$
$19$	4.62750	1.06162	0.530810	+	0.847491i	$0.321888\pi$
$20$	4.55816	1.01923
$21$	−5.45163	−1.18964
$22$	−0.138157	−0.0294552
$23$	1.54030	0.321174	0.160587	−	0.987022i	$-0.448661\pi$
$23$	1.54030	0.321174	0.160587	+	0.987022i	$0.448661\pi$
$24$	−0.973628	−0.198741
$25$	0.294780	0.0589560
$26$	0.570313	0.111848
$27$	5.07389	0.976470
$28$	−6.10035	−1.15286
$29$	2.75925	0.512381	0.256190	−	0.966626i	$-0.417533\pi$
$29$	2.75925	0.512381	0.256190	+	0.966626i	$0.417533\pi$
$30$	−0.562775	−0.102748
$31$	0.899523	0.161559	0.0807795	−	0.996732i	$-0.474259\pi$
$31$	0.899523	0.161559	0.0807795	+	0.996732i	$0.474259\pi$
$32$	−1.63684	−0.289355
$33$	−1.77026	−0.308163
$34$	−0.138157	−0.0236938
$35$	−7.08620	−1.19779
$36$	−0.265080	−0.0441800
$37$	−3.77749	−0.621015	−0.310508	−	0.950571i	$-0.600499\pi$
$37$	−3.77749	−0.621015	−0.310508	+	0.950571i	$0.600499\pi$
$38$	−0.639322	−0.103712
$39$	7.30763	1.17016
$40$	−1.26555	−0.200102
$41$	6.22956	0.972894	0.486447	−	0.873710i	$-0.338293\pi$
$41$	6.22956	0.972894	0.486447	+	0.873710i	$0.338293\pi$
$42$	0.753183	0.116219
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.98091	−0.298634
$45$	−0.307918	−0.0459017
$46$	−0.212803	−0.0313761
$47$	4.88646	0.712763	0.356381	−	0.934341i	$-0.384010\pi$
$47$	4.88646	0.712763	0.356381	+	0.934341i	$0.384010\pi$
$48$	−6.87894	−0.992890
$49$	2.48374	0.354819
$50$	−0.0407260	−0.00575952
$51$	−1.77026	−0.247886
$52$	8.17721	1.13397
$53$	−6.19798	−0.851358	−0.425679	−	0.904874i	$-0.639965\pi$
$53$	−6.19798	−0.851358	−0.425679	+	0.904874i	$0.639965\pi$
$54$	−0.700994	−0.0953932
$55$	−2.30104	−0.310272
$56$	1.69374	0.226335
$57$	−8.19187	−1.08504
$58$	−0.381211	−0.0500555
$59$	−10.5833	−1.37783	−0.688914	−	0.724843i	$-0.741912\pi$
$59$	−10.5833	−1.37783	−0.688914	+	0.724843i	$0.741912\pi$
$60$	−8.06912	−1.04172
$61$	14.6357	1.87391	0.936955	−	0.349451i	$-0.113632\pi$
$61$	14.6357	1.87391	0.936955	+	0.349451i	$0.113632\pi$
$62$	−0.124276	−0.0157830
$63$	0.412099	0.0519195
$64$	−7.54554	−0.943192
$65$	9.49869	1.17817
$66$	0.244574	0.0301050
$67$	−9.39569	−1.14787	−0.573933	−	0.818902i	$-0.694583\pi$
$67$	−9.39569	−1.14787	−0.573933	+	0.818902i	$0.694583\pi$
$68$	−1.98091	−0.240221
$69$	−2.72673	−0.328259
$70$	0.979011	0.117014
$71$	10.8128	1.28324	0.641620	−	0.767022i	$-0.278262\pi$
$71$	10.8128	1.28324	0.641620	+	0.767022i	$0.278262\pi$
$72$	0.0735983	0.00867364
$73$	−7.35850	−0.861247	−0.430623	−	0.902532i	$-0.641706\pi$
$73$	−7.35850	−0.861247	−0.430623	+	0.902532i	$0.641706\pi$
$74$	0.521888	0.0606682
$75$	−0.521837	−0.0602565
$76$	−9.16667	−1.05149
$77$	3.07957	0.350949
$78$	−1.00960	−0.114315
$79$	16.4825	1.85443	0.927214	−	0.374532i	$-0.122197\pi$
$79$	16.4825	1.85443	0.927214	+	0.374532i	$0.122197\pi$
$80$	−8.94147	−0.999687
$81$	−9.38354	−1.04262
$82$	−0.860659	−0.0950439
$83$	−8.51612	−0.934766	−0.467383	−	0.884055i	$-0.654803\pi$
$83$	−8.51612	−0.934766	−0.467383	+	0.884055i	$0.654803\pi$
$84$	10.7992	1.17829
$85$	−2.30104	−0.249583
$86$	−0.138157	−0.0148979
$87$	−4.88460	−0.523684
$88$	0.549992	0.0586294
$89$	13.2611	1.40567	0.702835	−	0.711353i	$-0.251917\pi$
$89$	13.2611	1.40567	0.702835	+	0.711353i	$0.251917\pi$
$90$	0.0425411	0.00448423
$91$	−12.7125	−1.33263
$92$	−3.05120	−0.318109
$93$	−1.59239	−0.165123
$94$	−0.675099	−0.0696312
$95$	−10.6480	−1.09247
$96$	2.89763	0.295738
$97$	3.98635	0.404753	0.202376	−	0.979308i	$-0.435134\pi$
$97$	3.98635	0.404753	0.202376	+	0.979308i	$0.435134\pi$
$98$	−0.343146	−0.0346630
$99$	0.133817	0.0134491
$100$	−0.583933	−0.0583933
$101$	−8.82813	−0.878432	−0.439216	−	0.898382i	$-0.644744\pi$
$101$	−8.82813	−0.878432	−0.439216	+	0.898382i	$0.644744\pi$
$102$	0.244574	0.0242165
$103$	−8.55177	−0.842631	−0.421315	−	0.906914i	$-0.638431\pi$
$103$	−8.55177	−0.842631	−0.421315	+	0.906914i	$0.638431\pi$
$104$	−2.27037	−0.222628
$105$	12.5444	1.22421
$106$	0.856296	0.0831708
$107$	−13.3237	−1.28805	−0.644025	−	0.765005i	$-0.722737\pi$
$107$	−13.3237	−1.28805	−0.644025	+	0.765005i	$0.722737\pi$
$108$	−10.0509	−0.967151
$109$	−12.9073	−1.23629	−0.618146	−	0.786063i	$-0.712116\pi$
$109$	−12.9073	−1.23629	−0.618146	+	0.786063i	$0.712116\pi$
$110$	0.317905	0.0303111
$111$	6.68713	0.634715
$112$	11.9667	1.13075
$113$	3.62698	0.341197	0.170599	−	0.985341i	$-0.445430\pi$
$113$	3.62698	0.341197	0.170599	+	0.985341i	$0.445430\pi$
$114$	1.13177	0.106000
$115$	−3.54429	−0.330506
$116$	−5.46584	−0.507491
$117$	−0.552397	−0.0510691
$118$	1.46216	0.134603
$119$	3.07957	0.282303
$120$	2.24036	0.204516
$121$	1.00000	0.0909091
$122$	−2.02203	−0.183066
$123$	−11.0279	−0.994355
$124$	−1.78188	−0.160017
$125$	10.8269	0.968387
$126$	−0.0569344	−0.00507212
$127$	−17.0513	−1.51306	−0.756528	−	0.653961i	$-0.773106\pi$
$127$	−17.0513	−1.51306	−0.756528	+	0.653961i	$0.773106\pi$
$128$	4.31615	0.381498
$129$	−1.77026	−0.155863
$130$	−1.31231	−0.115097
$131$	−20.7712	−1.81479	−0.907395	−	0.420278i	$-0.861933\pi$
$131$	−20.7712	−1.81479	−0.907395	+	0.420278i	$0.861933\pi$
$132$	3.50673	0.305222
$133$	14.2507	1.23569
$134$	1.29808	0.112137
$135$	−11.6752	−1.00484
$136$	0.549992	0.0471614
$137$	−11.8344	−1.01108	−0.505542	−	0.862802i	$-0.668707\pi$
$137$	−11.8344	−1.01108	−0.505542	+	0.862802i	$0.668707\pi$
$138$	0.376717	0.0320683
$139$	15.0965	1.28047	0.640236	−	0.768178i	$-0.278837\pi$
$139$	15.0965	1.28047	0.640236	+	0.768178i	$0.278837\pi$
$140$	14.0372	1.18636
$141$	−8.65029	−0.728486
$142$	−1.49386	−0.125362
$143$	−4.12800	−0.345201
$144$	0.519992	0.0433326
$145$	−6.34915	−0.527268
$146$	1.01663	0.0841369
$147$	−4.39686	−0.362647
$148$	7.48288	0.615089
$149$	6.92757	0.567529	0.283764	−	0.958894i	$-0.408417\pi$
$149$	6.92757	0.567529	0.283764	+	0.958894i	$0.408417\pi$
$150$	0.0720956	0.00588658
$151$	0.590593	0.0480618	0.0240309	−	0.999711i	$-0.492350\pi$
$151$	0.590593	0.0480618	0.0240309	+	0.999711i	$0.492350\pi$
$152$	2.54509	0.206434
$153$	0.133817	0.0108185
$154$	−0.425465	−0.0342849
$155$	−2.06984	−0.166253
$156$	−14.4758	−1.15899
$157$	−7.94091	−0.633754	−0.316877	−	0.948467i	$-0.602634\pi$
$157$	−7.94091	−0.633754	−0.316877	+	0.948467i	$0.602634\pi$
$158$	−2.27718	−0.181163
$159$	10.9720	0.870138
$160$	3.76644	0.297763
$161$	4.74345	0.373836
$162$	1.29640	0.101855
$163$	−1.41514	−0.110842	−0.0554212	−	0.998463i	$-0.517650\pi$
$163$	−1.41514	−0.110842	−0.0554212	+	0.998463i	$0.517650\pi$
$164$	−12.3402	−0.963609
$165$	4.07343	0.317116
$166$	1.17656	0.0913191
$167$	−4.02234	−0.311258	−0.155629	−	0.987816i	$-0.549740\pi$
$167$	−4.02234	−0.311258	−0.155629	+	0.987816i	$0.549740\pi$
$168$	−2.99835	−0.231328
$169$	4.04039	0.310799
$170$	0.317905	0.0243822
$171$	0.619238	0.0473543
$172$	−1.98091	−0.151043
$173$	−13.0145	−0.989475	−0.494738	−	0.869042i	$-0.664736\pi$
$173$	−13.0145	−0.989475	−0.494738	+	0.869042i	$0.664736\pi$
$174$	0.674842	0.0511597
$175$	0.907795	0.0686228
$176$	3.88584	0.292906
$177$	18.7352	1.40822
$178$	−1.83211	−0.137323
$179$	17.4569	1.30479	0.652394	−	0.757880i	$-0.273765\pi$
$179$	17.4569	1.30479	0.652394	+	0.757880i	$0.273765\pi$
$180$	0.609959	0.0454637
$181$	−23.0538	−1.71357	−0.856787	−	0.515671i	$-0.827543\pi$
$181$	−23.0538	−1.71357	−0.856787	+	0.515671i	$0.827543\pi$
$182$	1.75632	0.130187
$183$	−25.9090	−1.91525
$184$	0.847152	0.0624529
$185$	8.69215	0.639060
$186$	0.220000	0.0161312
$187$	1.00000	0.0731272
$188$	−9.67964	−0.705960
$189$	15.6254	1.13658
$190$	1.47111	0.106725
$191$	−8.04808	−0.582338	−0.291169	−	0.956672i	$-0.594044\pi$
$191$	−8.04808	−0.582338	−0.291169	+	0.956672i	$0.594044\pi$
$192$	13.3576	0.963999
$193$	18.9095	1.36113	0.680567	−	0.732686i	$-0.261734\pi$
$193$	18.9095	1.36113	0.680567	+	0.732686i	$0.261734\pi$
$194$	−0.550744	−0.0395411
$195$	−16.8151	−1.20416
$196$	−4.92006	−0.351433
$197$	1.83126	0.130472	0.0652360	−	0.997870i	$-0.479220\pi$
$197$	1.83126	0.130472	0.0652360	+	0.997870i	$0.479220\pi$
$198$	−0.0184878	−0.00131387
$199$	4.46656	0.316626	0.158313	−	0.987389i	$-0.449394\pi$
$199$	4.46656	0.316626	0.158313	+	0.987389i	$0.449394\pi$
$200$	0.162127	0.0114641
$201$	16.6328	1.17319
$202$	1.21967	0.0858157
$203$	8.49731	0.596394
$204$	3.50673	0.245520
$205$	−14.3345	−1.00116
$206$	1.18149	0.0823182
$207$	0.206118	0.0143262
$208$	−16.0407	−1.11223
$209$	4.62750	0.320091
$210$	−1.73310	−0.119595
$211$	10.2266	0.704028	0.352014	−	0.935995i	$-0.385497\pi$
$211$	10.2266	0.704028	0.352014	+	0.935995i	$0.385497\pi$
$212$	12.2777	0.843233
$213$	−19.1414	−1.31155
$214$	1.84076	0.125832
$215$	−2.30104	−0.156930
$216$	2.79060	0.189876
$217$	2.77014	0.188049
$218$	1.78323	0.120776
$219$	13.0264	0.880246
$220$	4.55816	0.307311
$221$	−4.12800	−0.277679
$222$	−0.923876	−0.0620065
$223$	12.6056	0.844133	0.422066	−	0.906565i	$-0.361305\pi$
$223$	12.6056	0.844133	0.422066	+	0.906565i	$0.361305\pi$
$224$	−5.04076	−0.336800
$225$	0.0394466	0.00262977
$226$	−0.501093	−0.0333322
$227$	−3.73386	−0.247825	−0.123913	−	0.992293i	$-0.539544\pi$
$227$	−3.73386	−0.247825	−0.123913	+	0.992293i	$0.539544\pi$
$228$	16.2274	1.07468
$229$	13.7928	0.911454	0.455727	−	0.890120i	$-0.349379\pi$
$229$	13.7928	0.911454	0.455727	+	0.890120i	$0.349379\pi$
$230$	0.489669	0.0322878
$231$	−5.45163	−0.358691
$232$	1.51757	0.0996332
$233$	12.3579	0.809596	0.404798	−	0.914406i	$-0.367342\pi$
$233$	12.3579	0.809596	0.404798	+	0.914406i	$0.367342\pi$
$234$	0.0763176	0.00498904
$235$	−11.2439	−0.733473
$236$	20.9646	1.36468
$237$	−29.1783	−1.89534
$238$	−0.425465	−0.0275788
$239$	3.87451	0.250621	0.125311	−	0.992118i	$-0.460007\pi$
$239$	3.87451	0.250621	0.125311	+	0.992118i	$0.460007\pi$
$240$	15.8287	1.02174
$241$	−1.32036	−0.0850519	−0.0425259	−	0.999095i	$-0.513541\pi$
$241$	−1.32036	−0.0850519	−0.0425259	+	0.999095i	$0.513541\pi$
$242$	−0.138157	−0.00888109
$243$	1.38964	0.0891458
$244$	−28.9920	−1.85603
$245$	−5.71517	−0.365129
$246$	1.52359	0.0971405
$247$	−19.1023	−1.21545
$248$	0.494730	0.0314154
$249$	15.0757	0.955386
$250$	−1.49581	−0.0946036
$251$	17.2433	1.08839	0.544193	−	0.838960i	$-0.316836\pi$
$251$	17.2433	1.08839	0.544193	+	0.838960i	$0.316836\pi$
$252$	−0.816331	−0.0514240
$253$	1.54030	0.0968377
$254$	2.35576	0.147813
$255$	4.07343	0.255088
$256$	14.4948	0.905923
$257$	8.37065	0.522147	0.261073	−	0.965319i	$-0.415924\pi$
$257$	8.37065	0.522147	0.261073	+	0.965319i	$0.415924\pi$
$258$	0.244574	0.0152265
$259$	−11.6330	−0.722842
$260$	−18.8161	−1.16692
$261$	0.369235	0.0228551
$262$	2.86970	0.177290
$263$	−8.70886	−0.537011	−0.268506	−	0.963278i	$-0.586530\pi$
$263$	−8.70886	−0.537011	−0.268506	+	0.963278i	$0.586530\pi$
$264$	−0.973628	−0.0599227
$265$	14.2618	0.876095
$266$	−1.96884	−0.120717
$267$	−23.4755	−1.43668
$268$	18.6120	1.13691
$269$	30.5399	1.86205	0.931025	−	0.364956i	$-0.118916\pi$
$269$	30.5399	1.86205	0.931025	+	0.364956i	$0.118916\pi$
$270$	1.61302	0.0981650
$271$	8.18863	0.497424	0.248712	−	0.968577i	$-0.419993\pi$
$271$	8.18863	0.497424	0.248712	+	0.968577i	$0.419993\pi$
$272$	3.88584	0.235614
$273$	22.5043	1.36202
$274$	1.63501	0.0987747
$275$	0.294780	0.0177759
$276$	5.40141	0.325126
$277$	23.8389	1.43234	0.716170	−	0.697926i	$-0.245894\pi$
$277$	23.8389	1.43234	0.716170	+	0.697926i	$0.245894\pi$
$278$	−2.08570	−0.125092
$279$	0.120371	0.00720645
$280$	−3.89736	−0.232912
$281$	−12.7470	−0.760425	−0.380213	−	0.924899i	$-0.624149\pi$
$281$	−12.7470	−0.760425	−0.380213	+	0.924899i	$0.624149\pi$
$282$	1.19510	0.0711672
$283$	8.69109	0.516632	0.258316	−	0.966060i	$-0.416832\pi$
$283$	8.69109	0.516632	0.258316	+	0.966060i	$0.416832\pi$
$284$	−21.4192	−1.27099
$285$	18.8498	1.11657
$286$	0.570313	0.0337233
$287$	19.1843	1.13242
$288$	−0.219037	−0.0129069
$289$	1.00000	0.0588235
$290$	0.877182	0.0515099
$291$	−7.05688	−0.413682
$292$	14.5765	0.853027
$293$	20.5332	1.19956	0.599781	−	0.800165i	$-0.295255\pi$
$293$	20.5332	1.19956	0.599781	+	0.800165i	$0.295255\pi$
$294$	0.607458	0.0354276
$295$	24.3526	1.41786
$296$	−2.07759	−0.120757
$297$	5.07389	0.294417
$298$	−0.957094	−0.0554430
$299$	−6.35835	−0.367713
$300$	1.03371	0.0596815
$301$	3.07957	0.177503
$302$	−0.0815947	−0.00469525
$303$	15.6281	0.897810
$304$	17.9817	1.03132
$305$	−33.6773	−1.92836
$306$	−0.0184878	−0.00105688
$307$	−30.5261	−1.74222	−0.871109	−	0.491089i	$-0.836599\pi$
$307$	−30.5261	−1.74222	−0.871109	+	0.491089i	$0.836599\pi$
$308$	−6.10035	−0.347600
$309$	15.1388	0.861219
$310$	0.285963	0.0162416
$311$	−24.6726	−1.39906	−0.699529	−	0.714605i	$-0.746607\pi$
$311$	−24.6726	−1.39906	−0.699529	+	0.714605i	$0.746607\pi$
$312$	4.01914	0.227539
$313$	−2.05516	−0.116165	−0.0580824	−	0.998312i	$-0.518499\pi$
$313$	−2.05516	−0.116165	−0.0580824	+	0.998312i	$0.518499\pi$
$314$	1.09709	0.0619126
$315$	−0.948255	−0.0534281
$316$	−32.6504	−1.83673
$317$	1.82245	0.102359	0.0511795	−	0.998689i	$-0.483702\pi$
$317$	1.82245	0.102359	0.0511795	+	0.998689i	$0.483702\pi$
$318$	−1.51587	−0.0850055
$319$	2.75925	0.154489
$320$	17.3626	0.970598
$321$	23.5864	1.31646
$322$	−0.655342	−0.0365208
$323$	4.62750	0.257481
$324$	18.5880	1.03267
$325$	−1.21685	−0.0674988
$326$	0.195512	0.0108284
$327$	22.8492	1.26356
$328$	3.42621	0.189181
$329$	15.0482	0.829632
$330$	−0.562775	−0.0309797
$331$	−20.6240	−1.13360	−0.566798	−	0.823857i	$-0.691818\pi$
$331$	−20.6240	−1.13360	−0.566798	+	0.823857i	$0.691818\pi$
$332$	16.8697	0.925844
$333$	−0.505492	−0.0277008
$334$	0.555715	0.0304074
$335$	21.6198	1.18122
$336$	−21.1842	−1.15569
$337$	15.2351	0.829911	0.414955	−	0.909842i	$-0.363797\pi$
$337$	15.2351	0.829911	0.414955	+	0.909842i	$0.363797\pi$
$338$	−0.558209	−0.0303626
$339$	−6.42069	−0.348724
$340$	4.55816	0.247201
$341$	0.899523	0.0487119
$342$	−0.0855522	−0.00462613
$343$	−13.9081	−0.750969
$344$	0.549992	0.0296536
$345$	6.27430	0.337797
$346$	1.79805	0.0966637
$347$	24.2964	1.30430	0.652150	−	0.758090i	$-0.273867\pi$
$347$	24.2964	1.30430	0.652150	+	0.758090i	$0.273867\pi$
$348$	9.67596	0.518686
$349$	9.47095	0.506968	0.253484	−	0.967340i	$-0.418423\pi$
$349$	9.47095	0.506968	0.253484	+	0.967340i	$0.418423\pi$
$350$	−0.125418	−0.00670390
$351$	−20.9450	−1.11796
$352$	−1.63684	−0.0872439
$353$	3.70159	0.197016	0.0985078	−	0.995136i	$-0.468593\pi$
$353$	3.70159	0.197016	0.0985078	+	0.995136i	$0.468593\pi$
$354$	−2.58840	−0.137572
$355$	−24.8806	−1.32053
$356$	−26.2690	−1.39225
$357$	−5.45163	−0.288531
$358$	−2.41179	−0.127467
$359$	6.72368	0.354862	0.177431	−	0.984133i	$-0.443221\pi$
$359$	6.72368	0.354862	0.177431	+	0.984133i	$0.443221\pi$
$360$	−0.169353	−0.00892566
$361$	2.41372	0.127038
$362$	3.18505	0.167402
$363$	−1.77026	−0.0929145
$364$	25.1823	1.31991
$365$	16.9322	0.886271
$366$	3.57951	0.187104
$367$	−25.1418	−1.31239	−0.656196	−	0.754590i	$-0.727836\pi$
$367$	−25.1418	−1.31239	−0.656196	+	0.754590i	$0.727836\pi$
$368$	5.98535	0.312008
$369$	0.833621	0.0433966
$370$	−1.20088	−0.0624310
$371$	−19.0871	−0.990953
$372$	3.15438	0.163547
$373$	−17.5440	−0.908394	−0.454197	−	0.890901i	$-0.650074\pi$
$373$	−17.5440	−0.908394	−0.454197	+	0.890901i	$0.650074\pi$
$374$	−0.138157	−0.00714394
$375$	−19.1664	−0.989749
$376$	2.68751	0.138598
$377$	−11.3902	−0.586625
$378$	−2.15876	−0.111035
$379$	5.61567	0.288458	0.144229	−	0.989544i	$-0.453930\pi$
$379$	5.61567	0.288458	0.144229	+	0.989544i	$0.453930\pi$
$380$	21.0929	1.08204
$381$	30.1852	1.54643
$382$	1.11190	0.0568898
$383$	34.9972	1.78827	0.894136	−	0.447796i	$-0.147791\pi$
$383$	34.9972	1.78827	0.894136	+	0.447796i	$0.147791\pi$
$384$	−7.64071	−0.389913
$385$	−7.08620	−0.361146
$386$	−2.61248	−0.132972
$387$	0.133817	0.00680230
$388$	−7.89662	−0.400890
$389$	35.5299	1.80144	0.900718	−	0.434405i	$-0.143041\pi$
$389$	35.5299	1.80144	0.900718	+	0.434405i	$0.143041\pi$
$390$	2.32313	0.117636
$391$	1.54030	0.0778962
$392$	1.36603	0.0689952
$393$	36.7705	1.85482
$394$	−0.253002	−0.0127461
$395$	−37.9269	−1.90831
$396$	−0.265080	−0.0133208
$397$	−15.4672	−0.776278	−0.388139	−	0.921601i	$-0.626882\pi$
$397$	−15.4672	−0.776278	−0.388139	+	0.921601i	$0.626882\pi$
$398$	−0.617088	−0.0309318
$399$	−25.2274	−1.26295
$400$	1.14547	0.0572734
$401$	5.70405	0.284847	0.142423	−	0.989806i	$-0.454511\pi$
$401$	5.70405	0.284847	0.142423	+	0.989806i	$0.454511\pi$
$402$	−2.29794	−0.114611
$403$	−3.71323	−0.184969
$404$	17.4878	0.870048
$405$	21.5919	1.07291
$406$	−1.17397	−0.0582629
$407$	−3.77749	−0.187243
$408$	−0.973628	−0.0482018
$409$	8.70768	0.430567	0.215284	−	0.976552i	$-0.430932\pi$
$409$	8.70768	0.430567	0.215284	+	0.976552i	$0.430932\pi$
$410$	1.98041	0.0978055
$411$	20.9500	1.03339
$412$	16.9403	0.834589
$413$	−32.5920	−1.60375
$414$	−0.0284767	−0.00139955
$415$	19.5959	0.961926
$416$	6.75688	0.331283
$417$	−26.7248	−1.30872
$418$	−0.639322	−0.0312703
$419$	−12.8534	−0.627928	−0.313964	−	0.949435i	$-0.601657\pi$
$419$	−12.8534	−0.627928	−0.313964	+	0.949435i	$0.601657\pi$
$420$	−24.8494	−1.21253
$421$	−23.6749	−1.15384	−0.576922	−	0.816799i	$-0.695746\pi$
$421$	−23.6749	−1.15384	−0.576922	+	0.816799i	$0.695746\pi$
$422$	−1.41288	−0.0687778
$423$	0.653891	0.0317933
$424$	−3.40884	−0.165548
$425$	0.294780	0.0142989
$426$	2.64453	0.128128
$427$	45.0716	2.18117
$428$	26.3931	1.27576
$429$	7.30763	0.352816
$430$	0.317905	0.0153308
$431$	−28.3297	−1.36459	−0.682296	−	0.731076i	$-0.739018\pi$
$431$	−28.3297	−1.36459	−0.682296	+	0.731076i	$0.739018\pi$
$432$	19.7163	0.948601
$433$	12.8062	0.615427	0.307714	−	0.951479i	$-0.400436\pi$
$433$	12.8062	0.615427	0.307714	+	0.951479i	$0.400436\pi$
$434$	−0.382715	−0.0183709
$435$	11.2396	0.538900
$436$	25.5682	1.22449
$437$	7.12772	0.340965
$438$	−1.79970	−0.0859929
$439$	25.6553	1.22446	0.612231	−	0.790679i	$-0.290272\pi$
$439$	25.6553	1.22446	0.612231	+	0.790679i	$0.290272\pi$
$440$	−1.26555	−0.0603329
$441$	0.332366	0.0158270
$442$	0.570313	0.0271270
$443$	−25.2589	−1.20009	−0.600044	−	0.799967i	$-0.704850\pi$
$443$	−25.2589	−1.20009	−0.600044	+	0.799967i	$0.704850\pi$
$444$	−13.2466	−0.628657
$445$	−30.5142	−1.44651
$446$	−1.74155	−0.0824650
$447$	−12.2636	−0.580048
$448$	−23.2370	−1.09784
$449$	27.1753	1.28248	0.641241	−	0.767339i	$-0.278420\pi$
$449$	27.1753	1.28248	0.641241	+	0.767339i	$0.278420\pi$
$450$	−0.00544983	−0.000256908 0
$451$	6.22956	0.293338
$452$	−7.18472	−0.337941
$453$	−1.04550	−0.0491220
$454$	0.515861	0.0242105
$455$	29.2519	1.37135
$456$	−4.50546	−0.210988
$457$	20.6255	0.964818	0.482409	−	0.875946i	$-0.339762\pi$
$457$	20.6255	0.964818	0.482409	+	0.875946i	$0.339762\pi$
$458$	−1.90558	−0.0890417
$459$	5.07389	0.236829
$460$	7.02092	0.327352
$461$	0.277404	0.0129200	0.00646000	−	0.999979i	$-0.497944\pi$
$461$	0.277404	0.0129200	0.00646000	+	0.999979i	$0.497944\pi$
$462$	0.753183	0.0350412
$463$	−34.3694	−1.59728	−0.798640	−	0.601809i	$-0.794447\pi$
$463$	−34.3694	−1.59728	−0.798640	+	0.601809i	$0.794447\pi$
$464$	10.7220	0.497757
$465$	3.66415	0.169921
$466$	−1.70734	−0.0790910
$467$	13.6174	0.630137	0.315069	−	0.949069i	$-0.397972\pi$
$467$	13.6174	0.630137	0.315069	+	0.949069i	$0.397972\pi$
$468$	1.09425	0.0505817
$469$	−28.9347	−1.33608
$470$	1.55343	0.0716544
$471$	14.0575	0.647734
$472$	−5.82073	−0.267921
$473$	1.00000	0.0459800
$474$	4.03120	0.185159
$475$	1.36409	0.0625889
$476$	−6.10035	−0.279609
$477$	−0.829395	−0.0379754
$478$	−0.535292	−0.0244837
$479$	−13.8599	−0.633274	−0.316637	−	0.948547i	$-0.602554\pi$
$479$	−13.8599	−0.633274	−0.316637	+	0.948547i	$0.602554\pi$
$480$	−6.66757	−0.304331
$481$	15.5935	0.711001
$482$	0.182417	0.00830888
$483$	−8.39714	−0.382083
$484$	−1.98091	−0.0900415
$485$	−9.17276	−0.416513
$486$	−0.191990	−0.00870882
$487$	15.7869	0.715372	0.357686	−	0.933842i	$-0.383566\pi$
$487$	15.7869	0.715372	0.357686	+	0.933842i	$0.383566\pi$
$488$	8.04952	0.364385
$489$	2.50516	0.113287
$490$	0.789593	0.0356702
$491$	38.6960	1.74633	0.873163	−	0.487428i	$-0.162065\pi$
$491$	38.6960	1.74633	0.873163	+	0.487428i	$0.162065\pi$
$492$	21.8454	0.984865
$493$	2.75925	0.124271
$494$	2.63912	0.118740
$495$	−0.307918	−0.0138399
$496$	3.49540	0.156948
$497$	33.2987	1.49365
$498$	−2.08282	−0.0933335
$499$	6.91948	0.309758	0.154879	−	0.987933i	$-0.450501\pi$
$499$	6.91948	0.309758	0.154879	+	0.987933i	$0.450501\pi$
$500$	−21.4471	−0.959145
$501$	7.12058	0.318124
$502$	−2.38229	−0.106327
$503$	−1.86296	−0.0830655	−0.0415327	−	0.999137i	$-0.513224\pi$
$503$	−1.86296	−0.0830655	−0.0415327	+	0.999137i	$0.513224\pi$
$504$	0.226651	0.0100958
$505$	20.3139	0.903955
$506$	−0.212803	−0.00946026
$507$	−7.15253	−0.317655
$508$	33.7771	1.49862
$509$	−5.74198	−0.254509	−0.127254	−	0.991870i	$-0.540616\pi$
$509$	−5.74198	−0.254509	−0.127254	+	0.991870i	$0.540616\pi$
$510$	−0.562775	−0.0249201
$511$	−22.6610	−1.00246
$512$	−10.6349	−0.469999
$513$	23.4794	1.03664
$514$	−1.15647	−0.0510095
$515$	19.6780	0.867114
$516$	3.50673	0.154375
$517$	4.88646	0.214906
$518$	1.60719	0.0706158
$519$	23.0391	1.01130
$520$	5.22420	0.229096
$521$	9.12112	0.399604	0.199802	−	0.979836i	$-0.435970\pi$
$521$	9.12112	0.399604	0.199802	+	0.979836i	$0.435970\pi$
$522$	−0.0510125	−0.00223276
$523$	21.2529	0.929323	0.464661	−	0.885488i	$-0.346176\pi$
$523$	21.2529	0.929323	0.464661	+	0.885488i	$0.346176\pi$
$524$	41.1460	1.79747
$525$	−1.60703	−0.0701366
$526$	1.20319	0.0524617
$527$	0.899523	0.0391838
$528$	−6.87894	−0.299368
$529$	−20.6275	−0.896847
$530$	−1.97037	−0.0855874
$531$	−1.41623	−0.0614590
$532$	−28.2294	−1.22390
$533$	−25.7156	−1.11387
$534$	3.24331	0.140352
$535$	30.6583	1.32548
$536$	−5.16755	−0.223204
$537$	−30.9032	−1.33357
$538$	−4.21931	−0.181907
$539$	2.48374	0.106982
$540$	23.1276	0.995252
$541$	23.6471	1.01667	0.508334	−	0.861160i	$-0.330261\pi$
$541$	23.6471	1.01667	0.508334	+	0.861160i	$0.330261\pi$
$542$	−1.13132	−0.0485943
$543$	40.8111	1.75137
$544$	−1.63684	−0.0701790
$545$	29.7001	1.27221
$546$	−3.10914	−0.133059
$547$	−5.62048	−0.240314	−0.120157	−	0.992755i	$-0.538340\pi$
$547$	−5.62048	−0.240314	−0.120157	+	0.992755i	$0.538340\pi$
$548$	23.4430	1.00143
$549$	1.95851	0.0835870
$550$	−0.0407260	−0.00173656
$551$	12.7684	0.543954
$552$	−1.49968	−0.0638305
$553$	50.7590	2.15849
$554$	−3.29351	−0.139928
$555$	−15.3874	−0.653157
$556$	−29.9049	−1.26825
$557$	5.96256	0.252642	0.126321	−	0.991989i	$-0.459683\pi$
$557$	5.96256	0.252642	0.126321	+	0.991989i	$0.459683\pi$
$558$	−0.0166302	−0.000704012 0
$559$	−4.12800	−0.174596
$560$	−27.5359	−1.16360
$561$	−1.77026	−0.0747404
$562$	1.76110	0.0742874
$563$	−4.64622	−0.195815	−0.0979074	−	0.995196i	$-0.531215\pi$
$563$	−4.64622	−0.195815	−0.0979074	+	0.995196i	$0.531215\pi$
$564$	17.1355	0.721534
$565$	−8.34581	−0.351111
$566$	−1.20074	−0.0504708
$567$	−28.8973	−1.21357
$568$	5.94694	0.249528
$569$	35.3502	1.48196	0.740979	−	0.671528i	$-0.234362\pi$
$569$	35.3502	1.48196	0.740979	+	0.671528i	$0.234362\pi$
$570$	−2.60424	−0.109080
$571$	39.4058	1.64908	0.824540	−	0.565803i	$-0.191434\pi$
$571$	39.4058	1.64908	0.824540	+	0.565803i	$0.191434\pi$
$572$	8.17721	0.341906
$573$	14.2472	0.595185
$574$	−2.65046	−0.110628
$575$	0.454049	0.0189351
$576$	−1.00972	−0.0420717
$577$	18.4164	0.766683	0.383341	−	0.923607i	$-0.374773\pi$
$577$	18.4164	0.766683	0.383341	+	0.923607i	$0.374773\pi$
$578$	−0.138157	−0.00574659
$579$	−33.4747	−1.39116
$580$	12.5771	0.522236
$581$	−26.2260	−1.08804
$582$	0.974959	0.0404134
$583$	−6.19798	−0.256694
$584$	−4.04711	−0.167471
$585$	1.27109	0.0525530
$586$	−2.83681	−0.117187
$587$	3.85601	0.159154	0.0795772	−	0.996829i	$-0.474643\pi$
$587$	3.85601	0.159154	0.0795772	+	0.996829i	$0.474643\pi$
$588$	8.70979	0.359186
$589$	4.16254	0.171514
$590$	−3.36449	−0.138514
$591$	−3.24181	−0.133350
$592$	−14.6787	−0.603292
$593$	−5.60940	−0.230351	−0.115175	−	0.993345i	$-0.536743\pi$
$593$	−5.60940	−0.230351	−0.115175	+	0.993345i	$0.536743\pi$
$594$	−0.700994	−0.0287621
$595$	−7.08620	−0.290506
$596$	−13.7229	−0.562112
$597$	−7.90697	−0.323611
$598$	0.878452	0.0359226
$599$	21.7083	0.886977	0.443489	−	0.896280i	$-0.353741\pi$
$599$	21.7083	0.886977	0.443489	+	0.896280i	$0.353741\pi$
$600$	−0.287006	−0.0117170
$601$	7.42094	0.302706	0.151353	−	0.988480i	$-0.451637\pi$
$601$	7.42094	0.302706	0.151353	+	0.988480i	$0.451637\pi$
$602$	−0.425465	−0.0173406
$603$	−1.25730	−0.0512014
$604$	−1.16991	−0.0476031
$605$	−2.30104	−0.0935505
$606$	−2.15913	−0.0877088
$607$	25.7097	1.04353	0.521763	−	0.853091i	$-0.325275\pi$
$607$	25.7097	1.04353	0.521763	+	0.853091i	$0.325275\pi$
$608$	−7.57448	−0.307186
$609$	−15.0424	−0.609550
$610$	4.65277	0.188385
$611$	−20.1713	−0.816043
$612$	−0.265080	−0.0107152
$613$	−16.9266	−0.683658	−0.341829	−	0.939762i	$-0.611046\pi$
$613$	−16.9266	−0.683658	−0.341829	+	0.939762i	$0.611046\pi$
$614$	4.21741	0.170201
$615$	25.3757	1.02325
$616$	1.69374	0.0682426
$617$	4.46848	0.179894	0.0899472	−	0.995947i	$-0.471330\pi$
$617$	4.46848	0.179894	0.0899472	+	0.995947i	$0.471330\pi$
$618$	−2.09154	−0.0841341
$619$	37.7703	1.51812	0.759059	−	0.651022i	$-0.225659\pi$
$619$	37.7703	1.51812	0.759059	+	0.651022i	$0.225659\pi$
$620$	4.10016	0.164667
$621$	7.81530	0.313617
$622$	3.40870	0.136677
$623$	40.8383	1.63615
$624$	28.3963	1.13676
$625$	−26.3870	−1.05548
$626$	0.283936	0.0113484
$627$	−8.19187	−0.327152
$628$	15.7302	0.627705
$629$	−3.77749	−0.150618
$630$	0.131008	0.00521950
$631$	−17.6976	−0.704531	−0.352265	−	0.935900i	$-0.614589\pi$
$631$	−17.6976	−0.704531	−0.352265	+	0.935900i	$0.614589\pi$
$632$	9.06525	0.360596
$633$	−18.1037	−0.719558
$634$	−0.251785	−0.00999966
$635$	39.2356	1.55702
$636$	−21.7346	−0.861834
$637$	−10.2529	−0.406233
$638$	−0.381211	−0.0150923
$639$	1.44693	0.0572398
$640$	−9.93164	−0.392582
$641$	17.6465	0.696996	0.348498	−	0.937310i	$-0.386692\pi$
$641$	17.6465	0.696996	0.348498	+	0.937310i	$0.386692\pi$
$642$	−3.25863	−0.128608
$643$	−2.35587	−0.0929065	−0.0464532	−	0.998920i	$-0.514792\pi$
$643$	−2.35587	−0.0929065	−0.0464532	+	0.998920i	$0.514792\pi$
$644$	−9.39636	−0.370269
$645$	4.07343	0.160391
$646$	−0.639322	−0.0251538
$647$	−3.10039	−0.121889	−0.0609445	−	0.998141i	$-0.519411\pi$
$647$	−3.10039	−0.121889	−0.0609445	+	0.998141i	$0.519411\pi$
$648$	−5.16087	−0.202738
$649$	−10.5833	−0.415431
$650$	0.168117	0.00659409
$651$	−4.90387	−0.192198
$652$	2.80327	0.109784
$653$	−3.41715	−0.133723	−0.0668617	−	0.997762i	$-0.521299\pi$
$653$	−3.41715	−0.133723	−0.0668617	+	0.997762i	$0.521299\pi$
$654$	−3.15678	−0.123440
$655$	47.7954	1.86752
$656$	24.2071	0.945127
$657$	−0.984692	−0.0384165
$658$	−2.07901	−0.0810484
$659$	10.1749	0.396358	0.198179	−	0.980166i	$-0.436497\pi$
$659$	10.1749	0.396358	0.198179	+	0.980166i	$0.436497\pi$
$660$	−8.06912	−0.314090
$661$	−47.7452	−1.85707	−0.928537	−	0.371240i	$-0.878933\pi$
$661$	−47.7452	−1.85707	−0.928537	+	0.371240i	$0.878933\pi$
$662$	2.84935	0.110743
$663$	7.30763	0.283805
$664$	−4.68380	−0.181767
$665$	−32.7914	−1.27160
$666$	0.0698375	0.00270615
$667$	4.25007	0.164564
$668$	7.96790	0.308287
$669$	−22.3152	−0.862754
$670$	−2.98694	−0.115396
$671$	14.6357	0.565005
$672$	8.92346	0.344230
$673$	2.28727	0.0881678	0.0440839	−	0.999028i	$-0.485963\pi$
$673$	2.28727	0.0881678	0.0440839	+	0.999028i	$0.485963\pi$
$674$	−2.10485	−0.0810756
$675$	1.49568	0.0575687
$676$	−8.00365	−0.307833
$677$	43.7037	1.67967	0.839835	−	0.542842i	$-0.182652\pi$
$677$	43.7037	1.67967	0.839835	+	0.542842i	$0.182652\pi$
$678$	0.887064	0.0340675
$679$	12.2762	0.471119
$680$	−1.26555	−0.0485317
$681$	6.60991	0.253292
$682$	−0.124276	−0.00475876
$683$	−3.83454	−0.146725	−0.0733624	−	0.997305i	$-0.523373\pi$
$683$	−3.83454	−0.146725	−0.0733624	+	0.997305i	$0.523373\pi$
$684$	−1.22666	−0.0469024
$685$	27.2315	1.04046
$686$	1.92151	0.0733636
$687$	−24.4168	−0.931560
$688$	3.88584	0.148146
$689$	25.5853	0.974721
$690$	−0.866841	−0.0330001
$691$	−33.5064	−1.27464	−0.637321	−	0.770599i	$-0.719957\pi$
$691$	−33.5064	−1.27464	−0.637321	+	0.770599i	$0.719957\pi$
$692$	25.7806	0.980032
$693$	0.412099	0.0156543
$694$	−3.35673	−0.127420
$695$	−34.7377	−1.31768
$696$	−2.68649	−0.101831
$697$	6.22956	0.235961
$698$	−1.30848	−0.0495267
$699$	−21.8768	−0.827456
$700$	−1.79826	−0.0679679
$701$	35.2029	1.32959	0.664797	−	0.747024i	$-0.268518\pi$
$701$	35.2029	1.32959	0.664797	+	0.747024i	$0.268518\pi$
$702$	2.89370	0.109216
$703$	−17.4803	−0.659283
$704$	−7.54554	−0.284383
$705$	19.9047	0.749653
$706$	−0.511401	−0.0192468
$707$	−27.1868	−1.02247
$708$	−37.1128	−1.39478
$709$	2.94762	0.110700	0.0553501	−	0.998467i	$-0.482372\pi$
$709$	2.94762	0.110700	0.0553501	+	0.998467i	$0.482372\pi$
$710$	3.43744	0.129005
$711$	2.20564	0.0827180
$712$	7.29348	0.273335
$713$	1.38553	0.0518886
$714$	0.753183	0.0281872
$715$	9.49869	0.355231
$716$	−34.5805	−1.29234
$717$	−6.85889	−0.256150
$718$	−0.928925	−0.0346672
$719$	−43.5442	−1.62392	−0.811961	−	0.583711i	$-0.801600\pi$
$719$	−43.5442	−1.62392	−0.811961	+	0.583711i	$0.801600\pi$
$720$	−1.19652	−0.0445917
$721$	−26.3357	−0.980795
$722$	−0.333474	−0.0124106
$723$	2.33738	0.0869281
$724$	45.6675	1.69722
$725$	0.813373	0.0302079
$726$	0.244574	0.00907700
$727$	−6.54347	−0.242684	−0.121342	−	0.992611i	$-0.538720\pi$
$727$	−6.54347	−0.242684	−0.121342	+	0.992611i	$0.538720\pi$
$728$	−6.99175	−0.259131
$729$	25.6906	0.951504
$730$	−2.33930	−0.0865815
$731$	1.00000	0.0369863
$732$	51.3234	1.89697
$733$	−44.3787	−1.63916	−0.819582	−	0.572962i	$-0.805794\pi$
$733$	−44.3787	−1.63916	−0.819582	+	0.572962i	$0.805794\pi$
$734$	3.47353	0.128210
$735$	10.1173	0.373184
$736$	−2.52122	−0.0929335
$737$	−9.39569	−0.346095
$738$	−0.115171	−0.00423950
$739$	5.78885	0.212946	0.106473	−	0.994316i	$-0.466044\pi$
$739$	5.78885	0.212946	0.106473	+	0.994316i	$0.466044\pi$
$740$	−17.2184	−0.632961
$741$	33.8160	1.24226
$742$	2.63702	0.0968081
$743$	25.4463	0.933533	0.466766	−	0.884381i	$-0.345419\pi$
$743$	25.4463	0.933533	0.466766	+	0.884381i	$0.345419\pi$
$744$	−0.875801	−0.0321084
$745$	−15.9406	−0.584019
$746$	2.42383	0.0887428
$747$	−1.13960	−0.0416959
$748$	−1.98091	−0.0724293
$749$	−41.0312	−1.49925
$750$	2.64798	0.0966905
$751$	−35.8014	−1.30641	−0.653205	−	0.757181i	$-0.726576\pi$
$751$	−35.8014	−1.30641	−0.653205	+	0.757181i	$0.726576\pi$
$752$	18.9880	0.692420
$753$	−30.5251	−1.11240
$754$	1.57364	0.0573086
$755$	−1.35898	−0.0494582
$756$	−30.9525	−1.12573
$757$	−1.58977	−0.0577811	−0.0288905	−	0.999583i	$-0.509197\pi$
$757$	−1.58977	−0.0577811	−0.0288905	+	0.999583i	$0.509197\pi$
$758$	−0.775846	−0.0281800
$759$	−2.72673	−0.0989739
$760$	−5.85634	−0.212432
$761$	28.3291	1.02693	0.513464	−	0.858111i	$-0.328362\pi$
$761$	28.3291	1.02693	0.513464	+	0.858111i	$0.328362\pi$
$762$	−4.17030	−0.151074
$763$	−39.7488	−1.43900
$764$	15.9425	0.576781
$765$	−0.307918	−0.0111328
$766$	−4.83511	−0.174700
$767$	43.6879	1.57748
$768$	−25.6595	−0.925907
$769$	23.0893	0.832620	0.416310	−	0.909223i	$-0.363323\pi$
$769$	23.0893	0.832620	0.416310	+	0.909223i	$0.363323\pi$
$770$	0.979011	0.0352811
$771$	−14.8182	−0.533665
$772$	−37.4580	−1.34814
$773$	17.8305	0.641320	0.320660	−	0.947194i	$-0.396095\pi$
$773$	17.8305	0.641320	0.320660	+	0.947194i	$0.396095\pi$
$774$	−0.0184878	−0.000664530 0
$775$	0.265161	0.00952487
$776$	2.19246	0.0787048
$777$	20.5935	0.738787
$778$	−4.90871	−0.175986
$779$	28.8273	1.03284
$780$	33.3093	1.19267
$781$	10.8128	0.386912
$782$	−0.212803	−0.00760983
$783$	14.0001	0.500324
$784$	9.65140	0.344693
$785$	18.2723	0.652168
$786$	−5.08011	−0.181201
$787$	55.4821	1.97772	0.988862	−	0.148833i	$-0.0475516\pi$
$787$	55.4821	1.97772	0.988862	+	0.148833i	$0.0475516\pi$
$788$	−3.62757	−0.129227
$789$	15.4169	0.548857
$790$	5.23988	0.186427
$791$	11.1695	0.397142
$792$	0.0735983	0.00261520
$793$	−60.4162	−2.14544
$794$	2.13691	0.0758361
$795$	−25.2471	−0.895421
$796$	−8.84787	−0.313604
$797$	52.4481	1.85781	0.928904	−	0.370320i	$-0.120752\pi$
$797$	52.4481	1.85781	0.928904	+	0.370320i	$0.120752\pi$
$798$	3.48535	0.123380
$799$	4.88646	0.172870
$800$	−0.482508	−0.0170592
$801$	1.77456	0.0627008
$802$	−0.788056	−0.0278272
$803$	−7.35850	−0.259676
$804$	−32.9481	−1.16199
$805$	−10.9149	−0.384699
$806$	0.513010	0.0180700
$807$	−54.0635	−1.90313
$808$	−4.85540	−0.170812
$809$	7.08594	0.249129	0.124564	−	0.992212i	$-0.460247\pi$
$809$	7.08594	0.249129	0.124564	+	0.992212i	$0.460247\pi$
$810$	−2.98308	−0.104815
$811$	13.0009	0.456523	0.228261	−	0.973600i	$-0.426696\pi$
$811$	13.0009	0.456523	0.228261	+	0.973600i	$0.426696\pi$
$812$	−16.8324	−0.590702
$813$	−14.4960	−0.508397
$814$	0.521888	0.0182922
$815$	3.25629	0.114063
$816$	−6.87894	−0.240811
$817$	4.62750	0.161896
$818$	−1.20303	−0.0420630
$819$	−1.70114	−0.0594428
$820$	28.3953	0.991607
$821$	29.8974	1.04342	0.521712	−	0.853121i	$-0.325293\pi$
$821$	29.8974	1.04342	0.521712	+	0.853121i	$0.325293\pi$
$822$	−2.89440	−0.100954
$823$	9.11474	0.317720	0.158860	−	0.987301i	$-0.449218\pi$
$823$	9.11474	0.317720	0.158860	+	0.987301i	$0.449218\pi$
$824$	−4.70340	−0.163851
$825$	−0.521837	−0.0181680
$826$	4.50282	0.156673
$827$	−33.1796	−1.15377	−0.576884	−	0.816826i	$-0.695732\pi$
$827$	−33.1796	−1.15377	−0.576884	+	0.816826i	$0.695732\pi$
$828$	−0.408302	−0.0141895
$829$	−22.0439	−0.765616	−0.382808	−	0.923828i	$-0.625043\pi$
$829$	−22.0439	−0.765616	−0.382808	+	0.923828i	$0.625043\pi$
$830$	−2.70732	−0.0939724
$831$	−42.2010	−1.46394
$832$	31.1480	1.07986
$833$	2.48374	0.0860563
$834$	3.69223	0.127851
$835$	9.25555	0.320302
$836$	−9.16667	−0.317036
$837$	4.56408	0.157758
$838$	1.77579	0.0613435
$839$	19.2015	0.662910	0.331455	−	0.943471i	$-0.392460\pi$
$839$	19.2015	0.662910	0.331455	+	0.943471i	$0.392460\pi$
$840$	6.89933	0.238049
$841$	−21.3865	−0.737466
$842$	3.27086	0.112721
$843$	22.5656	0.777200
$844$	−20.2580	−0.697309
$845$	−9.29709	−0.319830
$846$	−0.0903398	−0.00310595
$847$	3.07957	0.105815
$848$	−24.0844	−0.827060
$849$	−15.3855	−0.528029
$850$	−0.0407260	−0.00139689
$851$	−5.81846	−0.199454
$852$	37.9175	1.29903
$853$	−57.0430	−1.95311	−0.976557	−	0.215259i	$-0.930940\pi$
$853$	−57.0430	−1.95311	−0.976557	+	0.215259i	$0.930940\pi$
$854$	−6.22697	−0.213083
$855$	−1.42489	−0.0487302
$856$	−7.32792	−0.250463
$857$	7.98504	0.272764	0.136382	−	0.990656i	$-0.456453\pi$
$857$	7.98504	0.272764	0.136382	+	0.990656i	$0.456453\pi$
$858$	−1.00960	−0.0344673
$859$	−4.37811	−0.149379	−0.0746896	−	0.997207i	$-0.523797\pi$
$859$	−4.37811	−0.149379	−0.0746896	+	0.997207i	$0.523797\pi$
$860$	4.55816	0.155432
$861$	−33.9613	−1.15740
$862$	3.91395	0.133310
$863$	−34.7551	−1.18308	−0.591538	−	0.806277i	$-0.701479\pi$
$863$	−34.7551	−1.18308	−0.591538	+	0.806277i	$0.701479\pi$
$864$	−8.30515	−0.282547
$865$	29.9469	1.01823
$866$	−1.76927	−0.0601223
$867$	−1.77026	−0.0601211
$868$	−5.48741	−0.186255
$869$	16.4825	0.559131
$870$	−1.55284	−0.0526462
$871$	38.7854	1.31419
$872$	−7.09889	−0.240399
$873$	0.533442	0.0180543
$874$	−0.984747	−0.0333096
$875$	33.3422	1.12717
$876$	−25.8042	−0.871845
$877$	−2.87400	−0.0970480	−0.0485240	−	0.998822i	$-0.515452\pi$
$877$	−2.87400	−0.0970480	−0.0485240	+	0.998822i	$0.515452\pi$
$878$	−3.54447	−0.119620
$879$	−36.3490	−1.22602
$880$	−8.94147	−0.301417
$881$	−27.0492	−0.911310	−0.455655	−	0.890156i	$-0.650595\pi$
$881$	−27.0492	−0.911310	−0.455655	+	0.890156i	$0.650595\pi$
$882$	−0.0459188	−0.00154617
$883$	5.83645	0.196412	0.0982061	−	0.995166i	$-0.468690\pi$
$883$	5.83645	0.196412	0.0982061	+	0.995166i	$0.468690\pi$
$884$	8.17721	0.275029
$885$	−43.1104	−1.44914
$886$	3.48971	0.117239
$887$	50.5458	1.69716	0.848580	−	0.529067i	$-0.177458\pi$
$887$	50.5458	1.69716	0.848580	+	0.529067i	$0.177458\pi$
$888$	3.67787	0.123421
$889$	−52.5106	−1.76115
$890$	4.21576	0.141313
$891$	−9.38354	−0.314361
$892$	−24.9706	−0.836077
$893$	22.6121	0.756684
$894$	1.69430	0.0566660
$895$	−40.1689	−1.34270
$896$	13.2919	0.444051
$897$	11.2559	0.375825
$898$	−3.75447	−0.125288
$899$	2.48201	0.0827797
$900$	−0.0781402	−0.00260467
$901$	−6.19798	−0.206485
$902$	−0.860659	−0.0286568
$903$	−5.45163	−0.181419
$904$	1.99481	0.0663463
$905$	53.0476	1.76336
$906$	0.144444	0.00479882
$907$	0.983339	0.0326512	0.0163256	−	0.999867i	$-0.494803\pi$
$907$	0.983339	0.0326512	0.0163256	+	0.999867i	$0.494803\pi$
$908$	7.39646	0.245460
$909$	−1.18135	−0.0391830
$910$	−4.04136	−0.133970
$911$	20.5089	0.679490	0.339745	−	0.940518i	$-0.389659\pi$
$911$	20.5089	0.679490	0.339745	+	0.940518i	$0.389659\pi$
$912$	−31.8323	−1.05407
$913$	−8.51612	−0.281842
$914$	−2.84956	−0.0942550
$915$	59.6176	1.97090
$916$	−27.3223	−0.902755
$917$	−63.9664	−2.11236
$918$	−0.700994	−0.0231363
$919$	−21.3956	−0.705777	−0.352888	−	0.935665i	$-0.614800\pi$
$919$	−21.3956	−0.705777	−0.352888	+	0.935665i	$0.614800\pi$
$920$	−1.94933	−0.0642675
$921$	54.0392	1.78065
$922$	−0.0383254	−0.00126218
$923$	−44.6352	−1.46918
$924$	10.7992	0.355268
$925$	−1.11353	−0.0366126
$926$	4.74838	0.156041
$927$	−1.14437	−0.0375861
$928$	−4.51646	−0.148260
$929$	−11.3533	−0.372490	−0.186245	−	0.982503i	$-0.559632\pi$
$929$	−11.3533	−0.372490	−0.186245	+	0.982503i	$0.559632\pi$
$930$	−0.506229	−0.0165999
$931$	11.4935	0.376684
$932$	−24.4800	−0.801870
$933$	43.6770	1.42992
$934$	−1.88134	−0.0615593
$935$	−2.30104	−0.0752520
$936$	−0.303814	−0.00993047
$937$	−2.86395	−0.0935613	−0.0467806	−	0.998905i	$-0.514896\pi$
$937$	−2.86395	−0.0935613	−0.0467806	+	0.998905i	$0.514896\pi$
$938$	3.99753	0.130524
$939$	3.63817	0.118727
$940$	22.2732	0.726473
$941$	3.91894	0.127754	0.0638770	−	0.997958i	$-0.479653\pi$
$941$	3.91894	0.127754	0.0638770	+	0.997958i	$0.479653\pi$
$942$	−1.94214	−0.0632784
$943$	9.59538	0.312468
$944$	−41.1250	−1.33850
$945$	−35.9546	−1.16960
$946$	−0.138157	−0.00449188
$947$	36.3951	1.18268	0.591340	−	0.806422i	$-0.298599\pi$
$947$	36.3951	1.18268	0.591340	+	0.806422i	$0.298599\pi$
$948$	57.7997	1.87725
$949$	30.3759	0.986043
$950$	−0.188459	−0.00611443
$951$	−3.22621	−0.104617
$952$	1.69374	0.0548944
$953$	7.18545	0.232759	0.116380	−	0.993205i	$-0.462871\pi$
$953$	7.18545	0.232759	0.116380	+	0.993205i	$0.462871\pi$
$954$	0.114587	0.00370989
$955$	18.5189	0.599259
$956$	−7.67507	−0.248229
$957$	−4.88460	−0.157897
$958$	1.91484	0.0618658
$959$	−36.4449	−1.17687
$960$	−30.7363	−0.992008
$961$	−30.1909	−0.973899
$962$	−2.15435	−0.0694591
$963$	−1.78294	−0.0574543
$964$	2.61552	0.0842402
$965$	−43.5114	−1.40068
$966$	1.16013	0.0373264
$967$	61.3144	1.97174	0.985869	−	0.167521i	$-0.0535761\pi$
$967$	61.3144	1.97174	0.985869	+	0.167521i	$0.0535761\pi$
$968$	0.549992	0.0176774
$969$	−8.19187	−0.263161
$970$	1.26728	0.0406900
$971$	−52.0087	−1.66904	−0.834519	−	0.550979i	$-0.814255\pi$
$971$	−52.0087	−1.66904	−0.834519	+	0.550979i	$0.814255\pi$
$972$	−2.75277	−0.0882950
$973$	46.4908	1.49043
$974$	−2.18107	−0.0698860
$975$	2.15414	0.0689878
$976$	56.8720	1.82043
$977$	2.10850	0.0674571	0.0337285	−	0.999431i	$-0.489262\pi$
$977$	2.10850	0.0674571	0.0337285	+	0.999431i	$0.489262\pi$
$978$	−0.346107	−0.0110673
$979$	13.2611	0.423825
$980$	11.3213	0.361644
$981$	−1.72721	−0.0551456
$982$	−5.34613	−0.170602
$983$	29.5347	0.942010	0.471005	−	0.882130i	$-0.343891\pi$
$983$	29.5347	0.942010	0.471005	+	0.882130i	$0.343891\pi$
$984$	−6.06528	−0.193354
$985$	−4.21380	−0.134263
$986$	−0.381211	−0.0121402
$987$	−26.6392	−0.847934
$988$	37.8400	1.20385
$989$	1.54030	0.0489786
$990$	0.0425411	0.00135205
$991$	−3.12428	−0.0992461	−0.0496231	−	0.998768i	$-0.515802\pi$
$991$	−3.12428	−0.0992461	−0.0496231	+	0.998768i	$0.515802\pi$
$992$	−1.47238	−0.0467480
$993$	36.5098	1.15860
$994$	−4.60046	−0.145918
$995$	−10.2777	−0.325826
$996$	−29.8637	−0.946268
$997$	−6.94729	−0.220023	−0.110012	−	0.993930i	$-0.535089\pi$
$997$	−6.94729	−0.220023	−0.110012	+	0.993930i	$0.535089\pi$
$998$	−0.955976	−0.0302609
$999$	−19.1666	−0.606403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.40	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.40	✓	82	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-0.138157 q^{2} -1.77026 q^{3} -1.98091 q^{4} -2.30104 q^{5} +0.244574 q^{6} +3.07957 q^{7} +0.549992 q^{8} +0.133817 q^{9} +O(q^{10})\)	\(q-0.138157 q^{2} -1.77026 q^{3} -1.98091 q^{4} -2.30104 q^{5} +0.244574 q^{6} +3.07957 q^{7} +0.549992 q^{8} +0.133817 q^{9} +0.317905 q^{10} +1.00000 q^{11} +3.50673 q^{12} -4.12800 q^{13} -0.425465 q^{14} +4.07343 q^{15} +3.88584 q^{16} +1.00000 q^{17} -0.0184878 q^{18} +4.62750 q^{19} +4.55816 q^{20} -5.45163 q^{21} -0.138157 q^{22} +1.54030 q^{23} -0.973628 q^{24} +0.294780 q^{25} +0.570313 q^{26} +5.07389 q^{27} -6.10035 q^{28} +2.75925 q^{29} -0.562775 q^{30} +0.899523 q^{31} -1.63684 q^{32} -1.77026 q^{33} -0.138157 q^{34} -7.08620 q^{35} -0.265080 q^{36} -3.77749 q^{37} -0.639322 q^{38} +7.30763 q^{39} -1.26555 q^{40} +6.22956 q^{41} +0.753183 q^{42} +1.00000 q^{43} -1.98091 q^{44} -0.307918 q^{45} -0.212803 q^{46} +4.88646 q^{47} -6.87894 q^{48} +2.48374 q^{49} -0.0407260 q^{50} -1.77026 q^{51} +8.17721 q^{52} -6.19798 q^{53} -0.700994 q^{54} -2.30104 q^{55} +1.69374 q^{56} -8.19187 q^{57} -0.381211 q^{58} -10.5833 q^{59} -8.06912 q^{60} +14.6357 q^{61} -0.124276 q^{62} +0.412099 q^{63} -7.54554 q^{64} +9.49869 q^{65} +0.244574 q^{66} -9.39569 q^{67} -1.98091 q^{68} -2.72673 q^{69} +0.979011 q^{70} +10.8128 q^{71} +0.0735983 q^{72} -7.35850 q^{73} +0.521888 q^{74} -0.521837 q^{75} -9.16667 q^{76} +3.07957 q^{77} -1.00960 q^{78} +16.4825 q^{79} -8.94147 q^{80} -9.38354 q^{81} -0.860659 q^{82} -8.51612 q^{83} +10.7992 q^{84} -2.30104 q^{85} -0.138157 q^{86} -4.88460 q^{87} +0.549992 q^{88} +13.2611 q^{89} +0.0425411 q^{90} -12.7125 q^{91} -3.05120 q^{92} -1.59239 q^{93} -0.675099 q^{94} -10.6480 q^{95} +2.89763 q^{96} +3.98635 q^{97} -0.343146 q^{98} +0.133817 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9} + q^{10} + 82 q^{11} + 3 q^{12} + 26 q^{13} + 17 q^{14} + 66 q^{15} + 122 q^{16} + 82 q^{17} + 18 q^{18} + 12 q^{19} + 9 q^{20} + 22 q^{21} + 8 q^{22} + 50 q^{23} + 15 q^{24} + 117 q^{25} + 36 q^{26} + 30 q^{27} + 11 q^{28} + 33 q^{29} - 26 q^{30} + 40 q^{31} + 58 q^{32} + 6 q^{33} + 8 q^{34} + 16 q^{35} + 160 q^{36} + 31 q^{37} + 18 q^{38} + 41 q^{39} - 29 q^{40} + 42 q^{41} - 51 q^{42} + 82 q^{43} + 98 q^{44} - 2 q^{45} - 19 q^{46} + 84 q^{47} - 46 q^{48} + 136 q^{49} + 59 q^{50} + 6 q^{51} + 45 q^{52} + 83 q^{53} + 24 q^{54} + 11 q^{55} + 21 q^{56} + 23 q^{57} + 14 q^{58} + 96 q^{59} + 184 q^{60} - 6 q^{61} - 23 q^{62} + 8 q^{63} + 148 q^{64} + 5 q^{65} + 10 q^{66} + 78 q^{67} + 98 q^{68} + 61 q^{69} - 3 q^{70} + 155 q^{71} + 50 q^{72} - 23 q^{73} + 10 q^{74} - 19 q^{75} + 44 q^{76} + 8 q^{77} - 27 q^{78} + 31 q^{79} + 19 q^{80} + 150 q^{81} - 12 q^{82} + 54 q^{83} + 8 q^{84} + 11 q^{85} + 8 q^{86} + 20 q^{87} + 30 q^{88} + 25 q^{89} - 81 q^{90} - 14 q^{91} + 60 q^{92} + 36 q^{93} + 19 q^{94} + 111 q^{95} - 6 q^{96} + 2 q^{97} - 5 q^{98} + 108 q^{99}+O(q^{100}) \) 82 * q + 8 * q^2 + 6 * q^3 + 98 * q^4 + 11 * q^5 + 10 * q^6 + 8 * q^7 + 30 * q^8 + 108 * q^9 + q^10 + 82 * q^11 + 3 * q^12 + 26 * q^13 + 17 * q^14 + 66 * q^15 + 122 * q^16 + 82 * q^17 + 18 * q^18 + 12 * q^19 + 9 * q^20 + 22 * q^21 + 8 * q^22 + 50 * q^23 + 15 * q^24 + 117 * q^25 + 36 * q^26 + 30 * q^27 + 11 * q^28 + 33 * q^29 - 26 * q^30 + 40 * q^31 + 58 * q^32 + 6 * q^33 + 8 * q^34 + 16 * q^35 + 160 * q^36 + 31 * q^37 + 18 * q^38 + 41 * q^39 - 29 * q^40 + 42 * q^41 - 51 * q^42 + 82 * q^43 + 98 * q^44 - 2 * q^45 - 19 * q^46 + 84 * q^47 - 46 * q^48 + 136 * q^49 + 59 * q^50 + 6 * q^51 + 45 * q^52 + 83 * q^53 + 24 * q^54 + 11 * q^55 + 21 * q^56 + 23 * q^57 + 14 * q^58 + 96 * q^59 + 184 * q^60 - 6 * q^61 - 23 * q^62 + 8 * q^63 + 148 * q^64 + 5 * q^65 + 10 * q^66 + 78 * q^67 + 98 * q^68 + 61 * q^69 - 3 * q^70 + 155 * q^71 + 50 * q^72 - 23 * q^73 + 10 * q^74 - 19 * q^75 + 44 * q^76 + 8 * q^77 - 27 * q^78 + 31 * q^79 + 19 * q^80 + 150 * q^81 - 12 * q^82 + 54 * q^83 + 8 * q^84 + 11 * q^85 + 8 * q^86 + 20 * q^87 + 30 * q^88 + 25 * q^89 - 81 * q^90 - 14 * q^91 + 60 * q^92 + 36 * q^93 + 19 * q^94 + 111 * q^95 - 6 * q^96 + 2 * q^97 - 5 * q^98 + 108 * q^99

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