LMFDB - Embedded newform 8041.2.a.j.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.22059 q^{2} -3.23881 q^{3} +2.93104 q^{4} -1.33112 q^{5} +7.19209 q^{6} -0.932335 q^{7} -2.06746 q^{8} +7.48990 q^{9} +O(q^{10})$	\(q-2.22059 q^{2} -3.23881 q^{3} +2.93104 q^{4} -1.33112 q^{5} +7.19209 q^{6} -0.932335 q^{7} -2.06746 q^{8} +7.48990 q^{9} +2.95587 q^{10} +1.00000 q^{11} -9.49308 q^{12} +4.80259 q^{13} +2.07034 q^{14} +4.31124 q^{15} -1.27109 q^{16} +1.00000 q^{17} -16.6320 q^{18} +0.807270 q^{19} -3.90156 q^{20} +3.01966 q^{21} -2.22059 q^{22} -8.62067 q^{23} +6.69612 q^{24} -3.22813 q^{25} -10.6646 q^{26} -14.5419 q^{27} -2.73271 q^{28} -7.30946 q^{29} -9.57351 q^{30} +8.01755 q^{31} +6.95749 q^{32} -3.23881 q^{33} -2.22059 q^{34} +1.24105 q^{35} +21.9532 q^{36} -10.7508 q^{37} -1.79262 q^{38} -15.5547 q^{39} +2.75203 q^{40} +8.36668 q^{41} -6.70543 q^{42} +1.00000 q^{43} +2.93104 q^{44} -9.96994 q^{45} +19.1430 q^{46} +11.5760 q^{47} +4.11681 q^{48} -6.13075 q^{49} +7.16836 q^{50} -3.23881 q^{51} +14.0766 q^{52} +10.7135 q^{53} +32.2918 q^{54} -1.33112 q^{55} +1.92757 q^{56} -2.61460 q^{57} +16.2314 q^{58} +10.2059 q^{59} +12.6364 q^{60} -0.149587 q^{61} -17.8037 q^{62} -6.98310 q^{63} -12.9076 q^{64} -6.39281 q^{65} +7.19209 q^{66} -9.07168 q^{67} +2.93104 q^{68} +27.9207 q^{69} -2.75586 q^{70} +10.2411 q^{71} -15.4851 q^{72} +13.5574 q^{73} +23.8732 q^{74} +10.4553 q^{75} +2.36614 q^{76} -0.932335 q^{77} +34.5407 q^{78} +2.14236 q^{79} +1.69197 q^{80} +24.6289 q^{81} -18.5790 q^{82} +8.57869 q^{83} +8.85073 q^{84} -1.33112 q^{85} -2.22059 q^{86} +23.6740 q^{87} -2.06746 q^{88} -8.59733 q^{89} +22.1392 q^{90} -4.47762 q^{91} -25.2675 q^{92} -25.9673 q^{93} -25.7057 q^{94} -1.07457 q^{95} -22.5340 q^{96} -19.2144 q^{97} +13.6139 q^{98} +7.48990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.22059	−1.57020	−0.785099	−	0.619371i	$-0.787388\pi$
$2$	−2.22059	−1.57020	−0.785099	+	0.619371i	$0.787388\pi$
$3$	−3.23881	−1.86993	−0.934964	−	0.354741i	$-0.884569\pi$
$3$	−3.23881	−1.86993	−0.934964	+	0.354741i	$0.884569\pi$
$4$	2.93104	1.46552
$5$	−1.33112	−0.595294	−0.297647	−	0.954676i	$-0.596202\pi$
$5$	−1.33112	−0.595294	−0.297647	+	0.954676i	$0.596202\pi$
$6$	7.19209	2.93616
$7$	−0.932335	−0.352389	−0.176195	−	0.984355i	$-0.556379\pi$
$7$	−0.932335	−0.352389	−0.176195	+	0.984355i	$0.556379\pi$
$8$	−2.06746	−0.730958
$9$	7.48990	2.49663
$10$	2.95587	0.934729
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−9.49308	−2.74042
$13$	4.80259	1.33200	0.666000	−	0.745952i	$-0.268005\pi$
$13$	4.80259	1.33200	0.666000	+	0.745952i	$0.268005\pi$
$14$	2.07034	0.553321
$15$	4.31124	1.11316
$16$	−1.27109	−0.317772
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−16.6320	−3.92021
$19$	0.807270	0.185201	0.0926003	−	0.995703i	$-0.470482\pi$
$19$	0.807270	0.185201	0.0926003	+	0.995703i	$0.470482\pi$
$20$	−3.90156	−0.872415
$21$	3.01966	0.658943
$22$	−2.22059	−0.473432
$23$	−8.62067	−1.79753	−0.898767	−	0.438427i	$-0.855536\pi$
$23$	−8.62067	−1.79753	−0.898767	+	0.438427i	$0.855536\pi$
$24$	6.69612	1.36684
$25$	−3.22813	−0.645625
$26$	−10.6646	−2.09150
$27$	−14.5419	−2.79860
$28$	−2.73271	−0.516434
$29$	−7.30946	−1.35733	−0.678667	−	0.734446i	$-0.737442\pi$
$29$	−7.30946	−1.35733	−0.678667	+	0.734446i	$0.737442\pi$
$30$	−9.57351	−1.74788
$31$	8.01755	1.43999	0.719997	−	0.693977i	$-0.244143\pi$
$31$	8.01755	1.43999	0.719997	+	0.693977i	$0.244143\pi$
$32$	6.95749	1.22992
$33$	−3.23881	−0.563805
$34$	−2.22059	−0.380829
$35$	1.24105	0.209775
$36$	21.9532	3.65887
$37$	−10.7508	−1.76742	−0.883712	−	0.468030i	$-0.844964\pi$
$37$	−10.7508	−1.76742	−0.883712	+	0.468030i	$0.844964\pi$
$38$	−1.79262	−0.290801
$39$	−15.5547	−2.49074
$40$	2.75203	0.435135
$41$	8.36668	1.30666	0.653328	−	0.757075i	$-0.273372\pi$
$41$	8.36668	1.30666	0.653328	+	0.757075i	$0.273372\pi$
$42$	−6.70543	−1.03467
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	2.93104	0.441871
$45$	−9.96994	−1.48623
$46$	19.1430	2.82248
$47$	11.5760	1.68854	0.844268	−	0.535920i	$-0.180035\pi$
$47$	11.5760	1.68854	0.844268	+	0.535920i	$0.180035\pi$
$48$	4.11681	0.594211
$49$	−6.13075	−0.875822
$50$	7.16836	1.01376
$51$	−3.23881	−0.453524
$52$	14.0766	1.95207
$53$	10.7135	1.47162	0.735808	−	0.677190i	$-0.236803\pi$
$53$	10.7135	1.47162	0.735808	+	0.677190i	$0.236803\pi$
$54$	32.2918	4.39435
$55$	−1.33112	−0.179488
$56$	1.92757	0.257582
$57$	−2.61460	−0.346312
$58$	16.2314	2.13128
$59$	10.2059	1.32870	0.664349	−	0.747423i	$-0.268709\pi$
$59$	10.2059	1.32870	0.664349	+	0.747423i	$0.268709\pi$
$60$	12.6364	1.63135
$61$	−0.149587	−0.0191527	−0.00957636	−	0.999954i	$-0.503048\pi$
$61$	−0.149587	−0.0191527	−0.00957636	+	0.999954i	$0.503048\pi$
$62$	−17.8037	−2.26108
$63$	−6.98310	−0.879788
$64$	−12.9076	−1.61345
$65$	−6.39281	−0.792931
$66$	7.19209	0.885285
$67$	−9.07168	−1.10828	−0.554141	−	0.832423i	$-0.686953\pi$
$67$	−9.07168	−1.10828	−0.554141	+	0.832423i	$0.686953\pi$
$68$	2.93104	0.355441
$69$	27.9207	3.36126
$70$	−2.75586	−0.329389
$71$	10.2411	1.21540	0.607700	−	0.794167i	$-0.292093\pi$
$71$	10.2411	1.21540	0.607700	+	0.794167i	$0.292093\pi$
$72$	−15.4851	−1.82493
$73$	13.5574	1.58677	0.793387	−	0.608718i	$-0.208316\pi$
$73$	13.5574	1.58677	0.793387	+	0.608718i	$0.208316\pi$
$74$	23.8732	2.77521
$75$	10.4553	1.20727
$76$	2.36614	0.271415
$77$	−0.932335	−0.106249
$78$	34.5407	3.91096
$79$	2.14236	0.241034	0.120517	−	0.992711i	$-0.461545\pi$
$79$	2.14236	0.241034	0.120517	+	0.992711i	$0.461545\pi$
$80$	1.69197	0.189168
$81$	24.6289	2.73655
$82$	−18.5790	−2.05171
$83$	8.57869	0.941634	0.470817	−	0.882231i	$-0.343959\pi$
$83$	8.57869	0.941634	0.470817	+	0.882231i	$0.343959\pi$
$84$	8.85073	0.965694
$85$	−1.33112	−0.144380
$86$	−2.22059	−0.239453
$87$	23.6740	2.53812
$88$	−2.06746	−0.220392
$89$	−8.59733	−0.911315	−0.455658	−	0.890155i	$-0.650596\pi$
$89$	−8.59733	−0.911315	−0.455658	+	0.890155i	$0.650596\pi$
$90$	22.1392	2.33368
$91$	−4.47762	−0.469383
$92$	−25.2675	−2.63432
$93$	−25.9673	−2.69269
$94$	−25.7057	−2.65134
$95$	−1.07457	−0.110249
$96$	−22.5340	−2.29987
$97$	−19.2144	−1.95092	−0.975461	−	0.220170i	$-0.929339\pi$
$97$	−19.2144	−1.95092	−0.975461	+	0.220170i	$0.929339\pi$
$98$	13.6139	1.37521
$99$	7.48990	0.752763
$100$	−9.46176	−0.946176
$101$	11.7453	1.16870	0.584349	−	0.811503i	$-0.301350\pi$
$101$	11.7453	1.16870	0.584349	+	0.811503i	$0.301350\pi$
$102$	7.19209	0.712123
$103$	0.676477	0.0666553	0.0333276	−	0.999444i	$-0.489390\pi$
$103$	0.676477	0.0666553	0.0333276	+	0.999444i	$0.489390\pi$
$104$	−9.92917	−0.973635
$105$	−4.01952	−0.392265
$106$	−23.7904	−2.31073
$107$	−7.43546	−0.718813	−0.359406	−	0.933181i	$-0.617021\pi$
$107$	−7.43546	−0.718813	−0.359406	+	0.933181i	$0.617021\pi$
$108$	−42.6230	−4.10140
$109$	−14.3239	−1.37198	−0.685990	−	0.727611i	$-0.740630\pi$
$109$	−14.3239	−1.37198	−0.685990	+	0.727611i	$0.740630\pi$
$110$	2.95587	0.281831
$111$	34.8199	3.30496
$112$	1.18508	0.111979
$113$	−12.6686	−1.19176	−0.595879	−	0.803074i	$-0.703196\pi$
$113$	−12.6686	−1.19176	−0.595879	+	0.803074i	$0.703196\pi$
$114$	5.80596	0.543778
$115$	11.4751	1.07006
$116$	−21.4243	−1.98920
$117$	35.9709	3.32551
$118$	−22.6632	−2.08632
$119$	−0.932335	−0.0854670
$120$	−8.91332	−0.813671
$121$	1.00000	0.0909091
$122$	0.332173	0.0300735
$123$	−27.0981	−2.44336
$124$	23.4998	2.11034
$125$	10.9526	0.979631
$126$	15.5066	1.38144
$127$	10.5483	0.936013	0.468007	−	0.883725i	$-0.344972\pi$
$127$	10.5483	0.936013	0.468007	+	0.883725i	$0.344972\pi$
$128$	14.7475	1.30351
$129$	−3.23881	−0.285161
$130$	14.1958	1.24506
$131$	9.37849	0.819403	0.409701	−	0.912220i	$-0.365633\pi$
$131$	9.37849	0.819403	0.409701	+	0.912220i	$0.365633\pi$
$132$	−9.49308	−0.826267
$133$	−0.752646	−0.0652627
$134$	20.1445	1.74022
$135$	19.3570	1.66599
$136$	−2.06746	−0.177283
$137$	−5.92747	−0.506418	−0.253209	−	0.967412i	$-0.581486\pi$
$137$	−5.92747	−0.506418	−0.253209	+	0.967412i	$0.581486\pi$
$138$	−62.0006	−5.27784
$139$	−1.05055	−0.0891066	−0.0445533	−	0.999007i	$-0.514186\pi$
$139$	−1.05055	−0.0891066	−0.0445533	+	0.999007i	$0.514186\pi$
$140$	3.63756	0.307430
$141$	−37.4926	−3.15744
$142$	−22.7414	−1.90842
$143$	4.80259	0.401613
$144$	−9.52032	−0.793360
$145$	9.72975	0.808012
$146$	−30.1055	−2.49155
$147$	19.8564	1.63772
$148$	−31.5111	−2.59020
$149$	8.26366	0.676985	0.338493	−	0.940969i	$-0.390083\pi$
$149$	8.26366	0.676985	0.338493	+	0.940969i	$0.390083\pi$
$150$	−23.2170	−1.89566
$151$	9.80243	0.797710	0.398855	−	0.917014i	$-0.369408\pi$
$151$	9.80243	0.797710	0.398855	+	0.917014i	$0.369408\pi$
$152$	−1.66900	−0.135374
$153$	7.48990	0.605523
$154$	2.07034	0.166833
$155$	−10.6723	−0.857220
$156$	−45.5914	−3.65023
$157$	−10.6114	−0.846884	−0.423442	−	0.905923i	$-0.639178\pi$
$157$	−10.6114	−0.846884	−0.423442	+	0.905923i	$0.639178\pi$
$158$	−4.75731	−0.378471
$159$	−34.6991	−2.75182
$160$	−9.26124	−0.732165
$161$	8.03735	0.633432
$162$	−54.6909	−4.29692
$163$	−17.3561	−1.35943	−0.679716	−	0.733475i	$-0.737897\pi$
$163$	−17.3561	−1.35943	−0.679716	+	0.733475i	$0.737897\pi$
$164$	24.5231	1.91493
$165$	4.31124	0.335630
$166$	−19.0498	−1.47855
$167$	−21.3077	−1.64884	−0.824421	−	0.565978i	$-0.808499\pi$
$167$	−21.3077	−1.64884	−0.824421	+	0.565978i	$0.808499\pi$
$168$	−6.24302	−0.481660
$169$	10.0649	0.774222
$170$	2.95587	0.226705
$171$	6.04638	0.462378
$172$	2.93104	0.223490
$173$	24.2718	1.84535	0.922676	−	0.385575i	$-0.125997\pi$
$173$	24.2718	1.84535	0.922676	+	0.385575i	$0.125997\pi$
$174$	−52.5703	−3.98534
$175$	3.00969	0.227512
$176$	−1.27109	−0.0958118
$177$	−33.0551	−2.48457
$178$	19.0912	1.43094
$179$	11.1232	0.831389	0.415694	−	0.909504i	$-0.363539\pi$
$179$	11.1232	0.831389	0.415694	+	0.909504i	$0.363539\pi$
$180$	−29.2223	−2.17810
$181$	−6.48195	−0.481799	−0.240900	−	0.970550i	$-0.577442\pi$
$181$	−6.48195	−0.481799	−0.240900	+	0.970550i	$0.577442\pi$
$182$	9.94299	0.737023
$183$	0.484486	0.0358142
$184$	17.8229	1.31392
$185$	14.3106	1.05214
$186$	57.6629	4.22805
$187$	1.00000	0.0731272
$188$	33.9298	2.47458
$189$	13.5580	0.986197
$190$	2.38619	0.173112
$191$	5.43991	0.393618	0.196809	−	0.980442i	$-0.436942\pi$
$191$	5.43991	0.393618	0.196809	+	0.980442i	$0.436942\pi$
$192$	41.8053	3.01703
$193$	−4.53753	−0.326619	−0.163309	−	0.986575i	$-0.552217\pi$
$193$	−4.53753	−0.326619	−0.163309	+	0.986575i	$0.552217\pi$
$194$	42.6673	3.06333
$195$	20.7051	1.48272
$196$	−17.9695	−1.28353
$197$	−16.0137	−1.14093	−0.570466	−	0.821322i	$-0.693237\pi$
$197$	−16.0137	−1.14093	−0.570466	+	0.821322i	$0.693237\pi$
$198$	−16.6320	−1.18199
$199$	8.62260	0.611240	0.305620	−	0.952154i	$-0.401136\pi$
$199$	8.62260	0.611240	0.305620	+	0.952154i	$0.401136\pi$
$200$	6.67402	0.471925
$201$	29.3815	2.07241
$202$	−26.0815	−1.83509
$203$	6.81487	0.478310
$204$	−9.49308	−0.664649
$205$	−11.1370	−0.777845
$206$	−1.50218	−0.104662
$207$	−64.5680	−4.48778
$208$	−6.10451	−0.423272
$209$	0.807270	0.0558401
$210$	8.92572	0.615933
$211$	17.3751	1.19615	0.598074	−	0.801441i	$-0.295933\pi$
$211$	17.3751	1.19615	0.598074	+	0.801441i	$0.295933\pi$
$212$	31.4018	2.15668
$213$	−33.1691	−2.27271
$214$	16.5111	1.12868
$215$	−1.33112	−0.0907815
$216$	30.0649	2.04566
$217$	−7.47504	−0.507439
$218$	31.8075	2.15428
$219$	−43.9099	−2.96715
$220$	−3.90156	−0.263043
$221$	4.80259	0.323057
$222$	−77.3209	−5.18944
$223$	15.5189	1.03922	0.519611	−	0.854403i	$-0.326077\pi$
$223$	15.5189	1.03922	0.519611	+	0.854403i	$0.326077\pi$
$224$	−6.48671	−0.433412
$225$	−24.1783	−1.61189
$226$	28.1318	1.87130
$227$	−1.61241	−0.107019	−0.0535097	−	0.998567i	$-0.517041\pi$
$227$	−1.61241	−0.107019	−0.0535097	+	0.998567i	$0.517041\pi$
$228$	−7.66349	−0.507527
$229$	−14.9324	−0.986759	−0.493380	−	0.869814i	$-0.664239\pi$
$229$	−14.9324	−0.986759	−0.493380	+	0.869814i	$0.664239\pi$
$230$	−25.4816	−1.68021
$231$	3.01966	0.198679
$232$	15.1120	0.992153
$233$	13.9882	0.916398	0.458199	−	0.888850i	$-0.348495\pi$
$233$	13.9882	0.916398	0.458199	+	0.888850i	$0.348495\pi$
$234$	−79.8769	−5.22171
$235$	−15.4091	−1.00518
$236$	29.9140	1.94723
$237$	−6.93870	−0.450717
$238$	2.07034	0.134200
$239$	2.07630	0.134304	0.0671522	−	0.997743i	$-0.478609\pi$
$239$	2.07630	0.134304	0.0671522	+	0.997743i	$0.478609\pi$
$240$	−5.47996	−0.353730
$241$	16.4376	1.05884	0.529421	−	0.848359i	$-0.322409\pi$
$241$	16.4376	1.05884	0.529421	+	0.848359i	$0.322409\pi$
$242$	−2.22059	−0.142745
$243$	−36.1426	−2.31855
$244$	−0.438447	−0.0280687
$245$	8.16075	0.521371
$246$	60.1739	3.83655
$247$	3.87699	0.246687
$248$	−16.5760	−1.05257
$249$	−27.7848	−1.76079
$250$	−24.3213	−1.53821
$251$	−23.5430	−1.48602	−0.743010	−	0.669281i	$-0.766602\pi$
$251$	−23.5430	−1.48602	−0.743010	+	0.669281i	$0.766602\pi$
$252$	−20.4677	−1.28935
$253$	−8.62067	−0.541977
$254$	−23.4236	−1.46973
$255$	4.31124	0.269980
$256$	−6.93312	−0.433320
$257$	−1.99334	−0.124341	−0.0621705	−	0.998066i	$-0.519802\pi$
$257$	−1.99334	−0.124341	−0.0621705	+	0.998066i	$0.519802\pi$
$258$	7.19209	0.447760
$259$	10.0234	0.622822
$260$	−18.7376	−1.16206
$261$	−54.7472	−3.38876
$262$	−20.8258	−1.28662
$263$	−18.8731	−1.16376	−0.581882	−	0.813273i	$-0.697684\pi$
$263$	−18.8731	−1.16376	−0.581882	+	0.813273i	$0.697684\pi$
$264$	6.69612	0.412117
$265$	−14.2610	−0.876044
$266$	1.67132	0.102475
$267$	27.8451	1.70409
$268$	−26.5894	−1.62421
$269$	−19.1525	−1.16775	−0.583873	−	0.811845i	$-0.698463\pi$
$269$	−19.1525	−1.16775	−0.583873	+	0.811845i	$0.698463\pi$
$270$	−42.9841	−2.61593
$271$	9.31968	0.566130	0.283065	−	0.959101i	$-0.408649\pi$
$271$	9.31968	0.566130	0.283065	+	0.959101i	$0.408649\pi$
$272$	−1.27109	−0.0770710
$273$	14.5022	0.877712
$274$	13.1625	0.795176
$275$	−3.22813	−0.194663
$276$	81.8367	4.92599
$277$	9.57319	0.575197	0.287599	−	0.957751i	$-0.407143\pi$
$277$	9.57319	0.575197	0.287599	+	0.957751i	$0.407143\pi$
$278$	2.33285	0.139915
$279$	60.0507	3.59514
$280$	−2.56582	−0.153337
$281$	3.93684	0.234852	0.117426	−	0.993082i	$-0.462536\pi$
$281$	3.93684	0.234852	0.117426	+	0.993082i	$0.462536\pi$
$282$	83.2558	4.95781
$283$	21.8578	1.29931	0.649654	−	0.760230i	$-0.274914\pi$
$283$	21.8578	1.29931	0.649654	+	0.760230i	$0.274914\pi$
$284$	30.0172	1.78119
$285$	3.48034	0.206157
$286$	−10.6646	−0.630612
$287$	−7.80055	−0.460452
$288$	52.1109	3.07067
$289$	1.00000	0.0588235
$290$	−21.6058	−1.26874
$291$	62.2317	3.64809
$292$	39.7373	2.32545
$293$	−17.4790	−1.02113	−0.510567	−	0.859838i	$-0.670565\pi$
$293$	−17.4790	−1.02113	−0.510567	+	0.859838i	$0.670565\pi$
$294$	−44.0929	−2.57155
$295$	−13.5853	−0.790966
$296$	22.2269	1.29191
$297$	−14.5419	−0.843809
$298$	−18.3502	−1.06300
$299$	−41.4015	−2.39431
$300$	30.6449	1.76928
$301$	−0.932335	−0.0537389
$302$	−21.7672	−1.25256
$303$	−38.0407	−2.18538
$304$	−1.02611	−0.0588515
$305$	0.199119	0.0114015
$306$	−16.6320	−0.950790
$307$	3.32392	0.189706	0.0948530	−	0.995491i	$-0.469762\pi$
$307$	3.32392	0.189706	0.0948530	+	0.995491i	$0.469762\pi$
$308$	−2.73271	−0.155711
$309$	−2.19098	−0.124641
$310$	23.6988	1.34600
$311$	14.0796	0.798379	0.399190	−	0.916868i	$-0.369291\pi$
$311$	14.0796	0.798379	0.399190	+	0.916868i	$0.369291\pi$
$312$	32.1587	1.82063
$313$	−1.65434	−0.0935086	−0.0467543	−	0.998906i	$-0.514888\pi$
$313$	−1.65434	−0.0935086	−0.0467543	+	0.998906i	$0.514888\pi$
$314$	23.5637	1.32977
$315$	9.29532	0.523732
$316$	6.27934	0.353240
$317$	9.77596	0.549072	0.274536	−	0.961577i	$-0.411476\pi$
$317$	9.77596	0.549072	0.274536	+	0.961577i	$0.411476\pi$
$318$	77.0526	4.32090
$319$	−7.30946	−0.409251
$320$	17.1815	0.960476
$321$	24.0820	1.34413
$322$	−17.8477	−0.994613
$323$	0.807270	0.0449177
$324$	72.1884	4.01046
$325$	−15.5034	−0.859972
$326$	38.5408	2.13458
$327$	46.3924	2.56550
$328$	−17.2978	−0.955111
$329$	−10.7927	−0.595023
$330$	−9.57351	−0.527005
$331$	−7.80926	−0.429236	−0.214618	−	0.976698i	$-0.568851\pi$
$331$	−7.80926	−0.429236	−0.214618	+	0.976698i	$0.568851\pi$
$332$	25.1445	1.37998
$333$	−80.5226	−4.41261
$334$	47.3158	2.58901
$335$	12.0755	0.659753
$336$	−3.83825	−0.209394
$337$	−8.72374	−0.475213	−0.237606	−	0.971362i	$-0.576363\pi$
$337$	−8.72374	−0.475213	−0.237606	+	0.971362i	$0.576363\pi$
$338$	−22.3500	−1.21568
$339$	41.0311	2.22850
$340$	−3.90156	−0.211592
$341$	8.01755	0.434175
$342$	−13.4266	−0.726025
$343$	12.2423	0.661020
$344$	−2.06746	−0.111470
$345$	−37.1658	−2.00094
$346$	−53.8979	−2.89757
$347$	14.5666	0.781976	0.390988	−	0.920396i	$-0.372133\pi$
$347$	14.5666	0.781976	0.390988	+	0.920396i	$0.372133\pi$
$348$	69.3894	3.71966
$349$	−25.6913	−1.37522	−0.687612	−	0.726079i	$-0.741341\pi$
$349$	−25.6913	−1.37522	−0.687612	+	0.726079i	$0.741341\pi$
$350$	−6.68331	−0.357238
$351$	−69.8390	−3.72773
$352$	6.95749	0.370835
$353$	18.5988	0.989915	0.494958	−	0.868917i	$-0.335184\pi$
$353$	18.5988	0.989915	0.494958	+	0.868917i	$0.335184\pi$
$354$	73.4019	3.90126
$355$	−13.6322	−0.723520
$356$	−25.1991	−1.33555
$357$	3.01966	0.159817
$358$	−24.7002	−1.30544
$359$	3.74162	0.197475	0.0987375	−	0.995114i	$-0.468520\pi$
$359$	3.74162	0.197475	0.0987375	+	0.995114i	$0.468520\pi$
$360$	20.6125	1.08637
$361$	−18.3483	−0.965701
$362$	14.3938	0.756520
$363$	−3.23881	−0.169994
$364$	−13.1241	−0.687889
$365$	−18.0465	−0.944596
$366$	−1.07585	−0.0562354
$367$	−13.3254	−0.695581	−0.347790	−	0.937572i	$-0.613068\pi$
$367$	−13.3254	−0.695581	−0.347790	+	0.937572i	$0.613068\pi$
$368$	10.9576	0.571205
$369$	62.6657	3.26224
$370$	−31.7781	−1.65206
$371$	−9.98860	−0.518582
$372$	−76.1113	−3.94619
$373$	−26.2400	−1.35866	−0.679328	−	0.733834i	$-0.737729\pi$
$373$	−26.2400	−1.35866	−0.679328	+	0.733834i	$0.737729\pi$
$374$	−2.22059	−0.114824
$375$	−35.4734	−1.83184
$376$	−23.9330	−1.23425
$377$	−35.1044	−1.80797
$378$	−30.1067	−1.54852
$379$	25.4656	1.30808	0.654040	−	0.756460i	$-0.273073\pi$
$379$	25.4656	1.30808	0.654040	+	0.756460i	$0.273073\pi$
$380$	−3.14961	−0.161572
$381$	−34.1641	−1.75028
$382$	−12.0798	−0.618059
$383$	−7.17364	−0.366556	−0.183278	−	0.983061i	$-0.558671\pi$
$383$	−7.17364	−0.366556	−0.183278	+	0.983061i	$0.558671\pi$
$384$	−47.7645	−2.43747
$385$	1.24105	0.0632496
$386$	10.0760	0.512856
$387$	7.48990	0.380733
$388$	−56.3181	−2.85912
$389$	16.9227	0.858012	0.429006	−	0.903302i	$-0.358864\pi$
$389$	16.9227	0.858012	0.429006	+	0.903302i	$0.358864\pi$
$390$	−45.9777	−2.32817
$391$	−8.62067	−0.435966
$392$	12.6751	0.640189
$393$	−30.3752	−1.53222
$394$	35.5600	1.79149
$395$	−2.85173	−0.143486
$396$	21.9532	1.10319
$397$	−17.5239	−0.879498	−0.439749	−	0.898121i	$-0.644933\pi$
$397$	−17.5239	−0.879498	−0.439749	+	0.898121i	$0.644933\pi$
$398$	−19.1473	−0.959768
$399$	2.43768	0.122037
$400$	4.10323	0.205161
$401$	−10.5042	−0.524554	−0.262277	−	0.964993i	$-0.584473\pi$
$401$	−10.5042	−0.524554	−0.262277	+	0.964993i	$0.584473\pi$
$402$	−65.2443	−3.25409
$403$	38.5050	1.91807
$404$	34.4258	1.71275
$405$	−32.7840	−1.62905
$406$	−15.1331	−0.751041
$407$	−10.7508	−0.532899
$408$	6.69612	0.331507
$409$	−15.4454	−0.763724	−0.381862	−	0.924219i	$-0.624717\pi$
$409$	−15.4454	−0.763724	−0.381862	+	0.924219i	$0.624717\pi$
$410$	24.7309	1.22137
$411$	19.1980	0.946965
$412$	1.98278	0.0976846
$413$	−9.51533	−0.468219
$414$	143.379	7.04671
$415$	−11.4192	−0.560549
$416$	33.4140	1.63826
$417$	3.40254	0.166623
$418$	−1.79262	−0.0876799
$419$	11.3979	0.556826	0.278413	−	0.960461i	$-0.410192\pi$
$419$	11.3979	0.556826	0.278413	+	0.960461i	$0.410192\pi$
$420$	−11.7814	−0.574872
$421$	−25.9949	−1.26691	−0.633457	−	0.773778i	$-0.718365\pi$
$421$	−25.9949	−1.26691	−0.633457	+	0.773778i	$0.718365\pi$
$422$	−38.5830	−1.87819
$423$	86.7033	4.21566
$424$	−22.1498	−1.07569
$425$	−3.22813	−0.156587
$426$	73.6551	3.56860
$427$	0.139466	0.00674921
$428$	−21.7936	−1.05343
$429$	−15.5547	−0.750988
$430$	2.95587	0.142545
$431$	22.2699	1.07271	0.536353	−	0.843994i	$-0.319802\pi$
$431$	22.2699	1.07271	0.536353	+	0.843994i	$0.319802\pi$
$432$	18.4841	0.889316
$433$	37.6567	1.80966	0.904832	−	0.425769i	$-0.139996\pi$
$433$	37.6567	1.80966	0.904832	+	0.425769i	$0.139996\pi$
$434$	16.5990	0.796779
$435$	−31.5128	−1.51093
$436$	−41.9839	−2.01066
$437$	−6.95921	−0.332904
$438$	97.5060	4.65902
$439$	15.9729	0.762347	0.381173	−	0.924504i	$-0.375520\pi$
$439$	15.9729	0.762347	0.381173	+	0.924504i	$0.375520\pi$
$440$	2.75203	0.131198
$441$	−45.9187	−2.18661
$442$	−10.6646	−0.507264
$443$	−2.44955	−0.116382	−0.0581908	−	0.998305i	$-0.518533\pi$
$443$	−2.44955	−0.116382	−0.0581908	+	0.998305i	$0.518533\pi$
$444$	102.058	4.84348
$445$	11.4441	0.542500
$446$	−34.4612	−1.63178
$447$	−26.7644	−1.26591
$448$	12.0342	0.568562
$449$	−20.0298	−0.945265	−0.472632	−	0.881260i	$-0.656696\pi$
$449$	−20.0298	−0.945265	−0.472632	+	0.881260i	$0.656696\pi$
$450$	53.6903	2.53099
$451$	8.36668	0.393972
$452$	−37.1321	−1.74655
$453$	−31.7482	−1.49166
$454$	3.58051	0.168041
$455$	5.96024	0.279421
$456$	5.40558	0.253139
$457$	−22.2696	−1.04173	−0.520864	−	0.853640i	$-0.674390\pi$
$457$	−22.2696	−1.04173	−0.520864	+	0.853640i	$0.674390\pi$
$458$	33.1588	1.54941
$459$	−14.5419	−0.678760
$460$	33.6340	1.56819
$461$	1.41068	0.0657018	0.0328509	−	0.999460i	$-0.489541\pi$
$461$	1.41068	0.0657018	0.0328509	+	0.999460i	$0.489541\pi$
$462$	−6.70543	−0.311965
$463$	−25.3233	−1.17687	−0.588436	−	0.808544i	$-0.700256\pi$
$463$	−25.3233	−1.17687	−0.588436	+	0.808544i	$0.700256\pi$
$464$	9.29096	0.431322
$465$	34.5656	1.60294
$466$	−31.0621	−1.43893
$467$	0.313198	0.0144931	0.00724654	−	0.999974i	$-0.497693\pi$
$467$	0.313198	0.0144931	0.00724654	+	0.999974i	$0.497693\pi$
$468$	105.432	4.87361
$469$	8.45784	0.390547
$470$	34.2173	1.57832
$471$	34.3684	1.58361
$472$	−21.1003	−0.971222
$473$	1.00000	0.0459800
$474$	15.4080	0.707715
$475$	−2.60597	−0.119570
$476$	−2.73271	−0.125254
$477$	80.2433	3.67409
$478$	−4.61061	−0.210884
$479$	−1.08888	−0.0497524	−0.0248762	−	0.999691i	$-0.507919\pi$
$479$	−1.08888	−0.0497524	−0.0248762	+	0.999691i	$0.507919\pi$
$480$	29.9954	1.36910
$481$	−51.6318	−2.35421
$482$	−36.5013	−1.66259
$483$	−26.0315	−1.18447
$484$	2.93104	0.133229
$485$	25.5766	1.16137
$486$	80.2581	3.64058
$487$	−37.3112	−1.69073	−0.845367	−	0.534186i	$-0.820618\pi$
$487$	−37.3112	−1.69073	−0.845367	+	0.534186i	$0.820618\pi$
$488$	0.309266	0.0139998
$489$	56.2131	2.54204
$490$	−18.1217	−0.818656
$491$	−30.7080	−1.38583	−0.692917	−	0.721017i	$-0.743675\pi$
$491$	−30.7080	−1.38583	−0.692917	+	0.721017i	$0.743675\pi$
$492$	−79.4256	−3.58078
$493$	−7.30946	−0.329202
$494$	−8.60922	−0.387347
$495$	−9.96994	−0.448115
$496$	−10.1910	−0.457590
$497$	−9.54817	−0.428294
$498$	61.6987	2.76479
$499$	22.7886	1.02016	0.510080	−	0.860127i	$-0.329616\pi$
$499$	22.7886	1.02016	0.510080	+	0.860127i	$0.329616\pi$
$500$	32.1025	1.43567
$501$	69.0117	3.08322
$502$	52.2794	2.33334
$503$	−20.9566	−0.934408	−0.467204	−	0.884149i	$-0.654739\pi$
$503$	−20.9566	−0.934408	−0.467204	+	0.884149i	$0.654739\pi$
$504$	14.4373	0.643087
$505$	−15.6343	−0.695718
$506$	19.1430	0.851010
$507$	−32.5983	−1.44774
$508$	30.9176	1.37175
$509$	−35.8907	−1.59083	−0.795414	−	0.606066i	$-0.792747\pi$
$509$	−35.8907	−1.59083	−0.795414	+	0.606066i	$0.792747\pi$
$510$	−9.57351	−0.423922
$511$	−12.6400	−0.559162
$512$	−14.0994	−0.623112
$513$	−11.7393	−0.518302
$514$	4.42639	0.195240
$515$	−0.900471	−0.0396795
$516$	−9.49308	−0.417910
$517$	11.5760	0.509113
$518$	−22.2578	−0.977953
$519$	−78.6119	−3.45068
$520$	13.2169	0.579599
$521$	−4.88369	−0.213958	−0.106979	−	0.994261i	$-0.534118\pi$
$521$	−4.88369	−0.213958	−0.106979	+	0.994261i	$0.534118\pi$
$522$	121.571	5.32103
$523$	−3.63027	−0.158741	−0.0793704	−	0.996845i	$-0.525291\pi$
$523$	−3.63027	−0.158741	−0.0793704	+	0.996845i	$0.525291\pi$
$524$	27.4887	1.20085
$525$	−9.74783	−0.425430
$526$	41.9095	1.82734
$527$	8.01755	0.349250
$528$	4.11681	0.179161
$529$	51.3159	2.23113
$530$	31.6678	1.37556
$531$	76.4413	3.31727
$532$	−2.20604	−0.0956438
$533$	40.1818	1.74047
$534$	−61.8328	−2.67576
$535$	9.89747	0.427905
$536$	18.7553	0.810107
$537$	−36.0260	−1.55464
$538$	42.5298	1.83359
$539$	−6.13075	−0.264070
$540$	56.7363	2.44154
$541$	27.6169	1.18734	0.593672	−	0.804707i	$-0.297678\pi$
$541$	27.6169	1.18734	0.593672	+	0.804707i	$0.297678\pi$
$542$	−20.6952	−0.888936
$543$	20.9938	0.900931
$544$	6.95749	0.298300
$545$	19.0668	0.816731
$546$	−32.2035	−1.37818
$547$	−5.88658	−0.251692	−0.125846	−	0.992050i	$-0.540165\pi$
$547$	−5.88658	−0.251692	−0.125846	+	0.992050i	$0.540165\pi$
$548$	−17.3736	−0.742165
$549$	−1.12040	−0.0478173
$550$	7.16836	0.305660
$551$	−5.90071	−0.251379
$552$	−57.7250	−2.45694
$553$	−1.99740	−0.0849379
$554$	−21.2582	−0.903174
$555$	−46.3494	−1.96742
$556$	−3.07921	−0.130588
$557$	−17.7215	−0.750886	−0.375443	−	0.926846i	$-0.622509\pi$
$557$	−17.7215	−0.750886	−0.375443	+	0.926846i	$0.622509\pi$
$558$	−133.348	−5.64508
$559$	4.80259	0.203128
$560$	−1.57748	−0.0666607
$561$	−3.23881	−0.136743
$562$	−8.74213	−0.368765
$563$	−19.5992	−0.826006	−0.413003	−	0.910730i	$-0.635520\pi$
$563$	−19.5992	−0.826006	−0.413003	+	0.910730i	$0.635520\pi$
$564$	−109.892	−4.62730
$565$	16.8634	0.709447
$566$	−48.5372	−2.04017
$567$	−22.9624	−0.964330
$568$	−21.1731	−0.888405
$569$	23.8377	0.999327	0.499664	−	0.866219i	$-0.333457\pi$
$569$	23.8377	0.999327	0.499664	+	0.866219i	$0.333457\pi$
$570$	−7.72842	−0.323708
$571$	−15.1843	−0.635445	−0.317722	−	0.948184i	$-0.602918\pi$
$571$	−15.1843	−0.635445	−0.317722	+	0.948184i	$0.602918\pi$
$572$	14.0766	0.588572
$573$	−17.6189	−0.736038
$574$	17.3219	0.723001
$575$	27.8286	1.16053
$576$	−96.6766	−4.02819
$577$	−12.8644	−0.535552	−0.267776	−	0.963481i	$-0.586289\pi$
$577$	−12.8644	−0.535552	−0.267776	+	0.963481i	$0.586289\pi$
$578$	−2.22059	−0.0923645
$579$	14.6962	0.610754
$580$	28.5183	1.18416
$581$	−7.99822	−0.331822
$582$	−138.191	−5.72822
$583$	10.7135	0.443709
$584$	−28.0294	−1.15986
$585$	−47.8816	−1.97966
$586$	38.8138	1.60338
$587$	27.1321	1.11986	0.559931	−	0.828539i	$-0.310827\pi$
$587$	27.1321	1.11986	0.559931	+	0.828539i	$0.310827\pi$
$588$	58.1997	2.40012
$589$	6.47233	0.266688
$590$	30.1674	1.24197
$591$	51.8655	2.13346
$592$	13.6652	0.561638
$593$	18.9468	0.778054	0.389027	−	0.921226i	$-0.372811\pi$
$593$	18.9468	0.778054	0.389027	+	0.921226i	$0.372811\pi$
$594$	32.2918	1.32495
$595$	1.24105	0.0508780
$596$	24.2211	0.992135
$597$	−27.9270	−1.14298
$598$	91.9360	3.75954
$599$	4.37119	0.178602	0.0893010	−	0.996005i	$-0.471537\pi$
$599$	4.37119	0.178602	0.0893010	+	0.996005i	$0.471537\pi$
$600$	−21.6159	−0.882466
$601$	31.4728	1.28380	0.641901	−	0.766787i	$-0.278146\pi$
$601$	31.4728	1.28380	0.641901	+	0.766787i	$0.278146\pi$
$602$	2.07034	0.0843807
$603$	−67.9460	−2.76697
$604$	28.7313	1.16906
$605$	−1.33112	−0.0541176
$606$	84.4729	3.43148
$607$	13.6521	0.554121	0.277061	−	0.960852i	$-0.410640\pi$
$607$	13.6521	0.554121	0.277061	+	0.960852i	$0.410640\pi$
$608$	5.61658	0.227782
$609$	−22.0721	−0.894406
$610$	−0.442161	−0.0179026
$611$	55.5949	2.24913
$612$	21.9532	0.887405
$613$	7.09513	0.286570	0.143285	−	0.989681i	$-0.454234\pi$
$613$	7.09513	0.286570	0.143285	+	0.989681i	$0.454234\pi$
$614$	−7.38107	−0.297876
$615$	36.0708	1.45451
$616$	1.92757	0.0776638
$617$	25.3337	1.01990	0.509949	−	0.860205i	$-0.329664\pi$
$617$	25.3337	1.01990	0.509949	+	0.860205i	$0.329664\pi$
$618$	4.86528	0.195710
$619$	25.3955	1.02073	0.510366	−	0.859957i	$-0.329510\pi$
$619$	25.3955	1.02073	0.510366	+	0.859957i	$0.329510\pi$
$620$	−31.2809	−1.25627
$621$	125.361	5.03058
$622$	−31.2650	−1.25361
$623$	8.01559	0.321138
$624$	19.7714	0.791488
$625$	1.56143	0.0624571
$626$	3.67361	0.146827
$627$	−2.61460	−0.104417
$628$	−31.1025	−1.24113
$629$	−10.7508	−0.428663
$630$	−20.6411	−0.822363
$631$	−24.7758	−0.986310	−0.493155	−	0.869941i	$-0.664156\pi$
$631$	−24.7758	−0.986310	−0.493155	+	0.869941i	$0.664156\pi$
$632$	−4.42924	−0.176186
$633$	−56.2746	−2.23671
$634$	−21.7084	−0.862152
$635$	−14.0411	−0.557203
$636$	−101.704	−4.03284
$637$	−29.4435	−1.16659
$638$	16.2314	0.642605
$639$	76.7051	3.03441
$640$	−19.6307	−0.775972
$641$	−19.9885	−0.789497	−0.394748	−	0.918789i	$-0.629168\pi$
$641$	−19.9885	−0.789497	−0.394748	+	0.918789i	$0.629168\pi$
$642$	−53.4765	−2.11055
$643$	−31.7736	−1.25303	−0.626514	−	0.779410i	$-0.715519\pi$
$643$	−31.7736	−1.25303	−0.626514	+	0.779410i	$0.715519\pi$
$644$	23.5578	0.928307
$645$	4.31124	0.169755
$646$	−1.79262	−0.0705297
$647$	42.1715	1.65793	0.828966	−	0.559300i	$-0.188930\pi$
$647$	42.1715	1.65793	0.828966	+	0.559300i	$0.188930\pi$
$648$	−50.9193	−2.00030
$649$	10.2059	0.400617
$650$	34.4267	1.35033
$651$	24.2102	0.948874
$652$	−50.8713	−1.99228
$653$	−45.5674	−1.78319	−0.891595	−	0.452833i	$-0.850413\pi$
$653$	−45.5674	−1.78319	−0.891595	+	0.452833i	$0.850413\pi$
$654$	−103.019	−4.02835
$655$	−12.4839	−0.487785
$656$	−10.6348	−0.415219
$657$	101.544	3.96159
$658$	23.9663	0.934303
$659$	6.89142	0.268452	0.134226	−	0.990951i	$-0.457145\pi$
$659$	6.89142	0.268452	0.134226	+	0.990951i	$0.457145\pi$
$660$	12.6364	0.491872
$661$	−16.1336	−0.627526	−0.313763	−	0.949501i	$-0.601590\pi$
$661$	−16.1336	−0.627526	−0.313763	+	0.949501i	$0.601590\pi$
$662$	17.3412	0.673985
$663$	−15.5547	−0.604094
$664$	−17.7361	−0.688295
$665$	1.00186	0.0388505
$666$	178.808	6.92867
$667$	63.0124	2.43985
$668$	−62.4538	−2.41641
$669$	−50.2628	−1.94327
$670$	−26.8147	−1.03594
$671$	−0.149587	−0.00577476
$672$	21.0092	0.810449
$673$	9.63893	0.371554	0.185777	−	0.982592i	$-0.440520\pi$
$673$	9.63893	0.371554	0.185777	+	0.982592i	$0.440520\pi$
$674$	19.3719	0.746178
$675$	46.9432	1.80685
$676$	29.5006	1.13464
$677$	30.9794	1.19064	0.595318	−	0.803490i	$-0.297026\pi$
$677$	30.9794	1.19064	0.595318	+	0.803490i	$0.297026\pi$
$678$	−91.1135	−3.49919
$679$	17.9142	0.687485
$680$	2.75203	0.105536
$681$	5.22229	0.200119
$682$	−17.8037	−0.681740
$683$	9.47005	0.362361	0.181181	−	0.983450i	$-0.442008\pi$
$683$	9.47005	0.362361	0.181181	+	0.983450i	$0.442008\pi$
$684$	17.7222	0.677624
$685$	7.89016	0.301467
$686$	−27.1851	−1.03793
$687$	48.3632	1.84517
$688$	−1.27109	−0.0484597
$689$	51.4527	1.96019
$690$	82.5301	3.14187
$691$	−12.7430	−0.484766	−0.242383	−	0.970181i	$-0.577929\pi$
$691$	−12.7430	−0.484766	−0.242383	+	0.970181i	$0.577929\pi$
$692$	71.1417	2.70440
$693$	−6.98310	−0.265266
$694$	−32.3465	−1.22786
$695$	1.39841	0.0530446
$696$	−48.9450	−1.85526
$697$	8.36668	0.316911
$698$	57.0499	2.15937
$699$	−45.3052	−1.71360
$700$	8.82153	0.333423
$701$	0.760299	0.0287161	0.0143580	−	0.999897i	$-0.495430\pi$
$701$	0.760299	0.0287161	0.0143580	+	0.999897i	$0.495430\pi$
$702$	155.084	5.85328
$703$	−8.67882	−0.327328
$704$	−12.9076	−0.486473
$705$	49.9070	1.87961
$706$	−41.3004	−1.55436
$707$	−10.9505	−0.411837
$708$	−96.8857	−3.64119
$709$	31.7702	1.19316	0.596578	−	0.802555i	$-0.296527\pi$
$709$	31.7702	1.19316	0.596578	+	0.802555i	$0.296527\pi$
$710$	30.2715	1.13607
$711$	16.0461	0.601774
$712$	17.7746	0.666133
$713$	−69.1166	−2.58844
$714$	−6.70543	−0.250945
$715$	−6.39281	−0.239078
$716$	32.6026	1.21842
$717$	−6.72473	−0.251140
$718$	−8.30861	−0.310075
$719$	−36.0100	−1.34295	−0.671474	−	0.741028i	$-0.734338\pi$
$719$	−36.0100	−1.34295	−0.671474	+	0.741028i	$0.734338\pi$
$720$	12.6727	0.472282
$721$	−0.630703	−0.0234886
$722$	40.7442	1.51634
$723$	−53.2384	−1.97996
$724$	−18.9988	−0.706087
$725$	23.5959	0.876329
$726$	7.19209	0.266923
$727$	−38.0910	−1.41272	−0.706359	−	0.707854i	$-0.749664\pi$
$727$	−38.0910	−1.41272	−0.706359	+	0.707854i	$0.749664\pi$
$728$	9.25731	0.343099
$729$	43.1724	1.59898
$730$	40.0739	1.48320
$731$	1.00000	0.0369863
$732$	1.42005	0.0524864
$733$	28.7771	1.06291	0.531454	−	0.847087i	$-0.321646\pi$
$733$	28.7771	1.06291	0.531454	+	0.847087i	$0.321646\pi$
$734$	29.5903	1.09220
$735$	−26.4311	−0.974927
$736$	−59.9782	−2.21083
$737$	−9.07168	−0.334159
$738$	−139.155	−5.12237
$739$	−24.1005	−0.886549	−0.443275	−	0.896386i	$-0.646183\pi$
$739$	−24.1005	−0.886549	−0.443275	+	0.896386i	$0.646183\pi$
$740$	41.9450	1.54193
$741$	−12.5568	−0.461287
$742$	22.1806	0.814276
$743$	−22.3442	−0.819728	−0.409864	−	0.912147i	$-0.634424\pi$
$743$	−22.3442	−0.819728	−0.409864	+	0.912147i	$0.634424\pi$
$744$	53.6864	1.96824
$745$	−10.9999	−0.403005
$746$	58.2684	2.13336
$747$	64.2536	2.35092
$748$	2.93104	0.107169
$749$	6.93234	0.253302
$750$	78.7721	2.87635
$751$	28.9494	1.05638	0.528189	−	0.849127i	$-0.322871\pi$
$751$	28.9494	1.05638	0.528189	+	0.849127i	$0.322871\pi$
$752$	−14.7141	−0.536569
$753$	76.2512	2.77875
$754$	77.9526	2.83886
$755$	−13.0482	−0.474872
$756$	39.7389	1.44529
$757$	−20.4138	−0.741952	−0.370976	−	0.928642i	$-0.620977\pi$
$757$	−20.4138	−0.741952	−0.370976	+	0.928642i	$0.620977\pi$
$758$	−56.5488	−2.05394
$759$	27.9207	1.01346
$760$	2.22164	0.0805872
$761$	46.3201	1.67910	0.839551	−	0.543280i	$-0.182818\pi$
$761$	46.3201	1.67910	0.839551	+	0.543280i	$0.182818\pi$
$762$	75.8645	2.74828
$763$	13.3547	0.483471
$764$	15.9446	0.576856
$765$	−9.96994	−0.360464
$766$	15.9297	0.575565
$767$	49.0149	1.76982
$768$	22.4551	0.810278
$769$	−20.9153	−0.754223	−0.377112	−	0.926168i	$-0.623083\pi$
$769$	−20.9153	−0.754223	−0.377112	+	0.926168i	$0.623083\pi$
$770$	−2.75586	−0.0993144
$771$	6.45604	0.232509
$772$	−13.2997	−0.478666
$773$	−14.1945	−0.510542	−0.255271	−	0.966870i	$-0.582165\pi$
$773$	−14.1945	−0.510542	−0.255271	+	0.966870i	$0.582165\pi$
$774$	−16.6320	−0.597826
$775$	−25.8817	−0.929697
$776$	39.7249	1.42604
$777$	−32.4638	−1.16463
$778$	−37.5783	−1.34725
$779$	6.75418	0.241994
$780$	60.6875	2.17296
$781$	10.2411	0.366457
$782$	19.1430	0.684552
$783$	106.294	3.79863
$784$	7.79272	0.278311
$785$	14.1251	0.504145
$786$	67.4509	2.40590
$787$	22.0557	0.786201	0.393100	−	0.919496i	$-0.371402\pi$
$787$	22.0557	0.786201	0.393100	+	0.919496i	$0.371402\pi$
$788$	−46.9369	−1.67206
$789$	61.1264	2.17616
$790$	6.33254	0.225302
$791$	11.8114	0.419963
$792$	−15.4851	−0.550238
$793$	−0.718408	−0.0255114
$794$	38.9134	1.38099
$795$	46.1886	1.63814
$796$	25.2732	0.895784
$797$	1.90962	0.0676423	0.0338212	−	0.999428i	$-0.489232\pi$
$797$	1.90962	0.0676423	0.0338212	+	0.999428i	$0.489232\pi$
$798$	−5.41310	−0.191622
$799$	11.5760	0.409530
$800$	−22.4597	−0.794069
$801$	−64.3932	−2.27522
$802$	23.3255	0.823654
$803$	13.5574	0.478430
$804$	86.1182	3.03715
$805$	−10.6987	−0.377078
$806$	−85.5040	−3.01175
$807$	62.0312	2.18360
$808$	−24.2829	−0.854268
$809$	−16.0469	−0.564180	−0.282090	−	0.959388i	$-0.591028\pi$
$809$	−16.0469	−0.564180	−0.282090	+	0.959388i	$0.591028\pi$
$810$	72.8000	2.55793
$811$	−17.8474	−0.626708	−0.313354	−	0.949636i	$-0.601453\pi$
$811$	−17.8474	−0.626708	−0.313354	+	0.949636i	$0.601453\pi$
$812$	19.9746	0.700973
$813$	−30.1847	−1.05862
$814$	23.8732	0.836756
$815$	23.1030	0.809262
$816$	4.11681	0.144117
$817$	0.807270	0.0282428
$818$	34.2979	1.19920
$819$	−33.5370	−1.17188
$820$	−32.6431	−1.13995
$821$	27.8197	0.970915	0.485458	−	0.874260i	$-0.338653\pi$
$821$	27.8197	0.970915	0.485458	+	0.874260i	$0.338653\pi$
$822$	−42.6309	−1.48692
$823$	−28.2474	−0.984643	−0.492321	−	0.870413i	$-0.663852\pi$
$823$	−28.2474	−0.984643	−0.492321	+	0.870413i	$0.663852\pi$
$824$	−1.39859	−0.0487222
$825$	10.4553	0.364007
$826$	21.1297	0.735196
$827$	−13.0110	−0.452436	−0.226218	−	0.974077i	$-0.572636\pi$
$827$	−13.0110	−0.452436	−0.226218	+	0.974077i	$0.572636\pi$
$828$	−189.251	−6.57693
$829$	−0.125222	−0.00434914	−0.00217457	−	0.999998i	$-0.500692\pi$
$829$	−0.125222	−0.00434914	−0.00217457	+	0.999998i	$0.500692\pi$
$830$	25.3575	0.880172
$831$	−31.0058	−1.07558
$832$	−61.9899	−2.14911
$833$	−6.13075	−0.212418
$834$	−7.55566	−0.261631
$835$	28.3631	0.981545
$836$	2.36614	0.0818347
$837$	−116.591	−4.02997
$838$	−25.3102	−0.874327
$839$	44.9381	1.55143	0.775717	−	0.631080i	$-0.217388\pi$
$839$	44.9381	1.55143	0.775717	+	0.631080i	$0.217388\pi$
$840$	8.31020	0.286729
$841$	24.4282	0.842353
$842$	57.7241	1.98931
$843$	−12.7507	−0.439157
$844$	50.9270	1.75298
$845$	−13.3976	−0.460890
$846$	−192.533	−6.61942
$847$	−0.932335	−0.0320354
$848$	−13.6178	−0.467638
$849$	−70.7932	−2.42961
$850$	7.16836	0.245873
$851$	92.6793	3.17701
$852$	−97.2200	−3.33070
$853$	−10.8932	−0.372977	−0.186488	−	0.982457i	$-0.559711\pi$
$853$	−10.8932	−0.372977	−0.186488	+	0.982457i	$0.559711\pi$
$854$	−0.309697	−0.0105976
$855$	−8.04844	−0.275251
$856$	15.3725	0.525422
$857$	−19.4913	−0.665809	−0.332904	−	0.942961i	$-0.608029\pi$
$857$	−19.4913	−0.665809	−0.332904	+	0.942961i	$0.608029\pi$
$858$	34.5407	1.17920
$859$	−37.7299	−1.28733	−0.643664	−	0.765308i	$-0.722587\pi$
$859$	−37.7299	−1.28733	−0.643664	+	0.765308i	$0.722587\pi$
$860$	−3.90156	−0.133042
$861$	25.2645	0.861013
$862$	−49.4525	−1.68436
$863$	54.9779	1.87147	0.935734	−	0.352707i	$-0.114739\pi$
$863$	54.9779	1.87147	0.935734	+	0.352707i	$0.114739\pi$
$864$	−101.175	−3.44206
$865$	−32.3087	−1.09853
$866$	−83.6202	−2.84153
$867$	−3.23881	−0.109996
$868$	−21.9096	−0.743662
$869$	2.14236	0.0726746
$870$	69.9772	2.37245
$871$	−43.5676	−1.47623
$872$	29.6141	1.00286
$873$	−143.914	−4.87074
$874$	15.4536	0.522725
$875$	−10.2115	−0.345212
$876$	−128.701	−4.34842
$877$	−10.5383	−0.355852	−0.177926	−	0.984044i	$-0.556939\pi$
$877$	−10.5383	−0.355852	−0.177926	+	0.984044i	$0.556939\pi$
$878$	−35.4694	−1.19704
$879$	56.6112	1.90945
$880$	1.69197	0.0570362
$881$	−1.28919	−0.0434338	−0.0217169	−	0.999764i	$-0.506913\pi$
$881$	−1.28919	−0.0434338	−0.0217169	+	0.999764i	$0.506913\pi$
$882$	101.967	3.43340
$883$	13.3197	0.448245	0.224122	−	0.974561i	$-0.428048\pi$
$883$	13.3197	0.448245	0.224122	+	0.974561i	$0.428048\pi$
$884$	14.0766	0.473447
$885$	44.0002	1.47905
$886$	5.43946	0.182742
$887$	31.0808	1.04359	0.521796	−	0.853070i	$-0.325262\pi$
$887$	31.0808	1.04359	0.521796	+	0.853070i	$0.325262\pi$
$888$	−71.9888	−2.41579
$889$	−9.83458	−0.329841
$890$	−25.4126	−0.851833
$891$	24.6289	0.825100
$892$	45.4865	1.52300
$893$	9.34498	0.312718
$894$	59.4330	1.98774
$895$	−14.8063	−0.494921
$896$	−13.7496	−0.459343
$897$	134.092	4.47720
$898$	44.4781	1.48425
$899$	−58.6040	−1.95455
$900$	−70.8677	−2.36226
$901$	10.7135	0.356919
$902$	−18.5790	−0.618613
$903$	3.01966	0.100488
$904$	26.1918	0.871125
$905$	8.62824	0.286812
$906$	70.4999	2.34220
$907$	−31.0511	−1.03104	−0.515518	−	0.856879i	$-0.672400\pi$
$907$	−31.0511	−1.03104	−0.515518	+	0.856879i	$0.672400\pi$
$908$	−4.72603	−0.156839
$909$	87.9709	2.91781
$910$	−13.2353	−0.438745
$911$	1.94022	0.0642823	0.0321411	−	0.999483i	$-0.489767\pi$
$911$	1.94022	0.0642823	0.0321411	+	0.999483i	$0.489767\pi$
$912$	3.32338	0.110048
$913$	8.57869	0.283913
$914$	49.4517	1.63572
$915$	−0.644907	−0.0213200
$916$	−43.7674	−1.44612
$917$	−8.74390	−0.288749
$918$	32.2918	1.06579
$919$	6.35911	0.209768	0.104884	−	0.994484i	$-0.466553\pi$
$919$	6.35911	0.209768	0.104884	+	0.994484i	$0.466553\pi$
$920$	−23.7244	−0.782169
$921$	−10.7655	−0.354737
$922$	−3.13254	−0.103165
$923$	49.1840	1.61891
$924$	8.85073	0.291168
$925$	34.7050	1.14109
$926$	56.2327	1.84792
$927$	5.06675	0.166414
$928$	−50.8555	−1.66941
$929$	4.10078	0.134542	0.0672712	−	0.997735i	$-0.478571\pi$
$929$	4.10078	0.134542	0.0672712	+	0.997735i	$0.478571\pi$
$930$	−76.7561	−2.51693
$931$	−4.94917	−0.162203
$932$	41.0000	1.34300
$933$	−45.6011	−1.49291
$934$	−0.695486	−0.0227570
$935$	−1.33112	−0.0435322
$936$	−74.3685	−2.43081
$937$	31.6315	1.03335	0.516677	−	0.856180i	$-0.327169\pi$
$937$	31.6315	1.03335	0.516677	+	0.856180i	$0.327169\pi$
$938$	−18.7814	−0.613235
$939$	5.35808	0.174854
$940$	−45.1645	−1.47310
$941$	−19.8860	−0.648266	−0.324133	−	0.946011i	$-0.605073\pi$
$941$	−19.8860	−0.648266	−0.324133	+	0.946011i	$0.605073\pi$
$942$	−76.3183	−2.48658
$943$	−72.1264	−2.34876
$944$	−12.9726	−0.422223
$945$	−18.0472	−0.587077
$946$	−2.22059	−0.0721978
$947$	31.8193	1.03399	0.516994	−	0.855989i	$-0.327051\pi$
$947$	31.8193	1.03399	0.516994	+	0.855989i	$0.327051\pi$
$948$	−20.3376	−0.660535
$949$	65.1106	2.11358
$950$	5.78680	0.187749
$951$	−31.6625	−1.02673
$952$	1.92757	0.0624728
$953$	−39.9062	−1.29269	−0.646344	−	0.763046i	$-0.723703\pi$
$953$	−39.9062	−1.29269	−0.646344	+	0.763046i	$0.723703\pi$
$954$	−178.188	−5.76904
$955$	−7.24117	−0.234319
$956$	6.08571	0.196826
$957$	23.6740	0.765271
$958$	2.41797	0.0781211
$959$	5.52639	0.178456
$960$	−55.6477	−1.79602
$961$	33.2811	1.07358
$962$	114.653	3.69657
$963$	−55.6908	−1.79461
$964$	48.1794	1.55175
$965$	6.03999	0.194434
$966$	57.8053	1.85986
$967$	0.987880	0.0317681	0.0158840	−	0.999874i	$-0.494944\pi$
$967$	0.987880	0.0317681	0.0158840	+	0.999874i	$0.494944\pi$
$968$	−2.06746	−0.0664507
$969$	−2.61460	−0.0839930
$970$	−56.7952	−1.82358
$971$	−6.56596	−0.210712	−0.105356	−	0.994435i	$-0.533598\pi$
$971$	−6.56596	−0.210712	−0.105356	+	0.994435i	$0.533598\pi$
$972$	−105.935	−3.39788
$973$	0.979466	0.0314002
$974$	82.8531	2.65479
$975$	50.2125	1.60809
$976$	0.190139	0.00608619
$977$	23.3104	0.745765	0.372882	−	0.927879i	$-0.378369\pi$
$977$	23.3104	0.745765	0.372882	+	0.927879i	$0.378369\pi$
$978$	−124.826	−3.99151
$979$	−8.59733	−0.274772
$980$	23.9195	0.764080
$981$	−107.284	−3.42533
$982$	68.1901	2.17603
$983$	2.26795	0.0723365	0.0361682	−	0.999346i	$-0.488485\pi$
$983$	2.26795	0.0723365	0.0361682	+	0.999346i	$0.488485\pi$
$984$	56.0243	1.78599
$985$	21.3162	0.679189
$986$	16.2314	0.516912
$987$	34.9556	1.11265
$988$	11.3636	0.361525
$989$	−8.62067	−0.274121
$990$	22.1392	0.703630
$991$	10.1142	0.321289	0.160645	−	0.987012i	$-0.448643\pi$
$991$	10.1142	0.321289	0.160645	+	0.987012i	$0.448643\pi$
$992$	55.7820	1.77108
$993$	25.2927	0.802641
$994$	21.2026	0.672506
$995$	−11.4777	−0.363868
$996$	−81.4383	−2.58047
$997$	40.8609	1.29408	0.647038	−	0.762458i	$-0.276007\pi$
$997$	40.8609	1.29408	0.647038	+	0.762458i	$0.276007\pi$
$998$	−50.6043	−1.60185
$999$	156.338	4.94631

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.j.1.13	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.j.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.22059 q^{2} -3.23881 q^{3} +2.93104 q^{4} -1.33112 q^{5} +7.19209 q^{6} -0.932335 q^{7} -2.06746 q^{8} +7.48990 q^{9} +O(q^{10})\)	\(q-2.22059 q^{2} -3.23881 q^{3} +2.93104 q^{4} -1.33112 q^{5} +7.19209 q^{6} -0.932335 q^{7} -2.06746 q^{8} +7.48990 q^{9} +2.95587 q^{10} +1.00000 q^{11} -9.49308 q^{12} +4.80259 q^{13} +2.07034 q^{14} +4.31124 q^{15} -1.27109 q^{16} +1.00000 q^{17} -16.6320 q^{18} +0.807270 q^{19} -3.90156 q^{20} +3.01966 q^{21} -2.22059 q^{22} -8.62067 q^{23} +6.69612 q^{24} -3.22813 q^{25} -10.6646 q^{26} -14.5419 q^{27} -2.73271 q^{28} -7.30946 q^{29} -9.57351 q^{30} +8.01755 q^{31} +6.95749 q^{32} -3.23881 q^{33} -2.22059 q^{34} +1.24105 q^{35} +21.9532 q^{36} -10.7508 q^{37} -1.79262 q^{38} -15.5547 q^{39} +2.75203 q^{40} +8.36668 q^{41} -6.70543 q^{42} +1.00000 q^{43} +2.93104 q^{44} -9.96994 q^{45} +19.1430 q^{46} +11.5760 q^{47} +4.11681 q^{48} -6.13075 q^{49} +7.16836 q^{50} -3.23881 q^{51} +14.0766 q^{52} +10.7135 q^{53} +32.2918 q^{54} -1.33112 q^{55} +1.92757 q^{56} -2.61460 q^{57} +16.2314 q^{58} +10.2059 q^{59} +12.6364 q^{60} -0.149587 q^{61} -17.8037 q^{62} -6.98310 q^{63} -12.9076 q^{64} -6.39281 q^{65} +7.19209 q^{66} -9.07168 q^{67} +2.93104 q^{68} +27.9207 q^{69} -2.75586 q^{70} +10.2411 q^{71} -15.4851 q^{72} +13.5574 q^{73} +23.8732 q^{74} +10.4553 q^{75} +2.36614 q^{76} -0.932335 q^{77} +34.5407 q^{78} +2.14236 q^{79} +1.69197 q^{80} +24.6289 q^{81} -18.5790 q^{82} +8.57869 q^{83} +8.85073 q^{84} -1.33112 q^{85} -2.22059 q^{86} +23.6740 q^{87} -2.06746 q^{88} -8.59733 q^{89} +22.1392 q^{90} -4.47762 q^{91} -25.2675 q^{92} -25.9673 q^{93} -25.7057 q^{94} -1.07457 q^{95} -22.5340 q^{96} -19.2144 q^{97} +13.6139 q^{98} +7.48990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 8 q^{2} + 6 q^{3} + 98 q^{4} + 11 q^{5} + 10 q^{6} + 8 q^{7} + 30 q^{8} + 108 q^{9}+O(q^{10}) \) 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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