LMFDB - Embedded newform 6041.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2376278611$
Analytic rank:	$0$
Dimension:	$112$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80869 q^{2} +2.13107 q^{3} +5.88877 q^{4} -3.52544 q^{5} -5.98552 q^{6} -1.00000 q^{7} -10.9224 q^{8} +1.54145 q^{9} +O(q^{10})$	\(q-2.80869 q^{2} +2.13107 q^{3} +5.88877 q^{4} -3.52544 q^{5} -5.98552 q^{6} -1.00000 q^{7} -10.9224 q^{8} +1.54145 q^{9} +9.90189 q^{10} -1.46593 q^{11} +12.5494 q^{12} -4.10552 q^{13} +2.80869 q^{14} -7.51295 q^{15} +18.9000 q^{16} -4.94767 q^{17} -4.32945 q^{18} -0.218873 q^{19} -20.7605 q^{20} -2.13107 q^{21} +4.11734 q^{22} -1.85326 q^{23} -23.2763 q^{24} +7.42874 q^{25} +11.5312 q^{26} -3.10828 q^{27} -5.88877 q^{28} +0.0714707 q^{29} +21.1016 q^{30} -8.79785 q^{31} -31.2397 q^{32} -3.12399 q^{33} +13.8965 q^{34} +3.52544 q^{35} +9.07722 q^{36} -0.645944 q^{37} +0.614749 q^{38} -8.74914 q^{39} +38.5061 q^{40} +4.37374 q^{41} +5.98552 q^{42} -9.97214 q^{43} -8.63251 q^{44} -5.43428 q^{45} +5.20525 q^{46} -5.57618 q^{47} +40.2773 q^{48} +1.00000 q^{49} -20.8651 q^{50} -10.5438 q^{51} -24.1765 q^{52} -7.38341 q^{53} +8.73020 q^{54} +5.16804 q^{55} +10.9224 q^{56} -0.466434 q^{57} -0.200739 q^{58} -0.775751 q^{59} -44.2420 q^{60} +9.23557 q^{61} +24.7105 q^{62} -1.54145 q^{63} +49.9428 q^{64} +14.4738 q^{65} +8.77433 q^{66} +4.17349 q^{67} -29.1357 q^{68} -3.94942 q^{69} -9.90189 q^{70} +10.2711 q^{71} -16.8362 q^{72} +5.12492 q^{73} +1.81426 q^{74} +15.8311 q^{75} -1.28889 q^{76} +1.46593 q^{77} +24.5737 q^{78} +5.51200 q^{79} -66.6310 q^{80} -11.2483 q^{81} -12.2845 q^{82} -10.5691 q^{83} -12.5494 q^{84} +17.4427 q^{85} +28.0087 q^{86} +0.152309 q^{87} +16.0114 q^{88} -9.03534 q^{89} +15.2632 q^{90} +4.10552 q^{91} -10.9134 q^{92} -18.7488 q^{93} +15.6618 q^{94} +0.771625 q^{95} -66.5740 q^{96} -8.60312 q^{97} -2.80869 q^{98} -2.25965 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) $ 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * 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 $

$2$	−2.80869	−1.98605	−0.993024	−	0.117916i	$-0.962379\pi$
$2$	−2.80869	−1.98605	−0.993024	+	0.117916i	$0.962379\pi$
$3$	2.13107	1.23037	0.615186	−	0.788382i	$-0.289081\pi$
$3$	2.13107	1.23037	0.615186	+	0.788382i	$0.289081\pi$
$4$	5.88877	2.94438
$5$	−3.52544	−1.57663	−0.788313	−	0.615275i	$-0.789045\pi$
$5$	−3.52544	−1.57663	−0.788313	+	0.615275i	$0.789045\pi$
$6$	−5.98552	−2.44358
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.9224	−3.86164
$9$	1.54145	0.513815
$10$	9.90189	3.13125
$11$	−1.46593	−0.441994	−0.220997	−	0.975275i	$-0.570931\pi$
$11$	−1.46593	−0.441994	−0.220997	+	0.975275i	$0.570931\pi$
$12$	12.5494	3.62269
$13$	−4.10552	−1.13867	−0.569333	−	0.822107i	$-0.692799\pi$
$13$	−4.10552	−1.13867	−0.569333	+	0.822107i	$0.692799\pi$
$14$	2.80869	0.750655
$15$	−7.51295	−1.93984
$16$	18.9000	4.72501
$17$	−4.94767	−1.19999	−0.599993	−	0.800005i	$-0.704830\pi$
$17$	−4.94767	−1.19999	−0.599993	+	0.800005i	$0.704830\pi$
$18$	−4.32945	−1.02046
$19$	−0.218873	−0.0502130	−0.0251065	−	0.999685i	$-0.507992\pi$
$19$	−0.218873	−0.0502130	−0.0251065	+	0.999685i	$0.507992\pi$
$20$	−20.7605	−4.64219
$21$	−2.13107	−0.465037
$22$	4.11734	0.877821
$23$	−1.85326	−0.386432	−0.193216	−	0.981156i	$-0.561892\pi$
$23$	−1.85326	−0.386432	−0.193216	+	0.981156i	$0.561892\pi$
$24$	−23.2763	−4.75125
$25$	7.42874	1.48575
$26$	11.5312	2.26145
$27$	−3.10828	−0.598188
$28$	−5.88877	−1.11287
$29$	0.0714707	0.0132718	0.00663589	−	0.999978i	$-0.497888\pi$
$29$	0.0714707	0.0132718	0.00663589	+	0.999978i	$0.497888\pi$
$30$	21.1016	3.85261
$31$	−8.79785	−1.58014	−0.790071	−	0.613016i	$-0.789956\pi$
$31$	−8.79785	−1.58014	−0.790071	+	0.613016i	$0.789956\pi$
$32$	−31.2397	−5.52246
$33$	−3.12399	−0.543817
$34$	13.8965	2.38323
$35$	3.52544	0.595908
$36$	9.07722	1.51287
$37$	−0.645944	−0.106193	−0.0530963	−	0.998589i	$-0.516909\pi$
$37$	−0.645944	−0.106193	−0.0530963	+	0.998589i	$0.516909\pi$
$38$	0.614749	0.0997254
$39$	−8.74914	−1.40098
$40$	38.5061	6.08836
$41$	4.37374	0.683063	0.341532	−	0.939870i	$-0.389054\pi$
$41$	4.37374	0.683063	0.341532	+	0.939870i	$0.389054\pi$
$42$	5.98552	0.923585
$43$	−9.97214	−1.52074	−0.760369	−	0.649492i	$-0.774982\pi$
$43$	−9.97214	−1.52074	−0.760369	+	0.649492i	$0.774982\pi$
$44$	−8.63251	−1.30140
$45$	−5.43428	−0.810094
$46$	5.20525	0.767472
$47$	−5.57618	−0.813369	−0.406684	−	0.913569i	$-0.633315\pi$
$47$	−5.57618	−0.813369	−0.406684	+	0.913569i	$0.633315\pi$
$48$	40.2773	5.81352
$49$	1.00000	0.142857
$50$	−20.8651	−2.95076
$51$	−10.5438	−1.47643
$52$	−24.1765	−3.35267
$53$	−7.38341	−1.01419	−0.507094	−	0.861891i	$-0.669280\pi$
$53$	−7.38341	−1.01419	−0.507094	+	0.861891i	$0.669280\pi$
$54$	8.73020	1.18803
$55$	5.16804	0.696859
$56$	10.9224	1.45956
$57$	−0.466434	−0.0617807
$58$	−0.200739	−0.0263584
$59$	−0.775751	−0.100994	−0.0504971	−	0.998724i	$-0.516081\pi$
$59$	−0.775751	−0.100994	−0.0504971	+	0.998724i	$0.516081\pi$
$60$	−44.2420	−5.71162
$61$	9.23557	1.18249	0.591247	−	0.806491i	$-0.298636\pi$
$61$	9.23557	1.18249	0.591247	+	0.806491i	$0.298636\pi$
$62$	24.7105	3.13824
$63$	−1.54145	−0.194204
$64$	49.9428	6.24285
$65$	14.4738	1.79525
$66$	8.77433	1.08005
$67$	4.17349	0.509873	0.254936	−	0.966958i	$-0.417945\pi$
$67$	4.17349	0.509873	0.254936	+	0.966958i	$0.417945\pi$
$68$	−29.1357	−3.53322
$69$	−3.94942	−0.475455
$70$	−9.90189	−1.18350
$71$	10.2711	1.21896	0.609478	−	0.792803i	$-0.291379\pi$
$71$	10.2711	1.21896	0.609478	+	0.792803i	$0.291379\pi$
$72$	−16.8362	−1.98417
$73$	5.12492	0.599827	0.299913	−	0.953966i	$-0.403042\pi$
$73$	5.12492	0.599827	0.299913	+	0.953966i	$0.403042\pi$
$74$	1.81426	0.210903
$75$	15.8311	1.82802
$76$	−1.28889	−0.147846
$77$	1.46593	0.167058
$78$	24.5737	2.78242
$79$	5.51200	0.620149	0.310074	−	0.950712i	$-0.399646\pi$
$79$	5.51200	0.620149	0.310074	+	0.950712i	$0.399646\pi$
$80$	−66.6310	−7.44957
$81$	−11.2483	−1.24981
$82$	−12.2845	−1.35660
$83$	−10.5691	−1.16011	−0.580054	−	0.814578i	$-0.696969\pi$
$83$	−10.5691	−1.16011	−0.580054	+	0.814578i	$0.696969\pi$
$84$	−12.5494	−1.36925
$85$	17.4427	1.89193
$86$	28.0087	3.02026
$87$	0.152309	0.0163292
$88$	16.0114	1.70682
$89$	−9.03534	−0.957745	−0.478872	−	0.877885i	$-0.658954\pi$
$89$	−9.03534	−0.957745	−0.478872	+	0.877885i	$0.658954\pi$
$90$	15.2632	1.60889
$91$	4.10552	0.430376
$92$	−10.9134	−1.13780
$93$	−18.7488	−1.94416
$94$	15.6618	1.61539
$95$	0.771625	0.0791671
$96$	−66.5740	−6.79468
$97$	−8.60312	−0.873515	−0.436757	−	0.899579i	$-0.643873\pi$
$97$	−8.60312	−0.873515	−0.436757	+	0.899579i	$0.643873\pi$
$98$	−2.80869	−0.283721
$99$	−2.25965	−0.227103
$100$	43.7461	4.37461
$101$	−0.642844	−0.0639654	−0.0319827	−	0.999488i	$-0.510182\pi$
$101$	−0.642844	−0.0639654	−0.0319827	+	0.999488i	$0.510182\pi$
$102$	29.6144	2.93226
$103$	10.5427	1.03881	0.519403	−	0.854529i	$-0.326154\pi$
$103$	10.5427	1.03881	0.519403	+	0.854529i	$0.326154\pi$
$104$	44.8420	4.39712
$105$	7.51295	0.733189
$106$	20.7377	2.01423
$107$	−0.371273	−0.0358923	−0.0179461	−	0.999839i	$-0.505713\pi$
$107$	−0.371273	−0.0358923	−0.0179461	+	0.999839i	$0.505713\pi$
$108$	−18.3039	−1.76129
$109$	−18.9448	−1.81459	−0.907293	−	0.420498i	$-0.861855\pi$
$109$	−18.9448	−1.81459	−0.907293	+	0.420498i	$0.861855\pi$
$110$	−14.5155	−1.38399
$111$	−1.37655	−0.130656
$112$	−18.9000	−1.78589
$113$	−8.21280	−0.772595	−0.386298	−	0.922374i	$-0.626246\pi$
$113$	−8.21280	−0.772595	−0.386298	+	0.922374i	$0.626246\pi$
$114$	1.31007	0.122699
$115$	6.53356	0.609258
$116$	0.420874	0.0390772
$117$	−6.32844	−0.585064
$118$	2.17885	0.200579
$119$	4.94767	0.453552
$120$	82.0592	7.49094
$121$	−8.85106	−0.804642
$122$	−25.9399	−2.34849
$123$	9.32073	0.840422
$124$	−51.8085	−4.65254
$125$	−8.56237	−0.765841
$126$	4.32945	0.385698
$127$	5.58661	0.495732	0.247866	−	0.968794i	$-0.420271\pi$
$127$	5.58661	0.495732	0.247866	+	0.968794i	$0.420271\pi$
$128$	−77.7946	−6.87614
$129$	−21.2513	−1.87107
$130$	−40.6524	−3.56545
$131$	−11.2470	−0.982651	−0.491326	−	0.870976i	$-0.663487\pi$
$131$	−11.2470	−0.982651	−0.491326	+	0.870976i	$0.663487\pi$
$132$	−18.3964	−1.60121
$133$	0.218873	0.0189787
$134$	−11.7221	−1.01263
$135$	10.9580	0.943118
$136$	54.0402	4.63391
$137$	−16.9710	−1.44993	−0.724965	−	0.688786i	$-0.758144\pi$
$137$	−16.9710	−1.44993	−0.724965	+	0.688786i	$0.758144\pi$
$138$	11.0927	0.944276
$139$	18.5865	1.57648	0.788242	−	0.615366i	$-0.210992\pi$
$139$	18.5865	1.57648	0.788242	+	0.615366i	$0.210992\pi$
$140$	20.7605	1.75458
$141$	−11.8832	−1.00075
$142$	−28.8484	−2.42090
$143$	6.01840	0.503284
$144$	29.1334	2.42778
$145$	−0.251966	−0.0209246
$146$	−14.3943	−1.19128
$147$	2.13107	0.175767
$148$	−3.80381	−0.312672
$149$	6.30385	0.516431	0.258216	−	0.966087i	$-0.416865\pi$
$149$	6.30385	0.516431	0.258216	+	0.966087i	$0.416865\pi$
$150$	−44.4648	−3.63054
$151$	−15.6628	−1.27462	−0.637310	−	0.770607i	$-0.719953\pi$
$151$	−15.6628	−1.27462	−0.637310	+	0.770607i	$0.719953\pi$
$152$	2.39061	0.193904
$153$	−7.62657	−0.616571
$154$	−4.11734	−0.331785
$155$	31.0163	2.49129
$156$	−51.5216	−4.12503
$157$	13.9753	1.11535	0.557676	−	0.830058i	$-0.311693\pi$
$157$	13.9753	1.11535	0.557676	+	0.830058i	$0.311693\pi$
$158$	−15.4815	−1.23164
$159$	−15.7345	−1.24783
$160$	110.134	8.70685
$161$	1.85326	0.146057
$162$	31.5930	2.48218
$163$	−4.19046	−0.328222	−0.164111	−	0.986442i	$-0.552476\pi$
$163$	−4.19046	−0.328222	−0.164111	+	0.986442i	$0.552476\pi$
$164$	25.7559	2.01120
$165$	11.0134	0.857395
$166$	29.6853	2.30403
$167$	0.413491	0.0319969	0.0159985	−	0.999872i	$-0.494907\pi$
$167$	0.413491	0.0319969	0.0159985	+	0.999872i	$0.494907\pi$
$168$	23.2763	1.79580
$169$	3.85530	0.296562
$170$	−48.9913	−3.75746
$171$	−0.337381	−0.0258002
$172$	−58.7236	−4.47763
$173$	18.7110	1.42257	0.711285	−	0.702904i	$-0.248114\pi$
$173$	18.7110	1.42257	0.711285	+	0.702904i	$0.248114\pi$
$174$	−0.427789	−0.0324306
$175$	−7.42874	−0.561560
$176$	−27.7061	−2.08843
$177$	−1.65318	−0.124260
$178$	25.3775	1.90213
$179$	15.4247	1.15289	0.576447	−	0.817134i	$-0.304439\pi$
$179$	15.4247	1.15289	0.576447	+	0.817134i	$0.304439\pi$
$180$	−32.0012	−2.38523
$181$	23.1042	1.71732	0.858662	−	0.512542i	$-0.171296\pi$
$181$	23.1042	1.71732	0.858662	+	0.512542i	$0.171296\pi$
$182$	−11.5312	−0.854746
$183$	19.6816	1.45491
$184$	20.2420	1.49226
$185$	2.27724	0.167426
$186$	52.6597	3.86120
$187$	7.25293	0.530386
$188$	−32.8368	−2.39487
$189$	3.10828	0.226094
$190$	−2.16726	−0.157230
$191$	15.6344	1.13127	0.565634	−	0.824656i	$-0.308632\pi$
$191$	15.6344	1.13127	0.565634	+	0.824656i	$0.308632\pi$
$192$	106.431	7.68103
$193$	21.8813	1.57505	0.787526	−	0.616281i	$-0.211361\pi$
$193$	21.8813	1.57505	0.787526	+	0.616281i	$0.211361\pi$
$194$	24.1635	1.73484
$195$	30.8446	2.20883
$196$	5.88877	0.420626
$197$	−14.8640	−1.05901	−0.529506	−	0.848306i	$-0.677623\pi$
$197$	−14.8640	−1.05901	−0.529506	+	0.848306i	$0.677623\pi$
$198$	6.34666	0.451038
$199$	15.4817	1.09747	0.548736	−	0.835996i	$-0.315109\pi$
$199$	15.4817	1.09747	0.548736	+	0.835996i	$0.315109\pi$
$200$	−81.1393	−5.73742
$201$	8.89398	0.627333
$202$	1.80555	0.127038
$203$	−0.0714707	−0.00501626
$204$	−62.0901	−4.34718
$205$	−15.4194	−1.07693
$206$	−29.6113	−2.06312
$207$	−2.85670	−0.198555
$208$	−77.5945	−5.38021
$209$	0.320852	0.0221938
$210$	−21.1016	−1.45615
$211$	−19.2196	−1.32313	−0.661566	−	0.749887i	$-0.730108\pi$
$211$	−19.2196	−1.32313	−0.661566	+	0.749887i	$0.730108\pi$
$212$	−43.4792	−2.98616
$213$	21.8884	1.49977
$214$	1.04279	0.0712838
$215$	35.1562	2.39763
$216$	33.9497	2.30999
$217$	8.79785	0.597237
$218$	53.2103	3.60386
$219$	10.9215	0.738010
$220$	30.4334	2.05182
$221$	20.3128	1.36638
$222$	3.86631	0.259490
$223$	19.5116	1.30660	0.653298	−	0.757101i	$-0.273385\pi$
$223$	19.5116	1.30660	0.653298	+	0.757101i	$0.273385\pi$
$224$	31.2397	2.08729
$225$	11.4510	0.763400
$226$	23.0673	1.53441
$227$	−12.8656	−0.853917	−0.426959	−	0.904271i	$-0.640415\pi$
$227$	−12.8656	−0.853917	−0.426959	+	0.904271i	$0.640415\pi$
$228$	−2.74672	−0.181906
$229$	−12.4525	−0.822883	−0.411441	−	0.911436i	$-0.634975\pi$
$229$	−12.4525	−0.822883	−0.411441	+	0.911436i	$0.634975\pi$
$230$	−18.3508	−1.21002
$231$	3.12399	0.205543
$232$	−0.780629	−0.0512508
$233$	−17.4864	−1.14557	−0.572787	−	0.819704i	$-0.694138\pi$
$233$	−17.4864	−1.14557	−0.572787	+	0.819704i	$0.694138\pi$
$234$	17.7747	1.16197
$235$	19.6585	1.28238
$236$	−4.56822	−0.297366
$237$	11.7464	0.763014
$238$	−13.8965	−0.900776
$239$	13.1470	0.850410	0.425205	−	0.905097i	$-0.360202\pi$
$239$	13.1470	0.850410	0.425205	+	0.905097i	$0.360202\pi$
$240$	−141.995	−9.16575
$241$	−23.3870	−1.50649	−0.753244	−	0.657741i	$-0.771512\pi$
$241$	−23.3870	−1.50649	−0.753244	+	0.657741i	$0.771512\pi$
$242$	24.8599	1.59806
$243$	−14.6460	−0.939542
$244$	54.3861	3.48171
$245$	−3.52544	−0.225232
$246$	−26.1791	−1.66912
$247$	0.898589	0.0571759
$248$	96.0933	6.10193
$249$	−22.5234	−1.42736
$250$	24.0491	1.52100
$251$	−13.1557	−0.830378	−0.415189	−	0.909735i	$-0.636285\pi$
$251$	−13.1557	−0.830378	−0.415189	+	0.909735i	$0.636285\pi$
$252$	−9.07722	−0.571811
$253$	2.71675	0.170800
$254$	−15.6911	−0.984547
$255$	37.1716	2.32778
$256$	118.616	7.41349
$257$	−5.47491	−0.341515	−0.170758	−	0.985313i	$-0.554622\pi$
$257$	−5.47491	−0.341515	−0.170758	+	0.985313i	$0.554622\pi$
$258$	59.6884	3.71604
$259$	0.645944	0.0401370
$260$	85.2327	5.28591
$261$	0.110168	0.00681924
$262$	31.5893	1.95159
$263$	−8.80476	−0.542925	−0.271463	−	0.962449i	$-0.587507\pi$
$263$	−8.80476	−0.542925	−0.271463	+	0.962449i	$0.587507\pi$
$264$	34.1213	2.10002
$265$	26.0298	1.59900
$266$	−0.614749	−0.0376927
$267$	−19.2549	−1.17838
$268$	24.5767	1.50126
$269$	24.3298	1.48341	0.741706	−	0.670725i	$-0.234017\pi$
$269$	24.3298	1.48341	0.741706	+	0.670725i	$0.234017\pi$
$270$	−30.7778	−1.87308
$271$	23.6605	1.43727	0.718636	−	0.695387i	$-0.244767\pi$
$271$	23.6605	1.43727	0.718636	+	0.695387i	$0.244767\pi$
$272$	−93.5112	−5.66995
$273$	8.74914	0.529522
$274$	47.6663	2.87963
$275$	−10.8900	−0.656691
$276$	−23.2572	−1.39992
$277$	−5.04968	−0.303406	−0.151703	−	0.988426i	$-0.548476\pi$
$277$	−5.04968	−0.303406	−0.151703	+	0.988426i	$0.548476\pi$
$278$	−52.2037	−3.13097
$279$	−13.5614	−0.811901
$280$	−38.5061	−2.30118
$281$	−7.07090	−0.421815	−0.210907	−	0.977506i	$-0.567642\pi$
$281$	−7.07090	−0.421815	−0.210907	+	0.977506i	$0.567642\pi$
$282$	33.3763	1.98753
$283$	−8.87731	−0.527702	−0.263851	−	0.964564i	$-0.584993\pi$
$283$	−8.87731	−0.527702	−0.263851	+	0.964564i	$0.584993\pi$
$284$	60.4841	3.58907
$285$	1.64438	0.0974050
$286$	−16.9038	−0.999545
$287$	−4.37374	−0.258174
$288$	−48.1544	−2.83752
$289$	7.47944	0.439967
$290$	0.707695	0.0415573
$291$	−18.3338	−1.07475
$292$	30.1795	1.76612
$293$	26.3359	1.53856	0.769279	−	0.638914i	$-0.220616\pi$
$293$	26.3359	1.53856	0.769279	+	0.638914i	$0.220616\pi$
$294$	−5.98552	−0.349082
$295$	2.73486	0.159230
$296$	7.05524	0.410077
$297$	4.55651	0.264395
$298$	−17.7056	−1.02566
$299$	7.60860	0.440017
$300$	93.2259	5.38240
$301$	9.97214	0.574785
$302$	43.9920	2.53146
$303$	−1.36994	−0.0787012
$304$	−4.13672	−0.237257
$305$	−32.5594	−1.86435
$306$	21.4207	1.22454
$307$	10.7660	0.614448	0.307224	−	0.951637i	$-0.400600\pi$
$307$	10.7660	0.614448	0.307224	+	0.951637i	$0.400600\pi$
$308$	8.63251	0.491883
$309$	22.4673	1.27812
$310$	−87.1154	−4.94782
$311$	−21.5780	−1.22358	−0.611788	−	0.791022i	$-0.709549\pi$
$311$	−21.5780	−1.22358	−0.611788	+	0.791022i	$0.709549\pi$
$312$	95.5613	5.41009
$313$	6.62600	0.374524	0.187262	−	0.982310i	$-0.440039\pi$
$313$	6.62600	0.374524	0.187262	+	0.982310i	$0.440039\pi$
$314$	−39.2524	−2.21514
$315$	5.43428	0.306187
$316$	32.4589	1.82596
$317$	30.0822	1.68958	0.844792	−	0.535095i	$-0.179724\pi$
$317$	30.0822	1.68958	0.844792	+	0.535095i	$0.179724\pi$
$318$	44.1935	2.47825
$319$	−0.104771	−0.00586604
$320$	−176.070	−9.84264
$321$	−0.791207	−0.0441609
$322$	−5.20525	−0.290077
$323$	1.08291	0.0602549
$324$	−66.2385	−3.67992
$325$	−30.4988	−1.69177
$326$	11.7697	0.651865
$327$	−40.3727	−2.23262
$328$	−47.7716	−2.63774
$329$	5.57618	0.307425
$330$	−30.9334	−1.70283
$331$	7.13042	0.391923	0.195962	−	0.980612i	$-0.437217\pi$
$331$	7.13042	0.391923	0.195962	+	0.980612i	$0.437217\pi$
$332$	−62.2389	−3.41580
$333$	−0.995688	−0.0545634
$334$	−1.16137	−0.0635474
$335$	−14.7134	−0.803878
$336$	−40.2773	−2.19730
$337$	−22.3783	−1.21902	−0.609512	−	0.792777i	$-0.708635\pi$
$337$	−22.3783	−1.21902	−0.609512	+	0.792777i	$0.708635\pi$
$338$	−10.8284	−0.588985
$339$	−17.5020	−0.950580
$340$	102.716	5.57056
$341$	12.8970	0.698413
$342$	0.947602	0.0512404
$343$	−1.00000	−0.0539949
$344$	108.919	5.87254
$345$	13.9235	0.749614
$346$	−52.5535	−2.82529
$347$	−28.2185	−1.51485	−0.757425	−	0.652922i	$-0.773543\pi$
$347$	−28.2185	−1.51485	−0.757425	+	0.652922i	$0.773543\pi$
$348$	0.896911	0.0480795
$349$	−20.3764	−1.09073	−0.545363	−	0.838200i	$-0.683608\pi$
$349$	−20.3764	−1.09073	−0.545363	+	0.838200i	$0.683608\pi$
$350$	20.8651	1.11528
$351$	12.7611	0.681137
$352$	45.7952	2.44089
$353$	21.8424	1.16256	0.581278	−	0.813705i	$-0.302553\pi$
$353$	21.8424	1.16256	0.581278	+	0.813705i	$0.302553\pi$
$354$	4.64327	0.246787
$355$	−36.2102	−1.92184
$356$	−53.2070	−2.81997
$357$	10.5438	0.558038
$358$	−43.3232	−2.28970
$359$	−10.6003	−0.559463	−0.279732	−	0.960078i	$-0.590245\pi$
$359$	−10.6003	−0.559463	−0.279732	+	0.960078i	$0.590245\pi$
$360$	59.3551	3.12829
$361$	−18.9521	−0.997479
$362$	−64.8928	−3.41069
$363$	−18.8622	−0.990008
$364$	24.1765	1.26719
$365$	−18.0676	−0.945702
$366$	−55.2796	−2.88951
$367$	26.7588	1.39680	0.698399	−	0.715709i	$-0.253896\pi$
$367$	26.7588	1.39680	0.698399	+	0.715709i	$0.253896\pi$
$368$	−35.0267	−1.82589
$369$	6.74188	0.350968
$370$	−6.39607	−0.332516
$371$	7.38341	0.383327
$372$	−110.407	−5.72436
$373$	−5.78355	−0.299461	−0.149731	−	0.988727i	$-0.547841\pi$
$373$	−5.78355	−0.299461	−0.149731	+	0.988727i	$0.547841\pi$
$374$	−20.3713	−1.05337
$375$	−18.2470	−0.942270
$376$	60.9050	3.14094
$377$	−0.293424	−0.0151121
$378$	−8.73020	−0.449033
$379$	−36.3270	−1.86599	−0.932995	−	0.359889i	$-0.882815\pi$
$379$	−36.3270	−1.86599	−0.932995	+	0.359889i	$0.882815\pi$
$380$	4.54392	0.233098
$381$	11.9054	0.609935
$382$	−43.9123	−2.24675
$383$	28.0046	1.43097	0.715483	−	0.698630i	$-0.246207\pi$
$383$	28.0046	1.43097	0.715483	+	0.698630i	$0.246207\pi$
$384$	−165.786	−8.46021
$385$	−5.16804	−0.263388
$386$	−61.4580	−3.12813
$387$	−15.3715	−0.781378
$388$	−50.6618	−2.57196
$389$	29.5775	1.49964	0.749819	−	0.661643i	$-0.230141\pi$
$389$	29.5775	1.49964	0.749819	+	0.661643i	$0.230141\pi$
$390$	−86.6330	−4.38683
$391$	9.16933	0.463713
$392$	−10.9224	−0.551663
$393$	−23.9680	−1.20903
$394$	41.7483	2.10325
$395$	−19.4322	−0.977742
$396$	−13.3065	−0.668679
$397$	−19.5887	−0.983130	−0.491565	−	0.870841i	$-0.663575\pi$
$397$	−19.5887	−0.983130	−0.491565	+	0.870841i	$0.663575\pi$
$398$	−43.4835	−2.17963
$399$	0.466434	0.0233509
$400$	140.403	7.02017
$401$	21.2422	1.06078	0.530392	−	0.847752i	$-0.322045\pi$
$401$	21.2422	1.06078	0.530392	+	0.847752i	$0.322045\pi$
$402$	−24.9805	−1.24591
$403$	36.1198	1.79925
$404$	−3.78556	−0.188339
$405$	39.6552	1.97048
$406$	0.200739	0.00996253
$407$	0.946907	0.0469364
$408$	115.163	5.70144
$409$	−12.9000	−0.637862	−0.318931	−	0.947778i	$-0.603324\pi$
$409$	−12.9000	−0.637862	−0.318931	+	0.947778i	$0.603324\pi$
$410$	43.3083	2.13884
$411$	−36.1663	−1.78395
$412$	62.0837	3.05865
$413$	0.775751	0.0381722
$414$	8.02361	0.394339
$415$	37.2607	1.82906
$416$	128.255	6.28824
$417$	39.6090	1.93966
$418$	−0.901177	−0.0440780
$419$	18.1707	0.887698	0.443849	−	0.896102i	$-0.353613\pi$
$419$	18.1707	0.887698	0.443849	+	0.896102i	$0.353613\pi$
$420$	44.2420	2.15879
$421$	−37.7611	−1.84036	−0.920182	−	0.391491i	$-0.871960\pi$
$421$	−37.7611	−1.84036	−0.920182	+	0.391491i	$0.871960\pi$
$422$	53.9820	2.62780
$423$	−8.59537	−0.417921
$424$	80.6442	3.91643
$425$	−36.7549	−1.78288
$426$	−61.4779	−2.97861
$427$	−9.23557	−0.446940
$428$	−2.18634	−0.105681
$429$	12.8256	0.619226
$430$	−98.7430	−4.76181
$431$	−14.6959	−0.707875	−0.353938	−	0.935269i	$-0.615157\pi$
$431$	−14.6959	−0.707875	−0.353938	+	0.935269i	$0.615157\pi$
$432$	−58.7466	−2.82645
$433$	23.7260	1.14020	0.570100	−	0.821575i	$-0.306904\pi$
$433$	23.7260	1.14020	0.570100	+	0.821575i	$0.306904\pi$
$434$	−24.7105	−1.18614
$435$	−0.536956	−0.0257451
$436$	−111.562	−5.34284
$437$	0.405630	0.0194039
$438$	−30.6753	−1.46572
$439$	11.4265	0.545356	0.272678	−	0.962105i	$-0.412091\pi$
$439$	11.4265	0.545356	0.272678	+	0.962105i	$0.412091\pi$
$440$	−56.4472	−2.69102
$441$	1.54145	0.0734022
$442$	−57.0524	−2.71370
$443$	−0.886271	−0.0421080	−0.0210540	−	0.999778i	$-0.506702\pi$
$443$	−0.886271	−0.0421080	−0.0210540	+	0.999778i	$0.506702\pi$
$444$	−8.10618	−0.384702
$445$	31.8536	1.51000
$446$	−54.8022	−2.59496
$447$	13.4339	0.635403
$448$	−49.9428	−2.35958
$449$	4.49609	0.212183	0.106092	−	0.994356i	$-0.466166\pi$
$449$	4.49609	0.212183	0.106092	+	0.994356i	$0.466166\pi$
$450$	−32.1624	−1.51615
$451$	−6.41158	−0.301910
$452$	−48.3633	−2.27482
$453$	−33.3785	−1.56826
$454$	36.1354	1.69592
$455$	−14.4738	−0.678541
$456$	5.09456	0.238575
$457$	19.6994	0.921500	0.460750	−	0.887530i	$-0.347580\pi$
$457$	19.6994	0.921500	0.460750	+	0.887530i	$0.347580\pi$
$458$	34.9752	1.63428
$459$	15.3787	0.717817
$460$	38.4746	1.79389
$461$	30.0785	1.40090	0.700448	−	0.713703i	$-0.252983\pi$
$461$	30.0785	1.40090	0.700448	+	0.713703i	$0.252983\pi$
$462$	−8.77433	−0.408219
$463$	7.59284	0.352869	0.176435	−	0.984312i	$-0.443544\pi$
$463$	7.59284	0.352869	0.176435	+	0.984312i	$0.443544\pi$
$464$	1.35080	0.0627093
$465$	66.0978	3.06521
$466$	49.1141	2.27517
$467$	−16.2730	−0.753025	−0.376512	−	0.926412i	$-0.622877\pi$
$467$	−16.2730	−0.753025	−0.376512	+	0.926412i	$0.622877\pi$
$468$	−37.2667	−1.72265
$469$	−4.17349	−0.192714
$470$	−55.2147	−2.54686
$471$	29.7824	1.37230
$472$	8.47303	0.390003
$473$	14.6184	0.672156
$474$	−32.9922	−1.51538
$475$	−1.62595	−0.0746038
$476$	29.1357	1.33543
$477$	−11.3811	−0.521106
$478$	−36.9260	−1.68895
$479$	−39.8685	−1.82164	−0.910818	−	0.412808i	$-0.864548\pi$
$479$	−39.8685	−1.82164	−0.910818	+	0.412808i	$0.864548\pi$
$480$	234.703	10.7127
$481$	2.65194	0.120918
$482$	65.6869	2.99196
$483$	3.94942	0.179705
$484$	−52.1218	−2.36917
$485$	30.3298	1.37721
$486$	41.1362	1.86598
$487$	−10.4102	−0.471732	−0.235866	−	0.971786i	$-0.575793\pi$
$487$	−10.4102	−0.471732	−0.235866	+	0.971786i	$0.575793\pi$
$488$	−100.874	−4.56636
$489$	−8.93015	−0.403835
$490$	9.90189	0.447322
$491$	7.35864	0.332091	0.166045	−	0.986118i	$-0.446900\pi$
$491$	7.35864	0.332091	0.166045	+	0.986118i	$0.446900\pi$
$492$	54.8876	2.47452
$493$	−0.353613	−0.0159260
$494$	−2.52386	−0.113554
$495$	7.96626	0.358057
$496$	−166.280	−7.46619
$497$	−10.2711	−0.460722
$498$	63.2614	2.83481
$499$	15.4701	0.692535	0.346268	−	0.938136i	$-0.387449\pi$
$499$	15.4701	0.692535	0.346268	+	0.938136i	$0.387449\pi$
$500$	−50.4218	−2.25493
$501$	0.881177	0.0393681
$502$	36.9502	1.64917
$503$	−0.0725077	−0.00323296	−0.00161648	−	0.999999i	$-0.500515\pi$
$503$	−0.0725077	−0.00323296	−0.00161648	+	0.999999i	$0.500515\pi$
$504$	16.8362	0.749945
$505$	2.26631	0.100849
$506$	−7.63051	−0.339218
$507$	8.21590	0.364881
$508$	32.8983	1.45962
$509$	13.3432	0.591426	0.295713	−	0.955277i	$-0.404443\pi$
$509$	13.3432	0.591426	0.295713	+	0.955277i	$0.404443\pi$
$510$	−104.404	−4.62307
$511$	−5.12492	−0.226713
$512$	−177.566	−7.84740
$513$	0.680319	0.0300368
$514$	15.3773	0.678266
$515$	−37.1678	−1.63781
$516$	−125.144	−5.50916
$517$	8.17427	0.359504
$518$	−1.81426	−0.0797140
$519$	39.8744	1.75029
$520$	−158.088	−6.93261
$521$	15.2488	0.668060	0.334030	−	0.942562i	$-0.391591\pi$
$521$	15.2488	0.668060	0.334030	+	0.942562i	$0.391591\pi$
$522$	−0.309429	−0.0135433
$523$	−22.0030	−0.962122	−0.481061	−	0.876687i	$-0.659749\pi$
$523$	−22.0030	−0.962122	−0.481061	+	0.876687i	$0.659749\pi$
$524$	−66.2307	−2.89330
$525$	−15.8311	−0.690927
$526$	24.7299	1.07827
$527$	43.5289	1.89615
$528$	−59.0435	−2.56954
$529$	−19.5654	−0.850670
$530$	−73.1097	−3.17568
$531$	−1.19578	−0.0518923
$532$	1.28889	0.0558807
$533$	−17.9565	−0.777781
$534$	54.0812	2.34032
$535$	1.30890	0.0565887
$536$	−45.5843	−1.96894
$537$	32.8710	1.41849
$538$	−68.3349	−2.94613
$539$	−1.46593	−0.0631420
$540$	64.5294	2.77690
$541$	0.0643976	0.00276867	0.00138433	−	0.999999i	$-0.499559\pi$
$541$	0.0643976	0.00276867	0.00138433	+	0.999999i	$0.499559\pi$
$542$	−66.4551	−2.85449
$543$	49.2367	2.11295
$544$	154.564	6.62687
$545$	66.7889	2.86092
$546$	−24.5737	−1.05166
$547$	−41.5979	−1.77860	−0.889300	−	0.457325i	$-0.848808\pi$
$547$	−41.5979	−1.77860	−0.889300	+	0.457325i	$0.848808\pi$
$548$	−99.9382	−4.26915
$549$	14.2361	0.607583
$550$	30.5867	1.30422
$551$	−0.0156430	−0.000666416 0
$552$	43.1370	1.83603
$553$	−5.51200	−0.234394
$554$	14.1830	0.602578
$555$	4.85295	0.205996
$556$	109.451	4.64177
$557$	2.12504	0.0900410	0.0450205	−	0.998986i	$-0.485665\pi$
$557$	2.12504	0.0900410	0.0450205	+	0.998986i	$0.485665\pi$
$558$	38.0899	1.61247
$559$	40.9408	1.73161
$560$	66.6310	2.81567
$561$	15.4565	0.652573
$562$	19.8600	0.837744
$563$	14.5366	0.612645	0.306323	−	0.951928i	$-0.400901\pi$
$563$	14.5366	0.612645	0.306323	+	0.951928i	$0.400901\pi$
$564$	−69.9774	−2.94658
$565$	28.9538	1.21809
$566$	24.9337	1.04804
$567$	11.2483	0.472383
$568$	−112.185	−4.70716
$569$	6.42340	0.269283	0.134642	−	0.990894i	$-0.457012\pi$
$569$	6.42340	0.269283	0.134642	+	0.990894i	$0.457012\pi$
$570$	−4.61858	−0.193451
$571$	−23.9429	−1.00198	−0.500990	−	0.865453i	$-0.667031\pi$
$571$	−23.9429	−1.00198	−0.500990	+	0.865453i	$0.667031\pi$
$572$	35.4409	1.48186
$573$	33.3180	1.39188
$574$	12.2845	0.512745
$575$	−13.7674	−0.574140
$576$	76.9842	3.20767
$577$	27.9405	1.16318	0.581589	−	0.813483i	$-0.302431\pi$
$577$	27.9405	1.16318	0.581589	+	0.813483i	$0.302431\pi$
$578$	−21.0075	−0.873796
$579$	46.6306	1.93790
$580$	−1.48377	−0.0616101
$581$	10.5691	0.438480
$582$	51.4941	2.13450
$583$	10.8235	0.448265
$584$	−55.9762	−2.31631
$585$	22.3105	0.922427
$586$	−73.9694	−3.05565
$587$	17.6050	0.726634	0.363317	−	0.931665i	$-0.381644\pi$
$587$	17.6050	0.726634	0.363317	+	0.931665i	$0.381644\pi$
$588$	12.5494	0.517527
$589$	1.92562	0.0793436
$590$	−7.68140	−0.316238
$591$	−31.6761	−1.30298
$592$	−12.2084	−0.501761
$593$	25.0661	1.02934	0.514671	−	0.857388i	$-0.327914\pi$
$593$	25.0661	1.02934	0.514671	+	0.857388i	$0.327914\pi$
$594$	−12.7978	−0.525102
$595$	−17.4427	−0.715082
$596$	37.1219	1.52057
$597$	32.9926	1.35030
$598$	−21.3702	−0.873894
$599$	−16.4061	−0.670334	−0.335167	−	0.942159i	$-0.608793\pi$
$599$	−16.4061	−0.670334	−0.335167	+	0.942159i	$0.608793\pi$
$600$	−172.913	−7.05916
$601$	−19.6530	−0.801665	−0.400832	−	0.916151i	$-0.631279\pi$
$601$	−19.6530	−0.801665	−0.400832	+	0.916151i	$0.631279\pi$
$602$	−28.0087	−1.14155
$603$	6.43321	0.261980
$604$	−92.2346	−3.75297
$605$	31.2039	1.26862
$606$	3.84775	0.156304
$607$	−10.0463	−0.407768	−0.203884	−	0.978995i	$-0.565357\pi$
$607$	−10.0463	−0.407768	−0.203884	+	0.978995i	$0.565357\pi$
$608$	6.83755	0.277299
$609$	−0.152309	−0.00617187
$610$	91.4496	3.70268
$611$	22.8931	0.926156
$612$	−44.9111	−1.81542
$613$	−28.4289	−1.14823	−0.574117	−	0.818773i	$-0.694655\pi$
$613$	−28.4289	−1.14823	−0.574117	+	0.818773i	$0.694655\pi$
$614$	−30.2384	−1.22032
$615$	−32.8597	−1.32503
$616$	−16.0114	−0.645117
$617$	34.7864	1.40045	0.700224	−	0.713923i	$-0.253083\pi$
$617$	34.7864	1.40045	0.700224	+	0.713923i	$0.253083\pi$
$618$	−63.1037	−2.53840
$619$	−43.9385	−1.76604	−0.883019	−	0.469338i	$-0.844493\pi$
$619$	−43.9385	−1.76604	−0.883019	+	0.469338i	$0.844493\pi$
$620$	182.648	7.33532
$621$	5.76045	0.231159
$622$	60.6060	2.43008
$623$	9.03534	0.361993
$624$	−165.359	−6.61966
$625$	−6.95756	−0.278303
$626$	−18.6104	−0.743821
$627$	0.683758	0.0273067
$628$	82.2975	3.28403
$629$	3.19592	0.127430
$630$	−15.2632	−0.608102
$631$	−25.7430	−1.02481	−0.512406	−	0.858743i	$-0.671246\pi$
$631$	−25.7430	−1.02481	−0.512406	+	0.858743i	$0.671246\pi$
$632$	−60.2041	−2.39479
$633$	−40.9583	−1.62794
$634$	−84.4917	−3.35559
$635$	−19.6953	−0.781583
$636$	−92.6570	−3.67409
$637$	−4.10552	−0.162667
$638$	0.294269	0.0116502
$639$	15.8324	0.626318
$640$	274.260	10.8411
$641$	26.8490	1.06047	0.530235	−	0.847851i	$-0.322104\pi$
$641$	26.8490	1.06047	0.530235	+	0.847851i	$0.322104\pi$
$642$	2.22226	0.0877055
$643$	4.92411	0.194188	0.0970940	−	0.995275i	$-0.469045\pi$
$643$	4.92411	0.194188	0.0970940	+	0.995275i	$0.469045\pi$
$644$	10.9134	0.430049
$645$	74.9202	2.94998
$646$	−3.04157	−0.119669
$647$	23.6996	0.931728	0.465864	−	0.884856i	$-0.345744\pi$
$647$	23.6996	0.931728	0.465864	+	0.884856i	$0.345744\pi$
$648$	122.858	4.82631
$649$	1.13719	0.0446388
$650$	85.6619	3.35994
$651$	18.7488	0.734824
$652$	−24.6766	−0.966412
$653$	7.27866	0.284836	0.142418	−	0.989807i	$-0.454512\pi$
$653$	7.27866	0.284836	0.142418	+	0.989807i	$0.454512\pi$
$654$	113.395	4.43408
$655$	39.6505	1.54927
$656$	82.6639	3.22748
$657$	7.89979	0.308200
$658$	−15.6618	−0.610560
$659$	36.0813	1.40553	0.702764	−	0.711423i	$-0.251949\pi$
$659$	36.0813	1.40553	0.702764	+	0.711423i	$0.251949\pi$
$660$	64.8556	2.52450
$661$	−33.9308	−1.31975	−0.659877	−	0.751374i	$-0.729392\pi$
$661$	−33.9308	−1.31975	−0.659877	+	0.751374i	$0.729392\pi$
$662$	−20.0272	−0.778378
$663$	43.2879	1.68116
$664$	115.439	4.47992
$665$	−0.771625	−0.0299223
$666$	2.79658	0.108365
$667$	−0.132454	−0.00512864
$668$	2.43495	0.0942112
$669$	41.5806	1.60760
$670$	41.3254	1.59654
$671$	−13.5387	−0.522655
$672$	66.5740	2.56815
$673$	−41.7882	−1.61082	−0.805408	−	0.592721i	$-0.798054\pi$
$673$	−41.7882	−1.61082	−0.805408	+	0.592721i	$0.798054\pi$
$674$	62.8538	2.42104
$675$	−23.0906	−0.888756
$676$	22.7030	0.873191
$677$	−31.7650	−1.22083	−0.610414	−	0.792082i	$-0.708997\pi$
$677$	−31.7650	−1.22083	−0.610414	+	0.792082i	$0.708997\pi$
$678$	49.1579	1.88790
$679$	8.60312	0.330157
$680$	−190.516	−7.30594
$681$	−27.4174	−1.05064
$682$	−36.2238	−1.38708
$683$	10.1185	0.387174	0.193587	−	0.981083i	$-0.437988\pi$
$683$	10.1185	0.387174	0.193587	+	0.981083i	$0.437988\pi$
$684$	−1.98676	−0.0759657
$685$	59.8302	2.28600
$686$	2.80869	0.107236
$687$	−26.5371	−1.01245
$688$	−188.474	−7.18550
$689$	30.3127	1.15482
$690$	−39.1068	−1.48877
$691$	24.5760	0.934915	0.467457	−	0.884016i	$-0.345170\pi$
$691$	24.5760	0.934915	0.467457	+	0.884016i	$0.345170\pi$
$692$	110.185	4.18859
$693$	2.25965	0.0858369
$694$	79.2573	3.00856
$695$	−65.5255	−2.48552
$696$	−1.66357	−0.0630575
$697$	−21.6398	−0.819667
$698$	57.2312	2.16623
$699$	−37.2648	−1.40948
$700$	−43.7461	−1.65345
$701$	−34.4805	−1.30231	−0.651156	−	0.758944i	$-0.725716\pi$
$701$	−34.4805	−1.30231	−0.651156	+	0.758944i	$0.725716\pi$
$702$	−35.8420	−1.35277
$703$	0.141380	0.00533225
$704$	−73.2125	−2.75930
$705$	41.8935	1.57780
$706$	−61.3487	−2.30889
$707$	0.642844	0.0241766
$708$	−9.73517	−0.365870
$709$	7.99054	0.300091	0.150046	−	0.988679i	$-0.452058\pi$
$709$	7.99054	0.300091	0.150046	+	0.988679i	$0.452058\pi$
$710$	101.703	3.81686
$711$	8.49646	0.318642
$712$	98.6873	3.69846
$713$	16.3047	0.610617
$714$	−29.6144	−1.10829
$715$	−21.2175	−0.793489
$716$	90.8324	3.39456
$717$	28.0172	1.04632
$718$	29.7730	1.11112
$719$	17.9763	0.670403	0.335201	−	0.942146i	$-0.391196\pi$
$719$	17.9763	0.670403	0.335201	+	0.942146i	$0.391196\pi$
$720$	−102.708	−3.82770
$721$	−10.5427	−0.392632
$722$	53.2307	1.98104
$723$	−49.8392	−1.85354
$724$	136.055	5.05646
$725$	0.530937	0.0197185
$726$	52.9781	1.96620
$727$	19.3032	0.715915	0.357958	−	0.933738i	$-0.383473\pi$
$727$	19.3032	0.715915	0.357958	+	0.933738i	$0.383473\pi$
$728$	−44.8420	−1.66195
$729$	2.53321	0.0938227
$730$	50.7464	1.87821
$731$	49.3389	1.82486
$732$	115.900	4.28380
$733$	−34.9301	−1.29017	−0.645086	−	0.764110i	$-0.723178\pi$
$733$	−34.9301	−1.29017	−0.645086	+	0.764110i	$0.723178\pi$
$734$	−75.1573	−2.77411
$735$	−7.51295	−0.277119
$736$	57.8954	2.13405
$737$	−6.11803	−0.225361
$738$	−18.9359	−0.697040
$739$	−14.2336	−0.523593	−0.261796	−	0.965123i	$-0.584315\pi$
$739$	−14.2336	−0.523593	−0.261796	+	0.965123i	$0.584315\pi$
$740$	13.4101	0.492966
$741$	1.91495	0.0703476
$742$	−20.7377	−0.761306
$743$	−36.7682	−1.34890	−0.674448	−	0.738323i	$-0.735618\pi$
$743$	−36.7682	−1.34890	−0.674448	+	0.738323i	$0.735618\pi$
$744$	204.781	7.50765
$745$	−22.2238	−0.814219
$746$	16.2442	0.594744
$747$	−16.2917	−0.596081
$748$	42.7108	1.56166
$749$	0.371273	0.0135660
$750$	51.2502	1.87139
$751$	39.7072	1.44893	0.724467	−	0.689309i	$-0.242086\pi$
$751$	39.7072	1.44893	0.724467	+	0.689309i	$0.242086\pi$
$752$	−105.390	−3.84318
$753$	−28.0356	−1.02167
$754$	0.824140	0.0300134
$755$	55.2183	2.00960
$756$	18.3039	0.665707
$757$	20.7662	0.754759	0.377380	−	0.926059i	$-0.376825\pi$
$757$	20.7662	0.754759	0.377380	+	0.926059i	$0.376825\pi$
$758$	102.031	3.70595
$759$	5.78957	0.210148
$760$	−8.42797	−0.305715
$761$	−3.39307	−0.122999	−0.0614993	−	0.998107i	$-0.519588\pi$
$761$	−3.39307	−0.122999	−0.0614993	+	0.998107i	$0.519588\pi$
$762$	−33.4388	−1.21136
$763$	18.9448	0.685849
$764$	92.0675	3.33089
$765$	26.8870	0.972102
$766$	−78.6563	−2.84197
$767$	3.18486	0.114999
$768$	252.778	9.12135
$769$	49.0167	1.76759	0.883793	−	0.467878i	$-0.154981\pi$
$769$	49.0167	1.76759	0.883793	+	0.467878i	$0.154981\pi$
$770$	14.5155	0.523101
$771$	−11.6674	−0.420191
$772$	128.854	4.63756
$773$	−46.2227	−1.66252	−0.831258	−	0.555887i	$-0.812379\pi$
$773$	−46.2227	−1.66252	−0.831258	+	0.555887i	$0.812379\pi$
$774$	43.1739	1.55185
$775$	−65.3569	−2.34769
$776$	93.9664	3.37320
$777$	1.37655	0.0493835
$778$	−83.0741	−2.97835
$779$	−0.957295	−0.0342987
$780$	181.637	6.50363
$781$	−15.0567	−0.538771
$782$	−25.7538	−0.920956
$783$	−0.222151	−0.00793902
$784$	18.9000	0.675002
$785$	−49.2692	−1.75849
$786$	67.3188	2.40118
$787$	11.2468	0.400904	0.200452	−	0.979704i	$-0.435759\pi$
$787$	11.2468	0.400904	0.200452	+	0.979704i	$0.435759\pi$
$788$	−87.5304	−3.11814
$789$	−18.7635	−0.668000
$790$	54.5792	1.94184
$791$	8.21280	0.292014
$792$	24.6807	0.876990
$793$	−37.9168	−1.34647
$794$	55.0188	1.95254
$795$	55.4712	1.96736
$796$	91.1684	3.23138
$797$	−26.8036	−0.949432	−0.474716	−	0.880139i	$-0.657449\pi$
$797$	−26.8036	−0.949432	−0.474716	+	0.880139i	$0.657449\pi$
$798$	−1.31007	−0.0463760
$799$	27.5891	0.976031
$800$	−232.072	−8.20498
$801$	−13.9275	−0.492104
$802$	−59.6628	−2.10677
$803$	−7.51276	−0.265120
$804$	52.3746	1.84711
$805$	−6.53356	−0.230278
$806$	−101.449	−3.57340
$807$	51.8484	1.82515
$808$	7.02137	0.247011
$809$	−31.5438	−1.10902	−0.554511	−	0.832176i	$-0.687095\pi$
$809$	−31.5438	−1.10902	−0.554511	+	0.832176i	$0.687095\pi$
$810$	−111.379	−3.91347
$811$	−17.1510	−0.602254	−0.301127	−	0.953584i	$-0.597363\pi$
$811$	−17.1510	−0.602254	−0.301127	+	0.953584i	$0.597363\pi$
$812$	−0.420874	−0.0147698
$813$	50.4221	1.76838
$814$	−2.65957	−0.0932180
$815$	14.7732	0.517483
$816$	−199.279	−6.97615
$817$	2.18264	0.0763608
$818$	36.2320	1.26682
$819$	6.32844	0.221134
$820$	−90.8010	−3.17091
$821$	28.8983	1.00856	0.504278	−	0.863541i	$-0.331759\pi$
$821$	28.8983	1.00856	0.504278	+	0.863541i	$0.331759\pi$
$822$	101.580	3.54301
$823$	−9.89019	−0.344750	−0.172375	−	0.985031i	$-0.555144\pi$
$823$	−9.89019	−0.344750	−0.172375	+	0.985031i	$0.555144\pi$
$824$	−115.152	−4.01150
$825$	−23.2073	−0.807974
$826$	−2.17885	−0.0758118
$827$	11.3559	0.394885	0.197442	−	0.980314i	$-0.436736\pi$
$827$	11.3559	0.394885	0.197442	+	0.980314i	$0.436736\pi$
$828$	−16.8225	−0.584621
$829$	17.3932	0.604089	0.302045	−	0.953294i	$-0.402331\pi$
$829$	17.3932	0.604089	0.302045	+	0.953294i	$0.402331\pi$
$830$	−104.654	−3.63259
$831$	−10.7612	−0.373302
$832$	−205.041	−7.10853
$833$	−4.94767	−0.171427
$834$	−111.250	−3.85226
$835$	−1.45774	−0.0504471
$836$	1.88943	0.0653472
$837$	27.3462	0.945222
$838$	−51.0360	−1.76301
$839$	−30.8958	−1.06664	−0.533321	−	0.845913i	$-0.679056\pi$
$839$	−30.8958	−1.06664	−0.533321	+	0.845913i	$0.679056\pi$
$840$	−82.0592	−2.83131
$841$	−28.9949	−0.999824
$842$	106.059	3.65505
$843$	−15.0686	−0.518989
$844$	−113.180	−3.89581
$845$	−13.5916	−0.467566
$846$	24.1418	0.830012
$847$	8.85106	0.304126
$848$	−139.547	−4.79205
$849$	−18.9181	−0.649269
$850$	103.233	3.54088
$851$	1.19710	0.0410362
$852$	128.896	4.41589
$853$	24.2429	0.830060	0.415030	−	0.909808i	$-0.363771\pi$
$853$	24.2429	0.830060	0.415030	+	0.909808i	$0.363771\pi$
$854$	25.9399	0.887645
$855$	1.18942	0.0406773
$856$	4.05517	0.138603
$857$	24.2811	0.829428	0.414714	−	0.909952i	$-0.363882\pi$
$857$	24.2811	0.829428	0.414714	+	0.909952i	$0.363882\pi$
$858$	−36.0232	−1.22981
$859$	−14.0058	−0.477871	−0.238936	−	0.971035i	$-0.576798\pi$
$859$	−14.0058	−0.477871	−0.238936	+	0.971035i	$0.576798\pi$
$860$	207.027	7.05955
$861$	−9.32073	−0.317650
$862$	41.2762	1.40587
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	97.1017	3.30347
$865$	−65.9645	−2.24286
$866$	−66.6392	−2.26449
$867$	15.9392	0.541323
$868$	51.8085	1.75850
$869$	−8.08020	−0.274102
$870$	1.50815	0.0511309
$871$	−17.1343	−0.580575
$872$	206.922	7.00728
$873$	−13.2612	−0.448825
$874$	−1.13929	−0.0385371
$875$	8.56237	0.289461
$876$	64.3145	2.17298
$877$	−8.07481	−0.272667	−0.136333	−	0.990663i	$-0.543532\pi$
$877$	−8.07481	−0.272667	−0.136333	+	0.990663i	$0.543532\pi$
$878$	−32.0935	−1.08310
$879$	56.1235	1.89300
$880$	97.6762	3.29266
$881$	33.4174	1.12586	0.562931	−	0.826504i	$-0.309674\pi$
$881$	33.4174	1.12586	0.562931	+	0.826504i	$0.309674\pi$
$882$	−4.32945	−0.145780
$883$	29.6780	0.998743	0.499371	−	0.866388i	$-0.333564\pi$
$883$	29.6780	0.998743	0.499371	+	0.866388i	$0.333564\pi$
$884$	119.617	4.02316
$885$	5.82818	0.195912
$886$	2.48926	0.0836285
$887$	−26.3363	−0.884287	−0.442144	−	0.896944i	$-0.645782\pi$
$887$	−26.3363	−0.884287	−0.442144	+	0.896944i	$0.645782\pi$
$888$	15.0352	0.504548
$889$	−5.58661	−0.187369
$890$	−89.4670	−2.99894
$891$	16.4892	0.552408
$892$	114.899	3.84712
$893$	1.22048	0.0408417
$894$	−37.7318	−1.26194
$895$	−54.3788	−1.81768
$896$	77.7946	2.59894
$897$	16.2144	0.541385
$898$	−12.6281	−0.421406
$899$	−0.628789	−0.0209713
$900$	67.4322	2.24774
$901$	36.5307	1.21701
$902$	18.0082	0.599607
$903$	21.2513	0.707199
$904$	89.7032	2.98348
$905$	−81.4526	−2.70758
$906$	93.7499	3.11463
$907$	56.1542	1.86457	0.932284	−	0.361727i	$-0.117813\pi$
$907$	56.1542	1.86457	0.932284	+	0.361727i	$0.117813\pi$
$908$	−75.7623	−2.51426
$909$	−0.990909	−0.0328664
$910$	40.6524	1.34761
$911$	11.5797	0.383652	0.191826	−	0.981429i	$-0.438559\pi$
$911$	11.5797	0.383652	0.191826	+	0.981429i	$0.438559\pi$
$912$	−8.81562	−0.291914
$913$	15.4935	0.512761
$914$	−55.3297	−1.83014
$915$	−69.3864	−2.29384
$916$	−73.3298	−2.42288
$917$	11.2470	0.371407
$918$	−43.1941	−1.42562
$919$	−6.06792	−0.200162	−0.100081	−	0.994979i	$-0.531910\pi$
$919$	−6.06792	−0.200162	−0.100081	+	0.994979i	$0.531910\pi$
$920$	−71.3620	−2.35273
$921$	22.9431	0.756000
$922$	−84.4814	−2.78225
$923$	−42.1682	−1.38798
$924$	18.3964	0.605199
$925$	−4.79855	−0.157775
$926$	−21.3260	−0.700815
$927$	16.2511	0.533755
$928$	−2.23273	−0.0732928
$929$	−9.22811	−0.302764	−0.151382	−	0.988475i	$-0.548372\pi$
$929$	−9.22811	−0.302764	−0.151382	+	0.988475i	$0.548372\pi$
$930$	−185.649	−6.08766
$931$	−0.218873	−0.00717328
$932$	−102.974	−3.37301
$933$	−45.9841	−1.50545
$934$	45.7059	1.49554
$935$	−25.5698	−0.836221
$936$	69.1215	2.25931
$937$	45.7328	1.49402	0.747012	−	0.664810i	$-0.231488\pi$
$937$	45.7328	1.49402	0.747012	+	0.664810i	$0.231488\pi$
$938$	11.7221	0.382739
$939$	14.1204	0.460803
$940$	115.764	3.77581
$941$	55.0841	1.79569	0.897845	−	0.440311i	$-0.145132\pi$
$941$	55.0841	1.79569	0.897845	+	0.440311i	$0.145132\pi$
$942$	−83.6496	−2.72545
$943$	−8.10568	−0.263957
$944$	−14.6617	−0.477199
$945$	−10.9580	−0.356465
$946$	−41.0587	−1.33493
$947$	3.05923	0.0994115	0.0497057	−	0.998764i	$-0.484172\pi$
$947$	3.05923	0.0994115	0.0497057	+	0.998764i	$0.484172\pi$
$948$	69.1721	2.24661
$949$	−21.0405	−0.683003
$950$	4.56680	0.148167
$951$	64.1072	2.07882
$952$	−54.0402	−1.75145
$953$	−6.63021	−0.214774	−0.107387	−	0.994217i	$-0.534248\pi$
$953$	−6.63021	−0.214774	−0.107387	+	0.994217i	$0.534248\pi$
$954$	31.9661	1.03494
$955$	−55.1183	−1.78359
$956$	77.4197	2.50393
$957$	−0.223274	−0.00721741
$958$	111.978	3.61786
$959$	16.9710	0.548022
$960$	−375.218	−12.1101
$961$	46.4022	1.49685
$962$	−7.44848	−0.240149
$963$	−0.572297	−0.0184420
$964$	−137.721	−4.43568
$965$	−77.1413	−2.48327
$966$	−11.0927	−0.356903
$967$	29.1452	0.937247	0.468624	−	0.883398i	$-0.344750\pi$
$967$	29.1452	0.937247	0.468624	+	0.883398i	$0.344750\pi$
$968$	96.6744	3.10723
$969$	2.30776	0.0741360
$970$	−85.1871	−2.73519
$971$	25.3752	0.814329	0.407164	−	0.913355i	$-0.366518\pi$
$971$	25.3752	0.814329	0.407164	+	0.913355i	$0.366518\pi$
$972$	−86.2470	−2.76637
$973$	−18.5865	−0.595855
$974$	29.2392	0.936883
$975$	−64.9950	−2.08151
$976$	174.553	5.58729
$977$	4.43122	0.141767	0.0708836	−	0.997485i	$-0.477418\pi$
$977$	4.43122	0.141767	0.0708836	+	0.997485i	$0.477418\pi$
$978$	25.0821	0.802036
$979$	13.2452	0.423317
$980$	−20.7605	−0.663170
$981$	−29.2025	−0.932363
$982$	−20.6682	−0.659548
$983$	9.50972	0.303313	0.151656	−	0.988433i	$-0.451539\pi$
$983$	9.50972	0.303313	0.151656	+	0.988433i	$0.451539\pi$
$984$	−101.804	−3.24541
$985$	52.4020	1.66967
$986$	0.993192	0.0316297
$987$	11.8832	0.378247
$988$	5.29158	0.168348
$989$	18.4810	0.587661
$990$	−22.3748	−0.711117
$991$	−5.19342	−0.164974	−0.0824872	−	0.996592i	$-0.526286\pi$
$991$	−5.19342	−0.164974	−0.0824872	+	0.996592i	$0.526286\pi$
$992$	274.843	8.72626
$993$	15.1954	0.482211
$994$	28.8484	0.915015
$995$	−54.5800	−1.73030
$996$	−132.635	−4.20271
$997$	20.2274	0.640609	0.320305	−	0.947315i	$-0.396215\pi$
$997$	20.2274	0.640609	0.320305	+	0.947315i	$0.396215\pi$
$998$	−43.4507	−1.37541
$999$	2.00777	0.0635231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.e.1.2	✓	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.e.1.2	✓	112	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.80869 q^{2} +2.13107 q^{3} +5.88877 q^{4} -3.52544 q^{5} -5.98552 q^{6} -1.00000 q^{7} -10.9224 q^{8} +1.54145 q^{9} +O(q^{10})\)	\(q-2.80869 q^{2} +2.13107 q^{3} +5.88877 q^{4} -3.52544 q^{5} -5.98552 q^{6} -1.00000 q^{7} -10.9224 q^{8} +1.54145 q^{9} +9.90189 q^{10} -1.46593 q^{11} +12.5494 q^{12} -4.10552 q^{13} +2.80869 q^{14} -7.51295 q^{15} +18.9000 q^{16} -4.94767 q^{17} -4.32945 q^{18} -0.218873 q^{19} -20.7605 q^{20} -2.13107 q^{21} +4.11734 q^{22} -1.85326 q^{23} -23.2763 q^{24} +7.42874 q^{25} +11.5312 q^{26} -3.10828 q^{27} -5.88877 q^{28} +0.0714707 q^{29} +21.1016 q^{30} -8.79785 q^{31} -31.2397 q^{32} -3.12399 q^{33} +13.8965 q^{34} +3.52544 q^{35} +9.07722 q^{36} -0.645944 q^{37} +0.614749 q^{38} -8.74914 q^{39} +38.5061 q^{40} +4.37374 q^{41} +5.98552 q^{42} -9.97214 q^{43} -8.63251 q^{44} -5.43428 q^{45} +5.20525 q^{46} -5.57618 q^{47} +40.2773 q^{48} +1.00000 q^{49} -20.8651 q^{50} -10.5438 q^{51} -24.1765 q^{52} -7.38341 q^{53} +8.73020 q^{54} +5.16804 q^{55} +10.9224 q^{56} -0.466434 q^{57} -0.200739 q^{58} -0.775751 q^{59} -44.2420 q^{60} +9.23557 q^{61} +24.7105 q^{62} -1.54145 q^{63} +49.9428 q^{64} +14.4738 q^{65} +8.77433 q^{66} +4.17349 q^{67} -29.1357 q^{68} -3.94942 q^{69} -9.90189 q^{70} +10.2711 q^{71} -16.8362 q^{72} +5.12492 q^{73} +1.81426 q^{74} +15.8311 q^{75} -1.28889 q^{76} +1.46593 q^{77} +24.5737 q^{78} +5.51200 q^{79} -66.6310 q^{80} -11.2483 q^{81} -12.2845 q^{82} -10.5691 q^{83} -12.5494 q^{84} +17.4427 q^{85} +28.0087 q^{86} +0.152309 q^{87} +16.0114 q^{88} -9.03534 q^{89} +15.2632 q^{90} +4.10552 q^{91} -10.9134 q^{92} -18.7488 q^{93} +15.6618 q^{94} +0.771625 q^{95} -66.5740 q^{96} -8.60312 q^{97} -2.80869 q^{98} -2.25965 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9}+O(q^{10}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9	\( 112 q - 3 q^{2} + 14 q^{3} + 131 q^{4} + 13 q^{5} + 18 q^{6} - 112 q^{7} - 9 q^{8} + 116 q^{9} + 32 q^{10} + 14 q^{11} + 36 q^{12} + 22 q^{13} + 3 q^{14} + 19 q^{15} + 169 q^{16} + 11 q^{17} - 18 q^{18} + 52 q^{19} + 40 q^{20} - 14 q^{21} + 16 q^{22} + 38 q^{23} + 64 q^{24} + 99 q^{25} + 45 q^{26} + 65 q^{27} - 131 q^{28} + 10 q^{29} + q^{30} + 133 q^{31} - 26 q^{32} + 27 q^{33} + 52 q^{34} - 13 q^{35} + 183 q^{36} - 13 q^{37} + 20 q^{38} + 74 q^{39} + 92 q^{40} + 25 q^{41} - 18 q^{42} - 11 q^{43} + 16 q^{44} + 63 q^{45} + 28 q^{46} + 71 q^{47} + 70 q^{48} + 112 q^{49} + 5 q^{50} + 57 q^{51} + 79 q^{52} - 10 q^{53} + 75 q^{54} + 146 q^{55} + 9 q^{56} - 83 q^{57} - 19 q^{58} + 56 q^{59} - 3 q^{60} + 80 q^{61} + 42 q^{62} - 116 q^{63} + 263 q^{64} - 26 q^{65} + 48 q^{66} + 29 q^{67} + 57 q^{68} + 56 q^{69} - 32 q^{70} + 100 q^{71} - 62 q^{72} + 73 q^{73} + 24 q^{74} + 89 q^{75} + 155 q^{76} - 14 q^{77} + 33 q^{78} + 140 q^{79} + 80 q^{80} + 120 q^{81} + 114 q^{82} + 36 q^{83} - 36 q^{84} - 2 q^{85} + 12 q^{86} + 96 q^{87} + 29 q^{88} + 47 q^{89} + 52 q^{90} - 22 q^{91} + 81 q^{92} - 10 q^{93} + 127 q^{94} + 96 q^{95} + 175 q^{96} + 80 q^{97} - 3 q^{98} + 74 q^{99}+O(q^{100}) \) 112 * q - 3 * q^2 + 14 * q^3 + 131 * q^4 + 13 * q^5 + 18 * q^6 - 112 * q^7 - 9 * q^8 + 116 * q^9 + 32 * q^10 + 14 * q^11 + 36 * q^12 + 22 * q^13 + 3 * q^14 + 19 * q^15 + 169 * q^16 + 11 * q^17 - 18 * q^18 + 52 * q^19 + 40 * q^20 - 14 * q^21 + 16 * q^22 + 38 * q^23 + 64 * q^24 + 99 * q^25 + 45 * q^26 + 65 * q^27 - 131 * q^28 + 10 * q^29 + q^30 + 133 * q^31 - 26 * q^32 + 27 * q^33 + 52 * q^34 - 13 * q^35 + 183 * q^36 - 13 * q^37 + 20 * q^38 + 74 * q^39 + 92 * q^40 + 25 * q^41 - 18 * q^42 - 11 * q^43 + 16 * q^44 + 63 * q^45 + 28 * q^46 + 71 * q^47 + 70 * q^48 + 112 * q^49 + 5 * q^50 + 57 * q^51 + 79 * q^52 - 10 * q^53 + 75 * q^54 + 146 * q^55 + 9 * q^56 - 83 * q^57 - 19 * q^58 + 56 * q^59 - 3 * q^60 + 80 * q^61 + 42 * q^62 - 116 * q^63 + 263 * q^64 - 26 * q^65 + 48 * q^66 + 29 * q^67 + 57 * q^68 + 56 * q^69 - 32 * q^70 + 100 * q^71 - 62 * q^72 + 73 * q^73 + 24 * q^74 + 89 * q^75 + 155 * q^76 - 14 * q^77 + 33 * q^78 + 140 * q^79 + 80 * q^80 + 120 * q^81 + 114 * q^82 + 36 * q^83 - 36 * q^84 - 2 * q^85 + 12 * q^86 + 96 * q^87 + 29 * q^88 + 47 * q^89 + 52 * q^90 - 22 * q^91 + 81 * q^92 - 10 * q^93 + 127 * q^94 + 96 * q^95 + 175 * q^96 + 80 * q^97 - 3 * q^98 + 74 * q^99

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