LMFDB - Embedded newform 8043.2.a.t.1.42

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.42
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00395 q^{2} -1.00000 q^{3} +2.01582 q^{4} -2.34473 q^{5} -2.00395 q^{6} +1.00000 q^{7} +0.0316991 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.00395 q^{2} -1.00000 q^{3} +2.01582 q^{4} -2.34473 q^{5} -2.00395 q^{6} +1.00000 q^{7} +0.0316991 q^{8} +1.00000 q^{9} -4.69872 q^{10} +5.04789 q^{11} -2.01582 q^{12} +3.07108 q^{13} +2.00395 q^{14} +2.34473 q^{15} -3.96811 q^{16} -0.729519 q^{17} +2.00395 q^{18} +7.23246 q^{19} -4.72655 q^{20} -1.00000 q^{21} +10.1157 q^{22} -1.34166 q^{23} -0.0316991 q^{24} +0.497753 q^{25} +6.15430 q^{26} -1.00000 q^{27} +2.01582 q^{28} -4.82472 q^{29} +4.69872 q^{30} -4.78966 q^{31} -8.01530 q^{32} -5.04789 q^{33} -1.46192 q^{34} -2.34473 q^{35} +2.01582 q^{36} +9.83203 q^{37} +14.4935 q^{38} -3.07108 q^{39} -0.0743258 q^{40} +6.82978 q^{41} -2.00395 q^{42} +0.698229 q^{43} +10.1756 q^{44} -2.34473 q^{45} -2.68862 q^{46} -13.4646 q^{47} +3.96811 q^{48} +1.00000 q^{49} +0.997472 q^{50} +0.729519 q^{51} +6.19075 q^{52} +6.63099 q^{53} -2.00395 q^{54} -11.8359 q^{55} +0.0316991 q^{56} -7.23246 q^{57} -9.66850 q^{58} +1.67507 q^{59} +4.72655 q^{60} -2.47849 q^{61} -9.59824 q^{62} +1.00000 q^{63} -8.12604 q^{64} -7.20086 q^{65} -10.1157 q^{66} -2.86329 q^{67} -1.47058 q^{68} +1.34166 q^{69} -4.69872 q^{70} +0.543792 q^{71} +0.0316991 q^{72} -2.15048 q^{73} +19.7029 q^{74} -0.497753 q^{75} +14.5793 q^{76} +5.04789 q^{77} -6.15430 q^{78} +13.9990 q^{79} +9.30415 q^{80} +1.00000 q^{81} +13.6865 q^{82} -10.6154 q^{83} -2.01582 q^{84} +1.71052 q^{85} +1.39922 q^{86} +4.82472 q^{87} +0.160014 q^{88} -1.16846 q^{89} -4.69872 q^{90} +3.07108 q^{91} -2.70455 q^{92} +4.78966 q^{93} -26.9823 q^{94} -16.9581 q^{95} +8.01530 q^{96} +11.1876 q^{97} +2.00395 q^{98} +5.04789 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) $ 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * 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 $

$2$	2.00395	1.41701	0.708504	−	0.705707i	$-0.249371\pi$
$2$	2.00395	1.41701	0.708504	+	0.705707i	$0.249371\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.01582	1.00791
$5$	−2.34473	−1.04859	−0.524297	−	0.851535i	$-0.675672\pi$
$5$	−2.34473	−1.04859	−0.524297	+	0.851535i	$0.675672\pi$
$6$	−2.00395	−0.818109
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.0316991	0.0112073
$9$	1.00000	0.333333
$10$	−4.69872	−1.48587
$11$	5.04789	1.52200	0.760998	−	0.648754i	$-0.224710\pi$
$11$	5.04789	1.52200	0.760998	+	0.648754i	$0.224710\pi$
$12$	−2.01582	−0.581917
$13$	3.07108	0.851766	0.425883	−	0.904778i	$-0.359964\pi$
$13$	3.07108	0.851766	0.425883	+	0.904778i	$0.359964\pi$
$14$	2.00395	0.535578
$15$	2.34473	0.605406
$16$	−3.96811	−0.992028
$17$	−0.729519	−0.176934	−0.0884672	−	0.996079i	$-0.528197\pi$
$17$	−0.729519	−0.176934	−0.0884672	+	0.996079i	$0.528197\pi$
$18$	2.00395	0.472336
$19$	7.23246	1.65924	0.829620	−	0.558329i	$-0.188557\pi$
$19$	7.23246	1.65924	0.829620	+	0.558329i	$0.188557\pi$
$20$	−4.72655	−1.05689
$21$	−1.00000	−0.218218
$22$	10.1157	2.15668
$23$	−1.34166	−0.279756	−0.139878	−	0.990169i	$-0.544671\pi$
$23$	−1.34166	−0.279756	−0.139878	+	0.990169i	$0.544671\pi$
$24$	−0.0316991	−0.00647056
$25$	0.497753	0.0995506
$26$	6.15430	1.20696
$27$	−1.00000	−0.192450
$28$	2.01582	0.380954
$29$	−4.82472	−0.895928	−0.447964	−	0.894052i	$-0.647851\pi$
$29$	−4.82472	−0.895928	−0.447964	+	0.894052i	$0.647851\pi$
$30$	4.69872	0.857865
$31$	−4.78966	−0.860248	−0.430124	−	0.902770i	$-0.641530\pi$
$31$	−4.78966	−0.860248	−0.430124	+	0.902770i	$0.641530\pi$
$32$	−8.01530	−1.41692
$33$	−5.04789	−0.878725
$34$	−1.46192	−0.250717
$35$	−2.34473	−0.396331
$36$	2.01582	0.335970
$37$	9.83203	1.61638	0.808188	−	0.588925i	$-0.200449\pi$
$37$	9.83203	1.61638	0.808188	+	0.588925i	$0.200449\pi$
$38$	14.4935	2.35115
$39$	−3.07108	−0.491767
$40$	−0.0743258	−0.0117519
$41$	6.82978	1.06663	0.533316	−	0.845916i	$-0.320946\pi$
$41$	6.82978	1.06663	0.533316	+	0.845916i	$0.320946\pi$
$42$	−2.00395	−0.309216
$43$	0.698229	0.106479	0.0532394	−	0.998582i	$-0.483045\pi$
$43$	0.698229	0.106479	0.0532394	+	0.998582i	$0.483045\pi$
$44$	10.1756	1.53403
$45$	−2.34473	−0.349532
$46$	−2.68862	−0.396416
$47$	−13.4646	−1.96401	−0.982003	−	0.188863i	$-0.939520\pi$
$47$	−13.4646	−1.96401	−0.982003	+	0.188863i	$0.939520\pi$
$48$	3.96811	0.572748
$49$	1.00000	0.142857
$50$	0.997472	0.141064
$51$	0.729519	0.102153
$52$	6.19075	0.858502
$53$	6.63099	0.910836	0.455418	−	0.890278i	$-0.349490\pi$
$53$	6.63099	0.910836	0.455418	+	0.890278i	$0.349490\pi$
$54$	−2.00395	−0.272703
$55$	−11.8359	−1.59596
$56$	0.0316991	0.00423597
$57$	−7.23246	−0.957962
$58$	−9.66850	−1.26954
$59$	1.67507	0.218076	0.109038	−	0.994038i	$-0.465223\pi$
$59$	1.67507	0.218076	0.109038	+	0.994038i	$0.465223\pi$
$60$	4.72655	0.610195
$61$	−2.47849	−0.317338	−0.158669	−	0.987332i	$-0.550720\pi$
$61$	−2.47849	−0.317338	−0.158669	+	0.987332i	$0.550720\pi$
$62$	−9.59824	−1.21898
$63$	1.00000	0.125988
$64$	−8.12604	−1.01576
$65$	−7.20086	−0.893157
$66$	−10.1157	−1.24516
$67$	−2.86329	−0.349807	−0.174903	−	0.984586i	$-0.555961\pi$
$67$	−2.86329	−0.349807	−0.174903	+	0.984586i	$0.555961\pi$
$68$	−1.47058	−0.178334
$69$	1.34166	0.161517
$70$	−4.69872	−0.561605
$71$	0.543792	0.0645362	0.0322681	−	0.999479i	$-0.489727\pi$
$71$	0.543792	0.0645362	0.0322681	+	0.999479i	$0.489727\pi$
$72$	0.0316991	0.00373578
$73$	−2.15048	−0.251694	−0.125847	−	0.992050i	$-0.540165\pi$
$73$	−2.15048	−0.251694	−0.125847	+	0.992050i	$0.540165\pi$
$74$	19.7029	2.29042
$75$	−0.497753	−0.0574756
$76$	14.5793	1.67236
$77$	5.04789	0.575260
$78$	−6.15430	−0.696838
$79$	13.9990	1.57501	0.787506	−	0.616308i	$-0.211372\pi$
$79$	13.9990	1.57501	0.787506	+	0.616308i	$0.211372\pi$
$80$	9.30415	1.04024
$81$	1.00000	0.111111
$82$	13.6865	1.51143
$83$	−10.6154	−1.16520	−0.582598	−	0.812760i	$-0.697964\pi$
$83$	−10.6154	−1.16520	−0.582598	+	0.812760i	$0.697964\pi$
$84$	−2.01582	−0.219944
$85$	1.71052	0.185532
$86$	1.39922	0.150881
$87$	4.82472	0.517264
$88$	0.160014	0.0170575
$89$	−1.16846	−0.123856	−0.0619281	−	0.998081i	$-0.519725\pi$
$89$	−1.16846	−0.123856	−0.0619281	+	0.998081i	$0.519725\pi$
$90$	−4.69872	−0.495289
$91$	3.07108	0.321937
$92$	−2.70455	−0.281968
$93$	4.78966	0.496665
$94$	−26.9823	−2.78301
$95$	−16.9581	−1.73987
$96$	8.01530	0.818058
$97$	11.1876	1.13593	0.567963	−	0.823054i	$-0.307732\pi$
$97$	11.1876	1.13593	0.567963	+	0.823054i	$0.307732\pi$
$98$	2.00395	0.202430
$99$	5.04789	0.507332
$100$	1.00338	0.100338
$101$	−11.2713	−1.12154	−0.560768	−	0.827973i	$-0.689494\pi$
$101$	−11.2713	−1.12154	−0.560768	+	0.827973i	$0.689494\pi$
$102$	1.46192	0.144752
$103$	15.0910	1.48696	0.743479	−	0.668760i	$-0.233174\pi$
$103$	15.0910	1.48696	0.743479	+	0.668760i	$0.233174\pi$
$104$	0.0973507	0.00954602
$105$	2.34473	0.228822
$106$	13.2882	1.29066
$107$	−0.273142	−0.0264056	−0.0132028	−	0.999913i	$-0.504203\pi$
$107$	−0.273142	−0.0264056	−0.0132028	+	0.999913i	$0.504203\pi$
$108$	−2.01582	−0.193972
$109$	6.89733	0.660645	0.330322	−	0.943868i	$-0.392843\pi$
$109$	6.89733	0.660645	0.330322	+	0.943868i	$0.392843\pi$
$110$	−23.7186	−2.26148
$111$	−9.83203	−0.933215
$112$	−3.96811	−0.374951
$113$	14.4997	1.36402	0.682010	−	0.731343i	$-0.261106\pi$
$113$	14.4997	1.36402	0.682010	+	0.731343i	$0.261106\pi$
$114$	−14.4935	−1.35744
$115$	3.14583	0.293350
$116$	−9.72575	−0.903014
$117$	3.07108	0.283922
$118$	3.35676	0.309015
$119$	−0.729519	−0.0668749
$120$	0.0743258	0.00678499
$121$	14.4812	1.31647
$122$	−4.96676	−0.449670
$123$	−6.82978	−0.615821
$124$	−9.65508	−0.867052
$125$	10.5565	0.944206
$126$	2.00395	0.178526
$127$	15.9269	1.41328	0.706641	−	0.707572i	$-0.250210\pi$
$127$	15.9269	1.41328	0.706641	+	0.707572i	$0.250210\pi$
$128$	−0.253585	−0.0224140
$129$	−0.698229	−0.0614756
$130$	−14.4302	−1.26561
$131$	6.79637	0.593801	0.296901	−	0.954908i	$-0.404047\pi$
$131$	6.79637	0.593801	0.296901	+	0.954908i	$0.404047\pi$
$132$	−10.1756	−0.885675
$133$	7.23246	0.627133
$134$	−5.73790	−0.495679
$135$	2.34473	0.201802
$136$	−0.0231251	−0.00198296
$137$	20.9722	1.79177	0.895887	−	0.444281i	$-0.146541\pi$
$137$	20.9722	1.79177	0.895887	+	0.444281i	$0.146541\pi$
$138$	2.68862	0.228871
$139$	−4.07206	−0.345388	−0.172694	−	0.984976i	$-0.555247\pi$
$139$	−4.07206	−0.345388	−0.172694	+	0.984976i	$0.555247\pi$
$140$	−4.72655	−0.399466
$141$	13.4646	1.13392
$142$	1.08973	0.0914482
$143$	15.5025	1.29638
$144$	−3.96811	−0.330676
$145$	11.3127	0.939465
$146$	−4.30945	−0.356652
$147$	−1.00000	−0.0824786
$148$	19.8196	1.62916
$149$	7.17354	0.587679	0.293840	−	0.955855i	$-0.405067\pi$
$149$	7.17354	0.587679	0.293840	+	0.955855i	$0.405067\pi$
$150$	−0.997472	−0.0814433
$151$	13.6698	1.11243	0.556216	−	0.831038i	$-0.312253\pi$
$151$	13.6698	1.11243	0.556216	+	0.831038i	$0.312253\pi$
$152$	0.229263	0.0185956
$153$	−0.729519	−0.0589781
$154$	10.1157	0.815148
$155$	11.2305	0.902052
$156$	−6.19075	−0.495657
$157$	−8.71292	−0.695366	−0.347683	−	0.937612i	$-0.613032\pi$
$157$	−8.71292	−0.695366	−0.347683	+	0.937612i	$0.613032\pi$
$158$	28.0533	2.23180
$159$	−6.63099	−0.525872
$160$	18.7937	1.48577
$161$	−1.34166	−0.105738
$162$	2.00395	0.157445
$163$	−8.59604	−0.673294	−0.336647	−	0.941631i	$-0.609293\pi$
$163$	−8.59604	−0.673294	−0.336647	+	0.941631i	$0.609293\pi$
$164$	13.7676	1.07507
$165$	11.8359	0.921426
$166$	−21.2728	−1.65109
$167$	5.51024	0.426395	0.213198	−	0.977009i	$-0.431612\pi$
$167$	5.51024	0.426395	0.213198	+	0.977009i	$0.431612\pi$
$168$	−0.0316991	−0.00244564
$169$	−3.56844	−0.274495
$170$	3.42781	0.262901
$171$	7.23246	0.553080
$172$	1.40750	0.107321
$173$	−9.02736	−0.686337	−0.343169	−	0.939274i	$-0.611500\pi$
$173$	−9.02736	−0.686337	−0.343169	+	0.939274i	$0.611500\pi$
$174$	9.66850	0.732967
$175$	0.497753	0.0376266
$176$	−20.0306	−1.50986
$177$	−1.67507	−0.125906
$178$	−2.34153	−0.175505
$179$	9.61377	0.718567	0.359284	−	0.933228i	$-0.383021\pi$
$179$	9.61377	0.718567	0.359284	+	0.933228i	$0.383021\pi$
$180$	−4.72655	−0.352296
$181$	−8.75593	−0.650823	−0.325412	−	0.945572i	$-0.605503\pi$
$181$	−8.75593	−0.650823	−0.325412	+	0.945572i	$0.605503\pi$
$182$	6.15430	0.456187
$183$	2.47849	0.183215
$184$	−0.0425295	−0.00313532
$185$	−23.0534	−1.69492
$186$	9.59824	0.703777
$187$	−3.68253	−0.269293
$188$	−27.1421	−1.97954
$189$	−1.00000	−0.0727393
$190$	−33.9833	−2.46541
$191$	14.1480	1.02371	0.511857	−	0.859071i	$-0.328958\pi$
$191$	14.1480	1.02371	0.511857	+	0.859071i	$0.328958\pi$
$192$	8.12604	0.586447
$193$	21.8612	1.57360	0.786801	−	0.617206i	$-0.211736\pi$
$193$	21.8612	1.57360	0.786801	+	0.617206i	$0.211736\pi$
$194$	22.4193	1.60962
$195$	7.20086	0.515664
$196$	2.01582	0.143987
$197$	−15.7301	−1.12072	−0.560362	−	0.828248i	$-0.689338\pi$
$197$	−15.7301	−1.12072	−0.560362	+	0.828248i	$0.689338\pi$
$198$	10.1157	0.718893
$199$	−12.6260	−0.895035	−0.447517	−	0.894275i	$-0.647692\pi$
$199$	−12.6260	−0.895035	−0.447517	+	0.894275i	$0.647692\pi$
$200$	0.0157783	0.00111570
$201$	2.86329	0.201961
$202$	−22.5871	−1.58923
$203$	−4.82472	−0.338629
$204$	1.47058	0.102961
$205$	−16.0140	−1.11847
$206$	30.2416	2.10703
$207$	−1.34166	−0.0932519
$208$	−12.1864	−0.844976
$209$	36.5086	2.52536
$210$	4.69872	0.324243
$211$	−19.2408	−1.32459	−0.662294	−	0.749244i	$-0.730417\pi$
$211$	−19.2408	−1.32459	−0.662294	+	0.749244i	$0.730417\pi$
$212$	13.3669	0.918040
$213$	−0.543792	−0.0372600
$214$	−0.547363	−0.0374170
$215$	−1.63716	−0.111653
$216$	−0.0316991	−0.00215685
$217$	−4.78966	−0.325143
$218$	13.8219	0.936138
$219$	2.15048	0.145316
$220$	−23.8591	−1.60858
$221$	−2.24041	−0.150707
$222$	−19.7029	−1.32237
$223$	11.0462	0.739706	0.369853	−	0.929090i	$-0.379408\pi$
$223$	11.0462	0.739706	0.369853	+	0.929090i	$0.379408\pi$
$224$	−8.01530	−0.535545
$225$	0.497753	0.0331835
$226$	29.0568	1.93283
$227$	−13.9807	−0.927929	−0.463964	−	0.885854i	$-0.653573\pi$
$227$	−13.9807	−0.927929	−0.463964	+	0.885854i	$0.653573\pi$
$228$	−14.5793	−0.965539
$229$	3.97787	0.262865	0.131432	−	0.991325i	$-0.458042\pi$
$229$	3.97787	0.262865	0.131432	+	0.991325i	$0.458042\pi$
$230$	6.30409	0.415680
$231$	−5.04789	−0.332127
$232$	−0.152939	−0.0100410
$233$	−8.75737	−0.573714	−0.286857	−	0.957973i	$-0.592611\pi$
$233$	−8.75737	−0.573714	−0.286857	+	0.957973i	$0.592611\pi$
$234$	6.15430	0.402319
$235$	31.5707	2.05945
$236$	3.37664	0.219800
$237$	−13.9990	−0.909333
$238$	−1.46192	−0.0947622
$239$	22.5925	1.46139	0.730694	−	0.682705i	$-0.239197\pi$
$239$	22.5925	1.46139	0.730694	+	0.682705i	$0.239197\pi$
$240$	−9.30415	−0.600580
$241$	−14.4187	−0.928792	−0.464396	−	0.885628i	$-0.653729\pi$
$241$	−14.4187	−0.928792	−0.464396	+	0.885628i	$0.653729\pi$
$242$	29.0196	1.86545
$243$	−1.00000	−0.0641500
$244$	−4.99618	−0.319847
$245$	−2.34473	−0.149799
$246$	−13.6865	−0.872622
$247$	22.2115	1.41328
$248$	−0.151828	−0.00964109
$249$	10.6154	0.672727
$250$	21.1548	1.33795
$251$	9.97594	0.629676	0.314838	−	0.949145i	$-0.398050\pi$
$251$	9.97594	0.629676	0.314838	+	0.949145i	$0.398050\pi$
$252$	2.01582	0.126985
$253$	−6.77256	−0.425787
$254$	31.9167	2.00263
$255$	−1.71052	−0.107117
$256$	15.7439	0.983995
$257$	−17.3428	−1.08181	−0.540907	−	0.841082i	$-0.681919\pi$
$257$	−17.3428	−1.08181	−0.540907	+	0.841082i	$0.681919\pi$
$258$	−1.39922	−0.0871114
$259$	9.83203	0.610933
$260$	−14.5156	−0.900221
$261$	−4.82472	−0.298643
$262$	13.6196	0.841421
$263$	28.0413	1.72910	0.864551	−	0.502546i	$-0.167603\pi$
$263$	28.0413	1.72910	0.864551	+	0.502546i	$0.167603\pi$
$264$	−0.160014	−0.00984816
$265$	−15.5479	−0.955098
$266$	14.4935	0.888653
$267$	1.16846	0.0715084
$268$	−5.77188	−0.352573
$269$	10.7254	0.653938	0.326969	−	0.945035i	$-0.393973\pi$
$269$	10.7254	0.653938	0.326969	+	0.945035i	$0.393973\pi$
$270$	4.69872	0.285955
$271$	12.6053	0.765718	0.382859	−	0.923807i	$-0.374940\pi$
$271$	12.6053	0.765718	0.382859	+	0.923807i	$0.374940\pi$
$272$	2.89481	0.175524
$273$	−3.07108	−0.185871
$274$	42.0272	2.53896
$275$	2.51260	0.151516
$276$	2.70455	0.162795
$277$	29.5992	1.77844	0.889222	−	0.457476i	$-0.151247\pi$
$277$	29.5992	1.77844	0.889222	+	0.457476i	$0.151247\pi$
$278$	−8.16022	−0.489417
$279$	−4.78966	−0.286749
$280$	−0.0743258	−0.00444182
$281$	−17.5698	−1.04813	−0.524063	−	0.851680i	$-0.675584\pi$
$281$	−17.5698	−1.04813	−0.524063	+	0.851680i	$0.675584\pi$
$282$	26.9823	1.60677
$283$	18.1164	1.07691	0.538455	−	0.842654i	$-0.319008\pi$
$283$	18.1164	1.07691	0.538455	+	0.842654i	$0.319008\pi$
$284$	1.09618	0.0650466
$285$	16.9581	1.00451
$286$	31.0662	1.83699
$287$	6.82978	0.403149
$288$	−8.01530	−0.472306
$289$	−16.4678	−0.968694
$290$	22.6700	1.33123
$291$	−11.1876	−0.655827
$292$	−4.33497	−0.253685
$293$	−18.2544	−1.06643	−0.533216	−	0.845979i	$-0.679017\pi$
$293$	−18.2544	−1.06643	−0.533216	+	0.845979i	$0.679017\pi$
$294$	−2.00395	−0.116873
$295$	−3.92759	−0.228673
$296$	0.311667	0.0181153
$297$	−5.04789	−0.292908
$298$	14.3754	0.832746
$299$	−4.12036	−0.238286
$300$	−1.00338	−0.0579301
$301$	0.698229	0.0402452
$302$	27.3936	1.57632
$303$	11.2713	0.647520
$304$	−28.6992	−1.64601
$305$	5.81138	0.332758
$306$	−1.46192	−0.0835724
$307$	12.9783	0.740710	0.370355	−	0.928890i	$-0.379236\pi$
$307$	12.9783	0.740710	0.370355	+	0.928890i	$0.379236\pi$
$308$	10.1756	0.579810
$309$	−15.0910	−0.858495
$310$	22.5053	1.27821
$311$	19.5106	1.10635	0.553173	−	0.833067i	$-0.313417\pi$
$311$	19.5106	1.10635	0.553173	+	0.833067i	$0.313417\pi$
$312$	−0.0973507	−0.00551140
$313$	17.4693	0.987425	0.493713	−	0.869625i	$-0.335639\pi$
$313$	17.4693	0.987425	0.493713	+	0.869625i	$0.335639\pi$
$314$	−17.4603	−0.985339
$315$	−2.34473	−0.132110
$316$	28.2194	1.58747
$317$	24.4847	1.37520	0.687600	−	0.726089i	$-0.258664\pi$
$317$	24.4847	1.37520	0.687600	+	0.726089i	$0.258664\pi$
$318$	−13.2882	−0.745164
$319$	−24.3546	−1.36360
$320$	19.0534	1.06512
$321$	0.273142	0.0152453
$322$	−2.68862	−0.149831
$323$	−5.27621	−0.293576
$324$	2.01582	0.111990
$325$	1.52864	0.0847938
$326$	−17.2260	−0.954063
$327$	−6.89733	−0.381423
$328$	0.216498	0.0119541
$329$	−13.4646	−0.742325
$330$	23.7186	1.30567
$331$	0.968122	0.0532128	0.0266064	−	0.999646i	$-0.491530\pi$
$331$	0.968122	0.0532128	0.0266064	+	0.999646i	$0.491530\pi$
$332$	−21.3988	−1.17441
$333$	9.83203	0.538792
$334$	11.0422	0.604205
$335$	6.71364	0.366805
$336$	3.96811	0.216478
$337$	−28.9166	−1.57519	−0.787594	−	0.616194i	$-0.788674\pi$
$337$	−28.9166	−1.57519	−0.787594	+	0.616194i	$0.788674\pi$
$338$	−7.15097	−0.388962
$339$	−14.4997	−0.787518
$340$	3.44811	0.187000
$341$	−24.1777	−1.30929
$342$	14.4935	0.783718
$343$	1.00000	0.0539949
$344$	0.0221332	0.00119334
$345$	−3.14583	−0.169366
$346$	−18.0904	−0.972545
$347$	20.6733	1.10980	0.554900	−	0.831917i	$-0.312756\pi$
$347$	20.6733	1.10980	0.554900	+	0.831917i	$0.312756\pi$
$348$	9.72575	0.521355
$349$	11.2410	0.601716	0.300858	−	0.953669i	$-0.402727\pi$
$349$	11.2410	0.601716	0.300858	+	0.953669i	$0.402727\pi$
$350$	0.997472	0.0533171
$351$	−3.07108	−0.163922
$352$	−40.4604	−2.15654
$353$	−23.1271	−1.23093	−0.615466	−	0.788164i	$-0.711032\pi$
$353$	−23.1271	−1.23093	−0.615466	+	0.788164i	$0.711032\pi$
$354$	−3.35676	−0.178410
$355$	−1.27504	−0.0676723
$356$	−2.35540	−0.124836
$357$	0.729519	0.0386102
$358$	19.2655	1.01821
$359$	−3.98399	−0.210267	−0.105133	−	0.994458i	$-0.533527\pi$
$359$	−3.98399	−0.210267	−0.105133	+	0.994458i	$0.533527\pi$
$360$	−0.0743258	−0.00391732
$361$	33.3084	1.75307
$362$	−17.5465	−0.922222
$363$	−14.4812	−0.760066
$364$	6.19075	0.324483
$365$	5.04228	0.263925
$366$	4.96676	0.259617
$367$	−10.9658	−0.572409	−0.286204	−	0.958169i	$-0.592394\pi$
$367$	−10.9658	−0.572409	−0.286204	+	0.958169i	$0.592394\pi$
$368$	5.32387	0.277526
$369$	6.82978	0.355544
$370$	−46.1980	−2.40172
$371$	6.63099	0.344264
$372$	9.65508	0.500593
$373$	17.5568	0.909059	0.454530	−	0.890732i	$-0.349807\pi$
$373$	17.5568	0.909059	0.454530	+	0.890732i	$0.349807\pi$
$374$	−7.37961	−0.381591
$375$	−10.5565	−0.545138
$376$	−0.426814	−0.0220113
$377$	−14.8171	−0.763120
$378$	−2.00395	−0.103072
$379$	3.11193	0.159849	0.0799245	−	0.996801i	$-0.474532\pi$
$379$	3.11193	0.159849	0.0799245	+	0.996801i	$0.474532\pi$
$380$	−34.1845	−1.75363
$381$	−15.9269	−0.815959
$382$	28.3519	1.45061
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	0.253585	0.0129407
$385$	−11.8359	−0.603215
$386$	43.8087	2.22981
$387$	0.698229	0.0354930
$388$	22.5521	1.14491
$389$	5.91366	0.299834	0.149917	−	0.988699i	$-0.452099\pi$
$389$	5.91366	0.299834	0.149917	+	0.988699i	$0.452099\pi$
$390$	14.4302	0.730700
$391$	0.978768	0.0494984
$392$	0.0316991	0.00160105
$393$	−6.79637	−0.342831
$394$	−31.5224	−1.58807
$395$	−32.8239	−1.65155
$396$	10.1756	0.511345
$397$	25.0413	1.25679	0.628394	−	0.777895i	$-0.283713\pi$
$397$	25.0413	1.25679	0.628394	+	0.777895i	$0.283713\pi$
$398$	−25.3019	−1.26827
$399$	−7.23246	−0.362076
$400$	−1.97514	−0.0987570
$401$	−12.5428	−0.626358	−0.313179	−	0.949694i	$-0.601394\pi$
$401$	−12.5428	−0.626358	−0.313179	+	0.949694i	$0.601394\pi$
$402$	5.73790	0.286180
$403$	−14.7094	−0.732730
$404$	−22.7209	−1.13041
$405$	−2.34473	−0.116511
$406$	−9.66850	−0.479839
$407$	49.6310	2.46012
$408$	0.0231251	0.00114486
$409$	−29.6276	−1.46499	−0.732494	−	0.680773i	$-0.761644\pi$
$409$	−29.6276	−1.46499	−0.732494	+	0.680773i	$0.761644\pi$
$410$	−32.0912	−1.58487
$411$	−20.9722	−1.03448
$412$	30.4206	1.49872
$413$	1.67507	0.0824249
$414$	−2.68862	−0.132139
$415$	24.8903	1.22182
$416$	−24.6157	−1.20688
$417$	4.07206	0.199410
$418$	73.1615	3.57845
$419$	36.2117	1.76906	0.884528	−	0.466487i	$-0.154481\pi$
$419$	36.2117	1.76906	0.884528	+	0.466487i	$0.154481\pi$
$420$	4.72655	0.230632
$421$	−19.7921	−0.964609	−0.482304	−	0.876004i	$-0.660200\pi$
$421$	−19.7921	−0.964609	−0.482304	+	0.876004i	$0.660200\pi$
$422$	−38.5575	−1.87695
$423$	−13.4646	−0.654669
$424$	0.210197	0.0102080
$425$	−0.363120	−0.0176139
$426$	−1.08973	−0.0527977
$427$	−2.47849	−0.119942
$428$	−0.550604	−0.0266145
$429$	−15.5025	−0.748468
$430$	−3.28078	−0.158213
$431$	−28.6707	−1.38102	−0.690510	−	0.723323i	$-0.742614\pi$
$431$	−28.6707	−1.38102	−0.690510	+	0.723323i	$0.742614\pi$
$432$	3.96811	0.190916
$433$	35.7436	1.71773	0.858863	−	0.512205i	$-0.171171\pi$
$433$	35.7436	1.71773	0.858863	+	0.512205i	$0.171171\pi$
$434$	−9.59824	−0.460730
$435$	−11.3127	−0.542400
$436$	13.9038	0.665870
$437$	−9.70351	−0.464182
$438$	4.30945	0.205913
$439$	−13.6015	−0.649164	−0.324582	−	0.945858i	$-0.605224\pi$
$439$	−13.6015	−0.649164	−0.324582	+	0.945858i	$0.605224\pi$
$440$	−0.375189	−0.0178864
$441$	1.00000	0.0476190
$442$	−4.48968	−0.213552
$443$	−17.2519	−0.819661	−0.409830	−	0.912162i	$-0.634412\pi$
$443$	−17.2519	−0.819661	−0.409830	+	0.912162i	$0.634412\pi$
$444$	−19.8196	−0.940596
$445$	2.73971	0.129875
$446$	22.1360	1.04817
$447$	−7.17354	−0.339297
$448$	−8.12604	−0.383919
$449$	−33.1627	−1.56504	−0.782522	−	0.622623i	$-0.786067\pi$
$449$	−33.1627	−1.56504	−0.782522	+	0.622623i	$0.786067\pi$
$450$	0.997472	0.0470213
$451$	34.4760	1.62341
$452$	29.2288	1.37481
$453$	−13.6698	−0.642263
$454$	−28.0165	−1.31488
$455$	−7.20086	−0.337582
$456$	−0.229263	−0.0107362
$457$	−25.7435	−1.20423	−0.602115	−	0.798409i	$-0.705675\pi$
$457$	−25.7435	−1.20423	−0.602115	+	0.798409i	$0.705675\pi$
$458$	7.97145	0.372481
$459$	0.729519	0.0340510
$460$	6.34143	0.295671
$461$	14.8806	0.693057	0.346529	−	0.938039i	$-0.387360\pi$
$461$	14.8806	0.693057	0.346529	+	0.938039i	$0.387360\pi$
$462$	−10.1157	−0.470626
$463$	13.3969	0.622606	0.311303	−	0.950311i	$-0.399235\pi$
$463$	13.3969	0.622606	0.311303	+	0.950311i	$0.399235\pi$
$464$	19.1450	0.888785
$465$	−11.2305	−0.520800
$466$	−17.5493	−0.812957
$467$	−10.0605	−0.465545	−0.232773	−	0.972531i	$-0.574780\pi$
$467$	−10.0605	−0.465545	−0.232773	+	0.972531i	$0.574780\pi$
$468$	6.19075	0.286167
$469$	−2.86329	−0.132215
$470$	63.2662	2.91825
$471$	8.71292	0.401470
$472$	0.0530983	0.00244405
$473$	3.52458	0.162060
$474$	−28.0533	−1.28853
$475$	3.59998	0.165178
$476$	−1.47058	−0.0674038
$477$	6.63099	0.303612
$478$	45.2743	2.07080
$479$	−15.4611	−0.706434	−0.353217	−	0.935541i	$-0.614912\pi$
$479$	−15.4611	−0.706434	−0.353217	+	0.935541i	$0.614912\pi$
$480$	−18.7937	−0.857811
$481$	30.1950	1.37677
$482$	−28.8944	−1.31611
$483$	1.34166	0.0610477
$484$	29.1915	1.32688
$485$	−26.2318	−1.19113
$486$	−2.00395	−0.0909010
$487$	24.7393	1.12105	0.560523	−	0.828139i	$-0.310600\pi$
$487$	24.7393	1.12105	0.560523	+	0.828139i	$0.310600\pi$
$488$	−0.0785658	−0.00355651
$489$	8.59604	0.388727
$490$	−4.69872	−0.212267
$491$	−12.4306	−0.560984	−0.280492	−	0.959856i	$-0.590498\pi$
$491$	−12.4306	−0.560984	−0.280492	+	0.959856i	$0.590498\pi$
$492$	−13.7676	−0.620691
$493$	3.51972	0.158520
$494$	44.5107	2.00263
$495$	−11.8359	−0.531986
$496$	19.0059	0.853391
$497$	0.543792	0.0243924
$498$	21.2728	0.953258
$499$	−33.0273	−1.47850	−0.739252	−	0.673429i	$-0.764821\pi$
$499$	−33.0273	−1.47850	−0.739252	+	0.673429i	$0.764821\pi$
$500$	21.2801	0.951674
$501$	−5.51024	−0.246179
$502$	19.9913	0.892255
$503$	−14.4182	−0.642876	−0.321438	−	0.946931i	$-0.604166\pi$
$503$	−14.4182	−0.642876	−0.321438	+	0.946931i	$0.604166\pi$
$504$	0.0316991	0.00141199
$505$	26.4282	1.17604
$506$	−13.5719	−0.603344
$507$	3.56844	0.158480
$508$	32.1057	1.42446
$509$	−2.84745	−0.126211	−0.0631055	−	0.998007i	$-0.520100\pi$
$509$	−2.84745	−0.126211	−0.0631055	+	0.998007i	$0.520100\pi$
$510$	−3.42781	−0.151786
$511$	−2.15048	−0.0951315
$512$	32.0572	1.41674
$513$	−7.23246	−0.319321
$514$	−34.7541	−1.53294
$515$	−35.3842	−1.55922
$516$	−1.40750	−0.0619618
$517$	−67.9676	−2.98921
$518$	19.7029	0.865696
$519$	9.02736	0.396257
$520$	−0.228261	−0.0100099
$521$	20.9001	0.915650	0.457825	−	0.889042i	$-0.348629\pi$
$521$	20.9001	0.915650	0.457825	+	0.889042i	$0.348629\pi$
$522$	−9.66850	−0.423179
$523$	−26.1473	−1.14334	−0.571671	−	0.820483i	$-0.693705\pi$
$523$	−26.1473	−1.14334	−0.571671	+	0.820483i	$0.693705\pi$
$524$	13.7002	0.598498
$525$	−0.497753	−0.0217237
$526$	56.1934	2.45015
$527$	3.49415	0.152207
$528$	20.0306	0.871720
$529$	−21.1999	−0.921737
$530$	−31.1572	−1.35338
$531$	1.67507	0.0726919
$532$	14.5793	0.632094
$533$	20.9748	0.908521
$534$	2.34153	0.101328
$535$	0.640444	0.0276888
$536$	−0.0907638	−0.00392040
$537$	−9.61377	−0.414865
$538$	21.4931	0.926635
$539$	5.04789	0.217428
$540$	4.72655	0.203398
$541$	25.1910	1.08304	0.541522	−	0.840686i	$-0.317848\pi$
$541$	25.1910	1.08304	0.541522	+	0.840686i	$0.317848\pi$
$542$	25.2604	1.08503
$543$	8.75593	0.375753
$544$	5.84732	0.250702
$545$	−16.1724	−0.692749
$546$	−6.15430	−0.263380
$547$	45.4503	1.94331	0.971657	−	0.236397i	$-0.0759667\pi$
$547$	45.4503	1.94331	0.971657	+	0.236397i	$0.0759667\pi$
$548$	42.2761	1.80595
$549$	−2.47849	−0.105779
$550$	5.03513	0.214699
$551$	−34.8946	−1.48656
$552$	0.0425295	0.00181018
$553$	13.9990	0.595298
$554$	59.3153	2.52007
$555$	23.0534	0.978564
$556$	−8.20854	−0.348120
$557$	3.34686	0.141811	0.0709056	−	0.997483i	$-0.477411\pi$
$557$	3.34686	0.141811	0.0709056	+	0.997483i	$0.477411\pi$
$558$	−9.59824	−0.406326
$559$	2.14432	0.0906951
$560$	9.30415	0.393172
$561$	3.68253	0.155477
$562$	−35.2090	−1.48520
$563$	−18.8627	−0.794970	−0.397485	−	0.917609i	$-0.630117\pi$
$563$	−18.8627	−0.794970	−0.397485	+	0.917609i	$0.630117\pi$
$564$	27.1421	1.14289
$565$	−33.9979	−1.43030
$566$	36.3045	1.52599
$567$	1.00000	0.0419961
$568$	0.0172377	0.000723278 0
$569$	13.1879	0.552867	0.276433	−	0.961033i	$-0.410847\pi$
$569$	13.1879	0.552867	0.276433	+	0.961033i	$0.410847\pi$
$570$	33.9833	1.42340
$571$	17.0346	0.712878	0.356439	−	0.934319i	$-0.383991\pi$
$571$	17.0346	0.712878	0.356439	+	0.934319i	$0.383991\pi$
$572$	31.2502	1.30664
$573$	−14.1480	−0.591042
$574$	13.6865	0.571265
$575$	−0.667816	−0.0278499
$576$	−8.12604	−0.338585
$577$	26.2219	1.09163	0.545815	−	0.837906i	$-0.316220\pi$
$577$	26.2219	1.09163	0.545815	+	0.837906i	$0.316220\pi$
$578$	−33.0007	−1.37265
$579$	−21.8612	−0.908520
$580$	22.8043	0.946895
$581$	−10.6154	−0.440403
$582$	−22.4193	−0.929312
$583$	33.4725	1.38629
$584$	−0.0681682	−0.00282082
$585$	−7.20086	−0.297719
$586$	−36.5809	−1.51114
$587$	−18.0745	−0.746014	−0.373007	−	0.927829i	$-0.621673\pi$
$587$	−18.0745	−0.746014	−0.373007	+	0.927829i	$0.621673\pi$
$588$	−2.01582	−0.0831309
$589$	−34.6410	−1.42736
$590$	−7.87069	−0.324031
$591$	15.7301	0.647050
$592$	−39.0146	−1.60349
$593$	−0.0936878	−0.00384730	−0.00192365	−	0.999998i	$-0.500612\pi$
$593$	−0.0936878	−0.00384730	−0.00192365	+	0.999998i	$0.500612\pi$
$594$	−10.1157	−0.415053
$595$	1.71052	0.0701247
$596$	14.4606	0.592328
$597$	12.6260	0.516748
$598$	−8.25699	−0.337654
$599$	−39.8788	−1.62940	−0.814701	−	0.579881i	$-0.803099\pi$
$599$	−39.8788	−1.62940	−0.814701	+	0.579881i	$0.803099\pi$
$600$	−0.0157783	−0.000644148 0
$601$	−32.8971	−1.34190	−0.670951	−	0.741502i	$-0.734114\pi$
$601$	−32.8971	−1.34190	−0.670951	+	0.741502i	$0.734114\pi$
$602$	1.39922	0.0570278
$603$	−2.86329	−0.116602
$604$	27.5558	1.12123
$605$	−33.9545	−1.38045
$606$	22.5871	0.917540
$607$	11.7637	0.477474	0.238737	−	0.971084i	$-0.423267\pi$
$607$	11.7637	0.477474	0.238737	+	0.971084i	$0.423267\pi$
$608$	−57.9703	−2.35101
$609$	4.82472	0.195507
$610$	11.6457	0.471521
$611$	−41.3508	−1.67287
$612$	−1.47058	−0.0594446
$613$	−42.3560	−1.71074	−0.855372	−	0.518015i	$-0.826671\pi$
$613$	−42.3560	−1.71074	−0.855372	+	0.518015i	$0.826671\pi$
$614$	26.0079	1.04959
$615$	16.0140	0.645746
$616$	0.160014	0.00644714
$617$	−14.7345	−0.593189	−0.296594	−	0.955004i	$-0.595851\pi$
$617$	−14.7345	−0.593189	−0.296594	+	0.955004i	$0.595851\pi$
$618$	−30.2416	−1.21649
$619$	−11.1004	−0.446163	−0.223082	−	0.974800i	$-0.571612\pi$
$619$	−11.1004	−0.446163	−0.223082	+	0.974800i	$0.571612\pi$
$620$	22.6385	0.909186
$621$	1.34166	0.0538390
$622$	39.0983	1.56770
$623$	−1.16846	−0.0468132
$624$	12.1864	0.487847
$625$	−27.2410	−1.08964
$626$	35.0077	1.39919
$627$	−36.5086	−1.45801
$628$	−17.5637	−0.700866
$629$	−7.17265	−0.285992
$630$	−4.69872	−0.187202
$631$	−1.13747	−0.0452819	−0.0226409	−	0.999744i	$-0.507207\pi$
$631$	−1.13747	−0.0452819	−0.0226409	+	0.999744i	$0.507207\pi$
$632$	0.443756	0.0176517
$633$	19.2408	0.764752
$634$	49.0662	1.94867
$635$	−37.3442	−1.48196
$636$	−13.3669	−0.530031
$637$	3.07108	0.121681
$638$	−48.8055	−1.93223
$639$	0.543792	0.0215121
$640$	0.594588	0.0235032
$641$	−5.14525	−0.203225	−0.101613	−	0.994824i	$-0.532400\pi$
$641$	−5.14525	−0.203225	−0.101613	+	0.994824i	$0.532400\pi$
$642$	0.547363	0.0216027
$643$	−36.9008	−1.45523	−0.727613	−	0.685988i	$-0.759370\pi$
$643$	−36.9008	−1.45523	−0.727613	+	0.685988i	$0.759370\pi$
$644$	−2.70455	−0.106574
$645$	1.63716	0.0644630
$646$	−10.5733	−0.416000
$647$	−10.5297	−0.413964	−0.206982	−	0.978345i	$-0.566364\pi$
$647$	−10.5297	−0.413964	−0.206982	+	0.978345i	$0.566364\pi$
$648$	0.0316991	0.00124526
$649$	8.45557	0.331910
$650$	3.06332	0.120153
$651$	4.78966	0.187722
$652$	−17.3281	−0.678619
$653$	33.9358	1.32801	0.664005	−	0.747728i	$-0.268855\pi$
$653$	33.9358	1.32801	0.664005	+	0.747728i	$0.268855\pi$
$654$	−13.8219	−0.540480
$655$	−15.9356	−0.622657
$656$	−27.1013	−1.05813
$657$	−2.15048	−0.0838981
$658$	−26.9823	−1.05188
$659$	−10.5971	−0.412805	−0.206402	−	0.978467i	$-0.566176\pi$
$659$	−10.5971	−0.412805	−0.206402	+	0.978467i	$0.566176\pi$
$660$	23.8591	0.928714
$661$	15.7027	0.610763	0.305382	−	0.952230i	$-0.401216\pi$
$661$	15.7027	0.610763	0.305382	+	0.952230i	$0.401216\pi$
$662$	1.94007	0.0754029
$663$	2.24041	0.0870105
$664$	−0.336500	−0.0130587
$665$	−16.9581	−0.657609
$666$	19.7029	0.763472
$667$	6.47314	0.250641
$668$	11.1076	0.429767
$669$	−11.0462	−0.427069
$670$	13.4538	0.519766
$671$	−12.5111	−0.482987
$672$	8.01530	0.309197
$673$	18.0269	0.694884	0.347442	−	0.937701i	$-0.387050\pi$
$673$	18.0269	0.694884	0.347442	+	0.937701i	$0.387050\pi$
$674$	−57.9475	−2.23205
$675$	−0.497753	−0.0191585
$676$	−7.19332	−0.276666
$677$	1.92316	0.0739131	0.0369565	−	0.999317i	$-0.488234\pi$
$677$	1.92316	0.0739131	0.0369565	+	0.999317i	$0.488234\pi$
$678$	−29.0568	−1.11592
$679$	11.1876	0.429340
$680$	0.0542221	0.00207932
$681$	13.9807	0.535740
$682$	−48.4509	−1.85528
$683$	−19.3353	−0.739844	−0.369922	−	0.929063i	$-0.620616\pi$
$683$	−19.3353	−0.739844	−0.369922	+	0.929063i	$0.620616\pi$
$684$	14.5793	0.557454
$685$	−49.1741	−1.87885
$686$	2.00395	0.0765112
$687$	−3.97787	−0.151765
$688$	−2.77065	−0.105630
$689$	20.3643	0.775819
$690$	−6.30409	−0.239993
$691$	37.8915	1.44146	0.720730	−	0.693216i	$-0.243807\pi$
$691$	37.8915	1.44146	0.720730	+	0.693216i	$0.243807\pi$
$692$	−18.1975	−0.691766
$693$	5.04789	0.191753
$694$	41.4283	1.57259
$695$	9.54789	0.362172
$696$	0.152939	0.00579715
$697$	−4.98246	−0.188724
$698$	22.5264	0.852635
$699$	8.75737	0.331234
$700$	1.00338	0.0379242
$701$	−49.8490	−1.88277	−0.941385	−	0.337335i	$-0.890474\pi$
$701$	−49.8490	−1.88277	−0.941385	+	0.337335i	$0.890474\pi$
$702$	−6.15430	−0.232279
$703$	71.1097	2.68195
$704$	−41.0194	−1.54598
$705$	−31.5707	−1.18902
$706$	−46.3456	−1.74424
$707$	−11.2713	−0.423901
$708$	−3.37664	−0.126902
$709$	−4.29929	−0.161463	−0.0807316	−	0.996736i	$-0.525726\pi$
$709$	−4.29929	−0.161463	−0.0807316	+	0.996736i	$0.525726\pi$
$710$	−2.55512	−0.0958921
$711$	13.9990	0.525004
$712$	−0.0370391	−0.00138810
$713$	6.42610	0.240659
$714$	1.46192	0.0547110
$715$	−36.3492	−1.35938
$716$	19.3796	0.724250
$717$	−22.5925	−0.843732
$718$	−7.98371	−0.297949
$719$	12.5747	0.468957	0.234478	−	0.972121i	$-0.424662\pi$
$719$	12.5747	0.468957	0.234478	+	0.972121i	$0.424662\pi$
$720$	9.30415	0.346745
$721$	15.0910	0.562017
$722$	66.7484	2.48412
$723$	14.4187	0.536238
$724$	−17.6504	−0.655971
$725$	−2.40152	−0.0891901
$726$	−29.0196	−1.07702
$727$	−0.814496	−0.0302080	−0.0151040	−	0.999886i	$-0.504808\pi$
$727$	−0.814496	−0.0302080	−0.0151040	+	0.999886i	$0.504808\pi$
$728$	0.0973507	0.00360806
$729$	1.00000	0.0370370
$730$	10.1045	0.373984
$731$	−0.509371	−0.0188398
$732$	4.99618	0.184664
$733$	20.0350	0.740008	0.370004	−	0.929030i	$-0.379356\pi$
$733$	20.0350	0.740008	0.370004	+	0.929030i	$0.379356\pi$
$734$	−21.9749	−0.811107
$735$	2.34473	0.0864866
$736$	10.7538	0.396391
$737$	−14.4536	−0.532405
$738$	13.6865	0.503809
$739$	0.441963	0.0162579	0.00812893	−	0.999967i	$-0.497412\pi$
$739$	0.441963	0.0162579	0.00812893	+	0.999967i	$0.497412\pi$
$740$	−46.4716	−1.70833
$741$	−22.2115	−0.815959
$742$	13.2882	0.487824
$743$	2.42325	0.0889004	0.0444502	−	0.999012i	$-0.485846\pi$
$743$	2.42325	0.0889004	0.0444502	+	0.999012i	$0.485846\pi$
$744$	0.151828	0.00556628
$745$	−16.8200	−0.616237
$746$	35.1831	1.28814
$747$	−10.6154	−0.388399
$748$	−7.42332	−0.271423
$749$	−0.273142	−0.00998039
$750$	−21.1548	−0.772464
$751$	41.8907	1.52861	0.764307	−	0.644853i	$-0.223081\pi$
$751$	41.8907	1.52861	0.764307	+	0.644853i	$0.223081\pi$
$752$	53.4289	1.94835
$753$	−9.97594	−0.363544
$754$	−29.6928	−1.08135
$755$	−32.0520	−1.16649
$756$	−2.01582	−0.0733146
$757$	−0.269845	−0.00980770	−0.00490385	−	0.999988i	$-0.501561\pi$
$757$	−0.269845	−0.00980770	−0.00490385	+	0.999988i	$0.501561\pi$
$758$	6.23615	0.226507
$759$	6.77256	0.245828
$760$	−0.537558	−0.0194993
$761$	9.86312	0.357538	0.178769	−	0.983891i	$-0.442789\pi$
$761$	9.86312	0.357538	0.178769	+	0.983891i	$0.442789\pi$
$762$	−31.9167	−1.15622
$763$	6.89733	0.249700
$764$	28.5198	1.03181
$765$	1.71052	0.0618441
$766$	−2.00395	−0.0724057
$767$	5.14428	0.185749
$768$	−15.7439	−0.568110
$769$	−15.7198	−0.566870	−0.283435	−	0.958991i	$-0.591474\pi$
$769$	−15.7198	−0.566870	−0.283435	+	0.958991i	$0.591474\pi$
$770$	−23.7186	−0.854760
$771$	17.3428	0.624586
$772$	44.0682	1.58605
$773$	2.27737	0.0819112	0.0409556	−	0.999161i	$-0.486960\pi$
$773$	2.27737	0.0819112	0.0409556	+	0.999161i	$0.486960\pi$
$774$	1.39922	0.0502938
$775$	−2.38407	−0.0856382
$776$	0.354636	0.0127307
$777$	−9.83203	−0.352722
$778$	11.8507	0.424868
$779$	49.3961	1.76980
$780$	14.5156	0.519743
$781$	2.74500	0.0982238
$782$	1.96140	0.0701396
$783$	4.82472	0.172421
$784$	−3.96811	−0.141718
$785$	20.4294	0.729157
$786$	−13.6196	−0.485795
$787$	−17.4444	−0.621826	−0.310913	−	0.950438i	$-0.600635\pi$
$787$	−17.4444	−0.621826	−0.310913	+	0.950438i	$0.600635\pi$
$788$	−31.7091	−1.12959
$789$	−28.0413	−0.998297
$790$	−65.7774	−2.34026
$791$	14.4997	0.515551
$792$	0.160014	0.00568584
$793$	−7.61164	−0.270297
$794$	50.1816	1.78088
$795$	15.5479	0.551426
$796$	−25.4518	−0.902114
$797$	−24.6711	−0.873894	−0.436947	−	0.899487i	$-0.643940\pi$
$797$	−24.6711	−0.873894	−0.436947	+	0.899487i	$0.643940\pi$
$798$	−14.4935	−0.513064
$799$	9.82265	0.347500
$800$	−3.98964	−0.141055
$801$	−1.16846	−0.0412854
$802$	−25.1352	−0.887554
$803$	−10.8554	−0.383078
$804$	5.77188	0.203558
$805$	3.14583	0.110876
$806$	−29.4770	−1.03828
$807$	−10.7254	−0.377551
$808$	−0.357291	−0.0125694
$809$	−1.67506	−0.0588919	−0.0294459	−	0.999566i	$-0.509374\pi$
$809$	−1.67506	−0.0588919	−0.0294459	+	0.999566i	$0.509374\pi$
$810$	−4.69872	−0.165096
$811$	−27.9630	−0.981912	−0.490956	−	0.871184i	$-0.663352\pi$
$811$	−27.9630	−0.981912	−0.490956	+	0.871184i	$0.663352\pi$
$812$	−9.72575	−0.341307
$813$	−12.6053	−0.442087
$814$	99.4581	3.48600
$815$	20.1554	0.706013
$816$	−2.89481	−0.101339
$817$	5.04991	0.176674
$818$	−59.3722	−2.07590
$819$	3.07108	0.107312
$820$	−32.2813	−1.12731
$821$	39.7645	1.38779	0.693896	−	0.720075i	$-0.255893\pi$
$821$	39.7645	1.38779	0.693896	+	0.720075i	$0.255893\pi$
$822$	−42.0272	−1.46587
$823$	−24.9131	−0.868417	−0.434208	−	0.900812i	$-0.642972\pi$
$823$	−24.9131	−0.868417	−0.434208	+	0.900812i	$0.642972\pi$
$824$	0.478370	0.0166648
$825$	−2.51260	−0.0874776
$826$	3.35676	0.116797
$827$	−40.0021	−1.39101	−0.695505	−	0.718521i	$-0.744819\pi$
$827$	−40.0021	−1.39101	−0.695505	+	0.718521i	$0.744819\pi$
$828$	−2.70455	−0.0939895
$829$	−38.2635	−1.32894	−0.664472	−	0.747313i	$-0.731344\pi$
$829$	−38.2635	−1.32894	−0.664472	+	0.747313i	$0.731344\pi$
$830$	49.8790	1.73133
$831$	−29.5992	−1.02678
$832$	−24.9558	−0.865185
$833$	−0.729519	−0.0252763
$834$	8.16022	0.282565
$835$	−12.9200	−0.447116
$836$	73.5948	2.54533
$837$	4.78966	0.165555
$838$	72.5664	2.50676
$839$	47.8706	1.65268	0.826338	−	0.563175i	$-0.190420\pi$
$839$	47.8706	1.65268	0.826338	+	0.563175i	$0.190420\pi$
$840$	0.0743258	0.00256449
$841$	−5.72210	−0.197314
$842$	−39.6624	−1.36686
$843$	17.5698	0.605136
$844$	−38.7859	−1.33507
$845$	8.36702	0.287834
$846$	−26.9823	−0.927670
$847$	14.4812	0.497580
$848$	−26.3125	−0.903575
$849$	−18.1164	−0.621755
$850$	−0.727675	−0.0249590
$851$	−13.1913	−0.452191
$852$	−1.09618	−0.0375547
$853$	−6.73261	−0.230520	−0.115260	−	0.993335i	$-0.536770\pi$
$853$	−6.73261	−0.230520	−0.115260	+	0.993335i	$0.536770\pi$
$854$	−4.96676	−0.169959
$855$	−16.9581	−0.579956
$856$	−0.00865836	−0.000295937 0
$857$	−33.8875	−1.15757	−0.578787	−	0.815479i	$-0.696474\pi$
$857$	−33.8875	−1.15757	−0.578787	+	0.815479i	$0.696474\pi$
$858$	−31.0662	−1.06058
$859$	22.4449	0.765811	0.382906	−	0.923787i	$-0.374923\pi$
$859$	22.4449	0.765811	0.382906	+	0.923787i	$0.374923\pi$
$860$	−3.30021	−0.112536
$861$	−6.82978	−0.232758
$862$	−57.4547	−1.95691
$863$	54.4699	1.85418	0.927089	−	0.374842i	$-0.122303\pi$
$863$	54.4699	1.85418	0.927089	+	0.374842i	$0.122303\pi$
$864$	8.01530	0.272686
$865$	21.1667	0.719689
$866$	71.6284	2.43403
$867$	16.4678	0.559276
$868$	−9.65508	−0.327715
$869$	70.6654	2.39716
$870$	−22.6700	−0.768585
$871$	−8.79341	−0.297953
$872$	0.218639	0.00740407
$873$	11.1876	0.378642
$874$	−19.4454	−0.657749
$875$	10.5565	0.356876
$876$	4.33497	0.146465
$877$	−6.04205	−0.204026	−0.102013	−	0.994783i	$-0.532528\pi$
$877$	−6.04205	−0.204026	−0.102013	+	0.994783i	$0.532528\pi$
$878$	−27.2567	−0.919870
$879$	18.2544	0.615705
$880$	46.9663	1.58323
$881$	12.2605	0.413067	0.206533	−	0.978440i	$-0.433782\pi$
$881$	12.2605	0.413067	0.206533	+	0.978440i	$0.433782\pi$
$882$	2.00395	0.0674765
$883$	−6.28955	−0.211660	−0.105830	−	0.994384i	$-0.533750\pi$
$883$	−6.28955	−0.211660	−0.105830	+	0.994384i	$0.533750\pi$
$884$	−4.51627	−0.151899
$885$	3.92759	0.132024
$886$	−34.5719	−1.16146
$887$	6.27966	0.210850	0.105425	−	0.994427i	$-0.466380\pi$
$887$	6.27966	0.210850	0.105425	+	0.994427i	$0.466380\pi$
$888$	−0.311667	−0.0104588
$889$	15.9269	0.534170
$890$	5.49025	0.184034
$891$	5.04789	0.169111
$892$	22.2671	0.745556
$893$	−97.3818	−3.25876
$894$	−14.3754	−0.480786
$895$	−22.5417	−0.753486
$896$	−0.253585	−0.00847168
$897$	4.12036	0.137575
$898$	−66.4564	−2.21768
$899$	23.1088	0.770720
$900$	1.00338	0.0334460
$901$	−4.83743	−0.161158
$902$	69.0882	2.30038
$903$	−0.698229	−0.0232356
$904$	0.459629	0.0152870
$905$	20.5303	0.682450
$906$	−27.3936	−0.910091
$907$	−18.1575	−0.602909	−0.301455	−	0.953481i	$-0.597472\pi$
$907$	−18.1575	−0.602909	−0.301455	+	0.953481i	$0.597472\pi$
$908$	−28.1825	−0.935268
$909$	−11.2713	−0.373846
$910$	−14.4302	−0.478355
$911$	−55.0263	−1.82310	−0.911551	−	0.411188i	$-0.865114\pi$
$911$	−55.0263	−1.82310	−0.911551	+	0.411188i	$0.865114\pi$
$912$	28.6992	0.950326
$913$	−53.5856	−1.77342
$914$	−51.5887	−1.70640
$915$	−5.81138	−0.192118
$916$	8.01866	0.264944
$917$	6.79637	0.224436
$918$	1.46192	0.0482506
$919$	−44.4659	−1.46679	−0.733397	−	0.679801i	$-0.762066\pi$
$919$	−44.4659	−1.46679	−0.733397	+	0.679801i	$0.762066\pi$
$920$	0.0997202	0.00328768
$921$	−12.9783	−0.427649
$922$	29.8199	0.982067
$923$	1.67003	0.0549697
$924$	−10.1756	−0.334754
$925$	4.89392	0.160911
$926$	26.8467	0.882237
$927$	15.0910	0.495652
$928$	38.6716	1.26946
$929$	37.8357	1.24135	0.620674	−	0.784069i	$-0.286859\pi$
$929$	37.8357	1.24135	0.620674	+	0.784069i	$0.286859\pi$
$930$	−22.5053	−0.737977
$931$	7.23246	0.237034
$932$	−17.6533	−0.578252
$933$	−19.5106	−0.638749
$934$	−20.1608	−0.659681
$935$	8.63454	0.282380
$936$	0.0973507	0.00318201
$937$	−15.2522	−0.498267	−0.249134	−	0.968469i	$-0.580146\pi$
$937$	−15.2522	−0.498267	−0.249134	+	0.968469i	$0.580146\pi$
$938$	−5.73790	−0.187349
$939$	−17.4693	−0.570090
$940$	63.6408	2.07574
$941$	7.82646	0.255135	0.127568	−	0.991830i	$-0.459283\pi$
$941$	7.82646	0.255135	0.127568	+	0.991830i	$0.459283\pi$
$942$	17.4603	0.568886
$943$	−9.16326	−0.298397
$944$	−6.64687	−0.216337
$945$	2.34473	0.0762740
$946$	7.06309	0.229641
$947$	−49.6280	−1.61269	−0.806346	−	0.591444i	$-0.798558\pi$
$947$	−49.6280	−1.61269	−0.806346	+	0.591444i	$0.798558\pi$
$948$	−28.2194	−0.916525
$949$	−6.60429	−0.214384
$950$	7.21417	0.234059
$951$	−24.4847	−0.793972
$952$	−0.0231251	−0.000749489 0
$953$	−26.1985	−0.848653	−0.424327	−	0.905509i	$-0.639489\pi$
$953$	−26.1985	−0.848653	−0.424327	+	0.905509i	$0.639489\pi$
$954$	13.2882	0.430220
$955$	−33.1732	−1.07346
$956$	45.5424	1.47295
$957$	24.3546	0.787274
$958$	−30.9832	−1.00102
$959$	20.9722	0.677227
$960$	−19.0534	−0.614945
$961$	−8.05917	−0.259973
$962$	60.5093	1.95090
$963$	−0.273142	−0.00880187
$964$	−29.0655	−0.936138
$965$	−51.2586	−1.65007
$966$	2.68862	0.0865051
$967$	38.3554	1.23343	0.616713	−	0.787188i	$-0.288464\pi$
$967$	38.3554	1.23343	0.616713	+	0.787188i	$0.288464\pi$
$968$	0.459041	0.0147541
$969$	5.27621	0.169496
$970$	−52.5673	−1.68783
$971$	28.6440	0.919229	0.459615	−	0.888119i	$-0.347988\pi$
$971$	28.6440	0.919229	0.459615	+	0.888119i	$0.347988\pi$
$972$	−2.01582	−0.0646574
$973$	−4.07206	−0.130544
$974$	49.5764	1.58853
$975$	−1.52864	−0.0489557
$976$	9.83491	0.314808
$977$	54.4920	1.74335	0.871677	−	0.490081i	$-0.163033\pi$
$977$	54.4920	1.74335	0.871677	+	0.490081i	$0.163033\pi$
$978$	17.2260	0.550828
$979$	−5.89824	−0.188509
$980$	−4.72655	−0.150984
$981$	6.89733	0.220215
$982$	−24.9103	−0.794919
$983$	−12.4799	−0.398047	−0.199023	−	0.979995i	$-0.563777\pi$
$983$	−12.4799	−0.398047	−0.199023	+	0.979995i	$0.563777\pi$
$984$	−0.216498	−0.00690171
$985$	36.8829	1.17519
$986$	7.05335	0.224624
$987$	13.4646	0.428581
$988$	44.7743	1.42446
$989$	−0.936787	−0.0297881
$990$	−23.7186	−0.753827
$991$	−47.0618	−1.49497	−0.747484	−	0.664280i	$-0.768738\pi$
$991$	−47.0618	−1.49497	−0.747484	+	0.664280i	$0.768738\pi$
$992$	38.3906	1.21890
$993$	−0.968122	−0.0307224
$994$	1.08973	0.0345642
$995$	29.6046	0.938528
$996$	21.3988	0.678047
$997$	16.0010	0.506758	0.253379	−	0.967367i	$-0.418458\pi$
$997$	16.0010	0.506758	0.253379	+	0.967367i	$0.418458\pi$
$998$	−66.1850	−2.09505
$999$	−9.83203	−0.311072

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.t.1.42	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.t.1.42	✓	52	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00395 q^{2} -1.00000 q^{3} +2.01582 q^{4} -2.34473 q^{5} -2.00395 q^{6} +1.00000 q^{7} +0.0316991 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.00395 q^{2} -1.00000 q^{3} +2.01582 q^{4} -2.34473 q^{5} -2.00395 q^{6} +1.00000 q^{7} +0.0316991 q^{8} +1.00000 q^{9} -4.69872 q^{10} +5.04789 q^{11} -2.01582 q^{12} +3.07108 q^{13} +2.00395 q^{14} +2.34473 q^{15} -3.96811 q^{16} -0.729519 q^{17} +2.00395 q^{18} +7.23246 q^{19} -4.72655 q^{20} -1.00000 q^{21} +10.1157 q^{22} -1.34166 q^{23} -0.0316991 q^{24} +0.497753 q^{25} +6.15430 q^{26} -1.00000 q^{27} +2.01582 q^{28} -4.82472 q^{29} +4.69872 q^{30} -4.78966 q^{31} -8.01530 q^{32} -5.04789 q^{33} -1.46192 q^{34} -2.34473 q^{35} +2.01582 q^{36} +9.83203 q^{37} +14.4935 q^{38} -3.07108 q^{39} -0.0743258 q^{40} +6.82978 q^{41} -2.00395 q^{42} +0.698229 q^{43} +10.1756 q^{44} -2.34473 q^{45} -2.68862 q^{46} -13.4646 q^{47} +3.96811 q^{48} +1.00000 q^{49} +0.997472 q^{50} +0.729519 q^{51} +6.19075 q^{52} +6.63099 q^{53} -2.00395 q^{54} -11.8359 q^{55} +0.0316991 q^{56} -7.23246 q^{57} -9.66850 q^{58} +1.67507 q^{59} +4.72655 q^{60} -2.47849 q^{61} -9.59824 q^{62} +1.00000 q^{63} -8.12604 q^{64} -7.20086 q^{65} -10.1157 q^{66} -2.86329 q^{67} -1.47058 q^{68} +1.34166 q^{69} -4.69872 q^{70} +0.543792 q^{71} +0.0316991 q^{72} -2.15048 q^{73} +19.7029 q^{74} -0.497753 q^{75} +14.5793 q^{76} +5.04789 q^{77} -6.15430 q^{78} +13.9990 q^{79} +9.30415 q^{80} +1.00000 q^{81} +13.6865 q^{82} -10.6154 q^{83} -2.01582 q^{84} +1.71052 q^{85} +1.39922 q^{86} +4.82472 q^{87} +0.160014 q^{88} -1.16846 q^{89} -4.69872 q^{90} +3.07108 q^{91} -2.70455 q^{92} +4.78966 q^{93} -26.9823 q^{94} -16.9581 q^{95} +8.01530 q^{96} +11.1876 q^{97} +2.00395 q^{98} +5.04789 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9}+O(q^{10}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9	\( 52 q + 3 q^{2} - 52 q^{3} + 61 q^{4} - 7 q^{5} - 3 q^{6} + 52 q^{7} + 24 q^{8} + 52 q^{9} - 2 q^{10} + 9 q^{11} - 61 q^{12} + 44 q^{13} + 3 q^{14} + 7 q^{15} + 95 q^{16} - 6 q^{17} + 3 q^{18} + 7 q^{19} - 21 q^{20} - 52 q^{21} + 19 q^{22} - 4 q^{23} - 24 q^{24} + 83 q^{25} - 5 q^{26} - 52 q^{27} + 61 q^{28} + 31 q^{29} + 2 q^{30} + 11 q^{31} + 71 q^{32} - 9 q^{33} + 17 q^{34} - 7 q^{35} + 61 q^{36} + 71 q^{37} - 8 q^{38} - 44 q^{39} + 20 q^{40} - 25 q^{41} - 3 q^{42} + 75 q^{43} + 14 q^{44} - 7 q^{45} + 36 q^{46} - 20 q^{47} - 95 q^{48} + 52 q^{49} + 26 q^{50} + 6 q^{51} + 88 q^{52} + 70 q^{53} - 3 q^{54} + 12 q^{55} + 24 q^{56} - 7 q^{57} + 48 q^{58} - 27 q^{59} + 21 q^{60} + 59 q^{61} - 23 q^{62} + 52 q^{63} + 138 q^{64} + 44 q^{65} - 19 q^{66} + 65 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{70} - 11 q^{71} + 24 q^{72} + 34 q^{73} + 38 q^{74} - 83 q^{75} + 31 q^{76} + 9 q^{77} + 5 q^{78} + 74 q^{79} - 5 q^{80} + 52 q^{81} + 51 q^{82} - 30 q^{83} - 61 q^{84} + 70 q^{85} + 29 q^{86} - 31 q^{87} + 90 q^{88} - q^{89} - 2 q^{90} + 44 q^{91} + 34 q^{92} - 11 q^{93} + 27 q^{94} + 9 q^{95} - 71 q^{96} + 73 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 52 * q + 3 * q^2 - 52 * q^3 + 61 * q^4 - 7 * q^5 - 3 * q^6 + 52 * q^7 + 24 * q^8 + 52 * q^9 - 2 * q^10 + 9 * q^11 - 61 * q^12 + 44 * q^13 + 3 * q^14 + 7 * q^15 + 95 * q^16 - 6 * q^17 + 3 * q^18 + 7 * q^19 - 21 * q^20 - 52 * q^21 + 19 * q^22 - 4 * q^23 - 24 * q^24 + 83 * q^25 - 5 * q^26 - 52 * q^27 + 61 * q^28 + 31 * q^29 + 2 * q^30 + 11 * q^31 + 71 * q^32 - 9 * q^33 + 17 * q^34 - 7 * q^35 + 61 * q^36 + 71 * q^37 - 8 * q^38 - 44 * q^39 + 20 * q^40 - 25 * q^41 - 3 * q^42 + 75 * q^43 + 14 * q^44 - 7 * q^45 + 36 * q^46 - 20 * q^47 - 95 * q^48 + 52 * q^49 + 26 * q^50 + 6 * q^51 + 88 * q^52 + 70 * q^53 - 3 * q^54 + 12 * q^55 + 24 * q^56 - 7 * q^57 + 48 * q^58 - 27 * q^59 + 21 * q^60 + 59 * q^61 - 23 * q^62 + 52 * q^63 + 138 * q^64 + 44 * q^65 - 19 * q^66 + 65 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^70 - 11 * q^71 + 24 * q^72 + 34 * q^73 + 38 * q^74 - 83 * q^75 + 31 * q^76 + 9 * q^77 + 5 * q^78 + 74 * q^79 - 5 * q^80 + 52 * q^81 + 51 * q^82 - 30 * q^83 - 61 * q^84 + 70 * q^85 + 29 * q^86 - 31 * q^87 + 90 * q^88 - q^89 - 2 * q^90 + 44 * q^91 + 34 * q^92 - 11 * q^93 + 27 * q^94 + 9 * q^95 - 71 * q^96 + 73 * q^97 + 3 * q^98 + 9 * q^99

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