LMFDB - Embedded newform 8011.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8011,2,Mod(1,8011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8011, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8011.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:	$63.9681570592$
Analytic rank:	$0$
Dimension:	$358$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61809 q^{2} -3.37147 q^{3} +4.85437 q^{4} +3.62871 q^{5} +8.82680 q^{6} -2.17662 q^{7} -7.47299 q^{8} +8.36681 q^{9} +O(q^{10})$	\(q-2.61809 q^{2} -3.37147 q^{3} +4.85437 q^{4} +3.62871 q^{5} +8.82680 q^{6} -2.17662 q^{7} -7.47299 q^{8} +8.36681 q^{9} -9.50027 q^{10} -5.68339 q^{11} -16.3664 q^{12} -3.89143 q^{13} +5.69858 q^{14} -12.2341 q^{15} +9.85618 q^{16} -4.90540 q^{17} -21.9050 q^{18} +3.00670 q^{19} +17.6151 q^{20} +7.33841 q^{21} +14.8796 q^{22} +1.00449 q^{23} +25.1950 q^{24} +8.16751 q^{25} +10.1881 q^{26} -18.0940 q^{27} -10.5661 q^{28} +3.18572 q^{29} +32.0299 q^{30} -4.93247 q^{31} -10.8584 q^{32} +19.1614 q^{33} +12.8428 q^{34} -7.89832 q^{35} +40.6156 q^{36} -9.30560 q^{37} -7.87180 q^{38} +13.1198 q^{39} -27.1173 q^{40} -1.24511 q^{41} -19.2126 q^{42} -5.29208 q^{43} -27.5893 q^{44} +30.3607 q^{45} -2.62985 q^{46} -0.229215 q^{47} -33.2298 q^{48} -2.26232 q^{49} -21.3833 q^{50} +16.5384 q^{51} -18.8905 q^{52} -8.56333 q^{53} +47.3717 q^{54} -20.6234 q^{55} +16.2659 q^{56} -10.1370 q^{57} -8.34048 q^{58} -9.35565 q^{59} -59.3888 q^{60} +1.01390 q^{61} +12.9136 q^{62} -18.2114 q^{63} +8.71573 q^{64} -14.1209 q^{65} -50.1662 q^{66} -4.22483 q^{67} -23.8126 q^{68} -3.38662 q^{69} +20.6785 q^{70} -4.82623 q^{71} -62.5251 q^{72} +10.1842 q^{73} +24.3628 q^{74} -27.5365 q^{75} +14.5956 q^{76} +12.3706 q^{77} -34.3489 q^{78} -14.8509 q^{79} +35.7652 q^{80} +35.9030 q^{81} +3.25981 q^{82} -1.48956 q^{83} +35.6234 q^{84} -17.8003 q^{85} +13.8551 q^{86} -10.7406 q^{87} +42.4719 q^{88} +0.582583 q^{89} -79.4869 q^{90} +8.47017 q^{91} +4.87618 q^{92} +16.6297 q^{93} +0.600104 q^{94} +10.9104 q^{95} +36.6086 q^{96} -8.11866 q^{97} +5.92295 q^{98} -47.5519 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) $ 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * 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 $

$2$	−2.61809	−1.85127	−0.925633	−	0.378422i	$-0.876467\pi$
$2$	−2.61809	−1.85127	−0.925633	+	0.378422i	$0.876467\pi$
$3$	−3.37147	−1.94652	−0.973259	−	0.229709i	$-0.926223\pi$
$3$	−3.37147	−1.94652	−0.973259	+	0.229709i	$0.926223\pi$
$4$	4.85437	2.42719
$5$	3.62871	1.62281	0.811404	−	0.584486i	$-0.198704\pi$
$5$	3.62871	1.62281	0.811404	+	0.584486i	$0.198704\pi$
$6$	8.82680	3.60352
$7$	−2.17662	−0.822685	−0.411343	−	0.911481i	$-0.634940\pi$
$7$	−2.17662	−0.822685	−0.411343	+	0.911481i	$0.634940\pi$
$8$	−7.47299	−2.64210
$9$	8.36681	2.78894
$10$	−9.50027	−3.00425
$11$	−5.68339	−1.71361	−0.856804	−	0.515642i	$-0.827553\pi$
$11$	−5.68339	−1.71361	−0.856804	+	0.515642i	$0.827553\pi$
$12$	−16.3664	−4.72456
$13$	−3.89143	−1.07929	−0.539645	−	0.841893i	$-0.681441\pi$
$13$	−3.89143	−1.07929	−0.539645	+	0.841893i	$0.681441\pi$
$14$	5.69858	1.52301
$15$	−12.2341	−3.15882
$16$	9.85618	2.46405
$17$	−4.90540	−1.18973	−0.594867	−	0.803824i	$-0.702795\pi$
$17$	−4.90540	−1.18973	−0.594867	+	0.803824i	$0.702795\pi$
$18$	−21.9050	−5.16306
$19$	3.00670	0.689784	0.344892	−	0.938642i	$-0.387916\pi$
$19$	3.00670	0.689784	0.344892	+	0.938642i	$0.387916\pi$
$20$	17.6151	3.93885
$21$	7.33841	1.60137
$22$	14.8796	3.17234
$23$	1.00449	0.209451	0.104726	−	0.994501i	$-0.466604\pi$
$23$	1.00449	0.209451	0.104726	+	0.994501i	$0.466604\pi$
$24$	25.1950	5.14290
$25$	8.16751	1.63350
$26$	10.1881	1.99805
$27$	−18.0940	−3.48220
$28$	−10.5661	−1.99681
$29$	3.18572	0.591573	0.295786	−	0.955254i	$-0.404418\pi$
$29$	3.18572	0.591573	0.295786	+	0.955254i	$0.404418\pi$
$30$	32.0299	5.84782
$31$	−4.93247	−0.885898	−0.442949	−	0.896547i	$-0.646068\pi$
$31$	−4.93247	−0.885898	−0.442949	+	0.896547i	$0.646068\pi$
$32$	−10.8584	−1.91950
$33$	19.1614	3.33557
$34$	12.8428	2.20252
$35$	−7.89832	−1.33506
$36$	40.6156	6.76927
$37$	−9.30560	−1.52983	−0.764915	−	0.644131i	$-0.777219\pi$
$37$	−9.30560	−1.52983	−0.764915	+	0.644131i	$0.777219\pi$
$38$	−7.87180	−1.27697
$39$	13.1198	2.10086
$40$	−27.1173	−4.28762
$41$	−1.24511	−0.194454	−0.0972271	−	0.995262i	$-0.530997\pi$
$41$	−1.24511	−0.194454	−0.0972271	+	0.995262i	$0.530997\pi$
$42$	−19.2126	−2.96457
$43$	−5.29208	−0.807035	−0.403518	−	0.914972i	$-0.632213\pi$
$43$	−5.29208	−0.807035	−0.403518	+	0.914972i	$0.632213\pi$
$44$	−27.5893	−4.15924
$45$	30.3607	4.52590
$46$	−2.62985	−0.387750
$47$	−0.229215	−0.0334344	−0.0167172	−	0.999860i	$-0.505322\pi$
$47$	−0.229215	−0.0334344	−0.0167172	+	0.999860i	$0.505322\pi$
$48$	−33.2298	−4.79631
$49$	−2.26232	−0.323189
$50$	−21.3833	−3.02405
$51$	16.5384	2.31584
$52$	−18.8905	−2.61964
$53$	−8.56333	−1.17626	−0.588132	−	0.808765i	$-0.700136\pi$
$53$	−8.56333	−1.17626	−0.588132	+	0.808765i	$0.700136\pi$
$54$	47.3717	6.44647
$55$	−20.6234	−2.78085
$56$	16.2659	2.17362
$57$	−10.1370	−1.34268
$58$	−8.34048	−1.09516
$59$	−9.35565	−1.21800	−0.609001	−	0.793170i	$-0.708429\pi$
$59$	−9.35565	−1.21800	−0.609001	+	0.793170i	$0.708429\pi$
$60$	−59.3888	−7.66706
$61$	1.01390	0.129816	0.0649082	−	0.997891i	$-0.479325\pi$
$61$	1.01390	0.129816	0.0649082	+	0.997891i	$0.479325\pi$
$62$	12.9136	1.64003
$63$	−18.2114	−2.29442
$64$	8.71573	1.08947
$65$	−14.1209	−1.75148
$66$	−50.1662	−6.17503
$67$	−4.22483	−0.516145	−0.258072	−	0.966126i	$-0.583087\pi$
$67$	−4.22483	−0.516145	−0.258072	+	0.966126i	$0.583087\pi$
$68$	−23.8126	−2.88771
$69$	−3.38662	−0.407701
$70$	20.6785	2.47155
$71$	−4.82623	−0.572768	−0.286384	−	0.958115i	$-0.592453\pi$
$71$	−4.82623	−0.572768	−0.286384	+	0.958115i	$0.592453\pi$
$72$	−62.5251	−7.36865
$73$	10.1842	1.19197	0.595984	−	0.802996i	$-0.296762\pi$
$73$	10.1842	1.19197	0.595984	+	0.802996i	$0.296762\pi$
$74$	24.3628	2.83212
$75$	−27.5365	−3.17964
$76$	14.5956	1.67423
$77$	12.3706	1.40976
$78$	−34.3489	−3.88925
$79$	−14.8509	−1.67086	−0.835430	−	0.549596i	$-0.814782\pi$
$79$	−14.8509	−1.67086	−0.835430	+	0.549596i	$0.814782\pi$
$80$	35.7652	3.99867
$81$	35.9030	3.98923
$82$	3.25981	0.359986
$83$	−1.48956	−0.163500	−0.0817502	−	0.996653i	$-0.526051\pi$
$83$	−1.48956	−0.163500	−0.0817502	+	0.996653i	$0.526051\pi$
$84$	35.6234	3.88683
$85$	−17.8003	−1.93071
$86$	13.8551	1.49404
$87$	−10.7406	−1.15151
$88$	42.4719	4.52753
$89$	0.582583	0.0617537	0.0308769	−	0.999523i	$-0.490170\pi$
$89$	0.582583	0.0617537	0.0308769	+	0.999523i	$0.490170\pi$
$90$	−79.4869	−8.37865
$91$	8.47017	0.887915
$92$	4.87618	0.508377
$93$	16.6297	1.72442
$94$	0.600104	0.0618960
$95$	10.9104	1.11939
$96$	36.6086	3.73635
$97$	−8.11866	−0.824325	−0.412162	−	0.911110i	$-0.635226\pi$
$97$	−8.11866	−0.824325	−0.412162	+	0.911110i	$0.635226\pi$
$98$	5.92295	0.598309
$99$	−47.5519	−4.77914
$100$	39.6482	3.96482
$101$	18.4015	1.83102	0.915509	−	0.402298i	$-0.131788\pi$
$101$	18.4015	1.83102	0.915509	+	0.402298i	$0.131788\pi$
$102$	−43.2990	−4.28724
$103$	9.25067	0.911496	0.455748	−	0.890109i	$-0.349372\pi$
$103$	9.25067	0.911496	0.455748	+	0.890109i	$0.349372\pi$
$104$	29.0806	2.85159
$105$	26.6289	2.59872
$106$	22.4195	2.17758
$107$	6.29314	0.608381	0.304190	−	0.952611i	$-0.401614\pi$
$107$	6.29314	0.608381	0.304190	+	0.952611i	$0.401614\pi$
$108$	−87.8352	−8.45194
$109$	−12.3273	−1.18074	−0.590370	−	0.807133i	$-0.701018\pi$
$109$	−12.3273	−1.18074	−0.590370	+	0.807133i	$0.701018\pi$
$110$	53.9937	5.14810
$111$	31.3735	2.97784
$112$	−21.4532	−2.02713
$113$	0.723465	0.0680579	0.0340289	−	0.999421i	$-0.489166\pi$
$113$	0.723465	0.0680579	0.0340289	+	0.999421i	$0.489166\pi$
$114$	26.5395	2.48565
$115$	3.64501	0.339899
$116$	15.4647	1.43586
$117$	−32.5589	−3.01007
$118$	24.4939	2.25484
$119$	10.6772	0.978777
$120$	91.4251	8.34593
$121$	21.3010	1.93645
$122$	−2.65447	−0.240325
$123$	4.19786	0.378509
$124$	−23.9441	−2.15024
$125$	11.4940	1.02805
$126$	47.6789	4.24758
$127$	12.9576	1.14980	0.574901	−	0.818223i	$-0.305041\pi$
$127$	12.9576	1.14980	0.574901	+	0.818223i	$0.305041\pi$
$128$	−1.10182	−0.0973882
$129$	17.8421	1.57091
$130$	36.9696	3.24245
$131$	−22.0159	−1.92354	−0.961769	−	0.273861i	$-0.911699\pi$
$131$	−22.0159	−1.92354	−0.961769	+	0.273861i	$0.911699\pi$
$132$	93.0165	8.09605
$133$	−6.54444	−0.567475
$134$	11.0610	0.955521
$135$	−65.6579	−5.65094
$136$	36.6580	3.14340
$137$	−19.1958	−1.64001	−0.820004	−	0.572357i	$-0.806029\pi$
$137$	−19.1958	−1.64001	−0.820004	+	0.572357i	$0.806029\pi$
$138$	8.86645	0.754763
$139$	3.97676	0.337305	0.168652	−	0.985676i	$-0.446058\pi$
$139$	3.97676	0.337305	0.168652	+	0.985676i	$0.446058\pi$
$140$	−38.3414	−3.24044
$141$	0.772791	0.0650807
$142$	12.6355	1.06035
$143$	22.1165	1.84948
$144$	82.4648	6.87207
$145$	11.5600	0.960009
$146$	−26.6631	−2.20665
$147$	7.62735	0.629093
$148$	−45.1728	−3.71318
$149$	−5.11471	−0.419013	−0.209507	−	0.977807i	$-0.567186\pi$
$149$	−5.11471	−0.419013	−0.209507	+	0.977807i	$0.567186\pi$
$150$	72.0930	5.88637
$151$	−23.5475	−1.91626	−0.958132	−	0.286326i	$-0.907566\pi$
$151$	−23.5475	−1.91626	−0.958132	+	0.286326i	$0.907566\pi$
$152$	−22.4690	−1.82248
$153$	−41.0426	−3.31809
$154$	−32.3873	−2.60984
$155$	−17.8985	−1.43764
$156$	63.6886	5.09917
$157$	−8.61895	−0.687867	−0.343934	−	0.938994i	$-0.611760\pi$
$157$	−8.61895	−0.687867	−0.343934	+	0.938994i	$0.611760\pi$
$158$	38.8810	3.09321
$159$	28.8710	2.28962
$160$	−39.4018	−3.11498
$161$	−2.18640	−0.172312
$162$	−93.9973	−7.38512
$163$	−9.04156	−0.708190	−0.354095	−	0.935210i	$-0.615211\pi$
$163$	−9.04156	−0.708190	−0.354095	+	0.935210i	$0.615211\pi$
$164$	−6.04425	−0.471976
$165$	69.5311	5.41299
$166$	3.89979	0.302683
$167$	−20.6179	−1.59546	−0.797730	−	0.603015i	$-0.793966\pi$
$167$	−20.6179	−1.59546	−0.797730	+	0.603015i	$0.793966\pi$
$168$	−54.8399	−4.23099
$169$	2.14325	0.164865
$170$	46.6026	3.57426
$171$	25.1565	1.92376
$172$	−25.6897	−1.95882
$173$	12.1203	0.921488	0.460744	−	0.887533i	$-0.347583\pi$
$173$	12.1203	0.921488	0.460744	+	0.887533i	$0.347583\pi$
$174$	28.1197	2.13175
$175$	−17.7776	−1.34386
$176$	−56.0166	−4.22241
$177$	31.5423	2.37086
$178$	−1.52525	−0.114323
$179$	9.02400	0.674486	0.337243	−	0.941418i	$-0.390506\pi$
$179$	9.02400	0.674486	0.337243	+	0.941418i	$0.390506\pi$
$180$	147.382	10.9852
$181$	6.14583	0.456816	0.228408	−	0.973566i	$-0.426648\pi$
$181$	6.14583	0.456816	0.228408	+	0.973566i	$0.426648\pi$
$182$	−22.1756	−1.64377
$183$	−3.41833	−0.252690
$184$	−7.50656	−0.553391
$185$	−33.7673	−2.48262
$186$	−43.5379	−3.19236
$187$	27.8793	2.03874
$188$	−1.11269	−0.0811516
$189$	39.3838	2.86475
$190$	−28.5644	−2.07228
$191$	−6.22183	−0.450196	−0.225098	−	0.974336i	$-0.572270\pi$
$191$	−6.22183	−0.450196	−0.225098	+	0.974336i	$0.572270\pi$
$192$	−29.3848	−2.12067
$193$	−15.9712	−1.14964	−0.574818	−	0.818282i	$-0.694927\pi$
$193$	−15.9712	−1.14964	−0.574818	+	0.818282i	$0.694927\pi$
$194$	21.2553	1.52604
$195$	47.6081	3.40929
$196$	−10.9822	−0.784439
$197$	16.8874	1.20318	0.601590	−	0.798805i	$-0.294534\pi$
$197$	16.8874	1.20318	0.601590	+	0.798805i	$0.294534\pi$
$198$	124.495	8.84746
$199$	−0.997807	−0.0707327	−0.0353663	−	0.999374i	$-0.511260\pi$
$199$	−0.997807	−0.0707327	−0.0353663	+	0.999374i	$0.511260\pi$
$200$	−61.0358	−4.31588
$201$	14.2439	1.00469
$202$	−48.1767	−3.38970
$203$	−6.93410	−0.486678
$204$	80.2836	5.62098
$205$	−4.51815	−0.315562
$206$	−24.2190	−1.68742
$207$	8.40440	0.584146
$208$	−38.3547	−2.65942
$209$	−17.0883	−1.18202
$210$	−69.7169	−4.81092
$211$	14.4529	0.994982	0.497491	−	0.867469i	$-0.334255\pi$
$211$	14.4529	0.994982	0.497491	+	0.867469i	$0.334255\pi$
$212$	−41.5696	−2.85501
$213$	16.2715	1.11490
$214$	−16.4760	−1.12627
$215$	−19.2034	−1.30966
$216$	135.217	9.20032
$217$	10.7361	0.728815
$218$	32.2739	2.18586
$219$	−34.3357	−2.32019
$220$	−100.114	−6.74965
$221$	19.0890	1.28407
$222$	−82.1386	−5.51278
$223$	−21.4093	−1.43368	−0.716838	−	0.697240i	$-0.754411\pi$
$223$	−21.4093	−1.43368	−0.716838	+	0.697240i	$0.754411\pi$
$224$	23.6345	1.57915
$225$	68.3360	4.55573
$226$	−1.89409	−0.125993
$227$	18.7585	1.24505	0.622524	−	0.782601i	$-0.286107\pi$
$227$	18.7585	1.24505	0.622524	+	0.782601i	$0.286107\pi$
$228$	−49.2087	−3.25893
$229$	3.54506	0.234264	0.117132	−	0.993116i	$-0.462630\pi$
$229$	3.54506	0.234264	0.117132	+	0.993116i	$0.462630\pi$
$230$	−9.54295	−0.629243
$231$	−41.7071	−2.74412
$232$	−23.8068	−1.56300
$233$	−8.91016	−0.583724	−0.291862	−	0.956460i	$-0.594275\pi$
$233$	−8.91016	−0.583724	−0.291862	+	0.956460i	$0.594275\pi$
$234$	85.2419	5.57244
$235$	−0.831753	−0.0542576
$236$	−45.4158	−2.95632
$237$	50.0695	3.25236
$238$	−27.9538	−1.81198
$239$	−0.324371	−0.0209818	−0.0104909	−	0.999945i	$-0.503339\pi$
$239$	−0.324371	−0.0209818	−0.0104909	+	0.999945i	$0.503339\pi$
$240$	−120.581	−7.78349
$241$	17.1949	1.10762	0.553810	−	0.832643i	$-0.313174\pi$
$241$	17.1949	1.10762	0.553810	+	0.832643i	$0.313174\pi$
$242$	−55.7678	−3.58489
$243$	−66.7640	−4.28291
$244$	4.92184	0.315089
$245$	−8.20930	−0.524473
$246$	−10.9904	−0.700720
$247$	−11.7004	−0.744477
$248$	36.8603	2.34063
$249$	5.02200	0.318257
$250$	−30.0922	−1.90320
$251$	22.1029	1.39512	0.697561	−	0.716525i	$-0.254268\pi$
$251$	22.1029	1.39512	0.697561	+	0.716525i	$0.254268\pi$
$252$	−88.4048	−5.56898
$253$	−5.70893	−0.358917
$254$	−33.9241	−2.12859
$255$	60.0131	3.75816
$256$	−14.5468	−0.909175
$257$	26.8063	1.67213	0.836066	−	0.548628i	$-0.184850\pi$
$257$	26.8063	1.67213	0.836066	+	0.548628i	$0.184850\pi$
$258$	−46.7121	−2.90817
$259$	20.2548	1.25857
$260$	−68.5480	−4.25116
$261$	26.6543	1.64986
$262$	57.6395	3.56098
$263$	23.7722	1.46586	0.732928	−	0.680306i	$-0.238153\pi$
$263$	23.7722	1.46586	0.732928	+	0.680306i	$0.238153\pi$
$264$	−143.193	−8.81291
$265$	−31.0738	−1.90885
$266$	17.1339	1.05055
$267$	−1.96416	−0.120205
$268$	−20.5089	−1.25278
$269$	12.3870	0.755249	0.377625	−	0.925959i	$-0.376741\pi$
$269$	12.3870	0.755249	0.377625	+	0.925959i	$0.376741\pi$
$270$	171.898	10.4614
$271$	−29.7418	−1.80669	−0.903344	−	0.428917i	$-0.858895\pi$
$271$	−29.7418	−1.80669	−0.903344	+	0.428917i	$0.858895\pi$
$272$	−48.3485	−2.93156
$273$	−28.5569	−1.72834
$274$	50.2563	3.03609
$275$	−46.4192	−2.79918
$276$	−16.4399	−0.989566
$277$	27.2473	1.63713	0.818565	−	0.574413i	$-0.194770\pi$
$277$	27.2473	1.63713	0.818565	+	0.574413i	$0.194770\pi$
$278$	−10.4115	−0.624441
$279$	−41.2690	−2.47071
$280$	59.0241	3.52736
$281$	−30.6829	−1.83039	−0.915195	−	0.403012i	$-0.867963\pi$
$281$	−30.6829	−1.83039	−0.915195	+	0.403012i	$0.867963\pi$
$282$	−2.02323	−0.120482
$283$	15.7351	0.935357	0.467679	−	0.883899i	$-0.345090\pi$
$283$	15.7351	0.935357	0.467679	+	0.883899i	$0.345090\pi$
$284$	−23.4283	−1.39021
$285$	−36.7842	−2.17891
$286$	−57.9030	−3.42388
$287$	2.71014	0.159975
$288$	−90.8498	−5.35337
$289$	7.06297	0.415469
$290$	−30.2652	−1.77723
$291$	27.3718	1.60456
$292$	49.4378	2.89313
$293$	9.33066	0.545103	0.272552	−	0.962141i	$-0.412132\pi$
$293$	9.33066	0.545103	0.272552	+	0.962141i	$0.412132\pi$
$294$	−19.9691	−1.16462
$295$	−33.9489	−1.97658
$296$	69.5406	4.04197
$297$	102.835	5.96712
$298$	13.3907	0.775705
$299$	−3.90892	−0.226058
$300$	−133.673	−7.71759
$301$	11.5189	0.663936
$302$	61.6492	3.54752
$303$	−62.0401	−3.56411
$304$	29.6346	1.69966
$305$	3.67914	0.210667
$306$	107.453	6.14267
$307$	22.8399	1.30354	0.651772	−	0.758415i	$-0.274026\pi$
$307$	22.8399	1.30354	0.651772	+	0.758415i	$0.274026\pi$
$308$	60.0515	3.42175
$309$	−31.1884	−1.77424
$310$	46.8598	2.66146
$311$	−22.5780	−1.28028	−0.640141	−	0.768257i	$-0.721124\pi$
$311$	−22.5780	−1.28028	−0.640141	+	0.768257i	$0.721124\pi$
$312$	−98.0445	−5.55068
$313$	−21.5233	−1.21657	−0.608285	−	0.793719i	$-0.708142\pi$
$313$	−21.5233	−1.21657	−0.608285	+	0.793719i	$0.708142\pi$
$314$	22.5652	1.27343
$315$	−66.0837	−3.72340
$316$	−72.0920	−4.05549
$317$	−26.1263	−1.46740	−0.733699	−	0.679474i	$-0.762208\pi$
$317$	−26.1263	−1.46740	−0.733699	+	0.679474i	$0.762208\pi$
$318$	−75.5868	−4.23870
$319$	−18.1057	−1.01372
$320$	31.6268	1.76799
$321$	−21.2171	−1.18422
$322$	5.72418	0.318996
$323$	−14.7491	−0.820660
$324$	174.287	9.68260
$325$	−31.7833	−1.76302
$326$	23.6716	1.31105
$327$	41.5611	2.29833
$328$	9.30472	0.513767
$329$	0.498914	0.0275060
$330$	−182.038	−10.0209
$331$	−25.6465	−1.40966	−0.704831	−	0.709375i	$-0.748977\pi$
$331$	−25.6465	−1.40966	−0.704831	+	0.709375i	$0.748977\pi$
$332$	−7.23088	−0.396846
$333$	−77.8581	−4.26660
$334$	53.9794	2.95362
$335$	−15.3307	−0.837603
$336$	72.3287	3.94586
$337$	−3.88890	−0.211842	−0.105921	−	0.994375i	$-0.533779\pi$
$337$	−3.88890	−0.211842	−0.105921	+	0.994375i	$0.533779\pi$
$338$	−5.61121	−0.305210
$339$	−2.43914	−0.132476
$340$	−86.4091	−4.68619
$341$	28.0332	1.51808
$342$	−65.8618	−3.56140
$343$	20.1606	1.08857
$344$	39.5477	2.13227
$345$	−12.2890	−0.661620
$346$	−31.7319	−1.70592
$347$	11.4154	0.612810	0.306405	−	0.951901i	$-0.400874\pi$
$347$	11.4154	0.612810	0.306405	+	0.951901i	$0.400874\pi$
$348$	−52.1386	−2.79492
$349$	17.0860	0.914591	0.457296	−	0.889315i	$-0.348818\pi$
$349$	17.0860	0.914591	0.457296	+	0.889315i	$0.348818\pi$
$350$	46.5432	2.48784
$351$	70.4117	3.75830
$352$	61.7123	3.28928
$353$	1.36994	0.0729146	0.0364573	−	0.999335i	$-0.488393\pi$
$353$	1.36994	0.0729146	0.0364573	+	0.999335i	$0.488393\pi$
$354$	−82.5804	−4.38910
$355$	−17.5130	−0.929492
$356$	2.82808	0.149888
$357$	−35.9979	−1.90521
$358$	−23.6256	−1.24865
$359$	3.68956	0.194728	0.0973638	−	0.995249i	$-0.468959\pi$
$359$	3.68956	0.194728	0.0973638	+	0.995249i	$0.468959\pi$
$360$	−226.885	−11.9579
$361$	−9.95976	−0.524198
$362$	−16.0903	−0.845687
$363$	−71.8156	−3.76934
$364$	41.1174	2.15514
$365$	36.9554	1.93434
$366$	8.94948	0.467797
$367$	−11.1288	−0.580920	−0.290460	−	0.956887i	$-0.593808\pi$
$367$	−11.1288	−0.580920	−0.290460	+	0.956887i	$0.593808\pi$
$368$	9.90047	0.516097
$369$	−10.4176	−0.542320
$370$	88.4056	4.59599
$371$	18.6391	0.967695
$372$	80.7266	4.18548
$373$	−6.28098	−0.325217	−0.162608	−	0.986691i	$-0.551991\pi$
$373$	−6.28098	−0.325217	−0.162608	+	0.986691i	$0.551991\pi$
$374$	−72.9905	−3.77425
$375$	−38.7516	−2.00112
$376$	1.71292	0.0883371
$377$	−12.3970	−0.638478
$378$	−103.110	−5.30342
$379$	9.69666	0.498084	0.249042	−	0.968493i	$-0.419884\pi$
$379$	9.69666	0.498084	0.249042	+	0.968493i	$0.419884\pi$
$380$	52.9633	2.71696
$381$	−43.6862	−2.23811
$382$	16.2893	0.833433
$383$	−28.7181	−1.46743	−0.733714	−	0.679459i	$-0.762215\pi$
$383$	−28.7181	−1.46743	−0.733714	+	0.679459i	$0.762215\pi$
$384$	3.71476	0.189568
$385$	44.8893	2.28777
$386$	41.8141	2.12828
$387$	−44.2778	−2.25077
$388$	−39.4110	−2.00079
$389$	4.91637	0.249270	0.124635	−	0.992203i	$-0.460224\pi$
$389$	4.91637	0.249270	0.124635	+	0.992203i	$0.460224\pi$
$390$	−124.642	−6.31150
$391$	−4.92744	−0.249191
$392$	16.9063	0.853898
$393$	74.2260	3.74420
$394$	−44.2127	−2.22740
$395$	−53.8897	−2.71148
$396$	−230.834	−11.5999
$397$	−18.7084	−0.938947	−0.469473	−	0.882947i	$-0.655556\pi$
$397$	−18.7084	−0.938947	−0.469473	+	0.882947i	$0.655556\pi$
$398$	2.61234	0.130945
$399$	22.0644	1.10460
$400$	80.5005	4.02503
$401$	2.59028	0.129352	0.0646762	−	0.997906i	$-0.479399\pi$
$401$	2.59028	0.129352	0.0646762	+	0.997906i	$0.479399\pi$
$402$	−37.2917	−1.85994
$403$	19.1944	0.956140
$404$	89.3277	4.44422
$405$	130.282	6.47375
$406$	18.1541	0.900971
$407$	52.8874	2.62153
$408$	−123.591	−6.11869
$409$	10.9505	0.541466	0.270733	−	0.962654i	$-0.412734\pi$
$409$	10.9505	0.541466	0.270733	+	0.962654i	$0.412734\pi$
$410$	11.8289	0.584188
$411$	64.7181	3.19231
$412$	44.9062	2.21237
$413$	20.3637	1.00203
$414$	−22.0034	−1.08141
$415$	−5.40517	−0.265330
$416$	42.2546	2.07170
$417$	−13.4075	−0.656570
$418$	44.7385	2.18823
$419$	−8.89545	−0.434571	−0.217286	−	0.976108i	$-0.569720\pi$
$419$	−8.89545	−0.434571	−0.217286	+	0.976108i	$0.569720\pi$
$420$	129.267	6.30757
$421$	−40.1677	−1.95766	−0.978828	−	0.204686i	$-0.934383\pi$
$421$	−40.1677	−1.95766	−0.978828	+	0.204686i	$0.934383\pi$
$422$	−37.8390	−1.84198
$423$	−1.91780	−0.0932465
$424$	63.9937	3.10781
$425$	−40.0649	−1.94343
$426$	−42.6001	−2.06398
$427$	−2.20687	−0.106798
$428$	30.5492	1.47665
$429$	−74.5653	−3.60004
$430$	50.2762	2.42453
$431$	13.4589	0.648290	0.324145	−	0.946007i	$-0.394923\pi$
$431$	13.4589	0.648290	0.324145	+	0.946007i	$0.394923\pi$
$432$	−178.338	−8.58030
$433$	−15.5724	−0.748360	−0.374180	−	0.927356i	$-0.622076\pi$
$433$	−15.5724	−0.748360	−0.374180	+	0.927356i	$0.622076\pi$
$434$	−28.1081	−1.34923
$435$	−38.9743	−1.86868
$436$	−59.8412	−2.86588
$437$	3.02021	0.144476
$438$	89.8937	4.29529
$439$	35.0255	1.67168	0.835839	−	0.548975i	$-0.184982\pi$
$439$	35.0255	1.67168	0.835839	+	0.548975i	$0.184982\pi$
$440$	154.118	7.34730
$441$	−18.9284	−0.901353
$442$	−49.9767	−2.37715
$443$	23.5558	1.11917	0.559585	−	0.828773i	$-0.310961\pi$
$443$	23.5558	1.11917	0.559585	+	0.828773i	$0.310961\pi$
$444$	152.299	7.22778
$445$	2.11402	0.100214
$446$	56.0515	2.65412
$447$	17.2441	0.815617
$448$	−18.9708	−0.896288
$449$	−2.33777	−0.110326	−0.0551632	−	0.998477i	$-0.517568\pi$
$449$	−2.33777	−0.110326	−0.0551632	+	0.998477i	$0.517568\pi$
$450$	−178.910	−8.43388
$451$	7.07647	0.333218
$452$	3.51197	0.165189
$453$	79.3895	3.73004
$454$	−49.1115	−2.30491
$455$	30.7358	1.44092
$456$	75.7537	3.54749
$457$	−16.6574	−0.779199	−0.389600	−	0.920984i	$-0.627387\pi$
$457$	−16.6574	−0.779199	−0.389600	+	0.920984i	$0.627387\pi$
$458$	−9.28128	−0.433686
$459$	88.7585	4.14289
$460$	17.6942	0.824998
$461$	−28.9584	−1.34873	−0.674363	−	0.738400i	$-0.735582\pi$
$461$	−28.9584	−1.34873	−0.674363	+	0.738400i	$0.735582\pi$
$462$	109.193	5.08010
$463$	−0.195048	−0.00906467	−0.00453234	−	0.999990i	$-0.501443\pi$
$463$	−0.195048	−0.00906467	−0.00453234	+	0.999990i	$0.501443\pi$
$464$	31.3990	1.45766
$465$	60.3442	2.79840
$466$	23.3276	1.08063
$467$	−0.436989	−0.0202215	−0.0101107	−	0.999949i	$-0.503218\pi$
$467$	−0.436989	−0.0202215	−0.0101107	+	0.999949i	$0.503218\pi$
$468$	−158.053	−7.30600
$469$	9.19585	0.424625
$470$	2.17760	0.100445
$471$	29.0585	1.33895
$472$	69.9147	3.21808
$473$	30.0770	1.38294
$474$	−131.086	−6.02099
$475$	24.5573	1.12676
$476$	51.8311	2.37567
$477$	−71.6477	−3.28052
$478$	0.849231	0.0388429
$479$	−26.9684	−1.23222	−0.616108	−	0.787662i	$-0.711291\pi$
$479$	−26.9684	−1.23222	−0.616108	+	0.787662i	$0.711291\pi$
$480$	132.842	6.06338
$481$	36.2121	1.65113
$482$	−45.0177	−2.05050
$483$	7.37138	0.335409
$484$	103.403	4.70013
$485$	−29.4602	−1.33772
$486$	174.794	7.92881
$487$	15.0000	0.679715	0.339858	−	0.940477i	$-0.389621\pi$
$487$	15.0000	0.679715	0.339858	+	0.940477i	$0.389621\pi$
$488$	−7.57685	−0.342988
$489$	30.4833	1.37850
$490$	21.4927	0.970939
$491$	−7.32141	−0.330411	−0.165205	−	0.986259i	$-0.552829\pi$
$491$	−7.32141	−0.330411	−0.165205	+	0.986259i	$0.552829\pi$
$492$	20.3780	0.918711
$493$	−15.6272	−0.703815
$494$	30.6326	1.37822
$495$	−172.552	−7.75563
$496$	−48.6153	−2.18289
$497$	10.5049	0.471208
$498$	−13.1480	−0.589178
$499$	−34.6430	−1.55083	−0.775416	−	0.631451i	$-0.782460\pi$
$499$	−34.6430	−1.55083	−0.775416	+	0.631451i	$0.782460\pi$
$500$	55.7961	2.49528
$501$	69.5126	3.10559
$502$	−57.8673	−2.58274
$503$	−14.4771	−0.645500	−0.322750	−	0.946484i	$-0.604607\pi$
$503$	−14.4771	−0.645500	−0.322750	+	0.946484i	$0.604607\pi$
$504$	136.093	6.06208
$505$	66.7736	2.97139
$506$	14.9465	0.664451
$507$	−7.22590	−0.320914
$508$	62.9011	2.79078
$509$	5.00509	0.221847	0.110923	−	0.993829i	$-0.464619\pi$
$509$	5.00509	0.221847	0.110923	+	0.993829i	$0.464619\pi$
$510$	−157.119	−6.95736
$511$	−22.1671	−0.980615
$512$	40.2884	1.78051
$513$	−54.4033	−2.40196
$514$	−70.1813	−3.09556
$515$	33.5680	1.47918
$516$	86.6122	3.81289
$517$	1.30272	0.0572935
$518$	−53.0287	−2.32995
$519$	−40.8632	−1.79369
$520$	105.525	4.62758
$521$	13.7342	0.601708	0.300854	−	0.953670i	$-0.402728\pi$
$521$	13.7342	0.601708	0.300854	+	0.953670i	$0.402728\pi$
$522$	−69.7832	−3.05433
$523$	−35.6959	−1.56087	−0.780437	−	0.625235i	$-0.785003\pi$
$523$	−35.6959	−1.56087	−0.780437	+	0.625235i	$0.785003\pi$
$524$	−106.873	−4.66879
$525$	59.9366	2.61585
$526$	−62.2376	−2.71369
$527$	24.1958	1.05398
$528$	188.858	8.21900
$529$	−21.9910	−0.956130
$530$	81.3539	3.53379
$531$	−78.2769	−3.39693
$532$	−31.7692	−1.37737
$533$	4.84528	0.209872
$534$	5.14234	0.222531
$535$	22.8360	0.987285
$536$	31.5721	1.36371
$537$	−30.4241	−1.31290
$538$	−32.4302	−1.39817
$539$	12.8577	0.553819
$540$	−318.728	−13.7159
$541$	3.02386	0.130006	0.0650029	−	0.997885i	$-0.479294\pi$
$541$	3.02386	0.130006	0.0650029	+	0.997885i	$0.479294\pi$
$542$	77.8667	3.34466
$543$	−20.7205	−0.889200
$544$	53.2646	2.28370
$545$	−44.7321	−1.91611
$546$	74.7645	3.19963
$547$	7.00312	0.299432	0.149716	−	0.988729i	$-0.452164\pi$
$547$	7.00312	0.299432	0.149716	+	0.988729i	$0.452164\pi$
$548$	−93.1836	−3.98061
$549$	8.48309	0.362050
$550$	121.529	5.18203
$551$	9.57849	0.408058
$552$	25.3082	1.07719
$553$	32.3249	1.37459
$554$	−71.3357	−3.03076
$555$	113.845	4.83247
$556$	19.3047	0.818701
$557$	4.87347	0.206495	0.103248	−	0.994656i	$-0.467077\pi$
$557$	4.87347	0.206495	0.103248	+	0.994656i	$0.467077\pi$
$558$	108.046	4.57395
$559$	20.5938	0.871024
$560$	−77.8473	−3.28965
$561$	−93.9943	−3.96844
$562$	80.3305	3.38854
$563$	−10.2589	−0.432362	−0.216181	−	0.976353i	$-0.569360\pi$
$563$	−10.2589	−0.432362	−0.216181	+	0.976353i	$0.569360\pi$
$564$	3.75141	0.157963
$565$	2.62524	0.110445
$566$	−41.1959	−1.73159
$567$	−78.1473	−3.28188
$568$	36.0664	1.51331
$569$	−44.9732	−1.88537	−0.942687	−	0.333678i	$-0.891710\pi$
$569$	−44.9732	−1.88537	−0.942687	+	0.333678i	$0.891710\pi$
$570$	96.3041	4.03374
$571$	−2.23429	−0.0935022	−0.0467511	−	0.998907i	$-0.514887\pi$
$571$	−2.23429	−0.0935022	−0.0467511	+	0.998907i	$0.514887\pi$
$572$	107.362	4.48903
$573$	20.9767	0.876315
$574$	−7.09538	−0.296155
$575$	8.20421	0.342139
$576$	72.9228	3.03845
$577$	9.18651	0.382439	0.191220	−	0.981547i	$-0.438756\pi$
$577$	9.18651	0.382439	0.191220	+	0.981547i	$0.438756\pi$
$578$	−18.4914	−0.769143
$579$	53.8466	2.23779
$580$	56.1167	2.33012
$581$	3.24221	0.134509
$582$	−71.6617	−2.97047
$583$	48.6688	2.01565
$584$	−76.1063	−3.14930
$585$	−118.147	−4.88476
$586$	−24.4285	−1.00913
$587$	−24.9695	−1.03060	−0.515300	−	0.857010i	$-0.672320\pi$
$587$	−24.9695	−1.03060	−0.515300	+	0.857010i	$0.672320\pi$
$588$	37.0260	1.52693
$589$	−14.8305	−0.611078
$590$	88.8811	3.65918
$591$	−56.9354	−2.34201
$592$	−91.7177	−3.76957
$593$	−23.2337	−0.954094	−0.477047	−	0.878878i	$-0.658293\pi$
$593$	−23.2337	−0.954094	−0.477047	+	0.878878i	$0.658293\pi$
$594$	−269.232	−11.0467
$595$	38.7444	1.58837
$596$	−24.8287	−1.01702
$597$	3.36408	0.137682
$598$	10.2339	0.418494
$599$	43.7371	1.78705	0.893524	−	0.449016i	$-0.148225\pi$
$599$	43.7371	1.78705	0.893524	+	0.449016i	$0.148225\pi$
$600$	205.780	8.40094
$601$	−5.55625	−0.226644	−0.113322	−	0.993558i	$-0.536149\pi$
$601$	−5.55625	−0.226644	−0.113322	+	0.993558i	$0.536149\pi$
$602$	−30.1574	−1.22912
$603$	−35.3483	−1.43949
$604$	−114.308	−4.65113
$605$	77.2950	3.14249
$606$	162.426	6.59812
$607$	3.78453	0.153609	0.0768046	−	0.997046i	$-0.475528\pi$
$607$	3.78453	0.153609	0.0768046	+	0.997046i	$0.475528\pi$
$608$	−32.6478	−1.32404
$609$	23.3781	0.947329
$610$	−9.63231	−0.390001
$611$	0.891974	0.0360854
$612$	−199.236	−8.05363
$613$	11.6003	0.468533	0.234266	−	0.972172i	$-0.424731\pi$
$613$	11.6003	0.468533	0.234266	+	0.972172i	$0.424731\pi$
$614$	−59.7969	−2.41321
$615$	15.2328	0.614246
$616$	−92.4453	−3.72473
$617$	27.7427	1.11688	0.558440	−	0.829545i	$-0.311400\pi$
$617$	27.7427	1.11688	0.558440	+	0.829545i	$0.311400\pi$
$618$	81.6538	3.28460
$619$	−28.0199	−1.12622	−0.563108	−	0.826383i	$-0.690394\pi$
$619$	−28.0199	−1.12622	−0.563108	+	0.826383i	$0.690394\pi$
$620$	−86.8859	−3.48942
$621$	−18.1753	−0.729351
$622$	59.1112	2.37014
$623$	−1.26806	−0.0508039
$624$	129.312	5.17661
$625$	0.870715	0.0348286
$626$	56.3499	2.25219
$627$	57.6125	2.30082
$628$	−41.8396	−1.66958
$629$	45.6477	1.82009
$630$	173.013	6.89300
$631$	−29.0374	−1.15596	−0.577980	−	0.816051i	$-0.696159\pi$
$631$	−29.0374	−1.15596	−0.577980	+	0.816051i	$0.696159\pi$
$632$	110.981	4.41458
$633$	−48.7277	−1.93675
$634$	68.4009	2.71655
$635$	47.0194	1.86591
$636$	140.151	5.55733
$637$	8.80367	0.348814
$638$	47.4022	1.87667
$639$	−40.3801	−1.59741
$640$	−3.99819	−0.158042
$641$	16.6843	0.658989	0.329495	−	0.944157i	$-0.393122\pi$
$641$	16.6843	0.658989	0.329495	+	0.944157i	$0.393122\pi$
$642$	55.5483	2.19232
$643$	−8.56361	−0.337716	−0.168858	−	0.985640i	$-0.554008\pi$
$643$	−8.56361	−0.337716	−0.168858	+	0.985640i	$0.554008\pi$
$644$	−10.6136	−0.418234
$645$	64.7437	2.54928
$646$	38.6143	1.51926
$647$	48.2731	1.89781	0.948906	−	0.315558i	$-0.102192\pi$
$647$	48.2731	1.89781	0.948906	+	0.315558i	$0.102192\pi$
$648$	−268.303	−10.5399
$649$	53.1718	2.08718
$650$	83.2115	3.26382
$651$	−36.1965	−1.41865
$652$	−43.8911	−1.71891
$653$	−21.5108	−0.841784	−0.420892	−	0.907111i	$-0.638283\pi$
$653$	−21.5108	−0.841784	−0.420892	+	0.907111i	$0.638283\pi$
$654$	−108.810	−4.25483
$655$	−79.8893	−3.12153
$656$	−12.2721	−0.479144
$657$	85.2091	3.32432
$658$	−1.30620	−0.0509209
$659$	38.6137	1.50418	0.752089	−	0.659062i	$-0.229047\pi$
$659$	38.6137	1.50418	0.752089	+	0.659062i	$0.229047\pi$
$660$	337.530	13.1383
$661$	20.2078	0.785993	0.392997	−	0.919540i	$-0.371438\pi$
$661$	20.2078	0.785993	0.392997	+	0.919540i	$0.371438\pi$
$662$	67.1448	2.60966
$663$	−64.3581	−2.49946
$664$	11.1315	0.431985
$665$	−23.7479	−0.920903
$666$	203.839	7.89861
$667$	3.20003	0.123906
$668$	−100.087	−3.87248
$669$	72.1810	2.79068
$670$	40.1370	1.55063
$671$	−5.76239	−0.222454
$672$	−79.6831	−3.07384
$673$	−44.4790	−1.71454	−0.857270	−	0.514867i	$-0.827841\pi$
$673$	−44.4790	−1.71454	−0.857270	+	0.514867i	$0.827841\pi$
$674$	10.1815	0.392176
$675$	−147.783	−5.68818
$676$	10.4041	0.400159
$677$	−36.6478	−1.40849	−0.704245	−	0.709957i	$-0.748714\pi$
$677$	−36.6478	−1.40849	−0.704245	+	0.709957i	$0.748714\pi$
$678$	6.38588	0.245248
$679$	17.6712	0.678160
$680$	133.021	5.10113
$681$	−63.2438	−2.42351
$682$	−73.3933	−2.81037
$683$	52.1166	1.99419	0.997093	−	0.0761997i	$-0.0242787\pi$
$683$	52.1166	1.99419	0.997093	+	0.0761997i	$0.0242787\pi$
$684$	122.119	4.66933
$685$	−69.6560	−2.66142
$686$	−52.7821	−2.01523
$687$	−11.9521	−0.456000
$688$	−52.1598	−1.98857
$689$	33.3236	1.26953
$690$	32.1738	1.22483
$691$	−42.4202	−1.61374	−0.806871	−	0.590728i	$-0.798841\pi$
$691$	−42.4202	−1.61374	−0.806871	+	0.590728i	$0.798841\pi$
$692$	58.8364	2.23662
$693$	103.502	3.93173
$694$	−29.8865	−1.13447
$695$	14.4305	0.547380
$696$	80.2640	3.04240
$697$	6.10778	0.231349
$698$	−44.7325	−1.69315
$699$	30.0403	1.13623
$700$	−86.2990	−3.26180
$701$	27.2622	1.02968	0.514839	−	0.857287i	$-0.327852\pi$
$701$	27.2622	1.02968	0.514839	+	0.857287i	$0.327852\pi$
$702$	−184.344	−6.95761
$703$	−27.9791	−1.05525
$704$	−49.5349	−1.86692
$705$	2.80423	0.105613
$706$	−3.58662	−0.134984
$707$	−40.0531	−1.50635
$708$	153.118	5.75453
$709$	−5.14111	−0.193078	−0.0965391	−	0.995329i	$-0.530777\pi$
$709$	−5.14111	−0.193078	−0.0965391	+	0.995329i	$0.530777\pi$
$710$	45.8505	1.72074
$711$	−124.255	−4.65992
$712$	−4.35364	−0.163160
$713$	−4.95463	−0.185552
$714$	94.2455	3.52705
$715$	80.2545	3.00135
$716$	43.8059	1.63710
$717$	1.09361	0.0408415
$718$	−9.65958	−0.360492
$719$	48.4957	1.80858	0.904292	−	0.426914i	$-0.140399\pi$
$719$	48.4957	1.80858	0.904292	+	0.426914i	$0.140399\pi$
$720$	299.241	11.1520
$721$	−20.1352	−0.749874
$722$	26.0755	0.970430
$723$	−57.9720	−2.15600
$724$	29.8341	1.10878
$725$	26.0194	0.966336
$726$	188.019	6.97805
$727$	13.9737	0.518258	0.259129	−	0.965843i	$-0.416565\pi$
$727$	13.9737	0.518258	0.259129	+	0.965843i	$0.416565\pi$
$728$	−63.2975	−2.34596
$729$	117.383	4.34754
$730$	−96.7525	−3.58097
$731$	25.9598	0.960158
$732$	−16.5938	−0.613326
$733$	−15.0944	−0.557525	−0.278763	−	0.960360i	$-0.589924\pi$
$733$	−15.0944	−0.557525	−0.278763	+	0.960360i	$0.589924\pi$
$734$	29.1362	1.07544
$735$	27.6774	1.02090
$736$	−10.9071	−0.402042
$737$	24.0114	0.884470
$738$	27.2742	1.00398
$739$	39.3054	1.44587	0.722937	−	0.690914i	$-0.242792\pi$
$739$	39.3054	1.44587	0.722937	+	0.690914i	$0.242792\pi$
$740$	−163.919	−6.02578
$741$	39.4474	1.44914
$742$	−48.7988	−1.79146
$743$	−32.8300	−1.20441	−0.602207	−	0.798340i	$-0.705712\pi$
$743$	−32.8300	−1.20441	−0.602207	+	0.798340i	$0.705712\pi$
$744$	−124.273	−4.55608
$745$	−18.5598	−0.679978
$746$	16.4441	0.602063
$747$	−12.4629	−0.455992
$748$	135.337	4.94840
$749$	−13.6978	−0.500506
$750$	101.455	3.70461
$751$	33.2676	1.21395	0.606976	−	0.794720i	$-0.292382\pi$
$751$	33.2676	1.21395	0.606976	+	0.794720i	$0.292382\pi$
$752$	−2.25918	−0.0823840
$753$	−74.5193	−2.71563
$754$	32.4564	1.18199
$755$	−85.4468	−3.10973
$756$	191.184	6.95329
$757$	3.38338	0.122971	0.0614855	−	0.998108i	$-0.480416\pi$
$757$	3.38338	0.122971	0.0614855	+	0.998108i	$0.480416\pi$
$758$	−25.3867	−0.922086
$759$	19.2475	0.698639
$760$	−81.5335	−2.95753
$761$	36.2469	1.31395	0.656975	−	0.753912i	$-0.271836\pi$
$761$	36.2469	1.31395	0.656975	+	0.753912i	$0.271836\pi$
$762$	114.374	4.14334
$763$	26.8318	0.971377
$764$	−30.2031	−1.09271
$765$	−148.931	−5.38463
$766$	75.1865	2.71660
$767$	36.4069	1.31458
$768$	49.0441	1.76973
$769$	5.33480	0.192378	0.0961888	−	0.995363i	$-0.469335\pi$
$769$	5.33480	0.192378	0.0961888	+	0.995363i	$0.469335\pi$
$770$	−117.524	−4.23527
$771$	−90.3767	−3.25484
$772$	−77.5303	−2.79038
$773$	37.0231	1.33163	0.665814	−	0.746118i	$-0.268085\pi$
$773$	37.0231	1.33163	0.665814	+	0.746118i	$0.268085\pi$
$774$	115.923	4.16677
$775$	−40.2860	−1.44712
$776$	60.6707	2.17795
$777$	−68.2883	−2.44983
$778$	−12.8715	−0.461465
$779$	−3.74368	−0.134131
$780$	231.107	8.27497
$781$	27.4294	0.981500
$782$	12.9005	0.461320
$783$	−57.6425	−2.05997
$784$	−22.2979	−0.796352
$785$	−31.2756	−1.11628
$786$	−194.330	−6.93152
$787$	9.00298	0.320922	0.160461	−	0.987042i	$-0.448702\pi$
$787$	9.00298	0.320922	0.160461	+	0.987042i	$0.448702\pi$
$788$	81.9778	2.92034
$789$	−80.1472	−2.85332
$790$	141.088	5.01968
$791$	−1.57471	−0.0559902
$792$	355.355	12.6270
$793$	−3.94552	−0.140109
$794$	48.9802	1.73824
$795$	104.764	3.71561
$796$	−4.84373	−0.171681
$797$	−39.0230	−1.38227	−0.691133	−	0.722727i	$-0.742888\pi$
$797$	−39.0230	−1.38227	−0.691133	+	0.722727i	$0.742888\pi$
$798$	−57.7665	−2.04491
$799$	1.12439	0.0397781
$800$	−88.6858	−3.13552
$801$	4.87436	0.172227
$802$	−6.78158	−0.239466
$803$	−57.8807	−2.04257
$804$	69.1451	2.43856
$805$	−7.93380	−0.279630
$806$	−50.2525	−1.77007
$807$	−41.7624	−1.47011
$808$	−137.514	−4.83773
$809$	−2.59145	−0.0911106	−0.0455553	−	0.998962i	$-0.514506\pi$
$809$	−2.59145	−0.0911106	−0.0455553	+	0.998962i	$0.514506\pi$
$810$	−341.088	−11.9846
$811$	−37.8238	−1.32817	−0.664086	−	0.747656i	$-0.731179\pi$
$811$	−37.8238	−1.32817	−0.664086	+	0.747656i	$0.731179\pi$
$812$	−33.6607	−1.18126
$813$	100.274	3.51675
$814$	−138.464	−4.85315
$815$	−32.8092	−1.14925
$816$	163.006	5.70634
$817$	−15.9117	−0.556680
$818$	−28.6693	−1.00240
$819$	70.8683	2.47634
$820$	−21.9328	−0.765927
$821$	43.8766	1.53130	0.765652	−	0.643255i	$-0.222417\pi$
$821$	43.8766	1.53130	0.765652	+	0.643255i	$0.222417\pi$
$822$	−169.438	−5.90981
$823$	34.4813	1.20194	0.600972	−	0.799270i	$-0.294780\pi$
$823$	34.4813	1.20194	0.600972	+	0.799270i	$0.294780\pi$
$824$	−69.1302	−2.40826
$825$	156.501	5.44866
$826$	−53.3139	−1.85503
$827$	40.2493	1.39961	0.699803	−	0.714336i	$-0.253271\pi$
$827$	40.2493	1.39961	0.699803	+	0.714336i	$0.253271\pi$
$828$	40.7981	1.41783
$829$	−31.7610	−1.10311	−0.551553	−	0.834140i	$-0.685965\pi$
$829$	−31.7610	−1.10311	−0.551553	+	0.834140i	$0.685965\pi$
$830$	14.1512	0.491196
$831$	−91.8634	−3.18671
$832$	−33.9167	−1.17585
$833$	11.0976	0.384509
$834$	35.1021	1.21549
$835$	−74.8163	−2.58912
$836$	−82.9527	−2.86898
$837$	89.2483	3.08487
$838$	23.2891	0.804507
$839$	−1.35259	−0.0466964	−0.0233482	−	0.999727i	$-0.507433\pi$
$839$	−1.35259	−0.0466964	−0.0233482	+	0.999727i	$0.507433\pi$
$840$	−198.998	−6.86608
$841$	−18.8512	−0.650041
$842$	105.163	3.62414
$843$	103.447	3.56289
$844$	70.1600	2.41501
$845$	7.77723	0.267545
$846$	5.02096	0.172624
$847$	−46.3641	−1.59309
$848$	−84.4018	−2.89837
$849$	−53.0506	−1.82069
$850$	104.893	3.59782
$851$	−9.34740	−0.320425
$852$	78.9878	2.70608
$853$	−31.3775	−1.07435	−0.537173	−	0.843472i	$-0.680508\pi$
$853$	−31.3775	−1.07435	−0.537173	+	0.843472i	$0.680508\pi$
$854$	5.77778	0.197712
$855$	91.2855	3.12190
$856$	−47.0286	−1.60740
$857$	−18.9530	−0.647421	−0.323711	−	0.946156i	$-0.604930\pi$
$857$	−18.9530	−0.647421	−0.323711	+	0.946156i	$0.604930\pi$
$858$	195.218	6.66464
$859$	5.15902	0.176024	0.0880118	−	0.996119i	$-0.471949\pi$
$859$	5.15902	0.176024	0.0880118	+	0.996119i	$0.471949\pi$
$860$	−93.2205	−3.17879
$861$	−9.13716	−0.311394
$862$	−35.2364	−1.20016
$863$	−29.4534	−1.00261	−0.501303	−	0.865272i	$-0.667146\pi$
$863$	−29.4534	−1.00261	−0.501303	+	0.865272i	$0.667146\pi$
$864$	196.471	6.68409
$865$	43.9810	1.49540
$866$	40.7698	1.38541
$867$	−23.8126	−0.808717
$868$	52.1171	1.76897
$869$	84.4037	2.86320
$870$	102.038	3.45941
$871$	16.4406	0.557069
$872$	92.1217	3.11963
$873$	−67.9273	−2.29899
$874$	−7.90716	−0.267464
$875$	−25.0180	−0.845764
$876$	−166.678	−5.63153
$877$	−30.5542	−1.03174	−0.515871	−	0.856666i	$-0.672532\pi$
$877$	−30.5542	−1.03174	−0.515871	+	0.856666i	$0.672532\pi$
$878$	−91.6998	−3.09472
$879$	−31.4581	−1.06105
$880$	−203.268	−6.85215
$881$	8.45654	0.284908	0.142454	−	0.989801i	$-0.454501\pi$
$881$	8.45654	0.284908	0.142454	+	0.989801i	$0.454501\pi$
$882$	49.5562	1.66864
$883$	9.13229	0.307326	0.153663	−	0.988123i	$-0.450893\pi$
$883$	9.13229	0.307326	0.153663	+	0.988123i	$0.450893\pi$
$884$	92.6653	3.11667
$885$	114.458	3.84745
$886$	−61.6711	−2.07188
$887$	−27.7218	−0.930808	−0.465404	−	0.885098i	$-0.654091\pi$
$887$	−27.7218	−0.930808	−0.465404	+	0.885098i	$0.654091\pi$
$888$	−234.454	−7.86777
$889$	−28.2038	−0.945925
$890$	−5.53470	−0.185523
$891$	−204.051	−6.83597
$892$	−103.929	−3.47980
$893$	−0.689180	−0.0230625
$894$	−45.1465	−1.50992
$895$	32.7455	1.09456
$896$	2.39825	0.0801199
$897$	13.1788	0.440027
$898$	6.12049	0.204243
$899$	−15.7135	−0.524073
$900$	331.728	11.0576
$901$	42.0066	1.39944
$902$	−18.5268	−0.616875
$903$	−38.8355	−1.29236
$904$	−5.40645	−0.179816
$905$	22.3014	0.741324
$906$	−207.849	−6.90531
$907$	−16.8880	−0.560758	−0.280379	−	0.959889i	$-0.590460\pi$
$907$	−16.8880	−0.560758	−0.280379	+	0.959889i	$0.590460\pi$
$908$	91.0609	3.02196
$909$	153.962	5.10659
$910$	−80.4689	−2.66752
$911$	−42.7644	−1.41685	−0.708424	−	0.705787i	$-0.750593\pi$
$911$	−42.7644	−1.41685	−0.708424	+	0.705787i	$0.750593\pi$
$912$	−99.9121	−3.30842
$913$	8.46575	0.280176
$914$	43.6104	1.44251
$915$	−12.4041	−0.410067
$916$	17.2091	0.568603
$917$	47.9203	1.58247
$918$	−232.377	−7.66959
$919$	−39.3199	−1.29704	−0.648521	−	0.761197i	$-0.724612\pi$
$919$	−39.3199	−1.29704	−0.648521	+	0.761197i	$0.724612\pi$
$920$	−27.2391	−0.898047
$921$	−77.0042	−2.53737
$922$	75.8155	2.49685
$923$	18.7809	0.618182
$924$	−202.462	−6.66050
$925$	−76.0036	−2.49898
$926$	0.510654	0.0167811
$927$	77.3986	2.54210
$928$	−34.5917	−1.13553
$929$	−12.5528	−0.411843	−0.205922	−	0.978568i	$-0.566019\pi$
$929$	−12.5528	−0.411843	−0.205922	+	0.978568i	$0.566019\pi$
$930$	−157.986	−5.18058
$931$	−6.80212	−0.222931
$932$	−43.2532	−1.41681
$933$	76.1212	2.49209
$934$	1.14408	0.0374353
$935$	101.166	3.30848
$936$	243.312	7.95291
$937$	30.0404	0.981376	0.490688	−	0.871335i	$-0.336746\pi$
$937$	30.0404	0.981376	0.490688	+	0.871335i	$0.336746\pi$
$938$	−24.0755	−0.786093
$939$	72.5652	2.36808
$940$	−4.03764	−0.131693
$941$	42.7095	1.39229	0.696146	−	0.717900i	$-0.254897\pi$
$941$	42.7095	1.39229	0.696146	+	0.717900i	$0.254897\pi$
$942$	−76.0777	−2.47875
$943$	−1.25071	−0.0407287
$944$	−92.2110	−3.00121
$945$	142.912	4.64894
$946$	−78.7441	−2.56019
$947$	−19.0392	−0.618691	−0.309345	−	0.950950i	$-0.600110\pi$
$947$	−19.0392	−0.618691	−0.309345	+	0.950950i	$0.600110\pi$
$948$	243.056	7.89409
$949$	−39.6311	−1.28648
$950$	−64.2930	−2.08594
$951$	88.0840	2.85632
$952$	−79.7906	−2.58603
$953$	−3.48043	−0.112742	−0.0563710	−	0.998410i	$-0.517953\pi$
$953$	−3.48043	−0.112742	−0.0563710	+	0.998410i	$0.517953\pi$
$954$	187.580	6.07312
$955$	−22.5772	−0.730581
$956$	−1.57462	−0.0509268
$957$	61.0428	1.97323
$958$	70.6055	2.28116
$959$	41.7820	1.34921
$960$	−106.629	−3.44143
$961$	−6.67073	−0.215185
$962$	−94.8064	−3.05668
$963$	52.6535	1.69674
$964$	83.4703	2.68840
$965$	−57.9550	−1.86564
$966$	−19.2989	−0.620932
$967$	−21.7410	−0.699142	−0.349571	−	0.936910i	$-0.613673\pi$
$967$	−21.7410	−0.699142	−0.349571	+	0.936910i	$0.613673\pi$
$968$	−159.182	−5.11630
$969$	49.7260	1.59743
$970$	77.1294	2.47648
$971$	42.3396	1.35874	0.679371	−	0.733795i	$-0.262253\pi$
$971$	42.3396	1.35874	0.679371	+	0.733795i	$0.262253\pi$
$972$	−324.097	−10.3954
$973$	−8.65591	−0.277496
$974$	−39.2713	−1.25833
$975$	107.157	3.43176
$976$	9.99317	0.319874
$977$	49.8498	1.59484	0.797418	−	0.603427i	$-0.206199\pi$
$977$	49.8498	1.59484	0.797418	+	0.603427i	$0.206199\pi$
$978$	−79.8080	−2.55198
$979$	−3.31105	−0.105822
$980$	−39.8510	−1.27299
$981$	−103.140	−3.29301
$982$	19.1681	0.611678
$983$	16.8279	0.536727	0.268364	−	0.963318i	$-0.413517\pi$
$983$	16.8279	0.536727	0.268364	+	0.963318i	$0.413517\pi$
$984$	−31.3706	−1.00006
$985$	61.2795	1.95253
$986$	40.9134	1.30295
$987$	−1.68207	−0.0535410
$988$	−56.7979	−1.80698
$989$	−5.31586	−0.169034
$990$	451.755	14.3577
$991$	31.1482	0.989455	0.494728	−	0.869048i	$-0.335268\pi$
$991$	31.1482	0.989455	0.494728	+	0.869048i	$0.335268\pi$
$992$	53.5585	1.70048
$993$	86.4665	2.74393
$994$	−27.5026	−0.872331
$995$	−3.62075	−0.114785
$996$	24.3787	0.772468
$997$	17.0965	0.541451	0.270726	−	0.962657i	$-0.412736\pi$
$997$	17.0965	0.541451	0.270726	+	0.962657i	$0.412736\pi$
$998$	90.6983	2.87100
$999$	168.376	5.32717

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.14	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.14	✓	358	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:	\( N \)	\(=\)	\( 8011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61809 q^{2} -3.37147 q^{3} +4.85437 q^{4} +3.62871 q^{5} +8.82680 q^{6} -2.17662 q^{7} -7.47299 q^{8} +8.36681 q^{9} +O(q^{10})\)	\(q-2.61809 q^{2} -3.37147 q^{3} +4.85437 q^{4} +3.62871 q^{5} +8.82680 q^{6} -2.17662 q^{7} -7.47299 q^{8} +8.36681 q^{9} -9.50027 q^{10} -5.68339 q^{11} -16.3664 q^{12} -3.89143 q^{13} +5.69858 q^{14} -12.2341 q^{15} +9.85618 q^{16} -4.90540 q^{17} -21.9050 q^{18} +3.00670 q^{19} +17.6151 q^{20} +7.33841 q^{21} +14.8796 q^{22} +1.00449 q^{23} +25.1950 q^{24} +8.16751 q^{25} +10.1881 q^{26} -18.0940 q^{27} -10.5661 q^{28} +3.18572 q^{29} +32.0299 q^{30} -4.93247 q^{31} -10.8584 q^{32} +19.1614 q^{33} +12.8428 q^{34} -7.89832 q^{35} +40.6156 q^{36} -9.30560 q^{37} -7.87180 q^{38} +13.1198 q^{39} -27.1173 q^{40} -1.24511 q^{41} -19.2126 q^{42} -5.29208 q^{43} -27.5893 q^{44} +30.3607 q^{45} -2.62985 q^{46} -0.229215 q^{47} -33.2298 q^{48} -2.26232 q^{49} -21.3833 q^{50} +16.5384 q^{51} -18.8905 q^{52} -8.56333 q^{53} +47.3717 q^{54} -20.6234 q^{55} +16.2659 q^{56} -10.1370 q^{57} -8.34048 q^{58} -9.35565 q^{59} -59.3888 q^{60} +1.01390 q^{61} +12.9136 q^{62} -18.2114 q^{63} +8.71573 q^{64} -14.1209 q^{65} -50.1662 q^{66} -4.22483 q^{67} -23.8126 q^{68} -3.38662 q^{69} +20.6785 q^{70} -4.82623 q^{71} -62.5251 q^{72} +10.1842 q^{73} +24.3628 q^{74} -27.5365 q^{75} +14.5956 q^{76} +12.3706 q^{77} -34.3489 q^{78} -14.8509 q^{79} +35.7652 q^{80} +35.9030 q^{81} +3.25981 q^{82} -1.48956 q^{83} +35.6234 q^{84} -17.8003 q^{85} +13.8551 q^{86} -10.7406 q^{87} +42.4719 q^{88} +0.582583 q^{89} -79.4869 q^{90} +8.47017 q^{91} +4.87618 q^{92} +16.6297 q^{93} +0.600104 q^{94} +10.9104 q^{95} +36.6086 q^{96} -8.11866 q^{97} +5.92295 q^{98} -47.5519 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9} + 21 q^{10} + 70 q^{11} + 20 q^{12} + 53 q^{13} + 69 q^{14} + 28 q^{15} + 449 q^{16} + 88 q^{17} + 86 q^{18} + 44 q^{19} + 136 q^{20} + 125 q^{21} + 17 q^{22} + 104 q^{23} + 84 q^{24} + 444 q^{25} + 100 q^{26} + 32 q^{27} + 46 q^{28} + 373 q^{29} + 99 q^{30} + 30 q^{31} + 221 q^{32} + 56 q^{33} + 26 q^{34} + 164 q^{35} + 599 q^{36} + 81 q^{37} + 66 q^{38} + 143 q^{39} + 42 q^{40} + 182 q^{41} + 32 q^{42} + 40 q^{43} + 184 q^{44} + 198 q^{45} + 54 q^{46} + 66 q^{47} + 5 q^{48} + 479 q^{49} + 184 q^{50} + 123 q^{51} + 64 q^{52} + 221 q^{53} + 67 q^{54} + 38 q^{55} + 174 q^{56} + 84 q^{57} + 44 q^{58} + 127 q^{59} + 29 q^{60} + 174 q^{61} + 86 q^{62} + 48 q^{63} + 549 q^{64} + 202 q^{65} + 32 q^{66} + 29 q^{67} + 172 q^{68} + 249 q^{69} + 12 q^{70} + 185 q^{71} + 218 q^{72} + 57 q^{73} + 272 q^{74} + 24 q^{75} + 84 q^{76} + 384 q^{77} + 12 q^{78} + 93 q^{79} + 215 q^{80} + 702 q^{81} + 48 q^{82} + 121 q^{83} + 179 q^{84} + 177 q^{85} + 209 q^{86} + 91 q^{87} + 36 q^{88} + 186 q^{89} + 66 q^{90} + 32 q^{91} + 272 q^{92} + 220 q^{93} + 60 q^{94} + 170 q^{95} + 162 q^{96} + 22 q^{97} + 196 q^{98} + 152 q^{99}+O(q^{100}) \) 358 * q + 33 * q^2 + 11 * q^3 + 391 * q^4 + 76 * q^5 + 32 * q^6 + 19 * q^7 + 99 * q^8 + 451 * q^9 + 21 * q^10 + 70 * q^11 + 20 * q^12 + 53 * q^13 + 69 * q^14 + 28 * q^15 + 449 * q^16 + 88 * q^17 + 86 * q^18 + 44 * q^19 + 136 * q^20 + 125 * q^21 + 17 * q^22 + 104 * q^23 + 84 * q^24 + 444 * q^25 + 100 * q^26 + 32 * q^27 + 46 * q^28 + 373 * q^29 + 99 * q^30 + 30 * q^31 + 221 * q^32 + 56 * q^33 + 26 * q^34 + 164 * q^35 + 599 * q^36 + 81 * q^37 + 66 * q^38 + 143 * q^39 + 42 * q^40 + 182 * q^41 + 32 * q^42 + 40 * q^43 + 184 * q^44 + 198 * q^45 + 54 * q^46 + 66 * q^47 + 5 * q^48 + 479 * q^49 + 184 * q^50 + 123 * q^51 + 64 * q^52 + 221 * q^53 + 67 * q^54 + 38 * q^55 + 174 * q^56 + 84 * q^57 + 44 * q^58 + 127 * q^59 + 29 * q^60 + 174 * q^61 + 86 * q^62 + 48 * q^63 + 549 * q^64 + 202 * q^65 + 32 * q^66 + 29 * q^67 + 172 * q^68 + 249 * q^69 + 12 * q^70 + 185 * q^71 + 218 * q^72 + 57 * q^73 + 272 * q^74 + 24 * q^75 + 84 * q^76 + 384 * q^77 + 12 * q^78 + 93 * q^79 + 215 * q^80 + 702 * q^81 + 48 * q^82 + 121 * q^83 + 179 * q^84 + 177 * q^85 + 209 * q^86 + 91 * q^87 + 36 * q^88 + 186 * q^89 + 66 * q^90 + 32 * q^91 + 272 * q^92 + 220 * q^93 + 60 * q^94 + 170 * q^95 + 162 * q^96 + 22 * q^97 + 196 * q^98 + 152 * q^99

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