LMFDB - Embedded newform 8011.2.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q-2.59714 q^{2} -2.89463 q^{3} +4.74512 q^{4} +2.71586 q^{5} +7.51774 q^{6} -3.02593 q^{7} -7.12945 q^{8} +5.37887 q^{9} +O(q^{10})$	\(q-2.59714 q^{2} -2.89463 q^{3} +4.74512 q^{4} +2.71586 q^{5} +7.51774 q^{6} -3.02593 q^{7} -7.12945 q^{8} +5.37887 q^{9} -7.05346 q^{10} +6.06893 q^{11} -13.7354 q^{12} -0.0981225 q^{13} +7.85875 q^{14} -7.86141 q^{15} +9.02592 q^{16} +1.66842 q^{17} -13.9697 q^{18} +1.73026 q^{19} +12.8871 q^{20} +8.75894 q^{21} -15.7618 q^{22} +0.496599 q^{23} +20.6371 q^{24} +2.37590 q^{25} +0.254838 q^{26} -6.88595 q^{27} -14.3584 q^{28} -3.28894 q^{29} +20.4171 q^{30} +4.68386 q^{31} -9.18265 q^{32} -17.5673 q^{33} -4.33311 q^{34} -8.21800 q^{35} +25.5234 q^{36} +8.03219 q^{37} -4.49371 q^{38} +0.284028 q^{39} -19.3626 q^{40} +1.40866 q^{41} -22.7482 q^{42} +9.32188 q^{43} +28.7978 q^{44} +14.6083 q^{45} -1.28974 q^{46} -4.83030 q^{47} -26.1267 q^{48} +2.15625 q^{49} -6.17054 q^{50} -4.82944 q^{51} -0.465603 q^{52} -8.62023 q^{53} +17.8837 q^{54} +16.4824 q^{55} +21.5732 q^{56} -5.00845 q^{57} +8.54183 q^{58} +10.5661 q^{59} -37.3033 q^{60} +9.06527 q^{61} -12.1646 q^{62} -16.2761 q^{63} +5.79675 q^{64} -0.266487 q^{65} +45.6247 q^{66} -9.24343 q^{67} +7.91683 q^{68} -1.43747 q^{69} +21.3433 q^{70} -5.78055 q^{71} -38.3484 q^{72} +10.7832 q^{73} -20.8607 q^{74} -6.87735 q^{75} +8.21027 q^{76} -18.3642 q^{77} -0.737660 q^{78} -7.18491 q^{79} +24.5131 q^{80} +3.79564 q^{81} -3.65849 q^{82} -5.11825 q^{83} +41.5622 q^{84} +4.53119 q^{85} -24.2102 q^{86} +9.52026 q^{87} -43.2681 q^{88} +13.8596 q^{89} -37.9397 q^{90} +0.296912 q^{91} +2.35642 q^{92} -13.5580 q^{93} +12.5449 q^{94} +4.69913 q^{95} +26.5803 q^{96} +6.33446 q^{97} -5.60007 q^{98} +32.6440 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.59714	−1.83645	−0.918227	−	0.396056i	$-0.870379\pi$
$2$	−2.59714	−1.83645	−0.918227	+	0.396056i	$0.870379\pi$
$3$	−2.89463	−1.67121	−0.835607	−	0.549328i	$-0.814884\pi$
$3$	−2.89463	−1.67121	−0.835607	+	0.549328i	$0.814884\pi$
$4$	4.74512	2.37256
$5$	2.71586	1.21457	0.607285	−	0.794484i	$-0.292259\pi$
$5$	2.71586	1.21457	0.607285	+	0.794484i	$0.292259\pi$
$6$	7.51774	3.06911
$7$	−3.02593	−1.14369	−0.571847	−	0.820360i	$-0.693773\pi$
$7$	−3.02593	−1.14369	−0.571847	+	0.820360i	$0.693773\pi$
$8$	−7.12945	−2.52064
$9$	5.37887	1.79296
$10$	−7.05346	−2.23050
$11$	6.06893	1.82985	0.914926	−	0.403622i	$-0.132249\pi$
$11$	6.06893	1.82985	0.914926	+	0.403622i	$0.132249\pi$
$12$	−13.7354	−3.96506
$13$	−0.0981225	−0.0272143	−0.0136071	−	0.999907i	$-0.504331\pi$
$13$	−0.0981225	−0.0272143	−0.0136071	+	0.999907i	$0.504331\pi$
$14$	7.85875	2.10034
$15$	−7.86141	−2.02981
$16$	9.02592	2.25648
$17$	1.66842	0.404650	0.202325	−	0.979318i	$-0.435150\pi$
$17$	1.66842	0.404650	0.202325	+	0.979318i	$0.435150\pi$
$18$	−13.9697	−3.29268
$19$	1.73026	0.396948	0.198474	−	0.980106i	$-0.436401\pi$
$19$	1.73026	0.396948	0.198474	+	0.980106i	$0.436401\pi$
$20$	12.8871	2.88164
$21$	8.75894	1.91136
$22$	−15.7618	−3.36044
$23$	0.496599	0.103548	0.0517741	−	0.998659i	$-0.483512\pi$
$23$	0.496599	0.103548	0.0517741	+	0.998659i	$0.483512\pi$
$24$	20.6371	4.21253
$25$	2.37590	0.475180
$26$	0.254838	0.0499778
$27$	−6.88595	−1.32520
$28$	−14.3584	−2.71348
$29$	−3.28894	−0.610741	−0.305370	−	0.952234i	$-0.598780\pi$
$29$	−3.28894	−0.610741	−0.305370	+	0.952234i	$0.598780\pi$
$30$	20.4171	3.72764
$31$	4.68386	0.841246	0.420623	−	0.907235i	$-0.361811\pi$
$31$	4.68386	0.841246	0.420623	+	0.907235i	$0.361811\pi$
$32$	−9.18265	−1.62328
$33$	−17.5673	−3.05807
$34$	−4.33311	−0.743121
$35$	−8.21800	−1.38910
$36$	25.5234	4.25390
$37$	8.03219	1.32048	0.660242	−	0.751053i	$-0.270454\pi$
$37$	8.03219	1.32048	0.660242	+	0.751053i	$0.270454\pi$
$38$	−4.49371	−0.728976
$39$	0.284028	0.0454809
$40$	−19.3626	−3.06150
$41$	1.40866	0.219996	0.109998	−	0.993932i	$-0.464916\pi$
$41$	1.40866	0.219996	0.109998	+	0.993932i	$0.464916\pi$
$42$	−22.7482	−3.51012
$43$	9.32188	1.42157	0.710787	−	0.703408i	$-0.248339\pi$
$43$	9.32188	1.42157	0.710787	+	0.703408i	$0.248339\pi$
$44$	28.7978	4.34143
$45$	14.6083	2.17767
$46$	−1.28974	−0.190161
$47$	−4.83030	−0.704572	−0.352286	−	0.935892i	$-0.614595\pi$
$47$	−4.83030	−0.704572	−0.352286	+	0.935892i	$0.614595\pi$
$48$	−26.1267	−3.77106
$49$	2.15625	0.308035
$50$	−6.17054	−0.872646
$51$	−4.82944	−0.676257
$52$	−0.465603	−0.0645675
$53$	−8.62023	−1.18408	−0.592040	−	0.805909i	$-0.701677\pi$
$53$	−8.62023	−1.18408	−0.592040	+	0.805909i	$0.701677\pi$
$54$	17.8837	2.43367
$55$	16.4824	2.22248
$56$	21.5732	2.88284
$57$	−5.00845	−0.663385
$58$	8.54183	1.12160
$59$	10.5661	1.37558	0.687792	−	0.725907i	$-0.258580\pi$
$59$	10.5661	1.37558	0.687792	+	0.725907i	$0.258580\pi$
$60$	−37.3033	−4.81584
$61$	9.06527	1.16069	0.580344	−	0.814371i	$-0.302918\pi$
$61$	9.06527	1.16069	0.580344	+	0.814371i	$0.302918\pi$
$62$	−12.1646	−1.54491
$63$	−16.2761	−2.05059
$64$	5.79675	0.724594
$65$	−0.266487	−0.0330537
$66$	45.6247	5.61601
$67$	−9.24343	−1.12926	−0.564632	−	0.825343i	$-0.690982\pi$
$67$	−9.24343	−1.12926	−0.564632	+	0.825343i	$0.690982\pi$
$68$	7.91683	0.960057
$69$	−1.43747	−0.173051
$70$	21.3433	2.55101
$71$	−5.78055	−0.686025	−0.343013	−	0.939331i	$-0.611447\pi$
$71$	−5.78055	−0.686025	−0.343013	+	0.939331i	$0.611447\pi$
$72$	−38.3484	−4.51940
$73$	10.7832	1.26207	0.631036	−	0.775753i	$-0.282630\pi$
$73$	10.7832	1.26207	0.631036	+	0.775753i	$0.282630\pi$
$74$	−20.8607	−2.42501
$75$	−6.87735	−0.794127
$76$	8.21027	0.941783
$77$	−18.3642	−2.09279
$78$	−0.737660	−0.0835236
$79$	−7.18491	−0.808366	−0.404183	−	0.914678i	$-0.632444\pi$
$79$	−7.18491	−0.808366	−0.404183	+	0.914678i	$0.632444\pi$
$80$	24.5131	2.74065
$81$	3.79564	0.421738
$82$	−3.65849	−0.404013
$83$	−5.11825	−0.561801	−0.280900	−	0.959737i	$-0.590633\pi$
$83$	−5.11825	−0.561801	−0.280900	+	0.959737i	$0.590633\pi$
$84$	41.5622	4.53481
$85$	4.53119	0.491476
$86$	−24.2102	−2.61065
$87$	9.52026	1.02068
$88$	−43.2681	−4.61240
$89$	13.8596	1.46911	0.734557	−	0.678547i	$-0.237390\pi$
$89$	13.8596	1.46911	0.734557	+	0.678547i	$0.237390\pi$
$90$	−37.9397	−3.99919
$91$	0.296912	0.0311248
$92$	2.35642	0.245674
$93$	−13.5580	−1.40590
$94$	12.5449	1.29391
$95$	4.69913	0.482121
$96$	26.5803	2.71284
$97$	6.33446	0.643167	0.321583	−	0.946881i	$-0.395785\pi$
$97$	6.33446	0.643167	0.321583	+	0.946881i	$0.395785\pi$
$98$	−5.60007	−0.565692
$99$	32.6440	3.28084
$100$	11.2739	1.12739
$101$	11.2066	1.11510	0.557548	−	0.830144i	$-0.311742\pi$
$101$	11.2066	1.11510	0.557548	+	0.830144i	$0.311742\pi$
$102$	12.5427	1.24192
$103$	0.458394	0.0451669	0.0225835	−	0.999745i	$-0.492811\pi$
$103$	0.458394	0.0451669	0.0225835	+	0.999745i	$0.492811\pi$
$104$	0.699560	0.0685975
$105$	23.7881	2.32148
$106$	22.3879	2.17451
$107$	−4.29940	−0.415639	−0.207820	−	0.978167i	$-0.566637\pi$
$107$	−4.29940	−0.415639	−0.207820	+	0.978167i	$0.566637\pi$
$108$	−32.6746	−3.14412
$109$	10.0608	0.963645	0.481823	−	0.876269i	$-0.339975\pi$
$109$	10.0608	0.963645	0.481823	+	0.876269i	$0.339975\pi$
$110$	−42.8070	−4.08148
$111$	−23.2502	−2.20681
$112$	−27.3118	−2.58072
$113$	3.18818	0.299919	0.149959	−	0.988692i	$-0.452086\pi$
$113$	3.18818	0.299919	0.149959	+	0.988692i	$0.452086\pi$
$114$	13.0076	1.21828
$115$	1.34869	0.125766
$116$	−15.6064	−1.44902
$117$	−0.527788	−0.0487941
$118$	−27.4415	−2.52620
$119$	−5.04851	−0.462796
$120$	56.0475	5.11641
$121$	25.8319	2.34836
$122$	−23.5437	−2.13155
$123$	−4.07756	−0.367661
$124$	22.2255	1.99591
$125$	−7.12669	−0.637431
$126$	42.2712	3.76582
$127$	−3.53871	−0.314009	−0.157005	−	0.987598i	$-0.550184\pi$
$127$	−3.53871	−0.314009	−0.157005	+	0.987598i	$0.550184\pi$
$128$	3.31034	0.292596
$129$	−26.9834	−2.37575
$130$	0.692104	0.0607015
$131$	11.8037	1.03130	0.515648	−	0.856801i	$-0.327551\pi$
$131$	11.8037	1.03130	0.515648	+	0.856801i	$0.327551\pi$
$132$	−83.3589	−7.25546
$133$	−5.23563	−0.453987
$134$	24.0064	2.07384
$135$	−18.7013	−1.60955
$136$	−11.8949	−1.01998
$137$	19.6492	1.67874	0.839372	−	0.543558i	$-0.182923\pi$
$137$	19.6492	1.67874	0.839372	+	0.543558i	$0.182923\pi$
$138$	3.73331	0.317800
$139$	−6.58463	−0.558501	−0.279251	−	0.960218i	$-0.590086\pi$
$139$	−6.58463	−0.558501	−0.279251	+	0.960218i	$0.590086\pi$
$140$	−38.9954	−3.29571
$141$	13.9819	1.17749
$142$	15.0129	1.25985
$143$	−0.595499	−0.0497981
$144$	48.5493	4.04577
$145$	−8.93231	−0.741788
$146$	−28.0053	−2.31774
$147$	−6.24153	−0.514793
$148$	38.1137	3.13293
$149$	−1.94877	−0.159650	−0.0798248	−	0.996809i	$-0.525436\pi$
$149$	−1.94877	−0.159650	−0.0798248	+	0.996809i	$0.525436\pi$
$150$	17.8614	1.45838
$151$	−1.22636	−0.0997997	−0.0498999	−	0.998754i	$-0.515890\pi$
$151$	−1.22636	−0.0997997	−0.0498999	+	0.998754i	$0.515890\pi$
$152$	−12.3358	−1.00056
$153$	8.97420	0.725521
$154$	47.6942	3.84331
$155$	12.7207	1.02175
$156$	1.34775	0.107906
$157$	−0.822846	−0.0656703	−0.0328351	−	0.999461i	$-0.510454\pi$
$157$	−0.822846	−0.0656703	−0.0328351	+	0.999461i	$0.510454\pi$
$158$	18.6602	1.48453
$159$	24.9524	1.97885
$160$	−24.9388	−1.97158
$161$	−1.50267	−0.118427
$162$	−9.85779	−0.774501
$163$	17.1774	1.34544	0.672719	−	0.739898i	$-0.265126\pi$
$163$	17.1774	1.34544	0.672719	+	0.739898i	$0.265126\pi$
$164$	6.68427	0.521954
$165$	−47.7103	−3.71424
$166$	13.2928	1.03172
$167$	12.1266	0.938383	0.469192	−	0.883096i	$-0.344545\pi$
$167$	12.1266	0.938383	0.469192	+	0.883096i	$0.344545\pi$
$168$	−62.4464	−4.81785
$169$	−12.9904	−0.999259
$170$	−11.7681	−0.902573
$171$	9.30682	0.711711
$172$	44.2334	3.37277
$173$	12.4508	0.946620	0.473310	−	0.880896i	$-0.343059\pi$
$173$	12.4508	0.946620	0.473310	+	0.880896i	$0.343059\pi$
$174$	−24.7254	−1.87443
$175$	−7.18930	−0.543460
$176$	54.7777	4.12902
$177$	−30.5848	−2.29890
$178$	−35.9952	−2.69796
$179$	−13.3545	−0.998160	−0.499080	−	0.866556i	$-0.666329\pi$
$179$	−13.3545	−0.998160	−0.499080	+	0.866556i	$0.666329\pi$
$180$	69.3180	5.16666
$181$	14.6248	1.08705	0.543527	−	0.839392i	$-0.317088\pi$
$181$	14.6248	1.08705	0.543527	+	0.839392i	$0.317088\pi$
$182$	−0.771121	−0.0571593
$183$	−26.2406	−1.93976
$184$	−3.54048	−0.261008
$185$	21.8143	1.60382
$186$	35.2121	2.58187
$187$	10.1255	0.740450
$188$	−22.9203	−1.67164
$189$	20.8364	1.51562
$190$	−12.2043	−0.885393
$191$	2.79999	0.202600	0.101300	−	0.994856i	$-0.467700\pi$
$191$	2.79999	0.202600	0.101300	+	0.994856i	$0.467700\pi$
$192$	−16.7794	−1.21095
$193$	1.56415	0.112590	0.0562949	−	0.998414i	$-0.482071\pi$
$193$	1.56415	0.112590	0.0562949	+	0.998414i	$0.482071\pi$
$194$	−16.4515	−1.18115
$195$	0.771381	0.0552398
$196$	10.2317	0.730832
$197$	27.4718	1.95728	0.978641	−	0.205575i	$-0.0659066\pi$
$197$	27.4718	1.95728	0.978641	+	0.205575i	$0.0659066\pi$
$198$	−84.7809	−6.02512
$199$	−9.83964	−0.697513	−0.348757	−	0.937213i	$-0.613396\pi$
$199$	−9.83964	−0.697513	−0.348757	+	0.937213i	$0.613396\pi$
$200$	−16.9389	−1.19776
$201$	26.7563	1.88724
$202$	−29.1050	−2.04782
$203$	9.95210	0.698501
$204$	−22.9163	−1.60446
$205$	3.82573	0.267201
$206$	−1.19051	−0.0829469
$207$	2.67114	0.185657
$208$	−0.885646	−0.0614085
$209$	10.5008	0.726356
$210$	−61.7808	−4.26328
$211$	−24.3900	−1.67908	−0.839540	−	0.543299i	$-0.817175\pi$
$211$	−24.3900	−1.67908	−0.839540	+	0.543299i	$0.817175\pi$
$212$	−40.9040	−2.80930
$213$	16.7325	1.14650
$214$	11.1661	0.763302
$215$	25.3169	1.72660
$216$	49.0930	3.34036
$217$	−14.1730	−0.962128
$218$	−26.1292	−1.76969
$219$	−31.2132	−2.10919
$220$	78.2108	5.27297
$221$	−0.163709	−0.0110123
$222$	60.3839	4.05270
$223$	4.27847	0.286508	0.143254	−	0.989686i	$-0.454243\pi$
$223$	4.27847	0.286508	0.143254	+	0.989686i	$0.454243\pi$
$224$	27.7860	1.85653
$225$	12.7797	0.851977
$226$	−8.28014	−0.550787
$227$	−8.16005	−0.541601	−0.270801	−	0.962635i	$-0.587288\pi$
$227$	−8.16005	−0.541601	−0.270801	+	0.962635i	$0.587288\pi$
$228$	−23.7657	−1.57392
$229$	13.9408	0.921231	0.460616	−	0.887600i	$-0.347629\pi$
$229$	13.9408	0.921231	0.460616	+	0.887600i	$0.347629\pi$
$230$	−3.50274	−0.230964
$231$	53.1574	3.49750
$232$	23.4483	1.53946
$233$	11.9464	0.782635	0.391317	−	0.920256i	$-0.372019\pi$
$233$	11.9464	0.782635	0.391317	+	0.920256i	$0.372019\pi$
$234$	1.37074	0.0896080
$235$	−13.1184	−0.855751
$236$	50.1373	3.26366
$237$	20.7977	1.35095
$238$	13.1117	0.849903
$239$	0.176706	0.0114302	0.00571508	−	0.999984i	$-0.498181\pi$
$239$	0.176706	0.0114302	0.00571508	+	0.999984i	$0.498181\pi$
$240$	−70.9564	−4.58022
$241$	−8.02085	−0.516669	−0.258334	−	0.966056i	$-0.583174\pi$
$241$	−8.02085	−0.516669	−0.258334	+	0.966056i	$0.583174\pi$
$242$	−67.0890	−4.31265
$243$	9.67088	0.620387
$244$	43.0158	2.75380
$245$	5.85607	0.374130
$246$	10.5900	0.675192
$247$	−0.169777	−0.0108027
$248$	−33.3934	−2.12048
$249$	14.8154	0.938890
$250$	18.5090	1.17061
$251$	−20.2483	−1.27806	−0.639030	−	0.769182i	$-0.720664\pi$
$251$	−20.2483	−1.27806	−0.639030	+	0.769182i	$0.720664\pi$
$252$	−77.2320	−4.86516
$253$	3.01383	0.189478
$254$	9.19050	0.576663
$255$	−13.1161	−0.821362
$256$	−20.1909	−1.26193
$257$	−25.7707	−1.60753	−0.803765	−	0.594947i	$-0.797173\pi$
$257$	−25.7707	−1.60753	−0.803765	+	0.594947i	$0.797173\pi$
$258$	70.0795	4.36296
$259$	−24.3048	−1.51023
$260$	−1.26451	−0.0784218
$261$	−17.6908	−1.09503
$262$	−30.6559	−1.89393
$263$	0.484360	0.0298669	0.0149335	−	0.999888i	$-0.495246\pi$
$263$	0.484360	0.0298669	0.0149335	+	0.999888i	$0.495246\pi$
$264$	125.245	7.70831
$265$	−23.4114	−1.43815
$266$	13.5977	0.833726
$267$	−40.1184	−2.45520
$268$	−43.8612	−2.67925
$269$	−26.4394	−1.61204	−0.806020	−	0.591888i	$-0.798383\pi$
$269$	−26.4394	−1.61204	−0.806020	+	0.591888i	$0.798383\pi$
$270$	48.5698	2.95586
$271$	15.9879	0.971198	0.485599	−	0.874182i	$-0.338602\pi$
$271$	15.9879	0.971198	0.485599	+	0.874182i	$0.338602\pi$
$272$	15.0590	0.913085
$273$	−0.859449	−0.0520162
$274$	−51.0316	−3.08293
$275$	14.4192	0.869509
$276$	−6.82097	−0.410574
$277$	22.8402	1.37233	0.686167	−	0.727444i	$-0.259292\pi$
$277$	22.8402	1.37233	0.686167	+	0.727444i	$0.259292\pi$
$278$	17.1012	1.02566
$279$	25.1939	1.50832
$280$	58.5898	3.50141
$281$	−16.0046	−0.954755	−0.477378	−	0.878698i	$-0.658413\pi$
$281$	−16.0046	−0.954755	−0.477378	+	0.878698i	$0.658413\pi$
$282$	−36.3130	−2.16241
$283$	−11.7723	−0.699792	−0.349896	−	0.936789i	$-0.613783\pi$
$283$	−11.7723	−0.699792	−0.349896	+	0.936789i	$0.613783\pi$
$284$	−27.4294	−1.62764
$285$	−13.6022	−0.805728
$286$	1.54659	0.0914519
$287$	−4.26251	−0.251608
$288$	−49.3923	−2.91047
$289$	−14.2164	−0.836258
$290$	23.1984	1.36226
$291$	−18.3359	−1.07487
$292$	51.1673	2.99434
$293$	−8.54120	−0.498982	−0.249491	−	0.968377i	$-0.580263\pi$
$293$	−8.54120	−0.498982	−0.249491	+	0.968377i	$0.580263\pi$
$294$	16.2101	0.945393
$295$	28.6960	1.67074
$296$	−57.2651	−3.32846
$297$	−41.7903	−2.42492
$298$	5.06123	0.293189
$299$	−0.0487276	−0.00281799
$300$	−32.6338	−1.88411
$301$	−28.2074	−1.62584
$302$	3.18502	0.183278
$303$	−32.4389	−1.86357
$304$	15.6172	0.895705
$305$	24.6200	1.40974
$306$	−23.3072	−1.33238
$307$	−23.6764	−1.35128	−0.675641	−	0.737231i	$-0.736133\pi$
$307$	−23.6764	−1.35128	−0.675641	+	0.737231i	$0.736133\pi$
$308$	−87.1401	−4.96527
$309$	−1.32688	−0.0754836
$310$	−33.0374	−1.87640
$311$	−20.6475	−1.17081	−0.585407	−	0.810739i	$-0.699065\pi$
$311$	−20.6475	−1.17081	−0.585407	+	0.810739i	$0.699065\pi$
$312$	−2.02497	−0.114641
$313$	4.35880	0.246374	0.123187	−	0.992383i	$-0.460689\pi$
$313$	4.35880	0.246374	0.123187	+	0.992383i	$0.460689\pi$
$314$	2.13704	0.120600
$315$	−44.2036	−2.49059
$316$	−34.0933	−1.91790
$317$	−6.06362	−0.340567	−0.170283	−	0.985395i	$-0.554468\pi$
$317$	−6.06362	−0.340567	−0.170283	+	0.985395i	$0.554468\pi$
$318$	−64.8047	−3.63407
$319$	−19.9604	−1.11757
$320$	15.7432	0.880070
$321$	12.4452	0.694622
$322$	3.90265	0.217486
$323$	2.88679	0.160625
$324$	18.0108	1.00060
$325$	−0.233129	−0.0129317
$326$	−44.6120	−2.47083
$327$	−29.1221	−1.61046
$328$	−10.0430	−0.554532
$329$	14.6161	0.805814
$330$	123.910	6.82103
$331$	−20.5564	−1.12988	−0.564941	−	0.825131i	$-0.691101\pi$
$331$	−20.5564	−1.12988	−0.564941	+	0.825131i	$0.691101\pi$
$332$	−24.2867	−1.33291
$333$	43.2041	2.36757
$334$	−31.4944	−1.72330
$335$	−25.1039	−1.37157
$336$	79.0575	4.31294
$337$	−4.34845	−0.236875	−0.118438	−	0.992962i	$-0.537789\pi$
$337$	−4.34845	−0.236875	−0.118438	+	0.992962i	$0.537789\pi$
$338$	33.7378	1.83509
$339$	−9.22860	−0.501229
$340$	21.5010	1.16606
$341$	28.4260	1.53936
$342$	−24.1711	−1.30702
$343$	14.6569	0.791396
$344$	−66.4599	−3.58328
$345$	−3.90397	−0.210183
$346$	−32.3366	−1.73842
$347$	2.72968	0.146537	0.0732684	−	0.997312i	$-0.476657\pi$
$347$	2.72968	0.146537	0.0732684	+	0.997312i	$0.476657\pi$
$348$	45.1748	2.42162
$349$	−32.7936	−1.75540	−0.877701	−	0.479209i	$-0.840924\pi$
$349$	−32.7936	−1.75540	−0.877701	+	0.479209i	$0.840924\pi$
$350$	18.6716	0.998039
$351$	0.675666	0.0360644
$352$	−55.7288	−2.97036
$353$	27.2244	1.44901	0.724503	−	0.689271i	$-0.242069\pi$
$353$	27.2244	1.44901	0.724503	+	0.689271i	$0.242069\pi$
$354$	79.4330	4.22182
$355$	−15.6992	−0.833226
$356$	65.7654	3.48556
$357$	14.6136	0.773431
$358$	34.6834	1.83307
$359$	1.33938	0.0706900	0.0353450	−	0.999375i	$-0.488747\pi$
$359$	1.33938	0.0706900	0.0353450	+	0.999375i	$0.488747\pi$
$360$	−104.149	−5.48913
$361$	−16.0062	−0.842432
$362$	−37.9827	−1.99632
$363$	−74.7738	−3.92461
$364$	1.40888	0.0738455
$365$	29.2855	1.53288
$366$	68.1504	3.56228
$367$	−9.84862	−0.514094	−0.257047	−	0.966399i	$-0.582750\pi$
$367$	−9.84862	−0.514094	−0.257047	+	0.966399i	$0.582750\pi$
$368$	4.48227	0.233654
$369$	7.57702	0.394444
$370$	−56.6547	−2.94534
$371$	26.0842	1.35423
$372$	−64.3345	−3.33559
$373$	−23.0121	−1.19152	−0.595761	−	0.803162i	$-0.703149\pi$
$373$	−23.0121	−1.19152	−0.595761	+	0.803162i	$0.703149\pi$
$374$	−26.2973	−1.35980
$375$	20.6291	1.06528
$376$	34.4374	1.77597
$377$	0.322719	0.0166209
$378$	−54.1149	−2.78337
$379$	9.17747	0.471415	0.235708	−	0.971824i	$-0.424259\pi$
$379$	9.17747	0.471415	0.235708	+	0.971824i	$0.424259\pi$
$380$	22.2980	1.14386
$381$	10.2432	0.524777
$382$	−7.27196	−0.372066
$383$	−31.9832	−1.63427	−0.817133	−	0.576449i	$-0.804438\pi$
$383$	−31.9832	−1.63427	−0.817133	+	0.576449i	$0.804438\pi$
$384$	−9.58221	−0.488990
$385$	−49.8745	−2.54184
$386$	−4.06231	−0.206766
$387$	50.1412	2.54882
$388$	30.0578	1.52595
$389$	−3.12544	−0.158466	−0.0792331	−	0.996856i	$-0.525247\pi$
$389$	−3.12544	−0.158466	−0.0792331	+	0.996856i	$0.525247\pi$
$390$	−2.00338	−0.101445
$391$	0.828534	0.0419008
$392$	−15.3729	−0.776447
$393$	−34.1674	−1.72352
$394$	−71.3479	−3.59446
$395$	−19.5132	−0.981817
$396$	154.900	7.78400
$397$	−10.6864	−0.536333	−0.268167	−	0.963373i	$-0.586418\pi$
$397$	−10.6864	−0.536333	−0.268167	+	0.963373i	$0.586418\pi$
$398$	25.5549	1.28095
$399$	15.1552	0.758709
$400$	21.4447	1.07223
$401$	−0.332411	−0.0165998	−0.00829991	−	0.999966i	$-0.502642\pi$
$401$	−0.332411	−0.0165998	−0.00829991	+	0.999966i	$0.502642\pi$
$402$	−69.4897	−3.46583
$403$	−0.459592	−0.0228939
$404$	53.1766	2.64563
$405$	10.3084	0.512230
$406$	−25.8470	−1.28276
$407$	48.7468	2.41629
$408$	34.4313	1.70460
$409$	30.4365	1.50499	0.752494	−	0.658599i	$-0.228850\pi$
$409$	30.4365	1.50499	0.752494	+	0.658599i	$0.228850\pi$
$410$	−9.93595	−0.490702
$411$	−56.8771	−2.80554
$412$	2.17513	0.107161
$413$	−31.9722	−1.57325
$414$	−6.93733	−0.340951
$415$	−13.9005	−0.682346
$416$	0.901025	0.0441764
$417$	19.0601	0.933375
$418$	−27.2720	−1.33392
$419$	23.6660	1.15616	0.578081	−	0.815979i	$-0.303802\pi$
$419$	23.6660	1.15616	0.578081	+	0.815979i	$0.303802\pi$
$420$	112.877	5.50784
$421$	−20.1969	−0.984336	−0.492168	−	0.870500i	$-0.663795\pi$
$421$	−20.1969	−0.984336	−0.492168	+	0.870500i	$0.663795\pi$
$422$	63.3443	3.08355
$423$	−25.9816	−1.26327
$424$	61.4575	2.98464
$425$	3.96399	0.192282
$426$	−43.4567	−2.10548
$427$	−27.4309	−1.32747
$428$	−20.4012	−0.986129
$429$	1.72375	0.0832233
$430$	−65.7515	−3.17082
$431$	22.0200	1.06067	0.530333	−	0.847790i	$-0.322067\pi$
$431$	22.0200	1.06067	0.530333	+	0.847790i	$0.322067\pi$
$432$	−62.1520	−2.99029
$433$	−0.379633	−0.0182440	−0.00912200	−	0.999958i	$-0.502904\pi$
$433$	−0.379633	−0.0182440	−0.00912200	+	0.999958i	$0.502904\pi$
$434$	36.8093	1.76690
$435$	25.8557	1.23969
$436$	47.7395	2.28631
$437$	0.859244	0.0411032
$438$	81.0650	3.87343
$439$	14.0233	0.669295	0.334648	−	0.942343i	$-0.391383\pi$
$439$	14.0233	0.669295	0.334648	+	0.942343i	$0.391383\pi$
$440$	−117.510	−5.60208
$441$	11.5982	0.552294
$442$	0.425175	0.0202235
$443$	20.4338	0.970838	0.485419	−	0.874282i	$-0.338667\pi$
$443$	20.4338	0.970838	0.485419	+	0.874282i	$0.338667\pi$
$444$	−110.325	−5.23579
$445$	37.6407	1.78434
$446$	−11.1118	−0.526158
$447$	5.64097	0.266809
$448$	−17.5406	−0.828713
$449$	13.4696	0.635671	0.317836	−	0.948146i	$-0.397044\pi$
$449$	13.4696	0.635671	0.317836	+	0.948146i	$0.397044\pi$
$450$	−33.1905	−1.56462
$451$	8.54908	0.402560
$452$	15.1283	0.711575
$453$	3.54985	0.166787
$454$	21.1928	0.994626
$455$	0.806371	0.0378033
$456$	35.7075	1.67216
$457$	−30.2430	−1.41471	−0.707354	−	0.706859i	$-0.750111\pi$
$457$	−30.2430	−1.41471	−0.707354	+	0.706859i	$0.750111\pi$
$458$	−36.2061	−1.69180
$459$	−11.4886	−0.536243
$460$	6.39972	0.298388
$461$	6.73713	0.313779	0.156890	−	0.987616i	$-0.449853\pi$
$461$	6.73713	0.313779	0.156890	+	0.987616i	$0.449853\pi$
$462$	−138.057	−6.42299
$463$	22.8093	1.06004	0.530019	−	0.847986i	$-0.322185\pi$
$463$	22.8093	1.06004	0.530019	+	0.847986i	$0.322185\pi$
$464$	−29.6857	−1.37812
$465$	−36.8217	−1.70757
$466$	−31.0264	−1.43727
$467$	8.37717	0.387649	0.193825	−	0.981036i	$-0.437911\pi$
$467$	8.37717	0.387649	0.193825	+	0.981036i	$0.437911\pi$
$468$	−2.50442	−0.115767
$469$	27.9700	1.29153
$470$	34.0703	1.57155
$471$	2.38183	0.109749
$472$	−75.3303	−3.46736
$473$	56.5738	2.60127
$474$	−54.0143	−2.48096
$475$	4.11092	0.188622
$476$	−23.9558	−1.09801
$477$	−46.3671	−2.12300
$478$	−0.458929	−0.0209909
$479$	12.1559	0.555415	0.277708	−	0.960666i	$-0.410425\pi$
$479$	12.1559	0.555415	0.277708	+	0.960666i	$0.410425\pi$
$480$	72.1885	3.29494
$481$	−0.788138	−0.0359360
$482$	20.8313	0.948838
$483$	4.34968	0.197917
$484$	122.576	5.57161
$485$	17.2035	0.781171
$486$	−25.1166	−1.13931
$487$	7.52557	0.341016	0.170508	−	0.985356i	$-0.445459\pi$
$487$	7.52557	0.341016	0.170508	+	0.985356i	$0.445459\pi$
$488$	−64.6304	−2.92568
$489$	−49.7222	−2.24851
$490$	−15.2090	−0.687073
$491$	−39.2892	−1.77310	−0.886548	−	0.462637i	$-0.846903\pi$
$491$	−39.2892	−1.77310	−0.886548	+	0.462637i	$0.846903\pi$
$492$	−19.3485	−0.872297
$493$	−5.48732	−0.247137
$494$	0.440934	0.0198386
$495$	88.6565	3.98481
$496$	42.2761	1.89826
$497$	17.4915	0.784603
$498$	−38.4777	−1.72423
$499$	−5.45682	−0.244281	−0.122140	−	0.992513i	$-0.538976\pi$
$499$	−5.45682	−0.244281	−0.122140	+	0.992513i	$0.538976\pi$
$500$	−33.8170	−1.51234
$501$	−35.1020	−1.56824
$502$	52.5875	2.34710
$503$	18.7083	0.834164	0.417082	−	0.908869i	$-0.363053\pi$
$503$	18.7083	0.834164	0.417082	+	0.908869i	$0.363053\pi$
$504$	116.040	5.16881
$505$	30.4355	1.35436
$506$	−7.82732	−0.347967
$507$	37.6023	1.66998
$508$	−16.7916	−0.745006
$509$	3.60880	0.159957	0.0799786	−	0.996797i	$-0.474515\pi$
$509$	3.60880	0.159957	0.0799786	+	0.996797i	$0.474515\pi$
$510$	34.0643	1.50839
$511$	−32.6291	−1.44342
$512$	45.8179	2.02488
$513$	−11.9144	−0.526036
$514$	66.9299	2.95215
$515$	1.24493	0.0548584
$516$	−128.039	−5.63662
$517$	−29.3147	−1.28926
$518$	63.1230	2.77346
$519$	−36.0406	−1.58201
$520$	1.89991	0.0833164
$521$	39.7585	1.74185	0.870926	−	0.491414i	$-0.163520\pi$
$521$	39.7585	1.74185	0.870926	+	0.491414i	$0.163520\pi$
$522$	45.9454	2.01098
$523$	−30.3451	−1.32690	−0.663450	−	0.748221i	$-0.730908\pi$
$523$	−30.3451	−1.32690	−0.663450	+	0.748221i	$0.730908\pi$
$524$	56.0101	2.44681
$525$	20.8104	0.908239
$526$	−1.25795	−0.0548492
$527$	7.81463	0.340411
$528$	−158.561	−6.90048
$529$	−22.7534	−0.989278
$530$	60.8025	2.64109
$531$	56.8335	2.46636
$532$	−24.8437	−1.07711
$533$	−0.138222	−0.00598704
$534$	104.193	4.50887
$535$	−11.6766	−0.504823
$536$	65.9006	2.84647
$537$	38.6562	1.66814
$538$	68.6668	2.96044
$539$	13.0861	0.563659
$540$	−88.7398	−3.81875
$541$	−23.3703	−1.00477	−0.502383	−	0.864645i	$-0.667543\pi$
$541$	−23.3703	−1.00477	−0.502383	+	0.864645i	$0.667543\pi$
$542$	−41.5228	−1.78356
$543$	−42.3334	−1.81670
$544$	−15.3205	−0.656860
$545$	27.3236	1.17041
$546$	2.23211	0.0955254
$547$	−23.7302	−1.01463	−0.507315	−	0.861761i	$-0.669362\pi$
$547$	−23.7302	−1.01463	−0.507315	+	0.861761i	$0.669362\pi$
$548$	93.2377	3.98292
$549$	48.7609	2.08106
$550$	−37.4486	−1.59681
$551$	−5.69071	−0.242432
$552$	10.2484	0.436200
$553$	21.7410	0.924523
$554$	−59.3191	−2.52023
$555$	−63.1443	−2.68033
$556$	−31.2449	−1.32508
$557$	8.58077	0.363579	0.181789	−	0.983337i	$-0.441811\pi$
$557$	8.58077	0.363579	0.181789	+	0.983337i	$0.441811\pi$
$558$	−65.4320	−2.76996
$559$	−0.914687	−0.0386871
$560$	−74.1750	−3.13447
$561$	−29.3096	−1.23745
$562$	41.5662	1.75336
$563$	−11.3497	−0.478334	−0.239167	−	0.970978i	$-0.576874\pi$
$563$	−11.3497	−0.478334	−0.239167	+	0.970978i	$0.576874\pi$
$564$	66.3459	2.79367
$565$	8.65866	0.364272
$566$	30.5743	1.28514
$567$	−11.4853	−0.482339
$568$	41.2122	1.72922
$569$	23.5185	0.985948	0.492974	−	0.870044i	$-0.335910\pi$
$569$	23.5185	0.985948	0.492974	+	0.870044i	$0.335910\pi$
$570$	35.3269	1.47968
$571$	10.1200	0.423508	0.211754	−	0.977323i	$-0.432082\pi$
$571$	10.1200	0.423508	0.211754	+	0.977323i	$0.432082\pi$
$572$	−2.82571	−0.118149
$573$	−8.10493	−0.338588
$574$	11.0703	0.462067
$575$	1.17987	0.0492040
$576$	31.1800	1.29917
$577$	−13.1026	−0.545468	−0.272734	−	0.962089i	$-0.587928\pi$
$577$	−13.1026	−0.545468	−0.272734	+	0.962089i	$0.587928\pi$
$578$	36.9219	1.53575
$579$	−4.52763	−0.188162
$580$	−42.3849	−1.75994
$581$	15.4875	0.642528
$582$	47.6208	1.97395
$583$	−52.3156	−2.16669
$584$	−76.8779	−3.18123
$585$	−1.43340	−0.0592638
$586$	22.1827	0.916358
$587$	−22.3414	−0.922130	−0.461065	−	0.887366i	$-0.652532\pi$
$587$	−22.3414	−0.922130	−0.461065	+	0.887366i	$0.652532\pi$
$588$	−29.6168	−1.22138
$589$	8.10428	0.333931
$590$	−74.5274	−3.06824
$591$	−79.5206	−3.27104
$592$	72.4979	2.97964
$593$	41.0860	1.68720	0.843600	−	0.536972i	$-0.180432\pi$
$593$	41.0860	1.68720	0.843600	+	0.536972i	$0.180432\pi$
$594$	108.535	4.45325
$595$	−13.7110	−0.562098
$596$	−9.24715	−0.378778
$597$	28.4821	1.16569
$598$	0.126552	0.00517511
$599$	−44.3917	−1.81380	−0.906898	−	0.421350i	$-0.861556\pi$
$599$	−44.3917	−1.81380	−0.906898	+	0.421350i	$0.861556\pi$
$600$	49.0317	2.00171
$601$	−32.8064	−1.33820	−0.669101	−	0.743171i	$-0.733321\pi$
$601$	−32.8064	−1.33820	−0.669101	+	0.743171i	$0.733321\pi$
$602$	73.2584	2.98579
$603$	−49.7192	−2.02472
$604$	−5.81922	−0.236781
$605$	70.1559	2.85224
$606$	84.2482	3.42235
$607$	21.4982	0.872584	0.436292	−	0.899805i	$-0.356291\pi$
$607$	21.4982	0.872584	0.436292	+	0.899805i	$0.356291\pi$
$608$	−15.8883	−0.644357
$609$	−28.8076	−1.16734
$610$	−63.9415	−2.58892
$611$	0.473961	0.0191744
$612$	42.5836	1.72134
$613$	−23.2765	−0.940130	−0.470065	−	0.882632i	$-0.655770\pi$
$613$	−23.2765	−0.940130	−0.470065	+	0.882632i	$0.655770\pi$
$614$	61.4908	2.48157
$615$	−11.0741	−0.446550
$616$	130.926	5.27517
$617$	−43.0031	−1.73124	−0.865620	−	0.500701i	$-0.833075\pi$
$617$	−43.0031	−1.73124	−0.865620	+	0.500701i	$0.833075\pi$
$618$	3.44609	0.138622
$619$	8.88564	0.357144	0.178572	−	0.983927i	$-0.442852\pi$
$619$	8.88564	0.357144	0.178572	+	0.983927i	$0.442852\pi$
$620$	60.3613	2.42417
$621$	−3.41956	−0.137222
$622$	53.6245	2.15015
$623$	−41.9381	−1.68022
$624$	2.56362	0.102627
$625$	−31.2346	−1.24938
$626$	−11.3204	−0.452454
$627$	−30.3959	−1.21390
$628$	−3.90450	−0.155807
$629$	13.4010	0.534334
$630$	114.803	4.57385
$631$	17.9842	0.715942	0.357971	−	0.933733i	$-0.383469\pi$
$631$	17.9842	0.715942	0.357971	+	0.933733i	$0.383469\pi$
$632$	51.2245	2.03760
$633$	70.6001	2.80610
$634$	15.7480	0.625435
$635$	−9.61063	−0.381386
$636$	118.402	4.69494
$637$	−0.211576	−0.00838297
$638$	51.8398	2.05236
$639$	−31.0928	−1.23001
$640$	8.99043	0.355378
$641$	42.5720	1.68149	0.840746	−	0.541430i	$-0.182117\pi$
$641$	42.5720	1.68149	0.840746	+	0.541430i	$0.182117\pi$
$642$	−32.3218	−1.27564
$643$	−5.20691	−0.205341	−0.102670	−	0.994715i	$-0.532739\pi$
$643$	−5.20691	−0.205341	−0.102670	+	0.994715i	$0.532739\pi$
$644$	−7.13037	−0.280976
$645$	−73.2831	−2.88552
$646$	−7.49738	−0.294981
$647$	−14.0356	−0.551796	−0.275898	−	0.961187i	$-0.588975\pi$
$647$	−14.0356	−0.551796	−0.275898	+	0.961187i	$0.588975\pi$
$648$	−27.0608	−1.06305
$649$	64.1247	2.51712
$650$	0.605469	0.0237484
$651$	41.0256	1.60792
$652$	81.5088	3.19213
$653$	22.3561	0.874861	0.437431	−	0.899252i	$-0.355889\pi$
$653$	22.3561	0.874861	0.437431	+	0.899252i	$0.355889\pi$
$654$	75.6342	2.95753
$655$	32.0573	1.25258
$656$	12.7145	0.496417
$657$	58.0012	2.26284
$658$	−37.9601	−1.47984
$659$	−9.99227	−0.389244	−0.194622	−	0.980878i	$-0.562348\pi$
$659$	−9.99227	−0.389244	−0.194622	+	0.980878i	$0.562348\pi$
$660$	−226.391	−8.81227
$661$	45.9954	1.78901	0.894507	−	0.447055i	$-0.147527\pi$
$661$	45.9954	1.78901	0.894507	+	0.447055i	$0.147527\pi$
$662$	53.3878	2.07498
$663$	0.473877	0.0184039
$664$	36.4903	1.41610
$665$	−14.2192	−0.551399
$666$	−112.207	−4.34793
$667$	−1.63329	−0.0632411
$668$	57.5421	2.22637
$669$	−12.3846	−0.478816
$670$	65.1982	2.51882
$671$	55.0165	2.12389
$672$	−80.4302	−3.10266
$673$	11.3273	0.436634	0.218317	−	0.975878i	$-0.429943\pi$
$673$	11.3273	0.436634	0.218317	+	0.975878i	$0.429943\pi$
$674$	11.2935	0.435010
$675$	−16.3603	−0.629709
$676$	−61.6409	−2.37080
$677$	−21.0450	−0.808826	−0.404413	−	0.914576i	$-0.632524\pi$
$677$	−21.0450	−0.808826	−0.404413	+	0.914576i	$0.632524\pi$
$678$	23.9679	0.920483
$679$	−19.1676	−0.735586
$680$	−32.3049	−1.23884
$681$	23.6203	0.905132
$682$	−73.8263	−2.82695
$683$	−9.78428	−0.374385	−0.187193	−	0.982323i	$-0.559939\pi$
$683$	−9.78428	−0.374385	−0.187193	+	0.982323i	$0.559939\pi$
$684$	44.1620	1.68858
$685$	53.3644	2.03895
$686$	−38.0658	−1.45336
$687$	−40.3533	−1.53957
$688$	84.1385	3.20775
$689$	0.845839	0.0322239
$690$	10.1391	0.385991
$691$	24.7012	0.939679	0.469839	−	0.882752i	$-0.344312\pi$
$691$	24.7012	0.939679	0.469839	+	0.882752i	$0.344312\pi$
$692$	59.0808	2.24591
$693$	−98.7784	−3.75228
$694$	−7.08935	−0.269108
$695$	−17.8829	−0.678339
$696$	−67.8742	−2.57277
$697$	2.35024	0.0890215
$698$	85.1695	3.22371
$699$	−34.5804	−1.30795
$700$	−34.1141	−1.28939
$701$	−1.66130	−0.0627465	−0.0313733	−	0.999508i	$-0.509988\pi$
$701$	−1.66130	−0.0627465	−0.0313733	+	0.999508i	$0.509988\pi$
$702$	−1.75480	−0.0662306
$703$	13.8977	0.524163
$704$	35.1801	1.32590
$705$	37.9729	1.43014
$706$	−70.7054	−2.66103
$707$	−33.9103	−1.27533
$708$	−145.129	−5.45427
$709$	5.08840	0.191099	0.0955494	−	0.995425i	$-0.469539\pi$
$709$	5.08840	0.191099	0.0955494	+	0.995425i	$0.469539\pi$
$710$	40.7729	1.53018
$711$	−38.6467	−1.44937
$712$	−98.8113	−3.70311
$713$	2.32600	0.0871095
$714$	−37.9534	−1.42037
$715$	−1.61729	−0.0604833
$716$	−63.3685	−2.36819
$717$	−0.511498	−0.0191022
$718$	−3.47857	−0.129819
$719$	3.62884	0.135333	0.0676664	−	0.997708i	$-0.478445\pi$
$719$	3.62884	0.135333	0.0676664	+	0.997708i	$0.478445\pi$
$720$	131.853	4.91387
$721$	−1.38707	−0.0516571
$722$	41.5703	1.54709
$723$	23.2174	0.863464
$724$	69.3965	2.57910
$725$	−7.81419	−0.290212
$726$	194.198	7.20735
$727$	−31.0204	−1.15048	−0.575242	−	0.817983i	$-0.695092\pi$
$727$	−31.0204	−1.15048	−0.575242	+	0.817983i	$0.695092\pi$
$728$	−2.11682	−0.0784545
$729$	−39.3805	−1.45854
$730$	−76.0585	−2.81505
$731$	15.5528	0.575240
$732$	−124.515	−4.60219
$733$	5.94675	0.219648	0.109824	−	0.993951i	$-0.464971\pi$
$733$	5.94675	0.219648	0.109824	+	0.993951i	$0.464971\pi$
$734$	25.5782	0.944109
$735$	−16.9511	−0.625252
$736$	−4.56010	−0.168087
$737$	−56.0977	−2.06639
$738$	−19.6785	−0.724377
$739$	14.0384	0.516412	0.258206	−	0.966090i	$-0.416869\pi$
$739$	14.0384	0.516412	0.258206	+	0.966090i	$0.416869\pi$
$740$	103.511	3.80516
$741$	0.491442	0.0180536
$742$	−67.7443	−2.48697
$743$	36.6943	1.34618	0.673092	−	0.739559i	$-0.264966\pi$
$743$	36.6943	1.34618	0.673092	+	0.739559i	$0.264966\pi$
$744$	96.6613	3.54378
$745$	−5.29259	−0.193906
$746$	59.7656	2.18817
$747$	−27.5304	−1.00728
$748$	48.0467	1.75676
$749$	13.0097	0.475364
$750$	−53.5766	−1.95634
$751$	25.9446	0.946730	0.473365	−	0.880866i	$-0.343039\pi$
$751$	25.9446	0.946730	0.473365	+	0.880866i	$0.343039\pi$
$752$	−43.5979	−1.58985
$753$	58.6112	2.13591
$754$	−0.838146	−0.0305235
$755$	−3.33062	−0.121214
$756$	98.8711	3.59591
$757$	4.58366	0.166596	0.0832980	−	0.996525i	$-0.473455\pi$
$757$	4.58366	0.166596	0.0832980	+	0.996525i	$0.473455\pi$
$758$	−23.8352	−0.865732
$759$	−8.72391	−0.316658
$760$	−33.5022	−1.21525
$761$	44.9563	1.62967	0.814833	−	0.579696i	$-0.196829\pi$
$761$	44.9563	1.62967	0.814833	+	0.579696i	$0.196829\pi$
$762$	−26.6031	−0.963728
$763$	−30.4431	−1.10212
$764$	13.2863	0.480681
$765$	24.3727	0.881196
$766$	83.0648	3.00125
$767$	−1.03677	−0.0374356
$768$	58.4452	2.10896
$769$	−34.5558	−1.24611	−0.623057	−	0.782176i	$-0.714110\pi$
$769$	−34.5558	−1.24611	−0.623057	+	0.782176i	$0.714110\pi$
$770$	129.531	4.66797
$771$	74.5965	2.68653
$772$	7.42207	0.267126
$773$	39.4155	1.41768	0.708838	−	0.705372i	$-0.249220\pi$
$773$	39.4155	1.41768	0.708838	+	0.705372i	$0.249220\pi$
$774$	−130.224	−4.68079
$775$	11.1284	0.399743
$776$	−45.1612	−1.62119
$777$	70.3534	2.52392
$778$	8.11720	0.291016
$779$	2.43735	0.0873270
$780$	3.66030	0.131060
$781$	−35.0818	−1.25532
$782$	−2.15182	−0.0769488
$783$	22.6475	0.809354
$784$	19.4621	0.695076
$785$	−2.23474	−0.0797611
$786$	88.7374	3.16516
$787$	−31.9260	−1.13804	−0.569019	−	0.822324i	$-0.692677\pi$
$787$	−31.9260	−1.13804	−0.569019	+	0.822324i	$0.692677\pi$
$788$	130.357	4.64377
$789$	−1.40204	−0.0499140
$790$	50.6785	1.80306
$791$	−9.64721	−0.343015
$792$	−232.734	−8.26983
$793$	−0.889507	−0.0315873
$794$	27.7539	0.984951
$795$	67.7672	2.40345
$796$	−46.6903	−1.65489
$797$	4.12973	0.146283	0.0731413	−	0.997322i	$-0.476698\pi$
$797$	4.12973	0.146283	0.0731413	+	0.997322i	$0.476698\pi$
$798$	−39.3601	−1.39333
$799$	−8.05895	−0.285105
$800$	−21.8170	−0.771349
$801$	74.5489	2.63406
$802$	0.863317	0.0304848
$803$	65.4422	2.30940
$804$	126.962	4.47760
$805$	−4.08105	−0.143838
$806$	1.19362	0.0420436
$807$	76.5323	2.69407
$808$	−79.8968	−2.81076
$809$	−26.3280	−0.925642	−0.462821	−	0.886452i	$-0.653163\pi$
$809$	−26.3280	−0.925642	−0.462821	+	0.886452i	$0.653163\pi$
$810$	−26.7724	−0.940686
$811$	38.6183	1.35607	0.678036	−	0.735029i	$-0.262831\pi$
$811$	38.6183	1.35607	0.678036	+	0.735029i	$0.262831\pi$
$812$	47.2239	1.65723
$813$	−46.2791	−1.62308
$814$	−126.602	−4.43740
$815$	46.6514	1.63413
$816$	−43.5902	−1.52596
$817$	16.1292	0.564291
$818$	−79.0478	−2.76384
$819$	1.59705	0.0558055
$820$	18.1536	0.633950
$821$	34.6345	1.20875	0.604375	−	0.796700i	$-0.293423\pi$
$821$	34.6345	1.20875	0.604375	+	0.796700i	$0.293423\pi$
$822$	147.718	5.15224
$823$	−0.673535	−0.0234780	−0.0117390	−	0.999931i	$-0.503737\pi$
$823$	−0.673535	−0.0234780	−0.0117390	+	0.999931i	$0.503737\pi$
$824$	−3.26810	−0.113850
$825$	−41.7381	−1.45314
$826$	83.0361	2.88920
$827$	31.7288	1.10332	0.551660	−	0.834069i	$-0.313995\pi$
$827$	31.7288	1.10332	0.551660	+	0.834069i	$0.313995\pi$
$828$	12.6749	0.440483
$829$	31.9368	1.10921	0.554605	−	0.832114i	$-0.312869\pi$
$829$	31.9368	1.10921	0.554605	+	0.832114i	$0.312869\pi$
$830$	36.1014	1.25310
$831$	−66.1139	−2.29346
$832$	−0.568792	−0.0197193
$833$	3.59752	0.124647
$834$	−49.5016	−1.71410
$835$	32.9341	1.13973
$836$	49.8276	1.72332
$837$	−32.2528	−1.11482
$838$	−61.4639	−2.12324
$839$	−28.2199	−0.974259	−0.487129	−	0.873330i	$-0.661956\pi$
$839$	−28.2199	−0.974259	−0.487129	+	0.873330i	$0.661956\pi$
$840$	−169.596	−5.85161
$841$	−18.1829	−0.626995
$842$	52.4541	1.80769
$843$	46.3274	1.59560
$844$	−115.734	−3.98372
$845$	−35.2800	−1.21367
$846$	67.4777	2.31993
$847$	−78.1655	−2.68580
$848$	−77.8055	−2.67185
$849$	34.0765	1.16950
$850$	−10.2950	−0.353116
$851$	3.98878	0.136734
$852$	79.3979	2.72013
$853$	−33.3188	−1.14081	−0.570407	−	0.821362i	$-0.693215\pi$
$853$	−33.3188	−1.14081	−0.570407	+	0.821362i	$0.693215\pi$
$854$	71.2417	2.43784
$855$	25.2760	0.864422
$856$	30.6524	1.04768
$857$	−15.4129	−0.526495	−0.263248	−	0.964728i	$-0.584794\pi$
$857$	−15.4129	−0.526495	−0.263248	+	0.964728i	$0.584794\pi$
$858$	−4.47681	−0.152836
$859$	−44.1927	−1.50783	−0.753917	−	0.656970i	$-0.771838\pi$
$859$	−44.1927	−1.50783	−0.753917	+	0.656970i	$0.771838\pi$
$860$	120.132	4.09646
$861$	12.3384	0.420491
$862$	−57.1889	−1.94786
$863$	−41.6241	−1.41690	−0.708450	−	0.705761i	$-0.750605\pi$
$863$	−41.6241	−1.41690	−0.708450	+	0.705761i	$0.750605\pi$
$864$	63.2312	2.15117
$865$	33.8148	1.14974
$866$	0.985959	0.0335042
$867$	41.1512	1.39757
$868$	−67.2527	−2.28271
$869$	−43.6047	−1.47919
$870$	−67.1508	−2.27662
$871$	0.906989	0.0307321
$872$	−71.7276	−2.42900
$873$	34.0722	1.15317
$874$	−2.23157	−0.0754841
$875$	21.5649	0.729025
$876$	−148.110	−5.00419
$877$	52.2061	1.76287	0.881437	−	0.472302i	$-0.156577\pi$
$877$	52.2061	1.76287	0.881437	+	0.472302i	$0.156577\pi$
$878$	−36.4204	−1.22913
$879$	24.7236	0.833906
$880$	148.769	5.01499
$881$	20.9233	0.704925	0.352463	−	0.935826i	$-0.385344\pi$
$881$	20.9233	0.704925	0.352463	+	0.935826i	$0.385344\pi$
$882$	−30.1221	−1.01426
$883$	17.5012	0.588961	0.294480	−	0.955657i	$-0.404853\pi$
$883$	17.5012	0.588961	0.294480	+	0.955657i	$0.404853\pi$
$884$	−0.776820	−0.0261273
$885$	−83.0641	−2.79217
$886$	−53.0693	−1.78290
$887$	31.3614	1.05301	0.526507	−	0.850171i	$-0.323501\pi$
$887$	31.3614	1.05301	0.526507	+	0.850171i	$0.323501\pi$
$888$	165.761	5.56258
$889$	10.7079	0.359130
$890$	−97.7581	−3.27686
$891$	23.0355	0.771717
$892$	20.3019	0.679757
$893$	−8.35766	−0.279678
$894$	−14.6504	−0.489981
$895$	−36.2689	−1.21233
$896$	−10.0169	−0.334640
$897$	0.141048	0.00470946
$898$	−34.9825	−1.16738
$899$	−15.4049	−0.513784
$900$	60.6410	2.02137
$901$	−14.3821	−0.479138
$902$	−22.2031	−0.739283
$903$	81.6498	2.71713
$904$	−22.7300	−0.755988
$905$	39.7190	1.32030
$906$	−9.21946	−0.306296
$907$	−6.95136	−0.230816	−0.115408	−	0.993318i	$-0.536818\pi$
$907$	−6.95136	−0.230816	−0.115408	+	0.993318i	$0.536818\pi$
$908$	−38.7204	−1.28498
$909$	60.2788	1.99932
$910$	−2.09426	−0.0694239
$911$	−0.791263	−0.0262157	−0.0131079	−	0.999914i	$-0.504172\pi$
$911$	−0.791263	−0.0262157	−0.0131079	+	0.999914i	$0.504172\pi$
$912$	−45.2058	−1.49692
$913$	−31.0623	−1.02801
$914$	78.5452	2.59805
$915$	−71.2657	−2.35597
$916$	66.1506	2.18568
$917$	−35.7172	−1.17949
$918$	29.8375	0.984785
$919$	30.8388	1.01728	0.508639	−	0.860980i	$-0.330149\pi$
$919$	30.8388	1.01728	0.508639	+	0.860980i	$0.330149\pi$
$920$	−9.61545	−0.317012
$921$	68.5343	2.25828
$922$	−17.4972	−0.576241
$923$	0.567202	0.0186697
$924$	252.238	8.29803
$925$	19.0837	0.627467
$926$	−59.2388	−1.94671
$927$	2.46564	0.0809823
$928$	30.2012	0.991402
$929$	−5.21718	−0.171170	−0.0855851	−	0.996331i	$-0.527276\pi$
$929$	−5.21718	−0.171170	−0.0855851	+	0.996331i	$0.527276\pi$
$930$	95.6311	3.13587
$931$	3.73086	0.122274
$932$	56.6871	1.85685
$933$	59.7670	1.95668
$934$	−21.7567	−0.711900
$935$	27.4995	0.899328
$936$	3.76284	0.122992
$937$	−21.7090	−0.709202	−0.354601	−	0.935018i	$-0.615383\pi$
$937$	−21.7090	−0.709202	−0.354601	+	0.935018i	$0.615383\pi$
$938$	−72.6418	−2.37184
$939$	−12.6171	−0.411744
$940$	−62.2485	−2.03032
$941$	15.9003	0.518334	0.259167	−	0.965833i	$-0.416552\pi$
$941$	15.9003	0.518334	0.259167	+	0.965833i	$0.416552\pi$
$942$	−6.18595	−0.201549
$943$	0.699541	0.0227802
$944$	95.3685	3.10398
$945$	56.5887	1.84083
$946$	−146.930	−4.77711
$947$	7.70460	0.250366	0.125183	−	0.992134i	$-0.460048\pi$
$947$	7.70460	0.250366	0.125183	+	0.992134i	$0.460048\pi$
$948$	98.6873	3.20522
$949$	−1.05807	−0.0343464
$950$	−10.6766	−0.346395
$951$	17.5519	0.569160
$952$	35.9931	1.16654
$953$	56.5495	1.83182	0.915909	−	0.401385i	$-0.131471\pi$
$953$	56.5495	1.83182	0.915909	+	0.401385i	$0.131471\pi$
$954$	120.422	3.89880
$955$	7.60438	0.246072
$956$	0.838491	0.0271187
$957$	57.7778	1.86769
$958$	−31.5704	−1.01999
$959$	−59.4570	−1.91997
$960$	−45.5706	−1.47078
$961$	−9.06145	−0.292305
$962$	2.04690	0.0659948
$963$	−23.1259	−0.745223
$964$	−38.0599	−1.22583
$965$	4.24801	0.136748
$966$	−11.2967	−0.363466
$967$	6.47417	0.208195	0.104098	−	0.994567i	$-0.466805\pi$
$967$	6.47417	0.208195	0.104098	+	0.994567i	$0.466805\pi$
$968$	−184.167	−5.91936
$969$	−8.35618	−0.268439
$970$	−44.6799	−1.43458
$971$	−6.52729	−0.209471	−0.104735	−	0.994500i	$-0.533400\pi$
$971$	−6.52729	−0.209471	−0.104735	+	0.994500i	$0.533400\pi$
$972$	45.8895	1.47191
$973$	19.9246	0.638754
$974$	−19.5449	−0.626260
$975$	0.674823	0.0216116
$976$	81.8224	2.61907
$977$	30.8621	0.987365	0.493683	−	0.869642i	$-0.335650\pi$
$977$	30.8621	0.987365	0.493683	+	0.869642i	$0.335650\pi$
$978$	129.135	4.12929
$979$	84.1129	2.68826
$980$	27.7877	0.887647
$981$	54.1155	1.72777
$982$	102.039	3.25621
$983$	−50.6469	−1.61538	−0.807692	−	0.589604i	$-0.799284\pi$
$983$	−50.6469	−1.61538	−0.807692	+	0.589604i	$0.799284\pi$
$984$	29.0707	0.926741
$985$	74.6095	2.37726
$986$	14.2513	0.453855
$987$	−42.3083	−1.34669
$988$	−0.805613	−0.0256300
$989$	4.62924	0.147201
$990$	−230.253	−7.31793
$991$	1.87369	0.0595198	0.0297599	−	0.999557i	$-0.490526\pi$
$991$	1.87369	0.0595198	0.0297599	+	0.999557i	$0.490526\pi$
$992$	−43.0102	−1.36558
$993$	59.5031	1.88827
$994$	−45.4279	−1.44089
$995$	−26.7231	−0.847179
$996$	70.3010	2.22757
$997$	−16.9000	−0.535229	−0.267614	−	0.963526i	$-0.586235\pi$
$997$	−16.9000	−0.535229	−0.267614	+	0.963526i	$0.586235\pi$
$998$	14.1721	0.448610
$999$	−55.3092	−1.74991

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8011.2.a.b.1.16	✓	358

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8011.2.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-2.59714 q^{2} -2.89463 q^{3} +4.74512 q^{4} +2.71586 q^{5} +7.51774 q^{6} -3.02593 q^{7} -7.12945 q^{8} +5.37887 q^{9} +O(q^{10})\)	\(q-2.59714 q^{2} -2.89463 q^{3} +4.74512 q^{4} +2.71586 q^{5} +7.51774 q^{6} -3.02593 q^{7} -7.12945 q^{8} +5.37887 q^{9} -7.05346 q^{10} +6.06893 q^{11} -13.7354 q^{12} -0.0981225 q^{13} +7.85875 q^{14} -7.86141 q^{15} +9.02592 q^{16} +1.66842 q^{17} -13.9697 q^{18} +1.73026 q^{19} +12.8871 q^{20} +8.75894 q^{21} -15.7618 q^{22} +0.496599 q^{23} +20.6371 q^{24} +2.37590 q^{25} +0.254838 q^{26} -6.88595 q^{27} -14.3584 q^{28} -3.28894 q^{29} +20.4171 q^{30} +4.68386 q^{31} -9.18265 q^{32} -17.5673 q^{33} -4.33311 q^{34} -8.21800 q^{35} +25.5234 q^{36} +8.03219 q^{37} -4.49371 q^{38} +0.284028 q^{39} -19.3626 q^{40} +1.40866 q^{41} -22.7482 q^{42} +9.32188 q^{43} +28.7978 q^{44} +14.6083 q^{45} -1.28974 q^{46} -4.83030 q^{47} -26.1267 q^{48} +2.15625 q^{49} -6.17054 q^{50} -4.82944 q^{51} -0.465603 q^{52} -8.62023 q^{53} +17.8837 q^{54} +16.4824 q^{55} +21.5732 q^{56} -5.00845 q^{57} +8.54183 q^{58} +10.5661 q^{59} -37.3033 q^{60} +9.06527 q^{61} -12.1646 q^{62} -16.2761 q^{63} +5.79675 q^{64} -0.266487 q^{65} +45.6247 q^{66} -9.24343 q^{67} +7.91683 q^{68} -1.43747 q^{69} +21.3433 q^{70} -5.78055 q^{71} -38.3484 q^{72} +10.7832 q^{73} -20.8607 q^{74} -6.87735 q^{75} +8.21027 q^{76} -18.3642 q^{77} -0.737660 q^{78} -7.18491 q^{79} +24.5131 q^{80} +3.79564 q^{81} -3.65849 q^{82} -5.11825 q^{83} +41.5622 q^{84} +4.53119 q^{85} -24.2102 q^{86} +9.52026 q^{87} -43.2681 q^{88} +13.8596 q^{89} -37.9397 q^{90} +0.296912 q^{91} +2.35642 q^{92} -13.5580 q^{93} +12.5449 q^{94} +4.69913 q^{95} +26.5803 q^{96} +6.33446 q^{97} -5.60007 q^{98} +32.6440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 358 q + 33 q^{2} + 11 q^{3} + 391 q^{4} + 76 q^{5} + 32 q^{6} + 19 q^{7} + 99 q^{8} + 451 q^{9}+O(q^{10}) \) 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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