LMFDB - Embedded newform 8033.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8033,2,Mod(1,8033)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8033, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8033.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8033 = 29 \cdot 277 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8033.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1438279437$
Analytic rank:	$1$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8033.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25257 q^{2} -2.81760 q^{3} +3.07408 q^{4} -4.05860 q^{5} +6.34684 q^{6} -4.96798 q^{7} -2.41944 q^{8} +4.93885 q^{9} +O(q^{10})$	\(q-2.25257 q^{2} -2.81760 q^{3} +3.07408 q^{4} -4.05860 q^{5} +6.34684 q^{6} -4.96798 q^{7} -2.41944 q^{8} +4.93885 q^{9} +9.14228 q^{10} +5.90144 q^{11} -8.66152 q^{12} +6.26539 q^{13} +11.1907 q^{14} +11.4355 q^{15} -0.698189 q^{16} +2.92440 q^{17} -11.1251 q^{18} -7.18148 q^{19} -12.4765 q^{20} +13.9978 q^{21} -13.2934 q^{22} -8.02976 q^{23} +6.81702 q^{24} +11.4722 q^{25} -14.1132 q^{26} -5.46291 q^{27} -15.2720 q^{28} -1.00000 q^{29} -25.7593 q^{30} +3.72773 q^{31} +6.41161 q^{32} -16.6279 q^{33} -6.58741 q^{34} +20.1630 q^{35} +15.1824 q^{36} +2.74292 q^{37} +16.1768 q^{38} -17.6533 q^{39} +9.81955 q^{40} +1.26054 q^{41} -31.5310 q^{42} -7.87552 q^{43} +18.1415 q^{44} -20.0448 q^{45} +18.0876 q^{46} -10.2359 q^{47} +1.96721 q^{48} +17.6809 q^{49} -25.8420 q^{50} -8.23977 q^{51} +19.2603 q^{52} +0.911333 q^{53} +12.3056 q^{54} -23.9515 q^{55} +12.0198 q^{56} +20.2345 q^{57} +2.25257 q^{58} +1.15197 q^{59} +35.1536 q^{60} -2.00053 q^{61} -8.39698 q^{62} -24.5361 q^{63} -13.0462 q^{64} -25.4287 q^{65} +37.4555 q^{66} -4.40580 q^{67} +8.98983 q^{68} +22.6246 q^{69} -45.4187 q^{70} -3.73848 q^{71} -11.9493 q^{72} -2.87305 q^{73} -6.17862 q^{74} -32.3240 q^{75} -22.0764 q^{76} -29.3182 q^{77} +39.7654 q^{78} -0.176415 q^{79} +2.83366 q^{80} +0.575710 q^{81} -2.83946 q^{82} -7.62554 q^{83} +43.0303 q^{84} -11.8689 q^{85} +17.7402 q^{86} +2.81760 q^{87} -14.2782 q^{88} +7.69461 q^{89} +45.1524 q^{90} -31.1263 q^{91} -24.6841 q^{92} -10.5032 q^{93} +23.0572 q^{94} +29.1467 q^{95} -18.0653 q^{96} -0.449984 q^{97} -39.8274 q^{98} +29.1463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) $ 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * 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 $

$2$	−2.25257	−1.59281	−0.796404	−	0.604764i	$-0.793267\pi$
$2$	−2.25257	−1.59281	−0.796404	+	0.604764i	$0.793267\pi$
$3$	−2.81760	−1.62674	−0.813370	−	0.581746i	$-0.802370\pi$
$3$	−2.81760	−1.62674	−0.813370	+	0.581746i	$0.802370\pi$
$4$	3.07408	1.53704
$5$	−4.05860	−1.81506	−0.907530	−	0.419988i	$-0.862034\pi$
$5$	−4.05860	−1.81506	−0.907530	+	0.419988i	$0.862034\pi$
$6$	6.34684	2.59109
$7$	−4.96798	−1.87772	−0.938861	−	0.344297i	$-0.888117\pi$
$7$	−4.96798	−1.87772	−0.938861	+	0.344297i	$0.888117\pi$
$8$	−2.41944	−0.855403
$9$	4.93885	1.64628
$10$	9.14228	2.89104
$11$	5.90144	1.77935	0.889675	−	0.456594i	$-0.150931\pi$
$11$	5.90144	1.77935	0.889675	+	0.456594i	$0.150931\pi$
$12$	−8.66152	−2.50037
$13$	6.26539	1.73771	0.868853	−	0.495070i	$-0.164858\pi$
$13$	6.26539	1.73771	0.868853	+	0.495070i	$0.164858\pi$
$14$	11.1907	2.99085
$15$	11.4355	2.95263
$16$	−0.698189	−0.174547
$17$	2.92440	0.709270	0.354635	−	0.935005i	$-0.384605\pi$
$17$	2.92440	0.709270	0.354635	+	0.935005i	$0.384605\pi$
$18$	−11.1251	−2.62222
$19$	−7.18148	−1.64754	−0.823772	−	0.566921i	$-0.808134\pi$
$19$	−7.18148	−1.64754	−0.823772	+	0.566921i	$0.808134\pi$
$20$	−12.4765	−2.78982
$21$	13.9978	3.05457
$22$	−13.2934	−2.83417
$23$	−8.02976	−1.67432	−0.837160	−	0.546958i	$-0.815786\pi$
$23$	−8.02976	−1.67432	−0.837160	+	0.546958i	$0.815786\pi$
$24$	6.81702	1.39152
$25$	11.4722	2.29444
$26$	−14.1132	−2.76783
$27$	−5.46291	−1.05134
$28$	−15.2720	−2.88613
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−25.7593	−4.70298
$31$	3.72773	0.669520	0.334760	−	0.942303i	$-0.391345\pi$
$31$	3.72773	0.669520	0.334760	+	0.942303i	$0.391345\pi$
$32$	6.41161	1.13342
$33$	−16.6279	−2.89454
$34$	−6.58741	−1.12973
$35$	20.1630	3.40818
$36$	15.1824	2.53041
$37$	2.74292	0.450933	0.225466	−	0.974251i	$-0.427609\pi$
$37$	2.74292	0.450933	0.225466	+	0.974251i	$0.427609\pi$
$38$	16.1768	2.62422
$39$	−17.6533	−2.82680
$40$	9.81955	1.55261
$41$	1.26054	0.196863	0.0984317	−	0.995144i	$-0.468617\pi$
$41$	1.26054	0.196863	0.0984317	+	0.995144i	$0.468617\pi$
$42$	−31.5310	−4.86534
$43$	−7.87552	−1.20100	−0.600502	−	0.799623i	$-0.705033\pi$
$43$	−7.87552	−1.20100	−0.600502	+	0.799623i	$0.705033\pi$
$44$	18.1415	2.73493
$45$	−20.0448	−2.98810
$46$	18.0876	2.66687
$47$	−10.2359	−1.49306	−0.746532	−	0.665350i	$-0.768282\pi$
$47$	−10.2359	−1.49306	−0.746532	+	0.665350i	$0.768282\pi$
$48$	1.96721	0.283943
$49$	17.6809	2.52584
$50$	−25.8420	−3.65460
$51$	−8.23977	−1.15380
$52$	19.2603	2.67092
$53$	0.911333	0.125181	0.0625906	−	0.998039i	$-0.480064\pi$
$53$	0.911333	0.125181	0.0625906	+	0.998039i	$0.480064\pi$
$54$	12.3056	1.67458
$55$	−23.9515	−3.22963
$56$	12.0198	1.60621
$57$	20.2345	2.68013
$58$	2.25257	0.295777
$59$	1.15197	0.149974	0.0749871	−	0.997185i	$-0.476108\pi$
$59$	1.15197	0.149974	0.0749871	+	0.997185i	$0.476108\pi$
$60$	35.1536	4.53831
$61$	−2.00053	−0.256142	−0.128071	−	0.991765i	$-0.540879\pi$
$61$	−2.00053	−0.256142	−0.128071	+	0.991765i	$0.540879\pi$
$62$	−8.39698	−1.06642
$63$	−24.5361	−3.09126
$64$	−13.0462	−1.63078
$65$	−25.4287	−3.15404
$66$	37.4555	4.61045
$67$	−4.40580	−0.538255	−0.269127	−	0.963105i	$-0.586735\pi$
$67$	−4.40580	−0.538255	−0.269127	+	0.963105i	$0.586735\pi$
$68$	8.98983	1.09018
$69$	22.6246	2.72368
$70$	−45.4187	−5.42857
$71$	−3.73848	−0.443676	−0.221838	−	0.975084i	$-0.571206\pi$
$71$	−3.73848	−0.443676	−0.221838	+	0.975084i	$0.571206\pi$
$72$	−11.9493	−1.40824
$73$	−2.87305	−0.336265	−0.168133	−	0.985764i	$-0.553774\pi$
$73$	−2.87305	−0.336265	−0.168133	+	0.985764i	$0.553774\pi$
$74$	−6.17862	−0.718250
$75$	−32.3240	−3.73246
$76$	−22.0764	−2.53234
$77$	−29.3182	−3.34112
$78$	39.7654	4.50255
$79$	−0.176415	−0.0198482	−0.00992410	−	0.999951i	$-0.503159\pi$
$79$	−0.176415	−0.0198482	−0.00992410	+	0.999951i	$0.503159\pi$
$80$	2.83366	0.316813
$81$	0.575710	0.0639678
$82$	−2.83946	−0.313566
$83$	−7.62554	−0.837012	−0.418506	−	0.908214i	$-0.637446\pi$
$83$	−7.62554	−0.837012	−0.418506	+	0.908214i	$0.637446\pi$
$84$	43.0303	4.69499
$85$	−11.8689	−1.28737
$86$	17.7402	1.91297
$87$	2.81760	0.302078
$88$	−14.2782	−1.52206
$89$	7.69461	0.815627	0.407814	−	0.913065i	$-0.366291\pi$
$89$	7.69461	0.815627	0.407814	+	0.913065i	$0.366291\pi$
$90$	45.1524	4.75948
$91$	−31.1263	−3.26293
$92$	−24.6841	−2.57350
$93$	−10.5032	−1.08914
$94$	23.0572	2.37816
$95$	29.1467	2.99039
$96$	−18.0653	−1.84379
$97$	−0.449984	−0.0456890	−0.0228445	−	0.999739i	$-0.507272\pi$
$97$	−0.449984	−0.0456890	−0.0228445	+	0.999739i	$0.507272\pi$
$98$	−39.8274	−4.02318
$99$	29.1463	2.92932
$100$	35.2665	3.52665
$101$	−8.94454	−0.890015	−0.445007	−	0.895527i	$-0.646799\pi$
$101$	−8.94454	−0.890015	−0.445007	+	0.895527i	$0.646799\pi$
$102$	18.5607	1.83778
$103$	−5.86538	−0.577933	−0.288966	−	0.957339i	$-0.593312\pi$
$103$	−5.86538	−0.577933	−0.288966	+	0.957339i	$0.593312\pi$
$104$	−15.1588	−1.48644
$105$	−56.8113	−5.54422
$106$	−2.05284	−0.199390
$107$	6.96451	0.673285	0.336642	−	0.941633i	$-0.390709\pi$
$107$	6.96451	0.673285	0.336642	+	0.941633i	$0.390709\pi$
$108$	−16.7934	−1.61595
$109$	15.3468	1.46996	0.734978	−	0.678090i	$-0.237192\pi$
$109$	15.3468	1.46996	0.734978	+	0.678090i	$0.237192\pi$
$110$	53.9526	5.14418
$111$	−7.72843	−0.733550
$112$	3.46859	0.327751
$113$	1.30597	0.122855	0.0614276	−	0.998112i	$-0.480435\pi$
$113$	1.30597	0.122855	0.0614276	+	0.998112i	$0.480435\pi$
$114$	−45.5797	−4.26893
$115$	32.5895	3.03899
$116$	−3.07408	−0.285421
$117$	30.9438	2.86076
$118$	−2.59490	−0.238880
$119$	−14.5283	−1.33181
$120$	−27.6675	−2.52569
$121$	23.8270	2.16609
$122$	4.50635	0.407985
$123$	−3.55169	−0.320246
$124$	11.4593	1.02908
$125$	−26.2680	−2.34948
$126$	55.2694	4.92379
$127$	−8.96340	−0.795373	−0.397686	−	0.917521i	$-0.630187\pi$
$127$	−8.96340	−0.795373	−0.397686	+	0.917521i	$0.630187\pi$
$128$	16.5644	1.46410
$129$	22.1900	1.95372
$130$	57.2799	5.02378
$131$	0.666873	0.0582649	0.0291325	−	0.999576i	$-0.490726\pi$
$131$	0.666873	0.0582649	0.0291325	+	0.999576i	$0.490726\pi$
$132$	−51.1154	−4.44903
$133$	35.6775	3.09363
$134$	9.92439	0.857337
$135$	22.1717	1.90824
$136$	−7.07541	−0.606712
$137$	17.0901	1.46011	0.730054	−	0.683389i	$-0.239495\pi$
$137$	17.0901	1.46011	0.730054	+	0.683389i	$0.239495\pi$
$138$	−50.9636	−4.33831
$139$	9.60437	0.814632	0.407316	−	0.913287i	$-0.366465\pi$
$139$	9.60437	0.814632	0.407316	+	0.913287i	$0.366465\pi$
$140$	61.9828	5.23850
$141$	28.8407	2.42883
$142$	8.42119	0.706691
$143$	36.9748	3.09199
$144$	−3.44825	−0.287354
$145$	4.05860	0.337048
$146$	6.47176	0.535607
$147$	−49.8176	−4.10888
$148$	8.43195	0.693102
$149$	12.7703	1.04618	0.523092	−	0.852276i	$-0.324778\pi$
$149$	12.7703	1.04618	0.523092	+	0.852276i	$0.324778\pi$
$150$	72.8122	5.94509
$151$	−17.9826	−1.46340	−0.731700	−	0.681627i	$-0.761273\pi$
$151$	−17.9826	−1.46340	−0.731700	+	0.681627i	$0.761273\pi$
$152$	17.3752	1.40931
$153$	14.4432	1.16766
$154$	66.0415	5.32177
$155$	−15.1293	−1.21522
$156$	−54.2678	−4.34490
$157$	−24.7938	−1.97876	−0.989382	−	0.145339i	$-0.953573\pi$
$157$	−24.7938	−1.97876	−0.989382	+	0.145339i	$0.953573\pi$
$158$	0.397387	0.0316144
$159$	−2.56777	−0.203637
$160$	−26.0221	−2.05723
$161$	39.8917	3.14391
$162$	−1.29683	−0.101889
$163$	−5.06376	−0.396624	−0.198312	−	0.980139i	$-0.563546\pi$
$163$	−5.06376	−0.396624	−0.198312	+	0.980139i	$0.563546\pi$
$164$	3.87500	0.302587
$165$	67.4858	5.25376
$166$	17.1771	1.33320
$167$	8.55847	0.662274	0.331137	−	0.943583i	$-0.392568\pi$
$167$	8.55847	0.662274	0.331137	+	0.943583i	$0.392568\pi$
$168$	−33.8668	−2.61288
$169$	26.2551	2.01962
$170$	26.7356	2.05053
$171$	−35.4683	−2.71233
$172$	−24.2100	−1.84599
$173$	−5.80224	−0.441136	−0.220568	−	0.975372i	$-0.570791\pi$
$173$	−5.80224	−0.441136	−0.220568	+	0.975372i	$0.570791\pi$
$174$	−6.34684	−0.481153
$175$	−56.9937	−4.30832
$176$	−4.12032	−0.310581
$177$	−3.24580	−0.243969
$178$	−17.3327	−1.29914
$179$	−5.52580	−0.413018	−0.206509	−	0.978445i	$-0.566210\pi$
$179$	−5.52580	−0.413018	−0.206509	+	0.978445i	$0.566210\pi$
$180$	−61.6194	−4.59284
$181$	0.428180	0.0318264	0.0159132	−	0.999873i	$-0.494934\pi$
$181$	0.428180	0.0318264	0.0159132	+	0.999873i	$0.494934\pi$
$182$	70.1143	5.19722
$183$	5.63670	0.416677
$184$	19.4276	1.43222
$185$	−11.1324	−0.818470
$186$	23.6593	1.73478
$187$	17.2581	1.26204
$188$	−31.4661	−2.29490
$189$	27.1396	1.97412
$190$	−65.6551	−4.76312
$191$	0.117389	0.00849394	0.00424697	−	0.999991i	$-0.498648\pi$
$191$	0.117389	0.00849394	0.00424697	+	0.999991i	$0.498648\pi$
$192$	36.7590	2.65285
$193$	−11.1394	−0.801834	−0.400917	−	0.916114i	$-0.631308\pi$
$193$	−11.1394	−0.801834	−0.400917	+	0.916114i	$0.631308\pi$
$194$	1.01362	0.0727738
$195$	71.6478	5.13080
$196$	54.3524	3.88231
$197$	19.5247	1.39108	0.695540	−	0.718487i	$-0.255165\pi$
$197$	19.5247	1.39108	0.695540	+	0.718487i	$0.255165\pi$
$198$	−65.6542	−4.66584
$199$	5.23982	0.371441	0.185721	−	0.982603i	$-0.440538\pi$
$199$	5.23982	0.371441	0.185721	+	0.982603i	$0.440538\pi$
$200$	−27.7563	−1.96267
$201$	12.4138	0.875600
$202$	20.1482	1.41762
$203$	4.96798	0.348684
$204$	−25.3297	−1.77343
$205$	−5.11602	−0.357319
$206$	13.2122	0.920537
$207$	−39.6578	−2.75641
$208$	−4.37442	−0.303312
$209$	−42.3810	−2.93156
$210$	127.972	8.83088
$211$	−0.170046	−0.0117064	−0.00585321	−	0.999983i	$-0.501863\pi$
$211$	−0.170046	−0.0117064	−0.00585321	+	0.999983i	$0.501863\pi$
$212$	2.80151	0.192409
$213$	10.5335	0.721745
$214$	−15.6881	−1.07241
$215$	31.9635	2.17989
$216$	13.2172	0.899317
$217$	−18.5193	−1.25717
$218$	−34.5698	−2.34136
$219$	8.09511	0.547017
$220$	−73.6290	−4.96407
$221$	18.3225	1.23250
$222$	17.4089	1.16841
$223$	1.95609	0.130989	0.0654947	−	0.997853i	$-0.479137\pi$
$223$	1.95609	0.130989	0.0654947	+	0.997853i	$0.479137\pi$
$224$	−31.8528	−2.12825
$225$	56.6595	3.77730
$226$	−2.94179	−0.195685
$227$	10.2020	0.677129	0.338564	−	0.940943i	$-0.390059\pi$
$227$	10.2020	0.677129	0.338564	+	0.940943i	$0.390059\pi$
$228$	62.2025	4.11946
$229$	−4.05548	−0.267993	−0.133997	−	0.990982i	$-0.542781\pi$
$229$	−4.05548	−0.267993	−0.133997	+	0.990982i	$0.542781\pi$
$230$	−73.4103	−4.84053
$231$	82.6070	5.43514
$232$	2.41944	0.158844
$233$	−0.256575	−0.0168088	−0.00840440	−	0.999965i	$-0.502675\pi$
$233$	−0.256575	−0.0168088	−0.00840440	+	0.999965i	$0.502675\pi$
$234$	−69.7032	−4.55664
$235$	41.5435	2.71000
$236$	3.54126	0.230516
$237$	0.497065	0.0322879
$238$	32.7262	2.12132
$239$	21.0698	1.36289	0.681446	−	0.731868i	$-0.261351\pi$
$239$	21.0698	1.36289	0.681446	+	0.731868i	$0.261351\pi$
$240$	−7.98413	−0.515373
$241$	0.372371	0.0239865	0.0119933	−	0.999928i	$-0.496182\pi$
$241$	0.372371	0.0239865	0.0119933	+	0.999928i	$0.496182\pi$
$242$	−53.6720	−3.45016
$243$	14.7666	0.947278
$244$	−6.14980	−0.393701
$245$	−71.7595	−4.58454
$246$	8.00045	0.510090
$247$	−44.9947	−2.86295
$248$	−9.01904	−0.572709
$249$	21.4857	1.36160
$250$	59.1706	3.74228
$251$	11.1080	0.701132	0.350566	−	0.936538i	$-0.385989\pi$
$251$	11.1080	0.701132	0.350566	+	0.936538i	$0.385989\pi$
$252$	−75.4261	−4.75140
$253$	−47.3871	−2.97920
$254$	20.1907	1.26688
$255$	33.4419	2.09421
$256$	−11.2200	−0.701247
$257$	10.4094	0.649321	0.324660	−	0.945831i	$-0.394750\pi$
$257$	10.4094	0.649321	0.324660	+	0.945831i	$0.394750\pi$
$258$	−49.9846	−3.11191
$259$	−13.6268	−0.846726
$260$	−78.1698	−4.84788
$261$	−4.93885	−0.305707
$262$	−1.50218	−0.0928049
$263$	26.9543	1.66207	0.831035	−	0.556219i	$-0.187749\pi$
$263$	26.9543	1.66207	0.831035	+	0.556219i	$0.187749\pi$
$264$	40.2302	2.47600
$265$	−3.69873	−0.227211
$266$	−80.3661	−4.92756
$267$	−21.6803	−1.32681
$268$	−13.5438	−0.827319
$269$	−0.811016	−0.0494485	−0.0247242	−	0.999694i	$-0.507871\pi$
$269$	−0.811016	−0.0494485	−0.0247242	+	0.999694i	$0.507871\pi$
$270$	−49.9434	−3.03946
$271$	15.3336	0.931447	0.465723	−	0.884930i	$-0.345794\pi$
$271$	15.3336	0.931447	0.465723	+	0.884930i	$0.345794\pi$
$272$	−2.04178	−0.123801
$273$	87.7015	5.30794
$274$	−38.4968	−2.32567
$275$	67.7025	4.08261
$276$	69.5499	4.18641
$277$	−1.00000	−0.0600842
$277$	−1.00000	−0.0600842
$278$	−21.6345	−1.29755
$279$	18.4107	1.10222
$280$	−48.7834	−2.91536
$281$	0.541350	0.0322943	0.0161471	−	0.999870i	$-0.494860\pi$
$281$	0.541350	0.0322943	0.0161471	+	0.999870i	$0.494860\pi$
$282$	−64.9658	−3.86866
$283$	−23.6592	−1.40639	−0.703196	−	0.710997i	$-0.748244\pi$
$283$	−23.6592	−1.40639	−0.703196	+	0.710997i	$0.748244\pi$
$284$	−11.4924	−0.681948
$285$	−82.1237	−4.86459
$286$	−83.2884	−4.92495
$287$	−6.26234	−0.369654
$288$	31.6660	1.86594
$289$	−8.44791	−0.496936
$290$	−9.14228	−0.536853
$291$	1.26787	0.0743241
$292$	−8.83200	−0.516854
$293$	−24.8314	−1.45066	−0.725332	−	0.688399i	$-0.758314\pi$
$293$	−24.8314	−1.45066	−0.725332	+	0.688399i	$0.758314\pi$
$294$	112.218	6.54466
$295$	−4.67540	−0.272212
$296$	−6.63633	−0.385729
$297$	−32.2390	−1.87070
$298$	−28.7660	−1.66637
$299$	−50.3095	−2.90948
$300$	−99.3667	−5.73694
$301$	39.1254	2.25515
$302$	40.5070	2.33092
$303$	25.2021	1.44782
$304$	5.01403	0.287574
$305$	8.11936	0.464913
$306$	−32.5343	−1.85986
$307$	6.61243	0.377391	0.188696	−	0.982036i	$-0.439574\pi$
$307$	6.61243	0.377391	0.188696	+	0.982036i	$0.439574\pi$
$308$	−90.1267	−5.13544
$309$	16.5263	0.940147
$310$	34.0800	1.93561
$311$	24.7889	1.40565	0.702826	−	0.711362i	$-0.251921\pi$
$311$	24.7889	1.40565	0.702826	+	0.711362i	$0.251921\pi$
$312$	42.7113	2.41805
$313$	−9.13631	−0.516415	−0.258207	−	0.966090i	$-0.583132\pi$
$313$	−9.13631	−0.516415	−0.258207	+	0.966090i	$0.583132\pi$
$314$	55.8499	3.15179
$315$	99.5823	5.61083
$316$	−0.542313	−0.0305075
$317$	23.7269	1.33264	0.666318	−	0.745668i	$-0.267870\pi$
$317$	23.7269	1.33264	0.666318	+	0.745668i	$0.267870\pi$
$318$	5.78409	0.324355
$319$	−5.90144	−0.330417
$320$	52.9494	2.95996
$321$	−19.6232	−1.09526
$322$	−89.8589	−5.00764
$323$	−21.0015	−1.16855
$324$	1.76978	0.0983211
$325$	71.8778	3.98706
$326$	11.4065	0.631747
$327$	−43.2411	−2.39124
$328$	−3.04981	−0.168397
$329$	50.8519	2.80356
$330$	−152.017	−8.36824
$331$	1.57105	0.0863525	0.0431762	−	0.999067i	$-0.486252\pi$
$331$	1.57105	0.0863525	0.0431762	+	0.999067i	$0.486252\pi$
$332$	−23.4415	−1.28652
$333$	13.5469	0.742363
$334$	−19.2786	−1.05488
$335$	17.8814	0.976964
$336$	−9.77309	−0.533166
$337$	15.1364	0.824531	0.412266	−	0.911064i	$-0.364738\pi$
$337$	15.1364	0.824531	0.412266	+	0.911064i	$0.364738\pi$
$338$	−59.1414	−3.21687
$339$	−3.67970	−0.199854
$340$	−36.4861	−1.97874
$341$	21.9990	1.19131
$342$	79.8948	4.32022
$343$	−53.0624	−2.86510
$344$	19.0544	1.02734
$345$	−91.8242	−4.94365
$346$	13.0700	0.702645
$347$	8.78297	0.471495	0.235747	−	0.971814i	$-0.424246\pi$
$347$	8.78297	0.471495	0.235747	+	0.971814i	$0.424246\pi$
$348$	8.66152	0.464306
$349$	−6.27286	−0.335778	−0.167889	−	0.985806i	$-0.553695\pi$
$349$	−6.27286	−0.335778	−0.167889	+	0.985806i	$0.553695\pi$
$350$	128.382	6.86233
$351$	−34.2272	−1.82691
$352$	37.8377	2.01676
$353$	−13.5130	−0.719223	−0.359611	−	0.933102i	$-0.617091\pi$
$353$	−13.5130	−0.719223	−0.359611	+	0.933102i	$0.617091\pi$
$354$	7.31139	0.388596
$355$	15.1730	0.805298
$356$	23.6539	1.25365
$357$	40.9350	2.16651
$358$	12.4473	0.657859
$359$	−34.1153	−1.80054	−0.900268	−	0.435335i	$-0.856630\pi$
$359$	−34.1153	−1.80054	−0.900268	+	0.435335i	$0.856630\pi$
$360$	48.4973	2.55603
$361$	32.5736	1.71440
$362$	−0.964507	−0.0506934
$363$	−67.1348	−3.52366
$364$	−95.6849	−5.01525
$365$	11.6606	0.610342
$366$	−12.6971	−0.663686
$367$	−14.0902	−0.735502	−0.367751	−	0.929924i	$-0.619872\pi$
$367$	−14.0902	−0.735502	−0.367751	+	0.929924i	$0.619872\pi$
$368$	5.60628	0.292248
$369$	6.22562	0.324093
$370$	25.0765	1.30367
$371$	−4.52749	−0.235055
$372$	−32.2878	−1.67405
$373$	−6.12580	−0.317182	−0.158591	−	0.987344i	$-0.550695\pi$
$373$	−6.12580	−0.317182	−0.158591	+	0.987344i	$0.550695\pi$
$374$	−38.8752	−2.01019
$375$	74.0127	3.82200
$376$	24.7653	1.27717
$377$	−6.26539	−0.322684
$378$	−61.1340	−3.14439
$379$	−29.1114	−1.49535	−0.747676	−	0.664064i	$-0.768830\pi$
$379$	−29.1114	−1.49535	−0.747676	+	0.664064i	$0.768830\pi$
$380$	89.5993	4.59635
$381$	25.2552	1.29387
$382$	−0.264426	−0.0135292
$383$	10.8015	0.551929	0.275965	−	0.961168i	$-0.411003\pi$
$383$	10.8015	0.551929	0.275965	+	0.961168i	$0.411003\pi$
$384$	−46.6717	−2.38171
$385$	118.991	6.06434
$386$	25.0924	1.27717
$387$	−38.8960	−1.97720
$388$	−1.38329	−0.0702258
$389$	0.598634	0.0303519	0.0151760	−	0.999885i	$-0.495169\pi$
$389$	0.598634	0.0303519	0.0151760	+	0.999885i	$0.495169\pi$
$390$	−161.392	−8.17239
$391$	−23.4822	−1.18755
$392$	−42.7779	−2.16061
$393$	−1.87898	−0.0947819
$394$	−43.9809	−2.21572
$395$	0.715996	0.0360256
$396$	89.5982	4.50248
$397$	−5.83199	−0.292699	−0.146350	−	0.989233i	$-0.546752\pi$
$397$	−5.83199	−0.292699	−0.146350	+	0.989233i	$0.546752\pi$
$398$	−11.8031	−0.591635
$399$	−100.525	−5.03253
$400$	−8.00976	−0.400488
$401$	−8.76492	−0.437699	−0.218850	−	0.975759i	$-0.570230\pi$
$401$	−8.76492	−0.437699	−0.218850	+	0.975759i	$0.570230\pi$
$402$	−27.9629	−1.39466
$403$	23.3557	1.16343
$404$	−27.4962	−1.36799
$405$	−2.33658	−0.116105
$406$	−11.1907	−0.555387
$407$	16.1872	0.802367
$408$	19.9357	0.986962
$409$	−33.1477	−1.63905	−0.819525	−	0.573043i	$-0.805763\pi$
$409$	−33.1477	−1.63905	−0.819525	+	0.573043i	$0.805763\pi$
$410$	11.5242	0.569140
$411$	−48.1531	−2.37522
$412$	−18.0306	−0.888306
$413$	−5.72299	−0.281610
$414$	89.3320	4.39043
$415$	30.9490	1.51923
$416$	40.1712	1.96956
$417$	−27.0612	−1.32519
$418$	95.4663	4.66941
$419$	−28.8767	−1.41072	−0.705361	−	0.708848i	$-0.749215\pi$
$419$	−28.8767	−1.41072	−0.705361	+	0.708848i	$0.749215\pi$
$420$	−174.643	−8.52169
$421$	−16.3030	−0.794561	−0.397281	−	0.917697i	$-0.630046\pi$
$421$	−16.3030	−0.794561	−0.397281	+	0.917697i	$0.630046\pi$
$422$	0.383040	0.0186461
$423$	−50.5537	−2.45801
$424$	−2.20492	−0.107080
$425$	33.5492	1.62738
$426$	−23.7275	−1.14960
$427$	9.93862	0.480963
$428$	21.4095	1.03487
$429$	−104.180	−5.02986
$430$	−72.0002	−3.47216
$431$	24.0453	1.15822	0.579111	−	0.815248i	$-0.303400\pi$
$431$	24.0453	1.15822	0.579111	+	0.815248i	$0.303400\pi$
$432$	3.81414	0.183508
$433$	−3.94047	−0.189367	−0.0946835	−	0.995507i	$-0.530184\pi$
$433$	−3.94047	−0.189367	−0.0946835	+	0.995507i	$0.530184\pi$
$434$	41.7161	2.00244
$435$	−11.4355	−0.548290
$436$	47.1773	2.25938
$437$	57.6655	2.75852
$438$	−18.2348	−0.871293
$439$	−9.99513	−0.477042	−0.238521	−	0.971137i	$-0.576663\pi$
$439$	−9.99513	−0.477042	−0.238521	+	0.971137i	$0.576663\pi$
$440$	57.9494	2.76263
$441$	87.3232	4.15825
$442$	−41.2727	−1.96314
$443$	19.5440	0.928562	0.464281	−	0.885688i	$-0.346313\pi$
$443$	19.5440	0.928562	0.464281	+	0.885688i	$0.346313\pi$
$444$	−23.7578	−1.12750
$445$	−31.2293	−1.48041
$446$	−4.40623	−0.208641
$447$	−35.9816	−1.70187
$448$	64.8135	3.06215
$449$	6.98594	0.329687	0.164843	−	0.986320i	$-0.447288\pi$
$449$	6.98594	0.329687	0.164843	+	0.986320i	$0.447288\pi$
$450$	−127.630	−6.01652
$451$	7.43900	0.350289
$452$	4.01466	0.188833
$453$	50.6676	2.38057
$454$	−22.9807	−1.07854
$455$	126.329	5.92241
$456$	−48.9563	−2.29259
$457$	−30.2453	−1.41482	−0.707409	−	0.706805i	$-0.750136\pi$
$457$	−30.2453	−1.41482	−0.707409	+	0.706805i	$0.750136\pi$
$458$	9.13526	0.426862
$459$	−15.9757	−0.745682
$460$	100.183	4.67105
$461$	−23.8344	−1.11008	−0.555038	−	0.831825i	$-0.687296\pi$
$461$	−23.8344	−1.11008	−0.555038	+	0.831825i	$0.687296\pi$
$462$	−186.078	−8.65714
$463$	29.5964	1.37546	0.687731	−	0.725965i	$-0.258607\pi$
$463$	29.5964	1.37546	0.687731	+	0.725965i	$0.258607\pi$
$464$	0.698189	0.0324126
$465$	42.6284	1.97685
$466$	0.577954	0.0267732
$467$	15.2695	0.706588	0.353294	−	0.935512i	$-0.385061\pi$
$467$	15.2695	0.706588	0.353294	+	0.935512i	$0.385061\pi$
$468$	95.1238	4.39710
$469$	21.8880	1.01069
$470$	−93.5797	−4.31651
$471$	69.8591	3.21894
$472$	−2.78714	−0.128288
$473$	−46.4769	−2.13701
$474$	−1.11968	−0.0514284
$475$	−82.3873	−3.78019
$476$	−44.6613	−2.04705
$477$	4.50094	0.206084
$478$	−47.4613	−2.17083
$479$	32.5072	1.48529	0.742647	−	0.669684i	$-0.233570\pi$
$479$	32.5072	1.48529	0.742647	+	0.669684i	$0.233570\pi$
$480$	73.3199	3.34658
$481$	17.1854	0.783588
$482$	−0.838793	−0.0382060
$483$	−112.399	−5.11432
$484$	73.2460	3.32936
$485$	1.82630	0.0829282
$486$	−33.2628	−1.50883
$487$	−15.8106	−0.716448	−0.358224	−	0.933636i	$-0.616618\pi$
$487$	−15.8106	−0.716448	−0.358224	+	0.933636i	$0.616618\pi$
$488$	4.84018	0.219105
$489$	14.2676	0.645205
$490$	161.643	7.30230
$491$	43.4874	1.96256	0.981280	−	0.192587i	$-0.0616879\pi$
$491$	43.4874	1.96256	0.981280	+	0.192587i	$0.0616879\pi$
$492$	−10.9182	−0.492230
$493$	−2.92440	−0.131708
$494$	101.354	4.56013
$495$	−118.293	−5.31688
$496$	−2.60266	−0.116863
$497$	18.5727	0.833099
$498$	−48.3981	−2.16877
$499$	34.8815	1.56151	0.780756	−	0.624836i	$-0.214834\pi$
$499$	34.8815	1.56151	0.780756	+	0.624836i	$0.214834\pi$
$500$	−80.7501	−3.61125
$501$	−24.1143	−1.07735
$502$	−25.0216	−1.11677
$503$	4.31267	0.192293	0.0961463	−	0.995367i	$-0.469348\pi$
$503$	4.31267	0.192293	0.0961463	+	0.995367i	$0.469348\pi$
$504$	59.3638	2.64428
$505$	36.3023	1.61543
$506$	106.743	4.74530
$507$	−73.9762	−3.28540
$508$	−27.5542	−1.22252
$509$	7.93819	0.351854	0.175927	−	0.984403i	$-0.443708\pi$
$509$	7.93819	0.351854	0.175927	+	0.984403i	$0.443708\pi$
$510$	−75.3302	−3.33568
$511$	14.2733	0.631413
$512$	−7.85497	−0.347144
$513$	39.2317	1.73212
$514$	−23.4479	−1.03424
$515$	23.8052	1.04898
$516$	68.2139	3.00295
$517$	−60.4067	−2.65668
$518$	30.6953	1.34867
$519$	16.3484	0.717613
$520$	61.5233	2.69797
$521$	11.8731	0.520170	0.260085	−	0.965586i	$-0.416249\pi$
$521$	11.8731	0.520170	0.260085	+	0.965586i	$0.416249\pi$
$522$	11.1251	0.486933
$523$	−7.03706	−0.307709	−0.153855	−	0.988093i	$-0.549169\pi$
$523$	−7.03706	−0.307709	−0.153855	+	0.988093i	$0.549169\pi$
$524$	2.05002	0.0895555
$525$	160.585	7.00852
$526$	−60.7164	−2.64736
$527$	10.9014	0.474871
$528$	11.6094	0.505234
$529$	41.4770	1.80335
$530$	8.33166	0.361904
$531$	5.68943	0.246900
$532$	109.675	4.75503
$533$	7.89777	0.342091
$534$	48.8365	2.11336
$535$	−28.2661	−1.22205
$536$	10.6596	0.460424
$537$	15.5695	0.671873
$538$	1.82687	0.0787620
$539$	104.343	4.49435
$540$	68.1577	2.93304
$541$	−12.1850	−0.523875	−0.261937	−	0.965085i	$-0.584361\pi$
$541$	−12.1850	−0.523875	−0.261937	+	0.965085i	$0.584361\pi$
$542$	−34.5399	−1.48362
$543$	−1.20644	−0.0517733
$544$	18.7501	0.803903
$545$	−62.2865	−2.66806
$546$	−197.554	−8.45453
$547$	5.08852	0.217569	0.108785	−	0.994065i	$-0.465304\pi$
$547$	5.08852	0.217569	0.108785	+	0.994065i	$0.465304\pi$
$548$	52.5365	2.24425
$549$	−9.88034	−0.421683
$550$	−152.505	−6.50282
$551$	7.18148	0.305941
$552$	−54.7390	−2.32985
$553$	0.876425	0.0372694
$554$	2.25257	0.0957026
$555$	31.3666	1.33144
$556$	29.5246	1.25212
$557$	−3.28064	−0.139005	−0.0695025	−	0.997582i	$-0.522141\pi$
$557$	−3.28064	−0.139005	−0.0695025	+	0.997582i	$0.522141\pi$
$558$	−41.4715	−1.75563
$559$	−49.3432	−2.08699
$560$	−14.0776	−0.594887
$561$	−48.6265	−2.05301
$562$	−1.21943	−0.0514386
$563$	36.7479	1.54874	0.774370	−	0.632733i	$-0.218067\pi$
$563$	36.7479	1.54874	0.774370	+	0.632733i	$0.218067\pi$
$564$	88.6587	3.73320
$565$	−5.30040	−0.222990
$566$	53.2940	2.24011
$567$	−2.86012	−0.120114
$568$	9.04504	0.379521
$569$	−35.1983	−1.47559	−0.737795	−	0.675025i	$-0.764133\pi$
$569$	−35.1983	−1.47559	−0.737795	+	0.675025i	$0.764133\pi$
$570$	184.990	7.74836
$571$	32.6201	1.36511	0.682554	−	0.730835i	$-0.260869\pi$
$571$	32.6201	1.36511	0.682554	+	0.730835i	$0.260869\pi$
$572$	113.664	4.75251
$573$	−0.330754	−0.0138174
$574$	14.1064	0.588789
$575$	−92.1190	−3.84163
$576$	−64.4334	−2.68473
$577$	24.9054	1.03683	0.518413	−	0.855130i	$-0.326523\pi$
$577$	24.9054	1.03683	0.518413	+	0.855130i	$0.326523\pi$
$578$	19.0295	0.791524
$579$	31.3864	1.30438
$580$	12.4765	0.518056
$581$	37.8836	1.57168
$582$	−2.85598	−0.118384
$583$	5.37818	0.222741
$584$	6.95119	0.287642
$585$	−125.588	−5.19244
$586$	55.9345	2.31063
$587$	−0.387276	−0.0159846	−0.00799231	−	0.999968i	$-0.502544\pi$
$587$	−0.387276	−0.0159846	−0.00799231	+	0.999968i	$0.502544\pi$
$588$	−153.143	−6.31552
$589$	−26.7706	−1.10306
$590$	10.5317	0.433582
$591$	−55.0128	−2.26293
$592$	−1.91507	−0.0787090
$593$	35.0796	1.44055	0.720273	−	0.693691i	$-0.244017\pi$
$593$	35.0796	1.44055	0.720273	+	0.693691i	$0.244017\pi$
$594$	72.6207	2.97966
$595$	58.9647	2.41732
$596$	39.2569	1.60803
$597$	−14.7637	−0.604238
$598$	113.326	4.63424
$599$	−26.9977	−1.10310	−0.551548	−	0.834143i	$-0.685963\pi$
$599$	−26.9977	−1.10310	−0.551548	+	0.834143i	$0.685963\pi$
$600$	78.2062	3.19275
$601$	46.8773	1.91216	0.956082	−	0.293098i	$-0.0946863\pi$
$601$	46.8773	1.91216	0.956082	+	0.293098i	$0.0946863\pi$
$602$	−88.1329	−3.59203
$603$	−21.7596	−0.886120
$604$	−55.2798	−2.24931
$605$	−96.7040	−3.93158
$606$	−56.7696	−2.30611
$607$	−41.3049	−1.67651	−0.838256	−	0.545276i	$-0.816425\pi$
$607$	−41.3049	−1.67651	−0.838256	+	0.545276i	$0.816425\pi$
$608$	−46.0448	−1.86736
$609$	−13.9978	−0.567219
$610$	−18.2894	−0.740517
$611$	−64.1320	−2.59450
$612$	44.3994	1.79474
$613$	−30.3557	−1.22606	−0.613028	−	0.790061i	$-0.710049\pi$
$613$	−30.3557	−1.22606	−0.613028	+	0.790061i	$0.710049\pi$
$614$	−14.8950	−0.601112
$615$	14.4149	0.581265
$616$	70.9339	2.85801
$617$	27.6700	1.11395	0.556975	−	0.830529i	$-0.311962\pi$
$617$	27.6700	1.11395	0.556975	+	0.830529i	$0.311962\pi$
$618$	−37.2266	−1.49747
$619$	19.3328	0.777052	0.388526	−	0.921438i	$-0.372984\pi$
$619$	19.3328	0.777052	0.388526	+	0.921438i	$0.372984\pi$
$620$	−46.5088	−1.86784
$621$	43.8658	1.76027
$622$	−55.8389	−2.23894
$623$	−38.2267	−1.53152
$624$	12.3254	0.493409
$625$	49.2503	1.97001
$626$	20.5802	0.822550
$627$	119.413	4.76888
$628$	−76.2183	−3.04144
$629$	8.02137	0.319833
$630$	−224.316	−8.93697
$631$	32.8229	1.30666	0.653330	−	0.757073i	$-0.273371\pi$
$631$	32.8229	1.30666	0.653330	+	0.757073i	$0.273371\pi$
$632$	0.426825	0.0169782
$633$	0.479120	0.0190433
$634$	−53.4465	−2.12263
$635$	36.3788	1.44365
$636$	−7.89353	−0.312999
$637$	110.777	4.38916
$638$	13.2934	0.526291
$639$	−18.4638	−0.730416
$640$	−67.2281	−2.65742
$641$	−20.3923	−0.805446	−0.402723	−	0.915322i	$-0.631936\pi$
$641$	−20.3923	−0.805446	−0.402723	+	0.915322i	$0.631936\pi$
$642$	44.2026	1.74454
$643$	14.5000	0.571824	0.285912	−	0.958256i	$-0.407704\pi$
$643$	14.5000	0.571824	0.285912	+	0.958256i	$0.407704\pi$
$644$	122.630	4.83231
$645$	−90.0604	−3.54612
$646$	47.3073	1.86128
$647$	−25.8656	−1.01688	−0.508442	−	0.861096i	$-0.669778\pi$
$647$	−25.8656	−1.01688	−0.508442	+	0.861096i	$0.669778\pi$
$648$	−1.39290	−0.0547183
$649$	6.79830	0.266857
$650$	−161.910	−6.35063
$651$	52.1799	2.04509
$652$	−15.5664	−0.609628
$653$	15.9555	0.624386	0.312193	−	0.950019i	$-0.398936\pi$
$653$	15.9555	0.624386	0.312193	+	0.950019i	$0.398936\pi$
$654$	97.4037	3.80879
$655$	−2.70657	−0.105754
$656$	−0.880095	−0.0343619
$657$	−14.1896	−0.553589
$658$	−114.548	−4.46553
$659$	−1.13271	−0.0441242	−0.0220621	−	0.999757i	$-0.507023\pi$
$659$	−1.13271	−0.0441242	−0.0220621	+	0.999757i	$0.507023\pi$
$660$	207.457	8.07525
$661$	−0.467581	−0.0181868	−0.00909339	−	0.999959i	$-0.502895\pi$
$661$	−0.467581	−0.0181868	−0.00909339	+	0.999959i	$0.502895\pi$
$662$	−3.53889	−0.137543
$663$	−51.6253	−2.00496
$664$	18.4496	0.715983
$665$	−144.800	−5.61512
$666$	−30.5153	−1.18244
$667$	8.02976	0.310913
$668$	26.3094	1.01794
$669$	−5.51147	−0.213086
$670$	−40.2791	−1.55612
$671$	−11.8060	−0.455766
$672$	89.7483	3.46211
$673$	37.8691	1.45975	0.729873	−	0.683582i	$-0.239579\pi$
$673$	37.8691	1.45975	0.729873	+	0.683582i	$0.239579\pi$
$674$	−34.0958	−1.31332
$675$	−62.6715	−2.41223
$676$	80.7102	3.10424
$677$	−14.0665	−0.540618	−0.270309	−	0.962774i	$-0.587126\pi$
$677$	−14.0665	−0.540618	−0.270309	+	0.962774i	$0.587126\pi$
$678$	8.28878	0.318329
$679$	2.23551	0.0857912
$680$	28.7162	1.10122
$681$	−28.7450	−1.10151
$682$	−49.5543	−1.89753
$683$	−24.6685	−0.943914	−0.471957	−	0.881621i	$-0.656452\pi$
$683$	−24.6685	−0.943914	−0.471957	+	0.881621i	$0.656452\pi$
$684$	−109.032	−4.16895
$685$	−69.3619	−2.65018
$686$	119.527	4.56355
$687$	11.4267	0.435956
$688$	5.49859	0.209632
$689$	5.70985	0.217528
$690$	206.841	7.87429
$691$	−8.01279	−0.304821	−0.152411	−	0.988317i	$-0.548704\pi$
$691$	−8.01279	−0.304821	−0.152411	+	0.988317i	$0.548704\pi$
$692$	−17.8365	−0.678044
$693$	−144.799	−5.50044
$694$	−19.7843	−0.751001
$695$	−38.9802	−1.47860
$696$	−6.81702	−0.258398
$697$	3.68632	0.139629
$698$	14.1301	0.534831
$699$	0.722926	0.0273436
$700$	−175.203	−6.62206
$701$	−33.9678	−1.28295	−0.641473	−	0.767146i	$-0.721676\pi$
$701$	−33.9678	−1.28295	−0.641473	+	0.767146i	$0.721676\pi$
$702$	77.0993	2.90993
$703$	−19.6982	−0.742931
$704$	−76.9915	−2.90173
$705$	−117.053	−4.40846
$706$	30.4389	1.14558
$707$	44.4363	1.67120
$708$	−9.97784	−0.374990
$709$	−12.5848	−0.472631	−0.236316	−	0.971676i	$-0.575940\pi$
$709$	−12.5848	−0.472631	−0.236316	+	0.971676i	$0.575940\pi$
$710$	−34.1782	−1.28269
$711$	−0.871286	−0.0326758
$712$	−18.6167	−0.697690
$713$	−29.9328	−1.12099
$714$	−92.2091	−3.45084
$715$	−150.066	−5.61214
$716$	−16.9868	−0.634825
$717$	−59.3662	−2.21707
$718$	76.8472	2.86791
$719$	−28.9159	−1.07838	−0.539190	−	0.842184i	$-0.681269\pi$
$719$	−28.9159	−1.07838	−0.539190	+	0.842184i	$0.681269\pi$
$720$	13.9951	0.521565
$721$	29.1391	1.08520
$722$	−73.3744	−2.73071
$723$	−1.04919	−0.0390198
$724$	1.31626	0.0489184
$725$	−11.4722	−0.426067
$726$	151.226	5.61252
$727$	48.5761	1.80159	0.900794	−	0.434247i	$-0.142985\pi$
$727$	48.5761	1.80159	0.900794	+	0.434247i	$0.142985\pi$
$728$	75.3085	2.79112
$729$	−43.3335	−1.60494
$730$	−26.2663	−0.972158
$731$	−23.0311	−0.851837
$732$	17.3277	0.640449
$733$	−20.6037	−0.761016	−0.380508	−	0.924778i	$-0.624251\pi$
$733$	−20.6037	−0.761016	−0.380508	+	0.924778i	$0.624251\pi$
$734$	31.7392	1.17151
$735$	202.189	7.45786
$736$	−51.4837	−1.89771
$737$	−26.0006	−0.957744
$738$	−14.0237	−0.516218
$739$	35.1923	1.29457	0.647284	−	0.762249i	$-0.275905\pi$
$739$	35.1923	1.29457	0.647284	+	0.762249i	$0.275905\pi$
$740$	−34.2219	−1.25802
$741$	126.777	4.65727
$742$	10.1985	0.374398
$743$	−3.49787	−0.128324	−0.0641622	−	0.997939i	$-0.520438\pi$
$743$	−3.49787	−0.128324	−0.0641622	+	0.997939i	$0.520438\pi$
$744$	25.4120	0.931650
$745$	−51.8295	−1.89889
$746$	13.7988	0.505210
$747$	−37.6614	−1.37796
$748$	53.0529	1.93981
$749$	−34.5996	−1.26424
$750$	−166.719	−6.08772
$751$	12.8673	0.469535	0.234768	−	0.972052i	$-0.424567\pi$
$751$	12.8673	0.469535	0.234768	+	0.972052i	$0.424567\pi$
$752$	7.14661	0.260610
$753$	−31.2979	−1.14056
$754$	14.1132	0.513974
$755$	72.9839	2.65616
$756$	83.4294	3.03430
$757$	31.2921	1.13733	0.568665	−	0.822569i	$-0.307460\pi$
$757$	31.2921	1.13733	0.568665	+	0.822569i	$0.307460\pi$
$758$	65.5755	2.38181
$759$	133.518	4.84639
$760$	−70.5189	−2.55799
$761$	−19.9628	−0.723650	−0.361825	−	0.932246i	$-0.617846\pi$
$761$	−19.9628	−0.723650	−0.361825	+	0.932246i	$0.617846\pi$
$762$	−56.8892	−2.06088
$763$	−76.2427	−2.76017
$764$	0.360862	0.0130555
$765$	−58.6189	−2.11937
$766$	−24.3311	−0.879118
$767$	7.21756	0.260611
$768$	31.6133	1.14075
$769$	−37.1336	−1.33907	−0.669536	−	0.742780i	$-0.733507\pi$
$769$	−37.1336	−1.33907	−0.669536	+	0.742780i	$0.733507\pi$
$770$	−268.036	−9.65933
$771$	−29.3295	−1.05628
$772$	−34.2435	−1.23245
$773$	30.9749	1.11409	0.557045	−	0.830482i	$-0.311935\pi$
$773$	30.9749	1.11409	0.557045	+	0.830482i	$0.311935\pi$
$774$	87.6161	3.14929
$775$	42.7653	1.53617
$776$	1.08871	0.0390825
$777$	38.3947	1.37740
$778$	−1.34847	−0.0483448
$779$	−9.05254	−0.324341
$780$	220.251	7.88625
$781$	−22.0624	−0.789455
$782$	52.8953	1.89153
$783$	5.46291	0.195228
$784$	−12.3446	−0.440878
$785$	100.628	3.59157
$786$	4.23253	0.150969
$787$	−16.9594	−0.604537	−0.302268	−	0.953223i	$-0.597744\pi$
$787$	−16.9594	−0.604537	−0.302268	+	0.953223i	$0.597744\pi$
$788$	60.0206	2.13815
$789$	−75.9462	−2.70376
$790$	−1.61283	−0.0573820
$791$	−6.48803	−0.230688
$792$	−70.5179	−2.50575
$793$	−12.5341	−0.445099
$794$	13.1370	0.466214
$795$	10.4215	0.369614
$796$	16.1076	0.570920
$797$	49.9341	1.76876	0.884379	−	0.466770i	$-0.154582\pi$
$797$	49.9341	1.76876	0.884379	+	0.466770i	$0.154582\pi$
$798$	226.439	8.01586
$799$	−29.9339	−1.05898
$800$	73.5552	2.60057
$801$	38.0025	1.34275
$802$	19.7436	0.697172
$803$	−16.9551	−0.598334
$804$	38.1610	1.34583
$805$	−161.904	−5.70638
$806$	−52.6103	−1.85312
$807$	2.28512	0.0804399
$808$	21.6408	0.761321
$809$	31.5750	1.11012	0.555059	−	0.831811i	$-0.312696\pi$
$809$	31.5750	1.11012	0.555059	+	0.831811i	$0.312696\pi$
$810$	5.26330	0.184934
$811$	24.1557	0.848222	0.424111	−	0.905610i	$-0.360587\pi$
$811$	24.1557	0.848222	0.424111	+	0.905610i	$0.360587\pi$
$812$	15.2720	0.535942
$813$	−43.2038	−1.51522
$814$	−36.4627	−1.27802
$815$	20.5518	0.719897
$816$	5.75291	0.201392
$817$	56.5578	1.97871
$818$	74.6677	2.61069
$819$	−153.728	−5.37171
$820$	−15.7271	−0.549213
$821$	13.2610	0.462811	0.231405	−	0.972857i	$-0.425668\pi$
$821$	13.2610	0.462811	0.231405	+	0.972857i	$0.425668\pi$
$822$	108.468	3.78327
$823$	9.80760	0.341872	0.170936	−	0.985282i	$-0.445321\pi$
$823$	9.80760	0.341872	0.170936	+	0.985282i	$0.445321\pi$
$824$	14.1910	0.494365
$825$	−190.758	−6.64135
$826$	12.8914	0.448551
$827$	44.4584	1.54597	0.772986	−	0.634423i	$-0.218762\pi$
$827$	44.4584	1.54597	0.772986	+	0.634423i	$0.218762\pi$
$828$	−121.911	−4.23671
$829$	−37.4630	−1.30114	−0.650572	−	0.759445i	$-0.725471\pi$
$829$	−37.4630	−1.30114	−0.650572	+	0.759445i	$0.725471\pi$
$830$	−69.7149	−2.41984
$831$	2.81760	0.0977414
$832$	−81.7397	−2.83381
$833$	51.7058	1.79150
$834$	60.9574	2.11078
$835$	−34.7354	−1.20207
$836$	−130.283	−4.50592
$837$	−20.3642	−0.703891
$838$	65.0470	2.24701
$839$	−13.3132	−0.459622	−0.229811	−	0.973235i	$-0.573811\pi$
$839$	−13.3132	−0.459622	−0.229811	+	0.973235i	$0.573811\pi$
$840$	137.452	4.74254
$841$	1.00000	0.0344828
$842$	36.7238	1.26558
$843$	−1.52531	−0.0525344
$844$	−0.522734	−0.0179933
$845$	−106.559	−3.66573
$846$	113.876	3.91513
$847$	−118.372	−4.06731
$848$	−0.636282	−0.0218500
$849$	66.6620	2.28783
$850$	−75.5721	−2.59210
$851$	−22.0250	−0.755006
$852$	32.3809	1.10935
$853$	25.5509	0.874846	0.437423	−	0.899256i	$-0.355891\pi$
$853$	25.5509	0.874846	0.437423	+	0.899256i	$0.355891\pi$
$854$	−22.3875	−0.766083
$855$	143.951	4.92303
$856$	−16.8503	−0.575930
$857$	−50.3076	−1.71848	−0.859238	−	0.511576i	$-0.829062\pi$
$857$	−50.3076	−1.71848	−0.859238	+	0.511576i	$0.829062\pi$
$858$	234.673	8.01161
$859$	36.1581	1.23370	0.616850	−	0.787081i	$-0.288409\pi$
$859$	36.1581	1.23370	0.616850	+	0.787081i	$0.288409\pi$
$860$	98.2585	3.35059
$861$	17.6448	0.601332
$862$	−54.1638	−1.84483
$863$	−21.8520	−0.743849	−0.371925	−	0.928263i	$-0.621302\pi$
$863$	−21.8520	−0.743849	−0.371925	+	0.928263i	$0.621302\pi$
$864$	−35.0260	−1.19161
$865$	23.5489	0.800688
$866$	8.87619	0.301625
$867$	23.8028	0.808386
$868$	−56.9298	−1.93232
$869$	−1.04110	−0.0353169
$870$	25.7593	0.873321
$871$	−27.6041	−0.935328
$872$	−37.1307	−1.25741
$873$	−2.22241	−0.0752170
$874$	−129.896	−4.39379
$875$	130.499	4.41168
$876$	24.8850	0.840787
$877$	−19.0294	−0.642576	−0.321288	−	0.946982i	$-0.604116\pi$
$877$	−19.0294	−0.642576	−0.321288	+	0.946982i	$0.604116\pi$
$878$	22.5148	0.759836
$879$	69.9648	2.35985
$880$	16.7227	0.563722
$881$	−50.3886	−1.69763	−0.848817	−	0.528687i	$-0.822685\pi$
$881$	−50.3886	−1.69763	−0.848817	+	0.528687i	$0.822685\pi$
$882$	−196.702	−6.62329
$883$	−10.5574	−0.355286	−0.177643	−	0.984095i	$-0.556847\pi$
$883$	−10.5574	−0.355286	−0.177643	+	0.984095i	$0.556847\pi$
$884$	56.3247	1.89441
$885$	13.1734	0.442818
$886$	−44.0242	−1.47902
$887$	43.1301	1.44817	0.724083	−	0.689713i	$-0.242263\pi$
$887$	43.1301	1.44817	0.724083	+	0.689713i	$0.242263\pi$
$888$	18.6985	0.627481
$889$	44.5300	1.49349
$890$	70.3463	2.35801
$891$	3.39752	0.113821
$892$	6.01317	0.201336
$893$	73.5091	2.45989
$894$	81.0511	2.71075
$895$	22.4270	0.749652
$896$	−82.2915	−2.74917
$897$	141.752	4.73296
$898$	−15.7363	−0.525128
$899$	−3.72773	−0.124327
$900$	174.176	5.80586
$901$	2.66510	0.0887873
$902$	−16.7569	−0.557943
$903$	−110.240	−3.66855
$904$	−3.15972	−0.105091
$905$	−1.73781	−0.0577668
$906$	−114.132	−3.79180
$907$	7.66555	0.254531	0.127265	−	0.991869i	$-0.459380\pi$
$907$	7.66555	0.254531	0.127265	+	0.991869i	$0.459380\pi$
$908$	31.3617	1.04077
$909$	−44.1758	−1.46522
$910$	−284.566	−9.43326
$911$	20.3786	0.675173	0.337587	−	0.941295i	$-0.390389\pi$
$911$	20.3786	0.675173	0.337587	+	0.941295i	$0.390389\pi$
$912$	−14.1275	−0.467808
$913$	−45.0017	−1.48934
$914$	68.1298	2.25353
$915$	−22.8771	−0.756293
$916$	−12.4669	−0.411917
$917$	−3.31301	−0.109405
$918$	35.9864	1.18773
$919$	−46.8828	−1.54652	−0.773261	−	0.634088i	$-0.781376\pi$
$919$	−46.8828	−1.54652	−0.773261	+	0.634088i	$0.781376\pi$
$920$	−78.8486	−2.59956
$921$	−18.6312	−0.613918
$922$	53.6886	1.76814
$923$	−23.4230	−0.770978
$924$	253.941	8.35403
$925$	31.4673	1.03464
$926$	−66.6681	−2.19085
$927$	−28.9682	−0.951442
$928$	−6.41161	−0.210471
$929$	28.8103	0.945234	0.472617	−	0.881268i	$-0.343309\pi$
$929$	28.8103	0.945234	0.472617	+	0.881268i	$0.343309\pi$
$930$	−96.0236	−3.14874
$931$	−126.975	−4.16143
$932$	−0.788733	−0.0258358
$933$	−69.8453	−2.28663
$934$	−34.3957	−1.12546
$935$	−70.0438	−2.29068
$936$	−74.8669	−2.44710
$937$	−27.1981	−0.888524	−0.444262	−	0.895897i	$-0.646534\pi$
$937$	−27.1981	−0.888524	−0.444262	+	0.895897i	$0.646534\pi$
$938$	−49.3042	−1.60984
$939$	25.7424	0.840073
$940$	127.708	4.16538
$941$	0.657579	0.0214365	0.0107182	−	0.999943i	$-0.496588\pi$
$941$	0.657579	0.0214365	0.0107182	+	0.999943i	$0.496588\pi$
$942$	−157.363	−5.12715
$943$	−10.1218	−0.329612
$944$	−0.804295	−0.0261776
$945$	−110.149	−3.58314
$946$	104.692	3.40385
$947$	53.3148	1.73250	0.866250	−	0.499611i	$-0.166524\pi$
$947$	53.3148	1.73250	0.866250	+	0.499611i	$0.166524\pi$
$948$	1.52802	0.0496278
$949$	−18.0008	−0.584330
$950$	185.583	6.02112
$951$	−66.8528	−2.16785
$952$	35.1505	1.13924
$953$	8.47456	0.274518	0.137259	−	0.990535i	$-0.456171\pi$
$953$	8.47456	0.274518	0.137259	+	0.990535i	$0.456171\pi$
$954$	−10.1387	−0.328252
$955$	−0.476433	−0.0154170
$956$	64.7703	2.09482
$957$	16.6279	0.537503
$958$	−73.2249	−2.36579
$959$	−84.9035	−2.74168
$960$	−149.190	−4.81509
$961$	−17.1040	−0.551743
$962$	−38.7114	−1.24811
$963$	34.3967	1.10842
$964$	1.14470	0.0368683
$965$	45.2104	1.45538
$966$	253.186	8.14614
$967$	0.774766	0.0249148	0.0124574	−	0.999922i	$-0.496035\pi$
$967$	0.774766	0.0249148	0.0124574	+	0.999922i	$0.496035\pi$
$968$	−57.6480	−1.85288
$969$	59.1737	1.90093
$970$	−4.11388	−0.132089
$971$	42.6153	1.36759	0.683795	−	0.729674i	$-0.260328\pi$
$971$	42.6153	1.36759	0.683795	+	0.729674i	$0.260328\pi$
$972$	45.3937	1.45600
$973$	−47.7143	−1.52965
$974$	35.6146	1.14116
$975$	−202.523	−6.48591
$976$	1.39675	0.0447089
$977$	−55.9095	−1.78870	−0.894352	−	0.447364i	$-0.852363\pi$
$977$	−55.9095	−1.78870	−0.894352	+	0.447364i	$0.852363\pi$
$978$	−32.1389	−1.02769
$979$	45.4093	1.45129
$980$	−220.594	−7.04663
$981$	75.7956	2.41997
$982$	−97.9585	−3.12598
$983$	−5.85459	−0.186732	−0.0933662	−	0.995632i	$-0.529763\pi$
$983$	−5.85459	−0.186732	−0.0933662	+	0.995632i	$0.529763\pi$
$984$	8.59313	0.273939
$985$	−79.2430	−2.52489
$986$	6.58741	0.209786
$987$	−143.280	−4.56066
$988$	−138.317	−4.40046
$989$	63.2385	2.01087
$990$	266.464	8.46878
$991$	0.636396	0.0202158	0.0101079	−	0.999949i	$-0.496783\pi$
$991$	0.636396	0.0202158	0.0101079	+	0.999949i	$0.496783\pi$
$992$	23.9007	0.758850
$993$	−4.42657	−0.140473
$994$	−41.8363	−1.32697
$995$	−21.2663	−0.674187
$996$	66.0488	2.09284
$997$	−44.6539	−1.41420	−0.707102	−	0.707112i	$-0.749998\pi$
$997$	−44.6539	−1.41420	−0.707102	+	0.707112i	$0.749998\pi$
$998$	−78.5732	−2.48719
$999$	−14.9843	−0.474082

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8033.2.a.b.1.17	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8033.2.a.b.1.17	✓	153	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:	\( N \)	\(=\)	\( 8033 = 29 \cdot 277 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8033.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25257 q^{2} -2.81760 q^{3} +3.07408 q^{4} -4.05860 q^{5} +6.34684 q^{6} -4.96798 q^{7} -2.41944 q^{8} +4.93885 q^{9} +O(q^{10})\)	\(q-2.25257 q^{2} -2.81760 q^{3} +3.07408 q^{4} -4.05860 q^{5} +6.34684 q^{6} -4.96798 q^{7} -2.41944 q^{8} +4.93885 q^{9} +9.14228 q^{10} +5.90144 q^{11} -8.66152 q^{12} +6.26539 q^{13} +11.1907 q^{14} +11.4355 q^{15} -0.698189 q^{16} +2.92440 q^{17} -11.1251 q^{18} -7.18148 q^{19} -12.4765 q^{20} +13.9978 q^{21} -13.2934 q^{22} -8.02976 q^{23} +6.81702 q^{24} +11.4722 q^{25} -14.1132 q^{26} -5.46291 q^{27} -15.2720 q^{28} -1.00000 q^{29} -25.7593 q^{30} +3.72773 q^{31} +6.41161 q^{32} -16.6279 q^{33} -6.58741 q^{34} +20.1630 q^{35} +15.1824 q^{36} +2.74292 q^{37} +16.1768 q^{38} -17.6533 q^{39} +9.81955 q^{40} +1.26054 q^{41} -31.5310 q^{42} -7.87552 q^{43} +18.1415 q^{44} -20.0448 q^{45} +18.0876 q^{46} -10.2359 q^{47} +1.96721 q^{48} +17.6809 q^{49} -25.8420 q^{50} -8.23977 q^{51} +19.2603 q^{52} +0.911333 q^{53} +12.3056 q^{54} -23.9515 q^{55} +12.0198 q^{56} +20.2345 q^{57} +2.25257 q^{58} +1.15197 q^{59} +35.1536 q^{60} -2.00053 q^{61} -8.39698 q^{62} -24.5361 q^{63} -13.0462 q^{64} -25.4287 q^{65} +37.4555 q^{66} -4.40580 q^{67} +8.98983 q^{68} +22.6246 q^{69} -45.4187 q^{70} -3.73848 q^{71} -11.9493 q^{72} -2.87305 q^{73} -6.17862 q^{74} -32.3240 q^{75} -22.0764 q^{76} -29.3182 q^{77} +39.7654 q^{78} -0.176415 q^{79} +2.83366 q^{80} +0.575710 q^{81} -2.83946 q^{82} -7.62554 q^{83} +43.0303 q^{84} -11.8689 q^{85} +17.7402 q^{86} +2.81760 q^{87} -14.2782 q^{88} +7.69461 q^{89} +45.1524 q^{90} -31.1263 q^{91} -24.6841 q^{92} -10.5032 q^{93} +23.0572 q^{94} +29.1467 q^{95} -18.0653 q^{96} -0.449984 q^{97} -39.8274 q^{98} +29.1463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9}+O(q^{10}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9	\( 153 q - 3 q^{2} - 12 q^{3} + 135 q^{4} - 11 q^{5} - 17 q^{6} - 76 q^{7} - 12 q^{8} + 133 q^{9} - 30 q^{10} + 4 q^{11} - 39 q^{12} - 65 q^{13} + q^{14} - 26 q^{15} + 107 q^{16} - 20 q^{17} - 21 q^{18} - 65 q^{19} - 23 q^{20} - 24 q^{21} - 59 q^{22} - 62 q^{23} - 59 q^{24} + 102 q^{25} - 18 q^{26} - 57 q^{27} - 155 q^{28} - 153 q^{29} - 82 q^{30} - 49 q^{31} - 17 q^{32} - 59 q^{33} - 68 q^{34} - 36 q^{35} + 74 q^{36} - 30 q^{37} - 67 q^{38} - 47 q^{39} - 108 q^{40} - 9 q^{41} - 62 q^{42} - 90 q^{43} - 14 q^{44} - 56 q^{45} - 52 q^{46} - 54 q^{47} - 76 q^{48} + 101 q^{49} - 36 q^{50} - 60 q^{51} - 191 q^{52} - 38 q^{53} - 82 q^{54} - 215 q^{55} + 24 q^{56} - 52 q^{57} + 3 q^{58} - 55 q^{59} - 60 q^{60} - 90 q^{61} - 66 q^{62} - 229 q^{63} + 52 q^{64} - 67 q^{65} - 29 q^{66} - 114 q^{67} - 78 q^{68} - 68 q^{69} - 61 q^{70} - 52 q^{71} - 47 q^{72} - 83 q^{73} - 21 q^{74} - 47 q^{75} - 100 q^{76} - 32 q^{77} - 17 q^{78} - 151 q^{79} - 24 q^{80} + 81 q^{81} - 151 q^{82} - 94 q^{83} - 84 q^{84} - 77 q^{85} - 43 q^{86} + 12 q^{87} - 121 q^{88} + 11 q^{89} - 14 q^{90} - 66 q^{91} - 156 q^{92} - 66 q^{93} - 22 q^{94} - 67 q^{95} - 131 q^{96} - 78 q^{97} - 67 q^{98} - 41 q^{99}+O(q^{100}) \) 153 * q - 3 * q^2 - 12 * q^3 + 135 * q^4 - 11 * q^5 - 17 * q^6 - 76 * q^7 - 12 * q^8 + 133 * q^9 - 30 * q^10 + 4 * q^11 - 39 * q^12 - 65 * q^13 + q^14 - 26 * q^15 + 107 * q^16 - 20 * q^17 - 21 * q^18 - 65 * q^19 - 23 * q^20 - 24 * q^21 - 59 * q^22 - 62 * q^23 - 59 * q^24 + 102 * q^25 - 18 * q^26 - 57 * q^27 - 155 * q^28 - 153 * q^29 - 82 * q^30 - 49 * q^31 - 17 * q^32 - 59 * q^33 - 68 * q^34 - 36 * q^35 + 74 * q^36 - 30 * q^37 - 67 * q^38 - 47 * q^39 - 108 * q^40 - 9 * q^41 - 62 * q^42 - 90 * q^43 - 14 * q^44 - 56 * q^45 - 52 * q^46 - 54 * q^47 - 76 * q^48 + 101 * q^49 - 36 * q^50 - 60 * q^51 - 191 * q^52 - 38 * q^53 - 82 * q^54 - 215 * q^55 + 24 * q^56 - 52 * q^57 + 3 * q^58 - 55 * q^59 - 60 * q^60 - 90 * q^61 - 66 * q^62 - 229 * q^63 + 52 * q^64 - 67 * q^65 - 29 * q^66 - 114 * q^67 - 78 * q^68 - 68 * q^69 - 61 * q^70 - 52 * q^71 - 47 * q^72 - 83 * q^73 - 21 * q^74 - 47 * q^75 - 100 * q^76 - 32 * q^77 - 17 * q^78 - 151 * q^79 - 24 * q^80 + 81 * q^81 - 151 * q^82 - 94 * q^83 - 84 * q^84 - 77 * q^85 - 43 * q^86 + 12 * q^87 - 121 * q^88 + 11 * q^89 - 14 * q^90 - 66 * q^91 - 156 * q^92 - 66 * q^93 - 22 * q^94 - 67 * q^95 - 131 * q^96 - 78 * q^97 - 67 * q^98 - 41 * q^99

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