LMFDB - Embedded newform 1511.2.a.b.1.74

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1511,2,Mod(1,1511)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1511, 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("1511.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1511 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1511.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:	$12.0653957454$
Analytic rank:	$0$
Dimension:	$87$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.74
Character	$\chi$	$=$	1511.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.28620 q^{2} +1.47354 q^{3} +3.22671 q^{4} +1.42894 q^{5} +3.36880 q^{6} +3.91535 q^{7} +2.80451 q^{8} -0.828685 q^{9} +O(q^{10})$	\(q+2.28620 q^{2} +1.47354 q^{3} +3.22671 q^{4} +1.42894 q^{5} +3.36880 q^{6} +3.91535 q^{7} +2.80451 q^{8} -0.828685 q^{9} +3.26685 q^{10} +3.36521 q^{11} +4.75468 q^{12} -6.36993 q^{13} +8.95127 q^{14} +2.10560 q^{15} -0.0417542 q^{16} +5.56034 q^{17} -1.89454 q^{18} -5.42263 q^{19} +4.61079 q^{20} +5.76941 q^{21} +7.69354 q^{22} -4.62606 q^{23} +4.13255 q^{24} -2.95812 q^{25} -14.5629 q^{26} -5.64171 q^{27} +12.6337 q^{28} -8.19214 q^{29} +4.81383 q^{30} +1.94184 q^{31} -5.70448 q^{32} +4.95876 q^{33} +12.7120 q^{34} +5.59481 q^{35} -2.67393 q^{36} -6.23906 q^{37} -12.3972 q^{38} -9.38634 q^{39} +4.00748 q^{40} -3.91278 q^{41} +13.1900 q^{42} +5.53951 q^{43} +10.8586 q^{44} -1.18414 q^{45} -10.5761 q^{46} +12.2276 q^{47} -0.0615265 q^{48} +8.32994 q^{49} -6.76286 q^{50} +8.19337 q^{51} -20.5539 q^{52} +6.01963 q^{53} -12.8981 q^{54} +4.80869 q^{55} +10.9806 q^{56} -7.99046 q^{57} -18.7289 q^{58} +14.1788 q^{59} +6.79417 q^{60} +5.61169 q^{61} +4.43943 q^{62} -3.24459 q^{63} -12.9581 q^{64} -9.10227 q^{65} +11.3367 q^{66} +12.0834 q^{67} +17.9416 q^{68} -6.81667 q^{69} +12.7908 q^{70} -10.3637 q^{71} -2.32405 q^{72} -2.33015 q^{73} -14.2637 q^{74} -4.35891 q^{75} -17.4973 q^{76} +13.1760 q^{77} -21.4591 q^{78} +6.37528 q^{79} -0.0596644 q^{80} -5.82723 q^{81} -8.94540 q^{82} +2.84392 q^{83} +18.6162 q^{84} +7.94540 q^{85} +12.6644 q^{86} -12.0714 q^{87} +9.43776 q^{88} +1.12904 q^{89} -2.70719 q^{90} -24.9405 q^{91} -14.9270 q^{92} +2.86137 q^{93} +27.9547 q^{94} -7.74863 q^{95} -8.40577 q^{96} -14.3903 q^{97} +19.0439 q^{98} -2.78870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) $ 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * 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 $

$2$	2.28620	1.61659	0.808294	−	0.588779i	$-0.200391\pi$
$2$	2.28620	1.61659	0.808294	+	0.588779i	$0.200391\pi$
$3$	1.47354	0.850748	0.425374	−	0.905018i	$-0.360143\pi$
$3$	1.47354	0.850748	0.425374	+	0.905018i	$0.360143\pi$
$4$	3.22671	1.61336
$5$	1.42894	0.639043	0.319521	−	0.947579i	$-0.396478\pi$
$5$	1.42894	0.639043	0.319521	+	0.947579i	$0.396478\pi$
$6$	3.36880	1.37531
$7$	3.91535	1.47986	0.739931	−	0.672683i	$-0.234858\pi$
$7$	3.91535	1.47986	0.739931	+	0.672683i	$0.234858\pi$
$8$	2.80451	0.991544
$9$	−0.828685	−0.276228
$10$	3.26685	1.03307
$11$	3.36521	1.01465	0.507324	−	0.861755i	$-0.330635\pi$
$11$	3.36521	1.01465	0.507324	+	0.861755i	$0.330635\pi$
$12$	4.75468	1.37256
$13$	−6.36993	−1.76670	−0.883351	−	0.468712i	$-0.844718\pi$
$13$	−6.36993	−1.76670	−0.883351	+	0.468712i	$0.844718\pi$
$14$	8.95127	2.39233
$15$	2.10560	0.543664
$16$	−0.0417542	−0.0104386
$17$	5.56034	1.34858	0.674290	−	0.738467i	$-0.264450\pi$
$17$	5.56034	1.34858	0.674290	+	0.738467i	$0.264450\pi$
$18$	−1.89454	−0.446547
$19$	−5.42263	−1.24404	−0.622018	−	0.783003i	$-0.713687\pi$
$19$	−5.42263	−1.24404	−0.622018	+	0.783003i	$0.713687\pi$
$20$	4.61079	1.03100
$21$	5.76941	1.25899
$22$	7.69354	1.64027
$23$	−4.62606	−0.964600	−0.482300	−	0.876006i	$-0.660198\pi$
$23$	−4.62606	−0.964600	−0.482300	+	0.876006i	$0.660198\pi$
$24$	4.13255	0.843554
$25$	−2.95812	−0.591624
$26$	−14.5629	−2.85603
$27$	−5.64171	−1.08575
$28$	12.6337	2.38754
$29$	−8.19214	−1.52124	−0.760621	−	0.649196i	$-0.775105\pi$
$29$	−8.19214	−1.52124	−0.760621	+	0.649196i	$0.775105\pi$
$30$	4.81383	0.878881
$31$	1.94184	0.348764	0.174382	−	0.984678i	$-0.444207\pi$
$31$	1.94184	0.348764	0.174382	+	0.984678i	$0.444207\pi$
$32$	−5.70448	−1.00842
$33$	4.95876	0.863210
$34$	12.7120	2.18010
$35$	5.59481	0.945695
$36$	−2.67393	−0.445655
$37$	−6.23906	−1.02569	−0.512847	−	0.858480i	$-0.671409\pi$
$37$	−6.23906	−1.02569	−0.512847	+	0.858480i	$0.671409\pi$
$38$	−12.3972	−2.01109
$39$	−9.38634	−1.50302
$40$	4.00748	0.633639
$41$	−3.91278	−0.611074	−0.305537	−	0.952180i	$-0.598836\pi$
$41$	−3.91278	−0.611074	−0.305537	+	0.952180i	$0.598836\pi$
$42$	13.1900	2.03527
$43$	5.53951	0.844768	0.422384	−	0.906417i	$-0.361193\pi$
$43$	5.53951	0.844768	0.422384	+	0.906417i	$0.361193\pi$
$44$	10.8586	1.63699
$45$	−1.18414	−0.176522
$46$	−10.5761	−1.55936
$47$	12.2276	1.78357	0.891787	−	0.452456i	$-0.149452\pi$
$47$	12.2276	1.78357	0.891787	+	0.452456i	$0.149452\pi$
$48$	−0.0615265	−0.00888058
$49$	8.32994	1.18999
$50$	−6.76286	−0.956413
$51$	8.19337	1.14730
$52$	−20.5539	−2.85032
$53$	6.01963	0.826859	0.413430	−	0.910536i	$-0.364331\pi$
$53$	6.01963	0.826859	0.413430	+	0.910536i	$0.364331\pi$
$54$	−12.8981	−1.75521
$55$	4.80869	0.648404
$56$	10.9806	1.46735
$57$	−7.99046	−1.05836
$58$	−18.7289	−2.45922
$59$	14.1788	1.84592	0.922960	−	0.384896i	$-0.125763\pi$
$59$	14.1788	1.84592	0.922960	+	0.384896i	$0.125763\pi$
$60$	6.79417	0.877124
$61$	5.61169	0.718504	0.359252	−	0.933241i	$-0.383032\pi$
$61$	5.61169	0.718504	0.359252	+	0.933241i	$0.383032\pi$
$62$	4.43943	0.563808
$63$	−3.24459	−0.408780
$64$	−12.9581	−1.61976
$65$	−9.10227	−1.12900
$66$	11.3367	1.39545
$67$	12.0834	1.47622	0.738111	−	0.674679i	$-0.235718\pi$
$67$	12.0834	1.47622	0.738111	+	0.674679i	$0.235718\pi$
$68$	17.9416	2.17574
$69$	−6.81667	−0.820631
$70$	12.7908	1.52880
$71$	−10.3637	−1.22994	−0.614972	−	0.788549i	$-0.710833\pi$
$71$	−10.3637	−1.22994	−0.614972	+	0.788549i	$0.710833\pi$
$72$	−2.32405	−0.273892
$73$	−2.33015	−0.272723	−0.136362	−	0.990659i	$-0.543541\pi$
$73$	−2.33015	−0.272723	−0.136362	+	0.990659i	$0.543541\pi$
$74$	−14.2637	−1.65813
$75$	−4.35891	−0.503323
$76$	−17.4973	−2.00707
$77$	13.1760	1.50154
$78$	−21.4591	−2.42976
$79$	6.37528	0.717274	0.358637	−	0.933477i	$-0.383242\pi$
$79$	6.37528	0.717274	0.358637	+	0.933477i	$0.383242\pi$
$80$	−0.0596644	−0.00667069
$81$	−5.82723	−0.647470
$82$	−8.94540	−0.987855
$83$	2.84392	0.312161	0.156080	−	0.987744i	$-0.450114\pi$
$83$	2.84392	0.312161	0.156080	+	0.987744i	$0.450114\pi$
$84$	18.6162	2.03120
$85$	7.94540	0.861800
$86$	12.6644	1.36564
$87$	−12.0714	−1.29419
$88$	9.43776	1.00607
$89$	1.12904	0.119678	0.0598389	−	0.998208i	$-0.480941\pi$
$89$	1.12904	0.119678	0.0598389	+	0.998208i	$0.480941\pi$
$90$	−2.70719	−0.285363
$91$	−24.9405	−2.61447
$92$	−14.9270	−1.55624
$93$	2.86137	0.296711
$94$	27.9547	2.88330
$95$	−7.74863	−0.794993
$96$	−8.40577	−0.857910
$97$	−14.3903	−1.46111	−0.730557	−	0.682852i	$-0.760740\pi$
$97$	−14.3903	−1.46111	−0.730557	+	0.682852i	$0.760740\pi$
$98$	19.0439	1.92373
$99$	−2.78870	−0.280275
$100$	−9.54501	−0.954501
$101$	8.15298	0.811251	0.405626	−	0.914039i	$-0.367054\pi$
$101$	8.15298	0.811251	0.405626	+	0.914039i	$0.367054\pi$
$102$	18.7317	1.85471
$103$	−14.8672	−1.46491	−0.732454	−	0.680817i	$-0.761625\pi$
$103$	−14.8672	−1.46491	−0.732454	+	0.680817i	$0.761625\pi$
$104$	−17.8645	−1.75176
$105$	8.24416	0.804548
$106$	13.7621	1.33669
$107$	19.1565	1.85193	0.925963	−	0.377615i	$-0.123256\pi$
$107$	19.1565	1.85193	0.925963	+	0.377615i	$0.123256\pi$
$108$	−18.2042	−1.75170
$109$	−12.9731	−1.24260	−0.621298	−	0.783575i	$-0.713394\pi$
$109$	−12.9731	−1.24260	−0.621298	+	0.783575i	$0.713394\pi$
$110$	10.9936	1.04820
$111$	−9.19349	−0.872607
$112$	−0.163482	−0.0154476
$113$	16.3418	1.53731	0.768654	−	0.639665i	$-0.220927\pi$
$113$	16.3418	1.53731	0.768654	+	0.639665i	$0.220927\pi$
$114$	−18.2678	−1.71093
$115$	−6.61037	−0.616420
$116$	−26.4337	−2.45430
$117$	5.27867	0.488013
$118$	32.4155	2.98409
$119$	21.7706	1.99571
$120$	5.90518	0.539067
$121$	0.324632	0.0295120
$122$	12.8295	1.16152
$123$	−5.76563	−0.519870
$124$	6.26575	0.562681
$125$	−11.3717	−1.01712
$126$	−7.41778	−0.660828
$127$	9.62588	0.854159	0.427079	−	0.904214i	$-0.359542\pi$
$127$	9.62588	0.854159	0.427079	+	0.904214i	$0.359542\pi$
$128$	−18.2158	−1.61006
$129$	8.16269	0.718684
$130$	−20.8096	−1.82512
$131$	−3.34710	−0.292438	−0.146219	−	0.989252i	$-0.546710\pi$
$131$	−3.34710	−0.292438	−0.146219	+	0.989252i	$0.546710\pi$
$132$	16.0005	1.39267
$133$	−21.2315	−1.84100
$134$	27.6251	2.38644
$135$	−8.06169	−0.693840
$136$	15.5940	1.33718
$137$	−1.32740	−0.113408	−0.0567039	−	0.998391i	$-0.518059\pi$
$137$	−1.32740	−0.113408	−0.0567039	+	0.998391i	$0.518059\pi$
$138$	−15.5843	−1.32662
$139$	8.89284	0.754281	0.377141	−	0.926156i	$-0.376907\pi$
$139$	8.89284	0.754281	0.377141	+	0.926156i	$0.376907\pi$
$140$	18.0528	1.52574
$141$	18.0178	1.51737
$142$	−23.6935	−1.98831
$143$	−21.4362	−1.79258
$144$	0.0346011	0.00288343
$145$	−11.7061	−0.972139
$146$	−5.32719	−0.440881
$147$	12.2745	1.01238
$148$	−20.1316	−1.65481
$149$	2.84763	0.233287	0.116643	−	0.993174i	$-0.462787\pi$
$149$	2.84763	0.233287	0.116643	+	0.993174i	$0.462787\pi$
$150$	−9.96533	−0.813666
$151$	2.55716	0.208099	0.104049	−	0.994572i	$-0.466820\pi$
$151$	2.55716	0.208099	0.104049	+	0.994572i	$0.466820\pi$
$152$	−15.2078	−1.23352
$153$	−4.60777	−0.372516
$154$	30.1229	2.42737
$155$	2.77478	0.222875
$156$	−30.2870	−2.42490
$157$	8.46930	0.675924	0.337962	−	0.941160i	$-0.390262\pi$
$157$	8.46930	0.675924	0.337962	+	0.941160i	$0.390262\pi$
$158$	14.5752	1.15954
$159$	8.87015	0.703449
$160$	−8.15137	−0.644423
$161$	−18.1126	−1.42747
$162$	−13.3222	−1.04669
$163$	7.94237	0.622094	0.311047	−	0.950394i	$-0.399320\pi$
$163$	7.94237	0.622094	0.311047	+	0.950394i	$0.399320\pi$
$164$	−12.6254	−0.985880
$165$	7.08579	0.551628
$166$	6.50177	0.504635
$167$	18.4984	1.43145	0.715724	−	0.698383i	$-0.246097\pi$
$167$	18.4984	1.43145	0.715724	+	0.698383i	$0.246097\pi$
$168$	16.1804	1.24834
$169$	27.5760	2.12123
$170$	18.1648	1.39318
$171$	4.49365	0.343638
$172$	17.8744	1.36291
$173$	−7.09705	−0.539579	−0.269789	−	0.962919i	$-0.586954\pi$
$173$	−7.09705	−0.539579	−0.269789	+	0.962919i	$0.586954\pi$
$174$	−27.5977	−2.09218
$175$	−11.5821	−0.875522
$176$	−0.140512	−0.0105915
$177$	20.8930	1.57041
$178$	2.58121	0.193470
$179$	−12.7484	−0.952858	−0.476429	−	0.879213i	$-0.658069\pi$
$179$	−12.7484	−0.952858	−0.476429	+	0.879213i	$0.658069\pi$
$180$	−3.82089	−0.284792
$181$	−26.2349	−1.95003	−0.975014	−	0.222143i	$-0.928695\pi$
$181$	−26.2349	−1.95003	−0.975014	+	0.222143i	$0.928695\pi$
$182$	−57.0190	−4.22653
$183$	8.26905	0.611265
$184$	−12.9738	−0.956443
$185$	−8.91526	−0.655463
$186$	6.54167	0.479659
$187$	18.7117	1.36833
$188$	39.4548	2.87754
$189$	−22.0893	−1.60676
$190$	−17.7149	−1.28518
$191$	16.9008	1.22290	0.611451	−	0.791282i	$-0.290586\pi$
$191$	16.9008	1.22290	0.611451	+	0.791282i	$0.290586\pi$
$192$	−19.0942	−1.37801
$193$	6.86216	0.493949	0.246974	−	0.969022i	$-0.420564\pi$
$193$	6.86216	0.493949	0.246974	+	0.969022i	$0.420564\pi$
$194$	−32.8991	−2.36202
$195$	−13.4125	−0.960492
$196$	26.8783	1.91988
$197$	−10.9214	−0.778119	−0.389060	−	0.921213i	$-0.627200\pi$
$197$	−10.9214	−0.778119	−0.389060	+	0.921213i	$0.627200\pi$
$198$	−6.37552	−0.453089
$199$	20.3726	1.44417	0.722086	−	0.691803i	$-0.243183\pi$
$199$	20.3726	1.44417	0.722086	+	0.691803i	$0.243183\pi$
$200$	−8.29608	−0.586621
$201$	17.8054	1.25589
$202$	18.6393	1.31146
$203$	−32.0751	−2.25123
$204$	26.4376	1.85101
$205$	−5.59114	−0.390502
$206$	−33.9894	−2.36815
$207$	3.83354	0.266450
$208$	0.265972	0.0184418
$209$	−18.2483	−1.26226
$210$	18.8478	1.30062
$211$	−17.1093	−1.17786	−0.588928	−	0.808186i	$-0.700450\pi$
$211$	−17.1093	−1.17786	−0.588928	+	0.808186i	$0.700450\pi$
$212$	19.4236	1.33402
$213$	−15.2713	−1.04637
$214$	43.7955	2.99380
$215$	7.91565	0.539843
$216$	−15.8222	−1.07657
$217$	7.60297	0.516123
$218$	−29.6590	−2.00876
$219$	−3.43356	−0.232019
$220$	15.5163	1.04611
$221$	−35.4190	−2.38254
$222$	−21.0182	−1.41065
$223$	1.50122	0.100529	0.0502645	−	0.998736i	$-0.483994\pi$
$223$	1.50122	0.100529	0.0502645	+	0.998736i	$0.483994\pi$
$224$	−22.3350	−1.49232
$225$	2.45135	0.163423
$226$	37.3606	2.48519
$227$	−0.512532	−0.0340180	−0.0170090	−	0.999855i	$-0.505414\pi$
$227$	−0.512532	−0.0340180	−0.0170090	+	0.999855i	$0.505414\pi$
$228$	−25.7829	−1.70751
$229$	−3.52274	−0.232789	−0.116395	−	0.993203i	$-0.537134\pi$
$229$	−3.52274	−0.232789	−0.116395	+	0.993203i	$0.537134\pi$
$230$	−15.1126	−0.996497
$231$	19.4153	1.27743
$232$	−22.9749	−1.50838
$233$	10.0356	0.657452	0.328726	−	0.944425i	$-0.393381\pi$
$233$	10.0356	0.657452	0.328726	+	0.944425i	$0.393381\pi$
$234$	12.0681	0.788916
$235$	17.4725	1.13978
$236$	45.7508	2.97813
$237$	9.39421	0.610220
$238$	49.7721	3.22624
$239$	2.20627	0.142712	0.0713560	−	0.997451i	$-0.477267\pi$
$239$	2.20627	0.142712	0.0713560	+	0.997451i	$0.477267\pi$
$240$	−0.0879178	−0.00567507
$241$	−22.0468	−1.42016	−0.710081	−	0.704120i	$-0.751342\pi$
$241$	−22.0468	−1.42016	−0.710081	+	0.704120i	$0.751342\pi$
$242$	0.742174	0.0477088
$243$	8.33850	0.534915
$244$	18.1073	1.15920
$245$	11.9030	0.760455
$246$	−13.1814	−0.840415
$247$	34.5418	2.19784
$248$	5.44590	0.345815
$249$	4.19063	0.265570
$250$	−25.9980	−1.64426
$251$	9.93119	0.626851	0.313426	−	0.949613i	$-0.398523\pi$
$251$	9.93119	0.626851	0.313426	+	0.949613i	$0.398523\pi$
$252$	−10.4694	−0.659507
$253$	−15.5676	−0.978730
$254$	22.0067	1.38082
$255$	11.7079	0.733174
$256$	−15.7288	−0.983050
$257$	−10.4778	−0.653586	−0.326793	−	0.945096i	$-0.605968\pi$
$257$	−10.4778	−0.653586	−0.326793	+	0.945096i	$0.605968\pi$
$258$	18.6615	1.16182
$259$	−24.4281	−1.51789
$260$	−29.3704	−1.82148
$261$	6.78870	0.420210
$262$	−7.65215	−0.472751
$263$	−24.2824	−1.49732	−0.748659	−	0.662955i	$-0.769302\pi$
$263$	−24.2824	−1.49732	−0.748659	+	0.662955i	$0.769302\pi$
$264$	13.9069	0.855911
$265$	8.60170	0.528399
$266$	−48.5394	−2.97614
$267$	1.66368	0.101816
$268$	38.9897	2.38167
$269$	−22.7677	−1.38817	−0.694086	−	0.719892i	$-0.744191\pi$
$269$	−22.7677	−1.38817	−0.694086	+	0.719892i	$0.744191\pi$
$270$	−18.4306	−1.12165
$271$	0.797329	0.0484343	0.0242171	−	0.999707i	$-0.492291\pi$
$271$	0.797329	0.0484343	0.0242171	+	0.999707i	$0.492291\pi$
$272$	−0.232168	−0.0140772
$273$	−36.7508	−2.22426
$274$	−3.03471	−0.183334
$275$	−9.95470	−0.600291
$276$	−21.9954	−1.32397
$277$	−26.4421	−1.58875	−0.794377	−	0.607425i	$-0.792203\pi$
$277$	−26.4421	−1.58875	−0.794377	+	0.607425i	$0.792203\pi$
$278$	20.3308	1.21936
$279$	−1.60917	−0.0963386
$280$	15.6907	0.937698
$281$	17.8350	1.06394	0.531972	−	0.846762i	$-0.321451\pi$
$281$	17.8350	1.06394	0.531972	+	0.846762i	$0.321451\pi$
$282$	41.1923	2.45296
$283$	1.20137	0.0714143	0.0357072	−	0.999362i	$-0.488632\pi$
$283$	1.20137	0.0714143	0.0357072	+	0.999362i	$0.488632\pi$
$284$	−33.4407	−1.98434
$285$	−11.4179	−0.676338
$286$	−49.0073	−2.89787
$287$	−15.3199	−0.904305
$288$	4.72721	0.278554
$289$	13.9173	0.818667
$290$	−26.7625	−1.57155
$291$	−21.2047	−1.24304
$292$	−7.51872	−0.440000
$293$	−19.7434	−1.15342	−0.576712	−	0.816948i	$-0.695664\pi$
$293$	−19.7434	−1.15342	−0.576712	+	0.816948i	$0.695664\pi$
$294$	28.0619	1.63661
$295$	20.2607	1.17962
$296$	−17.4975	−1.01702
$297$	−18.9855	−1.10165
$298$	6.51025	0.377129
$299$	29.4677	1.70416
$300$	−14.0649	−0.812039
$301$	21.6891	1.25014
$302$	5.84618	0.336410
$303$	12.0137	0.690170
$304$	0.226418	0.0129860
$305$	8.01879	0.459155
$306$	−10.5343	−0.602205
$307$	−20.6355	−1.17773	−0.588867	−	0.808230i	$-0.700426\pi$
$307$	−20.6355	−1.17773	−0.588867	+	0.808230i	$0.700426\pi$
$308$	42.5150	2.42252
$309$	−21.9074	−1.24627
$310$	6.34369	0.360298
$311$	−8.04574	−0.456232	−0.228116	−	0.973634i	$-0.573257\pi$
$311$	−8.04574	−0.456232	−0.228116	+	0.973634i	$0.573257\pi$
$312$	−26.3241	−1.49031
$313$	14.5251	0.821006	0.410503	−	0.911859i	$-0.365353\pi$
$313$	14.5251	0.821006	0.410503	+	0.911859i	$0.365353\pi$
$314$	19.3625	1.09269
$315$	−4.63633	−0.261228
$316$	20.5712	1.15722
$317$	0.914131	0.0513427	0.0256714	−	0.999670i	$-0.491828\pi$
$317$	0.914131	0.0513427	0.0256714	+	0.999670i	$0.491828\pi$
$318$	20.2789	1.13719
$319$	−27.5683	−1.54353
$320$	−18.5163	−1.03509
$321$	28.2278	1.57552
$322$	−41.4091	−2.30764
$323$	−30.1517	−1.67768
$324$	−18.8028	−1.04460
$325$	18.8430	1.04522
$326$	18.1578	1.00567
$327$	−19.1163	−1.05714
$328$	−10.9734	−0.605906
$329$	47.8752	2.63944
$330$	16.1995	0.891755
$331$	27.1684	1.49331	0.746656	−	0.665211i	$-0.231658\pi$
$331$	27.1684	1.49331	0.746656	+	0.665211i	$0.231658\pi$
$332$	9.17651	0.503627
$333$	5.17021	0.283326
$334$	42.2910	2.31406
$335$	17.2665	0.943370
$336$	−0.240897	−0.0131420
$337$	−24.6727	−1.34401	−0.672003	−	0.740549i	$-0.734566\pi$
$337$	−24.6727	−1.34401	−0.672003	+	0.740549i	$0.734566\pi$
$338$	63.0444	3.42916
$339$	24.0803	1.30786
$340$	25.6375	1.39039
$341$	6.53469	0.353873
$342$	10.2734	0.555521
$343$	5.20718	0.281161
$344$	15.5356	0.837624
$345$	−9.74064	−0.524418
$346$	−16.2253	−0.872276
$347$	12.0907	0.649064	0.324532	−	0.945875i	$-0.394793\pi$
$347$	12.0907	0.649064	0.324532	+	0.945875i	$0.394793\pi$
$348$	−38.9510	−2.08799
$349$	−2.93717	−0.157223	−0.0786116	−	0.996905i	$-0.525049\pi$
$349$	−2.93717	−0.157223	−0.0786116	+	0.996905i	$0.525049\pi$
$350$	−26.4789	−1.41536
$351$	35.9373	1.91819
$352$	−19.1968	−1.02319
$353$	−14.3740	−0.765050	−0.382525	−	0.923945i	$-0.624945\pi$
$353$	−14.3740	−0.765050	−0.382525	+	0.923945i	$0.624945\pi$
$354$	47.7655	2.53871
$355$	−14.8091	−0.785987
$356$	3.64308	0.193083
$357$	32.0799	1.69785
$358$	−29.1453	−1.54038
$359$	32.8489	1.73370	0.866849	−	0.498571i	$-0.166142\pi$
$359$	32.8489	1.73370	0.866849	+	0.498571i	$0.166142\pi$
$360$	−3.32094	−0.175029
$361$	10.4049	0.547628
$362$	−59.9783	−3.15239
$363$	0.478358	0.0251073
$364$	−80.4758	−4.21808
$365$	−3.32965	−0.174282
$366$	18.9047	0.988164
$367$	23.1761	1.20978	0.604891	−	0.796308i	$-0.293217\pi$
$367$	23.1761	1.20978	0.604891	+	0.796308i	$0.293217\pi$
$368$	0.193157	0.0100690
$369$	3.24246	0.168796
$370$	−20.3821	−1.05961
$371$	23.5689	1.22364
$372$	9.23283	0.478700
$373$	18.6275	0.964494	0.482247	−	0.876035i	$-0.339821\pi$
$373$	18.6275	0.964494	0.482247	+	0.876035i	$0.339821\pi$
$374$	42.7787	2.21203
$375$	−16.7566	−0.865309
$376$	34.2923	1.76849
$377$	52.1834	2.68758
$378$	−50.5005	−2.59746
$379$	−26.8669	−1.38006	−0.690030	−	0.723781i	$-0.742403\pi$
$379$	−26.8669	−1.38006	−0.690030	+	0.723781i	$0.742403\pi$
$380$	−25.0026	−1.28261
$381$	14.1841	0.726674
$382$	38.6387	1.97693
$383$	−29.2760	−1.49593	−0.747967	−	0.663735i	$-0.768970\pi$
$383$	−29.2760	−1.49593	−0.747967	+	0.663735i	$0.768970\pi$
$384$	−26.8417	−1.36976
$385$	18.8277	0.959548
$386$	15.6883	0.798511
$387$	−4.59051	−0.233349
$388$	−46.4334	−2.35730
$389$	−12.1195	−0.614483	−0.307241	−	0.951632i	$-0.599406\pi$
$389$	−12.1195	−0.614483	−0.307241	+	0.951632i	$0.599406\pi$
$390$	−30.6638	−1.55272
$391$	−25.7224	−1.30084
$392$	23.3614	1.17993
$393$	−4.93208	−0.248791
$394$	−24.9686	−1.25790
$395$	9.10990	0.458369
$396$	−8.99832	−0.452183
$397$	7.15547	0.359123	0.179561	−	0.983747i	$-0.442532\pi$
$397$	7.15547	0.359123	0.179561	+	0.983747i	$0.442532\pi$
$398$	46.5758	2.33463
$399$	−31.2854	−1.56623
$400$	0.123514	0.00617571
$401$	0.600991	0.0300120	0.0150060	−	0.999887i	$-0.495223\pi$
$401$	0.600991	0.0300120	0.0150060	+	0.999887i	$0.495223\pi$
$402$	40.7066	2.03026
$403$	−12.3694	−0.616163
$404$	26.3073	1.30884
$405$	−8.32678	−0.413761
$406$	−73.3300	−3.63931
$407$	−20.9957	−1.04072
$408$	22.9784	1.13760
$409$	15.2958	0.756327	0.378164	−	0.925739i	$-0.376556\pi$
$409$	15.2958	0.756327	0.378164	+	0.925739i	$0.376556\pi$
$410$	−12.7825	−0.631281
$411$	−1.95598	−0.0964815
$412$	−47.9721	−2.36342
$413$	55.5148	2.73171
$414$	8.76425	0.430739
$415$	4.06380	0.199484
$416$	36.3371	1.78157
$417$	13.1039	0.641703
$418$	−41.7192	−2.04055
$419$	−28.7791	−1.40595	−0.702975	−	0.711215i	$-0.748145\pi$
$419$	−28.7791	−1.40595	−0.702975	+	0.711215i	$0.748145\pi$
$420$	26.6015	1.29802
$421$	−4.47024	−0.217866	−0.108933	−	0.994049i	$-0.534743\pi$
$421$	−4.47024	−0.217866	−0.108933	+	0.994049i	$0.534743\pi$
$422$	−39.1154	−1.90411
$423$	−10.1328	−0.492673
$424$	16.8821	0.819867
$425$	−16.4482	−0.797853
$426$	−34.9133	−1.69155
$427$	21.9717	1.06329
$428$	61.8124	2.98781
$429$	−31.5870	−1.52503
$430$	18.0968	0.872703
$431$	−39.3002	−1.89303	−0.946513	−	0.322666i	$-0.895421\pi$
$431$	−39.3002	−1.89303	−0.946513	+	0.322666i	$0.895421\pi$
$432$	0.235565	0.0113336
$433$	−7.40971	−0.356088	−0.178044	−	0.984023i	$-0.556977\pi$
$433$	−7.40971	−0.356088	−0.178044	+	0.984023i	$0.556977\pi$
$434$	17.3819	0.834359
$435$	−17.2494	−0.827045
$436$	−41.8604	−2.00475
$437$	25.0854	1.20000
$438$	−7.84982	−0.375079
$439$	2.16953	0.103546	0.0517730	−	0.998659i	$-0.483513\pi$
$439$	2.16953	0.103546	0.0517730	+	0.998659i	$0.483513\pi$
$440$	13.4860	0.642921
$441$	−6.90289	−0.328709
$442$	−80.9749	−3.85158
$443$	13.9189	0.661306	0.330653	−	0.943752i	$-0.392731\pi$
$443$	13.9189	0.661306	0.330653	+	0.943752i	$0.392731\pi$
$444$	−29.6647	−1.40783
$445$	1.61333	0.0764793
$446$	3.43209	0.162514
$447$	4.19609	0.198468
$448$	−50.7353	−2.39702
$449$	−6.13771	−0.289656	−0.144828	−	0.989457i	$-0.546263\pi$
$449$	−6.13771	−0.289656	−0.144828	+	0.989457i	$0.546263\pi$
$450$	5.60428	0.264188
$451$	−13.1673	−0.620025
$452$	52.7303	2.48022
$453$	3.76808	0.177040
$454$	−1.17175	−0.0549930
$455$	−35.6385	−1.67076
$456$	−22.4093	−1.04941
$457$	−26.4722	−1.23832	−0.619159	−	0.785266i	$-0.712526\pi$
$457$	−26.4722	−1.23832	−0.619159	+	0.785266i	$0.712526\pi$
$458$	−8.05369	−0.376324
$459$	−31.3698	−1.46422
$460$	−21.3298	−0.994505
$461$	15.1734	0.706694	0.353347	−	0.935492i	$-0.385043\pi$
$461$	15.1734	0.706694	0.353347	+	0.935492i	$0.385043\pi$
$462$	44.3872	2.06508
$463$	24.7168	1.14869	0.574344	−	0.818614i	$-0.305257\pi$
$463$	24.7168	1.14869	0.574344	+	0.818614i	$0.305257\pi$
$464$	0.342057	0.0158796
$465$	4.08874	0.189611
$466$	22.9433	1.06283
$467$	−1.76305	−0.0815843	−0.0407922	−	0.999168i	$-0.512988\pi$
$467$	−1.76305	−0.0815843	−0.0407922	+	0.999168i	$0.512988\pi$
$468$	17.0327	0.787339
$469$	47.3107	2.18461
$470$	39.9456	1.84255
$471$	12.4798	0.575041
$472$	39.7645	1.83031
$473$	18.6416	0.857143
$474$	21.4771	0.986474
$475$	16.0408	0.736003
$476$	70.2476	3.21979
$477$	−4.98837	−0.228402
$478$	5.04398	0.230706
$479$	4.97645	0.227380	0.113690	−	0.993516i	$-0.463733\pi$
$479$	4.97645	0.227380	0.113690	+	0.993516i	$0.463733\pi$
$480$	−12.0114	−0.548241
$481$	39.7424	1.81210
$482$	−50.4035	−2.29582
$483$	−26.6896	−1.21442
$484$	1.04749	0.0476134
$485$	−20.5629	−0.933714
$486$	19.0635	0.864737
$487$	38.2247	1.73213	0.866063	−	0.499934i	$-0.166642\pi$
$487$	38.2247	1.73213	0.866063	+	0.499934i	$0.166642\pi$
$488$	15.7380	0.712428
$489$	11.7034	0.529245
$490$	27.2127	1.22934
$491$	−13.8838	−0.626566	−0.313283	−	0.949660i	$-0.601429\pi$
$491$	−13.8838	−0.626566	−0.313283	+	0.949660i	$0.601429\pi$
$492$	−18.6040	−0.838735
$493$	−45.5511	−2.05152
$494$	78.9695	3.55300
$495$	−3.98489	−0.179107
$496$	−0.0810800	−0.00364060
$497$	−40.5775	−1.82015
$498$	9.58061	0.429317
$499$	−16.5910	−0.742715	−0.371357	−	0.928490i	$-0.621108\pi$
$499$	−16.5910	−0.742715	−0.371357	+	0.928490i	$0.621108\pi$
$500$	−36.6932	−1.64097
$501$	27.2581	1.21780
$502$	22.7047	1.01336
$503$	6.64906	0.296467	0.148233	−	0.988952i	$-0.452641\pi$
$503$	6.64906	0.296467	0.148233	+	0.988952i	$0.452641\pi$
$504$	−9.09948	−0.405323
$505$	11.6501	0.518424
$506$	−35.5908	−1.58220
$507$	40.6344	1.80464
$508$	31.0599	1.37806
$509$	1.41429	0.0626875	0.0313437	−	0.999509i	$-0.490021\pi$
$509$	1.41429	0.0626875	0.0313437	+	0.999509i	$0.490021\pi$
$510$	26.7665	1.18524
$511$	−9.12334	−0.403593
$512$	0.472386	0.0208767
$513$	30.5929	1.35071
$514$	−23.9543	−1.05658
$515$	−21.2444	−0.936139
$516$	26.3386	1.15949
$517$	41.1483	1.80970
$518$	−55.8475	−2.45380
$519$	−10.4578	−0.459045
$520$	−25.5274	−1.11945
$521$	−3.09366	−0.135536	−0.0677679	−	0.997701i	$-0.521588\pi$
$521$	−3.09366	−0.135536	−0.0677679	+	0.997701i	$0.521588\pi$
$522$	15.5203	0.679306
$523$	17.0109	0.743833	0.371916	−	0.928266i	$-0.378701\pi$
$523$	17.0109	0.743833	0.371916	+	0.928266i	$0.378701\pi$
$524$	−10.8001	−0.471806
$525$	−17.0666	−0.744849
$526$	−55.5145	−2.42055
$527$	10.7973	0.470337
$528$	−0.207049	−0.00901067
$529$	−1.59960	−0.0695478
$530$	19.6652	0.854203
$531$	−11.7497	−0.509895
$532$	−68.5079	−2.97019
$533$	24.9242	1.07959
$534$	3.80351	0.164594
$535$	27.3735	1.18346
$536$	33.8880	1.46374
$537$	−18.7852	−0.810642
$538$	−52.0516	−2.24410
$539$	28.0320	1.20742
$540$	−26.0127	−1.11941
$541$	0.0989551	0.00425441	0.00212721	−	0.999998i	$-0.499323\pi$
$541$	0.0989551	0.00425441	0.00212721	+	0.999998i	$0.499323\pi$
$542$	1.82285	0.0782982
$543$	−38.6582	−1.65898
$544$	−31.7188	−1.35993
$545$	−18.5378	−0.794071
$546$	−84.0196	−3.59571
$547$	28.1152	1.20212	0.601059	−	0.799204i	$-0.294746\pi$
$547$	28.1152	1.20212	0.601059	+	0.799204i	$0.294746\pi$
$548$	−4.28315	−0.182967
$549$	−4.65033	−0.198471
$550$	−22.7584	−0.970423
$551$	44.4230	1.89248
$552$	−19.1174	−0.813691
$553$	24.9614	1.06147
$554$	−60.4520	−2.56836
$555$	−13.1370	−0.557633
$556$	28.6946	1.21692
$557$	31.9538	1.35392	0.676962	−	0.736018i	$-0.263296\pi$
$557$	31.9538	1.35392	0.676962	+	0.736018i	$0.263296\pi$
$558$	−3.67889	−0.155740
$559$	−35.2863	−1.49245
$560$	−0.233607	−0.00987169
$561$	27.5724	1.16411
$562$	40.7743	1.71996
$563$	22.5379	0.949858	0.474929	−	0.880024i	$-0.342474\pi$
$563$	22.5379	0.949858	0.474929	+	0.880024i	$0.342474\pi$
$564$	58.1382	2.44806
$565$	23.3515	0.982405
$566$	2.74658	0.115447
$567$	−22.8156	−0.958166
$568$	−29.0651	−1.21954
$569$	−9.83705	−0.412391	−0.206195	−	0.978511i	$-0.566108\pi$
$569$	−9.83705	−0.412391	−0.206195	+	0.978511i	$0.566108\pi$
$570$	−26.1036	−1.09336
$571$	31.4302	1.31531	0.657657	−	0.753317i	$-0.271548\pi$
$571$	31.4302	1.31531	0.657657	+	0.753317i	$0.271548\pi$
$572$	−69.1683	−2.89207
$573$	24.9040	1.04038
$574$	−35.0244	−1.46189
$575$	13.6844	0.570681
$576$	10.7382	0.447423
$577$	26.8303	1.11696	0.558479	−	0.829518i	$-0.311385\pi$
$577$	26.8303	1.11696	0.558479	+	0.829518i	$0.311385\pi$
$578$	31.8178	1.32345
$579$	10.1116	0.420226
$580$	−37.7722	−1.56841
$581$	11.1349	0.461955
$582$	−48.4781	−2.00948
$583$	20.2573	0.838972
$584$	−6.53493	−0.270417
$585$	7.54291	0.311861
$586$	−45.1374	−1.86461
$587$	−38.7259	−1.59839	−0.799195	−	0.601071i	$-0.794741\pi$
$587$	−38.7259	−1.59839	−0.799195	+	0.601071i	$0.794741\pi$
$588$	39.6062	1.63333
$589$	−10.5299	−0.433876
$590$	46.3199	1.90696
$591$	−16.0931	−0.661983
$592$	0.260507	0.0107068
$593$	16.2736	0.668276	0.334138	−	0.942524i	$-0.391555\pi$
$593$	16.2736	0.668276	0.334138	+	0.942524i	$0.391555\pi$
$594$	−43.4048	−1.78092
$595$	31.1090	1.27535
$596$	9.18848	0.376375
$597$	30.0198	1.22863
$598$	67.3690	2.75492
$599$	−1.61316	−0.0659120	−0.0329560	−	0.999457i	$-0.510492\pi$
$599$	−1.61316	−0.0659120	−0.0329560	+	0.999457i	$0.510492\pi$
$600$	−12.2246	−0.499067
$601$	28.4347	1.15987	0.579937	−	0.814661i	$-0.303077\pi$
$601$	28.4347	1.15987	0.579937	+	0.814661i	$0.303077\pi$
$602$	49.5857	2.02096
$603$	−10.0133	−0.407774
$604$	8.25122	0.335738
$605$	0.463881	0.0188594
$606$	27.4658	1.11572
$607$	19.2504	0.781348	0.390674	−	0.920529i	$-0.372242\pi$
$607$	19.2504	0.781348	0.390674	+	0.920529i	$0.372242\pi$
$608$	30.9333	1.25451
$609$	−47.2638	−1.91523
$610$	18.3326	0.742264
$611$	−77.8888	−3.15104
$612$	−14.8679	−0.601001
$613$	17.8457	0.720781	0.360390	−	0.932802i	$-0.382643\pi$
$613$	17.8457	0.720781	0.360390	+	0.932802i	$0.382643\pi$
$614$	−47.1770	−1.90391
$615$	−8.23876	−0.332219
$616$	36.9521	1.48884
$617$	−0.996905	−0.0401339	−0.0200669	−	0.999799i	$-0.506388\pi$
$617$	−0.996905	−0.0401339	−0.0200669	+	0.999799i	$0.506388\pi$
$618$	−50.0846	−2.01470
$619$	−41.9133	−1.68464	−0.842319	−	0.538980i	$-0.818810\pi$
$619$	−41.9133	−1.68464	−0.842319	+	0.538980i	$0.818810\pi$
$620$	8.95340	0.359577
$621$	26.0989	1.04731
$622$	−18.3942	−0.737539
$623$	4.42058	0.177107
$624$	0.391919	0.0156893
$625$	−1.45890	−0.0583562
$626$	33.2072	1.32723
$627$	−26.8896	−1.07387
$628$	27.3280	1.09051
$629$	−34.6913	−1.38323
$630$	−10.5996	−0.422297
$631$	49.1527	1.95674	0.978369	−	0.206867i	$-0.0663266\pi$
$631$	49.1527	1.95674	0.978369	+	0.206867i	$0.0663266\pi$
$632$	17.8795	0.711209
$633$	−25.2113	−1.00206
$634$	2.08989	0.0830000
$635$	13.7548	0.545844
$636$	28.6214	1.13491
$637$	−53.0612	−2.10236
$638$	−63.0266	−2.49525
$639$	8.58824	0.339746
$640$	−26.0293	−1.02890
$641$	−9.53312	−0.376536	−0.188268	−	0.982118i	$-0.560287\pi$
$641$	−9.53312	−0.376536	−0.188268	+	0.982118i	$0.560287\pi$
$642$	64.5344	2.54697
$643$	−37.1595	−1.46543	−0.732715	−	0.680536i	$-0.761747\pi$
$643$	−37.1595	−1.46543	−0.732715	+	0.680536i	$0.761747\pi$
$644$	−58.4442	−2.30302
$645$	11.6640	0.459270
$646$	−68.9327	−2.71212
$647$	−42.5615	−1.67327	−0.836634	−	0.547763i	$-0.815480\pi$
$647$	−42.5615	−1.67327	−0.836634	+	0.547763i	$0.815480\pi$
$648$	−16.3425	−0.641994
$649$	47.7146	1.87296
$650$	43.0790	1.68970
$651$	11.2033	0.439091
$652$	25.6277	1.00366
$653$	5.92139	0.231722	0.115861	−	0.993265i	$-0.463037\pi$
$653$	5.92139	0.231722	0.115861	+	0.993265i	$0.463037\pi$
$654$	−43.7037	−1.70895
$655$	−4.78282	−0.186880
$656$	0.163375	0.00637873
$657$	1.93096	0.0753339
$658$	109.452	4.26689
$659$	−21.2582	−0.828102	−0.414051	−	0.910254i	$-0.635887\pi$
$659$	−21.2582	−0.828102	−0.414051	+	0.910254i	$0.635887\pi$
$660$	22.8638	0.889973
$661$	12.4631	0.484759	0.242379	−	0.970182i	$-0.422072\pi$
$661$	12.4631	0.484759	0.242379	+	0.970182i	$0.422072\pi$
$662$	62.1124	2.41407
$663$	−52.1912	−2.02694
$664$	7.97580	0.309521
$665$	−30.3386	−1.17648
$666$	11.8201	0.458021
$667$	37.8973	1.46739
$668$	59.6890	2.30943
$669$	2.21210	0.0855249
$670$	39.4747	1.52504
$671$	18.8845	0.729029
$672$	−32.9115	−1.26959
$673$	−38.6797	−1.49099	−0.745496	−	0.666510i	$-0.767787\pi$
$673$	−38.6797	−1.49099	−0.745496	+	0.666510i	$0.767787\pi$
$674$	−56.4066	−2.17270
$675$	16.6889	0.642355
$676$	88.9800	3.42231
$677$	10.6729	0.410193	0.205097	−	0.978742i	$-0.434249\pi$
$677$	10.6729	0.410193	0.205097	+	0.978742i	$0.434249\pi$
$678$	55.0523	2.11427
$679$	−56.3430	−2.16225
$680$	22.2830	0.854512
$681$	−0.755236	−0.0289407
$682$	14.9396	0.572067
$683$	8.02103	0.306916	0.153458	−	0.988155i	$-0.450959\pi$
$683$	8.02103	0.306916	0.153458	+	0.988155i	$0.450959\pi$
$684$	14.4997	0.554411
$685$	−1.89679	−0.0724725
$686$	11.9046	0.454522
$687$	−5.19089	−0.198045
$688$	−0.231298	−0.00881816
$689$	−38.3446	−1.46081
$690$	−22.2690	−0.847768
$691$	−29.5257	−1.12321	−0.561605	−	0.827405i	$-0.689816\pi$
$691$	−29.5257	−1.12321	−0.561605	+	0.827405i	$0.689816\pi$
$692$	−22.9001	−0.870532
$693$	−10.9187	−0.414768
$694$	27.6418	1.04927
$695$	12.7074	0.482018
$696$	−33.8544	−1.28325
$697$	−21.7564	−0.824082
$698$	−6.71496	−0.254165
$699$	14.7878	0.559326
$700$	−37.3720	−1.41253
$701$	3.71329	0.140249	0.0701245	−	0.997538i	$-0.477660\pi$
$701$	3.71329	0.140249	0.0701245	+	0.997538i	$0.477660\pi$
$702$	82.1600	3.10093
$703$	33.8321	1.27600
$704$	−43.6066	−1.64349
$705$	25.7464	0.969665
$706$	−32.8618	−1.23677
$707$	31.9217	1.20054
$708$	67.4156	2.53363
$709$	−28.7293	−1.07895	−0.539476	−	0.842001i	$-0.681378\pi$
$709$	−28.7293	−1.07895	−0.539476	+	0.842001i	$0.681378\pi$
$710$	−33.8567	−1.27062
$711$	−5.28309	−0.198131
$712$	3.16640	0.118666
$713$	−8.98305	−0.336418
$714$	73.3410	2.74472
$715$	−30.6310	−1.14554
$716$	−41.1353	−1.53730
$717$	3.25103	0.121412
$718$	75.0991	2.80267
$719$	−24.7246	−0.922071	−0.461035	−	0.887382i	$-0.652522\pi$
$719$	−24.7246	−0.922071	−0.461035	+	0.887382i	$0.652522\pi$
$720$	0.0494430	0.00184263
$721$	−58.2102	−2.16786
$722$	23.7878	0.885289
$723$	−32.4869	−1.20820
$724$	−84.6526	−3.14609
$725$	24.2333	0.900004
$726$	1.09362	0.0405881
$727$	−2.33920	−0.0867560	−0.0433780	−	0.999059i	$-0.513812\pi$
$727$	−2.33920	−0.0867560	−0.0433780	+	0.999059i	$0.513812\pi$
$728$	−69.9458	−2.59237
$729$	29.7688	1.10255
$730$	−7.61225	−0.281742
$731$	30.8016	1.13924
$732$	26.6818	0.986189
$733$	−16.4973	−0.609343	−0.304672	−	0.952457i	$-0.598547\pi$
$733$	−16.4973	−0.609343	−0.304672	+	0.952457i	$0.598547\pi$
$734$	52.9852	1.95572
$735$	17.5395	0.646956
$736$	26.3892	0.972720
$737$	40.6632	1.49785
$738$	7.41292	0.272873
$739$	−3.76870	−0.138634	−0.0693169	−	0.997595i	$-0.522082\pi$
$739$	−3.76870	−0.138634	−0.0693169	+	0.997595i	$0.522082\pi$
$740$	−28.7670	−1.05749
$741$	50.8987	1.86981
$742$	53.8833	1.97812
$743$	−32.4920	−1.19201	−0.596007	−	0.802979i	$-0.703247\pi$
$743$	−32.4920	−1.19201	−0.596007	+	0.802979i	$0.703247\pi$
$744$	8.02475	0.294202
$745$	4.06910	0.149080
$746$	42.5861	1.55919
$747$	−2.35671	−0.0862276
$748$	60.3773	2.20761
$749$	75.0042	2.74059
$750$	−38.3090	−1.39885
$751$	−6.22970	−0.227325	−0.113662	−	0.993519i	$-0.536258\pi$
$751$	−6.22970	−0.227325	−0.113662	+	0.993519i	$0.536258\pi$
$752$	−0.510553	−0.0186179
$753$	14.6340	0.533292
$754$	119.302	4.34471
$755$	3.65404	0.132984
$756$	−71.2757	−2.59227
$757$	13.7985	0.501516	0.250758	−	0.968050i	$-0.419320\pi$
$757$	13.7985	0.501516	0.250758	+	0.968050i	$0.419320\pi$
$758$	−61.4231	−2.23099
$759$	−22.9395	−0.832652
$760$	−21.7311	−0.788270
$761$	35.6749	1.29321	0.646607	−	0.762823i	$-0.276187\pi$
$761$	35.6749	1.29321	0.646607	+	0.762823i	$0.276187\pi$
$762$	32.4277	1.17473
$763$	−50.7941	−1.83887
$764$	54.5341	1.97298
$765$	−6.58424	−0.238054
$766$	−66.9309	−2.41831
$767$	−90.3179	−3.26119
$768$	−23.1770	−0.836328
$769$	50.4120	1.81790	0.908951	−	0.416903i	$-0.136885\pi$
$769$	50.4120	1.81790	0.908951	+	0.416903i	$0.136885\pi$
$770$	43.0439	1.55119
$771$	−15.4394	−0.556037
$772$	22.1422	0.796915
$773$	−1.94835	−0.0700774	−0.0350387	−	0.999386i	$-0.511155\pi$
$773$	−1.94835	−0.0700774	−0.0350387	+	0.999386i	$0.511155\pi$
$774$	−10.4948	−0.377229
$775$	−5.74420	−0.206338
$776$	−40.3577	−1.44876
$777$	−35.9957	−1.29134
$778$	−27.7076	−0.993365
$779$	21.2176	0.760199
$780$	−43.2784	−1.54962
$781$	−34.8760	−1.24796
$782$	−58.8066	−2.10292
$783$	46.2177	1.65169
$784$	−0.347810	−0.0124218
$785$	12.1022	0.431944
$786$	−11.2757	−0.402192
$787$	−14.8705	−0.530076	−0.265038	−	0.964238i	$-0.585385\pi$
$787$	−14.8705	−0.530076	−0.265038	+	0.964238i	$0.585385\pi$
$788$	−35.2403	−1.25538
$789$	−35.7811	−1.27384
$790$	20.8271	0.740994
$791$	63.9838	2.27500
$792$	−7.82093	−0.277905
$793$	−35.7461	−1.26938
$794$	16.3588	0.580553
$795$	12.6749	0.449534
$796$	65.7364	2.32996
$797$	32.7474	1.15997	0.579986	−	0.814626i	$-0.303058\pi$
$797$	32.7474	1.15997	0.579986	+	0.814626i	$0.303058\pi$
$798$	−71.5247	−2.53195
$799$	67.9894	2.40529
$800$	16.8745	0.596605
$801$	−0.935617	−0.0330584
$802$	1.37399	0.0485171
$803$	−7.84144	−0.276718
$804$	57.4528	2.02620
$805$	−25.8819	−0.912217
$806$	−28.2789	−0.996081
$807$	−33.5491	−1.18098
$808$	22.8651	0.804391
$809$	−29.9924	−1.05448	−0.527238	−	0.849717i	$-0.676773\pi$
$809$	−29.9924	−1.05448	−0.527238	+	0.849717i	$0.676773\pi$
$810$	−19.0367	−0.668881
$811$	−40.2422	−1.41309	−0.706547	−	0.707666i	$-0.749748\pi$
$811$	−40.2422	−1.41309	−0.706547	+	0.707666i	$0.749748\pi$
$812$	−103.497	−3.63203
$813$	1.17489	0.0412053
$814$	−48.0004	−1.68241
$815$	11.3492	0.397545
$816$	−0.342108	−0.0119762
$817$	−30.0387	−1.05092
$818$	34.9692	1.22267
$819$	20.6678	0.722192
$820$	−18.0410	−0.630019
$821$	10.7150	0.373956	0.186978	−	0.982364i	$-0.440131\pi$
$821$	10.7150	0.373956	0.186978	+	0.982364i	$0.440131\pi$
$822$	−4.47177	−0.155971
$823$	21.8882	0.762976	0.381488	−	0.924374i	$-0.375412\pi$
$823$	21.8882	0.762976	0.381488	+	0.924374i	$0.375412\pi$
$824$	−41.6952	−1.45252
$825$	−14.6686	−0.510696
$826$	126.918	4.41604
$827$	−27.0162	−0.939446	−0.469723	−	0.882814i	$-0.655646\pi$
$827$	−27.0162	−0.939446	−0.469723	+	0.882814i	$0.655646\pi$
$828$	12.3697	0.429878
$829$	26.3511	0.915210	0.457605	−	0.889156i	$-0.348707\pi$
$829$	26.3511	0.915210	0.457605	+	0.889156i	$0.348707\pi$
$830$	9.29066	0.322484
$831$	−38.9635	−1.35163
$832$	82.5420	2.86163
$833$	46.3173	1.60480
$834$	29.9582	1.03737
$835$	26.4331	0.914756
$836$	−58.8820	−2.03648
$837$	−10.9553	−0.378670
$838$	−65.7947	−2.27284
$839$	−50.6828	−1.74976	−0.874882	−	0.484336i	$-0.839061\pi$
$839$	−50.6828	−1.74976	−0.874882	+	0.484336i	$0.839061\pi$
$840$	23.1208	0.797744
$841$	38.1111	1.31418
$842$	−10.2199	−0.352199
$843$	26.2805	0.905148
$844$	−55.2069	−1.90030
$845$	39.4046	1.35556
$846$	−23.1656	−0.796450
$847$	1.27105	0.0436737
$848$	−0.251345	−0.00863122
$849$	1.77027	0.0607556
$850$	−37.6038	−1.28980
$851$	28.8622	0.989384
$852$	−49.2761	−1.68817
$853$	−27.6006	−0.945027	−0.472513	−	0.881323i	$-0.656653\pi$
$853$	−27.6006	−0.945027	−0.472513	+	0.881323i	$0.656653\pi$
$854$	50.2318	1.71890
$855$	6.42117	0.219599
$856$	53.7245	1.83626
$857$	9.83641	0.336005	0.168003	−	0.985787i	$-0.446268\pi$
$857$	9.83641	0.336005	0.168003	+	0.985787i	$0.446268\pi$
$858$	−72.2142	−2.46535
$859$	14.2531	0.486308	0.243154	−	0.969988i	$-0.421818\pi$
$859$	14.2531	0.486308	0.243154	+	0.969988i	$0.421818\pi$
$860$	25.5415	0.870959
$861$	−22.5745	−0.769335
$862$	−89.8482	−3.06024
$863$	−26.0290	−0.886039	−0.443020	−	0.896512i	$-0.646093\pi$
$863$	−26.0290	−0.886039	−0.443020	+	0.896512i	$0.646093\pi$
$864$	32.1830	1.09489
$865$	−10.1413	−0.344814
$866$	−16.9401	−0.575647
$867$	20.5077	0.696479
$868$	24.5326	0.832691
$869$	21.4541	0.727782
$870$	−39.4356	−1.33699
$871$	−76.9705	−2.60805
$872$	−36.3831	−1.23209
$873$	11.9250	0.403601
$874$	57.3503	1.93990
$875$	−44.5242	−1.50519
$876$	−11.0791	−0.374329
$877$	13.8037	0.466119	0.233059	−	0.972463i	$-0.425126\pi$
$877$	13.8037	0.466119	0.233059	+	0.972463i	$0.425126\pi$
$878$	4.95998	0.167391
$879$	−29.0927	−0.981272
$880$	−0.200783	−0.00676840
$881$	−42.5711	−1.43426	−0.717128	−	0.696942i	$-0.754544\pi$
$881$	−42.5711	−1.43426	−0.717128	+	0.696942i	$0.754544\pi$
$882$	−15.7814	−0.531387
$883$	23.6400	0.795551	0.397775	−	0.917483i	$-0.369782\pi$
$883$	23.6400	0.795551	0.397775	+	0.917483i	$0.369782\pi$
$884$	−114.287	−3.84388
$885$	29.8549	1.00356
$886$	31.8213	1.06906
$887$	−40.7883	−1.36954	−0.684768	−	0.728761i	$-0.740097\pi$
$887$	−40.7883	−1.36954	−0.684768	+	0.728761i	$0.740097\pi$
$888$	−25.7832	−0.865228
$889$	37.6887	1.26404
$890$	3.68840	0.123635
$891$	−19.6098	−0.656954
$892$	4.84400	0.162189
$893$	−66.3056	−2.21883
$894$	9.59311	0.320841
$895$	−18.2167	−0.608917
$896$	−71.3211	−2.38267
$897$	43.4217	1.44981
$898$	−14.0320	−0.468255
$899$	−15.9078	−0.530555
$900$	7.90980	0.263660
$901$	33.4712	1.11509
$902$	−30.1032	−1.00233
$903$	31.9597	1.06355
$904$	45.8307	1.52431
$905$	−37.4882	−1.24615
$906$	8.61458	0.286200
$907$	30.7199	1.02004	0.510018	−	0.860164i	$-0.329639\pi$
$907$	30.7199	1.02004	0.510018	+	0.860164i	$0.329639\pi$
$908$	−1.65379	−0.0548831
$909$	−6.75625	−0.224091
$910$	−81.4769	−2.70093
$911$	−33.9035	−1.12327	−0.561637	−	0.827384i	$-0.689828\pi$
$911$	−33.9035	−1.12327	−0.561637	+	0.827384i	$0.689828\pi$
$912$	0.333635	0.0110478
$913$	9.57039	0.316734
$914$	−60.5208	−2.00185
$915$	11.8160	0.390625
$916$	−11.3669	−0.375572
$917$	−13.1051	−0.432767
$918$	−71.7177	−2.36704
$919$	2.07305	0.0683836	0.0341918	−	0.999415i	$-0.489114\pi$
$919$	2.07305	0.0683836	0.0341918	+	0.999415i	$0.489114\pi$
$920$	−18.5388	−0.611208
$921$	−30.4073	−1.00195
$922$	34.6894	1.14243
$923$	66.0161	2.17295
$924$	62.6475	2.06095
$925$	18.4559	0.606826
$926$	56.5076	1.85696
$927$	12.3202	0.404649
$928$	46.7319	1.53405
$929$	31.2835	1.02638	0.513190	−	0.858275i	$-0.328464\pi$
$929$	31.2835	1.02638	0.513190	+	0.858275i	$0.328464\pi$
$930$	9.34768	0.306522
$931$	−45.1702	−1.48039
$932$	32.3819	1.06070
$933$	−11.8557	−0.388138
$934$	−4.03069	−0.131888
$935$	26.7379	0.874424
$936$	14.8041	0.483886
$937$	−34.4990	−1.12703	−0.563517	−	0.826104i	$-0.690552\pi$
$937$	−34.4990	−1.12703	−0.563517	+	0.826104i	$0.690552\pi$
$938$	108.162	3.53161
$939$	21.4033	0.698469
$940$	56.3787	1.83887
$941$	−17.7332	−0.578085	−0.289043	−	0.957316i	$-0.593337\pi$
$941$	−17.7332	−0.578085	−0.289043	+	0.957316i	$0.593337\pi$
$942$	28.5314	0.929604
$943$	18.1008	0.589442
$944$	−0.592024	−0.0192687
$945$	−31.5643	−1.02679
$946$	42.6185	1.38565
$947$	23.8339	0.774498	0.387249	−	0.921975i	$-0.373425\pi$
$947$	23.8339	0.774498	0.387249	+	0.921975i	$0.373425\pi$
$948$	30.3124	0.984502
$949$	14.8429	0.481821
$950$	36.6725	1.18981
$951$	1.34701	0.0436797
$952$	61.0560	1.97884
$953$	14.2584	0.461874	0.230937	−	0.972969i	$-0.425821\pi$
$953$	14.2584	0.461874	0.230937	+	0.972969i	$0.425821\pi$
$954$	−11.4044	−0.369232
$955$	24.1503	0.781486
$956$	7.11901	0.230245
$957$	−40.6229	−1.31315
$958$	11.3772	0.367580
$959$	−5.19725	−0.167828
$960$	−27.2845	−0.880605
$961$	−27.2293	−0.878363
$962$	90.8590	2.92941
$963$	−15.8747	−0.511554
$964$	−71.1388	−2.29123
$965$	9.80563	0.315654
$966$	−61.0179	−1.96322
$967$	50.5397	1.62525	0.812623	−	0.582789i	$-0.198039\pi$
$967$	50.5397	1.62525	0.812623	+	0.582789i	$0.198039\pi$
$968$	0.910434	0.0292625
$969$	−44.4296	−1.42729
$970$	−47.0110	−1.50943
$971$	26.2760	0.843236	0.421618	−	0.906774i	$-0.361462\pi$
$971$	26.2760	0.843236	0.421618	+	0.906774i	$0.361462\pi$
$972$	26.9059	0.863008
$973$	34.8186	1.11623
$974$	87.3893	2.80014
$975$	27.7659	0.889222
$976$	−0.234312	−0.00750014
$977$	27.6010	0.883034	0.441517	−	0.897253i	$-0.354440\pi$
$977$	27.6010	0.883034	0.441517	+	0.897253i	$0.354440\pi$
$978$	26.7563	0.855572
$979$	3.79945	0.121431
$980$	38.4076	1.22689
$981$	10.7506	0.343240
$982$	−31.7411	−1.01290
$983$	54.7261	1.74549	0.872746	−	0.488175i	$-0.162337\pi$
$983$	54.7261	1.74549	0.872746	+	0.488175i	$0.162337\pi$
$984$	−16.1698	−0.515474
$985$	−15.6061	−0.497251
$986$	−104.139	−3.31646
$987$	70.5459	2.24550
$988$	111.456	3.54590
$989$	−25.6261	−0.814863
$990$	−9.11026	−0.289543
$991$	51.1162	1.62376	0.811880	−	0.583825i	$-0.198445\pi$
$991$	51.1162	1.62376	0.811880	+	0.583825i	$0.198445\pi$
$992$	−11.0772	−0.351701
$993$	40.0337	1.27043
$994$	−92.7682	−2.94243
$995$	29.1112	0.922888
$996$	13.5219	0.428459
$997$	−30.7867	−0.975024	−0.487512	−	0.873116i	$-0.662095\pi$
$997$	−30.7867	−0.975024	−0.487512	+	0.873116i	$0.662095\pi$
$998$	−37.9303	−1.20066
$999$	35.1990	1.11365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1511.2.a.b.1.74	✓	87

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1511.2.a.b.1.74	✓	87	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:	\( N \)	\(=\)	\( 1511 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1511.a (trivial)

\(f(q)\)	\(=\)	\(q+2.28620 q^{2} +1.47354 q^{3} +3.22671 q^{4} +1.42894 q^{5} +3.36880 q^{6} +3.91535 q^{7} +2.80451 q^{8} -0.828685 q^{9} +O(q^{10})\)	\(q+2.28620 q^{2} +1.47354 q^{3} +3.22671 q^{4} +1.42894 q^{5} +3.36880 q^{6} +3.91535 q^{7} +2.80451 q^{8} -0.828685 q^{9} +3.26685 q^{10} +3.36521 q^{11} +4.75468 q^{12} -6.36993 q^{13} +8.95127 q^{14} +2.10560 q^{15} -0.0417542 q^{16} +5.56034 q^{17} -1.89454 q^{18} -5.42263 q^{19} +4.61079 q^{20} +5.76941 q^{21} +7.69354 q^{22} -4.62606 q^{23} +4.13255 q^{24} -2.95812 q^{25} -14.5629 q^{26} -5.64171 q^{27} +12.6337 q^{28} -8.19214 q^{29} +4.81383 q^{30} +1.94184 q^{31} -5.70448 q^{32} +4.95876 q^{33} +12.7120 q^{34} +5.59481 q^{35} -2.67393 q^{36} -6.23906 q^{37} -12.3972 q^{38} -9.38634 q^{39} +4.00748 q^{40} -3.91278 q^{41} +13.1900 q^{42} +5.53951 q^{43} +10.8586 q^{44} -1.18414 q^{45} -10.5761 q^{46} +12.2276 q^{47} -0.0615265 q^{48} +8.32994 q^{49} -6.76286 q^{50} +8.19337 q^{51} -20.5539 q^{52} +6.01963 q^{53} -12.8981 q^{54} +4.80869 q^{55} +10.9806 q^{56} -7.99046 q^{57} -18.7289 q^{58} +14.1788 q^{59} +6.79417 q^{60} +5.61169 q^{61} +4.43943 q^{62} -3.24459 q^{63} -12.9581 q^{64} -9.10227 q^{65} +11.3367 q^{66} +12.0834 q^{67} +17.9416 q^{68} -6.81667 q^{69} +12.7908 q^{70} -10.3637 q^{71} -2.32405 q^{72} -2.33015 q^{73} -14.2637 q^{74} -4.35891 q^{75} -17.4973 q^{76} +13.1760 q^{77} -21.4591 q^{78} +6.37528 q^{79} -0.0596644 q^{80} -5.82723 q^{81} -8.94540 q^{82} +2.84392 q^{83} +18.6162 q^{84} +7.94540 q^{85} +12.6644 q^{86} -12.0714 q^{87} +9.43776 q^{88} +1.12904 q^{89} -2.70719 q^{90} -24.9405 q^{91} -14.9270 q^{92} +2.86137 q^{93} +27.9547 q^{94} -7.74863 q^{95} -8.40577 q^{96} -14.3903 q^{97} +19.0439 q^{98} -2.78870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9}+O(q^{10}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9	\( 87 q + 6 q^{2} + 4 q^{3} + 110 q^{4} + 10 q^{5} + 8 q^{6} + 21 q^{7} + 15 q^{8} + 133 q^{9} + 25 q^{10} + 17 q^{11} + 34 q^{13} + 12 q^{14} + 16 q^{15} + 152 q^{16} + 32 q^{17} + 14 q^{18} + 56 q^{19} + 3 q^{20} + 38 q^{21} + 32 q^{22} + 8 q^{23} + 8 q^{24} + 179 q^{25} + 11 q^{26} - 2 q^{27} + 45 q^{28} + 40 q^{29} + 24 q^{30} + 31 q^{31} + 26 q^{32} + 31 q^{33} + 31 q^{34} + 22 q^{35} + 180 q^{36} + 35 q^{37} - 15 q^{38} + 59 q^{39} + 42 q^{40} + 45 q^{41} - 30 q^{42} + 82 q^{43} + 25 q^{44} + 20 q^{45} + 69 q^{46} - 7 q^{47} - 39 q^{48} + 222 q^{49} + 17 q^{50} + 53 q^{51} + 54 q^{52} + 16 q^{53} - 7 q^{54} + 49 q^{55} + 12 q^{56} + 52 q^{57} + 17 q^{58} - 7 q^{59} - 6 q^{60} + 131 q^{61} - 8 q^{62} + 19 q^{63} + 213 q^{64} + 57 q^{65} + 17 q^{66} + 38 q^{67} + 13 q^{68} + 45 q^{69} - 5 q^{71} + 4 q^{72} + 91 q^{73} + q^{74} - 44 q^{75} + 150 q^{76} + 5 q^{77} - 87 q^{78} + 120 q^{79} - 41 q^{80} + 247 q^{81} + 20 q^{82} - 33 q^{83} - 16 q^{84} + 110 q^{85} - 22 q^{86} - 13 q^{87} + 78 q^{88} + 53 q^{89} - 33 q^{90} + 32 q^{91} - 31 q^{92} + 13 q^{93} + 79 q^{94} - 25 q^{95} - 51 q^{96} + 92 q^{97} - 36 q^{98} + 35 q^{99}+O(q^{100}) \) 87 * q + 6 * q^2 + 4 * q^3 + 110 * q^4 + 10 * q^5 + 8 * q^6 + 21 * q^7 + 15 * q^8 + 133 * q^9 + 25 * q^10 + 17 * q^11 + 34 * q^13 + 12 * q^14 + 16 * q^15 + 152 * q^16 + 32 * q^17 + 14 * q^18 + 56 * q^19 + 3 * q^20 + 38 * q^21 + 32 * q^22 + 8 * q^23 + 8 * q^24 + 179 * q^25 + 11 * q^26 - 2 * q^27 + 45 * q^28 + 40 * q^29 + 24 * q^30 + 31 * q^31 + 26 * q^32 + 31 * q^33 + 31 * q^34 + 22 * q^35 + 180 * q^36 + 35 * q^37 - 15 * q^38 + 59 * q^39 + 42 * q^40 + 45 * q^41 - 30 * q^42 + 82 * q^43 + 25 * q^44 + 20 * q^45 + 69 * q^46 - 7 * q^47 - 39 * q^48 + 222 * q^49 + 17 * q^50 + 53 * q^51 + 54 * q^52 + 16 * q^53 - 7 * q^54 + 49 * q^55 + 12 * q^56 + 52 * q^57 + 17 * q^58 - 7 * q^59 - 6 * q^60 + 131 * q^61 - 8 * q^62 + 19 * q^63 + 213 * q^64 + 57 * q^65 + 17 * q^66 + 38 * q^67 + 13 * q^68 + 45 * q^69 - 5 * q^71 + 4 * q^72 + 91 * q^73 + q^74 - 44 * q^75 + 150 * q^76 + 5 * q^77 - 87 * q^78 + 120 * q^79 - 41 * q^80 + 247 * q^81 + 20 * q^82 - 33 * q^83 - 16 * q^84 + 110 * q^85 - 22 * q^86 - 13 * q^87 + 78 * q^88 + 53 * q^89 - 33 * q^90 + 32 * q^91 - 31 * q^92 + 13 * q^93 + 79 * q^94 - 25 * q^95 - 51 * q^96 + 92 * q^97 - 36 * q^98 + 35 * q^99

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