LMFDB - Embedded newform 8035.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.71462 q^{2} +2.16303 q^{3} +5.36914 q^{4} +1.00000 q^{5} -5.87179 q^{6} -4.59135 q^{7} -9.14592 q^{8} +1.67870 q^{9} +O(q^{10})$	\(q-2.71462 q^{2} +2.16303 q^{3} +5.36914 q^{4} +1.00000 q^{5} -5.87179 q^{6} -4.59135 q^{7} -9.14592 q^{8} +1.67870 q^{9} -2.71462 q^{10} -1.85768 q^{11} +11.6136 q^{12} -0.473422 q^{13} +12.4637 q^{14} +2.16303 q^{15} +14.0894 q^{16} +5.22842 q^{17} -4.55702 q^{18} +6.43407 q^{19} +5.36914 q^{20} -9.93122 q^{21} +5.04289 q^{22} -6.10480 q^{23} -19.7829 q^{24} +1.00000 q^{25} +1.28516 q^{26} -2.85802 q^{27} -24.6516 q^{28} +10.6754 q^{29} -5.87179 q^{30} -3.89035 q^{31} -19.9554 q^{32} -4.01822 q^{33} -14.1932 q^{34} -4.59135 q^{35} +9.01316 q^{36} -0.772275 q^{37} -17.4660 q^{38} -1.02403 q^{39} -9.14592 q^{40} -10.3158 q^{41} +26.9595 q^{42} -4.44984 q^{43} -9.97416 q^{44} +1.67870 q^{45} +16.5722 q^{46} -3.40537 q^{47} +30.4758 q^{48} +14.0805 q^{49} -2.71462 q^{50} +11.3092 q^{51} -2.54187 q^{52} +11.2491 q^{53} +7.75842 q^{54} -1.85768 q^{55} +41.9921 q^{56} +13.9171 q^{57} -28.9797 q^{58} +11.4392 q^{59} +11.6136 q^{60} +11.4994 q^{61} +10.5608 q^{62} -7.70748 q^{63} +25.9925 q^{64} -0.473422 q^{65} +10.9079 q^{66} -1.03348 q^{67} +28.0721 q^{68} -13.2049 q^{69} +12.4637 q^{70} -13.1791 q^{71} -15.3532 q^{72} -13.9911 q^{73} +2.09643 q^{74} +2.16303 q^{75} +34.5454 q^{76} +8.52927 q^{77} +2.77984 q^{78} -0.947999 q^{79} +14.0894 q^{80} -11.2181 q^{81} +28.0035 q^{82} +5.84937 q^{83} -53.3221 q^{84} +5.22842 q^{85} +12.0796 q^{86} +23.0913 q^{87} +16.9902 q^{88} -14.0004 q^{89} -4.55702 q^{90} +2.17365 q^{91} -32.7775 q^{92} -8.41493 q^{93} +9.24428 q^{94} +6.43407 q^{95} -43.1642 q^{96} -4.41652 q^{97} -38.2231 q^{98} -3.11849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.71462	−1.91952	−0.959762	−	0.280816i	$-0.909395\pi$
$2$	−2.71462	−1.91952	−0.959762	+	0.280816i	$0.909395\pi$
$3$	2.16303	1.24883	0.624413	−	0.781094i	$-0.285338\pi$
$3$	2.16303	1.24883	0.624413	+	0.781094i	$0.285338\pi$
$4$	5.36914	2.68457
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.87179	−2.39715
$7$	−4.59135	−1.73537	−0.867683	−	0.497117i	$-0.834392\pi$
$7$	−4.59135	−1.73537	−0.867683	+	0.497117i	$0.834392\pi$
$8$	−9.14592	−3.23357
$9$	1.67870	0.559566
$10$	−2.71462	−0.858437
$11$	−1.85768	−0.560112	−0.280056	−	0.959984i	$-0.590353\pi$
$11$	−1.85768	−0.560112	−0.280056	+	0.959984i	$0.590353\pi$
$12$	11.6136	3.35256
$13$	−0.473422	−0.131304	−0.0656519	−	0.997843i	$-0.520913\pi$
$13$	−0.473422	−0.131304	−0.0656519	+	0.997843i	$0.520913\pi$
$14$	12.4637	3.33108
$15$	2.16303	0.558492
$16$	14.0894	3.52235
$17$	5.22842	1.26808	0.634039	−	0.773301i	$-0.281396\pi$
$17$	5.22842	1.26808	0.634039	+	0.773301i	$0.281396\pi$
$18$	−4.55702	−1.07410
$19$	6.43407	1.47608	0.738038	−	0.674759i	$-0.235753\pi$
$19$	6.43407	1.47608	0.738038	+	0.674759i	$0.235753\pi$
$20$	5.36914	1.20058
$21$	−9.93122	−2.16717
$22$	5.04289	1.07515
$23$	−6.10480	−1.27294	−0.636469	−	0.771302i	$-0.719606\pi$
$23$	−6.10480	−1.27294	−0.636469	+	0.771302i	$0.719606\pi$
$24$	−19.7829	−4.03817
$25$	1.00000	0.200000
$26$	1.28516	0.252041
$27$	−2.85802	−0.550026
$28$	−24.6516	−4.65871
$29$	10.6754	1.98238	0.991188	−	0.132461i	$-0.0422878\pi$
$29$	10.6754	1.98238	0.991188	+	0.132461i	$0.0422878\pi$
$30$	−5.87179	−1.07204
$31$	−3.89035	−0.698727	−0.349363	−	0.936987i	$-0.613602\pi$
$31$	−3.89035	−0.698727	−0.349363	+	0.936987i	$0.613602\pi$
$32$	−19.9554	−3.52765
$33$	−4.01822	−0.699483
$34$	−14.1932	−2.43411
$35$	−4.59135	−0.776080
$36$	9.01316	1.50219
$37$	−0.772275	−0.126961	−0.0634806	−	0.997983i	$-0.520220\pi$
$37$	−0.772275	−0.126961	−0.0634806	+	0.997983i	$0.520220\pi$
$38$	−17.4660	−2.83336
$39$	−1.02403	−0.163976
$40$	−9.14592	−1.44610
$41$	−10.3158	−1.61106	−0.805532	−	0.592553i	$-0.798120\pi$
$41$	−10.3158	−1.61106	−0.805532	+	0.592553i	$0.798120\pi$
$42$	26.9595	4.15993
$43$	−4.44984	−0.678594	−0.339297	−	0.940679i	$-0.610189\pi$
$43$	−4.44984	−0.678594	−0.339297	+	0.940679i	$0.610189\pi$
$44$	−9.97416	−1.50366
$45$	1.67870	0.250245
$46$	16.5722	2.44343
$47$	−3.40537	−0.496725	−0.248362	−	0.968667i	$-0.579892\pi$
$47$	−3.40537	−0.496725	−0.248362	+	0.968667i	$0.579892\pi$
$48$	30.4758	4.39880
$49$	14.0805	2.01150
$50$	−2.71462	−0.383905
$51$	11.3092	1.58361
$52$	−2.54187	−0.352494
$53$	11.2491	1.54518	0.772592	−	0.634903i	$-0.218960\pi$
$53$	11.2491	1.54518	0.772592	+	0.634903i	$0.218960\pi$
$54$	7.75842	1.05579
$55$	−1.85768	−0.250490
$56$	41.9921	5.61143
$57$	13.9171	1.84336
$58$	−28.9797	−3.80522
$59$	11.4392	1.48926	0.744630	−	0.667478i	$-0.232626\pi$
$59$	11.4392	1.48926	0.744630	+	0.667478i	$0.232626\pi$
$60$	11.6136	1.49931
$61$	11.4994	1.47235	0.736175	−	0.676792i	$-0.236630\pi$
$61$	11.4994	1.47235	0.736175	+	0.676792i	$0.236630\pi$
$62$	10.5608	1.34122
$63$	−7.70748	−0.971052
$64$	25.9925	3.24907
$65$	−0.473422	−0.0587208
$66$	10.9079	1.34267
$67$	−1.03348	−0.126260	−0.0631298	−	0.998005i	$-0.520108\pi$
$67$	−1.03348	−0.126260	−0.0631298	+	0.998005i	$0.520108\pi$
$68$	28.0721	3.40425
$69$	−13.2049	−1.58968
$70$	12.4637	1.48970
$71$	−13.1791	−1.56407	−0.782036	−	0.623234i	$-0.785819\pi$
$71$	−13.1791	−1.56407	−0.782036	+	0.623234i	$0.785819\pi$
$72$	−15.3532	−1.80940
$73$	−13.9911	−1.63754	−0.818769	−	0.574123i	$-0.805343\pi$
$73$	−13.9911	−1.63754	−0.818769	+	0.574123i	$0.805343\pi$
$74$	2.09643	0.243705
$75$	2.16303	0.249765
$76$	34.5454	3.96263
$77$	8.52927	0.972000
$78$	2.77984	0.314755
$79$	−0.947999	−0.106658	−0.0533291	−	0.998577i	$-0.516983\pi$
$79$	−0.947999	−0.106658	−0.0533291	+	0.998577i	$0.516983\pi$
$80$	14.0894	1.57524
$81$	−11.2181	−1.24645
$82$	28.0035	3.09247
$83$	5.84937	0.642052	0.321026	−	0.947070i	$-0.395972\pi$
$83$	5.84937	0.642052	0.321026	+	0.947070i	$0.395972\pi$
$84$	−53.3221	−5.81792
$85$	5.22842	0.567102
$86$	12.0796	1.30258
$87$	23.0913	2.47564
$88$	16.9902	1.81116
$89$	−14.0004	−1.48404	−0.742021	−	0.670377i	$-0.766133\pi$
$89$	−14.0004	−1.48404	−0.742021	+	0.670377i	$0.766133\pi$
$90$	−4.55702	−0.480352
$91$	2.17365	0.227860
$92$	−32.7775	−3.41729
$93$	−8.41493	−0.872588
$94$	9.24428	0.953475
$95$	6.43407	0.660121
$96$	−43.1642	−4.40542
$97$	−4.41652	−0.448430	−0.224215	−	0.974540i	$-0.571982\pi$
$97$	−4.41652	−0.448430	−0.224215	+	0.974540i	$0.571982\pi$
$98$	−38.2231	−3.86112
$99$	−3.11849	−0.313420
$100$	5.36914	0.536914
$101$	10.8134	1.07597	0.537986	−	0.842954i	$-0.319185\pi$
$101$	10.8134	1.07597	0.537986	+	0.842954i	$0.319185\pi$
$102$	−30.7002	−3.03977
$103$	−3.23224	−0.318482	−0.159241	−	0.987240i	$-0.550905\pi$
$103$	−3.23224	−0.318482	−0.159241	+	0.987240i	$0.550905\pi$
$104$	4.32988	0.424580
$105$	−9.93122	−0.969188
$106$	−30.5370	−2.96602
$107$	6.02632	0.582586	0.291293	−	0.956634i	$-0.405915\pi$
$107$	6.02632	0.582586	0.291293	+	0.956634i	$0.405915\pi$
$108$	−15.3451	−1.47658
$109$	10.0825	0.965729	0.482865	−	0.875695i	$-0.339596\pi$
$109$	10.0825	0.965729	0.482865	+	0.875695i	$0.339596\pi$
$110$	5.04289	0.480821
$111$	−1.67045	−0.158552
$112$	−64.6893	−6.11256
$113$	10.6378	1.00072	0.500359	−	0.865818i	$-0.333201\pi$
$113$	10.6378	1.00072	0.500359	+	0.865818i	$0.333201\pi$
$114$	−37.7795	−3.53838
$115$	−6.10480	−0.569275
$116$	57.3178	5.32183
$117$	−0.794733	−0.0734731
$118$	−31.0531	−2.85867
$119$	−24.0055	−2.20058
$120$	−19.7829	−1.80592
$121$	−7.54902	−0.686274
$122$	−31.2165	−2.82621
$123$	−22.3135	−2.01194
$124$	−20.8878	−1.87578
$125$	1.00000	0.0894427
$126$	20.9229	1.86396
$127$	−7.34283	−0.651571	−0.325786	−	0.945444i	$-0.605629\pi$
$127$	−7.34283	−0.651571	−0.325786	+	0.945444i	$0.605629\pi$
$128$	−30.6489	−2.70901
$129$	−9.62513	−0.847445
$130$	1.28516	0.112716
$131$	1.66472	0.145448	0.0727238	−	0.997352i	$-0.476831\pi$
$131$	1.66472	0.145448	0.0727238	+	0.997352i	$0.476831\pi$
$132$	−21.5744	−1.87781
$133$	−29.5410	−2.56153
$134$	2.80550	0.242358
$135$	−2.85802	−0.245979
$136$	−47.8187	−4.10042
$137$	12.9232	1.10410	0.552052	−	0.833810i	$-0.313845\pi$
$137$	12.9232	1.10410	0.552052	+	0.833810i	$0.313845\pi$
$138$	35.8461	3.05142
$139$	13.2138	1.12078	0.560391	−	0.828228i	$-0.310651\pi$
$139$	13.2138	1.12078	0.560391	+	0.828228i	$0.310651\pi$
$140$	−24.6516	−2.08344
$141$	−7.36592	−0.620323
$142$	35.7762	3.00227
$143$	0.879469	0.0735449
$144$	23.6518	1.97098
$145$	10.6754	0.886546
$146$	37.9805	3.14329
$147$	30.4565	2.51201
$148$	−4.14645	−0.340836
$149$	−2.56859	−0.210427	−0.105214	−	0.994450i	$-0.533553\pi$
$149$	−2.56859	−0.210427	−0.105214	+	0.994450i	$0.533553\pi$
$150$	−5.87179	−0.479430
$151$	11.4536	0.932085	0.466042	−	0.884762i	$-0.345679\pi$
$151$	11.4536	0.932085	0.466042	+	0.884762i	$0.345679\pi$
$152$	−58.8455	−4.77300
$153$	8.77694	0.709573
$154$	−23.1537	−1.86578
$155$	−3.89035	−0.312480
$156$	−5.49814	−0.440204
$157$	5.26533	0.420219	0.210110	−	0.977678i	$-0.432618\pi$
$157$	5.26533	0.420219	0.210110	+	0.977678i	$0.432618\pi$
$158$	2.57345	0.204733
$159$	24.3322	1.92967
$160$	−19.9554	−1.57761
$161$	28.0292	2.20901
$162$	30.4527	2.39259
$163$	1.84492	0.144505	0.0722527	−	0.997386i	$-0.476981\pi$
$163$	1.84492	0.144505	0.0722527	+	0.997386i	$0.476981\pi$
$164$	−55.3872	−4.32501
$165$	−4.01822	−0.312818
$166$	−15.8788	−1.23243
$167$	13.3144	1.03030	0.515150	−	0.857100i	$-0.327736\pi$
$167$	13.3144	1.03030	0.515150	+	0.857100i	$0.327736\pi$
$168$	90.8302	7.00770
$169$	−12.7759	−0.982759
$170$	−14.1932	−1.08857
$171$	10.8008	0.825961
$172$	−23.8918	−1.82173
$173$	7.40702	0.563146	0.281573	−	0.959540i	$-0.409144\pi$
$173$	7.40702	0.563146	0.281573	+	0.959540i	$0.409144\pi$
$174$	−62.6839	−4.75205
$175$	−4.59135	−0.347073
$176$	−26.1736	−1.97291
$177$	24.7434	1.85983
$178$	38.0058	2.84865
$179$	−6.72200	−0.502426	−0.251213	−	0.967932i	$-0.580829\pi$
$179$	−6.72200	−0.502426	−0.251213	+	0.967932i	$0.580829\pi$
$180$	9.01316	0.671801
$181$	15.6894	1.16618	0.583090	−	0.812407i	$-0.301843\pi$
$181$	15.6894	1.16618	0.583090	+	0.812407i	$0.301843\pi$
$182$	−5.90062	−0.437383
$183$	24.8736	1.83871
$184$	55.8340	4.11614
$185$	−0.772275	−0.0567788
$186$	22.8433	1.67495
$187$	−9.71275	−0.710266
$188$	−18.2839	−1.33349
$189$	13.1222	0.954496
$190$	−17.4660	−1.26712
$191$	−14.8665	−1.07570	−0.537852	−	0.843039i	$-0.680764\pi$
$191$	−14.8665	−1.07570	−0.537852	+	0.843039i	$0.680764\pi$
$192$	56.2226	4.05752
$193$	13.6442	0.982128	0.491064	−	0.871123i	$-0.336608\pi$
$193$	13.6442	0.982128	0.491064	+	0.871123i	$0.336608\pi$
$194$	11.9892	0.860771
$195$	−1.02403	−0.0733321
$196$	75.6001	5.40000
$197$	7.06266	0.503194	0.251597	−	0.967832i	$-0.419044\pi$
$197$	7.06266	0.503194	0.251597	+	0.967832i	$0.419044\pi$
$198$	8.46549	0.601616
$199$	−5.74325	−0.407128	−0.203564	−	0.979062i	$-0.565252\pi$
$199$	−5.74325	−0.407128	−0.203564	+	0.979062i	$0.565252\pi$
$200$	−9.14592	−0.646714
$201$	−2.23545	−0.157676
$202$	−29.3542	−2.06535
$203$	−49.0146	−3.44015
$204$	60.7208	4.25131
$205$	−10.3158	−0.720489
$206$	8.77430	0.611334
$207$	−10.2481	−0.712292
$208$	−6.67023	−0.462497
$209$	−11.9525	−0.826768
$210$	26.9595	1.86038
$211$	−17.2763	−1.18935	−0.594675	−	0.803966i	$-0.702719\pi$
$211$	−17.2763	−1.18935	−0.594675	+	0.803966i	$0.702719\pi$
$212$	60.3981	4.14816
$213$	−28.5068	−1.95325
$214$	−16.3591	−1.11829
$215$	−4.44984	−0.303476
$216$	26.1392	1.77855
$217$	17.8619	1.21255
$218$	−27.3701	−1.85374
$219$	−30.2632	−2.04500
$220$	−9.97416	−0.672458
$221$	−2.47525	−0.166504
$222$	4.53464	0.304345
$223$	8.27151	0.553901	0.276951	−	0.960884i	$-0.410676\pi$
$223$	8.27151	0.553901	0.276951	+	0.960884i	$0.410676\pi$
$224$	91.6223	6.12177
$225$	1.67870	0.111913
$226$	−28.8775	−1.92090
$227$	−28.3564	−1.88208	−0.941039	−	0.338298i	$-0.890149\pi$
$227$	−28.3564	−1.88208	−0.941039	+	0.338298i	$0.890149\pi$
$228$	74.7227	4.94863
$229$	1.40391	0.0927727	0.0463864	−	0.998924i	$-0.485229\pi$
$229$	1.40391	0.0927727	0.0463864	+	0.998924i	$0.485229\pi$
$230$	16.5722	1.09274
$231$	18.4491	1.21386
$232$	−97.6366	−6.41016
$233$	8.57750	0.561930	0.280965	−	0.959718i	$-0.409345\pi$
$233$	8.57750	0.561930	0.280965	+	0.959718i	$0.409345\pi$
$234$	2.15739	0.141033
$235$	−3.40537	−0.222142
$236$	61.4188	3.99802
$237$	−2.05055	−0.133198
$238$	65.1657	4.22407
$239$	22.9997	1.48773	0.743863	−	0.668332i	$-0.232991\pi$
$239$	22.9997	1.48773	0.743863	+	0.668332i	$0.232991\pi$
$240$	30.4758	1.96720
$241$	−1.99067	−0.128230	−0.0641150	−	0.997943i	$-0.520422\pi$
$241$	−1.99067	−0.128230	−0.0641150	+	0.997943i	$0.520422\pi$
$242$	20.4927	1.31732
$243$	−15.6910	−1.00658
$244$	61.7420	3.95262
$245$	14.0805	0.899569
$246$	60.5725	3.86196
$247$	−3.04603	−0.193814
$248$	35.5808	2.25938
$249$	12.6524	0.801811
$250$	−2.71462	−0.171687
$251$	26.6081	1.67949	0.839745	−	0.542981i	$-0.182704\pi$
$251$	26.6081	1.67949	0.839745	+	0.542981i	$0.182704\pi$
$252$	−41.3826	−2.60686
$253$	11.3408	0.712988
$254$	19.9330	1.25071
$255$	11.3092	0.708212
$256$	31.2150	1.95094
$257$	−12.8591	−0.802128	−0.401064	−	0.916050i	$-0.631360\pi$
$257$	−12.8591	−0.802128	−0.401064	+	0.916050i	$0.631360\pi$
$258$	26.1285	1.62669
$259$	3.54578	0.220324
$260$	−2.54187	−0.157640
$261$	17.9208	1.10927
$262$	−4.51908	−0.279190
$263$	−5.06534	−0.312342	−0.156171	−	0.987730i	$-0.549915\pi$
$263$	−5.06534	−0.312342	−0.156171	+	0.987730i	$0.549915\pi$
$264$	36.7503	2.26183
$265$	11.2491	0.691027
$266$	80.1926	4.91692
$267$	−30.2833	−1.85331
$268$	−5.54889	−0.338953
$269$	13.4607	0.820715	0.410358	−	0.911925i	$-0.365404\pi$
$269$	13.4607	0.820715	0.410358	+	0.911925i	$0.365404\pi$
$270$	7.75842	0.472162
$271$	1.68890	0.102593	0.0512967	−	0.998683i	$-0.483665\pi$
$271$	1.68890	0.102593	0.0512967	+	0.998683i	$0.483665\pi$
$272$	73.6652	4.46661
$273$	4.70166	0.284558
$274$	−35.0815	−2.11935
$275$	−1.85768	−0.112022
$276$	−70.8987	−4.26760
$277$	20.8013	1.24983	0.624914	−	0.780694i	$-0.285134\pi$
$277$	20.8013	1.24983	0.624914	+	0.780694i	$0.285134\pi$
$278$	−35.8704	−2.15137
$279$	−6.53071	−0.390984
$280$	41.9921	2.50951
$281$	20.4815	1.22183	0.610913	−	0.791697i	$-0.290802\pi$
$281$	20.4815	1.22183	0.610913	+	0.791697i	$0.290802\pi$
$282$	19.9957	1.19072
$283$	−28.8233	−1.71336	−0.856682	−	0.515845i	$-0.827478\pi$
$283$	−28.8233	−1.71336	−0.856682	+	0.515845i	$0.827478\pi$
$284$	−70.7604	−4.19886
$285$	13.9171	0.824376
$286$	−2.38742	−0.141171
$287$	47.3636	2.79579
$288$	−33.4991	−1.97395
$289$	10.3364	0.608023
$290$	−28.9797	−1.70175
$291$	−9.55306	−0.560010
$292$	−75.1203	−4.39608
$293$	18.0456	1.05423	0.527116	−	0.849793i	$-0.323273\pi$
$293$	18.0456	1.05423	0.527116	+	0.849793i	$0.323273\pi$
$294$	−82.6777	−4.82186
$295$	11.4392	0.666017
$296$	7.06317	0.410538
$297$	5.30929	0.308076
$298$	6.97275	0.403920
$299$	2.89015	0.167142
$300$	11.6136	0.670512
$301$	20.4307	1.17761
$302$	−31.0923	−1.78916
$303$	23.3897	1.34370
$304$	90.6520	5.19925
$305$	11.4994	0.658455
$306$	−23.8260	−1.36204
$307$	24.7404	1.41201	0.706004	−	0.708208i	$-0.250496\pi$
$307$	24.7404	1.41201	0.706004	+	0.708208i	$0.250496\pi$
$308$	45.7948	2.60940
$309$	−6.99144	−0.397729
$310$	10.5608	0.599813
$311$	20.4487	1.15954	0.579770	−	0.814780i	$-0.303143\pi$
$311$	20.4487	1.15954	0.579770	+	0.814780i	$0.303143\pi$
$312$	9.36567	0.530227
$313$	−7.29020	−0.412067	−0.206033	−	0.978545i	$-0.566056\pi$
$313$	−7.29020	−0.412067	−0.206033	+	0.978545i	$0.566056\pi$
$314$	−14.2934	−0.806621
$315$	−7.70748	−0.434267
$316$	−5.08994	−0.286332
$317$	18.2687	1.02607	0.513036	−	0.858367i	$-0.328521\pi$
$317$	18.2687	1.02607	0.513036	+	0.858367i	$0.328521\pi$
$318$	−66.0525	−3.70404
$319$	−19.8315	−1.11035
$320$	25.9925	1.45303
$321$	13.0351	0.727548
$322$	−76.0886	−4.24025
$323$	33.6400	1.87178
$324$	−60.2314	−3.34619
$325$	−0.473422	−0.0262608
$326$	−5.00825	−0.277381
$327$	21.8088	1.20603
$328$	94.3478	5.20949
$329$	15.6353	0.862000
$330$	10.9079	0.600462
$331$	16.0487	0.882114	0.441057	−	0.897479i	$-0.354604\pi$
$331$	16.0487	0.882114	0.441057	+	0.897479i	$0.354604\pi$
$332$	31.4061	1.72363
$333$	−1.29642	−0.0710431
$334$	−36.1435	−1.97768
$335$	−1.03348	−0.0564650
$336$	−139.925	−7.63352
$337$	0.487635	0.0265631	0.0132816	−	0.999912i	$-0.495772\pi$
$337$	0.487635	0.0265631	0.0132816	+	0.999912i	$0.495772\pi$
$338$	34.6816	1.88643
$339$	23.0099	1.24972
$340$	28.0721	1.52243
$341$	7.22703	0.391366
$342$	−29.3202	−1.58545
$343$	−32.5090	−1.75532
$344$	40.6978	2.19428
$345$	−13.2049	−0.710925
$346$	−20.1072	−1.08097
$347$	21.5002	1.15419	0.577096	−	0.816676i	$-0.304186\pi$
$347$	21.5002	1.15419	0.577096	+	0.816676i	$0.304186\pi$
$348$	123.980	6.64604
$349$	32.5827	1.74411	0.872055	−	0.489408i	$-0.162787\pi$
$349$	32.5827	1.74411	0.872055	+	0.489408i	$0.162787\pi$
$350$	12.4637	0.666215
$351$	1.35305	0.0722204
$352$	37.0708	1.97588
$353$	10.2565	0.545900	0.272950	−	0.962028i	$-0.412001\pi$
$353$	10.2565	0.545900	0.272950	+	0.962028i	$0.412001\pi$
$354$	−67.1687	−3.56998
$355$	−13.1791	−0.699474
$356$	−75.1702	−3.98401
$357$	−51.9246	−2.74814
$358$	18.2477	0.964419
$359$	−1.38544	−0.0731206	−0.0365603	−	0.999331i	$-0.511640\pi$
$359$	−1.38544	−0.0731206	−0.0365603	+	0.999331i	$0.511640\pi$
$360$	−15.3532	−0.809186
$361$	22.3972	1.17880
$362$	−42.5906	−2.23851
$363$	−16.3287	−0.857037
$364$	11.6706	0.611707
$365$	−13.9911	−0.732329
$366$	−67.5222	−3.52944
$367$	−18.0906	−0.944323	−0.472162	−	0.881512i	$-0.656526\pi$
$367$	−18.0906	−0.944323	−0.472162	+	0.881512i	$0.656526\pi$
$368$	−86.0128	−4.48373
$369$	−17.3172	−0.901496
$370$	2.09643	0.108988
$371$	−51.6486	−2.68146
$372$	−45.1810	−2.34252
$373$	−10.8785	−0.563265	−0.281633	−	0.959522i	$-0.590876\pi$
$373$	−10.8785	−0.563265	−0.281633	+	0.959522i	$0.590876\pi$
$374$	26.3664	1.36337
$375$	2.16303	0.111698
$376$	31.1453	1.60619
$377$	−5.05399	−0.260294
$378$	−35.6216	−1.83218
$379$	28.8532	1.48209	0.741044	−	0.671457i	$-0.234331\pi$
$379$	28.8532	1.48209	0.741044	+	0.671457i	$0.234331\pi$
$380$	34.5454	1.77214
$381$	−15.8828	−0.813699
$382$	40.3569	2.06484
$383$	22.4715	1.14824	0.574120	−	0.818771i	$-0.305344\pi$
$383$	22.4715	1.14824	0.574120	+	0.818771i	$0.305344\pi$
$384$	−66.2945	−3.38308
$385$	8.52927	0.434692
$386$	−37.0387	−1.88522
$387$	−7.46993	−0.379718
$388$	−23.7129	−1.20384
$389$	−3.04352	−0.154313	−0.0771564	−	0.997019i	$-0.524584\pi$
$389$	−3.04352	−0.154313	−0.0771564	+	0.997019i	$0.524584\pi$
$390$	2.77984	0.140763
$391$	−31.9185	−1.61419
$392$	−128.779	−6.50432
$393$	3.60085	0.181639
$394$	−19.1724	−0.965892
$395$	−0.947999	−0.0476990
$396$	−16.7436	−0.841397
$397$	−3.22830	−0.162024	−0.0810119	−	0.996713i	$-0.525815\pi$
$397$	−3.22830	−0.162024	−0.0810119	+	0.996713i	$0.525815\pi$
$398$	15.5907	0.781492
$399$	−63.8981	−3.19891
$400$	14.0894	0.704469
$401$	−6.54361	−0.326772	−0.163386	−	0.986562i	$-0.552242\pi$
$401$	−6.54361	−0.326772	−0.163386	+	0.986562i	$0.552242\pi$
$402$	6.06838	0.302663
$403$	1.84178	0.0917455
$404$	58.0586	2.88852
$405$	−11.2181	−0.557430
$406$	133.056	6.60345
$407$	1.43464	0.0711125
$408$	−103.433	−5.12071
$409$	−14.5883	−0.721347	−0.360674	−	0.932692i	$-0.617453\pi$
$409$	−14.5883	−0.721347	−0.360674	+	0.932692i	$0.617453\pi$
$410$	28.0035	1.38300
$411$	27.9533	1.37883
$412$	−17.3544	−0.854988
$413$	−52.5214	−2.58441
$414$	27.8197	1.36726
$415$	5.84937	0.287134
$416$	9.44735	0.463194
$417$	28.5819	1.39966
$418$	32.4463	1.58700
$419$	14.1897	0.693210	0.346605	−	0.938011i	$-0.387334\pi$
$419$	14.1897	0.693210	0.346605	+	0.938011i	$0.387334\pi$
$420$	−53.3221	−2.60185
$421$	−9.79635	−0.477445	−0.238722	−	0.971088i	$-0.576729\pi$
$421$	−9.79635	−0.477445	−0.238722	+	0.971088i	$0.576729\pi$
$422$	46.8985	2.28299
$423$	−5.71659	−0.277950
$424$	−102.883	−4.99646
$425$	5.22842	0.253616
$426$	77.3850	3.74931
$427$	−52.7978	−2.55507
$428$	32.3561	1.56399
$429$	1.90232	0.0918447
$430$	12.0796	0.582530
$431$	17.1929	0.828151	0.414076	−	0.910242i	$-0.364105\pi$
$431$	17.1929	0.828151	0.414076	+	0.910242i	$0.364105\pi$
$432$	−40.2677	−1.93738
$433$	31.4216	1.51002	0.755012	−	0.655711i	$-0.227631\pi$
$433$	31.4216	1.51002	0.755012	+	0.655711i	$0.227631\pi$
$434$	−48.4883	−2.32751
$435$	23.0913	1.10714
$436$	54.1344	2.59257
$437$	−39.2787	−1.87895
$438$	82.1530	3.92542
$439$	20.0153	0.955279	0.477640	−	0.878556i	$-0.341493\pi$
$439$	20.0153	0.955279	0.477640	+	0.878556i	$0.341493\pi$
$440$	16.9902	0.809977
$441$	23.6369	1.12556
$442$	6.71936	0.319607
$443$	−13.3353	−0.633578	−0.316789	−	0.948496i	$-0.602605\pi$
$443$	−13.3353	−0.633578	−0.316789	+	0.948496i	$0.602605\pi$
$444$	−8.96890	−0.425645
$445$	−14.0004	−0.663684
$446$	−22.4540	−1.06323
$447$	−5.55594	−0.262787
$448$	−119.341	−5.63832
$449$	−4.24194	−0.200189	−0.100095	−	0.994978i	$-0.531915\pi$
$449$	−4.24194	−0.200189	−0.100095	+	0.994978i	$0.531915\pi$
$450$	−4.55702	−0.214820
$451$	19.1635	0.902376
$452$	57.1158	2.68650
$453$	24.7746	1.16401
$454$	76.9766	3.61269
$455$	2.17365	0.101902
$456$	−127.284	−5.96064
$457$	5.40125	0.252660	0.126330	−	0.991988i	$-0.459680\pi$
$457$	5.40125	0.252660	0.126330	+	0.991988i	$0.459680\pi$
$458$	−3.81107	−0.178079
$459$	−14.9429	−0.697476
$460$	−32.7775	−1.52826
$461$	−11.3261	−0.527510	−0.263755	−	0.964590i	$-0.584961\pi$
$461$	−11.3261	−0.527510	−0.263755	+	0.964590i	$0.584961\pi$
$462$	−50.0821	−2.33003
$463$	−1.91560	−0.0890255	−0.0445128	−	0.999009i	$-0.514174\pi$
$463$	−1.91560	−0.0890255	−0.0445128	+	0.999009i	$0.514174\pi$
$464$	150.410	6.98262
$465$	−8.41493	−0.390233
$466$	−23.2846	−1.07864
$467$	2.00150	0.0926183	0.0463091	−	0.998927i	$-0.485254\pi$
$467$	2.00150	0.0926183	0.0463091	+	0.998927i	$0.485254\pi$
$468$	−4.26703	−0.197244
$469$	4.74506	0.219107
$470$	9.24428	0.426407
$471$	11.3891	0.524781
$472$	−104.622	−4.81563
$473$	8.26638	0.380089
$474$	5.56646	0.255676
$475$	6.43407	0.295215
$476$	−128.889	−5.90761
$477$	18.8839	0.864632
$478$	−62.4353	−2.85573
$479$	43.6414	1.99402	0.997012	−	0.0772433i	$-0.0246118\pi$
$479$	43.6414	1.99402	0.997012	+	0.0772433i	$0.0246118\pi$
$480$	−43.1642	−1.97017
$481$	0.365612	0.0166705
$482$	5.40389	0.246141
$483$	60.6281	2.75867
$484$	−40.5317	−1.84235
$485$	−4.41652	−0.200544
$486$	42.5949	1.93215
$487$	−18.1831	−0.823954	−0.411977	−	0.911194i	$-0.635162\pi$
$487$	−18.1831	−0.823954	−0.411977	+	0.911194i	$0.635162\pi$
$488$	−105.173	−4.76095
$489$	3.99062	0.180462
$490$	−38.2231	−1.72674
$491$	−10.6416	−0.480248	−0.240124	−	0.970742i	$-0.577188\pi$
$491$	−10.6416	−0.480248	−0.240124	+	0.970742i	$0.577188\pi$
$492$	−119.804	−5.40119
$493$	55.8156	2.51381
$494$	8.26881	0.372031
$495$	−3.11849	−0.140166
$496$	−54.8126	−2.46116
$497$	60.5098	2.71424
$498$	−34.3463	−1.53909
$499$	12.2641	0.549014	0.274507	−	0.961585i	$-0.411485\pi$
$499$	12.2641	0.549014	0.274507	+	0.961585i	$0.411485\pi$
$500$	5.36914	0.240115
$501$	28.7995	1.28666
$502$	−72.2309	−3.22382
$503$	35.5286	1.58414	0.792070	−	0.610430i	$-0.209003\pi$
$503$	35.5286	1.58414	0.792070	+	0.610430i	$0.209003\pi$
$504$	70.4920	3.13996
$505$	10.8134	0.481189
$506$	−30.7858	−1.36860
$507$	−27.6346	−1.22730
$508$	−39.4247	−1.74919
$509$	−15.3898	−0.682143	−0.341072	−	0.940037i	$-0.610790\pi$
$509$	−15.3898	−0.682143	−0.341072	+	0.940037i	$0.610790\pi$
$510$	−30.7002	−1.35943
$511$	64.2381	2.84173
$512$	−23.4388	−1.03586
$513$	−18.3887	−0.811880
$514$	34.9075	1.53970
$515$	−3.23224	−0.142430
$516$	−51.6786	−2.27503
$517$	6.32610	0.278222
$518$	−9.62544	−0.422918
$519$	16.0216	0.703271
$520$	4.32988	0.189878
$521$	−3.45053	−0.151171	−0.0755853	−	0.997139i	$-0.524083\pi$
$521$	−3.45053	−0.151171	−0.0755853	+	0.997139i	$0.524083\pi$
$522$	−48.6481	−2.12927
$523$	−33.8358	−1.47954	−0.739768	−	0.672862i	$-0.765065\pi$
$523$	−33.8358	−1.47954	−0.739768	+	0.672862i	$0.765065\pi$
$524$	8.93813	0.390464
$525$	−9.93122	−0.433434
$526$	13.7504	0.599548
$527$	−20.3404	−0.886041
$528$	−56.6143	−2.46382
$529$	14.2685	0.620371
$530$	−30.5370	−1.32644
$531$	19.2030	0.833338
$532$	−158.610	−6.87661
$533$	4.88375	0.211539
$534$	82.2076	3.55747
$535$	6.02632	0.260540
$536$	9.45212	0.408269
$537$	−14.5399	−0.627443
$538$	−36.5407	−1.57538
$539$	−26.1571	−1.12666
$540$	−15.3451	−0.660348
$541$	−0.0378167	−0.00162587	−0.000812934	−	1.00000i	$-0.500259\pi$
$541$	−0.0378167	−0.00162587	−0.000812934		1.00000i	$0.500259\pi$
$542$	−4.58471	−0.196930
$543$	33.9365	1.45636
$544$	−104.335	−4.47334
$545$	10.0825	0.431887
$546$	−12.7632	−0.546215
$547$	−34.8702	−1.49094	−0.745470	−	0.666539i	$-0.767775\pi$
$547$	−34.8702	−1.49094	−0.745470	+	0.666539i	$0.767775\pi$
$548$	69.3865	2.96404
$549$	19.3040	0.823876
$550$	5.04289	0.215030
$551$	68.6864	2.92614
$552$	120.771	5.14034
$553$	4.35260	0.185091
$554$	−56.4675	−2.39907
$555$	−1.67045	−0.0709068
$556$	70.9468	3.00882
$557$	22.5273	0.954513	0.477257	−	0.878764i	$-0.341631\pi$
$557$	22.5273	0.954513	0.477257	+	0.878764i	$0.341631\pi$
$558$	17.7284	0.750502
$559$	2.10665	0.0891019
$560$	−64.6893	−2.73362
$561$	−21.0090	−0.886999
$562$	−55.5995	−2.34533
$563$	−30.8732	−1.30115	−0.650576	−	0.759441i	$-0.725472\pi$
$563$	−30.8732	−1.30115	−0.650576	+	0.759441i	$0.725472\pi$
$564$	−39.5487	−1.66530
$565$	10.6378	0.447535
$566$	78.2441	3.28884
$567$	51.5061	2.16305
$568$	120.535	5.05754
$569$	−33.0178	−1.38418	−0.692088	−	0.721813i	$-0.743309\pi$
$569$	−33.0178	−1.38418	−0.692088	+	0.721813i	$0.743309\pi$
$570$	−37.7795	−1.58241
$571$	−24.9929	−1.04592	−0.522961	−	0.852357i	$-0.675173\pi$
$571$	−24.9929	−1.04592	−0.522961	+	0.852357i	$0.675173\pi$
$572$	4.72199	0.197436
$573$	−32.1567	−1.34337
$574$	−128.574	−5.36657
$575$	−6.10480	−0.254588
$576$	43.6336	1.81807
$577$	−39.1167	−1.62845	−0.814225	−	0.580550i	$-0.802838\pi$
$577$	−39.1167	−1.62845	−0.814225	+	0.580550i	$0.802838\pi$
$578$	−28.0594	−1.16712
$579$	29.5127	1.22651
$580$	57.3178	2.37999
$581$	−26.8565	−1.11420
$582$	25.9329	1.07495
$583$	−20.8973	−0.865477
$584$	127.962	5.29510
$585$	−0.794733	−0.0328582
$586$	−48.9867	−2.02362
$587$	11.0489	0.456037	0.228019	−	0.973657i	$-0.426775\pi$
$587$	11.0489	0.456037	0.228019	+	0.973657i	$0.426775\pi$
$588$	163.525	6.74367
$589$	−25.0307	−1.03137
$590$	−31.0531	−1.27844
$591$	15.2767	0.628401
$592$	−10.8809	−0.447201
$593$	19.0114	0.780704	0.390352	−	0.920666i	$-0.372353\pi$
$593$	19.0114	0.780704	0.390352	+	0.920666i	$0.372353\pi$
$594$	−14.4127	−0.591359
$595$	−24.0055	−0.984130
$596$	−13.7911	−0.564907
$597$	−12.4228	−0.508432
$598$	−7.84564	−0.320832
$599$	16.1809	0.661133	0.330566	−	0.943783i	$-0.392760\pi$
$599$	16.1809	0.661133	0.330566	+	0.943783i	$0.392760\pi$
$600$	−19.7829	−0.807633
$601$	25.5018	1.04024	0.520120	−	0.854093i	$-0.325887\pi$
$601$	25.5018	1.04024	0.520120	+	0.854093i	$0.325887\pi$
$602$	−55.4616	−2.26045
$603$	−1.73490	−0.0706505
$604$	61.4962	2.50225
$605$	−7.54902	−0.306911
$606$	−63.4940	−2.57927
$607$	5.88688	0.238941	0.119470	−	0.992838i	$-0.461880\pi$
$607$	5.88688	0.238941	0.119470	+	0.992838i	$0.461880\pi$
$608$	−128.395	−5.20708
$609$	−106.020	−4.29615
$610$	−31.2165	−1.26392
$611$	1.61218	0.0652218
$612$	47.1246	1.90490
$613$	−17.0543	−0.688817	−0.344408	−	0.938820i	$-0.611920\pi$
$613$	−17.0543	−0.688817	−0.344408	+	0.938820i	$0.611920\pi$
$614$	−67.1606	−2.71038
$615$	−22.3135	−0.899766
$616$	−78.0080	−3.14303
$617$	48.9846	1.97205	0.986023	−	0.166608i	$-0.0532815\pi$
$617$	48.9846	1.97205	0.986023	+	0.166608i	$0.0532815\pi$
$618$	18.9791	0.763450
$619$	−3.64627	−0.146556	−0.0732780	−	0.997312i	$-0.523346\pi$
$619$	−3.64627	−0.146556	−0.0732780	+	0.997312i	$0.523346\pi$
$620$	−20.8878	−0.838875
$621$	17.4476	0.700149
$622$	−55.5104	−2.22576
$623$	64.2808	2.57536
$624$	−14.4279	−0.577579
$625$	1.00000	0.0400000
$626$	19.7901	0.790972
$627$	−25.8535	−1.03249
$628$	28.2703	1.12811
$629$	−4.03778	−0.160997
$630$	20.9229	0.833587
$631$	−18.8477	−0.750316	−0.375158	−	0.926961i	$-0.622412\pi$
$631$	−18.8477	−0.750316	−0.375158	+	0.926961i	$0.622412\pi$
$632$	8.67033	0.344887
$633$	−37.3692	−1.48529
$634$	−49.5925	−1.96957
$635$	−7.34283	−0.291392
$636$	130.643	5.18032
$637$	−6.66602	−0.264117
$638$	53.8350	2.13135
$639$	−22.1237	−0.875201
$640$	−30.6489	−1.21151
$641$	9.33283	0.368624	0.184312	−	0.982868i	$-0.440994\pi$
$641$	9.33283	0.368624	0.184312	+	0.982868i	$0.440994\pi$
$642$	−35.3853	−1.39655
$643$	13.2374	0.522030	0.261015	−	0.965335i	$-0.415943\pi$
$643$	13.2374	0.522030	0.261015	+	0.965335i	$0.415943\pi$
$644$	150.493	5.93025
$645$	−9.62513	−0.378989
$646$	−91.3197	−3.59293
$647$	5.29686	0.208241	0.104121	−	0.994565i	$-0.466797\pi$
$647$	5.29686	0.208241	0.104121	+	0.994565i	$0.466797\pi$
$648$	102.600	4.03049
$649$	−21.2504	−0.834152
$650$	1.28516	0.0504081
$651$	38.6359	1.51426
$652$	9.90564	0.387935
$653$	12.8603	0.503262	0.251631	−	0.967823i	$-0.419033\pi$
$653$	12.8603	0.503262	0.251631	+	0.967823i	$0.419033\pi$
$654$	−59.2024	−2.31500
$655$	1.66472	0.0650461
$656$	−145.344	−5.67472
$657$	−23.4869	−0.916310
$658$	−42.4437	−1.65463
$659$	39.0287	1.52034	0.760172	−	0.649722i	$-0.225115\pi$
$659$	39.0287	1.52034	0.760172	+	0.649722i	$0.225115\pi$
$660$	−21.5744	−0.839782
$661$	−14.7477	−0.573620	−0.286810	−	0.957987i	$-0.592595\pi$
$661$	−14.7477	−0.573620	−0.286810	+	0.957987i	$0.592595\pi$
$662$	−43.5660	−1.69324
$663$	−5.35404	−0.207934
$664$	−53.4979	−2.07612
$665$	−29.5410	−1.14555
$666$	3.51927	0.136369
$667$	−65.1713	−2.52344
$668$	71.4869	2.76591
$669$	17.8915	0.691726
$670$	2.80550	0.108386
$671$	−21.3623	−0.824681
$672$	198.182	7.64503
$673$	49.3395	1.90190	0.950950	−	0.309346i	$-0.100110\pi$
$673$	49.3395	1.90190	0.950950	+	0.309346i	$0.100110\pi$
$674$	−1.32374	−0.0509886
$675$	−2.85802	−0.110005
$676$	−68.5954	−2.63829
$677$	47.2300	1.81520	0.907599	−	0.419838i	$-0.137913\pi$
$677$	47.2300	1.81520	0.907599	+	0.419838i	$0.137913\pi$
$678$	−62.4629	−2.39887
$679$	20.2778	0.778190
$680$	−47.8187	−1.83376
$681$	−61.3357	−2.35039
$682$	−19.6186	−0.751235
$683$	23.4646	0.897847	0.448923	−	0.893570i	$-0.351808\pi$
$683$	23.4646	0.897847	0.448923	+	0.893570i	$0.351808\pi$
$684$	57.9913	2.21735
$685$	12.9232	0.493770
$686$	88.2493	3.36937
$687$	3.03669	0.115857
$688$	−62.6954	−2.39024
$689$	−5.32558	−0.202889
$690$	35.8461	1.36464
$691$	−51.4409	−1.95690	−0.978452	−	0.206475i	$-0.933801\pi$
$691$	−51.4409	−1.95690	−0.978452	+	0.206475i	$0.933801\pi$
$692$	39.7694	1.51180
$693$	14.3181	0.543898
$694$	−58.3648	−2.21550
$695$	13.2138	0.501229
$696$	−211.191	−8.00517
$697$	−53.9356	−2.04295
$698$	−88.4494	−3.34786
$699$	18.5534	0.701753
$700$	−24.6516	−0.931743
$701$	46.4415	1.75407	0.877036	−	0.480425i	$-0.159518\pi$
$701$	46.4415	1.75407	0.877036	+	0.480425i	$0.159518\pi$
$702$	−3.67301	−0.138629
$703$	−4.96887	−0.187404
$704$	−48.2859	−1.81984
$705$	−7.36592	−0.277417
$706$	−27.8426	−1.04787
$707$	−49.6480	−1.86721
$708$	132.851	4.99283
$709$	−17.2120	−0.646409	−0.323205	−	0.946329i	$-0.604760\pi$
$709$	−17.2120	−0.646409	−0.323205	+	0.946329i	$0.604760\pi$
$710$	35.7762	1.34266
$711$	−1.59140	−0.0596823
$712$	128.047	4.79876
$713$	23.7498	0.889436
$714$	140.955	5.27512
$715$	0.879469	0.0328903
$716$	−36.0914	−1.34880
$717$	49.7490	1.85791
$718$	3.76093	0.140357
$719$	30.6922	1.14463	0.572313	−	0.820035i	$-0.306046\pi$
$719$	30.6922	1.14463	0.572313	+	0.820035i	$0.306046\pi$
$720$	23.6518	0.881451
$721$	14.8403	0.552684
$722$	−60.7998	−2.26273
$723$	−4.30587	−0.160137
$724$	84.2383	3.13069
$725$	10.6754	0.396475
$726$	44.3263	1.64510
$727$	3.97684	0.147493	0.0737465	−	0.997277i	$-0.476504\pi$
$727$	3.97684	0.147493	0.0737465	+	0.997277i	$0.476504\pi$
$728$	−19.8800	−0.736802
$729$	−0.285808	−0.0105855
$730$	37.9805	1.40572
$731$	−23.2656	−0.860510
$732$	133.550	4.93614
$733$	10.9841	0.405705	0.202853	−	0.979209i	$-0.434979\pi$
$733$	10.9841	0.405705	0.202853	+	0.979209i	$0.434979\pi$
$734$	49.1091	1.81265
$735$	30.4565	1.12340
$736$	121.824	4.49048
$737$	1.91988	0.0707195
$738$	47.0095	1.73044
$739$	45.6054	1.67762	0.838811	−	0.544423i	$-0.183251\pi$
$739$	45.6054	1.67762	0.838811	+	0.544423i	$0.183251\pi$
$740$	−4.14645	−0.152427
$741$	−6.58866	−0.242040
$742$	140.206	5.14713
$743$	19.1849	0.703824	0.351912	−	0.936033i	$-0.385532\pi$
$743$	19.1849	0.703824	0.351912	+	0.936033i	$0.385532\pi$
$744$	76.9623	2.82158
$745$	−2.56859	−0.0941060
$746$	29.5308	1.08120
$747$	9.81932	0.359270
$748$	−52.1491	−1.90676
$749$	−27.6689	−1.01100
$750$	−5.87179	−0.214408
$751$	−16.4894	−0.601706	−0.300853	−	0.953671i	$-0.597271\pi$
$751$	−16.4894	−0.601706	−0.300853	+	0.953671i	$0.597271\pi$
$752$	−47.9796	−1.74964
$753$	57.5542	2.09739
$754$	13.7196	0.499639
$755$	11.4536	0.416841
$756$	70.4547	2.56241
$757$	−14.6475	−0.532374	−0.266187	−	0.963921i	$-0.585764\pi$
$757$	−14.6475	−0.532374	−0.266187	+	0.963921i	$0.585764\pi$
$758$	−78.3253	−2.84490
$759$	24.5304	0.890398
$760$	−58.8455	−2.13455
$761$	−44.8079	−1.62429	−0.812143	−	0.583458i	$-0.801699\pi$
$761$	−44.8079	−1.62429	−0.812143	+	0.583458i	$0.801699\pi$
$762$	43.1156	1.56191
$763$	−46.2923	−1.67589
$764$	−79.8205	−2.88780
$765$	8.77694	0.317331
$766$	−61.0015	−2.20407
$767$	−5.41558	−0.195545
$768$	67.5189	2.43638
$769$	34.5856	1.24719	0.623593	−	0.781749i	$-0.285672\pi$
$769$	34.5856	1.24719	0.623593	+	0.781749i	$0.285672\pi$
$770$	−23.1537	−0.834401
$771$	−27.8146	−1.00172
$772$	73.2574	2.63659
$773$	12.4708	0.448543	0.224271	−	0.974527i	$-0.428000\pi$
$773$	12.4708	0.448543	0.224271	+	0.974527i	$0.428000\pi$
$774$	20.2780	0.728877
$775$	−3.89035	−0.139745
$776$	40.3931	1.45003
$777$	7.66963	0.275147
$778$	8.26200	0.296207
$779$	−66.3728	−2.37805
$780$	−5.49814	−0.196865
$781$	24.4826	0.876056
$782$	86.6463	3.09847
$783$	−30.5105	−1.09036
$784$	198.385	7.08519
$785$	5.26533	0.187928
$786$	−9.77491	−0.348660
$787$	−44.7357	−1.59466	−0.797328	−	0.603547i	$-0.793754\pi$
$787$	−44.7357	−1.59466	−0.797328	+	0.603547i	$0.793754\pi$
$788$	37.9204	1.35086
$789$	−10.9565	−0.390061
$790$	2.57345	0.0915594
$791$	−48.8418	−1.73661
$792$	28.5214	1.01346
$793$	−5.44408	−0.193325
$794$	8.76360	0.311009
$795$	24.3322	0.862973
$796$	−30.8363	−1.09296
$797$	−45.6179	−1.61587	−0.807935	−	0.589272i	$-0.799415\pi$
$797$	−45.6179	−1.61587	−0.807935	+	0.589272i	$0.799415\pi$
$798$	173.459	6.14038
$799$	−17.8047	−0.629886
$800$	−19.9554	−0.705531
$801$	−23.5025	−0.830419
$802$	17.7634	0.627247
$803$	25.9911	0.917205
$804$	−12.0024	−0.423293
$805$	28.0292	0.987901
$806$	−4.99972	−0.176108
$807$	29.1160	1.02493
$808$	−98.8984	−3.47923
$809$	−3.88125	−0.136457	−0.0682287	−	0.997670i	$-0.521735\pi$
$809$	−3.88125	−0.136457	−0.0682287	+	0.997670i	$0.521735\pi$
$810$	30.4527	1.07000
$811$	30.9222	1.08582	0.542912	−	0.839790i	$-0.317322\pi$
$811$	30.9222	1.08582	0.542912	+	0.839790i	$0.317322\pi$
$812$	−263.166	−9.23532
$813$	3.65314	0.128121
$814$	−3.89450	−0.136502
$815$	1.84492	0.0646247
$816$	159.340	5.57802
$817$	−28.6305	−1.00166
$818$	39.6017	1.38464
$819$	3.64890	0.127503
$820$	−55.3872	−1.93420
$821$	13.3888	0.467273	0.233636	−	0.972324i	$-0.424937\pi$
$821$	13.3888	0.467273	0.233636	+	0.972324i	$0.424937\pi$
$822$	−75.8824	−2.64670
$823$	13.2266	0.461052	0.230526	−	0.973066i	$-0.425955\pi$
$823$	13.2266	0.461052	0.230526	+	0.973066i	$0.425955\pi$
$824$	29.5618	1.02984
$825$	−4.01822	−0.139897
$826$	142.576	4.96084
$827$	25.6976	0.893593	0.446796	−	0.894636i	$-0.352565\pi$
$827$	25.6976	0.893593	0.446796	+	0.894636i	$0.352565\pi$
$828$	−55.0235	−1.91220
$829$	−8.70771	−0.302431	−0.151216	−	0.988501i	$-0.548319\pi$
$829$	−8.70771	−0.302431	−0.151216	+	0.988501i	$0.548319\pi$
$830$	−15.8788	−0.551161
$831$	44.9938	1.56082
$832$	−12.3055	−0.426615
$833$	73.6187	2.55074
$834$	−77.5888	−2.68668
$835$	13.3144	0.460764
$836$	−64.1744	−2.21952
$837$	11.1187	0.384318
$838$	−38.5195	−1.33063
$839$	51.3648	1.77331	0.886654	−	0.462433i	$-0.153023\pi$
$839$	51.3648	1.77331	0.886654	+	0.462433i	$0.153023\pi$
$840$	90.8302	3.13394
$841$	84.9647	2.92982
$842$	26.5933	0.916467
$843$	44.3022	1.52585
$844$	−92.7589	−3.19289
$845$	−12.7759	−0.439503
$846$	15.5183	0.533532
$847$	34.6602	1.19094
$848$	158.493	5.44267
$849$	−62.3455	−2.13969
$850$	−14.1932	−0.486821
$851$	4.71458	0.161614
$852$	−153.057	−5.24364
$853$	31.4584	1.07712	0.538558	−	0.842588i	$-0.318969\pi$
$853$	31.4584	1.07712	0.538558	+	0.842588i	$0.318969\pi$
$854$	143.326	4.90451
$855$	10.8008	0.369381
$856$	−55.1162	−1.88383
$857$	35.2659	1.20466	0.602329	−	0.798248i	$-0.294239\pi$
$857$	35.2659	1.20466	0.602329	+	0.798248i	$0.294239\pi$
$858$	−5.16406	−0.176298
$859$	−47.8773	−1.63355	−0.816775	−	0.576956i	$-0.804241\pi$
$859$	−47.8773	−1.63355	−0.816775	+	0.576956i	$0.804241\pi$
$860$	−23.8918	−0.814703
$861$	102.449	3.49145
$862$	−46.6720	−1.58966
$863$	10.7149	0.364738	0.182369	−	0.983230i	$-0.441623\pi$
$863$	10.7149	0.364738	0.182369	+	0.983230i	$0.441623\pi$
$864$	57.0329	1.94030
$865$	7.40702	0.251846
$866$	−85.2974	−2.89853
$867$	22.3579	0.759315
$868$	95.9032	3.25517
$869$	1.76108	0.0597406
$870$	−62.6839	−2.12518
$871$	0.489272	0.0165784
$872$	−92.2138	−3.12275
$873$	−7.41400	−0.250926
$874$	106.626	3.60669
$875$	−4.59135	−0.155216
$876$	−162.487	−5.48994
$877$	0.488875	0.0165081	0.00825407	−	0.999966i	$-0.497373\pi$
$877$	0.488875	0.0165081	0.00825407	+	0.999966i	$0.497373\pi$
$878$	−54.3339	−1.83368
$879$	39.0331	1.31655
$880$	−26.1736	−0.882312
$881$	−45.6713	−1.53870	−0.769352	−	0.638825i	$-0.779421\pi$
$881$	−45.6713	−1.53870	−0.769352	+	0.638825i	$0.779421\pi$
$882$	−64.1650	−2.16055
$883$	10.9258	0.367682	0.183841	−	0.982956i	$-0.441147\pi$
$883$	10.9258	0.367682	0.183841	+	0.982956i	$0.441147\pi$
$884$	−13.2900	−0.446990
$885$	24.7434	0.831739
$886$	36.2002	1.21617
$887$	−52.2265	−1.75359	−0.876797	−	0.480860i	$-0.840325\pi$
$887$	−52.2265	−1.75359	−0.876797	+	0.480860i	$0.840325\pi$
$888$	15.2778	0.512691
$889$	33.7135	1.13071
$890$	38.0058	1.27396
$891$	20.8396	0.698153
$892$	44.4109	1.48699
$893$	−21.9104	−0.733203
$894$	15.0823	0.504426
$895$	−6.72200	−0.224692
$896$	140.720	4.70112
$897$	6.25148	0.208731
$898$	11.5152	0.384268
$899$	−41.5311	−1.38514
$900$	9.01316	0.300439
$901$	58.8151	1.95942
$902$	−52.0217	−1.73213
$903$	44.1923	1.47063
$904$	−97.2924	−3.23590
$905$	15.6894	0.521532
$906$	−67.2535	−2.23435
$907$	−47.6697	−1.58285	−0.791423	−	0.611269i	$-0.790659\pi$
$907$	−47.6697	−1.58285	−0.791423	+	0.611269i	$0.790659\pi$
$908$	−152.249	−5.05257
$909$	18.1524	0.602077
$910$	−5.90062	−0.195604
$911$	8.80254	0.291641	0.145821	−	0.989311i	$-0.453418\pi$
$911$	8.80254	0.291641	0.145821	+	0.989311i	$0.453418\pi$
$912$	196.083	6.49296
$913$	−10.8663	−0.359621
$914$	−14.6623	−0.484986
$915$	24.8736	0.822295
$916$	7.53777	0.249055
$917$	−7.64332	−0.252405
$918$	40.5643	1.33882
$919$	−55.7361	−1.83856	−0.919282	−	0.393600i	$-0.871230\pi$
$919$	−55.7361	−1.83856	−0.919282	+	0.393600i	$0.871230\pi$
$920$	55.8340	1.84079
$921$	53.5142	1.76335
$922$	30.7461	1.01257
$923$	6.23928	0.205368
$924$	99.0556	3.25869
$925$	−0.772275	−0.0253922
$926$	5.20012	0.170887
$927$	−5.42596	−0.178212
$928$	−213.033	−6.99314
$929$	20.6778	0.678417	0.339208	−	0.940711i	$-0.389841\pi$
$929$	20.6778	0.678417	0.339208	+	0.940711i	$0.389841\pi$
$930$	22.8433	0.749062
$931$	90.5947	2.96912
$932$	46.0538	1.50854
$933$	44.2311	1.44806
$934$	−5.43330	−0.177783
$935$	−9.71275	−0.317641
$936$	7.26856	0.237580
$937$	−14.6793	−0.479553	−0.239777	−	0.970828i	$-0.577074\pi$
$937$	−14.6793	−0.479553	−0.239777	+	0.970828i	$0.577074\pi$
$938$	−12.8810	−0.420580
$939$	−15.7689	−0.514600
$940$	−18.2839	−0.596356
$941$	−0.641329	−0.0209067	−0.0104534	−	0.999945i	$-0.503327\pi$
$941$	−0.641329	−0.0209067	−0.0104534	+	0.999945i	$0.503327\pi$
$942$	−30.9170	−1.00733
$943$	62.9761	2.05078
$944$	161.172	5.24569
$945$	13.1222	0.426864
$946$	−22.4400	−0.729589
$947$	28.8281	0.936788	0.468394	−	0.883520i	$-0.344833\pi$
$947$	28.8281	0.936788	0.468394	+	0.883520i	$0.344833\pi$
$948$	−11.0097	−0.357578
$949$	6.62371	0.215015
$950$	−17.4660	−0.566672
$951$	39.5157	1.28139
$952$	219.552	7.11574
$953$	15.9453	0.516520	0.258260	−	0.966075i	$-0.416851\pi$
$953$	15.9453	0.516520	0.258260	+	0.966075i	$0.416851\pi$
$954$	−51.2624	−1.65968
$955$	−14.8665	−0.481070
$956$	123.489	3.99391
$957$	−42.8962	−1.38664
$958$	−118.470	−3.82758
$959$	−59.3349	−1.91603
$960$	56.2226	1.81458
$961$	−15.8652	−0.511781
$962$	−0.992497	−0.0319994
$963$	10.1164	0.325995
$964$	−10.6882	−0.344242
$965$	13.6442	0.439221
$966$	−164.582	−5.29534
$967$	44.8189	1.44128	0.720639	−	0.693311i	$-0.243849\pi$
$967$	44.8189	1.44128	0.720639	+	0.693311i	$0.243849\pi$
$968$	69.0427	2.21912
$969$	72.7643	2.33753
$970$	11.9892	0.384949
$971$	−46.9691	−1.50731	−0.753656	−	0.657270i	$-0.771711\pi$
$971$	−46.9691	−1.50731	−0.753656	+	0.657270i	$0.771711\pi$
$972$	−84.2470	−2.70222
$973$	−60.6692	−1.94497
$974$	49.3601	1.58160
$975$	−1.02403	−0.0327951
$976$	162.020	5.18612
$977$	−15.6897	−0.501959	−0.250979	−	0.967992i	$-0.580753\pi$
$977$	−15.6897	−0.501959	−0.250979	+	0.967992i	$0.580753\pi$
$978$	−10.8330	−0.346401
$979$	26.0083	0.831230
$980$	75.6001	2.41496
$981$	16.9255	0.540389
$982$	28.8878	0.921846
$983$	−38.1280	−1.21609	−0.608047	−	0.793901i	$-0.708047\pi$
$983$	−38.1280	−1.21609	−0.608047	+	0.793901i	$0.708047\pi$
$984$	204.077	6.50574
$985$	7.06266	0.225035
$986$	−151.518	−4.82532
$987$	33.8195	1.07649
$988$	−16.3546	−0.520308
$989$	27.1653	0.863807
$990$	8.46549	0.269051
$991$	−36.3979	−1.15622	−0.578108	−	0.815960i	$-0.696209\pi$
$991$	−36.3979	−1.15622	−0.578108	+	0.815960i	$0.696209\pi$
$992$	77.6335	2.46487
$993$	34.7137	1.10161
$994$	−164.261	−5.21004
$995$	−5.74325	−0.182073
$996$	67.9323	2.15252
$997$	−9.28675	−0.294114	−0.147057	−	0.989128i	$-0.546980\pi$
$997$	−9.28675	−0.294114	−0.147057	+	0.989128i	$0.546980\pi$
$998$	−33.2922	−1.05385
$999$	2.20718	0.0698319

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.2	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.2	✓	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.71462 q^{2} +2.16303 q^{3} +5.36914 q^{4} +1.00000 q^{5} -5.87179 q^{6} -4.59135 q^{7} -9.14592 q^{8} +1.67870 q^{9} +O(q^{10})\)	\(q-2.71462 q^{2} +2.16303 q^{3} +5.36914 q^{4} +1.00000 q^{5} -5.87179 q^{6} -4.59135 q^{7} -9.14592 q^{8} +1.67870 q^{9} -2.71462 q^{10} -1.85768 q^{11} +11.6136 q^{12} -0.473422 q^{13} +12.4637 q^{14} +2.16303 q^{15} +14.0894 q^{16} +5.22842 q^{17} -4.55702 q^{18} +6.43407 q^{19} +5.36914 q^{20} -9.93122 q^{21} +5.04289 q^{22} -6.10480 q^{23} -19.7829 q^{24} +1.00000 q^{25} +1.28516 q^{26} -2.85802 q^{27} -24.6516 q^{28} +10.6754 q^{29} -5.87179 q^{30} -3.89035 q^{31} -19.9554 q^{32} -4.01822 q^{33} -14.1932 q^{34} -4.59135 q^{35} +9.01316 q^{36} -0.772275 q^{37} -17.4660 q^{38} -1.02403 q^{39} -9.14592 q^{40} -10.3158 q^{41} +26.9595 q^{42} -4.44984 q^{43} -9.97416 q^{44} +1.67870 q^{45} +16.5722 q^{46} -3.40537 q^{47} +30.4758 q^{48} +14.0805 q^{49} -2.71462 q^{50} +11.3092 q^{51} -2.54187 q^{52} +11.2491 q^{53} +7.75842 q^{54} -1.85768 q^{55} +41.9921 q^{56} +13.9171 q^{57} -28.9797 q^{58} +11.4392 q^{59} +11.6136 q^{60} +11.4994 q^{61} +10.5608 q^{62} -7.70748 q^{63} +25.9925 q^{64} -0.473422 q^{65} +10.9079 q^{66} -1.03348 q^{67} +28.0721 q^{68} -13.2049 q^{69} +12.4637 q^{70} -13.1791 q^{71} -15.3532 q^{72} -13.9911 q^{73} +2.09643 q^{74} +2.16303 q^{75} +34.5454 q^{76} +8.52927 q^{77} +2.77984 q^{78} -0.947999 q^{79} +14.0894 q^{80} -11.2181 q^{81} +28.0035 q^{82} +5.84937 q^{83} -53.3221 q^{84} +5.22842 q^{85} +12.0796 q^{86} +23.0913 q^{87} +16.9902 q^{88} -14.0004 q^{89} -4.55702 q^{90} +2.17365 q^{91} -32.7775 q^{92} -8.41493 q^{93} +9.24428 q^{94} +6.43407 q^{95} -43.1642 q^{96} -4.41652 q^{97} -38.2231 q^{98} -3.11849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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