LMFDB - Embedded newform 2563.2.a.j.1.33

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2563,2,Mod(1,2563)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2563, 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("2563.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2563 = 11 \cdot 233 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2563.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:	$20.4656580381$
Analytic rank:	$0$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.33
Character	$\chi$	$=$	2563.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.82613 q^{2} -1.94946 q^{3} +1.33474 q^{4} -2.55095 q^{5} -3.55996 q^{6} -2.25972 q^{7} -1.21485 q^{8} +0.800392 q^{9} +O(q^{10})$	\(q+1.82613 q^{2} -1.94946 q^{3} +1.33474 q^{4} -2.55095 q^{5} -3.55996 q^{6} -2.25972 q^{7} -1.21485 q^{8} +0.800392 q^{9} -4.65836 q^{10} -1.00000 q^{11} -2.60202 q^{12} -5.29275 q^{13} -4.12654 q^{14} +4.97297 q^{15} -4.88795 q^{16} -0.162306 q^{17} +1.46162 q^{18} +5.27683 q^{19} -3.40485 q^{20} +4.40524 q^{21} -1.82613 q^{22} +1.31030 q^{23} +2.36830 q^{24} +1.50734 q^{25} -9.66523 q^{26} +4.28805 q^{27} -3.01614 q^{28} -6.69569 q^{29} +9.08128 q^{30} +3.95367 q^{31} -6.49632 q^{32} +1.94946 q^{33} -0.296391 q^{34} +5.76444 q^{35} +1.06831 q^{36} +4.25441 q^{37} +9.63616 q^{38} +10.3180 q^{39} +3.09902 q^{40} -5.70838 q^{41} +8.04453 q^{42} +7.30095 q^{43} -1.33474 q^{44} -2.04176 q^{45} +2.39277 q^{46} +3.66086 q^{47} +9.52886 q^{48} -1.89365 q^{49} +2.75260 q^{50} +0.316409 q^{51} -7.06444 q^{52} +8.78812 q^{53} +7.83052 q^{54} +2.55095 q^{55} +2.74522 q^{56} -10.2870 q^{57} -12.2272 q^{58} -3.99554 q^{59} +6.63763 q^{60} -5.14145 q^{61} +7.21990 q^{62} -1.80866 q^{63} -2.08720 q^{64} +13.5015 q^{65} +3.55996 q^{66} -12.3762 q^{67} -0.216636 q^{68} -2.55437 q^{69} +10.5266 q^{70} +10.3480 q^{71} -0.972355 q^{72} -5.89103 q^{73} +7.76910 q^{74} -2.93851 q^{75} +7.04319 q^{76} +2.25972 q^{77} +18.8420 q^{78} -8.33979 q^{79} +12.4689 q^{80} -10.7605 q^{81} -10.4242 q^{82} +13.2591 q^{83} +5.87985 q^{84} +0.414034 q^{85} +13.3325 q^{86} +13.0530 q^{87} +1.21485 q^{88} -0.443840 q^{89} -3.72851 q^{90} +11.9602 q^{91} +1.74890 q^{92} -7.70752 q^{93} +6.68519 q^{94} -13.4609 q^{95} +12.6643 q^{96} +13.5384 q^{97} -3.45804 q^{98} -0.800392 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q + 12 q^{2} + 5 q^{3} + 54 q^{4} + 29 q^{5} - 2 q^{6} - 22 q^{7} + 36 q^{8} + 52 q^{9}+O(q^{10}) $ 45 * q + 12 * q^2 + 5 * q^3 + 54 * q^4 + 29 * q^5 - 2 * q^6 - 22 * q^7 + 36 * q^8 + 52 * q^9	\( 45 q + 12 q^{2} + 5 q^{3} + 54 q^{4} + 29 q^{5} - 2 q^{6} - 22 q^{7} + 36 q^{8} + 52 q^{9} + 10 q^{10} - 45 q^{11} + 39 q^{12} + 8 q^{13} + 24 q^{14} + 42 q^{15} + 64 q^{16} + 20 q^{17} + 27 q^{18} - 20 q^{19} + 66 q^{20} - 8 q^{21} - 12 q^{22} + 22 q^{23} - 2 q^{24} + 80 q^{25} + 26 q^{26} + 32 q^{27} - 39 q^{28} + 12 q^{29} + 16 q^{30} + 32 q^{31} + 79 q^{32} - 5 q^{33} + 47 q^{34} + 24 q^{35} + 70 q^{36} + 33 q^{37} + 46 q^{38} + 17 q^{40} + 9 q^{41} + 6 q^{42} - 22 q^{43} - 54 q^{44} + 83 q^{45} + 13 q^{46} + 85 q^{47} + 62 q^{48} + 67 q^{49} + 27 q^{50} + 8 q^{51} + 9 q^{52} + 56 q^{53} - 35 q^{54} - 29 q^{55} + 6 q^{56} + 14 q^{57} + 42 q^{58} + 28 q^{59} + 115 q^{60} + 6 q^{61} + 57 q^{62} - 52 q^{63} + 152 q^{64} + 31 q^{65} + 2 q^{66} + 23 q^{67} - 2 q^{68} + 28 q^{69} + 85 q^{70} + 6 q^{71} + 45 q^{72} + 17 q^{73} - 14 q^{74} + 76 q^{75} + 19 q^{76} + 22 q^{77} - 106 q^{78} - 75 q^{79} + 41 q^{80} + 101 q^{81} + 69 q^{82} + 43 q^{83} + 5 q^{84} + 42 q^{85} + 57 q^{86} + 19 q^{87} - 36 q^{88} + 5 q^{89} + 52 q^{90} - 7 q^{91} + 64 q^{92} + 81 q^{93} - 40 q^{94} + 9 q^{95} + 39 q^{96} + 58 q^{97} + 90 q^{98} - 52 q^{99}+O(q^{100}) \) 45 * q + 12 * q^2 + 5 * q^3 + 54 * q^4 + 29 * q^5 - 2 * q^6 - 22 * q^7 + 36 * q^8 + 52 * q^9 + 10 * q^10 - 45 * q^11 + 39 * q^12 + 8 * q^13 + 24 * q^14 + 42 * q^15 + 64 * q^16 + 20 * q^17 + 27 * q^18 - 20 * q^19 + 66 * q^20 - 8 * q^21 - 12 * q^22 + 22 * q^23 - 2 * q^24 + 80 * q^25 + 26 * q^26 + 32 * q^27 - 39 * q^28 + 12 * q^29 + 16 * q^30 + 32 * q^31 + 79 * q^32 - 5 * q^33 + 47 * q^34 + 24 * q^35 + 70 * q^36 + 33 * q^37 + 46 * q^38 + 17 * q^40 + 9 * q^41 + 6 * q^42 - 22 * q^43 - 54 * q^44 + 83 * q^45 + 13 * q^46 + 85 * q^47 + 62 * q^48 + 67 * q^49 + 27 * q^50 + 8 * q^51 + 9 * q^52 + 56 * q^53 - 35 * q^54 - 29 * q^55 + 6 * q^56 + 14 * q^57 + 42 * q^58 + 28 * q^59 + 115 * q^60 + 6 * q^61 + 57 * q^62 - 52 * q^63 + 152 * q^64 + 31 * q^65 + 2 * q^66 + 23 * q^67 - 2 * q^68 + 28 * q^69 + 85 * q^70 + 6 * q^71 + 45 * q^72 + 17 * q^73 - 14 * q^74 + 76 * q^75 + 19 * q^76 + 22 * q^77 - 106 * q^78 - 75 * q^79 + 41 * q^80 + 101 * q^81 + 69 * q^82 + 43 * q^83 + 5 * q^84 + 42 * q^85 + 57 * q^86 + 19 * q^87 - 36 * q^88 + 5 * q^89 + 52 * q^90 - 7 * q^91 + 64 * q^92 + 81 * q^93 - 40 * q^94 + 9 * q^95 + 39 * q^96 + 58 * q^97 + 90 * q^98 - 52 * 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 $

$2$	1.82613	1.29127	0.645633	−	0.763647i	$-0.276593\pi$
$2$	1.82613	1.29127	0.645633	+	0.763647i	$0.276593\pi$
$3$	−1.94946	−1.12552	−0.562760	−	0.826620i	$-0.690261\pi$
$3$	−1.94946	−1.12552	−0.562760	+	0.826620i	$0.690261\pi$
$4$	1.33474	0.667370
$5$	−2.55095	−1.14082	−0.570410	−	0.821360i	$-0.693216\pi$
$5$	−2.55095	−1.14082	−0.570410	+	0.821360i	$0.693216\pi$
$6$	−3.55996	−1.45335
$7$	−2.25972	−0.854095	−0.427048	−	0.904229i	$-0.640446\pi$
$7$	−2.25972	−0.854095	−0.427048	+	0.904229i	$0.640446\pi$
$8$	−1.21485	−0.429514
$9$	0.800392	0.266797
$10$	−4.65836	−1.47310
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.60202	−0.751139
$13$	−5.29275	−1.46794	−0.733972	−	0.679180i	$-0.762336\pi$
$13$	−5.29275	−1.46794	−0.733972	+	0.679180i	$0.762336\pi$
$14$	−4.12654	−1.10287
$15$	4.97297	1.28402
$16$	−4.88795	−1.22199
$17$	−0.162306	−0.0393650	−0.0196825	−	0.999806i	$-0.506266\pi$
$17$	−0.162306	−0.0393650	−0.0196825	+	0.999806i	$0.506266\pi$
$18$	1.46162	0.344506
$19$	5.27683	1.21059	0.605294	−	0.796002i	$-0.293056\pi$
$19$	5.27683	1.21059	0.605294	+	0.796002i	$0.293056\pi$
$20$	−3.40485	−0.761349
$21$	4.40524	0.961302
$22$	−1.82613	−0.389332
$23$	1.31030	0.273216	0.136608	−	0.990625i	$-0.456380\pi$
$23$	1.31030	0.273216	0.136608	+	0.990625i	$0.456380\pi$
$24$	2.36830	0.483427
$25$	1.50734	0.301469
$26$	−9.66523	−1.89551
$27$	4.28805	0.825235
$28$	−3.01614	−0.569998
$29$	−6.69569	−1.24336	−0.621679	−	0.783272i	$-0.713549\pi$
$29$	−6.69569	−1.24336	−0.621679	+	0.783272i	$0.713549\pi$
$30$	9.08128	1.65801
$31$	3.95367	0.710100	0.355050	−	0.934847i	$-0.384464\pi$
$31$	3.95367	0.710100	0.355050	+	0.934847i	$0.384464\pi$
$32$	−6.49632	−1.14840
$33$	1.94946	0.339357
$34$	−0.296391	−0.0508307
$35$	5.76444	0.974369
$36$	1.06831	0.178052
$37$	4.25441	0.699421	0.349711	−	0.936858i	$-0.386280\pi$
$37$	4.25441	0.699421	0.349711	+	0.936858i	$0.386280\pi$
$38$	9.63616	1.56319
$39$	10.3180	1.65220
$40$	3.09902	0.489998
$41$	−5.70838	−0.891498	−0.445749	−	0.895158i	$-0.647063\pi$
$41$	−5.70838	−0.891498	−0.445749	+	0.895158i	$0.647063\pi$
$42$	8.04453	1.24130
$43$	7.30095	1.11338	0.556692	−	0.830719i	$-0.312070\pi$
$43$	7.30095	1.11338	0.556692	+	0.830719i	$0.312070\pi$
$44$	−1.33474	−0.201220
$45$	−2.04176	−0.304367
$46$	2.39277	0.352794
$47$	3.66086	0.533991	0.266996	−	0.963698i	$-0.413969\pi$
$47$	3.66086	0.533991	0.266996	+	0.963698i	$0.413969\pi$
$48$	9.52886	1.37537
$49$	−1.89365	−0.270521
$50$	2.75260	0.389277
$51$	0.316409	0.0443061
$52$	−7.06444	−0.979662
$53$	8.78812	1.20714	0.603570	−	0.797310i	$-0.293744\pi$
$53$	8.78812	1.20714	0.603570	+	0.797310i	$0.293744\pi$
$54$	7.83052	1.06560
$55$	2.55095	0.343970
$56$	2.74522	0.366846
$57$	−10.2870	−1.36254
$58$	−12.2272	−1.60551
$59$	−3.99554	−0.520174	−0.260087	−	0.965585i	$-0.583751\pi$
$59$	−3.99554	−0.520174	−0.260087	+	0.965585i	$0.583751\pi$
$60$	6.63763	0.856914
$61$	−5.14145	−0.658295	−0.329147	−	0.944279i	$-0.606761\pi$
$61$	−5.14145	−0.658295	−0.329147	+	0.944279i	$0.606761\pi$
$62$	7.21990	0.916928
$63$	−1.80866	−0.227870
$64$	−2.08720	−0.260900
$65$	13.5015	1.67466
$66$	3.55996	0.438201
$67$	−12.3762	−1.51200	−0.755998	−	0.654574i	$-0.772848\pi$
$67$	−12.3762	−1.51200	−0.755998	+	0.654574i	$0.772848\pi$
$68$	−0.216636	−0.0262710
$69$	−2.55437	−0.307510
$70$	10.5266	1.25817
$71$	10.3480	1.22808	0.614040	−	0.789275i	$-0.289544\pi$
$71$	10.3480	1.22808	0.614040	+	0.789275i	$0.289544\pi$
$72$	−0.972355	−0.114593
$73$	−5.89103	−0.689493	−0.344746	−	0.938696i	$-0.612035\pi$
$73$	−5.89103	−0.689493	−0.344746	+	0.938696i	$0.612035\pi$
$74$	7.76910	0.903139
$75$	−2.93851	−0.339310
$76$	7.04319	0.807910
$77$	2.25972	0.257519
$78$	18.8420	2.13343
$79$	−8.33979	−0.938299	−0.469150	−	0.883119i	$-0.655440\pi$
$79$	−8.33979	−0.938299	−0.469150	+	0.883119i	$0.655440\pi$
$80$	12.4689	1.39407
$81$	−10.7605	−1.19562
$82$	−10.4242	−1.15116
$83$	13.2591	1.45537	0.727686	−	0.685910i	$-0.240596\pi$
$83$	13.2591	1.45537	0.727686	+	0.685910i	$0.240596\pi$
$84$	5.87985	0.641544
$85$	0.414034	0.0449083
$86$	13.3325	1.43768
$87$	13.0530	1.39942
$88$	1.21485	0.129503
$89$	−0.443840	−0.0470470	−0.0235235	−	0.999723i	$-0.507488\pi$
$89$	−0.443840	−0.0470470	−0.0235235	+	0.999723i	$0.507488\pi$
$90$	−3.72851	−0.393020
$91$	11.9602	1.25376
$92$	1.74890	0.182336
$93$	−7.70752	−0.799232
$94$	6.68519	0.689525
$95$	−13.4609	−1.38106
$96$	12.6643	1.29255
$97$	13.5384	1.37461	0.687306	−	0.726368i	$-0.258793\pi$
$97$	13.5384	1.37461	0.687306	+	0.726368i	$0.258793\pi$
$98$	−3.45804	−0.349315
$99$	−0.800392	−0.0804424
$100$	2.01191	0.201191
$101$	15.8938	1.58149	0.790745	−	0.612146i	$-0.209693\pi$
$101$	15.8938	1.58149	0.790745	+	0.612146i	$0.209693\pi$
$102$	0.577803	0.0572110
$103$	4.92702	0.485474	0.242737	−	0.970092i	$-0.421955\pi$
$103$	4.92702	0.485474	0.242737	+	0.970092i	$0.421955\pi$
$104$	6.42989	0.630503
$105$	−11.2375	−1.09667
$106$	16.0482	1.55874
$107$	−15.8380	−1.53111	−0.765557	−	0.643369i	$-0.777536\pi$
$107$	−15.8380	−1.53111	−0.765557	+	0.643369i	$0.777536\pi$
$108$	5.72343	0.550737
$109$	−2.49847	−0.239310	−0.119655	−	0.992816i	$-0.538179\pi$
$109$	−2.49847	−0.239310	−0.119655	+	0.992816i	$0.538179\pi$
$110$	4.65836	0.444157
$111$	−8.29380	−0.787213
$112$	11.0454	1.04369
$113$	−20.0199	−1.88331	−0.941656	−	0.336577i	$-0.890731\pi$
$113$	−20.0199	−1.88331	−0.941656	+	0.336577i	$0.890731\pi$
$114$	−18.7853	−1.75940
$115$	−3.34250	−0.311690
$116$	−8.93700	−0.829780
$117$	−4.23627	−0.391643
$118$	−7.29635	−0.671684
$119$	0.366767	0.0336214
$120$	−6.04141	−0.551503
$121$	1.00000	0.0909091
$122$	−9.38894	−0.850034
$123$	11.1282	1.00340
$124$	5.27712	0.473899
$125$	8.90959	0.796898
$126$	−3.30285	−0.294241
$127$	−10.5346	−0.934793	−0.467396	−	0.884048i	$-0.654808\pi$
$127$	−10.5346	−0.934793	−0.467396	+	0.884048i	$0.654808\pi$
$128$	9.18114	0.811505
$129$	−14.2329	−1.25314
$130$	24.6555	2.16243
$131$	15.8261	1.38273	0.691365	−	0.722506i	$-0.257010\pi$
$131$	15.8261	1.38273	0.691365	+	0.722506i	$0.257010\pi$
$132$	2.60202	0.226477
$133$	−11.9242	−1.03396
$134$	−22.6006	−1.95239
$135$	−10.9386	−0.941444
$136$	0.197177	0.0169078
$137$	16.5401	1.41312	0.706559	−	0.707654i	$-0.250246\pi$
$137$	16.5401	1.41312	0.706559	+	0.707654i	$0.250246\pi$
$138$	−4.66460	−0.397077
$139$	−21.6730	−1.83828	−0.919140	−	0.393932i	$-0.871114\pi$
$139$	−21.6730	−1.83828	−0.919140	+	0.393932i	$0.871114\pi$
$140$	7.69403	0.650264
$141$	−7.13669	−0.601018
$142$	18.8967	1.58578
$143$	5.29275	0.442602
$144$	−3.91227	−0.326023
$145$	17.0804	1.41845
$146$	−10.7578	−0.890319
$147$	3.69159	0.304477
$148$	5.67853	0.466773
$149$	4.99449	0.409165	0.204582	−	0.978849i	$-0.434416\pi$
$149$	4.99449	0.409165	0.204582	+	0.978849i	$0.434416\pi$
$150$	−5.36609	−0.438139
$151$	−0.701311	−0.0570719	−0.0285360	−	0.999593i	$-0.509085\pi$
$151$	−0.701311	−0.0570719	−0.0285360	+	0.999593i	$0.509085\pi$
$152$	−6.41055	−0.519964
$153$	−0.129908	−0.0105025
$154$	4.12654	0.332526
$155$	−10.0856	−0.810096
$156$	13.7718	1.10263
$157$	−10.9672	−0.875279	−0.437639	−	0.899151i	$-0.644185\pi$
$157$	−10.9672	−0.875279	−0.437639	+	0.899151i	$0.644185\pi$
$158$	−15.2295	−1.21159
$159$	−17.1321	−1.35866
$160$	16.5718	1.31011
$161$	−2.96091	−0.233352
$162$	−19.6501	−1.54386
$163$	17.2382	1.35020	0.675101	−	0.737725i	$-0.264100\pi$
$163$	17.2382	1.35020	0.675101	+	0.737725i	$0.264100\pi$
$164$	−7.61920	−0.594959
$165$	−4.97297	−0.387145
$166$	24.2128	1.87927
$167$	−21.1979	−1.64034	−0.820170	−	0.572119i	$-0.806121\pi$
$167$	−21.1979	−1.64034	−0.820170	+	0.572119i	$0.806121\pi$
$168$	−5.35170	−0.412893
$169$	15.0132	1.15486
$170$	0.756079	0.0579886
$171$	4.22353	0.322981
$172$	9.74487	0.743040
$173$	6.43123	0.488957	0.244479	−	0.969655i	$-0.421383\pi$
$173$	6.43123	0.488957	0.244479	+	0.969655i	$0.421383\pi$
$174$	23.8364	1.80703
$175$	−3.40618	−0.257483
$176$	4.88795	0.368443
$177$	7.78913	0.585467
$178$	−0.810509	−0.0607502
$179$	−12.8005	−0.956753	−0.478377	−	0.878155i	$-0.658775\pi$
$179$	−12.8005	−0.956753	−0.478377	+	0.878155i	$0.658775\pi$
$180$	−2.72522	−0.203126
$181$	18.3760	1.36588	0.682938	−	0.730476i	$-0.260702\pi$
$181$	18.3760	1.36588	0.682938	+	0.730476i	$0.260702\pi$
$182$	21.8408	1.61894
$183$	10.0230	0.740925
$184$	−1.59181	−0.117350
$185$	−10.8528	−0.797913
$186$	−14.0749	−1.03202
$187$	0.162306	0.0118690
$188$	4.88629	0.356370
$189$	−9.68980	−0.704829
$190$	−24.5814	−1.78332
$191$	1.31366	0.0950531	0.0475265	−	0.998870i	$-0.484866\pi$
$191$	1.31366	0.0950531	0.0475265	+	0.998870i	$0.484866\pi$
$192$	4.06892	0.293649
$193$	4.22792	0.304332	0.152166	−	0.988355i	$-0.451375\pi$
$193$	4.22792	0.304332	0.152166	+	0.988355i	$0.451375\pi$
$194$	24.7227	1.77499
$195$	−26.3207	−1.88486
$196$	−2.52753	−0.180538
$197$	−21.7857	−1.55217	−0.776084	−	0.630629i	$-0.782797\pi$
$197$	−21.7857	−1.55217	−0.776084	+	0.630629i	$0.782797\pi$
$198$	−1.46162	−0.103873
$199$	26.5200	1.87995	0.939976	−	0.341240i	$-0.110847\pi$
$199$	26.5200	1.87995	0.939976	+	0.341240i	$0.110847\pi$
$200$	−1.83120	−0.129485
$201$	24.1269	1.70178
$202$	29.0241	2.04213
$203$	15.1304	1.06195
$204$	0.422324	0.0295686
$205$	14.5618	1.01704
$206$	8.99736	0.626876
$207$	1.04875	0.0728931
$208$	25.8707	1.79381
$209$	−5.27683	−0.365006
$210$	−20.5212	−1.41610
$211$	−0.328006	−0.0225809	−0.0112904	−	0.999936i	$-0.503594\pi$
$211$	−0.328006	−0.0225809	−0.0112904	+	0.999936i	$0.503594\pi$
$212$	11.7299	0.805610
$213$	−20.1730	−1.38223
$214$	−28.9221	−1.97708
$215$	−18.6244	−1.27017
$216$	−5.20933	−0.354450
$217$	−8.93420	−0.606493
$218$	−4.56251	−0.309012
$219$	11.4843	0.776039
$220$	3.40485	0.229555
$221$	0.859044	0.0577856
$222$	−15.1455	−1.01650
$223$	−5.84881	−0.391665	−0.195833	−	0.980637i	$-0.562741\pi$
$223$	−5.84881	−0.391665	−0.195833	+	0.980637i	$0.562741\pi$
$224$	14.6799	0.980841
$225$	1.20647	0.0804311
$226$	−36.5588	−2.43186
$227$	13.3240	0.884346	0.442173	−	0.896930i	$-0.354208\pi$
$227$	13.3240	0.884346	0.442173	+	0.896930i	$0.354208\pi$
$228$	−13.7304	−0.909319
$229$	9.40951	0.621798	0.310899	−	0.950443i	$-0.399370\pi$
$229$	9.40951	0.621798	0.310899	+	0.950443i	$0.399370\pi$
$230$	−6.10383	−0.402474
$231$	−4.40524	−0.289844
$232$	8.13425	0.534039
$233$	1.00000	0.0655122
$233$	1.00000	0.0655122
$234$	−7.73597	−0.505716
$235$	−9.33867	−0.609187
$236$	−5.33300	−0.347149
$237$	16.2581	1.05608
$238$	0.669762	0.0434143
$239$	−14.0797	−0.910739	−0.455369	−	0.890303i	$-0.650493\pi$
$239$	−14.0797	−0.910739	−0.455369	+	0.890303i	$0.650493\pi$
$240$	−24.3076	−1.56905
$241$	4.53774	0.292302	0.146151	−	0.989262i	$-0.453312\pi$
$241$	4.53774	0.292302	0.146151	+	0.989262i	$0.453312\pi$
$242$	1.82613	0.117388
$243$	8.11311	0.520456
$244$	−6.86250	−0.439326
$245$	4.83060	0.308616
$246$	20.3216	1.29566
$247$	−27.9289	−1.77707
$248$	−4.80311	−0.304998
$249$	−25.8480	−1.63805
$250$	16.2700	1.02901
$251$	5.67163	0.357990	0.178995	−	0.983850i	$-0.442715\pi$
$251$	5.67163	0.357990	0.178995	+	0.983850i	$0.442715\pi$
$252$	−2.41410	−0.152074
$253$	−1.31030	−0.0823776
$254$	−19.2375	−1.20707
$255$	−0.807143	−0.0505453
$256$	20.9403	1.30877
$257$	17.2959	1.07889	0.539444	−	0.842022i	$-0.318635\pi$
$257$	17.2959	1.07889	0.539444	+	0.842022i	$0.318635\pi$
$258$	−25.9911	−1.61814
$259$	−9.61380	−0.597372
$260$	18.0210	1.11762
$261$	−5.35917	−0.331724
$262$	28.9004	1.78547
$263$	7.76833	0.479016	0.239508	−	0.970894i	$-0.423014\pi$
$263$	7.76833	0.479016	0.239508	+	0.970894i	$0.423014\pi$
$264$	−2.36830	−0.145759
$265$	−22.4181	−1.37713
$266$	−21.7751	−1.33511
$267$	0.865249	0.0529524
$268$	−16.5190	−1.00906
$269$	23.0331	1.40435	0.702177	−	0.712002i	$-0.252211\pi$
$269$	23.0331	1.40435	0.702177	+	0.712002i	$0.252211\pi$
$270$	−19.9753	−1.21566
$271$	−21.7763	−1.32281	−0.661407	−	0.750028i	$-0.730040\pi$
$271$	−21.7763	−1.32281	−0.661407	+	0.750028i	$0.730040\pi$
$272$	0.793343	0.0481035
$273$	−23.3158	−1.41114
$274$	30.2044	1.82471
$275$	−1.50734	−0.0908963
$276$	−3.40942	−0.205223
$277$	19.9145	1.19655	0.598274	−	0.801291i	$-0.295853\pi$
$277$	19.9145	1.19655	0.598274	+	0.801291i	$0.295853\pi$
$278$	−39.5776	−2.37371
$279$	3.16448	0.189453
$280$	−7.00293	−0.418505
$281$	−21.7781	−1.29917	−0.649587	−	0.760287i	$-0.725058\pi$
$281$	−21.7781	−1.29917	−0.649587	+	0.760287i	$0.725058\pi$
$282$	−13.0325	−0.776075
$283$	−9.60924	−0.571210	−0.285605	−	0.958347i	$-0.592195\pi$
$283$	−9.60924	−0.571210	−0.285605	+	0.958347i	$0.592195\pi$
$284$	13.8119	0.819583
$285$	26.2415	1.55441
$286$	9.66523	0.571517
$287$	12.8994	0.761425
$288$	−5.19960	−0.306389
$289$	−16.9737	−0.998450
$290$	31.1909	1.83159
$291$	−26.3925	−1.54715
$292$	−7.86299	−0.460147
$293$	30.8713	1.80352	0.901759	−	0.432238i	$-0.142276\pi$
$293$	30.8713	1.80352	0.901759	+	0.432238i	$0.142276\pi$
$294$	6.74131	0.393161
$295$	10.1924	0.593425
$296$	−5.16847	−0.300411
$297$	−4.28805	−0.248818
$298$	9.12058	0.528341
$299$	−6.93506	−0.401065
$300$	−3.92214	−0.226445
$301$	−16.4981	−0.950937
$302$	−1.28068	−0.0736951
$303$	−30.9843	−1.78000
$304$	−25.7929	−1.47932
$305$	13.1156	0.750996
$306$	−0.237229	−0.0135615
$307$	−31.2879	−1.78569	−0.892846	−	0.450361i	$-0.851295\pi$
$307$	−31.2879	−1.78569	−0.892846	+	0.450361i	$0.851295\pi$
$308$	3.01614	0.171861
$309$	−9.60502	−0.546411
$310$	−18.4176	−1.04605
$311$	−9.10324	−0.516197	−0.258099	−	0.966119i	$-0.583096\pi$
$311$	−9.10324	−0.516197	−0.258099	+	0.966119i	$0.583096\pi$
$312$	−12.5348	−0.709644
$313$	−1.20217	−0.0679508	−0.0339754	−	0.999423i	$-0.510817\pi$
$313$	−1.20217	−0.0679508	−0.0339754	+	0.999423i	$0.510817\pi$
$314$	−20.0275	−1.13022
$315$	4.61381	0.259959
$316$	−11.1314	−0.626193
$317$	−1.97581	−0.110973	−0.0554864	−	0.998459i	$-0.517671\pi$
$317$	−1.97581	−0.110973	−0.0554864	+	0.998459i	$0.517671\pi$
$318$	−31.2854	−1.75440
$319$	6.69569	0.374886
$320$	5.32435	0.297640
$321$	30.8755	1.72330
$322$	−5.40699	−0.301320
$323$	−0.856460	−0.0476547
$324$	−14.3625	−0.797919
$325$	−7.97799	−0.442539
$326$	31.4792	1.74347
$327$	4.87066	0.269348
$328$	6.93481	0.382911
$329$	−8.27253	−0.456079
$330$	−9.08128	−0.499908
$331$	14.8170	0.814414	0.407207	−	0.913336i	$-0.366503\pi$
$331$	14.8170	0.814414	0.407207	+	0.913336i	$0.366503\pi$
$332$	17.6974	0.971272
$333$	3.40520	0.186604
$334$	−38.7100	−2.11812
$335$	31.5711	1.72491
$336$	−21.5326	−1.17470
$337$	33.0098	1.79816	0.899080	−	0.437785i	$-0.144237\pi$
$337$	33.0098	1.79816	0.899080	+	0.437785i	$0.144237\pi$
$338$	27.4160	1.49123
$339$	39.0279	2.11971
$340$	0.552628	0.0299705
$341$	−3.95367	−0.214103
$342$	7.71270	0.417055
$343$	20.0972	1.08515
$344$	−8.86955	−0.478214
$345$	6.51606	0.350813
$346$	11.7442	0.631374
$347$	−1.51594	−0.0813801	−0.0406901	−	0.999172i	$-0.512956\pi$
$347$	−1.51594	−0.0813801	−0.0406901	+	0.999172i	$0.512956\pi$
$348$	17.4223	0.933934
$349$	−24.2455	−1.29783	−0.648916	−	0.760860i	$-0.724777\pi$
$349$	−24.2455	−1.29783	−0.648916	+	0.760860i	$0.724777\pi$
$350$	−6.22012	−0.332480
$351$	−22.6956	−1.21140
$352$	6.49632	0.346255
$353$	2.74807	0.146265	0.0731326	−	0.997322i	$-0.476700\pi$
$353$	2.74807	0.146265	0.0731326	+	0.997322i	$0.476700\pi$
$354$	14.2239	0.755994
$355$	−26.3972	−1.40102
$356$	−0.592412	−0.0313977
$357$	−0.714997	−0.0378416
$358$	−23.3753	−1.23542
$359$	−30.7173	−1.62120	−0.810599	−	0.585601i	$-0.800858\pi$
$359$	−30.7173	−1.62120	−0.810599	+	0.585601i	$0.800858\pi$
$360$	2.48043	0.130730
$361$	8.84491	0.465522
$362$	33.5569	1.76371
$363$	−1.94946	−0.102320
$364$	15.9637	0.836725
$365$	15.0277	0.786587
$366$	18.3033	0.956731
$367$	−8.09884	−0.422756	−0.211378	−	0.977404i	$-0.567795\pi$
$367$	−8.09884	−0.422756	−0.211378	+	0.977404i	$0.567795\pi$
$368$	−6.40466	−0.333866
$369$	−4.56894	−0.237849
$370$	−19.8186	−1.03032
$371$	−19.8587	−1.03101
$372$	−10.2875	−0.533384
$373$	−0.204014	−0.0105634	−0.00528172	−	0.999986i	$-0.501681\pi$
$373$	−0.204014	−0.0105634	−0.00528172	+	0.999986i	$0.501681\pi$
$374$	0.296391	0.0153260
$375$	−17.3689	−0.896925
$376$	−4.44739	−0.229357
$377$	35.4386	1.82518
$378$	−17.6948	−0.910123
$379$	26.5170	1.36209	0.681044	−	0.732243i	$-0.261526\pi$
$379$	26.5170	1.36209	0.681044	+	0.732243i	$0.261526\pi$
$380$	−17.9668	−0.921679
$381$	20.5367	1.05213
$382$	2.39891	0.122739
$383$	28.0053	1.43100	0.715502	−	0.698611i	$-0.246198\pi$
$383$	28.0053	1.43100	0.715502	+	0.698611i	$0.246198\pi$
$384$	−17.8983	−0.913366
$385$	−5.76444	−0.293783
$386$	7.72072	0.392974
$387$	5.84362	0.297048
$388$	18.0702	0.917374
$389$	7.36373	0.373356	0.186678	−	0.982421i	$-0.440228\pi$
$389$	7.36373	0.373356	0.186678	+	0.982421i	$0.440228\pi$
$390$	−48.0649	−2.43386
$391$	−0.212669	−0.0107551
$392$	2.30049	0.116193
$393$	−30.8523	−1.55629
$394$	−39.7835	−2.00426
$395$	21.2744	1.07043
$396$	−1.06831	−0.0536848
$397$	−32.7519	−1.64377	−0.821886	−	0.569651i	$-0.807078\pi$
$397$	−32.7519	−1.64377	−0.821886	+	0.569651i	$0.807078\pi$
$398$	48.4289	2.42752
$399$	23.2457	1.16374
$400$	−7.36782	−0.368391
$401$	−16.6422	−0.831073	−0.415536	−	0.909577i	$-0.636406\pi$
$401$	−16.6422	−0.831073	−0.415536	+	0.909577i	$0.636406\pi$
$402$	44.0589	2.19746
$403$	−20.9258	−1.04239
$404$	21.2141	1.05544
$405$	27.4496	1.36398
$406$	27.6300	1.37126
$407$	−4.25441	−0.210883
$408$	−0.384389	−0.0190301
$409$	−17.8869	−0.884450	−0.442225	−	0.896904i	$-0.645811\pi$
$409$	−17.8869	−0.884450	−0.442225	+	0.896904i	$0.645811\pi$
$410$	26.5917	1.31327
$411$	−32.2443	−1.59049
$412$	6.57629	0.323991
$413$	9.02881	0.444279
$414$	1.91515	0.0941245
$415$	−33.8232	−1.66032
$416$	34.3834	1.68578
$417$	42.2506	2.06902
$418$	−9.63616	−0.471320
$419$	−21.9771	−1.07365	−0.536827	−	0.843693i	$-0.680377\pi$
$419$	−21.9771	−1.07365	−0.536827	+	0.843693i	$0.680377\pi$
$420$	−14.9992	−0.731886
$421$	30.8000	1.50110	0.750550	−	0.660814i	$-0.229789\pi$
$421$	30.8000	1.50110	0.750550	+	0.660814i	$0.229789\pi$
$422$	−0.598981	−0.0291579
$423$	2.93012	0.142467
$424$	−10.6762	−0.518484
$425$	−0.244651	−0.0118673
$426$	−36.8384	−1.78483
$427$	11.6183	0.562247
$428$	−21.1396	−1.02182
$429$	−10.3180	−0.498158
$430$	−34.0104	−1.64013
$431$	−11.1617	−0.537639	−0.268819	−	0.963191i	$-0.586633\pi$
$431$	−11.1617	−0.537639	−0.268819	+	0.963191i	$0.586633\pi$
$432$	−20.9598	−1.00843
$433$	40.4703	1.94488	0.972440	−	0.233155i	$-0.0749048\pi$
$433$	40.4703	1.94488	0.972440	+	0.233155i	$0.0749048\pi$
$434$	−16.3150	−0.783144
$435$	−33.2975	−1.59649
$436$	−3.33480	−0.159708
$437$	6.91420	0.330751
$438$	20.9718	1.00207
$439$	13.2420	0.632007	0.316003	−	0.948758i	$-0.397659\pi$
$439$	13.2420	0.632007	0.316003	+	0.948758i	$0.397659\pi$
$440$	−3.09902	−0.147740
$441$	−1.51566	−0.0721742
$442$	1.56872	0.0746166
$443$	10.6742	0.507148	0.253574	−	0.967316i	$-0.418394\pi$
$443$	10.6742	0.507148	0.253574	+	0.967316i	$0.418394\pi$
$444$	−11.0701	−0.525362
$445$	1.13221	0.0536721
$446$	−10.6807	−0.505744
$447$	−9.73656	−0.460523
$448$	4.71651	0.222834
$449$	−32.2024	−1.51973	−0.759864	−	0.650082i	$-0.774734\pi$
$449$	−32.2024	−1.51973	−0.759864	+	0.650082i	$0.774734\pi$
$450$	2.20316	0.103858
$451$	5.70838	0.268797
$452$	−26.7213	−1.25687
$453$	1.36718	0.0642356
$454$	24.3314	1.14193
$455$	−30.5097	−1.43032
$456$	12.4971	0.585231
$457$	17.8077	0.833010	0.416505	−	0.909133i	$-0.363255\pi$
$457$	17.8077	0.833010	0.416505	+	0.909133i	$0.363255\pi$
$458$	17.1830	0.802907
$459$	−0.695975	−0.0324854
$460$	−4.46137	−0.208012
$461$	12.1678	0.566709	0.283355	−	0.959015i	$-0.408553\pi$
$461$	12.1678	0.566709	0.283355	+	0.959015i	$0.408553\pi$
$462$	−8.04453	−0.374265
$463$	−13.8986	−0.645921	−0.322960	−	0.946412i	$-0.604678\pi$
$463$	−13.8986	−0.645921	−0.322960	+	0.946412i	$0.604678\pi$
$464$	32.7282	1.51937
$465$	19.6615	0.911780
$466$	1.82613	0.0845937
$467$	19.2931	0.892778	0.446389	−	0.894839i	$-0.352710\pi$
$467$	19.2931	0.892778	0.446389	+	0.894839i	$0.352710\pi$
$468$	−5.65432	−0.261371
$469$	27.9668	1.29139
$470$	−17.0536	−0.786623
$471$	21.3801	0.985145
$472$	4.85397	0.223422
$473$	−7.30095	−0.335698
$474$	29.6893	1.36368
$475$	7.95400	0.364954
$476$	0.489538	0.0224379
$477$	7.03394	0.322062
$478$	−25.7113	−1.17601
$479$	−5.11089	−0.233522	−0.116761	−	0.993160i	$-0.537251\pi$
$479$	−5.11089	−0.233522	−0.116761	+	0.993160i	$0.537251\pi$
$480$	−32.3060	−1.47456
$481$	−22.5175	−1.02671
$482$	8.28650	0.377440
$483$	5.77217	0.262643
$484$	1.33474	0.0606700
$485$	−34.5357	−1.56818
$486$	14.8156	0.672048
$487$	28.4064	1.28722	0.643609	−	0.765355i	$-0.277436\pi$
$487$	28.4064	1.28722	0.643609	+	0.765355i	$0.277436\pi$
$488$	6.24608	0.282747
$489$	−33.6052	−1.51968
$490$	8.82128	0.398505
$491$	1.53232	0.0691527	0.0345763	−	0.999402i	$-0.488992\pi$
$491$	1.53232	0.0691527	0.0345763	+	0.999402i	$0.488992\pi$
$492$	14.8533	0.669639
$493$	1.08675	0.0489447
$494$	−51.0018	−2.29468
$495$	2.04176	0.0917702
$496$	−19.3253	−0.867733
$497$	−23.3836	−1.04890
$498$	−47.2018	−2.11516
$499$	11.1415	0.498763	0.249382	−	0.968405i	$-0.419773\pi$
$499$	11.1415	0.498763	0.249382	+	0.968405i	$0.419773\pi$
$500$	11.8920	0.531826
$501$	41.3244	1.84624
$502$	10.3571	0.462260
$503$	41.8139	1.86439	0.932194	−	0.361958i	$-0.117892\pi$
$503$	41.8139	1.86439	0.932194	+	0.361958i	$0.117892\pi$
$504$	2.19725	0.0978735
$505$	−40.5442	−1.80419
$506$	−2.39277	−0.106371
$507$	−29.2676	−1.29982
$508$	−14.0609	−0.623853
$509$	23.9999	1.06378	0.531888	−	0.846815i	$-0.321483\pi$
$509$	23.9999	1.06378	0.531888	+	0.846815i	$0.321483\pi$
$510$	−1.47395	−0.0652674
$511$	13.3121	0.588893
$512$	19.8774	0.878467
$513$	22.6273	0.999019
$514$	31.5845	1.39313
$515$	−12.5686	−0.553838
$516$	−18.9972	−0.836307
$517$	−3.66086	−0.161004
$518$	−17.5560	−0.771367
$519$	−12.5374	−0.550332
$520$	−16.4023	−0.719290
$521$	−33.5160	−1.46836	−0.734182	−	0.678953i	$-0.762434\pi$
$521$	−33.5160	−1.46836	−0.734182	+	0.678953i	$0.762434\pi$
$522$	−9.78653	−0.428345
$523$	−4.49486	−0.196547	−0.0982733	−	0.995159i	$-0.531332\pi$
$523$	−4.49486	−0.196547	−0.0982733	+	0.995159i	$0.531332\pi$
$524$	21.1237	0.922792
$525$	6.64021	0.289803
$526$	14.1860	0.618537
$527$	−0.641704	−0.0279531
$528$	−9.52886	−0.414690
$529$	−21.2831	−0.925353
$530$	−40.9382	−1.77824
$531$	−3.19799	−0.138781
$532$	−15.9157	−0.690032
$533$	30.2130	1.30867
$534$	1.58005	0.0683756
$535$	40.4018	1.74672
$536$	15.0352	0.649424
$537$	24.9540	1.07685
$538$	42.0614	1.81340
$539$	1.89365	0.0815651
$540$	−14.6002	−0.628292
$541$	3.82763	0.164563	0.0822814	−	0.996609i	$-0.473779\pi$
$541$	3.82763	0.164563	0.0822814	+	0.996609i	$0.473779\pi$
$542$	−39.7662	−1.70810
$543$	−35.8232	−1.53732
$544$	1.05439	0.0452066
$545$	6.37346	0.273009
$546$	−42.5777	−1.82216
$547$	−5.18931	−0.221879	−0.110939	−	0.993827i	$-0.535386\pi$
$547$	−5.18931	−0.221879	−0.110939	+	0.993827i	$0.535386\pi$
$548$	22.0768	0.943073
$549$	−4.11517	−0.175631
$550$	−2.75260	−0.117371
$551$	−35.3320	−1.50519
$552$	3.10317	0.132080
$553$	18.8456	0.801397
$554$	36.3665	1.54506
$555$	21.1571	0.898068
$556$	−28.9278	−1.22681
$557$	40.4551	1.71414	0.857069	−	0.515202i	$-0.172283\pi$
$557$	40.4551	1.71414	0.857069	+	0.515202i	$0.172283\pi$
$558$	5.77875	0.244634
$559$	−38.6421	−1.63439
$560$	−28.1763	−1.19067
$561$	−0.316409	−0.0133588
$562$	−39.7696	−1.67758
$563$	35.9113	1.51348	0.756741	−	0.653714i	$-0.226790\pi$
$563$	35.9113	1.51348	0.756741	+	0.653714i	$0.226790\pi$
$564$	−9.52563	−0.401101
$565$	51.0697	2.14852
$566$	−17.5477	−0.737585
$567$	24.3159	1.02117
$568$	−12.5712	−0.527477
$569$	−27.0660	−1.13466	−0.567332	−	0.823489i	$-0.692024\pi$
$569$	−27.0660	−1.13466	−0.567332	+	0.823489i	$0.692024\pi$
$570$	47.9204	2.00716
$571$	13.7252	0.574381	0.287191	−	0.957873i	$-0.407279\pi$
$571$	13.7252	0.574381	0.287191	+	0.957873i	$0.407279\pi$
$572$	7.06444	0.295379
$573$	−2.56093	−0.106984
$574$	23.5559	0.983203
$575$	1.97507	0.0823660
$576$	−1.67058	−0.0696075
$577$	−16.2784	−0.677680	−0.338840	−	0.940844i	$-0.610035\pi$
$577$	−16.2784	−0.677680	−0.338840	+	0.940844i	$0.610035\pi$
$578$	−30.9961	−1.28927
$579$	−8.24216	−0.342532
$580$	22.7978	0.946629
$581$	−29.9619	−1.24303
$582$	−48.1960	−1.99779
$583$	−8.78812	−0.363967
$584$	7.15671	0.296147
$585$	10.8065	0.446794
$586$	56.3749	2.32882
$587$	−25.1696	−1.03886	−0.519431	−	0.854513i	$-0.673856\pi$
$587$	−25.1696	−1.03886	−0.519431	+	0.854513i	$0.673856\pi$
$588$	4.92731	0.203199
$589$	20.8628	0.859638
$590$	18.6126	0.766270
$591$	42.4704	1.74700
$592$	−20.7953	−0.854684
$593$	44.5275	1.82853	0.914263	−	0.405121i	$-0.132771\pi$
$593$	44.5275	1.82853	0.914263	+	0.405121i	$0.132771\pi$
$594$	−7.83052	−0.321290
$595$	−0.935603	−0.0383560
$596$	6.66635	0.273064
$597$	−51.6996	−2.11593
$598$	−12.6643	−0.517882
$599$	26.7349	1.09236	0.546179	−	0.837669i	$-0.316082\pi$
$599$	26.7349	1.09236	0.546179	+	0.837669i	$0.316082\pi$
$600$	3.56984	0.145738
$601$	−13.4571	−0.548927	−0.274464	−	0.961597i	$-0.588500\pi$
$601$	−13.4571	−0.548927	−0.274464	+	0.961597i	$0.588500\pi$
$602$	−30.1277	−1.22791
$603$	−9.90583	−0.403396
$604$	−0.936068	−0.0380881
$605$	−2.55095	−0.103711
$606$	−56.5812	−2.29846
$607$	20.4978	0.831980	0.415990	−	0.909369i	$-0.363435\pi$
$607$	20.4978	0.831980	0.415990	+	0.909369i	$0.363435\pi$
$608$	−34.2800	−1.39024
$609$	−29.4961	−1.19524
$610$	23.9507	0.969736
$611$	−19.3760	−0.783869
$612$	−0.173394	−0.00700903
$613$	−27.2229	−1.09952	−0.549760	−	0.835322i	$-0.685281\pi$
$613$	−27.2229	−1.09952	−0.549760	+	0.835322i	$0.685281\pi$
$614$	−57.1356	−2.30581
$615$	−28.3876	−1.14470
$616$	−2.74522	−0.110608
$617$	−25.7401	−1.03626	−0.518128	−	0.855303i	$-0.673371\pi$
$617$	−25.7401	−1.03626	−0.518128	+	0.855303i	$0.673371\pi$
$618$	−17.5400	−0.705562
$619$	−35.3754	−1.42186	−0.710928	−	0.703265i	$-0.751725\pi$
$619$	−35.3754	−1.42186	−0.710928	+	0.703265i	$0.751725\pi$
$620$	−13.4617	−0.540634
$621$	5.61861	0.225467
$622$	−16.6237	−0.666548
$623$	1.00296	0.0401826
$624$	−50.4338	−2.01897
$625$	−30.2646	−1.21059
$626$	−2.19532	−0.0877426
$627$	10.2870	0.410822
$628$	−14.6384	−0.584135
$629$	−0.690516	−0.0275327
$630$	8.42541	0.335676
$631$	27.4499	1.09276	0.546382	−	0.837536i	$-0.316005\pi$
$631$	27.4499	1.09276	0.546382	+	0.837536i	$0.316005\pi$
$632$	10.1316	0.403013
$633$	0.639435	0.0254152
$634$	−3.60809	−0.143295
$635$	26.8732	1.06643
$636$	−22.8669	−0.906731
$637$	10.0226	0.397110
$638$	12.2272	0.484078
$639$	8.28244	0.327648
$640$	−23.4206	−0.925781
$641$	−11.5387	−0.455751	−0.227876	−	0.973690i	$-0.573178\pi$
$641$	−11.5387	−0.455751	−0.227876	+	0.973690i	$0.573178\pi$
$642$	56.3825	2.22524
$643$	−17.3558	−0.684446	−0.342223	−	0.939619i	$-0.611180\pi$
$643$	−17.3558	−0.684446	−0.342223	+	0.939619i	$0.611180\pi$
$644$	−3.95204	−0.155732
$645$	36.3074	1.42960
$646$	−1.56401	−0.0615350
$647$	39.1616	1.53960	0.769800	−	0.638285i	$-0.220356\pi$
$647$	39.1616	1.53960	0.769800	+	0.638285i	$0.220356\pi$
$648$	13.0724	0.513534
$649$	3.99554	0.156838
$650$	−14.5688	−0.571437
$651$	17.4169	0.682621
$652$	23.0086	0.901085
$653$	5.72864	0.224179	0.112090	−	0.993698i	$-0.464246\pi$
$653$	5.72864	0.224179	0.112090	+	0.993698i	$0.464246\pi$
$654$	8.89444	0.347800
$655$	−40.3715	−1.57744
$656$	27.9022	1.08940
$657$	−4.71513	−0.183955
$658$	−15.1067	−0.588920
$659$	42.8613	1.66964	0.834820	−	0.550523i	$-0.185571\pi$
$659$	42.8613	1.66964	0.834820	+	0.550523i	$0.185571\pi$
$660$	−6.63763	−0.258369
$661$	27.1683	1.05672	0.528362	−	0.849019i	$-0.322807\pi$
$661$	27.1683	1.05672	0.528362	+	0.849019i	$0.322807\pi$
$662$	27.0576	1.05163
$663$	−1.67467	−0.0650389
$664$	−16.1078	−0.625103
$665$	30.4180	1.17956
$666$	6.21832	0.240955
$667$	−8.77333	−0.339705
$668$	−28.2937	−1.09471
$669$	11.4020	0.440827
$670$	57.6529	2.22733
$671$	5.14145	0.198483
$672$	−28.6178	−1.10396
$673$	−13.3362	−0.514075	−0.257037	−	0.966401i	$-0.582746\pi$
$673$	−13.3362	−0.514075	−0.257037	+	0.966401i	$0.582746\pi$
$674$	60.2801	2.32190
$675$	6.46356	0.248783
$676$	20.0387	0.770719
$677$	47.7982	1.83703	0.918516	−	0.395383i	$-0.129388\pi$
$677$	47.7982	1.83703	0.918516	+	0.395383i	$0.129388\pi$
$678$	71.2700	2.73711
$679$	−30.5929	−1.17405
$680$	−0.502989	−0.0192888
$681$	−25.9746	−0.995350
$682$	−7.21990	−0.276464
$683$	1.46459	0.0560408	0.0280204	−	0.999607i	$-0.491080\pi$
$683$	1.46459	0.0560408	0.0280204	+	0.999607i	$0.491080\pi$
$684$	5.63731	0.215548
$685$	−42.1930	−1.61211
$686$	36.7000	1.40121
$687$	−18.3435	−0.699847
$688$	−35.6867	−1.36054
$689$	−46.5133	−1.77202
$690$	11.8992	0.452993
$691$	−18.5824	−0.706906	−0.353453	−	0.935452i	$-0.614993\pi$
$691$	−18.5824	−0.706906	−0.353453	+	0.935452i	$0.614993\pi$
$692$	8.58402	0.326315
$693$	1.80866	0.0687055
$694$	−2.76831	−0.105083
$695$	55.2867	2.09714
$696$	−15.8574	−0.601073
$697$	0.926503	0.0350938
$698$	−44.2754	−1.67585
$699$	−1.94946	−0.0737353
$700$	−4.54637	−0.171837
$701$	45.2365	1.70856	0.854279	−	0.519814i	$-0.173999\pi$
$701$	45.2365	1.70856	0.854279	+	0.519814i	$0.173999\pi$
$702$	−41.4450	−1.56424
$703$	22.4498	0.846710
$704$	2.08720	0.0786645
$705$	18.2053	0.685653
$706$	5.01833	0.188867
$707$	−35.9156	−1.35074
$708$	10.3965	0.390723
$709$	6.85497	0.257444	0.128722	−	0.991681i	$-0.458913\pi$
$709$	6.85497	0.257444	0.128722	+	0.991681i	$0.458913\pi$
$710$	−48.2046	−1.80909
$711$	−6.67510	−0.250336
$712$	0.539199	0.0202073
$713$	5.18047	0.194010
$714$	−1.30567	−0.0488636
$715$	−13.5015	−0.504929
$716$	−17.0853	−0.638508
$717$	27.4478	1.02506
$718$	−56.0937	−2.09340
$719$	−42.3612	−1.57981	−0.789903	−	0.613232i	$-0.789869\pi$
$719$	−42.3612	−1.57981	−0.789903	+	0.613232i	$0.789869\pi$
$720$	9.98001	0.371933
$721$	−11.1337	−0.414641
$722$	16.1519	0.601113
$723$	−8.84615	−0.328992
$724$	24.5272	0.911545
$725$	−10.0927	−0.374834
$726$	−3.55996	−0.132123
$727$	13.9531	0.517491	0.258745	−	0.965946i	$-0.416691\pi$
$727$	13.9531	0.517491	0.258745	+	0.965946i	$0.416691\pi$
$728$	−14.5298	−0.538509
$729$	16.4655	0.609832
$730$	27.4425	1.01569
$731$	−1.18499	−0.0438284
$732$	13.3782	0.494471
$733$	−9.60086	−0.354616	−0.177308	−	0.984155i	$-0.556739\pi$
$733$	−9.60086	−0.354616	−0.177308	+	0.984155i	$0.556739\pi$
$734$	−14.7895	−0.545890
$735$	−9.41705	−0.347353
$736$	−8.51210	−0.313760
$737$	12.3762	0.455884
$738$	−8.34346	−0.307127
$739$	−11.7419	−0.431934	−0.215967	−	0.976401i	$-0.569290\pi$
$739$	−11.7419	−0.431934	−0.215967	+	0.976401i	$0.569290\pi$
$740$	−14.4857	−0.532503
$741$	54.4463	2.00013
$742$	−36.2646	−1.33131
$743$	−13.6357	−0.500244	−0.250122	−	0.968214i	$-0.580471\pi$
$743$	−13.6357	−0.500244	−0.250122	+	0.968214i	$0.580471\pi$
$744$	9.36347	0.343281
$745$	−12.7407	−0.466783
$746$	−0.372555	−0.0136402
$747$	10.6125	0.388289
$748$	0.216636	0.00792101
$749$	35.7894	1.30772
$750$	−31.7178	−1.15817
$751$	−10.1075	−0.368826	−0.184413	−	0.982849i	$-0.559038\pi$
$751$	−10.1075	−0.368826	−0.184413	+	0.982849i	$0.559038\pi$
$752$	−17.8941	−0.652530
$753$	−11.0566	−0.402925
$754$	64.7153	2.35679
$755$	1.78901	0.0651087
$756$	−12.9334	−0.470382
$757$	11.5605	0.420172	0.210086	−	0.977683i	$-0.432626\pi$
$757$	11.5605	0.420172	0.210086	+	0.977683i	$0.432626\pi$
$758$	48.4234	1.75882
$759$	2.55437	0.0927177
$760$	16.3530	0.593185
$761$	44.8101	1.62437	0.812183	−	0.583403i	$-0.198279\pi$
$761$	44.8101	1.62437	0.812183	+	0.583403i	$0.198279\pi$
$762$	37.5027	1.35858
$763$	5.64584	0.204393
$764$	1.75339	0.0634356
$765$	0.331390	0.0119814
$766$	51.1412	1.84781
$767$	21.1474	0.763587
$768$	−40.8223	−1.47305
$769$	9.91129	0.357410	0.178705	−	0.983903i	$-0.442809\pi$
$769$	9.91129	0.357410	0.178705	+	0.983903i	$0.442809\pi$
$770$	−10.5266	−0.379353
$771$	−33.7176	−1.21431
$772$	5.64317	0.203102
$773$	−20.2979	−0.730063	−0.365032	−	0.930995i	$-0.618942\pi$
$773$	−20.2979	−0.730063	−0.365032	+	0.930995i	$0.618942\pi$
$774$	10.6712	0.383568
$775$	5.95954	0.214073
$776$	−16.4471	−0.590415
$777$	18.7417	0.672355
$778$	13.4471	0.482102
$779$	−30.1221	−1.07924
$780$	−35.1313	−1.25790
$781$	−10.3480	−0.370280
$782$	−0.388360	−0.0138877
$783$	−28.7114	−1.02606
$784$	9.25605	0.330573
$785$	27.9768	0.998535
$786$	−56.3402	−2.00959
$787$	−5.97247	−0.212896	−0.106448	−	0.994318i	$-0.533948\pi$
$787$	−5.97247	−0.212896	−0.106448	+	0.994318i	$0.533948\pi$
$788$	−29.0783	−1.03587
$789$	−15.1440	−0.539142
$790$	38.8497	1.38221
$791$	45.2394	1.60853
$792$	0.972355	0.0345511
$793$	27.2124	0.966340
$794$	−59.8092	−2.12255
$795$	43.7031	1.54999
$796$	35.3973	1.25462
$797$	−0.761912	−0.0269883	−0.0134942	−	0.999909i	$-0.504295\pi$
$797$	−0.761912	−0.0269883	−0.0134942	+	0.999909i	$0.504295\pi$
$798$	42.4496	1.50270
$799$	−0.594179	−0.0210205
$800$	−9.79219	−0.346206
$801$	−0.355246	−0.0125520
$802$	−30.3908	−1.07314
$803$	5.89103	0.207890
$804$	32.2032	1.13572
$805$	7.55312	0.266213
$806$	−38.2131	−1.34600
$807$	−44.9021	−1.58063
$808$	−19.3085	−0.679272
$809$	−5.05115	−0.177589	−0.0887945	−	0.996050i	$-0.528301\pi$
$809$	−5.05115	−0.177589	−0.0887945	+	0.996050i	$0.528301\pi$
$810$	50.1265	1.76127
$811$	33.6953	1.18320	0.591601	−	0.806231i	$-0.298496\pi$
$811$	33.6953	1.18320	0.591601	+	0.806231i	$0.298496\pi$
$812$	20.1952	0.708711
$813$	42.4519	1.48885
$814$	−7.76910	−0.272307
$815$	−43.9739	−1.54034
$816$	−1.54659	−0.0541415
$817$	38.5259	1.34785
$818$	−32.6637	−1.14206
$819$	9.57281	0.334501
$820$	19.4362	0.678741
$821$	7.84854	0.273916	0.136958	−	0.990577i	$-0.456267\pi$
$821$	7.84854	0.273916	0.136958	+	0.990577i	$0.456267\pi$
$822$	−58.8822	−2.05375
$823$	−4.14332	−0.144427	−0.0722135	−	0.997389i	$-0.523006\pi$
$823$	−4.14332	−0.144427	−0.0722135	+	0.997389i	$0.523006\pi$
$824$	−5.98559	−0.208518
$825$	2.93851	0.102306
$826$	16.4877	0.573682
$827$	2.12323	0.0738319	0.0369159	−	0.999318i	$-0.488247\pi$
$827$	2.12323	0.0738319	0.0369159	+	0.999318i	$0.488247\pi$
$828$	1.39981	0.0486467
$829$	−10.6721	−0.370657	−0.185328	−	0.982677i	$-0.559335\pi$
$829$	−10.6721	−0.370657	−0.185328	+	0.982677i	$0.559335\pi$
$830$	−61.7655	−2.14391
$831$	−38.8226	−1.34674
$832$	11.0470	0.382987
$833$	0.307350	0.0106490
$834$	77.1550	2.67166
$835$	54.0747	1.87133
$836$	−7.04319	−0.243594
$837$	16.9535	0.585999
$838$	−40.1330	−1.38637
$839$	17.7918	0.614242	0.307121	−	0.951670i	$-0.400634\pi$
$839$	17.7918	0.614242	0.307121	+	0.951670i	$0.400634\pi$
$840$	13.6519	0.471036
$841$	15.8322	0.545938
$842$	56.2447	1.93832
$843$	42.4556	1.46225
$844$	−0.437803	−0.0150698
$845$	−38.2979	−1.31749
$846$	5.35077	0.183963
$847$	−2.25972	−0.0776450
$848$	−42.9559	−1.47511
$849$	18.7328	0.642909
$850$	−0.446764	−0.0153239
$851$	5.57454	0.191093
$852$	−26.9257	−0.922458
$853$	−6.94484	−0.237787	−0.118893	−	0.992907i	$-0.537935\pi$
$853$	−6.94484	−0.237787	−0.118893	+	0.992907i	$0.537935\pi$
$854$	21.2164	0.726011
$855$	−10.7740	−0.368463
$856$	19.2407	0.657635
$857$	25.8791	0.884012	0.442006	−	0.897012i	$-0.354267\pi$
$857$	25.8791	0.884012	0.442006	+	0.897012i	$0.354267\pi$
$858$	−18.8420	−0.643254
$859$	41.8318	1.42728	0.713641	−	0.700511i	$-0.247045\pi$
$859$	41.8318	1.42728	0.713641	+	0.700511i	$0.247045\pi$
$860$	−24.8587	−0.847674
$861$	−25.1468	−0.856999
$862$	−20.3826	−0.694235
$863$	33.3628	1.13568	0.567841	−	0.823138i	$-0.307779\pi$
$863$	33.3628	1.13568	0.567841	+	0.823138i	$0.307779\pi$
$864$	−27.8565	−0.947698
$865$	−16.4057	−0.557812
$866$	73.9039	2.51136
$867$	33.0895	1.12378
$868$	−11.9248	−0.404755
$869$	8.33979	0.282908
$870$	−60.8054	−2.06150
$871$	65.5042	2.21953
$872$	3.03526	0.102787
$873$	10.8360	0.366742
$874$	12.6262	0.427088
$875$	−20.1332	−0.680627
$876$	15.3286	0.517905
$877$	−24.3286	−0.821517	−0.410759	−	0.911744i	$-0.634736\pi$
$877$	−24.3286	−0.821517	−0.410759	+	0.911744i	$0.634736\pi$
$878$	24.1816	0.816089
$879$	−60.1823	−2.02990
$880$	−12.4689	−0.420327
$881$	33.7706	1.13776	0.568881	−	0.822420i	$-0.307377\pi$
$881$	33.7706	1.13776	0.568881	+	0.822420i	$0.307377\pi$
$882$	−2.76779	−0.0931962
$883$	27.1052	0.912162	0.456081	−	0.889938i	$-0.349253\pi$
$883$	27.1052	0.912162	0.456081	+	0.889938i	$0.349253\pi$
$884$	1.14660	0.0385644
$885$	−19.8697	−0.667912
$886$	19.4925	0.654863
$887$	36.5517	1.22729	0.613643	−	0.789584i	$-0.289703\pi$
$887$	36.5517	1.22729	0.613643	+	0.789584i	$0.289703\pi$
$888$	10.0757	0.338119
$889$	23.8052	0.798402
$890$	2.06757	0.0693050
$891$	10.7605	0.360492
$892$	−7.80664	−0.261386
$893$	19.3177	0.646443
$894$	−17.7802	−0.594659
$895$	32.6534	1.09148
$896$	−20.7468	−0.693103
$897$	13.5196	0.451407
$898$	−58.8058	−1.96237
$899$	−26.4725	−0.882908
$900$	1.61032	0.0536773
$901$	−1.42636	−0.0475191
$902$	10.4242	0.347088
$903$	32.1624	1.07030
$904$	24.3211	0.808909
$905$	−46.8762	−1.55822
$906$	2.49664	0.0829453
$907$	19.4865	0.647039	0.323520	−	0.946221i	$-0.395134\pi$
$907$	19.4865	0.647039	0.323520	+	0.946221i	$0.395134\pi$
$908$	17.7841	0.590186
$909$	12.7212	0.421937
$910$	−55.7147	−1.84692
$911$	−37.3542	−1.23760	−0.618800	−	0.785549i	$-0.712381\pi$
$911$	−37.3542	−1.23760	−0.618800	+	0.785549i	$0.712381\pi$
$912$	50.2821	1.66501
$913$	−13.2591	−0.438811
$914$	32.5192	1.07564
$915$	−25.5683	−0.845261
$916$	12.5593	0.414969
$917$	−35.7625	−1.18098
$918$	−1.27094	−0.0419473
$919$	1.12283	0.0370387	0.0185193	−	0.999829i	$-0.494105\pi$
$919$	1.12283	0.0370387	0.0185193	+	0.999829i	$0.494105\pi$
$920$	4.06063	0.133875
$921$	60.9944	2.00983
$922$	22.2199	0.731773
$923$	−54.7692	−1.80275
$924$	−5.87985	−0.193433
$925$	6.41286	0.210854
$926$	−25.3805	−0.834056
$927$	3.94355	0.129523
$928$	43.4973	1.42787
$929$	−20.0869	−0.659031	−0.329515	−	0.944150i	$-0.606885\pi$
$929$	−20.0869	−0.659031	−0.329515	+	0.944150i	$0.606885\pi$
$930$	35.9044	1.17735
$931$	−9.99245	−0.327489
$932$	1.33474	0.0437209
$933$	17.7464	0.580991
$934$	35.2316	1.15281
$935$	−0.414034	−0.0135404
$936$	5.14643	0.168216
$937$	−2.91397	−0.0951953	−0.0475976	−	0.998867i	$-0.515157\pi$
$937$	−2.91397	−0.0951953	−0.0475976	+	0.998867i	$0.515157\pi$
$938$	51.0710	1.66753
$939$	2.34359	0.0764801
$940$	−12.4647	−0.406553
$941$	58.3164	1.90106	0.950530	−	0.310634i	$-0.100541\pi$
$941$	58.3164	1.90106	0.950530	+	0.310634i	$0.100541\pi$
$942$	39.0428	1.27208
$943$	−7.47966	−0.243571
$944$	19.5300	0.635646
$945$	24.7182	0.804083
$946$	−13.3325	−0.433476
$947$	28.6045	0.929522	0.464761	−	0.885436i	$-0.346140\pi$
$947$	28.6045	0.929522	0.464761	+	0.885436i	$0.346140\pi$
$948$	21.7003	0.704793
$949$	31.1797	1.01214
$950$	14.5250	0.471254
$951$	3.85177	0.124902
$952$	−0.445566	−0.0144409
$953$	20.2187	0.654948	0.327474	−	0.944860i	$-0.393803\pi$
$953$	20.2187	0.654948	0.327474	+	0.944860i	$0.393803\pi$
$954$	12.8449	0.415868
$955$	−3.35108	−0.108438
$956$	−18.7927	−0.607800
$957$	−13.0530	−0.421942
$958$	−9.33313	−0.301540
$959$	−37.3761	−1.20694
$960$	−10.3796	−0.335000
$961$	−15.3685	−0.495758
$962$	−41.1199	−1.32576
$963$	−12.6766	−0.408497
$964$	6.05671	0.195073
$965$	−10.7852	−0.347188
$966$	10.5407	0.339142
$967$	−2.84404	−0.0914581	−0.0457290	−	0.998954i	$-0.514561\pi$
$967$	−2.84404	−0.0914581	−0.0457290	+	0.998954i	$0.514561\pi$
$968$	−1.21485	−0.0390467
$969$	1.66963	0.0536364
$970$	−63.0665	−2.02494
$971$	−50.0076	−1.60482	−0.802411	−	0.596772i	$-0.796449\pi$
$971$	−50.0076	−1.60482	−0.802411	+	0.596772i	$0.796449\pi$
$972$	10.8289	0.347337
$973$	48.9750	1.57007
$974$	51.8737	1.66214
$975$	15.5528	0.498087
$976$	25.1311	0.804428
$977$	−27.9692	−0.894815	−0.447407	−	0.894330i	$-0.647653\pi$
$977$	−27.9692	−0.894815	−0.447407	+	0.894330i	$0.647653\pi$
$978$	−61.3674	−1.96231
$979$	0.443840	0.0141852
$980$	6.44759	0.205961
$981$	−1.99975	−0.0638471
$982$	2.79821	0.0892945
$983$	20.8155	0.663911	0.331956	−	0.943295i	$-0.392292\pi$
$983$	20.8155	0.663911	0.331956	+	0.943295i	$0.392292\pi$
$984$	−13.5191	−0.430974
$985$	55.5743	1.77074
$986$	1.98454	0.0632007
$987$	16.1270	0.513327
$988$	−37.2778	−1.18597
$989$	9.56640	0.304194
$990$	3.72851	0.118500
$991$	−31.2849	−0.993799	−0.496899	−	0.867808i	$-0.665528\pi$
$991$	−31.2849	−0.993799	−0.496899	+	0.867808i	$0.665528\pi$
$992$	−25.6843	−0.815477
$993$	−28.8851	−0.916639
$994$	−42.7014	−1.35441
$995$	−67.6512	−2.14469
$996$	−34.5004	−1.09319
$997$	0.476353	0.0150862	0.00754312	−	0.999972i	$-0.497599\pi$
$997$	0.476353	0.0150862	0.00754312	+	0.999972i	$0.497599\pi$
$998$	20.3458	0.644036
$999$	18.2431	0.577187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2563.2.a.j.1.33	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2563.2.a.j.1.33	✓	45	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:	\( N \)	\(=\)	\( 2563 = 11 \cdot 233 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2563.a (trivial)

\(f(q)\)	\(=\)	\(q+1.82613 q^{2} -1.94946 q^{3} +1.33474 q^{4} -2.55095 q^{5} -3.55996 q^{6} -2.25972 q^{7} -1.21485 q^{8} +0.800392 q^{9} +O(q^{10})\)	\(q+1.82613 q^{2} -1.94946 q^{3} +1.33474 q^{4} -2.55095 q^{5} -3.55996 q^{6} -2.25972 q^{7} -1.21485 q^{8} +0.800392 q^{9} -4.65836 q^{10} -1.00000 q^{11} -2.60202 q^{12} -5.29275 q^{13} -4.12654 q^{14} +4.97297 q^{15} -4.88795 q^{16} -0.162306 q^{17} +1.46162 q^{18} +5.27683 q^{19} -3.40485 q^{20} +4.40524 q^{21} -1.82613 q^{22} +1.31030 q^{23} +2.36830 q^{24} +1.50734 q^{25} -9.66523 q^{26} +4.28805 q^{27} -3.01614 q^{28} -6.69569 q^{29} +9.08128 q^{30} +3.95367 q^{31} -6.49632 q^{32} +1.94946 q^{33} -0.296391 q^{34} +5.76444 q^{35} +1.06831 q^{36} +4.25441 q^{37} +9.63616 q^{38} +10.3180 q^{39} +3.09902 q^{40} -5.70838 q^{41} +8.04453 q^{42} +7.30095 q^{43} -1.33474 q^{44} -2.04176 q^{45} +2.39277 q^{46} +3.66086 q^{47} +9.52886 q^{48} -1.89365 q^{49} +2.75260 q^{50} +0.316409 q^{51} -7.06444 q^{52} +8.78812 q^{53} +7.83052 q^{54} +2.55095 q^{55} +2.74522 q^{56} -10.2870 q^{57} -12.2272 q^{58} -3.99554 q^{59} +6.63763 q^{60} -5.14145 q^{61} +7.21990 q^{62} -1.80866 q^{63} -2.08720 q^{64} +13.5015 q^{65} +3.55996 q^{66} -12.3762 q^{67} -0.216636 q^{68} -2.55437 q^{69} +10.5266 q^{70} +10.3480 q^{71} -0.972355 q^{72} -5.89103 q^{73} +7.76910 q^{74} -2.93851 q^{75} +7.04319 q^{76} +2.25972 q^{77} +18.8420 q^{78} -8.33979 q^{79} +12.4689 q^{80} -10.7605 q^{81} -10.4242 q^{82} +13.2591 q^{83} +5.87985 q^{84} +0.414034 q^{85} +13.3325 q^{86} +13.0530 q^{87} +1.21485 q^{88} -0.443840 q^{89} -3.72851 q^{90} +11.9602 q^{91} +1.74890 q^{92} -7.70752 q^{93} +6.68519 q^{94} -13.4609 q^{95} +12.6643 q^{96} +13.5384 q^{97} -3.45804 q^{98} -0.800392 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q + 12 q^{2} + 5 q^{3} + 54 q^{4} + 29 q^{5} - 2 q^{6} - 22 q^{7} + 36 q^{8} + 52 q^{9}+O(q^{10}) \) 45 * q + 12 * q^2 + 5 * q^3 + 54 * q^4 + 29 * q^5 - 2 * q^6 - 22 * q^7 + 36 * q^8 + 52 * q^9	\( 45 q + 12 q^{2} + 5 q^{3} + 54 q^{4} + 29 q^{5} - 2 q^{6} - 22 q^{7} + 36 q^{8} + 52 q^{9} + 10 q^{10} - 45 q^{11} + 39 q^{12} + 8 q^{13} + 24 q^{14} + 42 q^{15} + 64 q^{16} + 20 q^{17} + 27 q^{18} - 20 q^{19} + 66 q^{20} - 8 q^{21} - 12 q^{22} + 22 q^{23} - 2 q^{24} + 80 q^{25} + 26 q^{26} + 32 q^{27} - 39 q^{28} + 12 q^{29} + 16 q^{30} + 32 q^{31} + 79 q^{32} - 5 q^{33} + 47 q^{34} + 24 q^{35} + 70 q^{36} + 33 q^{37} + 46 q^{38} + 17 q^{40} + 9 q^{41} + 6 q^{42} - 22 q^{43} - 54 q^{44} + 83 q^{45} + 13 q^{46} + 85 q^{47} + 62 q^{48} + 67 q^{49} + 27 q^{50} + 8 q^{51} + 9 q^{52} + 56 q^{53} - 35 q^{54} - 29 q^{55} + 6 q^{56} + 14 q^{57} + 42 q^{58} + 28 q^{59} + 115 q^{60} + 6 q^{61} + 57 q^{62} - 52 q^{63} + 152 q^{64} + 31 q^{65} + 2 q^{66} + 23 q^{67} - 2 q^{68} + 28 q^{69} + 85 q^{70} + 6 q^{71} + 45 q^{72} + 17 q^{73} - 14 q^{74} + 76 q^{75} + 19 q^{76} + 22 q^{77} - 106 q^{78} - 75 q^{79} + 41 q^{80} + 101 q^{81} + 69 q^{82} + 43 q^{83} + 5 q^{84} + 42 q^{85} + 57 q^{86} + 19 q^{87} - 36 q^{88} + 5 q^{89} + 52 q^{90} - 7 q^{91} + 64 q^{92} + 81 q^{93} - 40 q^{94} + 9 q^{95} + 39 q^{96} + 58 q^{97} + 90 q^{98} - 52 q^{99}+O(q^{100}) \) 45 * q + 12 * q^2 + 5 * q^3 + 54 * q^4 + 29 * q^5 - 2 * q^6 - 22 * q^7 + 36 * q^8 + 52 * q^9 + 10 * q^10 - 45 * q^11 + 39 * q^12 + 8 * q^13 + 24 * q^14 + 42 * q^15 + 64 * q^16 + 20 * q^17 + 27 * q^18 - 20 * q^19 + 66 * q^20 - 8 * q^21 - 12 * q^22 + 22 * q^23 - 2 * q^24 + 80 * q^25 + 26 * q^26 + 32 * q^27 - 39 * q^28 + 12 * q^29 + 16 * q^30 + 32 * q^31 + 79 * q^32 - 5 * q^33 + 47 * q^34 + 24 * q^35 + 70 * q^36 + 33 * q^37 + 46 * q^38 + 17 * q^40 + 9 * q^41 + 6 * q^42 - 22 * q^43 - 54 * q^44 + 83 * q^45 + 13 * q^46 + 85 * q^47 + 62 * q^48 + 67 * q^49 + 27 * q^50 + 8 * q^51 + 9 * q^52 + 56 * q^53 - 35 * q^54 - 29 * q^55 + 6 * q^56 + 14 * q^57 + 42 * q^58 + 28 * q^59 + 115 * q^60 + 6 * q^61 + 57 * q^62 - 52 * q^63 + 152 * q^64 + 31 * q^65 + 2 * q^66 + 23 * q^67 - 2 * q^68 + 28 * q^69 + 85 * q^70 + 6 * q^71 + 45 * q^72 + 17 * q^73 - 14 * q^74 + 76 * q^75 + 19 * q^76 + 22 * q^77 - 106 * q^78 - 75 * q^79 + 41 * q^80 + 101 * q^81 + 69 * q^82 + 43 * q^83 + 5 * q^84 + 42 * q^85 + 57 * q^86 + 19 * q^87 - 36 * q^88 + 5 * q^89 + 52 * q^90 - 7 * q^91 + 64 * q^92 + 81 * q^93 - 40 * q^94 + 9 * q^95 + 39 * q^96 + 58 * q^97 + 90 * q^98 - 52 * q^99

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