LMFDB - Embedded newform 4029.2.a.i.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.495377 q^{2} -1.00000 q^{3} -1.75460 q^{4} -3.92669 q^{5} +0.495377 q^{6} +0.792012 q^{7} +1.85994 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.495377 q^{2} -1.00000 q^{3} -1.75460 q^{4} -3.92669 q^{5} +0.495377 q^{6} +0.792012 q^{7} +1.85994 q^{8} +1.00000 q^{9} +1.94519 q^{10} +3.60141 q^{11} +1.75460 q^{12} -4.35807 q^{13} -0.392345 q^{14} +3.92669 q^{15} +2.58783 q^{16} +1.00000 q^{17} -0.495377 q^{18} +5.25644 q^{19} +6.88978 q^{20} -0.792012 q^{21} -1.78406 q^{22} -4.05074 q^{23} -1.85994 q^{24} +10.4189 q^{25} +2.15889 q^{26} -1.00000 q^{27} -1.38967 q^{28} -2.38181 q^{29} -1.94519 q^{30} -3.27296 q^{31} -5.00184 q^{32} -3.60141 q^{33} -0.495377 q^{34} -3.10999 q^{35} -1.75460 q^{36} -8.28956 q^{37} -2.60392 q^{38} +4.35807 q^{39} -7.30342 q^{40} +5.75442 q^{41} +0.392345 q^{42} +2.25024 q^{43} -6.31904 q^{44} -3.92669 q^{45} +2.00664 q^{46} -12.5423 q^{47} -2.58783 q^{48} -6.37272 q^{49} -5.16128 q^{50} -1.00000 q^{51} +7.64668 q^{52} -9.15188 q^{53} +0.495377 q^{54} -14.1416 q^{55} +1.47310 q^{56} -5.25644 q^{57} +1.17989 q^{58} -11.9524 q^{59} -6.88978 q^{60} +5.37127 q^{61} +1.62135 q^{62} +0.792012 q^{63} -2.69786 q^{64} +17.1128 q^{65} +1.78406 q^{66} +7.52829 q^{67} -1.75460 q^{68} +4.05074 q^{69} +1.54062 q^{70} +8.83540 q^{71} +1.85994 q^{72} -8.78515 q^{73} +4.10646 q^{74} -10.4189 q^{75} -9.22295 q^{76} +2.85236 q^{77} -2.15889 q^{78} -1.00000 q^{79} -10.1616 q^{80} +1.00000 q^{81} -2.85061 q^{82} +8.41255 q^{83} +1.38967 q^{84} -3.92669 q^{85} -1.11472 q^{86} +2.38181 q^{87} +6.69842 q^{88} +8.58421 q^{89} +1.94519 q^{90} -3.45165 q^{91} +7.10744 q^{92} +3.27296 q^{93} +6.21316 q^{94} -20.6404 q^{95} +5.00184 q^{96} +5.86365 q^{97} +3.15690 q^{98} +3.60141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * 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 $

$2$	−0.495377	−0.350284	−0.175142	−	0.984543i	$-0.556039\pi$
$2$	−0.495377	−0.350284	−0.175142	+	0.984543i	$0.556039\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.75460	−0.877301
$5$	−3.92669	−1.75607	−0.878035	−	0.478597i	$-0.841146\pi$
$5$	−3.92669	−1.75607	−0.878035	+	0.478597i	$0.841146\pi$
$6$	0.495377	0.202237
$7$	0.792012	0.299352	0.149676	−	0.988735i	$-0.452177\pi$
$7$	0.792012	0.299352	0.149676	+	0.988735i	$0.452177\pi$
$8$	1.85994	0.657589
$9$	1.00000	0.333333
$10$	1.94519	0.615124
$11$	3.60141	1.08587	0.542933	−	0.839776i	$-0.317314\pi$
$11$	3.60141	1.08587	0.542933	+	0.839776i	$0.317314\pi$
$12$	1.75460	0.506510
$13$	−4.35807	−1.20871	−0.604356	−	0.796714i	$-0.706570\pi$
$13$	−4.35807	−1.20871	−0.604356	+	0.796714i	$0.706570\pi$
$14$	−0.392345	−0.104858
$15$	3.92669	1.01387
$16$	2.58783	0.646957
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.495377	−0.116761
$19$	5.25644	1.20591	0.602955	−	0.797775i	$-0.293990\pi$
$19$	5.25644	1.20591	0.602955	+	0.797775i	$0.293990\pi$
$20$	6.88978	1.54060
$21$	−0.792012	−0.172831
$22$	−1.78406	−0.380362
$23$	−4.05074	−0.844638	−0.422319	−	0.906447i	$-0.638784\pi$
$23$	−4.05074	−0.844638	−0.422319	+	0.906447i	$0.638784\pi$
$24$	−1.85994	−0.379659
$25$	10.4189	2.08378
$26$	2.15889	0.423393
$27$	−1.00000	−0.192450
$28$	−1.38967	−0.262622
$29$	−2.38181	−0.442291	−0.221145	−	0.975241i	$-0.570980\pi$
$29$	−2.38181	−0.442291	−0.221145	+	0.975241i	$0.570980\pi$
$30$	−1.94519	−0.355142
$31$	−3.27296	−0.587841	−0.293920	−	0.955830i	$-0.594960\pi$
$31$	−3.27296	−0.587841	−0.293920	+	0.955830i	$0.594960\pi$
$32$	−5.00184	−0.884209
$33$	−3.60141	−0.626925
$34$	−0.495377	−0.0849565
$35$	−3.10999	−0.525684
$36$	−1.75460	−0.292434
$37$	−8.28956	−1.36280	−0.681398	−	0.731913i	$-0.738628\pi$
$37$	−8.28956	−1.36280	−0.681398	+	0.731913i	$0.738628\pi$
$38$	−2.60392	−0.422411
$39$	4.35807	0.697850
$40$	−7.30342	−1.15477
$41$	5.75442	0.898690	0.449345	−	0.893358i	$-0.351657\pi$
$41$	5.75442	0.898690	0.449345	+	0.893358i	$0.351657\pi$
$42$	0.392345	0.0605401
$43$	2.25024	0.343159	0.171580	−	0.985170i	$-0.445113\pi$
$43$	2.25024	0.343159	0.171580	+	0.985170i	$0.445113\pi$
$44$	−6.31904	−0.952631
$45$	−3.92669	−0.585357
$46$	2.00664	0.295864
$47$	−12.5423	−1.82948	−0.914740	−	0.404043i	$-0.867605\pi$
$47$	−12.5423	−1.82948	−0.914740	+	0.404043i	$0.867605\pi$
$48$	−2.58783	−0.373521
$49$	−6.37272	−0.910388
$50$	−5.16128	−0.729916
$51$	−1.00000	−0.140028
$52$	7.64668	1.06040
$53$	−9.15188	−1.25711	−0.628554	−	0.777766i	$-0.716353\pi$
$53$	−9.15188	−1.25711	−0.628554	+	0.777766i	$0.716353\pi$
$54$	0.495377	0.0674123
$55$	−14.1416	−1.90686
$56$	1.47310	0.196851
$57$	−5.25644	−0.696232
$58$	1.17989	0.154928
$59$	−11.9524	−1.55607	−0.778033	−	0.628223i	$-0.783782\pi$
$59$	−11.9524	−1.55607	−0.778033	+	0.628223i	$0.783782\pi$
$60$	−6.88978	−0.889466
$61$	5.37127	0.687720	0.343860	−	0.939021i	$-0.388265\pi$
$61$	5.37127	0.687720	0.343860	+	0.939021i	$0.388265\pi$
$62$	1.62135	0.205911
$63$	0.792012	0.0997841
$64$	−2.69786	−0.337233
$65$	17.1128	2.12258
$66$	1.78406	0.219602
$67$	7.52829	0.919727	0.459863	−	0.887990i	$-0.347898\pi$
$67$	7.52829	0.919727	0.459863	+	0.887990i	$0.347898\pi$
$68$	−1.75460	−0.212777
$69$	4.05074	0.487652
$70$	1.54062	0.184139
$71$	8.83540	1.04857	0.524284	−	0.851543i	$-0.324333\pi$
$71$	8.83540	1.04857	0.524284	+	0.851543i	$0.324333\pi$
$72$	1.85994	0.219196
$73$	−8.78515	−1.02822	−0.514112	−	0.857723i	$-0.671879\pi$
$73$	−8.78515	−1.02822	−0.514112	+	0.857723i	$0.671879\pi$
$74$	4.10646	0.477366
$75$	−10.4189	−1.20307
$76$	−9.22295	−1.05795
$77$	2.85236	0.325057
$78$	−2.15889	−0.244446
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−10.1616	−1.13610
$81$	1.00000	0.111111
$82$	−2.85061	−0.314797
$83$	8.41255	0.923398	0.461699	−	0.887037i	$-0.347240\pi$
$83$	8.41255	0.923398	0.461699	+	0.887037i	$0.347240\pi$
$84$	1.38967	0.151625
$85$	−3.92669	−0.425909
$86$	−1.11472	−0.120203
$87$	2.38181	0.255357
$88$	6.69842	0.714054
$89$	8.58421	0.909925	0.454962	−	0.890511i	$-0.349653\pi$
$89$	8.58421	0.909925	0.454962	+	0.890511i	$0.349653\pi$
$90$	1.94519	0.205041
$91$	−3.45165	−0.361831
$92$	7.10744	0.741001
$93$	3.27296	0.339390
$94$	6.21316	0.640838
$95$	−20.6404	−2.11766
$96$	5.00184	0.510498
$97$	5.86365	0.595363	0.297682	−	0.954665i	$-0.403787\pi$
$97$	5.86365	0.595363	0.297682	+	0.954665i	$0.403787\pi$
$98$	3.15690	0.318895
$99$	3.60141	0.361955
$100$	−18.2810	−1.82810
$101$	17.3359	1.72499	0.862495	−	0.506065i	$-0.168900\pi$
$101$	17.3359	1.72499	0.862495	+	0.506065i	$0.168900\pi$
$102$	0.495377	0.0490496
$103$	−5.69401	−0.561048	−0.280524	−	0.959847i	$-0.590508\pi$
$103$	−5.69401	−0.561048	−0.280524	+	0.959847i	$0.590508\pi$
$104$	−8.10577	−0.794836
$105$	3.10999	0.303504
$106$	4.53363	0.440345
$107$	10.6660	1.03112	0.515561	−	0.856853i	$-0.327584\pi$
$107$	10.6660	1.03112	0.515561	+	0.856853i	$0.327584\pi$
$108$	1.75460	0.168837
$109$	12.5951	1.20639	0.603194	−	0.797594i	$-0.293894\pi$
$109$	12.5951	1.20639	0.603194	+	0.797594i	$0.293894\pi$
$110$	7.00544	0.667942
$111$	8.28956	0.786810
$112$	2.04959	0.193668
$113$	−20.5979	−1.93769	−0.968845	−	0.247667i	$-0.920336\pi$
$113$	−20.5979	−1.93769	−0.968845	+	0.247667i	$0.920336\pi$
$114$	2.60392	0.243879
$115$	15.9060	1.48324
$116$	4.17913	0.388022
$117$	−4.35807	−0.402904
$118$	5.92093	0.545066
$119$	0.792012	0.0726036
$120$	7.30342	0.666708
$121$	1.97016	0.179105
$122$	−2.66080	−0.240898
$123$	−5.75442	−0.518859
$124$	5.74274	0.515713
$125$	−21.2783	−1.90319
$126$	−0.392345	−0.0349528
$127$	6.86580	0.609241	0.304621	−	0.952474i	$-0.401470\pi$
$127$	6.86580	0.609241	0.304621	+	0.952474i	$0.401470\pi$
$128$	11.3401	1.00234
$129$	−2.25024	−0.198123
$130$	−8.47729	−0.743508
$131$	−8.05414	−0.703693	−0.351847	−	0.936058i	$-0.614446\pi$
$131$	−8.05414	−0.703693	−0.351847	+	0.936058i	$0.614446\pi$
$132$	6.31904	0.550002
$133$	4.16316	0.360992
$134$	−3.72934	−0.322166
$135$	3.92669	0.337956
$136$	1.85994	0.159489
$137$	−19.6064	−1.67509	−0.837544	−	0.546371i	$-0.816009\pi$
$137$	−19.6064	−1.67509	−0.837544	+	0.546371i	$0.816009\pi$
$138$	−2.00664	−0.170817
$139$	16.2142	1.37527	0.687635	−	0.726056i	$-0.258649\pi$
$139$	16.2142	1.37527	0.687635	+	0.726056i	$0.258649\pi$
$140$	5.45679	0.461183
$141$	12.5423	1.05625
$142$	−4.37685	−0.367297
$143$	−15.6952	−1.31250
$144$	2.58783	0.215652
$145$	9.35263	0.776694
$146$	4.35196	0.360171
$147$	6.37272	0.525613
$148$	14.5449	1.19558
$149$	−20.2760	−1.66108	−0.830538	−	0.556962i	$-0.811967\pi$
$149$	−20.2760	−1.66108	−0.830538	+	0.556962i	$0.811967\pi$
$150$	5.16128	0.421417
$151$	−13.3506	−1.08646	−0.543228	−	0.839585i	$-0.682798\pi$
$151$	−13.3506	−1.08646	−0.543228	+	0.839585i	$0.682798\pi$
$152$	9.77668	0.792993
$153$	1.00000	0.0808452
$154$	−1.41299	−0.113862
$155$	12.8519	1.03229
$156$	−7.64668	−0.612225
$157$	6.98952	0.557824	0.278912	−	0.960317i	$-0.410026\pi$
$157$	6.98952	0.557824	0.278912	+	0.960317i	$0.410026\pi$
$158$	0.495377	0.0394101
$159$	9.15188	0.725791
$160$	19.6407	1.55273
$161$	−3.20824	−0.252844
$162$	−0.495377	−0.0389205
$163$	−14.4956	−1.13538	−0.567690	−	0.823242i	$-0.692163\pi$
$163$	−14.4956	−1.13538	−0.567690	+	0.823242i	$0.692163\pi$
$164$	−10.0967	−0.788422
$165$	14.1416	1.10092
$166$	−4.16739	−0.323452
$167$	−5.23555	−0.405139	−0.202570	−	0.979268i	$-0.564929\pi$
$167$	−5.23555	−0.405139	−0.202570	+	0.979268i	$0.564929\pi$
$168$	−1.47310	−0.113652
$169$	5.99281	0.460986
$170$	1.94519	0.149189
$171$	5.25644	0.401970
$172$	−3.94828	−0.301054
$173$	13.6838	1.04036	0.520179	−	0.854058i	$-0.325865\pi$
$173$	13.6838	1.04036	0.520179	+	0.854058i	$0.325865\pi$
$174$	−1.17989	−0.0894475
$175$	8.25189	0.623785
$176$	9.31984	0.702509
$177$	11.9524	0.898395
$178$	−4.25242	−0.318732
$179$	−14.9123	−1.11460	−0.557299	−	0.830312i	$-0.688162\pi$
$179$	−14.9123	−1.11460	−0.557299	+	0.830312i	$0.688162\pi$
$180$	6.88978	0.513534
$181$	19.2519	1.43098	0.715492	−	0.698621i	$-0.246203\pi$
$181$	19.2519	1.43098	0.715492	+	0.698621i	$0.246203\pi$
$182$	1.70987	0.126744
$183$	−5.37127	−0.397055
$184$	−7.53415	−0.555425
$185$	32.5505	2.39316
$186$	−1.62135	−0.118883
$187$	3.60141	0.263361
$188$	22.0067	1.60500
$189$	−0.792012	−0.0576104
$190$	10.2248	0.741784
$191$	0.704658	0.0509873	0.0254936	−	0.999675i	$-0.491884\pi$
$191$	0.704658	0.0509873	0.0254936	+	0.999675i	$0.491884\pi$
$192$	2.69786	0.194702
$193$	8.38827	0.603801	0.301900	−	0.953339i	$-0.402379\pi$
$193$	8.38827	0.603801	0.301900	+	0.953339i	$0.402379\pi$
$194$	−2.90472	−0.208546
$195$	−17.1128	−1.22547
$196$	11.1816	0.798684
$197$	−21.0730	−1.50139	−0.750696	−	0.660648i	$-0.770282\pi$
$197$	−21.0730	−1.50139	−0.750696	+	0.660648i	$0.770282\pi$
$198$	−1.78406	−0.126787
$199$	22.5529	1.59873	0.799365	−	0.600845i	$-0.205169\pi$
$199$	22.5529	1.59873	0.799365	+	0.600845i	$0.205169\pi$
$200$	19.3786	1.37027
$201$	−7.52829	−0.531004
$202$	−8.58783	−0.604238
$203$	−1.88642	−0.132401
$204$	1.75460	0.122847
$205$	−22.5958	−1.57816
$206$	2.82068	0.196526
$207$	−4.05074	−0.281546
$208$	−11.2780	−0.781985
$209$	18.9306	1.30946
$210$	−1.54062	−0.106313
$211$	−3.98425	−0.274287	−0.137144	−	0.990551i	$-0.543792\pi$
$211$	−3.98425	−0.274287	−0.137144	+	0.990551i	$0.543792\pi$
$212$	16.0579	1.10286
$213$	−8.83540	−0.605391
$214$	−5.28370	−0.361186
$215$	−8.83601	−0.602611
$216$	−1.85994	−0.126553
$217$	−2.59222	−0.175972
$218$	−6.23930	−0.422579
$219$	8.78515	0.593646
$220$	24.8129	1.67289
$221$	−4.35807	−0.293156
$222$	−4.10646	−0.275607
$223$	−29.6728	−1.98704	−0.993521	−	0.113653i	$-0.963745\pi$
$223$	−29.6728	−1.98704	−0.993521	+	0.113653i	$0.963745\pi$
$224$	−3.96152	−0.264690
$225$	10.4189	0.694593
$226$	10.2037	0.678743
$227$	−26.6083	−1.76605	−0.883026	−	0.469323i	$-0.844498\pi$
$227$	−26.6083	−1.76605	−0.883026	+	0.469323i	$0.844498\pi$
$228$	9.22295	0.610805
$229$	20.9131	1.38198	0.690989	−	0.722865i	$-0.257175\pi$
$229$	20.9131	1.38198	0.690989	+	0.722865i	$0.257175\pi$
$230$	−7.87947	−0.519557
$231$	−2.85236	−0.187672
$232$	−4.43003	−0.290846
$233$	3.11401	0.204006	0.102003	−	0.994784i	$-0.467475\pi$
$233$	3.11401	0.204006	0.102003	+	0.994784i	$0.467475\pi$
$234$	2.15889	0.141131
$235$	49.2497	3.21269
$236$	20.9717	1.36514
$237$	1.00000	0.0649570
$238$	−0.392345	−0.0254319
$239$	1.29460	0.0837408	0.0418704	−	0.999123i	$-0.486668\pi$
$239$	1.29460	0.0837408	0.0418704	+	0.999123i	$0.486668\pi$
$240$	10.1616	0.655929
$241$	24.4731	1.57645	0.788224	−	0.615388i	$-0.211001\pi$
$241$	24.4731	1.57645	0.788224	+	0.615388i	$0.211001\pi$
$242$	−0.975970	−0.0627377
$243$	−1.00000	−0.0641500
$244$	−9.42443	−0.603337
$245$	25.0237	1.59870
$246$	2.85061	0.181748
$247$	−22.9079	−1.45760
$248$	−6.08752	−0.386558
$249$	−8.41255	−0.533124
$250$	10.5408	0.666659
$251$	−4.52016	−0.285310	−0.142655	−	0.989772i	$-0.545564\pi$
$251$	−4.52016	−0.285310	−0.142655	+	0.989772i	$0.545564\pi$
$252$	−1.38967	−0.0875407
$253$	−14.5884	−0.917164
$254$	−3.40116	−0.213408
$255$	3.92669	0.245899
$256$	−0.221918	−0.0138698
$257$	27.0863	1.68959	0.844797	−	0.535087i	$-0.179721\pi$
$257$	27.0863	1.68959	0.844797	+	0.535087i	$0.179721\pi$
$258$	1.11472	0.0693994
$259$	−6.56543	−0.407956
$260$	−30.0262	−1.86214
$261$	−2.38181	−0.147430
$262$	3.98984	0.246493
$263$	−16.7569	−1.03327	−0.516637	−	0.856205i	$-0.672816\pi$
$263$	−16.7569	−1.03327	−0.516637	+	0.856205i	$0.672816\pi$
$264$	−6.69842	−0.412259
$265$	35.9366	2.20757
$266$	−2.06233	−0.126450
$267$	−8.58421	−0.525345
$268$	−13.2091	−0.806877
$269$	13.3950	0.816710	0.408355	−	0.912823i	$-0.366103\pi$
$269$	13.3950	0.816710	0.408355	+	0.912823i	$0.366103\pi$
$270$	−1.94519	−0.118381
$271$	20.6607	1.25505	0.627523	−	0.778598i	$-0.284069\pi$
$271$	20.6607	1.25505	0.627523	+	0.778598i	$0.284069\pi$
$272$	2.58783	0.156910
$273$	3.45165	0.208903
$274$	9.71256	0.586757
$275$	37.5227	2.26271
$276$	−7.10744	−0.427817
$277$	15.5579	0.934784	0.467392	−	0.884050i	$-0.345194\pi$
$277$	15.5579	0.934784	0.467392	+	0.884050i	$0.345194\pi$
$278$	−8.03214	−0.481736
$279$	−3.27296	−0.195947
$280$	−5.78440	−0.345684
$281$	3.42774	0.204482	0.102241	−	0.994760i	$-0.467399\pi$
$281$	3.42774	0.204482	0.102241	+	0.994760i	$0.467399\pi$
$282$	−6.21316	−0.369988
$283$	4.99808	0.297105	0.148553	−	0.988905i	$-0.452539\pi$
$283$	4.99808	0.297105	0.148553	+	0.988905i	$0.452539\pi$
$284$	−15.5026	−0.919910
$285$	20.6404	1.22263
$286$	7.77505	0.459748
$287$	4.55757	0.269025
$288$	−5.00184	−0.294736
$289$	1.00000	0.0588235
$290$	−4.63308	−0.272064
$291$	−5.86365	−0.343733
$292$	15.4144	0.902062
$293$	29.0788	1.69880	0.849401	−	0.527748i	$-0.176963\pi$
$293$	29.0788	1.69880	0.849401	+	0.527748i	$0.176963\pi$
$294$	−3.15690	−0.184114
$295$	46.9333	2.73256
$296$	−15.4181	−0.896160
$297$	−3.60141	−0.208975
$298$	10.0443	0.581849
$299$	17.6534	1.02092
$300$	18.2810	1.05546
$301$	1.78222	0.102725
$302$	6.61358	0.380569
$303$	−17.3359	−0.995924
$304$	13.6028	0.780172
$305$	−21.0913	−1.20768
$306$	−0.495377	−0.0283188
$307$	23.6235	1.34826	0.674131	−	0.738612i	$-0.264518\pi$
$307$	23.6235	1.34826	0.674131	+	0.738612i	$0.264518\pi$
$308$	−5.00476	−0.285172
$309$	5.69401	0.323921
$310$	−6.36653	−0.361595
$311$	13.4375	0.761972	0.380986	−	0.924581i	$-0.375585\pi$
$311$	13.4375	0.761972	0.380986	+	0.924581i	$0.375585\pi$
$312$	8.10577	0.458899
$313$	23.5037	1.32851	0.664254	−	0.747507i	$-0.268749\pi$
$313$	23.5037	1.32851	0.664254	+	0.747507i	$0.268749\pi$
$314$	−3.46245	−0.195397
$315$	−3.10999	−0.175228
$316$	1.75460	0.0987040
$317$	12.7005	0.713329	0.356664	−	0.934233i	$-0.383914\pi$
$317$	12.7005	0.713329	0.356664	+	0.934233i	$0.383914\pi$
$318$	−4.53363	−0.254233
$319$	−8.57787	−0.480269
$320$	10.5937	0.592204
$321$	−10.6660	−0.595318
$322$	1.58929	0.0885675
$323$	5.25644	0.292476
$324$	−1.75460	−0.0974779
$325$	−45.4063	−2.51869
$326$	7.18078	0.397706
$327$	−12.5951	−0.696508
$328$	10.7029	0.590969
$329$	−9.93364	−0.547659
$330$	−7.00544	−0.385637
$331$	−3.69932	−0.203333	−0.101666	−	0.994819i	$-0.532417\pi$
$331$	−3.69932	−0.203333	−0.101666	+	0.994819i	$0.532417\pi$
$332$	−14.7607	−0.810098
$333$	−8.28956	−0.454265
$334$	2.59357	0.141914
$335$	−29.5613	−1.61510
$336$	−2.04959	−0.111814
$337$	3.58777	0.195438	0.0977191	−	0.995214i	$-0.468845\pi$
$337$	3.58777	0.195438	0.0977191	+	0.995214i	$0.468845\pi$
$338$	−2.96870	−0.161476
$339$	20.5979	1.11873
$340$	6.88978	0.373651
$341$	−11.7873	−0.638316
$342$	−2.60392	−0.140804
$343$	−10.5914	−0.571879
$344$	4.18533	0.225658
$345$	−15.9060	−0.856351
$346$	−6.77862	−0.364421
$347$	1.39029	0.0746349	0.0373174	−	0.999303i	$-0.488119\pi$
$347$	1.39029	0.0746349	0.0373174	+	0.999303i	$0.488119\pi$
$348$	−4.17913	−0.224025
$349$	17.8730	0.956722	0.478361	−	0.878163i	$-0.341231\pi$
$349$	17.8730	0.956722	0.478361	+	0.878163i	$0.341231\pi$
$350$	−4.08780	−0.218502
$351$	4.35807	0.232617
$352$	−18.0137	−0.960132
$353$	14.8977	0.792925	0.396462	−	0.918051i	$-0.370238\pi$
$353$	14.8977	0.792925	0.396462	+	0.918051i	$0.370238\pi$
$354$	−5.92093	−0.314694
$355$	−34.6939	−1.84136
$356$	−15.0619	−0.798278
$357$	−0.792012	−0.0419177
$358$	7.38721	0.390426
$359$	−33.1403	−1.74908	−0.874540	−	0.484953i	$-0.838837\pi$
$359$	−33.1403	−1.74908	−0.874540	+	0.484953i	$0.838837\pi$
$360$	−7.30342	−0.384924
$361$	8.63014	0.454218
$362$	−9.53696	−0.501251
$363$	−1.97016	−0.103406
$364$	6.05627	0.317435
$365$	34.4966	1.80563
$366$	2.66080	0.139082
$367$	−16.2431	−0.847881	−0.423940	−	0.905690i	$-0.639353\pi$
$367$	−16.2431	−0.847881	−0.423940	+	0.905690i	$0.639353\pi$
$368$	−10.4826	−0.546445
$369$	5.75442	0.299563
$370$	−16.1248	−0.838288
$371$	−7.24840	−0.376318
$372$	−5.74274	−0.297747
$373$	16.1495	0.836189	0.418094	−	0.908404i	$-0.362698\pi$
$373$	16.1495	0.836189	0.418094	+	0.908404i	$0.362698\pi$
$374$	−1.78406	−0.0922513
$375$	21.2783	1.09881
$376$	−23.3279	−1.20305
$377$	10.3801	0.534602
$378$	0.392345	0.0201800
$379$	1.44922	0.0744414	0.0372207	−	0.999307i	$-0.488150\pi$
$379$	1.44922	0.0744414	0.0372207	+	0.999307i	$0.488150\pi$
$380$	36.2157	1.85783
$381$	−6.86580	−0.351746
$382$	−0.349071	−0.0178601
$383$	−15.3908	−0.786432	−0.393216	−	0.919446i	$-0.628638\pi$
$383$	−15.3908	−0.786432	−0.393216	+	0.919446i	$0.628638\pi$
$384$	−11.3401	−0.578699
$385$	−11.2003	−0.570822
$386$	−4.15536	−0.211502
$387$	2.25024	0.114386
$388$	−10.2884	−0.522312
$389$	−28.3777	−1.43881	−0.719404	−	0.694592i	$-0.755585\pi$
$389$	−28.3777	−1.43881	−0.719404	+	0.694592i	$0.755585\pi$
$390$	8.47729	0.429264
$391$	−4.05074	−0.204855
$392$	−11.8529	−0.598662
$393$	8.05414	0.406278
$394$	10.4391	0.525914
$395$	3.92669	0.197573
$396$	−6.31904	−0.317544
$397$	−9.06834	−0.455127	−0.227564	−	0.973763i	$-0.573076\pi$
$397$	−9.06834	−0.455127	−0.227564	+	0.973763i	$0.573076\pi$
$398$	−11.1722	−0.560011
$399$	−4.16316	−0.208419
$400$	26.9623	1.34812
$401$	−23.3030	−1.16369	−0.581847	−	0.813298i	$-0.697670\pi$
$401$	−23.3030	−1.16369	−0.581847	+	0.813298i	$0.697670\pi$
$402$	3.72934	0.186003
$403$	14.2638	0.710530
$404$	−30.4177	−1.51334
$405$	−3.92669	−0.195119
$406$	0.934490	0.0463780
$407$	−29.8541	−1.47981
$408$	−1.85994	−0.0920809
$409$	−32.5065	−1.60734	−0.803671	−	0.595074i	$-0.797123\pi$
$409$	−32.5065	−1.60734	−0.803671	+	0.595074i	$0.797123\pi$
$410$	11.1935	0.552806
$411$	19.6064	0.967112
$412$	9.99072	0.492208
$413$	−9.46642	−0.465812
$414$	2.00664	0.0986212
$415$	−33.0335	−1.62155
$416$	21.7984	1.06875
$417$	−16.2142	−0.794013
$418$	−9.37778	−0.458682
$419$	−1.02269	−0.0499618	−0.0249809	−	0.999688i	$-0.507953\pi$
$419$	−1.02269	−0.0499618	−0.0249809	+	0.999688i	$0.507953\pi$
$420$	−5.45679	−0.266264
$421$	15.8912	0.774491	0.387246	−	0.921977i	$-0.373427\pi$
$421$	15.8912	0.774491	0.387246	+	0.921977i	$0.373427\pi$
$422$	1.97371	0.0960786
$423$	−12.5423	−0.609827
$424$	−17.0220	−0.826660
$425$	10.4189	0.505391
$426$	4.37685	0.212059
$427$	4.25411	0.205871
$428$	−18.7146	−0.904604
$429$	15.6952	0.757772
$430$	4.37716	0.211085
$431$	26.7563	1.28880	0.644402	−	0.764687i	$-0.277107\pi$
$431$	26.7563	1.28880	0.644402	+	0.764687i	$0.277107\pi$
$432$	−2.58783	−0.124507
$433$	−8.32382	−0.400017	−0.200009	−	0.979794i	$-0.564097\pi$
$433$	−8.32382	−0.400017	−0.200009	+	0.979794i	$0.564097\pi$
$434$	1.28413	0.0616401
$435$	−9.35263	−0.448424
$436$	−22.0993	−1.05837
$437$	−21.2925	−1.01856
$438$	−4.35196	−0.207945
$439$	−30.2260	−1.44261	−0.721303	−	0.692619i	$-0.756457\pi$
$439$	−30.2260	−1.44261	−0.721303	+	0.692619i	$0.756457\pi$
$440$	−26.3026	−1.25393
$441$	−6.37272	−0.303463
$442$	2.15889	0.102688
$443$	18.7955	0.893001	0.446500	−	0.894783i	$-0.352670\pi$
$443$	18.7955	0.893001	0.446500	+	0.894783i	$0.352670\pi$
$444$	−14.5449	−0.690269
$445$	−33.7075	−1.59789
$446$	14.6992	0.696030
$447$	20.2760	0.959023
$448$	−2.13674	−0.100951
$449$	35.1265	1.65772	0.828861	−	0.559455i	$-0.188990\pi$
$449$	35.1265	1.65772	0.828861	+	0.559455i	$0.188990\pi$
$450$	−5.16128	−0.243305
$451$	20.7240	0.975857
$452$	36.1412	1.69994
$453$	13.3506	0.627266
$454$	13.1811	0.618621
$455$	13.5536	0.635400
$456$	−9.77668	−0.457835
$457$	11.7903	0.551526	0.275763	−	0.961226i	$-0.411069\pi$
$457$	11.7903	0.551526	0.275763	+	0.961226i	$0.411069\pi$
$458$	−10.3599	−0.484086
$459$	−1.00000	−0.0466760
$460$	−27.9087	−1.30125
$461$	−7.13431	−0.332278	−0.166139	−	0.986102i	$-0.553130\pi$
$461$	−7.13431	−0.332278	−0.166139	+	0.986102i	$0.553130\pi$
$462$	1.41299	0.0657384
$463$	36.5804	1.70003	0.850017	−	0.526755i	$-0.176591\pi$
$463$	36.5804	1.70003	0.850017	+	0.526755i	$0.176591\pi$
$464$	−6.16372	−0.286143
$465$	−12.8519	−0.595992
$466$	−1.54261	−0.0714600
$467$	26.5379	1.22803	0.614014	−	0.789295i	$-0.289554\pi$
$467$	26.5379	1.22803	0.614014	+	0.789295i	$0.289554\pi$
$468$	7.64668	0.353468
$469$	5.96249	0.275322
$470$	−24.3972	−1.12536
$471$	−6.98952	−0.322060
$472$	−22.2307	−1.02325
$473$	8.10405	0.372625
$474$	−0.495377	−0.0227534
$475$	54.7663	2.51285
$476$	−1.38967	−0.0636952
$477$	−9.15188	−0.419036
$478$	−0.641316	−0.0293331
$479$	11.7997	0.539142	0.269571	−	0.962981i	$-0.413118\pi$
$479$	11.7997	0.539142	0.269571	+	0.962981i	$0.413118\pi$
$480$	−19.6407	−0.896470
$481$	36.1265	1.64723
$482$	−12.1234	−0.552206
$483$	3.20824	0.145980
$484$	−3.45684	−0.157129
$485$	−23.0247	−1.04550
$486$	0.495377	0.0224708
$487$	−1.77231	−0.0803109	−0.0401554	−	0.999193i	$-0.512785\pi$
$487$	−1.77231	−0.0803109	−0.0401554	+	0.999193i	$0.512785\pi$
$488$	9.99025	0.452237
$489$	14.4956	0.655513
$490$	−12.3962	−0.560002
$491$	−18.3073	−0.826198	−0.413099	−	0.910686i	$-0.635554\pi$
$491$	−18.3073	−0.826198	−0.413099	+	0.910686i	$0.635554\pi$
$492$	10.0967	0.455195
$493$	−2.38181	−0.107271
$494$	11.3481	0.510574
$495$	−14.1416	−0.635619
$496$	−8.46986	−0.380308
$497$	6.99774	0.313892
$498$	4.16739	0.186745
$499$	−13.6566	−0.611356	−0.305678	−	0.952135i	$-0.598883\pi$
$499$	−13.6566	−0.611356	−0.305678	+	0.952135i	$0.598883\pi$
$500$	37.3350	1.66967
$501$	5.23555	0.233907
$502$	2.23918	0.0999396
$503$	26.0719	1.16249	0.581244	−	0.813729i	$-0.302566\pi$
$503$	26.0719	1.16249	0.581244	+	0.813729i	$0.302566\pi$
$504$	1.47310	0.0656170
$505$	−68.0729	−3.02920
$506$	7.22675	0.321268
$507$	−5.99281	−0.266150
$508$	−12.0467	−0.534488
$509$	12.5753	0.557392	0.278696	−	0.960379i	$-0.410098\pi$
$509$	12.5753	0.557392	0.278696	+	0.960379i	$0.410098\pi$
$510$	−1.94519	−0.0861346
$511$	−6.95795	−0.307801
$512$	−22.5703	−0.997478
$513$	−5.25644	−0.232077
$514$	−13.4179	−0.591839
$515$	22.3586	0.985239
$516$	3.94828	0.173813
$517$	−45.1699	−1.98657
$518$	3.25236	0.142901
$519$	−13.6838	−0.600650
$520$	31.8289	1.39579
$521$	−18.1821	−0.796571	−0.398286	−	0.917261i	$-0.630395\pi$
$521$	−18.1821	−0.796571	−0.398286	+	0.917261i	$0.630395\pi$
$522$	1.17989	0.0516425
$523$	−14.8318	−0.648547	−0.324274	−	0.945963i	$-0.605120\pi$
$523$	−14.8318	−0.648547	−0.324274	+	0.945963i	$0.605120\pi$
$524$	14.1318	0.617351
$525$	−8.25189	−0.360142
$526$	8.30097	0.361940
$527$	−3.27296	−0.142572
$528$	−9.31984	−0.405594
$529$	−6.59150	−0.286587
$530$	−17.8022	−0.773277
$531$	−11.9524	−0.518689
$532$	−7.30469	−0.316698
$533$	−25.0782	−1.08626
$534$	4.25242	0.184020
$535$	−41.8821	−1.81072
$536$	14.0022	0.604802
$537$	14.9123	0.643513
$538$	−6.63560	−0.286081
$539$	−22.9508	−0.988560
$540$	−6.88978	−0.296489
$541$	26.4803	1.13848	0.569238	−	0.822173i	$-0.307238\pi$
$541$	26.4803	1.13848	0.569238	+	0.822173i	$0.307238\pi$
$542$	−10.2348	−0.439623
$543$	−19.2519	−0.826179
$544$	−5.00184	−0.214452
$545$	−49.4569	−2.11850
$546$	−1.70987	−0.0731755
$547$	26.7236	1.14262	0.571310	−	0.820734i	$-0.306435\pi$
$547$	26.7236	1.14262	0.571310	+	0.820734i	$0.306435\pi$
$548$	34.4014	1.46956
$549$	5.37127	0.229240
$550$	−18.5879	−0.792591
$551$	−12.5198	−0.533363
$552$	7.53415	0.320675
$553$	−0.792012	−0.0336798
$554$	−7.70703	−0.327440
$555$	−32.5505	−1.38169
$556$	−28.4495	−1.20653
$557$	−22.9463	−0.972267	−0.486133	−	0.873885i	$-0.661593\pi$
$557$	−22.9463	−0.972267	−0.486133	+	0.873885i	$0.661593\pi$
$558$	1.62135	0.0686372
$559$	−9.80673	−0.414781
$560$	−8.04811	−0.340095
$561$	−3.60141	−0.152052
$562$	−1.69802	−0.0716268
$563$	40.0035	1.68595	0.842973	−	0.537956i	$-0.180803\pi$
$563$	40.0035	1.68595	0.842973	+	0.537956i	$0.180803\pi$
$564$	−22.0067	−0.926650
$565$	80.8817	3.40272
$566$	−2.47593	−0.104071
$567$	0.792012	0.0332614
$568$	16.4333	0.689528
$569$	−19.0081	−0.796863	−0.398431	−	0.917198i	$-0.630445\pi$
$569$	−19.0081	−0.796863	−0.398431	+	0.917198i	$0.630445\pi$
$570$	−10.2248	−0.428269
$571$	23.6266	0.988742	0.494371	−	0.869251i	$-0.335398\pi$
$571$	23.6266	0.988742	0.494371	+	0.869251i	$0.335398\pi$
$572$	27.5388	1.15146
$573$	−0.704658	−0.0294375
$574$	−2.25772	−0.0942353
$575$	−42.2043	−1.76004
$576$	−2.69786	−0.112411
$577$	19.3914	0.807273	0.403637	−	0.914919i	$-0.367746\pi$
$577$	19.3914	0.807273	0.403637	+	0.914919i	$0.367746\pi$
$578$	−0.495377	−0.0206050
$579$	−8.38827	−0.348604
$580$	−16.4101	−0.681394
$581$	6.66284	0.276421
$582$	2.90472	0.120404
$583$	−32.9597	−1.36505
$584$	−16.3399	−0.676149
$585$	17.1128	0.707528
$586$	−14.4050	−0.595064
$587$	19.2357	0.793942	0.396971	−	0.917831i	$-0.370061\pi$
$587$	19.2357	0.793942	0.396971	+	0.917831i	$0.370061\pi$
$588$	−11.1816	−0.461121
$589$	−17.2041	−0.708883
$590$	−23.2497	−0.957174
$591$	21.0730	0.866829
$592$	−21.4520	−0.881671
$593$	3.61238	0.148343	0.0741714	−	0.997246i	$-0.476369\pi$
$593$	3.61238	0.148343	0.0741714	+	0.997246i	$0.476369\pi$
$594$	1.78406	0.0732007
$595$	−3.10999	−0.127497
$596$	35.5763	1.45726
$597$	−22.5529	−0.923028
$598$	−8.74511	−0.357614
$599$	17.9370	0.732886	0.366443	−	0.930441i	$-0.380576\pi$
$599$	17.9370	0.732886	0.366443	+	0.930441i	$0.380576\pi$
$600$	−19.3786	−0.791127
$601$	−1.01370	−0.0413498	−0.0206749	−	0.999786i	$-0.506581\pi$
$601$	−1.01370	−0.0413498	−0.0206749	+	0.999786i	$0.506581\pi$
$602$	−0.882871	−0.0359831
$603$	7.52829	0.306576
$604$	23.4250	0.953149
$605$	−7.73619	−0.314521
$606$	8.58783	0.348857
$607$	−17.8098	−0.722877	−0.361438	−	0.932396i	$-0.617714\pi$
$607$	−17.8098	−0.722877	−0.361438	+	0.932396i	$0.617714\pi$
$608$	−26.2919	−1.06628
$609$	1.88642	0.0764416
$610$	10.4481	0.423033
$611$	54.6602	2.21132
$612$	−1.75460	−0.0709256
$613$	43.1244	1.74178	0.870890	−	0.491479i	$-0.163543\pi$
$613$	43.1244	1.74178	0.870890	+	0.491479i	$0.163543\pi$
$614$	−11.7025	−0.472275
$615$	22.5958	0.911153
$616$	5.30523	0.213754
$617$	41.9429	1.68856	0.844279	−	0.535904i	$-0.180029\pi$
$617$	41.9429	1.68856	0.844279	+	0.535904i	$0.180029\pi$
$618$	−2.82068	−0.113465
$619$	12.8511	0.516531	0.258265	−	0.966074i	$-0.416849\pi$
$619$	12.8511	0.516531	0.258265	+	0.966074i	$0.416849\pi$
$620$	−22.5500	−0.905628
$621$	4.05074	0.162551
$622$	−6.65664	−0.266907
$623$	6.79880	0.272388
$624$	11.2780	0.451480
$625$	31.4590	1.25836
$626$	−11.6432	−0.465356
$627$	−18.9306	−0.756015
$628$	−12.2638	−0.489380
$629$	−8.28956	−0.330526
$630$	1.54062	0.0613796
$631$	−9.62468	−0.383152	−0.191576	−	0.981478i	$-0.561360\pi$
$631$	−9.62468	−0.383152	−0.191576	+	0.981478i	$0.561360\pi$
$632$	−1.85994	−0.0739846
$633$	3.98425	0.158360
$634$	−6.29152	−0.249868
$635$	−26.9599	−1.06987
$636$	−16.0579	−0.636737
$637$	27.7728	1.10040
$638$	4.24928	0.168231
$639$	8.83540	0.349523
$640$	−44.5292	−1.76017
$641$	17.7457	0.700912	0.350456	−	0.936579i	$-0.386027\pi$
$641$	17.7457	0.700912	0.350456	+	0.936579i	$0.386027\pi$
$642$	5.28370	0.208531
$643$	39.9832	1.57678	0.788391	−	0.615175i	$-0.210915\pi$
$643$	39.9832	1.57678	0.788391	+	0.615175i	$0.210915\pi$
$644$	5.62917	0.221821
$645$	8.83601	0.347918
$646$	−2.60392	−0.102450
$647$	25.2225	0.991598	0.495799	−	0.868437i	$-0.334875\pi$
$647$	25.2225	0.991598	0.495799	+	0.868437i	$0.334875\pi$
$648$	1.85994	0.0730655
$649$	−43.0454	−1.68968
$650$	22.4933	0.882258
$651$	2.59222	0.101597
$652$	25.4340	0.996071
$653$	−42.7676	−1.67363	−0.836814	−	0.547488i	$-0.815584\pi$
$653$	−42.7676	−1.67363	−0.836814	+	0.547488i	$0.815584\pi$
$654$	6.23930	0.243976
$655$	31.6261	1.23573
$656$	14.8915	0.581414
$657$	−8.78515	−0.342741
$658$	4.92090	0.191837
$659$	17.1039	0.666274	0.333137	−	0.942878i	$-0.391893\pi$
$659$	17.1039	0.666274	0.333137	+	0.942878i	$0.391893\pi$
$660$	−24.8129	−0.965841
$661$	−11.1344	−0.433079	−0.216540	−	0.976274i	$-0.569477\pi$
$661$	−11.1344	−0.433079	−0.216540	+	0.976274i	$0.569477\pi$
$662$	1.83256	0.0712244
$663$	4.35807	0.169254
$664$	15.6469	0.607217
$665$	−16.3474	−0.633927
$666$	4.10646	0.159122
$667$	9.64809	0.373576
$668$	9.18630	0.355429
$669$	29.6728	1.14722
$670$	14.6440	0.565746
$671$	19.3441	0.746772
$672$	3.96152	0.152819
$673$	18.1149	0.698280	0.349140	−	0.937071i	$-0.386474\pi$
$673$	18.1149	0.698280	0.349140	+	0.937071i	$0.386474\pi$
$674$	−1.77730	−0.0684590
$675$	−10.4189	−0.401024
$676$	−10.5150	−0.404423
$677$	−24.6404	−0.947007	−0.473503	−	0.880792i	$-0.657011\pi$
$677$	−24.6404	−0.947007	−0.473503	+	0.880792i	$0.657011\pi$
$678$	−10.2037	−0.391872
$679$	4.64408	0.178223
$680$	−7.30342	−0.280073
$681$	26.6083	1.01963
$682$	5.83914	0.223592
$683$	−36.0127	−1.37799	−0.688994	−	0.724767i	$-0.741947\pi$
$683$	−36.0127	−1.37799	−0.688994	+	0.724767i	$0.741947\pi$
$684$	−9.22295	−0.352648
$685$	76.9882	2.94157
$686$	5.24671	0.200320
$687$	−20.9131	−0.797886
$688$	5.82325	0.222009
$689$	39.8846	1.51948
$690$	7.87947	0.299966
$691$	32.6885	1.24353	0.621764	−	0.783205i	$-0.286416\pi$
$691$	32.6885	1.24353	0.621764	+	0.783205i	$0.286416\pi$
$692$	−24.0095	−0.912706
$693$	2.85236	0.108352
$694$	−0.688719	−0.0261434
$695$	−63.6681	−2.41507
$696$	4.43003	0.167920
$697$	5.75442	0.217964
$698$	−8.85390	−0.335125
$699$	−3.11401	−0.117783
$700$	−14.4788	−0.547247
$701$	−30.8554	−1.16539	−0.582696	−	0.812690i	$-0.698002\pi$
$701$	−30.8554	−1.16539	−0.582696	+	0.812690i	$0.698002\pi$
$702$	−2.15889	−0.0814821
$703$	−43.5736	−1.64341
$704$	−9.71611	−0.366190
$705$	−49.2497	−1.85485
$706$	−7.37998	−0.277749
$707$	13.7303	0.516380
$708$	−20.9717	−0.788163
$709$	0.552903	0.0207647	0.0103823	−	0.999946i	$-0.496695\pi$
$709$	0.552903	0.0207647	0.0103823	+	0.999946i	$0.496695\pi$
$710$	17.1865	0.645000
$711$	−1.00000	−0.0375029
$712$	15.9661	0.598357
$713$	13.2579	0.496513
$714$	0.392345	0.0146831
$715$	61.6303	2.30484
$716$	26.1651	0.977837
$717$	−1.29460	−0.0483478
$718$	16.4170	0.612676
$719$	−21.2962	−0.794214	−0.397107	−	0.917772i	$-0.629986\pi$
$719$	−21.2962	−0.794214	−0.397107	+	0.917772i	$0.629986\pi$
$720$	−10.1616	−0.378701
$721$	−4.50973	−0.167951
$722$	−4.27517	−0.159105
$723$	−24.4731	−0.910163
$724$	−33.7794	−1.25540
$725$	−24.8158	−0.921637
$726$	0.975970	0.0362216
$727$	−35.5209	−1.31740	−0.658698	−	0.752408i	$-0.728892\pi$
$727$	−35.5209	−1.31740	−0.658698	+	0.752408i	$0.728892\pi$
$728$	−6.41987	−0.237936
$729$	1.00000	0.0370370
$730$	−17.0888	−0.632485
$731$	2.25024	0.0832283
$732$	9.42443	0.348337
$733$	17.5317	0.647550	0.323775	−	0.946134i	$-0.395048\pi$
$733$	17.5317	0.647550	0.323775	+	0.946134i	$0.395048\pi$
$734$	8.04644	0.296999
$735$	−25.0237	−0.923013
$736$	20.2612	0.746836
$737$	27.1124	0.998700
$738$	−2.85061	−0.104932
$739$	28.7687	1.05827	0.529137	−	0.848536i	$-0.322516\pi$
$739$	28.7687	1.05827	0.529137	+	0.848536i	$0.322516\pi$
$740$	−57.1132	−2.09952
$741$	22.9079	0.841544
$742$	3.59069	0.131818
$743$	−38.6159	−1.41668	−0.708340	−	0.705871i	$-0.750556\pi$
$743$	−38.6159	−1.41668	−0.708340	+	0.705871i	$0.750556\pi$
$744$	6.08752	0.223179
$745$	79.6177	2.91697
$746$	−8.00009	−0.292904
$747$	8.41255	0.307799
$748$	−6.31904	−0.231047
$749$	8.44761	0.308669
$750$	−10.5408	−0.384896
$751$	−5.76962	−0.210537	−0.105268	−	0.994444i	$-0.533570\pi$
$751$	−5.76962	−0.210537	−0.105268	+	0.994444i	$0.533570\pi$
$752$	−32.4573	−1.18360
$753$	4.52016	0.164724
$754$	−5.14206	−0.187263
$755$	52.4237	1.90789
$756$	1.38967	0.0505416
$757$	13.4890	0.490267	0.245133	−	0.969489i	$-0.421168\pi$
$757$	13.4890	0.490267	0.245133	+	0.969489i	$0.421168\pi$
$758$	−0.717910	−0.0260757
$759$	14.5884	0.529525
$760$	−38.3900	−1.39255
$761$	−18.3884	−0.666577	−0.333289	−	0.942825i	$-0.608158\pi$
$761$	−18.3884	−0.666577	−0.333289	+	0.942825i	$0.608158\pi$
$762$	3.40116	0.123211
$763$	9.97544	0.361135
$764$	−1.23639	−0.0447312
$765$	−3.92669	−0.141970
$766$	7.62424	0.275475
$767$	52.0893	1.88084
$768$	0.221918	0.00800776
$769$	−29.2070	−1.05323	−0.526615	−	0.850104i	$-0.676539\pi$
$769$	−29.2070	−1.05323	−0.526615	+	0.850104i	$0.676539\pi$
$770$	5.54839	0.199950
$771$	−27.0863	−0.975487
$772$	−14.7181	−0.529715
$773$	13.4818	0.484907	0.242454	−	0.970163i	$-0.422048\pi$
$773$	13.4818	0.484907	0.242454	+	0.970163i	$0.422048\pi$
$774$	−1.11472	−0.0400678
$775$	−34.1006	−1.22493
$776$	10.9061	0.391504
$777$	6.56543	0.235534
$778$	14.0577	0.503992
$779$	30.2478	1.08374
$780$	30.0262	1.07511
$781$	31.8199	1.13861
$782$	2.00664	0.0717575
$783$	2.38181	0.0851189
$784$	−16.4915	−0.588982
$785$	−27.4457	−0.979578
$786$	−3.98984	−0.142313
$787$	29.1255	1.03821	0.519107	−	0.854709i	$-0.326265\pi$
$787$	29.1255	1.03821	0.519107	+	0.854709i	$0.326265\pi$
$788$	36.9748	1.31717
$789$	16.7569	0.596561
$790$	−1.94519	−0.0692068
$791$	−16.3138	−0.580052
$792$	6.69842	0.238018
$793$	−23.4084	−0.831256
$794$	4.49225	0.159424
$795$	−35.9366	−1.27454
$796$	−39.5713	−1.40257
$797$	50.5438	1.79035	0.895176	−	0.445713i	$-0.147050\pi$
$797$	50.5438	1.79035	0.895176	+	0.445713i	$0.147050\pi$
$798$	2.06233	0.0730059
$799$	−12.5423	−0.443714
$800$	−52.1137	−1.84250
$801$	8.58421	0.303308
$802$	11.5438	0.407624
$803$	−31.6389	−1.11651
$804$	13.2091	0.465851
$805$	12.5977	0.444012
$806$	−7.06596	−0.248888
$807$	−13.3950	−0.471528
$808$	32.2439	1.13434
$809$	−26.5517	−0.933509	−0.466755	−	0.884387i	$-0.654577\pi$
$809$	−26.5517	−0.933509	−0.466755	+	0.884387i	$0.654577\pi$
$810$	1.94519	0.0683471
$811$	5.23369	0.183780	0.0918898	−	0.995769i	$-0.470709\pi$
$811$	5.23369	0.183780	0.0918898	+	0.995769i	$0.470709\pi$
$812$	3.30992	0.116155
$813$	−20.6607	−0.724601
$814$	14.7890	0.518356
$815$	56.9196	1.99381
$816$	−2.58783	−0.0905922
$817$	11.8283	0.413819
$818$	16.1030	0.563027
$819$	−3.45165	−0.120610
$820$	39.6467	1.38452
$821$	5.58871	0.195047	0.0975237	−	0.995233i	$-0.468908\pi$
$821$	5.58871	0.195047	0.0975237	+	0.995233i	$0.468908\pi$
$822$	−9.71256	−0.338764
$823$	17.8202	0.621171	0.310586	−	0.950545i	$-0.399475\pi$
$823$	17.8202	0.621171	0.310586	+	0.950545i	$0.399475\pi$
$824$	−10.5905	−0.368939
$825$	−37.5227	−1.30637
$826$	4.68945	0.163167
$827$	41.1804	1.43198	0.715991	−	0.698110i	$-0.245975\pi$
$827$	41.1804	1.43198	0.715991	+	0.698110i	$0.245975\pi$
$828$	7.10744	0.247000
$829$	−44.2796	−1.53789	−0.768947	−	0.639312i	$-0.779219\pi$
$829$	−44.2796	−1.53789	−0.768947	+	0.639312i	$0.779219\pi$
$830$	16.3640	0.568004
$831$	−15.5579	−0.539698
$832$	11.7575	0.407618
$833$	−6.37272	−0.220802
$834$	8.03214	0.278130
$835$	20.5584	0.711452
$836$	−33.2156	−1.14879
$837$	3.27296	0.113130
$838$	0.506619	0.0175009
$839$	−8.39870	−0.289955	−0.144978	−	0.989435i	$-0.546311\pi$
$839$	−8.39870	−0.289955	−0.144978	+	0.989435i	$0.546311\pi$
$840$	5.78440	0.199581
$841$	−23.3270	−0.804379
$842$	−7.87215	−0.271292
$843$	−3.42774	−0.118058
$844$	6.99078	0.240633
$845$	−23.5319	−0.809523
$846$	6.21316	0.213613
$847$	1.56039	0.0536155
$848$	−23.6835	−0.813295
$849$	−4.99808	−0.171534
$850$	−5.16128	−0.177031
$851$	33.5789	1.15107
$852$	15.5026	0.531110
$853$	40.8685	1.39931	0.699656	−	0.714480i	$-0.253337\pi$
$853$	40.8685	1.39931	0.699656	+	0.714480i	$0.253337\pi$
$854$	−2.10739	−0.0721133
$855$	−20.6404	−0.705887
$856$	19.8382	0.678055
$857$	−47.8137	−1.63329	−0.816643	−	0.577143i	$-0.804167\pi$
$857$	−47.8137	−1.63329	−0.816643	+	0.577143i	$0.804167\pi$
$858$	−7.77505	−0.265436
$859$	−25.9929	−0.886867	−0.443433	−	0.896307i	$-0.646240\pi$
$859$	−25.9929	−0.886867	−0.443433	+	0.896307i	$0.646240\pi$
$860$	15.5037	0.528671
$861$	−4.55757	−0.155322
$862$	−13.2544	−0.451448
$863$	−16.0387	−0.545965	−0.272982	−	0.962019i	$-0.588010\pi$
$863$	−16.0387	−0.545965	−0.272982	+	0.962019i	$0.588010\pi$
$864$	5.00184	0.170166
$865$	−53.7319	−1.82694
$866$	4.12343	0.140120
$867$	−1.00000	−0.0339618
$868$	4.54832	0.154380
$869$	−3.60141	−0.122169
$870$	4.63308	0.157076
$871$	−32.8088	−1.11168
$872$	23.4261	0.793308
$873$	5.86365	0.198454
$874$	10.5478	0.356785
$875$	−16.8527	−0.569725
$876$	−15.4144	−0.520806
$877$	7.11057	0.240107	0.120054	−	0.992767i	$-0.461693\pi$
$877$	7.11057	0.240107	0.120054	+	0.992767i	$0.461693\pi$
$878$	14.9732	0.505323
$879$	−29.0788	−0.980804
$880$	−36.5961	−1.23365
$881$	40.6863	1.37076	0.685378	−	0.728188i	$-0.259637\pi$
$881$	40.6863	1.37076	0.685378	+	0.728188i	$0.259637\pi$
$882$	3.15690	0.106298
$883$	−27.2209	−0.916055	−0.458027	−	0.888938i	$-0.651444\pi$
$883$	−27.2209	−0.916055	−0.458027	+	0.888938i	$0.651444\pi$
$884$	7.64668	0.257186
$885$	−46.9333	−1.57764
$886$	−9.31086	−0.312804
$887$	32.7743	1.10045	0.550227	−	0.835015i	$-0.314541\pi$
$887$	32.7743	1.10045	0.550227	+	0.835015i	$0.314541\pi$
$888$	15.4181	0.517398
$889$	5.43779	0.182378
$890$	16.6979	0.559716
$891$	3.60141	0.120652
$892$	52.0640	1.74323
$893$	−65.9277	−2.20619
$894$	−10.0443	−0.335931
$895$	58.5560	1.95731
$896$	8.98152	0.300052
$897$	−17.6534	−0.589431
$898$	−17.4009	−0.580674
$899$	7.79556	0.259997
$900$	−18.2810	−0.609367
$901$	−9.15188	−0.304893
$902$	−10.2662	−0.341828
$903$	−1.78222	−0.0593086
$904$	−38.3110	−1.27420
$905$	−75.5963	−2.51291
$906$	−6.61358	−0.219721
$907$	−25.2980	−0.840007	−0.420003	−	0.907523i	$-0.637971\pi$
$907$	−25.2980	−0.840007	−0.420003	+	0.907523i	$0.637971\pi$
$908$	46.6869	1.54936
$909$	17.3359	0.574997
$910$	−6.71412	−0.222571
$911$	43.0898	1.42763	0.713814	−	0.700335i	$-0.246966\pi$
$911$	43.0898	1.42763	0.713814	+	0.700335i	$0.246966\pi$
$912$	−13.6028	−0.450433
$913$	30.2971	1.00269
$914$	−5.84064	−0.193191
$915$	21.0913	0.697257
$916$	−36.6942	−1.21241
$917$	−6.37897	−0.210652
$918$	0.495377	0.0163499
$919$	41.6507	1.37393	0.686965	−	0.726690i	$-0.258942\pi$
$919$	41.6507	1.37393	0.686965	+	0.726690i	$0.258942\pi$
$920$	29.5843	0.975365
$921$	−23.6235	−0.778420
$922$	3.53417	0.116392
$923$	−38.5053	−1.26742
$924$	5.00476	0.164644
$925$	−86.3681	−2.83977
$926$	−18.1211	−0.595496
$927$	−5.69401	−0.187016
$928$	11.9134	0.391077
$929$	−24.1981	−0.793912	−0.396956	−	0.917838i	$-0.629934\pi$
$929$	−24.1981	−0.793912	−0.396956	+	0.917838i	$0.629934\pi$
$930$	6.36653	0.208767
$931$	−33.4978	−1.09785
$932$	−5.46385	−0.178974
$933$	−13.4375	−0.439925
$934$	−13.1463	−0.430159
$935$	−14.1416	−0.462481
$936$	−8.10577	−0.264945
$937$	41.5780	1.35829	0.679146	−	0.734003i	$-0.262350\pi$
$937$	41.5780	1.35829	0.679146	+	0.734003i	$0.262350\pi$
$938$	−2.95368	−0.0964411
$939$	−23.5037	−0.767015
$940$	−86.4135	−2.81850
$941$	−34.4303	−1.12240	−0.561198	−	0.827681i	$-0.689660\pi$
$941$	−34.4303	−1.12240	−0.561198	+	0.827681i	$0.689660\pi$
$942$	3.46245	0.112813
$943$	−23.3097	−0.759068
$944$	−30.9307	−1.00671
$945$	3.10999	0.101168
$946$	−4.01456	−0.130525
$947$	41.0605	1.33429	0.667144	−	0.744929i	$-0.267517\pi$
$947$	41.0605	1.33429	0.667144	+	0.744929i	$0.267517\pi$
$948$	−1.75460	−0.0569868
$949$	38.2864	1.24283
$950$	−27.1300	−0.880213
$951$	−12.7005	−0.411841
$952$	1.47310	0.0477434
$953$	−21.3535	−0.691706	−0.345853	−	0.938289i	$-0.612410\pi$
$953$	−21.3535	−0.691706	−0.345853	+	0.938289i	$0.612410\pi$
$954$	4.53363	0.146782
$955$	−2.76697	−0.0895372
$956$	−2.27151	−0.0734658
$957$	8.57787	0.277283
$958$	−5.84530	−0.188853
$959$	−15.5285	−0.501441
$960$	−10.5937	−0.341909
$961$	−20.2877	−0.654443
$962$	−17.8962	−0.576998
$963$	10.6660	0.343707
$964$	−42.9405	−1.38302
$965$	−32.9381	−1.06032
$966$	−1.58929	−0.0511344
$967$	2.54388	0.0818056	0.0409028	−	0.999163i	$-0.486977\pi$
$967$	2.54388	0.0818056	0.0409028	+	0.999163i	$0.486977\pi$
$968$	3.66438	0.117778
$969$	−5.25644	−0.168861
$970$	11.4059	0.366222
$971$	−4.88648	−0.156815	−0.0784073	−	0.996921i	$-0.524983\pi$
$971$	−4.88648	−0.156815	−0.0784073	+	0.996921i	$0.524983\pi$
$972$	1.75460	0.0562789
$973$	12.8418	0.411690
$974$	0.877960	0.0281317
$975$	45.4063	1.45417
$976$	13.8999	0.444926
$977$	43.4594	1.39039	0.695195	−	0.718821i	$-0.255318\pi$
$977$	43.4594	1.39039	0.695195	+	0.718821i	$0.255318\pi$
$978$	−7.18078	−0.229616
$979$	30.9153	0.988056
$980$	−43.9066	−1.40255
$981$	12.5951	0.402129
$982$	9.06903	0.289404
$983$	16.8858	0.538573	0.269287	−	0.963060i	$-0.413212\pi$
$983$	16.8858	0.538573	0.269287	+	0.963060i	$0.413212\pi$
$984$	−10.7029	−0.341196
$985$	82.7473	2.63655
$986$	1.17989	0.0375755
$987$	9.93364	0.316191
$988$	40.1943	1.27875
$989$	−9.11516	−0.289845
$990$	7.00544	0.222647
$991$	18.3162	0.581835	0.290917	−	0.956748i	$-0.406040\pi$
$991$	18.3162	0.581835	0.290917	+	0.956748i	$0.406040\pi$
$992$	16.3708	0.519774
$993$	3.69932	0.117394
$994$	−3.46652	−0.109951
$995$	−88.5582	−2.80748
$996$	14.7607	0.467710
$997$	−11.4370	−0.362213	−0.181107	−	0.983463i	$-0.557968\pi$
$997$	−11.4370	−0.362213	−0.181107	+	0.983463i	$0.557968\pi$
$998$	6.76519	0.214148
$999$	8.28956	0.262270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.12	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-0.495377 q^{2} -1.00000 q^{3} -1.75460 q^{4} -3.92669 q^{5} +0.495377 q^{6} +0.792012 q^{7} +1.85994 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.495377 q^{2} -1.00000 q^{3} -1.75460 q^{4} -3.92669 q^{5} +0.495377 q^{6} +0.792012 q^{7} +1.85994 q^{8} +1.00000 q^{9} +1.94519 q^{10} +3.60141 q^{11} +1.75460 q^{12} -4.35807 q^{13} -0.392345 q^{14} +3.92669 q^{15} +2.58783 q^{16} +1.00000 q^{17} -0.495377 q^{18} +5.25644 q^{19} +6.88978 q^{20} -0.792012 q^{21} -1.78406 q^{22} -4.05074 q^{23} -1.85994 q^{24} +10.4189 q^{25} +2.15889 q^{26} -1.00000 q^{27} -1.38967 q^{28} -2.38181 q^{29} -1.94519 q^{30} -3.27296 q^{31} -5.00184 q^{32} -3.60141 q^{33} -0.495377 q^{34} -3.10999 q^{35} -1.75460 q^{36} -8.28956 q^{37} -2.60392 q^{38} +4.35807 q^{39} -7.30342 q^{40} +5.75442 q^{41} +0.392345 q^{42} +2.25024 q^{43} -6.31904 q^{44} -3.92669 q^{45} +2.00664 q^{46} -12.5423 q^{47} -2.58783 q^{48} -6.37272 q^{49} -5.16128 q^{50} -1.00000 q^{51} +7.64668 q^{52} -9.15188 q^{53} +0.495377 q^{54} -14.1416 q^{55} +1.47310 q^{56} -5.25644 q^{57} +1.17989 q^{58} -11.9524 q^{59} -6.88978 q^{60} +5.37127 q^{61} +1.62135 q^{62} +0.792012 q^{63} -2.69786 q^{64} +17.1128 q^{65} +1.78406 q^{66} +7.52829 q^{67} -1.75460 q^{68} +4.05074 q^{69} +1.54062 q^{70} +8.83540 q^{71} +1.85994 q^{72} -8.78515 q^{73} +4.10646 q^{74} -10.4189 q^{75} -9.22295 q^{76} +2.85236 q^{77} -2.15889 q^{78} -1.00000 q^{79} -10.1616 q^{80} +1.00000 q^{81} -2.85061 q^{82} +8.41255 q^{83} +1.38967 q^{84} -3.92669 q^{85} -1.11472 q^{86} +2.38181 q^{87} +6.69842 q^{88} +8.58421 q^{89} +1.94519 q^{90} -3.45165 q^{91} +7.10744 q^{92} +3.27296 q^{93} +6.21316 q^{94} -20.6404 q^{95} +5.00184 q^{96} +5.86365 q^{97} +3.15690 q^{98} +3.60141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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