LMFDB - Embedded newform 4029.2.a.j.1.8

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			1.8
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)

$f(q)$	$=$	$q-0.991328 q^{2} +1.00000 q^{3} -1.01727 q^{4} +3.49390 q^{5} -0.991328 q^{6} -2.79439 q^{7} +2.99110 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.991328 q^{2} +1.00000 q^{3} -1.01727 q^{4} +3.49390 q^{5} -0.991328 q^{6} -2.79439 q^{7} +2.99110 q^{8} +1.00000 q^{9} -3.46360 q^{10} +2.06029 q^{11} -1.01727 q^{12} -4.67690 q^{13} +2.77015 q^{14} +3.49390 q^{15} -0.930626 q^{16} -1.00000 q^{17} -0.991328 q^{18} +6.84116 q^{19} -3.55423 q^{20} -2.79439 q^{21} -2.04242 q^{22} -0.328472 q^{23} +2.99110 q^{24} +7.20731 q^{25} +4.63634 q^{26} +1.00000 q^{27} +2.84264 q^{28} -3.28926 q^{29} -3.46360 q^{30} -2.75526 q^{31} -5.05965 q^{32} +2.06029 q^{33} +0.991328 q^{34} -9.76330 q^{35} -1.01727 q^{36} +3.98500 q^{37} -6.78184 q^{38} -4.67690 q^{39} +10.4506 q^{40} +5.45094 q^{41} +2.77015 q^{42} +9.05063 q^{43} -2.09587 q^{44} +3.49390 q^{45} +0.325623 q^{46} -0.439021 q^{47} -0.930626 q^{48} +0.808597 q^{49} -7.14480 q^{50} -1.00000 q^{51} +4.75767 q^{52} +2.45884 q^{53} -0.991328 q^{54} +7.19843 q^{55} -8.35830 q^{56} +6.84116 q^{57} +3.26074 q^{58} -0.718665 q^{59} -3.55423 q^{60} +9.44856 q^{61} +2.73137 q^{62} -2.79439 q^{63} +6.87703 q^{64} -16.3406 q^{65} -2.04242 q^{66} -2.15845 q^{67} +1.01727 q^{68} -0.328472 q^{69} +9.67863 q^{70} -14.5077 q^{71} +2.99110 q^{72} +4.46045 q^{73} -3.95044 q^{74} +7.20731 q^{75} -6.95930 q^{76} -5.75724 q^{77} +4.63634 q^{78} -1.00000 q^{79} -3.25151 q^{80} +1.00000 q^{81} -5.40367 q^{82} +12.7620 q^{83} +2.84264 q^{84} -3.49390 q^{85} -8.97214 q^{86} -3.28926 q^{87} +6.16253 q^{88} +11.2726 q^{89} -3.46360 q^{90} +13.0691 q^{91} +0.334144 q^{92} -2.75526 q^{93} +0.435214 q^{94} +23.9023 q^{95} -5.05965 q^{96} +6.16257 q^{97} -0.801585 q^{98} +2.06029 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * 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 $

$2$	−0.991328	−0.700975	−0.350487	−	0.936567i	$-0.613984\pi$
$2$	−0.991328	−0.700975	−0.350487	+	0.936567i	$0.613984\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.01727	−0.508634
$5$	3.49390	1.56252	0.781259	−	0.624207i	$-0.214578\pi$
$5$	3.49390	1.56252	0.781259	+	0.624207i	$0.214578\pi$
$6$	−0.991328	−0.404708
$7$	−2.79439	−1.05618	−0.528089	−	0.849189i	$-0.677091\pi$
$7$	−2.79439	−1.05618	−0.528089	+	0.849189i	$0.677091\pi$
$8$	2.99110	1.05751
$9$	1.00000	0.333333
$10$	−3.46360	−1.09529
$11$	2.06029	0.621200	0.310600	−	0.950541i	$-0.399470\pi$
$11$	2.06029	0.621200	0.310600	+	0.950541i	$0.399470\pi$
$12$	−1.01727	−0.293660
$13$	−4.67690	−1.29714	−0.648570	−	0.761155i	$-0.724632\pi$
$13$	−4.67690	−1.29714	−0.648570	+	0.761155i	$0.724632\pi$
$14$	2.77015	0.740355
$15$	3.49390	0.902120
$16$	−0.930626	−0.232657
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.991328	−0.233658
$19$	6.84116	1.56947	0.784735	−	0.619831i	$-0.212799\pi$
$19$	6.84116	1.56947	0.784735	+	0.619831i	$0.212799\pi$
$20$	−3.55423	−0.794750
$21$	−2.79439	−0.609785
$22$	−2.04242	−0.435445
$23$	−0.328472	−0.0684911	−0.0342455	−	0.999413i	$-0.510903\pi$
$23$	−0.328472	−0.0684911	−0.0342455	+	0.999413i	$0.510903\pi$
$24$	2.99110	0.610556
$25$	7.20731	1.44146
$26$	4.63634	0.909262
$27$	1.00000	0.192450
$28$	2.84264	0.537209
$29$	−3.28926	−0.610801	−0.305401	−	0.952224i	$-0.598790\pi$
$29$	−3.28926	−0.610801	−0.305401	+	0.952224i	$0.598790\pi$
$30$	−3.46360	−0.632363
$31$	−2.75526	−0.494859	−0.247430	−	0.968906i	$-0.579586\pi$
$31$	−2.75526	−0.494859	−0.247430	+	0.968906i	$0.579586\pi$
$32$	−5.05965	−0.894428
$33$	2.06029	0.358650
$34$	0.991328	0.170011
$35$	−9.76330	−1.65030
$36$	−1.01727	−0.169545
$37$	3.98500	0.655130	0.327565	−	0.944829i	$-0.393772\pi$
$37$	3.98500	0.655130	0.327565	+	0.944829i	$0.393772\pi$
$38$	−6.78184	−1.10016
$39$	−4.67690	−0.748904
$40$	10.4506	1.65239
$41$	5.45094	0.851294	0.425647	−	0.904889i	$-0.360047\pi$
$41$	5.45094	0.851294	0.425647	+	0.904889i	$0.360047\pi$
$42$	2.77015	0.427444
$43$	9.05063	1.38021	0.690104	−	0.723710i	$-0.257565\pi$
$43$	9.05063	1.38021	0.690104	+	0.723710i	$0.257565\pi$
$44$	−2.09587	−0.315964
$45$	3.49390	0.520839
$46$	0.325623	0.0480105
$47$	−0.439021	−0.0640378	−0.0320189	−	0.999487i	$-0.510194\pi$
$47$	−0.439021	−0.0640378	−0.0320189	+	0.999487i	$0.510194\pi$
$48$	−0.930626	−0.134324
$49$	0.808597	0.115514
$50$	−7.14480	−1.01043
$51$	−1.00000	−0.140028
$52$	4.75767	0.659770
$53$	2.45884	0.337748	0.168874	−	0.985638i	$-0.445987\pi$
$53$	2.45884	0.337748	0.168874	+	0.985638i	$0.445987\pi$
$54$	−0.991328	−0.134903
$55$	7.19843	0.970635
$56$	−8.35830	−1.11692
$57$	6.84116	0.906134
$58$	3.26074	0.428156
$59$	−0.718665	−0.0935622	−0.0467811	−	0.998905i	$-0.514896\pi$
$59$	−0.718665	−0.0935622	−0.0467811	+	0.998905i	$0.514896\pi$
$60$	−3.55423	−0.458849
$61$	9.44856	1.20976	0.604882	−	0.796315i	$-0.293220\pi$
$61$	9.44856	1.20976	0.604882	+	0.796315i	$0.293220\pi$
$62$	2.73137	0.346884
$63$	−2.79439	−0.352060
$64$	6.87703	0.859628
$65$	−16.3406	−2.02680
$66$	−2.04242	−0.251404
$67$	−2.15845	−0.263696	−0.131848	−	0.991270i	$-0.542091\pi$
$67$	−2.15845	−0.263696	−0.131848	+	0.991270i	$0.542091\pi$
$68$	1.01727	0.123362
$69$	−0.328472	−0.0395433
$70$	9.67863	1.15682
$71$	−14.5077	−1.72174	−0.860871	−	0.508824i	$-0.830081\pi$
$71$	−14.5077	−1.72174	−0.860871	+	0.508824i	$0.830081\pi$
$72$	2.99110	0.352505
$73$	4.46045	0.522057	0.261028	−	0.965331i	$-0.415938\pi$
$73$	4.46045	0.522057	0.261028	+	0.965331i	$0.415938\pi$
$74$	−3.95044	−0.459229
$75$	7.20731	0.832228
$76$	−6.95930	−0.798287
$77$	−5.75724	−0.656098
$78$	4.63634	0.524962
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−3.25151	−0.363530
$81$	1.00000	0.111111
$82$	−5.40367	−0.596735
$83$	12.7620	1.40081	0.700404	−	0.713746i	$-0.253003\pi$
$83$	12.7620	1.40081	0.700404	+	0.713746i	$0.253003\pi$
$84$	2.84264	0.310158
$85$	−3.49390	−0.378966
$86$	−8.97214	−0.967491
$87$	−3.28926	−0.352646
$88$	6.16253	0.656928
$89$	11.2726	1.19490	0.597449	−	0.801907i	$-0.296181\pi$
$89$	11.2726	1.19490	0.597449	+	0.801907i	$0.296181\pi$
$90$	−3.46360	−0.365095
$91$	13.0691	1.37001
$92$	0.334144	0.0348369
$93$	−2.75526	−0.285707
$94$	0.435214	0.0448889
$95$	23.9023	2.45233
$96$	−5.05965	−0.516398
$97$	6.16257	0.625714	0.312857	−	0.949800i	$-0.398714\pi$
$97$	6.16257	0.625714	0.312857	+	0.949800i	$0.398714\pi$
$98$	−0.801585	−0.0809723
$99$	2.06029	0.207067
$100$	−7.33177	−0.733177
$101$	−2.71522	−0.270174	−0.135087	−	0.990834i	$-0.543131\pi$
$101$	−2.71522	−0.270174	−0.135087	+	0.990834i	$0.543131\pi$
$102$	0.991328	0.0981561
$103$	2.41319	0.237779	0.118889	−	0.992908i	$-0.462067\pi$
$103$	2.41319	0.237779	0.118889	+	0.992908i	$0.462067\pi$
$104$	−13.9891	−1.37174
$105$	−9.76330	−0.952800
$106$	−2.43752	−0.236753
$107$	19.8612	1.92005	0.960026	−	0.279911i	$-0.0903048\pi$
$107$	19.8612	1.92005	0.960026	+	0.279911i	$0.0903048\pi$
$108$	−1.01727	−0.0978867
$109$	−0.394736	−0.0378089	−0.0189044	−	0.999821i	$-0.506018\pi$
$109$	−0.394736	−0.0378089	−0.0189044	+	0.999821i	$0.506018\pi$
$110$	−7.13600	−0.680391
$111$	3.98500	0.378239
$112$	2.60053	0.245727
$113$	5.77373	0.543146	0.271573	−	0.962418i	$-0.412456\pi$
$113$	5.77373	0.543146	0.271573	+	0.962418i	$0.412456\pi$
$114$	−6.78184	−0.635177
$115$	−1.14765	−0.107018
$116$	3.34607	0.310674
$117$	−4.67690	−0.432380
$118$	0.712433	0.0655847
$119$	2.79439	0.256161
$120$	10.4506	0.954005
$121$	−6.75522	−0.614111
$122$	−9.36662	−0.848014
$123$	5.45094	0.491495
$124$	2.80284	0.251702
$125$	7.71210	0.689791
$126$	2.77015	0.246785
$127$	−5.56748	−0.494034	−0.247017	−	0.969011i	$-0.579450\pi$
$127$	−5.56748	−0.494034	−0.247017	+	0.969011i	$0.579450\pi$
$128$	3.30191	0.291851
$129$	9.05063	0.796863
$130$	16.1989	1.42074
$131$	−5.98816	−0.523188	−0.261594	−	0.965178i	$-0.584248\pi$
$131$	−5.98816	−0.523188	−0.261594	+	0.965178i	$0.584248\pi$
$132$	−2.09587	−0.182422
$133$	−19.1169	−1.65764
$134$	2.13973	0.184845
$135$	3.49390	0.300707
$136$	−2.99110	−0.256485
$137$	5.80816	0.496225	0.248113	−	0.968731i	$-0.420190\pi$
$137$	5.80816	0.496225	0.248113	+	0.968731i	$0.420190\pi$
$138$	0.325623	0.0277189
$139$	7.67802	0.651241	0.325621	−	0.945500i	$-0.394427\pi$
$139$	7.67802	0.651241	0.325621	+	0.945500i	$0.394427\pi$
$140$	9.93190	0.839399
$141$	−0.439021	−0.0369723
$142$	14.3818	1.20690
$143$	−9.63576	−0.805782
$144$	−0.930626	−0.0775522
$145$	−11.4923	−0.954388
$146$	−4.42177	−0.365949
$147$	0.808597	0.0666920
$148$	−4.05382	−0.333222
$149$	9.78724	0.801802	0.400901	−	0.916121i	$-0.368697\pi$
$149$	9.78724	0.801802	0.400901	+	0.916121i	$0.368697\pi$
$150$	−7.14480	−0.583371
$151$	20.3598	1.65685	0.828427	−	0.560097i	$-0.189236\pi$
$151$	20.3598	1.65685	0.828427	+	0.560097i	$0.189236\pi$
$152$	20.4626	1.65974
$153$	−1.00000	−0.0808452
$154$	5.70731	0.459908
$155$	−9.62659	−0.773226
$156$	4.75767	0.380918
$157$	−9.17308	−0.732091	−0.366046	−	0.930597i	$-0.619289\pi$
$157$	−9.17308	−0.732091	−0.366046	+	0.930597i	$0.619289\pi$
$158$	0.991328	0.0788658
$159$	2.45884	0.194999
$160$	−17.6779	−1.39756
$161$	0.917877	0.0723388
$162$	−0.991328	−0.0778861
$163$	−18.9443	−1.48383	−0.741917	−	0.670492i	$-0.766083\pi$
$163$	−18.9443	−1.48383	−0.741917	+	0.670492i	$0.766083\pi$
$164$	−5.54507	−0.432997
$165$	7.19843	0.560397
$166$	−12.6513	−0.981932
$167$	−17.1994	−1.33093	−0.665464	−	0.746430i	$-0.731766\pi$
$167$	−17.1994	−1.33093	−0.665464	+	0.746430i	$0.731766\pi$
$168$	−8.35830	−0.644857
$169$	8.87341	0.682570
$170$	3.46360	0.265646
$171$	6.84116	0.523157
$172$	−9.20692	−0.702021
$173$	−22.6231	−1.72001	−0.860003	−	0.510289i	$-0.829539\pi$
$173$	−22.6231	−1.72001	−0.860003	+	0.510289i	$0.829539\pi$
$174$	3.26074	0.247196
$175$	−20.1400	−1.52244
$176$	−1.91736	−0.144526
$177$	−0.718665	−0.0540182
$178$	−11.1749	−0.837593
$179$	9.74334	0.728251	0.364126	−	0.931350i	$-0.381368\pi$
$179$	9.74334	0.728251	0.364126	+	0.931350i	$0.381368\pi$
$180$	−3.55423	−0.264917
$181$	4.70316	0.349583	0.174792	−	0.984605i	$-0.444075\pi$
$181$	4.70316	0.349583	0.174792	+	0.984605i	$0.444075\pi$
$182$	−12.9557	−0.960343
$183$	9.44856	0.698458
$184$	−0.982492	−0.0724303
$185$	13.9232	1.02365
$186$	2.73137	0.200273
$187$	−2.06029	−0.150663
$188$	0.446603	0.0325719
$189$	−2.79439	−0.203262
$190$	−23.6950	−1.71902
$191$	1.11126	0.0804079	0.0402039	−	0.999191i	$-0.487199\pi$
$191$	1.11126	0.0804079	0.0402039	+	0.999191i	$0.487199\pi$
$192$	6.87703	0.496307
$193$	13.3537	0.961221	0.480610	−	0.876934i	$-0.340415\pi$
$193$	13.3537	0.961221	0.480610	+	0.876934i	$0.340415\pi$
$194$	−6.10912	−0.438610
$195$	−16.3406	−1.17018
$196$	−0.822561	−0.0587543
$197$	−11.9207	−0.849316	−0.424658	−	0.905354i	$-0.639606\pi$
$197$	−11.9207	−0.849316	−0.424658	+	0.905354i	$0.639606\pi$
$198$	−2.04242	−0.145148
$199$	10.0598	0.713118	0.356559	−	0.934273i	$-0.383950\pi$
$199$	10.0598	0.713118	0.356559	+	0.934273i	$0.383950\pi$
$200$	21.5578	1.52437
$201$	−2.15845	−0.152245
$202$	2.69167	0.189385
$203$	9.19148	0.645115
$204$	1.01727	0.0712231
$205$	19.0450	1.33016
$206$	−2.39226	−0.166677
$207$	−0.328472	−0.0228304
$208$	4.35245	0.301788
$209$	14.0948	0.974955
$210$	9.67863	0.667889
$211$	−3.92218	−0.270014	−0.135007	−	0.990845i	$-0.543106\pi$
$211$	−3.92218	−0.270014	−0.135007	+	0.990845i	$0.543106\pi$
$212$	−2.50131	−0.171790
$213$	−14.5077	−0.994048
$214$	−19.6889	−1.34591
$215$	31.6220	2.15660
$216$	2.99110	0.203519
$217$	7.69926	0.522660
$218$	0.391313	0.0265031
$219$	4.46045	0.301410
$220$	−7.32273	−0.493699
$221$	4.67690	0.314602
$222$	−3.95044	−0.265136
$223$	−0.888526	−0.0595001	−0.0297501	−	0.999557i	$-0.509471\pi$
$223$	−0.888526	−0.0595001	−0.0297501	+	0.999557i	$0.509471\pi$
$224$	14.1386	0.944676
$225$	7.20731	0.480487
$226$	−5.72366	−0.380732
$227$	9.97312	0.661939	0.330970	−	0.943641i	$-0.392624\pi$
$227$	9.97312	0.661939	0.330970	+	0.943641i	$0.392624\pi$
$228$	−6.95930	−0.460891
$229$	19.8364	1.31083	0.655413	−	0.755271i	$-0.272495\pi$
$229$	19.8364	1.31083	0.655413	+	0.755271i	$0.272495\pi$
$230$	1.13769	0.0750173
$231$	−5.75724	−0.378798
$232$	−9.83853	−0.645931
$233$	−9.97366	−0.653396	−0.326698	−	0.945129i	$-0.605936\pi$
$233$	−9.97366	−0.653396	−0.326698	+	0.945129i	$0.605936\pi$
$234$	4.63634	0.303087
$235$	−1.53389	−0.100060
$236$	0.731076	0.0475890
$237$	−1.00000	−0.0649570
$238$	−2.77015	−0.179562
$239$	−2.92719	−0.189344	−0.0946721	−	0.995509i	$-0.530180\pi$
$239$	−2.92719	−0.189344	−0.0946721	+	0.995509i	$0.530180\pi$
$240$	−3.25151	−0.209884
$241$	10.9297	0.704045	0.352022	−	0.935992i	$-0.385494\pi$
$241$	10.9297	0.704045	0.352022	+	0.935992i	$0.385494\pi$
$242$	6.69664	0.430476
$243$	1.00000	0.0641500
$244$	−9.61173	−0.615328
$245$	2.82515	0.180492
$246$	−5.40367	−0.344525
$247$	−31.9954	−2.03582
$248$	−8.24127	−0.523321
$249$	12.7620	0.808757
$250$	−7.64522	−0.483526
$251$	21.4151	1.35171	0.675853	−	0.737036i	$-0.263775\pi$
$251$	21.4151	1.35171	0.675853	+	0.737036i	$0.263775\pi$
$252$	2.84264	0.179070
$253$	−0.676746	−0.0425466
$254$	5.51920	0.346306
$255$	−3.49390	−0.218796
$256$	−17.0273	−1.06421
$257$	9.35016	0.583247	0.291623	−	0.956533i	$-0.405805\pi$
$257$	9.35016	0.583247	0.291623	+	0.956533i	$0.405805\pi$
$258$	−8.97214	−0.558581
$259$	−11.1356	−0.691934
$260$	16.6228	1.03090
$261$	−3.28926	−0.203600
$262$	5.93623	0.366741
$263$	29.9542	1.84706	0.923528	−	0.383530i	$-0.125292\pi$
$263$	29.9542	1.84706	0.923528	+	0.383530i	$0.125292\pi$
$264$	6.16253	0.379277
$265$	8.59095	0.527738
$266$	18.9511	1.16196
$267$	11.2726	0.689874
$268$	2.19572	0.134125
$269$	−12.4442	−0.758735	−0.379367	−	0.925246i	$-0.623858\pi$
$269$	−12.4442	−0.758735	−0.379367	+	0.925246i	$0.623858\pi$
$270$	−3.46360	−0.210788
$271$	2.59372	0.157557	0.0787786	−	0.996892i	$-0.474898\pi$
$271$	2.59372	0.157557	0.0787786	+	0.996892i	$0.474898\pi$
$272$	0.930626	0.0564275
$273$	13.0691	0.790976
$274$	−5.75780	−0.347841
$275$	14.8491	0.895435
$276$	0.334144	0.0201131
$277$	22.1230	1.32924	0.664620	−	0.747181i	$-0.268593\pi$
$277$	22.1230	1.32924	0.664620	+	0.747181i	$0.268593\pi$
$278$	−7.61144	−0.456504
$279$	−2.75526	−0.164953
$280$	−29.2030	−1.74521
$281$	−26.1676	−1.56103	−0.780514	−	0.625138i	$-0.785043\pi$
$281$	−26.1676	−1.56103	−0.780514	+	0.625138i	$0.785043\pi$
$282$	0.435214	0.0259166
$283$	3.58067	0.212849	0.106424	−	0.994321i	$-0.466060\pi$
$283$	3.58067	0.212849	0.106424	+	0.994321i	$0.466060\pi$
$284$	14.7582	0.875737
$285$	23.9023	1.41585
$286$	9.55219	0.564833
$287$	−15.2320	−0.899118
$288$	−5.05965	−0.298143
$289$	1.00000	0.0588235
$290$	11.3927	0.669002
$291$	6.16257	0.361256
$292$	−4.53748	−0.265536
$293$	10.2402	0.598241	0.299121	−	0.954215i	$-0.403307\pi$
$293$	10.2402	0.598241	0.299121	+	0.954215i	$0.403307\pi$
$294$	−0.801585	−0.0467494
$295$	−2.51094	−0.146193
$296$	11.9195	0.692809
$297$	2.06029	0.119550
$298$	−9.70237	−0.562043
$299$	1.53623	0.0888424
$300$	−7.33177	−0.423300
$301$	−25.2910	−1.45775
$302$	−20.1832	−1.16141
$303$	−2.71522	−0.155985
$304$	−6.36657	−0.365148
$305$	33.0123	1.89028
$306$	0.991328	0.0566704
$307$	−23.7263	−1.35413	−0.677065	−	0.735924i	$-0.736748\pi$
$307$	−23.7263	−1.35413	−0.677065	+	0.735924i	$0.736748\pi$
$308$	5.85666	0.333714
$309$	2.41319	0.137281
$310$	9.54311	0.542012
$311$	3.40626	0.193151	0.0965757	−	0.995326i	$-0.469211\pi$
$311$	3.40626	0.193151	0.0965757	+	0.995326i	$0.469211\pi$
$312$	−13.9891	−0.791976
$313$	−18.3253	−1.03581	−0.517903	−	0.855440i	$-0.673287\pi$
$313$	−18.3253	−1.03581	−0.517903	+	0.855440i	$0.673287\pi$
$314$	9.09353	0.513178
$315$	−9.76330	−0.550099
$316$	1.01727	0.0572258
$317$	18.2163	1.02313	0.511566	−	0.859244i	$-0.329066\pi$
$317$	18.2163	1.02313	0.511566	+	0.859244i	$0.329066\pi$
$318$	−2.43752	−0.136689
$319$	−6.77683	−0.379429
$320$	24.0276	1.34318
$321$	19.8612	1.10854
$322$	−0.909917	−0.0507077
$323$	−6.84116	−0.380653
$324$	−1.01727	−0.0565149
$325$	−33.7079	−1.86978
$326$	18.7800	1.04013
$327$	−0.394736	−0.0218290
$328$	16.3043	0.900255
$329$	1.22680	0.0676354
$330$	−7.13600	−0.392824
$331$	27.5193	1.51260	0.756298	−	0.654227i	$-0.227006\pi$
$331$	27.5193	1.51260	0.756298	+	0.654227i	$0.227006\pi$
$332$	−12.9824	−0.712500
$333$	3.98500	0.218377
$334$	17.0502	0.932946
$335$	−7.54139	−0.412030
$336$	2.60053	0.141871
$337$	−11.1177	−0.605621	−0.302811	−	0.953051i	$-0.597925\pi$
$337$	−11.1177	−0.605621	−0.302811	+	0.953051i	$0.597925\pi$
$338$	−8.79646	−0.478464
$339$	5.77373	0.313586
$340$	3.55423	0.192755
$341$	−5.67662	−0.307406
$342$	−6.78184	−0.366720
$343$	17.3012	0.934176
$344$	27.0714	1.45959
$345$	−1.14765	−0.0617872
$346$	22.4270	1.20568
$347$	−25.9711	−1.39420	−0.697102	−	0.716972i	$-0.745527\pi$
$347$	−25.9711	−1.39420	−0.697102	+	0.716972i	$0.745527\pi$
$348$	3.34607	0.179368
$349$	−4.57781	−0.245045	−0.122522	−	0.992466i	$-0.539098\pi$
$349$	−4.57781	−0.245045	−0.122522	+	0.992466i	$0.539098\pi$
$350$	19.9653	1.06719
$351$	−4.67690	−0.249635
$352$	−10.4243	−0.555619
$353$	−5.73490	−0.305238	−0.152619	−	0.988285i	$-0.548771\pi$
$353$	−5.73490	−0.305238	−0.152619	+	0.988285i	$0.548771\pi$
$354$	0.712433	0.0378654
$355$	−50.6882	−2.69025
$356$	−11.4673	−0.607766
$357$	2.79439	0.147895
$358$	−9.65884	−0.510486
$359$	−3.68443	−0.194457	−0.0972284	−	0.995262i	$-0.530998\pi$
$359$	−3.68443	−0.194457	−0.0972284	+	0.995262i	$0.530998\pi$
$360$	10.4506	0.550795
$361$	27.8015	1.46324
$362$	−4.66237	−0.245049
$363$	−6.75522	−0.354557
$364$	−13.2948	−0.696835
$365$	15.5844	0.815723
$366$	−9.36662	−0.489601
$367$	−12.9631	−0.676666	−0.338333	−	0.941026i	$-0.609863\pi$
$367$	−12.9631	−0.676666	−0.338333	+	0.941026i	$0.609863\pi$
$368$	0.305684	0.0159349
$369$	5.45094	0.283765
$370$	−13.8024	−0.717554
$371$	−6.87096	−0.356723
$372$	2.80284	0.145321
$373$	−8.88886	−0.460248	−0.230124	−	0.973161i	$-0.573913\pi$
$373$	−8.88886	−0.460248	−0.230124	+	0.973161i	$0.573913\pi$
$374$	2.04242	0.105611
$375$	7.71210	0.398251
$376$	−1.31316	−0.0677210
$377$	15.3836	0.792294
$378$	2.77015	0.142481
$379$	20.2721	1.04131	0.520654	−	0.853768i	$-0.325688\pi$
$379$	20.2721	1.04131	0.520654	+	0.853768i	$0.325688\pi$
$380$	−24.3151	−1.24734
$381$	−5.56748	−0.285231
$382$	−1.10162	−0.0563639
$383$	−18.5714	−0.948952	−0.474476	−	0.880268i	$-0.657362\pi$
$383$	−18.5714	−0.948952	−0.474476	+	0.880268i	$0.657362\pi$
$384$	3.30191	0.168500
$385$	−20.1152	−1.02516
$386$	−13.2379	−0.673791
$387$	9.05063	0.460069
$388$	−6.26899	−0.318260
$389$	35.5781	1.80388	0.901942	−	0.431857i	$-0.142142\pi$
$389$	35.5781	1.80388	0.901942	+	0.431857i	$0.142142\pi$
$390$	16.1989	0.820263
$391$	0.328472	0.0166115
$392$	2.41860	0.122158
$393$	−5.98816	−0.302063
$394$	11.8173	0.595349
$395$	−3.49390	−0.175797
$396$	−2.09587	−0.105321
$397$	−5.09114	−0.255517	−0.127759	−	0.991805i	$-0.540778\pi$
$397$	−5.09114	−0.255517	−0.127759	+	0.991805i	$0.540778\pi$
$398$	−9.97252	−0.499877
$399$	−19.1169	−0.957040
$400$	−6.70731	−0.335365
$401$	15.0174	0.749933	0.374967	−	0.927038i	$-0.377654\pi$
$401$	15.0174	0.749933	0.374967	+	0.927038i	$0.377654\pi$
$402$	2.13973	0.106720
$403$	12.8861	0.641901
$404$	2.76211	0.137420
$405$	3.49390	0.173613
$406$	−9.11177	−0.452209
$407$	8.21024	0.406966
$408$	−2.99110	−0.148082
$409$	7.76251	0.383832	0.191916	−	0.981411i	$-0.438530\pi$
$409$	7.76251	0.383832	0.191916	+	0.981411i	$0.438530\pi$
$410$	−18.8799	−0.932409
$411$	5.80816	0.286496
$412$	−2.45486	−0.120942
$413$	2.00823	0.0988184
$414$	0.325623	0.0160035
$415$	44.5890	2.18879
$416$	23.6635	1.16020
$417$	7.67802	0.375994
$418$	−13.9725	−0.683419
$419$	−2.04638	−0.0999724	−0.0499862	−	0.998750i	$-0.515918\pi$
$419$	−2.04638	−0.0999724	−0.0499862	+	0.998750i	$0.515918\pi$
$420$	9.93190	0.484627
$421$	−6.39633	−0.311738	−0.155869	−	0.987778i	$-0.549818\pi$
$421$	−6.39633	−0.311738	−0.155869	+	0.987778i	$0.549818\pi$
$422$	3.88817	0.189273
$423$	−0.439021	−0.0213459
$424$	7.35466	0.357174
$425$	−7.20731	−0.349606
$426$	14.3818	0.696803
$427$	−26.4029	−1.27773
$428$	−20.2042	−0.976605
$429$	−9.63576	−0.465219
$430$	−31.3477	−1.51172
$431$	13.9233	0.670664	0.335332	−	0.942100i	$-0.391151\pi$
$431$	13.9233	0.670664	0.335332	+	0.942100i	$0.391151\pi$
$432$	−0.930626	−0.0447748
$433$	−23.5683	−1.13262	−0.566310	−	0.824192i	$-0.691629\pi$
$433$	−23.5683	−1.13262	−0.566310	+	0.824192i	$0.691629\pi$
$434$	−7.63249	−0.366371
$435$	−11.4923	−0.551016
$436$	0.401553	0.0192309
$437$	−2.24713	−0.107495
$438$	−4.42177	−0.211280
$439$	34.0006	1.62276	0.811381	−	0.584517i	$-0.198716\pi$
$439$	34.0006	1.62276	0.811381	+	0.584517i	$0.198716\pi$
$440$	21.5312	1.02646
$441$	0.808597	0.0385046
$442$	−4.63634	−0.220528
$443$	7.48089	0.355428	0.177714	−	0.984082i	$-0.443130\pi$
$443$	7.48089	0.355428	0.177714	+	0.984082i	$0.443130\pi$
$444$	−4.05382	−0.192386
$445$	39.3854	1.86705
$446$	0.880821	0.0417081
$447$	9.78724	0.462921
$448$	−19.2171	−0.907921
$449$	39.7163	1.87433	0.937164	−	0.348889i	$-0.113441\pi$
$449$	39.7163	1.87433	0.937164	+	0.348889i	$0.113441\pi$
$450$	−7.14480	−0.336809
$451$	11.2305	0.528823
$452$	−5.87343	−0.276263
$453$	20.3598	0.956585
$454$	−9.88663	−0.464003
$455$	45.6620	2.14067
$456$	20.4626	0.958250
$457$	19.2861	0.902163	0.451082	−	0.892483i	$-0.351038\pi$
$457$	19.2861	0.902163	0.451082	+	0.892483i	$0.351038\pi$
$458$	−19.6644	−0.918855
$459$	−1.00000	−0.0466760
$460$	1.16746	0.0544333
$461$	−17.1278	−0.797723	−0.398861	−	0.917011i	$-0.630595\pi$
$461$	−17.1278	−0.797723	−0.398861	+	0.917011i	$0.630595\pi$
$462$	5.70731	0.265528
$463$	−21.5674	−1.00232	−0.501161	−	0.865354i	$-0.667094\pi$
$463$	−21.5674	−1.00232	−0.501161	+	0.865354i	$0.667094\pi$
$464$	3.06108	0.142107
$465$	−9.62659	−0.446422
$466$	9.88717	0.458014
$467$	22.8087	1.05546	0.527730	−	0.849412i	$-0.323043\pi$
$467$	22.8087	1.05546	0.527730	+	0.849412i	$0.323043\pi$
$468$	4.75767	0.219923
$469$	6.03154	0.278511
$470$	1.52059	0.0701397
$471$	−9.17308	−0.422673
$472$	−2.14960	−0.0989434
$473$	18.6469	0.857385
$474$	0.991328	0.0455332
$475$	49.3064	2.26233
$476$	−2.84264	−0.130292
$477$	2.45884	0.112583
$478$	2.90180	0.132725
$479$	−5.60943	−0.256301	−0.128151	−	0.991755i	$-0.540904\pi$
$479$	−5.60943	−0.256301	−0.128151	+	0.991755i	$0.540904\pi$
$480$	−17.6779	−0.806882
$481$	−18.6375	−0.849795
$482$	−10.8349	−0.493518
$483$	0.917877	0.0417648
$484$	6.87188	0.312358
$485$	21.5314	0.977689
$486$	−0.991328	−0.0449675
$487$	−0.322759	−0.0146256	−0.00731279	−	0.999973i	$-0.502328\pi$
$487$	−0.322759	−0.0146256	−0.00731279	+	0.999973i	$0.502328\pi$
$488$	28.2616	1.27934
$489$	−18.9443	−0.856692
$490$	−2.80065	−0.126521
$491$	17.8366	0.804953	0.402476	−	0.915430i	$-0.368150\pi$
$491$	17.8366	0.804953	0.402476	+	0.915430i	$0.368150\pi$
$492$	−5.54507	−0.249991
$493$	3.28926	0.148141
$494$	31.7180	1.42706
$495$	7.19843	0.323545
$496$	2.56412	0.115132
$497$	40.5400	1.81847
$498$	−12.6513	−0.566918
$499$	34.9468	1.56443	0.782216	−	0.623007i	$-0.214089\pi$
$499$	34.9468	1.56443	0.782216	+	0.623007i	$0.214089\pi$
$500$	−7.84528	−0.350852
$501$	−17.1994	−0.768411
$502$	−21.2293	−0.947512
$503$	−3.45827	−0.154196	−0.0770982	−	0.997024i	$-0.524566\pi$
$503$	−3.45827	−0.154196	−0.0770982	+	0.997024i	$0.524566\pi$
$504$	−8.35830	−0.372308
$505$	−9.48669	−0.422152
$506$	0.670877	0.0298241
$507$	8.87341	0.394082
$508$	5.66363	0.251283
$509$	−1.65347	−0.0732888	−0.0366444	−	0.999328i	$-0.511667\pi$
$509$	−1.65347	−0.0732888	−0.0366444	+	0.999328i	$0.511667\pi$
$510$	3.46360	0.153371
$511$	−12.4642	−0.551385
$512$	10.2758	0.454132
$513$	6.84116	0.302045
$514$	−9.26907	−0.408841
$515$	8.43143	0.371533
$516$	−9.20692	−0.405312
$517$	−0.904510	−0.0397803
$518$	11.0391	0.485029
$519$	−22.6231	−0.993046
$520$	−48.8764	−2.14337
$521$	−39.1390	−1.71471	−0.857354	−	0.514726i	$-0.827894\pi$
$521$	−39.1390	−1.71471	−0.857354	+	0.514726i	$0.827894\pi$
$522$	3.26074	0.142719
$523$	40.3303	1.76352	0.881761	−	0.471696i	$-0.156358\pi$
$523$	40.3303	1.76352	0.881761	+	0.471696i	$0.156358\pi$
$524$	6.09157	0.266111
$525$	−20.1400	−0.878982
$526$	−29.6945	−1.29474
$527$	2.75526	0.120021
$528$	−1.91736	−0.0834422
$529$	−22.8921	−0.995309
$530$	−8.51645	−0.369931
$531$	−0.718665	−0.0311874
$532$	19.4470	0.843134
$533$	−25.4935	−1.10425
$534$	−11.1749	−0.483584
$535$	69.3929	3.00012
$536$	−6.45614	−0.278863
$537$	9.74334	0.420456
$538$	12.3363	0.531854
$539$	1.66594	0.0717572
$540$	−3.55423	−0.152950
$541$	−39.5878	−1.70201	−0.851006	−	0.525156i	$-0.824007\pi$
$541$	−39.5878	−1.70201	−0.851006	+	0.525156i	$0.824007\pi$
$542$	−2.57123	−0.110444
$543$	4.70316	0.201832
$544$	5.05965	0.216931
$545$	−1.37917	−0.0590771
$546$	−12.9557	−0.554454
$547$	8.50789	0.363771	0.181886	−	0.983320i	$-0.441780\pi$
$547$	8.50789	0.363771	0.181886	+	0.983320i	$0.441780\pi$
$548$	−5.90847	−0.252397
$549$	9.44856	0.403255
$550$	−14.7203	−0.627678
$551$	−22.5024	−0.958634
$552$	−0.982492	−0.0418177
$553$	2.79439	0.118829
$554$	−21.9311	−0.931764
$555$	13.9232	0.591006
$556$	−7.81061	−0.331244
$557$	−41.2729	−1.74879	−0.874395	−	0.485214i	$-0.838742\pi$
$557$	−41.2729	−1.74879	−0.874395	+	0.485214i	$0.838742\pi$
$558$	2.73137	0.115628
$559$	−42.3289	−1.79032
$560$	9.08598	0.383953
$561$	−2.06029	−0.0869854
$562$	25.9407	1.09424
$563$	39.9931	1.68551	0.842755	−	0.538298i	$-0.180932\pi$
$563$	39.9931	1.68551	0.842755	+	0.538298i	$0.180932\pi$
$564$	0.446603	0.0188054
$565$	20.1728	0.848676
$566$	−3.54962	−0.149202
$567$	−2.79439	−0.117353
$568$	−43.3939	−1.82077
$569$	−1.72896	−0.0724820	−0.0362410	−	0.999343i	$-0.511538\pi$
$569$	−1.72896	−0.0724820	−0.0362410	+	0.999343i	$0.511538\pi$
$570$	−23.6950	−0.992476
$571$	−33.8495	−1.41656	−0.708278	−	0.705934i	$-0.750528\pi$
$571$	−33.8495	−1.41656	−0.708278	+	0.705934i	$0.750528\pi$
$572$	9.80215	0.409849
$573$	1.11126	0.0464235
$574$	15.0999	0.630259
$575$	−2.36740	−0.0987272
$576$	6.87703	0.286543
$577$	−18.3404	−0.763520	−0.381760	−	0.924262i	$-0.624682\pi$
$577$	−18.3404	−0.763520	−0.381760	+	0.924262i	$0.624682\pi$
$578$	−0.991328	−0.0412338
$579$	13.3537	0.554961
$580$	11.6908	0.485434
$581$	−35.6619	−1.47950
$582$	−6.10912	−0.253231
$583$	5.06592	0.209809
$584$	13.3417	0.552083
$585$	−16.3406	−0.675601
$586$	−10.1514	−0.419352
$587$	16.4753	0.680007	0.340003	−	0.940424i	$-0.389572\pi$
$587$	16.4753	0.680007	0.340003	+	0.940424i	$0.389572\pi$
$588$	−0.822561	−0.0339218
$589$	−18.8492	−0.776667
$590$	2.48917	0.102477
$591$	−11.9207	−0.490353
$592$	−3.70855	−0.152420
$593$	−7.82463	−0.321319	−0.160659	−	0.987010i	$-0.551362\pi$
$593$	−7.82463	−0.321319	−0.160659	+	0.987010i	$0.551362\pi$
$594$	−2.04242	−0.0838015
$595$	9.76330	0.400256
$596$	−9.95626	−0.407824
$597$	10.0598	0.411719
$598$	−1.52291	−0.0622763
$599$	28.2270	1.15332	0.576662	−	0.816983i	$-0.304355\pi$
$599$	28.2270	1.15332	0.576662	+	0.816983i	$0.304355\pi$
$600$	21.5578	0.880093
$601$	14.1800	0.578416	0.289208	−	0.957266i	$-0.406608\pi$
$601$	14.1800	0.578416	0.289208	+	0.957266i	$0.406608\pi$
$602$	25.0716	1.02184
$603$	−2.15845	−0.0878988
$604$	−20.7114	−0.842733
$605$	−23.6020	−0.959559
$606$	2.69167	0.109342
$607$	2.32882	0.0945239	0.0472619	−	0.998883i	$-0.484950\pi$
$607$	2.32882	0.0945239	0.0472619	+	0.998883i	$0.484950\pi$
$608$	−34.6139	−1.40378
$609$	9.19148	0.372457
$610$	−32.7260	−1.32504
$611$	2.05326	0.0830660
$612$	1.01727	0.0411207
$613$	31.3935	1.26797	0.633985	−	0.773345i	$-0.281418\pi$
$613$	31.3935	1.26797	0.633985	+	0.773345i	$0.281418\pi$
$614$	23.5205	0.949210
$615$	19.0450	0.767969
$616$	−17.2205	−0.693833
$617$	−40.9336	−1.64792	−0.823961	−	0.566646i	$-0.808241\pi$
$617$	−40.9336	−1.64792	−0.823961	+	0.566646i	$0.808241\pi$
$618$	−2.39226	−0.0962309
$619$	−25.2554	−1.01510	−0.507551	−	0.861622i	$-0.669449\pi$
$619$	−25.2554	−1.01510	−0.507551	+	0.861622i	$0.669449\pi$
$620$	9.79283	0.393290
$621$	−0.328472	−0.0131811
$622$	−3.37672	−0.135394
$623$	−31.5001	−1.26203
$624$	4.35245	0.174237
$625$	−9.09126	−0.363650
$626$	18.1663	0.726073
$627$	14.0948	0.562890
$628$	9.33149	0.372367
$629$	−3.98500	−0.158892
$630$	9.67863	0.385606
$631$	−19.5526	−0.778378	−0.389189	−	0.921158i	$-0.627245\pi$
$631$	−19.5526	−0.778378	−0.389189	+	0.921158i	$0.627245\pi$
$632$	−2.99110	−0.118980
$633$	−3.92218	−0.155893
$634$	−18.0584	−0.717189
$635$	−19.4522	−0.771937
$636$	−2.50131	−0.0991832
$637$	−3.78173	−0.149838
$638$	6.71806	0.265970
$639$	−14.5077	−0.573914
$640$	11.5365	0.456022
$641$	−7.86380	−0.310602	−0.155301	−	0.987867i	$-0.549635\pi$
$641$	−7.86380	−0.310602	−0.155301	+	0.987867i	$0.549635\pi$
$642$	−19.6889	−0.777060
$643$	−26.2950	−1.03697	−0.518486	−	0.855086i	$-0.673504\pi$
$643$	−26.2950	−1.03697	−0.518486	+	0.855086i	$0.673504\pi$
$644$	−0.933727	−0.0367940
$645$	31.6220	1.24511
$646$	6.78184	0.266828
$647$	−31.1963	−1.22645	−0.613226	−	0.789908i	$-0.710128\pi$
$647$	−31.1963	−1.22645	−0.613226	+	0.789908i	$0.710128\pi$
$648$	2.99110	0.117502
$649$	−1.48066	−0.0581208
$650$	33.4155	1.31067
$651$	7.69926	0.301758
$652$	19.2715	0.754729
$653$	−33.4104	−1.30745	−0.653724	−	0.756733i	$-0.726794\pi$
$653$	−33.4104	−1.30745	−0.653724	+	0.756733i	$0.726794\pi$
$654$	0.391313	0.0153016
$655$	−20.9220	−0.817490
$656$	−5.07279	−0.198059
$657$	4.46045	0.174019
$658$	−1.21616	−0.0474107
$659$	15.9141	0.619926	0.309963	−	0.950749i	$-0.399683\pi$
$659$	15.9141	0.619926	0.309963	+	0.950749i	$0.399683\pi$
$660$	−7.32273	−0.285037
$661$	4.40702	0.171413	0.0857066	−	0.996320i	$-0.472685\pi$
$661$	4.40702	0.171413	0.0857066	+	0.996320i	$0.472685\pi$
$662$	−27.2806	−1.06029
$663$	4.67690	0.181636
$664$	38.1724	1.48138
$665$	−66.7923	−2.59009
$666$	−3.95044	−0.153076
$667$	1.08043	0.0418344
$668$	17.4964	0.676955
$669$	−0.888526	−0.0343524
$670$	7.47599	0.288823
$671$	19.4667	0.751505
$672$	14.1386	0.545409
$673$	−1.64869	−0.0635522	−0.0317761	−	0.999495i	$-0.510116\pi$
$673$	−1.64869	−0.0635522	−0.0317761	+	0.999495i	$0.510116\pi$
$674$	11.0213	0.424525
$675$	7.20731	0.277409
$676$	−9.02664	−0.347179
$677$	−18.4591	−0.709442	−0.354721	−	0.934972i	$-0.615424\pi$
$677$	−18.4591	−0.709442	−0.354721	+	0.934972i	$0.615424\pi$
$678$	−5.72366	−0.219816
$679$	−17.2206	−0.660866
$680$	−10.4506	−0.400762
$681$	9.97312	0.382171
$682$	5.62740	0.215484
$683$	−50.6993	−1.93996	−0.969978	−	0.243191i	$-0.921806\pi$
$683$	−50.6993	−1.93996	−0.969978	+	0.243191i	$0.921806\pi$
$684$	−6.95930	−0.266096
$685$	20.2931	0.775360
$686$	−17.1511	−0.654833
$687$	19.8364	0.756805
$688$	−8.42275	−0.321114
$689$	−11.4998	−0.438107
$690$	1.13769	0.0433112
$691$	28.3590	1.07883	0.539413	−	0.842041i	$-0.318646\pi$
$691$	28.3590	1.07883	0.539413	+	0.842041i	$0.318646\pi$
$692$	23.0138	0.874854
$693$	−5.75724	−0.218699
$694$	25.7459	0.977302
$695$	26.8262	1.01758
$696$	−9.83853	−0.372928
$697$	−5.45094	−0.206469
$698$	4.53811	0.171770
$699$	−9.97366	−0.377239
$700$	20.4878	0.774366
$701$	−1.90709	−0.0720298	−0.0360149	−	0.999351i	$-0.511466\pi$
$701$	−1.90709	−0.0720298	−0.0360149	+	0.999351i	$0.511466\pi$
$702$	4.63634	0.174987
$703$	27.2620	1.02821
$704$	14.1686	0.534001
$705$	−1.53389	−0.0577698
$706$	5.68517	0.213964
$707$	7.58737	0.285352
$708$	0.731076	0.0274755
$709$	−31.9998	−1.20178	−0.600889	−	0.799332i	$-0.705187\pi$
$709$	−31.9998	−1.20178	−0.600889	+	0.799332i	$0.705187\pi$
$710$	50.2487	1.88580
$711$	−1.00000	−0.0375029
$712$	33.7176	1.26362
$713$	0.905025	0.0338934
$714$	−2.77015	−0.103670
$715$	−33.6663	−1.25905
$716$	−9.91159	−0.370414
$717$	−2.92719	−0.109318
$718$	3.65248	0.136309
$719$	38.5433	1.43742	0.718712	−	0.695308i	$-0.244732\pi$
$719$	38.5433	1.43742	0.718712	+	0.695308i	$0.244732\pi$
$720$	−3.25151	−0.121177
$721$	−6.74338	−0.251137
$722$	−27.5604	−1.02569
$723$	10.9297	0.406481
$724$	−4.78438	−0.177810
$725$	−23.7067	−0.880446
$726$	6.69664	0.248536
$727$	42.8716	1.59002	0.795009	−	0.606597i	$-0.207466\pi$
$727$	42.8716	1.59002	0.795009	+	0.606597i	$0.207466\pi$
$728$	39.0909	1.44881
$729$	1.00000	0.0370370
$730$	−15.4492	−0.571801
$731$	−9.05063	−0.334750
$732$	−9.61173	−0.355260
$733$	9.29166	0.343195	0.171598	−	0.985167i	$-0.445107\pi$
$733$	9.29166	0.343195	0.171598	+	0.985167i	$0.445107\pi$
$734$	12.8506	0.474326
$735$	2.82515	0.104207
$736$	1.66195	0.0612603
$737$	−4.44702	−0.163808
$738$	−5.40367	−0.198912
$739$	26.5349	0.976103	0.488051	−	0.872815i	$-0.337708\pi$
$739$	26.5349	0.976103	0.488051	+	0.872815i	$0.337708\pi$
$740$	−14.1636	−0.520665
$741$	−31.9954	−1.17538
$742$	6.81138	0.250054
$743$	16.9372	0.621364	0.310682	−	0.950514i	$-0.399443\pi$
$743$	16.9372	0.621364	0.310682	+	0.950514i	$0.399443\pi$
$744$	−8.24127	−0.302139
$745$	34.1956	1.25283
$746$	8.81178	0.322622
$747$	12.7620	0.466936
$748$	2.09587	0.0766324
$749$	−55.4998	−2.02792
$750$	−7.64522	−0.279164
$751$	7.03495	0.256709	0.128354	−	0.991728i	$-0.459031\pi$
$751$	7.03495	0.256709	0.128354	+	0.991728i	$0.459031\pi$
$752$	0.408565	0.0148988
$753$	21.4151	0.780408
$754$	−15.2502	−0.555378
$755$	71.1349	2.58886
$756$	2.84264	0.103386
$757$	−28.0614	−1.01991	−0.509954	−	0.860202i	$-0.670338\pi$
$757$	−28.0614	−1.01991	−0.509954	+	0.860202i	$0.670338\pi$
$758$	−20.0963	−0.729931
$759$	−0.676746	−0.0245643
$760$	71.4943	2.59337
$761$	−11.8995	−0.431355	−0.215677	−	0.976465i	$-0.569196\pi$
$761$	−11.8995	−0.431355	−0.215677	+	0.976465i	$0.569196\pi$
$762$	5.51920	0.199940
$763$	1.10305	0.0399330
$764$	−1.13045	−0.0408982
$765$	−3.49390	−0.126322
$766$	18.4103	0.665191
$767$	3.36113	0.121363
$768$	−17.0273	−0.614421
$769$	19.2831	0.695368	0.347684	−	0.937612i	$-0.386968\pi$
$769$	19.2831	0.695368	0.347684	+	0.937612i	$0.386968\pi$
$770$	19.9407	0.718615
$771$	9.35016	0.336738
$772$	−13.5843	−0.488910
$773$	11.8275	0.425405	0.212702	−	0.977117i	$-0.431774\pi$
$773$	11.8275	0.425405	0.212702	+	0.977117i	$0.431774\pi$
$774$	−8.97214	−0.322497
$775$	−19.8580	−0.713321
$776$	18.4329	0.661701
$777$	−11.1356	−0.399489
$778$	−35.2696	−1.26448
$779$	37.2908	1.33608
$780$	16.6228	0.595191
$781$	−29.8899	−1.06955
$782$	−0.325623	−0.0116443
$783$	−3.28926	−0.117549
$784$	−0.752502	−0.0268751
$785$	−32.0498	−1.14391
$786$	5.93623	0.211738
$787$	−4.40985	−0.157194	−0.0785970	−	0.996906i	$-0.525044\pi$
$787$	−4.40985	−0.157194	−0.0785970	+	0.996906i	$0.525044\pi$
$788$	12.1266	0.431992
$789$	29.9542	1.06640
$790$	3.46360	0.123229
$791$	−16.1340	−0.573660
$792$	6.16253	0.218976
$793$	−44.1900	−1.56923
$794$	5.04699	0.179111
$795$	8.59095	0.304689
$796$	−10.2335	−0.362716
$797$	−32.8245	−1.16270	−0.581351	−	0.813653i	$-0.697476\pi$
$797$	−32.8245	−1.16270	−0.581351	+	0.813653i	$0.697476\pi$
$798$	18.9511	0.670861
$799$	0.439021	0.0155315
$800$	−36.4665	−1.28928
$801$	11.2726	0.398299
$802$	−14.8872	−0.525684
$803$	9.18981	0.324301
$804$	2.19572	0.0774372
$805$	3.20697	0.113031
$806$	−12.7743	−0.449957
$807$	−12.4442	−0.438056
$808$	−8.12150	−0.285713
$809$	18.1444	0.637924	0.318962	−	0.947767i	$-0.396666\pi$
$809$	18.1444	0.637924	0.318962	+	0.947767i	$0.396666\pi$
$810$	−3.46360	−0.121698
$811$	−0.355085	−0.0124687	−0.00623437	−	0.999981i	$-0.501984\pi$
$811$	−0.355085	−0.0124687	−0.00623437	+	0.999981i	$0.501984\pi$
$812$	−9.35020	−0.328128
$813$	2.59372	0.0909657
$814$	−8.13904	−0.285273
$815$	−66.1895	−2.31852
$816$	0.930626	0.0325784
$817$	61.9168	2.16620
$818$	−7.69520	−0.269056
$819$	13.0691	0.456670
$820$	−19.3739	−0.676566
$821$	−5.80576	−0.202623	−0.101311	−	0.994855i	$-0.532304\pi$
$821$	−5.80576	−0.202623	−0.101311	+	0.994855i	$0.532304\pi$
$822$	−5.75780	−0.200826
$823$	−25.2951	−0.881733	−0.440866	−	0.897573i	$-0.645329\pi$
$823$	−25.2951	−0.881733	−0.440866	+	0.897573i	$0.645329\pi$
$824$	7.21810	0.251454
$825$	14.8491	0.516980
$826$	−1.99081	−0.0692692
$827$	38.2337	1.32952	0.664758	−	0.747059i	$-0.268535\pi$
$827$	38.2337	1.32952	0.664758	+	0.747059i	$0.268535\pi$
$828$	0.334144	0.0116123
$829$	−21.7196	−0.754354	−0.377177	−	0.926141i	$-0.623105\pi$
$829$	−21.7196	−0.754354	−0.377177	+	0.926141i	$0.623105\pi$
$830$	−44.2023	−1.53429
$831$	22.1230	0.767438
$832$	−32.1632	−1.11506
$833$	−0.808597	−0.0280162
$834$	−7.61144	−0.263563
$835$	−60.0928	−2.07960
$836$	−14.3382	−0.495896
$837$	−2.75526	−0.0952357
$838$	2.02864	0.0700781
$839$	21.2699	0.734318	0.367159	−	0.930158i	$-0.380331\pi$
$839$	21.2699	0.734318	0.367159	+	0.930158i	$0.380331\pi$
$840$	−29.2030	−1.00760
$841$	−18.1807	−0.626922
$842$	6.34087	0.218521
$843$	−26.1676	−0.901260
$844$	3.98991	0.137338
$845$	31.0028	1.06653
$846$	0.435214	0.0149630
$847$	18.8767	0.648611
$848$	−2.28827	−0.0785794
$849$	3.58067	0.122888
$850$	7.14480	0.245065
$851$	−1.30896	−0.0448705
$852$	14.7582	0.505607
$853$	−22.8045	−0.780812	−0.390406	−	0.920643i	$-0.627665\pi$
$853$	−22.8045	−0.780812	−0.390406	+	0.920643i	$0.627665\pi$
$854$	26.1740	0.895655
$855$	23.9023	0.817442
$856$	59.4068	2.03048
$857$	7.90001	0.269859	0.134930	−	0.990855i	$-0.456919\pi$
$857$	7.90001	0.269859	0.134930	+	0.990855i	$0.456919\pi$
$858$	9.55219	0.326107
$859$	−45.4649	−1.55124	−0.775621	−	0.631198i	$-0.782563\pi$
$859$	−45.4649	−1.55124	−0.775621	+	0.631198i	$0.782563\pi$
$860$	−32.1680	−1.09692
$861$	−15.2320	−0.519106
$862$	−13.8026	−0.470119
$863$	−46.4328	−1.58059	−0.790296	−	0.612725i	$-0.790073\pi$
$863$	−46.4328	−1.58059	−0.790296	+	0.612725i	$0.790073\pi$
$864$	−5.05965	−0.172133
$865$	−79.0429	−2.68754
$866$	23.3639	0.793938
$867$	1.00000	0.0339618
$868$	−7.83222	−0.265843
$869$	−2.06029	−0.0698904
$870$	11.3927	0.386248
$871$	10.0949	0.342051
$872$	−1.18070	−0.0399835
$873$	6.16257	0.208571
$874$	2.22764	0.0753511
$875$	−21.5506	−0.728543
$876$	−4.53748	−0.153307
$877$	−35.9536	−1.21407	−0.607034	−	0.794676i	$-0.707641\pi$
$877$	−35.9536	−1.21407	−0.607034	+	0.794676i	$0.707641\pi$
$878$	−33.7058	−1.13752
$879$	10.2402	0.345395
$880$	−6.69904	−0.225825
$881$	−44.2858	−1.49203	−0.746014	−	0.665931i	$-0.768035\pi$
$881$	−44.2858	−1.49203	−0.746014	+	0.665931i	$0.768035\pi$
$882$	−0.801585	−0.0269908
$883$	−21.9952	−0.740197	−0.370099	−	0.928992i	$-0.620676\pi$
$883$	−21.9952	−0.740197	−0.370099	+	0.928992i	$0.620676\pi$
$884$	−4.75767	−0.160018
$885$	−2.51094	−0.0844043
$886$	−7.41601	−0.249146
$887$	7.42890	0.249438	0.124719	−	0.992192i	$-0.460197\pi$
$887$	7.42890	0.249438	0.124719	+	0.992192i	$0.460197\pi$
$888$	11.9195	0.399994
$889$	15.5577	0.521789
$890$	−39.0439	−1.30875
$891$	2.06029	0.0690222
$892$	0.903870	0.0302638
$893$	−3.00342	−0.100506
$894$	−9.70237	−0.324496
$895$	34.0422	1.13791
$896$	−9.22682	−0.308246
$897$	1.53623	0.0512932
$898$	−39.3719	−1.31386
$899$	9.06278	0.302261
$900$	−7.33177	−0.244392
$901$	−2.45884	−0.0819160
$902$	−11.1331	−0.370692
$903$	−25.2910	−0.841630
$904$	17.2698	0.574385
$905$	16.4324	0.546230
$906$	−20.1832	−0.670542
$907$	−45.8042	−1.52090	−0.760452	−	0.649394i	$-0.775023\pi$
$907$	−45.8042	−1.52090	−0.760452	+	0.649394i	$0.775023\pi$
$908$	−10.1453	−0.336685
$909$	−2.71522	−0.0900581
$910$	−45.2660	−1.50055
$911$	2.58702	0.0857119	0.0428559	−	0.999081i	$-0.486354\pi$
$911$	2.58702	0.0857119	0.0428559	+	0.999081i	$0.486354\pi$
$912$	−6.36657	−0.210818
$913$	26.2933	0.870182
$914$	−19.1188	−0.632394
$915$	33.0123	1.09135
$916$	−20.1789	−0.666731
$917$	16.7332	0.552580
$918$	0.991328	0.0327187
$919$	−18.5473	−0.611818	−0.305909	−	0.952061i	$-0.598960\pi$
$919$	−18.5473	−0.611818	−0.305909	+	0.952061i	$0.598960\pi$
$920$	−3.43273	−0.113174
$921$	−23.7263	−0.781807
$922$	16.9793	0.559184
$923$	67.8509	2.23334
$924$	5.85666	0.192670
$925$	28.7211	0.944344
$926$	21.3804	0.702602
$927$	2.41319	0.0792595
$928$	16.6425	0.546318
$929$	−7.93535	−0.260350	−0.130175	−	0.991491i	$-0.541554\pi$
$929$	−7.93535	−0.260350	−0.130175	+	0.991491i	$0.541554\pi$
$930$	9.54311	0.312931
$931$	5.53175	0.181296
$932$	10.1459	0.332340
$933$	3.40626	0.111516
$934$	−22.6109	−0.739850
$935$	−7.19843	−0.235414
$936$	−13.9891	−0.457248
$937$	−47.8134	−1.56200	−0.780998	−	0.624534i	$-0.785289\pi$
$937$	−47.8134	−1.56200	−0.780998	+	0.624534i	$0.785289\pi$
$938$	−5.97923	−0.195229
$939$	−18.3253	−0.598022
$940$	1.56038	0.0508941
$941$	0.520904	0.0169810	0.00849050	−	0.999964i	$-0.497297\pi$
$941$	0.520904	0.0169810	0.00849050	+	0.999964i	$0.497297\pi$
$942$	9.09353	0.296283
$943$	−1.79048	−0.0583060
$944$	0.668808	0.0217679
$945$	−9.76330	−0.317600
$946$	−18.4852	−0.601005
$947$	48.9766	1.59153	0.795763	−	0.605609i	$-0.207070\pi$
$947$	48.9766	1.59153	0.795763	+	0.605609i	$0.207070\pi$
$948$	1.01727	0.0330394
$949$	−20.8611	−0.677180
$950$	−48.8788	−1.58584
$951$	18.2163	0.590705
$952$	8.35830	0.270894
$953$	−28.4810	−0.922589	−0.461295	−	0.887247i	$-0.652615\pi$
$953$	−28.4810	−0.922589	−0.461295	+	0.887247i	$0.652615\pi$
$954$	−2.43752	−0.0789177
$955$	3.88262	0.125639
$956$	2.97774	0.0963069
$957$	−6.77683	−0.219064
$958$	5.56078	0.179661
$959$	−16.2303	−0.524102
$960$	24.0276	0.775488
$961$	−23.4085	−0.755114
$962$	18.4758	0.595685
$963$	19.8612	0.640017
$964$	−11.1185	−0.358102
$965$	46.6565	1.50192
$966$	−0.909917	−0.0292761
$967$	−58.1614	−1.87034	−0.935172	−	0.354195i	$-0.884755\pi$
$967$	−58.1614	−1.87034	−0.935172	+	0.354195i	$0.884755\pi$
$968$	−20.2056	−0.649431
$969$	−6.84116	−0.219770
$970$	−21.3446	−0.685335
$971$	−55.4179	−1.77845	−0.889223	−	0.457474i	$-0.848754\pi$
$971$	−55.4179	−1.77845	−0.889223	+	0.457474i	$0.848754\pi$
$972$	−1.01727	−0.0326289
$973$	−21.4554	−0.687827
$974$	0.319960	0.0102522
$975$	−33.7079	−1.07952
$976$	−8.79308	−0.281460
$977$	11.3882	0.364342	0.182171	−	0.983267i	$-0.441688\pi$
$977$	11.3882	0.364342	0.182171	+	0.983267i	$0.441688\pi$
$978$	18.7800	0.600519
$979$	23.2249	0.742270
$980$	−2.87394	−0.0918047
$981$	−0.394736	−0.0126030
$982$	−17.6819	−0.564251
$983$	−26.6417	−0.849738	−0.424869	−	0.905255i	$-0.639680\pi$
$983$	−26.6417	−0.849738	−0.424869	+	0.905255i	$0.639680\pi$
$984$	16.3043	0.519763
$985$	−41.6498	−1.32707
$986$	−3.26074	−0.103843
$987$	1.22680	0.0390493
$988$	32.5480	1.03549
$989$	−2.97287	−0.0945319
$990$	−7.13600	−0.226797
$991$	13.8043	0.438509	0.219255	−	0.975668i	$-0.429637\pi$
$991$	13.8043	0.438509	0.219255	+	0.975668i	$0.429637\pi$
$992$	13.9407	0.442616
$993$	27.5193	0.873298
$994$	−40.1884	−1.27470
$995$	35.1478	1.11426
$996$	−12.9824	−0.411362
$997$	51.9147	1.64415	0.822077	−	0.569376i	$-0.192815\pi$
$997$	51.9147	1.64415	0.822077	+	0.569376i	$0.192815\pi$
$998$	−34.6437	−1.09663
$999$	3.98500	0.126080

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.8	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-0.991328 q^{2} +1.00000 q^{3} -1.01727 q^{4} +3.49390 q^{5} -0.991328 q^{6} -2.79439 q^{7} +2.99110 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.991328 q^{2} +1.00000 q^{3} -1.01727 q^{4} +3.49390 q^{5} -0.991328 q^{6} -2.79439 q^{7} +2.99110 q^{8} +1.00000 q^{9} -3.46360 q^{10} +2.06029 q^{11} -1.01727 q^{12} -4.67690 q^{13} +2.77015 q^{14} +3.49390 q^{15} -0.930626 q^{16} -1.00000 q^{17} -0.991328 q^{18} +6.84116 q^{19} -3.55423 q^{20} -2.79439 q^{21} -2.04242 q^{22} -0.328472 q^{23} +2.99110 q^{24} +7.20731 q^{25} +4.63634 q^{26} +1.00000 q^{27} +2.84264 q^{28} -3.28926 q^{29} -3.46360 q^{30} -2.75526 q^{31} -5.05965 q^{32} +2.06029 q^{33} +0.991328 q^{34} -9.76330 q^{35} -1.01727 q^{36} +3.98500 q^{37} -6.78184 q^{38} -4.67690 q^{39} +10.4506 q^{40} +5.45094 q^{41} +2.77015 q^{42} +9.05063 q^{43} -2.09587 q^{44} +3.49390 q^{45} +0.325623 q^{46} -0.439021 q^{47} -0.930626 q^{48} +0.808597 q^{49} -7.14480 q^{50} -1.00000 q^{51} +4.75767 q^{52} +2.45884 q^{53} -0.991328 q^{54} +7.19843 q^{55} -8.35830 q^{56} +6.84116 q^{57} +3.26074 q^{58} -0.718665 q^{59} -3.55423 q^{60} +9.44856 q^{61} +2.73137 q^{62} -2.79439 q^{63} +6.87703 q^{64} -16.3406 q^{65} -2.04242 q^{66} -2.15845 q^{67} +1.01727 q^{68} -0.328472 q^{69} +9.67863 q^{70} -14.5077 q^{71} +2.99110 q^{72} +4.46045 q^{73} -3.95044 q^{74} +7.20731 q^{75} -6.95930 q^{76} -5.75724 q^{77} +4.63634 q^{78} -1.00000 q^{79} -3.25151 q^{80} +1.00000 q^{81} -5.40367 q^{82} +12.7620 q^{83} +2.84264 q^{84} -3.49390 q^{85} -8.97214 q^{86} -3.28926 q^{87} +6.16253 q^{88} +11.2726 q^{89} -3.46360 q^{90} +13.0691 q^{91} +0.334144 q^{92} -2.75526 q^{93} +0.435214 q^{94} +23.9023 q^{95} -5.05965 q^{96} +6.16257 q^{97} -0.801585 q^{98} +2.06029 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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