LMFDB - Embedded newform 8018.2.a.f.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.994559 q^{3} +1.00000 q^{4} -3.18772 q^{5} -0.994559 q^{6} -0.721856 q^{7} -1.00000 q^{8} -2.01085 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.994559 q^{3} +1.00000 q^{4} -3.18772 q^{5} -0.994559 q^{6} -0.721856 q^{7} -1.00000 q^{8} -2.01085 q^{9} +3.18772 q^{10} -1.88674 q^{11} +0.994559 q^{12} +1.86235 q^{13} +0.721856 q^{14} -3.17037 q^{15} +1.00000 q^{16} +2.19676 q^{17} +2.01085 q^{18} -1.00000 q^{19} -3.18772 q^{20} -0.717929 q^{21} +1.88674 q^{22} +3.75056 q^{23} -0.994559 q^{24} +5.16153 q^{25} -1.86235 q^{26} -4.98359 q^{27} -0.721856 q^{28} +5.55874 q^{29} +3.17037 q^{30} +2.69501 q^{31} -1.00000 q^{32} -1.87647 q^{33} -2.19676 q^{34} +2.30107 q^{35} -2.01085 q^{36} -5.33254 q^{37} +1.00000 q^{38} +1.85221 q^{39} +3.18772 q^{40} +10.8945 q^{41} +0.717929 q^{42} -2.68486 q^{43} -1.88674 q^{44} +6.41002 q^{45} -3.75056 q^{46} -10.2574 q^{47} +0.994559 q^{48} -6.47892 q^{49} -5.16153 q^{50} +2.18480 q^{51} +1.86235 q^{52} -0.302806 q^{53} +4.98359 q^{54} +6.01438 q^{55} +0.721856 q^{56} -0.994559 q^{57} -5.55874 q^{58} +12.1685 q^{59} -3.17037 q^{60} +0.637129 q^{61} -2.69501 q^{62} +1.45155 q^{63} +1.00000 q^{64} -5.93663 q^{65} +1.87647 q^{66} -3.50262 q^{67} +2.19676 q^{68} +3.73015 q^{69} -2.30107 q^{70} +1.48701 q^{71} +2.01085 q^{72} +12.4849 q^{73} +5.33254 q^{74} +5.13345 q^{75} -1.00000 q^{76} +1.36195 q^{77} -1.85221 q^{78} -5.56487 q^{79} -3.18772 q^{80} +1.07608 q^{81} -10.8945 q^{82} -5.62995 q^{83} -0.717929 q^{84} -7.00263 q^{85} +2.68486 q^{86} +5.52850 q^{87} +1.88674 q^{88} +5.68927 q^{89} -6.41002 q^{90} -1.34435 q^{91} +3.75056 q^{92} +2.68034 q^{93} +10.2574 q^{94} +3.18772 q^{95} -0.994559 q^{96} +18.7000 q^{97} +6.47892 q^{98} +3.79395 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.994559	0.574209	0.287105	−	0.957899i	$-0.407307\pi$
$3$	0.994559	0.574209	0.287105	+	0.957899i	$0.407307\pi$
$4$	1.00000	0.500000
$5$	−3.18772	−1.42559	−0.712795	−	0.701373i	$-0.752571\pi$
$5$	−3.18772	−1.42559	−0.712795	+	0.701373i	$0.752571\pi$
$6$	−0.994559	−0.406027
$7$	−0.721856	−0.272836	−0.136418	−	0.990651i	$-0.543559\pi$
$7$	−0.721856	−0.272836	−0.136418	+	0.990651i	$0.543559\pi$
$8$	−1.00000	−0.353553
$9$	−2.01085	−0.670284
$10$	3.18772	1.00804
$11$	−1.88674	−0.568872	−0.284436	−	0.958695i	$-0.591806\pi$
$11$	−1.88674	−0.568872	−0.284436	+	0.958695i	$0.591806\pi$
$12$	0.994559	0.287105
$13$	1.86235	0.516522	0.258261	−	0.966075i	$-0.416851\pi$
$13$	1.86235	0.516522	0.258261	+	0.966075i	$0.416851\pi$
$14$	0.721856	0.192924
$15$	−3.17037	−0.818586
$16$	1.00000	0.250000
$17$	2.19676	0.532792	0.266396	−	0.963864i	$-0.414167\pi$
$17$	2.19676	0.532792	0.266396	+	0.963864i	$0.414167\pi$
$18$	2.01085	0.473962
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−3.18772	−0.712795
$21$	−0.717929	−0.156665
$22$	1.88674	0.402254
$23$	3.75056	0.782045	0.391023	−	0.920381i	$-0.372121\pi$
$23$	3.75056	0.782045	0.391023	+	0.920381i	$0.372121\pi$
$24$	−0.994559	−0.203014
$25$	5.16153	1.03231
$26$	−1.86235	−0.365236
$27$	−4.98359	−0.959092
$28$	−0.721856	−0.136418
$29$	5.55874	1.03223	0.516116	−	0.856519i	$-0.327377\pi$
$29$	5.55874	1.03223	0.516116	+	0.856519i	$0.327377\pi$
$30$	3.17037	0.578828
$31$	2.69501	0.484038	0.242019	−	0.970272i	$-0.422190\pi$
$31$	2.69501	0.484038	0.242019	+	0.970272i	$0.422190\pi$
$32$	−1.00000	−0.176777
$33$	−1.87647	−0.326652
$34$	−2.19676	−0.376741
$35$	2.30107	0.388952
$36$	−2.01085	−0.335142
$37$	−5.33254	−0.876665	−0.438332	−	0.898813i	$-0.644431\pi$
$37$	−5.33254	−0.876665	−0.438332	+	0.898813i	$0.644431\pi$
$38$	1.00000	0.162221
$39$	1.85221	0.296592
$40$	3.18772	0.504022
$41$	10.8945	1.70144	0.850720	−	0.525619i	$-0.176166\pi$
$41$	10.8945	1.70144	0.850720	+	0.525619i	$0.176166\pi$
$42$	0.717929	0.110779
$43$	−2.68486	−0.409438	−0.204719	−	0.978821i	$-0.565628\pi$
$43$	−2.68486	−0.409438	−0.204719	+	0.978821i	$0.565628\pi$
$44$	−1.88674	−0.284436
$45$	6.41002	0.955550
$46$	−3.75056	−0.552990
$47$	−10.2574	−1.49620	−0.748099	−	0.663587i	$-0.769033\pi$
$47$	−10.2574	−1.49620	−0.748099	+	0.663587i	$0.769033\pi$
$48$	0.994559	0.143552
$49$	−6.47892	−0.925561
$50$	−5.16153	−0.729950
$51$	2.18480	0.305934
$52$	1.86235	0.258261
$53$	−0.302806	−0.0415937	−0.0207968	−	0.999784i	$-0.506620\pi$
$53$	−0.302806	−0.0415937	−0.0207968	+	0.999784i	$0.506620\pi$
$54$	4.98359	0.678181
$55$	6.01438	0.810979
$56$	0.721856	0.0964621
$57$	−0.994559	−0.131733
$58$	−5.55874	−0.729898
$59$	12.1685	1.58420	0.792099	−	0.610393i	$-0.208989\pi$
$59$	12.1685	1.58420	0.792099	+	0.610393i	$0.208989\pi$
$60$	−3.17037	−0.409293
$61$	0.637129	0.0815759	0.0407880	−	0.999168i	$-0.487013\pi$
$61$	0.637129	0.0815759	0.0407880	+	0.999168i	$0.487013\pi$
$62$	−2.69501	−0.342266
$63$	1.45155	0.182878
$64$	1.00000	0.125000
$65$	−5.93663	−0.736348
$66$	1.87647	0.230978
$67$	−3.50262	−0.427913	−0.213957	−	0.976843i	$-0.568635\pi$
$67$	−3.50262	−0.427913	−0.213957	+	0.976843i	$0.568635\pi$
$68$	2.19676	0.266396
$69$	3.73015	0.449057
$70$	−2.30107	−0.275031
$71$	1.48701	0.176476	0.0882379	−	0.996099i	$-0.471876\pi$
$71$	1.48701	0.176476	0.0882379	+	0.996099i	$0.471876\pi$
$72$	2.01085	0.236981
$73$	12.4849	1.46125	0.730626	−	0.682778i	$-0.239228\pi$
$73$	12.4849	1.46125	0.730626	+	0.682778i	$0.239228\pi$
$74$	5.33254	0.619896
$75$	5.13345	0.592759
$76$	−1.00000	−0.114708
$77$	1.36195	0.155209
$78$	−1.85221	−0.209722
$79$	−5.56487	−0.626097	−0.313048	−	0.949737i	$-0.601350\pi$
$79$	−5.56487	−0.626097	−0.313048	+	0.949737i	$0.601350\pi$
$80$	−3.18772	−0.356397
$81$	1.07608	0.119564
$82$	−10.8945	−1.20310
$83$	−5.62995	−0.617967	−0.308983	−	0.951067i	$-0.599989\pi$
$83$	−5.62995	−0.617967	−0.308983	+	0.951067i	$0.599989\pi$
$84$	−0.717929	−0.0783324
$85$	−7.00263	−0.759542
$86$	2.68486	0.289516
$87$	5.52850	0.592717
$88$	1.88674	0.201127
$89$	5.68927	0.603061	0.301531	−	0.953456i	$-0.402502\pi$
$89$	5.68927	0.603061	0.301531	+	0.953456i	$0.402502\pi$
$90$	−6.41002	−0.675676
$91$	−1.34435	−0.140926
$92$	3.75056	0.391023
$93$	2.68034	0.277939
$94$	10.2574	1.05797
$95$	3.18772	0.327053
$96$	−0.994559	−0.101507
$97$	18.7000	1.89870	0.949348	−	0.314226i	$-0.101745\pi$
$97$	18.7000	1.89870	0.949348	+	0.314226i	$0.101745\pi$
$98$	6.47892	0.654470
$99$	3.79395	0.381306
$100$	5.16153	0.516153
$101$	2.82835	0.281431	0.140716	−	0.990050i	$-0.455060\pi$
$101$	2.82835	0.281431	0.140716	+	0.990050i	$0.455060\pi$
$102$	−2.18480	−0.216328
$103$	−18.7443	−1.84693	−0.923464	−	0.383685i	$-0.874655\pi$
$103$	−18.7443	−1.84693	−0.923464	+	0.383685i	$0.874655\pi$
$104$	−1.86235	−0.182618
$105$	2.28855	0.223340
$106$	0.302806	0.0294112
$107$	8.14423	0.787332	0.393666	−	0.919253i	$-0.371207\pi$
$107$	8.14423	0.787332	0.393666	+	0.919253i	$0.371207\pi$
$108$	−4.98359	−0.479546
$109$	1.95164	0.186933	0.0934664	−	0.995622i	$-0.470205\pi$
$109$	1.95164	0.186933	0.0934664	+	0.995622i	$0.470205\pi$
$110$	−6.01438	−0.573449
$111$	−5.30353	−0.503389
$112$	−0.721856	−0.0682090
$113$	−7.49146	−0.704737	−0.352369	−	0.935861i	$-0.614624\pi$
$113$	−7.49146	−0.704737	−0.352369	+	0.935861i	$0.614624\pi$
$114$	0.994559	0.0931490
$115$	−11.9557	−1.11488
$116$	5.55874	0.516116
$117$	−3.74490	−0.346216
$118$	−12.1685	−1.12020
$119$	−1.58574	−0.145365
$120$	3.17037	0.289414
$121$	−7.44023	−0.676384
$122$	−0.637129	−0.0576829
$123$	10.8353	0.976982
$124$	2.69501	0.242019
$125$	−0.514905	−0.0460545
$126$	−1.45155	−0.129314
$127$	17.4951	1.55244	0.776220	−	0.630462i	$-0.217134\pi$
$127$	17.4951	1.55244	0.776220	+	0.630462i	$0.217134\pi$
$128$	−1.00000	−0.0883883
$129$	−2.67025	−0.235103
$130$	5.93663	0.520677
$131$	−6.66336	−0.582180	−0.291090	−	0.956696i	$-0.594018\pi$
$131$	−6.66336	−0.582180	−0.291090	+	0.956696i	$0.594018\pi$
$132$	−1.87647	−0.163326
$133$	0.721856	0.0625929
$134$	3.50262	0.302580
$135$	15.8863	1.36727
$136$	−2.19676	−0.188370
$137$	−7.53527	−0.643781	−0.321891	−	0.946777i	$-0.604318\pi$
$137$	−7.53527	−0.643781	−0.321891	+	0.946777i	$0.604318\pi$
$138$	−3.73015	−0.317532
$139$	−14.8868	−1.26268	−0.631339	−	0.775507i	$-0.717494\pi$
$139$	−14.8868	−1.26268	−0.631339	+	0.775507i	$0.717494\pi$
$140$	2.30107	0.194476
$141$	−10.2016	−0.859130
$142$	−1.48701	−0.124787
$143$	−3.51376	−0.293835
$144$	−2.01085	−0.167571
$145$	−17.7197	−1.47154
$146$	−12.4849	−1.03326
$147$	−6.44367	−0.531465
$148$	−5.33254	−0.438332
$149$	21.5573	1.76604	0.883021	−	0.469333i	$-0.155506\pi$
$149$	21.5573	1.76604	0.883021	+	0.469333i	$0.155506\pi$
$150$	−5.13345	−0.419144
$151$	−11.2237	−0.913375	−0.456688	−	0.889627i	$-0.650964\pi$
$151$	−11.2237	−0.913375	−0.456688	+	0.889627i	$0.650964\pi$
$152$	1.00000	0.0811107
$153$	−4.41735	−0.357122
$154$	−1.36195	−0.109749
$155$	−8.59092	−0.690039
$156$	1.85221	0.148296
$157$	9.65400	0.770473	0.385237	−	0.922818i	$-0.374120\pi$
$157$	9.65400	0.770473	0.385237	+	0.922818i	$0.374120\pi$
$158$	5.56487	0.442717
$159$	−0.301159	−0.0238835
$160$	3.18772	0.252011
$161$	−2.70736	−0.213370
$162$	−1.07608	−0.0845449
$163$	0.658760	0.0515981	0.0257991	−	0.999667i	$-0.491787\pi$
$163$	0.658760	0.0515981	0.0257991	+	0.999667i	$0.491787\pi$
$164$	10.8945	0.850720
$165$	5.98166	0.465671
$166$	5.62995	0.436969
$167$	1.69848	0.131432	0.0657160	−	0.997838i	$-0.479067\pi$
$167$	1.69848	0.131432	0.0657160	+	0.997838i	$0.479067\pi$
$168$	0.717929	0.0553894
$169$	−9.53167	−0.733205
$170$	7.00263	0.537077
$171$	2.01085	0.153774
$172$	−2.68486	−0.204719
$173$	−16.1442	−1.22742	−0.613711	−	0.789531i	$-0.710324\pi$
$173$	−16.1442	−1.22742	−0.613711	+	0.789531i	$0.710324\pi$
$174$	−5.52850	−0.419114
$175$	−3.72588	−0.281650
$176$	−1.88674	−0.142218
$177$	12.1022	0.909660
$178$	−5.68927	−0.426429
$179$	7.10877	0.531334	0.265667	−	0.964065i	$-0.414408\pi$
$179$	7.10877	0.531334	0.265667	+	0.964065i	$0.414408\pi$
$180$	6.41002	0.477775
$181$	15.8357	1.17706	0.588529	−	0.808476i	$-0.299707\pi$
$181$	15.8357	1.17706	0.588529	+	0.808476i	$0.299707\pi$
$182$	1.34435	0.0996495
$183$	0.633662	0.0468417
$184$	−3.75056	−0.276495
$185$	16.9986	1.24976
$186$	−2.68034	−0.196532
$187$	−4.14470	−0.303090
$188$	−10.2574	−0.748099
$189$	3.59743	0.261675
$190$	−3.18772	−0.231261
$191$	7.53684	0.545347	0.272673	−	0.962107i	$-0.412092\pi$
$191$	7.53684	0.545347	0.272673	+	0.962107i	$0.412092\pi$
$192$	0.994559	0.0717761
$193$	−9.85398	−0.709305	−0.354652	−	0.934998i	$-0.615401\pi$
$193$	−9.85398	−0.709305	−0.354652	+	0.934998i	$0.615401\pi$
$194$	−18.7000	−1.34258
$195$	−5.90433	−0.422818
$196$	−6.47892	−0.462780
$197$	−2.15032	−0.153204	−0.0766019	−	0.997062i	$-0.524407\pi$
$197$	−2.15032	−0.153204	−0.0766019	+	0.997062i	$0.524407\pi$
$198$	−3.79395	−0.269624
$199$	0.101812	0.00721726	0.00360863	−	0.999993i	$-0.498851\pi$
$199$	0.101812	0.00721726	0.00360863	+	0.999993i	$0.498851\pi$
$200$	−5.16153	−0.364975
$201$	−3.48356	−0.245712
$202$	−2.82835	−0.199002
$203$	−4.01261	−0.281630
$204$	2.18480	0.152967
$205$	−34.7287	−2.42556
$206$	18.7443	1.30598
$207$	−7.54181	−0.524192
$208$	1.86235	0.129130
$209$	1.88674	0.130508
$210$	−2.28855	−0.157925
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−0.302806	−0.0207968
$213$	1.47892	0.101334
$214$	−8.14423	−0.556728
$215$	8.55857	0.583690
$216$	4.98359	0.339090
$217$	−1.94541	−0.132063
$218$	−1.95164	−0.132181
$219$	12.4170	0.839065
$220$	6.01438	0.405489
$221$	4.09112	0.275198
$222$	5.30353	0.355950
$223$	−21.1981	−1.41953	−0.709765	−	0.704439i	$-0.751199\pi$
$223$	−21.1981	−1.41953	−0.709765	+	0.704439i	$0.751199\pi$
$224$	0.721856	0.0482310
$225$	−10.3791	−0.691938
$226$	7.49146	0.498324
$227$	−12.9478	−0.859376	−0.429688	−	0.902977i	$-0.641376\pi$
$227$	−12.9478	−0.859376	−0.429688	+	0.902977i	$0.641376\pi$
$228$	−0.994559	−0.0658663
$229$	−12.8068	−0.846300	−0.423150	−	0.906060i	$-0.639076\pi$
$229$	−12.8068	−0.846300	−0.423150	+	0.906060i	$0.639076\pi$
$230$	11.9557	0.788336
$231$	1.35454	0.0891223
$232$	−5.55874	−0.364949
$233$	−22.9645	−1.50445	−0.752226	−	0.658905i	$-0.771020\pi$
$233$	−22.9645	−1.50445	−0.752226	+	0.658905i	$0.771020\pi$
$234$	3.74490	0.244812
$235$	32.6977	2.13296
$236$	12.1685	0.792099
$237$	−5.53459	−0.359511
$238$	1.58574	0.102788
$239$	−23.8796	−1.54464	−0.772321	−	0.635233i	$-0.780904\pi$
$239$	−23.8796	−1.54464	−0.772321	+	0.635233i	$0.780904\pi$
$240$	−3.17037	−0.204647
$241$	−5.53155	−0.356318	−0.178159	−	0.984002i	$-0.557014\pi$
$241$	−5.53155	−0.356318	−0.178159	+	0.984002i	$0.557014\pi$
$242$	7.44023	0.478276
$243$	16.0210	1.02775
$244$	0.637129	0.0407880
$245$	20.6530	1.31947
$246$	−10.8353	−0.690831
$247$	−1.86235	−0.118498
$248$	−2.69501	−0.171133
$249$	−5.59932	−0.354842
$250$	0.514905	0.0325655
$251$	−17.3718	−1.09650	−0.548250	−	0.836315i	$-0.684706\pi$
$251$	−17.3718	−1.09650	−0.548250	+	0.836315i	$0.684706\pi$
$252$	1.45155	0.0914388
$253$	−7.07631	−0.444884
$254$	−17.4951	−1.09774
$255$	−6.96453	−0.436136
$256$	1.00000	0.0625000
$257$	2.15996	0.134734	0.0673672	−	0.997728i	$-0.478540\pi$
$257$	2.15996	0.134734	0.0673672	+	0.997728i	$0.478540\pi$
$258$	2.67025	0.166243
$259$	3.84933	0.239186
$260$	−5.93663	−0.368174
$261$	−11.1778	−0.691889
$262$	6.66336	0.411663
$263$	11.3713	0.701183	0.350591	−	0.936529i	$-0.385981\pi$
$263$	11.3713	0.701183	0.350591	+	0.936529i	$0.385981\pi$
$264$	1.87647	0.115489
$265$	0.965260	0.0592955
$266$	−0.721856	−0.0442598
$267$	5.65832	0.346283
$268$	−3.50262	−0.213957
$269$	−12.6591	−0.771837	−0.385919	−	0.922533i	$-0.626115\pi$
$269$	−12.6591	−0.771837	−0.385919	+	0.922533i	$0.626115\pi$
$270$	−15.8863	−0.966807
$271$	−30.6640	−1.86270	−0.931352	−	0.364121i	$-0.881370\pi$
$271$	−30.6640	−1.86270	−0.931352	+	0.364121i	$0.881370\pi$
$272$	2.19676	0.133198
$273$	−1.33703	−0.0809208
$274$	7.53527	0.455222
$275$	−9.73844	−0.587250
$276$	3.73015	0.224529
$277$	−9.85161	−0.591926	−0.295963	−	0.955199i	$-0.595640\pi$
$277$	−9.85161	−0.591926	−0.295963	+	0.955199i	$0.595640\pi$
$278$	14.8868	0.892848
$279$	−5.41926	−0.324443
$280$	−2.30107	−0.137515
$281$	20.2029	1.20520	0.602601	−	0.798043i	$-0.294131\pi$
$281$	20.2029	1.20520	0.602601	+	0.798043i	$0.294131\pi$
$282$	10.2016	0.607497
$283$	−21.8065	−1.29626	−0.648132	−	0.761528i	$-0.724450\pi$
$283$	−21.8065	−1.29626	−0.648132	+	0.761528i	$0.724450\pi$
$284$	1.48701	0.0882379
$285$	3.17037	0.187797
$286$	3.51376	0.207773
$287$	−7.86428	−0.464214
$288$	2.01085	0.118491
$289$	−12.1743	−0.716133
$290$	17.7197	1.04054
$291$	18.5982	1.09025
$292$	12.4849	0.730626
$293$	16.5822	0.968740	0.484370	−	0.874863i	$-0.339049\pi$
$293$	16.5822	0.968740	0.484370	+	0.874863i	$0.339049\pi$
$294$	6.44367	0.375803
$295$	−38.7896	−2.25842
$296$	5.33254	0.309948
$297$	9.40272	0.545601
$298$	−21.5573	−1.24878
$299$	6.98483	0.403943
$300$	5.13345	0.296380
$301$	1.93808	0.111709
$302$	11.2237	0.645854
$303$	2.81296	0.161600
$304$	−1.00000	−0.0573539
$305$	−2.03098	−0.116294
$306$	4.41735	0.252523
$307$	−6.86076	−0.391564	−0.195782	−	0.980647i	$-0.562725\pi$
$307$	−6.86076	−0.391564	−0.195782	+	0.980647i	$0.562725\pi$
$308$	1.36195	0.0776044
$309$	−18.6423	−1.06052
$310$	8.59092	0.487931
$311$	5.16375	0.292809	0.146405	−	0.989225i	$-0.453230\pi$
$311$	5.16375	0.292809	0.146405	+	0.989225i	$0.453230\pi$
$312$	−1.85221	−0.104861
$313$	−19.6548	−1.11095	−0.555477	−	0.831532i	$-0.687464\pi$
$313$	−19.6548	−1.11095	−0.555477	+	0.831532i	$0.687464\pi$
$314$	−9.65400	−0.544807
$315$	−4.62711	−0.260708
$316$	−5.56487	−0.313048
$317$	11.2578	0.632304	0.316152	−	0.948709i	$-0.397609\pi$
$317$	11.2578	0.632304	0.316152	+	0.948709i	$0.397609\pi$
$318$	0.301159	0.0168882
$319$	−10.4879	−0.587208
$320$	−3.18772	−0.178199
$321$	8.09992	0.452093
$322$	2.70736	0.150875
$323$	−2.19676	−0.122231
$324$	1.07608	0.0597822
$325$	9.61255	0.533208
$326$	−0.658760	−0.0364854
$327$	1.94102	0.107339
$328$	−10.8945	−0.601550
$329$	7.40438	0.408216
$330$	−5.98166	−0.329279
$331$	7.81406	0.429500	0.214750	−	0.976669i	$-0.431106\pi$
$331$	7.81406	0.429500	0.214750	+	0.976669i	$0.431106\pi$
$332$	−5.62995	−0.308983
$333$	10.7230	0.587614
$334$	−1.69848	−0.0929364
$335$	11.1654	0.610028
$336$	−0.717929	−0.0391662
$337$	−0.463821	−0.0252659	−0.0126330	−	0.999920i	$-0.504021\pi$
$337$	−0.463821	−0.0252659	−0.0126330	+	0.999920i	$0.504021\pi$
$338$	9.53167	0.518454
$339$	−7.45070	−0.404666
$340$	−7.00263	−0.379771
$341$	−5.08477	−0.275356
$342$	−2.01085	−0.108734
$343$	9.72984	0.525362
$344$	2.68486	0.144758
$345$	−11.8907	−0.640172
$346$	16.1442	0.867918
$347$	−20.2158	−1.08524	−0.542619	−	0.839979i	$-0.682567\pi$
$347$	−20.2158	−1.08524	−0.542619	+	0.839979i	$0.682567\pi$
$348$	5.52850	0.296359
$349$	−22.4771	−1.20317	−0.601587	−	0.798807i	$-0.705465\pi$
$349$	−22.4771	−1.20317	−0.601587	+	0.798807i	$0.705465\pi$
$350$	3.72588	0.199157
$351$	−9.28117	−0.495392
$352$	1.88674	0.100563
$353$	−14.8736	−0.791642	−0.395821	−	0.918328i	$-0.629540\pi$
$353$	−14.8736	−0.791642	−0.395821	+	0.918328i	$0.629540\pi$
$354$	−12.1022	−0.643227
$355$	−4.74017	−0.251582
$356$	5.68927	0.301531
$357$	−1.57711	−0.0834697
$358$	−7.10877	−0.375710
$359$	−14.7547	−0.778725	−0.389362	−	0.921085i	$-0.627305\pi$
$359$	−14.7547	−0.778725	−0.389362	+	0.921085i	$0.627305\pi$
$360$	−6.41002	−0.337838
$361$	1.00000	0.0526316
$362$	−15.8357	−0.832306
$363$	−7.39975	−0.388386
$364$	−1.34435	−0.0704628
$365$	−39.7985	−2.08315
$366$	−0.633662	−0.0331220
$367$	−14.6163	−0.762965	−0.381482	−	0.924376i	$-0.624586\pi$
$367$	−14.6163	−0.762965	−0.381482	+	0.924376i	$0.624586\pi$
$368$	3.75056	0.195511
$369$	−21.9073	−1.14045
$370$	−16.9986	−0.883717
$371$	0.218583	0.0113482
$372$	2.68034	0.138969
$373$	9.03773	0.467956	0.233978	−	0.972242i	$-0.424826\pi$
$373$	9.03773	0.467956	0.233978	+	0.972242i	$0.424826\pi$
$374$	4.14470	0.214317
$375$	−0.512104	−0.0264449
$376$	10.2574	0.528986
$377$	10.3523	0.533170
$378$	−3.59743	−0.185032
$379$	3.04627	0.156476	0.0782382	−	0.996935i	$-0.475071\pi$
$379$	3.04627	0.156476	0.0782382	+	0.996935i	$0.475071\pi$
$380$	3.18772	0.163526
$381$	17.3999	0.891425
$382$	−7.53684	−0.385618
$383$	−22.9135	−1.17083	−0.585413	−	0.810735i	$-0.699068\pi$
$383$	−22.9135	−1.17083	−0.585413	+	0.810735i	$0.699068\pi$
$384$	−0.994559	−0.0507534
$385$	−4.34152	−0.221264
$386$	9.85398	0.501554
$387$	5.39886	0.274439
$388$	18.7000	0.949348
$389$	−4.68637	−0.237609	−0.118804	−	0.992918i	$-0.537906\pi$
$389$	−4.68637	−0.237609	−0.118804	+	0.992918i	$0.537906\pi$
$390$	5.90433	0.298977
$391$	8.23906	0.416667
$392$	6.47892	0.327235
$393$	−6.62710	−0.334293
$394$	2.15032	0.108332
$395$	17.7392	0.892557
$396$	3.79395	0.190653
$397$	5.49380	0.275726	0.137863	−	0.990451i	$-0.455977\pi$
$397$	5.49380	0.275726	0.137863	+	0.990451i	$0.455977\pi$
$398$	−0.101812	−0.00510337
$399$	0.717929	0.0359414
$400$	5.16153	0.258076
$401$	15.0000	0.749065	0.374533	−	0.927214i	$-0.377803\pi$
$401$	15.0000	0.749065	0.374533	+	0.927214i	$0.377803\pi$
$402$	3.48356	0.173744
$403$	5.01904	0.250016
$404$	2.82835	0.140716
$405$	−3.43024	−0.170450
$406$	4.01261	0.199142
$407$	10.0611	0.498710
$408$	−2.18480	−0.108164
$409$	−22.1504	−1.09527	−0.547634	−	0.836718i	$-0.684471\pi$
$409$	−22.1504	−1.09527	−0.547634	+	0.836718i	$0.684471\pi$
$410$	34.7287	1.71513
$411$	−7.49427	−0.369665
$412$	−18.7443	−0.923464
$413$	−8.78387	−0.432226
$414$	7.54181	0.370660
$415$	17.9467	0.880967
$416$	−1.86235	−0.0913090
$417$	−14.8058	−0.725041
$418$	−1.88674	−0.0922833
$419$	2.96078	0.144644	0.0723219	−	0.997381i	$-0.476959\pi$
$419$	2.96078	0.144644	0.0723219	+	0.997381i	$0.476959\pi$
$420$	2.28855	0.111670
$421$	−24.2352	−1.18115	−0.590576	−	0.806982i	$-0.701099\pi$
$421$	−24.2352	−1.18115	−0.590576	+	0.806982i	$0.701099\pi$
$422$	1.00000	0.0486792
$423$	20.6261	1.00288
$424$	0.302806	0.0147056
$425$	11.3386	0.550004
$426$	−1.47892	−0.0716540
$427$	−0.459915	−0.0222568
$428$	8.14423	0.393666
$429$	−3.49464	−0.168723
$430$	−8.55857	−0.412731
$431$	−16.5726	−0.798276	−0.399138	−	0.916891i	$-0.630691\pi$
$431$	−16.5726	−0.798276	−0.399138	+	0.916891i	$0.630691\pi$
$432$	−4.98359	−0.239773
$433$	−19.5675	−0.940354	−0.470177	−	0.882572i	$-0.655810\pi$
$433$	−19.5675	−0.940354	−0.470177	+	0.882572i	$0.655810\pi$
$434$	1.94541	0.0933825
$435$	−17.6233	−0.844971
$436$	1.95164	0.0934664
$437$	−3.75056	−0.179413
$438$	−12.4170	−0.593308
$439$	−10.0394	−0.479156	−0.239578	−	0.970877i	$-0.577009\pi$
$439$	−10.0394	−0.479156	−0.239578	+	0.970877i	$0.577009\pi$
$440$	−6.01438	−0.286724
$441$	13.0282	0.620388
$442$	−4.09112	−0.194595
$443$	3.74979	0.178158	0.0890789	−	0.996025i	$-0.471608\pi$
$443$	3.74979	0.178158	0.0890789	+	0.996025i	$0.471608\pi$
$444$	−5.30353	−0.251694
$445$	−18.1358	−0.859718
$446$	21.1981	1.00376
$447$	21.4400	1.01408
$448$	−0.721856	−0.0341045
$449$	34.5318	1.62966	0.814829	−	0.579702i	$-0.196831\pi$
$449$	34.5318	1.62966	0.814829	+	0.579702i	$0.196831\pi$
$450$	10.3791	0.489274
$451$	−20.5551	−0.967902
$452$	−7.49146	−0.352369
$453$	−11.1627	−0.524468
$454$	12.9478	0.607670
$455$	4.28539	0.200902
$456$	0.994559	0.0465745
$457$	−20.6178	−0.964458	−0.482229	−	0.876045i	$-0.660173\pi$
$457$	−20.6178	−0.964458	−0.482229	+	0.876045i	$0.660173\pi$
$458$	12.8068	0.598425
$459$	−10.9477	−0.510996
$460$	−11.9557	−0.557438
$461$	−8.33906	−0.388389	−0.194194	−	0.980963i	$-0.562209\pi$
$461$	−8.33906	−0.388389	−0.194194	+	0.980963i	$0.562209\pi$
$462$	−1.35454	−0.0630190
$463$	−11.4598	−0.532584	−0.266292	−	0.963892i	$-0.585799\pi$
$463$	−11.4598	−0.532584	−0.266292	+	0.963892i	$0.585799\pi$
$464$	5.55874	0.258058
$465$	−8.54417	−0.396227
$466$	22.9645	1.06381
$467$	18.8303	0.871362	0.435681	−	0.900101i	$-0.356508\pi$
$467$	18.8303	0.871362	0.435681	+	0.900101i	$0.356508\pi$
$468$	−3.74490	−0.173108
$469$	2.52839	0.116750
$470$	−32.6977	−1.50823
$471$	9.60148	0.442413
$472$	−12.1685	−0.560098
$473$	5.06563	0.232918
$474$	5.53459	0.254212
$475$	−5.16153	−0.236827
$476$	−1.58574	−0.0726823
$477$	0.608899	0.0278796
$478$	23.8796	1.09223
$479$	5.02945	0.229801	0.114901	−	0.993377i	$-0.463345\pi$
$479$	5.02945	0.229801	0.114901	+	0.993377i	$0.463345\pi$
$480$	3.17037	0.144707
$481$	−9.93104	−0.452816
$482$	5.53155	0.251955
$483$	−2.69263	−0.122519
$484$	−7.44023	−0.338192
$485$	−59.6102	−2.70676
$486$	−16.0210	−0.726727
$487$	36.0613	1.63409	0.817046	−	0.576572i	$-0.195610\pi$
$487$	36.0613	1.63409	0.817046	+	0.576572i	$0.195610\pi$
$488$	−0.637129	−0.0288415
$489$	0.655176	0.0296281
$490$	−20.6530	−0.933006
$491$	23.1166	1.04324	0.521619	−	0.853178i	$-0.325328\pi$
$491$	23.1166	1.04324	0.521619	+	0.853178i	$0.325328\pi$
$492$	10.8353	0.488491
$493$	12.2112	0.549965
$494$	1.86235	0.0837909
$495$	−12.0940	−0.543586
$496$	2.69501	0.121009
$497$	−1.07341	−0.0481490
$498$	5.59932	0.250911
$499$	28.2985	1.26681	0.633407	−	0.773819i	$-0.281656\pi$
$499$	28.2985	1.26681	0.633407	+	0.773819i	$0.281656\pi$
$500$	−0.514905	−0.0230273
$501$	1.68923	0.0754694
$502$	17.3718	0.775342
$503$	−11.7075	−0.522011	−0.261006	−	0.965337i	$-0.584054\pi$
$503$	−11.7075	−0.522011	−0.261006	+	0.965337i	$0.584054\pi$
$504$	−1.45155	−0.0646570
$505$	−9.01597	−0.401205
$506$	7.07631	0.314581
$507$	−9.47981	−0.421013
$508$	17.4951	0.776220
$509$	7.22643	0.320306	0.160153	−	0.987092i	$-0.448801\pi$
$509$	7.22643	0.320306	0.160153	+	0.987092i	$0.448801\pi$
$510$	6.96453	0.308395
$511$	−9.01233	−0.398682
$512$	−1.00000	−0.0441942
$513$	4.98359	0.220031
$514$	−2.15996	−0.0952717
$515$	59.7514	2.63296
$516$	−2.67025	−0.117551
$517$	19.3530	0.851146
$518$	−3.84933	−0.169130
$519$	−16.0564	−0.704797
$520$	5.93663	0.260338
$521$	11.8773	0.520354	0.260177	−	0.965561i	$-0.416219\pi$
$521$	11.8773	0.520354	0.260177	+	0.965561i	$0.416219\pi$
$522$	11.1778	0.489239
$523$	−21.7126	−0.949427	−0.474714	−	0.880140i	$-0.657448\pi$
$523$	−21.7126	−0.949427	−0.474714	+	0.880140i	$0.657448\pi$
$524$	−6.66336	−0.291090
$525$	−3.70561	−0.161726
$526$	−11.3713	−0.495811
$527$	5.92027	0.257891
$528$	−1.87647	−0.0816629
$529$	−8.93332	−0.388405
$530$	−0.965260	−0.0419282
$531$	−24.4690	−1.06186
$532$	0.721856	0.0312964
$533$	20.2894	0.878831
$534$	−5.65832	−0.244859
$535$	−25.9615	−1.12241
$536$	3.50262	0.151290
$537$	7.07009	0.305097
$538$	12.6591	0.545771
$539$	12.2240	0.526526
$540$	15.8863	0.683636
$541$	−26.4304	−1.13633	−0.568166	−	0.822914i	$-0.692347\pi$
$541$	−26.4304	−1.13633	−0.568166	+	0.822914i	$0.692347\pi$
$542$	30.6640	1.31713
$543$	15.7495	0.675878
$544$	−2.19676	−0.0941851
$545$	−6.22126	−0.266490
$546$	1.33703	0.0572197
$547$	26.1072	1.11626	0.558131	−	0.829753i	$-0.311519\pi$
$547$	26.1072	1.11626	0.558131	+	0.829753i	$0.311519\pi$
$548$	−7.53527	−0.321891
$549$	−1.28117	−0.0546790
$550$	9.73844	0.415249
$551$	−5.55874	−0.236810
$552$	−3.73015	−0.158766
$553$	4.01704	0.170822
$554$	9.85161	0.418555
$555$	16.9061	0.717626
$556$	−14.8868	−0.631339
$557$	−2.67458	−0.113326	−0.0566629	−	0.998393i	$-0.518046\pi$
$557$	−2.67458	−0.113326	−0.0566629	+	0.998393i	$0.518046\pi$
$558$	5.41926	0.229416
$559$	−5.00014	−0.211483
$560$	2.30107	0.0972380
$561$	−4.12215	−0.174037
$562$	−20.2029	−0.852207
$563$	−15.7110	−0.662139	−0.331069	−	0.943606i	$-0.607409\pi$
$563$	−15.7110	−0.662139	−0.331069	+	0.943606i	$0.607409\pi$
$564$	−10.2016	−0.429565
$565$	23.8806	1.00467
$566$	21.8065	0.916597
$567$	−0.776775	−0.0326215
$568$	−1.48701	−0.0623936
$569$	14.4072	0.603982	0.301991	−	0.953311i	$-0.402349\pi$
$569$	14.4072	0.603982	0.301991	+	0.953311i	$0.402349\pi$
$570$	−3.17037	−0.132792
$571$	−21.4394	−0.897211	−0.448605	−	0.893730i	$-0.648079\pi$
$571$	−21.4394	−0.897211	−0.448605	+	0.893730i	$0.648079\pi$
$572$	−3.51376	−0.146918
$573$	7.49584	0.313143
$574$	7.86428	0.328249
$575$	19.3586	0.807310
$576$	−2.01085	−0.0837855
$577$	40.3744	1.68081	0.840404	−	0.541961i	$-0.182318\pi$
$577$	40.3744	1.68081	0.840404	+	0.541961i	$0.182318\pi$
$578$	12.1743	0.506383
$579$	−9.80036	−0.407289
$580$	−17.7197	−0.735770
$581$	4.06401	0.168604
$582$	−18.5982	−0.770922
$583$	0.571316	0.0236615
$584$	−12.4849	−0.516631
$585$	11.9377	0.493562
$586$	−16.5822	−0.685003
$587$	−1.27372	−0.0525721	−0.0262861	−	0.999654i	$-0.508368\pi$
$587$	−1.27372	−0.0525721	−0.0262861	+	0.999654i	$0.508368\pi$
$588$	−6.44367	−0.265733
$589$	−2.69501	−0.111046
$590$	38.7896	1.59694
$591$	−2.13862	−0.0879711
$592$	−5.33254	−0.219166
$593$	−17.1214	−0.703090	−0.351545	−	0.936171i	$-0.614344\pi$
$593$	−17.1214	−0.703090	−0.351545	+	0.936171i	$0.614344\pi$
$594$	−9.40272	−0.385798
$595$	5.05489	0.207230
$596$	21.5573	0.883021
$597$	0.101258	0.00414421
$598$	−6.98483	−0.285631
$599$	7.19078	0.293807	0.146904	−	0.989151i	$-0.453069\pi$
$599$	7.19078	0.293807	0.146904	+	0.989151i	$0.453069\pi$
$600$	−5.13345	−0.209572
$601$	−14.2428	−0.580977	−0.290489	−	0.956878i	$-0.593818\pi$
$601$	−14.2428	−0.580977	−0.290489	+	0.956878i	$0.593818\pi$
$602$	−1.93808	−0.0789904
$603$	7.04325	0.286823
$604$	−11.2237	−0.456688
$605$	23.7173	0.964246
$606$	−2.81296	−0.114269
$607$	9.58209	0.388925	0.194463	−	0.980910i	$-0.437704\pi$
$607$	9.58209	0.388925	0.194463	+	0.980910i	$0.437704\pi$
$608$	1.00000	0.0405554
$609$	−3.99078	−0.161715
$610$	2.03098	0.0822321
$611$	−19.1029	−0.772819
$612$	−4.41735	−0.178561
$613$	−15.0392	−0.607429	−0.303714	−	0.952763i	$-0.598227\pi$
$613$	−15.0392	−0.607429	−0.303714	+	0.952763i	$0.598227\pi$
$614$	6.86076	0.276878
$615$	−34.5397	−1.39278
$616$	−1.36195	−0.0548746
$617$	−31.3535	−1.26225	−0.631123	−	0.775683i	$-0.717406\pi$
$617$	−31.3535	−1.26225	−0.631123	+	0.775683i	$0.717406\pi$
$618$	18.6423	0.749903
$619$	40.7615	1.63834	0.819172	−	0.573548i	$-0.194433\pi$
$619$	40.7615	1.63834	0.819172	+	0.573548i	$0.194433\pi$
$620$	−8.59092	−0.345019
$621$	−18.6912	−0.750054
$622$	−5.16375	−0.207047
$623$	−4.10683	−0.164537
$624$	1.85221	0.0741479
$625$	−24.1663	−0.966651
$626$	19.6548	0.785563
$627$	1.87647	0.0749390
$628$	9.65400	0.385237
$629$	−11.7143	−0.467080
$630$	4.62711	0.184349
$631$	31.3886	1.24956	0.624779	−	0.780801i	$-0.285189\pi$
$631$	31.3886	1.24956	0.624779	+	0.780801i	$0.285189\pi$
$632$	5.56487	0.221359
$633$	−0.994559	−0.0395302
$634$	−11.2578	−0.447106
$635$	−55.7694	−2.21314
$636$	−0.301159	−0.0119417
$637$	−12.0660	−0.478072
$638$	10.4879	0.415219
$639$	−2.99016	−0.118289
$640$	3.18772	0.126006
$641$	−2.31164	−0.0913041	−0.0456521	−	0.998957i	$-0.514537\pi$
$641$	−2.31164	−0.0913041	−0.0456521	+	0.998957i	$0.514537\pi$
$642$	−8.09992	−0.319678
$643$	−25.0442	−0.987646	−0.493823	−	0.869562i	$-0.664401\pi$
$643$	−25.0442	−0.987646	−0.493823	+	0.869562i	$0.664401\pi$
$644$	−2.70736	−0.106685
$645$	8.51201	0.335160
$646$	2.19676	0.0864302
$647$	−27.5161	−1.08177	−0.540886	−	0.841096i	$-0.681911\pi$
$647$	−27.5161	−1.08177	−0.540886	+	0.841096i	$0.681911\pi$
$648$	−1.07608	−0.0422724
$649$	−22.9587	−0.901206
$650$	−9.61255	−0.377035
$651$	−1.93482	−0.0758317
$652$	0.658760	0.0257991
$653$	−7.78075	−0.304484	−0.152242	−	0.988343i	$-0.548649\pi$
$653$	−7.78075	−0.304484	−0.152242	+	0.988343i	$0.548649\pi$
$654$	−1.94102	−0.0758998
$655$	21.2409	0.829950
$656$	10.8945	0.425360
$657$	−25.1054	−0.979454
$658$	−7.40438	−0.288653
$659$	30.8510	1.20178	0.600892	−	0.799330i	$-0.294812\pi$
$659$	30.8510	1.20178	0.600892	+	0.799330i	$0.294812\pi$
$660$	5.98166	0.232836
$661$	−19.7607	−0.768601	−0.384300	−	0.923208i	$-0.625557\pi$
$661$	−19.7607	−0.768601	−0.384300	+	0.923208i	$0.625557\pi$
$662$	−7.81406	−0.303702
$663$	4.06886	0.158021
$664$	5.62995	0.218484
$665$	−2.30107	−0.0892317
$666$	−10.7230	−0.415506
$667$	20.8484	0.807252
$668$	1.69848	0.0657160
$669$	−21.0828	−0.815107
$670$	−11.1654	−0.431355
$671$	−1.20209	−0.0464063
$672$	0.717929	0.0276947
$673$	8.37179	0.322709	0.161354	−	0.986897i	$-0.448414\pi$
$673$	8.37179	0.322709	0.161354	+	0.986897i	$0.448414\pi$
$674$	0.463821	0.0178657
$675$	−25.7229	−0.990076
$676$	−9.53167	−0.366603
$677$	40.2806	1.54811	0.774054	−	0.633120i	$-0.218226\pi$
$677$	40.2806	1.54811	0.774054	+	0.633120i	$0.218226\pi$
$678$	7.45070	0.286142
$679$	−13.4987	−0.518032
$680$	7.00263	0.268539
$681$	−12.8774	−0.493461
$682$	5.08477	0.194706
$683$	46.8472	1.79256	0.896280	−	0.443489i	$-0.146260\pi$
$683$	46.8472	1.79256	0.896280	+	0.443489i	$0.146260\pi$
$684$	2.01085	0.0768868
$685$	24.0203	0.917768
$686$	−9.72984	−0.371487
$687$	−12.7372	−0.485953
$688$	−2.68486	−0.102359
$689$	−0.563930	−0.0214840
$690$	11.8907	0.452670
$691$	−15.5847	−0.592871	−0.296435	−	0.955053i	$-0.595798\pi$
$691$	−15.5847	−0.592871	−0.296435	+	0.955053i	$0.595798\pi$
$692$	−16.1442	−0.613711
$693$	−2.73868	−0.104034
$694$	20.2158	0.767380
$695$	47.4547	1.80006
$696$	−5.52850	−0.209557
$697$	23.9326	0.906513
$698$	22.4771	0.850773
$699$	−22.8395	−0.863870
$700$	−3.72588	−0.140825
$701$	−42.0011	−1.58636	−0.793180	−	0.608987i	$-0.791576\pi$
$701$	−42.0011	−1.58636	−0.793180	+	0.608987i	$0.791576\pi$
$702$	9.28117	0.350295
$703$	5.33254	0.201121
$704$	−1.88674	−0.0711091
$705$	32.5198	1.22477
$706$	14.8736	0.559775
$707$	−2.04166	−0.0767845
$708$	12.1022	0.454830
$709$	3.35816	0.126118	0.0630591	−	0.998010i	$-0.479914\pi$
$709$	3.35816	0.126118	0.0630591	+	0.998010i	$0.479914\pi$
$710$	4.74017	0.177895
$711$	11.1901	0.419663
$712$	−5.68927	−0.213214
$713$	10.1078	0.378539
$714$	1.57711	0.0590220
$715$	11.2009	0.418888
$716$	7.10877	0.265667
$717$	−23.7497	−0.886947
$718$	14.7547	0.550642
$719$	−8.18796	−0.305359	−0.152680	−	0.988276i	$-0.548790\pi$
$719$	−8.18796	−0.305359	−0.152680	+	0.988276i	$0.548790\pi$
$720$	6.41002	0.238887
$721$	13.5307	0.503908
$722$	−1.00000	−0.0372161
$723$	−5.50145	−0.204601
$724$	15.8357	0.588529
$725$	28.6916	1.06558
$726$	7.39975	0.274630
$727$	2.69900	0.100101	0.0500503	−	0.998747i	$-0.484062\pi$
$727$	2.69900	0.100101	0.0500503	+	0.998747i	$0.484062\pi$
$728$	1.34435	0.0498248
$729$	12.7056	0.470577
$730$	39.7985	1.47301
$731$	−5.89798	−0.218145
$732$	0.633662	0.0234208
$733$	−25.1206	−0.927852	−0.463926	−	0.885874i	$-0.653560\pi$
$733$	−25.1206	−0.927852	−0.463926	+	0.885874i	$0.653560\pi$
$734$	14.6163	0.539497
$735$	20.5406	0.757651
$736$	−3.75056	−0.138247
$737$	6.60852	0.243428
$738$	21.9073	0.806418
$739$	48.9411	1.80033	0.900164	−	0.435550i	$-0.143446\pi$
$739$	48.9411	1.80033	0.900164	+	0.435550i	$0.143446\pi$
$740$	16.9986	0.624882
$741$	−1.85221	−0.0680428
$742$	−0.218583	−0.00802442
$743$	20.5513	0.753954	0.376977	−	0.926223i	$-0.376964\pi$
$743$	20.5513	0.753954	0.376977	+	0.926223i	$0.376964\pi$
$744$	−2.68034	−0.0982662
$745$	−68.7185	−2.51765
$746$	−9.03773	−0.330895
$747$	11.3210	0.414213
$748$	−4.14470	−0.151545
$749$	−5.87896	−0.214813
$750$	0.512104	0.0186994
$751$	16.5466	0.603793	0.301896	−	0.953341i	$-0.402380\pi$
$751$	16.5466	0.603793	0.301896	+	0.953341i	$0.402380\pi$
$752$	−10.2574	−0.374049
$753$	−17.2773	−0.629620
$754$	−10.3523	−0.377008
$755$	35.7781	1.30210
$756$	3.59743	0.130837
$757$	−1.06705	−0.0387826	−0.0193913	−	0.999812i	$-0.506173\pi$
$757$	−1.06705	−0.0387826	−0.0193913	+	0.999812i	$0.506173\pi$
$758$	−3.04627	−0.110645
$759$	−7.03781	−0.255456
$760$	−3.18772	−0.115631
$761$	5.18965	0.188125	0.0940624	−	0.995566i	$-0.470015\pi$
$761$	5.18965	0.188125	0.0940624	+	0.995566i	$0.470015\pi$
$762$	−17.3999	−0.630333
$763$	−1.40880	−0.0510020
$764$	7.53684	0.272673
$765$	14.0813	0.509109
$766$	22.9135	0.827899
$767$	22.6619	0.818272
$768$	0.994559	0.0358881
$769$	34.2318	1.23443	0.617216	−	0.786794i	$-0.288261\pi$
$769$	34.2318	1.23443	0.617216	+	0.786794i	$0.288261\pi$
$770$	4.34152	0.156457
$771$	2.14821	0.0773658
$772$	−9.85398	−0.354652
$773$	20.2659	0.728913	0.364457	−	0.931220i	$-0.381255\pi$
$773$	20.2659	0.728913	0.364457	+	0.931220i	$0.381255\pi$
$774$	−5.39886	−0.194058
$775$	13.9104	0.499675
$776$	−18.7000	−0.671290
$777$	3.82839	0.137343
$778$	4.68637	0.168015
$779$	−10.8945	−0.390337
$780$	−5.90433	−0.211409
$781$	−2.80560	−0.100392
$782$	−8.23906	−0.294628
$783$	−27.7025	−0.990006
$784$	−6.47892	−0.231390
$785$	−30.7742	−1.09838
$786$	6.62710	0.236381
$787$	35.1885	1.25434	0.627168	−	0.778884i	$-0.284214\pi$
$787$	35.1885	1.25434	0.627168	+	0.778884i	$0.284214\pi$
$788$	−2.15032	−0.0766019
$789$	11.3094	0.402625
$790$	−17.7392	−0.631133
$791$	5.40775	0.192278
$792$	−3.79395	−0.134812
$793$	1.18655	0.0421358
$794$	−5.49380	−0.194968
$795$	0.960009	0.0340480
$796$	0.101812	0.00360863
$797$	13.6822	0.484648	0.242324	−	0.970195i	$-0.422090\pi$
$797$	13.6822	0.484648	0.242324	+	0.970195i	$0.422090\pi$
$798$	−0.717929	−0.0254144
$799$	−22.5330	−0.797161
$800$	−5.16153	−0.182488
$801$	−11.4403	−0.404222
$802$	−15.0000	−0.529669
$803$	−23.5558	−0.831266
$804$	−3.48356	−0.122856
$805$	8.63030	0.304178
$806$	−5.01904	−0.176788
$807$	−12.5902	−0.443196
$808$	−2.82835	−0.0995009
$809$	−35.0254	−1.23143	−0.615714	−	0.787970i	$-0.711132\pi$
$809$	−35.0254	−1.23143	−0.615714	+	0.787970i	$0.711132\pi$
$810$	3.43024	0.120526
$811$	−19.4275	−0.682190	−0.341095	−	0.940029i	$-0.610798\pi$
$811$	−19.4275	−0.682190	−0.341095	+	0.940029i	$0.610798\pi$
$812$	−4.01261	−0.140815
$813$	−30.4971	−1.06958
$814$	−10.0611	−0.352642
$815$	−2.09994	−0.0735577
$816$	2.18480	0.0764834
$817$	2.68486	0.0939314
$818$	22.1504	0.774471
$819$	2.70328	0.0944602
$820$	−34.7287	−1.21278
$821$	28.9473	1.01027	0.505134	−	0.863041i	$-0.331443\pi$
$821$	28.9473	1.01027	0.505134	+	0.863041i	$0.331443\pi$
$822$	7.49427	0.261393
$823$	0.848515	0.0295774	0.0147887	−	0.999891i	$-0.495292\pi$
$823$	0.848515	0.0295774	0.0147887	+	0.999891i	$0.495292\pi$
$824$	18.7443	0.652988
$825$	−9.68546	−0.337204
$826$	8.78387	0.305630
$827$	24.4475	0.850124	0.425062	−	0.905164i	$-0.360252\pi$
$827$	24.4475	0.850124	0.425062	+	0.905164i	$0.360252\pi$
$828$	−7.54181	−0.262096
$829$	6.63673	0.230503	0.115252	−	0.993336i	$-0.463233\pi$
$829$	6.63673	0.230503	0.115252	+	0.993336i	$0.463233\pi$
$830$	−17.9467	−0.622938
$831$	−9.79801	−0.339889
$832$	1.86235	0.0645652
$833$	−14.2326	−0.493131
$834$	14.8058	0.512682
$835$	−5.41425	−0.187368
$836$	1.88674	0.0652541
$837$	−13.4308	−0.464237
$838$	−2.96078	−0.102279
$839$	32.4444	1.12010	0.560052	−	0.828457i	$-0.310781\pi$
$839$	32.4444	1.12010	0.560052	+	0.828457i	$0.310781\pi$
$840$	−2.28855	−0.0789625
$841$	1.89960	0.0655034
$842$	24.2352	0.835200
$843$	20.0930	0.692038
$844$	−1.00000	−0.0344214
$845$	30.3842	1.04525
$846$	−20.6261	−0.709141
$847$	5.37077	0.184542
$848$	−0.302806	−0.0103984
$849$	−21.6879	−0.744327
$850$	−11.3386	−0.388911
$851$	−20.0000	−0.685592
$852$	1.47892	0.0506670
$853$	9.60311	0.328804	0.164402	−	0.986393i	$-0.447431\pi$
$853$	9.60311	0.328804	0.164402	+	0.986393i	$0.447431\pi$
$854$	0.459915	0.0157380
$855$	−6.41002	−0.219218
$856$	−8.14423	−0.278364
$857$	−45.1311	−1.54165	−0.770825	−	0.637048i	$-0.780155\pi$
$857$	−45.1311	−1.54165	−0.770825	+	0.637048i	$0.780155\pi$
$858$	3.49464	0.119305
$859$	−42.8624	−1.46245	−0.731223	−	0.682138i	$-0.761050\pi$
$859$	−42.8624	−1.46245	−0.731223	+	0.682138i	$0.761050\pi$
$860$	8.55857	0.291845
$861$	−7.82150	−0.266556
$862$	16.5726	0.564466
$863$	−40.5692	−1.38099	−0.690496	−	0.723337i	$-0.742608\pi$
$863$	−40.5692	−1.38099	−0.690496	+	0.723337i	$0.742608\pi$
$864$	4.98359	0.169545
$865$	51.4632	1.74980
$866$	19.5675	0.664931
$867$	−12.1080	−0.411210
$868$	−1.94541	−0.0660314
$869$	10.4994	0.356169
$870$	17.6233	0.597485
$871$	−6.52309	−0.221026
$872$	−1.95164	−0.0660907
$873$	−37.6029	−1.27267
$874$	3.75056	0.126864
$875$	0.371687	0.0125653
$876$	12.4170	0.419532
$877$	4.23013	0.142841	0.0714206	−	0.997446i	$-0.477247\pi$
$877$	4.23013	0.142841	0.0714206	+	0.997446i	$0.477247\pi$
$878$	10.0394	0.338815
$879$	16.4919	0.556259
$880$	6.01438	0.202745
$881$	−7.78759	−0.262371	−0.131185	−	0.991358i	$-0.541878\pi$
$881$	−7.78759	−0.262371	−0.131185	+	0.991358i	$0.541878\pi$
$882$	−13.0282	−0.438681
$883$	−20.2444	−0.681280	−0.340640	−	0.940194i	$-0.610644\pi$
$883$	−20.2444	−0.681280	−0.340640	+	0.940194i	$0.610644\pi$
$884$	4.09112	0.137599
$885$	−38.5785	−1.29680
$886$	−3.74979	−0.125977
$887$	−20.3263	−0.682490	−0.341245	−	0.939974i	$-0.610849\pi$
$887$	−20.3263	−0.682490	−0.341245	+	0.939974i	$0.610849\pi$
$888$	5.30353	0.177975
$889$	−12.6290	−0.423562
$890$	18.1358	0.607912
$891$	−2.03028	−0.0680169
$892$	−21.1981	−0.709765
$893$	10.2574	0.343251
$894$	−21.4400	−0.717061
$895$	−22.6607	−0.757464
$896$	0.721856	0.0241155
$897$	6.94683	0.231948
$898$	−34.5318	−1.15234
$899$	14.9808	0.499639
$900$	−10.3791	−0.345969
$901$	−0.665192	−0.0221607
$902$	20.5551	0.684410
$903$	1.92754	0.0641445
$904$	7.49146	0.249162
$905$	−50.4797	−1.67800
$906$	11.1627	0.370855
$907$	0.547462	0.0181782	0.00908908	−	0.999959i	$-0.497107\pi$
$907$	0.547462	0.0181782	0.00908908	+	0.999959i	$0.497107\pi$
$908$	−12.9478	−0.429688
$909$	−5.68739	−0.188639
$910$	−4.28539	−0.142059
$911$	−30.2801	−1.00322	−0.501612	−	0.865092i	$-0.667260\pi$
$911$	−30.2801	−1.00322	−0.501612	+	0.865092i	$0.667260\pi$
$912$	−0.994559	−0.0329331
$913$	10.6222	0.351544
$914$	20.6178	0.681975
$915$	−2.01993	−0.0667770
$916$	−12.8068	−0.423150
$917$	4.80998	0.158840
$918$	10.9477	0.361329
$919$	−58.0617	−1.91528	−0.957640	−	0.287969i	$-0.907020\pi$
$919$	−58.0617	−1.91528	−0.957640	+	0.287969i	$0.907020\pi$
$920$	11.9557	0.394168
$921$	−6.82343	−0.224840
$922$	8.33906	0.274632
$923$	2.76933	0.0911536
$924$	1.35454	0.0445612
$925$	−27.5241	−0.904986
$926$	11.4598	0.376594
$927$	37.6920	1.23797
$928$	−5.55874	−0.182475
$929$	−45.9324	−1.50699	−0.753496	−	0.657452i	$-0.771634\pi$
$929$	−45.9324	−1.50699	−0.753496	+	0.657452i	$0.771634\pi$
$930$	8.54417	0.280175
$931$	6.47892	0.212338
$932$	−22.9645	−0.752226
$933$	5.13565	0.168134
$934$	−18.8303	−0.616146
$935$	13.2121	0.432083
$936$	3.74490	0.122406
$937$	5.73070	0.187214	0.0936070	−	0.995609i	$-0.470160\pi$
$937$	5.73070	0.187214	0.0936070	+	0.995609i	$0.470160\pi$
$938$	−2.52839	−0.0825547
$939$	−19.5479	−0.637920
$940$	32.6977	1.06648
$941$	−23.3541	−0.761321	−0.380661	−	0.924715i	$-0.624303\pi$
$941$	−23.3541	−0.761321	−0.380661	+	0.924715i	$0.624303\pi$
$942$	−9.60148	−0.312833
$943$	40.8606	1.33060
$944$	12.1685	0.396049
$945$	−11.4676	−0.373041
$946$	−5.06563	−0.164698
$947$	17.7981	0.578361	0.289180	−	0.957275i	$-0.406617\pi$
$947$	17.7981	0.578361	0.289180	+	0.957275i	$0.406617\pi$
$948$	−5.53459	−0.179755
$949$	23.2513	0.754769
$950$	5.16153	0.167462
$951$	11.1966	0.363074
$952$	1.58574	0.0513942
$953$	50.7880	1.64519	0.822593	−	0.568631i	$-0.192527\pi$
$953$	50.7880	1.64519	0.822593	+	0.568631i	$0.192527\pi$
$954$	−0.608899	−0.0197138
$955$	−24.0253	−0.777441
$956$	−23.8796	−0.772321
$957$	−10.4308	−0.337180
$958$	−5.02945	−0.162494
$959$	5.43938	0.175647
$960$	−3.17037	−0.102323
$961$	−23.7369	−0.765708
$962$	9.93104	0.320190
$963$	−16.3768	−0.527736
$964$	−5.53155	−0.178159
$965$	31.4117	1.01118
$966$	2.69263	0.0866340
$967$	−18.9052	−0.607949	−0.303974	−	0.952680i	$-0.598314\pi$
$967$	−18.9052	−0.607949	−0.303974	+	0.952680i	$0.598314\pi$
$968$	7.44023	0.239138
$969$	−2.18480	−0.0701860
$970$	59.6102	1.91397
$971$	44.4734	1.42722	0.713609	−	0.700544i	$-0.247059\pi$
$971$	44.4734	1.42722	0.713609	+	0.700544i	$0.247059\pi$
$972$	16.0210	0.513874
$973$	10.7461	0.344504
$974$	−36.0613	−1.15548
$975$	9.56025	0.306173
$976$	0.637129	0.0203940
$977$	9.66945	0.309353	0.154677	−	0.987965i	$-0.450566\pi$
$977$	9.66945	0.309353	0.154677	+	0.987965i	$0.450566\pi$
$978$	−0.655176	−0.0209502
$979$	−10.7342	−0.343065
$980$	20.6530	0.659735
$981$	−3.92445	−0.125298
$982$	−23.1166	−0.737681
$983$	30.0061	0.957044	0.478522	−	0.878075i	$-0.341173\pi$
$983$	30.0061	0.957044	0.478522	+	0.878075i	$0.341173\pi$
$984$	−10.8353	−0.345415
$985$	6.85460	0.218406
$986$	−12.2112	−0.388884
$987$	7.36409	0.234402
$988$	−1.86235	−0.0592491
$989$	−10.0697	−0.320199
$990$	12.0940	0.384373
$991$	−26.3366	−0.836610	−0.418305	−	0.908307i	$-0.637376\pi$
$991$	−26.3366	−0.836610	−0.418305	+	0.908307i	$0.637376\pi$
$992$	−2.69501	−0.0855666
$993$	7.77155	0.246623
$994$	1.07341	0.0340465
$995$	−0.324547	−0.0102888
$996$	−5.59932	−0.177421
$997$	58.0345	1.83797	0.918985	−	0.394291i	$-0.129010\pi$
$997$	58.0345	1.83797	0.918985	+	0.394291i	$0.129010\pi$
$998$	−28.2985	−0.895773
$999$	26.5752	0.840802

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.22	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.22	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.994559 q^{3} +1.00000 q^{4} -3.18772 q^{5} -0.994559 q^{6} -0.721856 q^{7} -1.00000 q^{8} -2.01085 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.994559 q^{3} +1.00000 q^{4} -3.18772 q^{5} -0.994559 q^{6} -0.721856 q^{7} -1.00000 q^{8} -2.01085 q^{9} +3.18772 q^{10} -1.88674 q^{11} +0.994559 q^{12} +1.86235 q^{13} +0.721856 q^{14} -3.17037 q^{15} +1.00000 q^{16} +2.19676 q^{17} +2.01085 q^{18} -1.00000 q^{19} -3.18772 q^{20} -0.717929 q^{21} +1.88674 q^{22} +3.75056 q^{23} -0.994559 q^{24} +5.16153 q^{25} -1.86235 q^{26} -4.98359 q^{27} -0.721856 q^{28} +5.55874 q^{29} +3.17037 q^{30} +2.69501 q^{31} -1.00000 q^{32} -1.87647 q^{33} -2.19676 q^{34} +2.30107 q^{35} -2.01085 q^{36} -5.33254 q^{37} +1.00000 q^{38} +1.85221 q^{39} +3.18772 q^{40} +10.8945 q^{41} +0.717929 q^{42} -2.68486 q^{43} -1.88674 q^{44} +6.41002 q^{45} -3.75056 q^{46} -10.2574 q^{47} +0.994559 q^{48} -6.47892 q^{49} -5.16153 q^{50} +2.18480 q^{51} +1.86235 q^{52} -0.302806 q^{53} +4.98359 q^{54} +6.01438 q^{55} +0.721856 q^{56} -0.994559 q^{57} -5.55874 q^{58} +12.1685 q^{59} -3.17037 q^{60} +0.637129 q^{61} -2.69501 q^{62} +1.45155 q^{63} +1.00000 q^{64} -5.93663 q^{65} +1.87647 q^{66} -3.50262 q^{67} +2.19676 q^{68} +3.73015 q^{69} -2.30107 q^{70} +1.48701 q^{71} +2.01085 q^{72} +12.4849 q^{73} +5.33254 q^{74} +5.13345 q^{75} -1.00000 q^{76} +1.36195 q^{77} -1.85221 q^{78} -5.56487 q^{79} -3.18772 q^{80} +1.07608 q^{81} -10.8945 q^{82} -5.62995 q^{83} -0.717929 q^{84} -7.00263 q^{85} +2.68486 q^{86} +5.52850 q^{87} +1.88674 q^{88} +5.68927 q^{89} -6.41002 q^{90} -1.34435 q^{91} +3.75056 q^{92} +2.68034 q^{93} +10.2574 q^{94} +3.18772 q^{95} -0.994559 q^{96} +18.7000 q^{97} +6.47892 q^{98} +3.79395 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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