LMFDB - Embedded newform 4017.2.a.k.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46454 q^{2} +1.00000 q^{3} +0.144881 q^{4} +1.31201 q^{5} -1.46454 q^{6} +2.70261 q^{7} +2.71690 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.46454 q^{2} +1.00000 q^{3} +0.144881 q^{4} +1.31201 q^{5} -1.46454 q^{6} +2.70261 q^{7} +2.71690 q^{8} +1.00000 q^{9} -1.92149 q^{10} -1.08894 q^{11} +0.144881 q^{12} +1.00000 q^{13} -3.95808 q^{14} +1.31201 q^{15} -4.26877 q^{16} +7.41452 q^{17} -1.46454 q^{18} -2.05209 q^{19} +0.190085 q^{20} +2.70261 q^{21} +1.59480 q^{22} +2.65511 q^{23} +2.71690 q^{24} -3.27863 q^{25} -1.46454 q^{26} +1.00000 q^{27} +0.391555 q^{28} -2.42268 q^{29} -1.92149 q^{30} +2.29972 q^{31} +0.817993 q^{32} -1.08894 q^{33} -10.8589 q^{34} +3.54585 q^{35} +0.144881 q^{36} +6.46505 q^{37} +3.00537 q^{38} +1.00000 q^{39} +3.56460 q^{40} +10.0094 q^{41} -3.95808 q^{42} +5.63104 q^{43} -0.157767 q^{44} +1.31201 q^{45} -3.88852 q^{46} -1.52512 q^{47} -4.26877 q^{48} +0.304081 q^{49} +4.80168 q^{50} +7.41452 q^{51} +0.144881 q^{52} -9.33590 q^{53} -1.46454 q^{54} -1.42871 q^{55} +7.34271 q^{56} -2.05209 q^{57} +3.54811 q^{58} -8.84831 q^{59} +0.190085 q^{60} +9.82229 q^{61} -3.36804 q^{62} +2.70261 q^{63} +7.33956 q^{64} +1.31201 q^{65} +1.59480 q^{66} -2.42605 q^{67} +1.07422 q^{68} +2.65511 q^{69} -5.19304 q^{70} -1.05553 q^{71} +2.71690 q^{72} -1.00361 q^{73} -9.46833 q^{74} -3.27863 q^{75} -0.297308 q^{76} -2.94298 q^{77} -1.46454 q^{78} +12.1425 q^{79} -5.60068 q^{80} +1.00000 q^{81} -14.6592 q^{82} +5.65779 q^{83} +0.391555 q^{84} +9.72794 q^{85} -8.24689 q^{86} -2.42268 q^{87} -2.95855 q^{88} -2.96108 q^{89} -1.92149 q^{90} +2.70261 q^{91} +0.384674 q^{92} +2.29972 q^{93} +2.23360 q^{94} -2.69237 q^{95} +0.817993 q^{96} +17.5915 q^{97} -0.445339 q^{98} -1.08894 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	−1.46454	−1.03559	−0.517793	−	0.855506i	$-0.673246\pi$
$2$	−1.46454	−1.03559	−0.517793	+	0.855506i	$0.673246\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.144881	0.0724403
$5$	1.31201	0.586749	0.293375	−	0.955998i	$-0.405222\pi$
$5$	1.31201	0.586749	0.293375	+	0.955998i	$0.405222\pi$
$6$	−1.46454	−0.597896
$7$	2.70261	1.02149	0.510745	−	0.859733i	$-0.329370\pi$
$7$	2.70261	1.02149	0.510745	+	0.859733i	$0.329370\pi$
$8$	2.71690	0.960569
$9$	1.00000	0.333333
$10$	−1.92149	−0.607630
$11$	−1.08894	−0.328329	−0.164164	−	0.986433i	$-0.552493\pi$
$11$	−1.08894	−0.328329	−0.164164	+	0.986433i	$0.552493\pi$
$12$	0.144881	0.0418234
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.95808	−1.05784
$15$	1.31201	0.338760
$16$	−4.26877	−1.06719
$17$	7.41452	1.79829	0.899143	−	0.437655i	$-0.144191\pi$
$17$	7.41452	1.79829	0.899143	+	0.437655i	$0.144191\pi$
$18$	−1.46454	−0.345196
$19$	−2.05209	−0.470782	−0.235391	−	0.971901i	$-0.575637\pi$
$19$	−2.05209	−0.470782	−0.235391	+	0.971901i	$0.575637\pi$
$20$	0.190085	0.0425043
$21$	2.70261	0.589757
$22$	1.59480	0.340013
$23$	2.65511	0.553629	0.276815	−	0.960923i	$-0.410721\pi$
$23$	2.65511	0.553629	0.276815	+	0.960923i	$0.410721\pi$
$24$	2.71690	0.554585
$25$	−3.27863	−0.655725
$26$	−1.46454	−0.287220
$27$	1.00000	0.192450
$28$	0.391555	0.0739970
$29$	−2.42268	−0.449880	−0.224940	−	0.974373i	$-0.572219\pi$
$29$	−2.42268	−0.449880	−0.224940	+	0.974373i	$0.572219\pi$
$30$	−1.92149	−0.350815
$31$	2.29972	0.413042	0.206521	−	0.978442i	$-0.433786\pi$
$31$	2.29972	0.413042	0.206521	+	0.978442i	$0.433786\pi$
$32$	0.817993	0.144602
$33$	−1.08894	−0.189561
$34$	−10.8589	−1.86228
$35$	3.54585	0.599358
$36$	0.144881	0.0241468
$37$	6.46505	1.06285	0.531424	−	0.847106i	$-0.321657\pi$
$37$	6.46505	1.06285	0.531424	+	0.847106i	$0.321657\pi$
$38$	3.00537	0.487536
$39$	1.00000	0.160128
$40$	3.56460	0.563613
$41$	10.0094	1.56321	0.781606	−	0.623772i	$-0.214401\pi$
$41$	10.0094	1.56321	0.781606	+	0.623772i	$0.214401\pi$
$42$	−3.95808	−0.610745
$43$	5.63104	0.858726	0.429363	−	0.903132i	$-0.358738\pi$
$43$	5.63104	0.858726	0.429363	+	0.903132i	$0.358738\pi$
$44$	−0.157767	−0.0237842
$45$	1.31201	0.195583
$46$	−3.88852	−0.573331
$47$	−1.52512	−0.222462	−0.111231	−	0.993795i	$-0.535479\pi$
$47$	−1.52512	−0.222462	−0.111231	+	0.993795i	$0.535479\pi$
$48$	−4.26877	−0.616144
$49$	0.304081	0.0434401
$50$	4.80168	0.679061
$51$	7.41452	1.03824
$52$	0.144881	0.0200913
$53$	−9.33590	−1.28238	−0.641192	−	0.767380i	$-0.721560\pi$
$53$	−9.33590	−1.28238	−0.641192	+	0.767380i	$0.721560\pi$
$54$	−1.46454	−0.199299
$55$	−1.42871	−0.192647
$56$	7.34271	0.981211
$57$	−2.05209	−0.271806
$58$	3.54811	0.465890
$59$	−8.84831	−1.15195	−0.575976	−	0.817467i	$-0.695378\pi$
$59$	−8.84831	−1.15195	−0.575976	+	0.817467i	$0.695378\pi$
$60$	0.190085	0.0245399
$61$	9.82229	1.25762	0.628808	−	0.777561i	$-0.283543\pi$
$61$	9.82229	1.25762	0.628808	+	0.777561i	$0.283543\pi$
$62$	−3.36804	−0.427741
$63$	2.70261	0.340496
$64$	7.33956	0.917445
$65$	1.31201	0.162735
$66$	1.59480	0.196306
$67$	−2.42605	−0.296389	−0.148194	−	0.988958i	$-0.547346\pi$
$67$	−2.42605	−0.296389	−0.148194	+	0.988958i	$0.547346\pi$
$68$	1.07422	0.130268
$69$	2.65511	0.319638
$70$	−5.19304	−0.620687
$71$	−1.05553	−0.125269	−0.0626344	−	0.998037i	$-0.519950\pi$
$71$	−1.05553	−0.125269	−0.0626344	+	0.998037i	$0.519950\pi$
$72$	2.71690	0.320190
$73$	−1.00361	−0.117463	−0.0587316	−	0.998274i	$-0.518706\pi$
$73$	−1.00361	−0.117463	−0.0587316	+	0.998274i	$0.518706\pi$
$74$	−9.46833	−1.10067
$75$	−3.27863	−0.378583
$76$	−0.297308	−0.0341036
$77$	−2.94298	−0.335384
$78$	−1.46454	−0.165827
$79$	12.1425	1.36614	0.683070	−	0.730353i	$-0.260644\pi$
$79$	12.1425	1.36614	0.683070	+	0.730353i	$0.260644\pi$
$80$	−5.60068	−0.626175
$81$	1.00000	0.111111
$82$	−14.6592	−1.61884
$83$	5.65779	0.621023	0.310512	−	0.950570i	$-0.399500\pi$
$83$	5.65779	0.621023	0.310512	+	0.950570i	$0.399500\pi$
$84$	0.391555	0.0427222
$85$	9.72794	1.05514
$86$	−8.24689	−0.889285
$87$	−2.42268	−0.259738
$88$	−2.95855	−0.315382
$89$	−2.96108	−0.313874	−0.156937	−	0.987609i	$-0.550162\pi$
$89$	−2.96108	−0.313874	−0.156937	+	0.987609i	$0.550162\pi$
$90$	−1.92149	−0.202543
$91$	2.70261	0.283310
$92$	0.384674	0.0401050
$93$	2.29972	0.238470
$94$	2.23360	0.230378
$95$	−2.69237	−0.276231
$96$	0.817993	0.0834860
$97$	17.5915	1.78615	0.893073	−	0.449912i	$-0.148545\pi$
$97$	17.5915	1.78615	0.893073	+	0.449912i	$0.148545\pi$
$98$	−0.445339	−0.0449860
$99$	−1.08894	−0.109443
$100$	−0.475009	−0.0475009
$101$	−6.75158	−0.671807	−0.335904	−	0.941896i	$-0.609042\pi$
$101$	−6.75158	−0.671807	−0.335904	+	0.941896i	$0.609042\pi$
$102$	−10.8589	−1.07519
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	2.71690	0.266414
$105$	3.54585	0.346040
$106$	13.6728	1.32802
$107$	9.16882	0.886384	0.443192	−	0.896427i	$-0.353846\pi$
$107$	9.16882	0.886384	0.443192	+	0.896427i	$0.353846\pi$
$108$	0.144881	0.0139411
$109$	−16.2127	−1.55290	−0.776448	−	0.630181i	$-0.782981\pi$
$109$	−16.2127	−1.55290	−0.776448	+	0.630181i	$0.782981\pi$
$110$	2.09240	0.199502
$111$	6.46505	0.613636
$112$	−11.5368	−1.09013
$113$	−16.4085	−1.54358	−0.771789	−	0.635878i	$-0.780638\pi$
$113$	−16.4085	−1.54358	−0.771789	+	0.635878i	$0.780638\pi$
$114$	3.00537	0.281479
$115$	3.48354	0.324841
$116$	−0.350999	−0.0325894
$117$	1.00000	0.0924500
$118$	12.9587	1.19295
$119$	20.0385	1.83693
$120$	3.56460	0.325402
$121$	−9.81420	−0.892200
$122$	−14.3851	−1.30237
$123$	10.0094	0.902521
$124$	0.333185	0.0299209
$125$	−10.8617	−0.971496
$126$	−3.95808	−0.352614
$127$	−6.20891	−0.550952	−0.275476	−	0.961308i	$-0.588835\pi$
$127$	−6.20891	−0.550952	−0.275476	+	0.961308i	$0.588835\pi$
$128$	−12.3851	−1.09470
$129$	5.63104	0.495786
$130$	−1.92149	−0.168526
$131$	5.01336	0.438020	0.219010	−	0.975723i	$-0.429717\pi$
$131$	5.01336	0.438020	0.219010	+	0.975723i	$0.429717\pi$
$132$	−0.157767	−0.0137318
$133$	−5.54600	−0.480899
$134$	3.55305	0.306936
$135$	1.31201	0.112920
$136$	20.1445	1.72738
$137$	−17.1276	−1.46331	−0.731654	−	0.681676i	$-0.761251\pi$
$137$	−17.1276	−1.46331	−0.731654	+	0.681676i	$0.761251\pi$
$138$	−3.88852	−0.331013
$139$	6.45085	0.547154	0.273577	−	0.961850i	$-0.411793\pi$
$139$	6.45085	0.547154	0.273577	+	0.961850i	$0.411793\pi$
$140$	0.513725	0.0434177
$141$	−1.52512	−0.128438
$142$	1.54587	0.129727
$143$	−1.08894	−0.0910620
$144$	−4.26877	−0.355731
$145$	−3.17858	−0.263967
$146$	1.46982	0.121643
$147$	0.304081	0.0250802
$148$	0.936660	0.0769930
$149$	14.2501	1.16741	0.583707	−	0.811965i	$-0.301602\pi$
$149$	14.2501	1.16741	0.583707	+	0.811965i	$0.301602\pi$
$150$	4.80168	0.392056
$151$	13.0990	1.06598	0.532992	−	0.846120i	$-0.321067\pi$
$151$	13.0990	1.06598	0.532992	+	0.846120i	$0.321067\pi$
$152$	−5.57533	−0.452219
$153$	7.41452	0.599429
$154$	4.31012	0.347319
$155$	3.01726	0.242352
$156$	0.144881	0.0115997
$157$	−7.34103	−0.585878	−0.292939	−	0.956131i	$-0.594633\pi$
$157$	−7.34103	−0.585878	−0.292939	+	0.956131i	$0.594633\pi$
$158$	−17.7832	−1.41476
$159$	−9.33590	−0.740385
$160$	1.07322	0.0848452
$161$	7.17572	0.565526
$162$	−1.46454	−0.115065
$163$	−18.0338	−1.41252	−0.706260	−	0.707953i	$-0.749619\pi$
$163$	−18.0338	−1.41252	−0.706260	+	0.707953i	$0.749619\pi$
$164$	1.45017	0.113240
$165$	−1.42871	−0.111225
$166$	−8.28607	−0.643124
$167$	−12.1275	−0.938452	−0.469226	−	0.883078i	$-0.655467\pi$
$167$	−12.1275	−0.938452	−0.469226	+	0.883078i	$0.655467\pi$
$168$	7.34271	0.566502
$169$	1.00000	0.0769231
$170$	−14.2470	−1.09269
$171$	−2.05209	−0.156927
$172$	0.815828	0.0622063
$173$	11.9700	0.910060	0.455030	−	0.890476i	$-0.349629\pi$
$173$	11.9700	0.910060	0.455030	+	0.890476i	$0.349629\pi$
$174$	3.54811	0.268981
$175$	−8.86084	−0.669816
$176$	4.64845	0.350390
$177$	−8.84831	−0.665080
$178$	4.33662	0.325044
$179$	6.91187	0.516618	0.258309	−	0.966062i	$-0.416835\pi$
$179$	6.91187	0.516618	0.258309	+	0.966062i	$0.416835\pi$
$180$	0.190085	0.0141681
$181$	−8.52500	−0.633659	−0.316829	−	0.948483i	$-0.602618\pi$
$181$	−8.52500	−0.633659	−0.316829	+	0.948483i	$0.602618\pi$
$182$	−3.95808	−0.293392
$183$	9.82229	0.726085
$184$	7.21367	0.531799
$185$	8.48222	0.623625
$186$	−3.36804	−0.246957
$187$	−8.07399	−0.590429
$188$	−0.220960	−0.0161152
$189$	2.70261	0.196586
$190$	3.94308	0.286061
$191$	−5.76811	−0.417366	−0.208683	−	0.977983i	$-0.566918\pi$
$191$	−5.76811	−0.417366	−0.208683	+	0.977983i	$0.566918\pi$
$192$	7.33956	0.529687
$193$	9.99639	0.719556	0.359778	−	0.933038i	$-0.382852\pi$
$193$	9.99639	0.719556	0.359778	+	0.933038i	$0.382852\pi$
$194$	−25.7635	−1.84971
$195$	1.31201	0.0939551
$196$	0.0440554	0.00314681
$197$	3.34134	0.238061	0.119030	−	0.992891i	$-0.462021\pi$
$197$	3.34134	0.238061	0.119030	+	0.992891i	$0.462021\pi$
$198$	1.59480	0.113338
$199$	12.7999	0.907358	0.453679	−	0.891165i	$-0.350111\pi$
$199$	12.7999	0.907358	0.453679	+	0.891165i	$0.350111\pi$
$200$	−8.90770	−0.629869
$201$	−2.42605	−0.171120
$202$	9.88797	0.695715
$203$	−6.54754	−0.459547
$204$	1.07422	0.0752105
$205$	13.1325	0.917214
$206$	−1.46454	−0.102039
$207$	2.65511	0.184543
$208$	−4.26877	−0.295986
$209$	2.23461	0.154571
$210$	−5.19304	−0.358354
$211$	4.16769	0.286916	0.143458	−	0.989656i	$-0.454178\pi$
$211$	4.16769	0.286916	0.143458	+	0.989656i	$0.454178\pi$
$212$	−1.35259	−0.0928963
$213$	−1.05553	−0.0723240
$214$	−13.4281	−0.917927
$215$	7.38799	0.503857
$216$	2.71690	0.184862
$217$	6.21524	0.421918
$218$	23.7442	1.60816
$219$	−1.00361	−0.0678175
$220$	−0.206992	−0.0139554
$221$	7.41452	0.498755
$222$	−9.46833	−0.635473
$223$	15.8109	1.05878	0.529389	−	0.848379i	$-0.322421\pi$
$223$	15.8109	1.05878	0.529389	+	0.848379i	$0.322421\pi$
$224$	2.21071	0.147709
$225$	−3.27863	−0.218575
$226$	24.0309	1.59851
$227$	−20.6012	−1.36735	−0.683674	−	0.729788i	$-0.739619\pi$
$227$	−20.6012	−1.36735	−0.683674	+	0.729788i	$0.739619\pi$
$228$	−0.297308	−0.0196897
$229$	−22.5594	−1.49076	−0.745382	−	0.666637i	$-0.767733\pi$
$229$	−22.5594	−1.49076	−0.745382	+	0.666637i	$0.767733\pi$
$230$	−5.10178	−0.336402
$231$	−2.94298	−0.193634
$232$	−6.58217	−0.432140
$233$	−13.6385	−0.893490	−0.446745	−	0.894661i	$-0.647417\pi$
$233$	−13.6385	−0.893490	−0.446745	+	0.894661i	$0.647417\pi$
$234$	−1.46454	−0.0957400
$235$	−2.00098	−0.130529
$236$	−1.28195	−0.0834477
$237$	12.1425	0.788741
$238$	−29.3473	−1.90230
$239$	−14.5653	−0.942149	−0.471074	−	0.882094i	$-0.656134\pi$
$239$	−14.5653	−0.942149	−0.471074	+	0.882094i	$0.656134\pi$
$240$	−5.60068	−0.361522
$241$	23.8400	1.53567	0.767834	−	0.640649i	$-0.221335\pi$
$241$	23.8400	1.53567	0.767834	+	0.640649i	$0.221335\pi$
$242$	14.3733	0.923951
$243$	1.00000	0.0641500
$244$	1.42306	0.0911020
$245$	0.398957	0.0254884
$246$	−14.6592	−0.934639
$247$	−2.05209	−0.130572
$248$	6.24811	0.396756
$249$	5.65779	0.358548
$250$	15.9073	1.00607
$251$	−0.218852	−0.0138138	−0.00690692	−	0.999976i	$-0.502199\pi$
$251$	−0.218852	−0.0138138	−0.00690692	+	0.999976i	$0.502199\pi$
$252$	0.391555	0.0246657
$253$	−2.89126	−0.181772
$254$	9.09321	0.570559
$255$	9.72794	0.609187
$256$	3.45933	0.216208
$257$	−4.37036	−0.272616	−0.136308	−	0.990667i	$-0.543524\pi$
$257$	−4.37036	−0.272616	−0.136308	+	0.990667i	$0.543524\pi$
$258$	−8.24689	−0.513429
$259$	17.4725	1.08569
$260$	0.190085	0.0117886
$261$	−2.42268	−0.149960
$262$	−7.34228	−0.453607
$263$	14.2403	0.878093	0.439047	−	0.898464i	$-0.355316\pi$
$263$	14.2403	0.878093	0.439047	+	0.898464i	$0.355316\pi$
$264$	−2.95855	−0.182086
$265$	−12.2488	−0.752438
$266$	8.12234	0.498013
$267$	−2.96108	−0.181215
$268$	−0.351487	−0.0214705
$269$	25.6262	1.56246	0.781229	−	0.624245i	$-0.214593\pi$
$269$	25.6262	1.56246	0.781229	+	0.624245i	$0.214593\pi$
$270$	−1.92149	−0.116938
$271$	19.3718	1.17675	0.588376	−	0.808587i	$-0.299768\pi$
$271$	19.3718	1.17675	0.588376	+	0.808587i	$0.299768\pi$
$272$	−31.6509	−1.91912
$273$	2.70261	0.163569
$274$	25.0841	1.51538
$275$	3.57024	0.215293
$276$	0.384674	0.0231547
$277$	14.5288	0.872954	0.436477	−	0.899715i	$-0.356226\pi$
$277$	14.5288	0.872954	0.436477	+	0.899715i	$0.356226\pi$
$278$	−9.44754	−0.566626
$279$	2.29972	0.137681
$280$	9.63371	0.575725
$281$	13.7480	0.820135	0.410068	−	0.912055i	$-0.365505\pi$
$281$	13.7480	0.820135	0.410068	+	0.912055i	$0.365505\pi$
$282$	2.23360	0.133009
$283$	18.6559	1.10898	0.554490	−	0.832191i	$-0.312914\pi$
$283$	18.6559	1.10898	0.554490	+	0.832191i	$0.312914\pi$
$284$	−0.152926	−0.00907451
$285$	−2.69237	−0.159482
$286$	1.59480	0.0943026
$287$	27.0516	1.59680
$288$	0.817993	0.0482007
$289$	37.9752	2.23383
$290$	4.65516	0.273360
$291$	17.5915	1.03123
$292$	−0.145403	−0.00850907
$293$	−31.0389	−1.81331	−0.906656	−	0.421871i	$-0.861374\pi$
$293$	−31.0389	−1.81331	−0.906656	+	0.421871i	$0.861374\pi$
$294$	−0.445339	−0.0259727
$295$	−11.6091	−0.675907
$296$	17.5649	1.02094
$297$	−1.08894	−0.0631869
$298$	−20.8698	−1.20896
$299$	2.65511	0.153549
$300$	−0.475009	−0.0274247
$301$	15.2185	0.877179
$302$	−19.1841	−1.10392
$303$	−6.75158	−0.387868
$304$	8.75991	0.502416
$305$	12.8870	0.737905
$306$	−10.8589	−0.620761
$307$	34.0648	1.94418	0.972091	−	0.234603i	$-0.0753791\pi$
$307$	34.0648	1.94418	0.972091	+	0.234603i	$0.0753791\pi$
$308$	−0.426381	−0.0242953
$309$	1.00000	0.0568880
$310$	−4.41890	−0.250977
$311$	−20.6694	−1.17205	−0.586026	−	0.810292i	$-0.699308\pi$
$311$	−20.6694	−1.17205	−0.586026	+	0.810292i	$0.699308\pi$
$312$	2.71690	0.153814
$313$	0.685951	0.0387723	0.0193861	−	0.999812i	$-0.493829\pi$
$313$	0.685951	0.0387723	0.0193861	+	0.999812i	$0.493829\pi$
$314$	10.7512	0.606728
$315$	3.54585	0.199786
$316$	1.75921	0.0989636
$317$	13.9736	0.784837	0.392419	−	0.919787i	$-0.371638\pi$
$317$	13.9736	0.784837	0.392419	+	0.919787i	$0.371638\pi$
$318$	13.6728	0.766733
$319$	2.63816	0.147708
$320$	9.62958	0.538310
$321$	9.16882	0.511754
$322$	−10.5091	−0.585651
$323$	−15.2153	−0.846602
$324$	0.144881	0.00804892
$325$	−3.27863	−0.181865
$326$	26.4113	1.46279
$327$	−16.2127	−0.896565
$328$	27.1946	1.50157
$329$	−4.12180	−0.227242
$330$	2.09240	0.115183
$331$	15.2911	0.840473	0.420237	−	0.907415i	$-0.361947\pi$
$331$	15.2911	0.840473	0.420237	+	0.907415i	$0.361947\pi$
$332$	0.819704	0.0449871
$333$	6.46505	0.354283
$334$	17.7612	0.971848
$335$	−3.18300	−0.173906
$336$	−11.5368	−0.629384
$337$	−17.3722	−0.946326	−0.473163	−	0.880975i	$-0.656888\pi$
$337$	−17.3722	−0.946326	−0.473163	+	0.880975i	$0.656888\pi$
$338$	−1.46454	−0.0796605
$339$	−16.4085	−0.891186
$340$	1.40939	0.0764349
$341$	−2.50427	−0.135614
$342$	3.00537	0.162512
$343$	−18.0964	−0.977116
$344$	15.2990	0.824865
$345$	3.48354	0.187547
$346$	−17.5305	−0.942446
$347$	−16.6923	−0.896092	−0.448046	−	0.894010i	$-0.647880\pi$
$347$	−16.6923	−0.896092	−0.448046	+	0.894010i	$0.647880\pi$
$348$	−0.350999	−0.0188155
$349$	8.35276	0.447113	0.223557	−	0.974691i	$-0.428233\pi$
$349$	8.35276	0.447113	0.223557	+	0.974691i	$0.428233\pi$
$350$	12.9771	0.693653
$351$	1.00000	0.0533761
$352$	−0.890747	−0.0474770
$353$	0.335115	0.0178364	0.00891819	−	0.999960i	$-0.497161\pi$
$353$	0.335115	0.0178364	0.00891819	+	0.999960i	$0.497161\pi$
$354$	12.9587	0.688748
$355$	−1.38487	−0.0735014
$356$	−0.429003	−0.0227371
$357$	20.0385	1.06055
$358$	−10.1227	−0.535003
$359$	3.78196	0.199604	0.0998021	−	0.995007i	$-0.468179\pi$
$359$	3.78196	0.199604	0.0998021	+	0.995007i	$0.468179\pi$
$360$	3.56460	0.187871
$361$	−14.7889	−0.778364
$362$	12.4852	0.656209
$363$	−9.81420	−0.515112
$364$	0.391555	0.0205231
$365$	−1.31674	−0.0689215
$366$	−14.3851	−0.751924
$367$	−1.67029	−0.0871883	−0.0435942	−	0.999049i	$-0.513881\pi$
$367$	−1.67029	−0.0871883	−0.0435942	+	0.999049i	$0.513881\pi$
$368$	−11.3341	−0.590829
$369$	10.0094	0.521071
$370$	−12.4226	−0.645818
$371$	−25.2313	−1.30994
$372$	0.333185	0.0172748
$373$	−12.3168	−0.637739	−0.318869	−	0.947799i	$-0.603303\pi$
$373$	−12.3168	−0.637739	−0.318869	+	0.947799i	$0.603303\pi$
$374$	11.8247	0.611440
$375$	−10.8617	−0.560893
$376$	−4.14360	−0.213690
$377$	−2.42268	−0.124774
$378$	−3.95808	−0.203582
$379$	−5.13683	−0.263861	−0.131931	−	0.991259i	$-0.542118\pi$
$379$	−5.13683	−0.263861	−0.131931	+	0.991259i	$0.542118\pi$
$380$	−0.390072	−0.0200103
$381$	−6.20891	−0.318092
$382$	8.44764	0.432219
$383$	7.86643	0.401956	0.200978	−	0.979596i	$-0.435588\pi$
$383$	7.86643	0.401956	0.200978	+	0.979596i	$0.435588\pi$
$384$	−12.3851	−0.632023
$385$	−3.86123	−0.196786
$386$	−14.6401	−0.745163
$387$	5.63104	0.286242
$388$	2.54867	0.129389
$389$	−12.8768	−0.652880	−0.326440	−	0.945218i	$-0.605849\pi$
$389$	−12.8768	−0.652880	−0.326440	+	0.945218i	$0.605849\pi$
$390$	−1.92149	−0.0972987
$391$	19.6864	0.995584
$392$	0.826156	0.0417272
$393$	5.01336	0.252891
$394$	−4.89353	−0.246533
$395$	15.9311	0.801582
$396$	−0.157767	−0.00792807
$397$	16.7506	0.840687	0.420343	−	0.907365i	$-0.361910\pi$
$397$	16.7506	0.840687	0.420343	+	0.907365i	$0.361910\pi$
$398$	−18.7459	−0.939648
$399$	−5.54600	−0.277647
$400$	13.9957	0.699785
$401$	13.0443	0.651402	0.325701	−	0.945473i	$-0.394400\pi$
$401$	13.0443	0.651402	0.325701	+	0.945473i	$0.394400\pi$
$402$	3.55305	0.177210
$403$	2.29972	0.114557
$404$	−0.978173	−0.0486659
$405$	1.31201	0.0651944
$406$	9.58914	0.475901
$407$	−7.04007	−0.348963
$408$	20.1445	0.997302
$409$	5.16928	0.255604	0.127802	−	0.991800i	$-0.459208\pi$
$409$	5.16928	0.255604	0.127802	+	0.991800i	$0.459208\pi$
$410$	−19.2331	−0.949854
$411$	−17.1276	−0.844842
$412$	0.144881	0.00713775
$413$	−23.9135	−1.17671
$414$	−3.88852	−0.191110
$415$	7.42309	0.364385
$416$	0.817993	0.0401054
$417$	6.45085	0.315900
$418$	−3.27268	−0.160072
$419$	1.10787	0.0541232	0.0270616	−	0.999634i	$-0.491385\pi$
$419$	1.10787	0.0541232	0.0270616	+	0.999634i	$0.491385\pi$
$420$	0.513725	0.0250672
$421$	−19.3830	−0.944670	−0.472335	−	0.881419i	$-0.656589\pi$
$421$	−19.3830	−0.944670	−0.472335	+	0.881419i	$0.656589\pi$
$422$	−6.10376	−0.297126
$423$	−1.52512	−0.0741539
$424$	−25.3647	−1.23182
$425$	−24.3095	−1.17918
$426$	1.54587	0.0748978
$427$	26.5458	1.28464
$428$	1.32838	0.0642099
$429$	−1.08894	−0.0525746
$430$	−10.8200	−0.521787
$431$	3.49610	0.168401	0.0842006	−	0.996449i	$-0.473166\pi$
$431$	3.49610	0.168401	0.0842006	+	0.996449i	$0.473166\pi$
$432$	−4.26877	−0.205381
$433$	−36.3256	−1.74570	−0.872849	−	0.487990i	$-0.837730\pi$
$433$	−36.3256	−1.74570	−0.872849	+	0.487990i	$0.837730\pi$
$434$	−9.10248	−0.436933
$435$	−3.17858	−0.152401
$436$	−2.34891	−0.112492
$437$	−5.44854	−0.260639
$438$	1.46982	0.0702309
$439$	24.3278	1.16110	0.580552	−	0.814223i	$-0.302837\pi$
$439$	24.3278	1.16110	0.580552	+	0.814223i	$0.302837\pi$
$440$	−3.88165	−0.185050
$441$	0.304081	0.0144800
$442$	−10.8589	−0.516504
$443$	0.951663	0.0452149	0.0226074	−	0.999744i	$-0.492803\pi$
$443$	0.951663	0.0452149	0.0226074	+	0.999744i	$0.492803\pi$
$444$	0.936660	0.0444519
$445$	−3.88497	−0.184165
$446$	−23.1557	−1.09646
$447$	14.2501	0.674006
$448$	19.8359	0.937160
$449$	13.5092	0.637538	0.318769	−	0.947832i	$-0.396731\pi$
$449$	13.5092	0.637538	0.318769	+	0.947832i	$0.396731\pi$
$450$	4.80168	0.226354
$451$	−10.8997	−0.513247
$452$	−2.37727	−0.111817
$453$	13.0990	0.615447
$454$	30.1713	1.41601
$455$	3.54585	0.166232
$456$	−5.57533	−0.261089
$457$	23.6897	1.10816	0.554079	−	0.832464i	$-0.313071\pi$
$457$	23.6897	1.10816	0.554079	+	0.832464i	$0.313071\pi$
$458$	33.0391	1.54382
$459$	7.41452	0.346080
$460$	0.504697	0.0235316
$461$	−4.16382	−0.193929	−0.0969643	−	0.995288i	$-0.530913\pi$
$461$	−4.16382	−0.193929	−0.0969643	+	0.995288i	$0.530913\pi$
$462$	4.31012	0.200525
$463$	−20.4988	−0.952662	−0.476331	−	0.879266i	$-0.658034\pi$
$463$	−20.4988	−0.952662	−0.476331	+	0.879266i	$0.658034\pi$
$464$	10.3419	0.480108
$465$	3.01726	0.139922
$466$	19.9742	0.925287
$467$	−27.9350	−1.29268	−0.646339	−	0.763050i	$-0.723701\pi$
$467$	−27.9350	−1.29268	−0.646339	+	0.763050i	$0.723701\pi$
$468$	0.144881	0.00669711
$469$	−6.55665	−0.302758
$470$	2.93051	0.135174
$471$	−7.34103	−0.338257
$472$	−24.0400	−1.10653
$473$	−6.13188	−0.281944
$474$	−17.7832	−0.816810
$475$	6.72805	0.308704
$476$	2.90320	0.133068
$477$	−9.33590	−0.427462
$478$	21.3314	0.975677
$479$	32.2388	1.47303	0.736513	−	0.676423i	$-0.236471\pi$
$479$	32.2388	1.47303	0.736513	+	0.676423i	$0.236471\pi$
$480$	1.07322	0.0489854
$481$	6.46505	0.294781
$482$	−34.9146	−1.59032
$483$	7.17572	0.326507
$484$	−1.42189	−0.0646312
$485$	23.0802	1.04802
$486$	−1.46454	−0.0664329
$487$	34.4308	1.56021	0.780104	−	0.625650i	$-0.215166\pi$
$487$	34.4308	1.56021	0.780104	+	0.625650i	$0.215166\pi$
$488$	26.6862	1.20803
$489$	−18.0338	−0.815519
$490$	−0.584289	−0.0263955
$491$	−6.76359	−0.305237	−0.152618	−	0.988285i	$-0.548771\pi$
$491$	−6.76359	−0.305237	−0.152618	+	0.988285i	$0.548771\pi$
$492$	1.45017	0.0653789
$493$	−17.9630	−0.809013
$494$	3.00537	0.135218
$495$	−1.42871	−0.0642155
$496$	−9.81699	−0.440796
$497$	−2.85269	−0.127961
$498$	−8.28607	−0.371308
$499$	38.6701	1.73111	0.865555	−	0.500814i	$-0.166966\pi$
$499$	38.6701	1.73111	0.865555	+	0.500814i	$0.166966\pi$
$500$	−1.57364	−0.0703754
$501$	−12.1275	−0.541815
$502$	0.320518	0.0143054
$503$	20.7007	0.923000	0.461500	−	0.887140i	$-0.347311\pi$
$503$	20.7007	0.923000	0.461500	+	0.887140i	$0.347311\pi$
$504$	7.34271	0.327070
$505$	−8.85815	−0.394182
$506$	4.23438	0.188241
$507$	1.00000	0.0444116
$508$	−0.899551	−0.0399111
$509$	−1.56148	−0.0692112	−0.0346056	−	0.999401i	$-0.511018\pi$
$509$	−1.56148	−0.0692112	−0.0346056	+	0.999401i	$0.511018\pi$
$510$	−14.2470	−0.630866
$511$	−2.71235	−0.119987
$512$	19.7038	0.870794
$513$	−2.05209	−0.0906021
$514$	6.40057	0.282317
$515$	1.31201	0.0578141
$516$	0.815828	0.0359148
$517$	1.66077	0.0730406
$518$	−25.5892	−1.12432
$519$	11.9700	0.525423
$520$	3.56460	0.156318
$521$	7.57814	0.332005	0.166002	−	0.986125i	$-0.446914\pi$
$521$	7.57814	0.332005	0.166002	+	0.986125i	$0.446914\pi$
$522$	3.54811	0.155297
$523$	25.2775	1.10531	0.552653	−	0.833411i	$-0.313615\pi$
$523$	25.2775	1.10531	0.552653	+	0.833411i	$0.313615\pi$
$524$	0.726339	0.0317303
$525$	−8.86084	−0.386719
$526$	−20.8555	−0.909342
$527$	17.0513	0.742768
$528$	4.64845	0.202298
$529$	−15.9504	−0.693495
$530$	17.9389	0.779215
$531$	−8.84831	−0.383984
$532$	−0.803507	−0.0348365
$533$	10.0094	0.433557
$534$	4.33662	0.187664
$535$	12.0296	0.520085
$536$	−6.59133	−0.284702
$537$	6.91187	0.298269
$538$	−37.5306	−1.61806
$539$	−0.331126	−0.0142626
$540$	0.190085	0.00817995
$541$	−11.3686	−0.488775	−0.244388	−	0.969678i	$-0.578587\pi$
$541$	−11.3686	−0.488775	−0.244388	+	0.969678i	$0.578587\pi$
$542$	−28.3708	−1.21863
$543$	−8.52500	−0.365843
$544$	6.06503	0.260036
$545$	−21.2713	−0.911160
$546$	−3.95808	−0.169390
$547$	−7.46973	−0.319383	−0.159691	−	0.987167i	$-0.551050\pi$
$547$	−7.46973	−0.319383	−0.159691	+	0.987167i	$0.551050\pi$
$548$	−2.48145	−0.106002
$549$	9.82229	0.419205
$550$	−5.22876	−0.222955
$551$	4.97156	0.211795
$552$	7.21367	0.307034
$553$	32.8164	1.39550
$554$	−21.2781	−0.904020
$555$	8.48222	0.360050
$556$	0.934603	0.0396360
$557$	28.5936	1.21155	0.605775	−	0.795636i	$-0.292863\pi$
$557$	28.5936	1.21155	0.605775	+	0.795636i	$0.292863\pi$
$558$	−3.36804	−0.142580
$559$	5.63104	0.238168
$560$	−15.1364	−0.639630
$561$	−8.07399	−0.340884
$562$	−20.1345	−0.849321
$563$	−17.0166	−0.717164	−0.358582	−	0.933498i	$-0.616740\pi$
$563$	−17.0166	−0.717164	−0.358582	+	0.933498i	$0.616740\pi$
$564$	−0.220960	−0.00930411
$565$	−21.5281	−0.905694
$566$	−27.3224	−1.14844
$567$	2.70261	0.113499
$568$	−2.86778	−0.120329
$569$	−32.5815	−1.36589	−0.682943	−	0.730472i	$-0.739300\pi$
$569$	−32.5815	−1.36589	−0.682943	+	0.730472i	$0.739300\pi$
$570$	3.94308	0.165158
$571$	36.1407	1.51244	0.756220	−	0.654317i	$-0.227044\pi$
$571$	36.1407	1.51244	0.756220	+	0.654317i	$0.227044\pi$
$572$	−0.157767	−0.00659655
$573$	−5.76811	−0.240966
$574$	−39.6181	−1.65363
$575$	−8.70512	−0.363029
$576$	7.33956	0.305815
$577$	30.4881	1.26924	0.634618	−	0.772826i	$-0.281157\pi$
$577$	30.4881	1.26924	0.634618	+	0.772826i	$0.281157\pi$
$578$	−55.6162	−2.31333
$579$	9.99639	0.415436
$580$	−0.460514	−0.0191218
$581$	15.2908	0.634369
$582$	−25.7635	−1.06793
$583$	10.1663	0.421044
$584$	−2.72670	−0.112832
$585$	1.31201	0.0542450
$586$	45.4577	1.87784
$587$	34.1612	1.40998	0.704992	−	0.709215i	$-0.250950\pi$
$587$	34.1612	1.40998	0.704992	+	0.709215i	$0.250950\pi$
$588$	0.0440554	0.00181681
$589$	−4.71924	−0.194453
$590$	17.0020	0.699960
$591$	3.34134	0.137444
$592$	−27.5978	−1.13426
$593$	24.8172	1.01912	0.509561	−	0.860435i	$-0.329808\pi$
$593$	24.8172	1.01912	0.509561	+	0.860435i	$0.329808\pi$
$594$	1.59480	0.0654355
$595$	26.2908	1.07782
$596$	2.06456	0.0845677
$597$	12.7999	0.523863
$598$	−3.88852	−0.159013
$599$	−26.8187	−1.09578	−0.547892	−	0.836549i	$-0.684570\pi$
$599$	−26.8187	−1.09578	−0.547892	+	0.836549i	$0.684570\pi$
$600$	−8.90770	−0.363655
$601$	41.2847	1.68404	0.842019	−	0.539449i	$-0.181367\pi$
$601$	41.2847	1.68404	0.842019	+	0.539449i	$0.181367\pi$
$602$	−22.2881	−0.908395
$603$	−2.42605	−0.0987963
$604$	1.89780	0.0772202
$605$	−12.8763	−0.523498
$606$	9.88797	0.401671
$607$	39.9052	1.61970	0.809851	−	0.586636i	$-0.199548\pi$
$607$	39.9052	1.61970	0.809851	+	0.586636i	$0.199548\pi$
$608$	−1.67860	−0.0680761
$609$	−6.54754	−0.265320
$610$	−18.8735	−0.764165
$611$	−1.52512	−0.0616998
$612$	1.07422	0.0434228
$613$	−28.8267	−1.16430	−0.582149	−	0.813082i	$-0.697788\pi$
$613$	−28.8267	−1.16430	−0.582149	+	0.813082i	$0.697788\pi$
$614$	−49.8893	−2.01337
$615$	13.1325	0.529554
$616$	−7.99579	−0.322159
$617$	15.6371	0.629528	0.314764	−	0.949170i	$-0.398075\pi$
$617$	15.6371	0.629528	0.314764	+	0.949170i	$0.398075\pi$
$618$	−1.46454	−0.0589125
$619$	22.2989	0.896270	0.448135	−	0.893966i	$-0.352088\pi$
$619$	22.2989	0.896270	0.448135	+	0.893966i	$0.352088\pi$
$620$	0.437143	0.0175561
$621$	2.65511	0.106546
$622$	30.2711	1.21376
$623$	−8.00263	−0.320619
$624$	−4.26877	−0.170888
$625$	2.14252	0.0857009
$626$	−1.00460	−0.0401520
$627$	2.23461	0.0892418
$628$	−1.06357	−0.0424412
$629$	47.9353	1.91130
$630$	−5.19304	−0.206896
$631$	−42.3927	−1.68763	−0.843814	−	0.536636i	$-0.819695\pi$
$631$	−42.3927	−1.68763	−0.843814	+	0.536636i	$0.819695\pi$
$632$	32.9900	1.31227
$633$	4.16769	0.165651
$634$	−20.4650	−0.812767
$635$	−8.14617	−0.323271
$636$	−1.35259	−0.0536337
$637$	0.304081	0.0120481
$638$	−3.86369	−0.152965
$639$	−1.05553	−0.0417563
$640$	−16.2493	−0.642312
$641$	−14.8876	−0.588025	−0.294012	−	0.955802i	$-0.594991\pi$
$641$	−14.8876	−0.588025	−0.294012	+	0.955802i	$0.594991\pi$
$642$	−13.4281	−0.529966
$643$	−10.0465	−0.396195	−0.198097	−	0.980182i	$-0.563476\pi$
$643$	−10.0465	−0.396195	−0.198097	+	0.980182i	$0.563476\pi$
$644$	1.03962	0.0409669
$645$	7.38799	0.290902
$646$	22.2834	0.876729
$647$	−28.2708	−1.11144	−0.555720	−	0.831369i	$-0.687557\pi$
$647$	−28.2708	−1.11144	−0.555720	+	0.831369i	$0.687557\pi$
$648$	2.71690	0.106730
$649$	9.63530	0.378219
$650$	4.80168	0.188338
$651$	6.21524	0.243595
$652$	−2.61275	−0.102323
$653$	−11.9833	−0.468943	−0.234471	−	0.972123i	$-0.575336\pi$
$653$	−11.9833	−0.468943	−0.234471	+	0.972123i	$0.575336\pi$
$654$	23.7442	0.928471
$655$	6.57759	0.257008
$656$	−42.7280	−1.66825
$657$	−1.00361	−0.0391544
$658$	6.03655	0.235329
$659$	−43.9683	−1.71276	−0.856382	−	0.516343i	$-0.827293\pi$
$659$	−43.9683	−1.71276	−0.856382	+	0.516343i	$0.827293\pi$
$660$	−0.206992	−0.00805714
$661$	27.3386	1.06335	0.531674	−	0.846949i	$-0.321563\pi$
$661$	27.3386	1.06335	0.531674	+	0.846949i	$0.321563\pi$
$662$	−22.3944	−0.870383
$663$	7.41452	0.287956
$664$	15.3717	0.596536
$665$	−7.27641	−0.282167
$666$	−9.46833	−0.366890
$667$	−6.43248	−0.249067
$668$	−1.75703	−0.0679817
$669$	15.8109	0.611286
$670$	4.66164	0.180095
$671$	−10.6959	−0.412911
$672$	2.21071	0.0852801
$673$	−29.1732	−1.12455	−0.562273	−	0.826952i	$-0.690073\pi$
$673$	−29.1732	−1.12455	−0.562273	+	0.826952i	$0.690073\pi$
$674$	25.4424	0.980003
$675$	−3.27863	−0.126194
$676$	0.144881	0.00557233
$677$	−44.1712	−1.69764	−0.848818	−	0.528684i	$-0.822685\pi$
$677$	−44.1712	−1.69764	−0.848818	+	0.528684i	$0.822685\pi$
$678$	24.0309	0.922900
$679$	47.5429	1.82453
$680$	26.4298	1.01354
$681$	−20.6012	−0.789439
$682$	3.66760	0.140440
$683$	−18.6089	−0.712049	−0.356024	−	0.934477i	$-0.615868\pi$
$683$	−18.6089	−0.712049	−0.356024	+	0.934477i	$0.615868\pi$
$684$	−0.297308	−0.0113679
$685$	−22.4716	−0.858595
$686$	26.5030	1.01189
$687$	−22.5594	−0.860693
$688$	−24.0376	−0.916426
$689$	−9.33590	−0.355669
$690$	−5.10178	−0.194222
$691$	−14.6611	−0.557736	−0.278868	−	0.960329i	$-0.589959\pi$
$691$	−14.6611	−0.557736	−0.278868	+	0.960329i	$0.589959\pi$
$692$	1.73422	0.0659250
$693$	−2.94298	−0.111795
$694$	24.4466	0.927981
$695$	8.46359	0.321042
$696$	−6.58217	−0.249496
$697$	74.2153	2.81110
$698$	−12.2330	−0.463025
$699$	−13.6385	−0.515857
$700$	−1.28376	−0.0485217
$701$	10.0542	0.379741	0.189870	−	0.981809i	$-0.439193\pi$
$701$	10.0542	0.379741	0.189870	+	0.981809i	$0.439193\pi$
$702$	−1.46454	−0.0552755
$703$	−13.2669	−0.500370
$704$	−7.99236	−0.301223
$705$	−2.00098	−0.0753611
$706$	−0.490790	−0.0184711
$707$	−18.2469	−0.686244
$708$	−1.28195	−0.0481785
$709$	−4.78641	−0.179757	−0.0898786	−	0.995953i	$-0.528648\pi$
$709$	−4.78641	−0.179757	−0.0898786	+	0.995953i	$0.528648\pi$
$710$	2.02820	0.0761171
$711$	12.1425	0.455380
$712$	−8.04495	−0.301497
$713$	6.10602	0.228672
$714$	−29.3473	−1.09829
$715$	−1.42871	−0.0534305
$716$	1.00140	0.0374239
$717$	−14.5653	−0.543950
$718$	−5.53883	−0.206707
$719$	33.7823	1.25987	0.629933	−	0.776649i	$-0.283082\pi$
$719$	33.7823	1.25987	0.629933	+	0.776649i	$0.283082\pi$
$720$	−5.60068	−0.208725
$721$	2.70261	0.100650
$722$	21.6590	0.806064
$723$	23.8400	0.886618
$724$	−1.23511	−0.0459024
$725$	7.94305	0.294998
$726$	14.3733	0.533443
$727$	−20.5729	−0.763005	−0.381503	−	0.924368i	$-0.624593\pi$
$727$	−20.5729	−0.763005	−0.381503	+	0.924368i	$0.624593\pi$
$728$	7.34271	0.272139
$729$	1.00000	0.0370370
$730$	1.92842	0.0713742
$731$	41.7515	1.54423
$732$	1.42306	0.0525978
$733$	17.2334	0.636531	0.318265	−	0.948002i	$-0.396900\pi$
$733$	17.2334	0.636531	0.318265	+	0.948002i	$0.396900\pi$
$734$	2.44621	0.0902911
$735$	0.398957	0.0147158
$736$	2.17186	0.0800559
$737$	2.64183	0.0973129
$738$	−14.6592	−0.539614
$739$	−43.5360	−1.60150	−0.800749	−	0.599000i	$-0.795565\pi$
$739$	−43.5360	−1.60150	−0.800749	+	0.599000i	$0.795565\pi$
$740$	1.22891	0.0451756
$741$	−2.05209	−0.0753855
$742$	36.9522	1.35656
$743$	−28.8845	−1.05967	−0.529835	−	0.848101i	$-0.677746\pi$
$743$	−28.8845	−1.05967	−0.529835	+	0.848101i	$0.677746\pi$
$744$	6.24811	0.229067
$745$	18.6963	0.684979
$746$	18.0384	0.660434
$747$	5.65779	0.207008
$748$	−1.16976	−0.0427708
$749$	24.7797	0.905431
$750$	15.9073	0.580854
$751$	−42.3250	−1.54446	−0.772231	−	0.635342i	$-0.780859\pi$
$751$	−42.3250	−1.54446	−0.772231	+	0.635342i	$0.780859\pi$
$752$	6.51039	0.237410
$753$	−0.218852	−0.00797543
$754$	3.54811	0.129215
$755$	17.1861	0.625466
$756$	0.391555	0.0142407
$757$	9.32398	0.338886	0.169443	−	0.985540i	$-0.445803\pi$
$757$	9.32398	0.338886	0.169443	+	0.985540i	$0.445803\pi$
$758$	7.52309	0.273251
$759$	−2.89126	−0.104946
$760$	−7.31489	−0.265339
$761$	40.6832	1.47477	0.737383	−	0.675475i	$-0.236061\pi$
$761$	40.6832	1.47477	0.737383	+	0.675475i	$0.236061\pi$
$762$	9.09321	0.329412
$763$	−43.8166	−1.58627
$764$	−0.835687	−0.0302341
$765$	9.72794	0.351714
$766$	−11.5207	−0.416260
$767$	−8.84831	−0.319494
$768$	3.45933	0.124828
$769$	29.5556	1.06580	0.532902	−	0.846177i	$-0.321102\pi$
$769$	29.5556	1.06580	0.532902	+	0.846177i	$0.321102\pi$
$770$	5.65493	0.203789
$771$	−4.37036	−0.157395
$772$	1.44828	0.0521248
$773$	−36.6138	−1.31691	−0.658453	−	0.752622i	$-0.728789\pi$
$773$	−36.6138	−1.31691	−0.658453	+	0.752622i	$0.728789\pi$
$774$	−8.24689	−0.296428
$775$	−7.53993	−0.270842
$776$	47.7943	1.71572
$777$	17.4725	0.626822
$778$	18.8586	0.676114
$779$	−20.5403	−0.735933
$780$	0.190085	0.00680613
$781$	1.14942	0.0411294
$782$	−28.8315	−1.03101
$783$	−2.42268	−0.0865794
$784$	−1.29805	−0.0463590
$785$	−9.63151	−0.343763
$786$	−7.34228	−0.261890
$787$	−52.6342	−1.87621	−0.938103	−	0.346356i	$-0.887419\pi$
$787$	−52.6342	−1.87621	−0.938103	+	0.346356i	$0.887419\pi$
$788$	0.484095	0.0172452
$789$	14.2403	0.506967
$790$	−23.3318	−0.830108
$791$	−44.3456	−1.57675
$792$	−2.95855	−0.105127
$793$	9.82229	0.348800
$794$	−24.5319	−0.870604
$795$	−12.2488	−0.434420
$796$	1.85445	0.0657292
$797$	−3.01822	−0.106911	−0.0534555	−	0.998570i	$-0.517024\pi$
$797$	−3.01822	−0.106911	−0.0534555	+	0.998570i	$0.517024\pi$
$798$	8.12234	0.287528
$799$	−11.3080	−0.400050
$800$	−2.68189	−0.0948192
$801$	−2.96108	−0.104625
$802$	−19.1039	−0.674584
$803$	1.09287	0.0385666
$804$	−0.351487	−0.0123960
$805$	9.41463	0.331822
$806$	−3.36804	−0.118634
$807$	25.6262	0.902085
$808$	−18.3434	−0.645317
$809$	−9.21408	−0.323950	−0.161975	−	0.986795i	$-0.551786\pi$
$809$	−9.21408	−0.323950	−0.161975	+	0.986795i	$0.551786\pi$
$810$	−1.92149	−0.0675144
$811$	−24.9392	−0.875733	−0.437867	−	0.899040i	$-0.644266\pi$
$811$	−24.9392	−0.875733	−0.437867	+	0.899040i	$0.644266\pi$
$812$	−0.948611	−0.0332897
$813$	19.3718	0.679398
$814$	10.3105	0.361382
$815$	−23.6606	−0.828795
$816$	−31.6509	−1.10800
$817$	−11.5554	−0.404273
$818$	−7.57062	−0.264701
$819$	2.70261	0.0944367
$820$	1.90264	0.0664432
$821$	−11.0189	−0.384563	−0.192282	−	0.981340i	$-0.561589\pi$
$821$	−11.0189	−0.384563	−0.192282	+	0.981340i	$0.561589\pi$
$822$	25.0841	0.874907
$823$	11.0068	0.383674	0.191837	−	0.981427i	$-0.438556\pi$
$823$	11.0068	0.383674	0.191837	+	0.981427i	$0.438556\pi$
$824$	2.71690	0.0946476
$825$	3.57024	0.124300
$826$	35.0223	1.21858
$827$	15.0382	0.522929	0.261464	−	0.965213i	$-0.415795\pi$
$827$	15.0382	0.522929	0.261464	+	0.965213i	$0.415795\pi$
$828$	0.384674	0.0133683
$829$	−25.5942	−0.888923	−0.444462	−	0.895798i	$-0.646605\pi$
$829$	−25.5942	−0.888923	−0.444462	+	0.895798i	$0.646605\pi$
$830$	−10.8714	−0.377352
$831$	14.5288	0.504000
$832$	7.33956	0.254453
$833$	2.25461	0.0781177
$834$	−9.44754	−0.327141
$835$	−15.9114	−0.550636
$836$	0.323752	0.0111972
$837$	2.29972	0.0794900
$838$	−1.62253	−0.0560492
$839$	−4.89303	−0.168926	−0.0844631	−	0.996427i	$-0.526917\pi$
$839$	−4.89303	−0.168926	−0.0844631	+	0.996427i	$0.526917\pi$
$840$	9.63371	0.332395
$841$	−23.1306	−0.797608
$842$	28.3872	0.978288
$843$	13.7480	0.473505
$844$	0.603818	0.0207843
$845$	1.31201	0.0451346
$846$	2.23360	0.0767928
$847$	−26.5239	−0.911373
$848$	39.8528	1.36855
$849$	18.6559	0.640269
$850$	35.6022	1.22115
$851$	17.1654	0.588423
$852$	−0.152926	−0.00523917
$853$	−41.6885	−1.42739	−0.713694	−	0.700458i	$-0.752979\pi$
$853$	−41.6885	−1.42739	−0.713694	+	0.700458i	$0.752979\pi$
$854$	−38.8774	−1.33036
$855$	−2.69237	−0.0920771
$856$	24.9108	0.851432
$857$	−3.06381	−0.104658	−0.0523288	−	0.998630i	$-0.516664\pi$
$857$	−3.06381	−0.104658	−0.0523288	+	0.998630i	$0.516664\pi$
$858$	1.59480	0.0544456
$859$	−5.80827	−0.198175	−0.0990877	−	0.995079i	$-0.531592\pi$
$859$	−5.80827	−0.198175	−0.0990877	+	0.995079i	$0.531592\pi$
$860$	1.07038	0.0364995
$861$	27.0516	0.921915
$862$	−5.12018	−0.174394
$863$	−13.2389	−0.450659	−0.225329	−	0.974283i	$-0.572346\pi$
$863$	−13.2389	−0.450659	−0.225329	+	0.974283i	$0.572346\pi$
$864$	0.817993	0.0278287
$865$	15.7047	0.533977
$866$	53.2004	1.80782
$867$	37.9752	1.28970
$868$	0.900468	0.0305639
$869$	−13.2225	−0.448543
$870$	4.65516	0.157825
$871$	−2.42605	−0.0822035
$872$	−44.0483	−1.49166
$873$	17.5915	0.595382
$874$	7.97960	0.269914
$875$	−29.3548	−0.992372
$876$	−0.145403	−0.00491272
$877$	−44.3084	−1.49619	−0.748095	−	0.663592i	$-0.769031\pi$
$877$	−44.3084	−1.49619	−0.748095	+	0.663592i	$0.769031\pi$
$878$	−35.6291	−1.20242
$879$	−31.0389	−1.04692
$880$	6.09881	0.205591
$881$	−33.7974	−1.13866	−0.569332	−	0.822108i	$-0.692798\pi$
$881$	−33.7974	−1.13866	−0.569332	+	0.822108i	$0.692798\pi$
$882$	−0.445339	−0.0149953
$883$	20.5022	0.689955	0.344977	−	0.938611i	$-0.387887\pi$
$883$	20.5022	0.689955	0.344977	+	0.938611i	$0.387887\pi$
$884$	1.07422	0.0361299
$885$	−11.6091	−0.390235
$886$	−1.39375	−0.0468239
$887$	53.8882	1.80939	0.904695	−	0.426060i	$-0.140099\pi$
$887$	53.8882	1.80939	0.904695	+	0.426060i	$0.140099\pi$
$888$	17.5649	0.589439
$889$	−16.7803	−0.562792
$890$	5.68970	0.190719
$891$	−1.08894	−0.0364810
$892$	2.29070	0.0766982
$893$	3.12969	0.104731
$894$	−20.8698	−0.697992
$895$	9.06846	0.303125
$896$	−33.4720	−1.11822
$897$	2.65511	0.0886516
$898$	−19.7848	−0.660226
$899$	−5.57148	−0.185819
$900$	−0.475009	−0.0158336
$901$	−69.2213	−2.30609
$902$	15.9631	0.531512
$903$	15.2185	0.506440
$904$	−44.5801	−1.48271
$905$	−11.1849	−0.371799
$906$	−19.1841	−0.637349
$907$	−35.7316	−1.18645	−0.593225	−	0.805037i	$-0.702145\pi$
$907$	−35.7316	−1.18645	−0.593225	+	0.805037i	$0.702145\pi$
$908$	−2.98471	−0.0990511
$909$	−6.75158	−0.223936
$910$	−5.19304	−0.172148
$911$	−17.5143	−0.580276	−0.290138	−	0.956985i	$-0.593701\pi$
$911$	−17.5143	−0.580276	−0.290138	+	0.956985i	$0.593701\pi$
$912$	8.75991	0.290070
$913$	−6.16101	−0.203900
$914$	−34.6946	−1.14759
$915$	12.8870	0.426030
$916$	−3.26841	−0.107991
$917$	13.5491	0.447432
$918$	−10.8589	−0.358396
$919$	−30.1738	−0.995340	−0.497670	−	0.867366i	$-0.665811\pi$
$919$	−30.1738	−0.995340	−0.497670	+	0.867366i	$0.665811\pi$
$920$	9.46442	0.312033
$921$	34.0648	1.12247
$922$	6.09809	0.200830
$923$	−1.05553	−0.0347433
$924$	−0.426381	−0.0140269
$925$	−21.1965	−0.696936
$926$	30.0214	0.986564
$927$	1.00000	0.0328443
$928$	−1.98173	−0.0650535
$929$	−33.0828	−1.08541	−0.542706	−	0.839923i	$-0.682600\pi$
$929$	−33.0828	−1.08541	−0.542706	+	0.839923i	$0.682600\pi$
$930$	−4.41890	−0.144902
$931$	−0.624002	−0.0204508
$932$	−1.97596	−0.0647247
$933$	−20.6694	−0.676684
$934$	40.9120	1.33868
$935$	−10.5932	−0.346434
$936$	2.71690	0.0888046
$937$	26.0492	0.850991	0.425496	−	0.904960i	$-0.360100\pi$
$937$	26.0492	0.850991	0.425496	+	0.904960i	$0.360100\pi$
$938$	9.60249	0.313532
$939$	0.685951	0.0223852
$940$	−0.289902	−0.00945558
$941$	39.1288	1.27556	0.637782	−	0.770217i	$-0.279852\pi$
$941$	39.1288	1.27556	0.637782	+	0.770217i	$0.279852\pi$
$942$	10.7512	0.350294
$943$	26.5762	0.865440
$944$	37.7714	1.22935
$945$	3.54585	0.115347
$946$	8.98039	0.291978
$947$	−30.3431	−0.986019	−0.493009	−	0.870024i	$-0.664103\pi$
$947$	−30.3431	−0.986019	−0.493009	+	0.870024i	$0.664103\pi$
$948$	1.75921	0.0571366
$949$	−1.00361	−0.0325785
$950$	−9.85350	−0.319690
$951$	13.9736	0.453126
$952$	54.4427	1.76450
$953$	−23.3508	−0.756406	−0.378203	−	0.925723i	$-0.623458\pi$
$953$	−23.3508	−0.756406	−0.378203	+	0.925723i	$0.623458\pi$
$954$	13.6728	0.442674
$955$	−7.56783	−0.244889
$956$	−2.11022	−0.0682495
$957$	2.63816	0.0852795
$958$	−47.2150	−1.52545
$959$	−46.2891	−1.49475
$960$	9.62958	0.310793
$961$	−25.7113	−0.829396
$962$	−9.46833	−0.305271
$963$	9.16882	0.295461
$964$	3.45395	0.111244
$965$	13.1154	0.422199
$966$	−10.5091	−0.338126
$967$	−39.2810	−1.26319	−0.631596	−	0.775298i	$-0.717600\pi$
$967$	−39.2810	−1.26319	−0.631596	+	0.775298i	$0.717600\pi$
$968$	−26.6642	−0.857020
$969$	−15.2153	−0.488786
$970$	−33.8020	−1.08532
$971$	−43.4713	−1.39506	−0.697530	−	0.716555i	$-0.745718\pi$
$971$	−43.4713	−1.39506	−0.697530	+	0.716555i	$0.745718\pi$
$972$	0.144881	0.00464705
$973$	17.4341	0.558912
$974$	−50.4253	−1.61573
$975$	−3.27863	−0.105000
$976$	−41.9291	−1.34212
$977$	31.7703	1.01642	0.508211	−	0.861232i	$-0.330307\pi$
$977$	31.7703	1.01642	0.508211	+	0.861232i	$0.330307\pi$
$978$	26.4113	0.844541
$979$	3.22445	0.103054
$980$	0.0578012	0.00184639
$981$	−16.2127	−0.517632
$982$	9.90556	0.316099
$983$	9.00553	0.287232	0.143616	−	0.989634i	$-0.454127\pi$
$983$	9.00553	0.287232	0.143616	+	0.989634i	$0.454127\pi$
$984$	27.1946	0.866933
$985$	4.38388	0.139682
$986$	26.3075	0.837803
$987$	−4.12180	−0.131198
$988$	−0.297308	−0.00945864
$989$	14.9510	0.475416
$990$	2.09240	0.0665008
$991$	9.20747	0.292485	0.146243	−	0.989249i	$-0.453282\pi$
$991$	9.20747	0.292485	0.146243	+	0.989249i	$0.453282\pi$
$992$	1.88116	0.0597268
$993$	15.2911	0.485248
$994$	4.17789	0.132515
$995$	16.7936	0.532391
$996$	0.819704	0.0259733
$997$	6.44863	0.204230	0.102115	−	0.994773i	$-0.467439\pi$
$997$	6.44863	0.204230	0.102115	+	0.994773i	$0.467439\pi$
$998$	−56.6339	−1.79271
$999$	6.46505	0.204545

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.9	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.9	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.46454 q^{2} +1.00000 q^{3} +0.144881 q^{4} +1.31201 q^{5} -1.46454 q^{6} +2.70261 q^{7} +2.71690 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.46454 q^{2} +1.00000 q^{3} +0.144881 q^{4} +1.31201 q^{5} -1.46454 q^{6} +2.70261 q^{7} +2.71690 q^{8} +1.00000 q^{9} -1.92149 q^{10} -1.08894 q^{11} +0.144881 q^{12} +1.00000 q^{13} -3.95808 q^{14} +1.31201 q^{15} -4.26877 q^{16} +7.41452 q^{17} -1.46454 q^{18} -2.05209 q^{19} +0.190085 q^{20} +2.70261 q^{21} +1.59480 q^{22} +2.65511 q^{23} +2.71690 q^{24} -3.27863 q^{25} -1.46454 q^{26} +1.00000 q^{27} +0.391555 q^{28} -2.42268 q^{29} -1.92149 q^{30} +2.29972 q^{31} +0.817993 q^{32} -1.08894 q^{33} -10.8589 q^{34} +3.54585 q^{35} +0.144881 q^{36} +6.46505 q^{37} +3.00537 q^{38} +1.00000 q^{39} +3.56460 q^{40} +10.0094 q^{41} -3.95808 q^{42} +5.63104 q^{43} -0.157767 q^{44} +1.31201 q^{45} -3.88852 q^{46} -1.52512 q^{47} -4.26877 q^{48} +0.304081 q^{49} +4.80168 q^{50} +7.41452 q^{51} +0.144881 q^{52} -9.33590 q^{53} -1.46454 q^{54} -1.42871 q^{55} +7.34271 q^{56} -2.05209 q^{57} +3.54811 q^{58} -8.84831 q^{59} +0.190085 q^{60} +9.82229 q^{61} -3.36804 q^{62} +2.70261 q^{63} +7.33956 q^{64} +1.31201 q^{65} +1.59480 q^{66} -2.42605 q^{67} +1.07422 q^{68} +2.65511 q^{69} -5.19304 q^{70} -1.05553 q^{71} +2.71690 q^{72} -1.00361 q^{73} -9.46833 q^{74} -3.27863 q^{75} -0.297308 q^{76} -2.94298 q^{77} -1.46454 q^{78} +12.1425 q^{79} -5.60068 q^{80} +1.00000 q^{81} -14.6592 q^{82} +5.65779 q^{83} +0.391555 q^{84} +9.72794 q^{85} -8.24689 q^{86} -2.42268 q^{87} -2.95855 q^{88} -2.96108 q^{89} -1.92149 q^{90} +2.70261 q^{91} +0.384674 q^{92} +2.29972 q^{93} +2.23360 q^{94} -2.69237 q^{95} +0.817993 q^{96} +17.5915 q^{97} -0.445339 q^{98} -1.08894 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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