LMFDB - Embedded newform 6019.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.88082 q^{2} -1.45946 q^{3} +1.53747 q^{4} +1.38464 q^{5} +2.74498 q^{6} -0.844871 q^{7} +0.869931 q^{8} -0.869978 q^{9} +O(q^{10})$	\(q-1.88082 q^{2} -1.45946 q^{3} +1.53747 q^{4} +1.38464 q^{5} +2.74498 q^{6} -0.844871 q^{7} +0.869931 q^{8} -0.869978 q^{9} -2.60424 q^{10} +1.27066 q^{11} -2.24388 q^{12} +1.00000 q^{13} +1.58905 q^{14} -2.02082 q^{15} -4.71112 q^{16} +2.69251 q^{17} +1.63627 q^{18} +1.83970 q^{19} +2.12884 q^{20} +1.23306 q^{21} -2.38988 q^{22} +1.10350 q^{23} -1.26963 q^{24} -3.08279 q^{25} -1.88082 q^{26} +5.64808 q^{27} -1.29897 q^{28} +7.07199 q^{29} +3.80079 q^{30} -10.5386 q^{31} +7.12090 q^{32} -1.85447 q^{33} -5.06411 q^{34} -1.16984 q^{35} -1.33757 q^{36} -4.85993 q^{37} -3.46014 q^{38} -1.45946 q^{39} +1.20454 q^{40} +2.77030 q^{41} -2.31915 q^{42} -10.5608 q^{43} +1.95360 q^{44} -1.20460 q^{45} -2.07547 q^{46} +4.00051 q^{47} +6.87569 q^{48} -6.28619 q^{49} +5.79816 q^{50} -3.92961 q^{51} +1.53747 q^{52} -3.78372 q^{53} -10.6230 q^{54} +1.75940 q^{55} -0.734980 q^{56} -2.68497 q^{57} -13.3011 q^{58} +9.28024 q^{59} -3.10695 q^{60} -0.0371063 q^{61} +19.8212 q^{62} +0.735020 q^{63} -3.97086 q^{64} +1.38464 q^{65} +3.48793 q^{66} +6.85927 q^{67} +4.13965 q^{68} -1.61051 q^{69} +2.20025 q^{70} +5.80401 q^{71} -0.756821 q^{72} +6.93910 q^{73} +9.14064 q^{74} +4.49920 q^{75} +2.82849 q^{76} -1.07354 q^{77} +2.74498 q^{78} +12.2936 q^{79} -6.52319 q^{80} -5.63320 q^{81} -5.21043 q^{82} -9.95179 q^{83} +1.89579 q^{84} +3.72814 q^{85} +19.8628 q^{86} -10.3213 q^{87} +1.10539 q^{88} -16.0018 q^{89} +2.26564 q^{90} -0.844871 q^{91} +1.69659 q^{92} +15.3806 q^{93} -7.52424 q^{94} +2.54731 q^{95} -10.3927 q^{96} -15.7433 q^{97} +11.8232 q^{98} -1.10545 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−1.88082	−1.32994	−0.664969	−	0.746871i	$-0.731555\pi$
$2$	−1.88082	−1.32994	−0.664969	+	0.746871i	$0.731555\pi$
$3$	−1.45946	−0.842619	−0.421310	−	0.906917i	$-0.638429\pi$
$3$	−1.45946	−0.842619	−0.421310	+	0.906917i	$0.638429\pi$
$4$	1.53747	0.768736
$5$	1.38464	0.619228	0.309614	−	0.950862i	$-0.399800\pi$
$5$	1.38464	0.619228	0.309614	+	0.950862i	$0.399800\pi$
$6$	2.74498	1.12063
$7$	−0.844871	−0.319331	−0.159666	−	0.987171i	$-0.551042\pi$
$7$	−0.844871	−0.319331	−0.159666	+	0.987171i	$0.551042\pi$
$8$	0.869931	0.307567
$9$	−0.869978	−0.289993
$10$	−2.60424	−0.823534
$11$	1.27066	0.383118	0.191559	−	0.981481i	$-0.438646\pi$
$11$	1.27066	0.383118	0.191559	+	0.981481i	$0.438646\pi$
$12$	−2.24388	−0.647752
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.58905	0.424691
$15$	−2.02082	−0.521773
$16$	−4.71112	−1.17778
$17$	2.69251	0.653029	0.326515	−	0.945192i	$-0.394126\pi$
$17$	2.69251	0.653029	0.326515	+	0.945192i	$0.394126\pi$
$18$	1.63627	0.385672
$19$	1.83970	0.422056	0.211028	−	0.977480i	$-0.432319\pi$
$19$	1.83970	0.422056	0.211028	+	0.977480i	$0.432319\pi$
$20$	2.12884	0.476022
$21$	1.23306	0.269075
$22$	−2.38988	−0.509523
$23$	1.10350	0.230095	0.115047	−	0.993360i	$-0.463298\pi$
$23$	1.10350	0.230095	0.115047	+	0.993360i	$0.463298\pi$
$24$	−1.26963	−0.259162
$25$	−3.08279	−0.616557
$26$	−1.88082	−0.368859
$27$	5.64808	1.08697
$28$	−1.29897	−0.245481
$29$	7.07199	1.31323	0.656617	−	0.754224i	$-0.271987\pi$
$29$	7.07199	1.31323	0.656617	+	0.754224i	$0.271987\pi$
$30$	3.80079	0.693926
$31$	−10.5386	−1.89279	−0.946393	−	0.323016i	$-0.895303\pi$
$31$	−10.5386	−1.89279	−0.946393	+	0.323016i	$0.895303\pi$
$32$	7.12090	1.25881
$33$	−1.85447	−0.322823
$34$	−5.06411	−0.868488
$35$	−1.16984	−0.197739
$36$	−1.33757	−0.222928
$37$	−4.85993	−0.798967	−0.399484	−	0.916740i	$-0.630811\pi$
$37$	−4.85993	−0.798967	−0.399484	+	0.916740i	$0.630811\pi$
$38$	−3.46014	−0.561309
$39$	−1.45946	−0.233701
$40$	1.20454	0.190454
$41$	2.77030	0.432648	0.216324	−	0.976322i	$-0.430593\pi$
$41$	2.77030	0.432648	0.216324	+	0.976322i	$0.430593\pi$
$42$	−2.31915	−0.357853
$43$	−10.5608	−1.61050	−0.805250	−	0.592936i	$-0.797969\pi$
$43$	−10.5608	−1.61050	−0.805250	+	0.592936i	$0.797969\pi$
$44$	1.95360	0.294517
$45$	−1.20460	−0.179572
$46$	−2.07547	−0.306012
$47$	4.00051	0.583535	0.291768	−	0.956489i	$-0.405757\pi$
$47$	4.00051	0.583535	0.291768	+	0.956489i	$0.405757\pi$
$48$	6.87569	0.992421
$49$	−6.28619	−0.898027
$50$	5.79816	0.819983
$51$	−3.92961	−0.550255
$52$	1.53747	0.213209
$53$	−3.78372	−0.519734	−0.259867	−	0.965644i	$-0.583679\pi$
$53$	−3.78372	−0.519734	−0.259867	+	0.965644i	$0.583679\pi$
$54$	−10.6230	−1.44561
$55$	1.75940	0.237237
$56$	−0.734980	−0.0982158
$57$	−2.68497	−0.355633
$58$	−13.3011	−1.74652
$59$	9.28024	1.20818	0.604092	−	0.796914i	$-0.293536\pi$
$59$	9.28024	1.20818	0.604092	+	0.796914i	$0.293536\pi$
$60$	−3.10695	−0.401106
$61$	−0.0371063	−0.00475098	−0.00237549	−	0.999997i	$-0.500756\pi$
$61$	−0.0371063	−0.00475098	−0.00237549	+	0.999997i	$0.500756\pi$
$62$	19.8212	2.51729
$63$	0.735020	0.0926038
$64$	−3.97086	−0.496357
$65$	1.38464	0.171743
$66$	3.48793	0.429334
$67$	6.85927	0.837993	0.418997	−	0.907988i	$-0.362382\pi$
$67$	6.85927	0.837993	0.418997	+	0.907988i	$0.362382\pi$
$68$	4.13965	0.502007
$69$	−1.61051	−0.193882
$70$	2.20025	0.262980
$71$	5.80401	0.688809	0.344405	−	0.938821i	$-0.388081\pi$
$71$	5.80401	0.688809	0.344405	+	0.938821i	$0.388081\pi$
$72$	−0.756821	−0.0891922
$73$	6.93910	0.812160	0.406080	−	0.913838i	$-0.366895\pi$
$73$	6.93910	0.812160	0.406080	+	0.913838i	$0.366895\pi$
$74$	9.14064	1.06258
$75$	4.49920	0.519523
$76$	2.82849	0.324450
$77$	−1.07354	−0.122342
$78$	2.74498	0.310807
$79$	12.2936	1.38314	0.691571	−	0.722308i	$-0.256919\pi$
$79$	12.2936	1.38314	0.691571	+	0.722308i	$0.256919\pi$
$80$	−6.52319	−0.729315
$81$	−5.63320	−0.625911
$82$	−5.21043	−0.575396
$83$	−9.95179	−1.09235	−0.546176	−	0.837671i	$-0.683917\pi$
$83$	−9.95179	−1.09235	−0.546176	+	0.837671i	$0.683917\pi$
$84$	1.89579	0.206847
$85$	3.72814	0.404374
$86$	19.8628	2.14186
$87$	−10.3213	−1.10656
$88$	1.10539	0.117835
$89$	−16.0018	−1.69619	−0.848093	−	0.529848i	$-0.822249\pi$
$89$	−16.0018	−1.69619	−0.848093	+	0.529848i	$0.822249\pi$
$90$	2.26564	0.238819
$91$	−0.844871	−0.0885666
$92$	1.69659	0.176882
$93$	15.3806	1.59490
$94$	−7.52424	−0.776066
$95$	2.54731	0.261349
$96$	−10.3927	−1.06070
$97$	−15.7433	−1.59849	−0.799247	−	0.601003i	$-0.794768\pi$
$97$	−15.7433	−1.59849	−0.799247	+	0.601003i	$0.794768\pi$
$98$	11.8232	1.19432
$99$	−1.10545	−0.111101
$100$	−4.73970	−0.473970
$101$	−1.67173	−0.166343	−0.0831717	−	0.996535i	$-0.526505\pi$
$101$	−1.67173	−0.166343	−0.0831717	+	0.996535i	$0.526505\pi$
$102$	7.39087	0.731805
$103$	−1.97186	−0.194294	−0.0971468	−	0.995270i	$-0.530972\pi$
$103$	−1.97186	−0.194294	−0.0971468	+	0.995270i	$0.530972\pi$
$104$	0.869931	0.0853038
$105$	1.70733	0.166619
$106$	7.11648	0.691214
$107$	−10.8829	−1.05209	−0.526043	−	0.850458i	$-0.676325\pi$
$107$	−10.8829	−1.05209	−0.526043	+	0.850458i	$0.676325\pi$
$108$	8.68376	0.835595
$109$	−17.6569	−1.69122	−0.845612	−	0.533799i	$-0.820764\pi$
$109$	−17.6569	−1.69122	−0.845612	+	0.533799i	$0.820764\pi$
$110$	−3.30911	−0.315511
$111$	7.09287	0.673225
$112$	3.98029	0.376102
$113$	0.0204520	0.00192396	0.000961981	−	1.00000i	$-0.499694\pi$
$113$	0.0204520	0.00192396	0.000961981		1.00000i	$0.499694\pi$
$114$	5.04993	0.472970
$115$	1.52794	0.142481
$116$	10.8730	1.00953
$117$	−0.869978	−0.0804295
$118$	−17.4544	−1.60681
$119$	−2.27482	−0.208533
$120$	−1.75797	−0.160480
$121$	−9.38543	−0.853221
$122$	0.0697902	0.00631851
$123$	−4.04314	−0.364558
$124$	−16.2028	−1.45505
$125$	−11.1917	−1.00102
$126$	−1.38244	−0.123157
$127$	−10.1625	−0.901775	−0.450888	−	0.892581i	$-0.648892\pi$
$127$	−10.1625	−0.901775	−0.450888	+	0.892581i	$0.648892\pi$
$128$	−6.77334	−0.598685
$129$	15.4130	1.35704
$130$	−2.60424	−0.228407
$131$	−12.9445	−1.13097	−0.565483	−	0.824760i	$-0.691310\pi$
$131$	−12.9445	−1.13097	−0.565483	+	0.824760i	$0.691310\pi$
$132$	−2.85120	−0.248165
$133$	−1.55431	−0.134776
$134$	−12.9010	−1.11448
$135$	7.82052	0.673084
$136$	2.34230	0.200850
$137$	21.9413	1.87457	0.937284	−	0.348567i	$-0.113332\pi$
$137$	21.9413	1.87457	0.937284	+	0.348567i	$0.113332\pi$
$138$	3.02907	0.257851
$139$	18.1993	1.54365	0.771823	−	0.635837i	$-0.219345\pi$
$139$	18.1993	1.54365	0.771823	+	0.635837i	$0.219345\pi$
$140$	−1.79859	−0.152009
$141$	−5.83859	−0.491698
$142$	−10.9163	−0.916074
$143$	1.27066	0.106258
$144$	4.09858	0.341548
$145$	9.79212	0.813191
$146$	−13.0512	−1.08012
$147$	9.17444	0.756695
$148$	−7.47200	−0.614195
$149$	19.6898	1.61305	0.806527	−	0.591198i	$-0.201345\pi$
$149$	19.6898	1.61305	0.806527	+	0.591198i	$0.201345\pi$
$150$	−8.46217	−0.690933
$151$	4.55926	0.371027	0.185514	−	0.982642i	$-0.440605\pi$
$151$	4.55926	0.371027	0.185514	+	0.982642i	$0.440605\pi$
$152$	1.60041	0.129811
$153$	−2.34242	−0.189374
$154$	2.01914	0.162707
$155$	−14.5921	−1.17207
$156$	−2.24388	−0.179654
$157$	9.01678	0.719617	0.359809	−	0.933026i	$-0.382842\pi$
$157$	9.01678	0.719617	0.359809	+	0.933026i	$0.382842\pi$
$158$	−23.1221	−1.83949
$159$	5.52218	0.437938
$160$	9.85985	0.779489
$161$	−0.932312	−0.0734765
$162$	10.5950	0.832424
$163$	2.99532	0.234612	0.117306	−	0.993096i	$-0.462574\pi$
$163$	2.99532	0.234612	0.117306	+	0.993096i	$0.462574\pi$
$164$	4.25926	0.332592
$165$	−2.56777	−0.199901
$166$	18.7175	1.45276
$167$	−12.7700	−0.988169	−0.494084	−	0.869414i	$-0.664497\pi$
$167$	−12.7700	−0.988169	−0.494084	+	0.869414i	$0.664497\pi$
$168$	1.07267	0.0827586
$169$	1.00000	0.0769231
$170$	−7.01195	−0.537792
$171$	−1.60050	−0.122393
$172$	−16.2369	−1.23805
$173$	10.7583	0.817941	0.408970	−	0.912548i	$-0.365888\pi$
$173$	10.7583	0.817941	0.408970	+	0.912548i	$0.365888\pi$
$174$	19.4124	1.47165
$175$	2.60456	0.196886
$176$	−5.98623	−0.451229
$177$	−13.5441	−1.01804
$178$	30.0964	2.25582
$179$	0.976947	0.0730205	0.0365102	−	0.999333i	$-0.488376\pi$
$179$	0.976947	0.0730205	0.0365102	+	0.999333i	$0.488376\pi$
$180$	−1.85204	−0.138043
$181$	16.4985	1.22632	0.613162	−	0.789957i	$-0.289897\pi$
$181$	16.4985	1.22632	0.613162	+	0.789957i	$0.289897\pi$
$182$	1.58905	0.117788
$183$	0.0541552	0.00400327
$184$	0.959965	0.0707696
$185$	−6.72923	−0.494743
$186$	−28.9282	−2.12112
$187$	3.42126	0.250187
$188$	6.15068	0.448584
$189$	−4.77190	−0.347105
$190$	−4.79103	−0.347578
$191$	13.1930	0.954614	0.477307	−	0.878737i	$-0.341613\pi$
$191$	13.1930	0.954614	0.477307	+	0.878737i	$0.341613\pi$
$192$	5.79531	0.418240
$193$	7.79400	0.561025	0.280512	−	0.959850i	$-0.409496\pi$
$193$	7.79400	0.561025	0.280512	+	0.959850i	$0.409496\pi$
$194$	29.6103	2.12590
$195$	−2.02082	−0.144714
$196$	−9.66484	−0.690346
$197$	−6.21910	−0.443093	−0.221546	−	0.975150i	$-0.571110\pi$
$197$	−6.21910	−0.443093	−0.221546	+	0.975150i	$0.571110\pi$
$198$	2.07914	0.147758
$199$	23.4422	1.66177	0.830886	−	0.556442i	$-0.187834\pi$
$199$	23.4422	1.66177	0.830886	+	0.556442i	$0.187834\pi$
$200$	−2.68181	−0.189633
$201$	−10.0108	−0.706109
$202$	3.14422	0.221226
$203$	−5.97492	−0.419357
$204$	−6.04166	−0.423001
$205$	3.83586	0.267908
$206$	3.70872	0.258398
$207$	−0.960017	−0.0667258
$208$	−4.71112	−0.326658
$209$	2.33763	0.161697
$210$	−3.21118	−0.221592
$211$	6.16452	0.424383	0.212192	−	0.977228i	$-0.431940\pi$
$211$	6.16452	0.424383	0.212192	+	0.977228i	$0.431940\pi$
$212$	−5.81736	−0.399538
$213$	−8.47072	−0.580404
$214$	20.4687	1.39921
$215$	−14.6228	−0.997266
$216$	4.91344	0.334317
$217$	8.90375	0.604426
$218$	33.2094	2.24922
$219$	−10.1273	−0.684342
$220$	2.70503	0.182373
$221$	2.69251	0.181118
$222$	−13.3404	−0.895348
$223$	7.81376	0.523248	0.261624	−	0.965170i	$-0.415742\pi$
$223$	7.81376	0.523248	0.261624	+	0.965170i	$0.415742\pi$
$224$	−6.01624	−0.401977
$225$	2.68196	0.178797
$226$	−0.0384665	−0.00255875
$227$	29.3203	1.94606	0.973029	−	0.230682i	$-0.0740956\pi$
$227$	29.3203	1.94606	0.973029	+	0.230682i	$0.0740956\pi$
$228$	−4.12806	−0.273388
$229$	−18.7461	−1.23878	−0.619389	−	0.785084i	$-0.712620\pi$
$229$	−18.7461	−1.23878	−0.619389	+	0.785084i	$0.712620\pi$
$230$	−2.87377	−0.189491
$231$	1.56679	0.103087
$232$	6.15214	0.403908
$233$	−7.05725	−0.462336	−0.231168	−	0.972914i	$-0.574255\pi$
$233$	−7.05725	−0.462336	−0.231168	+	0.972914i	$0.574255\pi$
$234$	1.63627	0.106966
$235$	5.53925	0.361341
$236$	14.2681	0.928775
$237$	−17.9421	−1.16546
$238$	4.27853	0.277336
$239$	−15.1115	−0.977480	−0.488740	−	0.872429i	$-0.662543\pi$
$239$	−15.1115	−0.977480	−0.488740	+	0.872429i	$0.662543\pi$
$240$	9.52033	0.614534
$241$	−24.7812	−1.59630	−0.798150	−	0.602459i	$-0.794188\pi$
$241$	−24.7812	−1.59630	−0.798150	+	0.602459i	$0.794188\pi$
$242$	17.6523	1.13473
$243$	−8.72280	−0.559568
$244$	−0.0570499	−0.00365225
$245$	−8.70408	−0.556083
$246$	7.60441	0.484839
$247$	1.83970	0.117057
$248$	−9.16785	−0.582159
$249$	14.5242	0.920436
$250$	21.0496	1.33129
$251$	−2.06205	−0.130155	−0.0650776	−	0.997880i	$-0.520729\pi$
$251$	−2.06205	−0.130155	−0.0650776	+	0.997880i	$0.520729\pi$
$252$	1.13007	0.0711878
$253$	1.40217	0.0881535
$254$	19.1138	1.19931
$255$	−5.44107	−0.340733
$256$	20.6811	1.29257
$257$	−7.25586	−0.452608	−0.226304	−	0.974057i	$-0.572664\pi$
$257$	−7.25586	−0.452608	−0.226304	+	0.974057i	$0.572664\pi$
$258$	−28.9890	−1.80478
$259$	4.10602	0.255135
$260$	2.12884	0.132025
$261$	−6.15247	−0.380829
$262$	24.3462	1.50411
$263$	−2.58518	−0.159409	−0.0797044	−	0.996819i	$-0.525398\pi$
$263$	−2.58518	−0.159409	−0.0797044	+	0.996819i	$0.525398\pi$
$264$	−1.61327	−0.0992896
$265$	−5.23907	−0.321833
$266$	2.92337	0.179244
$267$	23.3539	1.42924
$268$	10.5459	0.644196
$269$	13.1456	0.801501	0.400750	−	0.916187i	$-0.368750\pi$
$269$	13.1456	0.801501	0.400750	+	0.916187i	$0.368750\pi$
$270$	−14.7090	−0.895160
$271$	−23.4768	−1.42611	−0.713057	−	0.701106i	$-0.752690\pi$
$271$	−23.4768	−1.42611	−0.713057	+	0.701106i	$0.752690\pi$
$272$	−12.6847	−0.769125
$273$	1.23306	0.0746279
$274$	−41.2675	−2.49306
$275$	−3.91717	−0.236214
$276$	−2.47611	−0.149044
$277$	−8.64758	−0.519583	−0.259791	−	0.965665i	$-0.583654\pi$
$277$	−8.64758	−0.519583	−0.259791	+	0.965665i	$0.583654\pi$
$278$	−34.2296	−2.05295
$279$	9.16834	0.548894
$280$	−1.01768	−0.0608180
$281$	−1.21871	−0.0727019	−0.0363509	−	0.999339i	$-0.511573\pi$
$281$	−1.21871	−0.0727019	−0.0363509	+	0.999339i	$0.511573\pi$
$282$	10.9813	0.653928
$283$	17.1865	1.02163	0.510815	−	0.859691i	$-0.329344\pi$
$283$	17.1865	1.02163	0.510815	+	0.859691i	$0.329344\pi$
$284$	8.92350	0.529512
$285$	−3.71770	−0.220218
$286$	−2.38988	−0.141316
$287$	−2.34055	−0.138158
$288$	−6.19503	−0.365045
$289$	−9.75040	−0.573553
$290$	−18.4172	−1.08149
$291$	22.9768	1.34692
$292$	10.6687	0.624336
$293$	19.1594	1.11931	0.559653	−	0.828727i	$-0.310935\pi$
$293$	19.1594	1.11931	0.559653	+	0.828727i	$0.310935\pi$
$294$	−17.2554	−1.00636
$295$	12.8498	0.748141
$296$	−4.22780	−0.245736
$297$	7.17678	0.416439
$298$	−37.0330	−2.14526
$299$	1.10350	0.0638168
$300$	6.91739	0.399376
$301$	8.92248	0.514283
$302$	−8.57513	−0.493443
$303$	2.43982	0.140164
$304$	−8.66706	−0.497090
$305$	−0.0513787	−0.00294194
$306$	4.40567	0.251855
$307$	16.3289	0.931941	0.465970	−	0.884800i	$-0.345705\pi$
$307$	16.3289	0.931941	0.465970	+	0.884800i	$0.345705\pi$
$308$	−1.65054	−0.0940484
$309$	2.87786	0.163716
$310$	27.4451	1.55878
$311$	13.2479	0.751221	0.375610	−	0.926778i	$-0.377433\pi$
$311$	13.2479	0.751221	0.375610	+	0.926778i	$0.377433\pi$
$312$	−1.26963	−0.0718786
$313$	−11.1002	−0.627418	−0.313709	−	0.949519i	$-0.601572\pi$
$313$	−11.1002	−0.627418	−0.313709	+	0.949519i	$0.601572\pi$
$314$	−16.9589	−0.957046
$315$	1.01773	0.0573428
$316$	18.9011	1.06327
$317$	10.1350	0.569237	0.284618	−	0.958641i	$-0.408133\pi$
$317$	10.1350	0.569237	0.284618	+	0.958641i	$0.408133\pi$
$318$	−10.3862	−0.582430
$319$	8.98608	0.503124
$320$	−5.49819	−0.307358
$321$	15.8831	0.886509
$322$	1.75351	0.0977192
$323$	4.95341	0.275615
$324$	−8.66089	−0.481161
$325$	−3.08279	−0.171002
$326$	−5.63366	−0.312019
$327$	25.7695	1.42506
$328$	2.40997	0.133068
$329$	−3.37992	−0.186341
$330$	4.82951	0.265856
$331$	−27.2478	−1.49768	−0.748838	−	0.662753i	$-0.769388\pi$
$331$	−27.2478	−1.49768	−0.748838	+	0.662753i	$0.769388\pi$
$332$	−15.3006	−0.839729
$333$	4.22803	0.231695
$334$	24.0179	1.31420
$335$	9.49759	0.518909
$336$	−5.80908	−0.316911
$337$	−31.9340	−1.73956	−0.869779	−	0.493441i	$-0.835739\pi$
$337$	−31.9340	−1.73956	−0.869779	+	0.493441i	$0.835739\pi$
$338$	−1.88082	−0.102303
$339$	−0.0298489	−0.00162117
$340$	5.73191	0.310856
$341$	−13.3910	−0.725161
$342$	3.01025	0.162775
$343$	11.2251	0.606100
$344$	−9.18713	−0.495337
$345$	−2.22996	−0.120057
$346$	−20.2344	−1.08781
$347$	8.54629	0.458789	0.229394	−	0.973334i	$-0.426325\pi$
$347$	8.54629	0.458789	0.229394	+	0.973334i	$0.426325\pi$
$348$	−15.8687	−0.850650
$349$	−29.2065	−1.56339	−0.781694	−	0.623663i	$-0.785644\pi$
$349$	−29.2065	−1.56339	−0.781694	+	0.623663i	$0.785644\pi$
$350$	−4.89870	−0.261846
$351$	5.64808	0.301472
$352$	9.04823	0.482272
$353$	−5.07943	−0.270351	−0.135175	−	0.990822i	$-0.543160\pi$
$353$	−5.07943	−0.270351	−0.135175	+	0.990822i	$0.543160\pi$
$354$	25.4740	1.35393
$355$	8.03644	0.426530
$356$	−24.6023	−1.30392
$357$	3.32001	0.175714
$358$	−1.83746	−0.0971127
$359$	0.810903	0.0427978	0.0213989	−	0.999771i	$-0.493188\pi$
$359$	0.810903	0.0427978	0.0213989	+	0.999771i	$0.493188\pi$
$360$	−1.04792	−0.0552303
$361$	−15.6155	−0.821869
$362$	−31.0306	−1.63093
$363$	13.6976	0.718940
$364$	−1.29897	−0.0680843
$365$	9.60812	0.502912
$366$	−0.101856	−0.00532410
$367$	35.1725	1.83599	0.917996	−	0.396590i	$-0.129806\pi$
$367$	35.1725	1.83599	0.917996	+	0.396590i	$0.129806\pi$
$368$	−5.19871	−0.271001
$369$	−2.41010	−0.125465
$370$	12.6564	0.657977
$371$	3.19676	0.165967
$372$	23.6473	1.22606
$373$	13.3269	0.690043	0.345021	−	0.938595i	$-0.387872\pi$
$373$	13.3269	0.690043	0.345021	+	0.938595i	$0.387872\pi$
$374$	−6.43476	−0.332734
$375$	16.3338	0.843476
$376$	3.48017	0.179476
$377$	7.07199	0.364226
$378$	8.97507	0.461628
$379$	−28.5920	−1.46867	−0.734337	−	0.678785i	$-0.762507\pi$
$379$	−28.5920	−1.46867	−0.734337	+	0.678785i	$0.762507\pi$
$380$	3.91642	0.200908
$381$	14.8317	0.759853
$382$	−24.8137	−1.26958
$383$	−28.4699	−1.45474	−0.727372	−	0.686243i	$-0.759259\pi$
$383$	−28.4699	−1.45474	−0.727372	+	0.686243i	$0.759259\pi$
$384$	9.88542	0.504463
$385$	−1.48647	−0.0757573
$386$	−14.6591	−0.746128
$387$	9.18762	0.467033
$388$	−24.2049	−1.22882
$389$	−13.6156	−0.690339	−0.345170	−	0.938540i	$-0.612179\pi$
$389$	−13.6156	−0.690339	−0.345170	+	0.938540i	$0.612179\pi$
$390$	3.80079	0.192460
$391$	2.97117	0.150259
$392$	−5.46855	−0.276204
$393$	18.8920	0.952973
$394$	11.6970	0.589286
$395$	17.0222	0.856480
$396$	−1.69959	−0.0854077
$397$	−12.7084	−0.637818	−0.318909	−	0.947785i	$-0.603317\pi$
$397$	−12.7084	−0.637818	−0.318909	+	0.947785i	$0.603317\pi$
$398$	−44.0905	−2.21006
$399$	2.26845	0.113565
$400$	14.5234	0.726169
$401$	−11.7677	−0.587651	−0.293826	−	0.955859i	$-0.594929\pi$
$401$	−11.7677	−0.587651	−0.293826	+	0.955859i	$0.594929\pi$
$402$	18.8285	0.939082
$403$	−10.5386	−0.524965
$404$	−2.57024	−0.127874
$405$	−7.79993	−0.387582
$406$	11.2377	0.557719
$407$	−6.17531	−0.306099
$408$	−3.41849	−0.169240
$409$	−11.1270	−0.550194	−0.275097	−	0.961416i	$-0.588710\pi$
$409$	−11.1270	−0.550194	−0.275097	+	0.961416i	$0.588710\pi$
$410$	−7.21454	−0.356301
$411$	−32.0224	−1.57955
$412$	−3.03169	−0.149360
$413$	−7.84061	−0.385811
$414$	1.80562	0.0887412
$415$	−13.7796	−0.676414
$416$	7.12090	0.349131
$417$	−26.5612	−1.30071
$418$	−4.39666	−0.215047
$419$	−37.9641	−1.85467	−0.927333	−	0.374237i	$-0.877905\pi$
$419$	−37.9641	−1.85467	−0.927333	+	0.374237i	$0.877905\pi$
$420$	2.62497	0.128086
$421$	10.5100	0.512224	0.256112	−	0.966647i	$-0.417558\pi$
$421$	10.5100	0.512224	0.256112	+	0.966647i	$0.417558\pi$
$422$	−11.5943	−0.564404
$423$	−3.48036	−0.169221
$424$	−3.29157	−0.159853
$425$	−8.30042	−0.402630
$426$	15.9319	0.771902
$427$	0.0313501	0.00151714
$428$	−16.7321	−0.808777
$429$	−1.85447	−0.0895349
$430$	27.5028	1.32630
$431$	−19.2917	−0.929249	−0.464625	−	0.885508i	$-0.653811\pi$
$431$	−19.2917	−0.929249	−0.464625	+	0.885508i	$0.653811\pi$
$432$	−26.6088	−1.28022
$433$	11.4322	0.549397	0.274699	−	0.961530i	$-0.411422\pi$
$433$	11.4322	0.549397	0.274699	+	0.961530i	$0.411422\pi$
$434$	−16.7463	−0.803850
$435$	−14.2912	−0.685211
$436$	−27.1470	−1.30010
$437$	2.03010	0.0971129
$438$	19.0477	0.910132
$439$	−23.3296	−1.11346	−0.556731	−	0.830693i	$-0.687945\pi$
$439$	−23.3296	−1.11346	−0.556731	+	0.830693i	$0.687945\pi$
$440$	1.53056	0.0729664
$441$	5.46885	0.260421
$442$	−5.06411	−0.240875
$443$	38.1909	1.81450	0.907252	−	0.420588i	$-0.138176\pi$
$443$	38.1909	1.81450	0.907252	+	0.420588i	$0.138176\pi$
$444$	10.9051	0.517532
$445$	−22.1566	−1.05032
$446$	−14.6963	−0.695888
$447$	−28.7365	−1.35919
$448$	3.35486	0.158502
$449$	−17.7756	−0.838884	−0.419442	−	0.907782i	$-0.637774\pi$
$449$	−17.7756	−0.838884	−0.419442	+	0.907782i	$0.637774\pi$
$450$	−5.04427	−0.237789
$451$	3.52011	0.165755
$452$	0.0314444	0.00147902
$453$	−6.65405	−0.312635
$454$	−55.1462	−2.58814
$455$	−1.16984	−0.0548429
$456$	−2.33574	−0.109381
$457$	−1.66368	−0.0778237	−0.0389118	−	0.999243i	$-0.512389\pi$
$457$	−1.66368	−0.0778237	−0.0389118	+	0.999243i	$0.512389\pi$
$458$	35.2580	1.64750
$459$	15.2075	0.709825
$460$	2.34916	0.109530
$461$	6.47840	0.301729	0.150865	−	0.988554i	$-0.451794\pi$
$461$	6.47840	0.301729	0.150865	+	0.988554i	$0.451794\pi$
$462$	−2.94685	−0.137100
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	−33.3170	−1.54670
$465$	21.2966	0.987605
$466$	13.2734	0.614878
$467$	9.60850	0.444628	0.222314	−	0.974975i	$-0.428639\pi$
$467$	9.60850	0.444628	0.222314	+	0.974975i	$0.428639\pi$
$468$	−1.33757	−0.0618290
$469$	−5.79520	−0.267598
$470$	−10.4183	−0.480561
$471$	−13.1596	−0.606363
$472$	8.07317	0.371598
$473$	−13.4191	−0.617011
$474$	33.7457	1.54999
$475$	−5.67140	−0.260222
$476$	−3.49748	−0.160307
$477$	3.29175	0.150719
$478$	28.4219	1.29999
$479$	0.568894	0.0259934	0.0129967	−	0.999916i	$-0.495863\pi$
$479$	0.568894	0.0259934	0.0129967	+	0.999916i	$0.495863\pi$
$480$	−14.3900	−0.656813
$481$	−4.85993	−0.221594
$482$	46.6089	2.12298
$483$	1.36067	0.0619127
$484$	−14.4298	−0.655901
$485$	−21.7988	−0.989832
$486$	16.4060	0.744190
$487$	11.3241	0.513146	0.256573	−	0.966525i	$-0.417407\pi$
$487$	11.3241	0.513146	0.256573	+	0.966525i	$0.417407\pi$
$488$	−0.0322799	−0.00146124
$489$	−4.37155	−0.197688
$490$	16.3708	0.739557
$491$	−16.1911	−0.730696	−0.365348	−	0.930871i	$-0.619050\pi$
$491$	−16.1911	−0.730696	−0.365348	+	0.930871i	$0.619050\pi$
$492$	−6.21622	−0.280249
$493$	19.0414	0.857580
$494$	−3.46014	−0.155679
$495$	−1.53064	−0.0687971
$496$	49.6486	2.22929
$497$	−4.90364	−0.219958
$498$	−27.3174	−1.22412
$499$	7.20398	0.322494	0.161247	−	0.986914i	$-0.448448\pi$
$499$	7.20398	0.322494	0.161247	+	0.986914i	$0.448448\pi$
$500$	−17.2069	−0.769517
$501$	18.6372	0.832650
$502$	3.87833	0.173098
$503$	−28.3322	−1.26327	−0.631635	−	0.775266i	$-0.717616\pi$
$503$	−28.3322	−1.26327	−0.631635	+	0.775266i	$0.717616\pi$
$504$	0.639417	0.0284819
$505$	−2.31474	−0.103004
$506$	−2.63722	−0.117239
$507$	−1.45946	−0.0648169
$508$	−15.6245	−0.693227
$509$	−19.0344	−0.843683	−0.421842	−	0.906670i	$-0.638616\pi$
$509$	−19.0344	−0.843683	−0.421842	+	0.906670i	$0.638616\pi$
$510$	10.2337	0.453154
$511$	−5.86265	−0.259348
$512$	−25.3507	−1.12035
$513$	10.3908	0.458764
$514$	13.6469	0.601941
$515$	−2.73031	−0.120312
$516$	23.6970	1.04320
$517$	5.08329	0.223563
$518$	−7.72266	−0.339314
$519$	−15.7013	−0.689213
$520$	1.20454	0.0528224
$521$	−18.2157	−0.798044	−0.399022	−	0.916941i	$-0.630650\pi$
$521$	−18.2157	−0.798044	−0.399022	+	0.916941i	$0.630650\pi$
$522$	11.5717	0.506478
$523$	33.1030	1.44749	0.723746	−	0.690066i	$-0.242419\pi$
$523$	33.1030	1.44749	0.723746	+	0.690066i	$0.242419\pi$
$524$	−19.9018	−0.869414
$525$	−3.80125	−0.165900
$526$	4.86224	0.212004
$527$	−28.3752	−1.23604
$528$	8.73666	0.380214
$529$	−21.7823	−0.947056
$530$	9.85373	0.428019
$531$	−8.07361	−0.350365
$532$	−2.38971	−0.103607
$533$	2.77030	0.119995
$534$	−43.9245	−1.90080
$535$	−15.0688	−0.651481
$536$	5.96709	0.257739
$537$	−1.42582	−0.0615285
$538$	−24.7244	−1.06595
$539$	−7.98761	−0.344051
$540$	12.0238	0.517423
$541$	15.1781	0.652559	0.326279	−	0.945273i	$-0.394205\pi$
$541$	15.1781	0.652559	0.326279	+	0.945273i	$0.394205\pi$
$542$	44.1556	1.89664
$543$	−24.0789	−1.03332
$544$	19.1731	0.822039
$545$	−24.4483	−1.04725
$546$	−2.31915	−0.0992505
$547$	−2.63712	−0.112755	−0.0563775	−	0.998410i	$-0.517955\pi$
$547$	−2.63712	−0.112755	−0.0563775	+	0.998410i	$0.517955\pi$
$548$	33.7340	1.44105
$549$	0.0322817	0.00137775
$550$	7.36748	0.314150
$551$	13.0103	0.554259
$552$	−1.40103	−0.0596318
$553$	−10.3865	−0.441681
$554$	16.2645	0.691013
$555$	9.82103	0.416880
$556$	27.9809	1.18666
$557$	−34.6366	−1.46760	−0.733800	−	0.679366i	$-0.762255\pi$
$557$	−34.6366	−1.46760	−0.733800	+	0.679366i	$0.762255\pi$
$558$	−17.2440	−0.729996
$559$	−10.5608	−0.446672
$560$	5.51126	0.232893
$561$	−4.99319	−0.210813
$562$	2.29216	0.0966890
$563$	−22.8263	−0.962016	−0.481008	−	0.876716i	$-0.659729\pi$
$563$	−22.8263	−0.962016	−0.481008	+	0.876716i	$0.659729\pi$
$564$	−8.97666	−0.377986
$565$	0.0283186	0.00119137
$566$	−32.3246	−1.35870
$567$	4.75933	0.199873
$568$	5.04909	0.211855
$569$	−28.5201	−1.19563	−0.597813	−	0.801635i	$-0.703964\pi$
$569$	−28.5201	−1.19563	−0.597813	+	0.801635i	$0.703964\pi$
$570$	6.99231	0.292876
$571$	−21.0983	−0.882938	−0.441469	−	0.897276i	$-0.645542\pi$
$571$	−21.0983	−0.882938	−0.441469	+	0.897276i	$0.645542\pi$
$572$	1.95360	0.0816842
$573$	−19.2547	−0.804376
$574$	4.40214	0.183742
$575$	−3.40184	−0.141867
$576$	3.45456	0.143940
$577$	8.70903	0.362561	0.181281	−	0.983431i	$-0.441976\pi$
$577$	8.70903	0.362561	0.181281	+	0.983431i	$0.441976\pi$
$578$	18.3387	0.762790
$579$	−11.3750	−0.472730
$580$	15.0551	0.625129
$581$	8.40799	0.348822
$582$	−43.2151	−1.79132
$583$	−4.80782	−0.199119
$584$	6.03654	0.249794
$585$	−1.20460	−0.0498042
$586$	−36.0354	−1.48861
$587$	13.6139	0.561907	0.280954	−	0.959721i	$-0.409349\pi$
$587$	13.6139	0.561907	0.280954	+	0.959721i	$0.409349\pi$
$588$	14.1054	0.581699
$589$	−19.3879	−0.798862
$590$	−24.1680	−0.994982
$591$	9.07653	0.373359
$592$	22.8957	0.941009
$593$	−19.5945	−0.804649	−0.402325	−	0.915497i	$-0.631798\pi$
$593$	−19.5945	−0.804649	−0.402325	+	0.915497i	$0.631798\pi$
$594$	−13.4982	−0.553838
$595$	−3.14980	−0.129129
$596$	30.2725	1.24001
$597$	−34.2129	−1.40024
$598$	−2.07547	−0.0848724
$599$	3.09625	0.126509	0.0632547	−	0.997997i	$-0.479852\pi$
$599$	3.09625	0.126509	0.0632547	+	0.997997i	$0.479852\pi$
$600$	3.91399	0.159788
$601$	−27.7468	−1.13181	−0.565907	−	0.824469i	$-0.691474\pi$
$601$	−27.7468	−1.13181	−0.565907	+	0.824469i	$0.691474\pi$
$602$	−16.7815	−0.683965
$603$	−5.96742	−0.243012
$604$	7.00973	0.285222
$605$	−12.9954	−0.528338
$606$	−4.58886	−0.186410
$607$	−28.4267	−1.15380	−0.576901	−	0.816814i	$-0.695738\pi$
$607$	−28.4267	−1.15380	−0.576901	+	0.816814i	$0.695738\pi$
$608$	13.1003	0.531288
$609$	8.72015	0.353358
$610$	0.0966339	0.00391259
$611$	4.00051	0.161844
$612$	−3.60141	−0.145578
$613$	10.4225	0.420963	0.210481	−	0.977598i	$-0.432497\pi$
$613$	10.4225	0.420963	0.210481	+	0.977598i	$0.432497\pi$
$614$	−30.7117	−1.23942
$615$	−5.59828	−0.225744
$616$	−0.933909	−0.0376283
$617$	41.6385	1.67630	0.838152	−	0.545437i	$-0.183636\pi$
$617$	41.6385	1.67630	0.838152	+	0.545437i	$0.183636\pi$
$618$	−5.41272	−0.217732
$619$	−47.5119	−1.90966	−0.954832	−	0.297146i	$-0.903965\pi$
$619$	−47.5119	−1.90966	−0.954832	+	0.297146i	$0.903965\pi$
$620$	−22.4349	−0.901009
$621$	6.23263	0.250107
$622$	−24.9169	−0.999077
$623$	13.5194	0.541645
$624$	6.87569	0.275248
$625$	−0.0825019	−0.00330008
$626$	20.8774	0.834428
$627$	−3.41168	−0.136249
$628$	13.8630	0.553195
$629$	−13.0854	−0.521749
$630$	−1.91417	−0.0762624
$631$	−38.2812	−1.52395	−0.761975	−	0.647606i	$-0.775770\pi$
$631$	−38.2812	−1.52395	−0.761975	+	0.647606i	$0.775770\pi$
$632$	10.6946	0.425409
$633$	−8.99687	−0.357594
$634$	−19.0620	−0.757049
$635$	−14.0713	−0.558404
$636$	8.49020	0.336658
$637$	−6.28619	−0.249068
$638$	−16.9012	−0.669124
$639$	−5.04936	−0.199750
$640$	−9.37861	−0.370722
$641$	20.4789	0.808869	0.404434	−	0.914567i	$-0.367468\pi$
$641$	20.4789	0.808869	0.404434	+	0.914567i	$0.367468\pi$
$642$	−29.8732	−1.17900
$643$	−2.51939	−0.0993552	−0.0496776	−	0.998765i	$-0.515819\pi$
$643$	−2.51939	−0.0993552	−0.0496776	+	0.998765i	$0.515819\pi$
$644$	−1.43340	−0.0564840
$645$	21.3414	0.840315
$646$	−9.31645	−0.366551
$647$	−7.29503	−0.286797	−0.143399	−	0.989665i	$-0.545803\pi$
$647$	−7.29503	−0.286797	−0.143399	+	0.989665i	$0.545803\pi$
$648$	−4.90050	−0.192510
$649$	11.7920	0.462877
$650$	5.79816	0.227422
$651$	−12.9947	−0.509301
$652$	4.60523	0.180355
$653$	−4.91885	−0.192489	−0.0962447	−	0.995358i	$-0.530683\pi$
$653$	−4.91885	−0.192489	−0.0962447	+	0.995358i	$0.530683\pi$
$654$	−48.4677	−1.89524
$655$	−17.9234	−0.700325
$656$	−13.0512	−0.509565
$657$	−6.03686	−0.235520
$658$	6.35701	0.247822
$659$	1.87428	0.0730117	0.0365058	−	0.999333i	$-0.488377\pi$
$659$	1.87428	0.0730117	0.0365058	+	0.999333i	$0.488377\pi$
$660$	−3.94787	−0.153671
$661$	29.1227	1.13274	0.566371	−	0.824150i	$-0.308347\pi$
$661$	29.1227	1.13274	0.566371	+	0.824150i	$0.308347\pi$
$662$	51.2482	1.99182
$663$	−3.92961	−0.152613
$664$	−8.65737	−0.335971
$665$	−2.15215	−0.0834569
$666$	−7.95215	−0.308140
$667$	7.80391	0.302168
$668$	−19.6334	−0.759641
$669$	−11.4039	−0.440899
$670$	−17.8632	−0.690116
$671$	−0.0471495	−0.00182019
$672$	8.78046	0.338714
$673$	−0.732264	−0.0282267	−0.0141134	−	0.999900i	$-0.504493\pi$
$673$	−0.732264	−0.0282267	−0.0141134	+	0.999900i	$0.504493\pi$
$674$	60.0621	2.31351
$675$	−17.4118	−0.670181
$676$	1.53747	0.0591335
$677$	−46.9815	−1.80564	−0.902822	−	0.430014i	$-0.858509\pi$
$677$	−46.9815	−1.80564	−0.902822	+	0.430014i	$0.858509\pi$
$678$	0.0561403	0.00215605
$679$	13.3011	0.510449
$680$	3.24323	0.124372
$681$	−42.7918	−1.63979
$682$	25.1859	0.964419
$683$	27.3835	1.04780	0.523900	−	0.851779i	$-0.324476\pi$
$683$	27.3835	1.04780	0.523900	+	0.851779i	$0.324476\pi$
$684$	−2.46072	−0.0940881
$685$	30.3806	1.16078
$686$	−21.1124	−0.806075
$687$	27.3592	1.04382
$688$	49.7530	1.89682
$689$	−3.78372	−0.144148
$690$	4.19415	0.159669
$691$	−10.9111	−0.415077	−0.207539	−	0.978227i	$-0.566545\pi$
$691$	−10.9111	−0.415077	−0.207539	+	0.978227i	$0.566545\pi$
$692$	16.5406	0.628780
$693$	0.933959	0.0354782
$694$	−16.0740	−0.610161
$695$	25.1994	0.955868
$696$	−8.97880	−0.340341
$697$	7.45906	0.282532
$698$	54.9320	2.07921
$699$	10.2998	0.389573
$700$	4.00443	0.151353
$701$	21.9937	0.830691	0.415345	−	0.909664i	$-0.363661\pi$
$701$	21.9937	0.830691	0.415345	+	0.909664i	$0.363661\pi$
$702$	−10.6230	−0.400939
$703$	−8.94081	−0.337209
$704$	−5.04561	−0.190163
$705$	−8.08431	−0.304473
$706$	9.55348	0.359550
$707$	1.41240	0.0531187
$708$	−20.8237	−0.782604
$709$	13.7577	0.516682	0.258341	−	0.966054i	$-0.416824\pi$
$709$	13.7577	0.516682	0.258341	+	0.966054i	$0.416824\pi$
$710$	−15.1151	−0.567258
$711$	−10.6952	−0.401101
$712$	−13.9204	−0.521691
$713$	−11.6293	−0.435520
$714$	−6.24433	−0.233688
$715$	1.75940	0.0657978
$716$	1.50203	0.0561335
$717$	22.0546	0.823644
$718$	−1.52516	−0.0569184
$719$	−1.44716	−0.0539701	−0.0269851	−	0.999636i	$-0.508591\pi$
$719$	−1.44716	−0.0539701	−0.0269851	+	0.999636i	$0.508591\pi$
$720$	5.67503	0.211496
$721$	1.66597	0.0620440
$722$	29.3699	1.09303
$723$	36.1672	1.34507
$724$	25.3660	0.942719
$725$	−21.8014	−0.809684
$726$	−25.7628	−0.956146
$727$	−43.8880	−1.62771	−0.813857	−	0.581065i	$-0.802636\pi$
$727$	−43.8880	−1.62771	−0.813857	+	0.581065i	$0.802636\pi$
$728$	−0.734980	−0.0272402
$729$	29.6302	1.09741
$730$	−18.0711	−0.668842
$731$	−28.4349	−1.05170
$732$	0.0832620	0.00307745
$733$	−18.4114	−0.680042	−0.340021	−	0.940418i	$-0.610434\pi$
$733$	−18.4114	−0.680042	−0.340021	+	0.940418i	$0.610434\pi$
$734$	−66.1531	−2.44176
$735$	12.7033	0.468567
$736$	7.85788	0.289645
$737$	8.71579	0.321050
$738$	4.53296	0.166861
$739$	35.8179	1.31758	0.658791	−	0.752326i	$-0.271068\pi$
$739$	35.8179	1.31758	0.658791	+	0.752326i	$0.271068\pi$
$740$	−10.3460	−0.380326
$741$	−2.68497	−0.0986348
$742$	−6.01251	−0.220726
$743$	−26.6077	−0.976142	−0.488071	−	0.872804i	$-0.662299\pi$
$743$	−26.6077	−0.976142	−0.488071	+	0.872804i	$0.662299\pi$
$744$	13.3801	0.490538
$745$	27.2632	0.998847
$746$	−25.0655	−0.917714
$747$	8.65784	0.316774
$748$	5.26009	0.192328
$749$	9.19463	0.335964
$750$	−30.7210	−1.12177
$751$	−15.6637	−0.571575	−0.285788	−	0.958293i	$-0.592255\pi$
$751$	−15.6637	−0.571575	−0.285788	+	0.958293i	$0.592255\pi$
$752$	−18.8469	−0.687277
$753$	3.00947	0.109671
$754$	−13.3011	−0.484398
$755$	6.31291	0.229750
$756$	−7.33666	−0.266832
$757$	−45.6059	−1.65758	−0.828788	−	0.559563i	$-0.810969\pi$
$757$	−45.6059	−1.65758	−0.828788	+	0.559563i	$0.810969\pi$
$758$	53.7764	1.95325
$759$	−2.04641	−0.0742798
$760$	2.21599	0.0803823
$761$	−45.7697	−1.65915	−0.829576	−	0.558394i	$-0.811418\pi$
$761$	−45.7697	−1.65915	−0.829576	+	0.558394i	$0.811418\pi$
$762$	−27.8958	−1.01056
$763$	14.9178	0.540061
$764$	20.2839	0.733846
$765$	−3.24340	−0.117265
$766$	53.5467	1.93472
$767$	9.28024	0.335090
$768$	−30.1833	−1.08915
$769$	−7.08709	−0.255567	−0.127784	−	0.991802i	$-0.540786\pi$
$769$	−7.08709	−0.255567	−0.127784	+	0.991802i	$0.540786\pi$
$770$	2.79577	0.100753
$771$	10.5896	0.381376
$772$	11.9831	0.431280
$773$	53.1233	1.91071	0.955356	−	0.295457i	$-0.0954720\pi$
$773$	53.1233	1.91071	0.955356	+	0.295457i	$0.0954720\pi$
$774$	−17.2802	−0.621125
$775$	32.4882	1.16701
$776$	−13.6956	−0.491644
$777$	−5.99256	−0.214982
$778$	25.6085	0.918109
$779$	5.09652	0.182602
$780$	−3.10695	−0.111247
$781$	7.37492	0.263895
$782$	−5.58823	−0.199835
$783$	39.9431	1.42745
$784$	29.6150	1.05768
$785$	12.4849	0.445607
$786$	−35.5323	−1.26740
$787$	−14.3209	−0.510486	−0.255243	−	0.966877i	$-0.582156\pi$
$787$	−14.3209	−0.510486	−0.255243	+	0.966877i	$0.582156\pi$
$788$	−9.56170	−0.340621
$789$	3.77296	0.134321
$790$	−32.0157	−1.13907
$791$	−0.0172793	−0.000614382 0
$792$	−0.961661	−0.0341712
$793$	−0.0371063	−0.00131768
$794$	23.9023	0.848259
$795$	7.64621	0.271183
$796$	36.0417	1.27746
$797$	−8.97504	−0.317912	−0.158956	−	0.987286i	$-0.550813\pi$
$797$	−8.97504	−0.317912	−0.158956	+	0.987286i	$0.550813\pi$
$798$	−4.26654	−0.151034
$799$	10.7714	0.381065
$800$	−21.9522	−0.776128
$801$	13.9212	0.491881
$802$	22.1329	0.781540
$803$	8.81722	0.311153
$804$	−15.3914	−0.542812
$805$	−1.29091	−0.0454987
$806$	19.8212	0.698171
$807$	−19.1854	−0.675360
$808$	−1.45429	−0.0511618
$809$	−37.2173	−1.30849	−0.654246	−	0.756282i	$-0.727014\pi$
$809$	−37.2173	−1.30849	−0.654246	+	0.756282i	$0.727014\pi$
$810$	14.6702	0.515460
$811$	−7.94344	−0.278932	−0.139466	−	0.990227i	$-0.544539\pi$
$811$	−7.94344	−0.278932	−0.139466	+	0.990227i	$0.544539\pi$
$812$	−9.18627	−0.322375
$813$	34.2634	1.20167
$814$	11.6146	0.407093
$815$	4.14743	0.145278
$816$	18.5129	0.648080
$817$	−19.4286	−0.679721
$818$	20.9278	0.731724
$819$	0.735020	0.0256837
$820$	5.89752	0.205950
$821$	15.1171	0.527589	0.263795	−	0.964579i	$-0.415026\pi$
$821$	15.1171	0.527589	0.263795	+	0.964579i	$0.415026\pi$
$822$	60.2282	2.10070
$823$	−37.6366	−1.31193	−0.655964	−	0.754792i	$-0.727738\pi$
$823$	−37.6366	−1.31193	−0.655964	+	0.754792i	$0.727738\pi$
$824$	−1.71539	−0.0597583
$825$	5.71695	0.199039
$826$	14.7468	0.513105
$827$	3.56304	0.123899	0.0619495	−	0.998079i	$-0.480268\pi$
$827$	3.56304	0.123899	0.0619495	+	0.998079i	$0.480268\pi$
$828$	−1.47600	−0.0512945
$829$	−37.8912	−1.31601	−0.658007	−	0.753012i	$-0.728600\pi$
$829$	−37.8912	−1.31601	−0.658007	+	0.753012i	$0.728600\pi$
$830$	25.9169	0.899589
$831$	12.6208	0.437810
$832$	−3.97086	−0.137665
$833$	−16.9256	−0.586438
$834$	49.9567	1.72986
$835$	−17.6817	−0.611901
$836$	3.59404	0.124303
$837$	−59.5228	−2.05741
$838$	71.4034	2.46659
$839$	−7.08228	−0.244508	−0.122254	−	0.992499i	$-0.539012\pi$
$839$	−7.08228	−0.244508	−0.122254	+	0.992499i	$0.539012\pi$
$840$	1.48526	0.0512464
$841$	21.0130	0.724586
$842$	−19.7673	−0.681227
$843$	1.77865	0.0612600
$844$	9.47778	0.326239
$845$	1.38464	0.0476329
$846$	6.54592	0.225053
$847$	7.92948	0.272460
$848$	17.8256	0.612133
$849$	−25.0829	−0.860845
$850$	15.6116	0.535473
$851$	−5.36291	−0.183838
$852$	−13.0235	−0.446177
$853$	32.2458	1.10407	0.552037	−	0.833819i	$-0.313851\pi$
$853$	32.2458	1.10407	0.552037	+	0.833819i	$0.313851\pi$
$854$	−0.0589637	−0.00201770
$855$	−2.21611	−0.0757893
$856$	−9.46735	−0.323587
$857$	−50.6133	−1.72892	−0.864458	−	0.502705i	$-0.832338\pi$
$857$	−50.6133	−1.72892	−0.864458	+	0.502705i	$0.832338\pi$
$858$	3.48793	0.119076
$859$	−12.2227	−0.417035	−0.208517	−	0.978019i	$-0.566864\pi$
$859$	−12.2227	−0.417035	−0.208517	+	0.978019i	$0.566864\pi$
$860$	−22.4821	−0.766634
$861$	3.41593	0.116415
$862$	36.2842	1.23584
$863$	10.6300	0.361850	0.180925	−	0.983497i	$-0.442091\pi$
$863$	10.6300	0.361850	0.180925	+	0.983497i	$0.442091\pi$
$864$	40.2194	1.36829
$865$	14.8964	0.506491
$866$	−21.5019	−0.730665
$867$	14.2303	0.483287
$868$	13.6893	0.464644
$869$	15.6210	0.529907
$870$	26.8791	0.911288
$871$	6.85927	0.232418
$872$	−15.3603	−0.520165
$873$	13.6964	0.463552
$874$	−3.81825	−0.129154
$875$	9.45556	0.319656
$876$	−15.5705	−0.526078
$877$	−24.7425	−0.835494	−0.417747	−	0.908563i	$-0.637180\pi$
$877$	−24.7425	−0.835494	−0.417747	+	0.908563i	$0.637180\pi$
$878$	43.8788	1.48084
$879$	−27.9624	−0.943148
$880$	−8.28875	−0.279414
$881$	37.1268	1.25083	0.625417	−	0.780291i	$-0.284929\pi$
$881$	37.1268	1.25083	0.625417	+	0.780291i	$0.284929\pi$
$882$	−10.2859	−0.346344
$883$	17.5758	0.591472	0.295736	−	0.955270i	$-0.404435\pi$
$883$	17.5758	0.591472	0.295736	+	0.955270i	$0.404435\pi$
$884$	4.13965	0.139232
$885$	−18.7537	−0.630398
$886$	−71.8300	−2.41318
$887$	−40.0152	−1.34358	−0.671789	−	0.740743i	$-0.734474\pi$
$887$	−40.0152	−1.34358	−0.671789	+	0.740743i	$0.734474\pi$
$888$	6.17031	0.207062
$889$	8.58600	0.287965
$890$	41.6725	1.39687
$891$	−7.15788	−0.239798
$892$	12.0134	0.402240
$893$	7.35975	0.246285
$894$	54.0481	1.80764
$895$	1.35272	0.0452163
$896$	5.72260	0.191179
$897$	−1.61051	−0.0537733
$898$	33.4327	1.11566
$899$	−74.5288	−2.48567
$900$	4.12343	0.137448
$901$	−10.1877	−0.339401
$902$	−6.62068	−0.220444
$903$	−13.0220	−0.433345
$904$	0.0177918	0.000591748 0
$905$	22.8444	0.759373
$906$	12.5151	0.415785
$907$	6.23137	0.206909	0.103455	−	0.994634i	$-0.467010\pi$
$907$	6.23137	0.206909	0.103455	+	0.994634i	$0.467010\pi$
$908$	45.0792	1.49600
$909$	1.45437	0.0482384
$910$	2.20025	0.0729376
$911$	−22.9845	−0.761509	−0.380755	−	0.924676i	$-0.624336\pi$
$911$	−22.9845	−0.761509	−0.380755	+	0.924676i	$0.624336\pi$
$912$	12.6492	0.418857
$913$	−12.6453	−0.418499
$914$	3.12908	0.103501
$915$	0.0749851	0.00247893
$916$	−28.8216	−0.952293
$917$	10.9364	0.361153
$918$	−28.6025	−0.944023
$919$	−10.6916	−0.352683	−0.176341	−	0.984329i	$-0.556426\pi$
$919$	−10.6916	−0.352683	−0.176341	+	0.984329i	$0.556426\pi$
$920$	1.32920	0.0438225
$921$	−23.8314	−0.785271
$922$	−12.1847	−0.401281
$923$	5.80401	0.191041
$924$	2.40890	0.0792470
$925$	14.9821	0.492609
$926$	−1.88082	−0.0618075
$927$	1.71548	0.0563437
$928$	50.3589	1.65311
$929$	−13.1823	−0.432496	−0.216248	−	0.976338i	$-0.569382\pi$
$929$	−13.1823	−0.432496	−0.216248	+	0.976338i	$0.569382\pi$
$930$	−40.0550	−1.31345
$931$	−11.5647	−0.379018
$932$	−10.8503	−0.355414
$933$	−19.3348	−0.632993
$934$	−18.0718	−0.591328
$935$	4.73719	0.154923
$936$	−0.756821	−0.0247375
$937$	−12.3095	−0.402134	−0.201067	−	0.979578i	$-0.564441\pi$
$937$	−12.3095	−0.402134	−0.201067	+	0.979578i	$0.564441\pi$
$938$	10.8997	0.355888
$939$	16.2002	0.528675
$940$	8.51644	0.277776
$941$	−31.2492	−1.01870	−0.509348	−	0.860561i	$-0.670113\pi$
$941$	−31.2492	−1.01870	−0.509348	+	0.860561i	$0.670113\pi$
$942$	24.7508	0.806426
$943$	3.05702	0.0995501
$944$	−43.7204	−1.42298
$945$	−6.60734	−0.214937
$946$	25.2389	0.820587
$947$	−2.69892	−0.0877032	−0.0438516	−	0.999038i	$-0.513963\pi$
$947$	−2.69892	−0.0877032	−0.0438516	+	0.999038i	$0.513963\pi$
$948$	−27.5854	−0.895933
$949$	6.93910	0.225253
$950$	10.6669	0.346079
$951$	−14.7916	−0.479650
$952$	−1.97894	−0.0641378
$953$	−58.6079	−1.89850	−0.949248	−	0.314528i	$-0.898154\pi$
$953$	−58.6079	−1.89850	−0.949248	+	0.314528i	$0.898154\pi$
$954$	−6.19118	−0.200447
$955$	18.2675	0.591124
$956$	−23.2335	−0.751424
$957$	−13.1148	−0.423942
$958$	−1.06998	−0.0345696
$959$	−18.5375	−0.598608
$960$	8.02438	0.258986
$961$	80.0619	2.58264
$962$	9.14064	0.294706
$963$	9.46786	0.305098
$964$	−38.1004	−1.22713
$965$	10.7918	0.347402
$966$	−2.55917	−0.0823401
$967$	58.5146	1.88170	0.940851	−	0.338821i	$-0.110028\pi$
$967$	58.5146	1.88170	0.940851	+	0.338821i	$0.110028\pi$
$968$	−8.16467	−0.262423
$969$	−7.22930	−0.232238
$970$	40.9995	1.31641
$971$	17.5172	0.562155	0.281078	−	0.959685i	$-0.409308\pi$
$971$	17.5172	0.562155	0.281078	+	0.959685i	$0.409308\pi$
$972$	−13.4111	−0.430160
$973$	−15.3761	−0.492935
$974$	−21.2986	−0.682452
$975$	4.49920	0.144090
$976$	0.174812	0.00559561
$977$	38.5508	1.23335	0.616675	−	0.787218i	$-0.288479\pi$
$977$	38.5508	1.23335	0.616675	+	0.787218i	$0.288479\pi$
$978$	8.22209	0.262913
$979$	−20.3328	−0.649839
$980$	−13.3823	−0.427481
$981$	15.3611	0.490442
$982$	30.4526	0.971780
$983$	5.41797	0.172806	0.0864032	−	0.996260i	$-0.472463\pi$
$983$	5.41797	0.172806	0.0864032	+	0.996260i	$0.472463\pi$
$984$	−3.51725	−0.112126
$985$	−8.61119	−0.274375
$986$	−35.8133	−1.14053
$987$	4.93286	0.157015
$988$	2.82849	0.0899862
$989$	−11.6537	−0.370567
$990$	2.87885	0.0914959
$991$	−20.3509	−0.646469	−0.323234	−	0.946319i	$-0.604770\pi$
$991$	−20.3509	−0.646469	−0.323234	+	0.946319i	$0.604770\pi$
$992$	−75.0442	−2.38266
$993$	39.7671	1.26197
$994$	9.22286	0.292531
$995$	32.4589	1.02902
$996$	22.3306	0.707572
$997$	−35.8721	−1.13608	−0.568041	−	0.823000i	$-0.692298\pi$
$997$	−35.8721	−1.13608	−0.568041	+	0.823000i	$0.692298\pi$
$998$	−13.5494	−0.428897
$999$	−27.4492	−0.868456

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.20	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.20	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-1.88082 q^{2} -1.45946 q^{3} +1.53747 q^{4} +1.38464 q^{5} +2.74498 q^{6} -0.844871 q^{7} +0.869931 q^{8} -0.869978 q^{9} +O(q^{10})\)	\(q-1.88082 q^{2} -1.45946 q^{3} +1.53747 q^{4} +1.38464 q^{5} +2.74498 q^{6} -0.844871 q^{7} +0.869931 q^{8} -0.869978 q^{9} -2.60424 q^{10} +1.27066 q^{11} -2.24388 q^{12} +1.00000 q^{13} +1.58905 q^{14} -2.02082 q^{15} -4.71112 q^{16} +2.69251 q^{17} +1.63627 q^{18} +1.83970 q^{19} +2.12884 q^{20} +1.23306 q^{21} -2.38988 q^{22} +1.10350 q^{23} -1.26963 q^{24} -3.08279 q^{25} -1.88082 q^{26} +5.64808 q^{27} -1.29897 q^{28} +7.07199 q^{29} +3.80079 q^{30} -10.5386 q^{31} +7.12090 q^{32} -1.85447 q^{33} -5.06411 q^{34} -1.16984 q^{35} -1.33757 q^{36} -4.85993 q^{37} -3.46014 q^{38} -1.45946 q^{39} +1.20454 q^{40} +2.77030 q^{41} -2.31915 q^{42} -10.5608 q^{43} +1.95360 q^{44} -1.20460 q^{45} -2.07547 q^{46} +4.00051 q^{47} +6.87569 q^{48} -6.28619 q^{49} +5.79816 q^{50} -3.92961 q^{51} +1.53747 q^{52} -3.78372 q^{53} -10.6230 q^{54} +1.75940 q^{55} -0.734980 q^{56} -2.68497 q^{57} -13.3011 q^{58} +9.28024 q^{59} -3.10695 q^{60} -0.0371063 q^{61} +19.8212 q^{62} +0.735020 q^{63} -3.97086 q^{64} +1.38464 q^{65} +3.48793 q^{66} +6.85927 q^{67} +4.13965 q^{68} -1.61051 q^{69} +2.20025 q^{70} +5.80401 q^{71} -0.756821 q^{72} +6.93910 q^{73} +9.14064 q^{74} +4.49920 q^{75} +2.82849 q^{76} -1.07354 q^{77} +2.74498 q^{78} +12.2936 q^{79} -6.52319 q^{80} -5.63320 q^{81} -5.21043 q^{82} -9.95179 q^{83} +1.89579 q^{84} +3.72814 q^{85} +19.8628 q^{86} -10.3213 q^{87} +1.10539 q^{88} -16.0018 q^{89} +2.26564 q^{90} -0.844871 q^{91} +1.69659 q^{92} +15.3806 q^{93} -7.52424 q^{94} +2.54731 q^{95} -10.3927 q^{96} -15.7433 q^{97} +11.8232 q^{98} -1.10545 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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