LMFDB - Embedded newform 6015.2.a.i.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63729 q^{2} +1.00000 q^{3} +4.95532 q^{4} +1.00000 q^{5} -2.63729 q^{6} +3.21800 q^{7} -7.79405 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.63729 q^{2} +1.00000 q^{3} +4.95532 q^{4} +1.00000 q^{5} -2.63729 q^{6} +3.21800 q^{7} -7.79405 q^{8} +1.00000 q^{9} -2.63729 q^{10} +3.01409 q^{11} +4.95532 q^{12} +4.14997 q^{13} -8.48682 q^{14} +1.00000 q^{15} +10.6446 q^{16} +0.987925 q^{17} -2.63729 q^{18} +1.25888 q^{19} +4.95532 q^{20} +3.21800 q^{21} -7.94904 q^{22} -9.12768 q^{23} -7.79405 q^{24} +1.00000 q^{25} -10.9447 q^{26} +1.00000 q^{27} +15.9462 q^{28} -2.91280 q^{29} -2.63729 q^{30} +4.89429 q^{31} -12.4848 q^{32} +3.01409 q^{33} -2.60545 q^{34} +3.21800 q^{35} +4.95532 q^{36} +2.06393 q^{37} -3.32004 q^{38} +4.14997 q^{39} -7.79405 q^{40} -8.91825 q^{41} -8.48682 q^{42} -5.34567 q^{43} +14.9358 q^{44} +1.00000 q^{45} +24.0724 q^{46} +10.3270 q^{47} +10.6446 q^{48} +3.35554 q^{49} -2.63729 q^{50} +0.987925 q^{51} +20.5645 q^{52} +6.13045 q^{53} -2.63729 q^{54} +3.01409 q^{55} -25.0813 q^{56} +1.25888 q^{57} +7.68191 q^{58} -0.853562 q^{59} +4.95532 q^{60} +9.70717 q^{61} -12.9077 q^{62} +3.21800 q^{63} +11.6368 q^{64} +4.14997 q^{65} -7.94904 q^{66} -12.1013 q^{67} +4.89549 q^{68} -9.12768 q^{69} -8.48682 q^{70} +13.1563 q^{71} -7.79405 q^{72} -6.60906 q^{73} -5.44320 q^{74} +1.00000 q^{75} +6.23816 q^{76} +9.69935 q^{77} -10.9447 q^{78} +0.0984439 q^{79} +10.6446 q^{80} +1.00000 q^{81} +23.5201 q^{82} +7.53490 q^{83} +15.9462 q^{84} +0.987925 q^{85} +14.0981 q^{86} -2.91280 q^{87} -23.4920 q^{88} +2.26998 q^{89} -2.63729 q^{90} +13.3546 q^{91} -45.2306 q^{92} +4.89429 q^{93} -27.2353 q^{94} +1.25888 q^{95} -12.4848 q^{96} +9.34835 q^{97} -8.84955 q^{98} +3.01409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.63729	−1.86485	−0.932424	−	0.361365i	$-0.882311\pi$
$2$	−2.63729	−1.86485	−0.932424	+	0.361365i	$0.882311\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.95532	2.47766
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.63729	−1.07667
$7$	3.21800	1.21629	0.608145	−	0.793826i	$-0.291914\pi$
$7$	3.21800	1.21629	0.608145	+	0.793826i	$0.291914\pi$
$8$	−7.79405	−2.75561
$9$	1.00000	0.333333
$10$	−2.63729	−0.833986
$11$	3.01409	0.908783	0.454391	−	0.890802i	$-0.349857\pi$
$11$	3.01409	0.908783	0.454391	+	0.890802i	$0.349857\pi$
$12$	4.95532	1.43048
$13$	4.14997	1.15100	0.575498	−	0.817803i	$-0.304808\pi$
$13$	4.14997	1.15100	0.575498	+	0.817803i	$0.304808\pi$
$14$	−8.48682	−2.26820
$15$	1.00000	0.258199
$16$	10.6446	2.66114
$17$	0.987925	0.239607	0.119804	−	0.992798i	$-0.461774\pi$
$17$	0.987925	0.239607	0.119804	+	0.992798i	$0.461774\pi$
$18$	−2.63729	−0.621616
$19$	1.25888	0.288807	0.144403	−	0.989519i	$-0.453874\pi$
$19$	1.25888	0.288807	0.144403	+	0.989519i	$0.453874\pi$
$20$	4.95532	1.10804
$21$	3.21800	0.702226
$22$	−7.94904	−1.69474
$23$	−9.12768	−1.90325	−0.951626	−	0.307259i	$-0.900588\pi$
$23$	−9.12768	−1.90325	−0.951626	+	0.307259i	$0.900588\pi$
$24$	−7.79405	−1.59095
$25$	1.00000	0.200000
$26$	−10.9447	−2.14643
$27$	1.00000	0.192450
$28$	15.9462	3.01356
$29$	−2.91280	−0.540894	−0.270447	−	0.962735i	$-0.587171\pi$
$29$	−2.91280	−0.540894	−0.270447	+	0.962735i	$0.587171\pi$
$30$	−2.63729	−0.481502
$31$	4.89429	0.879040	0.439520	−	0.898233i	$-0.355149\pi$
$31$	4.89429	0.879040	0.439520	+	0.898233i	$0.355149\pi$
$32$	−12.4848	−2.20701
$33$	3.01409	0.524686
$34$	−2.60545	−0.446831
$35$	3.21800	0.543942
$36$	4.95532	0.825887
$37$	2.06393	0.339309	0.169654	−	0.985504i	$-0.445735\pi$
$37$	2.06393	0.339309	0.169654	+	0.985504i	$0.445735\pi$
$38$	−3.32004	−0.538581
$39$	4.14997	0.664528
$40$	−7.79405	−1.23235
$41$	−8.91825	−1.39280	−0.696399	−	0.717655i	$-0.745215\pi$
$41$	−8.91825	−1.39280	−0.696399	+	0.717655i	$0.745215\pi$
$42$	−8.48682	−1.30954
$43$	−5.34567	−0.815207	−0.407604	−	0.913159i	$-0.633635\pi$
$43$	−5.34567	−0.815207	−0.407604	+	0.913159i	$0.633635\pi$
$44$	14.9358	2.25165
$45$	1.00000	0.149071
$46$	24.0724	3.54928
$47$	10.3270	1.50634	0.753171	−	0.657824i	$-0.228523\pi$
$47$	10.3270	1.50634	0.753171	+	0.657824i	$0.228523\pi$
$48$	10.6446	1.53641
$49$	3.35554	0.479363
$50$	−2.63729	−0.372970
$51$	0.987925	0.138337
$52$	20.5645	2.85178
$53$	6.13045	0.842082	0.421041	−	0.907042i	$-0.361665\pi$
$53$	6.13045	0.842082	0.421041	+	0.907042i	$0.361665\pi$
$54$	−2.63729	−0.358890
$55$	3.01409	0.406420
$56$	−25.0813	−3.35163
$57$	1.25888	0.166743
$58$	7.68191	1.00868
$59$	−0.853562	−0.111124	−0.0555622	−	0.998455i	$-0.517695\pi$
$59$	−0.853562	−0.111124	−0.0555622	+	0.998455i	$0.517695\pi$
$60$	4.95532	0.639729
$61$	9.70717	1.24288	0.621438	−	0.783463i	$-0.286549\pi$
$61$	9.70717	1.24288	0.621438	+	0.783463i	$0.286549\pi$
$62$	−12.9077	−1.63928
$63$	3.21800	0.405430
$64$	11.6368	1.45460
$65$	4.14997	0.514741
$66$	−7.94904	−0.978460
$67$	−12.1013	−1.47841	−0.739204	−	0.673482i	$-0.764798\pi$
$67$	−12.1013	−1.47841	−0.739204	+	0.673482i	$0.764798\pi$
$68$	4.89549	0.593665
$69$	−9.12768	−1.09884
$70$	−8.48682	−1.01437
$71$	13.1563	1.56137	0.780683	−	0.624927i	$-0.214871\pi$
$71$	13.1563	1.56137	0.780683	+	0.624927i	$0.214871\pi$
$72$	−7.79405	−0.918538
$73$	−6.60906	−0.773532	−0.386766	−	0.922178i	$-0.626408\pi$
$73$	−6.60906	−0.773532	−0.386766	+	0.922178i	$0.626408\pi$
$74$	−5.44320	−0.632759
$75$	1.00000	0.115470
$76$	6.23816	0.715566
$77$	9.69935	1.10534
$78$	−10.9447	−1.23924
$79$	0.0984439	0.0110758	0.00553790	−	0.999985i	$-0.498237\pi$
$79$	0.0984439	0.0110758	0.00553790	+	0.999985i	$0.498237\pi$
$80$	10.6446	1.19010
$81$	1.00000	0.111111
$82$	23.5201	2.59736
$83$	7.53490	0.827063	0.413531	−	0.910490i	$-0.364295\pi$
$83$	7.53490	0.827063	0.413531	+	0.910490i	$0.364295\pi$
$84$	15.9462	1.73988
$85$	0.987925	0.107156
$86$	14.0981	1.52024
$87$	−2.91280	−0.312285
$88$	−23.4920	−2.50425
$89$	2.26998	0.240617	0.120309	−	0.992737i	$-0.461612\pi$
$89$	2.26998	0.240617	0.120309	+	0.992737i	$0.461612\pi$
$90$	−2.63729	−0.277995
$91$	13.3546	1.39995
$92$	−45.2306	−4.71561
$93$	4.89429	0.507514
$94$	−27.2353	−2.80910
$95$	1.25888	0.129158
$96$	−12.4848	−1.27422
$97$	9.34835	0.949181	0.474591	−	0.880207i	$-0.342596\pi$
$97$	9.34835	0.949181	0.474591	+	0.880207i	$0.342596\pi$
$98$	−8.84955	−0.893940
$99$	3.01409	0.302928
$100$	4.95532	0.495532
$101$	10.7074	1.06543	0.532713	−	0.846296i	$-0.321172\pi$
$101$	10.7074	1.06543	0.532713	+	0.846296i	$0.321172\pi$
$102$	−2.60545	−0.257978
$103$	−9.99101	−0.984443	−0.492222	−	0.870470i	$-0.663815\pi$
$103$	−9.99101	−0.984443	−0.492222	+	0.870470i	$0.663815\pi$
$104$	−32.3451	−3.17170
$105$	3.21800	0.314045
$106$	−16.1678	−1.57036
$107$	−15.5029	−1.49872	−0.749360	−	0.662163i	$-0.769639\pi$
$107$	−15.5029	−1.49872	−0.749360	+	0.662163i	$0.769639\pi$
$108$	4.95532	0.476826
$109$	13.0248	1.24755	0.623773	−	0.781606i	$-0.285599\pi$
$109$	13.0248	1.24755	0.623773	+	0.781606i	$0.285599\pi$
$110$	−7.94904	−0.757912
$111$	2.06393	0.195900
$112$	34.2543	3.23672
$113$	−0.563425	−0.0530026	−0.0265013	−	0.999649i	$-0.508437\pi$
$113$	−0.563425	−0.0530026	−0.0265013	+	0.999649i	$0.508437\pi$
$114$	−3.32004	−0.310950
$115$	−9.12768	−0.851160
$116$	−14.4339	−1.34015
$117$	4.14997	0.383665
$118$	2.25109	0.207230
$119$	3.17915	0.291432
$120$	−7.79405	−0.711496
$121$	−1.91526	−0.174114
$122$	−25.6007	−2.31778
$123$	−8.91825	−0.804132
$124$	24.2528	2.17796
$125$	1.00000	0.0894427
$126$	−8.48682	−0.756066
$127$	14.5337	1.28965	0.644827	−	0.764329i	$-0.276930\pi$
$127$	14.5337	1.28965	0.644827	+	0.764329i	$0.276930\pi$
$128$	−5.72025	−0.505604
$129$	−5.34567	−0.470660
$130$	−10.9447	−0.959914
$131$	−6.30402	−0.550785	−0.275393	−	0.961332i	$-0.588808\pi$
$131$	−6.30402	−0.550785	−0.275393	+	0.961332i	$0.588808\pi$
$132$	14.9358	1.29999
$133$	4.05108	0.351273
$134$	31.9146	2.75701
$135$	1.00000	0.0860663
$136$	−7.69994	−0.660264
$137$	−7.00396	−0.598389	−0.299194	−	0.954192i	$-0.596718\pi$
$137$	−7.00396	−0.598389	−0.299194	+	0.954192i	$0.596718\pi$
$138$	24.0724	2.04918
$139$	17.4668	1.48151	0.740756	−	0.671774i	$-0.234467\pi$
$139$	17.4668	1.48151	0.740756	+	0.671774i	$0.234467\pi$
$140$	15.9462	1.34770
$141$	10.3270	0.869687
$142$	−34.6971	−2.91171
$143$	12.5084	1.04600
$144$	10.6446	0.887047
$145$	−2.91280	−0.241895
$146$	17.4300	1.44252
$147$	3.35554	0.276761
$148$	10.2275	0.840692
$149$	7.11382	0.582786	0.291393	−	0.956603i	$-0.405881\pi$
$149$	7.11382	0.582786	0.291393	+	0.956603i	$0.405881\pi$
$150$	−2.63729	−0.215334
$151$	12.4836	1.01590	0.507950	−	0.861386i	$-0.330403\pi$
$151$	12.4836	1.01590	0.507950	+	0.861386i	$0.330403\pi$
$152$	−9.81178	−0.795840
$153$	0.987925	0.0798690
$154$	−25.5800	−2.06130
$155$	4.89429	0.393119
$156$	20.5645	1.64647
$157$	−9.21631	−0.735542	−0.367771	−	0.929916i	$-0.619879\pi$
$157$	−9.21631	−0.735542	−0.367771	+	0.929916i	$0.619879\pi$
$158$	−0.259626	−0.0206547
$159$	6.13045	0.486176
$160$	−12.4848	−0.987007
$161$	−29.3729	−2.31491
$162$	−2.63729	−0.207205
$163$	1.74256	0.136488	0.0682440	−	0.997669i	$-0.478260\pi$
$163$	1.74256	0.136488	0.0682440	+	0.997669i	$0.478260\pi$
$164$	−44.1928	−3.45088
$165$	3.01409	0.234647
$166$	−19.8718	−1.54235
$167$	−0.270268	−0.0209140	−0.0104570	−	0.999945i	$-0.503329\pi$
$167$	−0.270268	−0.0209140	−0.0104570	+	0.999945i	$0.503329\pi$
$168$	−25.0813	−1.93506
$169$	4.22228	0.324791
$170$	−2.60545	−0.199829
$171$	1.25888	0.0962690
$172$	−26.4895	−2.01981
$173$	22.9508	1.74492	0.872458	−	0.488689i	$-0.162525\pi$
$173$	22.9508	1.74492	0.872458	+	0.488689i	$0.162525\pi$
$174$	7.68191	0.582364
$175$	3.21800	0.243258
$176$	32.0837	2.41840
$177$	−0.853562	−0.0641576
$178$	−5.98660	−0.448715
$179$	7.55584	0.564750	0.282375	−	0.959304i	$-0.408878\pi$
$179$	7.55584	0.564750	0.282375	+	0.959304i	$0.408878\pi$
$180$	4.95532	0.369348
$181$	0.184950	0.0137473	0.00687363	−	0.999976i	$-0.497812\pi$
$181$	0.184950	0.0137473	0.00687363	+	0.999976i	$0.497812\pi$
$182$	−35.2201	−2.61069
$183$	9.70717	0.717575
$184$	71.1416	5.24463
$185$	2.06393	0.151743
$186$	−12.9077	−0.946437
$187$	2.97770	0.217751
$188$	51.1734	3.73221
$189$	3.21800	0.234075
$190$	−3.32004	−0.240861
$191$	−3.97908	−0.287916	−0.143958	−	0.989584i	$-0.545983\pi$
$191$	−3.97908	−0.287916	−0.143958	+	0.989584i	$0.545983\pi$
$192$	11.6368	0.839816
$193$	1.57936	0.113685	0.0568424	−	0.998383i	$-0.481897\pi$
$193$	1.57936	0.113685	0.0568424	+	0.998383i	$0.481897\pi$
$194$	−24.6543	−1.77008
$195$	4.14997	0.297186
$196$	16.6278	1.18770
$197$	16.2314	1.15644	0.578220	−	0.815881i	$-0.303747\pi$
$197$	16.2314	1.15644	0.578220	+	0.815881i	$0.303747\pi$
$198$	−7.94904	−0.564914
$199$	23.2554	1.64853	0.824266	−	0.566203i	$-0.191588\pi$
$199$	23.2554	1.64853	0.824266	+	0.566203i	$0.191588\pi$
$200$	−7.79405	−0.551123
$201$	−12.1013	−0.853559
$202$	−28.2386	−1.98686
$203$	−9.37340	−0.657884
$204$	4.89549	0.342753
$205$	−8.91825	−0.622878
$206$	26.3492	1.83584
$207$	−9.12768	−0.634417
$208$	44.1747	3.06296
$209$	3.79438	0.262463
$210$	−8.48682	−0.585646
$211$	0.739210	0.0508893	0.0254447	−	0.999676i	$-0.491900\pi$
$211$	0.739210	0.0508893	0.0254447	+	0.999676i	$0.491900\pi$
$212$	30.3784	2.08639
$213$	13.1563	0.901455
$214$	40.8856	2.79488
$215$	−5.34567	−0.364572
$216$	−7.79405	−0.530318
$217$	15.7498	1.06917
$218$	−34.3501	−2.32648
$219$	−6.60906	−0.446599
$220$	14.9358	1.00697
$221$	4.09986	0.275787
$222$	−5.44320	−0.365324
$223$	2.94509	0.197218	0.0986090	−	0.995126i	$-0.468561\pi$
$223$	2.94509	0.197218	0.0986090	+	0.995126i	$0.468561\pi$
$224$	−40.1760	−2.68437
$225$	1.00000	0.0666667
$226$	1.48592	0.0988418
$227$	−22.5101	−1.49405	−0.747024	−	0.664797i	$-0.768518\pi$
$227$	−22.5101	−1.49405	−0.747024	+	0.664797i	$0.768518\pi$
$228$	6.23816	0.413132
$229$	13.5102	0.892782	0.446391	−	0.894838i	$-0.352709\pi$
$229$	13.5102	0.892782	0.446391	+	0.894838i	$0.352709\pi$
$230$	24.0724	1.58728
$231$	9.69935	0.638171
$232$	22.7025	1.49049
$233$	−21.5119	−1.40929	−0.704646	−	0.709560i	$-0.748894\pi$
$233$	−21.5119	−1.40929	−0.704646	+	0.709560i	$0.748894\pi$
$234$	−10.9447	−0.715478
$235$	10.3270	0.673657
$236$	−4.22967	−0.275328
$237$	0.0984439	0.00639462
$238$	−8.38434	−0.543476
$239$	7.68849	0.497327	0.248663	−	0.968590i	$-0.420009\pi$
$239$	7.68849	0.497327	0.248663	+	0.968590i	$0.420009\pi$
$240$	10.6446	0.687104
$241$	−10.3787	−0.668549	−0.334275	−	0.942476i	$-0.608491\pi$
$241$	−10.3787	−0.668549	−0.334275	+	0.942476i	$0.608491\pi$
$242$	5.05110	0.324697
$243$	1.00000	0.0641500
$244$	48.1021	3.07942
$245$	3.35554	0.214378
$246$	23.5201	1.49958
$247$	5.22432	0.332416
$248$	−38.1463	−2.42230
$249$	7.53490	0.477505
$250$	−2.63729	−0.166797
$251$	−22.1308	−1.39688	−0.698441	−	0.715668i	$-0.746122\pi$
$251$	−22.1308	−1.39688	−0.698441	+	0.715668i	$0.746122\pi$
$252$	15.9462	1.00452
$253$	−27.5116	−1.72964
$254$	−38.3295	−2.40501
$255$	0.987925	0.0618663
$256$	−8.18768	−0.511730
$257$	14.5169	0.905537	0.452768	−	0.891628i	$-0.350436\pi$
$257$	14.5169	0.905537	0.452768	+	0.891628i	$0.350436\pi$
$258$	14.0981	0.877710
$259$	6.64175	0.412698
$260$	20.5645	1.27535
$261$	−2.91280	−0.180298
$262$	16.6256	1.02713
$263$	−25.5810	−1.57739	−0.788696	−	0.614783i	$-0.789244\pi$
$263$	−25.5810	−1.57739	−0.788696	+	0.614783i	$0.789244\pi$
$264$	−23.4920	−1.44583
$265$	6.13045	0.376591
$266$	−10.6839	−0.655071
$267$	2.26998	0.138920
$268$	−59.9658	−3.66299
$269$	−25.3086	−1.54309	−0.771545	−	0.636175i	$-0.780516\pi$
$269$	−25.3086	−1.54309	−0.771545	+	0.636175i	$0.780516\pi$
$270$	−2.63729	−0.160501
$271$	7.92906	0.481656	0.240828	−	0.970568i	$-0.422581\pi$
$271$	7.92906	0.481656	0.240828	+	0.970568i	$0.422581\pi$
$272$	10.5160	0.637628
$273$	13.3546	0.808259
$274$	18.4715	1.11590
$275$	3.01409	0.181757
$276$	−45.2306	−2.72256
$277$	7.92553	0.476199	0.238099	−	0.971241i	$-0.423476\pi$
$277$	7.92553	0.476199	0.238099	+	0.971241i	$0.423476\pi$
$278$	−46.0650	−2.76280
$279$	4.89429	0.293013
$280$	−25.0813	−1.49889
$281$	7.29330	0.435082	0.217541	−	0.976051i	$-0.430196\pi$
$281$	7.29330	0.435082	0.217541	+	0.976051i	$0.430196\pi$
$282$	−27.2353	−1.62184
$283$	−13.0537	−0.775965	−0.387982	−	0.921667i	$-0.626828\pi$
$283$	−13.0537	−0.775965	−0.387982	+	0.921667i	$0.626828\pi$
$284$	65.1937	3.86854
$285$	1.25888	0.0745696
$286$	−32.9883	−1.95064
$287$	−28.6990	−1.69405
$288$	−12.4848	−0.735671
$289$	−16.0240	−0.942588
$290$	7.68191	0.451098
$291$	9.34835	0.548010
$292$	−32.7500	−1.91655
$293$	−26.7579	−1.56321	−0.781606	−	0.623773i	$-0.785599\pi$
$293$	−26.7579	−1.56321	−0.781606	+	0.623773i	$0.785599\pi$
$294$	−8.84955	−0.516116
$295$	−0.853562	−0.0496963
$296$	−16.0864	−0.935004
$297$	3.01409	0.174895
$298$	−18.7612	−1.08681
$299$	−37.8796	−2.19063
$300$	4.95532	0.286096
$301$	−17.2024	−0.991529
$302$	−32.9229	−1.89450
$303$	10.7074	0.615124
$304$	13.4002	0.768556
$305$	9.70717	0.555831
$306$	−2.60545	−0.148944
$307$	6.49037	0.370425	0.185212	−	0.982699i	$-0.440703\pi$
$307$	6.49037	0.370425	0.185212	+	0.982699i	$0.440703\pi$
$308$	48.0634	2.73867
$309$	−9.99101	−0.568369
$310$	−12.9077	−0.733107
$311$	0.912738	0.0517566	0.0258783	−	0.999665i	$-0.491762\pi$
$311$	0.912738	0.0517566	0.0258783	+	0.999665i	$0.491762\pi$
$312$	−32.3451	−1.83118
$313$	−12.5930	−0.711800	−0.355900	−	0.934524i	$-0.615826\pi$
$313$	−12.5930	−0.711800	−0.355900	+	0.934524i	$0.615826\pi$
$314$	24.3061	1.37167
$315$	3.21800	0.181314
$316$	0.487821	0.0274421
$317$	14.2764	0.801841	0.400921	−	0.916113i	$-0.368690\pi$
$317$	14.2764	0.801841	0.400921	+	0.916113i	$0.368690\pi$
$318$	−16.1678	−0.906645
$319$	−8.77945	−0.491555
$320$	11.6368	0.650519
$321$	−15.5029	−0.865286
$322$	77.4650	4.31695
$323$	1.24368	0.0692002
$324$	4.95532	0.275296
$325$	4.14997	0.230199
$326$	−4.59565	−0.254529
$327$	13.0248	0.720271
$328$	69.5093	3.83801
$329$	33.2322	1.83215
$330$	−7.94904	−0.437580
$331$	−0.477421	−0.0262414	−0.0131207	−	0.999914i	$-0.504177\pi$
$331$	−0.477421	−0.0262414	−0.0131207	+	0.999914i	$0.504177\pi$
$332$	37.3379	2.04918
$333$	2.06393	0.113103
$334$	0.712776	0.0390014
$335$	−12.1013	−0.661164
$336$	34.2543	1.86872
$337$	3.21596	0.175185	0.0875923	−	0.996156i	$-0.472083\pi$
$337$	3.21596	0.175185	0.0875923	+	0.996156i	$0.472083\pi$
$338$	−11.1354	−0.605686
$339$	−0.563425	−0.0306010
$340$	4.89549	0.265495
$341$	14.7518	0.798856
$342$	−3.32004	−0.179527
$343$	−11.7279	−0.633246
$344$	41.6644	2.24640
$345$	−9.12768	−0.491418
$346$	−60.5280	−3.25400
$347$	4.85709	0.260742	0.130371	−	0.991465i	$-0.458383\pi$
$347$	4.85709	0.260742	0.130371	+	0.991465i	$0.458383\pi$
$348$	−14.4339	−0.773736
$349$	2.39786	0.128354	0.0641771	−	0.997939i	$-0.479558\pi$
$349$	2.39786	0.128354	0.0641771	+	0.997939i	$0.479558\pi$
$350$	−8.48682	−0.453640
$351$	4.14997	0.221509
$352$	−37.6302	−2.00570
$353$	−4.44361	−0.236509	−0.118255	−	0.992983i	$-0.537730\pi$
$353$	−4.44361	−0.236509	−0.118255	+	0.992983i	$0.537730\pi$
$354$	2.25109	0.119644
$355$	13.1563	0.698264
$356$	11.2485	0.596168
$357$	3.17915	0.168258
$358$	−19.9270	−1.05317
$359$	−2.25472	−0.119000	−0.0594998	−	0.998228i	$-0.518951\pi$
$359$	−2.25472	−0.119000	−0.0594998	+	0.998228i	$0.518951\pi$
$360$	−7.79405	−0.410783
$361$	−17.4152	−0.916591
$362$	−0.487769	−0.0256365
$363$	−1.91526	−0.100525
$364$	66.1765	3.46859
$365$	−6.60906	−0.345934
$366$	−25.6007	−1.33817
$367$	−32.1738	−1.67946	−0.839729	−	0.543006i	$-0.817286\pi$
$367$	−32.1738	−1.67946	−0.839729	+	0.543006i	$0.817286\pi$
$368$	−97.1602	−5.06482
$369$	−8.91825	−0.464266
$370$	−5.44320	−0.282979
$371$	19.7278	1.02422
$372$	24.2528	1.25745
$373$	1.78362	0.0923521	0.0461761	−	0.998933i	$-0.485296\pi$
$373$	1.78362	0.0923521	0.0461761	+	0.998933i	$0.485296\pi$
$374$	−7.85306	−0.406072
$375$	1.00000	0.0516398
$376$	−80.4889	−4.15090
$377$	−12.0880	−0.622566
$378$	−8.48682	−0.436515
$379$	34.8881	1.79208	0.896040	−	0.443972i	$-0.146431\pi$
$379$	34.8881	1.79208	0.896040	+	0.443972i	$0.146431\pi$
$380$	6.23816	0.320011
$381$	14.5337	0.744582
$382$	10.4940	0.536920
$383$	26.6661	1.36258	0.681288	−	0.732016i	$-0.261420\pi$
$383$	26.6661	1.36258	0.681288	+	0.732016i	$0.261420\pi$
$384$	−5.72025	−0.291910
$385$	9.69935	0.494325
$386$	−4.16523	−0.212005
$387$	−5.34567	−0.271736
$388$	46.3241	2.35175
$389$	−33.1136	−1.67893	−0.839463	−	0.543417i	$-0.817130\pi$
$389$	−33.1136	−1.67893	−0.839463	+	0.543417i	$0.817130\pi$
$390$	−10.9447	−0.554207
$391$	−9.01746	−0.456033
$392$	−26.1533	−1.32094
$393$	−6.30402	−0.317996
$394$	−42.8070	−2.15659
$395$	0.0984439	0.00495325
$396$	14.9358	0.750552
$397$	10.6286	0.533436	0.266718	−	0.963775i	$-0.414061\pi$
$397$	10.6286	0.533436	0.266718	+	0.963775i	$0.414061\pi$
$398$	−61.3313	−3.07426
$399$	4.05108	0.202808
$400$	10.6446	0.532228
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	31.9146	1.59176
$403$	20.3112	1.01177
$404$	53.0586	2.63977
$405$	1.00000	0.0496904
$406$	24.7204	1.22685
$407$	6.22088	0.308358
$408$	−7.69994	−0.381204
$409$	−31.2488	−1.54515	−0.772577	−	0.634922i	$-0.781032\pi$
$409$	−31.2488	−1.54515	−0.772577	+	0.634922i	$0.781032\pi$
$410$	23.5201	1.16157
$411$	−7.00396	−0.345480
$412$	−49.5087	−2.43912
$413$	−2.74677	−0.135159
$414$	24.0724	1.18309
$415$	7.53490	0.369874
$416$	−51.8114	−2.54026
$417$	17.4668	0.855352
$418$	−10.0069	−0.489453
$419$	27.6492	1.35075	0.675376	−	0.737473i	$-0.263981\pi$
$419$	27.6492	1.35075	0.675376	+	0.737473i	$0.263981\pi$
$420$	15.9462	0.778097
$421$	30.9064	1.50629	0.753143	−	0.657857i	$-0.228537\pi$
$421$	30.9064	1.50629	0.753143	+	0.657857i	$0.228537\pi$
$422$	−1.94952	−0.0949009
$423$	10.3270	0.502114
$424$	−47.7811	−2.32045
$425$	0.987925	0.0479214
$426$	−34.6971	−1.68108
$427$	31.2377	1.51170
$428$	−76.8217	−3.71332
$429$	12.5084	0.603911
$430$	14.0981	0.679871
$431$	−5.86183	−0.282354	−0.141177	−	0.989984i	$-0.545089\pi$
$431$	−5.86183	−0.282354	−0.141177	+	0.989984i	$0.545089\pi$
$432$	10.6446	0.512137
$433$	−26.8036	−1.28810	−0.644050	−	0.764983i	$-0.722747\pi$
$433$	−26.8036	−1.28810	−0.644050	+	0.764983i	$0.722747\pi$
$434$	−41.5370	−1.99384
$435$	−2.91280	−0.139658
$436$	64.5419	3.09099
$437$	−11.4907	−0.549672
$438$	17.4300	0.832839
$439$	−11.3504	−0.541727	−0.270864	−	0.962618i	$-0.587309\pi$
$439$	−11.3504	−0.541727	−0.270864	+	0.962618i	$0.587309\pi$
$440$	−23.4920	−1.11994
$441$	3.35554	0.159788
$442$	−10.8125	−0.514300
$443$	−26.6844	−1.26781	−0.633907	−	0.773409i	$-0.718550\pi$
$443$	−26.6844	−1.26781	−0.633907	+	0.773409i	$0.718550\pi$
$444$	10.2275	0.485374
$445$	2.26998	0.107607
$446$	−7.76708	−0.367782
$447$	7.11382	0.336472
$448$	37.4474	1.76922
$449$	15.7179	0.741773	0.370886	−	0.928678i	$-0.379054\pi$
$449$	15.7179	0.741773	0.370886	+	0.928678i	$0.379054\pi$
$450$	−2.63729	−0.124323
$451$	−26.8804	−1.26575
$452$	−2.79195	−0.131322
$453$	12.4836	0.586531
$454$	59.3658	2.78617
$455$	13.3546	0.626075
$456$	−9.81178	−0.459479
$457$	−6.22270	−0.291086	−0.145543	−	0.989352i	$-0.546493\pi$
$457$	−6.22270	−0.291086	−0.145543	+	0.989352i	$0.546493\pi$
$458$	−35.6305	−1.66490
$459$	0.987925	0.0461124
$460$	−45.2306	−2.10889
$461$	−6.70482	−0.312275	−0.156137	−	0.987735i	$-0.549904\pi$
$461$	−6.70482	−0.312275	−0.156137	+	0.987735i	$0.549904\pi$
$462$	−25.5800	−1.19009
$463$	−13.3796	−0.621804	−0.310902	−	0.950442i	$-0.600631\pi$
$463$	−13.3796	−0.621804	−0.310902	+	0.950442i	$0.600631\pi$
$464$	−31.0055	−1.43939
$465$	4.89429	0.226967
$466$	56.7332	2.62811
$467$	12.7846	0.591601	0.295801	−	0.955250i	$-0.404414\pi$
$467$	12.7846	0.591601	0.295801	+	0.955250i	$0.404414\pi$
$468$	20.5645	0.950592
$469$	−38.9420	−1.79817
$470$	−27.2353	−1.25627
$471$	−9.21631	−0.424665
$472$	6.65271	0.306216
$473$	−16.1123	−0.740846
$474$	−0.259626	−0.0119250
$475$	1.25888	0.0577614
$476$	15.7537	0.722069
$477$	6.13045	0.280694
$478$	−20.2768	−0.927440
$479$	26.7959	1.22434	0.612168	−	0.790728i	$-0.290298\pi$
$479$	26.7959	1.22434	0.612168	+	0.790728i	$0.290298\pi$
$480$	−12.4848	−0.569848
$481$	8.56527	0.390543
$482$	27.3716	1.24674
$483$	−29.3729	−1.33651
$484$	−9.49072	−0.431396
$485$	9.34835	0.424487
$486$	−2.63729	−0.119630
$487$	−25.5839	−1.15932	−0.579658	−	0.814860i	$-0.696814\pi$
$487$	−25.5839	−1.15932	−0.579658	+	0.814860i	$0.696814\pi$
$488$	−75.6582	−3.42489
$489$	1.74256	0.0788014
$490$	−8.84955	−0.399782
$491$	−32.3706	−1.46086	−0.730432	−	0.682985i	$-0.760681\pi$
$491$	−32.3706	−1.46086	−0.730432	+	0.682985i	$0.760681\pi$
$492$	−44.1928	−1.99237
$493$	−2.87763	−0.129602
$494$	−13.7781	−0.619905
$495$	3.01409	0.135473
$496$	52.0976	2.33925
$497$	42.3370	1.89908
$498$	−19.8718	−0.890474
$499$	−25.7263	−1.15167	−0.575834	−	0.817566i	$-0.695323\pi$
$499$	−25.7263	−1.15167	−0.575834	+	0.817566i	$0.695323\pi$
$500$	4.95532	0.221609
$501$	−0.270268	−0.0120747
$502$	58.3653	2.60497
$503$	−29.4800	−1.31445	−0.657224	−	0.753695i	$-0.728269\pi$
$503$	−29.4800	−1.31445	−0.657224	+	0.753695i	$0.728269\pi$
$504$	−25.0813	−1.11721
$505$	10.7074	0.476473
$506$	72.5563	3.22552
$507$	4.22228	0.187518
$508$	72.0189	3.19532
$509$	28.5067	1.26354	0.631768	−	0.775157i	$-0.282330\pi$
$509$	28.5067	1.26354	0.631768	+	0.775157i	$0.282330\pi$
$510$	−2.60545	−0.115371
$511$	−21.2680	−0.940839
$512$	33.0338	1.45990
$513$	1.25888	0.0555809
$514$	−38.2852	−1.68869
$515$	−9.99101	−0.440257
$516$	−26.4895	−1.16614
$517$	31.1264	1.36894
$518$	−17.5162	−0.769619
$519$	22.9508	1.00743
$520$	−32.3451	−1.41843
$521$	2.24383	0.0983039	0.0491520	−	0.998791i	$-0.484348\pi$
$521$	2.24383	0.0983039	0.0491520	+	0.998791i	$0.484348\pi$
$522$	7.68191	0.336228
$523$	−28.5633	−1.24899	−0.624493	−	0.781031i	$-0.714694\pi$
$523$	−28.5633	−1.24899	−0.624493	+	0.781031i	$0.714694\pi$
$524$	−31.2385	−1.36466
$525$	3.21800	0.140445
$526$	67.4646	2.94160
$527$	4.83519	0.210624
$528$	32.0837	1.39626
$529$	60.3145	2.62237
$530$	−16.1678	−0.702285
$531$	−0.853562	−0.0370414
$532$	20.0744	0.870336
$533$	−37.0105	−1.60310
$534$	−5.98660	−0.259065
$535$	−15.5029	−0.670248
$536$	94.3180	4.07392
$537$	7.55584	0.326059
$538$	66.7461	2.87763
$539$	10.1139	0.435637
$540$	4.95532	0.213243
$541$	10.1766	0.437528	0.218764	−	0.975778i	$-0.429798\pi$
$541$	10.1766	0.437528	0.218764	+	0.975778i	$0.429798\pi$
$542$	−20.9113	−0.898215
$543$	0.184950	0.00793698
$544$	−12.3340	−0.528816
$545$	13.0248	0.557919
$546$	−35.2201	−1.50728
$547$	−37.0400	−1.58372	−0.791859	−	0.610704i	$-0.790886\pi$
$547$	−37.0400	−1.58372	−0.791859	+	0.610704i	$0.790886\pi$
$548$	−34.7069	−1.48260
$549$	9.70717	0.414292
$550$	−7.94904	−0.338948
$551$	−3.66687	−0.156214
$552$	71.1416	3.02799
$553$	0.316793	0.0134714
$554$	−20.9020	−0.888039
$555$	2.06393	0.0876091
$556$	86.5535	3.67069
$557$	−41.9397	−1.77704	−0.888522	−	0.458835i	$-0.848267\pi$
$557$	−41.9397	−1.77704	−0.888522	+	0.458835i	$0.848267\pi$
$558$	−12.9077	−0.546426
$559$	−22.1844	−0.938300
$560$	34.2543	1.44751
$561$	2.97770	0.125718
$562$	−19.2346	−0.811361
$563$	22.3552	0.942158	0.471079	−	0.882091i	$-0.343865\pi$
$563$	22.3552	0.942158	0.471079	+	0.882091i	$0.343865\pi$
$564$	51.1734	2.15479
$565$	−0.563425	−0.0237035
$566$	34.4266	1.44706
$567$	3.21800	0.135143
$568$	−102.541	−4.30252
$569$	44.8647	1.88083	0.940413	−	0.340035i	$-0.110439\pi$
$569$	44.8647	1.88083	0.940413	+	0.340035i	$0.110439\pi$
$570$	−3.32004	−0.139061
$571$	25.8659	1.08245	0.541227	−	0.840877i	$-0.317960\pi$
$571$	25.8659	1.08245	0.541227	+	0.840877i	$0.317960\pi$
$572$	61.9831	2.59165
$573$	−3.97908	−0.166229
$574$	75.6876	3.15914
$575$	−9.12768	−0.380650
$576$	11.6368	0.484868
$577$	−16.3966	−0.682599	−0.341299	−	0.939955i	$-0.610867\pi$
$577$	−16.3966	−0.682599	−0.341299	+	0.939955i	$0.610867\pi$
$578$	42.2600	1.75778
$579$	1.57936	0.0656359
$580$	−14.4339	−0.599334
$581$	24.2473	1.00595
$582$	−24.6543	−1.02196
$583$	18.4777	0.765270
$584$	51.5113	2.13155
$585$	4.14997	0.171580
$586$	70.5684	2.91515
$587$	22.8812	0.944408	0.472204	−	0.881489i	$-0.343459\pi$
$587$	22.8812	0.944408	0.472204	+	0.881489i	$0.343459\pi$
$588$	16.6278	0.685719
$589$	6.16132	0.253873
$590$	2.25109	0.0926761
$591$	16.2314	0.667671
$592$	21.9697	0.902949
$593$	14.0804	0.578212	0.289106	−	0.957297i	$-0.406642\pi$
$593$	14.0804	0.578212	0.289106	+	0.957297i	$0.406642\pi$
$594$	−7.94904	−0.326153
$595$	3.17915	0.130332
$596$	35.2512	1.44395
$597$	23.2554	0.951780
$598$	99.8997	4.08520
$599$	4.80985	0.196525	0.0982625	−	0.995161i	$-0.468672\pi$
$599$	4.80985	0.196525	0.0982625	+	0.995161i	$0.468672\pi$
$600$	−7.79405	−0.318191
$601$	25.2443	1.02974	0.514868	−	0.857269i	$-0.327841\pi$
$601$	25.2443	1.02974	0.514868	+	0.857269i	$0.327841\pi$
$602$	45.3677	1.84905
$603$	−12.1013	−0.492802
$604$	61.8603	2.51706
$605$	−1.91526	−0.0778663
$606$	−28.2386	−1.14711
$607$	−19.9140	−0.808285	−0.404142	−	0.914696i	$-0.632430\pi$
$607$	−19.9140	−0.808285	−0.404142	+	0.914696i	$0.632430\pi$
$608$	−15.7168	−0.637401
$609$	−9.37340	−0.379829
$610$	−25.6007	−1.03654
$611$	42.8566	1.73379
$612$	4.89549	0.197888
$613$	−21.0001	−0.848188	−0.424094	−	0.905618i	$-0.639407\pi$
$613$	−21.0001	−0.848188	−0.424094	+	0.905618i	$0.639407\pi$
$614$	−17.1170	−0.690786
$615$	−8.91825	−0.359619
$616$	−75.5973	−3.04590
$617$	12.2789	0.494332	0.247166	−	0.968973i	$-0.420501\pi$
$617$	12.2789	0.494332	0.247166	+	0.968973i	$0.420501\pi$
$618$	26.3492	1.05992
$619$	0.944428	0.0379598	0.0189799	−	0.999820i	$-0.493958\pi$
$619$	0.944428	0.0379598	0.0189799	+	0.999820i	$0.493958\pi$
$620$	24.2528	0.974015
$621$	−9.12768	−0.366281
$622$	−2.40716	−0.0965183
$623$	7.30479	0.292660
$624$	44.1747	1.76840
$625$	1.00000	0.0400000
$626$	33.2115	1.32740
$627$	3.79438	0.151533
$628$	−45.6698	−1.82242
$629$	2.03901	0.0813007
$630$	−8.48682	−0.338123
$631$	−12.7403	−0.507182	−0.253591	−	0.967311i	$-0.581612\pi$
$631$	−12.7403	−0.507182	−0.253591	+	0.967311i	$0.581612\pi$
$632$	−0.767277	−0.0305207
$633$	0.739210	0.0293810
$634$	−37.6510	−1.49531
$635$	14.5337	0.576751
$636$	30.3784	1.20458
$637$	13.9254	0.551745
$638$	23.1540	0.916675
$639$	13.1563	0.520455
$640$	−5.72025	−0.226113
$641$	20.8523	0.823617	0.411809	−	0.911270i	$-0.364897\pi$
$641$	20.8523	0.823617	0.411809	+	0.911270i	$0.364897\pi$
$642$	40.8856	1.61363
$643$	−9.83405	−0.387817	−0.193909	−	0.981020i	$-0.562117\pi$
$643$	−9.83405	−0.387817	−0.193909	+	0.981020i	$0.562117\pi$
$644$	−145.552	−5.73556
$645$	−5.34567	−0.210486
$646$	−3.27995	−0.129048
$647$	−14.1225	−0.555213	−0.277607	−	0.960695i	$-0.589541\pi$
$647$	−14.1225	−0.555213	−0.277607	+	0.960695i	$0.589541\pi$
$648$	−7.79405	−0.306179
$649$	−2.57271	−0.100988
$650$	−10.9447	−0.429287
$651$	15.7498	0.617285
$652$	8.63496	0.338171
$653$	33.7413	1.32040	0.660200	−	0.751090i	$-0.270472\pi$
$653$	33.7413	1.32040	0.660200	+	0.751090i	$0.270472\pi$
$654$	−34.3501	−1.34320
$655$	−6.30402	−0.246319
$656$	−94.9309	−3.70643
$657$	−6.60906	−0.257844
$658$	−87.6431	−3.41668
$659$	26.9040	1.04803	0.524015	−	0.851709i	$-0.324434\pi$
$659$	26.9040	1.04803	0.524015	+	0.851709i	$0.324434\pi$
$660$	14.9358	0.581375
$661$	−35.7141	−1.38912	−0.694560	−	0.719435i	$-0.744401\pi$
$661$	−35.7141	−1.38912	−0.694560	+	0.719435i	$0.744401\pi$
$662$	1.25910	0.0489363
$663$	4.09986	0.159226
$664$	−58.7274	−2.27907
$665$	4.05108	0.157094
$666$	−5.44320	−0.210920
$667$	26.5871	1.02946
$668$	−1.33927	−0.0518177
$669$	2.94509	0.113864
$670$	31.9146	1.23297
$671$	29.2583	1.12950
$672$	−40.1760	−1.54982
$673$	8.00333	0.308506	0.154253	−	0.988031i	$-0.450703\pi$
$673$	8.00333	0.308506	0.154253	+	0.988031i	$0.450703\pi$
$674$	−8.48144	−0.326693
$675$	1.00000	0.0384900
$676$	20.9228	0.804722
$677$	45.6697	1.75523	0.877614	−	0.479367i	$-0.159134\pi$
$677$	45.6697	1.75523	0.877614	+	0.479367i	$0.159134\pi$
$678$	1.48592	0.0570663
$679$	30.0830	1.15448
$680$	−7.69994	−0.295279
$681$	−22.5101	−0.862589
$682$	−38.9049	−1.48975
$683$	−9.27509	−0.354901	−0.177451	−	0.984130i	$-0.556785\pi$
$683$	−9.27509	−0.354901	−0.177451	+	0.984130i	$0.556785\pi$
$684$	6.23816	0.238522
$685$	−7.00396	−0.267608
$686$	30.9299	1.18091
$687$	13.5102	0.515448
$688$	−56.9024	−2.16938
$689$	25.4412	0.969233
$690$	24.0724	0.916419
$691$	−1.89807	−0.0722060	−0.0361030	−	0.999348i	$-0.511494\pi$
$691$	−1.89807	−0.0722060	−0.0361030	+	0.999348i	$0.511494\pi$
$692$	113.729	4.32331
$693$	9.69935	0.368448
$694$	−12.8096	−0.486245
$695$	17.4668	0.662553
$696$	22.7025	0.860537
$697$	−8.81057	−0.333724
$698$	−6.32385	−0.239361
$699$	−21.5119	−0.813655
$700$	15.9462	0.602711
$701$	−17.5572	−0.663126	−0.331563	−	0.943433i	$-0.607576\pi$
$701$	−17.5572	−0.663126	−0.331563	+	0.943433i	$0.607576\pi$
$702$	−10.9447	−0.413081
$703$	2.59825	0.0979947
$704$	35.0745	1.32192
$705$	10.3270	0.388936
$706$	11.7191	0.441054
$707$	34.4565	1.29587
$708$	−4.22967	−0.158961
$709$	−20.7659	−0.779881	−0.389941	−	0.920840i	$-0.627505\pi$
$709$	−20.7659	−0.779881	−0.389941	+	0.920840i	$0.627505\pi$
$710$	−34.6971	−1.30216
$711$	0.0984439	0.00369194
$712$	−17.6923	−0.663048
$713$	−44.6735	−1.67303
$714$	−8.38434	−0.313776
$715$	12.5084	0.467788
$716$	37.4416	1.39926
$717$	7.68849	0.287132
$718$	5.94636	0.221916
$719$	21.9139	0.817249	0.408625	−	0.912703i	$-0.366009\pi$
$719$	21.9139	0.817249	0.408625	+	0.912703i	$0.366009\pi$
$720$	10.6446	0.396700
$721$	−32.1511	−1.19737
$722$	45.9291	1.70930
$723$	−10.3787	−0.385987
$724$	0.916489	0.0340610
$725$	−2.91280	−0.108179
$726$	5.05110	0.187464
$727$	−14.4551	−0.536111	−0.268055	−	0.963404i	$-0.586381\pi$
$727$	−14.4551	−0.536111	−0.268055	+	0.963404i	$0.586381\pi$
$728$	−104.087	−3.85771
$729$	1.00000	0.0370370
$730$	17.4300	0.645114
$731$	−5.28112	−0.195329
$732$	48.1021	1.77791
$733$	27.9145	1.03104	0.515522	−	0.856876i	$-0.327598\pi$
$733$	27.9145	1.03104	0.515522	+	0.856876i	$0.327598\pi$
$734$	84.8517	3.13193
$735$	3.35554	0.123771
$736$	113.957	4.20050
$737$	−36.4744	−1.34355
$738$	23.5201	0.865785
$739$	36.8081	1.35401	0.677005	−	0.735979i	$-0.263278\pi$
$739$	36.8081	1.35401	0.677005	+	0.735979i	$0.263278\pi$
$740$	10.2275	0.375969
$741$	5.22432	0.191920
$742$	−52.0280	−1.91001
$743$	19.9897	0.733352	0.366676	−	0.930349i	$-0.380496\pi$
$743$	19.9897	0.733352	0.366676	+	0.930349i	$0.380496\pi$
$744$	−38.1463	−1.39851
$745$	7.11382	0.260630
$746$	−4.70392	−0.172223
$747$	7.53490	0.275688
$748$	14.7554	0.539512
$749$	−49.8883	−1.82288
$750$	−2.63729	−0.0963004
$751$	−46.2792	−1.68875	−0.844376	−	0.535751i	$-0.820028\pi$
$751$	−46.2792	−1.68875	−0.844376	+	0.535751i	$0.820028\pi$
$752$	109.926	4.00859
$753$	−22.1308	−0.806490
$754$	31.8797	1.16099
$755$	12.4836	0.454325
$756$	15.9462	0.579959
$757$	42.1909	1.53345	0.766727	−	0.641973i	$-0.221884\pi$
$757$	42.1909	1.53345	0.766727	+	0.641973i	$0.221884\pi$
$758$	−92.0102	−3.34196
$759$	−27.5116	−0.998609
$760$	−9.81178	−0.355911
$761$	26.5000	0.960626	0.480313	−	0.877097i	$-0.340523\pi$
$761$	26.5000	0.960626	0.480313	+	0.877097i	$0.340523\pi$
$762$	−38.3295	−1.38853
$763$	41.9137	1.51738
$764$	−19.7176	−0.713359
$765$	0.987925	0.0357185
$766$	−70.3264	−2.54100
$767$	−3.54226	−0.127904
$768$	−8.18768	−0.295448
$769$	−9.50856	−0.342887	−0.171444	−	0.985194i	$-0.554843\pi$
$769$	−9.50856	−0.342887	−0.171444	+	0.985194i	$0.554843\pi$
$770$	−25.5800	−0.921841
$771$	14.5169	0.522812
$772$	7.82623	0.281672
$773$	−37.6294	−1.35343	−0.676717	−	0.736243i	$-0.736598\pi$
$773$	−37.6294	−1.35343	−0.676717	+	0.736243i	$0.736598\pi$
$774$	14.0981	0.506746
$775$	4.89429	0.175808
$776$	−72.8615	−2.61558
$777$	6.64175	0.238271
$778$	87.3303	3.13094
$779$	−11.2270	−0.402249
$780$	20.5645	0.736326
$781$	39.6543	1.41894
$782$	23.7817	0.850432
$783$	−2.91280	−0.104095
$784$	35.7183	1.27565
$785$	−9.21631	−0.328944
$786$	16.6256	0.593014
$787$	33.5315	1.19527	0.597634	−	0.801769i	$-0.296107\pi$
$787$	33.5315	1.19527	0.597634	+	0.801769i	$0.296107\pi$
$788$	80.4319	2.86527
$789$	−25.5810	−0.910708
$790$	−0.259626	−0.00923707
$791$	−1.81310	−0.0644665
$792$	−23.4920	−0.834751
$793$	40.2845	1.43054
$794$	−28.0309	−0.994778
$795$	6.13045	0.217425
$796$	115.238	4.08450
$797$	33.4668	1.18545	0.592727	−	0.805404i	$-0.298051\pi$
$797$	33.4668	1.18545	0.592727	+	0.805404i	$0.298051\pi$
$798$	−10.6839	−0.378206
$799$	10.2023	0.360930
$800$	−12.4848	−0.441403
$801$	2.26998	0.0802057
$802$	−2.63729	−0.0931261
$803$	−19.9203	−0.702972
$804$	−59.9658	−2.11483
$805$	−29.3729	−1.03526
$806$	−53.5665	−1.88680
$807$	−25.3086	−0.890903
$808$	−83.4541	−2.93590
$809$	1.62547	0.0571484	0.0285742	−	0.999592i	$-0.490903\pi$
$809$	1.62547	0.0571484	0.0285742	+	0.999592i	$0.490903\pi$
$810$	−2.63729	−0.0926651
$811$	−3.21507	−0.112896	−0.0564482	−	0.998406i	$-0.517978\pi$
$811$	−3.21507	−0.112896	−0.0564482	+	0.998406i	$0.517978\pi$
$812$	−46.4482	−1.63001
$813$	7.92906	0.278084
$814$	−16.4063	−0.575041
$815$	1.74256	0.0610393
$816$	10.5160	0.368135
$817$	−6.72956	−0.235437
$818$	82.4122	2.88148
$819$	13.3546	0.466648
$820$	−44.1928	−1.54328
$821$	−35.6266	−1.24338	−0.621688	−	0.783265i	$-0.713553\pi$
$821$	−35.6266	−1.24338	−0.621688	+	0.783265i	$0.713553\pi$
$822$	18.4715	0.644268
$823$	21.9349	0.764603	0.382302	−	0.924038i	$-0.375132\pi$
$823$	21.9349	0.764603	0.382302	+	0.924038i	$0.375132\pi$
$824$	77.8705	2.71275
$825$	3.01409	0.104937
$826$	7.24403	0.252052
$827$	−15.9050	−0.553072	−0.276536	−	0.961004i	$-0.589187\pi$
$827$	−15.9050	−0.553072	−0.276536	+	0.961004i	$0.589187\pi$
$828$	−45.2306	−1.57187
$829$	−43.4197	−1.50803	−0.754014	−	0.656859i	$-0.771885\pi$
$829$	−43.4197	−1.50803	−0.754014	+	0.656859i	$0.771885\pi$
$830$	−19.8718	−0.689759
$831$	7.92553	0.274934
$832$	48.2926	1.67424
$833$	3.31503	0.114859
$834$	−46.0650	−1.59510
$835$	−0.270268	−0.00935301
$836$	18.8024	0.650294
$837$	4.89429	0.169171
$838$	−72.9191	−2.51895
$839$	17.8818	0.617348	0.308674	−	0.951168i	$-0.400115\pi$
$839$	17.8818	0.617348	0.308674	+	0.951168i	$0.400115\pi$
$840$	−25.0813	−0.865387
$841$	−20.5156	−0.707434
$842$	−81.5093	−2.80900
$843$	7.29330	0.251194
$844$	3.66303	0.126087
$845$	4.22228	0.145251
$846$	−27.2353	−0.936367
$847$	−6.16330	−0.211774
$848$	65.2560	2.24090
$849$	−13.0537	−0.448003
$850$	−2.60545	−0.0893662
$851$	−18.8389	−0.645790
$852$	65.1937	2.23350
$853$	−15.1351	−0.518215	−0.259107	−	0.965849i	$-0.583428\pi$
$853$	−15.1351	−0.518215	−0.259107	+	0.965849i	$0.583428\pi$
$854$	−82.3830	−2.81909
$855$	1.25888	0.0430528
$856$	120.830	4.12989
$857$	−11.4610	−0.391499	−0.195750	−	0.980654i	$-0.562714\pi$
$857$	−11.4610	−0.391499	−0.195750	+	0.980654i	$0.562714\pi$
$858$	−32.9883	−1.12620
$859$	−18.7399	−0.639398	−0.319699	−	0.947519i	$-0.603582\pi$
$859$	−18.7399	−0.639398	−0.319699	+	0.947519i	$0.603582\pi$
$860$	−26.4895	−0.903285
$861$	−28.6990	−0.978058
$862$	15.4594	0.526548
$863$	51.2147	1.74337	0.871685	−	0.490067i	$-0.163028\pi$
$863$	51.2147	1.74337	0.871685	+	0.490067i	$0.163028\pi$
$864$	−12.4848	−0.424740
$865$	22.9508	0.780350
$866$	70.6890	2.40211
$867$	−16.0240	−0.544204
$868$	78.0455	2.64904
$869$	0.296719	0.0100655
$870$	7.68191	0.260441
$871$	−50.2200	−1.70164
$872$	−101.516	−3.43775
$873$	9.34835	0.316394
$874$	30.3042	1.02506
$875$	3.21800	0.108788
$876$	−32.7500	−1.10652
$877$	−21.7801	−0.735460	−0.367730	−	0.929933i	$-0.619865\pi$
$877$	−21.7801	−0.735460	−0.367730	+	0.929933i	$0.619865\pi$
$878$	29.9345	1.01024
$879$	−26.7579	−0.902521
$880$	32.0837	1.08154
$881$	0.176517	0.00594700	0.00297350	−	0.999996i	$-0.499054\pi$
$881$	0.176517	0.00594700	0.00297350	+	0.999996i	$0.499054\pi$
$882$	−8.84955	−0.297980
$883$	−12.3597	−0.415936	−0.207968	−	0.978136i	$-0.566685\pi$
$883$	−12.3597	−0.415936	−0.207968	+	0.978136i	$0.566685\pi$
$884$	20.3161	0.683306
$885$	−0.853562	−0.0286922
$886$	70.3746	2.36428
$887$	−2.89339	−0.0971504	−0.0485752	−	0.998820i	$-0.515468\pi$
$887$	−2.89339	−0.0971504	−0.0485752	+	0.998820i	$0.515468\pi$
$888$	−16.0864	−0.539825
$889$	46.7693	1.56859
$890$	−5.98660	−0.200671
$891$	3.01409	0.100976
$892$	14.5939	0.488639
$893$	13.0004	0.435042
$894$	−18.7612	−0.627469
$895$	7.55584	0.252564
$896$	−18.4078	−0.614961
$897$	−37.8796	−1.26476
$898$	−41.4527	−1.38329
$899$	−14.2561	−0.475467
$900$	4.95532	0.165177
$901$	6.05643	0.201769
$902$	70.8916	2.36043
$903$	−17.2024	−0.572459
$904$	4.39136	0.146055
$905$	0.184950	0.00614796
$906$	−32.9229	−1.09379
$907$	28.4201	0.943675	0.471837	−	0.881686i	$-0.343591\pi$
$907$	28.4201	0.943675	0.471837	+	0.881686i	$0.343591\pi$
$908$	−111.545	−3.70174
$909$	10.7074	0.355142
$910$	−35.2201	−1.16753
$911$	49.9201	1.65393	0.826963	−	0.562256i	$-0.190067\pi$
$911$	49.9201	1.65393	0.826963	+	0.562256i	$0.190067\pi$
$912$	13.4002	0.443726
$913$	22.7109	0.751620
$914$	16.4111	0.542831
$915$	9.70717	0.320909
$916$	66.9476	2.21201
$917$	−20.2864	−0.669915
$918$	−2.60545	−0.0859926
$919$	27.3732	0.902957	0.451479	−	0.892282i	$-0.350897\pi$
$919$	27.3732	0.902957	0.451479	+	0.892282i	$0.350897\pi$
$920$	71.1416	2.34547
$921$	6.49037	0.213865
$922$	17.6826	0.582345
$923$	54.5983	1.79713
$924$	48.0634	1.58117
$925$	2.06393	0.0678617
$926$	35.2860	1.15957
$927$	−9.99101	−0.328148
$928$	36.3656	1.19376
$929$	−19.8986	−0.652851	−0.326426	−	0.945223i	$-0.605844\pi$
$929$	−19.8986	−0.652851	−0.326426	+	0.945223i	$0.605844\pi$
$930$	−12.9077	−0.423259
$931$	4.22423	0.138443
$932$	−106.598	−3.49175
$933$	0.912738	0.0298817
$934$	−33.7168	−1.10325
$935$	2.97770	0.0973811
$936$	−32.3451	−1.05723
$937$	16.3435	0.533917	0.266959	−	0.963708i	$-0.413981\pi$
$937$	16.3435	0.533917	0.266959	+	0.963708i	$0.413981\pi$
$938$	102.701	3.35332
$939$	−12.5930	−0.410958
$940$	51.1734	1.66909
$941$	49.1730	1.60299	0.801497	−	0.597998i	$-0.204037\pi$
$941$	49.1730	1.60299	0.801497	+	0.597998i	$0.204037\pi$
$942$	24.3061	0.791936
$943$	81.4029	2.65084
$944$	−9.08580	−0.295718
$945$	3.21800	0.104682
$946$	42.4930	1.38157
$947$	−39.7527	−1.29179	−0.645894	−	0.763427i	$-0.723515\pi$
$947$	−39.7527	−1.29179	−0.645894	+	0.763427i	$0.723515\pi$
$948$	0.487821	0.0158437
$949$	−27.4274	−0.890332
$950$	−3.32004	−0.107716
$951$	14.2764	0.462943
$952$	−24.7784	−0.803074
$953$	−0.335815	−0.0108781	−0.00543905	−	0.999985i	$-0.501731\pi$
$953$	−0.335815	−0.0108781	−0.00543905	+	0.999985i	$0.501731\pi$
$954$	−16.1678	−0.523452
$955$	−3.97908	−0.128760
$956$	38.0989	1.23221
$957$	−8.77945	−0.283799
$958$	−70.6686	−2.28320
$959$	−22.5388	−0.727815
$960$	11.6368	0.375577
$961$	−7.04594	−0.227288
$962$	−22.5891	−0.728303
$963$	−15.5029	−0.499573
$964$	−51.4297	−1.65644
$965$	1.57936	0.0508414
$966$	77.4650	2.49239
$967$	−17.6543	−0.567725	−0.283862	−	0.958865i	$-0.591616\pi$
$967$	−17.6543	−0.567725	−0.283862	+	0.958865i	$0.591616\pi$
$968$	14.9276	0.479792
$969$	1.24368	0.0399527
$970$	−24.6543	−0.791603
$971$	−20.4421	−0.656019	−0.328009	−	0.944674i	$-0.606378\pi$
$971$	−20.4421	−0.656019	−0.328009	+	0.944674i	$0.606378\pi$
$972$	4.95532	0.158942
$973$	56.2082	1.80195
$974$	67.4722	2.16195
$975$	4.14997	0.132906
$976$	103.329	3.30747
$977$	−3.43575	−0.109919	−0.0549597	−	0.998489i	$-0.517503\pi$
$977$	−3.43575	−0.109919	−0.0549597	+	0.998489i	$0.517503\pi$
$978$	−4.59565	−0.146953
$979$	6.84192	0.218669
$980$	16.6278	0.531155
$981$	13.0248	0.415848
$982$	85.3708	2.72429
$983$	−51.0361	−1.62780	−0.813899	−	0.581007i	$-0.802659\pi$
$983$	−51.0361	−1.62780	−0.813899	+	0.581007i	$0.802659\pi$
$984$	69.5093	2.21588
$985$	16.2314	0.517176
$986$	7.58916	0.241688
$987$	33.2322	1.05779
$988$	25.8882	0.823613
$989$	48.7935	1.55154
$990$	−7.94904	−0.252637
$991$	20.3020	0.644913	0.322456	−	0.946584i	$-0.395491\pi$
$991$	20.3020	0.644913	0.322456	+	0.946584i	$0.395491\pi$
$992$	−61.1040	−1.94005
$993$	−0.477421	−0.0151505
$994$	−111.655	−3.54149
$995$	23.2554	0.737245
$996$	37.3379	1.18310
$997$	3.08284	0.0976347	0.0488173	−	0.998808i	$-0.484455\pi$
$997$	3.08284	0.0976347	0.0488173	+	0.998808i	$0.484455\pi$
$998$	67.8479	2.14769
$999$	2.06393	0.0653000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.3	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.3	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63729 q^{2} +1.00000 q^{3} +4.95532 q^{4} +1.00000 q^{5} -2.63729 q^{6} +3.21800 q^{7} -7.79405 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.63729 q^{2} +1.00000 q^{3} +4.95532 q^{4} +1.00000 q^{5} -2.63729 q^{6} +3.21800 q^{7} -7.79405 q^{8} +1.00000 q^{9} -2.63729 q^{10} +3.01409 q^{11} +4.95532 q^{12} +4.14997 q^{13} -8.48682 q^{14} +1.00000 q^{15} +10.6446 q^{16} +0.987925 q^{17} -2.63729 q^{18} +1.25888 q^{19} +4.95532 q^{20} +3.21800 q^{21} -7.94904 q^{22} -9.12768 q^{23} -7.79405 q^{24} +1.00000 q^{25} -10.9447 q^{26} +1.00000 q^{27} +15.9462 q^{28} -2.91280 q^{29} -2.63729 q^{30} +4.89429 q^{31} -12.4848 q^{32} +3.01409 q^{33} -2.60545 q^{34} +3.21800 q^{35} +4.95532 q^{36} +2.06393 q^{37} -3.32004 q^{38} +4.14997 q^{39} -7.79405 q^{40} -8.91825 q^{41} -8.48682 q^{42} -5.34567 q^{43} +14.9358 q^{44} +1.00000 q^{45} +24.0724 q^{46} +10.3270 q^{47} +10.6446 q^{48} +3.35554 q^{49} -2.63729 q^{50} +0.987925 q^{51} +20.5645 q^{52} +6.13045 q^{53} -2.63729 q^{54} +3.01409 q^{55} -25.0813 q^{56} +1.25888 q^{57} +7.68191 q^{58} -0.853562 q^{59} +4.95532 q^{60} +9.70717 q^{61} -12.9077 q^{62} +3.21800 q^{63} +11.6368 q^{64} +4.14997 q^{65} -7.94904 q^{66} -12.1013 q^{67} +4.89549 q^{68} -9.12768 q^{69} -8.48682 q^{70} +13.1563 q^{71} -7.79405 q^{72} -6.60906 q^{73} -5.44320 q^{74} +1.00000 q^{75} +6.23816 q^{76} +9.69935 q^{77} -10.9447 q^{78} +0.0984439 q^{79} +10.6446 q^{80} +1.00000 q^{81} +23.5201 q^{82} +7.53490 q^{83} +15.9462 q^{84} +0.987925 q^{85} +14.0981 q^{86} -2.91280 q^{87} -23.4920 q^{88} +2.26998 q^{89} -2.63729 q^{90} +13.3546 q^{91} -45.2306 q^{92} +4.89429 q^{93} -27.2353 q^{94} +1.25888 q^{95} -12.4848 q^{96} +9.34835 q^{97} -8.84955 q^{98} +3.01409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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