LMFDB - Embedded newform 1441.2.a.f.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1441,2,Mod(1,1441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1441, 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("1441.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1441 = 11 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1441.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:	$11.5064429313$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	1441.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.00234753 q^{2} +2.44529 q^{3} -1.99999 q^{4} +1.45917 q^{5} +0.00574040 q^{6} +4.30357 q^{7} -0.00939012 q^{8} +2.97943 q^{9} +O(q^{10})$	\(q+0.00234753 q^{2} +2.44529 q^{3} -1.99999 q^{4} +1.45917 q^{5} +0.00574040 q^{6} +4.30357 q^{7} -0.00939012 q^{8} +2.97943 q^{9} +0.00342546 q^{10} -1.00000 q^{11} -4.89056 q^{12} +6.13170 q^{13} +0.0101028 q^{14} +3.56810 q^{15} +3.99997 q^{16} +3.35551 q^{17} +0.00699432 q^{18} -4.42221 q^{19} -2.91834 q^{20} +10.5235 q^{21} -0.00234753 q^{22} -6.97306 q^{23} -0.0229616 q^{24} -2.87082 q^{25} +0.0143944 q^{26} -0.0502907 q^{27} -8.60712 q^{28} +1.53797 q^{29} +0.00837622 q^{30} -2.56645 q^{31} +0.0281703 q^{32} -2.44529 q^{33} +0.00787716 q^{34} +6.27965 q^{35} -5.95885 q^{36} -8.05597 q^{37} -0.0103813 q^{38} +14.9938 q^{39} -0.0137018 q^{40} -0.972876 q^{41} +0.0247042 q^{42} +7.31076 q^{43} +1.99999 q^{44} +4.34751 q^{45} -0.0163695 q^{46} +8.14429 q^{47} +9.78107 q^{48} +11.5207 q^{49} -0.00673934 q^{50} +8.20518 q^{51} -12.2634 q^{52} +2.35904 q^{53} -0.000118059 q^{54} -1.45917 q^{55} -0.0404111 q^{56} -10.8136 q^{57} +0.00361045 q^{58} +5.79738 q^{59} -7.13617 q^{60} -8.35442 q^{61} -0.00602483 q^{62} +12.8222 q^{63} -7.99987 q^{64} +8.94720 q^{65} -0.00574040 q^{66} -7.08891 q^{67} -6.71099 q^{68} -17.0511 q^{69} +0.0147417 q^{70} +14.8118 q^{71} -0.0279772 q^{72} +0.310986 q^{73} -0.0189117 q^{74} -7.01998 q^{75} +8.84440 q^{76} -4.30357 q^{77} +0.0351984 q^{78} +1.50197 q^{79} +5.83664 q^{80} -9.06128 q^{81} -0.00228386 q^{82} -5.64172 q^{83} -21.0469 q^{84} +4.89626 q^{85} +0.0171623 q^{86} +3.76079 q^{87} +0.00939012 q^{88} +14.5922 q^{89} +0.0102059 q^{90} +26.3882 q^{91} +13.9461 q^{92} -6.27571 q^{93} +0.0191190 q^{94} -6.45277 q^{95} +0.0688845 q^{96} -6.91713 q^{97} +0.0270453 q^{98} -2.97943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.00234753	0.00165996	0.000829979	−	1.00000i	$-0.499736\pi$
$2$	0.00234753	0.00165996	0.000829979		1.00000i	$0.499736\pi$
$3$	2.44529	1.41179	0.705894	−	0.708318i	$-0.250546\pi$
$3$	2.44529	1.41179	0.705894	+	0.708318i	$0.250546\pi$
$4$	−1.99999	−0.999997
$5$	1.45917	0.652561	0.326281	−	0.945273i	$-0.394205\pi$
$5$	1.45917	0.652561	0.326281	+	0.945273i	$0.394205\pi$
$6$	0.00574040	0.00234351
$7$	4.30357	1.62660	0.813299	−	0.581846i	$-0.197670\pi$
$7$	4.30357	1.62660	0.813299	+	0.581846i	$0.197670\pi$
$8$	−0.00939012	−0.00331991
$9$	2.97943	0.993145
$10$	0.00342546	0.00108322
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−4.89056	−1.41178
$13$	6.13170	1.70063	0.850314	−	0.526276i	$-0.176412\pi$
$13$	6.13170	1.70063	0.850314	+	0.526276i	$0.176412\pi$
$14$	0.0101028	0.00270008
$15$	3.56810	0.921278
$16$	3.99997	0.999992
$17$	3.35551	0.813830	0.406915	−	0.913466i	$-0.366605\pi$
$17$	3.35551	0.813830	0.406915	+	0.913466i	$0.366605\pi$
$18$	0.00699432	0.00164858
$19$	−4.42221	−1.01453	−0.507263	−	0.861791i	$-0.669343\pi$
$19$	−4.42221	−1.01453	−0.507263	+	0.861791i	$0.669343\pi$
$20$	−2.91834	−0.652560
$21$	10.5235	2.29641
$22$	−0.00234753	−0.000500496 0
$23$	−6.97306	−1.45398	−0.726992	−	0.686646i	$-0.759082\pi$
$23$	−6.97306	−1.45398	−0.726992	+	0.686646i	$0.759082\pi$
$24$	−0.0229616	−0.00468701
$25$	−2.87082	−0.574164
$26$	0.0143944	0.00282297
$27$	−0.0502907	−0.00967844
$28$	−8.60712	−1.62659
$29$	1.53797	0.285595	0.142797	−	0.989752i	$-0.454390\pi$
$29$	1.53797	0.285595	0.142797	+	0.989752i	$0.454390\pi$
$30$	0.00837622	0.00152928
$31$	−2.56645	−0.460948	−0.230474	−	0.973078i	$-0.574028\pi$
$31$	−2.56645	−0.460948	−0.230474	+	0.973078i	$0.574028\pi$
$32$	0.0281703	0.00497985
$33$	−2.44529	−0.425670
$34$	0.00787716	0.00135092
$35$	6.27965	1.06145
$36$	−5.95885	−0.993142
$37$	−8.05597	−1.32439	−0.662197	−	0.749330i	$-0.730376\pi$
$37$	−8.05597	−1.32439	−0.662197	+	0.749330i	$0.730376\pi$
$38$	−0.0103813	−0.00168407
$39$	14.9938	2.40092
$40$	−0.0137018	−0.00216645
$41$	−0.972876	−0.151938	−0.0759688	−	0.997110i	$-0.524205\pi$
$41$	−0.972876	−0.151938	−0.0759688	+	0.997110i	$0.524205\pi$
$42$	0.0247042	0.00381194
$43$	7.31076	1.11488	0.557440	−	0.830217i	$-0.311784\pi$
$43$	7.31076	1.11488	0.557440	+	0.830217i	$0.311784\pi$
$44$	1.99999	0.301511
$45$	4.34751	0.648088
$46$	−0.0163695	−0.00241355
$47$	8.14429	1.18797	0.593983	−	0.804477i	$-0.297554\pi$
$47$	8.14429	1.18797	0.593983	+	0.804477i	$0.297554\pi$
$48$	9.78107	1.41178
$49$	11.5207	1.64582
$50$	−0.00673934	−0.000953087 0
$51$	8.20518	1.14895
$52$	−12.2634	−1.70062
$53$	2.35904	0.324039	0.162020	−	0.986788i	$-0.448199\pi$
$53$	2.35904	0.324039	0.162020	+	0.986788i	$0.448199\pi$
$54$	−0.000118059 0	−1.60658e−5 0
$55$	−1.45917	−0.196755
$56$	−0.0404111	−0.00540016
$57$	−10.8136	−1.43229
$58$	0.00361045	0.000474075 0
$59$	5.79738	0.754754	0.377377	−	0.926060i	$-0.376826\pi$
$59$	5.79738	0.754754	0.377377	+	0.926060i	$0.376826\pi$
$60$	−7.13617	−0.921276
$61$	−8.35442	−1.06967	−0.534837	−	0.844955i	$-0.679627\pi$
$61$	−8.35442	−1.06967	−0.534837	+	0.844955i	$0.679627\pi$
$62$	−0.00602483	−0.000765154 0
$63$	12.8222	1.61545
$64$	−7.99987	−0.999983
$65$	8.94720	1.10976
$66$	−0.00574040	−0.000706594 0
$67$	−7.08891	−0.866049	−0.433024	−	0.901382i	$-0.642554\pi$
$67$	−7.08891	−0.866049	−0.433024	+	0.901382i	$0.642554\pi$
$68$	−6.71099	−0.813827
$69$	−17.0511	−2.05272
$70$	0.0147417	0.00176197
$71$	14.8118	1.75784	0.878918	−	0.476974i	$-0.158266\pi$
$71$	14.8118	1.75784	0.878918	+	0.476974i	$0.158266\pi$
$72$	−0.0279772	−0.00329715
$73$	0.310986	0.0363981	0.0181991	−	0.999834i	$-0.494207\pi$
$73$	0.310986	0.0363981	0.0181991	+	0.999834i	$0.494207\pi$
$74$	−0.0189117	−0.00219844
$75$	−7.01998	−0.810597
$76$	8.84440	1.01452
$77$	−4.30357	−0.490438
$78$	0.0351984	0.00398543
$79$	1.50197	0.168984	0.0844922	−	0.996424i	$-0.473073\pi$
$79$	1.50197	0.168984	0.0844922	+	0.996424i	$0.473073\pi$
$80$	5.83664	0.652556
$81$	−9.06128	−1.00681
$82$	−0.00228386	−0.000252210 0
$83$	−5.64172	−0.619259	−0.309629	−	0.950857i	$-0.600205\pi$
$83$	−5.64172	−0.619259	−0.309629	+	0.950857i	$0.600205\pi$
$84$	−21.0469	−2.29640
$85$	4.89626	0.531074
$86$	0.0171623	0.00185065
$87$	3.76079	0.403199
$88$	0.00939012	0.00100099
$89$	14.5922	1.54677	0.773386	−	0.633935i	$-0.218561\pi$
$89$	14.5922	1.54677	0.773386	+	0.633935i	$0.218561\pi$
$90$	0.0102059	0.00107580
$91$	26.3882	2.76624
$92$	13.9461	1.45398
$93$	−6.27571	−0.650761
$94$	0.0191190	0.00197197
$95$	−6.45277	−0.662040
$96$	0.0688845	0.00703050
$97$	−6.91713	−0.702328	−0.351164	−	0.936314i	$-0.614214\pi$
$97$	−6.91713	−0.702328	−0.351164	+	0.936314i	$0.614214\pi$
$98$	0.0270453	0.00273199
$99$	−2.97943	−0.299444
$100$	5.74162	0.574162
$101$	−11.3766	−1.13202	−0.566009	−	0.824399i	$-0.691513\pi$
$101$	−11.3766	−1.13202	−0.566009	+	0.824399i	$0.691513\pi$
$102$	0.0192619	0.00190722
$103$	17.4100	1.71546	0.857729	−	0.514102i	$-0.171875\pi$
$103$	17.4100	1.71546	0.857729	+	0.514102i	$0.171875\pi$
$104$	−0.0575774	−0.00564593
$105$	15.3556	1.49855
$106$	0.00553793	0.000537892 0
$107$	10.7022	1.03463	0.517313	−	0.855796i	$-0.326932\pi$
$107$	10.7022	1.03463	0.517313	+	0.855796i	$0.326932\pi$
$108$	0.100581	0.00967841
$109$	−15.6770	−1.50158	−0.750791	−	0.660540i	$-0.770328\pi$
$109$	−15.6770	−1.50158	−0.750791	+	0.660540i	$0.770328\pi$
$110$	−0.00342546	−0.000326604 0
$111$	−19.6992	−1.86976
$112$	17.2141	1.62658
$113$	−4.51823	−0.425040	−0.212520	−	0.977157i	$-0.568167\pi$
$113$	−4.51823	−0.425040	−0.212520	+	0.977157i	$0.568167\pi$
$114$	−0.0253853	−0.00237755
$115$	−10.1749	−0.948813
$116$	−3.07594	−0.285594
$117$	18.2690	1.68897
$118$	0.0136095	0.00125286
$119$	14.4407	1.32377
$120$	−0.0335049	−0.00305856
$121$	1.00000	0.0909091
$122$	−0.0196123	−0.00177561
$123$	−2.37896	−0.214504
$124$	5.13289	0.460947
$125$	−11.4849	−1.02724
$126$	0.0301006	0.00268157
$127$	−18.3122	−1.62494	−0.812472	−	0.583001i	$-0.801878\pi$
$127$	−18.3122	−1.62494	−0.812472	+	0.583001i	$0.801878\pi$
$128$	−0.0751206	−0.00663978
$129$	17.8769	1.57397
$130$	0.0210039	0.00184216
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	4.89056	0.425669
$133$	−19.0313	−1.65022
$134$	−0.0166415	−0.00143760
$135$	−0.0733827	−0.00631578
$136$	−0.0315086	−0.00270184
$137$	−4.19800	−0.358659	−0.179330	−	0.983789i	$-0.557393\pi$
$137$	−4.19800	−0.358659	−0.179330	+	0.983789i	$0.557393\pi$
$138$	−0.0400281	−0.00340742
$139$	−10.0610	−0.853364	−0.426682	−	0.904402i	$-0.640318\pi$
$139$	−10.0610	−0.853364	−0.426682	+	0.904402i	$0.640318\pi$
$140$	−12.5593	−1.06145
$141$	19.9151	1.67716
$142$	0.0347712	0.00291793
$143$	−6.13170	−0.512758
$144$	11.9176	0.993136
$145$	2.24417	0.186368
$146$	0.000730049 0	6.04193e−5 0
$147$	28.1715	2.32355
$148$	16.1119	1.32439
$149$	−4.54037	−0.371962	−0.185981	−	0.982553i	$-0.559546\pi$
$149$	−4.54037	−0.371962	−0.185981	+	0.982553i	$0.559546\pi$
$150$	−0.0164796	−0.00134556
$151$	−9.46825	−0.770515	−0.385257	−	0.922809i	$-0.625887\pi$
$151$	−9.46825	−0.770515	−0.385257	+	0.922809i	$0.625887\pi$
$152$	0.0415251	0.00336813
$153$	9.99751	0.808250
$154$	−0.0101028	−0.000814105 0
$155$	−3.74489	−0.300797
$156$	−29.9875	−2.40092
$157$	−3.35944	−0.268113	−0.134056	−	0.990974i	$-0.542800\pi$
$157$	−3.35944	−0.268113	−0.134056	+	0.990974i	$0.542800\pi$
$158$	0.00352592	0.000280507 0
$159$	5.76854	0.457475
$160$	0.0411053	0.00324966
$161$	−30.0091	−2.36505
$162$	−0.0212717	−0.00167126
$163$	22.1853	1.73769	0.868843	−	0.495087i	$-0.164864\pi$
$163$	22.1853	1.73769	0.868843	+	0.495087i	$0.164864\pi$
$164$	1.94575	0.151937
$165$	−3.56810	−0.277776
$166$	−0.0132441	−0.00102794
$167$	−15.4480	−1.19540	−0.597702	−	0.801718i	$-0.703919\pi$
$167$	−15.4480	−1.19540	−0.597702	+	0.801718i	$0.703919\pi$
$168$	−0.0988167	−0.00762387
$169$	24.5977	1.89213
$170$	0.0114941	0.000881560 0
$171$	−13.1757	−1.00757
$172$	−14.6215	−1.11488
$173$	23.1026	1.75646	0.878230	−	0.478239i	$-0.158725\pi$
$173$	23.1026	1.75646	0.878230	+	0.478239i	$0.158725\pi$
$174$	0.00882858	0.000669293 0
$175$	−12.3548	−0.933933
$176$	−3.99997	−0.301509
$177$	14.1763	1.06555
$178$	0.0342557	0.00256758
$179$	−14.0041	−1.04671	−0.523357	−	0.852114i	$-0.675320\pi$
$179$	−14.0041	−1.04671	−0.523357	+	0.852114i	$0.675320\pi$
$180$	−8.69499	−0.648086
$181$	−3.20599	−0.238299	−0.119150	−	0.992876i	$-0.538017\pi$
$181$	−3.20599	−0.238299	−0.119150	+	0.992876i	$0.538017\pi$
$182$	0.0619472	0.00459183
$183$	−20.4290	−1.51015
$184$	0.0654779	0.00482709
$185$	−11.7550	−0.864248
$186$	−0.0147324	−0.00108024
$187$	−3.35551	−0.245379
$188$	−16.2885	−1.18796
$189$	−0.216429	−0.0157429
$190$	−0.0151481	−0.00109896
$191$	−4.48379	−0.324436	−0.162218	−	0.986755i	$-0.551865\pi$
$191$	−4.48379	−0.324436	−0.162218	+	0.986755i	$0.551865\pi$
$192$	−19.5620	−1.41176
$193$	5.02181	0.361478	0.180739	−	0.983531i	$-0.442151\pi$
$193$	5.02181	0.361478	0.180739	+	0.983531i	$0.442151\pi$
$194$	−0.0162382	−0.00116583
$195$	21.8785	1.56675
$196$	−23.0414	−1.64581
$197$	−2.23752	−0.159417	−0.0797084	−	0.996818i	$-0.525399\pi$
$197$	−2.23752	−0.159417	−0.0797084	+	0.996818i	$0.525399\pi$
$198$	−0.00699432	−0.000497065 0
$199$	−11.2516	−0.797602	−0.398801	−	0.917038i	$-0.630574\pi$
$199$	−11.2516	−0.797602	−0.398801	+	0.917038i	$0.630574\pi$
$200$	0.0269573	0.00190617
$201$	−17.3344	−1.22268
$202$	−0.0267070	−0.00187910
$203$	6.61878	0.464548
$204$	−16.4103	−1.14895
$205$	−1.41959	−0.0991487
$206$	0.0408706	0.00284759
$207$	−20.7758	−1.44402
$208$	24.5266	1.70061
$209$	4.42221	0.305891
$210$	0.0360477	0.00248753
$211$	1.36628	0.0940585	0.0470292	−	0.998894i	$-0.485025\pi$
$211$	1.36628	0.0940585	0.0470292	+	0.998894i	$0.485025\pi$
$212$	−4.71807	−0.324039
$213$	36.2191	2.48169
$214$	0.0251239	0.00171743
$215$	10.6677	0.727528
$216$	0.000472235 0	3.21316e−5 0
$217$	−11.0449	−0.749777
$218$	−0.0368022	−0.00249256
$219$	0.760449	0.0513864
$220$	2.91834	0.196754
$221$	20.5749	1.38402
$222$	−0.0462445	−0.00310373
$223$	−12.2795	−0.822295	−0.411147	−	0.911569i	$-0.634872\pi$
$223$	−12.2795	−0.822295	−0.411147	+	0.911569i	$0.634872\pi$
$224$	0.121233	0.00810022
$225$	−8.55341	−0.570227
$226$	−0.0106067	−0.000705547 0
$227$	−6.48358	−0.430330	−0.215165	−	0.976578i	$-0.569029\pi$
$227$	−6.48358	−0.430330	−0.215165	+	0.976578i	$0.569029\pi$
$228$	21.6271	1.43229
$229$	−13.8333	−0.914127	−0.457064	−	0.889434i	$-0.651099\pi$
$229$	−13.8333	−0.914127	−0.457064	+	0.889434i	$0.651099\pi$
$230$	−0.0238859	−0.00157499
$231$	−10.5235	−0.692394
$232$	−0.0144418	−0.000948149 0
$233$	22.6938	1.48672	0.743362	−	0.668890i	$-0.233230\pi$
$233$	22.6938	1.48672	0.743362	+	0.668890i	$0.233230\pi$
$234$	0.0428871	0.00280362
$235$	11.8839	0.775221
$236$	−11.5947	−0.754752
$237$	3.67274	0.238570
$238$	0.0338999	0.00219741
$239$	−0.731748	−0.0473329	−0.0236664	−	0.999720i	$-0.507534\pi$
$239$	−0.731748	−0.0473329	−0.0236664	+	0.999720i	$0.507534\pi$
$240$	14.2723	0.921271
$241$	5.43580	0.350151	0.175075	−	0.984555i	$-0.443983\pi$
$241$	5.43580	0.350151	0.175075	+	0.984555i	$0.443983\pi$
$242$	0.00234753	0.000150905 0
$243$	−22.0066	−1.41172
$244$	16.7088	1.06967
$245$	16.8107	1.07400
$246$	−0.00558469	−0.000356067 0
$247$	−27.1157	−1.72533
$248$	0.0240993	0.00153031
$249$	−13.7956	−0.874262
$250$	−0.0269611	−0.00170517
$251$	4.73370	0.298789	0.149394	−	0.988778i	$-0.452268\pi$
$251$	4.73370	0.298789	0.149394	+	0.988778i	$0.452268\pi$
$252$	−25.6443	−1.61544
$253$	6.97306	0.438392
$254$	−0.0429885	−0.00269734
$255$	11.9728	0.749763
$256$	15.9996	0.999972
$257$	−3.86301	−0.240968	−0.120484	−	0.992715i	$-0.538445\pi$
$257$	−3.86301	−0.240968	−0.120484	+	0.992715i	$0.538445\pi$
$258$	0.0419667	0.00261273
$259$	−34.6695	−2.15426
$260$	−17.8944	−1.10976
$261$	4.58229	0.283637
$262$	0.00234753	0.000145031 0
$263$	−15.5423	−0.958380	−0.479190	−	0.877711i	$-0.659070\pi$
$263$	−15.5423	−0.958380	−0.479190	+	0.877711i	$0.659070\pi$
$264$	0.0229616	0.00141319
$265$	3.44225	0.211456
$266$	−0.0446767	−0.00273930
$267$	35.6822	2.18372
$268$	14.1778	0.866046
$269$	−17.5719	−1.07138	−0.535689	−	0.844415i	$-0.679948\pi$
$269$	−17.5719	−1.07138	−0.535689	+	0.844415i	$0.679948\pi$
$270$	−0.000172268 0	−1.04839e−5 0
$271$	12.5745	0.763849	0.381924	−	0.924194i	$-0.375262\pi$
$271$	12.5745	0.763849	0.381924	+	0.924194i	$0.375262\pi$
$272$	13.4219	0.813823
$273$	64.5268	3.90534
$274$	−0.00985494	−0.000595359 0
$275$	2.87082	0.173117
$276$	34.1022	2.05271
$277$	0.914530	0.0549488	0.0274744	−	0.999623i	$-0.491254\pi$
$277$	0.914530	0.0549488	0.0274744	+	0.999623i	$0.491254\pi$
$278$	−0.0236186	−0.00141655
$279$	−7.64657	−0.457788
$280$	−0.0589667	−0.00352393
$281$	−27.1926	−1.62218	−0.811088	−	0.584924i	$-0.801124\pi$
$281$	−27.1926	−1.62218	−0.811088	+	0.584924i	$0.801124\pi$
$282$	0.0467514	0.00278401
$283$	33.3088	1.98000	0.990000	−	0.141065i	$-0.0450527\pi$
$283$	33.3088	1.98000	0.990000	+	0.141065i	$0.0450527\pi$
$284$	−29.6235	−1.75783
$285$	−15.7789	−0.934660
$286$	−0.0143944	−0.000851157 0
$287$	−4.18684	−0.247141
$288$	0.0839315	0.00494571
$289$	−5.74058	−0.337681
$290$	0.00526826	0.000309363 0
$291$	−16.9144	−0.991538
$292$	−0.621969	−0.0363980
$293$	9.68664	0.565899	0.282950	−	0.959135i	$-0.408687\pi$
$293$	9.68664	0.565899	0.282950	+	0.959135i	$0.408687\pi$
$294$	0.0661336	0.00385699
$295$	8.45937	0.492523
$296$	0.0756466	0.00439687
$297$	0.0502907	0.00291816
$298$	−0.0106587	−0.000617440 0
$299$	−42.7567	−2.47268
$300$	14.0399	0.810595
$301$	31.4624	1.81346
$302$	−0.0222270	−0.00127902
$303$	−27.8191	−1.59817
$304$	−17.6887	−1.01452
$305$	−12.1905	−0.698028
$306$	0.0234695	0.00134166
$307$	31.0554	1.77243	0.886213	−	0.463278i	$-0.153327\pi$
$307$	31.0554	1.77243	0.886213	+	0.463278i	$0.153327\pi$
$308$	8.60712	0.490436
$309$	42.5725	2.42186
$310$	−0.00879126	−0.000499310 0
$311$	29.4451	1.66968	0.834839	−	0.550495i	$-0.185561\pi$
$311$	29.4451	1.66968	0.834839	+	0.550495i	$0.185561\pi$
$312$	−0.140793	−0.00797085
$313$	−24.8400	−1.40404	−0.702020	−	0.712158i	$-0.747718\pi$
$313$	−24.8400	−1.40404	−0.702020	+	0.712158i	$0.747718\pi$
$314$	−0.00788641	−0.000445056 0
$315$	18.7098	1.05418
$316$	−3.00392	−0.168984
$317$	21.9029	1.23019	0.615094	−	0.788454i	$-0.289118\pi$
$317$	21.9029	1.23019	0.615094	+	0.788454i	$0.289118\pi$
$318$	0.0135418	0.000759389 0
$319$	−1.53797	−0.0861100
$320$	−11.6732	−0.652551
$321$	26.1701	1.46067
$322$	−0.0704473	−0.00392587
$323$	−14.8388	−0.825651
$324$	18.1225	1.00681
$325$	−17.6030	−0.976438
$326$	0.0520807	0.00288448
$327$	−38.3347	−2.11992
$328$	0.00913542	0.000504419 0
$329$	35.0495	1.93234
$330$	−0.00837622	−0.000461096 0
$331$	−28.0164	−1.53992	−0.769960	−	0.638092i	$-0.779724\pi$
$331$	−28.0164	−1.53992	−0.769960	+	0.638092i	$0.779724\pi$
$332$	11.2834	0.619257
$333$	−24.0022	−1.31531
$334$	−0.0362647	−0.00198432
$335$	−10.3439	−0.565150
$336$	42.0935	2.29639
$337$	1.65365	0.0900800	0.0450400	−	0.998985i	$-0.485658\pi$
$337$	1.65365	0.0900800	0.0450400	+	0.998985i	$0.485658\pi$
$338$	0.0577440	0.00314086
$339$	−11.0484	−0.600066
$340$	−9.79249	−0.531072
$341$	2.56645	0.138981
$342$	−0.0309304	−0.00167252
$343$	19.4553	1.05049
$344$	−0.0686489	−0.00370130
$345$	−24.8805	−1.33952
$346$	0.0542342	0.00291565
$347$	−23.3683	−1.25448	−0.627238	−	0.778828i	$-0.715815\pi$
$347$	−23.3683	−1.25448	−0.627238	+	0.778828i	$0.715815\pi$
$348$	−7.52156	−0.403198
$349$	−21.7573	−1.16464	−0.582320	−	0.812960i	$-0.697855\pi$
$349$	−21.7573	−1.16464	−0.582320	+	0.812960i	$0.697855\pi$
$350$	−0.0290032	−0.00155029
$351$	−0.308367	−0.0164594
$352$	−0.0281703	−0.00150148
$353$	−4.89666	−0.260623	−0.130312	−	0.991473i	$-0.541598\pi$
$353$	−4.89666	−0.260623	−0.130312	+	0.991473i	$0.541598\pi$
$354$	0.0332792	0.00176877
$355$	21.6129	1.14710
$356$	−29.1844	−1.54677
$357$	35.3116	1.86889
$358$	−0.0328750	−0.00173750
$359$	18.4726	0.974949	0.487474	−	0.873137i	$-0.337918\pi$
$359$	18.4726	0.974949	0.487474	+	0.873137i	$0.337918\pi$
$360$	−0.0408236	−0.00215159
$361$	0.555980	0.0292621
$362$	−0.00752616	−0.000395566 0
$363$	2.44529	0.128344
$364$	−52.7763	−2.76623
$365$	0.453781	0.0237520
$366$	−0.0479577	−0.00250679
$367$	4.85687	0.253526	0.126763	−	0.991933i	$-0.459541\pi$
$367$	4.85687	0.253526	0.126763	+	0.991933i	$0.459541\pi$
$368$	−27.8920	−1.45397
$369$	−2.89862	−0.150896
$370$	−0.0275954	−0.00143462
$371$	10.1523	0.527082
$372$	12.5514	0.650759
$373$	−31.3960	−1.62562	−0.812811	−	0.582528i	$-0.802064\pi$
$373$	−31.3960	−1.62562	−0.812811	+	0.582528i	$0.802064\pi$
$374$	−0.00787716	−0.000407318 0
$375$	−28.0838	−1.45024
$376$	−0.0764759	−0.00394394
$377$	9.43040	0.485690
$378$	−0.000508075 0	−2.61326e−5 0
$379$	−30.3948	−1.56128	−0.780639	−	0.624983i	$-0.785106\pi$
$379$	−30.3948	−1.56128	−0.780639	+	0.624983i	$0.785106\pi$
$380$	12.9055	0.662038
$381$	−44.7786	−2.29408
$382$	−0.0105258	−0.000538549 0
$383$	25.7939	1.31801	0.659004	−	0.752140i	$-0.270978\pi$
$383$	25.7939	1.31801	0.659004	+	0.752140i	$0.270978\pi$
$384$	−0.183691	−0.00937396
$385$	−6.27965	−0.320041
$386$	0.0117889	0.000600037 0
$387$	21.7819	1.10724
$388$	13.8342	0.702326
$389$	−33.0210	−1.67423	−0.837115	−	0.547027i	$-0.815759\pi$
$389$	−33.0210	−1.67423	−0.837115	+	0.547027i	$0.815759\pi$
$390$	0.0513605	0.00260074
$391$	−23.3981	−1.18329
$392$	−0.108181	−0.00546397
$393$	2.44529	0.123348
$394$	−0.00525265	−0.000264625 0
$395$	2.19163	0.110273
$396$	5.95885	0.299444
$397$	12.6785	0.636314	0.318157	−	0.948038i	$-0.396936\pi$
$397$	12.6785	0.636314	0.318157	+	0.948038i	$0.396936\pi$
$398$	−0.0264134	−0.00132398
$399$	−46.5371	−2.32977
$400$	−11.4832	−0.574159
$401$	26.1739	1.30706	0.653531	−	0.756900i	$-0.273287\pi$
$401$	26.1739	1.30706	0.653531	+	0.756900i	$0.273287\pi$
$402$	−0.0406932	−0.00202959
$403$	−15.7367	−0.783901
$404$	22.7532	1.13201
$405$	−13.2220	−0.657004
$406$	0.0155378	0.000771129 0
$407$	8.05597	0.399320
$408$	−0.0770476	−0.00381443
$409$	−4.05369	−0.200442	−0.100221	−	0.994965i	$-0.531955\pi$
$409$	−4.05369	−0.200442	−0.100221	+	0.994965i	$0.531955\pi$
$410$	−0.00333254	−0.000164583 0
$411$	−10.2653	−0.506351
$412$	−34.8199	−1.71545
$413$	24.9494	1.22768
$414$	−0.0487718	−0.00239700
$415$	−8.23223	−0.404104
$416$	0.172732	0.00846887
$417$	−24.6021	−1.20477
$418$	0.0103813	0.000507766 0
$419$	1.60775	0.0785438	0.0392719	−	0.999229i	$-0.487496\pi$
$419$	1.60775	0.0785438	0.0392719	+	0.999229i	$0.487496\pi$
$420$	−30.7110	−1.49854
$421$	32.0824	1.56360	0.781801	−	0.623528i	$-0.214301\pi$
$421$	32.0824	1.56360	0.781801	+	0.623528i	$0.214301\pi$
$422$	0.00320738	0.000156133 0
$423$	24.2654	1.17982
$424$	−0.0221517	−0.00107578
$425$	−9.63304	−0.467271
$426$	0.0850255	0.00411950
$427$	−35.9539	−1.73993
$428$	−21.4044	−1.03462
$429$	−14.9938	−0.723906
$430$	0.0250427	0.00120767
$431$	1.95025	0.0939404	0.0469702	−	0.998896i	$-0.485043\pi$
$431$	1.95025	0.0939404	0.0469702	+	0.998896i	$0.485043\pi$
$432$	−0.201161	−0.00967836
$433$	−14.0167	−0.673600	−0.336800	−	0.941576i	$-0.609345\pi$
$433$	−14.0167	−0.673600	−0.336800	+	0.941576i	$0.609345\pi$
$434$	−0.0259283	−0.00124460
$435$	5.48764	0.263112
$436$	31.3539	1.50158
$437$	30.8364	1.47510
$438$	0.00178518	8.52992e−5 0
$439$	1.00431	0.0479330	0.0239665	−	0.999713i	$-0.492370\pi$
$439$	1.00431	0.0479330	0.0239665	+	0.999713i	$0.492370\pi$
$440$	0.0137018	0.000653208 0
$441$	34.3253	1.63454
$442$	0.0483004	0.00229741
$443$	29.6935	1.41078	0.705391	−	0.708818i	$-0.250771\pi$
$443$	29.6935	1.41078	0.705391	+	0.708818i	$0.250771\pi$
$444$	39.3982	1.86976
$445$	21.2926	1.00936
$446$	−0.0288265	−0.00136497
$447$	−11.1025	−0.525131
$448$	−34.4280	−1.62657
$449$	−28.3906	−1.33984	−0.669918	−	0.742435i	$-0.733671\pi$
$449$	−28.3906	−1.33984	−0.669918	+	0.742435i	$0.733671\pi$
$450$	−0.0200794	−0.000946553 0
$451$	0.972876	0.0458109
$452$	9.03644	0.425038
$453$	−23.1526	−1.08780
$454$	−0.0152204	−0.000714329 0
$455$	38.5049	1.80514
$456$	0.101541	0.00475509
$457$	−22.4467	−1.05001	−0.525007	−	0.851098i	$-0.675937\pi$
$457$	−22.4467	−1.05001	−0.525007	+	0.851098i	$0.675937\pi$
$458$	−0.0324740	−0.00151741
$459$	−0.168751	−0.00787660
$460$	20.3497	0.948811
$461$	−10.0935	−0.470102	−0.235051	−	0.971983i	$-0.575526\pi$
$461$	−10.0935	−0.470102	−0.235051	+	0.971983i	$0.575526\pi$
$462$	−0.0247042	−0.00114934
$463$	32.3790	1.50478	0.752390	−	0.658717i	$-0.228901\pi$
$463$	32.3790	1.50478	0.752390	+	0.658717i	$0.228901\pi$
$464$	6.15185	0.285592
$465$	−9.15734	−0.424662
$466$	0.0532746	0.00246790
$467$	−9.36072	−0.433162	−0.216581	−	0.976265i	$-0.569491\pi$
$467$	−9.36072	−0.433162	−0.216581	+	0.976265i	$0.569491\pi$
$468$	−36.5379	−1.68896
$469$	−30.5076	−1.40871
$470$	0.0278979	0.00128683
$471$	−8.21481	−0.378518
$472$	−0.0544381	−0.00250571
$473$	−7.31076	−0.336149
$474$	0.00862188	0.000396016 0
$475$	12.6954	0.582504
$476$	−28.8812	−1.32377
$477$	7.02861	0.321818
$478$	−0.00171780	−7.85705e−5 0
$479$	−14.3168	−0.654151	−0.327075	−	0.944998i	$-0.606063\pi$
$479$	−14.3168	−0.654151	−0.327075	+	0.944998i	$0.606063\pi$
$480$	0.100514	0.00458783
$481$	−49.3968	−2.25230
$482$	0.0127607	0.000581235 0
$483$	−73.3808	−3.33894
$484$	−1.99999	−0.0909088
$485$	−10.0933	−0.458312
$486$	−0.0516611	−0.00234340
$487$	15.1448	0.686277	0.343139	−	0.939285i	$-0.388510\pi$
$487$	15.1448	0.686277	0.343139	+	0.939285i	$0.388510\pi$
$488$	0.0784490	0.00355122
$489$	54.2494	2.45324
$490$	0.0394638	0.00178279
$491$	13.9595	0.629981	0.314991	−	0.949095i	$-0.397999\pi$
$491$	13.9595	0.629981	0.314991	+	0.949095i	$0.397999\pi$
$492$	4.75791	0.214503
$493$	5.16068	0.232425
$494$	−0.0636550	−0.00286397
$495$	−4.34751	−0.195406
$496$	−10.2657	−0.460944
$497$	63.7436	2.85929
$498$	−0.0323857	−0.00145124
$499$	−24.3215	−1.08878	−0.544390	−	0.838833i	$-0.683239\pi$
$499$	−24.3215	−1.08878	−0.544390	+	0.838833i	$0.683239\pi$
$500$	22.9697	1.02724
$501$	−37.7749	−1.68766
$502$	0.0111125	0.000495976 0
$503$	25.4355	1.13411	0.567056	−	0.823679i	$-0.308082\pi$
$503$	25.4355	1.13411	0.567056	+	0.823679i	$0.308082\pi$
$504$	−0.120402	−0.00536314
$505$	−16.6005	−0.738711
$506$	0.0163695	0.000727713 0
$507$	60.1485	2.67129
$508$	36.6243	1.62494
$509$	6.33181	0.280653	0.140326	−	0.990105i	$-0.455185\pi$
$509$	6.33181	0.280653	0.140326	+	0.990105i	$0.455185\pi$
$510$	0.0281065	0.00124458
$511$	1.33835	0.0592051
$512$	0.187801	0.00829969
$513$	0.222396	0.00981903
$514$	−0.00906854	−0.000399996 0
$515$	25.4042	1.11944
$516$	−35.7537	−1.57397
$517$	−8.14429	−0.358185
$518$	−0.0813877	−0.00357597
$519$	56.4926	2.47975
$520$	−0.0840153	−0.00368432
$521$	41.1421	1.80247	0.901233	−	0.433334i	$-0.142663\pi$
$521$	41.1421	1.80247	0.901233	+	0.433334i	$0.142663\pi$
$522$	0.0107571	0.000470825 0
$523$	−8.72023	−0.381309	−0.190655	−	0.981657i	$-0.561061\pi$
$523$	−8.72023	−0.381309	−0.190655	+	0.981657i	$0.561061\pi$
$524$	−1.99999	−0.0873702
$525$	−30.2110	−1.31851
$526$	−0.0364861	−0.00159087
$527$	−8.61174	−0.375133
$528$	−9.78107	−0.425666
$529$	25.6235	1.11407
$530$	0.00808080	0.000351007 0
$531$	17.2729	0.749580
$532$	38.0625	1.65022
$533$	−5.96538	−0.258389
$534$	0.0837652	0.00362487
$535$	15.6164	0.675157
$536$	0.0665658	0.00287520
$537$	−34.2440	−1.47774
$538$	−0.0412507	−0.00177844
$539$	−11.5207	−0.496233
$540$	0.146765	0.00631576
$541$	−8.81265	−0.378885	−0.189443	−	0.981892i	$-0.560668\pi$
$541$	−8.81265	−0.378885	−0.189443	+	0.981892i	$0.560668\pi$
$542$	0.0295191	0.00126796
$543$	−7.83956	−0.336428
$544$	0.0945256	0.00405275
$545$	−22.8754	−0.979875
$546$	0.151479	0.00648269
$547$	3.14593	0.134510	0.0672552	−	0.997736i	$-0.478576\pi$
$547$	3.14593	0.134510	0.0672552	+	0.997736i	$0.478576\pi$
$548$	8.39597	0.358658
$549$	−24.8914	−1.06234
$550$	0.00673934	0.000287366 0
$551$	−6.80125	−0.289743
$552$	0.160112	0.00681483
$553$	6.46382	0.274870
$554$	0.00214689	9.12127e−5 0
$555$	−28.7445	−1.22014
$556$	20.1220	0.853362
$557$	−17.8404	−0.755921	−0.377961	−	0.925822i	$-0.623375\pi$
$557$	−17.8404	−0.755921	−0.377961	+	0.925822i	$0.623375\pi$
$558$	−0.0179506	−0.000759909 0
$559$	44.8274	1.89600
$560$	25.1184	1.06145
$561$	−8.20518	−0.346423
$562$	−0.0638356	−0.00269274
$563$	−27.3625	−1.15319	−0.576595	−	0.817030i	$-0.695619\pi$
$563$	−27.3625	−1.15319	−0.576595	+	0.817030i	$0.695619\pi$
$564$	−39.8302	−1.67715
$565$	−6.59288	−0.277364
$566$	0.0781935	0.00328672
$567$	−38.9959	−1.63767
$568$	−0.139084	−0.00583585
$569$	−41.2050	−1.72740	−0.863701	−	0.504004i	$-0.831859\pi$
$569$	−41.2050	−1.72740	−0.863701	+	0.504004i	$0.831859\pi$
$570$	−0.0370415	−0.00155150
$571$	1.55356	0.0650146	0.0325073	−	0.999471i	$-0.489651\pi$
$571$	1.55356	0.0650146	0.0325073	+	0.999471i	$0.489651\pi$
$572$	12.2634	0.512757
$573$	−10.9642	−0.458034
$574$	−0.00982875	−0.000410244 0
$575$	20.0184	0.834824
$576$	−23.8351	−0.993128
$577$	−29.5989	−1.23222	−0.616108	−	0.787661i	$-0.711292\pi$
$577$	−29.5989	−1.23222	−0.616108	+	0.787661i	$0.711292\pi$
$578$	−0.0134762	−0.000560537 0
$579$	12.2798	0.510330
$580$	−4.48833	−0.186368
$581$	−24.2795	−1.00728
$582$	−0.0397071	−0.00164591
$583$	−2.35904	−0.0977016
$584$	−0.00292019	−0.000120838 0
$585$	26.6576	1.10216
$586$	0.0227397	0.000939369 0
$587$	41.9776	1.73260	0.866300	−	0.499524i	$-0.166492\pi$
$587$	41.9776	1.73260	0.866300	+	0.499524i	$0.166492\pi$
$588$	−56.3429	−2.32354
$589$	11.3494	0.467644
$590$	0.0198586	0.000817568 0
$591$	−5.47138	−0.225063
$592$	−32.2236	−1.32438
$593$	11.0583	0.454111	0.227055	−	0.973882i	$-0.427090\pi$
$593$	11.0583	0.454111	0.227055	+	0.973882i	$0.427090\pi$
$594$	0.000118059 0	4.84402e−6 0
$595$	21.0714	0.863843
$596$	9.08071	0.371961
$597$	−27.5133	−1.12604
$598$	−0.100373	−0.00410455
$599$	−19.1667	−0.783132	−0.391566	−	0.920150i	$-0.628066\pi$
$599$	−19.1667	−0.783132	−0.391566	+	0.920150i	$0.628066\pi$
$600$	0.0659184	0.00269111
$601$	−6.05541	−0.247005	−0.123503	−	0.992344i	$-0.539413\pi$
$601$	−6.05541	−0.247005	−0.123503	+	0.992344i	$0.539413\pi$
$602$	0.0738590	0.00301027
$603$	−21.1209	−0.860111
$604$	18.9364	0.770513
$605$	1.45917	0.0593238
$606$	−0.0653064	−0.00265289
$607$	0.184430	0.00748578	0.00374289	−	0.999993i	$-0.498809\pi$
$607$	0.184430	0.00748578	0.00374289	+	0.999993i	$0.498809\pi$
$608$	−0.124575	−0.00505219
$609$	16.1848	0.655843
$610$	−0.0286177	−0.00115870
$611$	49.9383	2.02029
$612$	−19.9950	−0.808248
$613$	1.27623	0.0515463	0.0257731	−	0.999668i	$-0.491795\pi$
$613$	1.27623	0.0515463	0.0257731	+	0.999668i	$0.491795\pi$
$614$	0.0729036	0.00294215
$615$	−3.47131	−0.139977
$616$	0.0404111	0.00162821
$617$	19.4880	0.784559	0.392280	−	0.919846i	$-0.371687\pi$
$617$	19.4880	0.784559	0.392280	+	0.919846i	$0.371687\pi$
$618$	0.0999403	0.00402019
$619$	−7.60882	−0.305824	−0.152912	−	0.988240i	$-0.548865\pi$
$619$	−7.60882	−0.305824	−0.152912	+	0.988240i	$0.548865\pi$
$620$	7.48977	0.300796
$621$	0.350680	0.0140723
$622$	0.0691233	0.00277159
$623$	62.7987	2.51598
$624$	59.9746	2.40090
$625$	−2.40432	−0.0961727
$626$	−0.0583127	−0.00233064
$627$	10.8136	0.431853
$628$	6.71887	0.268112
$629$	−27.0319	−1.07783
$630$	0.0439219	0.00174989
$631$	−31.9087	−1.27026	−0.635132	−	0.772404i	$-0.719054\pi$
$631$	−31.9087	−1.27026	−0.635132	+	0.772404i	$0.719054\pi$
$632$	−0.0141036	−0.000561013 0
$633$	3.34094	0.132791
$634$	0.0514177	0.00204206
$635$	−26.7206	−1.06038
$636$	−11.5370	−0.457474
$637$	70.6417	2.79892
$638$	−0.00361045	−0.000142939 0
$639$	44.1307	1.74578
$640$	−0.109614	−0.00433287
$641$	−23.8038	−0.940193	−0.470096	−	0.882615i	$-0.655781\pi$
$641$	−23.8038	−0.940193	−0.470096	+	0.882615i	$0.655781\pi$
$642$	0.0614351	0.00242465
$643$	24.3152	0.958897	0.479448	−	0.877570i	$-0.340837\pi$
$643$	24.3152	0.958897	0.479448	+	0.877570i	$0.340837\pi$
$644$	60.0180	2.36504
$645$	26.0855	1.02712
$646$	−0.0348345	−0.00137055
$647$	−7.48331	−0.294199	−0.147100	−	0.989122i	$-0.546994\pi$
$647$	−7.48331	−0.294199	−0.147100	+	0.989122i	$0.546994\pi$
$648$	0.0850865	0.00334251
$649$	−5.79738	−0.227567
$650$	−0.0413236	−0.00162085
$651$	−27.0080	−1.05853
$652$	−44.3705	−1.73768
$653$	47.7287	1.86777	0.933885	−	0.357573i	$-0.116396\pi$
$653$	47.7287	1.86777	0.933885	+	0.357573i	$0.116396\pi$
$654$	−0.0899921	−0.00351897
$655$	1.45917	0.0570146
$656$	−3.89147	−0.151936
$657$	0.926561	0.0361486
$658$	0.0822800	0.00320761
$659$	38.1123	1.48465	0.742323	−	0.670042i	$-0.233724\pi$
$659$	38.1123	1.48465	0.742323	+	0.670042i	$0.233724\pi$
$660$	7.13617	0.277775
$661$	−32.6183	−1.26870	−0.634352	−	0.773044i	$-0.718733\pi$
$661$	−32.6183	−1.26870	−0.634352	+	0.773044i	$0.718733\pi$
$662$	−0.0657694	−0.00255620
$663$	50.3117	1.95394
$664$	0.0529764	0.00205588
$665$	−27.7700	−1.07687
$666$	−0.0563461	−0.00218337
$667$	−10.7244	−0.415250
$668$	30.8960	1.19540
$669$	−30.0269	−1.16091
$670$	−0.0242828	−0.000938125 0
$671$	8.35442	0.322519
$672$	0.296449	0.0114358
$673$	21.7239	0.837395	0.418697	−	0.908126i	$-0.362487\pi$
$673$	21.7239	0.837395	0.418697	+	0.908126i	$0.362487\pi$
$674$	0.00388200	0.000149529 0
$675$	0.144375	0.00555701
$676$	−49.1953	−1.89213
$677$	−8.18190	−0.314456	−0.157228	−	0.987562i	$-0.550256\pi$
$677$	−8.18190	−0.314456	−0.157228	+	0.987562i	$0.550256\pi$
$678$	−0.0259364	−0.000996083 0
$679$	−29.7684	−1.14240
$680$	−0.0459765	−0.00176312
$681$	−15.8542	−0.607535
$682$	0.00602483	0.000230703 0
$683$	22.3159	0.853896	0.426948	−	0.904276i	$-0.359589\pi$
$683$	22.3159	0.853896	0.426948	+	0.904276i	$0.359589\pi$
$684$	26.3513	1.00757
$685$	−6.12560	−0.234047
$686$	0.0456720	0.00174376
$687$	−33.8263	−1.29055
$688$	29.2428	1.11487
$689$	14.4649	0.551070
$690$	−0.0584079	−0.00222355
$691$	42.3853	1.61241	0.806207	−	0.591634i	$-0.201517\pi$
$691$	42.3853	1.61241	0.806207	+	0.591634i	$0.201517\pi$
$692$	−46.2051	−1.75645
$693$	−12.8222	−0.487075
$694$	−0.0548579	−0.00208238
$695$	−14.6807	−0.556873
$696$	−0.0353143	−0.00133858
$697$	−3.26449	−0.123651
$698$	−0.0510759	−0.00193325
$699$	55.4930	2.09894
$700$	24.7095	0.933930
$701$	12.5527	0.474107	0.237054	−	0.971497i	$-0.423818\pi$
$701$	12.5527	0.474107	0.237054	+	0.971497i	$0.423818\pi$
$702$	−0.000723902 0	−2.73219e−5 0
$703$	35.6252	1.34363
$704$	7.99987	0.301506
$705$	29.0596	1.09445
$706$	−0.0114951	−0.000432623 0
$707$	−48.9602	−1.84134
$708$	−28.3524	−1.06555
$709$	12.7941	0.480492	0.240246	−	0.970712i	$-0.422772\pi$
$709$	12.7941	0.480492	0.240246	+	0.970712i	$0.422772\pi$
$710$	0.0507371	0.00190413
$711$	4.47501	0.167826
$712$	−0.137023	−0.00513515
$713$	17.8960	0.670211
$714$	0.0828951	0.00310227
$715$	−8.94720	−0.334606
$716$	28.0081	1.04671
$717$	−1.78933	−0.0668239
$718$	0.0433652	0.00161837
$719$	25.5031	0.951104	0.475552	−	0.879688i	$-0.342248\pi$
$719$	25.5031	0.951104	0.475552	+	0.879688i	$0.342248\pi$
$720$	17.3899	0.648083
$721$	74.9252	2.79036
$722$	0.00130518	4.85739e−5 0
$723$	13.2921	0.494339
$724$	6.41196	0.238298
$725$	−4.41524	−0.163978
$726$	0.00574040	0.000213046 0
$727$	47.1654	1.74927	0.874634	−	0.484785i	$-0.161102\pi$
$727$	47.1654	1.74927	0.874634	+	0.484785i	$0.161102\pi$
$728$	−0.247788	−0.00918365
$729$	−26.6285	−0.986242
$730$	0.00106527	3.94273e−5 0
$731$	24.5313	0.907323
$732$	40.8578	1.51015
$733$	−1.29492	−0.0478288	−0.0239144	−	0.999714i	$-0.507613\pi$
$733$	−1.29492	−0.0478288	−0.0239144	+	0.999714i	$0.507613\pi$
$734$	0.0114017	0.000420843 0
$735$	41.1071	1.51626
$736$	−0.196433	−0.00724062
$737$	7.08891	0.261123
$738$	−0.00680460	−0.000250481 0
$739$	−5.76231	−0.211970	−0.105985	−	0.994368i	$-0.533800\pi$
$739$	−5.76231	−0.211970	−0.105985	+	0.994368i	$0.533800\pi$
$740$	23.5100	0.864246
$741$	−66.3057	−2.43580
$742$	0.0238329	0.000874933 0
$743$	−8.20380	−0.300968	−0.150484	−	0.988612i	$-0.548083\pi$
$743$	−8.20380	−0.300968	−0.150484	+	0.988612i	$0.548083\pi$
$744$	0.0589297	0.00216047
$745$	−6.62518	−0.242728
$746$	−0.0737031	−0.00269846
$747$	−16.8091	−0.615014
$748$	6.71099	0.245378
$749$	46.0579	1.68292
$750$	−0.0659277	−0.00240734
$751$	−10.2739	−0.374899	−0.187449	−	0.982274i	$-0.560022\pi$
$751$	−10.2739	−0.374899	−0.187449	+	0.982274i	$0.560022\pi$
$752$	32.5769	1.18796
$753$	11.5753	0.421826
$754$	0.0221382	0.000806225 0
$755$	−13.8158	−0.502808
$756$	0.432858	0.0157429
$757$	7.65614	0.278267	0.139134	−	0.990274i	$-0.455568\pi$
$757$	7.65614	0.278267	0.139134	+	0.990274i	$0.455568\pi$
$758$	−0.0713529	−0.00259165
$759$	17.0511	0.618917
$760$	0.0605923	0.00219791
$761$	−15.3878	−0.557806	−0.278903	−	0.960319i	$-0.589971\pi$
$761$	−15.3878	−0.557806	−0.278903	+	0.960319i	$0.589971\pi$
$762$	−0.105119	−0.00380807
$763$	−67.4670	−2.44247
$764$	8.96755	0.324435
$765$	14.5881	0.527433
$766$	0.0605521	0.00218784
$767$	35.5478	1.28356
$768$	39.1235	1.41175
$769$	−14.2477	−0.513785	−0.256892	−	0.966440i	$-0.582699\pi$
$769$	−14.2477	−0.513785	−0.256892	+	0.966440i	$0.582699\pi$
$770$	−0.0147417	−0.000531254 0
$771$	−9.44617	−0.340195
$772$	−10.0436	−0.361477
$773$	45.8783	1.65013	0.825064	−	0.565040i	$-0.191139\pi$
$773$	45.8783	1.65013	0.825064	+	0.565040i	$0.191139\pi$
$774$	0.0511338	0.00183797
$775$	7.36781	0.264660
$776$	0.0649527	0.00233167
$777$	−84.7768	−3.04135
$778$	−0.0775178	−0.00277915
$779$	4.30226	0.154145
$780$	−43.7568	−1.56675
$781$	−14.8118	−0.530007
$782$	−0.0549279	−0.00196422
$783$	−0.0773458	−0.00276411
$784$	46.0826	1.64581
$785$	−4.90201	−0.174960
$786$	0.00574040	0.000204753 0
$787$	−9.32611	−0.332440	−0.166220	−	0.986089i	$-0.553156\pi$
$787$	−9.32611	−0.332440	−0.166220	+	0.986089i	$0.553156\pi$
$788$	4.47503	0.159416
$789$	−38.0054	−1.35303
$790$	0.00514492	0.000183048 0
$791$	−19.4445	−0.691368
$792$	0.0279772	0.000994128 0
$793$	−51.2268	−1.81912
$794$	0.0297631	0.00105625
$795$	8.41729	0.298531
$796$	22.5031	0.797600
$797$	32.4703	1.15016	0.575079	−	0.818098i	$-0.304971\pi$
$797$	32.4703	1.15016	0.575079	+	0.818098i	$0.304971\pi$
$798$	−0.109247	−0.00386731
$799$	27.3282	0.966802
$800$	−0.0808718	−0.00285925
$801$	43.4766	1.53617
$802$	0.0614441	0.00216967
$803$	−0.310986	−0.0109744
$804$	34.6688	1.22267
$805$	−43.7884	−1.54334
$806$	−0.0369424	−0.00130124
$807$	−42.9684	−1.51256
$808$	0.106828	0.00375820
$809$	26.2612	0.923295	0.461647	−	0.887064i	$-0.347259\pi$
$809$	26.2612	0.923295	0.461647	+	0.887064i	$0.347259\pi$
$810$	−0.0310390	−0.00109060
$811$	27.3734	0.961209	0.480605	−	0.876937i	$-0.340417\pi$
$811$	27.3734	0.961209	0.480605	+	0.876937i	$0.340417\pi$
$812$	−13.2375	−0.464546
$813$	30.7484	1.07839
$814$	0.0189117	0.000662854 0
$815$	32.3722	1.13395
$816$	32.8204	1.14895
$817$	−32.3298	−1.13107
$818$	−0.00951618	−0.000332725 0
$819$	78.6219	2.74727
$820$	2.83918	0.0991484
$821$	−14.0706	−0.491068	−0.245534	−	0.969388i	$-0.578963\pi$
$821$	−14.0706	−0.491068	−0.245534	+	0.969388i	$0.578963\pi$
$822$	−0.0240982	−0.000840520 0
$823$	−17.6334	−0.614663	−0.307332	−	0.951602i	$-0.599436\pi$
$823$	−17.6334	−0.614663	−0.307332	+	0.951602i	$0.599436\pi$
$824$	−0.163482	−0.00569517
$825$	7.01998	0.244404
$826$	0.0585696	0.00203790
$827$	−10.3165	−0.358741	−0.179371	−	0.983782i	$-0.557406\pi$
$827$	−10.3165	−0.358741	−0.179371	+	0.983782i	$0.557406\pi$
$828$	41.5514	1.44401
$829$	11.9768	0.415971	0.207986	−	0.978132i	$-0.433309\pi$
$829$	11.9768	0.415971	0.207986	+	0.978132i	$0.433309\pi$
$830$	−0.0193254	−0.000670796 0
$831$	2.23629	0.0775761
$832$	−49.0528	−1.70060
$833$	38.6579	1.33942
$834$	−0.0577542	−0.00199986
$835$	−22.5413	−0.780074
$836$	−8.84440	−0.305890
$837$	0.129069	0.00446126
$838$	0.00377425	0.000130379 0
$839$	9.31499	0.321589	0.160795	−	0.986988i	$-0.448594\pi$
$839$	9.31499	0.321589	0.160795	+	0.986988i	$0.448594\pi$
$840$	−0.144191	−0.00497505
$841$	−26.6346	−0.918436
$842$	0.0753146	0.00259551
$843$	−66.4938	−2.29017
$844$	−2.73255	−0.0940582
$845$	35.8923	1.23473
$846$	0.0569638	0.00195845
$847$	4.30357	0.147872
$848$	9.43609	0.324037
$849$	81.4495	2.79534
$850$	−0.0226139	−0.000775650 0
$851$	56.1748	1.92565
$852$	−72.4380	−2.48168
$853$	54.3958	1.86248	0.931239	−	0.364409i	$-0.118729\pi$
$853$	54.3958	1.86248	0.931239	+	0.364409i	$0.118729\pi$
$854$	−0.0844029	−0.00288821
$855$	−19.2256	−0.657502
$856$	−0.100495	−0.00343486
$857$	51.6524	1.76441	0.882206	−	0.470864i	$-0.156058\pi$
$857$	51.6524	1.76441	0.882206	+	0.470864i	$0.156058\pi$
$858$	−0.0351984	−0.00120165
$859$	7.77320	0.265218	0.132609	−	0.991168i	$-0.457665\pi$
$859$	7.77320	0.265218	0.132609	+	0.991168i	$0.457665\pi$
$860$	−21.3353	−0.727526
$861$	−10.2380	−0.348911
$862$	0.00457828	0.000155937 0
$863$	5.03978	0.171556	0.0857781	−	0.996314i	$-0.472662\pi$
$863$	5.03978	0.171556	0.0857781	+	0.996314i	$0.472662\pi$
$864$	−0.00141670	−4.81972e−5 0
$865$	33.7107	1.14620
$866$	−0.0329047	−0.00111815
$867$	−14.0374	−0.476735
$868$	22.0898	0.749775
$869$	−1.50197	−0.0509507
$870$	0.0128824	0.000436755 0
$871$	−43.4671	−1.47283
$872$	0.147209	0.00498512
$873$	−20.6091	−0.697513
$874$	0.0723894	0.00244861
$875$	−49.4260	−1.67090
$876$	−1.52089	−0.0513863
$877$	−50.6572	−1.71057	−0.855287	−	0.518155i	$-0.826619\pi$
$877$	−50.6572	−1.71057	−0.855287	+	0.518155i	$0.826619\pi$
$878$	0.00235765	7.95667e−5 0
$879$	23.6866	0.798930
$880$	−5.83664	−0.196753
$881$	−24.6444	−0.830291	−0.415145	−	0.909755i	$-0.636269\pi$
$881$	−24.6444	−0.830291	−0.415145	+	0.909755i	$0.636269\pi$
$882$	0.0805797	0.00271326
$883$	−28.4054	−0.955918	−0.477959	−	0.878382i	$-0.658623\pi$
$883$	−28.4054	−0.955918	−0.477959	+	0.878382i	$0.658623\pi$
$884$	−41.1498	−1.38402
$885$	20.6856	0.695338
$886$	0.0697066	0.00234184
$887$	−45.2378	−1.51894	−0.759469	−	0.650543i	$-0.774541\pi$
$887$	−45.2378	−1.51894	−0.759469	+	0.650543i	$0.774541\pi$
$888$	0.184978	0.00620744
$889$	−78.8078	−2.64313
$890$	0.0499850	0.00167550
$891$	9.06128	0.303564
$892$	24.5589	0.822293
$893$	−36.0158	−1.20522
$894$	−0.0260635	−0.000871695 0
$895$	−20.4343	−0.683045
$896$	−0.323287	−0.0108003
$897$	−104.552	−3.49090
$898$	−0.0666479	−0.00222407
$899$	−3.94714	−0.131644
$900$	17.1068	0.570226
$901$	7.91578	0.263713
$902$	0.00228386	7.60442e−5 0
$903$	76.9346	2.56022
$904$	0.0424268	0.00141109
$905$	−4.67809	−0.155505
$906$	−0.0543515	−0.00180571
$907$	−10.1761	−0.337890	−0.168945	−	0.985625i	$-0.554036\pi$
$907$	−10.1761	−0.337890	−0.168945	+	0.985625i	$0.554036\pi$
$908$	12.9671	0.430329
$909$	−33.8959	−1.12426
$910$	0.0903916	0.00299645
$911$	20.9273	0.693354	0.346677	−	0.937985i	$-0.387310\pi$
$911$	20.9273	0.693354	0.346677	+	0.937985i	$0.387310\pi$
$912$	−43.2540	−1.43228
$913$	5.64172	0.186714
$914$	−0.0526945	−0.00174298
$915$	−29.8094	−0.985467
$916$	27.6664	0.914125
$917$	4.30357	0.142116
$918$	−0.000396148 0	−1.30748e−5 0
$919$	33.6605	1.11036	0.555179	−	0.831731i	$-0.312650\pi$
$919$	33.6605	1.11036	0.555179	+	0.831731i	$0.312650\pi$
$920$	0.0955435	0.00314997
$921$	75.9394	2.50229
$922$	−0.0236949	−0.000780349 0
$923$	90.8214	2.98942
$924$	21.0469	0.692392
$925$	23.1272	0.760419
$926$	0.0760109	0.00249787
$927$	51.8719	1.70370
$928$	0.0433252	0.00142222
$929$	53.4294	1.75296	0.876480	−	0.481438i	$-0.159885\pi$
$929$	53.4294	1.75296	0.876480	+	0.481438i	$0.159885\pi$
$930$	−0.0214972	−0.000704920 0
$931$	−50.9472	−1.66973
$932$	−45.3876	−1.48672
$933$	72.0017	2.35723
$934$	−0.0219746	−0.000719031 0
$935$	−4.89626	−0.160125
$936$	−0.171548	−0.00560722
$937$	44.3075	1.44746	0.723731	−	0.690082i	$-0.242426\pi$
$937$	44.3075	1.44746	0.723731	+	0.690082i	$0.242426\pi$
$938$	−0.0716177	−0.00233840
$939$	−60.7409	−1.98221
$940$	−23.7678	−0.775219
$941$	−48.7901	−1.59051	−0.795257	−	0.606273i	$-0.792664\pi$
$941$	−48.7901	−1.59051	−0.795257	+	0.606273i	$0.792664\pi$
$942$	−0.0192845	−0.000628324 0
$943$	6.78392	0.220915
$944$	23.1893	0.754748
$945$	−0.315808	−0.0102732
$946$	−0.0171623	−0.000557993 0
$947$	−20.4876	−0.665758	−0.332879	−	0.942970i	$-0.608020\pi$
$947$	−20.4876	−0.665758	−0.332879	+	0.942970i	$0.608020\pi$
$948$	−7.34546	−0.238569
$949$	1.90687	0.0618996
$950$	0.0298028	0.000966931 0
$951$	53.5588	1.73676
$952$	−0.135600	−0.00439481
$953$	18.5289	0.600210	0.300105	−	0.953906i	$-0.402978\pi$
$953$	18.5289	0.600210	0.300105	+	0.953906i	$0.402978\pi$
$954$	0.0164999	0.000534204 0
$955$	−6.54262	−0.211714
$956$	1.46349	0.0473327
$957$	−3.76079	−0.121569
$958$	−0.0336092	−0.00108586
$959$	−18.0664	−0.583394
$960$	−28.5443	−0.921263
$961$	−24.4133	−0.787527
$962$	−0.115961	−0.00373872
$963$	31.8866	1.02753
$964$	−10.8716	−0.350150
$965$	7.32768	0.235886
$966$	−0.172264	−0.00554250
$967$	−18.2392	−0.586533	−0.293267	−	0.956031i	$-0.594742\pi$
$967$	−18.2392	−0.586533	−0.293267	+	0.956031i	$0.594742\pi$
$968$	−0.00939012	−0.000301810 0
$969$	−36.2851	−1.16564
$970$	−0.0236943	−0.000760779 0
$971$	10.2243	0.328112	0.164056	−	0.986451i	$-0.447542\pi$
$971$	10.2243	0.328112	0.164056	+	0.986451i	$0.447542\pi$
$972$	44.0130	1.41172
$973$	−43.2983	−1.38808
$974$	0.0355530	0.00113919
$975$	−43.0444	−1.37852
$976$	−33.4174	−1.06967
$977$	56.1087	1.79508	0.897538	−	0.440937i	$-0.145354\pi$
$977$	56.1087	1.79508	0.897538	+	0.440937i	$0.145354\pi$
$978$	0.127352	0.00407228
$979$	−14.5922	−0.466370
$980$	−33.6214	−1.07400
$981$	−46.7085	−1.49129
$982$	0.0327703	0.00104574
$983$	3.26445	0.104120	0.0520600	−	0.998644i	$-0.483421\pi$
$983$	3.26445	0.104120	0.0520600	+	0.998644i	$0.483421\pi$
$984$	0.0223387	0.000712133 0
$985$	−3.26493	−0.104029
$986$	0.0121149	0.000385816 0
$987$	85.7062	2.72806
$988$	54.2312	1.72532
$989$	−50.9784	−1.62102
$990$	−0.0102059	−0.000324365 0
$991$	−0.738867	−0.0234709	−0.0117354	−	0.999931i	$-0.503736\pi$
$991$	−0.738867	−0.0234709	−0.0117354	+	0.999931i	$0.503736\pi$
$992$	−0.0722977	−0.00229545
$993$	−68.5082	−2.17404
$994$	0.149640	0.00474630
$995$	−16.4180	−0.520484
$996$	27.5912	0.874260
$997$	56.7682	1.79787	0.898933	−	0.438086i	$-0.144343\pi$
$997$	56.7682	1.79787	0.898933	+	0.438086i	$0.144343\pi$
$998$	−0.0570955	−0.00180733
$999$	0.405140	0.0128181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1441.2.a.f.1.15	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1441.2.a.f.1.15	✓	31	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:	\( N \)	\(=\)	\( 1441 = 11 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1441.a (trivial)

\(f(q)\)	\(=\)	\(q+0.00234753 q^{2} +2.44529 q^{3} -1.99999 q^{4} +1.45917 q^{5} +0.00574040 q^{6} +4.30357 q^{7} -0.00939012 q^{8} +2.97943 q^{9} +O(q^{10})\)	\(q+0.00234753 q^{2} +2.44529 q^{3} -1.99999 q^{4} +1.45917 q^{5} +0.00574040 q^{6} +4.30357 q^{7} -0.00939012 q^{8} +2.97943 q^{9} +0.00342546 q^{10} -1.00000 q^{11} -4.89056 q^{12} +6.13170 q^{13} +0.0101028 q^{14} +3.56810 q^{15} +3.99997 q^{16} +3.35551 q^{17} +0.00699432 q^{18} -4.42221 q^{19} -2.91834 q^{20} +10.5235 q^{21} -0.00234753 q^{22} -6.97306 q^{23} -0.0229616 q^{24} -2.87082 q^{25} +0.0143944 q^{26} -0.0502907 q^{27} -8.60712 q^{28} +1.53797 q^{29} +0.00837622 q^{30} -2.56645 q^{31} +0.0281703 q^{32} -2.44529 q^{33} +0.00787716 q^{34} +6.27965 q^{35} -5.95885 q^{36} -8.05597 q^{37} -0.0103813 q^{38} +14.9938 q^{39} -0.0137018 q^{40} -0.972876 q^{41} +0.0247042 q^{42} +7.31076 q^{43} +1.99999 q^{44} +4.34751 q^{45} -0.0163695 q^{46} +8.14429 q^{47} +9.78107 q^{48} +11.5207 q^{49} -0.00673934 q^{50} +8.20518 q^{51} -12.2634 q^{52} +2.35904 q^{53} -0.000118059 q^{54} -1.45917 q^{55} -0.0404111 q^{56} -10.8136 q^{57} +0.00361045 q^{58} +5.79738 q^{59} -7.13617 q^{60} -8.35442 q^{61} -0.00602483 q^{62} +12.8222 q^{63} -7.99987 q^{64} +8.94720 q^{65} -0.00574040 q^{66} -7.08891 q^{67} -6.71099 q^{68} -17.0511 q^{69} +0.0147417 q^{70} +14.8118 q^{71} -0.0279772 q^{72} +0.310986 q^{73} -0.0189117 q^{74} -7.01998 q^{75} +8.84440 q^{76} -4.30357 q^{77} +0.0351984 q^{78} +1.50197 q^{79} +5.83664 q^{80} -9.06128 q^{81} -0.00228386 q^{82} -5.64172 q^{83} -21.0469 q^{84} +4.89626 q^{85} +0.0171623 q^{86} +3.76079 q^{87} +0.00939012 q^{88} +14.5922 q^{89} +0.0102059 q^{90} +26.3882 q^{91} +13.9461 q^{92} -6.27571 q^{93} +0.0191190 q^{94} -6.45277 q^{95} +0.0688845 q^{96} -6.91713 q^{97} +0.0270453 q^{98} -2.97943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9	\( 31 q + 6 q^{2} + 4 q^{3} + 38 q^{4} + 8 q^{5} + 7 q^{6} + 4 q^{7} + 24 q^{8} + 45 q^{9} - 8 q^{10} - 31 q^{11} + 10 q^{12} - 8 q^{13} + 29 q^{14} + 36 q^{15} + 52 q^{16} - q^{17} + 33 q^{18} - 2 q^{19} + 22 q^{20} - 13 q^{21} - 6 q^{22} + 45 q^{23} + 16 q^{24} + 41 q^{25} + 24 q^{26} + 22 q^{27} + 17 q^{28} + 5 q^{29} + 29 q^{30} + 28 q^{31} + 69 q^{32} - 4 q^{33} + 14 q^{34} + 36 q^{35} + 63 q^{36} - 3 q^{37} + 4 q^{38} + 40 q^{39} - 48 q^{40} + 21 q^{41} - 9 q^{42} - 20 q^{43} - 38 q^{44} + 28 q^{45} - 24 q^{46} + 57 q^{47} - 46 q^{48} + 37 q^{49} + 64 q^{50} + 17 q^{51} - 11 q^{52} + 32 q^{53} - 26 q^{54} - 8 q^{55} + 84 q^{56} + 10 q^{57} - 17 q^{58} + 70 q^{59} - 33 q^{60} - 51 q^{61} - 34 q^{62} + 32 q^{63} + 80 q^{64} - q^{65} - 7 q^{66} + 24 q^{67} - 13 q^{68} + 19 q^{69} - 9 q^{70} + 128 q^{71} + 118 q^{72} - 27 q^{73} - 23 q^{74} + 41 q^{75} - 34 q^{76} - 4 q^{77} + 9 q^{78} + 2 q^{79} - 45 q^{80} + 43 q^{81} - 18 q^{82} + 46 q^{83} - 103 q^{84} - 50 q^{85} + 78 q^{86} - 9 q^{87} - 24 q^{88} + 52 q^{89} - 46 q^{90} + 38 q^{91} + 54 q^{92} + 4 q^{93} + 3 q^{94} + 70 q^{95} - 21 q^{96} + 3 q^{97} - 120 q^{98} - 45 q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 + 4 * q^3 + 38 * q^4 + 8 * q^5 + 7 * q^6 + 4 * q^7 + 24 * q^8 + 45 * q^9 - 8 * q^10 - 31 * q^11 + 10 * q^12 - 8 * q^13 + 29 * q^14 + 36 * q^15 + 52 * q^16 - q^17 + 33 * q^18 - 2 * q^19 + 22 * q^20 - 13 * q^21 - 6 * q^22 + 45 * q^23 + 16 * q^24 + 41 * q^25 + 24 * q^26 + 22 * q^27 + 17 * q^28 + 5 * q^29 + 29 * q^30 + 28 * q^31 + 69 * q^32 - 4 * q^33 + 14 * q^34 + 36 * q^35 + 63 * q^36 - 3 * q^37 + 4 * q^38 + 40 * q^39 - 48 * q^40 + 21 * q^41 - 9 * q^42 - 20 * q^43 - 38 * q^44 + 28 * q^45 - 24 * q^46 + 57 * q^47 - 46 * q^48 + 37 * q^49 + 64 * q^50 + 17 * q^51 - 11 * q^52 + 32 * q^53 - 26 * q^54 - 8 * q^55 + 84 * q^56 + 10 * q^57 - 17 * q^58 + 70 * q^59 - 33 * q^60 - 51 * q^61 - 34 * q^62 + 32 * q^63 + 80 * q^64 - q^65 - 7 * q^66 + 24 * q^67 - 13 * q^68 + 19 * q^69 - 9 * q^70 + 128 * q^71 + 118 * q^72 - 27 * q^73 - 23 * q^74 + 41 * q^75 - 34 * q^76 - 4 * q^77 + 9 * q^78 + 2 * q^79 - 45 * q^80 + 43 * q^81 - 18 * q^82 + 46 * q^83 - 103 * q^84 - 50 * q^85 + 78 * q^86 - 9 * q^87 - 24 * q^88 + 52 * q^89 - 46 * q^90 + 38 * q^91 + 54 * q^92 + 4 * q^93 + 3 * q^94 + 70 * q^95 - 21 * q^96 + 3 * q^97 - 120 * q^98 - 45 * q^99

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