LMFDB - Embedded newform 6025.2.a.m.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.833391 q^{2} -0.371715 q^{3} -1.30546 q^{4} +0.309784 q^{6} +3.36045 q^{7} +2.75474 q^{8} -2.86183 q^{9} +O(q^{10})$	\(q-0.833391 q^{2} -0.371715 q^{3} -1.30546 q^{4} +0.309784 q^{6} +3.36045 q^{7} +2.75474 q^{8} -2.86183 q^{9} +4.22461 q^{11} +0.485258 q^{12} -2.14707 q^{13} -2.80057 q^{14} +0.315140 q^{16} +5.91524 q^{17} +2.38502 q^{18} -1.05248 q^{19} -1.24913 q^{21} -3.52075 q^{22} -1.38872 q^{23} -1.02398 q^{24} +1.78935 q^{26} +2.17893 q^{27} -4.38693 q^{28} -8.76672 q^{29} -4.98104 q^{31} -5.77212 q^{32} -1.57035 q^{33} -4.92971 q^{34} +3.73600 q^{36} -5.08988 q^{37} +0.877131 q^{38} +0.798096 q^{39} -2.30662 q^{41} +1.04101 q^{42} +1.64001 q^{43} -5.51505 q^{44} +1.15735 q^{46} -1.94415 q^{47} -0.117142 q^{48} +4.29263 q^{49} -2.19878 q^{51} +2.80291 q^{52} -6.66307 q^{53} -1.81590 q^{54} +9.25717 q^{56} +0.391224 q^{57} +7.30611 q^{58} +0.478473 q^{59} -7.83890 q^{61} +4.15115 q^{62} -9.61703 q^{63} +4.18015 q^{64} +1.30872 q^{66} -2.44838 q^{67} -7.72210 q^{68} +0.516207 q^{69} +11.2029 q^{71} -7.88360 q^{72} -10.0541 q^{73} +4.24186 q^{74} +1.37397 q^{76} +14.1966 q^{77} -0.665127 q^{78} +1.27929 q^{79} +7.77554 q^{81} +1.92232 q^{82} +7.12327 q^{83} +1.63069 q^{84} -1.36677 q^{86} +3.25872 q^{87} +11.6377 q^{88} +6.89974 q^{89} -7.21511 q^{91} +1.81291 q^{92} +1.85153 q^{93} +1.62024 q^{94} +2.14558 q^{96} +4.38743 q^{97} -3.57744 q^{98} -12.0901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	$ 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) $ 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * 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 $

$2$	−0.833391	−0.589297	−0.294648	−	0.955606i	$-0.595203\pi$
$2$	−0.833391	−0.589297	−0.294648	+	0.955606i	$0.595203\pi$
$3$	−0.371715	−0.214610	−0.107305	−	0.994226i	$-0.534222\pi$
$3$	−0.371715	−0.214610	−0.107305	+	0.994226i	$0.534222\pi$
$4$	−1.30546	−0.652729
$5$	0	0
$5$	0	0
$6$	0.309784	0.126469
$7$	3.36045	1.27013	0.635066	−	0.772458i	$-0.280973\pi$
$7$	3.36045	1.27013	0.635066	+	0.772458i	$0.280973\pi$
$8$	2.75474	0.973948
$9$	−2.86183	−0.953943
$10$	0	0
$11$	4.22461	1.27377	0.636884	−	0.770960i	$-0.280223\pi$
$11$	4.22461	1.27377	0.636884	+	0.770960i	$0.280223\pi$
$12$	0.485258	0.140082
$13$	−2.14707	−0.595489	−0.297744	−	0.954646i	$-0.596234\pi$
$13$	−2.14707	−0.595489	−0.297744	+	0.954646i	$0.596234\pi$
$14$	−2.80057	−0.748484
$15$	0	0
$16$	0.315140	0.0787849
$17$	5.91524	1.43466	0.717328	−	0.696736i	$-0.245365\pi$
$17$	5.91524	1.43466	0.717328	+	0.696736i	$0.245365\pi$
$18$	2.38502	0.562155
$19$	−1.05248	−0.241456	−0.120728	−	0.992686i	$-0.538523\pi$
$19$	−1.05248	−0.241456	−0.120728	+	0.992686i	$0.538523\pi$
$20$	0	0
$21$	−1.24913	−0.272582
$22$	−3.52075	−0.750627
$23$	−1.38872	−0.289568	−0.144784	−	0.989463i	$-0.546249\pi$
$23$	−1.38872	−0.289568	−0.144784	+	0.989463i	$0.546249\pi$
$24$	−1.02398	−0.209019
$25$	0	0
$26$	1.78935	0.350920
$27$	2.17893	0.419335
$28$	−4.38693	−0.829052
$29$	−8.76672	−1.62794	−0.813969	−	0.580908i	$-0.802698\pi$
$29$	−8.76672	−1.62794	−0.813969	+	0.580908i	$0.802698\pi$
$30$	0	0
$31$	−4.98104	−0.894621	−0.447310	−	0.894379i	$-0.647618\pi$
$31$	−4.98104	−0.894621	−0.447310	+	0.894379i	$0.647618\pi$
$32$	−5.77212	−1.02038
$33$	−1.57035	−0.273363
$34$	−4.92971	−0.845438
$35$	0	0
$36$	3.73600	0.622666
$37$	−5.08988	−0.836771	−0.418386	−	0.908270i	$-0.637404\pi$
$37$	−5.08988	−0.836771	−0.418386	+	0.908270i	$0.637404\pi$
$38$	0.877131	0.142289
$39$	0.798096	0.127798
$40$	0	0
$41$	−2.30662	−0.360234	−0.180117	−	0.983645i	$-0.557648\pi$
$41$	−2.30662	−0.360234	−0.180117	+	0.983645i	$0.557648\pi$
$42$	1.04101	0.160632
$43$	1.64001	0.250100	0.125050	−	0.992150i	$-0.460091\pi$
$43$	1.64001	0.250100	0.125050	+	0.992150i	$0.460091\pi$
$44$	−5.51505	−0.831426
$45$	0	0
$46$	1.15735	0.170641
$47$	−1.94415	−0.283583	−0.141792	−	0.989897i	$-0.545286\pi$
$47$	−1.94415	−0.283583	−0.141792	+	0.989897i	$0.545286\pi$
$48$	−0.117142	−0.0169080
$49$	4.29263	0.613233
$50$	0	0
$51$	−2.19878	−0.307891
$52$	2.80291	0.388693
$53$	−6.66307	−0.915242	−0.457621	−	0.889147i	$-0.651298\pi$
$53$	−6.66307	−0.915242	−0.457621	+	0.889147i	$0.651298\pi$
$54$	−1.81590	−0.247113
$55$	0	0
$56$	9.25717	1.23704
$57$	0.391224	0.0518188
$58$	7.30611	0.959339
$59$	0.478473	0.0622919	0.0311460	−	0.999515i	$-0.490084\pi$
$59$	0.478473	0.0622919	0.0311460	+	0.999515i	$0.490084\pi$
$60$	0	0
$61$	−7.83890	−1.00367	−0.501834	−	0.864964i	$-0.667341\pi$
$61$	−7.83890	−1.00367	−0.501834	+	0.864964i	$0.667341\pi$
$62$	4.15115	0.527197
$63$	−9.61703	−1.21163
$64$	4.18015	0.522519
$65$	0	0
$66$	1.30872	0.161092
$67$	−2.44838	−0.299117	−0.149558	−	0.988753i	$-0.547785\pi$
$67$	−2.44838	−0.299117	−0.149558	+	0.988753i	$0.547785\pi$
$68$	−7.72210	−0.936442
$69$	0.516207	0.0621440
$70$	0	0
$71$	11.2029	1.32954	0.664768	−	0.747050i	$-0.268530\pi$
$71$	11.2029	1.32954	0.664768	+	0.747050i	$0.268530\pi$
$72$	−7.88360	−0.929091
$73$	−10.0541	−1.17674	−0.588372	−	0.808590i	$-0.700231\pi$
$73$	−10.0541	−1.17674	−0.588372	+	0.808590i	$0.700231\pi$
$74$	4.24186	0.493107
$75$	0	0
$76$	1.37397	0.157606
$77$	14.1966	1.61785
$78$	−0.665127	−0.0753108
$79$	1.27929	0.143931	0.0719656	−	0.997407i	$-0.477073\pi$
$79$	1.27929	0.143931	0.0719656	+	0.997407i	$0.477073\pi$
$80$	0	0
$81$	7.77554	0.863949
$82$	1.92232	0.212284
$83$	7.12327	0.781880	0.390940	−	0.920416i	$-0.372150\pi$
$83$	7.12327	0.781880	0.390940	+	0.920416i	$0.372150\pi$
$84$	1.63069	0.177923
$85$	0	0
$86$	−1.36677	−0.147383
$87$	3.25872	0.349371
$88$	11.6377	1.24058
$89$	6.89974	0.731371	0.365686	−	0.930738i	$-0.380835\pi$
$89$	6.89974	0.731371	0.365686	+	0.930738i	$0.380835\pi$
$90$	0	0
$91$	−7.21511	−0.756349
$92$	1.81291	0.189009
$93$	1.85153	0.191994
$94$	1.62024	0.167115
$95$	0	0
$96$	2.14558	0.218983
$97$	4.38743	0.445476	0.222738	−	0.974878i	$-0.428501\pi$
$97$	4.38743	0.445476	0.222738	+	0.974878i	$0.428501\pi$
$98$	−3.57744	−0.361376
$99$	−12.0901	−1.21510
$100$	0	0
$101$	−11.8105	−1.17519	−0.587593	−	0.809157i	$-0.699924\pi$
$101$	−11.8105	−1.17519	−0.587593	+	0.809157i	$0.699924\pi$
$102$	1.83245	0.181439
$103$	1.28910	0.127019	0.0635096	−	0.997981i	$-0.479771\pi$
$103$	1.28910	0.127019	0.0635096	+	0.997981i	$0.479771\pi$
$104$	−5.91461	−0.579975
$105$	0	0
$106$	5.55294	0.539349
$107$	−1.80397	−0.174396	−0.0871981	−	0.996191i	$-0.527791\pi$
$107$	−1.80397	−0.174396	−0.0871981	+	0.996191i	$0.527791\pi$
$108$	−2.84450	−0.273712
$109$	15.3587	1.47110	0.735551	−	0.677470i	$-0.236924\pi$
$109$	15.3587	1.47110	0.735551	+	0.677470i	$0.236924\pi$
$110$	0	0
$111$	1.89198	0.179579
$112$	1.05901	0.100067
$113$	−18.0793	−1.70075	−0.850376	−	0.526175i	$-0.823626\pi$
$113$	−18.0793	−1.70075	−0.850376	+	0.526175i	$0.823626\pi$
$114$	−0.326042	−0.0305367
$115$	0	0
$116$	11.4446	1.06260
$117$	6.14453	0.568062
$118$	−0.398756	−0.0367084
$119$	19.8779	1.82220
$120$	0	0
$121$	6.84733	0.622485
$122$	6.53287	0.591459
$123$	0.857405	0.0773096
$124$	6.50254	0.583945
$125$	0	0
$126$	8.01475	0.714011
$127$	−10.3671	−0.919932	−0.459966	−	0.887936i	$-0.652138\pi$
$127$	−10.3671	−0.919932	−0.459966	+	0.887936i	$0.652138\pi$
$128$	8.06053	0.712457
$129$	−0.609618	−0.0536739
$130$	0	0
$131$	−0.0351964	−0.00307512	−0.00153756	−	0.999999i	$-0.500489\pi$
$131$	−0.0351964	−0.00307512	−0.00153756	+	0.999999i	$0.500489\pi$
$132$	2.05003	0.178432
$133$	−3.53682	−0.306681
$134$	2.04046	0.176269
$135$	0	0
$136$	16.2949	1.39728
$137$	−12.1237	−1.03580	−0.517900	−	0.855441i	$-0.673286\pi$
$137$	−12.1237	−1.03580	−0.517900	+	0.855441i	$0.673286\pi$
$138$	−0.430203	−0.0366213
$139$	−9.63035	−0.816836	−0.408418	−	0.912795i	$-0.633919\pi$
$139$	−9.63035	−0.816836	−0.408418	+	0.912795i	$0.633919\pi$
$140$	0	0
$141$	0.722669	0.0608597
$142$	−9.33637	−0.783491
$143$	−9.07052	−0.758515
$144$	−0.901876	−0.0751563
$145$	0	0
$146$	8.37901	0.693452
$147$	−1.59564	−0.131606
$148$	6.64463	0.546185
$149$	15.8600	1.29930	0.649652	−	0.760231i	$-0.274914\pi$
$149$	15.8600	1.29930	0.649652	+	0.760231i	$0.274914\pi$
$150$	0	0
$151$	−11.7468	−0.955938	−0.477969	−	0.878377i	$-0.658627\pi$
$151$	−11.7468	−0.955938	−0.477969	+	0.878377i	$0.658627\pi$
$152$	−2.89932	−0.235166
$153$	−16.9284	−1.36858
$154$	−11.8313	−0.953395
$155$	0	0
$156$	−1.04188	−0.0834173
$157$	−23.3280	−1.86178	−0.930890	−	0.365299i	$-0.880967\pi$
$157$	−23.3280	−1.86178	−0.930890	+	0.365299i	$0.880967\pi$
$158$	−1.06615	−0.0848182
$159$	2.47676	0.196420
$160$	0	0
$161$	−4.66672	−0.367789
$162$	−6.48007	−0.509123
$163$	3.47161	0.271917	0.135959	−	0.990715i	$-0.456589\pi$
$163$	3.47161	0.271917	0.135959	+	0.990715i	$0.456589\pi$
$164$	3.01120	0.235135
$165$	0	0
$166$	−5.93647	−0.460760
$167$	12.7217	0.984431	0.492216	−	0.870473i	$-0.336187\pi$
$167$	12.7217	0.984431	0.492216	+	0.870473i	$0.336187\pi$
$168$	−3.44103	−0.265481
$169$	−8.39011	−0.645393
$170$	0	0
$171$	3.01203	0.230335
$172$	−2.14097	−0.163247
$173$	13.5079	1.02698	0.513492	−	0.858094i	$-0.328351\pi$
$173$	13.5079	1.02698	0.513492	+	0.858094i	$0.328351\pi$
$174$	−2.71579	−0.205883
$175$	0	0
$176$	1.33134	0.100354
$177$	−0.177856	−0.0133684
$178$	−5.75019	−0.430995
$179$	13.1010	0.979216	0.489608	−	0.871943i	$-0.337140\pi$
$179$	13.1010	0.979216	0.489608	+	0.871943i	$0.337140\pi$
$180$	0	0
$181$	3.60097	0.267658	0.133829	−	0.991004i	$-0.457273\pi$
$181$	3.60097	0.267658	0.133829	+	0.991004i	$0.457273\pi$
$182$	6.01301	0.445714
$183$	2.91384	0.215397
$184$	−3.82556	−0.282024
$185$	0	0
$186$	−1.54305	−0.113142
$187$	24.9896	1.82742
$188$	2.53801	0.185103
$189$	7.32218	0.532611
$190$	0	0
$191$	−8.09155	−0.585484	−0.292742	−	0.956191i	$-0.594568\pi$
$191$	−8.09155	−0.585484	−0.292742	+	0.956191i	$0.594568\pi$
$192$	−1.55383	−0.112138
$193$	−14.8451	−1.06857	−0.534286	−	0.845304i	$-0.679420\pi$
$193$	−14.8451	−1.06857	−0.534286	+	0.845304i	$0.679420\pi$
$194$	−3.65644	−0.262517
$195$	0	0
$196$	−5.60385	−0.400275
$197$	−22.5775	−1.60858	−0.804291	−	0.594236i	$-0.797455\pi$
$197$	−22.5775	−1.60858	−0.804291	+	0.594236i	$0.797455\pi$
$198$	10.0758	0.716055
$199$	−4.33812	−0.307521	−0.153761	−	0.988108i	$-0.549138\pi$
$199$	−4.33812	−0.307521	−0.153761	+	0.988108i	$0.549138\pi$
$200$	0	0
$201$	0.910098	0.0641933
$202$	9.84275	0.692533
$203$	−29.4601	−2.06770
$204$	2.87042	0.200969
$205$	0	0
$206$	−1.07433	−0.0748521
$207$	3.97427	0.276231
$208$	−0.676626	−0.0469156
$209$	−4.44633	−0.307559
$210$	0	0
$211$	18.7262	1.28917	0.644583	−	0.764535i	$-0.277031\pi$
$211$	18.7262	1.28917	0.644583	+	0.764535i	$0.277031\pi$
$212$	8.69836	0.597406
$213$	−4.16427	−0.285331
$214$	1.50341	0.102771
$215$	0	0
$216$	6.00238	0.408411
$217$	−16.7385	−1.13629
$218$	−12.7998	−0.866915
$219$	3.73726	0.252541
$220$	0	0
$221$	−12.7004	−0.854321
$222$	−1.57676	−0.105825
$223$	−11.6612	−0.780891	−0.390445	−	0.920626i	$-0.627679\pi$
$223$	−11.6612	−0.780891	−0.390445	+	0.920626i	$0.627679\pi$
$224$	−19.3969	−1.29601
$225$	0	0
$226$	15.0671	1.00225
$227$	9.25156	0.614048	0.307024	−	0.951702i	$-0.400667\pi$
$227$	9.25156	0.614048	0.307024	+	0.951702i	$0.400667\pi$
$228$	−0.510726	−0.0338237
$229$	−14.0844	−0.930724	−0.465362	−	0.885120i	$-0.654076\pi$
$229$	−14.0844	−0.930724	−0.465362	+	0.885120i	$0.654076\pi$
$230$	0	0
$231$	−5.27709	−0.347207
$232$	−24.1500	−1.58553
$233$	11.9530	0.783067	0.391533	−	0.920164i	$-0.371945\pi$
$233$	11.9530	0.783067	0.391533	+	0.920164i	$0.371945\pi$
$234$	−5.12080	−0.334757
$235$	0	0
$236$	−0.624627	−0.0406598
$237$	−0.475531	−0.0308890
$238$	−16.5660	−1.07382
$239$	21.6310	1.39919	0.699595	−	0.714539i	$-0.253364\pi$
$239$	21.6310	1.39919	0.699595	+	0.714539i	$0.253364\pi$
$240$	0	0
$241$	1.00000	0.0644157
$241$	1.00000	0.0644157
$242$	−5.70651	−0.366828
$243$	−9.42707	−0.604747
$244$	10.2334	0.655124
$245$	0	0
$246$	−0.714554	−0.0455583
$247$	2.25975	0.143784
$248$	−13.7215	−0.871314
$249$	−2.64783	−0.167799
$250$	0	0
$251$	30.7635	1.94178	0.970888	−	0.239536i	$-0.0769952\pi$
$251$	30.7635	1.94178	0.970888	+	0.239536i	$0.0769952\pi$
$252$	12.5546	0.790868
$253$	−5.86679	−0.368842
$254$	8.63986	0.542113
$255$	0	0
$256$	−15.0779	−0.942368
$257$	−14.4573	−0.901823	−0.450912	−	0.892569i	$-0.648901\pi$
$257$	−14.4573	−0.901823	−0.450912	+	0.892569i	$0.648901\pi$
$258$	0.508050	0.0316298
$259$	−17.1043	−1.06281
$260$	0	0
$261$	25.0888	1.55296
$262$	0.0293323	0.00181216
$263$	−15.6408	−0.964456	−0.482228	−	0.876046i	$-0.660172\pi$
$263$	−15.6408	−0.964456	−0.482228	+	0.876046i	$0.660172\pi$
$264$	−4.32591	−0.266241
$265$	0	0
$266$	2.94755	0.180726
$267$	−2.56474	−0.156959
$268$	3.19625	0.195242
$269$	−16.1628	−0.985462	−0.492731	−	0.870182i	$-0.664001\pi$
$269$	−16.1628	−0.985462	−0.492731	+	0.870182i	$0.664001\pi$
$270$	0	0
$271$	25.4407	1.54541	0.772705	−	0.634765i	$-0.218903\pi$
$271$	25.4407	1.54541	0.772705	+	0.634765i	$0.218903\pi$
$272$	1.86413	0.113029
$273$	2.68196	0.162320
$274$	10.1038	0.610394
$275$	0	0
$276$	−0.673887	−0.0405632
$277$	−15.9310	−0.957204	−0.478602	−	0.878032i	$-0.658856\pi$
$277$	−15.9310	−0.957204	−0.478602	+	0.878032i	$0.658856\pi$
$278$	8.02585	0.481359
$279$	14.2549	0.853417
$280$	0	0
$281$	2.48302	0.148125	0.0740624	−	0.997254i	$-0.476404\pi$
$281$	2.48302	0.148125	0.0740624	+	0.997254i	$0.476404\pi$
$282$	−0.602266	−0.0358644
$283$	21.5459	1.28077	0.640387	−	0.768053i	$-0.278774\pi$
$283$	21.5459	1.28077	0.640387	+	0.768053i	$0.278774\pi$
$284$	−14.6249	−0.867827
$285$	0	0
$286$	7.55929	0.446990
$287$	−7.75128	−0.457544
$288$	16.5188	0.973380
$289$	17.9900	1.05824
$290$	0	0
$291$	−1.63087	−0.0956034
$292$	13.1252	0.768096
$293$	−9.29499	−0.543019	−0.271510	−	0.962436i	$-0.587523\pi$
$293$	−9.29499	−0.543019	−0.271510	+	0.962436i	$0.587523\pi$
$294$	1.32979	0.0775549
$295$	0	0
$296$	−14.0213	−0.814972
$297$	9.20513	0.534136
$298$	−13.2176	−0.765676
$299$	2.98167	0.172434
$300$	0	0
$301$	5.51119	0.317660
$302$	9.78965	0.563331
$303$	4.39013	0.252206
$304$	−0.331679	−0.0190231
$305$	0	0
$306$	14.1080	0.806499
$307$	21.8059	1.24453	0.622265	−	0.782807i	$-0.286213\pi$
$307$	21.8059	1.24453	0.622265	+	0.782807i	$0.286213\pi$
$308$	−18.5331	−1.05602
$309$	−0.479180	−0.0272596
$310$	0	0
$311$	4.67118	0.264878	0.132439	−	0.991191i	$-0.457719\pi$
$311$	4.67118	0.264878	0.132439	+	0.991191i	$0.457719\pi$
$312$	2.19855	0.124468
$313$	−12.0596	−0.681651	−0.340826	−	0.940127i	$-0.610707\pi$
$313$	−12.0596	−0.681651	−0.340826	+	0.940127i	$0.610707\pi$
$314$	19.4414	1.09714
$315$	0	0
$316$	−1.67006	−0.0939481
$317$	28.8553	1.62068	0.810339	−	0.585962i	$-0.199283\pi$
$317$	28.8553	1.62068	0.810339	+	0.585962i	$0.199283\pi$
$318$	−2.06411	−0.115750
$319$	−37.0360	−2.07362
$320$	0	0
$321$	0.670562	0.0374271
$322$	3.88920	0.216737
$323$	−6.22569	−0.346406
$324$	−10.1507	−0.563925
$325$	0	0
$326$	−2.89321	−0.160240
$327$	−5.70908	−0.315713
$328$	−6.35414	−0.350849
$329$	−6.53322	−0.360188
$330$	0	0
$331$	11.8453	0.651075	0.325538	−	0.945529i	$-0.394455\pi$
$331$	11.8453	0.651075	0.325538	+	0.945529i	$0.394455\pi$
$332$	−9.29913	−0.510356
$333$	14.5664	0.798232
$334$	−10.6021	−0.580122
$335$	0	0
$336$	−0.393651	−0.0214754
$337$	−21.7114	−1.18270	−0.591348	−	0.806417i	$-0.701404\pi$
$337$	−21.7114	−1.18270	−0.591348	+	0.806417i	$0.701404\pi$
$338$	6.99225	0.380328
$339$	6.72033	0.364998
$340$	0	0
$341$	−21.0429	−1.13954
$342$	−2.51020	−0.135736
$343$	−9.09798	−0.491245
$344$	4.51781	0.243584
$345$	0	0
$346$	−11.2573	−0.605199
$347$	−18.8075	−1.00964	−0.504819	−	0.863225i	$-0.668441\pi$
$347$	−18.8075	−1.00964	−0.504819	+	0.863225i	$0.668441\pi$
$348$	−4.25412	−0.228045
$349$	−33.4897	−1.79266	−0.896331	−	0.443385i	$-0.853777\pi$
$349$	−33.4897	−1.79266	−0.896331	+	0.443385i	$0.853777\pi$
$350$	0	0
$351$	−4.67830	−0.249709
$352$	−24.3849	−1.29972
$353$	−10.3972	−0.553386	−0.276693	−	0.960958i	$-0.589238\pi$
$353$	−10.3972	−0.553386	−0.276693	+	0.960958i	$0.589238\pi$
$354$	0.148223	0.00787798
$355$	0	0
$356$	−9.00733	−0.477388
$357$	−7.38890	−0.391062
$358$	−10.9183	−0.577049
$359$	−34.8680	−1.84026	−0.920131	−	0.391612i	$-0.871918\pi$
$359$	−34.8680	−1.84026	−0.920131	+	0.391612i	$0.871918\pi$
$360$	0	0
$361$	−17.8923	−0.941699
$362$	−3.00102	−0.157730
$363$	−2.54526	−0.133591
$364$	9.41903	0.493691
$365$	0	0
$366$	−2.42837	−0.126933
$367$	10.5108	0.548662	0.274331	−	0.961635i	$-0.411544\pi$
$367$	10.5108	0.548662	0.274331	+	0.961635i	$0.411544\pi$
$368$	−0.437640	−0.0228136
$369$	6.60115	0.343642
$370$	0	0
$371$	−22.3909	−1.16248
$372$	−2.41709	−0.125320
$373$	8.81336	0.456338	0.228169	−	0.973622i	$-0.426726\pi$
$373$	8.81336	0.456338	0.228169	+	0.973622i	$0.426726\pi$
$374$	−20.8261	−1.07689
$375$	0	0
$376$	−5.35563	−0.276195
$377$	18.8227	0.969419
$378$	−6.10225	−0.313866
$379$	16.9301	0.869643	0.434822	−	0.900517i	$-0.356811\pi$
$379$	16.9301	0.869643	0.434822	+	0.900517i	$0.356811\pi$
$380$	0	0
$381$	3.85361	0.197426
$382$	6.74343	0.345024
$383$	−36.0980	−1.84452	−0.922261	−	0.386567i	$-0.873661\pi$
$383$	−36.0980	−1.84452	−0.922261	+	0.386567i	$0.873661\pi$
$384$	−2.99622	−0.152900
$385$	0	0
$386$	12.3718	0.629706
$387$	−4.69344	−0.238581
$388$	−5.72760	−0.290775
$389$	0.391503	0.0198500	0.00992499	−	0.999951i	$-0.496841\pi$
$389$	0.391503	0.0198500	0.00992499	+	0.999951i	$0.496841\pi$
$390$	0	0
$391$	−8.21459	−0.415430
$392$	11.8251	0.597257
$393$	0.0130830	0.000659951 0
$394$	18.8159	0.947932
$395$	0	0
$396$	15.7831	0.793133
$397$	−23.6812	−1.18852	−0.594262	−	0.804271i	$-0.702556\pi$
$397$	−23.6812	−1.18852	−0.594262	+	0.804271i	$0.702556\pi$
$398$	3.61535	0.181221
$399$	1.31469	0.0658167
$400$	0	0
$401$	−5.30878	−0.265108	−0.132554	−	0.991176i	$-0.542318\pi$
$401$	−5.30878	−0.265108	−0.132554	+	0.991176i	$0.542318\pi$
$402$	−0.758468	−0.0378289
$403$	10.6946	0.532737
$404$	15.4181	0.767079
$405$	0	0
$406$	24.5518	1.21849
$407$	−21.5028	−1.06585
$408$	−6.05707	−0.299870
$409$	−12.2278	−0.604624	−0.302312	−	0.953209i	$-0.597758\pi$
$409$	−12.2278	−0.604624	−0.302312	+	0.953209i	$0.597758\pi$
$410$	0	0
$411$	4.50657	0.222293
$412$	−1.68287	−0.0829092
$413$	1.60789	0.0791189
$414$	−3.31212	−0.162782
$415$	0	0
$416$	12.3931	0.607622
$417$	3.57975	0.175301
$418$	3.70553	0.181244
$419$	−28.2562	−1.38040	−0.690202	−	0.723617i	$-0.742478\pi$
$419$	−28.2562	−1.38040	−0.690202	+	0.723617i	$0.742478\pi$
$420$	0	0
$421$	8.28506	0.403789	0.201894	−	0.979407i	$-0.435290\pi$
$421$	8.28506	0.403789	0.201894	+	0.979407i	$0.435290\pi$
$422$	−15.6063	−0.759701
$423$	5.56382	0.270522
$424$	−18.3550	−0.891399
$425$	0	0
$426$	3.47047	0.168145
$427$	−26.3422	−1.27479
$428$	2.35501	0.113834
$429$	3.37165	0.162785
$430$	0	0
$431$	−34.1306	−1.64402	−0.822008	−	0.569476i	$-0.807146\pi$
$431$	−34.1306	−1.64402	−0.822008	+	0.569476i	$0.807146\pi$
$432$	0.686667	0.0330373
$433$	−8.70906	−0.418531	−0.209265	−	0.977859i	$-0.567107\pi$
$433$	−8.70906	−0.418531	−0.209265	+	0.977859i	$0.567107\pi$
$434$	13.9497	0.669609
$435$	0	0
$436$	−20.0502	−0.960231
$437$	1.46160	0.0699179
$438$	−3.11460	−0.148821
$439$	8.40802	0.401293	0.200646	−	0.979664i	$-0.435696\pi$
$439$	8.40802	0.401293	0.200646	+	0.979664i	$0.435696\pi$
$440$	0	0
$441$	−12.2848	−0.584989
$442$	10.5844	0.503449
$443$	11.2842	0.536128	0.268064	−	0.963401i	$-0.413616\pi$
$443$	11.2842	0.536128	0.268064	+	0.963401i	$0.413616\pi$
$444$	−2.46991	−0.117217
$445$	0	0
$446$	9.71833	0.460176
$447$	−5.89541	−0.278843
$448$	14.0472	0.663668
$449$	6.03919	0.285007	0.142504	−	0.989794i	$-0.454485\pi$
$449$	6.03919	0.285007	0.142504	+	0.989794i	$0.454485\pi$
$450$	0	0
$451$	−9.74457	−0.458854
$452$	23.6017	1.11013
$453$	4.36645	0.205154
$454$	−7.71017	−0.361856
$455$	0	0
$456$	1.07772	0.0504689
$457$	3.68220	0.172246	0.0861229	−	0.996285i	$-0.472552\pi$
$457$	3.68220	0.172246	0.0861229	+	0.996285i	$0.472552\pi$
$458$	11.7378	0.548473
$459$	12.8889	0.601601
$460$	0	0
$461$	−38.8887	−1.81123	−0.905613	−	0.424105i	$-0.860589\pi$
$461$	−38.8887	−1.81123	−0.905613	+	0.424105i	$0.860589\pi$
$462$	4.39788	0.204608
$463$	9.67761	0.449757	0.224878	−	0.974387i	$-0.427802\pi$
$463$	9.67761	0.449757	0.224878	+	0.974387i	$0.427802\pi$
$464$	−2.76274	−0.128257
$465$	0	0
$466$	−9.96152	−0.461459
$467$	11.5850	0.536092	0.268046	−	0.963406i	$-0.413622\pi$
$467$	11.5850	0.536092	0.268046	+	0.963406i	$0.413622\pi$
$468$	−8.02143	−0.370791
$469$	−8.22765	−0.379917
$470$	0	0
$471$	8.67138	0.399556
$472$	1.31807	0.0606691
$473$	6.92842	0.318569
$474$	0.396303	0.0182028
$475$	0	0
$476$	−25.9497	−1.18940
$477$	19.0685	0.873089
$478$	−18.0271	−0.824539
$479$	−19.4154	−0.887114	−0.443557	−	0.896246i	$-0.646284\pi$
$479$	−19.4154	−0.887114	−0.443557	+	0.896246i	$0.646284\pi$
$480$	0	0
$481$	10.9283	0.498288
$482$	−0.833391	−0.0379599
$483$	1.73469	0.0789311
$484$	−8.93891	−0.406314
$485$	0	0
$486$	7.85644	0.356375
$487$	−4.43936	−0.201167	−0.100583	−	0.994929i	$-0.532071\pi$
$487$	−4.43936	−0.201167	−0.100583	+	0.994929i	$0.532071\pi$
$488$	−21.5941	−0.977521
$489$	−1.29045	−0.0583561
$490$	0	0
$491$	−30.2554	−1.36541	−0.682703	−	0.730696i	$-0.739196\pi$
$491$	−30.2554	−1.36541	−0.682703	+	0.730696i	$0.739196\pi$
$492$	−1.11931	−0.0504623
$493$	−51.8572	−2.33553
$494$	−1.88326	−0.0847317
$495$	0	0
$496$	−1.56972	−0.0704826
$497$	37.6467	1.68868
$498$	2.20668	0.0988835
$499$	−8.06048	−0.360836	−0.180418	−	0.983590i	$-0.557745\pi$
$499$	−8.06048	−0.360836	−0.180418	+	0.983590i	$0.557745\pi$
$500$	0	0
$501$	−4.72883	−0.211268
$502$	−25.6380	−1.14428
$503$	15.5796	0.694660	0.347330	−	0.937743i	$-0.387088\pi$
$503$	15.5796	0.694660	0.347330	+	0.937743i	$0.387088\pi$
$504$	−26.4924	−1.18007
$505$	0	0
$506$	4.88933	0.217357
$507$	3.11873	0.138508
$508$	13.5338	0.600467
$509$	−7.48959	−0.331970	−0.165985	−	0.986128i	$-0.553080\pi$
$509$	−7.48959	−0.331970	−0.165985	+	0.986128i	$0.553080\pi$
$510$	0	0
$511$	−33.7863	−1.49462
$512$	−3.55528	−0.157123
$513$	−2.29329	−0.101251
$514$	12.0486	0.531442
$515$	0	0
$516$	0.795831	0.0350345
$517$	−8.21327	−0.361219
$518$	14.2546	0.626310
$519$	−5.02108	−0.220401
$520$	0	0
$521$	−34.0915	−1.49358	−0.746788	−	0.665063i	$-0.768405\pi$
$521$	−34.0915	−1.49358	−0.746788	+	0.665063i	$0.768405\pi$
$522$	−20.9088	−0.915154
$523$	27.0664	1.18353	0.591766	−	0.806110i	$-0.298431\pi$
$523$	27.0664	1.18353	0.591766	+	0.806110i	$0.298431\pi$
$524$	0.0459474	0.00200722
$525$	0	0
$526$	13.0349	0.568351
$527$	−29.4640	−1.28347
$528$	−0.494880	−0.0215369
$529$	−21.0715	−0.916151
$530$	0	0
$531$	−1.36931	−0.0594229
$532$	4.61717	0.200180
$533$	4.95246	0.214515
$534$	2.13743	0.0924957
$535$	0	0
$536$	−6.74464	−0.291324
$537$	−4.86984	−0.210149
$538$	13.4699	0.580730
$539$	18.1347	0.781117
$540$	0	0
$541$	19.4967	0.838228	0.419114	−	0.907934i	$-0.362341\pi$
$541$	19.4967	0.838228	0.419114	+	0.907934i	$0.362341\pi$
$542$	−21.2020	−0.910705
$543$	−1.33854	−0.0574421
$544$	−34.1434	−1.46389
$545$	0	0
$546$	−2.23513	−0.0956545
$547$	3.24176	0.138608	0.0693038	−	0.997596i	$-0.477922\pi$
$547$	3.24176	0.138608	0.0693038	+	0.997596i	$0.477922\pi$
$548$	15.8270	0.676097
$549$	22.4336	0.957442
$550$	0	0
$551$	9.22682	0.393076
$552$	1.42202	0.0605251
$553$	4.29899	0.182812
$554$	13.2768	0.564077
$555$	0	0
$556$	12.5720	0.533173
$557$	−31.5930	−1.33864	−0.669320	−	0.742974i	$-0.733414\pi$
$557$	−31.5930	−1.33864	−0.669320	+	0.742974i	$0.733414\pi$
$558$	−11.8799	−0.502916
$559$	−3.52122	−0.148932
$560$	0	0
$561$	−9.28899	−0.392182
$562$	−2.06933	−0.0872895
$563$	12.4549	0.524911	0.262456	−	0.964944i	$-0.415468\pi$
$563$	12.4549	0.524911	0.262456	+	0.964944i	$0.415468\pi$
$564$	−0.943415	−0.0397249
$565$	0	0
$566$	−17.9562	−0.754756
$567$	26.1293	1.09733
$568$	30.8610	1.29490
$569$	−3.78115	−0.158514	−0.0792571	−	0.996854i	$-0.525255\pi$
$569$	−3.78115	−0.158514	−0.0792571	+	0.996854i	$0.525255\pi$
$570$	0	0
$571$	22.2602	0.931561	0.465781	−	0.884900i	$-0.345774\pi$
$571$	22.2602	0.931561	0.465781	+	0.884900i	$0.345774\pi$
$572$	11.8412	0.495105
$573$	3.00775	0.125651
$574$	6.45985	0.269629
$575$	0	0
$576$	−11.9629	−0.498453
$577$	−7.65680	−0.318757	−0.159378	−	0.987218i	$-0.550949\pi$
$577$	−7.65680	−0.318757	−0.159378	+	0.987218i	$0.550949\pi$
$578$	−14.9927	−0.623615
$579$	5.51814	0.229326
$580$	0	0
$581$	23.9374	0.993091
$582$	1.35915	0.0563388
$583$	−28.1489	−1.16581
$584$	−27.6965	−1.14609
$585$	0	0
$586$	7.74636	0.319999
$587$	20.6739	0.853305	0.426652	−	0.904416i	$-0.359693\pi$
$587$	20.6739	0.853305	0.426652	+	0.904416i	$0.359693\pi$
$588$	2.08304	0.0859030
$589$	5.24246	0.216012
$590$	0	0
$591$	8.39240	0.345217
$592$	−1.60402	−0.0659250
$593$	−8.70880	−0.357628	−0.178814	−	0.983883i	$-0.557226\pi$
$593$	−8.70880	−0.357628	−0.178814	+	0.983883i	$0.557226\pi$
$594$	−7.67147	−0.314764
$595$	0	0
$596$	−20.7046	−0.848094
$597$	1.61254	0.0659970
$598$	−2.48490	−0.101615
$599$	−32.9380	−1.34581	−0.672905	−	0.739729i	$-0.734954\pi$
$599$	−32.9380	−1.34581	−0.672905	+	0.739729i	$0.734954\pi$
$600$	0	0
$601$	10.6152	0.433005	0.216502	−	0.976282i	$-0.430535\pi$
$601$	10.6152	0.433005	0.216502	+	0.976282i	$0.430535\pi$
$602$	−4.59298	−0.187196
$603$	7.00683	0.285340
$604$	15.3349	0.623969
$605$	0	0
$606$	−3.65870	−0.148624
$607$	−26.0431	−1.05706	−0.528529	−	0.848915i	$-0.677256\pi$
$607$	−26.0431	−1.05706	−0.528529	+	0.848915i	$0.677256\pi$
$608$	6.07506	0.246376
$609$	10.9508	0.443747
$610$	0	0
$611$	4.17422	0.168871
$612$	22.0993	0.893312
$613$	34.6771	1.40059	0.700297	−	0.713852i	$-0.253051\pi$
$613$	34.6771	1.40059	0.700297	+	0.713852i	$0.253051\pi$
$614$	−18.1729	−0.733398
$615$	0	0
$616$	39.1079	1.57570
$617$	−2.71361	−0.109246	−0.0546228	−	0.998507i	$-0.517396\pi$
$617$	−2.71361	−0.109246	−0.0546228	+	0.998507i	$0.517396\pi$
$618$	0.399344	0.0160640
$619$	23.0391	0.926020	0.463010	−	0.886353i	$-0.346769\pi$
$619$	23.0391	0.926020	0.463010	+	0.886353i	$0.346769\pi$
$620$	0	0
$621$	−3.02592	−0.121426
$622$	−3.89292	−0.156092
$623$	23.1863	0.928938
$624$	0.251512	0.0100685
$625$	0	0
$626$	10.0504	0.401695
$627$	1.65277	0.0660052
$628$	30.4538	1.21524
$629$	−30.1078	−1.20048
$630$	0	0
$631$	31.3266	1.24709	0.623547	−	0.781786i	$-0.285691\pi$
$631$	31.3266	1.24709	0.623547	+	0.781786i	$0.285691\pi$
$632$	3.52411	0.140182
$633$	−6.96081	−0.276667
$634$	−24.0478	−0.955060
$635$	0	0
$636$	−3.23331	−0.128209
$637$	−9.21656	−0.365174
$638$	30.8655	1.22197
$639$	−32.0607	−1.26830
$640$	0	0
$641$	48.6122	1.92007	0.960033	−	0.279887i	$-0.0902968\pi$
$641$	48.6122	1.92007	0.960033	+	0.279887i	$0.0902968\pi$
$642$	−0.558841	−0.0220557
$643$	−20.7459	−0.818138	−0.409069	−	0.912503i	$-0.634146\pi$
$643$	−20.7459	−0.818138	−0.409069	+	0.912503i	$0.634146\pi$
$644$	6.09221	0.240067
$645$	0	0
$646$	5.18843	0.204136
$647$	−10.6407	−0.418327	−0.209164	−	0.977881i	$-0.567074\pi$
$647$	−10.6407	−0.418327	−0.209164	+	0.977881i	$0.567074\pi$
$648$	21.4196	0.841442
$649$	2.02136	0.0793454
$650$	0	0
$651$	6.22196	0.243858
$652$	−4.53204	−0.177488
$653$	−15.4550	−0.604801	−0.302401	−	0.953181i	$-0.597788\pi$
$653$	−15.4550	−0.604801	−0.302401	+	0.953181i	$0.597788\pi$
$654$	4.75789	0.186048
$655$	0	0
$656$	−0.726908	−0.0283810
$657$	28.7731	1.12255
$658$	5.44473	0.212258
$659$	46.9947	1.83066	0.915328	−	0.402710i	$-0.131932\pi$
$659$	46.9947	1.83066	0.915328	+	0.402710i	$0.131932\pi$
$660$	0	0
$661$	2.24935	0.0874895	0.0437447	−	0.999043i	$-0.486071\pi$
$661$	2.24935	0.0874895	0.0437447	+	0.999043i	$0.486071\pi$
$662$	−9.87175	−0.383676
$663$	4.72093	0.183346
$664$	19.6228	0.761511
$665$	0	0
$666$	−12.1395	−0.470395
$667$	12.1745	0.471398
$668$	−16.6076	−0.642567
$669$	4.33464	0.167587
$670$	0	0
$671$	−33.1163	−1.27844
$672$	7.21012	0.278137
$673$	33.4046	1.28765	0.643827	−	0.765171i	$-0.277346\pi$
$673$	33.4046	1.28765	0.643827	+	0.765171i	$0.277346\pi$
$674$	18.0941	0.696959
$675$	0	0
$676$	10.9529	0.421267
$677$	−29.2070	−1.12251	−0.561257	−	0.827641i	$-0.689682\pi$
$677$	−29.2070	−1.12251	−0.561257	+	0.827641i	$0.689682\pi$
$678$	−5.60066	−0.215092
$679$	14.7437	0.565813
$680$	0	0
$681$	−3.43894	−0.131781
$682$	17.5370	0.671527
$683$	−17.3181	−0.662658	−0.331329	−	0.943515i	$-0.607497\pi$
$683$	−17.3181	−0.662658	−0.331329	+	0.943515i	$0.607497\pi$
$684$	−3.93208	−0.150347
$685$	0	0
$686$	7.58218	0.289489
$687$	5.23539	0.199742
$688$	0.516834	0.0197041
$689$	14.3060	0.545017
$690$	0	0
$691$	−23.4990	−0.893945	−0.446973	−	0.894548i	$-0.647498\pi$
$691$	−23.4990	−0.893945	−0.446973	+	0.894548i	$0.647498\pi$
$692$	−17.6340	−0.670343
$693$	−40.6282	−1.54334
$694$	15.6740	0.594976
$695$	0	0
$696$	8.97693	0.340270
$697$	−13.6442	−0.516811
$698$	27.9100	1.05641
$699$	−4.44311	−0.168054
$700$	0	0
$701$	−18.0415	−0.681417	−0.340709	−	0.940169i	$-0.610667\pi$
$701$	−18.0415	−0.681417	−0.340709	+	0.940169i	$0.610667\pi$
$702$	3.89886	0.147153
$703$	5.35701	0.202044
$704$	17.6595	0.665568
$705$	0	0
$706$	8.66492	0.326108
$707$	−39.6885	−1.49264
$708$	0.232183	0.00872598
$709$	2.47784	0.0930572	0.0465286	−	0.998917i	$-0.485184\pi$
$709$	2.47784	0.0930572	0.0465286	+	0.998917i	$0.485184\pi$
$710$	0	0
$711$	−3.66110	−0.137302
$712$	19.0070	0.712318
$713$	6.91725	0.259053
$714$	6.15784	0.230452
$715$	0	0
$716$	−17.1028	−0.639163
$717$	−8.04055	−0.300280
$718$	29.0587	1.08446
$719$	−12.3572	−0.460845	−0.230422	−	0.973091i	$-0.574011\pi$
$719$	−12.3572	−0.460845	−0.230422	+	0.973091i	$0.574011\pi$
$720$	0	0
$721$	4.33197	0.161331
$722$	14.9113	0.554940
$723$	−0.371715	−0.0138242
$724$	−4.70092	−0.174708
$725$	0	0
$726$	2.12119	0.0787249
$727$	28.0925	1.04189	0.520947	−	0.853589i	$-0.325579\pi$
$727$	28.0925	1.04189	0.520947	+	0.853589i	$0.325579\pi$
$728$	−19.8758	−0.736645
$729$	−19.8224	−0.734165
$730$	0	0
$731$	9.70107	0.358807
$732$	−3.80389	−0.140596
$733$	27.9632	1.03284	0.516422	−	0.856334i	$-0.327264\pi$
$733$	27.9632	1.03284	0.516422	+	0.856334i	$0.327264\pi$
$734$	−8.75965	−0.323325
$735$	0	0
$736$	8.01584	0.295468
$737$	−10.3434	−0.381005
$738$	−5.50134	−0.202507
$739$	3.51473	0.129291	0.0646456	−	0.997908i	$-0.479408\pi$
$739$	3.51473	0.129291	0.0646456	+	0.997908i	$0.479408\pi$
$740$	0	0
$741$	−0.839983	−0.0308575
$742$	18.6604	0.685044
$743$	−42.3152	−1.55239	−0.776197	−	0.630491i	$-0.782854\pi$
$743$	−42.3152	−1.55239	−0.776197	+	0.630491i	$0.782854\pi$
$744$	5.10047	0.186992
$745$	0	0
$746$	−7.34498	−0.268919
$747$	−20.3856	−0.745869
$748$	−32.6228	−1.19281
$749$	−6.06215	−0.221506
$750$	0	0
$751$	52.0561	1.89955	0.949776	−	0.312930i	$-0.101311\pi$
$751$	52.0561	1.89955	0.949776	+	0.312930i	$0.101311\pi$
$752$	−0.612679	−0.0223421
$753$	−11.4353	−0.416724
$754$	−15.6867	−0.571276
$755$	0	0
$756$	−9.55881	−0.347651
$757$	−43.0097	−1.56322	−0.781608	−	0.623770i	$-0.785600\pi$
$757$	−43.0097	−1.56322	−0.781608	+	0.623770i	$0.785600\pi$
$758$	−14.1094	−0.512478
$759$	2.18077	0.0791571
$760$	0	0
$761$	−8.00777	−0.290281	−0.145141	−	0.989411i	$-0.546363\pi$
$761$	−8.00777	−0.290281	−0.145141	+	0.989411i	$0.546363\pi$
$762$	−3.21157	−0.116343
$763$	51.6123	1.86849
$764$	10.5632	0.382163
$765$	0	0
$766$	30.0838	1.08697
$767$	−1.02731	−0.0370941
$768$	5.60467	0.202241
$769$	−4.40317	−0.158782	−0.0793912	−	0.996844i	$-0.525298\pi$
$769$	−4.40317	−0.158782	−0.0793912	+	0.996844i	$0.525298\pi$
$770$	0	0
$771$	5.37401	0.193540
$772$	19.3796	0.697489
$773$	−22.5902	−0.812512	−0.406256	−	0.913759i	$-0.633166\pi$
$773$	−22.5902	−0.812512	−0.406256	+	0.913759i	$0.633166\pi$
$774$	3.91147	0.140595
$775$	0	0
$776$	12.0862	0.433870
$777$	6.35792	0.228089
$778$	−0.326275	−0.0116975
$779$	2.42768	0.0869806
$780$	0	0
$781$	47.3278	1.69352
$782$	6.84597	0.244811
$783$	−19.1021	−0.682652
$784$	1.35278	0.0483135
$785$	0	0
$786$	−0.0109033	−0.000388907 0
$787$	33.1462	1.18153	0.590767	−	0.806842i	$-0.298825\pi$
$787$	33.1462	1.18153	0.590767	+	0.806842i	$0.298825\pi$
$788$	29.4740	1.04997
$789$	5.81394	0.206982
$790$	0	0
$791$	−60.7544	−2.16018
$792$	−33.3051	−1.18345
$793$	16.8306	0.597674
$794$	19.7357	0.700393
$795$	0	0
$796$	5.66324	0.200728
$797$	−6.60145	−0.233835	−0.116918	−	0.993142i	$-0.537301\pi$
$797$	−6.60145	−0.233835	−0.116918	+	0.993142i	$0.537301\pi$
$798$	−1.09565	−0.0387856
$799$	−11.5001	−0.406844
$800$	0	0
$801$	−19.7459	−0.697686
$802$	4.42429	0.156227
$803$	−42.4747	−1.49890
$804$	−1.18810	−0.0419009
$805$	0	0
$806$	−8.91280	−0.313940
$807$	6.00795	0.211490
$808$	−32.5348	−1.14457
$809$	−21.2748	−0.747983	−0.373991	−	0.927432i	$-0.622011\pi$
$809$	−21.2748	−0.747983	−0.373991	+	0.927432i	$0.622011\pi$
$810$	0	0
$811$	15.3810	0.540099	0.270049	−	0.962846i	$-0.412960\pi$
$811$	15.3810	0.540099	0.270049	+	0.962846i	$0.412960\pi$
$812$	38.4590	1.34965
$813$	−9.45667	−0.331660
$814$	17.9202	0.628103
$815$	0	0
$816$	−0.692923	−0.0242572
$817$	−1.72609	−0.0603882
$818$	10.1905	0.356303
$819$	20.6484	0.721514
$820$	0	0
$821$	4.07004	0.142045	0.0710227	−	0.997475i	$-0.477374\pi$
$821$	4.07004	0.142045	0.0710227	+	0.997475i	$0.477374\pi$
$822$	−3.75574	−0.130996
$823$	−43.2054	−1.50605	−0.753023	−	0.657994i	$-0.771405\pi$
$823$	−43.2054	−1.50605	−0.753023	+	0.657994i	$0.771405\pi$
$824$	3.55115	0.123710
$825$	0	0
$826$	−1.34000	−0.0466245
$827$	36.4276	1.26671	0.633356	−	0.773860i	$-0.281677\pi$
$827$	36.4276	1.26671	0.633356	+	0.773860i	$0.281677\pi$
$828$	−5.18825	−0.180304
$829$	35.6070	1.23668	0.618342	−	0.785909i	$-0.287805\pi$
$829$	35.6070	1.23668	0.618342	+	0.785909i	$0.287805\pi$
$830$	0	0
$831$	5.92181	0.205425
$832$	−8.97506	−0.311154
$833$	25.3919	0.879778
$834$	−2.98333	−0.103304
$835$	0	0
$836$	5.80450	0.200753
$837$	−10.8533	−0.375146
$838$	23.5484	0.813467
$839$	40.7536	1.40697	0.703485	−	0.710710i	$-0.251626\pi$
$839$	40.7536	1.40697	0.703485	+	0.710710i	$0.251626\pi$
$840$	0	0
$841$	47.8553	1.65018
$842$	−6.90470	−0.237952
$843$	−0.922977	−0.0317890
$844$	−24.4463	−0.841476
$845$	0	0
$846$	−4.63684	−0.159418
$847$	23.0101	0.790638
$848$	−2.09980	−0.0721073
$849$	−8.00895	−0.274866
$850$	0	0
$851$	7.06841	0.242302
$852$	5.43629	0.186244
$853$	20.5591	0.703929	0.351965	−	0.936013i	$-0.385514\pi$
$853$	20.5591	0.703929	0.351965	+	0.936013i	$0.385514\pi$
$854$	21.9534	0.751230
$855$	0	0
$856$	−4.96947	−0.169853
$857$	3.27915	0.112013	0.0560067	−	0.998430i	$-0.482163\pi$
$857$	3.27915	0.112013	0.0560067	+	0.998430i	$0.482163\pi$
$858$	−2.80990	−0.0959284
$859$	9.43081	0.321775	0.160888	−	0.986973i	$-0.448564\pi$
$859$	9.43081	0.321775	0.160888	+	0.986973i	$0.448564\pi$
$860$	0	0
$861$	2.88127	0.0981933
$862$	28.4442	0.968813
$863$	20.8526	0.709829	0.354915	−	0.934899i	$-0.384510\pi$
$863$	20.8526	0.709829	0.354915	+	0.934899i	$0.384510\pi$
$864$	−12.5770	−0.427879
$865$	0	0
$866$	7.25806	0.246639
$867$	−6.68716	−0.227108
$868$	21.8515	0.741687
$869$	5.40450	0.183335
$870$	0	0
$871$	5.25682	0.178121
$872$	42.3094	1.43278
$873$	−12.5561	−0.424958
$874$	−1.21809	−0.0412024
$875$	0	0
$876$	−4.87884	−0.164841
$877$	4.99069	0.168524	0.0842618	−	0.996444i	$-0.473147\pi$
$877$	4.99069	0.168524	0.0842618	+	0.996444i	$0.473147\pi$
$878$	−7.00717	−0.236480
$879$	3.45509	0.116537
$880$	0	0
$881$	−21.9617	−0.739908	−0.369954	−	0.929050i	$-0.620627\pi$
$881$	−21.9617	−0.739908	−0.369954	+	0.929050i	$0.620627\pi$
$882$	10.2380	0.344732
$883$	−24.4645	−0.823296	−0.411648	−	0.911343i	$-0.635047\pi$
$883$	−24.4645	−0.823296	−0.411648	+	0.911343i	$0.635047\pi$
$884$	16.5798	0.557641
$885$	0	0
$886$	−9.40414	−0.315938
$887$	−34.1997	−1.14831	−0.574156	−	0.818746i	$-0.694670\pi$
$887$	−34.1997	−1.14831	−0.574156	+	0.818746i	$0.694670\pi$
$888$	5.21193	0.174901
$889$	−34.8382	−1.16843
$890$	0	0
$891$	32.8486	1.10047
$892$	15.2232	0.509710
$893$	2.04618	0.0684729
$894$	4.91319	0.164322
$895$	0	0
$896$	27.0870	0.904914
$897$	−1.10833	−0.0370061
$898$	−5.03301	−0.167954
$899$	43.6673	1.45639
$900$	0	0
$901$	−39.4136	−1.31306
$902$	8.12104	0.270401
$903$	−2.04859	−0.0681728
$904$	−49.8037	−1.65645
$905$	0	0
$906$	−3.63896	−0.120896
$907$	−59.0699	−1.96138	−0.980692	−	0.195560i	$-0.937348\pi$
$907$	−59.0699	−1.96138	−0.980692	+	0.195560i	$0.937348\pi$
$908$	−12.0775	−0.400807
$909$	33.7995	1.12106
$910$	0	0
$911$	−5.86166	−0.194206	−0.0971028	−	0.995274i	$-0.530958\pi$
$911$	−5.86166	−0.194206	−0.0971028	+	0.995274i	$0.530958\pi$
$912$	0.123290	0.00408255
$913$	30.0930	0.995934
$914$	−3.06871	−0.101504
$915$	0	0
$916$	18.3866	0.607511
$917$	−0.118276	−0.00390581
$918$	−10.7415	−0.354522
$919$	43.5684	1.43719	0.718594	−	0.695430i	$-0.244786\pi$
$919$	43.5684	1.43719	0.718594	+	0.695430i	$0.244786\pi$
$920$	0	0
$921$	−8.10559	−0.267088
$922$	32.4095	1.06735
$923$	−24.0533	−0.791724
$924$	6.88902	0.226632
$925$	0	0
$926$	−8.06524	−0.265040
$927$	−3.68920	−0.121169
$928$	50.6025	1.66111
$929$	12.1238	0.397770	0.198885	−	0.980023i	$-0.436268\pi$
$929$	12.1238	0.397770	0.198885	+	0.980023i	$0.436268\pi$
$930$	0	0
$931$	−4.51792	−0.148069
$932$	−15.6041	−0.511131
$933$	−1.73635	−0.0568455
$934$	−9.65487	−0.315917
$935$	0	0
$936$	16.9266	0.553263
$937$	−33.2672	−1.08679	−0.543396	−	0.839476i	$-0.682862\pi$
$937$	−33.2672	−1.08679	−0.543396	+	0.839476i	$0.682862\pi$
$938$	6.85685	0.223884
$939$	4.48275	0.146289
$940$	0	0
$941$	−18.7091	−0.609901	−0.304950	−	0.952368i	$-0.598640\pi$
$941$	−18.7091	−0.609901	−0.304950	+	0.952368i	$0.598640\pi$
$942$	−7.22666	−0.235457
$943$	3.20324	0.104312
$944$	0.150786	0.00490766
$945$	0	0
$946$	−5.77409	−0.187732
$947$	−48.4778	−1.57532	−0.787658	−	0.616113i	$-0.788706\pi$
$947$	−48.4778	−1.57532	−0.787658	+	0.616113i	$0.788706\pi$
$948$	0.620786	0.0201622
$949$	21.5868	0.700738
$950$	0	0
$951$	−10.7260	−0.347813
$952$	54.7584	1.77473
$953$	7.61596	0.246705	0.123353	−	0.992363i	$-0.460635\pi$
$953$	7.61596	0.246705	0.123353	+	0.992363i	$0.460635\pi$
$954$	−15.8916	−0.514508
$955$	0	0
$956$	−28.2383	−0.913293
$957$	13.7668	0.445018
$958$	16.1807	0.522774
$959$	−40.7412	−1.31560
$960$	0	0
$961$	−6.18927	−0.199654
$962$	−9.10756	−0.293639
$963$	5.16265	0.166364
$964$	−1.30546	−0.0420460
$965$	0	0
$966$	−1.44567	−0.0465138
$967$	28.6688	0.921926	0.460963	−	0.887419i	$-0.347504\pi$
$967$	28.6688	0.921926	0.460963	+	0.887419i	$0.347504\pi$
$968$	18.8626	0.606268
$969$	2.31418	0.0743422
$970$	0	0
$971$	−8.91424	−0.286072	−0.143036	−	0.989718i	$-0.545686\pi$
$971$	−8.91424	−0.286072	−0.143036	+	0.989718i	$0.545686\pi$
$972$	12.3067	0.394736
$973$	−32.3623	−1.03749
$974$	3.69972	0.118547
$975$	0	0
$976$	−2.47035	−0.0790740
$977$	51.5292	1.64857	0.824283	−	0.566178i	$-0.191578\pi$
$977$	51.5292	1.64857	0.824283	+	0.566178i	$0.191578\pi$
$978$	1.07545	0.0343890
$979$	29.1487	0.931598
$980$	0	0
$981$	−43.9541	−1.40335
$982$	25.2146	0.804630
$983$	32.5428	1.03795	0.518977	−	0.854788i	$-0.326313\pi$
$983$	32.5428	1.03795	0.518977	+	0.854788i	$0.326313\pi$
$984$	2.36193	0.0752955
$985$	0	0
$986$	43.2173	1.37632
$987$	2.42849	0.0772998
$988$	−2.95001	−0.0938524
$989$	−2.27752	−0.0724208
$990$	0	0
$991$	0.356238	0.0113163	0.00565813	−	0.999984i	$-0.498199\pi$
$991$	0.356238	0.0113163	0.00565813	+	0.999984i	$0.498199\pi$
$992$	28.7511	0.912849
$993$	−4.40306	−0.139727
$994$	−31.3744	−0.995137
$995$	0	0
$996$	3.45663	0.109527
$997$	−17.9785	−0.569384	−0.284692	−	0.958619i	$-0.591891\pi$
$997$	−17.9785	−0.569384	−0.284692	+	0.958619i	$0.591891\pi$
$998$	6.71753	0.212640
$999$	−11.0905	−0.350888

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.m.1.17	✓	40
5.4	even	2		6025.2.a.n.1.24	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.m.1.17	✓	40	1.1	even	1	trivial
6025.2.a.n.1.24	yes	40	5.4	even	2

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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q-0.833391 q^{2} -0.371715 q^{3} -1.30546 q^{4} +0.309784 q^{6} +3.36045 q^{7} +2.75474 q^{8} -2.86183 q^{9} +O(q^{10})\)	\(q-0.833391 q^{2} -0.371715 q^{3} -1.30546 q^{4} +0.309784 q^{6} +3.36045 q^{7} +2.75474 q^{8} -2.86183 q^{9} +4.22461 q^{11} +0.485258 q^{12} -2.14707 q^{13} -2.80057 q^{14} +0.315140 q^{16} +5.91524 q^{17} +2.38502 q^{18} -1.05248 q^{19} -1.24913 q^{21} -3.52075 q^{22} -1.38872 q^{23} -1.02398 q^{24} +1.78935 q^{26} +2.17893 q^{27} -4.38693 q^{28} -8.76672 q^{29} -4.98104 q^{31} -5.77212 q^{32} -1.57035 q^{33} -4.92971 q^{34} +3.73600 q^{36} -5.08988 q^{37} +0.877131 q^{38} +0.798096 q^{39} -2.30662 q^{41} +1.04101 q^{42} +1.64001 q^{43} -5.51505 q^{44} +1.15735 q^{46} -1.94415 q^{47} -0.117142 q^{48} +4.29263 q^{49} -2.19878 q^{51} +2.80291 q^{52} -6.66307 q^{53} -1.81590 q^{54} +9.25717 q^{56} +0.391224 q^{57} +7.30611 q^{58} +0.478473 q^{59} -7.83890 q^{61} +4.15115 q^{62} -9.61703 q^{63} +4.18015 q^{64} +1.30872 q^{66} -2.44838 q^{67} -7.72210 q^{68} +0.516207 q^{69} +11.2029 q^{71} -7.88360 q^{72} -10.0541 q^{73} +4.24186 q^{74} +1.37397 q^{76} +14.1966 q^{77} -0.665127 q^{78} +1.27929 q^{79} +7.77554 q^{81} +1.92232 q^{82} +7.12327 q^{83} +1.63069 q^{84} -1.36677 q^{86} +3.25872 q^{87} +11.6377 q^{88} +6.89974 q^{89} -7.21511 q^{91} +1.81291 q^{92} +1.85153 q^{93} +1.62024 q^{94} +2.14558 q^{96} +4.38743 q^{97} -3.57744 q^{98} -12.0901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9	\( 40 q - 9 q^{2} - 8 q^{3} + 41 q^{4} + 3 q^{6} - 20 q^{7} - 27 q^{8} + 38 q^{9} + q^{11} - 26 q^{12} - 11 q^{13} - q^{14} + 43 q^{16} - 20 q^{17} - 18 q^{18} + 2 q^{21} - 23 q^{22} - 79 q^{23} - 2 q^{24} + 2 q^{26} - 26 q^{27} - 30 q^{28} + 2 q^{29} + q^{31} - 68 q^{32} - 20 q^{33} + 5 q^{34} + 32 q^{36} - 16 q^{37} - 45 q^{38} - 2 q^{39} - 2 q^{41} - 19 q^{42} - 25 q^{43} + 3 q^{44} + 14 q^{46} - 88 q^{47} - 75 q^{48} + 40 q^{49} - 10 q^{51} - 18 q^{52} - 34 q^{53} + 4 q^{54} - 15 q^{56} - 51 q^{57} - 53 q^{58} + q^{59} + 9 q^{61} - 39 q^{62} - 110 q^{63} + 17 q^{64} + 26 q^{66} - 30 q^{67} - 44 q^{68} - 7 q^{69} + 5 q^{71} - 18 q^{72} - 23 q^{73} - 18 q^{74} + 43 q^{76} - 30 q^{77} - 46 q^{78} + 5 q^{79} + 44 q^{81} - 5 q^{82} - 65 q^{83} - 65 q^{84} + 40 q^{86} - 33 q^{87} - 71 q^{88} - 9 q^{89} + q^{91} - 117 q^{92} - 68 q^{93} - 72 q^{94} + 83 q^{96} + 8 q^{97} - 76 q^{98} - 40 q^{99}+O(q^{100}) \) 40 * q - 9 * q^2 - 8 * q^3 + 41 * q^4 + 3 * q^6 - 20 * q^7 - 27 * q^8 + 38 * q^9 + q^11 - 26 * q^12 - 11 * q^13 - q^14 + 43 * q^16 - 20 * q^17 - 18 * q^18 + 2 * q^21 - 23 * q^22 - 79 * q^23 - 2 * q^24 + 2 * q^26 - 26 * q^27 - 30 * q^28 + 2 * q^29 + q^31 - 68 * q^32 - 20 * q^33 + 5 * q^34 + 32 * q^36 - 16 * q^37 - 45 * q^38 - 2 * q^39 - 2 * q^41 - 19 * q^42 - 25 * q^43 + 3 * q^44 + 14 * q^46 - 88 * q^47 - 75 * q^48 + 40 * q^49 - 10 * q^51 - 18 * q^52 - 34 * q^53 + 4 * q^54 - 15 * q^56 - 51 * q^57 - 53 * q^58 + q^59 + 9 * q^61 - 39 * q^62 - 110 * q^63 + 17 * q^64 + 26 * q^66 - 30 * q^67 - 44 * q^68 - 7 * q^69 + 5 * q^71 - 18 * q^72 - 23 * q^73 - 18 * q^74 + 43 * q^76 - 30 * q^77 - 46 * q^78 + 5 * q^79 + 44 * q^81 - 5 * q^82 - 65 * q^83 - 65 * q^84 + 40 * q^86 - 33 * q^87 - 71 * q^88 - 9 * q^89 + q^91 - 117 * q^92 - 68 * q^93 - 72 * q^94 + 83 * q^96 + 8 * q^97 - 76 * q^98 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more