LMFDB - Embedded newform 1725.2.b.m.1174.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1725,2,Mod(1174,1725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1725, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1725.1174");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1725 = 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1725.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$13.7741943487$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 345)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1174.1
Root			$-1.22474 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	1725.1174
Dual form			1725.2.b.m.1174.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.44949i q^{2} -1.00000i q^{3} -4.00000 q^{4} -2.44949 q^{6} -1.00000i q^{7} +4.89898i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.44949i q^{2} -1.00000i q^{3} -4.00000 q^{4} -2.44949 q^{6} -1.00000i q^{7} +4.89898i q^{8} -1.00000 q^{9} +2.44949 q^{11} +4.00000i q^{12} -4.44949i q^{13} -2.44949 q^{14} +4.00000 q^{16} -5.44949i q^{17} +2.44949i q^{18} -4.44949 q^{19} -1.00000 q^{21} -6.00000i q^{22} +1.00000i q^{23} +4.89898 q^{24} -10.8990 q^{26} +1.00000i q^{27} +4.00000i q^{28} -10.3485 q^{29} +0.101021 q^{31} -2.44949i q^{33} -13.3485 q^{34} +4.00000 q^{36} +3.89898i q^{37} +10.8990i q^{38} -4.44949 q^{39} +5.44949 q^{41} +2.44949i q^{42} -2.00000i q^{43} -9.79796 q^{44} +2.44949 q^{46} +8.44949i q^{47} -4.00000i q^{48} +6.00000 q^{49} -5.44949 q^{51} +17.7980i q^{52} -0.550510i q^{53} +2.44949 q^{54} +4.89898 q^{56} +4.44949i q^{57} +25.3485i q^{58} -10.3485 q^{59} +0.651531 q^{61} -0.247449i q^{62} +1.00000i q^{63} +8.00000 q^{64} -6.00000 q^{66} -7.00000i q^{67} +21.7980i q^{68} +1.00000 q^{69} -4.34847 q^{71} -4.89898i q^{72} +5.34847i q^{73} +9.55051 q^{74} +17.7980 q^{76} -2.44949i q^{77} +10.8990i q^{78} +4.00000 q^{79} +1.00000 q^{81} -13.3485i q^{82} -15.2474i q^{83} +4.00000 q^{84} -4.89898 q^{86} +10.3485i q^{87} +12.0000i q^{88} +16.8990 q^{89} -4.44949 q^{91} -4.00000i q^{92} -0.101021i q^{93} +20.6969 q^{94} +3.10102i q^{97} -14.6969i q^{98} -2.44949 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{4} - 4 q^{9}+O(q^{10}) $ 4 * q - 16 * q^4 - 4 * q^9	$ 4 q - 16 q^{4} - 4 q^{9} + 16 q^{16} - 8 q^{19} - 4 q^{21} - 24 q^{26} - 12 q^{29} + 20 q^{31} - 24 q^{34} + 16 q^{36} - 8 q^{39} + 12 q^{41} + 24 q^{49} - 12 q^{51} - 12 q^{59} + 32 q^{61} + 32 q^{64} - 24 q^{66} + 4 q^{69} + 12 q^{71} + 48 q^{74} + 32 q^{76} + 16 q^{79} + 4 q^{81} + 16 q^{84} + 48 q^{89} - 8 q^{91} + 24 q^{94}+O(q^{100}) $ 4 * q - 16 * q^4 - 4 * q^9 + 16 * q^16 - 8 * q^19 - 4 * q^21 - 24 * q^26 - 12 * q^29 + 20 * q^31 - 24 * q^34 + 16 * q^36 - 8 * q^39 + 12 * q^41 + 24 * q^49 - 12 * q^51 - 12 * q^59 + 32 * q^61 + 32 * q^64 - 24 * q^66 + 4 * q^69 + 12 * q^71 + 48 * q^74 + 32 * q^76 + 16 * q^79 + 4 * q^81 + 16 * q^84 + 48 * q^89 - 8 * q^91 + 24 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1725\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	− 2.44949i	− 1.73205i	−0.500000	−	0.866025i	$-0.666667\pi$
$2$	− 2.44949i	− 1.73205i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−4.00000	−2.00000
$5$	0	0
$5$	0	0
$6$	−2.44949	−1.00000
$7$	− 1.00000i	− 0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	− 1.00000i	− 0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$	4.89898i	1.73205i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	2.44949	0.738549	0.369274	−	0.929320i	$-0.379606\pi$
$11$	2.44949	0.738549	0.369274	+	0.929320i	$0.379606\pi$
$12$	4.00000i	1.15470i
$13$	− 4.44949i	− 1.23407i	−0.786937	−	0.617033i	$-0.788334\pi$
$13$	− 4.44949i	− 1.23407i	0.786937	−	0.617033i	$-0.211666\pi$
$14$	−2.44949	−0.654654
$15$	0	0
$16$	4.00000	1.00000
$17$	− 5.44949i	− 1.32170i	−0.750520	−	0.660848i	$-0.770197\pi$
$17$	− 5.44949i	− 1.32170i	0.750520	−	0.660848i	$-0.229803\pi$
$18$	2.44949i	0.577350i
$19$	−4.44949	−1.02078	−0.510391	−	0.859942i	$-0.670499\pi$
$19$	−4.44949	−1.02078	−0.510391	+	0.859942i	$0.670499\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	− 6.00000i	− 1.27920i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	4.89898	1.00000
$25$	0	0
$26$	−10.8990	−2.13747
$27$	1.00000i	0.192450i
$28$	4.00000i	0.755929i
$29$	−10.3485	−1.92166	−0.960831	−	0.277134i	$-0.910615\pi$
$29$	−10.3485	−1.92166	−0.960831	+	0.277134i	$0.910615\pi$
$30$	0	0
$31$	0.101021	0.0181438	0.00907191	−	0.999959i	$-0.497112\pi$
$31$	0.101021	0.0181438	0.00907191	+	0.999959i	$0.497112\pi$
$32$	0	0
$33$	− 2.44949i	− 0.426401i
$34$	−13.3485	−2.28924
$35$	0	0
$36$	4.00000	0.666667
$37$	3.89898i	0.640988i	0.947250	+	0.320494i	$0.103849\pi$
$37$	3.89898i	0.640988i	−0.947250	+	0.320494i	$0.896151\pi$
$38$	10.8990i	1.76805i
$39$	−4.44949	−0.712489
$40$	0	0
$41$	5.44949	0.851067	0.425534	−	0.904943i	$-0.360086\pi$
$41$	5.44949	0.851067	0.425534	+	0.904943i	$0.360086\pi$
$42$	2.44949i	0.377964i
$43$	− 2.00000i	− 0.304997i	−0.988304	−	0.152499i	$-0.951268\pi$
$43$	− 2.00000i	− 0.304997i	0.988304	−	0.152499i	$-0.0487319\pi$
$44$	−9.79796	−1.47710
$45$	0	0
$46$	2.44949	0.361158
$47$	8.44949i	1.23248i	0.787557	+	0.616242i	$0.211346\pi$
$47$	8.44949i	1.23248i	−0.787557	+	0.616242i	$0.788654\pi$
$48$	− 4.00000i	− 0.577350i
$49$	6.00000	0.857143
$50$	0	0
$51$	−5.44949	−0.763081
$52$	17.7980i	2.46813i
$53$	− 0.550510i	− 0.0756184i	−0.999285	−	0.0378092i	$-0.987962\pi$
$53$	− 0.550510i	− 0.0756184i	0.999285	−	0.0378092i	$-0.0120379\pi$
$54$	2.44949	0.333333
$55$	0	0
$56$	4.89898	0.654654
$57$	4.44949i	0.589349i
$58$	25.3485i	3.32842i
$59$	−10.3485	−1.34726	−0.673628	−	0.739071i	$-0.735265\pi$
$59$	−10.3485	−1.34726	−0.673628	+	0.739071i	$0.735265\pi$
$60$	0	0
$61$	0.651531	0.0834200	0.0417100	−	0.999130i	$-0.486719\pi$
$61$	0.651531	0.0834200	0.0417100	+	0.999130i	$0.486719\pi$
$62$	− 0.247449i	− 0.0314260i
$63$	1.00000i	0.125988i
$64$	8.00000	1.00000
$65$	0	0
$66$	−6.00000	−0.738549
$67$	− 7.00000i	− 0.855186i	−0.903971	−	0.427593i	$-0.859362\pi$
$67$	− 7.00000i	− 0.855186i	0.903971	−	0.427593i	$-0.140638\pi$
$68$	21.7980i	2.64339i
$69$	1.00000	0.120386
$70$	0	0
$71$	−4.34847	−0.516068	−0.258034	−	0.966136i	$-0.583075\pi$
$71$	−4.34847	−0.516068	−0.258034	+	0.966136i	$0.583075\pi$
$72$	− 4.89898i	− 0.577350i
$73$	5.34847i	0.625991i	0.949755	+	0.312995i	$0.101332\pi$
$73$	5.34847i	0.625991i	−0.949755	+	0.312995i	$0.898668\pi$
$74$	9.55051	1.11022
$75$	0	0
$76$	17.7980	2.04157
$77$	− 2.44949i	− 0.279145i
$78$	10.8990i	1.23407i
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 13.3485i	− 1.47409i
$83$	− 15.2474i	− 1.67362i	−0.547490	−	0.836812i	$-0.684416\pi$
$83$	− 15.2474i	− 1.67362i	0.547490	−	0.836812i	$-0.315584\pi$
$84$	4.00000	0.436436
$85$	0	0
$86$	−4.89898	−0.528271
$87$	10.3485i	1.10947i
$88$	12.0000i	1.27920i
$89$	16.8990	1.79129	0.895644	−	0.444771i	$-0.146715\pi$
$89$	16.8990	1.79129	0.895644	+	0.444771i	$0.146715\pi$
$90$	0	0
$91$	−4.44949	−0.466433
$92$	− 4.00000i	− 0.417029i
$93$	− 0.101021i	− 0.0104753i
$94$	20.6969	2.13473
$95$	0	0
$96$	0	0
$97$	3.10102i	0.314861i	0.987530	+	0.157430i	$0.0503210\pi$
$97$	3.10102i	0.314861i	−0.987530	+	0.157430i	$0.949679\pi$
$98$	− 14.6969i	− 1.48461i
$99$	−2.44949	−0.246183
$100$	0	0
$101$	−12.5505	−1.24882	−0.624411	−	0.781096i	$-0.714661\pi$
$101$	−12.5505	−1.24882	−0.624411	+	0.781096i	$0.714661\pi$
$102$	13.3485i	1.32170i
$103$	12.6969i	1.25107i	0.780198	+	0.625533i	$0.215119\pi$
$103$	12.6969i	1.25107i	−0.780198	+	0.625533i	$0.784881\pi$
$104$	21.7980	2.13747
$105$	0	0
$106$	−1.34847	−0.130975
$107$	− 5.44949i	− 0.526822i	−0.964684	−	0.263411i	$-0.915152\pi$
$107$	− 5.44949i	− 0.526822i	0.964684	−	0.263411i	$-0.0848475\pi$
$108$	− 4.00000i	− 0.384900i
$109$	−11.5505	−1.10634	−0.553169	−	0.833069i	$-0.686582\pi$
$109$	−11.5505	−1.10634	−0.553169	+	0.833069i	$0.686582\pi$
$110$	0	0
$111$	3.89898	0.370075
$112$	− 4.00000i	− 0.377964i
$113$	1.65153i	0.155363i	0.996978	+	0.0776815i	$0.0247517\pi$
$113$	1.65153i	0.155363i	−0.996978	+	0.0776815i	$0.975248\pi$
$114$	10.8990	1.02078
$115$	0	0
$116$	41.3939	3.84332
$117$	4.44949i	0.411355i
$118$	25.3485i	2.33352i
$119$	−5.44949	−0.499554
$120$	0	0
$121$	−5.00000	−0.454545
$122$	− 1.59592i	− 0.144488i
$123$	− 5.44949i	− 0.491364i
$124$	−0.404082	−0.0362876
$125$	0	0
$126$	2.44949	0.218218
$127$	− 1.55051i	− 0.137586i	−0.997631	−	0.0687928i	$-0.978085\pi$
$127$	− 1.55051i	− 0.137586i	0.997631	−	0.0687928i	$-0.0219147\pi$
$128$	− 19.5959i	− 1.73205i
$129$	−2.00000	−0.176090
$130$	0	0
$131$	−19.5959	−1.71210	−0.856052	−	0.516890i	$-0.827090\pi$
$131$	−19.5959	−1.71210	−0.856052	+	0.516890i	$0.827090\pi$
$132$	9.79796i	0.852803i
$133$	4.44949i	0.385820i
$134$	−17.1464	−1.48123
$135$	0	0
$136$	26.6969	2.28924
$137$	− 16.8990i	− 1.44378i	−0.692009	−	0.721889i	$-0.743274\pi$
$137$	− 16.8990i	− 1.44378i	0.692009	−	0.721889i	$-0.256726\pi$
$138$	− 2.44949i	− 0.208514i
$139$	4.79796	0.406958	0.203479	−	0.979079i	$-0.434775\pi$
$139$	4.79796	0.406958	0.203479	+	0.979079i	$0.434775\pi$
$140$	0	0
$141$	8.44949	0.711575
$142$	10.6515i	0.893857i
$143$	− 10.8990i	− 0.911418i
$144$	−4.00000	−0.333333
$145$	0	0
$146$	13.1010	1.08425
$147$	− 6.00000i	− 0.494872i
$148$	− 15.5959i	− 1.28198i
$149$	1.34847	0.110471	0.0552355	−	0.998473i	$-0.482409\pi$
$149$	1.34847	0.110471	0.0552355	+	0.998473i	$0.482409\pi$
$150$	0	0
$151$	14.0000	1.13930	0.569652	−	0.821886i	$-0.307078\pi$
$151$	14.0000	1.13930	0.569652	+	0.821886i	$0.307078\pi$
$152$	− 21.7980i	− 1.76805i
$153$	5.44949i	0.440565i
$154$	−6.00000	−0.483494
$155$	0	0
$156$	17.7980	1.42498
$157$	18.5959i	1.48412i	0.670336	+	0.742058i	$0.266150\pi$
$157$	18.5959i	1.48412i	−0.670336	+	0.742058i	$0.733850\pi$
$158$	− 9.79796i	− 0.779484i
$159$	−0.550510	−0.0436583
$160$	0	0
$161$	1.00000	0.0788110
$162$	− 2.44949i	− 0.192450i
$163$	10.0000i	0.783260i	0.920123	+	0.391630i	$0.128089\pi$
$163$	10.0000i	0.783260i	−0.920123	+	0.391630i	$0.871911\pi$
$164$	−21.7980	−1.70213
$165$	0	0
$166$	−37.3485	−2.89880
$167$	13.3485i	1.03294i	0.856307	+	0.516468i	$0.172753\pi$
$167$	13.3485i	1.03294i	−0.856307	+	0.516468i	$0.827247\pi$
$168$	− 4.89898i	− 0.377964i
$169$	−6.79796	−0.522920
$170$	0	0
$171$	4.44949	0.340261
$172$	8.00000i	0.609994i
$173$	− 19.5959i	− 1.48985i	−0.667148	−	0.744925i	$-0.732485\pi$
$173$	− 19.5959i	− 1.48985i	0.667148	−	0.744925i	$-0.267515\pi$
$174$	25.3485	1.92166
$175$	0	0
$176$	9.79796	0.738549
$177$	10.3485i	0.777839i
$178$	− 41.3939i	− 3.10260i
$179$	6.00000	0.448461	0.224231	−	0.974536i	$-0.428013\pi$
$179$	6.00000	0.448461	0.224231	+	0.974536i	$0.428013\pi$
$180$	0	0
$181$	−8.89898	−0.661456	−0.330728	−	0.943726i	$-0.607294\pi$
$181$	−8.89898	−0.661456	−0.330728	+	0.943726i	$0.607294\pi$
$182$	10.8990i	0.807886i
$183$	− 0.651531i	− 0.0481625i
$184$	−4.89898	−0.361158
$185$	0	0
$186$	−0.247449	−0.0181438
$187$	− 13.3485i	− 0.976137i
$188$	− 33.7980i	− 2.46497i
$189$	1.00000	0.0727393
$190$	0	0
$191$	−18.2474	−1.32034	−0.660170	−	0.751117i	$-0.729516\pi$
$191$	−18.2474	−1.32034	−0.660170	+	0.751117i	$0.729516\pi$
$192$	− 8.00000i	− 0.577350i
$193$	6.69694i	0.482056i	0.970518	+	0.241028i	$0.0774846\pi$
$193$	6.69694i	0.482056i	−0.970518	+	0.241028i	$0.922515\pi$
$194$	7.59592	0.545355
$195$	0	0
$196$	−24.0000	−1.71429
$197$	− 22.8990i	− 1.63148i	−0.578415	−	0.815742i	$-0.696329\pi$
$197$	− 22.8990i	− 1.63148i	0.578415	−	0.815742i	$-0.303671\pi$
$198$	6.00000i	0.426401i
$199$	2.89898	0.205503	0.102752	−	0.994707i	$-0.467235\pi$
$199$	2.89898	0.205503	0.102752	+	0.994707i	$0.467235\pi$
$200$	0	0
$201$	−7.00000	−0.493742
$202$	30.7423i	2.16302i
$203$	10.3485i	0.726320i
$204$	21.7980	1.52616
$205$	0	0
$206$	31.1010	2.16691
$207$	− 1.00000i	− 0.0695048i
$208$	− 17.7980i	− 1.23407i
$209$	−10.8990	−0.753898
$210$	0	0
$211$	11.0000	0.757271	0.378636	−	0.925546i	$-0.376393\pi$
$211$	11.0000	0.757271	0.378636	+	0.925546i	$0.376393\pi$
$212$	2.20204i	0.151237i
$213$	4.34847i	0.297952i
$214$	−13.3485	−0.912483
$215$	0	0
$216$	−4.89898	−0.333333
$217$	− 0.101021i	− 0.00685772i
$218$	28.2929i	1.91623i
$219$	5.34847	0.361416
$220$	0	0
$221$	−24.2474	−1.63106
$222$	− 9.55051i	− 0.640988i
$223$	− 21.5959i	− 1.44617i	−0.690759	−	0.723085i	$-0.742724\pi$
$223$	− 21.5959i	− 1.44617i	0.690759	−	0.723085i	$-0.257276\pi$
$224$	0	0
$225$	0	0
$226$	4.04541	0.269097
$227$	21.7980i	1.44678i	0.690439	+	0.723391i	$0.257417\pi$
$227$	21.7980i	1.44678i	−0.690439	+	0.723391i	$0.742583\pi$
$228$	− 17.7980i	− 1.17870i
$229$	28.4949	1.88300	0.941498	−	0.337019i	$-0.109419\pi$
$229$	28.4949	1.88300	0.941498	+	0.337019i	$0.109419\pi$
$230$	0	0
$231$	−2.44949	−0.161165
$232$	− 50.6969i	− 3.32842i
$233$	− 21.7980i	− 1.42803i	−0.700129	−	0.714016i	$-0.746874\pi$
$233$	− 21.7980i	− 1.42803i	0.700129	−	0.714016i	$-0.253126\pi$
$234$	10.8990	0.712489
$235$	0	0
$236$	41.3939	2.69451
$237$	− 4.00000i	− 0.259828i
$238$	13.3485i	0.865253i
$239$	−6.55051	−0.423717	−0.211859	−	0.977300i	$-0.567952\pi$
$239$	−6.55051	−0.423717	−0.211859	+	0.977300i	$0.567952\pi$
$240$	0	0
$241$	−29.3485	−1.89050	−0.945251	−	0.326346i	$-0.894183\pi$
$241$	−29.3485	−1.89050	−0.945251	+	0.326346i	$0.894183\pi$
$242$	12.2474i	0.787296i
$243$	− 1.00000i	− 0.0641500i
$244$	−2.60612	−0.166840
$245$	0	0
$246$	−13.3485	−0.851067
$247$	19.7980i	1.25971i
$248$	0.494897i	0.0314260i
$249$	−15.2474	−0.966268
$250$	0	0
$251$	18.0000	1.13615	0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000	1.13615	0.568075	+	0.822977i	$0.307688\pi$
$252$	− 4.00000i	− 0.251976i
$253$	2.44949i	0.153998i
$254$	−3.79796	−0.238305
$255$	0	0
$256$	−32.0000	−2.00000
$257$	− 25.3485i	− 1.58119i	−0.612337	−	0.790597i	$-0.709770\pi$
$257$	− 25.3485i	− 1.58119i	0.612337	−	0.790597i	$-0.290230\pi$
$258$	4.89898i	0.304997i
$259$	3.89898	0.242271
$260$	0	0
$261$	10.3485	0.640554
$262$	48.0000i	2.96545i
$263$	− 27.2474i	− 1.68015i	−0.542471	−	0.840075i	$-0.682511\pi$
$263$	− 27.2474i	− 1.68015i	0.542471	−	0.840075i	$-0.317489\pi$
$264$	12.0000	0.738549
$265$	0	0
$266$	10.8990	0.668259
$267$	− 16.8990i	− 1.03420i
$268$	28.0000i	1.71037i
$269$	5.44949	0.332261	0.166131	−	0.986104i	$-0.446873\pi$
$269$	5.44949	0.332261	0.166131	+	0.986104i	$0.446873\pi$
$270$	0	0
$271$	31.6969	1.92545	0.962726	−	0.270479i	$-0.0871820\pi$
$271$	31.6969	1.92545	0.962726	+	0.270479i	$0.0871820\pi$
$272$	− 21.7980i	− 1.32170i
$273$	4.44949i	0.269295i
$274$	−41.3939	−2.50070
$275$	0	0
$276$	−4.00000	−0.240772
$277$	− 10.0000i	− 0.600842i	−0.953807	−	0.300421i	$-0.902873\pi$
$277$	− 10.0000i	− 0.600842i	0.953807	−	0.300421i	$-0.0971271\pi$
$278$	− 11.7526i	− 0.704871i
$279$	−0.101021	−0.00604794
$280$	0	0
$281$	−19.3485	−1.15423	−0.577116	−	0.816662i	$-0.695822\pi$
$281$	−19.3485	−1.15423	−0.577116	+	0.816662i	$0.695822\pi$
$282$	− 20.6969i	− 1.23248i
$283$	2.10102i	0.124893i	0.998048	+	0.0624464i	$0.0198902\pi$
$283$	2.10102i	0.124893i	−0.998048	+	0.0624464i	$0.980110\pi$
$284$	17.3939	1.03214
$285$	0	0
$286$	−26.6969	−1.57862
$287$	− 5.44949i	− 0.321673i
$288$	0	0
$289$	−12.6969	−0.746879
$290$	0	0
$291$	3.10102	0.181785
$292$	− 21.3939i	− 1.25198i
$293$	21.2474i	1.24129i	0.784092	+	0.620645i	$0.213129\pi$
$293$	21.2474i	1.24129i	−0.784092	+	0.620645i	$0.786871\pi$
$294$	−14.6969	−0.857143
$295$	0	0
$296$	−19.1010	−1.11022
$297$	2.44949i	0.142134i
$298$	− 3.30306i	− 0.191341i
$299$	4.44949	0.257321
$300$	0	0
$301$	−2.00000	−0.115278
$302$	− 34.2929i	− 1.97333i
$303$	12.5505i	0.721008i
$304$	−17.7980	−1.02078
$305$	0	0
$306$	13.3485	0.763081
$307$	− 2.65153i	− 0.151331i	−0.997133	−	0.0756654i	$-0.975892\pi$
$307$	− 2.65153i	− 0.151331i	0.997133	−	0.0756654i	$-0.0241081\pi$
$308$	9.79796i	0.558291i
$309$	12.6969	0.722304
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	− 21.7980i	− 1.23407i
$313$	− 19.6969i	− 1.11334i	−0.830735	−	0.556668i	$-0.812079\pi$
$313$	− 19.6969i	− 1.11334i	0.830735	−	0.556668i	$-0.187921\pi$
$314$	45.5505	2.57056
$315$	0	0
$316$	−16.0000	−0.900070
$317$	6.24745i	0.350892i	0.984489	+	0.175446i	$0.0561367\pi$
$317$	6.24745i	0.350892i	−0.984489	+	0.175446i	$0.943863\pi$
$318$	1.34847i	0.0756184i
$319$	−25.3485	−1.41924
$320$	0	0
$321$	−5.44949	−0.304161
$322$	− 2.44949i	− 0.136505i
$323$	24.2474i	1.34916i
$324$	−4.00000	−0.222222
$325$	0	0
$326$	24.4949	1.35665
$327$	11.5505i	0.638745i
$328$	26.6969i	1.47409i
$329$	8.44949	0.465835
$330$	0	0
$331$	24.5959	1.35191	0.675957	−	0.736941i	$-0.263731\pi$
$331$	24.5959	1.35191	0.675957	+	0.736941i	$0.263731\pi$
$332$	60.9898i	3.34725i
$333$	− 3.89898i	− 0.213663i
$334$	32.6969	1.78910
$335$	0	0
$336$	−4.00000	−0.218218
$337$	− 19.7980i	− 1.07846i	−0.842157	−	0.539232i	$-0.818715\pi$
$337$	− 19.7980i	− 1.07846i	0.842157	−	0.539232i	$-0.181285\pi$
$338$	16.6515i	0.905724i
$339$	1.65153	0.0896988
$340$	0	0
$341$	0.247449	0.0134001
$342$	− 10.8990i	− 0.589349i
$343$	− 13.0000i	− 0.701934i
$344$	9.79796	0.528271
$345$	0	0
$346$	−48.0000	−2.58050
$347$	− 28.8990i	− 1.55138i	−0.631115	−	0.775689i	$-0.717402\pi$
$347$	− 28.8990i	− 1.55138i	0.631115	−	0.775689i	$-0.282598\pi$
$348$	− 41.3939i	− 2.21894i
$349$	−23.4949	−1.25765	−0.628827	−	0.777546i	$-0.716464\pi$
$349$	−23.4949	−1.25765	−0.628827	+	0.777546i	$0.716464\pi$
$350$	0	0
$351$	4.44949	0.237496
$352$	0	0
$353$	15.5505i	0.827670i	0.910352	+	0.413835i	$0.135811\pi$
$353$	15.5505i	0.827670i	−0.910352	+	0.413835i	$0.864189\pi$
$354$	25.3485	1.34726
$355$	0	0
$356$	−67.5959	−3.58258
$357$	5.44949i	0.288418i
$358$	− 14.6969i	− 0.776757i
$359$	3.55051	0.187389	0.0936944	−	0.995601i	$-0.470132\pi$
$359$	3.55051	0.187389	0.0936944	+	0.995601i	$0.470132\pi$
$360$	0	0
$361$	0.797959	0.0419978
$362$	21.7980i	1.14568i
$363$	5.00000i	0.262432i
$364$	17.7980	0.932867
$365$	0	0
$366$	−1.59592	−0.0834200
$367$	13.6969i	0.714974i	0.933918	+	0.357487i	$0.116366\pi$
$367$	13.6969i	0.714974i	−0.933918	+	0.357487i	$0.883634\pi$
$368$	4.00000i	0.208514i
$369$	−5.44949	−0.283689
$370$	0	0
$371$	−0.550510	−0.0285811
$372$	0.404082i	0.0209507i
$373$	− 27.5959i	− 1.42886i	−0.699706	−	0.714431i	$-0.746686\pi$
$373$	− 27.5959i	− 1.42886i	0.699706	−	0.714431i	$-0.253314\pi$
$374$	−32.6969	−1.69072
$375$	0	0
$376$	−41.3939	−2.13473
$377$	46.0454i	2.37146i
$378$	− 2.44949i	− 0.125988i
$379$	−25.3939	−1.30440	−0.652198	−	0.758049i	$-0.726153\pi$
$379$	−25.3939	−1.30440	−0.652198	+	0.758049i	$0.726153\pi$
$380$	0	0
$381$	−1.55051	−0.0794350
$382$	44.6969i	2.28689i
$383$	− 1.65153i	− 0.0843893i	−0.999109	−	0.0421946i	$-0.986565\pi$
$383$	− 1.65153i	− 0.0843893i	0.999109	−	0.0421946i	$-0.0134350\pi$
$384$	−19.5959	−1.00000
$385$	0	0
$386$	16.4041	0.834946
$387$	2.00000i	0.101666i
$388$	− 12.4041i	− 0.629722i
$389$	3.30306	0.167472	0.0837359	−	0.996488i	$-0.473315\pi$
$389$	3.30306	0.167472	0.0837359	+	0.996488i	$0.473315\pi$
$390$	0	0
$391$	5.44949	0.275593
$392$	29.3939i	1.48461i
$393$	19.5959i	0.988483i
$394$	−56.0908	−2.82581
$395$	0	0
$396$	9.79796	0.492366
$397$	− 13.7980i	− 0.692500i	−0.938142	−	0.346250i	$-0.887455\pi$
$397$	− 13.7980i	− 0.692500i	0.938142	−	0.346250i	$-0.112545\pi$
$398$	− 7.10102i	− 0.355942i
$399$	4.44949	0.222753
$400$	0	0
$401$	−13.1010	−0.654234	−0.327117	−	0.944984i	$-0.606077\pi$
$401$	−13.1010	−0.654234	−0.327117	+	0.944984i	$0.606077\pi$
$402$	17.1464i	0.855186i
$403$	− 0.449490i	− 0.0223907i
$404$	50.2020	2.49764
$405$	0	0
$406$	25.3485	1.25802
$407$	9.55051i	0.473401i
$408$	− 26.6969i	− 1.32170i
$409$	−21.8990	−1.08283	−0.541417	−	0.840754i	$-0.682112\pi$
$409$	−21.8990	−1.08283	−0.541417	+	0.840754i	$0.682112\pi$
$410$	0	0
$411$	−16.8990	−0.833565
$412$	− 50.7878i	− 2.50213i
$413$	10.3485i	0.509215i
$414$	−2.44949	−0.120386
$415$	0	0
$416$	0	0
$417$	− 4.79796i	− 0.234957i
$418$	26.6969i	1.30579i
$419$	−33.5505	−1.63905	−0.819525	−	0.573044i	$-0.805763\pi$
$419$	−33.5505	−1.63905	−0.819525	+	0.573044i	$0.805763\pi$
$420$	0	0
$421$	−22.2474	−1.08427	−0.542137	−	0.840290i	$-0.682385\pi$
$421$	−22.2474	−1.08427	−0.542137	+	0.840290i	$0.682385\pi$
$422$	− 26.9444i	− 1.31163i
$423$	− 8.44949i	− 0.410828i
$424$	2.69694	0.130975
$425$	0	0
$426$	10.6515	0.516068
$427$	− 0.651531i	− 0.0315298i
$428$	21.7980i	1.05364i
$429$	−10.8990	−0.526208
$430$	0	0
$431$	−24.4949	−1.17988	−0.589939	−	0.807448i	$-0.700848\pi$
$431$	−24.4949	−1.17988	−0.589939	+	0.807448i	$0.700848\pi$
$432$	4.00000i	0.192450i
$433$	− 2.79796i	− 0.134461i	−0.997737	−	0.0672307i	$-0.978584\pi$
$433$	− 2.79796i	− 0.134461i	0.997737	−	0.0672307i	$-0.0214163\pi$
$434$	−0.247449	−0.0118779
$435$	0	0
$436$	46.2020	2.21268
$437$	− 4.44949i	− 0.212848i
$438$	− 13.1010i	− 0.625991i
$439$	36.6969	1.75145	0.875725	−	0.482811i	$-0.160384\pi$
$439$	36.6969	1.75145	0.875725	+	0.482811i	$0.160384\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	59.3939i	2.82508i
$443$	20.4495i	0.971585i	0.874074	+	0.485792i	$0.161469\pi$
$443$	20.4495i	0.971585i	−0.874074	+	0.485792i	$0.838531\pi$
$444$	−15.5959	−0.740150
$445$	0	0
$446$	−52.8990	−2.50484
$447$	− 1.34847i	− 0.0637804i
$448$	− 8.00000i	− 0.377964i
$449$	21.2474	1.00273	0.501365	−	0.865236i	$-0.332832\pi$
$449$	21.2474	1.00273	0.501365	+	0.865236i	$0.332832\pi$
$450$	0	0
$451$	13.3485	0.628555
$452$	− 6.60612i	− 0.310726i
$453$	− 14.0000i	− 0.657777i
$454$	53.3939	2.50590
$455$	0	0
$456$	−21.7980	−1.02078
$457$	0.101021i	0.00472554i	0.999997	+	0.00236277i	$0.000752094\pi$
$457$	0.101021i	0.00472554i	−0.999997	+	0.00236277i	$0.999248\pi$
$458$	− 69.7980i	− 3.26144i
$459$	5.44949	0.254360
$460$	0	0
$461$	−18.4949	−0.861393	−0.430697	−	0.902497i	$-0.641732\pi$
$461$	−18.4949	−0.861393	−0.430697	+	0.902497i	$0.641732\pi$
$462$	6.00000i	0.279145i
$463$	24.9444i	1.15926i	0.814878	+	0.579632i	$0.196804\pi$
$463$	24.9444i	1.15926i	−0.814878	+	0.579632i	$0.803196\pi$
$464$	−41.3939	−1.92166
$465$	0	0
$466$	−53.3939	−2.47342
$467$	− 34.8434i	− 1.61236i	−0.591671	−	0.806179i	$-0.701532\pi$
$467$	− 34.8434i	− 1.61236i	0.591671	−	0.806179i	$-0.298468\pi$
$468$	− 17.7980i	− 0.822711i
$469$	−7.00000	−0.323230
$470$	0	0
$471$	18.5959	0.856855
$472$	− 50.6969i	− 2.33352i
$473$	− 4.89898i	− 0.225255i
$474$	−9.79796	−0.450035
$475$	0	0
$476$	21.7980	0.999108
$477$	0.550510i	0.0252061i
$478$	16.0454i	0.733900i
$479$	−32.9444	−1.50527	−0.752634	−	0.658439i	$-0.771217\pi$
$479$	−32.9444	−1.50527	−0.752634	+	0.658439i	$0.771217\pi$
$480$	0	0
$481$	17.3485	0.791022
$482$	71.8888i	3.27444i
$483$	− 1.00000i	− 0.0455016i
$484$	20.0000	0.909091
$485$	0	0
$486$	−2.44949	−0.111111
$487$	− 18.9444i	− 0.858452i	−0.903197	−	0.429226i	$-0.858786\pi$
$487$	− 18.9444i	− 0.858452i	0.903197	−	0.429226i	$-0.141214\pi$
$488$	3.19184i	0.144488i
$489$	10.0000	0.452216
$490$	0	0
$491$	12.5505	0.566397	0.283198	−	0.959061i	$-0.408605\pi$
$491$	12.5505	0.566397	0.283198	+	0.959061i	$0.408605\pi$
$492$	21.7980i	0.982728i
$493$	56.3939i	2.53985i
$494$	48.4949	2.18189
$495$	0	0
$496$	0.404082	0.0181438
$497$	4.34847i	0.195056i
$498$	37.3485i	1.67362i
$499$	1.00000	0.0447661	0.0223831	−	0.999749i	$-0.492875\pi$
$499$	1.00000	0.0447661	0.0223831	+	0.999749i	$0.492875\pi$
$500$	0	0
$501$	13.3485	0.596366
$502$	− 44.0908i	− 1.96787i
$503$	− 7.04541i	− 0.314139i	−0.987588	−	0.157070i	$-0.949795\pi$
$503$	− 7.04541i	− 0.314139i	0.987588	−	0.157070i	$-0.0502047\pi$
$504$	−4.89898	−0.218218
$505$	0	0
$506$	6.00000	0.266733
$507$	6.79796i	0.301908i
$508$	6.20204i	0.275171i
$509$	−28.8990	−1.28092	−0.640462	−	0.767990i	$-0.721257\pi$
$509$	−28.8990	−1.28092	−0.640462	+	0.767990i	$0.721257\pi$
$510$	0	0
$511$	5.34847	0.236602
$512$	39.1918i	1.73205i
$513$	− 4.44949i	− 0.196450i
$514$	−62.0908	−2.73871
$515$	0	0
$516$	8.00000	0.352180
$517$	20.6969i	0.910250i
$518$	− 9.55051i	− 0.419625i
$519$	−19.5959	−0.860165
$520$	0	0
$521$	−43.8434	−1.92081	−0.960406	−	0.278603i	$-0.910129\pi$
$521$	−43.8434	−1.92081	−0.960406	+	0.278603i	$0.910129\pi$
$522$	− 25.3485i	− 1.10947i
$523$	33.3939i	1.46021i	0.683334	+	0.730106i	$0.260529\pi$
$523$	33.3939i	1.46021i	−0.683334	+	0.730106i	$0.739471\pi$
$524$	78.3837	3.42421
$525$	0	0
$526$	−66.7423	−2.91010
$527$	− 0.550510i	− 0.0239806i
$528$	− 9.79796i	− 0.426401i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	10.3485	0.449085
$532$	− 17.7980i	− 0.771639i
$533$	− 24.2474i	− 1.05027i
$534$	−41.3939	−1.79129
$535$	0	0
$536$	34.2929	1.48123
$537$	− 6.00000i	− 0.258919i
$538$	− 13.3485i	− 0.575493i
$539$	14.6969	0.633042
$540$	0	0
$541$	12.8990	0.554570	0.277285	−	0.960788i	$-0.410565\pi$
$541$	12.8990	0.554570	0.277285	+	0.960788i	$0.410565\pi$
$542$	− 77.6413i	− 3.33498i
$543$	8.89898i	0.381892i
$544$	0	0
$545$	0	0
$546$	10.8990	0.466433
$547$	− 28.0000i	− 1.19719i	−0.801050	−	0.598597i	$-0.795725\pi$
$547$	− 28.0000i	− 1.19719i	0.801050	−	0.598597i	$-0.204275\pi$
$548$	67.5959i	2.88755i
$549$	−0.651531	−0.0278067
$550$	0	0
$551$	46.0454	1.96160
$552$	4.89898i	0.208514i
$553$	− 4.00000i	− 0.170097i
$554$	−24.4949	−1.04069
$555$	0	0
$556$	−19.1918	−0.813915
$557$	− 19.0454i	− 0.806980i	−0.914984	−	0.403490i	$-0.867797\pi$
$557$	− 19.0454i	− 0.806980i	0.914984	−	0.403490i	$-0.132203\pi$
$558$	0.247449i	0.0104753i
$559$	−8.89898	−0.376387
$560$	0	0
$561$	−13.3485	−0.563573
$562$	47.3939i	1.99919i
$563$	− 5.44949i	− 0.229669i	−0.993385	−	0.114834i	$-0.963366\pi$
$563$	− 5.44949i	− 0.229669i	0.993385	−	0.114834i	$-0.0366337\pi$
$564$	−33.7980	−1.42315
$565$	0	0
$566$	5.14643	0.216321
$567$	− 1.00000i	− 0.0419961i
$568$	− 21.3031i	− 0.893857i
$569$	28.2929	1.18610	0.593049	−	0.805166i	$-0.297924\pi$
$569$	28.2929	1.18610	0.593049	+	0.805166i	$0.297924\pi$
$570$	0	0
$571$	13.1464	0.550161	0.275080	−	0.961421i	$-0.411296\pi$
$571$	13.1464	0.550161	0.275080	+	0.961421i	$0.411296\pi$
$572$	43.5959i	1.82284i
$573$	18.2474i	0.762298i
$574$	−13.3485	−0.557154
$575$	0	0
$576$	−8.00000	−0.333333
$577$	− 28.0000i	− 1.16566i	−0.812596	−	0.582828i	$-0.801946\pi$
$577$	− 28.0000i	− 1.16566i	0.812596	−	0.582828i	$-0.198054\pi$
$578$	31.1010i	1.29363i
$579$	6.69694	0.278315
$580$	0	0
$581$	−15.2474	−0.632571
$582$	− 7.59592i	− 0.314861i
$583$	− 1.34847i	− 0.0558479i
$584$	−26.2020	−1.08425
$585$	0	0
$586$	52.0454	2.14998
$587$	− 6.00000i	− 0.247647i	−0.992304	−	0.123823i	$-0.960484\pi$
$587$	− 6.00000i	− 0.247647i	0.992304	−	0.123823i	$-0.0395156\pi$
$588$	24.0000i	0.989743i
$589$	−0.449490	−0.0185209
$590$	0	0
$591$	−22.8990	−0.941938
$592$	15.5959i	0.640988i
$593$	− 27.5505i	− 1.13136i	−0.824624	−	0.565682i	$-0.808613\pi$
$593$	− 27.5505i	− 1.13136i	0.824624	−	0.565682i	$-0.191387\pi$
$594$	6.00000	0.246183
$595$	0	0
$596$	−5.39388	−0.220942
$597$	− 2.89898i	− 0.118647i
$598$	− 10.8990i	− 0.445692i
$599$	2.69694	0.110194	0.0550970	−	0.998481i	$-0.482453\pi$
$599$	2.69694	0.110194	0.0550970	+	0.998481i	$0.482453\pi$
$600$	0	0
$601$	5.00000	0.203954	0.101977	−	0.994787i	$-0.467483\pi$
$601$	5.00000	0.203954	0.101977	+	0.994787i	$0.467483\pi$
$602$	4.89898i	0.199667i
$603$	7.00000i	0.285062i
$604$	−56.0000	−2.27861
$605$	0	0
$606$	30.7423	1.24882
$607$	− 16.2474i	− 0.659464i	−0.944075	−	0.329732i	$-0.893042\pi$
$607$	− 16.2474i	− 0.659464i	0.944075	−	0.329732i	$-0.106958\pi$
$608$	0	0
$609$	10.3485	0.419341
$610$	0	0
$611$	37.5959	1.52097
$612$	− 21.7980i	− 0.881130i
$613$	− 14.0000i	− 0.565455i	−0.959200	−	0.282727i	$-0.908761\pi$
$613$	− 14.0000i	− 0.565455i	0.959200	−	0.282727i	$-0.0912392\pi$
$614$	−6.49490	−0.262113
$615$	0	0
$616$	12.0000	0.483494
$617$	12.5505i	0.505265i	0.967562	+	0.252632i	$0.0812963\pi$
$617$	12.5505i	0.505265i	−0.967562	+	0.252632i	$0.918704\pi$
$618$	− 31.1010i	− 1.25107i
$619$	4.00000	0.160774	0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000	0.160774	0.0803868	+	0.996764i	$0.474384\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	− 29.3939i	− 1.17859i
$623$	− 16.8990i	− 0.677043i
$624$	−17.7980	−0.712489
$625$	0	0
$626$	−48.2474	−1.92836
$627$	10.8990i	0.435263i
$628$	− 74.3837i	− 2.96823i
$629$	21.2474	0.847191
$630$	0	0
$631$	29.5505	1.17639	0.588194	−	0.808720i	$-0.299839\pi$
$631$	29.5505	1.17639	0.588194	+	0.808720i	$0.299839\pi$
$632$	19.5959i	0.779484i
$633$	− 11.0000i	− 0.437211i
$634$	15.3031	0.607762
$635$	0	0
$636$	2.20204	0.0873166
$637$	− 26.6969i	− 1.05777i
$638$	62.0908i	2.45820i
$639$	4.34847	0.172023
$640$	0	0
$641$	26.9444	1.06424	0.532120	−	0.846669i	$-0.321396\pi$
$641$	26.9444	1.06424	0.532120	+	0.846669i	$0.321396\pi$
$642$	13.3485i	0.526822i
$643$	9.69694i	0.382410i	0.981550	+	0.191205i	$0.0612395\pi$
$643$	9.69694i	0.382410i	−0.981550	+	0.191205i	$0.938760\pi$
$644$	−4.00000	−0.157622
$645$	0	0
$646$	59.3939	2.33682
$647$	1.95459i	0.0768430i	0.999262	+	0.0384215i	$0.0122329\pi$
$647$	1.95459i	0.0768430i	−0.999262	+	0.0384215i	$0.987767\pi$
$648$	4.89898i	0.192450i
$649$	−25.3485	−0.995014
$650$	0	0
$651$	−0.101021	−0.00395931
$652$	− 40.0000i	− 1.56652i
$653$	− 43.8434i	− 1.71572i	−0.513881	−	0.857862i	$-0.671793\pi$
$653$	− 43.8434i	− 1.71572i	0.513881	−	0.857862i	$-0.328207\pi$
$654$	28.2929	1.10634
$655$	0	0
$656$	21.7980	0.851067
$657$	− 5.34847i	− 0.208664i
$658$	− 20.6969i	− 0.806851i
$659$	5.14643	0.200476	0.100238	−	0.994963i	$-0.468040\pi$
$659$	5.14643	0.200476	0.100238	+	0.994963i	$0.468040\pi$
$660$	0	0
$661$	46.0908	1.79272	0.896362	−	0.443322i	$-0.146200\pi$
$661$	46.0908	1.79272	0.896362	+	0.443322i	$0.146200\pi$
$662$	− 60.2474i	− 2.34158i
$663$	24.2474i	0.941693i
$664$	74.6969	2.89880
$665$	0	0
$666$	−9.55051	−0.370075
$667$	− 10.3485i	− 0.400694i
$668$	− 53.3939i	− 2.06587i
$669$	−21.5959	−0.834946
$670$	0	0
$671$	1.59592	0.0616097
$672$	0	0
$673$	− 22.4495i	− 0.865364i	−0.901547	−	0.432682i	$-0.857567\pi$
$673$	− 22.4495i	− 0.865364i	0.901547	−	0.432682i	$-0.142433\pi$
$674$	−48.4949	−1.86795
$675$	0	0
$676$	27.1918	1.04584
$677$	− 12.5505i	− 0.482355i	−0.970481	−	0.241178i	$-0.922466\pi$
$677$	− 12.5505i	− 0.482355i	0.970481	−	0.241178i	$-0.0775336\pi$
$678$	− 4.04541i	− 0.155363i
$679$	3.10102	0.119006
$680$	0	0
$681$	21.7980	0.835300
$682$	− 0.606123i	− 0.0232097i
$683$	− 18.2474i	− 0.698219i	−0.937082	−	0.349110i	$-0.886484\pi$
$683$	− 18.2474i	− 0.698219i	0.937082	−	0.349110i	$-0.113516\pi$
$684$	−17.7980	−0.680522
$685$	0	0
$686$	−31.8434	−1.21579
$687$	− 28.4949i	− 1.08715i
$688$	− 8.00000i	− 0.304997i
$689$	−2.44949	−0.0933181
$690$	0	0
$691$	16.2020	0.616355	0.308177	−	0.951329i	$-0.400281\pi$
$691$	16.2020	0.616355	0.308177	+	0.951329i	$0.400281\pi$
$692$	78.3837i	2.97970i
$693$	2.44949i	0.0930484i
$694$	−70.7878	−2.68707
$695$	0	0
$696$	−50.6969	−1.92166
$697$	− 29.6969i	− 1.12485i
$698$	57.5505i	2.17832i
$699$	−21.7980	−0.824475
$700$	0	0
$701$	−52.0454	−1.96573	−0.982864	−	0.184332i	$-0.940988\pi$
$701$	−52.0454	−1.96573	−0.982864	+	0.184332i	$0.940988\pi$
$702$	− 10.8990i	− 0.411355i
$703$	− 17.3485i	− 0.654310i
$704$	19.5959	0.738549
$705$	0	0
$706$	38.0908	1.43357
$707$	12.5505i	0.472011i
$708$	− 41.3939i	− 1.55568i
$709$	28.7423	1.07944	0.539721	−	0.841844i	$-0.318530\pi$
$709$	28.7423	1.07944	0.539721	+	0.841844i	$0.318530\pi$
$710$	0	0
$711$	−4.00000	−0.150012
$712$	82.7878i	3.10260i
$713$	0.101021i	0.00378325i
$714$	13.3485	0.499554
$715$	0	0
$716$	−24.0000	−0.896922
$717$	6.55051i	0.244633i
$718$	− 8.69694i	− 0.324567i
$719$	11.9444	0.445450	0.222725	−	0.974881i	$-0.428505\pi$
$719$	11.9444	0.445450	0.222725	+	0.974881i	$0.428505\pi$
$720$	0	0
$721$	12.6969	0.472859
$722$	− 1.95459i	− 0.0727424i
$723$	29.3485i	1.09148i
$724$	35.5959	1.32291
$725$	0	0
$726$	12.2474	0.454545
$727$	− 16.3031i	− 0.604647i	−0.953205	−	0.302324i	$-0.902238\pi$
$727$	− 16.3031i	− 0.604647i	0.953205	−	0.302324i	$-0.0977623\pi$
$728$	− 21.7980i	− 0.807886i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−10.8990	−0.403113
$732$	2.60612i	0.0963251i
$733$	8.59592i	0.317497i	0.987319	+	0.158749i	$0.0507460\pi$
$733$	8.59592i	0.317497i	−0.987319	+	0.158749i	$0.949254\pi$
$734$	33.5505	1.23837
$735$	0	0
$736$	0	0
$737$	− 17.1464i	− 0.631597i
$738$	13.3485i	0.491364i
$739$	9.20204	0.338503	0.169251	−	0.985573i	$-0.445865\pi$
$739$	9.20204	0.338503	0.169251	+	0.985573i	$0.445865\pi$
$740$	0	0
$741$	19.7980	0.727296
$742$	1.34847i	0.0495039i
$743$	21.7980i	0.799690i	0.916583	+	0.399845i	$0.130936\pi$
$743$	21.7980i	0.799690i	−0.916583	+	0.399845i	$0.869064\pi$
$744$	0.494897	0.0181438
$745$	0	0
$746$	−67.5959	−2.47486
$747$	15.2474i	0.557875i
$748$	53.3939i	1.95227i
$749$	−5.44949	−0.199120
$750$	0	0
$751$	30.6515	1.11849	0.559245	−	0.829002i	$-0.311091\pi$
$751$	30.6515	1.11849	0.559245	+	0.829002i	$0.311091\pi$
$752$	33.7980i	1.23248i
$753$	− 18.0000i	− 0.655956i
$754$	112.788	4.10749
$755$	0	0
$756$	−4.00000	−0.145479
$757$	− 3.69694i	− 0.134368i	−0.997741	−	0.0671838i	$-0.978599\pi$
$757$	− 3.69694i	− 0.134368i	0.997741	−	0.0671838i	$-0.0214014\pi$
$758$	62.2020i	2.25928i
$759$	2.44949	0.0889108
$760$	0	0
$761$	14.1464	0.512808	0.256404	−	0.966570i	$-0.417462\pi$
$761$	14.1464	0.512808	0.256404	+	0.966570i	$0.417462\pi$
$762$	3.79796i	0.137586i
$763$	11.5505i	0.418157i
$764$	72.9898	2.64068
$765$	0	0
$766$	−4.04541	−0.146167
$767$	46.0454i	1.66260i
$768$	32.0000i	1.15470i
$769$	−10.4495	−0.376818	−0.188409	−	0.982091i	$-0.560333\pi$
$769$	−10.4495	−0.376818	−0.188409	+	0.982091i	$0.560333\pi$
$770$	0	0
$771$	−25.3485	−0.912903
$772$	− 26.7878i	− 0.964112i
$773$	16.2929i	0.586013i	0.956110	+	0.293007i	$0.0946558\pi$
$773$	16.2929i	0.586013i	−0.956110	+	0.293007i	$0.905344\pi$
$774$	4.89898	0.176090
$775$	0	0
$776$	−15.1918	−0.545355
$777$	− 3.89898i	− 0.139875i
$778$	− 8.09082i	− 0.290070i
$779$	−24.2474	−0.868755
$780$	0	0
$781$	−10.6515	−0.381142
$782$	− 13.3485i	− 0.477340i
$783$	− 10.3485i	− 0.369824i
$784$	24.0000	0.857143
$785$	0	0
$786$	48.0000	1.71210
$787$	− 21.6969i	− 0.773412i	−0.922203	−	0.386706i	$-0.873613\pi$
$787$	− 21.6969i	− 0.773412i	0.922203	−	0.386706i	$-0.126387\pi$
$788$	91.5959i	3.26297i
$789$	−27.2474	−0.970035
$790$	0	0
$791$	1.65153	0.0587217
$792$	− 12.0000i	− 0.426401i
$793$	− 2.89898i	− 0.102946i
$794$	−33.7980	−1.19944
$795$	0	0
$796$	−11.5959	−0.411006
$797$	9.24745i	0.327561i	0.986497	+	0.163781i	$0.0523690\pi$
$797$	9.24745i	0.327561i	−0.986497	+	0.163781i	$0.947631\pi$
$798$	− 10.8990i	− 0.385820i
$799$	46.0454	1.62897
$800$	0	0
$801$	−16.8990	−0.597096
$802$	32.0908i	1.13317i
$803$	13.1010i	0.462325i
$804$	28.0000	0.987484
$805$	0	0
$806$	−1.10102	−0.0387818
$807$	− 5.44949i	− 0.191831i
$808$	− 61.4847i	− 2.16302i
$809$	−6.55051	−0.230304	−0.115152	−	0.993348i	$-0.536735\pi$
$809$	−6.55051	−0.230304	−0.115152	+	0.993348i	$0.536735\pi$
$810$	0	0
$811$	−42.3939	−1.48865	−0.744325	−	0.667817i	$-0.767229\pi$
$811$	−42.3939	−1.48865	−0.744325	+	0.667817i	$0.767229\pi$
$812$	− 41.3939i	− 1.45264i
$813$	− 31.6969i	− 1.11166i
$814$	23.3939	0.819955
$815$	0	0
$816$	−21.7980	−0.763081
$817$	8.89898i	0.311336i
$818$	53.6413i	1.87552i
$819$	4.44949	0.155478
$820$	0	0
$821$	21.3031	0.743482	0.371741	−	0.928336i	$-0.378761\pi$
$821$	21.3031	0.743482	0.371741	+	0.928336i	$0.378761\pi$
$822$	41.3939i	1.44378i
$823$	− 3.59592i	− 0.125346i	−0.998034	−	0.0626729i	$-0.980038\pi$
$823$	− 3.59592i	− 0.125346i	0.998034	−	0.0626729i	$-0.0199625\pi$
$824$	−62.2020	−2.16691
$825$	0	0
$826$	25.3485	0.881986
$827$	32.1464i	1.11784i	0.829221	+	0.558920i	$0.188784\pi$
$827$	32.1464i	1.11784i	−0.829221	+	0.558920i	$0.811216\pi$
$828$	4.00000i	0.139010i
$829$	27.6969	0.961954	0.480977	−	0.876733i	$-0.340282\pi$
$829$	27.6969	0.961954	0.480977	+	0.876733i	$0.340282\pi$
$830$	0	0
$831$	−10.0000	−0.346896
$832$	− 35.5959i	− 1.23407i
$833$	− 32.6969i	− 1.13288i
$834$	−11.7526	−0.406958
$835$	0	0
$836$	43.5959	1.50780
$837$	0.101021i	0.00349178i
$838$	82.1816i	2.83892i
$839$	45.1918	1.56020	0.780098	−	0.625658i	$-0.215169\pi$
$839$	45.1918	1.56020	0.780098	+	0.625658i	$0.215169\pi$
$840$	0	0
$841$	78.0908	2.69279
$842$	54.4949i	1.87802i
$843$	19.3485i	0.666397i
$844$	−44.0000	−1.51454
$845$	0	0
$846$	−20.6969	−0.711575
$847$	5.00000i	0.171802i
$848$	− 2.20204i	− 0.0756184i
$849$	2.10102	0.0721068
$850$	0	0
$851$	−3.89898	−0.133655
$852$	− 17.3939i	− 0.595904i
$853$	− 46.0908i	− 1.57812i	−0.614316	−	0.789060i	$-0.710568\pi$
$853$	− 46.0908i	− 1.57812i	0.614316	−	0.789060i	$-0.289432\pi$
$854$	−1.59592	−0.0546112
$855$	0	0
$856$	26.6969	0.912483
$857$	− 13.5959i	− 0.464428i	−0.972665	−	0.232214i	$-0.925403\pi$
$857$	− 13.5959i	− 0.464428i	0.972665	−	0.232214i	$-0.0745969\pi$
$858$	26.6969i	0.911418i
$859$	−38.1918	−1.30309	−0.651544	−	0.758611i	$-0.725879\pi$
$859$	−38.1918	−1.30309	−0.651544	+	0.758611i	$0.725879\pi$
$860$	0	0
$861$	−5.44949	−0.185718
$862$	60.0000i	2.04361i
$863$	− 6.49490i	− 0.221089i	−0.993871	−	0.110544i	$-0.964741\pi$
$863$	− 6.49490i	− 0.221089i	0.993871	−	0.110544i	$-0.0352595\pi$
$864$	0	0
$865$	0	0
$866$	−6.85357	−0.232894
$867$	12.6969i	0.431211i
$868$	0.404082i	0.0137154i
$869$	9.79796	0.332373
$870$	0	0
$871$	−31.1464	−1.05536
$872$	− 56.5857i	− 1.91623i
$873$	− 3.10102i	− 0.104954i
$874$	−10.8990	−0.368663
$875$	0	0
$876$	−21.3939	−0.722832
$877$	− 10.4949i	− 0.354388i	−0.984176	−	0.177194i	$-0.943298\pi$
$877$	− 10.4949i	− 0.354388i	0.984176	−	0.177194i	$-0.0567019\pi$
$878$	− 89.8888i	− 3.03360i
$879$	21.2474	0.716659
$880$	0	0
$881$	8.44949	0.284671	0.142335	−	0.989819i	$-0.454539\pi$
$881$	8.44949	0.284671	0.142335	+	0.989819i	$0.454539\pi$
$882$	14.6969i	0.494872i
$883$	37.5505i	1.26368i	0.775101	+	0.631838i	$0.217699\pi$
$883$	37.5505i	1.26368i	−0.775101	+	0.631838i	$0.782301\pi$
$884$	96.9898	3.26212
$885$	0	0
$886$	50.0908	1.68283
$887$	− 6.49490i	− 0.218077i	−0.994038	−	0.109039i	$-0.965223\pi$
$887$	− 6.49490i	− 0.218077i	0.994038	−	0.109039i	$-0.0347772\pi$
$888$	19.1010i	0.640988i
$889$	−1.55051	−0.0520024
$890$	0	0
$891$	2.44949	0.0820610
$892$	86.3837i	2.89234i
$893$	− 37.5959i	− 1.25810i
$894$	−3.30306	−0.110471
$895$	0	0
$896$	−19.5959	−0.654654
$897$	− 4.44949i	− 0.148564i
$898$	− 52.0454i	− 1.73678i
$899$	−1.04541	−0.0348663
$900$	0	0
$901$	−3.00000	−0.0999445
$902$	− 32.6969i	− 1.08869i
$903$	2.00000i	0.0665558i
$904$	−8.09082	−0.269097
$905$	0	0
$906$	−34.2929	−1.13930
$907$	38.7980i	1.28827i	0.764914	+	0.644133i	$0.222781\pi$
$907$	38.7980i	1.28827i	−0.764914	+	0.644133i	$0.777219\pi$
$908$	− 87.1918i	− 2.89356i
$909$	12.5505	0.416274
$910$	0	0
$911$	−14.2020	−0.470535	−0.235267	−	0.971931i	$-0.575597\pi$
$911$	−14.2020	−0.470535	−0.235267	+	0.971931i	$0.575597\pi$
$912$	17.7980i	0.589349i
$913$	− 37.3485i	− 1.23605i
$914$	0.247449	0.00818488
$915$	0	0
$916$	−113.980	−3.76599
$917$	19.5959i	0.647114i
$918$	− 13.3485i	− 0.440565i
$919$	45.3939	1.49741	0.748703	−	0.662906i	$-0.230677\pi$
$919$	45.3939	1.49741	0.748703	+	0.662906i	$0.230677\pi$
$920$	0	0
$921$	−2.65153	−0.0873709
$922$	45.3031i	1.49198i
$923$	19.3485i	0.636863i
$924$	9.79796	0.322329
$925$	0	0
$926$	61.1010	2.00790
$927$	− 12.6969i	− 0.417022i
$928$	0	0
$929$	−22.8434	−0.749467	−0.374733	−	0.927133i	$-0.622266\pi$
$929$	−22.8434	−0.749467	−0.374733	+	0.927133i	$0.622266\pi$
$930$	0	0
$931$	−26.6969	−0.874957
$932$	87.1918i	2.85606i
$933$	− 12.0000i	− 0.392862i
$934$	−85.3485	−2.79269
$935$	0	0
$936$	−21.7980	−0.712489
$937$	− 8.89898i	− 0.290717i	−0.989379	−	0.145358i	$-0.953566\pi$
$937$	− 8.89898i	− 0.290717i	0.989379	−	0.145358i	$-0.0464336\pi$
$938$	17.1464i	0.559851i
$939$	−19.6969	−0.642785
$940$	0	0
$941$	−24.8536	−0.810203	−0.405102	−	0.914272i	$-0.632764\pi$
$941$	−24.8536	−0.810203	−0.405102	+	0.914272i	$0.632764\pi$
$942$	− 45.5505i	− 1.48412i
$943$	5.44949i	0.177460i
$944$	−41.3939	−1.34726
$945$	0	0
$946$	−12.0000	−0.390154
$947$	− 0.494897i	− 0.0160820i	−0.999968	−	0.00804100i	$-0.997440\pi$
$947$	− 0.494897i	− 0.0160820i	0.999968	−	0.00804100i	$-0.00255956\pi$
$948$	16.0000i	0.519656i
$949$	23.7980	0.772514
$950$	0	0
$951$	6.24745	0.202587
$952$	− 26.6969i	− 0.865253i
$953$	− 10.4041i	− 0.337021i	−0.985700	−	0.168511i	$-0.946104\pi$
$953$	− 10.4041i	− 0.337021i	0.985700	−	0.168511i	$-0.0538958\pi$
$954$	1.34847	0.0436583
$955$	0	0
$956$	26.2020	0.847435
$957$	25.3485i	0.819400i
$958$	80.6969i	2.60720i
$959$	−16.8990	−0.545697
$960$	0	0
$961$	−30.9898	−0.999671
$962$	− 42.4949i	− 1.37009i
$963$	5.44949i	0.175607i
$964$	117.394	3.78100
$965$	0	0
$966$	−2.44949	−0.0788110
$967$	54.0454i	1.73798i	0.494827	+	0.868992i	$0.335231\pi$
$967$	54.0454i	1.73798i	−0.494827	+	0.868992i	$0.664769\pi$
$968$	− 24.4949i	− 0.787296i
$969$	24.2474	0.778940
$970$	0	0
$971$	22.2929	0.715412	0.357706	−	0.933834i	$-0.383559\pi$
$971$	22.2929	0.715412	0.357706	+	0.933834i	$0.383559\pi$
$972$	4.00000i	0.128300i
$973$	− 4.79796i	− 0.153816i
$974$	−46.4041	−1.48688
$975$	0	0
$976$	2.60612	0.0834200
$977$	19.6515i	0.628708i	0.949306	+	0.314354i	$0.101788\pi$
$977$	19.6515i	0.628708i	−0.949306	+	0.314354i	$0.898212\pi$
$978$	− 24.4949i	− 0.783260i
$979$	41.3939	1.32295
$980$	0	0
$981$	11.5505	0.368779
$982$	− 30.7423i	− 0.981028i
$983$	33.7423i	1.07621i	0.842877	+	0.538107i	$0.180860\pi$
$983$	33.7423i	1.07621i	−0.842877	+	0.538107i	$0.819140\pi$
$984$	26.6969	0.851067
$985$	0	0
$986$	138.136	4.39915
$987$	− 8.44949i	− 0.268950i
$988$	− 79.1918i	− 2.51943i
$989$	2.00000	0.0635963
$990$	0	0
$991$	57.7878	1.83569	0.917844	−	0.396941i	$-0.129928\pi$
$991$	57.7878	1.83569	0.917844	+	0.396941i	$0.129928\pi$
$992$	0	0
$993$	− 24.5959i	− 0.780528i
$994$	10.6515	0.337846
$995$	0	0
$996$	60.9898	1.93254
$997$	40.0908i	1.26969i	0.772640	+	0.634844i	$0.218936\pi$
$997$	40.0908i	1.26969i	−0.772640	+	0.634844i	$0.781064\pi$
$998$	− 2.44949i	− 0.0775372i
$999$	−3.89898	−0.123358

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1725.2.b.m.1174.1		4
5.2	odd	4		1725.2.a.y.1.2		2
5.3	odd	4		345.2.a.i.1.1	✓	2
5.4	even	2	inner	1725.2.b.m.1174.4		4
15.2	even	4		5175.2.a.bl.1.1		2
15.8	even	4		1035.2.a.k.1.2		2
20.3	even	4		5520.2.a.bi.1.1		2
115.68	even	4		7935.2.a.t.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.a.i.1.1	✓	2	5.3	odd	4
1035.2.a.k.1.2		2	15.8	even	4
1725.2.a.y.1.2		2	5.2	odd	4
1725.2.b.m.1174.1		4	1.1	even	1	trivial
1725.2.b.m.1174.4		4	5.4	even	2	inner
5175.2.a.bl.1.1		2	15.2	even	4
5520.2.a.bi.1.1		2	20.3	even	4
7935.2.a.t.1.1		2	115.68	even	4

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:	\( N \)	\(=\)	\( 1725 = 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1725.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2.44949i q^{2} -1.00000i q^{3} -4.00000 q^{4} -2.44949 q^{6} -1.00000i q^{7} +4.89898i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.44949i q^{2} -1.00000i q^{3} -4.00000 q^{4} -2.44949 q^{6} -1.00000i q^{7} +4.89898i q^{8} -1.00000 q^{9} +2.44949 q^{11} +4.00000i q^{12} -4.44949i q^{13} -2.44949 q^{14} +4.00000 q^{16} -5.44949i q^{17} +2.44949i q^{18} -4.44949 q^{19} -1.00000 q^{21} -6.00000i q^{22} +1.00000i q^{23} +4.89898 q^{24} -10.8990 q^{26} +1.00000i q^{27} +4.00000i q^{28} -10.3485 q^{29} +0.101021 q^{31} -2.44949i q^{33} -13.3485 q^{34} +4.00000 q^{36} +3.89898i q^{37} +10.8990i q^{38} -4.44949 q^{39} +5.44949 q^{41} +2.44949i q^{42} -2.00000i q^{43} -9.79796 q^{44} +2.44949 q^{46} +8.44949i q^{47} -4.00000i q^{48} +6.00000 q^{49} -5.44949 q^{51} +17.7980i q^{52} -0.550510i q^{53} +2.44949 q^{54} +4.89898 q^{56} +4.44949i q^{57} +25.3485i q^{58} -10.3485 q^{59} +0.651531 q^{61} -0.247449i q^{62} +1.00000i q^{63} +8.00000 q^{64} -6.00000 q^{66} -7.00000i q^{67} +21.7980i q^{68} +1.00000 q^{69} -4.34847 q^{71} -4.89898i q^{72} +5.34847i q^{73} +9.55051 q^{74} +17.7980 q^{76} -2.44949i q^{77} +10.8990i q^{78} +4.00000 q^{79} +1.00000 q^{81} -13.3485i q^{82} -15.2474i q^{83} +4.00000 q^{84} -4.89898 q^{86} +10.3485i q^{87} +12.0000i q^{88} +16.8990 q^{89} -4.44949 q^{91} -4.00000i q^{92} -0.101021i q^{93} +20.6969 q^{94} +3.10102i q^{97} -14.6969i q^{98} -2.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{4} - 4 q^{9}+O(q^{10}) \) 4 * q - 16 * q^4 - 4 * q^9	\( 4 q - 16 q^{4} - 4 q^{9} + 16 q^{16} - 8 q^{19} - 4 q^{21} - 24 q^{26} - 12 q^{29} + 20 q^{31} - 24 q^{34} + 16 q^{36} - 8 q^{39} + 12 q^{41} + 24 q^{49} - 12 q^{51} - 12 q^{59} + 32 q^{61} + 32 q^{64} - 24 q^{66} + 4 q^{69} + 12 q^{71} + 48 q^{74} + 32 q^{76} + 16 q^{79} + 4 q^{81} + 16 q^{84} + 48 q^{89} - 8 q^{91} + 24 q^{94}+O(q^{100}) \) 4 * q - 16 * q^4 - 4 * q^9 + 16 * q^16 - 8 * q^19 - 4 * q^21 - 24 * q^26 - 12 * q^29 + 20 * q^31 - 24 * q^34 + 16 * q^36 - 8 * q^39 + 12 * q^41 + 24 * q^49 - 12 * q^51 - 12 * q^59 + 32 * q^61 + 32 * q^64 - 24 * q^66 + 4 * q^69 + 12 * q^71 + 48 * q^74 + 32 * q^76 + 16 * q^79 + 4 * q^81 + 16 * q^84 + 48 * q^89 - 8 * q^91 + 24 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more