LMFDB - Embedded newform 3450.2.d.c.2899.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, 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("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.d (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:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.c.2899.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} +1.00000i q^{12} +1.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -1.00000 q^{21} +3.00000i q^{22} +1.00000i q^{23} +1.00000 q^{24} +1.00000 q^{26} +1.00000i q^{27} +1.00000i q^{28} +9.00000 q^{29} -4.00000 q^{31} -1.00000i q^{32} +3.00000i q^{33} +6.00000 q^{34} +1.00000 q^{36} -4.00000i q^{37} -1.00000i q^{38} +1.00000 q^{39} +9.00000 q^{41} +1.00000i q^{42} +1.00000i q^{43} +3.00000 q^{44} +1.00000 q^{46} +6.00000i q^{47} -1.00000i q^{48} +6.00000 q^{49} +6.00000 q^{51} -1.00000i q^{52} -12.0000i q^{53} +1.00000 q^{54} +1.00000 q^{56} -1.00000i q^{57} -9.00000i q^{58} +6.00000 q^{59} -4.00000 q^{61} +4.00000i q^{62} +1.00000i q^{63} -1.00000 q^{64} +3.00000 q^{66} -4.00000i q^{67} -6.00000i q^{68} +1.00000 q^{69} -6.00000 q^{71} -1.00000i q^{72} +7.00000i q^{73} -4.00000 q^{74} -1.00000 q^{76} +3.00000i q^{77} -1.00000i q^{78} +1.00000 q^{79} +1.00000 q^{81} -9.00000i q^{82} +15.0000i q^{83} +1.00000 q^{84} +1.00000 q^{86} -9.00000i q^{87} -3.00000i q^{88} +18.0000 q^{89} +1.00000 q^{91} -1.00000i q^{92} +4.00000i q^{93} +6.00000 q^{94} -1.00000 q^{96} -4.00000i q^{97} -6.00000i q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	$ 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} - 2 q^{14} + 2 q^{16} + 2 q^{19} - 2 q^{21} + 2 q^{24} + 2 q^{26} + 18 q^{29} - 8 q^{31} + 12 q^{34} + 2 q^{36} + 2 q^{39} + 18 q^{41} + 6 q^{44} + 2 q^{46} + 12 q^{49} + 12 q^{51} + 2 q^{54} + 2 q^{56} + 12 q^{59} - 8 q^{61} - 2 q^{64} + 6 q^{66} + 2 q^{69} - 12 q^{71} - 8 q^{74} - 2 q^{76} + 2 q^{79} + 2 q^{81} + 2 q^{84} + 2 q^{86} + 36 q^{89} + 2 q^{91} + 12 q^{94} - 2 q^{96} + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^11 - 2 * q^14 + 2 * q^16 + 2 * q^19 - 2 * q^21 + 2 * q^24 + 2 * q^26 + 18 * q^29 - 8 * q^31 + 12 * q^34 + 2 * q^36 + 2 * q^39 + 18 * q^41 + 6 * q^44 + 2 * q^46 + 12 * q^49 + 12 * q^51 + 2 * q^54 + 2 * q^56 + 12 * q^59 - 8 * q^61 - 2 * q^64 + 6 * q^66 + 2 * q^69 - 12 * q^71 - 8 * q^74 - 2 * q^76 + 2 * q^79 + 2 * q^81 + 2 * q^84 + 2 * q^86 + 36 * q^89 + 2 * q^91 + 12 * q^94 - 2 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

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

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 1.00000i	− 0.577350i
$3$	− 1.00000i	− 0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	− 1.00000i	− 0.377964i	−0.981981	−	0.188982i	$-0.939481\pi$
$7$	− 1.00000i	− 0.377964i	0.981981	−	0.188982i	$-0.0605189\pi$
$8$	1.00000i	0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	−3.00000	−0.904534	−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000	−0.904534	−0.452267	+	0.891883i	$0.649385\pi$
$12$	1.00000i	0.288675i
$13$	1.00000i	0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$	1.00000i	0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$	−1.00000	−0.267261
$15$	0	0
$16$	1.00000	0.250000
$17$	6.00000i	1.45521i	0.685994	+	0.727607i	$0.259367\pi$
$17$	6.00000i	1.45521i	−0.685994	+	0.727607i	$0.740633\pi$
$18$	1.00000i	0.235702i
$19$	1.00000	0.229416	0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000	0.229416	0.114708	+	0.993399i	$0.463407\pi$
$20$	0	0
$21$	−1.00000	−0.218218
$22$	3.00000i	0.639602i
$23$	1.00000i	0.208514i
$23$	1.00000i	0.208514i
$24$	1.00000	0.204124
$25$	0	0
$26$	1.00000	0.196116
$27$	1.00000i	0.192450i
$28$	1.00000i	0.188982i
$29$	9.00000	1.67126	0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000	1.67126	0.835629	+	0.549294i	$0.185103\pi$
$30$	0	0
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	− 1.00000i	− 0.176777i
$33$	3.00000i	0.522233i
$34$	6.00000	1.02899
$35$	0	0
$36$	1.00000	0.166667
$37$	− 4.00000i	− 0.657596i	−0.944400	−	0.328798i	$-0.893356\pi$
$37$	− 4.00000i	− 0.657596i	0.944400	−	0.328798i	$-0.106644\pi$
$38$	− 1.00000i	− 0.162221i
$39$	1.00000	0.160128
$40$	0	0
$41$	9.00000	1.40556	0.702782	−	0.711405i	$-0.251941\pi$
$41$	9.00000	1.40556	0.702782	+	0.711405i	$0.251941\pi$
$42$	1.00000i	0.154303i
$43$	1.00000i	0.152499i	0.997089	+	0.0762493i	$0.0242945\pi$
$43$	1.00000i	0.152499i	−0.997089	+	0.0762493i	$0.975706\pi$
$44$	3.00000	0.452267
$45$	0	0
$46$	1.00000	0.147442
$47$	6.00000i	0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$	6.00000i	0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	− 1.00000i	− 0.144338i
$49$	6.00000	0.857143
$50$	0	0
$51$	6.00000	0.840168
$52$	− 1.00000i	− 0.138675i
$53$	− 12.0000i	− 1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$	− 12.0000i	− 1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	1.00000	0.133631
$57$	− 1.00000i	− 0.132453i
$58$	− 9.00000i	− 1.18176i
$59$	6.00000	0.781133	0.390567	−	0.920575i	$-0.372279\pi$
$59$	6.00000	0.781133	0.390567	+	0.920575i	$0.372279\pi$
$60$	0	0
$61$	−4.00000	−0.512148	−0.256074	−	0.966657i	$-0.582429\pi$
$61$	−4.00000	−0.512148	−0.256074	+	0.966657i	$0.582429\pi$
$62$	4.00000i	0.508001i
$63$	1.00000i	0.125988i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	3.00000	0.369274
$67$	− 4.00000i	− 0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$	− 4.00000i	− 0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	− 6.00000i	− 0.727607i
$69$	1.00000	0.120386
$70$	0	0
$71$	−6.00000	−0.712069	−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000	−0.712069	−0.356034	+	0.934473i	$0.615871\pi$
$72$	− 1.00000i	− 0.117851i
$73$	7.00000i	0.819288i	0.912245	+	0.409644i	$0.134347\pi$
$73$	7.00000i	0.819288i	−0.912245	+	0.409644i	$0.865653\pi$
$74$	−4.00000	−0.464991
$75$	0	0
$76$	−1.00000	−0.114708
$77$	3.00000i	0.341882i
$78$	− 1.00000i	− 0.113228i
$79$	1.00000	0.112509	0.0562544	−	0.998416i	$-0.482084\pi$
$79$	1.00000	0.112509	0.0562544	+	0.998416i	$0.482084\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	− 9.00000i	− 0.993884i
$83$	15.0000i	1.64646i	0.567705	+	0.823232i	$0.307831\pi$
$83$	15.0000i	1.64646i	−0.567705	+	0.823232i	$0.692169\pi$
$84$	1.00000	0.109109
$85$	0	0
$86$	1.00000	0.107833
$87$	− 9.00000i	− 0.964901i
$88$	− 3.00000i	− 0.319801i
$89$	18.0000	1.90800	0.953998	−	0.299813i	$-0.0969242\pi$
$89$	18.0000	1.90800	0.953998	+	0.299813i	$0.0969242\pi$
$90$	0	0
$91$	1.00000	0.104828
$92$	− 1.00000i	− 0.104257i
$93$	4.00000i	0.414781i
$94$	6.00000	0.618853
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 4.00000i	− 0.406138i	−0.979164	−	0.203069i	$-0.934908\pi$
$97$	− 4.00000i	− 0.406138i	0.979164	−	0.203069i	$-0.0650917\pi$
$98$	− 6.00000i	− 0.606092i
$99$	3.00000	0.301511
$100$	0	0
$101$	6.00000	0.597022	0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000	0.597022	0.298511	+	0.954406i	$0.403510\pi$
$102$	− 6.00000i	− 0.594089i
$103$	7.00000i	0.689730i	0.938652	+	0.344865i	$0.112075\pi$
$103$	7.00000i	0.689730i	−0.938652	+	0.344865i	$0.887925\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	−12.0000	−1.16554
$107$	− 12.0000i	− 1.16008i	−0.814587	−	0.580042i	$-0.803036\pi$
$107$	− 12.0000i	− 1.16008i	0.814587	−	0.580042i	$-0.196964\pi$
$108$	− 1.00000i	− 0.0962250i
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	−4.00000	−0.379663
$112$	− 1.00000i	− 0.0944911i
$113$	− 18.0000i	− 1.69330i	−0.532152	−	0.846649i	$-0.678617\pi$
$113$	− 18.0000i	− 1.69330i	0.532152	−	0.846649i	$-0.321383\pi$
$114$	−1.00000	−0.0936586
$115$	0	0
$116$	−9.00000	−0.835629
$117$	− 1.00000i	− 0.0924500i
$118$	− 6.00000i	− 0.552345i
$119$	6.00000	0.550019
$120$	0	0
$121$	−2.00000	−0.181818
$122$	4.00000i	0.362143i
$123$	− 9.00000i	− 0.811503i
$124$	4.00000	0.359211
$125$	0	0
$126$	1.00000	0.0890871
$127$	14.0000i	1.24230i	0.783692	+	0.621150i	$0.213334\pi$
$127$	14.0000i	1.24230i	−0.783692	+	0.621150i	$0.786666\pi$
$128$	1.00000i	0.0883883i
$129$	1.00000	0.0880451
$130$	0	0
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	− 3.00000i	− 0.261116i
$133$	− 1.00000i	− 0.0867110i
$134$	−4.00000	−0.345547
$135$	0	0
$136$	−6.00000	−0.514496
$137$	− 12.0000i	− 1.02523i	−0.858619	−	0.512615i	$-0.828677\pi$
$137$	− 12.0000i	− 1.02523i	0.858619	−	0.512615i	$-0.171323\pi$
$138$	− 1.00000i	− 0.0851257i
$139$	10.0000	0.848189	0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000	0.848189	0.424094	+	0.905618i	$0.360592\pi$
$140$	0	0
$141$	6.00000	0.505291
$142$	6.00000i	0.503509i
$143$	− 3.00000i	− 0.250873i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	7.00000	0.579324
$147$	− 6.00000i	− 0.494872i
$148$	4.00000i	0.328798i
$149$	0	0		−	1.00000i	$-0.5\pi$
$149$	0	0			1.00000i	$0.5\pi$
$150$	0	0
$151$	−10.0000	−0.813788	−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000	−0.813788	−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.00000i	0.0811107i
$153$	− 6.00000i	− 0.485071i
$154$	3.00000	0.241747
$155$	0	0
$156$	−1.00000	−0.0800641
$157$	8.00000i	0.638470i	0.947676	+	0.319235i	$0.103426\pi$
$157$	8.00000i	0.638470i	−0.947676	+	0.319235i	$0.896574\pi$
$158$	− 1.00000i	− 0.0795557i
$159$	−12.0000	−0.951662
$160$	0	0
$161$	1.00000	0.0788110
$162$	− 1.00000i	− 0.0785674i
$163$	16.0000i	1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$	16.0000i	1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$	−9.00000	−0.702782
$165$	0	0
$166$	15.0000	1.16423
$167$	24.0000i	1.85718i	0.371113	+	0.928588i	$0.378976\pi$
$167$	24.0000i	1.85718i	−0.371113	+	0.928588i	$0.621024\pi$
$168$	− 1.00000i	− 0.0771517i
$169$	12.0000	0.923077
$170$	0	0
$171$	−1.00000	−0.0764719
$172$	− 1.00000i	− 0.0762493i
$173$	− 15.0000i	− 1.14043i	−0.821496	−	0.570214i	$-0.806860\pi$
$173$	− 15.0000i	− 1.14043i	0.821496	−	0.570214i	$-0.193140\pi$
$174$	−9.00000	−0.682288
$175$	0	0
$176$	−3.00000	−0.226134
$177$	− 6.00000i	− 0.450988i
$178$	− 18.0000i	− 1.34916i
$179$	18.0000	1.34538	0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000	1.34538	0.672692	+	0.739923i	$0.265138\pi$
$180$	0	0
$181$	14.0000	1.04061	0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000	1.04061	0.520306	+	0.853980i	$0.325818\pi$
$182$	− 1.00000i	− 0.0741249i
$183$	4.00000i	0.295689i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	4.00000	0.293294
$187$	− 18.0000i	− 1.31629i
$188$	− 6.00000i	− 0.437595i
$189$	1.00000	0.0727393
$190$	0	0
$191$	15.0000	1.08536	0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000	1.08536	0.542681	+	0.839939i	$0.317409\pi$
$192$	1.00000i	0.0721688i
$193$	− 2.00000i	− 0.143963i	−0.997406	−	0.0719816i	$-0.977068\pi$
$193$	− 2.00000i	− 0.143963i	0.997406	−	0.0719816i	$-0.0229323\pi$
$194$	−4.00000	−0.287183
$195$	0	0
$196$	−6.00000	−0.428571
$197$	− 9.00000i	− 0.641223i	−0.947211	−	0.320612i	$-0.896112\pi$
$197$	− 9.00000i	− 0.641223i	0.947211	−	0.320612i	$-0.103888\pi$
$198$	− 3.00000i	− 0.213201i
$199$	13.0000	0.921546	0.460773	−	0.887518i	$-0.347572\pi$
$199$	13.0000	0.921546	0.460773	+	0.887518i	$0.347572\pi$
$200$	0	0
$201$	−4.00000	−0.282138
$202$	− 6.00000i	− 0.422159i
$203$	− 9.00000i	− 0.631676i
$204$	−6.00000	−0.420084
$205$	0	0
$206$	7.00000	0.487713
$207$	− 1.00000i	− 0.0695048i
$208$	1.00000i	0.0693375i
$209$	−3.00000	−0.207514
$210$	0	0
$211$	−22.0000	−1.51454	−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000	−1.51454	−0.757271	+	0.653101i	$0.773468\pi$
$212$	12.0000i	0.824163i
$213$	6.00000i	0.411113i
$214$	−12.0000	−0.820303
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	4.00000i	0.271538i
$218$	− 4.00000i	− 0.270914i
$219$	7.00000	0.473016
$220$	0	0
$221$	−6.00000	−0.403604
$222$	4.00000i	0.268462i
$223$	10.0000i	0.669650i	0.942280	+	0.334825i	$0.108677\pi$
$223$	10.0000i	0.669650i	−0.942280	+	0.334825i	$0.891323\pi$
$224$	−1.00000	−0.0668153
$225$	0	0
$226$	−18.0000	−1.19734
$227$	− 24.0000i	− 1.59294i	−0.604681	−	0.796468i	$-0.706699\pi$
$227$	− 24.0000i	− 1.59294i	0.604681	−	0.796468i	$-0.293301\pi$
$228$	1.00000i	0.0662266i
$229$	4.00000	0.264327	0.132164	−	0.991228i	$-0.457808\pi$
$229$	4.00000	0.264327	0.132164	+	0.991228i	$0.457808\pi$
$230$	0	0
$231$	3.00000	0.197386
$232$	9.00000i	0.590879i
$233$	− 9.00000i	− 0.589610i	−0.955557	−	0.294805i	$-0.904745\pi$
$233$	− 9.00000i	− 0.589610i	0.955557	−	0.294805i	$-0.0952546\pi$
$234$	−1.00000	−0.0653720
$235$	0	0
$236$	−6.00000	−0.390567
$237$	− 1.00000i	− 0.0649570i
$238$	− 6.00000i	− 0.388922i
$239$	−12.0000	−0.776215	−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000	−0.776215	−0.388108	+	0.921614i	$0.626871\pi$
$240$	0	0
$241$	−10.0000	−0.644157	−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000	−0.644157	−0.322078	+	0.946713i	$0.604381\pi$
$242$	2.00000i	0.128565i
$243$	− 1.00000i	− 0.0641500i
$244$	4.00000	0.256074
$245$	0	0
$246$	−9.00000	−0.573819
$247$	1.00000i	0.0636285i
$248$	− 4.00000i	− 0.254000i
$249$	15.0000	0.950586
$250$	0	0
$251$	12.0000	0.757433	0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000	0.757433	0.378717	+	0.925513i	$0.376365\pi$
$252$	− 1.00000i	− 0.0629941i
$253$	− 3.00000i	− 0.188608i
$254$	14.0000	0.878438
$255$	0	0
$256$	1.00000	0.0625000
$257$	18.0000i	1.12281i	0.827541	+	0.561405i	$0.189739\pi$
$257$	18.0000i	1.12281i	−0.827541	+	0.561405i	$0.810261\pi$
$258$	− 1.00000i	− 0.0622573i
$259$	−4.00000	−0.248548
$260$	0	0
$261$	−9.00000	−0.557086
$262$	0	0
$263$	− 12.0000i	− 0.739952i	−0.929041	−	0.369976i	$-0.879366\pi$
$263$	− 12.0000i	− 0.739952i	0.929041	−	0.369976i	$-0.120634\pi$
$264$	−3.00000	−0.184637
$265$	0	0
$266$	−1.00000	−0.0613139
$267$	− 18.0000i	− 1.10158i
$268$	4.00000i	0.244339i
$269$	9.00000	0.548740	0.274370	−	0.961624i	$-0.411531\pi$
$269$	9.00000	0.548740	0.274370	+	0.961624i	$0.411531\pi$
$270$	0	0
$271$	8.00000	0.485965	0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000	0.485965	0.242983	+	0.970031i	$0.421874\pi$
$272$	6.00000i	0.363803i
$273$	− 1.00000i	− 0.0605228i
$274$	−12.0000	−0.724947
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	− 19.0000i	− 1.14160i	−0.821089	−	0.570800i	$-0.806633\pi$
$277$	− 19.0000i	− 1.14160i	0.821089	−	0.570800i	$-0.193367\pi$
$278$	− 10.0000i	− 0.599760i
$279$	4.00000	0.239474
$280$	0	0
$281$	−6.00000	−0.357930	−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000	−0.357930	−0.178965	+	0.983855i	$0.557275\pi$
$282$	− 6.00000i	− 0.357295i
$283$	4.00000i	0.237775i	0.992908	+	0.118888i	$0.0379328\pi$
$283$	4.00000i	0.237775i	−0.992908	+	0.118888i	$0.962067\pi$
$284$	6.00000	0.356034
$285$	0	0
$286$	−3.00000	−0.177394
$287$	− 9.00000i	− 0.531253i
$288$	1.00000i	0.0589256i
$289$	−19.0000	−1.11765
$290$	0	0
$291$	−4.00000	−0.234484
$292$	− 7.00000i	− 0.409644i
$293$	12.0000i	0.701047i	0.936554	+	0.350524i	$0.113996\pi$
$293$	12.0000i	0.701047i	−0.936554	+	0.350524i	$0.886004\pi$
$294$	−6.00000	−0.349927
$295$	0	0
$296$	4.00000	0.232495
$297$	− 3.00000i	− 0.174078i
$298$	0	0
$299$	−1.00000	−0.0578315
$300$	0	0
$301$	1.00000	0.0576390
$302$	10.0000i	0.575435i
$303$	− 6.00000i	− 0.344691i
$304$	1.00000	0.0573539
$305$	0	0
$306$	−6.00000	−0.342997
$307$	− 4.00000i	− 0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$	− 4.00000i	− 0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$	− 3.00000i	− 0.170941i
$309$	7.00000	0.398216
$310$	0	0
$311$	12.0000	0.680458	0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000	0.680458	0.340229	+	0.940343i	$0.389495\pi$
$312$	1.00000i	0.0566139i
$313$	− 8.00000i	− 0.452187i	−0.974106	−	0.226093i	$-0.927405\pi$
$313$	− 8.00000i	− 0.452187i	0.974106	−	0.226093i	$-0.0725954\pi$
$314$	8.00000	0.451466
$315$	0	0
$316$	−1.00000	−0.0562544
$317$	3.00000i	0.168497i	0.996445	+	0.0842484i	$0.0268489\pi$
$317$	3.00000i	0.168497i	−0.996445	+	0.0842484i	$0.973151\pi$
$318$	12.0000i	0.672927i
$319$	−27.0000	−1.51171
$320$	0	0
$321$	−12.0000	−0.669775
$322$	− 1.00000i	− 0.0557278i
$323$	6.00000i	0.333849i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	16.0000	0.886158
$327$	− 4.00000i	− 0.221201i
$328$	9.00000i	0.496942i
$329$	6.00000	0.330791
$330$	0	0
$331$	8.00000	0.439720	0.219860	−	0.975531i	$-0.429440\pi$
$331$	8.00000	0.439720	0.219860	+	0.975531i	$0.429440\pi$
$332$	− 15.0000i	− 0.823232i
$333$	4.00000i	0.219199i
$334$	24.0000	1.31322
$335$	0	0
$336$	−1.00000	−0.0545545
$337$	20.0000i	1.08947i	0.838608	+	0.544735i	$0.183370\pi$
$337$	20.0000i	1.08947i	−0.838608	+	0.544735i	$0.816630\pi$
$338$	− 12.0000i	− 0.652714i
$339$	−18.0000	−0.977626
$340$	0	0
$341$	12.0000	0.649836
$342$	1.00000i	0.0540738i
$343$	− 13.0000i	− 0.701934i
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−15.0000	−0.806405
$347$	12.0000i	0.644194i	0.946707	+	0.322097i	$0.104388\pi$
$347$	12.0000i	0.644194i	−0.946707	+	0.322097i	$0.895612\pi$
$348$	9.00000i	0.482451i
$349$	−5.00000	−0.267644	−0.133822	−	0.991005i	$-0.542725\pi$
$349$	−5.00000	−0.267644	−0.133822	+	0.991005i	$0.542725\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	3.00000i	0.159901i
$353$	9.00000i	0.479022i	0.970894	+	0.239511i	$0.0769871\pi$
$353$	9.00000i	0.479022i	−0.970894	+	0.239511i	$0.923013\pi$
$354$	−6.00000	−0.318896
$355$	0	0
$356$	−18.0000	−0.953998
$357$	− 6.00000i	− 0.317554i
$358$	− 18.0000i	− 0.951330i
$359$	3.00000	0.158334	0.0791670	−	0.996861i	$-0.474774\pi$
$359$	3.00000	0.158334	0.0791670	+	0.996861i	$0.474774\pi$
$360$	0	0
$361$	−18.0000	−0.947368
$362$	− 14.0000i	− 0.735824i
$363$	2.00000i	0.104973i
$364$	−1.00000	−0.0524142
$365$	0	0
$366$	4.00000	0.209083
$367$	− 37.0000i	− 1.93138i	−0.259690	−	0.965692i	$-0.583620\pi$
$367$	− 37.0000i	− 1.93138i	0.259690	−	0.965692i	$-0.416380\pi$
$368$	1.00000i	0.0521286i
$369$	−9.00000	−0.468521
$370$	0	0
$371$	−12.0000	−0.623009
$372$	− 4.00000i	− 0.207390i
$373$	10.0000i	0.517780i	0.965907	+	0.258890i	$0.0833568\pi$
$373$	10.0000i	0.517780i	−0.965907	+	0.258890i	$0.916643\pi$
$374$	−18.0000	−0.930758
$375$	0	0
$376$	−6.00000	−0.309426
$377$	9.00000i	0.463524i
$378$	− 1.00000i	− 0.0514344i
$379$	−20.0000	−1.02733	−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000	−1.02733	−0.513665	+	0.857991i	$0.671713\pi$
$380$	0	0
$381$	14.0000	0.717242
$382$	− 15.0000i	− 0.767467i
$383$	27.0000i	1.37964i	0.723983	+	0.689818i	$0.242309\pi$
$383$	27.0000i	1.37964i	−0.723983	+	0.689818i	$0.757691\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−2.00000	−0.101797
$387$	− 1.00000i	− 0.0508329i
$388$	4.00000i	0.203069i
$389$	30.0000	1.52106	0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000	1.52106	0.760530	+	0.649303i	$0.224939\pi$
$390$	0	0
$391$	−6.00000	−0.303433
$392$	6.00000i	0.303046i
$393$	0	0
$394$	−9.00000	−0.453413
$395$	0	0
$396$	−3.00000	−0.150756
$397$	2.00000i	0.100377i	0.998740	+	0.0501886i	$0.0159822\pi$
$397$	2.00000i	0.100377i	−0.998740	+	0.0501886i	$0.984018\pi$
$398$	− 13.0000i	− 0.651631i
$399$	−1.00000	−0.0500626
$400$	0	0
$401$	12.0000	0.599251	0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000	0.599251	0.299626	+	0.954057i	$0.403138\pi$
$402$	4.00000i	0.199502i
$403$	− 4.00000i	− 0.199254i
$404$	−6.00000	−0.298511
$405$	0	0
$406$	−9.00000	−0.446663
$407$	12.0000i	0.594818i
$408$	6.00000i	0.297044i
$409$	7.00000	0.346128	0.173064	−	0.984911i	$-0.444633\pi$
$409$	7.00000	0.346128	0.173064	+	0.984911i	$0.444633\pi$
$410$	0	0
$411$	−12.0000	−0.591916
$412$	− 7.00000i	− 0.344865i
$413$	− 6.00000i	− 0.295241i
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	1.00000	0.0490290
$417$	− 10.0000i	− 0.489702i
$418$	3.00000i	0.146735i
$419$	9.00000	0.439679	0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000	0.439679	0.219839	+	0.975536i	$0.429447\pi$
$420$	0	0
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	22.0000i	1.07094i
$423$	− 6.00000i	− 0.291730i
$424$	12.0000	0.582772
$425$	0	0
$426$	6.00000	0.290701
$427$	4.00000i	0.193574i
$428$	12.0000i	0.580042i
$429$	−3.00000	−0.144841
$430$	0	0
$431$	24.0000	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$432$	1.00000i	0.0481125i
$433$	28.0000i	1.34559i	0.739827	+	0.672797i	$0.234907\pi$
$433$	28.0000i	1.34559i	−0.739827	+	0.672797i	$0.765093\pi$
$434$	4.00000	0.192006
$435$	0	0
$436$	−4.00000	−0.191565
$437$	1.00000i	0.0478365i
$438$	− 7.00000i	− 0.334473i
$439$	−20.0000	−0.954548	−0.477274	−	0.878755i	$-0.658375\pi$
$439$	−20.0000	−0.954548	−0.477274	+	0.878755i	$0.658375\pi$
$440$	0	0
$441$	−6.00000	−0.285714
$442$	6.00000i	0.285391i
$443$	24.0000i	1.14027i	0.821549	+	0.570137i	$0.193110\pi$
$443$	24.0000i	1.14027i	−0.821549	+	0.570137i	$0.806890\pi$
$444$	4.00000	0.189832
$445$	0	0
$446$	10.0000	0.473514
$447$	0	0
$448$	1.00000i	0.0472456i
$449$	18.0000	0.849473	0.424736	−	0.905317i	$-0.360367\pi$
$449$	18.0000	0.849473	0.424736	+	0.905317i	$0.360367\pi$
$450$	0	0
$451$	−27.0000	−1.27138
$452$	18.0000i	0.846649i
$453$	10.0000i	0.469841i
$454$	−24.0000	−1.12638
$455$	0	0
$456$	1.00000	0.0468293
$457$	2.00000i	0.0935561i	0.998905	+	0.0467780i	$0.0148953\pi$
$457$	2.00000i	0.0935561i	−0.998905	+	0.0467780i	$0.985105\pi$
$458$	− 4.00000i	− 0.186908i
$459$	−6.00000	−0.280056
$460$	0	0
$461$	−21.0000	−0.978068	−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000	−0.978068	−0.489034	+	0.872265i	$0.662651\pi$
$462$	− 3.00000i	− 0.139573i
$463$	4.00000i	0.185896i	0.995671	+	0.0929479i	$0.0296290\pi$
$463$	4.00000i	0.185896i	−0.995671	+	0.0929479i	$0.970371\pi$
$464$	9.00000	0.417815
$465$	0	0
$466$	−9.00000	−0.416917
$467$	− 21.0000i	− 0.971764i	−0.874024	−	0.485882i	$-0.838498\pi$
$467$	− 21.0000i	− 0.971764i	0.874024	−	0.485882i	$-0.161502\pi$
$468$	1.00000i	0.0462250i
$469$	−4.00000	−0.184703
$470$	0	0
$471$	8.00000	0.368621
$472$	6.00000i	0.276172i
$473$	− 3.00000i	− 0.137940i
$474$	−1.00000	−0.0459315
$475$	0	0
$476$	−6.00000	−0.275010
$477$	12.0000i	0.549442i
$478$	12.0000i	0.548867i
$479$	−3.00000	−0.137073	−0.0685367	−	0.997649i	$-0.521833\pi$
$479$	−3.00000	−0.137073	−0.0685367	+	0.997649i	$0.521833\pi$
$480$	0	0
$481$	4.00000	0.182384
$482$	10.0000i	0.455488i
$483$	− 1.00000i	− 0.0455016i
$484$	2.00000	0.0909091
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	14.0000i	0.634401i	0.948359	+	0.317200i	$0.102743\pi$
$487$	14.0000i	0.634401i	−0.948359	+	0.317200i	$0.897257\pi$
$488$	− 4.00000i	− 0.181071i
$489$	16.0000	0.723545
$490$	0	0
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	9.00000i	0.405751i
$493$	54.0000i	2.43204i
$494$	1.00000	0.0449921
$495$	0	0
$496$	−4.00000	−0.179605
$497$	6.00000i	0.269137i
$498$	− 15.0000i	− 0.672166i
$499$	−26.0000	−1.16392	−0.581960	−	0.813217i	$-0.697714\pi$
$499$	−26.0000	−1.16392	−0.581960	+	0.813217i	$0.697714\pi$
$500$	0	0
$501$	24.0000	1.07224
$502$	− 12.0000i	− 0.535586i
$503$	9.00000i	0.401290i	0.979664	+	0.200645i	$0.0643038\pi$
$503$	9.00000i	0.401290i	−0.979664	+	0.200645i	$0.935696\pi$
$504$	−1.00000	−0.0445435
$505$	0	0
$506$	−3.00000	−0.133366
$507$	− 12.0000i	− 0.532939i
$508$	− 14.0000i	− 0.621150i
$509$	−30.0000	−1.32973	−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000	−1.32973	−0.664863	+	0.746965i	$0.731510\pi$
$510$	0	0
$511$	7.00000	0.309662
$512$	− 1.00000i	− 0.0441942i
$513$	1.00000i	0.0441511i
$514$	18.0000	0.793946
$515$	0	0
$516$	−1.00000	−0.0440225
$517$	− 18.0000i	− 0.791639i
$518$	4.00000i	0.175750i
$519$	−15.0000	−0.658427
$520$	0	0
$521$	36.0000	1.57719	0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000	1.57719	0.788594	+	0.614914i	$0.210809\pi$
$522$	9.00000i	0.393919i
$523$	31.0000i	1.35554i	0.735276	+	0.677768i	$0.237052\pi$
$523$	31.0000i	1.35554i	−0.735276	+	0.677768i	$0.762948\pi$
$524$	0	0
$525$	0	0
$526$	−12.0000	−0.523225
$527$	− 24.0000i	− 1.04546i
$528$	3.00000i	0.130558i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	−6.00000	−0.260378
$532$	1.00000i	0.0433555i
$533$	9.00000i	0.389833i
$534$	−18.0000	−0.778936
$535$	0	0
$536$	4.00000	0.172774
$537$	− 18.0000i	− 0.776757i
$538$	− 9.00000i	− 0.388018i
$539$	−18.0000	−0.775315
$540$	0	0
$541$	29.0000	1.24681	0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000	1.24681	0.623404	+	0.781900i	$0.285749\pi$
$542$	− 8.00000i	− 0.343629i
$543$	− 14.0000i	− 0.600798i
$544$	6.00000	0.257248
$545$	0	0
$546$	−1.00000	−0.0427960
$547$	26.0000i	1.11168i	0.831289	+	0.555840i	$0.187603\pi$
$547$	26.0000i	1.11168i	−0.831289	+	0.555840i	$0.812397\pi$
$548$	12.0000i	0.512615i
$549$	4.00000	0.170716
$550$	0	0
$551$	9.00000	0.383413
$552$	1.00000i	0.0425628i
$553$	− 1.00000i	− 0.0425243i
$554$	−19.0000	−0.807233
$555$	0	0
$556$	−10.0000	−0.424094
$557$	30.0000i	1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$	30.0000i	1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$	− 4.00000i	− 0.169334i
$559$	−1.00000	−0.0422955
$560$	0	0
$561$	−18.0000	−0.759961
$562$	6.00000i	0.253095i
$563$	− 21.0000i	− 0.885044i	−0.896758	−	0.442522i	$-0.854084\pi$
$563$	− 21.0000i	− 0.885044i	0.896758	−	0.442522i	$-0.145916\pi$
$564$	−6.00000	−0.252646
$565$	0	0
$566$	4.00000	0.168133
$567$	− 1.00000i	− 0.0419961i
$568$	− 6.00000i	− 0.251754i
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	0	0
$571$	−4.00000	−0.167395	−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000	−0.167395	−0.0836974	+	0.996491i	$0.526673\pi$
$572$	3.00000i	0.125436i
$573$	− 15.0000i	− 0.626634i
$574$	−9.00000	−0.375653
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 31.0000i	− 1.29055i	−0.763952	−	0.645273i	$-0.776743\pi$
$577$	− 31.0000i	− 1.29055i	0.763952	−	0.645273i	$-0.223257\pi$
$578$	19.0000i	0.790296i
$579$	−2.00000	−0.0831172
$580$	0	0
$581$	15.0000	0.622305
$582$	4.00000i	0.165805i
$583$	36.0000i	1.49097i
$584$	−7.00000	−0.289662
$585$	0	0
$586$	12.0000	0.495715
$587$	42.0000i	1.73353i	0.498721	+	0.866763i	$0.333803\pi$
$587$	42.0000i	1.73353i	−0.498721	+	0.866763i	$0.666197\pi$
$588$	6.00000i	0.247436i
$589$	−4.00000	−0.164817
$590$	0	0
$591$	−9.00000	−0.370211
$592$	− 4.00000i	− 0.164399i
$593$	− 21.0000i	− 0.862367i	−0.902264	−	0.431183i	$-0.858096\pi$
$593$	− 21.0000i	− 0.862367i	0.902264	−	0.431183i	$-0.141904\pi$
$594$	−3.00000	−0.123091
$595$	0	0
$596$	0	0
$597$	− 13.0000i	− 0.532055i
$598$	1.00000i	0.0408930i
$599$	−24.0000	−0.980613	−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000	−0.980613	−0.490307	+	0.871550i	$0.663115\pi$
$600$	0	0
$601$	−46.0000	−1.87638	−0.938190	−	0.346122i	$-0.887498\pi$
$601$	−46.0000	−1.87638	−0.938190	+	0.346122i	$0.887498\pi$
$602$	− 1.00000i	− 0.0407570i
$603$	4.00000i	0.162893i
$604$	10.0000	0.406894
$605$	0	0
$606$	−6.00000	−0.243733
$607$	− 34.0000i	− 1.38002i	−0.723801	−	0.690009i	$-0.757607\pi$
$607$	− 34.0000i	− 1.38002i	0.723801	−	0.690009i	$-0.242393\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	−9.00000	−0.364698
$610$	0	0
$611$	−6.00000	−0.242734
$612$	6.00000i	0.242536i
$613$	− 26.0000i	− 1.05013i	−0.851062	−	0.525065i	$-0.824041\pi$
$613$	− 26.0000i	− 1.05013i	0.851062	−	0.525065i	$-0.175959\pi$
$614$	−4.00000	−0.161427
$615$	0	0
$616$	−3.00000	−0.120873
$617$	6.00000i	0.241551i	0.992680	+	0.120775i	$0.0385381\pi$
$617$	6.00000i	0.241551i	−0.992680	+	0.120775i	$0.961462\pi$
$618$	− 7.00000i	− 0.281581i
$619$	28.0000	1.12542	0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000	1.12542	0.562708	+	0.826656i	$0.309760\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	− 12.0000i	− 0.481156i
$623$	− 18.0000i	− 0.721155i
$624$	1.00000	0.0400320
$625$	0	0
$626$	−8.00000	−0.319744
$627$	3.00000i	0.119808i
$628$	− 8.00000i	− 0.319235i
$629$	24.0000	0.956943
$630$	0	0
$631$	17.0000	0.676759	0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000	0.676759	0.338380	+	0.941010i	$0.390121\pi$
$632$	1.00000i	0.0397779i
$633$	22.0000i	0.874421i
$634$	3.00000	0.119145
$635$	0	0
$636$	12.0000	0.475831
$637$	6.00000i	0.237729i
$638$	27.0000i	1.06894i
$639$	6.00000	0.237356
$640$	0	0
$641$	36.0000	1.42191	0.710957	−	0.703235i	$-0.248262\pi$
$641$	36.0000	1.42191	0.710957	+	0.703235i	$0.248262\pi$
$642$	12.0000i	0.473602i
$643$	49.0000i	1.93237i	0.257847	+	0.966186i	$0.416987\pi$
$643$	49.0000i	1.93237i	−0.257847	+	0.966186i	$0.583013\pi$
$644$	−1.00000	−0.0394055
$645$	0	0
$646$	6.00000	0.236067
$647$	12.0000i	0.471769i	0.971781	+	0.235884i	$0.0757987\pi$
$647$	12.0000i	0.471769i	−0.971781	+	0.235884i	$0.924201\pi$
$648$	1.00000i	0.0392837i
$649$	−18.0000	−0.706562
$650$	0	0
$651$	4.00000	0.156772
$652$	− 16.0000i	− 0.626608i
$653$	39.0000i	1.52619i	0.646288	+	0.763094i	$0.276321\pi$
$653$	39.0000i	1.52619i	−0.646288	+	0.763094i	$0.723679\pi$
$654$	−4.00000	−0.156412
$655$	0	0
$656$	9.00000	0.351391
$657$	− 7.00000i	− 0.273096i
$658$	− 6.00000i	− 0.233904i
$659$	45.0000	1.75295	0.876476	−	0.481446i	$-0.159888\pi$
$659$	45.0000	1.75295	0.876476	+	0.481446i	$0.159888\pi$
$660$	0	0
$661$	−4.00000	−0.155582	−0.0777910	−	0.996970i	$-0.524787\pi$
$661$	−4.00000	−0.155582	−0.0777910	+	0.996970i	$0.524787\pi$
$662$	− 8.00000i	− 0.310929i
$663$	6.00000i	0.233021i
$664$	−15.0000	−0.582113
$665$	0	0
$666$	4.00000	0.154997
$667$	9.00000i	0.348481i
$668$	− 24.0000i	− 0.928588i
$669$	10.0000	0.386622
$670$	0	0
$671$	12.0000	0.463255
$672$	1.00000i	0.0385758i
$673$	− 35.0000i	− 1.34915i	−0.738206	−	0.674575i	$-0.764327\pi$
$673$	− 35.0000i	− 1.34915i	0.738206	−	0.674575i	$-0.235673\pi$
$674$	20.0000	0.770371
$675$	0	0
$676$	−12.0000	−0.461538
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	18.0000i	0.691286i
$679$	−4.00000	−0.153506
$680$	0	0
$681$	−24.0000	−0.919682
$682$	− 12.0000i	− 0.459504i
$683$	− 18.0000i	− 0.688751i	−0.938832	−	0.344375i	$-0.888091\pi$
$683$	− 18.0000i	− 0.688751i	0.938832	−	0.344375i	$-0.111909\pi$
$684$	1.00000	0.0382360
$685$	0	0
$686$	−13.0000	−0.496342
$687$	− 4.00000i	− 0.152610i
$688$	1.00000i	0.0381246i
$689$	12.0000	0.457164
$690$	0	0
$691$	50.0000	1.90209	0.951045	−	0.309053i	$-0.100012\pi$
$691$	50.0000	1.90209	0.951045	+	0.309053i	$0.100012\pi$
$692$	15.0000i	0.570214i
$693$	− 3.00000i	− 0.113961i
$694$	12.0000	0.455514
$695$	0	0
$696$	9.00000	0.341144
$697$	54.0000i	2.04540i
$698$	5.00000i	0.189253i
$699$	−9.00000	−0.340411
$700$	0	0
$701$	12.0000	0.453234	0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000	0.453234	0.226617	+	0.973984i	$0.427233\pi$
$702$	1.00000i	0.0377426i
$703$	− 4.00000i	− 0.150863i
$704$	3.00000	0.113067
$705$	0	0
$706$	9.00000	0.338719
$707$	− 6.00000i	− 0.225653i
$708$	6.00000i	0.225494i
$709$	−8.00000	−0.300446	−0.150223	−	0.988652i	$-0.547999\pi$
$709$	−8.00000	−0.300446	−0.150223	+	0.988652i	$0.547999\pi$
$710$	0	0
$711$	−1.00000	−0.0375029
$712$	18.0000i	0.674579i
$713$	− 4.00000i	− 0.149801i
$714$	−6.00000	−0.224544
$715$	0	0
$716$	−18.0000	−0.672692
$717$	12.0000i	0.448148i
$718$	− 3.00000i	− 0.111959i
$719$	18.0000	0.671287	0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000	0.671287	0.335643	+	0.941989i	$0.391046\pi$
$720$	0	0
$721$	7.00000	0.260694
$722$	18.0000i	0.669891i
$723$	10.0000i	0.371904i
$724$	−14.0000	−0.520306
$725$	0	0
$726$	2.00000	0.0742270
$727$	32.0000i	1.18681i	0.804902	+	0.593407i	$0.202218\pi$
$727$	32.0000i	1.18681i	−0.804902	+	0.593407i	$0.797782\pi$
$728$	1.00000i	0.0370625i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−6.00000	−0.221918
$732$	− 4.00000i	− 0.147844i
$733$	− 44.0000i	− 1.62518i	−0.582838	−	0.812589i	$-0.698058\pi$
$733$	− 44.0000i	− 1.62518i	0.582838	−	0.812589i	$-0.301942\pi$
$734$	−37.0000	−1.36569
$735$	0	0
$736$	1.00000	0.0368605
$737$	12.0000i	0.442026i
$738$	9.00000i	0.331295i
$739$	4.00000	0.147142	0.0735712	−	0.997290i	$-0.476560\pi$
$739$	4.00000	0.147142	0.0735712	+	0.997290i	$0.476560\pi$
$740$	0	0
$741$	1.00000	0.0367359
$742$	12.0000i	0.440534i
$743$	− 9.00000i	− 0.330178i	−0.986279	−	0.165089i	$-0.947209\pi$
$743$	− 9.00000i	− 0.330178i	0.986279	−	0.165089i	$-0.0527911\pi$
$744$	−4.00000	−0.146647
$745$	0	0
$746$	10.0000	0.366126
$747$	− 15.0000i	− 0.548821i
$748$	18.0000i	0.658145i
$749$	−12.0000	−0.438470
$750$	0	0
$751$	−31.0000	−1.13121	−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000	−1.13121	−0.565603	+	0.824678i	$0.691357\pi$
$752$	6.00000i	0.218797i
$753$	− 12.0000i	− 0.437304i
$754$	9.00000	0.327761
$755$	0	0
$756$	−1.00000	−0.0363696
$757$	− 4.00000i	− 0.145382i	−0.997354	−	0.0726912i	$-0.976841\pi$
$757$	− 4.00000i	− 0.145382i	0.997354	−	0.0726912i	$-0.0231588\pi$
$758$	20.0000i	0.726433i
$759$	−3.00000	−0.108893
$760$	0	0
$761$	27.0000	0.978749	0.489375	−	0.872074i	$-0.337225\pi$
$761$	27.0000	0.978749	0.489375	+	0.872074i	$0.337225\pi$
$762$	− 14.0000i	− 0.507166i
$763$	− 4.00000i	− 0.144810i
$764$	−15.0000	−0.542681
$765$	0	0
$766$	27.0000	0.975550
$767$	6.00000i	0.216647i
$768$	− 1.00000i	− 0.0360844i
$769$	−26.0000	−0.937584	−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000	−0.937584	−0.468792	+	0.883309i	$0.655311\pi$
$770$	0	0
$771$	18.0000	0.648254
$772$	2.00000i	0.0719816i
$773$	36.0000i	1.29483i	0.762138	+	0.647415i	$0.224150\pi$
$773$	36.0000i	1.29483i	−0.762138	+	0.647415i	$0.775850\pi$
$774$	−1.00000	−0.0359443
$775$	0	0
$776$	4.00000	0.143592
$777$	4.00000i	0.143499i
$778$	− 30.0000i	− 1.07555i
$779$	9.00000	0.322458
$780$	0	0
$781$	18.0000	0.644091
$782$	6.00000i	0.214560i
$783$	9.00000i	0.321634i
$784$	6.00000	0.214286
$785$	0	0
$786$	0	0
$787$	17.0000i	0.605985i	0.952993	+	0.302992i	$0.0979856\pi$
$787$	17.0000i	0.605985i	−0.952993	+	0.302992i	$0.902014\pi$
$788$	9.00000i	0.320612i
$789$	−12.0000	−0.427211
$790$	0	0
$791$	−18.0000	−0.640006
$792$	3.00000i	0.106600i
$793$	− 4.00000i	− 0.142044i
$794$	2.00000	0.0709773
$795$	0	0
$796$	−13.0000	−0.460773
$797$	18.0000i	0.637593i	0.947823	+	0.318796i	$0.103279\pi$
$797$	18.0000i	0.637593i	−0.947823	+	0.318796i	$0.896721\pi$
$798$	1.00000i	0.0353996i
$799$	−36.0000	−1.27359
$800$	0	0
$801$	−18.0000	−0.635999
$802$	− 12.0000i	− 0.423735i
$803$	− 21.0000i	− 0.741074i
$804$	4.00000	0.141069
$805$	0	0
$806$	−4.00000	−0.140894
$807$	− 9.00000i	− 0.316815i
$808$	6.00000i	0.211079i
$809$	−51.0000	−1.79306	−0.896532	−	0.442978i	$-0.853922\pi$
$809$	−51.0000	−1.79306	−0.896532	+	0.442978i	$0.853922\pi$
$810$	0	0
$811$	38.0000	1.33436	0.667180	−	0.744896i	$-0.267501\pi$
$811$	38.0000	1.33436	0.667180	+	0.744896i	$0.267501\pi$
$812$	9.00000i	0.315838i
$813$	− 8.00000i	− 0.280572i
$814$	12.0000	0.420600
$815$	0	0
$816$	6.00000	0.210042
$817$	1.00000i	0.0349856i
$818$	− 7.00000i	− 0.244749i
$819$	−1.00000	−0.0349428
$820$	0	0
$821$	45.0000	1.57051	0.785255	−	0.619172i	$-0.212532\pi$
$821$	45.0000	1.57051	0.785255	+	0.619172i	$0.212532\pi$
$822$	12.0000i	0.418548i
$823$	− 2.00000i	− 0.0697156i	−0.999392	−	0.0348578i	$-0.988902\pi$
$823$	− 2.00000i	− 0.0697156i	0.999392	−	0.0348578i	$-0.0110978\pi$
$824$	−7.00000	−0.243857
$825$	0	0
$826$	−6.00000	−0.208767
$827$	27.0000i	0.938882i	0.882964	+	0.469441i	$0.155545\pi$
$827$	27.0000i	0.938882i	−0.882964	+	0.469441i	$0.844455\pi$
$828$	1.00000i	0.0347524i
$829$	−29.0000	−1.00721	−0.503606	−	0.863934i	$-0.667994\pi$
$829$	−29.0000	−1.00721	−0.503606	+	0.863934i	$0.667994\pi$
$830$	0	0
$831$	−19.0000	−0.659103
$832$	− 1.00000i	− 0.0346688i
$833$	36.0000i	1.24733i
$834$	−10.0000	−0.346272
$835$	0	0
$836$	3.00000	0.103757
$837$	− 4.00000i	− 0.138260i
$838$	− 9.00000i	− 0.310900i
$839$	−3.00000	−0.103572	−0.0517858	−	0.998658i	$-0.516491\pi$
$839$	−3.00000	−0.103572	−0.0517858	+	0.998658i	$0.516491\pi$
$840$	0	0
$841$	52.0000	1.79310
$842$	− 14.0000i	− 0.482472i
$843$	6.00000i	0.206651i
$844$	22.0000	0.757271
$845$	0	0
$846$	−6.00000	−0.206284
$847$	2.00000i	0.0687208i
$848$	− 12.0000i	− 0.412082i
$849$	4.00000	0.137280
$850$	0	0
$851$	4.00000	0.137118
$852$	− 6.00000i	− 0.205557i
$853$	37.0000i	1.26686i	0.773802	+	0.633428i	$0.218353\pi$
$853$	37.0000i	1.26686i	−0.773802	+	0.633428i	$0.781647\pi$
$854$	4.00000	0.136877
$855$	0	0
$856$	12.0000	0.410152
$857$	54.0000i	1.84460i	0.386469	+	0.922302i	$0.373695\pi$
$857$	54.0000i	1.84460i	−0.386469	+	0.922302i	$0.626305\pi$
$858$	3.00000i	0.102418i
$859$	−38.0000	−1.29654	−0.648272	−	0.761409i	$-0.724508\pi$
$859$	−38.0000	−1.29654	−0.648272	+	0.761409i	$0.724508\pi$
$860$	0	0
$861$	−9.00000	−0.306719
$862$	− 24.0000i	− 0.817443i
$863$	− 6.00000i	− 0.204242i	−0.994772	−	0.102121i	$-0.967437\pi$
$863$	− 6.00000i	− 0.204242i	0.994772	−	0.102121i	$-0.0325630\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	28.0000	0.951479
$867$	19.0000i	0.645274i
$868$	− 4.00000i	− 0.135769i
$869$	−3.00000	−0.101768
$870$	0	0
$871$	4.00000	0.135535
$872$	4.00000i	0.135457i
$873$	4.00000i	0.135379i
$874$	1.00000	0.0338255
$875$	0	0
$876$	−7.00000	−0.236508
$877$	14.0000i	0.472746i	0.971662	+	0.236373i	$0.0759588\pi$
$877$	14.0000i	0.472746i	−0.971662	+	0.236373i	$0.924041\pi$
$878$	20.0000i	0.674967i
$879$	12.0000	0.404750
$880$	0	0
$881$	0	0		−	1.00000i	$-0.5\pi$
$881$	0	0			1.00000i	$0.5\pi$
$882$	6.00000i	0.202031i
$883$	− 8.00000i	− 0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$	− 8.00000i	− 0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	6.00000	0.201802
$885$	0	0
$886$	24.0000	0.806296
$887$	6.00000i	0.201460i	0.994914	+	0.100730i	$0.0321179\pi$
$887$	6.00000i	0.201460i	−0.994914	+	0.100730i	$0.967882\pi$
$888$	− 4.00000i	− 0.134231i
$889$	14.0000	0.469545
$890$	0	0
$891$	−3.00000	−0.100504
$892$	− 10.0000i	− 0.334825i
$893$	6.00000i	0.200782i
$894$	0	0
$895$	0	0
$896$	1.00000	0.0334077
$897$	1.00000i	0.0333890i
$898$	− 18.0000i	− 0.600668i
$899$	−36.0000	−1.20067
$900$	0	0
$901$	72.0000	2.39867
$902$	27.0000i	0.899002i
$903$	− 1.00000i	− 0.0332779i
$904$	18.0000	0.598671
$905$	0	0
$906$	10.0000	0.332228
$907$	− 19.0000i	− 0.630885i	−0.948945	−	0.315442i	$-0.897847\pi$
$907$	− 19.0000i	− 0.630885i	0.948945	−	0.315442i	$-0.102153\pi$
$908$	24.0000i	0.796468i
$909$	−6.00000	−0.199007
$910$	0	0
$911$	−27.0000	−0.894550	−0.447275	−	0.894397i	$-0.647605\pi$
$911$	−27.0000	−0.894550	−0.447275	+	0.894397i	$0.647605\pi$
$912$	− 1.00000i	− 0.0331133i
$913$	− 45.0000i	− 1.48928i
$914$	2.00000	0.0661541
$915$	0	0
$916$	−4.00000	−0.132164
$917$	0	0
$918$	6.00000i	0.198030i
$919$	4.00000	0.131948	0.0659739	−	0.997821i	$-0.478985\pi$
$919$	4.00000	0.131948	0.0659739	+	0.997821i	$0.478985\pi$
$920$	0	0
$921$	−4.00000	−0.131804
$922$	21.0000i	0.691598i
$923$	− 6.00000i	− 0.197492i
$924$	−3.00000	−0.0986928
$925$	0	0
$926$	4.00000	0.131448
$927$	− 7.00000i	− 0.229910i
$928$	− 9.00000i	− 0.295439i
$929$	27.0000	0.885841	0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000	0.885841	0.442921	+	0.896561i	$0.353942\pi$
$930$	0	0
$931$	6.00000	0.196642
$932$	9.00000i	0.294805i
$933$	− 12.0000i	− 0.392862i
$934$	−21.0000	−0.687141
$935$	0	0
$936$	1.00000	0.0326860
$937$	− 16.0000i	− 0.522697i	−0.965244	−	0.261349i	$-0.915833\pi$
$937$	− 16.0000i	− 0.522697i	0.965244	−	0.261349i	$-0.0841672\pi$
$938$	4.00000i	0.130605i
$939$	−8.00000	−0.261070
$940$	0	0
$941$	−60.0000	−1.95594	−0.977972	−	0.208736i	$-0.933065\pi$
$941$	−60.0000	−1.95594	−0.977972	+	0.208736i	$0.933065\pi$
$942$	− 8.00000i	− 0.260654i
$943$	9.00000i	0.293080i
$944$	6.00000	0.195283
$945$	0	0
$946$	−3.00000	−0.0975384
$947$	− 36.0000i	− 1.16984i	−0.811090	−	0.584921i	$-0.801125\pi$
$947$	− 36.0000i	− 1.16984i	0.811090	−	0.584921i	$-0.198875\pi$
$948$	1.00000i	0.0324785i
$949$	−7.00000	−0.227230
$950$	0	0
$951$	3.00000	0.0972817
$952$	6.00000i	0.194461i
$953$	− 12.0000i	− 0.388718i	−0.980930	−	0.194359i	$-0.937737\pi$
$953$	− 12.0000i	− 0.388718i	0.980930	−	0.194359i	$-0.0622627\pi$
$954$	12.0000	0.388514
$955$	0	0
$956$	12.0000	0.388108
$957$	27.0000i	0.872786i
$958$	3.00000i	0.0969256i
$959$	−12.0000	−0.387500
$960$	0	0
$961$	−15.0000	−0.483871
$962$	− 4.00000i	− 0.128965i
$963$	12.0000i	0.386695i
$964$	10.0000	0.322078
$965$	0	0
$966$	−1.00000	−0.0321745
$967$	− 16.0000i	− 0.514525i	−0.966342	−	0.257263i	$-0.917179\pi$
$967$	− 16.0000i	− 0.514525i	0.966342	−	0.257263i	$-0.0828206\pi$
$968$	− 2.00000i	− 0.0642824i
$969$	6.00000	0.192748
$970$	0	0
$971$	−9.00000	−0.288824	−0.144412	−	0.989518i	$-0.546129\pi$
$971$	−9.00000	−0.288824	−0.144412	+	0.989518i	$0.546129\pi$
$972$	1.00000i	0.0320750i
$973$	− 10.0000i	− 0.320585i
$974$	14.0000	0.448589
$975$	0	0
$976$	−4.00000	−0.128037
$977$	12.0000i	0.383914i	0.981403	+	0.191957i	$0.0614834\pi$
$977$	12.0000i	0.383914i	−0.981403	+	0.191957i	$0.938517\pi$
$978$	− 16.0000i	− 0.511624i
$979$	−54.0000	−1.72585
$980$	0	0
$981$	−4.00000	−0.127710
$982$	0	0
$983$	45.0000i	1.43528i	0.696416	+	0.717639i	$0.254777\pi$
$983$	45.0000i	1.43528i	−0.696416	+	0.717639i	$0.745223\pi$
$984$	9.00000	0.286910
$985$	0	0
$986$	54.0000	1.71971
$987$	− 6.00000i	− 0.190982i
$988$	− 1.00000i	− 0.0318142i
$989$	−1.00000	−0.0317982
$990$	0	0
$991$	−40.0000	−1.27064	−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000	−1.27064	−0.635321	+	0.772248i	$0.719132\pi$
$992$	4.00000i	0.127000i
$993$	− 8.00000i	− 0.253872i
$994$	6.00000	0.190308
$995$	0	0
$996$	−15.0000	−0.475293
$997$	53.0000i	1.67853i	0.543725	+	0.839263i	$0.317013\pi$
$997$	53.0000i	1.67853i	−0.543725	+	0.839263i	$0.682987\pi$
$998$	26.0000i	0.823016i
$999$	4.00000	0.126554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.c.2899.1		2
5.2	odd	4		3450.2.a.r.1.1	yes	1
5.3	odd	4		3450.2.a.i.1.1	✓	1
5.4	even	2	inner	3450.2.d.c.2899.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.i.1.1	✓	1	5.3	odd	4
3450.2.a.r.1.1	yes	1	5.2	odd	4
3450.2.d.c.2899.1		2	1.1	even	1	trivial
3450.2.d.c.2899.2		2	5.4	even	2	inner

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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} -1.00000i q^{7} +1.00000i q^{8} -1.00000 q^{9} -3.00000 q^{11} +1.00000i q^{12} +1.00000i q^{13} -1.00000 q^{14} +1.00000 q^{16} +6.00000i q^{17} +1.00000i q^{18} +1.00000 q^{19} -1.00000 q^{21} +3.00000i q^{22} +1.00000i q^{23} +1.00000 q^{24} +1.00000 q^{26} +1.00000i q^{27} +1.00000i q^{28} +9.00000 q^{29} -4.00000 q^{31} -1.00000i q^{32} +3.00000i q^{33} +6.00000 q^{34} +1.00000 q^{36} -4.00000i q^{37} -1.00000i q^{38} +1.00000 q^{39} +9.00000 q^{41} +1.00000i q^{42} +1.00000i q^{43} +3.00000 q^{44} +1.00000 q^{46} +6.00000i q^{47} -1.00000i q^{48} +6.00000 q^{49} +6.00000 q^{51} -1.00000i q^{52} -12.0000i q^{53} +1.00000 q^{54} +1.00000 q^{56} -1.00000i q^{57} -9.00000i q^{58} +6.00000 q^{59} -4.00000 q^{61} +4.00000i q^{62} +1.00000i q^{63} -1.00000 q^{64} +3.00000 q^{66} -4.00000i q^{67} -6.00000i q^{68} +1.00000 q^{69} -6.00000 q^{71} -1.00000i q^{72} +7.00000i q^{73} -4.00000 q^{74} -1.00000 q^{76} +3.00000i q^{77} -1.00000i q^{78} +1.00000 q^{79} +1.00000 q^{81} -9.00000i q^{82} +15.0000i q^{83} +1.00000 q^{84} +1.00000 q^{86} -9.00000i q^{87} -3.00000i q^{88} +18.0000 q^{89} +1.00000 q^{91} -1.00000i q^{92} +4.00000i q^{93} +6.00000 q^{94} -1.00000 q^{96} -4.00000i q^{97} -6.00000i q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9	\( 2 q - 2 q^{4} - 2 q^{6} - 2 q^{9} - 6 q^{11} - 2 q^{14} + 2 q^{16} + 2 q^{19} - 2 q^{21} + 2 q^{24} + 2 q^{26} + 18 q^{29} - 8 q^{31} + 12 q^{34} + 2 q^{36} + 2 q^{39} + 18 q^{41} + 6 q^{44} + 2 q^{46} + 12 q^{49} + 12 q^{51} + 2 q^{54} + 2 q^{56} + 12 q^{59} - 8 q^{61} - 2 q^{64} + 6 q^{66} + 2 q^{69} - 12 q^{71} - 8 q^{74} - 2 q^{76} + 2 q^{79} + 2 q^{81} + 2 q^{84} + 2 q^{86} + 36 q^{89} + 2 q^{91} + 12 q^{94} - 2 q^{96} + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^4 - 2 * q^6 - 2 * q^9 - 6 * q^11 - 2 * q^14 + 2 * q^16 + 2 * q^19 - 2 * q^21 + 2 * q^24 + 2 * q^26 + 18 * q^29 - 8 * q^31 + 12 * q^34 + 2 * q^36 + 2 * q^39 + 18 * q^41 + 6 * q^44 + 2 * q^46 + 12 * q^49 + 12 * q^51 + 2 * q^54 + 2 * q^56 + 12 * q^59 - 8 * q^61 - 2 * q^64 + 6 * q^66 + 2 * q^69 - 12 * q^71 - 8 * q^74 - 2 * q^76 + 2 * q^79 + 2 * q^81 + 2 * q^84 + 2 * q^86 + 36 * q^89 + 2 * q^91 + 12 * q^94 - 2 * q^96 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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