Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2900,1,Mod(127,2900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2900, base_ring=CyclotomicField(140))
chi = DirichletCharacter(H, H._module([70, 7, 125]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2900.127");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2900 = 2^{2} \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2900.da (of order \(140\), degree \(48\), 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: | \(1.44728853664\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Coefficient field: | \(\Q(\zeta_{140})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{48} + x^{46} - x^{38} - x^{36} - x^{34} - x^{32} + x^{28} + x^{26} + x^{24} + x^{22} + x^{20} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{140}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{140} - \cdots)\) |
Embedding invariants
Embedding label | 403.1 | ||
Root | \(0.919528 + 0.393025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2900.403 |
Dual form | 2900.1.da.a.367.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2900\mathbb{Z}\right)^\times\).
\(n\) | \(901\) | \(1277\) | \(1451\) |
\(\chi(n)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.995974 | − | 0.0896393i | −0.995974 | − | 0.0896393i | ||||
\(3\) | 0 | 0 | 0.880596 | − | 0.473869i | \(-0.157143\pi\) | ||||
−0.880596 | + | 0.473869i | \(0.842857\pi\) | |||||||
\(4\) | 0.983930 | + | 0.178557i | 0.983930 | + | 0.178557i | ||||
\(5\) | 0.998993 | + | 0.0448648i | 0.998993 | + | 0.0448648i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(8\) | −0.963963 | − | 0.266037i | −0.963963 | − | 0.266037i | ||||
\(9\) | 0.550897 | − | 0.834573i | 0.550897 | − | 0.834573i | ||||
\(10\) | −0.990950 | − | 0.134233i | −0.990950 | − | 0.134233i | ||||
\(11\) | 0 | 0 | 0.200589 | − | 0.979675i | \(-0.435714\pi\) | ||||
−0.200589 | + | 0.979675i | \(0.564286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.03701 | + | 0.471030i | −1.03701 | + | 0.471030i | −0.858449 | − | 0.512899i | \(-0.828571\pi\) |
−0.178557 | + | 0.983930i | \(0.557143\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.936235 | + | 0.351375i | 0.936235 | + | 0.351375i | ||||
\(17\) | 0.145039 | − | 0.105377i | 0.145039 | − | 0.105377i | −0.512899 | − | 0.858449i | \(-0.671429\pi\) |
0.657939 | + | 0.753071i | \(0.271429\pi\) | |||||||
\(18\) | −0.623490 | + | 0.781831i | −0.623490 | + | 0.781831i | ||||
\(19\) | 0 | 0 | −0.287599 | − | 0.957751i | \(-0.592857\pi\) | ||||
0.287599 | + | 0.957751i | \(0.407143\pi\) | |||||||
\(20\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.244340 | − | 0.969690i | \(-0.578571\pi\) | ||||
0.244340 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.995974 | + | 0.0896393i | 0.995974 | + | 0.0896393i | ||||
\(26\) | 1.07505 | − | 0.376178i | 1.07505 | − | 0.376178i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.834573 | − | 0.550897i | 0.834573 | − | 0.550897i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.0672690 | − | 0.997735i | \(-0.521429\pi\) | ||||
0.0672690 | + | 0.997735i | \(0.478571\pi\) | |||||||
\(32\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.153902 | + | 0.0919519i | −0.153902 | + | 0.0919519i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.691063 | − | 0.722795i | 0.691063 | − | 0.722795i | ||||
\(37\) | 1.15348 | + | 0.761409i | 1.15348 | + | 0.761409i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
0.178557 | + | 0.983930i | \(0.442857\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.951057 | − | 0.309017i | −0.951057 | − | 0.309017i | ||||
\(41\) | −0.512506 | − | 0.261135i | −0.512506 | − | 0.261135i | 0.178557 | − | 0.983930i | \(-0.442857\pi\) |
−0.691063 | + | 0.722795i | \(0.742857\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.587785 | − | 0.809017i | 0.587785 | − | 0.809017i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.266037 | − | 0.963963i | \(-0.585714\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.781831 | − | 0.623490i | 0.781831 | − | 0.623490i | ||||
\(50\) | −0.983930 | − | 0.178557i | −0.983930 | − | 0.178557i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.10445 | + | 0.278296i | −1.10445 | + | 0.278296i | ||||
\(53\) | 1.85203 | − | 0.742901i | 1.85203 | − | 0.742901i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
0.951057 | − | 0.309017i | \(-0.100000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.880596 | + | 0.473869i | −0.880596 | + | 0.473869i | ||||
\(59\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.134504 | − | 0.00301877i | 0.134504 | − | 0.00301877i | 0.0448648 | − | 0.998993i | \(-0.485714\pi\) |
0.0896393 | + | 0.995974i | \(0.471429\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.858449 | + | 0.512899i | 0.858449 | + | 0.512899i | ||||
\(65\) | −1.05709 | + | 0.424031i | −1.05709 | + | 0.424031i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.493508 | − | 0.869741i | \(-0.664286\pi\) | ||||
0.493508 | + | 0.869741i | \(0.335714\pi\) | |||||||
\(68\) | 0.161524 | − | 0.0777861i | 0.161524 | − | 0.0777861i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.266037 | − | 0.963963i | \(-0.585714\pi\) | ||||
0.266037 | + | 0.963963i | \(0.414286\pi\) | |||||||
\(72\) | −0.753071 | + | 0.657939i | −0.753071 | + | 0.657939i | ||||
\(73\) | −1.29295 | − | 0.772500i | −1.29295 | − | 0.772500i | −0.309017 | − | 0.951057i | \(-0.600000\pi\) |
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(74\) | −1.08059 | − | 0.861741i | −1.08059 | − | 0.861741i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.738119 | − | 0.674671i | \(-0.764286\pi\) | ||||
0.738119 | + | 0.674671i | \(0.235714\pi\) | |||||||
\(80\) | 0.919528 | + | 0.393025i | 0.919528 | + | 0.393025i | ||||
\(81\) | −0.393025 | − | 0.919528i | −0.393025 | − | 0.919528i | ||||
\(82\) | 0.487035 | + | 0.306024i | 0.487035 | + | 0.306024i | ||||
\(83\) | 0 | 0 | 0.957751 | − | 0.287599i | \(-0.0928571\pi\) | ||||
−0.957751 | + | 0.287599i | \(0.907143\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.149621 | − | 0.0987640i | 0.149621 | − | 0.0987640i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.39785 | + | 1.16701i | −1.39785 | + | 1.16701i | −0.433884 | + | 0.900969i | \(0.642857\pi\) |
−0.963963 | + | 0.266037i | \(0.914286\pi\) | |||||||
\(90\) | −0.657939 | + | 0.753071i | −0.657939 | + | 0.753071i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.353882 | + | 1.95005i | −0.353882 | + | 1.95005i | −0.0448648 | + | 0.998993i | \(0.514286\pi\) |
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(98\) | −0.834573 | + | 0.550897i | −0.834573 | + | 0.550897i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.963963 | + | 0.266037i | 0.963963 | + | 0.266037i | ||||
\(101\) | 0.700340 | − | 0.440053i | 0.700340 | − | 0.440053i | −0.134233 | − | 0.990950i | \(-0.542857\pi\) |
0.834573 | + | 0.550897i | \(0.185714\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | −0.869741 | − | 0.493508i | \(-0.835714\pi\) | ||||
0.869741 | + | 0.493508i | \(0.164286\pi\) | |||||||
\(104\) | 1.12495 | − | 0.178174i | 1.12495 | − | 0.178174i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.91116 | + | 0.573896i | −1.91116 | + | 0.573896i | ||||
\(107\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.236410 | + | 1.74525i | −0.236410 | + | 1.74525i | 0.351375 | + | 0.936235i | \(0.385714\pi\) |
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.251348 | − | 1.85552i | 0.251348 | − | 1.85552i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.473869 | − | 0.880596i | \(-0.342857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.919528 | − | 0.393025i | 0.919528 | − | 0.393025i | ||||
\(117\) | −0.178174 | + | 1.12495i | −0.178174 | + | 1.12495i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.919528 | − | 0.393025i | −0.919528 | − | 0.393025i | ||||
\(122\) | −0.134233 | − | 0.00905024i | −0.134233 | − | 0.00905024i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.990950 | + | 0.134233i | 0.990950 | + | 0.134233i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.550897 | − | 0.834573i | \(-0.685714\pi\) | ||||
0.550897 | + | 0.834573i | \(0.314286\pi\) | |||||||
\(128\) | −0.809017 | − | 0.587785i | −0.809017 | − | 0.587785i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.09085 | − | 0.327567i | 1.09085 | − | 0.327567i | ||||
\(131\) | 0 | 0 | −0.928115 | − | 0.372294i | \(-0.878571\pi\) | ||||
0.928115 | + | 0.372294i | \(0.121429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.167847 | + | 0.0629940i | −0.167847 | + | 0.0629940i | ||||
\(137\) | 0.293118 | − | 0.444054i | 0.293118 | − | 0.444054i | −0.657939 | − | 0.753071i | \(-0.728571\pi\) |
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.512899 | − | 0.858449i | \(-0.328571\pi\) | ||||
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(145\) | 0.858449 | − | 0.512899i | 0.858449 | − | 0.512899i | ||||
\(146\) | 1.21850 | + | 0.885289i | 1.21850 | + | 0.885289i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.998993 | + | 0.955135i | 0.998993 | + | 0.955135i | ||||
\(149\) | 0.708207 | − | 0.341054i | 0.708207 | − | 0.341054i | −0.0448648 | − | 0.998993i | \(-0.514286\pi\) |
0.753071 | + | 0.657939i | \(0.228571\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.00804330 | − | 0.179098i | −0.00804330 | − | 0.179098i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.66915i | 1.66915i | 0.550897 | + | 0.834573i | \(0.314286\pi\) | ||||
−0.550897 | + | 0.834573i | \(0.685714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.880596 | − | 0.473869i | −0.880596 | − | 0.473869i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.309017 | + | 0.951057i | 0.309017 | + | 0.951057i | ||||
\(163\) | 0 | 0 | −0.936235 | − | 0.351375i | \(-0.885714\pi\) | ||||
0.936235 | + | 0.351375i | \(0.114286\pi\) | |||||||
\(164\) | −0.457642 | − | 0.348450i | −0.457642 | − | 0.348450i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.822002 | − | 0.569484i | \(-0.807143\pi\) | ||||
0.822002 | + | 0.569484i | \(0.192857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.195573 | − | 0.223851i | 0.195573 | − | 0.223851i | ||||
\(170\) | −0.157872 | + | 0.0849545i | −0.157872 | + | 0.0849545i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.581903 | − | 1.14205i | −0.581903 | − | 1.14205i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.393025 | − | 0.919528i | \(-0.371429\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.49683 | − | 1.03701i | 1.49683 | − | 1.03701i | ||||
\(179\) | 0 | 0 | 0.393025 | − | 0.919528i | \(-0.371429\pi\) | ||||
−0.393025 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(180\) | 0.722795 | − | 0.691063i | 0.722795 | − | 0.691063i | ||||
\(181\) | −1.08409 | + | 0.196733i | −1.08409 | + | 0.196733i | −0.691063 | − | 0.722795i | \(-0.742857\pi\) |
−0.393025 | + | 0.919528i | \(0.628571\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.11816 | + | 0.812393i | 1.11816 | + | 0.812393i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.453990 | − | 0.891007i | \(-0.350000\pi\) | ||||
−0.453990 | + | 0.891007i | \(0.650000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.0389322 | − | 0.0808436i | −0.0389322 | − | 0.0808436i | 0.880596 | − | 0.473869i | \(-0.157143\pi\) |
−0.919528 | + | 0.393025i | \(0.871429\pi\) | |||||||
\(194\) | 0.527258 | − | 1.91048i | 0.527258 | − | 1.91048i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.880596 | − | 0.473869i | 0.880596 | − | 0.473869i | ||||
\(197\) | 0.0993051 | − | 1.47289i | 0.0993051 | − | 1.47289i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.722795 | − | 0.691063i | \(-0.242857\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(200\) | −0.936235 | − | 0.351375i | −0.936235 | − | 0.351375i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.736967 | + | 0.375503i | −0.736967 | + | 0.375503i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.500274 | − | 0.283865i | −0.500274 | − | 0.283865i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.13639 | + | 0.0766173i | −1.13639 | + | 0.0766173i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.413559 | − | 0.910478i | \(-0.364286\pi\) | ||||
−0.413559 | + | 0.910478i | \(0.635714\pi\) | |||||||
\(212\) | 1.95491 | − | 0.400270i | 1.95491 | − | 0.400270i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.391902 | − | 1.71703i | 0.391902 | − | 1.71703i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.100771 | + | 0.177595i | −0.100771 | + | 0.177595i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.910478 | − | 0.413559i | \(-0.864286\pi\) | ||||
0.910478 | + | 0.413559i | \(0.135714\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(226\) | −0.416664 | + | 1.82552i | −0.416664 | + | 1.82552i | ||||
\(227\) | 0 | 0 | 0.767645 | − | 0.640876i | \(-0.221429\pi\) | ||||
−0.767645 | + | 0.640876i | \(0.778571\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.214143 | − | 0.713129i | 0.214143 | − | 0.713129i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.995974 | − | 0.0896393i | \(-0.0285714\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.951057 | + | 0.309017i | −0.951057 | + | 0.309017i | ||||
\(233\) | −1.33273 | − | 0.211083i | −1.33273 | − | 0.211083i | −0.550897 | − | 0.834573i | \(-0.685714\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(234\) | 0.278296 | − | 1.10445i | 0.278296 | − | 1.10445i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.722795 | − | 0.691063i | \(-0.757143\pi\) | ||||
0.722795 | + | 0.691063i | \(0.242857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.66243 | + | 1.09736i | 1.66243 | + | 1.09736i | 0.880596 | + | 0.473869i | \(0.157143\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(242\) | 0.880596 | + | 0.473869i | 0.880596 | + | 0.473869i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.132882 | + | 0.0210464i | 0.132882 | + | 0.0210464i | ||||
\(245\) | 0.809017 | − | 0.587785i | 0.809017 | − | 0.587785i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.974928 | − | 0.222521i | −0.974928 | − | 0.222521i | ||||
\(251\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.753071 | + | 0.657939i | 0.753071 | + | 0.657939i | ||||
\(257\) | −0.542980 | + | 1.55175i | −0.542980 | + | 1.55175i | 0.266037 | + | 0.963963i | \(0.414286\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.11582 | + | 0.228465i | −1.11582 | + | 0.228465i | ||||
\(261\) | − | 1.00000i | − | 1.00000i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.512899 | − | 0.858449i | \(-0.671429\pi\) | ||||
0.512899 | + | 0.858449i | \(0.328571\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.88349 | − | 0.659062i | 1.88349 | − | 0.659062i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.487101 | − | 0.858449i | −0.487101 | − | 0.858449i | 0.512899 | − | 0.858449i | \(-0.328571\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.822002 | − | 0.569484i | \(-0.192857\pi\) | ||||
−0.822002 | + | 0.569484i | \(0.807143\pi\) | |||||||
\(272\) | 0.172818 | − | 0.0476947i | 0.172818 | − | 0.0476947i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.331743 | + | 0.415992i | −0.331743 | + | 0.415992i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.89996 | + | 0.389019i | 1.89996 | + | 0.389019i | 0.998993 | − | 0.0448648i | \(-0.0142857\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.344244 | + | 0.0950054i | 0.344244 | + | 0.0950054i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.0896393 | + | 0.995974i | \(0.528571\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.569484 | − | 0.822002i | \(-0.307143\pi\) | ||||
−0.569484 | + | 0.822002i | \(0.692857\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.858449 | + | 0.512899i | −0.858449 | + | 0.512899i | ||||
\(289\) | −0.299085 | + | 0.920489i | −0.299085 | + | 0.920489i | ||||
\(290\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.13423 | − | 0.990950i | −1.13423 | − | 0.990950i | ||||
\(293\) | −0.627218 | + | 1.30243i | −0.627218 | + | 1.30243i | 0.309017 | + | 0.951057i | \(0.400000\pi\) |
−0.936235 | + | 0.351375i | \(0.885714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.909354 | − | 1.04084i | −0.909354 | − | 1.04084i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.735927 | + | 0.276198i | −0.735927 | + | 0.276198i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.134504 | + | 0.00301877i | 0.134504 | + | 0.00301877i | ||||
\(306\) | −0.00804330 | + | 0.179098i | −0.00804330 | + | 0.179098i | ||||
\(307\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.910478 | − | 0.413559i | \(-0.864286\pi\) | ||||
0.910478 | + | 0.413559i | \(0.135714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.816823 | − | 0.681933i | −0.816823 | − | 0.681933i | 0.134233 | − | 0.990950i | \(-0.457143\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(314\) | 0.149621 | − | 1.66243i | 0.149621 | − | 1.66243i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.292810 | + | 0.335148i | −0.292810 | + | 0.335148i | −0.880596 | − | 0.473869i | \(-0.842857\pi\) |
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.834573 | + | 0.550897i | 0.834573 | + | 0.550897i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(325\) | −1.07505 | + | 0.376178i | −1.07505 | + | 0.376178i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.424565 | + | 0.388070i | 0.424565 | + | 0.388070i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.156434 | − | 0.987688i | \(-0.450000\pi\) | ||||
−0.156434 | + | 0.987688i | \(0.550000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.27090 | − | 0.543210i | 1.27090 | − | 0.543210i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.304912 | + | 0.812434i | −0.304912 | + | 0.812434i | 0.691063 | + | 0.722795i | \(0.257143\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(338\) | −0.214851 | + | 0.205419i | −0.214851 | + | 0.205419i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.164852 | − | 0.0704610i | 0.164852 | − | 0.0704610i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.477188 | + | 1.18961i | 0.477188 | + | 1.18961i | ||||
\(347\) | 0 | 0 | −0.156434 | − | 0.987688i | \(-0.550000\pi\) | ||||
0.156434 | + | 0.987688i | \(0.450000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.71690i | 1.71690i | 0.512899 | + | 0.858449i | \(0.328571\pi\) | ||||
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.245922 | − | 0.613074i | −0.245922 | − | 0.613074i | 0.753071 | − | 0.657939i | \(-0.228571\pi\) |
−0.998993 | + | 0.0448648i | \(0.985714\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.58376 | + | 0.898656i | −1.58376 | + | 0.898656i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.910478 | − | 0.413559i | \(-0.135714\pi\) | ||||
−0.910478 | + | 0.413559i | \(0.864286\pi\) | |||||||
\(360\) | −0.781831 | + | 0.623490i | −0.781831 | + | 0.623490i | ||||
\(361\) | −0.834573 | + | 0.550897i | −0.834573 | + | 0.550897i | ||||
\(362\) | 1.09736 | − | 0.0987640i | 1.09736 | − | 0.0987640i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.25699 | − | 0.829730i | −1.25699 | − | 0.829730i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.473869 | − | 0.880596i | \(-0.342857\pi\) | ||||
−0.473869 | + | 0.880596i | \(0.657143\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.500274 | + | 0.283865i | −0.500274 | + | 0.283865i | ||||
\(370\) | −1.04084 | − | 0.909354i | −1.04084 | − | 0.909354i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.135654 | − | 0.178163i | 0.135654 | − | 0.178163i | −0.722795 | − | 0.691063i | \(-0.757143\pi\) |
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.605968 | + | 0.964393i | −0.605968 | + | 0.964393i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.372294 | − | 0.928115i | \(-0.621429\pi\) | ||||
0.372294 | + | 0.928115i | \(0.378571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.928115 | − | 0.372294i | \(-0.878571\pi\) | ||||
0.928115 | + | 0.372294i | \(0.121429\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0315287 | + | 0.0840080i | 0.0315287 | + | 0.0840080i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.696390 | + | 1.85552i | −0.696390 | + | 1.85552i | ||||
\(389\) | −1.65391 | + | 0.842711i | −1.65391 | + | 0.842711i | −0.657939 | + | 0.753071i | \(0.728571\pi\) |
−0.995974 | + | 0.0896393i | \(0.971429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −0.919528 | + | 0.393025i | −0.919528 | + | 0.393025i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −0.230935 | + | 1.45806i | −0.230935 | + | 1.45806i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.24997 | − | 1.14252i | −1.24997 | − | 1.14252i | −0.983930 | − | 0.178557i | \(-0.942857\pi\) |
−0.266037 | − | 0.963963i | \(-0.585714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.900969 | + | 0.433884i | 0.900969 | + | 0.433884i | ||||
\(401\) | 0.210891 | + | 0.923976i | 0.210891 | + | 0.923976i | 0.963963 | + | 0.266037i | \(0.0857143\pi\) |
−0.753071 | + | 0.657939i | \(0.771429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.767660 | − | 0.307930i | 0.767660 | − | 0.307930i | ||||
\(405\) | −0.351375 | − | 0.936235i | −0.351375 | − | 0.936235i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.18696 | − | 1.55891i | −1.18696 | − | 1.55891i | −0.753071 | − | 0.657939i | \(-0.771429\pi\) |
−0.433884 | − | 0.900969i | \(-0.642857\pi\) | |||||||
\(410\) | 0.472814 | + | 0.327567i | 0.472814 | + | 0.327567i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.13868 | + | 0.0255563i | 1.13868 | + | 0.0255563i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.0448648 | − | 0.998993i | \(-0.485714\pi\) | ||||
−0.0448648 | + | 0.998993i | \(0.514286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.119874 | + | 1.77798i | −0.119874 | + | 1.77798i | 0.393025 | + | 0.919528i | \(0.371429\pi\) |
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.98292 | + | 0.223422i | −1.98292 | + | 0.223422i | ||||
\(425\) | 0.153902 | − | 0.0919519i | 0.153902 | − | 0.0919519i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.473869 | − | 0.880596i | \(-0.342857\pi\) | ||||
−0.473869 | + | 0.880596i | \(0.657143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.885289 | − | 0.773453i | −0.885289 | − | 0.773453i | 0.0896393 | − | 0.995974i | \(-0.471429\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.544238 | + | 1.67499i | −0.544238 | + | 1.67499i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.134233 | − | 0.990950i | \(-0.542857\pi\) | ||||
0.134233 | + | 0.990950i | \(0.457143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0896393 | − | 0.995974i | −0.0896393 | − | 0.995974i | ||||
\(442\) | 0.116285 | − | 0.167847i | 0.116285 | − | 0.167847i | ||||
\(443\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.44880 | + | 1.10312i | −1.44880 | + | 1.10312i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.259994 | − | 0.413778i | −0.259994 | − | 0.413778i | 0.691063 | − | 0.722795i | \(-0.257143\pi\) |
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(450\) | −0.691063 | + | 0.722795i | −0.691063 | + | 0.722795i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0.578625 | − | 1.78082i | 0.578625 | − | 1.78082i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.656405 | + | 1.87590i | 0.656405 | + | 1.87590i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(458\) | −0.277205 | + | 0.691063i | −0.277205 | + | 0.691063i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.0203733 | + | 0.907752i | 0.0203733 | + | 0.907752i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
−0.880596 | + | 0.473869i | \(0.842857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.891007 | − | 0.453990i | \(-0.850000\pi\) | ||||
0.891007 | + | 0.453990i | \(0.150000\pi\) | |||||||
\(464\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.30844 | + | 0.329699i | 1.30844 | + | 0.329699i | ||||
\(467\) | 0 | 0 | 0.983930 | − | 0.178557i | \(-0.0571429\pi\) | ||||
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(468\) | −0.376178 | + | 1.07505i | −0.376178 | + | 1.07505i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.400270 | − | 1.95491i | 0.400270 | − | 1.95491i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.997735 | − | 0.0672690i | \(-0.978571\pi\) | ||||
0.997735 | + | 0.0672690i | \(0.0214286\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.55482 | − | 0.246259i | −1.55482 | − | 0.246259i | ||||
\(482\) | −1.55737 | − | 1.24196i | −1.55737 | − | 1.24196i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.834573 | − | 0.550897i | −0.834573 | − | 0.550897i | ||||
\(485\) | −0.441014 | + | 1.93221i | −0.441014 | + | 1.93221i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0 | 0 | 0.640876 | − | 0.767645i | \(-0.278571\pi\) | ||||
−0.640876 | + | 0.767645i | \(0.721429\pi\) | |||||||
\(488\) | −0.130460 | − | 0.0328731i | −0.130460 | − | 0.0328731i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.858449 | + | 0.512899i | −0.858449 | + | 0.512899i | ||||
\(491\) | 0 | 0 | 0.244340 | − | 0.969690i | \(-0.421429\pi\) | ||||
−0.244340 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0629940 | − | 0.167847i | 0.0629940 | − | 0.167847i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(500\) | 0.951057 | + | 0.309017i | 0.951057 | + | 0.309017i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.983930 | − | 0.178557i | \(-0.942857\pi\) | ||||
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.719378 | − | 0.408189i | 0.719378 | − | 0.408189i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.0943324 | − | 0.251348i | 0.0943324 | − | 0.251348i | −0.880596 | − | 0.473869i | \(-0.842857\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.691063 | − | 0.722795i | −0.691063 | − | 0.722795i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.679892 | − | 1.49683i | 0.679892 | − | 1.49683i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.13181 | − | 0.127524i | 1.13181 | − | 0.127524i | ||||
\(521\) | −1.13321 | + | 1.55972i | −1.13321 | + | 1.55972i | −0.351375 | + | 0.936235i | \(0.614286\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(522\) | −0.0896393 | + | 0.995974i | −0.0896393 | + | 0.995974i | ||||
\(523\) | 0 | 0 | 0.891007 | − | 0.453990i | \(-0.150000\pi\) | ||||
−0.891007 | + | 0.453990i | \(0.850000\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.880596 | + | 0.473869i | −0.880596 | + | 0.473869i | ||||
\(530\) | −1.93499 | + | 0.487574i | −1.93499 | + | 0.487574i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.654474 | + | 0.0293925i | 0.654474 | + | 0.0293925i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.408189 | + | 0.898656i | 0.408189 | + | 0.898656i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.0357045 | − | 1.59085i | 0.0357045 | − | 1.59085i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.176398 | + | 0.0320114i | −0.176398 | + | 0.0320114i | ||||
\(545\) | −0.314473 | + | 1.73289i | −0.314473 | + | 1.73289i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 0.822002 | − | 0.569484i | \(-0.192857\pi\) | ||||
−0.822002 | + | 0.569484i | \(0.807143\pi\) | |||||||
\(548\) | 0.367696 | − | 0.384580i | 0.367696 | − | 0.384580i | ||||
\(549\) | 0.0715785 | − | 0.113917i | 0.0715785 | − | 0.113917i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.85744 | − | 0.557764i | −1.85744 | − | 0.557764i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.69302 | + | 1.06380i | −1.69302 | + | 1.06380i | −0.834573 | + | 0.550897i | \(0.814286\pi\) |
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.334342 | − | 0.125481i | −0.334342 | − | 0.125481i | ||||
\(563\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.334342 | − | 1.84238i | 0.334342 | − | 1.84238i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.47587 | + | 1.34900i | −1.47587 | + | 1.34900i | −0.722795 | + | 0.691063i | \(0.757143\pi\) |
−0.753071 | + | 0.657939i | \(0.771429\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.0448648 | − | 0.998993i | \(-0.514286\pi\) | ||||
0.0448648 | + | 0.998993i | \(0.485714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(577\) | −1.30243 | − | 1.24525i | −1.30243 | − | 1.24525i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
−0.351375 | − | 0.936235i | \(-0.614286\pi\) | |||||||
\(578\) | 0.380393 | − | 0.889973i | 0.380393 | − | 0.889973i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.936235 | − | 0.351375i | 0.936235 | − | 0.351375i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 1.04084 | + | 1.08863i | 1.04084 | + | 1.08863i | ||||
\(585\) | −0.228465 | + | 1.11582i | −0.228465 | + | 1.11582i | ||||
\(586\) | 0.741442 | − | 1.24096i | 0.741442 | − | 1.24096i | ||||
\(587\) | 0 | 0 | −0.605790 | − | 0.795625i | \(-0.707143\pi\) | ||||
0.605790 | + | 0.795625i | \(0.292857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.812393 | + | 1.11816i | 0.812393 | + | 1.11816i | ||||
\(593\) | −0.0547149 | − | 0.485608i | −0.0547149 | − | 0.485608i | −0.990950 | − | 0.134233i | \(-0.957143\pi\) |
0.936235 | − | 0.351375i | \(-0.114286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.757723 | − | 0.209118i | 0.757723 | − | 0.209118i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0350302 | − | 0.310902i | 0.0350302 | − | 0.310902i | −0.963963 | − | 0.266037i | \(-0.914286\pi\) |
0.998993 | − | 0.0448648i | \(-0.0142857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.133692 | − | 0.0150635i | −0.133692 | − | 0.0150635i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.0240652 | − | 0.177656i | 0.0240652 | − | 0.177656i | ||||
\(613\) | −1.59085 | − | 0.0357045i | −1.59085 | − | 0.0357045i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.531538 | − | 1.92598i | 0.531538 | − | 1.92598i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.309017 | − | 0.951057i | \(-0.400000\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.957751 | − | 0.287599i | \(-0.0928571\pi\) | ||||
−0.957751 | + | 0.287599i | \(0.907143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.983930 | + | 0.178557i | 0.983930 | + | 0.178557i | ||||
\(626\) | 0.752407 | + | 0.752407i | 0.752407 | + | 0.752407i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.298038 | + | 1.64232i | −0.298038 | + | 1.64232i | ||||
\(629\) | 0.247536 | − | 0.0111169i | 0.247536 | − | 0.0111169i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.178557 | − | 0.983930i | \(-0.557143\pi\) | ||||
0.178557 | + | 0.983930i | \(0.442857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.321674 | − | 0.307552i | 0.321674 | − | 0.307552i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.517081 | + | 1.01483i | −0.517081 | + | 1.01483i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(641\) | −1.12518 | + | 0.856716i | −1.12518 | + | 0.856716i | −0.990950 | − | 0.134233i | \(-0.957143\pi\) |
−0.134233 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.674671 | − | 0.738119i | \(-0.264286\pi\) | ||||
−0.674671 | + | 0.738119i | \(0.735714\pi\) | |||||||
\(648\) | 0.134233 | + | 0.990950i | 0.134233 | + | 0.990950i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 1.10445 | − | 0.278296i | 1.10445 | − | 0.278296i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.202174 | + | 0.176635i | −0.202174 | + | 0.176635i | −0.753071 | − | 0.657939i | \(-0.771429\pi\) |
0.550897 | + | 0.834573i | \(0.314286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.388070 | − | 0.424565i | −0.388070 | − | 0.424565i | ||||
\(657\) | −1.35699 | + | 0.653491i | −1.35699 | + | 0.653491i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.200589 | − | 0.979675i | \(-0.564286\pi\) | ||||
0.200589 | + | 0.979675i | \(0.435714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.54687 | − | 0.924213i | −1.54687 | − | 0.924213i | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) |
−0.550897 | − | 0.834573i | \(-0.685714\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.31448 | + | 0.427100i | −1.31448 | + | 0.427100i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.389019 | − | 0.0980242i | 0.389019 | − | 0.0980242i | −0.0448648 | − | 0.998993i | \(-0.514286\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(674\) | 0.376510 | − | 0.781831i | 0.376510 | − | 0.781831i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.232400 | − | 0.185333i | 0.232400 | − | 0.185333i | ||||
\(677\) | 1.54951 | − | 0.209896i | 1.54951 | − | 0.209896i | 0.691063 | − | 0.722795i | \(-0.257143\pi\) |
0.858449 | + | 0.512899i | \(0.171429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.170504 | + | 0.0554001i | −0.170504 | + | 0.0554001i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.738119 | − | 0.674671i | \(-0.235714\pi\) | ||||
−0.738119 | + | 0.674671i | \(0.764286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.312745 | − | 0.430457i | 0.312745 | − | 0.430457i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.57063 | + | 1.64275i | −1.57063 | + | 1.64275i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.858449 | − | 0.512899i | \(-0.171429\pi\) | ||||
−0.858449 | + | 0.512899i | \(0.828571\pi\) | |||||||
\(692\) | −0.368631 | − | 1.22760i | −0.368631 | − | 1.22760i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.101851 | + | 0.0161317i | −0.101851 | + | 0.0161317i | ||||
\(698\) | 0.153902 | − | 1.70999i | 0.153902 | − | 1.70999i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.79295 | − | 0.409228i | 1.79295 | − | 0.409228i | 0.809017 | − | 0.587785i | \(-0.200000\pi\) |
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.189976 | + | 0.632650i | 0.189976 | + | 0.632650i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.87058 | + | 0.702042i | 1.87058 | + | 0.702042i | 0.951057 | + | 0.309017i | \(0.100000\pi\) |
0.919528 | + | 0.393025i | \(0.128571\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.65794 | − | 0.753071i | 1.65794 | − | 0.753071i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.919528 | − | 0.393025i | \(-0.128571\pi\) | ||||
−0.919528 | + | 0.393025i | \(0.871429\pi\) | |||||||
\(720\) | 0.834573 | − | 0.550897i | 0.834573 | − | 0.550897i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0.880596 | − | 0.473869i | 0.880596 | − | 0.473869i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.10179 | −1.10179 | ||||||||
\(725\) | 0.880596 | − | 0.473869i | 0.880596 | − | 0.473869i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.995974 | − | 0.0896393i | \(-0.971429\pi\) | ||||
0.995974 | + | 0.0896393i | \(0.0285714\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −0.983930 | − | 0.178557i | −0.983930 | − | 0.178557i | ||||
\(730\) | 1.17755 | + | 0.939065i | 1.17755 | + | 0.939065i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.266037 | − | 0.963963i | \(-0.414286\pi\) | ||||
−0.266037 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0.523705 | − | 0.237878i | 0.523705 | − | 0.237878i | ||||
\(739\) | 0 | 0 | 0.969690 | − | 0.244340i | \(-0.0785714\pi\) | ||||
−0.969690 | + | 0.244340i | \(0.921429\pi\) | |||||||
\(740\) | 0.955135 | + | 0.998993i | 0.955135 | + | 0.998993i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.722795 | − | 0.308937i | 0.722795 | − | 0.308937i | ||||
\(746\) | −0.151078 | + | 0.165286i | −0.151078 | + | 0.165286i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.689976 | − | 0.906192i | 0.689976 | − | 0.906192i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.73700 | + | 0.836496i | 1.73700 | + | 0.836496i | 0.983930 | + | 0.178557i | \(0.0571429\pi\) |
0.753071 | + | 0.657939i | \(0.228571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.38073 | − | 1.44413i | 1.38073 | − | 1.44413i | 0.657939 | − | 0.753071i | \(-0.271429\pi\) |
0.722795 | − | 0.691063i | \(-0.242857\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − | 0.179279i | − | 0.179279i | ||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.739906 | − | 1.84456i | 0.739906 | − | 1.84456i | 0.266037 | − | 0.963963i | \(-0.414286\pi\) |
0.473869 | − | 0.880596i | \(-0.342857\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.0238714 | − | 0.0864961i | −0.0238714 | − | 0.0864961i | ||||
\(773\) | 1.91048 | − | 0.258792i | 1.91048 | − | 0.258792i | 0.919528 | − | 0.393025i | \(-0.128571\pi\) |
0.990950 | + | 0.134233i | \(0.0428571\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.859914 | − | 1.78563i | 0.859914 | − | 1.78563i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.72279 | − | 0.691063i | 1.72279 | − | 0.691063i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.951057 | − | 0.309017i | 0.951057 | − | 0.309017i | ||||
\(785\) | −0.0748860 | + | 1.66747i | −0.0748860 | + | 1.66747i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | 0.0224381 | − | 0.999748i | \(-0.492857\pi\) | ||||
−0.0224381 | + | 0.999748i | \(0.507143\pi\) | |||||||
\(788\) | 0.360705 | − | 1.43149i | 0.360705 | − | 1.43149i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.138060 | + | 0.0664860i | −0.138060 | + | 0.0664860i | ||||
\(794\) | 1.14252 | + | 1.24997i | 1.14252 | + | 1.24997i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.713714 | − | 0.623553i | 0.713714 | − | 0.623553i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.936235 | + | 0.351375i | \(0.114286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.858449 | − | 0.512899i | −0.858449 | − | 0.512899i | ||||
\(801\) | 0.203882 | + | 1.80951i | 0.203882 | + | 1.80951i | ||||
\(802\) | −0.127218 | − | 0.939160i | −0.127218 | − | 0.939160i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.792172 | + | 0.237878i | −0.792172 | + | 0.237878i | ||||
\(809\) | −0.963963 | + | 0.733963i | −0.963963 | + | 0.733963i | −0.963963 | − | 0.266037i | \(-0.914286\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0.266037 | + | 0.963963i | 0.266037 | + | 0.963963i | ||||
\(811\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 1.04244 | + | 1.65903i | 1.04244 | + | 1.65903i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.441548 | − | 0.368631i | −0.441548 | − | 0.368631i | ||||
\(821\) | −1.94789 | + | 0.0874800i | −1.94789 | + | 0.0874800i | −0.983930 | − | 0.178557i | \(-0.942857\pi\) |
−0.963963 | + | 0.266037i | \(0.914286\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.834573 | − | 0.550897i | \(-0.185714\pi\) | ||||
−0.834573 | + | 0.550897i | \(0.814286\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.512899 | − | 0.858449i | \(-0.328571\pi\) | ||||
−0.512899 | + | 0.858449i | \(0.671429\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.89192 | + | 0.299650i | −1.89192 | + | 0.299650i | −0.990950 | − | 0.134233i | \(-0.957143\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.13181 | − | 0.127524i | −1.13181 | − | 0.127524i | ||||
\(833\) | 0.0476947 | − | 0.172818i | 0.0476947 | − | 0.172818i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.640876 | − | 0.767645i | \(-0.721429\pi\) | ||||
0.640876 | + | 0.767645i | \(0.278571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.393025 | − | 0.919528i | 0.393025 | − | 0.919528i | ||||
\(842\) | 0.278768 | − | 1.76007i | 0.278768 | − | 1.76007i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.205419 | − | 0.214851i | 0.205419 | − | 0.214851i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.99497 | − | 0.0447745i | 1.99497 | − | 0.0447745i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.161524 | + | 0.0777861i | −0.161524 | + | 0.0777861i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.61640 | + | 1.17439i | 1.61640 | + | 1.17439i | 0.834573 | + | 0.550897i | \(0.185714\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.158342 | + | 1.40532i | 0.158342 | + | 1.40532i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.413559 | − | 0.910478i | \(-0.635714\pi\) | ||||
0.413559 | + | 0.910478i | \(0.364286\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.605790 | − | 0.795625i | \(-0.707143\pi\) | ||||
0.605790 | + | 0.795625i | \(0.292857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.530079 | − | 1.16701i | −0.530079 | − | 1.16701i | ||||
\(866\) | 0.812393 | + | 0.849696i | 0.812393 | + | 0.849696i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0.692192 | − | 1.61946i | 0.692192 | − | 1.61946i | ||||
\(873\) | 1.43251 | + | 1.36962i | 1.43251 | + | 1.36962i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.00702017 | − | 0.312790i | −0.00702017 | − | 0.312790i | −0.990950 | − | 0.134233i | \(-0.957143\pi\) |
0.983930 | − | 0.178557i | \(-0.0571429\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.24997 | + | 1.14252i | −1.24997 | + | 1.14252i | −0.266037 | + | 0.963963i | \(0.585714\pi\) |
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(882\) | 1.00000i | 1.00000i | ||||||||
\(883\) | 0 | 0 | −0.674671 | − | 0.738119i | \(-0.735714\pi\) | ||||
0.674671 | + | 0.738119i | \(0.264286\pi\) | |||||||
\(884\) | −0.130862 | + | 0.156748i | −0.130862 | + | 0.156748i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.54185 | − | 0.968807i | 1.54185 | − | 0.968807i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0.221856 | + | 0.435418i | 0.221856 | + | 0.435418i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.753071 | − | 0.657939i | 0.753071 | − | 0.657939i | ||||
\(901\) | 0.190332 | − | 0.302911i | 0.190332 | − | 0.302911i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −0.735927 | + | 1.72179i | −0.735927 | + | 1.72179i | ||||
\(905\) | −1.09182 | + | 0.147897i | −1.09182 | + | 0.147897i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0185589 | − | 0.826909i | 0.0185589 | − | 0.826909i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.453990 | − | 0.891007i | \(-0.650000\pi\) | ||||
0.453990 | + | 0.891007i | \(0.350000\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −0.485608 | − | 1.92718i | −0.485608 | − | 1.92718i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.338036 | − | 0.663432i | 0.338036 | − | 0.663432i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.266037 | − | 0.963963i | \(-0.414286\pi\) | ||||
−0.266037 | + | 0.963963i | \(0.585714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.0610790 | − | 0.905924i | 0.0610790 | − | 0.905924i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.08059 | + | 0.861741i | 1.08059 | + | 0.861741i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.990950 | + | 0.134233i | −0.990950 | + | 0.134233i | ||||
\(929\) | 0.849696 | − | 1.16951i | 0.849696 | − | 1.16951i | −0.134233 | − | 0.990950i | \(-0.542857\pi\) |
0.983930 | − | 0.178557i | \(-0.0571429\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.27362 | − | 0.445659i | −1.27362 | − | 0.445659i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.471030 | − | 1.03701i | 0.471030 | − | 1.03701i | ||||
\(937\) | −0.393025 | + | 0.0804722i | −0.393025 | + | 0.0804722i | −0.393025 | − | 0.919528i | \(-0.628571\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.668355 | + | 1.78082i | −0.668355 | + | 1.78082i | −0.0448648 | + | 0.998993i | \(0.514286\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.983930 | − | 0.178557i | \(-0.942857\pi\) | ||||
0.983930 | + | 0.178557i | \(0.0571429\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.70466 | + | 0.192069i | 1.70466 | + | 0.192069i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.906192 | − | 1.30801i | −0.906192 | − | 1.30801i | −0.951057 | − | 0.309017i | \(-0.900000\pi\) |
0.0448648 | − | 0.998993i | \(-0.485714\pi\) | |||||||
\(954\) | −0.573896 | + | 1.91116i | −0.573896 | + | 1.91116i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.990950 | + | 0.134233i | −0.990950 | + | 0.134233i | ||||
\(962\) | 1.52648 | + | 0.384640i | 1.52648 | + | 0.384640i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.43977 | + | 1.37656i | 1.43977 | + | 1.37656i | ||||
\(965\) | −0.0352660 | − | 0.0825089i | −0.0352660 | − | 0.0825089i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.880596 | − | 0.473869i | \(-0.842857\pi\) | ||||
0.880596 | + | 0.473869i | \(0.157143\pi\) | |||||||
\(968\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.612441 | − | 1.88490i | 0.612441 | − | 1.88490i | ||||
\(971\) | 0 | 0 | −0.997735 | − | 0.0672690i | \(-0.978571\pi\) | ||||
0.997735 | + | 0.0672690i | \(0.0214286\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.126988 | + | 0.0444351i | 0.126988 | + | 0.0444351i | ||||
\(977\) | 0.408189 | − | 0.898656i | 0.408189 | − | 0.898656i | −0.587785 | − | 0.809017i | \(-0.700000\pi\) |
0.995974 | − | 0.0896393i | \(-0.0285714\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(981\) | 1.32630 | + | 1.15876i | 1.32630 | + | 1.15876i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.983930 | − | 0.178557i | \(-0.0571429\pi\) | ||||
−0.983930 | + | 0.178557i | \(0.942857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.165286 | − | 1.46696i | 0.165286 | − | 1.46696i | ||||
\(986\) | −0.0777861 | + | 0.161524i | −0.0777861 | + | 0.161524i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.512899 | − | 0.858449i | \(-0.671429\pi\) | ||||
0.512899 | + | 0.858449i | \(0.328571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.20204 | − | 0.331743i | 1.20204 | − | 0.331743i | 0.393025 | − | 0.919528i | \(-0.371429\pi\) |
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2900.1.da.a.403.1 | yes | 48 | |
4.3 | odd | 2 | CM | 2900.1.da.a.403.1 | yes | 48 | |
25.17 | odd | 20 | 2900.1.cr.a.867.1 | ✓ | 48 | ||
29.19 | odd | 28 | 2900.1.cr.a.2803.1 | yes | 48 | ||
100.67 | even | 20 | 2900.1.cr.a.867.1 | ✓ | 48 | ||
116.19 | even | 28 | 2900.1.cr.a.2803.1 | yes | 48 | ||
725.367 | even | 140 | inner | 2900.1.da.a.367.1 | yes | 48 | |
2900.367 | odd | 140 | inner | 2900.1.da.a.367.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2900.1.cr.a.867.1 | ✓ | 48 | 25.17 | odd | 20 | ||
2900.1.cr.a.867.1 | ✓ | 48 | 100.67 | even | 20 | ||
2900.1.cr.a.2803.1 | yes | 48 | 29.19 | odd | 28 | ||
2900.1.cr.a.2803.1 | yes | 48 | 116.19 | even | 28 | ||
2900.1.da.a.367.1 | yes | 48 | 725.367 | even | 140 | inner | |
2900.1.da.a.367.1 | yes | 48 | 2900.367 | odd | 140 | inner | |
2900.1.da.a.403.1 | yes | 48 | 1.1 | even | 1 | trivial | |
2900.1.da.a.403.1 | yes | 48 | 4.3 | odd | 2 | CM |