Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,4,Mod(49,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.c (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: | \(23.6007640023\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.49 |
Dual form | 400.4.c.e.49.2 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(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 | 0 | ||||||||
\(3\) | − 7.00000i | − 1.34715i | −0.739119 | − | 0.673575i | \(-0.764758\pi\) | ||||
0.739119 | − | 0.673575i | \(-0.235242\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000i | 0.323970i | 0.986793 | + | 0.161985i | \(0.0517895\pi\) | ||||
−0.986793 | + | 0.161985i | \(0.948210\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −22.0000 | −0.814815 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 43.0000 | 1.17864 | 0.589318 | − | 0.807901i | \(-0.299397\pi\) | ||||
0.589318 | + | 0.807901i | \(0.299397\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 28.0000i | − 0.597369i | −0.954352 | − | 0.298685i | \(-0.903452\pi\) | ||||
0.954352 | − | 0.298685i | \(-0.0965479\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 91.0000i | − 1.29828i | −0.760669 | − | 0.649139i | \(-0.775129\pi\) | ||||
0.760669 | − | 0.649139i | \(-0.224871\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −35.0000 | −0.422608 | −0.211304 | − | 0.977420i | \(-0.567771\pi\) | ||||
−0.211304 | + | 0.977420i | \(0.567771\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.0000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 162.000i | − 1.46867i | −0.678789 | − | 0.734333i | \(-0.737495\pi\) | ||||
0.678789 | − | 0.734333i | \(-0.262505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 35.0000i | − 0.249472i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −160.000 | −1.02453 | −0.512263 | − | 0.858829i | \(-0.671193\pi\) | ||||
−0.512263 | + | 0.858829i | \(0.671193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −42.0000 | −0.243336 | −0.121668 | − | 0.992571i | \(-0.538824\pi\) | ||||
−0.121668 | + | 0.992571i | \(0.538824\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 301.000i | − 1.58780i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 314.000i | 1.39517i | 0.716502 | + | 0.697585i | \(0.245742\pi\) | ||||
−0.716502 | + | 0.697585i | \(0.754258\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −196.000 | −0.804747 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −203.000 | −0.773251 | −0.386625 | − | 0.922237i | \(-0.626359\pi\) | ||||
−0.386625 | + | 0.922237i | \(0.626359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 92.0000i | − 0.326276i | −0.986603 | − | 0.163138i | \(-0.947838\pi\) | ||||
0.986603 | − | 0.163138i | \(-0.0521616\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 196.000i | 0.608288i | 0.952626 | + | 0.304144i | \(0.0983704\pi\) | ||||
−0.952626 | + | 0.304144i | \(0.901630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 307.000 | 0.895044 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −637.000 | −1.74898 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 82.0000i | 0.212520i | 0.994338 | + | 0.106260i | \(0.0338876\pi\) | ||||
−0.994338 | + | 0.106260i | \(0.966112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 245.000i | 0.569317i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −280.000 | −0.617846 | −0.308923 | − | 0.951087i | \(-0.599968\pi\) | ||||
−0.308923 | + | 0.951087i | \(0.599968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −518.000 | −1.08726 | −0.543632 | − | 0.839324i | \(-0.682951\pi\) | ||||
−0.543632 | + | 0.839324i | \(0.682951\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 132.000i | − 0.263975i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 141.000i | 0.257103i | 0.991703 | + | 0.128551i | \(0.0410327\pi\) | ||||
−0.991703 | + | 0.128551i | \(0.958967\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1134.00 | −1.97852 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −412.000 | −0.688668 | −0.344334 | − | 0.938847i | \(-0.611895\pi\) | ||||
−0.344334 | + | 0.938847i | \(0.611895\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 763.000i | − 1.22332i | −0.791121 | − | 0.611660i | \(-0.790502\pi\) | ||||
0.791121 | − | 0.611660i | \(-0.209498\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 258.000i | 0.381842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 510.000 | 0.726323 | 0.363161 | − | 0.931726i | \(-0.381697\pi\) | ||||
0.363161 | + | 0.931726i | \(0.381697\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −839.000 | −1.15089 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 777.000i | − 1.02755i | −0.857924 | − | 0.513776i | \(-0.828246\pi\) | ||||
0.857924 | − | 0.513776i | \(-0.171754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1120.00i | 1.38019i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 945.000 | 1.12550 | 0.562752 | − | 0.826626i | \(-0.309743\pi\) | ||||
0.562752 | + | 0.826626i | \(0.309743\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 168.000 | 0.193530 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 294.000i | 0.327811i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1246.00i | − 1.30425i | −0.758112 | − | 0.652124i | \(-0.773878\pi\) | ||||
0.758112 | − | 0.652124i | \(-0.226122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −946.000 | −0.960369 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1302.00 | 1.28271 | 0.641356 | − | 0.767244i | \(-0.278372\pi\) | ||||
0.641356 | + | 0.767244i | \(0.278372\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 532.000i | − 0.508927i | −0.967082 | − | 0.254464i | \(-0.918101\pi\) | ||||
0.967082 | − | 0.254464i | \(-0.0818989\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 1269.00i | − 1.14653i | −0.819370 | − | 0.573266i | \(-0.805676\pi\) | ||||
0.819370 | − | 0.573266i | \(-0.194324\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1070.00 | −0.940251 | −0.470126 | − | 0.882599i | \(-0.655791\pi\) | ||||
−0.470126 | + | 0.882599i | \(0.655791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2198.00 | 1.87950 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 503.000i | − 0.418746i | −0.977836 | − | 0.209373i | \(-0.932858\pi\) | ||||
0.977836 | − | 0.209373i | \(-0.0671422\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 616.000i | 0.486745i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 546.000 | 0.420603 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 518.000 | 0.389181 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1421.00i | 1.04169i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 874.000i | − 0.610669i | −0.952245 | − | 0.305334i | \(-0.901232\pi\) | ||||
0.952245 | − | 0.305334i | \(-0.0987683\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −644.000 | −0.439543 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1092.00 | −0.728309 | −0.364155 | − | 0.931339i | \(-0.618642\pi\) | ||||
−0.364155 | + | 0.931339i | \(0.618642\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 210.000i | − 0.136912i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 411.000i | − 0.256307i | −0.991754 | − | 0.128154i | \(-0.959095\pi\) | ||||
0.991754 | − | 0.128154i | \(-0.0409051\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −595.000 | −0.363074 | −0.181537 | − | 0.983384i | \(-0.558107\pi\) | ||||
−0.181537 | + | 0.983384i | \(0.558107\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1372.00 | 0.819456 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 1204.00i | − 0.704081i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2149.00i | − 1.20576i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3200.00 | 1.75942 | 0.879712 | − | 0.475507i | \(-0.157735\pi\) | ||||
0.879712 | + | 0.475507i | \(0.157735\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −202.000 | −0.108864 | −0.0544322 | − | 0.998517i | \(-0.517335\pi\) | ||||
−0.0544322 | + | 0.998517i | \(0.517335\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2002.00i | 1.05786i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 406.000i | − 0.206384i | −0.994661 | − | 0.103192i | \(-0.967094\pi\) | ||||
0.994661 | − | 0.103192i | \(-0.0329057\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 574.000 | 0.286297 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 972.000 | 0.475803 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3803.00i | 1.82745i | 0.406336 | + | 0.913724i | \(0.366806\pi\) | ||||
−0.406336 | + | 0.913724i | \(0.633194\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4116.00i | 1.90722i | 0.301046 | + | 0.953610i | \(0.402664\pi\) | ||||
−0.301046 | + | 0.953610i | \(0.597336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1413.00 | 0.643150 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 770.000 | 0.344347 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1512.00i | 0.664481i | 0.943195 | + | 0.332241i | \(0.107805\pi\) | ||||
−0.943195 | + | 0.332241i | \(0.892195\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1960.00i | 0.832331i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2585.00 | 1.07940 | 0.539698 | − | 0.841859i | \(-0.318538\pi\) | ||||
0.539698 | + | 0.841859i | \(0.318538\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2758.00 | −1.13260 | −0.566300 | − | 0.824199i | \(-0.691626\pi\) | ||||
−0.566300 | + | 0.824199i | \(0.691626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3626.00i | 1.46471i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 3913.00i | − 1.53020i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 210.000 | 0.0808214 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2378.00 | 0.900869 | 0.450435 | − | 0.892809i | \(-0.351269\pi\) | ||||
0.450435 | + | 0.892809i | \(0.351269\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3067.00i | 1.14387i | 0.820298 | + | 0.571937i | \(0.193808\pi\) | ||||
−0.820298 | + | 0.571937i | \(0.806192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2346.00i | − 0.848455i | −0.905556 | − | 0.424227i | \(-0.860546\pi\) | ||||
0.905556 | − | 0.424227i | \(-0.139454\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4900.00 | 1.74549 | 0.872743 | − | 0.488180i | \(-0.162339\pi\) | ||||
0.872743 | + | 0.488180i | \(0.162339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 987.000 | 0.346356 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 960.000i | − 0.331915i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3564.00i | 1.19669i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1505.00 | −0.498101 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4307.00 | −1.40524 | −0.702621 | − | 0.711564i | \(-0.747987\pi\) | ||||
−0.702621 | + | 0.711564i | \(0.747987\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2884.00i | 0.927739i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 252.000i | − 0.0788335i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5341.00 | −1.64800 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2548.00 | −0.775552 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 2212.00i | − 0.664244i | −0.943236 | − | 0.332122i | \(-0.892235\pi\) | ||||
0.943236 | − | 0.332122i | \(-0.107765\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 476.000i | 0.139177i | 0.997576 | + | 0.0695886i | \(0.0221687\pi\) | ||||
−0.997576 | + | 0.0695886i | \(0.977831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2940.00 | 0.848387 | 0.424194 | − | 0.905572i | \(-0.360558\pi\) | ||||
0.424194 | + | 0.905572i | \(0.360558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1806.00 | 0.514399 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1002.00i | 0.281730i | 0.990029 | + | 0.140865i | \(0.0449884\pi\) | ||||
−0.990029 | + | 0.140865i | \(0.955012\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 3570.00i | − 0.978466i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2480.00 | 0.671204 | 0.335602 | − | 0.942004i | \(-0.391060\pi\) | ||||
0.335602 | + | 0.942004i | \(0.391060\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1897.00 | 0.507039 | 0.253520 | − | 0.967330i | \(-0.418412\pi\) | ||||
0.253520 | + | 0.967330i | \(0.418412\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4928.00i | 1.30095i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 980.000i | 0.252453i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5439.00 | −1.38427 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2373.00 | 0.596743 | 0.298371 | − | 0.954450i | \(-0.403557\pi\) | ||||
0.298371 | + | 0.954450i | \(0.403557\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6966.00i | − 1.73102i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4494.00i | 1.09077i | 0.838185 | + | 0.545385i | \(0.183617\pi\) | ||||
−0.838185 | + | 0.545385i | \(0.816383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1884.00 | −0.451993 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3520.00 | 0.834799 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 722.000i | − 0.169279i | −0.996412 | − | 0.0846396i | \(-0.973026\pi\) | ||||
0.996412 | − | 0.0846396i | \(-0.0269739\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6615.00i | − 1.51622i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6160.00 | 1.39621 | 0.698107 | − | 0.715993i | \(-0.254026\pi\) | ||||
0.698107 | + | 0.715993i | \(0.254026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7238.00 | 1.62243 | 0.811213 | − | 0.584751i | \(-0.198808\pi\) | ||||
0.811213 | + | 0.584751i | \(0.198808\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 1176.00i | − 0.260713i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1776.00i | − 0.385233i | −0.981274 | − | 0.192616i | \(-0.938303\pi\) | ||||
0.981274 | − | 0.192616i | \(-0.0616973\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 924.000 | 0.198274 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4542.00 | 0.964246 | 0.482123 | − | 0.876104i | \(-0.339866\pi\) | ||||
0.482123 | + | 0.876104i | \(0.339866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 7077.00i | − 1.48652i | −0.669005 | − | 0.743258i | \(-0.733280\pi\) | ||||
0.669005 | − | 0.743258i | \(-0.266720\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 1218.00i | − 0.250510i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3368.00 | −0.685528 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8722.00 | −1.75702 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 4158.00i | − 0.829054i | −0.910037 | − | 0.414527i | \(-0.863947\pi\) | ||||
0.910037 | − | 0.414527i | \(-0.136053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 1505.00i | − 0.294037i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4536.00 | −0.877337 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 552.000 | 0.105703 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 9114.00i | − 1.72801i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2569.00i | − 0.477591i | −0.971070 | − | 0.238796i | \(-0.923247\pi\) | ||||
0.971070 | − | 0.238796i | \(-0.0767526\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3724.00 | −0.685602 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2982.00 | −0.543710 | −0.271855 | − | 0.962338i | \(-0.587637\pi\) | ||||
−0.271855 | + | 0.962338i | \(0.587637\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2422.00i | 0.437379i | 0.975795 | + | 0.218689i | \(0.0701781\pi\) | ||||
−0.975795 | + | 0.218689i | \(0.929822\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9484.00i | 1.68036i | 0.542307 | + | 0.840181i | \(0.317551\pi\) | ||||
−0.542307 | + | 0.840181i | \(0.682449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6880.00 | −1.20754 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8883.00 | −1.54455 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3185.00i | 0.548663i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7490.00i | 1.26666i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1176.00 | −0.197067 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 183.000 | 0.0303885 | 0.0151942 | − | 0.999885i | \(-0.495163\pi\) | ||||
0.0151942 | + | 0.999885i | \(0.495163\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 6908.00i | − 1.13681i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2861.00i | − 0.462459i | −0.972899 | − | 0.231229i | \(-0.925725\pi\) | ||||
0.972899 | − | 0.231229i | \(-0.0742748\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3521.00 | −0.564113 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1806.00 | −0.286805 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3900.00i | 0.613936i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 629.000i | − 0.0973098i | −0.998816 | − | 0.0486549i | \(-0.984507\pi\) | ||||
0.998816 | − | 0.0486549i | \(-0.0154934\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5950.00 | −0.912597 | −0.456298 | − | 0.889827i | \(-0.650825\pi\) | ||||
−0.456298 | + | 0.889827i | \(0.650825\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −980.000 | −0.149027 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 11718.0i | − 1.76682i | −0.468604 | − | 0.883408i | \(-0.655243\pi\) | ||||
0.468604 | − | 0.883408i | \(-0.344757\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3822.00i | − 0.566615i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8070.00 | 1.18640 | 0.593201 | − | 0.805054i | \(-0.297864\pi\) | ||||
0.593201 | + | 0.805054i | \(0.297864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5634.00 | −0.821403 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 3626.00i | − 0.524286i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8316.00i | 1.18281i | 0.806374 | + | 0.591406i | \(0.201427\pi\) | ||||
−0.806374 | + | 0.591406i | \(0.798573\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4466.00 | 0.630056 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −492.000 | −0.0688500 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12062.0i | 1.67439i | 0.546906 | + | 0.837194i | \(0.315805\pi\) | ||||
−0.546906 | + | 0.837194i | \(0.684195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4480.00i | 0.612021i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1735.00 | 0.235148 | 0.117574 | − | 0.993064i | \(-0.462488\pi\) | ||||
0.117574 | + | 0.993064i | \(0.462488\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6118.00 | −0.822663 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 7602.00i | − 1.01421i | −0.861883 | − | 0.507107i | \(-0.830715\pi\) | ||||
0.861883 | − | 0.507107i | \(-0.169285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2024.00i | 0.265855i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3030.00 | −0.394928 | −0.197464 | − | 0.980310i | \(-0.563271\pi\) | ||||
−0.197464 | + | 0.980310i | \(0.563271\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14742.0 | −1.90674 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7644.00i | 0.981142i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1204.00i | 0.152209i | 0.997100 | + | 0.0761046i | \(0.0242483\pi\) | ||||
−0.997100 | + | 0.0761046i | \(0.975752\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1470.00 | −0.184441 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1077.00 | 0.134122 | 0.0670609 | − | 0.997749i | \(-0.478638\pi\) | ||||
0.0670609 | + | 0.997749i | \(0.478638\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1176.00i | 0.145362i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13502.0i | 1.64440i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3955.00 | 0.478147 | 0.239074 | − | 0.971001i | \(-0.423156\pi\) | ||||
0.239074 | + | 0.971001i | \(0.423156\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2877.00 | −0.345285 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1680.00i | − 0.200163i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4165.00i | 0.489115i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6265.00 | 0.730466 | 0.365233 | − | 0.930916i | \(-0.380989\pi\) | ||||
0.365233 | + | 0.930916i | \(0.380989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3788.00 | −0.438517 | −0.219259 | − | 0.975667i | \(-0.570364\pi\) | ||||
−0.219259 | + | 0.975667i | \(0.570364\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 4312.00i | − 0.495642i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3108.00i | − 0.352240i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8428.00 | −0.948503 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15258.0 | 1.70523 | 0.852613 | − | 0.522544i | \(-0.175017\pi\) | ||||
0.852613 | + | 0.522544i | \(0.175017\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 13573.0i | − 1.50641i | −0.657784 | − | 0.753206i | \(-0.728506\pi\) | ||||
0.657784 | − | 0.753206i | \(-0.271494\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5670.00i | 0.620670i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8120.00 | −0.882794 | −0.441397 | − | 0.897312i | \(-0.645517\pi\) | ||||
−0.441397 | + | 0.897312i | \(0.645517\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6754.00 | −0.729295 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6183.00i | 0.663122i | 0.943434 | + | 0.331561i | \(0.107575\pi\) | ||||
−0.943434 | + | 0.331561i | \(0.892425\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 22400.0i | − 2.37021i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1975.00 | 0.207586 | 0.103793 | − | 0.994599i | \(-0.466902\pi\) | ||||
0.103793 | + | 0.994599i | \(0.466902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8729.00 | −0.911380 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1414.00i | 0.146657i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 11831.0i | − 1.21101i | −0.795842 | − | 0.605504i | \(-0.792971\pi\) | ||||
0.795842 | − | 0.605504i | \(-0.207029\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3185.00 | −0.323885 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1932.00 | 0.195189 | 0.0975946 | − | 0.995226i | \(-0.468885\pi\) | ||||
0.0975946 | + | 0.995226i | \(0.468885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9228.00i | 0.926267i | 0.886289 | + | 0.463133i | \(0.153275\pi\) | ||||
−0.886289 | + | 0.463133i | \(0.846725\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13916.0i | 1.37892i | 0.724324 | + | 0.689460i | \(0.242152\pi\) | ||||
−0.724324 | + | 0.689460i | \(0.757848\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −846.000 | −0.0832935 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2842.00 | −0.278031 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 3956.00i | − 0.384560i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 1804.00i | − 0.173165i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2310.00 | 0.220348 | 0.110174 | − | 0.993912i | \(-0.464859\pi\) | ||||
0.110174 | + | 0.993912i | \(0.464859\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8792.00 | 0.833432 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 6804.00i | − 0.640979i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 17114.0i | − 1.59242i | −0.605019 | − | 0.796211i | \(-0.706835\pi\) | ||||
0.605019 | − | 0.796211i | \(-0.293165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 26621.0 | 2.46185 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17228.0 | 1.58348 | 0.791740 | − | 0.610858i | \(-0.209175\pi\) | ||||
0.791740 | + | 0.610858i | \(0.209175\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14560.0i | 1.33012i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2472.00i | − 0.223107i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12500.0 | −1.12140 | −0.560698 | − | 0.828020i | \(-0.689467\pi\) | ||||
−0.560698 | + | 0.828020i | \(0.689467\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 28812.0 | 2.56931 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 868.000i | 0.0769428i | 0.999260 | + | 0.0384714i | \(0.0122488\pi\) | ||||
−0.999260 | + | 0.0384714i | \(0.987751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9891.00i | − 0.866420i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13370.0 | −1.16427 | −0.582136 | − | 0.813091i | \(-0.697783\pi\) | ||||
−0.582136 | + | 0.813091i | \(0.697783\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4578.00 | 0.396319 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1225.00i | 0.105429i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8428.00i | 0.716950i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10584.0 | 0.895156 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21637.0 | 1.81945 | 0.909726 | − | 0.415210i | \(-0.136292\pi\) | ||||
0.909726 | + | 0.415210i | \(0.136292\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 287.000i | − 0.0239955i | −0.999928 | − | 0.0119977i | \(-0.996181\pi\) | ||||
0.999928 | − | 0.0119977i | \(-0.00381909\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3822.00i | 0.315918i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −14077.0 | −1.15698 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6160.00 | 0.503430 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5684.00i | 0.461916i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 18095.0i | − 1.45411i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13201.0 | 1.05493 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5328.00 | −0.423417 | −0.211709 | − | 0.977333i | \(-0.567903\pi\) | ||||
−0.211709 | + | 0.977333i | \(0.567903\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 19306.0i | 1.52578i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 71.0000i | 0.00554980i | 0.999996 | + | 0.00277490i | \(0.000883279\pi\) | ||||
−0.999996 | + | 0.00277490i | \(0.999117\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11396.0 | 0.885919 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5600.00 | 0.432973 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3060.00i | 0.235306i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18444.0i | 1.40305i | 0.712646 | + | 0.701524i | \(0.247497\pi\) | ||||
−0.712646 | + | 0.701524i | \(0.752503\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2576.00 | −0.194907 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −27391.0 | −2.06141 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 672.000i | − 0.0503045i | −0.999684 | − | 0.0251522i | \(-0.991993\pi\) | ||||
0.999684 | − | 0.0251522i | \(-0.00800705\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 5034.00i | − 0.372854i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10935.0 | 0.805657 | 0.402829 | − | 0.915275i | \(-0.368027\pi\) | ||||
0.402829 | + | 0.915275i | \(0.368027\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13588.0 | 0.995867 | 0.497934 | − | 0.867215i | \(-0.334092\pi\) | ||||
0.497934 | + | 0.867215i | \(0.334092\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 16646.0i | − 1.21361i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 8701.00i | − 0.627777i | −0.949460 | − | 0.313889i | \(-0.898368\pi\) | ||||
0.949460 | − | 0.313889i | \(-0.101632\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 21469.0 | 1.54097 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4662.00 | 0.332896 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3526.00i | 0.250484i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11361.0i | 0.798839i | 0.916768 | + | 0.399420i | \(0.130788\pi\) | ||||
−0.916768 | + | 0.399420i | \(0.869212\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1470.00 | 0.102836 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16422.0 | −1.14300 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11417.0i | 0.790624i | 0.918547 | + | 0.395312i | \(0.129364\pi\) | ||||
−0.918547 | + | 0.395312i | \(0.870636\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 34300.0i | − 2.35143i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21050.0 | −1.43586 | −0.717930 | − | 0.696116i | \(-0.754910\pi\) | ||||
−0.717930 | + | 0.696116i | \(0.754910\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7427.00 | 0.504083 | 0.252041 | − | 0.967716i | \(-0.418898\pi\) | ||||
0.252041 | + | 0.967716i | \(0.418898\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 3102.00i | − 0.209491i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 4144.00i | − 0.277100i | −0.990355 | − | 0.138550i | \(-0.955756\pi\) | ||||
0.990355 | − | 0.138550i | \(-0.0442442\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6720.00 | −0.447140 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5488.00 | 0.363373 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30122.0i | 1.98469i | 0.123489 | + | 0.992346i | \(0.460592\pi\) | ||||
−0.123489 | + | 0.992346i | \(0.539408\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11934.0i | 0.778679i | 0.921094 | + | 0.389339i | \(0.127297\pi\) | ||||
−0.921094 | + | 0.389339i | \(0.872703\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8540.00 | 0.554526 | 0.277263 | − | 0.960794i | \(-0.410573\pi\) | ||||
0.277263 | + | 0.960794i | \(0.410573\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5670.00 | −0.366392 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5670.00i | 0.364629i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10535.0i | 0.671017i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 28574.0 | 1.81132 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3158.00 | 0.199236 | 0.0996181 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996181 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30149.0i | 1.89307i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 8596.00i | − 0.534672i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9064.00 | 0.561137 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4278.00 | −0.263605 | −0.131803 | − | 0.991276i | \(-0.542076\pi\) | ||||
−0.131803 | + | 0.991276i | \(0.542076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11508.0i | 0.705803i | 0.935661 | + | 0.352901i | \(0.114805\pi\) | ||||
−0.935661 | + | 0.352901i | \(0.885195\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 8204.00i | − 0.498505i | −0.968439 | − | 0.249252i | \(-0.919815\pi\) | ||||
0.968439 | − | 0.249252i | \(-0.0801849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12040.0 | −0.728215 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1764.00 | −0.106201 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5518.00i | − 0.330683i | −0.986236 | − | 0.165342i | \(-0.947127\pi\) | ||||
0.986236 | − | 0.165342i | \(-0.0528726\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16786.0i | 0.996780i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13295.0 | 0.785887 | 0.392944 | − | 0.919563i | \(-0.371457\pi\) | ||||
0.392944 | + | 0.919563i | \(0.371457\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9968.00 | −0.586551 | −0.293276 | − | 0.956028i | \(-0.594745\pi\) | ||||
−0.293276 | + | 0.956028i | \(0.594745\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17836.0i | 1.04479i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25920.0i | 1.50469i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −15484.0 | −0.894837 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22274.0 | −1.28149 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 15738.0i | − 0.901419i | −0.892671 | − | 0.450710i | \(-0.851171\pi\) | ||||
0.892671 | − | 0.450710i | \(-0.148829\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19824.0i | 1.12540i | 0.826660 | + | 0.562702i | \(0.190238\pi\) | ||||
−0.826660 | + | 0.562702i | \(0.809762\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7476.00 | 0.422537 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3332.00 | 0.187493 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11073.0i | 0.620346i | 0.950680 | + | 0.310173i | \(0.100387\pi\) | ||||
−0.950680 | + | 0.310173i | \(0.899613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 20580.0i | − 1.14291i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2296.00 | 0.126953 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6503.00 | 0.358011 | 0.179006 | − | 0.983848i | \(-0.442712\pi\) | ||||
0.179006 | + | 0.983848i | \(0.442712\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 5676.00i | − 0.311130i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18473.0i | 1.00389i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7014.00 | 0.379533 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10148.0 | −0.546768 | −0.273384 | − | 0.961905i | \(-0.588143\pi\) | ||||
−0.273384 | + | 0.961905i | \(0.588143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 10990.0i | − 0.589610i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7812.00i | 0.415559i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9980.00 | 0.528641 | 0.264321 | − | 0.964435i | \(-0.414852\pi\) | ||||
0.264321 | + | 0.964435i | \(0.414852\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11220.0 | −0.591818 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6804.00i | 0.357380i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 17360.0i | − 0.904214i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −27510.0 | −1.42691 | −0.713456 | − | 0.700700i | \(-0.752871\pi\) | ||||
−0.713456 | + | 0.700700i | \(0.752871\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3192.00 | 0.164877 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 13279.0i | − 0.683059i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 17024.0i | − 0.868480i | −0.900797 | − | 0.434240i | \(-0.857017\pi\) | ||||
0.900797 | − | 0.434240i | \(-0.142983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11843.0 | 0.601687 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8372.00 | −0.423597 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 34748.0i | − 1.75095i | −0.483263 | − | 0.875475i | \(-0.660549\pi\) | ||||
0.483263 | − | 0.875475i | \(-0.339451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6063.00i | 0.303030i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12020.0 | −0.598326 | −0.299163 | − | 0.954202i | \(-0.596707\pi\) | ||||
−0.299163 | + | 0.954202i | \(0.596707\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6860.00 | 0.340092 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 28642.0i | − 1.41423i | −0.707098 | − | 0.707115i | \(-0.749996\pi\) | ||||
0.707098 | − | 0.707115i | \(-0.250004\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17094.0i | 0.837265i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7614.00 | 0.371441 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8752.00 | −0.425253 | −0.212627 | − | 0.977134i | \(-0.568202\pi\) | ||||
−0.212627 | + | 0.977134i | \(0.568202\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 16611.0i | − 0.803902i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 10256.0i | − 0.492418i | −0.969217 | − | 0.246209i | \(-0.920815\pi\) | ||||
0.969217 | − | 0.246209i | \(-0.0791850\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −48762.0 | −2.33195 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33957.0 | 1.61753 | 0.808765 | − | 0.588132i | \(-0.200136\pi\) | ||||
0.808765 | + | 0.588132i | \(0.200136\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 6420.00i | − 0.304613i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7840.00i | 0.369082i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −27965.0 | −1.31137 | −0.655685 | − | 0.755034i | \(-0.727620\pi\) | ||||
−0.655685 | + | 0.755034i | \(0.727620\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31458.0 | 1.46943 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9912.00i | 0.461203i | 0.973048 | + | 0.230601i | \(0.0740694\pi\) | ||||
−0.973048 | + | 0.230601i | \(0.925931\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13188.0i | 0.608902i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7105.00 | 0.326782 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17716.0 | −0.811688 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5600.00i | 0.255591i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 25564.0i | − 1.15789i | −0.815367 | − | 0.578944i | \(-0.803465\pi\) | ||||
0.815367 | − | 0.578944i | \(-0.196535\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5054.00 | −0.228045 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3018.00 | 0.135661 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14504.0i | 0.649498i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 12446.0i | − 0.553149i | −0.960992 | − | 0.276575i | \(-0.910801\pi\) | ||||
0.960992 | − | 0.276575i | \(-0.0891993\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17836.0 | 0.789728 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20790.0 | −0.917077 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 32809.0i | − 1.44185i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 43120.0i | − 1.88091i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33970.0 | −1.47629 | −0.738147 | − | 0.674640i | \(-0.764299\pi\) | ||||
−0.738147 | + | 0.674640i | \(0.764299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18732.0 | −0.811060 | −0.405530 | − | 0.914082i | \(-0.632913\pi\) | ||||
−0.405530 | + | 0.914082i | \(0.632913\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 50666.0i | − 2.18565i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3220.00i | 0.137887i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3696.00 | −0.157691 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6162.00 | 0.261943 | 0.130972 | − | 0.991386i | \(-0.458190\pi\) | ||||
0.130972 | + | 0.991386i | \(0.458190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25388.0i | 1.07530i | 0.843169 | + | 0.537649i | \(0.180687\pi\) | ||||
−0.843169 | + | 0.537649i | \(0.819313\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25201.0i | 1.05964i | 0.848109 | + | 0.529821i | \(0.177741\pi\) | ||||
−0.848109 | + | 0.529821i | \(0.822259\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19740.0 | 0.827019 | 0.413509 | − | 0.910500i | \(-0.364303\pi\) | ||||
0.413509 | + | 0.910500i | \(0.364303\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12432.0 | −0.518967 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 27937.0i | − 1.16202i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1470.00i | 0.0607057i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29680.0 | 1.22130 | 0.610648 | − | 0.791902i | \(-0.290909\pi\) | ||||
0.610648 | + | 0.791902i | \(0.290909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1211.00 | 0.0496535 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 31794.0i | − 1.29898i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3108.00i | 0.126083i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −49539.0 | −2.00256 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50868.0 | 2.04904 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 1218.00i | − 0.0488904i | −0.999701 | − | 0.0244452i | \(-0.992218\pi\) | ||||
0.999701 | − | 0.0244452i | \(-0.00778193\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 38731.0i | − 1.54379i | −0.635752 | − | 0.771894i | \(-0.719310\pi\) | ||||
0.635752 | − | 0.771894i | \(-0.280690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −23555.0 | −0.935607 | −0.467803 | − | 0.883833i | \(-0.654954\pi\) | ||||
−0.467803 | + | 0.883833i | \(0.654954\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8526.00 | −0.337474 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 24872.0i | − 0.981058i | −0.871425 | − | 0.490529i | \(-0.836804\pi\) | ||||
0.871425 | − | 0.490529i | \(-0.163196\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23576.0i | 0.923510i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21930.0 | 0.856069 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3948.00 | 0.153585 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27412.0i | 1.06272i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17124.0i | 0.659335i | 0.944097 | + | 0.329667i | \(0.106937\pi\) | ||||
−0.944097 | + | 0.329667i | \(0.893063\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −29106.0 | −1.11686 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −658.000 | −0.0251630 | −0.0125815 | − | 0.999921i | \(-0.504005\pi\) | ||||
−0.0125815 | + | 0.999921i | \(0.504005\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 33727.0i | − 1.28540i | −0.766120 | − | 0.642698i | \(-0.777815\pi\) | ||||
0.766120 | − | 0.642698i | \(-0.222185\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36036.0i | 1.36412i | 0.731298 | + | 0.682058i | \(0.238915\pi\) | ||||
−0.731298 | + | 0.682058i | \(0.761085\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5244.00 | 0.197838 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −36077.0 | −1.35648 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6860.00i | − 0.257067i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 31752.0i | 1.18190i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6720.00 | 0.249304 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7462.00 | 0.275910 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 3864.00i | − 0.142399i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 39156.0i | 1.43347i | 0.697348 | + | 0.716733i | \(0.254363\pi\) | ||||
−0.697348 | + | 0.716733i | \(0.745637\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28644.0 | −1.04517 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −43532.0 | −1.58318 | −0.791591 | − | 0.611051i | \(-0.790747\pi\) | ||||
−0.791591 | + | 0.611051i | \(0.790747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 33411.0i | − 1.21111i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 6552.00i | − 0.235950i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28610.0 | −1.02694 | −0.513469 | − | 0.858108i | \(-0.671640\pi\) | ||||
−0.513469 | + | 0.858108i | \(0.671640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17983.0 | −0.643388 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11536.0i | 0.411389i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11704.0i | 0.414682i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24290.0 | 0.857835 | 0.428918 | − | 0.903344i | \(-0.358895\pi\) | ||||
0.428918 | + | 0.903344i | \(0.358895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10745.0 | −0.378253 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20874.0i | 0.732459i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 34461.0i | − 1.20149i | −0.799442 | − | 0.600743i | \(-0.794872\pi\) | ||||
0.799442 | − | 0.600743i | \(-0.205128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16954.0 | 0.589215 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −40628.0 | −1.40748 | −0.703738 | − | 0.710460i | \(-0.748487\pi\) | ||||
−0.703738 | + | 0.710460i | \(0.748487\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32886.0i | 1.13565i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 20904.0i | − 0.717306i | −0.933471 | − | 0.358653i | \(-0.883236\pi\) | ||||
0.933471 | − | 0.358653i | \(-0.116764\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21364.0 | −0.730774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 66388.0 | 2.26370 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1807.00i | 0.0614213i | 0.999528 | + | 0.0307106i | \(0.00977704\pi\) | ||||
−0.999528 | + | 0.0307106i | \(0.990223\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 48160.0i | 1.62674i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2466.00 | 0.0830358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28027.0 | −0.940787 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 27918.0i | 0.934211i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 57584.0i | − 1.91497i | −0.288482 | − | 0.957485i | \(-0.593151\pi\) | ||||
0.288482 | − | 0.957485i | \(-0.406849\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22295.0 | 0.739132 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27237.0 | −0.900182 | −0.450091 | − | 0.892983i | \(-0.648608\pi\) | ||||
−0.450091 | + | 0.892983i | \(0.648608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 3570.00i | − 0.117625i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 13649.0i | 0.446950i | 0.974710 | + | 0.223475i | \(0.0717401\pi\) | ||||
−0.974710 | + | 0.223475i | \(0.928260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40635.0 | 1.32656 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23540.0 | 0.766131 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 16002.0i | − 0.519211i | −0.965715 | − | 0.259606i | \(-0.916407\pi\) | ||||
0.965715 | − | 0.259606i | \(-0.0835925\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8232.00i | 0.265479i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14904.0 | −0.479191 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37022.0 | −1.18672 | −0.593362 | − | 0.804936i | \(-0.702200\pi\) | ||||
−0.593362 | + | 0.804936i | \(0.702200\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1281.00i | − 0.0409379i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 18396.0i | − 0.584360i | −0.956363 | − | 0.292180i | \(-0.905619\pi\) | ||||
0.956363 | − | 0.292180i | \(-0.0943807\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10990.0 | 0.348056 |
(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 | 400.4.c.e.49.1 | 2 | ||
4.3 | odd | 2 | 25.4.b.b.24.1 | 2 | |||
5.2 | odd | 4 | 400.4.a.c.1.1 | 1 | |||
5.3 | odd | 4 | 400.4.a.s.1.1 | 1 | |||
5.4 | even | 2 | inner | 400.4.c.e.49.2 | 2 | ||
12.11 | even | 2 | 225.4.b.f.199.2 | 2 | |||
20.3 | even | 4 | 25.4.a.a.1.1 | ✓ | 1 | ||
20.7 | even | 4 | 25.4.a.b.1.1 | yes | 1 | ||
20.19 | odd | 2 | 25.4.b.b.24.2 | 2 | |||
40.3 | even | 4 | 1600.4.a.bt.1.1 | 1 | |||
40.13 | odd | 4 | 1600.4.a.h.1.1 | 1 | |||
40.27 | even | 4 | 1600.4.a.i.1.1 | 1 | |||
40.37 | odd | 4 | 1600.4.a.bs.1.1 | 1 | |||
60.23 | odd | 4 | 225.4.a.e.1.1 | 1 | |||
60.47 | odd | 4 | 225.4.a.c.1.1 | 1 | |||
60.59 | even | 2 | 225.4.b.f.199.1 | 2 | |||
140.27 | odd | 4 | 1225.4.a.i.1.1 | 1 | |||
140.83 | odd | 4 | 1225.4.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.4.a.a.1.1 | ✓ | 1 | 20.3 | even | 4 | ||
25.4.a.b.1.1 | yes | 1 | 20.7 | even | 4 | ||
25.4.b.b.24.1 | 2 | 4.3 | odd | 2 | |||
25.4.b.b.24.2 | 2 | 20.19 | odd | 2 | |||
225.4.a.c.1.1 | 1 | 60.47 | odd | 4 | |||
225.4.a.e.1.1 | 1 | 60.23 | odd | 4 | |||
225.4.b.f.199.1 | 2 | 60.59 | even | 2 | |||
225.4.b.f.199.2 | 2 | 12.11 | even | 2 | |||
400.4.a.c.1.1 | 1 | 5.2 | odd | 4 | |||
400.4.a.s.1.1 | 1 | 5.3 | odd | 4 | |||
400.4.c.e.49.1 | 2 | 1.1 | even | 1 | trivial | ||
400.4.c.e.49.2 | 2 | 5.4 | even | 2 | inner | ||
1225.4.a.h.1.1 | 1 | 140.83 | odd | 4 | |||
1225.4.a.i.1.1 | 1 | 140.27 | odd | 4 | |||
1600.4.a.h.1.1 | 1 | 40.13 | odd | 4 | |||
1600.4.a.i.1.1 | 1 | 40.27 | even | 4 | |||
1600.4.a.bs.1.1 | 1 | 40.37 | odd | 4 | |||
1600.4.a.bt.1.1 | 1 | 40.3 | even | 4 |