Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(199,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.199");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(72.1727189158\) |
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 150) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.199 |
Dual form | 450.6.c.g.199.2 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 79.0000i | − 0.609371i | −0.952453 | − | 0.304686i | \(-0.901449\pi\) | ||||
0.952453 | − | 0.304686i | \(-0.0985514\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −150.000 | −0.373774 | −0.186887 | − | 0.982381i | \(-0.559840\pi\) | ||||
−0.186887 | + | 0.982381i | \(0.559840\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 137.000i | − 0.224834i | −0.993661 | − | 0.112417i | \(-0.964141\pi\) | ||||
0.993661 | − | 0.112417i | \(-0.0358593\pi\) | |||||||
\(14\) | −316.000 | −0.430891 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 2034.00i | 1.70698i | 0.521109 | + | 0.853490i | \(0.325519\pi\) | ||||
−0.521109 | + | 0.853490i | \(0.674481\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1969.00 | 1.25130 | 0.625650 | − | 0.780104i | \(-0.284834\pi\) | ||||
0.625650 | + | 0.780104i | \(0.284834\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 600.000i | 0.264298i | ||||||||
\(23\) | − 1350.00i | − 0.532126i | −0.963956 | − | 0.266063i | \(-0.914277\pi\) | ||||
0.963956 | − | 0.266063i | \(-0.0857229\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −548.000 | −0.158982 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1264.00i | 0.304686i | ||||||||
\(29\) | −2946.00 | −0.650486 | −0.325243 | − | 0.945631i | \(-0.605446\pi\) | ||||
−0.325243 | + | 0.945631i | \(0.605446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 713.000 | 0.133256 | 0.0666278 | − | 0.997778i | \(-0.478776\pi\) | ||||
0.0666278 | + | 0.997778i | \(0.478776\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8136.00 | 1.20702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 3238.00i | − 0.388841i | −0.980918 | − | 0.194421i | \(-0.937717\pi\) | ||||
0.980918 | − | 0.194421i | \(-0.0622827\pi\) | |||||||
\(38\) | − 7876.00i | − 0.884803i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6564.00 | −0.609830 | −0.304915 | − | 0.952380i | \(-0.598628\pi\) | ||||
−0.304915 | + | 0.952380i | \(0.598628\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 19579.0i | 1.61480i | 0.590003 | + | 0.807401i | \(0.299127\pi\) | ||||
−0.590003 | + | 0.807401i | \(0.700873\pi\) | |||||||
\(44\) | 2400.00 | 0.186887 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5400.00 | −0.376270 | ||||||||
\(47\) | 21150.0i | 1.39658i | 0.715815 | + | 0.698290i | \(0.246055\pi\) | ||||
−0.715815 | + | 0.698290i | \(0.753945\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10566.0 | 0.628667 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2192.00i | 0.112417i | ||||||||
\(53\) | − 25896.0i | − 1.26632i | −0.774021 | − | 0.633159i | \(-0.781758\pi\) | ||||
0.774021 | − | 0.633159i | \(-0.218242\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5056.00 | 0.215445 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 11784.0i | 0.459963i | ||||||||
\(59\) | 25350.0 | 0.948086 | 0.474043 | − | 0.880502i | \(-0.342794\pi\) | ||||
0.474043 | + | 0.880502i | \(0.342794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 50615.0 | 1.74163 | 0.870813 | − | 0.491615i | \(-0.163593\pi\) | ||||
0.870813 | + | 0.491615i | \(0.163593\pi\) | |||||||
\(62\) | − 2852.00i | − 0.0942259i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 22519.0i | − 0.612861i | −0.951893 | − | 0.306431i | \(-0.900865\pi\) | ||||
0.951893 | − | 0.306431i | \(-0.0991347\pi\) | |||||||
\(68\) | − 32544.0i | − 0.853490i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −33900.0 | −0.798094 | −0.399047 | − | 0.916931i | \(-0.630659\pi\) | ||||
−0.399047 | + | 0.916931i | \(0.630659\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 82442.0i | − 1.81068i | −0.424689 | − | 0.905339i | \(-0.639617\pi\) | ||||
0.424689 | − | 0.905339i | \(-0.360383\pi\) | |||||||
\(74\) | −12952.0 | −0.274952 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −31504.0 | −0.625650 | ||||||||
\(77\) | 11850.0i | 0.227767i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 81472.0 | 1.46873 | 0.734363 | − | 0.678757i | \(-0.237481\pi\) | ||||
0.734363 | + | 0.678757i | \(0.237481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 26256.0i | 0.431215i | ||||||||
\(83\) | 25782.0i | 0.410791i | 0.978679 | + | 0.205396i | \(0.0658481\pi\) | ||||
−0.978679 | + | 0.205396i | \(0.934152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 78316.0 | 1.14184 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 9600.00i | − 0.132149i | ||||||||
\(89\) | 103728. | 1.38810 | 0.694050 | − | 0.719926i | \(-0.255824\pi\) | ||||
0.694050 | + | 0.719926i | \(0.255824\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10823.0 | −0.137007 | ||||||||
\(92\) | 21600.0i | 0.266063i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 84600.0 | 0.987531 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 57343.0i | − 0.618801i | −0.950932 | − | 0.309401i | \(-0.899872\pi\) | ||||
0.950932 | − | 0.309401i | \(-0.100128\pi\) | |||||||
\(98\) | − 42264.0i | − 0.444534i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 91032.0 | 0.887954 | 0.443977 | − | 0.896038i | \(-0.353567\pi\) | ||||
0.443977 | + | 0.896038i | \(0.353567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 191636.i | − 1.77985i | −0.456104 | − | 0.889926i | \(-0.650756\pi\) | ||||
0.456104 | − | 0.889926i | \(-0.349244\pi\) | |||||||
\(104\) | 8768.00 | 0.0794909 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −103584. | −0.895423 | ||||||||
\(107\) | − 9288.00i | − 0.0784265i | −0.999231 | − | 0.0392132i | \(-0.987515\pi\) | ||||
0.999231 | − | 0.0392132i | \(-0.0124852\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 20635.0 | 0.166356 | 0.0831780 | − | 0.996535i | \(-0.473493\pi\) | ||||
0.0831780 | + | 0.996535i | \(0.473493\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 20224.0i | − 0.152343i | ||||||||
\(113\) | 176892.i | 1.30320i | 0.758561 | + | 0.651602i | \(0.225903\pi\) | ||||
−0.758561 | + | 0.651602i | \(0.774097\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 47136.0 | 0.325243 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 101400.i | − 0.670398i | ||||||||
\(119\) | 160686. | 1.04019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −138551. | −0.860293 | ||||||||
\(122\) | − 202460.i | − 1.23151i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11408.0 | −0.0666278 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 256480.i | − 1.41106i | −0.708682 | − | 0.705528i | \(-0.750710\pi\) | ||||
0.708682 | − | 0.705528i | \(-0.249290\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −177600. | −0.904200 | −0.452100 | − | 0.891967i | \(-0.649325\pi\) | ||||
−0.452100 | + | 0.891967i | \(0.649325\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 155551.i | − 0.762507i | ||||||||
\(134\) | −90076.0 | −0.433358 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −130176. | −0.603509 | ||||||||
\(137\) | − 260886.i | − 1.18754i | −0.804634 | − | 0.593772i | \(-0.797638\pi\) | ||||
0.804634 | − | 0.593772i | \(-0.202362\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 217684. | 0.955629 | 0.477815 | − | 0.878461i | \(-0.341429\pi\) | ||||
0.477815 | + | 0.878461i | \(0.341429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 135600.i | 0.564337i | ||||||||
\(143\) | 20550.0i | 0.0840372i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −329768. | −1.28034 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 51808.0i | 0.194421i | ||||||||
\(149\) | 421794. | 1.55645 | 0.778224 | − | 0.627987i | \(-0.216121\pi\) | ||||
0.778224 | + | 0.627987i | \(0.216121\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −101917. | −0.363751 | −0.181876 | − | 0.983322i | \(-0.558217\pi\) | ||||
−0.181876 | + | 0.983322i | \(0.558217\pi\) | |||||||
\(152\) | 126016.i | 0.442402i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 47400.0 | 0.161056 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 101773.i | − 0.329521i | −0.986334 | − | 0.164761i | \(-0.947315\pi\) | ||||
0.986334 | − | 0.164761i | \(-0.0526852\pi\) | |||||||
\(158\) | − 325888.i | − 1.03855i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −106650. | −0.324262 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 202249.i | 0.596235i | 0.954529 | + | 0.298117i | \(0.0963587\pi\) | ||||
−0.954529 | + | 0.298117i | \(0.903641\pi\) | |||||||
\(164\) | 105024. | 0.304915 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 103128. | 0.290473 | ||||||||
\(167\) | − 231600.i | − 0.642610i | −0.946976 | − | 0.321305i | \(-0.895879\pi\) | ||||
0.946976 | − | 0.321305i | \(-0.104121\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 352524. | 0.949450 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 313264.i | − 0.807401i | ||||||||
\(173\) | − 174222.i | − 0.442576i | −0.975209 | − | 0.221288i | \(-0.928974\pi\) | ||||
0.975209 | − | 0.221288i | \(-0.0710261\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −38400.0 | −0.0934436 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 414912.i | − 0.981535i | ||||||||
\(179\) | −642066. | −1.49778 | −0.748888 | − | 0.662696i | \(-0.769412\pi\) | ||||
−0.748888 | + | 0.662696i | \(0.769412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −56071.0 | −0.127216 | −0.0636080 | − | 0.997975i | \(-0.520261\pi\) | ||||
−0.0636080 | + | 0.997975i | \(0.520261\pi\) | |||||||
\(182\) | 43292.0i | 0.0968789i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 86400.0 | 0.188135 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 305100.i | − 0.638026i | ||||||||
\(188\) | − 338400.i | − 0.698290i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 209694. | 0.415913 | 0.207957 | − | 0.978138i | \(-0.433319\pi\) | ||||
0.207957 | + | 0.978138i | \(0.433319\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 715597.i | 1.38285i | 0.722448 | + | 0.691425i | \(0.243017\pi\) | ||||
−0.722448 | + | 0.691425i | \(0.756983\pi\) | |||||||
\(194\) | −229372. | −0.437558 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −169056. | −0.314333 | ||||||||
\(197\) | − 508854.i | − 0.934174i | −0.884211 | − | 0.467087i | \(-0.845304\pi\) | ||||
0.884211 | − | 0.467087i | \(-0.154696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 986017. | 1.76503 | 0.882514 | − | 0.470286i | \(-0.155849\pi\) | ||||
0.882514 | + | 0.470286i | \(0.155849\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 364128.i | − 0.627879i | ||||||||
\(203\) | 232734.i | 0.396387i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −766544. | −1.25855 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 35072.0i | − 0.0562085i | ||||||||
\(209\) | −295350. | −0.467704 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 119495. | 0.184775 | 0.0923876 | − | 0.995723i | \(-0.470550\pi\) | ||||
0.0923876 | + | 0.995723i | \(0.470550\pi\) | |||||||
\(212\) | 414336.i | 0.633159i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −37152.0 | −0.0554559 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 56327.0i | − 0.0812021i | ||||||||
\(218\) | − 82540.0i | − 0.117631i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 278658. | 0.383788 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 48545.0i | − 0.0653706i | −0.999466 | − | 0.0326853i | \(-0.989594\pi\) | ||||
0.999466 | − | 0.0326853i | \(-0.0104059\pi\) | |||||||
\(224\) | −80896.0 | −0.107723 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 707568. | 0.921504 | ||||||||
\(227\) | 287652.i | 0.370512i | 0.982690 | + | 0.185256i | \(0.0593115\pi\) | ||||
−0.982690 | + | 0.185256i | \(0.940689\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −72065.0 | −0.0908104 | −0.0454052 | − | 0.998969i | \(-0.514458\pi\) | ||||
−0.0454052 | + | 0.998969i | \(0.514458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 188544.i | − 0.229981i | ||||||||
\(233\) | − 569148.i | − 0.686808i | −0.939188 | − | 0.343404i | \(-0.888420\pi\) | ||||
0.939188 | − | 0.343404i | \(-0.111580\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −405600. | −0.474043 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 642744.i | − 0.735522i | ||||||||
\(239\) | 696504. | 0.788731 | 0.394365 | − | 0.918954i | \(-0.370964\pi\) | ||||
0.394365 | + | 0.918954i | \(0.370964\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 576137. | 0.638974 | 0.319487 | − | 0.947591i | \(-0.396489\pi\) | ||||
0.319487 | + | 0.947591i | \(0.396489\pi\) | |||||||
\(242\) | 554204.i | 0.608319i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −809840. | −0.870813 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 269753.i | − 0.281335i | ||||||||
\(248\) | 45632.0i | 0.0471130i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.22492e6 | 1.22723 | 0.613613 | − | 0.789607i | \(-0.289715\pi\) | ||||
0.613613 | + | 0.789607i | \(0.289715\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 202500.i | 0.198895i | ||||||||
\(254\) | −1.02592e6 | −0.997767 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | − 972132.i | − 0.918105i | −0.888409 | − | 0.459053i | \(-0.848189\pi\) | ||||
0.888409 | − | 0.459053i | \(-0.151811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −255802. | −0.236949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 710400.i | 0.639366i | ||||||||
\(263\) | 1.76190e6i | 1.57070i | 0.619055 | + | 0.785348i | \(0.287516\pi\) | ||||
−0.619055 | + | 0.785348i | \(0.712484\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −622204. | −0.539174 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 360304.i | 0.306431i | ||||||||
\(269\) | 1.74383e6 | 1.46935 | 0.734674 | − | 0.678421i | \(-0.237335\pi\) | ||||
0.734674 | + | 0.678421i | \(0.237335\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.70426e6 | −1.40965 | −0.704826 | − | 0.709381i | \(-0.748975\pi\) | ||||
−0.704826 | + | 0.709381i | \(0.748975\pi\) | |||||||
\(272\) | 520704.i | 0.426745i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.04354e6 | −0.839720 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.46972e6i | 1.15089i | 0.817840 | + | 0.575446i | \(0.195171\pi\) | ||||
−0.817840 | + | 0.575446i | \(0.804829\pi\) | |||||||
\(278\) | − 870736.i | − 0.675732i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.22530e6 | 0.925715 | 0.462858 | − | 0.886433i | \(-0.346824\pi\) | ||||
0.462858 | + | 0.886433i | \(0.346824\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 637333.i | 0.473043i | 0.971626 | + | 0.236521i | \(0.0760073\pi\) | ||||
−0.971626 | + | 0.236521i | \(0.923993\pi\) | |||||||
\(284\) | 542400. | 0.399047 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 82200.0 | 0.0594233 | ||||||||
\(287\) | 518556.i | 0.371613i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.71730e6 | −1.91378 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.31907e6i | 0.905339i | ||||||||
\(293\) | 35094.0i | 0.0238816i | 0.999929 | + | 0.0119408i | \(0.00380097\pi\) | ||||
−0.999929 | + | 0.0119408i | \(0.996199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 207232. | 0.137476 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 1.68718e6i | − 1.10058i | ||||||||
\(299\) | −184950. | −0.119640 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.54674e6 | 0.984014 | ||||||||
\(302\) | 407668.i | 0.257211i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 504064. | 0.312825 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.88040e6i | 1.74424i | 0.489293 | + | 0.872120i | \(0.337255\pi\) | ||||
−0.489293 | + | 0.872120i | \(0.662745\pi\) | |||||||
\(308\) | − 189600.i | − 0.113884i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.38305e6 | 1.39712 | 0.698558 | − | 0.715554i | \(-0.253826\pi\) | ||||
0.698558 | + | 0.715554i | \(0.253826\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.93081e6i | 1.11399i | 0.830517 | + | 0.556993i | \(0.188045\pi\) | ||||
−0.830517 | + | 0.556993i | \(0.811955\pi\) | |||||||
\(314\) | −407092. | −0.233007 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.30355e6 | −0.734363 | ||||||||
\(317\) | 2.18995e6i | 1.22401i | 0.790852 | + | 0.612007i | \(0.209638\pi\) | ||||
−0.790852 | + | 0.612007i | \(0.790362\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 441900. | 0.243135 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 426600.i | 0.229288i | ||||||||
\(323\) | 4.00495e6i | 2.13595i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 808996. | 0.421602 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 420096.i | − 0.215608i | ||||||||
\(329\) | 1.67085e6 | 0.851036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.41429e6 | 0.709527 | 0.354764 | − | 0.934956i | \(-0.384561\pi\) | ||||
0.354764 | + | 0.934956i | \(0.384561\pi\) | |||||||
\(332\) | − 412512.i | − 0.205396i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −926400. | −0.454394 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.38208e6i | 0.662916i | 0.943470 | + | 0.331458i | \(0.107541\pi\) | ||||
−0.943470 | + | 0.331458i | \(0.892459\pi\) | |||||||
\(338\) | − 1.41010e6i | − 0.671362i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −106950. | −0.0498075 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 2.16247e6i | − 0.992463i | ||||||||
\(344\) | −1.25306e6 | −0.570919 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −696888. | −0.312948 | ||||||||
\(347\) | 283758.i | 0.126510i | 0.997997 | + | 0.0632549i | \(0.0201481\pi\) | ||||
−0.997997 | + | 0.0632549i | \(0.979852\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.13809e6 | −0.939642 | −0.469821 | − | 0.882762i | \(-0.655682\pi\) | ||||
−0.469821 | + | 0.882762i | \(0.655682\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 153600.i | 0.0660746i | ||||||||
\(353\) | 3.16015e6i | 1.34980i | 0.737908 | + | 0.674901i | \(0.235814\pi\) | ||||
−0.737908 | + | 0.674901i | \(0.764186\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.65965e6 | −0.694050 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.56826e6i | 1.05909i | ||||||||
\(359\) | −3.59564e6 | −1.47245 | −0.736225 | − | 0.676737i | \(-0.763393\pi\) | ||||
−0.736225 | + | 0.676737i | \(0.763393\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.40086e6 | 0.565754 | ||||||||
\(362\) | 224284.i | 0.0899553i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 173168. | 0.0685037 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.62043e6i | − 1.79068i | −0.445385 | − | 0.895339i | \(-0.646933\pi\) | ||||
0.445385 | − | 0.895339i | \(-0.353067\pi\) | |||||||
\(368\) | − 345600.i | − 0.133031i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.04578e6 | −0.771658 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.51983e6i | 1.30993i | 0.755657 | + | 0.654967i | \(0.227318\pi\) | ||||
−0.755657 | + | 0.654967i | \(0.772682\pi\) | |||||||
\(374\) | −1.22040e6 | −0.451152 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.35360e6 | −0.493765 | ||||||||
\(377\) | 403602.i | 0.146251i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −595061. | −0.212796 | −0.106398 | − | 0.994324i | \(-0.533932\pi\) | ||||
−0.106398 | + | 0.994324i | \(0.533932\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 838776.i | − 0.294095i | ||||||||
\(383\) | − 1.30050e6i | − 0.453016i | −0.974009 | − | 0.226508i | \(-0.927269\pi\) | ||||
0.974009 | − | 0.226508i | \(-0.0727309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.86239e6 | 0.977823 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 917488.i | 0.309401i | ||||||||
\(389\) | 620724. | 0.207981 | 0.103991 | − | 0.994578i | \(-0.466839\pi\) | ||||
0.103991 | + | 0.994578i | \(0.466839\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.74590e6 | 0.908328 | ||||||||
\(392\) | 676224.i | 0.222267i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.03542e6 | −0.660561 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.18622e6i | 0.377737i | 0.982002 | + | 0.188869i | \(0.0604821\pi\) | ||||
−0.982002 | + | 0.188869i | \(0.939518\pi\) | |||||||
\(398\) | − 3.94407e6i | − 1.24806i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.13334e6 | −0.973077 | −0.486538 | − | 0.873659i | \(-0.661741\pi\) | ||||
−0.486538 | + | 0.873659i | \(0.661741\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 97681.0i | − 0.0299604i | ||||||||
\(404\) | −1.45651e6 | −0.443977 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 930936. | 0.280288 | ||||||||
\(407\) | 485700.i | 0.145339i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −567581. | −0.167772 | −0.0838860 | − | 0.996475i | \(-0.526733\pi\) | ||||
−0.0838860 | + | 0.996475i | \(0.526733\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.06618e6i | 0.889926i | ||||||||
\(413\) | − 2.00265e6i | − 0.577737i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −140288. | −0.0397454 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.18140e6i | 0.330717i | ||||||||
\(419\) | −6.09000e6 | −1.69466 | −0.847329 | − | 0.531068i | \(-0.821791\pi\) | ||||
−0.847329 | + | 0.531068i | \(0.821791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.07139e6 | 0.844558 | 0.422279 | − | 0.906466i | \(-0.361230\pi\) | ||||
0.422279 | + | 0.906466i | \(0.361230\pi\) | |||||||
\(422\) | − 477980.i | − 0.130656i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.65734e6 | 0.447711 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 3.99858e6i | − 1.06130i | ||||||||
\(428\) | 148608.i | 0.0392132i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 669150. | 0.173512 | 0.0867562 | − | 0.996230i | \(-0.472350\pi\) | ||||
0.0867562 | + | 0.996230i | \(0.472350\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.25439e6i | 0.834161i | 0.908870 | + | 0.417080i | \(0.136947\pi\) | ||||
−0.908870 | + | 0.417080i | \(0.863053\pi\) | |||||||
\(434\) | −225308. | −0.0574186 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −330160. | −0.0831780 | ||||||||
\(437\) | − 2.65815e6i | − 0.665849i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.58759e6 | −0.393168 | −0.196584 | − | 0.980487i | \(-0.562985\pi\) | ||||
−0.196584 | + | 0.980487i | \(0.562985\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 1.11463e6i | − 0.271379i | ||||||||
\(443\) | − 213888.i | − 0.0517818i | −0.999665 | − | 0.0258909i | \(-0.991758\pi\) | ||||
0.999665 | − | 0.0258909i | \(-0.00824225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −194180. | −0.0462240 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 323584.i | 0.0761714i | ||||||||
\(449\) | 3.70724e6 | 0.867831 | 0.433916 | − | 0.900953i | \(-0.357132\pi\) | ||||
0.433916 | + | 0.900953i | \(0.357132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 984600. | 0.227939 | ||||||||
\(452\) | − 2.83027e6i | − 0.651602i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.15061e6 | 0.261992 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.83193e6i | 0.858275i | 0.903239 | + | 0.429138i | \(0.141182\pi\) | ||||
−0.903239 | + | 0.429138i | \(0.858818\pi\) | |||||||
\(458\) | 288260.i | 0.0642127i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.58672e6 | −1.22435 | −0.612174 | − | 0.790723i | \(-0.709705\pi\) | ||||
−0.612174 | + | 0.790723i | \(0.709705\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.40142e6i | 0.954203i | 0.878848 | + | 0.477101i | \(0.158313\pi\) | ||||
−0.878848 | + | 0.477101i | \(0.841687\pi\) | |||||||
\(464\) | −754176. | −0.162621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.27659e6 | −0.485647 | ||||||||
\(467\) | − 3.35225e6i | − 0.711287i | −0.934622 | − | 0.355643i | \(-0.884262\pi\) | ||||
0.934622 | − | 0.355643i | \(-0.115738\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.77900e6 | −0.373460 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.62240e6i | 0.335199i | ||||||||
\(473\) | − 2.93685e6i | − 0.603572i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.57098e6 | −0.520093 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 2.78602e6i | − 0.557717i | ||||||||
\(479\) | 909966. | 0.181212 | 0.0906059 | − | 0.995887i | \(-0.471120\pi\) | ||||
0.0906059 | + | 0.995887i | \(0.471120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −443606. | −0.0874248 | ||||||||
\(482\) | − 2.30455e6i | − 0.451823i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.21682e6 | 0.430146 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4.03579e6i | − 0.771093i | −0.922689 | − | 0.385546i | \(-0.874013\pi\) | ||||
0.922689 | − | 0.385546i | \(-0.125987\pi\) | |||||||
\(488\) | 3.23936e6i | 0.615757i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −379944. | −0.0711239 | −0.0355620 | − | 0.999367i | \(-0.511322\pi\) | ||||
−0.0355620 | + | 0.999367i | \(0.511322\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.99216e6i | − 1.11037i | ||||||||
\(494\) | −1.07901e6 | −0.198934 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 182528. | 0.0333139 | ||||||||
\(497\) | 2.67810e6i | 0.486335i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.42433e6 | 1.33477 | 0.667384 | − | 0.744714i | \(-0.267414\pi\) | ||||
0.667384 | + | 0.744714i | \(0.267414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 4.89970e6i | − 0.867780i | ||||||||
\(503\) | 2.29988e6i | 0.405309i | 0.979250 | + | 0.202654i | \(0.0649568\pi\) | ||||
−0.979250 | + | 0.202654i | \(0.935043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 810000. | 0.140640 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.10368e6i | 0.705528i | ||||||||
\(509\) | 6.73721e6 | 1.15262 | 0.576310 | − | 0.817231i | \(-0.304492\pi\) | ||||
0.576310 | + | 0.817231i | \(0.304492\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.51292e6 | −1.10338 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.88853e6 | −0.649198 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 3.17250e6i | − 0.522006i | ||||||||
\(518\) | 1.02321e6i | 0.167548i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.26806e6 | 1.49587 | 0.747936 | − | 0.663770i | \(-0.231045\pi\) | ||||
0.747936 | + | 0.663770i | \(0.231045\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 1.10620e7i | − 1.76839i | −0.467113 | − | 0.884197i | \(-0.654706\pi\) | ||||
0.467113 | − | 0.884197i | \(-0.345294\pi\) | |||||||
\(524\) | 2.84160e6 | 0.452100 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.04760e6 | 1.11065 | ||||||||
\(527\) | 1.45024e6i | 0.227465i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.61384e6 | 0.716842 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.48882e6i | 0.381253i | ||||||||
\(533\) | 899268.i | 0.137111i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.44122e6 | 0.216679 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 6.97534e6i | − 1.03899i | ||||||||
\(539\) | −1.58490e6 | −0.234979 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.30754e7 | −1.92072 | −0.960358 | − | 0.278771i | \(-0.910073\pi\) | ||||
−0.960358 | + | 0.278771i | \(0.910073\pi\) | |||||||
\(542\) | 6.81702e6i | 0.996774i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.08282e6 | 0.301754 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.84605e6i | − 0.263800i | −0.991263 | − | 0.131900i | \(-0.957892\pi\) | ||||
0.991263 | − | 0.131900i | \(-0.0421078\pi\) | |||||||
\(548\) | 4.17418e6i | 0.593772i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.80067e6 | −0.813953 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 6.43629e6i | − 0.894999i | ||||||||
\(554\) | 5.87887e6 | 0.813803 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.48294e6 | −0.477815 | ||||||||
\(557\) | − 6.48782e6i | − 0.886055i | −0.896508 | − | 0.443027i | \(-0.853904\pi\) | ||||
0.896508 | − | 0.443027i | \(-0.146096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.68232e6 | 0.363063 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 4.90121e6i | − 0.654579i | ||||||||
\(563\) | 3.01538e6i | 0.400932i | 0.979701 | + | 0.200466i | \(0.0642456\pi\) | ||||
−0.979701 | + | 0.200466i | \(0.935754\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.54933e6 | 0.334492 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 2.16960e6i | − 0.282169i | ||||||||
\(569\) | −3.49810e6 | −0.452952 | −0.226476 | − | 0.974017i | \(-0.572720\pi\) | ||||
−0.226476 | + | 0.974017i | \(0.572720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.23749e7 | −1.58837 | −0.794185 | − | 0.607676i | \(-0.792102\pi\) | ||||
−0.794185 | + | 0.607676i | \(0.792102\pi\) | |||||||
\(572\) | − 328800.i | − 0.0420186i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.07422e6 | 0.262770 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.80687e6i | 0.851153i | 0.904922 | + | 0.425577i | \(0.139929\pi\) | ||||
−0.904922 | + | 0.425577i | \(0.860071\pi\) | |||||||
\(578\) | 1.08692e7i | 1.35325i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.03678e6 | 0.250325 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.88440e6i | 0.473317i | ||||||||
\(584\) | 5.27629e6 | 0.640172 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 140376. | 0.0168869 | ||||||||
\(587\) | − 7.77113e6i | − 0.930870i | −0.885082 | − | 0.465435i | \(-0.845898\pi\) | ||||
0.885082 | − | 0.465435i | \(-0.154102\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.40390e6 | 0.166743 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 828928.i | − 0.0972104i | ||||||||
\(593\) | − 1.51222e7i | − 1.76595i | −0.469418 | − | 0.882976i | \(-0.655536\pi\) | ||||
0.469418 | − | 0.882976i | \(-0.344464\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.74870e6 | −0.778224 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 739800.i | 0.0845982i | ||||||||
\(599\) | −1.67012e6 | −0.190187 | −0.0950937 | − | 0.995468i | \(-0.530315\pi\) | ||||
−0.0950937 | + | 0.995468i | \(0.530315\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.12220e6 | 0.465525 | 0.232763 | − | 0.972534i | \(-0.425223\pi\) | ||||
0.232763 | + | 0.972534i | \(0.425223\pi\) | |||||||
\(602\) | − 6.18696e6i | − 0.695803i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.63067e6 | 0.181876 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.81870e6i | 0.751155i | 0.926791 | + | 0.375578i | \(0.122556\pi\) | ||||
−0.926791 | + | 0.375578i | \(0.877444\pi\) | |||||||
\(608\) | − 2.01626e6i | − 0.221201i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.89755e6 | 0.313999 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.59466e7i | − 1.71402i | −0.515300 | − | 0.857010i | \(-0.672319\pi\) | ||||
0.515300 | − | 0.857010i | \(-0.327681\pi\) | |||||||
\(614\) | 1.15216e7 | 1.23336 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −758400. | −0.0805279 | ||||||||
\(617\) | 8.21952e6i | 0.869228i | 0.900617 | + | 0.434614i | \(0.143115\pi\) | ||||
−0.900617 | + | 0.434614i | \(0.856885\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.23323e7 | 1.29366 | 0.646828 | − | 0.762636i | \(-0.276095\pi\) | ||||
0.646828 | + | 0.762636i | \(0.276095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 9.53220e6i | − 0.987910i | ||||||||
\(623\) | − 8.19451e6i | − 0.845869i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.72325e6 | 0.787706 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.62837e6i | 0.164761i | ||||||||
\(629\) | 6.58609e6 | 0.663745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.01912e6 | −0.301861 | −0.150931 | − | 0.988544i | \(-0.548227\pi\) | ||||
−0.150931 | + | 0.988544i | \(0.548227\pi\) | |||||||
\(632\) | 5.21421e6i | 0.519273i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.75981e6 | 0.865509 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.44754e6i | − 0.141346i | ||||||||
\(638\) | − 1.76760e6i | − 0.171922i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.18052e7 | 1.13482 | 0.567411 | − | 0.823435i | \(-0.307945\pi\) | ||||
0.567411 | + | 0.823435i | \(0.307945\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.85360e6i | 0.272186i | 0.990696 | + | 0.136093i | \(0.0434546\pi\) | ||||
−0.990696 | + | 0.136093i | \(0.956545\pi\) | |||||||
\(644\) | 1.70640e6 | 0.162131 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.60198e7 | 1.51034 | ||||||||
\(647\) | 3.40192e6i | 0.319494i | 0.987158 | + | 0.159747i | \(0.0510679\pi\) | ||||
−0.987158 | + | 0.159747i | \(0.948932\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.80250e6 | −0.354370 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 3.23598e6i | − 0.298117i | ||||||||
\(653\) | − 9.39166e6i | − 0.861905i | −0.902375 | − | 0.430953i | \(-0.858178\pi\) | ||||
0.902375 | − | 0.430953i | \(-0.141822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.68038e6 | −0.152458 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 6.68340e6i | − 0.601773i | ||||||||
\(659\) | 9.36659e6 | 0.840171 | 0.420086 | − | 0.907484i | \(-0.362000\pi\) | ||||
0.420086 | + | 0.907484i | \(0.362000\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57748e7 | 1.40430 | 0.702150 | − | 0.712029i | \(-0.252223\pi\) | ||||
0.702150 | + | 0.712029i | \(0.252223\pi\) | |||||||
\(662\) | − 5.65717e6i | − 0.501712i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.65005e6 | −0.145237 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.97710e6i | 0.346140i | ||||||||
\(668\) | 3.70560e6i | 0.321305i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.59225e6 | −0.650975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.64515e6i | 0.565545i | 0.959187 | + | 0.282773i | \(0.0912542\pi\) | ||||
−0.959187 | + | 0.282773i | \(0.908746\pi\) | |||||||
\(674\) | 5.52832e6 | 0.468753 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.64038e6 | −0.474725 | ||||||||
\(677\) | 1.57780e7i | 1.32306i | 0.749917 | + | 0.661532i | \(0.230094\pi\) | ||||
−0.749917 | + | 0.661532i | \(0.769906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.53010e6 | −0.377080 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 427800.i | 0.0352192i | ||||||||
\(683\) | − 1.96654e7i | − 1.61306i | −0.591190 | − | 0.806532i | \(-0.701342\pi\) | ||||
0.591190 | − | 0.806532i | \(-0.298658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.64987e6 | −0.701777 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.01222e6i | 0.403701i | ||||||||
\(689\) | −3.54775e6 | −0.284712 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 990464. | 0.0789121 | 0.0394560 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394560 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(692\) | 2.78755e6i | 0.221288i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.13503e6 | 0.0894560 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.33512e7i | − 1.04097i | ||||||||
\(698\) | 8.55236e6i | 0.664427i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.52919e6 | −0.501839 | −0.250920 | − | 0.968008i | \(-0.580733\pi\) | ||||
−0.250920 | + | 0.968008i | \(0.580733\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 6.37562e6i | − 0.486558i | ||||||||
\(704\) | 614400. | 0.0467218 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.26406e7 | 0.954455 | ||||||||
\(707\) | − 7.19153e6i | − 0.541094i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.02106e7 | 1.50996 | 0.754979 | − | 0.655749i | \(-0.227647\pi\) | ||||
0.754979 | + | 0.655749i | \(0.227647\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 6.63859e6i | 0.490768i | ||||||||
\(713\) | − 962550.i | − 0.0709087i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.02731e7 | 0.748888 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.43826e7i | 1.04118i | ||||||||
\(719\) | −2.27720e7 | −1.64277 | −0.821387 | − | 0.570371i | \(-0.806800\pi\) | ||||
−0.821387 | + | 0.570371i | \(0.806800\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.51392e7 | −1.08459 | ||||||||
\(722\) | − 5.60345e6i | − 0.400048i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 897136. | 0.0636080 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 7.09186e6i | − 0.497650i | −0.968548 | − | 0.248825i | \(-0.919956\pi\) | ||||
0.968548 | − | 0.248825i | \(-0.0800445\pi\) | |||||||
\(728\) | − 692672.i | − 0.0484394i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.98237e7 | −2.75644 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.38982e7i | 0.955432i | 0.878514 | + | 0.477716i | \(0.158535\pi\) | ||||
−0.878514 | + | 0.477716i | \(0.841465\pi\) | |||||||
\(734\) | −1.84817e7 | −1.26620 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.38240e6 | −0.0940674 | ||||||||
\(737\) | 3.37785e6i | 0.229072i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.54857e7 | −1.04309 | −0.521543 | − | 0.853225i | \(-0.674643\pi\) | ||||
−0.521543 | + | 0.853225i | \(0.674643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.18314e6i | 0.545645i | ||||||||
\(743\) | 159276.i | 0.0105847i | 0.999986 | + | 0.00529235i | \(0.00168461\pi\) | ||||
−0.999986 | + | 0.00529235i | \(0.998315\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.40793e7 | 0.926263 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.88160e6i | 0.319013i | ||||||||
\(749\) | −733752. | −0.0477908 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.15554e7 | 0.747625 | 0.373812 | − | 0.927504i | \(-0.378050\pi\) | ||||
0.373812 | + | 0.927504i | \(0.378050\pi\) | |||||||
\(752\) | 5.41440e6i | 0.349145i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.61441e6 | 0.103415 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 6.34402e6i | − 0.402369i | −0.979553 | − | 0.201185i | \(-0.935521\pi\) | ||||
0.979553 | − | 0.201185i | \(-0.0644792\pi\) | |||||||
\(758\) | 2.38024e6i | 0.150469i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.17748e7 | 0.737040 | 0.368520 | − | 0.929620i | \(-0.379865\pi\) | ||||
0.368520 | + | 0.929620i | \(0.379865\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.63016e6i | − 0.101373i | ||||||||
\(764\) | −3.35510e6 | −0.207957 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.20200e6 | −0.320331 | ||||||||
\(767\) | − 3.47295e6i | − 0.213162i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.47869e7 | 1.51149 | 0.755745 | − | 0.654865i | \(-0.227275\pi\) | ||||
0.755745 | + | 0.654865i | \(0.227275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1.14496e7i | − 0.691425i | ||||||||
\(773\) | − 1.38017e7i | − 0.830774i | −0.909645 | − | 0.415387i | \(-0.863646\pi\) | ||||
0.909645 | − | 0.415387i | \(-0.136354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.66995e6 | 0.218779 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 2.48290e6i | − 0.147065i | ||||||||
\(779\) | −1.29245e7 | −0.763081 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.08500e6 | 0.298307 | ||||||||
\(782\) | − 1.09836e7i | − 0.642285i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.70490e6 | 0.157167 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.53795e7i | − 0.885129i | −0.896737 | − | 0.442565i | \(-0.854069\pi\) | ||||
0.896737 | − | 0.442565i | \(-0.145931\pi\) | |||||||
\(788\) | 8.14166e6i | 0.467087i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.39745e7 | 0.794135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 6.93426e6i | − 0.391577i | ||||||||
\(794\) | 4.74489e6 | 0.267101 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.57763e7 | −0.882514 | ||||||||
\(797\) | 2.33978e7i | 1.30475i | 0.757894 | + | 0.652377i | \(0.226228\pi\) | ||||
−0.757894 | + | 0.652377i | \(0.773772\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.30191e7 | −2.38393 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.25334e7i | 0.688069i | ||||||||
\(803\) | 1.23663e7i | 0.676785i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −390724. | −0.0211852 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.82605e6i | 0.313939i | ||||||||
\(809\) | −2.80188e7 | −1.50515 | −0.752573 | − | 0.658509i | \(-0.771187\pi\) | ||||
−0.752573 | + | 0.658509i | \(0.771187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.65641e6 | −0.0884332 | −0.0442166 | − | 0.999022i | \(-0.514079\pi\) | ||||
−0.0442166 | + | 0.999022i | \(0.514079\pi\) | |||||||
\(812\) | − 3.72374e6i | − 0.198194i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.94280e6 | 0.102770 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.85511e7i | 2.02060i | ||||||||
\(818\) | 2.27032e6i | 0.118633i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.97382e7 | −1.53978 | −0.769888 | − | 0.638179i | \(-0.779688\pi\) | ||||
−0.769888 | + | 0.638179i | \(0.779688\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.60108e7i | 0.823972i | 0.911190 | + | 0.411986i | \(0.135165\pi\) | ||||
−0.911190 | + | 0.411986i | \(0.864835\pi\) | |||||||
\(824\) | 1.22647e7 | 0.629273 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.01060e6 | −0.408522 | ||||||||
\(827\) | − 2.54748e7i | − 1.29523i | −0.761969 | − | 0.647614i | \(-0.775767\pi\) | ||||
0.761969 | − | 0.647614i | \(-0.224233\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.89971e7 | −0.960064 | −0.480032 | − | 0.877251i | \(-0.659375\pi\) | ||||
−0.480032 | + | 0.877251i | \(0.659375\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 561152.i | 0.0281043i | ||||||||
\(833\) | 2.14912e7i | 1.07312i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.72560e6 | 0.233852 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.43600e7i | 1.19830i | ||||||||
\(839\) | 3.98539e7 | 1.95463 | 0.977317 | − | 0.211782i | \(-0.0679267\pi\) | ||||
0.977317 | + | 0.211782i | \(0.0679267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.18322e7 | −0.576868 | ||||||||
\(842\) | − 1.22856e7i | − 0.597193i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.91192e6 | −0.0923876 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.09455e7i | 0.524238i | ||||||||
\(848\) | − 6.62938e6i | − 0.316580i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.37130e6 | −0.206912 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 2.19179e7i | − 1.03140i | −0.856769 | − | 0.515700i | \(-0.827532\pi\) | ||||
0.856769 | − | 0.515700i | \(-0.172468\pi\) | |||||||
\(854\) | −1.59943e7 | −0.750450 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 594432. | 0.0277280 | ||||||||
\(857\) | 2.72213e7i | 1.26607i | 0.774125 | + | 0.633033i | \(0.218190\pi\) | ||||
−0.774125 | + | 0.633033i | \(0.781810\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.76214e7 | −1.73961 | −0.869805 | − | 0.493396i | \(-0.835755\pi\) | ||||
−0.869805 | + | 0.493396i | \(0.835755\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 2.67660e6i | − 0.122692i | ||||||||
\(863\) | 2.51995e7i | 1.15177i | 0.817531 | + | 0.575885i | \(0.195342\pi\) | ||||
−0.817531 | + | 0.575885i | \(0.804658\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.30176e7 | 0.589841 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 901232.i | 0.0406011i | ||||||||
\(869\) | −1.22208e7 | −0.548972 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.08510e6 | −0.137792 | ||||||||
\(872\) | 1.32064e6i | 0.0588157i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.06326e7 | −0.470826 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.77307e6i | 0.121748i | 0.998145 | + | 0.0608739i | \(0.0193888\pi\) | ||||
−0.998145 | + | 0.0608739i | \(0.980611\pi\) | |||||||
\(878\) | 6.35037e6i | 0.278012i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.37827e7 | 0.598268 | 0.299134 | − | 0.954211i | \(-0.403302\pi\) | ||||
0.299134 | + | 0.954211i | \(0.403302\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.96322e6i | 0.214221i | 0.994247 | + | 0.107110i | \(0.0341598\pi\) | ||||
−0.994247 | + | 0.107110i | \(0.965840\pi\) | |||||||
\(884\) | −4.45853e6 | −0.191894 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −855552. | −0.0366153 | ||||||||
\(887\) | − 4.12640e7i | − 1.76101i | −0.474037 | − | 0.880505i | \(-0.657204\pi\) | ||||
0.474037 | − | 0.880505i | \(-0.342796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.02619e7 | −0.859857 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 776720.i | 0.0326853i | ||||||||
\(893\) | 4.16444e7i | 1.74754i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.29434e6 | 0.0538613 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 1.48290e7i | − 0.613649i | ||||||||
\(899\) | −2.10050e6 | −0.0866808 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.26725e7 | 2.16158 | ||||||||
\(902\) | − 3.93840e6i | − 0.161177i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.13211e7 | −0.460752 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.66308e7i | 0.671268i | 0.941992 | + | 0.335634i | \(0.108951\pi\) | ||||
−0.941992 | + | 0.335634i | \(0.891049\pi\) | |||||||
\(908\) | − 4.60243e6i | − 0.185256i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.64995e7 | −1.45711 | −0.728554 | − | 0.684989i | \(-0.759807\pi\) | ||||
−0.728554 | + | 0.684989i | \(0.759807\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 3.86730e6i | − 0.153543i | ||||||||
\(914\) | 1.53277e7 | 0.606892 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.15304e6 | 0.0454052 | ||||||||
\(917\) | 1.40304e7i | 0.550994i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.83190e6 | −0.266841 | −0.133421 | − | 0.991060i | \(-0.542596\pi\) | ||||
−0.133421 | + | 0.991060i | \(0.542596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.23469e7i | 0.865744i | ||||||||
\(923\) | 4.64430e6i | 0.179439i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.76057e7 | 0.674723 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.01670e6i | 0.114991i | ||||||||
\(929\) | 5.05115e6 | 0.192022 | 0.0960111 | − | 0.995380i | \(-0.469392\pi\) | ||||
0.0960111 | + | 0.995380i | \(0.469392\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.08045e7 | 0.786651 | ||||||||
\(932\) | 9.10637e6i | 0.343404i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.34090e7 | −0.502956 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.30023e6i | 0.308845i | 0.988005 | + | 0.154423i | \(0.0493518\pi\) | ||||
−0.988005 | + | 0.154423i | \(0.950648\pi\) | |||||||
\(938\) | 7.11600e6i | 0.264076i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.87332e7 | 1.79412 | 0.897059 | − | 0.441910i | \(-0.145699\pi\) | ||||
0.897059 | + | 0.441910i | \(0.145699\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.86140e6i | 0.324506i | ||||||||
\(944\) | 6.48960e6 | 0.237022 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.17474e7 | −0.426790 | ||||||||
\(947\) | 7.34777e6i | 0.266245i | 0.991100 | + | 0.133122i | \(0.0425003\pi\) | ||||
−0.991100 | + | 0.133122i | \(0.957500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.12946e7 | −0.407102 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.02839e7i | 0.367761i | ||||||||
\(953\) | − 3.51437e7i | − 1.25347i | −0.779231 | − | 0.626737i | \(-0.784390\pi\) | ||||
0.779231 | − | 0.626737i | \(-0.215610\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.11441e7 | −0.394365 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 3.63986e6i | − 0.128136i | ||||||||
\(959\) | −2.06100e7 | −0.723655 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.81208e7 | −0.982243 | ||||||||
\(962\) | 1.77442e6i | 0.0618187i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.21819e6 | −0.319487 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.31186e6i | 0.0795050i | 0.999210 | + | 0.0397525i | \(0.0126570\pi\) | ||||
−0.999210 | + | 0.0397525i | \(0.987343\pi\) | |||||||
\(968\) | − 8.86726e6i | − 0.304159i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.73588e7 | 1.27158 | 0.635791 | − | 0.771861i | \(-0.280674\pi\) | ||||
0.635791 | + | 0.771861i | \(0.280674\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.71970e7i | − 0.582333i | ||||||||
\(974\) | −1.61432e7 | −0.545245 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.29574e7 | 0.435406 | ||||||||
\(977\) | 1.02666e7i | 0.344104i | 0.985088 | + | 0.172052i | \(0.0550397\pi\) | ||||
−0.985088 | + | 0.172052i | \(0.944960\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.55592e7 | −0.518837 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.51978e6i | 0.0502922i | ||||||||
\(983\) | 2.98404e7i | 0.984966i | 0.870322 | + | 0.492483i | \(0.163911\pi\) | ||||
−0.870322 | + | 0.492483i | \(0.836089\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −2.39687e7 | −0.785148 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.31605e6i | 0.140668i | ||||||||
\(989\) | 2.64316e7 | 0.859278 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.34222e7 | −0.757605 | −0.378803 | − | 0.925477i | \(-0.623664\pi\) | ||||
−0.378803 | + | 0.925477i | \(0.623664\pi\) | |||||||
\(992\) | − 730112.i | − 0.0235565i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.07124e7 | 0.343891 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 2.60709e7i | − 0.830651i | −0.909673 | − | 0.415326i | \(-0.863668\pi\) | ||||
0.909673 | − | 0.415326i | \(-0.136332\pi\) | |||||||
\(998\) | − 2.96973e7i | − 0.943824i | ||||||||
\(999\) | 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 | 450.6.c.g.199.1 | 2 | ||
3.2 | odd | 2 | 150.6.c.c.49.2 | 2 | |||
5.2 | odd | 4 | 450.6.a.t.1.1 | 1 | |||
5.3 | odd | 4 | 450.6.a.e.1.1 | 1 | |||
5.4 | even | 2 | inner | 450.6.c.g.199.2 | 2 | ||
15.2 | even | 4 | 150.6.a.g.1.1 | ✓ | 1 | ||
15.8 | even | 4 | 150.6.a.i.1.1 | yes | 1 | ||
15.14 | odd | 2 | 150.6.c.c.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
150.6.a.g.1.1 | ✓ | 1 | 15.2 | even | 4 | ||
150.6.a.i.1.1 | yes | 1 | 15.8 | even | 4 | ||
150.6.c.c.49.1 | 2 | 15.14 | odd | 2 | |||
150.6.c.c.49.2 | 2 | 3.2 | odd | 2 | |||
450.6.a.e.1.1 | 1 | 5.3 | odd | 4 | |||
450.6.a.t.1.1 | 1 | 5.2 | odd | 4 | |||
450.6.c.g.199.1 | 2 | 1.1 | even | 1 | trivial | ||
450.6.c.g.199.2 | 2 | 5.4 | even | 2 | inner |