Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,7,Mod(149,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.149");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(69.0162250860\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 406 x^{14} + 67561 x^{12} + 5921226 x^{10} + 291565644 x^{8} + 7924637994 x^{6} + \cdots + 276002078881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{30}\cdot 3^{18}\cdot 5^{26} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.13 | ||
Root | \(3.23723i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.149 |
Dual form | 300.7.b.e.149.14 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 15.3993 | − | 22.1779i | 0.570346 | − | 0.821405i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 437.053i | − | 1.27421i | −0.770778 | − | 0.637103i | \(-0.780132\pi\) | ||
0.770778 | − | 0.637103i | \(-0.219868\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −254.720 | − | 683.051i | −0.349411 | − | 0.936970i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1898.54i | − | 1.42640i | −0.700962 | − | 0.713199i | \(-0.747246\pi\) | ||
0.700962 | − | 0.713199i | \(-0.252754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2670.19i | − | 1.21538i | −0.794174 | − | 0.607691i | \(-0.792096\pi\) | ||
0.794174 | − | 0.607691i | \(-0.207904\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4521.29 | −0.920270 | −0.460135 | − | 0.887849i | \(-0.652199\pi\) | ||||
−0.460135 | + | 0.887849i | \(0.652199\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 9502.28 | 1.38537 | 0.692687 | − | 0.721238i | \(-0.256427\pi\) | ||||
0.692687 | + | 0.721238i | \(0.256427\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9692.93 | − | 6730.33i | −1.04664 | − | 0.726739i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 549.560 | 0.0451680 | 0.0225840 | − | 0.999745i | \(-0.492811\pi\) | ||||
0.0225840 | + | 0.999745i | \(0.492811\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19071.2 | − | 4869.36i | −0.968916 | − | 0.247389i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 43308.7i | 1.77575i | 0.460089 | + | 0.887873i | \(0.347818\pi\) | ||||
−0.460089 | + | 0.887873i | \(0.652182\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29588.2 | 0.993191 | 0.496596 | − | 0.867982i | \(-0.334583\pi\) | ||||
0.496596 | + | 0.867982i | \(0.334583\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −42105.6 | − | 29236.2i | −1.17165 | − | 0.813540i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 45794.0i | 0.904074i | 0.891999 | + | 0.452037i | \(0.149302\pi\) | ||||
−0.891999 | + | 0.452037i | \(0.850698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −59219.3 | − | 41119.2i | −0.998320 | − | 0.693188i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 114611.i | − | 1.66294i | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||
0.555570 | − | 0.831470i | \(-0.312500\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 24917.0i | − | 0.313394i | −0.987647 | − | 0.156697i | \(-0.949915\pi\) | ||
0.987647 | − | 0.156697i | \(-0.0500847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 18258.6 | 0.175863 | 0.0879313 | − | 0.996127i | \(-0.471974\pi\) | ||||
0.0879313 | + | 0.996127i | \(0.471974\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −73366.3 | −0.623603 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −69624.9 | + | 100273.i | −0.524873 | + | 0.755914i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −174021. | −1.16889 | −0.584444 | − | 0.811434i | \(-0.698687\pi\) | ||||
−0.584444 | + | 0.811434i | \(0.698687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 146329. | − | 210741.i | 0.790143 | − | 1.13795i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 67872.4i | 0.330474i | 0.986254 | + | 0.165237i | \(0.0528389\pi\) | ||||
−0.986254 | + | 0.165237i | \(0.947161\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 175028. | 0.771112 | 0.385556 | − | 0.922685i | \(-0.374010\pi\) | ||||
0.385556 | + | 0.922685i | \(0.374010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −298529. | + | 111326.i | −1.19389 | + | 0.445222i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 16056.7i | − | 0.0533865i | −0.999644 | − | 0.0266932i | \(-0.991502\pi\) | ||
0.999644 | − | 0.0266932i | \(-0.00849773\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8462.86 | − | 12188.1i | 0.0257614 | − | 0.0371012i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 222821.i | 0.622561i | 0.950318 | + | 0.311281i | \(0.100758\pi\) | ||||
−0.950318 | + | 0.311281i | \(0.899242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 620790.i | − | 1.59579i | −0.602796 | − | 0.797896i | \(-0.705947\pi\) | ||
0.602796 | − | 0.797896i | \(-0.294053\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −829761. | −1.81753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −525417. | −1.06567 | −0.532835 | − | 0.846219i | \(-0.678873\pi\) | ||||
−0.532835 | + | 0.846219i | \(0.678873\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −401676. | + | 347974.i | −0.755824 | + | 0.654775i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 790761. | 1.38296 | 0.691482 | − | 0.722394i | \(-0.256958\pi\) | ||||
0.691482 | + | 0.722394i | \(0.256958\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 960496. | + | 666925.i | 1.45861 | + | 1.01279i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.12565e6i | 1.59673i | 0.602172 | + | 0.798366i | \(0.294302\pi\) | ||||
−0.602172 | + | 0.798366i | \(0.705698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.16702e6 | −1.54865 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 455638. | − | 656204.i | 0.566463 | − | 0.815812i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 624200.i | 0.683925i | 0.939714 | + | 0.341963i | \(0.111092\pi\) | ||||
−0.939714 | + | 0.341963i | \(0.888908\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.29680e6 | + | 483596.i | −1.33649 | + | 0.498399i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 136558.i | − | 0.132542i | −0.997802 | − | 0.0662709i | \(-0.978890\pi\) | ||
0.997802 | − | 0.0662709i | \(-0.0211101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 244469.i | 0.223724i | 0.993724 | + | 0.111862i | \(0.0356814\pi\) | ||||
−0.993724 | + | 0.111862i | \(0.964319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.66094e6 | 1.35582 | 0.677912 | − | 0.735143i | \(-0.262885\pi\) | ||||
0.677912 | + | 0.735143i | \(0.262885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.14498e6 | −0.884138 | −0.442069 | − | 0.896981i | \(-0.645755\pi\) | ||||
−0.442069 | + | 0.896981i | \(0.645755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.01562e6 | + | 705198.i | 0.742610 | + | 0.515635i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.03300e6 | −0.715924 | −0.357962 | − | 0.933736i | \(-0.616528\pi\) | ||||
−0.357962 | + | 0.933736i | \(0.616528\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.82388e6 | + | 680153.i | −1.13878 | + | 0.424667i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.97604e6i | 1.17261i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.83288e6 | −1.03461 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.54184e6 | − | 1.76494e6i | −1.36595 | − | 0.948451i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.16679e6i | − | 1.54600i | −0.634408 | − | 0.772998i | \(-0.718756\pi\) | ||
0.634408 | − | 0.772998i | \(-0.281244\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −552608. | − | 383706.i | −0.257423 | − | 0.178743i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.06944e6i | 0.920533i | 0.887781 | + | 0.460266i | \(0.152246\pi\) | ||||
−0.887781 | + | 0.460266i | \(0.847754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 4.15300e6i | − | 1.76525i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 520796. | 0.202538 | 0.101269 | − | 0.994859i | \(-0.467710\pi\) | ||||
0.101269 | + | 0.994859i | \(0.467710\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.89209e6 | −1.44923 | −0.724616 | − | 0.689153i | \(-0.757983\pi\) | ||||
−0.724616 | + | 0.689153i | \(0.757983\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 281170. | − | 404937.i | 0.100303 | − | 0.144454i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.06946e6 | −1.73362 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.12979e6 | + | 1.62711e6i | −0.355670 | + | 0.512230i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2.27030e6i | − | 0.686318i | −0.939277 | − | 0.343159i | \(-0.888503\pi\) | ||
0.939277 | − | 0.343159i | \(-0.111497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.27718e6 | 0.370954 | 0.185477 | − | 0.982649i | \(-0.440617\pi\) | ||||
0.185477 | + | 0.982649i | \(0.440617\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.15166e6 | + | 3.08827e6i | 0.321552 | + | 0.862265i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.40437e6i | − | 0.362897i | −0.983400 | − | 0.181448i | \(-0.941921\pi\) | ||
0.983400 | − | 0.181448i | \(-0.0580786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.67980e6 | + | 3.85942e6i | −0.666671 | + | 0.960130i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 240187.i | − | 0.0575534i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.84510e6i | − | 1.11877i | −0.828909 | − | 0.559384i | \(-0.811038\pi\) | ||
0.828909 | − | 0.559384i | \(-0.188962\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 823298. | 0.176770 | 0.0883848 | − | 0.996086i | \(-0.471829\pi\) | ||||
0.0883848 | + | 0.996086i | \(0.471829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.30312e6 | −0.477152 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.42043e6 | − | 6.49054e6i | −0.484065 | − | 1.29805i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.06349e6 | −1.75048 | −0.875240 | − | 0.483689i | \(-0.839297\pi\) | ||||
−0.875240 | + | 0.483689i | \(0.839297\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.50527e6 | + | 1.04519e6i | 0.271453 | + | 0.188485i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.68808e6i | 1.16612i | 0.812430 | + | 0.583059i | \(0.198144\pi\) | ||||
−0.812430 | + | 0.583059i | \(0.801856\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −963367. | −0.162464 | −0.0812318 | − | 0.996695i | \(-0.525885\pi\) | ||||
−0.0812318 | + | 0.996695i | \(0.525885\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.69531e6 | − | 3.88175e6i | 0.439800 | − | 0.633395i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.58383e6i | 1.31267i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.12817e6 | + | 8.33511e6i | −0.315225 | + | 1.23460i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.37892e6i | − | 0.197896i | −0.995093 | − | 0.0989482i | \(-0.968452\pi\) | ||
0.995093 | − | 0.0989482i | \(-0.0315478\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 549967.i | 0.0765006i | 0.999268 | + | 0.0382503i | \(0.0121784\pi\) | ||||
−0.999268 | + | 0.0382503i | \(0.987822\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.23680e6 | −0.554166 | −0.277083 | − | 0.960846i | \(-0.589368\pi\) | ||||
−0.277083 | + | 0.960846i | \(0.589368\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.42388e7 | 1.80682 | 0.903411 | − | 0.428775i | \(-0.141055\pi\) | ||||
0.903411 | + | 0.428775i | \(0.141055\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −356104. | − | 247262.i | −0.0438519 | − | 0.0304488i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.89282e7 | 2.26267 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −139984. | − | 375377.i | −0.0157822 | − | 0.0423211i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.80404e7i | − | 1.97610i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 920077. | 0.0979437 | 0.0489719 | − | 0.998800i | \(-0.484406\pi\) | ||||
0.0489719 | + | 0.998800i | \(0.484406\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.94172e6 | + | 3.43130e6i | 0.511374 | + | 0.355075i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.29316e7i | − | 1.26553i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.37678e7 | − | 9.55976e6i | −1.31079 | − | 0.910153i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.20727e7i | 1.11848i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.23626e7i | 1.11479i | 0.830246 | + | 0.557397i | \(0.188200\pi\) | ||||
−0.830246 | + | 0.557397i | \(0.811800\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 447256. | 0.0382365 | 0.0191183 | − | 0.999817i | \(-0.493914\pi\) | ||||
0.0191183 | + | 0.999817i | \(0.493914\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.85551e7 | 1.54510 | 0.772550 | − | 0.634954i | \(-0.218981\pi\) | ||||
0.772550 | + | 0.634954i | \(0.218981\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.27778e7 | + | 1.84024e7i | −1.03662 | + | 1.49292i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.33318e6 | −0.105395 | −0.0526976 | − | 0.998611i | \(-0.516782\pi\) | ||||
−0.0526976 | + | 0.998611i | \(0.516782\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.09107e6 | + | 1.16526e7i | −0.607800 | + | 0.875346i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.84514e6i | 0.354905i | 0.984129 | + | 0.177453i | \(0.0567857\pi\) | ||||
−0.984129 | + | 0.177453i | \(0.943214\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.84505e7 | 1.31813 | 0.659063 | − | 0.752088i | \(-0.270953\pi\) | ||||
0.659063 | + | 0.752088i | \(0.270953\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.53180e6 | + | 1.42669e7i | 0.106754 | + | 0.994286i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.53729e7i | − | 1.68376i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.21772e7 | − | 1.75374e7i | 0.788768 | − | 1.13597i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.38133e7i | − | 0.873526i | −0.899577 | − | 0.436763i | \(-0.856125\pi\) | ||
0.899577 | − | 0.436763i | \(-0.143875\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 1.04336e6i | − | 0.0644276i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.89697e7 | 1.70665 | 0.853324 | − | 0.521381i | \(-0.174583\pi\) | ||||
0.853324 | + | 0.521381i | \(0.174583\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00144e7 | 1.15198 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.95820e7 | − | 1.10316e7i | 1.66382 | − | 0.620465i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.65865e7 | 0.911776 | 0.455888 | − | 0.890037i | \(-0.349322\pi\) | ||||
0.455888 | + | 0.890037i | \(0.349322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.49645e7 | + | 1.73342e7i | 1.31156 | + | 0.910690i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 230441.i | 0.0118387i | 0.999982 | + | 0.00591934i | \(0.00188420\pi\) | ||||
−0.999982 | + | 0.00591934i | \(0.998116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.94774e7 | −0.978638 | −0.489319 | − | 0.872105i | \(-0.662755\pi\) | ||||
−0.489319 | + | 0.872105i | \(0.662755\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.79713e7 | + | 2.58820e7i | −0.883265 | + | 1.27207i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 140418.i | − | 0.00660667i | −0.999995 | − | 0.00330334i | \(-0.998949\pi\) | ||
0.999995 | − | 0.00330334i | \(-0.00105149\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.53671e6 | − | 2.02102e7i | −0.347032 | − | 0.930590i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.34994e7i | − | 0.608407i | −0.952607 | − | 0.304203i | \(-0.901610\pi\) | ||
0.952607 | − | 0.304203i | \(-0.0983902\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.01080e7i | 0.887174i | 0.896231 | + | 0.443587i | \(0.146294\pi\) | ||||
−0.896231 | + | 0.443587i | \(0.853706\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.00913e7 | −2.11893 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.69552e6 | −0.153102 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.38435e7 | + | 9.61227e6i | 0.561779 | + | 0.390074i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.37099e7 | 1.73771 | 0.868854 | − | 0.495068i | \(-0.164857\pi\) | ||||
0.868854 | + | 0.495068i | \(0.164857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −9.24466e6 | + | 3.62073e7i | −0.352876 | + | 1.38206i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.46743e6i | − | 0.0548964i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.08901e7 | −0.399329 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.02857e6 | − | 2.10290e6i | −0.108870 | − | 0.0755947i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.79809e7i | − | 1.65826i | −0.559055 | − | 0.829131i | \(-0.688836\pi\) | ||
0.559055 | − | 0.829131i | \(-0.311164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.42181e6 | + | 3.76466e6i | 0.183768 | + | 0.127600i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.28475e7i | − | 0.759553i | −0.925078 | − | 0.379777i | \(-0.876001\pi\) | ||
0.925078 | − | 0.379777i | \(-0.123999\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.38707e7i | − | 0.778451i | −0.921142 | − | 0.389226i | \(-0.872743\pi\) | ||
0.921142 | − | 0.389226i | \(-0.127257\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.21703e7 | −0.382054 | −0.191027 | − | 0.981585i | \(-0.561182\pi\) | ||||
−0.191027 | + | 0.981585i | \(0.561182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.22230e7 | 2.53292 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.55774e7 | − | 3.68363e7i | 0.773289 | − | 1.11368i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.29626e7 | −1.27492 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.76320e7 | + | 2.53934e7i | −0.504265 | + | 0.726235i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7.97997e6i | − | 0.224085i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.94247e6 | −0.108714 | −0.0543569 | − | 0.998522i | \(-0.517311\pi\) | ||||
−0.0543569 | + | 0.998522i | \(0.517311\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.12797e7 | − | 1.16647e7i | 0.847090 | − | 0.315893i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3.45006e7i | − | 0.901439i | −0.892666 | − | 0.450720i | \(-0.851167\pi\) | ||
0.892666 | − | 0.450720i | \(-0.148833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.59076e7 | + | 2.29099e7i | −0.408324 | + | 0.588063i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.61742e7i | − | 1.41669i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.93539e7i | − | 0.479607i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.55712e7 | −1.33003 | −0.665015 | − | 0.746830i | \(-0.731575\pi\) | ||||
−0.665015 | + | 0.746830i | \(0.731575\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.36309e7 | 1.73214 | 0.866071 | − | 0.499921i | \(-0.166638\pi\) | ||||
0.866071 | + | 0.499921i | \(0.166638\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.30021e7 | + | 5.09237e7i | −0.300672 | + | 1.17760i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.13378e7 | −1.16711 | −0.583557 | − | 0.812072i | \(-0.698340\pi\) | ||||
−0.583557 | + | 0.812072i | \(0.698340\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 4.38245e7 | + | 3.04298e7i | 0.963191 | + | 0.668796i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.77258e7i | − | 1.03150i | −0.856739 | − | 0.515751i | \(-0.827513\pi\) | ||
0.856739 | − | 0.515751i | \(-0.172487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.32475e7 | 0.919263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.82251e7 | + | 4.06494e7i | −0.590086 | + | 0.849834i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 8.29285e7i | − | 1.67767i | −0.544388 | − | 0.838834i | \(-0.683238\pi\) | ||
0.544388 | − | 0.838834i | \(-0.316762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.82854e7 | + | 2.91939e7i | −1.55812 | + | 0.581049i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.60562e7i | 1.48941i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.09826e7i | 0.789719i | 0.918741 | + | 0.394860i | \(0.129207\pi\) | ||||
−0.918741 | + | 0.394860i | \(0.870793\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.15642e8 | 2.15821 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.54504e7 | −1.75332 | −0.876658 | − | 0.481114i | \(-0.840232\pi\) | ||||
−0.876658 | + | 0.481114i | \(0.840232\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.02329e7 | − | 4.87665e7i | −1.26989 | − | 0.881753i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.90198e7 | 0.872520 | 0.436260 | − | 0.899821i | \(-0.356303\pi\) | ||||
0.436260 | + | 0.899821i | \(0.356303\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.70196e7 | + | 6.34688e6i | −0.293641 | + | 0.109503i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 6.92192e6i | − | 0.117592i | −0.998270 | − | 0.0587960i | \(-0.981274\pi\) | ||
0.998270 | − | 0.0587960i | \(-0.0187262\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.48472e6 | −0.0415668 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.58959e7 | + | 3.18680e7i | 0.756130 | + | 0.525022i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.04166e8i | 1.66478i | 0.554191 | + | 0.832389i | \(0.313028\pi\) | ||||
−0.554191 | + | 0.832389i | \(0.686972\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.21049e7 | − | 6.39535e7i | −1.44999 | − | 1.00681i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.09926e8i | 1.70477i | 0.522911 | + | 0.852387i | \(0.324846\pi\) | ||||
−0.522911 | + | 0.852387i | \(0.675154\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 7.90061e7i | − | 1.20711i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.69416e7 | 1.28957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.73956e7 | 1.42354 | 0.711770 | − | 0.702413i | \(-0.247894\pi\) | ||||
0.711770 | + | 0.702413i | \(0.247894\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.01992e6 | − | 1.15502e7i | 0.115517 | − | 0.166365i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.96639e7 | 0.421092 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.99356e7 | + | 8.63184e7i | −0.826564 | + | 1.19041i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.80064e7i | 0.924501i | 0.886749 | + | 0.462251i | \(0.152958\pi\) | ||||
−0.886749 | + | 0.462251i | \(0.847042\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.17666e7 | 0.425720 | 0.212860 | − | 0.977083i | \(-0.431722\pi\) | ||||
0.212860 | + | 0.977083i | \(0.431722\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.65083e6 | − | 1.24715e7i | −0.0614483 | − | 0.164778i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.64964e7i | − | 0.982556i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.80663e7 | + | 1.12430e8i | −0.988762 | + | 1.42400i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.40240e7i | 1.04947i | 0.851264 | + | 0.524737i | \(0.175836\pi\) | ||||
−0.851264 | + | 0.524737i | \(0.824164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.82768e7i | − | 1.08738i | −0.839285 | − | 0.543692i | \(-0.817026\pi\) | ||
0.839285 | − | 0.543692i | \(-0.182974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.22207e6 | 0.0625747 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.03991e8 | −1.22914 | −0.614569 | − | 0.788863i | \(-0.710670\pi\) | ||||
−0.614569 | + | 0.788863i | \(0.710670\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.86879e7 | + | 5.01129e7i | 0.217894 | + | 0.584297i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.29638e8 | −1.49115 | −0.745575 | − | 0.666422i | \(-0.767825\pi\) | ||||
−0.745575 | + | 0.666422i | \(0.767825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.03506e7 | − | 3.49612e7i | −0.563745 | − | 0.391439i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.46554e7i | 1.04570i | 0.852425 | + | 0.522849i | \(0.175131\pi\) | ||||
−0.852425 | + | 0.522849i | \(0.824869\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.17594e8 | −2.37201 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.96677e7 | − | 2.83251e7i | 0.211572 | − | 0.304703i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 5.45336e7i | − | 0.571367i | −0.958324 | − | 0.285684i | \(-0.907779\pi\) | ||
0.958324 | − | 0.285684i | \(-0.0922206\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.62263e7 | + | 2.20158e7i | 0.891665 | + | 0.227665i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.37094e7i | − | 0.752350i | −0.926549 | − | 0.376175i | \(-0.877239\pi\) | ||
0.926549 | − | 0.376175i | \(-0.122761\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.87082e7i | − | 0.188490i | −0.995549 | − | 0.0942452i | \(-0.969956\pi\) | ||
0.995549 | − | 0.0942452i | \(-0.0300438\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.19481e8 | −1.17313 | −0.586567 | − | 0.809901i | \(-0.699521\pi\) | ||||
−0.586567 | + | 0.809901i | \(0.699521\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.01762e6 | −0.0680254 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.11461e7 | − | 2.16264e7i | −0.298085 | − | 0.206977i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.73059e7 | −0.447025 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.43266e7 | + | 1.18865e8i | 0.408422 | + | 1.09521i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.84244e7i | 0.167644i | 0.996481 | + | 0.0838220i | \(0.0267127\pi\) | ||||
−0.996481 | + | 0.0838220i | \(0.973287\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.22279e8 | 1.09879 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.32684e6 | − | 3.69872e6i | −0.0472747 | − | 0.0328254i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.48625e7i | − | 0.561574i | −0.959770 | − | 0.280787i | \(-0.909405\pi\) | ||
0.959770 | − | 0.280787i | \(-0.0905954\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.07454e8 | − | 7.46113e7i | −0.918961 | − | 0.638085i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.01202e8i | − | 0.854961i | −0.904025 | − | 0.427480i | \(-0.859401\pi\) | ||
0.904025 | − | 0.427480i | \(-0.140599\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.95811e8i | − | 1.63417i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.73848e7 | 0.793272 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.08259e7 | 0.248092 | 0.124046 | − | 0.992276i | \(-0.460413\pi\) | ||||
0.124046 | + | 0.992276i | \(0.460413\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.26782e7 | − | 1.82590e7i | 0.100820 | − | 0.145199i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.31110e8 | 1.03022 | 0.515111 | − | 0.857123i | \(-0.327751\pi\) | ||||
0.515111 | + | 0.857123i | \(0.327751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.54665e7 | + | 5.10784e7i | −0.272142 | + | 0.391935i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.77883e7i | − | 0.134890i | −0.997723 | − | 0.0674452i | \(-0.978515\pi\) | ||
0.997723 | − | 0.0674452i | \(-0.0214848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.71318e8 | −2.03337 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.81220e8 | − | 4.62701e7i | −1.34231 | − | 0.342727i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 3.46646e7i | − | 0.250850i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.39572e8 | + | 2.01009e8i | −0.998379 | + | 1.43785i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.90916e8i | − | 1.34999i | −0.737823 | − | 0.674994i | \(-0.764146\pi\) | ||
0.737823 | − | 0.674994i | \(-0.235854\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.68384e8i | − | 1.17705i | −0.808478 | − | 0.588527i | \(-0.799708\pi\) | ||
0.808478 | − | 0.588527i | \(-0.200292\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.33777e8 | −0.914005 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.47734e8 | −0.997960 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.63603e7 | − | 1.72885e7i | 0.309644 | − | 0.115471i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.06035e8 | −2.02111 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.48328e8 | + | 1.02992e8i | 0.957855 | + | 0.665091i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.39289e8i | 0.889506i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.49423e8 | 1.57523 | 0.787616 | − | 0.616167i | \(-0.211315\pi\) | ||||
0.787616 | + | 0.616167i | \(0.211315\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.48352e7 | + | 2.13655e7i | −0.0926605 | + | 0.133448i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.16411e8i | − | 0.711268i | −0.934625 | − | 0.355634i | \(-0.884265\pi\) | ||
0.934625 | − | 0.355634i | \(-0.115735\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.45831e7 | − | 1.19553e8i | −0.269435 | − | 0.722508i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.11531e8i | 2.46007i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.29635e8i | 1.35788i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.07511e8 | −1.20082 | −0.600408 | − | 0.799694i | \(-0.704995\pi\) | ||||
−0.600408 | + | 0.799694i | \(0.704995\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.65333e7 | −0.380894 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.90371e8 | + | 1.32185e8i | 1.07823 | + | 0.748677i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.47557e7 | −0.474945 | −0.237473 | − | 0.971394i | \(-0.576319\pi\) | ||||
−0.237473 | + | 0.971394i | \(0.576319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.52083e8 | + | 1.75554e8i | 0.834318 | + | 0.963076i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.84731e8i | − | 1.00278i | −0.865223 | − | 0.501388i | \(-0.832823\pi\) | ||
0.865223 | − | 0.501388i | \(-0.167177\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.60597e7 | 0.354837 | 0.177418 | − | 0.984136i | \(-0.443225\pi\) | ||||
0.177418 | + | 0.984136i | \(0.443225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −3.05815e7 | − | 2.12344e7i | −0.162553 | − | 0.112869i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 9.03538e7i | − | 0.470348i | −0.971953 | − | 0.235174i | \(-0.924434\pi\) | ||
0.971953 | − | 0.235174i | \(-0.0755659\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.21971e7 | + | 8.46913e6i | 0.0628379 | + | 0.0436318i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.45604e8i | − | 1.76218i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.30384e8i | 1.66730i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.74492e8 | 0.862704 | 0.431352 | − | 0.902184i | \(-0.358037\pi\) | ||||
0.431352 | + | 0.902184i | \(0.358037\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.81155e8 | 1.37594 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.52440e7 | + | 9.39635e7i | −0.316066 | + | 0.455194i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.18826e8 | 1.04938 | 0.524692 | − | 0.851292i | \(-0.324180\pi\) | ||||
0.524692 | + | 0.851292i | \(0.324180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.19269e8 | − | 3.15788e8i | 1.03051 | − | 1.48413i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.01081e8i | 1.40088i | 0.713709 | + | 0.700442i | \(0.247014\pi\) | ||||
−0.713709 | + | 0.700442i | \(0.752986\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.54238e8 | −1.17116 | −0.585582 | − | 0.810614i | \(-0.699134\pi\) | ||||
−0.585582 | + | 0.810614i | \(0.699134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.09675e7 | + | 4.08996e6i | −0.0500215 | + | 0.0186538i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.76940e8i | 0.791153i | 0.918433 | + | 0.395576i | \(0.129455\pi\) | ||||
−0.918433 | + | 0.395576i | \(0.870545\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.91482e8 | − | 4.19788e8i | 1.29050 | − | 1.85857i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.87539e7i | − | 0.213740i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.16816e8i | − | 0.507132i | −0.967318 | − | 0.253566i | \(-0.918397\pi\) | ||
0.967318 | − | 0.253566i | \(-0.0816034\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.32683e8 | −0.564886 | −0.282443 | − | 0.959284i | \(-0.591145\pi\) | ||||
−0.282443 | + | 0.959284i | \(0.591145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.63767e7 | −0.0690484 | −0.0345242 | − | 0.999404i | \(-0.510992\pi\) | ||||
−0.0345242 | + | 0.999404i | \(0.510992\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.04807e7 | − | 2.67601e6i | −0.0437641 | − | 0.0111741i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.91967e8 | 2.03457 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.00099e8 | − | 2.77811e8i | −1.62317 | − | 1.12706i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.07048e8i | − | 0.831992i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.22391e7 | −0.128320 | −0.0641600 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641600 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.41686e7 | − | 2.04054e7i | 0.0558618 | − | 0.0804514i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.95902e8i | 0.757916i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.52198e8 | − | 5.67572e7i | 0.583321 | − | 0.217530i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.81122e8i | 0.687698i | 0.939025 | + | 0.343849i | \(0.111731\pi\) | ||||
−0.939025 | + | 0.343849i | \(0.888269\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.65331e6i | − | 0.0287883i | −0.999896 | − | 0.0143942i | \(-0.995418\pi\) | ||
0.999896 | − | 0.0143942i | \(-0.00458196\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.31805e8 | 0.855875 | 0.427937 | − | 0.903808i | \(-0.359240\pi\) | ||||
0.427937 | + | 0.903808i | \(0.359240\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.28858e8 | 0.471388 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.86796e8 | − | 1.99138e8i | −1.03951 | − | 0.721791i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.95202e8 | 1.41932 | 0.709660 | − | 0.704545i | \(-0.248849\pi\) | ||||
0.709660 | + | 0.704545i | \(0.248849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.24031e8 | + | 1.58128e8i | −1.49521 | + | 0.557587i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.10657e8i | − | 1.78432i | −0.451719 | − | 0.892160i | \(-0.649189\pi\) | ||
0.451719 | − | 0.892160i | \(-0.350811\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.10564e8 | 1.42160 | 0.710799 | − | 0.703395i | \(-0.248333\pi\) | ||||
0.710799 | + | 0.703395i | \(0.248333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.67748e8 | + | 1.85912e8i | 0.918724 | + | 0.637920i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.38007e7i | 0.0802070i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.74176e8 | + | 1.90376e8i | 0.915696 | + | 0.635818i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 3.32296e8i | − | 1.09991i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.19215e7i | 0.301559i | 0.988567 | + | 0.150779i | \(0.0481783\pi\) | ||||
−0.988567 | + | 0.150779i | \(0.951822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.47302e8 | 0.474726 | 0.237363 | − | 0.971421i | \(-0.423717\pi\) | ||||
0.237363 | + | 0.971421i | \(0.423717\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.72809e8 | 0.871462 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.88744e6 | − | 9.91920e6i | 0.0218080 | − | 0.0314076i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.01111e8 | −0.317347 | −0.158673 | − | 0.987331i | \(-0.550722\pi\) | ||||
−0.158673 | + | 0.987331i | \(0.550722\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.85736e8 | − | 4.11513e8i | 0.881241 | − | 1.26915i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.64669e8i | 1.42065i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.65597e8 | 0.804987 | 0.402493 | − | 0.915423i | \(-0.368144\pi\) | ||||
0.402493 | + | 0.915423i | \(0.368144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.11357e8 | + | 5.66769e8i | 0.635063 | + | 1.70297i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.18191e8i | 1.53035i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.05301e7 | + | 2.95671e7i | −0.0601117 | + | 0.0865721i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.56699e8i | 1.32579i | 0.748711 | + | 0.662897i | \(0.230673\pi\) | ||||
−0.748711 | + | 0.662897i | \(0.769327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.35148e8i | 1.25248i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −5.96830e7 | −0.168886 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.21150e7 | 0.0620509 | 0.0310255 | − | 0.999519i | \(-0.490123\pi\) | ||||
0.0310255 | + | 0.999519i | \(0.490123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.33834e8 | + | 3.58886e8i | 0.372356 | + | 0.998500i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.62605e7 | 0.0448605 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.07455e8 | + | 7.46119e7i | 0.291521 | + | 0.202419i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1.60221e8i | − | 0.431054i | −0.976498 | − | 0.215527i | \(-0.930853\pi\) | ||
0.976498 | − | 0.215527i | \(-0.0691469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.06846e8 | 0.285070 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.84126e8 | − | 4.09194e8i | 0.751788 | − | 1.08271i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.41495e8i | 0.888753i | 0.895840 | + | 0.444376i | \(0.146575\pi\) | ||||
−0.895840 | + | 0.444376i | \(0.853425\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.39999e8 | + | 1.85729e8i | 0.877597 | + | 0.479399i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.12657e8i | 0.288407i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.06271e8i | 1.03158i | 0.856714 | + | 0.515791i | \(0.172502\pi\) | ||||
−0.856714 | + | 0.515791i | \(0.827498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.04842e7 | −0.0761503 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.06192e7 | −0.0263123 | −0.0131562 | − | 0.999913i | \(-0.504188\pi\) | ||||
−0.0131562 | + | 0.999913i | \(0.504188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.62719e8 | − | 3.90726e8i | −1.38305 | − | 0.960325i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.86011e8 | −1.42869 | −0.714347 | − | 0.699791i | \(-0.753276\pi\) | ||||
−0.714347 | + | 0.699791i | \(0.753276\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.01423e8 | − | 5.40130e8i | −0.483222 | − | 1.29579i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 7.25920e8i | − | 1.72760i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.96057e7 | 0.117115 | 0.0585574 | − | 0.998284i | \(-0.481350\pi\) | ||||
0.0585574 | + | 0.998284i | \(0.481350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.06350e8 | − | 2.12715e8i | −0.717518 | − | 0.498212i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 4.58919e7i | − | 0.105791i | −0.998600 | − | 0.0528955i | \(-0.983155\pi\) | ||
0.998600 | − | 0.0528955i | \(-0.0168450\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.31395e7 | − | 1.60670e7i | −0.0529211 | − | 0.0367460i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.06778e8i | − | 1.37682i | −0.725323 | − | 0.688408i | \(-0.758310\pi\) | ||
0.725323 | − | 0.688408i | \(-0.241690\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.00419e8i | 1.12658i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.81233e8 | 0.401652 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.78906e8 | −1.05310 | −0.526552 | − | 0.850143i | \(-0.676516\pi\) | ||||
−0.526552 | + | 0.850143i | \(0.676516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.46114e8 | − | 6.42487e8i | 0.973380 | − | 1.40185i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.49686e7 | 0.0757076 | 0.0378538 | − | 0.999283i | \(-0.487948\pi\) | ||||
0.0378538 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.08209e8 | − | 4.43878e8i | 0.657025 | − | 0.946239i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 1.08907e9i | − | 2.30379i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.23034e8 | 0.888020 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.10886e8 | − | 8.25947e8i | 0.439301 | − | 1.72055i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 3.11411e8i | − | 0.638866i | −0.947609 | − | 0.319433i | \(-0.896508\pi\) | ||
0.947609 | − | 0.319433i | \(-0.103492\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.55422e8 | − | 3.67855e8i | 0.520028 | − | 0.748937i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.51478e8i | 0.912235i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 4.67358e8i | − | 0.937195i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.48813e8 | −0.886525 | −0.443262 | − | 0.896392i | \(-0.646179\pi\) | ||||
−0.443262 | + | 0.896392i | \(0.646179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.25523e7 | −0.161841 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.68874e8 | − | 2.86725e8i | 1.49609 | − | 0.557915i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.17859e9 | −2.27623 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.11071e6 | + | 3.54864e6i | 0.00972435 | + | 0.00675215i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.94261e8i | 0.933493i | 0.884391 | + | 0.466746i | \(0.154574\pi\) | ||||
−0.884391 | + | 0.466746i | \(0.845426\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.89935e8 | −0.543549 | −0.271774 | − | 0.962361i | \(-0.587610\pi\) | ||||
−0.271774 | + | 0.962361i | \(0.587610\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.99939e8 | + | 4.31967e8i | −0.558162 | + | 0.803858i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 2.36769e8i | − | 0.434168i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.97263e8 | + | 7.97131e8i | 0.541114 | + | 1.45104i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.20406e8i | 0.217579i | 0.994065 | + | 0.108789i | \(0.0346974\pi\) | ||||
−0.994065 | + | 0.108789i | \(0.965303\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.61929e8i | 0.469878i | 0.972010 | + | 0.234939i | \(0.0754890\pi\) | ||||
−0.972010 | + | 0.234939i | \(0.924511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.59768e8 | −0.282471 | −0.141236 | − | 0.989976i | \(-0.545107\pi\) | ||||
−0.141236 | + | 0.989976i | \(0.545107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.51308e7 | −0.131873 | −0.0659363 | − | 0.997824i | \(-0.521003\pi\) | ||||
−0.0659363 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.11417e6 | − | 2.16234e6i | −0.00542675 | − | 0.00376809i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.31710e8 | 0.573884 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.64281e8 | − | 1.44076e8i | −0.962319 | − | 0.245705i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.46323e8i | 1.26369i | 0.775094 | + | 0.631846i | \(0.217702\pi\) | ||||
−0.775094 | + | 0.631846i | \(0.782298\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.28082e9 | −2.15327 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.99388e8 | − | 2.07881e8i | −0.499748 | − | 0.347002i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.01064e8i | 1.31831i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.45953e8 | + | 3.09649e8i | 0.728729 | + | 0.505996i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.51666e7i | 0.0408352i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7.32618e8i | − | 1.18040i | −0.807256 | − | 0.590201i | \(-0.799048\pi\) | ||
0.807256 | − | 0.590201i | \(-0.200952\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.41490e8 | 0.701420 | 0.350710 | − | 0.936484i | \(-0.385940\pi\) | ||||
0.350710 | + | 0.936484i | \(0.385940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.02777e8 | −1.26653 | −0.633265 | − | 0.773935i | \(-0.718286\pi\) | ||||
−0.633265 | + | 0.773935i | \(0.718286\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.71373e8 | + | 1.11092e9i | −1.20852 | + | 1.74050i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.01287e8 | 1.24668 | 0.623341 | − | 0.781950i | \(-0.285775\pi\) | ||||
0.623341 | + | 0.781950i | \(0.285775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.69085e7 | + | 8.19589e7i | −0.0873213 | + | 0.125759i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.97522e8i | 1.52007i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.28744e7 | −0.0648849 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.26360e8 | − | 1.58997e8i | 0.640817 | − | 0.238971i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.69001e8i | 1.14006i | 0.821623 | + | 0.570031i | \(0.193069\pi\) | ||||
−0.821623 | + | 0.570031i | \(0.806931\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.73104e8 | − | 9.69394e8i | 0.991095 | − | 1.42736i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9.64066e8i | − | 1.40987i | −0.709272 | − | 0.704935i | \(-0.750976\pi\) | ||
0.709272 | − | 0.704935i | \(-0.249024\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.12143e8i | 0.598639i | 0.954153 | + | 0.299320i | \(0.0967597\pi\) | ||||
−0.954153 | + | 0.299320i | \(0.903240\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.16317e8 | −0.739854 | −0.369927 | − | 0.929061i | \(-0.620617\pi\) | ||||
−0.369927 | + | 0.929061i | \(0.620617\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.38406e9 | −1.96992 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.60641e8 | + | 7.62596e8i | 0.933969 | + | 1.07811i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.73498e8 | 0.243636 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.25446e7 | − | 2.25975e7i | −0.0450922 | − | 0.0313099i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.28142e9i | 1.76366i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.86798e8 | 1.07569 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.67700e8 | + | 2.41519e8i | −0.227756 | + | 0.328011i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.20289e9i | 1.61214i | 0.591817 | + | 0.806072i | \(0.298411\pi\) | ||||
−0.591817 | + | 0.806072i | \(0.701589\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.32760e7 | + | 3.47841e7i | −0.124188 | + | 0.0463115i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.04819e8i | − | 0.270903i | −0.990784 | − | 0.135452i | \(-0.956751\pi\) | ||
0.990784 | − | 0.135452i | \(-0.0432485\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.50129e9i | − | 1.97266i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.04456e8 | 1.17295 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.07525e9 | −1.38536 | −0.692682 | − | 0.721243i | \(-0.743571\pi\) | ||||
−0.692682 | + | 0.721243i | \(0.743571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.06412e9 | − | 7.38874e8i | −1.36210 | − | 0.945783i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.94976e8 | 0.756649 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.66985e8 | − | 6.22712e7i | 0.209622 | − | 0.0781714i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 3.27972e8i | − | 0.409063i | −0.978860 | − | 0.204532i | \(-0.934433\pi\) | ||
0.978860 | − | 0.204532i | \(-0.0655671\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.97147e8 | −0.863924 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.06711e8 | − | 3.51837e8i | −0.623900 | − | 0.433208i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1.00558e8i | − | 0.122235i | −0.998131 | − | 0.0611177i | \(-0.980533\pi\) | ||
0.998131 | − | 0.0611177i | \(-0.0194665\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.29402e8 | − | 3.67592e8i | −0.639423 | − | 0.443987i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.31841e9i | 1.58227i | 0.611642 | + | 0.791134i | \(0.290509\pi\) | ||||
−0.611642 | + | 0.791134i | \(0.709491\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 6.29858e7i | − | 0.0751117i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.08841e8 | 0.834640 | 0.417320 | − | 0.908760i | \(-0.362969\pi\) | ||||
0.417320 | + | 0.908760i | \(0.362969\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.65763e9 | −1.93949 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.87415e8 | + | 2.69913e8i | −0.217903 | + | 0.313821i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.08239e8 | −0.471668 | −0.235834 | − | 0.971793i | \(-0.575782\pi\) | ||||
−0.235834 | + | 0.971793i | \(0.575782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.26618e9 | − | 1.82354e9i | 1.44464 | − | 2.08055i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.27615e8i | − | 0.258075i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.20442e7 | −0.0135709 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.23076e8 | − | 1.13451e9i | −0.473740 | − | 1.27037i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.53392e8i | − | 0.722594i | −0.932451 | − | 0.361297i | \(-0.882334\pi\) | ||
0.932451 | − | 0.361297i | \(-0.117666\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.61595e8 | + | 9.52821e8i | −0.727145 | + | 1.04722i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.53885e8i | − | 0.277319i | −0.990340 | − | 0.138659i | \(-0.955721\pi\) | ||
0.990340 | − | 0.138659i | \(-0.0442793\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.70105e9i | 1.84662i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.70410e8 | −0.504420 | −0.252210 | − | 0.967672i | \(-0.581157\pi\) | ||||
−0.252210 | + | 0.967672i | \(0.581157\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.13708e9 | 2.27758 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.91651e8 | + | 7.82083e8i | 0.308928 | + | 0.828411i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.68355e8 | 0.598355 | 0.299178 | − | 0.954197i | \(-0.403288\pi\) | ||||
0.299178 | + | 0.954197i | \(0.403288\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.76979e8 | − | 1.22886e8i | −0.184065 | − | 0.127806i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.36934e7i | − | 0.0141554i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.44684e8 | −0.354161 | −0.177080 | − | 0.984196i | \(-0.556665\pi\) | ||||
−0.177080 | + | 0.984196i | \(0.556665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −6.07115e7 | + | 8.74358e7i | −0.0620045 | + | 0.0892980i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.23493e8i | 0.427327i | 0.976907 | + | 0.213664i | \(0.0685397\pi\) | ||||
−0.976907 | + | 0.213664i | \(0.931460\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.22988e8 | − | 8.73346e8i | 0.223658 | − | 0.875972i |
(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 | 300.7.b.e.149.13 | 16 | ||
3.2 | odd | 2 | inner | 300.7.b.e.149.3 | 16 | ||
5.2 | odd | 4 | 60.7.g.a.41.3 | ✓ | 8 | ||
5.3 | odd | 4 | 300.7.g.h.101.6 | 8 | |||
5.4 | even | 2 | inner | 300.7.b.e.149.4 | 16 | ||
15.2 | even | 4 | 60.7.g.a.41.4 | yes | 8 | ||
15.8 | even | 4 | 300.7.g.h.101.5 | 8 | |||
15.14 | odd | 2 | inner | 300.7.b.e.149.14 | 16 | ||
20.7 | even | 4 | 240.7.l.c.161.6 | 8 | |||
60.47 | odd | 4 | 240.7.l.c.161.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.7.g.a.41.3 | ✓ | 8 | 5.2 | odd | 4 | ||
60.7.g.a.41.4 | yes | 8 | 15.2 | even | 4 | ||
240.7.l.c.161.5 | 8 | 60.47 | odd | 4 | |||
240.7.l.c.161.6 | 8 | 20.7 | even | 4 | |||
300.7.b.e.149.3 | 16 | 3.2 | odd | 2 | inner | ||
300.7.b.e.149.4 | 16 | 5.4 | even | 2 | inner | ||
300.7.b.e.149.13 | 16 | 1.1 | even | 1 | trivial | ||
300.7.b.e.149.14 | 16 | 15.14 | odd | 2 | inner | ||
300.7.g.h.101.5 | 8 | 15.8 | even | 4 | |||
300.7.g.h.101.6 | 8 | 5.3 | odd | 4 |