Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (of order \(2\), degree \(1\), 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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + 18093172325 x^{8} + 74958811500 x^{6} + 79355888475 x^{4} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.19 | ||
Root | \(-0.852576i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.a.383.20 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 15.4777 | − | 1.85457i | 0.992898 | − | 0.118971i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 55.8580i | 0.999219i | 0.866251 | + | 0.499610i | \(0.166523\pi\) | ||||
−0.866251 | + | 0.499610i | \(0.833477\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 225.953i | 1.74290i | 0.490480 | + | 0.871452i | \(0.336821\pi\) | ||||
−0.490480 | + | 0.871452i | \(0.663179\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 236.121 | − | 57.4091i | 0.971692 | − | 0.236251i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −36.9229 | −0.0920054 | −0.0460027 | − | 0.998941i | \(-0.514648\pi\) | ||||
−0.0460027 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 795.597 | 1.30567 | 0.652837 | − | 0.757499i | \(-0.273579\pi\) | ||||
0.652837 | + | 0.757499i | \(0.273579\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 103.593 | + | 864.557i | 0.118878 | + | 0.992122i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 129.541i | − | 0.108714i | −0.998522 | − | 0.0543568i | \(-0.982689\pi\) | ||
0.998522 | − | 0.0543568i | \(-0.0173108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 998.033i | − | 0.634251i | −0.948384 | − | 0.317125i | \(-0.897282\pi\) | ||
0.948384 | − | 0.317125i | \(-0.102718\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 419.046 | + | 3497.25i | 0.207354 | + | 1.73053i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3748.76 | 1.47764 | 0.738819 | − | 0.673904i | \(-0.235384\pi\) | ||||
0.738819 | + | 0.673904i | \(0.235384\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.87856 | 0.00156114 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3548.15 | − | 1326.47i | 0.936684 | − | 0.350176i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 921.479i | 0.203465i | 0.994812 | + | 0.101733i | \(0.0324386\pi\) | ||||
−0.994812 | + | 0.101733i | \(0.967561\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 423.688i | 0.0791849i | 0.999216 | + | 0.0395925i | \(0.0126060\pi\) | ||||
−0.999216 | + | 0.0395925i | \(0.987394\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −571.482 | + | 68.4759i | −0.0913520 | + | 0.0109459i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −12621.3 | −1.74154 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10929.6 | −1.31250 | −0.656249 | − | 0.754544i | \(-0.727858\pi\) | ||||
−0.656249 | + | 0.754544i | \(0.727858\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12314.0 | − | 1475.49i | 1.29640 | − | 0.155337i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 14465.5i | 1.34392i | 0.740586 | + | 0.671962i | \(0.234548\pi\) | ||||
−0.740586 | + | 0.671962i | \(0.765452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20897.9i | 1.72358i | 0.507268 | + | 0.861788i | \(0.330655\pi\) | ||||
−0.507268 | + | 0.861788i | \(0.669345\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3206.76 | + | 13189.3i | 0.236067 | + | 0.970933i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12002.2 | −0.792534 | −0.396267 | − | 0.918135i | \(-0.629695\pi\) | ||||
−0.396267 | + | 0.918135i | \(0.629695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −34247.9 | −2.03772 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −240.242 | − | 2005.00i | −0.0129337 | − | 0.107942i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11365.4i | − | 0.555769i | −0.960615 | − | 0.277884i | \(-0.910367\pi\) | ||
0.960615 | − | 0.277884i | \(-0.0896332\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2062.44i | − | 0.0919336i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1850.92 | − | 15447.3i | −0.0754572 | − | 0.629746i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −36606.6 | −1.36908 | −0.684542 | − | 0.728974i | \(-0.739998\pi\) | ||||
−0.684542 | + | 0.728974i | \(0.739998\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 38251.8 | 1.31622 | 0.658108 | − | 0.752923i | \(-0.271357\pi\) | ||||
0.658108 | + | 0.752923i | \(0.271357\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12971.8 | + | 53352.4i | 0.411763 | + | 1.69357i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44440.5i | 1.30465i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8975.18i | − | 0.244262i | −0.992514 | − | 0.122131i | \(-0.961027\pi\) | ||
0.992514 | − | 0.122131i | \(-0.0389728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 58022.3 | − | 6952.33i | 1.46714 | − | 0.175795i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −61606.6 | −1.45038 | −0.725189 | − | 0.688549i | \(-0.758248\pi\) | ||||
−0.725189 | + | 0.688549i | \(0.758248\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2569.04 | 0.0564240 | 0.0282120 | − | 0.999602i | \(-0.491019\pi\) | ||||
0.0282120 | + | 0.999602i | \(0.491019\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 75.5091 | − | 9.04762i | 0.00155005 | − | 0.000185730i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 8342.84i | − | 0.160357i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61551.9i | 1.10962i | 0.831978 | + | 0.554809i | \(0.187209\pi\) | ||||
−0.831978 | + | 0.554809i | \(0.812791\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 52457.4 | − | 27111.0i | 0.888371 | − | 0.459127i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 113300. | 1.80523 | 0.902617 | − | 0.430444i | \(-0.141643\pi\) | ||||
0.902617 | + | 0.430444i | \(0.141643\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7235.89 | 0.108629 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1708.95 | + | 14262.4i | 0.0242064 | + | 0.202020i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 125521.i | − | 1.67974i | −0.542790 | − | 0.839868i | \(-0.682632\pi\) | ||
0.542790 | − | 0.839868i | \(-0.317368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 179768.i | 2.27566i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 785.759 | + | 6557.74i | 0.00942067 | + | 0.0786225i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 55748.2 | 0.633756 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −156644. | −1.69038 | −0.845191 | − | 0.534465i | \(-0.820513\pi\) | ||||
−0.845191 | + | 0.534465i | \(0.820513\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8718.27 | + | 2119.71i | −0.0894010 | + | 0.0217364i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 34422.0i | − | 0.335763i | −0.985807 | − | 0.167881i | \(-0.946307\pi\) | ||
0.985807 | − | 0.167881i | \(-0.0536926\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 28205.4i | − | 0.261962i | −0.991385 | − | 0.130981i | \(-0.958187\pi\) | ||
0.991385 | − | 0.130981i | \(-0.0418127\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −195349. | + | 23407.1i | −1.72917 | + | 0.207192i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 42182.3 | 0.356181 | 0.178090 | − | 0.984014i | \(-0.443008\pi\) | ||||
0.178090 | + | 0.984014i | \(0.443008\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 88788.0 | 0.715794 | 0.357897 | − | 0.933761i | \(-0.383494\pi\) | ||||
0.357897 | + | 0.933761i | \(0.383494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −169165. | + | 20269.6i | −1.30318 | + | 0.156149i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 238904.i | − | 1.76006i | −0.474921 | − | 0.880028i | \(-0.657523\pi\) | ||
0.474921 | − | 0.880028i | \(-0.342477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 209398.i | 1.47648i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 187857. | − | 45674.5i | 1.26871 | − | 0.308467i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 29270.2 | 0.189477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −159688. | −0.991535 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 26827.3 | + | 223894.i | 0.159887 | + | 1.33438i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 174829.i | 1.00078i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 258860.i | 1.42415i | 0.702105 | + | 0.712074i | \(0.252244\pi\) | ||||
−0.702105 | + | 0.712074i | \(0.747756\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 38756.5 | + | 323452.i | 0.205055 | + | 1.71133i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9462.28 | 0.0481745 | 0.0240873 | − | 0.999710i | \(-0.492332\pi\) | ||||
0.0240873 | + | 0.999710i | \(0.492332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 225509. | 1.10544 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 74093.8 | + | 198193.i | 0.349903 | + | 0.935952i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 146703.i | − | 0.667788i | −0.942611 | − | 0.333894i | \(-0.891637\pi\) | ||
0.942611 | − | 0.333894i | \(-0.108363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 150825.i | − | 0.662119i | −0.943610 | − | 0.331060i | \(-0.892594\pi\) | ||
0.943610 | − | 0.331060i | \(-0.107406\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −185768. | + | 22259.0i | −0.786905 | + | 0.0942882i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −29375.7 | −0.120129 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −51472.0 | −0.203306 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −530080. | + | 63515.1i | −2.02324 | + | 0.242428i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 223409.i | − | 0.824396i | −0.911094 | − | 0.412198i | \(-0.864761\pi\) | ||
0.911094 | − | 0.412198i | \(-0.135239\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 398109.i | 1.42089i | 0.703754 | + | 0.710443i | \(0.251506\pi\) | ||||
−0.703754 | + | 0.710443i | \(0.748494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7436.81 | − | 30587.3i | −0.0256837 | − | 0.105636i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23666.4 | −0.0791231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 457758. | 1.48213 | 0.741066 | − | 0.671432i | \(-0.234320\pi\) | ||||
0.741066 | + | 0.671432i | \(0.234320\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −21077.9 | − | 175910.i | −0.0661202 | − | 0.551822i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 847044.i | 2.57538i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 90580.0i | − | 0.267032i | −0.991047 | − | 0.133516i | \(-0.957373\pi\) | ||
0.991047 | − | 0.133516i | \(-0.0426268\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3824.93 | − | 31921.9i | −0.0109374 | − | 0.0912807i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −160677. | −0.445822 | −0.222911 | − | 0.974839i | \(-0.571556\pi\) | ||||
−0.222911 | + | 0.974839i | \(0.571556\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 261681. | 0.704784 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −57296.2 | − | 235657.i | −0.149843 | − | 0.616296i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 425382.i | 1.08060i | 0.841473 | + | 0.540299i | \(0.181689\pi\) | ||||
−0.841473 | + | 0.540299i | \(0.818311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1102.33i | 0.00272092i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −566588. | + | 67889.5i | −1.35936 | + | 0.162881i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19674.5 | 0.0458956 | 0.0229478 | − | 0.999737i | \(-0.492695\pi\) | ||||
0.0229478 | + | 0.999737i | \(0.492695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −46347.1 | −0.105154 | −0.0525771 | − | 0.998617i | \(-0.516744\pi\) | ||||
−0.0525771 | + | 0.998617i | \(0.516744\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 592052. | − | 70940.6i | 1.30687 | − | 0.156591i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 610504.i | − | 1.31147i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4783.01i | 0.0100022i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 299719. | + | 801717.i | 0.610324 | + | 1.63255i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 57120.9 | 0.113295 | 0.0566476 | − | 0.998394i | \(-0.481959\pi\) | ||||
0.0566476 | + | 0.998394i | \(0.481959\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −257879. | −0.498336 | −0.249168 | − | 0.968460i | \(-0.580157\pi\) | ||||
−0.249168 | + | 0.968460i | \(0.580157\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 82417.9 | + | 687838.i | 0.155215 | + | 1.29539i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 704799.i | − | 1.29390i | −0.762534 | − | 0.646948i | \(-0.776045\pi\) | ||
0.762534 | − | 0.646948i | \(-0.223955\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 259574.i | 0.464654i | 0.972638 | + | 0.232327i | \(0.0746339\pi\) | ||||
−0.972638 | + | 0.232327i | \(0.925366\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −16645.1 | − | 138916.i | −0.0290600 | − | 0.242527i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −208211. | −0.354621 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −808016. | −1.34287 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 885161. | − | 215213.i | 1.43581 | − | 0.349094i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 36850.2i | 0.0583545i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 534281.i | 0.826159i | 0.910695 | + | 0.413080i | \(0.135547\pi\) | ||||
−0.910695 | + | 0.413080i | \(0.864453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −953531. | + | 114254.i | −1.44008 | + | 0.172552i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.16731e6 | −1.72223 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −95733.8 | −0.138012 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39762.9 | − | 4764.46i | 0.0560232 | − | 0.00671279i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 103062.i | − | 0.141945i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 864006.i | − | 1.16347i | −0.813379 | − | 0.581734i | \(-0.802374\pi\) | ||
0.813379 | − | 0.581734i | \(-0.197626\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1151.93 | − | 280.074i | 0.00151695 | − | 0.000368821i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 889864. | 1.14620 | 0.573098 | − | 0.819487i | \(-0.305741\pi\) | ||||
0.573098 | + | 0.819487i | \(0.305741\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 296508. | 0.373635 | 0.186818 | − | 0.982395i | \(-0.440183\pi\) | ||||
0.186818 | + | 0.982395i | \(0.440183\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15472.4 | − | 129128.i | −0.0190777 | − | 0.159218i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 763288.i | − | 0.921083i | −0.887638 | − | 0.460541i | \(-0.847655\pi\) | ||
0.887638 | − | 0.460541i | \(-0.152345\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 670422.i | − | 0.791915i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 114152. | + | 952684.i | 0.132012 | + | 1.10174i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 36450.5 | 0.0412771 | 0.0206385 | − | 0.999787i | \(-0.493430\pi\) | ||||
0.0206385 | + | 0.999787i | \(0.493430\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.29506e6 | 1.43631 | 0.718155 | − | 0.695884i | \(-0.244987\pi\) | ||||
0.718155 | + | 0.695884i | \(0.244987\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 761643. | − | 516903.i | 0.827439 | − | 0.561556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 1.91302e6i | − | 2.03613i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 794032.i | − | 0.828125i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.75362e6 | − | 210122.i | 1.79241 | − | 0.214770i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 466045. | 0.466921 | 0.233460 | − | 0.972366i | \(-0.424995\pi\) | ||||
0.233460 | + | 0.972366i | \(0.424995\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −138415. | −0.135951 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 111995. | − | 13419.5i | 0.107857 | − | 0.0129236i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 571612.i | − | 0.539844i | −0.962882 | − | 0.269922i | \(-0.913002\pi\) | ||
0.962882 | − | 0.269922i | \(-0.0869979\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.46957e6i | − | 2.28756i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 52901.2 | + | 217581.i | 0.0480689 | + | 0.197706i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −435018. | −0.387809 | −0.193905 | − | 0.981020i | \(-0.562115\pi\) | ||||
−0.193905 | + | 0.981020i | \(0.562115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 634848. | 0.555335 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −232787. | − | 1.94278e6i | −0.199839 | − | 1.66781i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.11982e6i | − | 0.943556i | −0.881717 | − | 0.471778i | \(-0.843612\pi\) | ||
0.881717 | − | 0.471778i | \(-0.156388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 201205.i | − | 0.166424i | −0.996532 | − | 0.0832118i | \(-0.973482\pi\) | ||
0.996532 | − | 0.0832118i | \(-0.0265178\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 333392. | + | 2.78240e6i | 0.270737 | + | 2.25950i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −180.130 | −0.000143633 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −302438. | −0.236830 | −0.118415 | − | 0.992964i | \(-0.537781\pi\) | ||||
−0.118415 | + | 0.992964i | \(0.537781\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24323.6 | + | 100042.i | 0.0187075 | + | 0.0769433i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.77044e6i | − | 1.33757i | −0.743457 | − | 0.668784i | \(-0.766815\pi\) | ||
0.743457 | − | 0.668784i | \(-0.233185\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 809916.i | 0.601138i | 0.953760 | + | 0.300569i | \(0.0971765\pi\) | ||||
−0.953760 | + | 0.300569i | \(0.902824\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 862856. | − | 103389.i | 0.629255 | − | 0.0753983i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.26853e6 | −2.34233 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.40308e6 | 0.988181 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.42450e6 | + | 290507.i | −1.67838 | + | 0.201106i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.73657e6i | − | 1.18174i | −0.806767 | − | 0.590870i | \(-0.798784\pi\) | ||
0.806767 | − | 0.590870i | \(-0.201216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.04478e6i | − | 1.36801i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −131008. | + | 48976.9i | −0.0861800 | + | 0.0322181i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.98250e6 | 1.92931 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.72194e6 | −3.00403 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −63837.9 | − | 532775.i | −0.0399459 | − | 0.333378i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.13667e6i | 1.31519i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 596701.i | 0.361335i | 0.983544 | + | 0.180668i | \(0.0578259\pi\) | ||||
−0.983544 | + | 0.180668i | \(0.942174\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −52308.8 | − | 436556.i | −0.0311658 | − | 0.260102i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.86268e6 | 1.67831 | 0.839154 | − | 0.543894i | \(-0.183051\pi\) | ||||
0.839154 | + | 0.543894i | \(0.183051\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.53442e6 | −0.885287 | −0.442644 | − | 0.896698i | \(-0.645959\pi\) | ||||
−0.442644 | + | 0.896698i | \(0.645959\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.98016e6 | + | 724578.i | −1.69224 | + | 0.411442i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.33250e6i | 1.86261i | 0.364241 | + | 0.931305i | \(0.381329\pi\) | ||||
−0.364241 | + | 0.931305i | \(0.618671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 34023.6i | − | 0.0187199i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 652886. | − | 78229.9i | 0.353651 | − | 0.0423750i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −129286. | −0.0689517 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3881.37 | 0.00203834 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.37424e6 | − | 164663.i | 0.710711 | − | 0.0851585i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.71195e6i | − | 1.38131i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.02136e6i | 1.01408i | 0.861922 | + | 0.507041i | \(0.169261\pi\) | ||||
−0.861922 | + | 0.507041i | \(0.830739\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.58070e6 | + | 627456.i | −1.27534 | + | 0.310079i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 501336. | 0.244071 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.12008e6 | −0.537249 | −0.268625 | − | 0.963245i | \(-0.586569\pi\) | ||||
−0.268625 | + | 0.963245i | \(0.586569\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −443063. | − | 3.69769e6i | −0.209395 | − | 1.74756i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15643.8i | − | 0.00728544i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.94083e6i | − | 1.80864i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 388343. | + | 3.24101e6i | 0.175658 | + | 1.46600i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.39720e6 | 1.06876 | 0.534380 | − | 0.845244i | \(-0.320545\pi\) | ||||
0.534380 | + | 0.845244i | \(0.320545\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.86085e6 | 0.817801 | 0.408900 | − | 0.912579i | \(-0.365912\pi\) | ||||
0.408900 | + | 0.912579i | \(0.365912\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.82290e6 | − | 1.05533e6i | 1.22300 | − | 0.457216i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.14786e6i | − | 0.917423i | −0.888585 | − | 0.458711i | \(-0.848311\pi\) | ||
0.888585 | − | 0.458711i | \(-0.151689\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.44122e6i | − | 1.44925i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 453036. | − | 54283.5i | 0.188132 | − | 0.0225423i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.48571e6 | −0.608412 | −0.304206 | − | 0.952606i | \(-0.598391\pi\) | ||||
−0.304206 | + | 0.952606i | \(0.598391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.48003e6 | 0.597726 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.47161e6 | + | 296152.i | −0.984493 | + | 0.117964i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 143501.i | 0.0563799i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.58403e6i | 1.00146i | 0.865604 | + | 0.500729i | \(0.166935\pi\) | ||||
−0.865604 | + | 0.500729i | \(0.833065\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 830452. | + | 3.41562e6i | 0.317504 | + | 1.30588i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.56804e6 | 0.968652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.75492e6 | −1.39743 | −0.698713 | − | 0.715402i | \(-0.746244\pi\) | ||||
−0.698713 | + | 0.715402i | \(0.746244\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 324232. | + | 2.70596e6i | 0.119063 | + | 0.993671i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 733126.i | 0.265659i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 4.37130e6i | − | 1.56319i | −0.623784 | − | 0.781597i | \(-0.714405\pi\) | ||
0.623784 | − | 0.781597i | \(-0.285595\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 480073. | + | 4.00656e6i | 0.169432 | + | 1.41403i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.26259e6 | 0.439812 | 0.219906 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219906 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 466015. | 0.160231 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.19973e6 | + | 4.93442e6i | 0.407197 | + | 1.67479i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.13040e6i | 0.713817i | 0.934139 | + | 0.356908i | \(0.116169\pi\) | ||||
−0.934139 | + | 0.356908i | \(0.883831\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 485617.i | − | 0.160639i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 146455. | − | 17548.4i | 0.0478324 | − | 0.00573135i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.43817e6 | −1.10875 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.68644e6 | 1.17390 | 0.586950 | − | 0.809623i | \(-0.300328\pi\) | ||||
0.586950 | + | 0.809623i | \(0.300328\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.49037e6 | − | 418222.i | 1.09759 | − | 0.131515i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 3.06338e6i | − | 0.951350i | −0.879621 | − | 0.475675i | \(-0.842204\pi\) | ||
0.879621 | − | 0.475675i | \(-0.157796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 337085.i | 0.103390i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.51437e6 | + | 2.93017e6i | 0.458768 | + | 0.887677i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 403551. | 0.120757 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.44429e6 | 1.31369 | 0.656847 | − | 0.754024i | \(-0.271890\pi\) | ||||
0.656847 | + | 0.754024i | \(0.271890\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −272071. | − | 2.27064e6i | −0.0794472 | − | 0.663046i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 8.27139e6i | − | 2.38618i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.32870e6i | 1.80382i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −279715. | − | 2.33443e6i | −0.0787727 | − | 0.657417i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.62681e6 | 0.452691 | 0.226346 | − | 0.974047i | \(-0.427322\pi\) | ||||
0.226346 | + | 0.974047i | \(0.427322\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.43223e6 | 0.393828 | 0.196914 | − | 0.980421i | \(-0.436908\pi\) | ||||
0.196914 | + | 0.980421i | \(0.436908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.83398e6 | + | 689038.i | −0.770099 | + | 0.187237i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 631.972i | − | 0.000169717i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.64312e6i | 2.29404i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −454670. | + | 54479.2i | −0.119276 | + | 0.0142918i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.60361e6 | −1.45303 | −0.726515 | − | 0.687151i | \(-0.758861\pi\) | ||||
−0.726515 | + | 0.687151i | \(0.758861\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.49780e6 | −1.15287 | −0.576435 | − | 0.817143i | \(-0.695557\pi\) | ||||
−0.576435 | + | 0.817143i | \(0.695557\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −796671. | + | 95458.3i | −0.201862 | + | 0.0241875i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 3.74139e6i | − | 0.937193i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.39182e6i | 1.33529i | 0.744481 | + | 0.667643i | \(0.232697\pi\) | ||||
−0.744481 | + | 0.667643i | \(0.767303\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.08665e6 | + | 1.96614e6i | −1.98003 | + | 0.481413i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 697144. | 0.168777 | 0.0843885 | − | 0.996433i | \(-0.473106\pi\) | ||||
0.0843885 | + | 0.996433i | \(0.473106\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.01136e6 | 1.67843 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −414328. | − | 3.45787e6i | −0.0980788 | − | 0.818541i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.66314e6i | 0.623416i | 0.950178 | + | 0.311708i | \(0.100901\pi\) | ||||
−0.950178 | + | 0.311708i | \(0.899099\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 534108.i | − | 0.123648i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 738320. | + | 6.16183e6i | 0.169044 | + | 1.41080i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.00415e7 | −2.27389 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.12657e6 | −0.476310 | −0.238155 | − | 0.971227i | \(-0.576543\pi\) | ||||
−0.238155 | + | 0.971227i | \(0.576543\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −171831. | − | 459630.i | −0.0380689 | − | 0.101830i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4.19441e6i | − | 0.919218i | −0.888121 | − | 0.459609i | \(-0.847989\pi\) | ||
0.888121 | − | 0.459609i | \(-0.152011\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.23099e6i | − | 0.917254i | −0.888629 | − | 0.458627i | \(-0.848341\pi\) | ||
0.888629 | − | 0.458627i | \(-0.151659\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −366303. | + | 43891.0i | −0.0785611 | + | 0.00941332i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.90063e6 | −1.03982 | −0.519912 | − | 0.854220i | \(-0.674035\pi\) | ||||
−0.519912 | + | 0.854220i | \(0.674035\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.02797e6 | 0.425726 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.08506e6 | − | 848944.i | 1.47161 | − | 0.176330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 771608.i | − | 0.158578i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4868.97i | − | 0.000990154i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −652476. | − | 2.68361e6i | −0.131301 | − | 0.540036i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.45294e6 | −0.687622 | −0.343811 | − | 0.939039i | \(-0.611718\pi\) | ||||
−0.343811 | + | 0.939039i | \(0.611718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.69553e6 | −1.71369 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.57090e6 | + | 1.31103e7i | 0.306395 | + | 2.55709i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.74983e6i | − | 1.68906i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.62872e6i | 0.311188i | 0.987821 | + | 0.155594i | \(0.0497292\pi\) | ||||
−0.987821 | + | 0.155594i | \(0.950271\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −167987. | − | 1.40197e6i | −0.0317690 | − | 0.265136i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.79077e6 | 1.08401 | 0.542004 | − | 0.840376i | \(-0.317666\pi\) | ||||
0.542004 | + | 0.840376i | \(0.317666\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 119369. | 0.0221195 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −118403. | − | 486985.i | −0.0217194 | − | 0.0893311i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.39202e7i | − | 2.52787i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.75964e6i | 0.855702i | 0.903849 | + | 0.427851i | \(0.140729\pi\) | ||||
−0.903849 | + | 0.427851i | \(0.859271\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.48691e6 | + | 297986.i | −0.442656 | + | 0.0530397i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 55691.2 | 0.00981446 | 0.00490723 | − | 0.999988i | \(-0.498438\pi\) | ||||
0.00490723 | + | 0.999988i | \(0.498438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.92275e6 | 0.335501 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.05024e6 | − | 485306.i | 0.699778 | − | 0.0838486i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.84383e6i | 0.486530i | 0.969960 | + | 0.243265i | \(0.0782185\pi\) | ||||
−0.969960 | + | 0.243265i | \(0.921781\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 580483.i | 0.0983416i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.32386e6 | − | 3.54118e6i | −0.222100 | − | 0.594093i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.57550e6 | 0.261758 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 443157. | 0.0729174 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 788900. | + | 6.58396e6i | 0.128559 | + | 1.07292i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.07097e7i | 1.72855i | 0.503019 | + | 0.864275i | \(0.332223\pi\) | ||||
−0.503019 | + | 0.864275i | \(0.667777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.05988e6i | 0.649022i | 0.945882 | + | 0.324511i | \(0.105200\pi\) | ||||
−0.945882 | + | 0.324511i | \(0.894800\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2044.34 | + | 17061.5i | 0.000323709 | + | 0.00270159i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 54884.9 | 0.00860848 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.61684e6 | 1.18341 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.64360e6 | + | 2.10155e6i | −1.33033 | + | 0.323448i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.15087e7i | 1.75473i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.35622e6i | 0.355903i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 304517. | − | 36487.7i | 0.0455696 | − | 0.00546022i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.26453e6 | 0.187481 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.26069e6 | 0.478979 | 0.239490 | − | 0.970899i | \(-0.423020\pi\) | ||||
0.239490 | + | 0.970899i | \(0.423020\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −717349. | + | 85953.9i | −0.104407 | + | 0.0125102i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.95953e6i | 0.715235i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.81195e6i | − | 0.830526i | −0.909701 | − | 0.415263i | \(-0.863690\pi\) | ||
0.909701 | − | 0.415263i | \(-0.136310\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.03206e6 | − | 2.19600e6i | 1.27896 | − | 0.310958i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 919667. | 0.129048 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.39078e7 | −1.93396 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.13222e6 | − | 9.44923e6i | −0.156027 | − | 1.30216i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 5.08607e6i | − | 0.694615i | −0.937751 | − | 0.347308i | \(-0.887096\pi\) | ||
0.937751 | − | 0.347308i | \(-0.112904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.66263e7i | 2.25043i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8870.42 | + | 74030.3i | 0.00118997 | + | 0.00993121i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.79359e6 | 1.30218 | 0.651090 | − | 0.759001i | \(-0.274312\pi\) | ||||
0.651090 | + | 0.759001i | \(0.274312\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.33447e7 | 1.75868 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 6.12582e6 | + | 1.18529e7i | 0.800214 | + | 1.54835i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 8.50753e6i | − | 1.10160i | −0.834638 | − | 0.550799i | \(-0.814323\pi\) | ||
0.834638 | − | 0.550799i | \(-0.185677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.37026e6i | 0.560941i | 0.959863 | + | 0.280470i | \(0.0904905\pi\) | ||||
−0.959863 | + | 0.280470i | \(0.909510\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 884103. | − | 105935.i | 0.112491 | − | 0.0134788i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 18288.5 | 0.00230680 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.87042e6 | 1.10919 | 0.554594 | − | 0.832121i | \(-0.312874\pi\) | ||||
0.554594 | + | 0.832121i | \(0.312874\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.99138e6 | + | 478254.i | −0.494797 | + | 0.0592874i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.56004e7i | 3.14635i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 419642.i | 0.0511338i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.55129e6 | + | 1.04933e7i | 0.308226 | + | 1.26772i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.40119e6 | −0.167842 | −0.0839209 | − | 0.996472i | \(-0.526744\pi\) | ||||
−0.0839209 | + | 0.996472i | \(0.526744\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 422855. | 0.0502231 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.30710e6 | − | 1.09087e7i | −0.153936 | − | 1.28471i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1.59083e7i | − | 1.85774i | −0.370401 | − | 0.928872i | \(-0.620780\pi\) | ||
0.370401 | − | 0.928872i | \(-0.379220\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.63497e6i | 0.189330i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 481398. | + | 4.01763e6i | 0.0552801 | + | 0.461353i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.27346e7 | 1.45017 | 0.725085 | − | 0.688660i | \(-0.241801\pi\) | ||||
0.725085 | + | 0.688660i | \(0.241801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.53611e6 | −0.963992 | −0.481996 | − | 0.876173i | \(-0.660088\pi\) | ||||
−0.481996 | + | 0.876173i | \(0.660088\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −515257. | − | 2.11923e6i | −0.0577072 | − | 0.237348i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 8.91984e6i | − | 0.990761i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.68744e6i | − | 0.406212i | −0.979157 | − | 0.203106i | \(-0.934896\pi\) | ||
0.979157 | − | 0.203106i | \(-0.0651036\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.22264e6 | + | 386142.i | −0.352102 | + | 0.0421894i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.54895e6 | −1.03479 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.99314e6 | −0.644174 | −0.322087 | − | 0.946710i | \(-0.604384\pi\) | ||||
−0.322087 | + | 0.946710i | \(0.604384\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.25063e7 | + | 1.49852e6i | −1.33334 | + | 0.159762i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.12913e7i | 1.19407i | 0.802215 | + | 0.597035i | \(0.203655\pi\) | ||||
−0.802215 | + | 0.597035i | \(0.796345\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.53091e6i | 0.789989i | 0.918684 | + | 0.394994i | \(0.129253\pi\) | ||||
−0.918684 | + | 0.394994i | \(0.870747\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.33012e7 | − | 4.97260e6i | 1.38408 | − | 0.517433i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.83619e7 | 2.92762 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.75036e6 | −0.998436 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 68341.3 | + | 570359.i | 0.00694247 | + | 0.0579401i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.41582e6i | 0.142686i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.39881e7i | − | 1.39858i | −0.714840 | − | 0.699289i | \(-0.753500\pi\) | ||
0.714840 | − | 0.699289i | \(-0.246500\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 990861. | + | 8.26947e6i | 0.0982887 | + | 0.820292i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.44594e7 | −1.42304 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.72475e7 | −2.66059 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.45466e7 | + | 3.53678e6i | −1.40932 | + | 0.342654i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.54988e6i | 0.918021i | 0.888431 | + | 0.459011i | \(0.151796\pi\) | ||||
−0.888431 | + | 0.459011i | \(0.848204\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.51800e6i | − | 0.144792i | −0.997376 | − | 0.0723959i | \(-0.976935\pi\) | ||
0.997376 | − | 0.0723959i | \(-0.0230645\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.80674e7 | + | 2.16486e6i | −1.71000 | + | 0.204895i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.58617e7 | −1.48967 | −0.744834 | − | 0.667250i | \(-0.767471\pi\) | ||||
−0.744834 | + | 0.667250i | \(0.767471\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.35162e6 | 0.125963 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.48174e6 | + | 177545.i | −0.137032 | + | 0.0164193i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 543838.i | − | 0.0499099i | −0.999689 | − | 0.0249549i | \(-0.992056\pi\) | ||
0.999689 | − | 0.0249549i | \(-0.00794423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 528544.i | 0.0481369i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 606604. | − | 147486.i | 0.0548267 | − | 0.0133302i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.06321e7 | 0.953685 | 0.476843 | − | 0.878989i | \(-0.341781\pi\) | ||||
0.476843 | + | 0.878989i | \(0.341781\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.47871e7 | −1.31638 | −0.658189 | − | 0.752853i | \(-0.728677\pi\) | ||||
−0.658189 | + | 0.752853i | \(0.728677\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −191136. | − | 1.59517e6i | −0.0168872 | − | 0.140936i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.25965e7i | 1.10458i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.45440e6i | 0.300648i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.60236e6 | − | 1.33729e7i | −0.138419 | − | 1.15521i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41237e6 | −0.121099 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.01183e7 | 0.861129 | 0.430565 | − | 0.902560i | \(-0.358314\pi\) | ||||
0.430565 | + | 0.902560i | \(0.358314\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 17309.9 | − | 6471.24i | 0.00146229 | − | 0.000546674i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.55270e6i | − | 0.801040i | −0.916288 | − | 0.400520i | \(-0.868829\pi\) | ||
0.916288 | − | 0.400520i | \(-0.131171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.53942e7i | − | 2.94617i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.37731e7 | − | 1.65031e6i | 1.13806 | − | 0.136364i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.31661e7 | −1.07995 | −0.539975 | − | 0.841681i | \(-0.681566\pi\) | ||||
−0.539975 | + | 0.841681i | \(0.681566\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.19457e6 | 0.667267 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.58928e6 | − | 549894.i | 0.370982 | − | 0.0444516i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.04226e6i | − | 0.725653i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.90008e7i | − | 1.51383i | −0.653516 | − | 0.756913i | \(-0.726707\pi\) | ||
0.653516 | − | 0.756913i | \(-0.273293\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −478955. | − | 1.96992e6i | −0.0378845 | − | 0.155817i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.42479e6 | 0.661602 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.87387e6 | 0.146103 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.41557e6 | − | 1.18140e7i | −0.109582 | − | 0.914541i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.43183e6i | 0.571216i | 0.958347 | + | 0.285608i | \(0.0921956\pi\) | ||||
−0.958347 | + | 0.285608i | \(0.907804\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.09081e7i | 0.832453i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.24334e6 | − | 1.03766e7i | −0.0942146 | − | 0.786291i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.77776e6 | 0.585202 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.49641e6 | 0.709486 | 0.354743 | − | 0.934964i | \(-0.384568\pi\) | ||||
0.354743 | + | 0.934964i | \(0.384568\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.53364e6 | + | 1.45337e7i | 0.262149 | + | 1.07821i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.58831e6i | 0.117007i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.64087e6i | − | 0.120035i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 564172. | − | 67600.0i | 0.0409839 | − | 0.00491076i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.25267e6 | −0.162508 | −0.0812541 | − | 0.996693i | \(-0.525893\pi\) | ||||
−0.0812541 | + | 0.996693i | \(0.525893\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.37310e6 | 0.456575 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.00446e7 | − | 2.40178e6i | 1.42611 | − | 0.170879i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4495.49i | 0.000317638i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.23196e6i | − | 0.647825i | −0.946087 | − | 0.323913i | \(-0.895002\pi\) | ||
0.946087 | − | 0.323913i | \(-0.104998\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.08299e7 | − | 9.41301e6i | 0.754753 | − | 0.656009i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.70712e6 | 0.187376 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.66782e6 | −0.252143 | −0.126072 | − | 0.992021i | \(-0.540237\pi\) | ||||
−0.126072 | + | 0.992021i | \(0.540237\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.54783e6 | − | 2.96092e7i | −0.242239 | − | 2.02166i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 331389.i | 0.0224734i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 2.25692e7i | − | 1.52022i | −0.649795 | − | 0.760109i | \(-0.725145\pi\) | ||
0.649795 | − | 0.760109i | \(-0.274855\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.47259e6 | − | 1.22898e7i | −0.0985225 | − | 0.822243i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.79409e7 | −1.19226 | −0.596130 | − | 0.802888i | \(-0.703296\pi\) | ||||
−0.596130 | + | 0.802888i | \(0.703296\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.24792e7 | 0.823752 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.67525e7 | − | 6.50443e6i | 1.75413 | − | 0.426489i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.53122e6i | 0.620789i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.43657e7i | 0.929451i | 0.885455 | + | 0.464726i | \(0.153847\pi\) | ||||
−0.885455 | + | 0.464726i | \(0.846153\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 7.21332e6 | − | 864311.i | 0.463605 | − | 0.0555498i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.22376e7 | −1.41978 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.10716e6 | 0.323922 | 0.161961 | − | 0.986797i | \(-0.448218\pi\) | ||||
0.161961 | + | 0.986797i | \(0.448218\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.14235e6 | + | 256700.i | −0.134985 | + | 0.0161741i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.66301e6i | 0.542260i | 0.962543 | + | 0.271130i | \(0.0873973\pi\) | ||||
−0.962543 | + | 0.271130i | \(0.912603\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.00619e7i | 1.24756i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.70855e6 | − | 415406.i | 0.105554 | − | 0.0256637i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.91241e7 | −1.78758 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.21621e6 | 0.0741639 | 0.0370819 | − | 0.999312i | \(-0.488194\pi\) | ||||
0.0370819 | + | 0.999312i | \(0.488194\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.06009e6 | − | 8.84726e6i | −0.0642256 | − | 0.536010i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.17432e6i | − | 0.0706867i | −0.999375 | − | 0.0353434i | \(-0.988748\pi\) | ||
0.999375 | − | 0.0353434i | \(-0.0112525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2066.99i | 0.000123619i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.57999e6 | − | 3.82234e7i | −0.272152 | − | 2.27131i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.44371e7 | 0.852384 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.27469e6 | 0.133443 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.22231e6 | + | 3.26955e6i | 0.0712487 | + | 0.190583i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.55695e7i | 1.48098i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.61589e7i | − | 0.929983i | −0.885315 | − | 0.464991i | \(-0.846057\pi\) | ||
0.885315 | − | 0.464991i | \(-0.153943\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.73310e6 | + | 806771.i | −0.385055 | + | 0.0461379i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.39811e7 | 3.06761 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.04330e7 | 1.71855 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.82601e6 | − | 1.17737e6i | 0.551391 | − | 0.0660685i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.59354e7i | − | 0.888622i | −0.895873 | − | 0.444311i | \(-0.853448\pi\) | ||
0.895873 | − | 0.444311i | \(-0.146552\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.55478e6i | 0.0861592i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.20604e6 | − | 2.96382e7i | −0.396840 | − | 1.63219i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −94856.2 | −0.00519131 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.73142e7 | −2.57337 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.07678e6 | − | 1.73323e7i | −0.112255 | − | 0.936855i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 8.21438e6i | − | 0.441269i | −0.975357 | − | 0.220635i | \(-0.929187\pi\) | ||
0.975357 | − | 0.220635i | \(-0.0708128\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.18134e7i | − | 1.16459i | −0.812979 | − | 0.582293i | \(-0.802156\pi\) | ||
0.812979 | − | 0.582293i | \(-0.197844\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −373148. | − | 3.11419e6i | −0.0197995 | − | 0.165242i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.05962e6 | 0.266824 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.08568e7 | 1.09318 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.03203e7 | + | 4.24470e7i | 0.537629 | + | 2.21125i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.73324e6i | 0.452186i | 0.974106 | + | 0.226093i | \(0.0725954\pi\) | ||||
−0.974106 | + | 0.226093i | \(0.927405\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.88986e6i | − | 0.303114i | −0.988449 | − | 0.151557i | \(-0.951571\pi\) | ||
0.988449 | − | 0.151557i | \(-0.0484287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2788.01 | + | 334.064i | −0.000142613 | + | 1.70881e-5i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.33435e7 | 1.18687 | 0.593435 | − | 0.804882i | \(-0.297771\pi\) | ||||
0.593435 | + | 0.804882i | \(0.297771\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.06227e7 | −0.536846 | −0.268423 | − | 0.963301i | \(-0.586502\pi\) | ||||
−0.268423 | + | 0.963301i | \(0.586502\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.68106e6 | + | 560892.i | −0.235148 | + | 0.0281758i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.43650e6i | 0.221528i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 8.97508e6i | − | 0.445474i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 562008. | + | 1.50331e6i | 0.0277287 | + | 0.0741712i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.24424e7 | −1.10069 | −0.550345 | − | 0.834937i | \(-0.685504\pi\) | ||||
−0.550345 | + | 0.834937i | \(0.685504\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.96620e7 | 0.958602 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.28341e6 | − | 2.74025e7i | −0.159131 | − | 1.32807i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.46170e7i | 0.704234i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.60820e7i | − | 1.72815i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.50204e6 | + | 1.25357e7i | 0.0715177 | + | 0.596868i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.09723e7 | −1.93940 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.61531e7 | 1.23070 | 0.615348 | − | 0.788256i | \(-0.289015\pi\) | ||||
0.615348 | + | 0.788256i | \(0.289015\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.31633e7 | − | 3.20045e6i | 0.615815 | − | 0.149726i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.20270e7i | 0.559380i | 0.960090 | + | 0.279690i | \(0.0902316\pi\) | ||||
−0.960090 | + | 0.279690i | \(0.909768\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.12884e7i | 1.44677i | 0.690443 | + | 0.723387i | \(0.257416\pi\) | ||||
−0.690443 | + | 0.723387i | \(0.742584\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.05895e7 | + | 6.06172e6i | −2.32569 | + | 0.278668i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.08600e7 | 0.496368 | 0.248184 | − | 0.968713i | \(-0.420166\pi\) | ||||
0.248184 | + | 0.968713i | \(0.420166\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.37610e7 | −1.07975 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.17165e7 | − | 2.60210e6i | 0.981163 | − | 0.117565i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.27267e6i | − | 0.102091i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 7.14063e6i | − | 0.318927i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.69870e7 | + | 8.99279e6i | −1.64253 | + | 0.399355i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.95032e7 | −1.74426 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.30114e7 | 0.571248 | 0.285624 | − | 0.958342i | \(-0.407799\pi\) | ||||
0.285624 | + | 0.958342i | \(0.407799\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.22058e6 | − | 2.68781e7i | −0.140592 | − | 1.17335i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.19604e7i | 1.82138i | 0.413092 | + | 0.910689i | \(0.364449\pi\) | ||||
−0.413092 | + | 0.910689i | \(0.635551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 2.89203e7i | − | 1.24825i | −0.781325 | − | 0.624124i | \(-0.785456\pi\) | ||
0.781325 | − | 0.624124i | \(-0.214544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.79218e6 | − | 3.16485e7i | −0.162753 | − | 1.35830i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.04342e7 | 1.29883 | 0.649415 | − | 0.760434i | \(-0.275014\pi\) | ||||
0.649415 | + | 0.760434i | \(0.275014\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.84902e7 | −2.48215 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.93688e6 | + | 1.00102e6i | −0.0817349 | + | 0.0422422i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.19786e7i | 0.502665i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.09898e6i | 0.0458597i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 4.61624e7 | − | 5.53125e6i | 1.91561 | − | 0.229531i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −390420. | −0.0161114 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.47228e6 | −0.0604197 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.30850e7 | + | 8.75716e6i | −2.98269 | + | 0.357391i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.58886e6i | − | 0.105072i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.69233e7i | − | 1.08670i | −0.839506 | − | 0.543350i | \(-0.817156\pi\) | ||
0.839506 | − | 0.543350i | \(-0.182844\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.97613e6 | − | 8.12776e6i | −0.0793244 | − | 0.326258i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.27099e7 | 1.30582 | 0.652910 | − | 0.757435i | \(-0.273548\pi\) | ||||
0.652910 | + | 0.757435i | \(0.273548\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.18335e6 | −0.166091 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.96260e6 | + | 3.30709e7i | 0.156469 | + | 1.30585i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.13803e6i | 0.0839636i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.99356e7i | 0.778648i | 0.921101 | + | 0.389324i | \(0.127291\pi\) | ||||
−0.921101 | + | 0.389324i | \(0.872709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.10662e6 | + | 9.23558e6i | 0.0429883 | + | 0.358769i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.90140e7 | −1.89372 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −53320.6 | −0.00204899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.61924e6 | − | 6.65989e6i | −0.0618889 | − | 0.254547i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 6.13766e6i | − | 0.233326i | −0.993172 | − | 0.116663i | \(-0.962780\pi\) | ||
0.993172 | − | 0.116663i | \(-0.0372198\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.41805e7i | 1.29242i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.43078e7 | − | 5.30903e6i | 1.66639 | − | 0.199669i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −267170. | −0.00999444 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.01876e7 | 0.751166 | 0.375583 | − | 0.926789i | \(-0.377443\pi\) | ||||
0.375583 | + | 0.926789i | \(0.377443\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.37494e7 | + | 2.84569e6i | −0.879000 | + | 0.105323i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.23966e7i | 1.56083i | 0.625259 | + | 0.780417i | \(0.284993\pi\) | ||||
−0.625259 | + | 0.780417i | \(0.715007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.42277e7i | 1.98583i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.47824e7 | + | 1.67417e7i | −1.63128 | + | 0.609847i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.58224e6 | −0.166036 | −0.0830181 | − | 0.996548i | \(-0.526456\pi\) | ||||
−0.0830181 | + | 0.996548i | \(0.526456\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.04392e6 | 0.0736713 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.18035e6 | + | 5.15796e7i | 0.221596 | + | 1.84938i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 2.70977e7i | − | 0.966498i | −0.875483 | − | 0.483249i | \(-0.839457\pi\) | ||
0.875483 | − | 0.483249i | \(-0.160543\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.19066e6i | 0.113207i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −63099.1 | − | 526609.i | −0.00222712 | − | 0.0185870i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.31481e7 | 1.16389 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.84496e7 | 0.993730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.96012e6 | − | 2.42164e6i | 0.346098 | − | 0.0841481i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 1.44046e7i | − | 0.497947i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.22367e7i | 0.764724i | 0.924013 | + | 0.382362i | \(0.124889\pi\) | ||||
−0.924013 | + | 0.382362i | \(0.875111\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.00106e6 | + | 239770.i | −0.0684620 | + | 0.00820323i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.88599e7 | 1.32267 | 0.661337 | − | 0.750089i | \(-0.269989\pi\) | ||||
0.661337 | + | 0.750089i | \(0.269989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.40794e7 | 1.15401 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 60074.8 | − | 7198.26i | 0.00202386 | − | 0.000242502i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.97266e7i | 1.33151i | 0.746169 | + | 0.665756i | \(0.231891\pi\) | ||||
−0.746169 | + | 0.665756i | \(0.768109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.63459e6i | 0.154545i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.09647e7 | − | 5.09724e6i | 0.695532 | − | 0.169107i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.21692e6 | 0.238215 | 0.119107 | − | 0.992881i | \(-0.461997\pi\) | ||||
0.119107 | + | 0.992881i | \(0.461997\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.93687e7 | 1.29289 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.02949e6 | − | 4.19748e7i | −0.164335 | − | 1.37150i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.83410e7i | 2.54682i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.46570e7i | 0.797545i | 0.917050 | + | 0.398773i | \(0.130564\pi\) | ||||
−0.917050 | + | 0.398773i | \(0.869436\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.74875e6 | + | 3.12861e7i | 0.120646 | + | 1.00688i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.44993e7 | −0.464291 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.96664e7 | 0.626596 | 0.313298 | − | 0.949655i | \(-0.398566\pi\) | ||||
0.313298 | + | 0.949655i | \(0.398566\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.87798e7 | + | 1.44977e7i | −1.22940 | + | 0.459606i |
(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 | 384.6.c.a.383.19 | ✓ | 20 | |
3.2 | odd | 2 | 384.6.c.d.383.1 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.d.383.2 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.b.383.19 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.c.383.2 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.a.383.20 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.b.383.20 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.c.383.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.19 | ✓ | 20 | 1.1 | even | 1 | trivial | |
384.6.c.a.383.20 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.b.383.19 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.b.383.20 | yes | 20 | 24.5 | odd | 2 | ||
384.6.c.c.383.1 | yes | 20 | 24.11 | even | 2 | ||
384.6.c.c.383.2 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.d.383.1 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.d.383.2 | yes | 20 | 4.3 | odd | 2 |