Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(1,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.a (trivial) |
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: | yes |
Analytic conductor: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 140x^{2} - 84x + 3103 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.80512\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(3\) | −25.7605 | −1.65254 | −0.826270 | − | 0.563274i | \(-0.809541\pi\) | ||||
−0.826270 | + | 0.563274i | \(0.809541\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −109.245 | −1.95424 | −0.977118 | − | 0.212696i | \(-0.931776\pi\) | ||||
−0.977118 | + | 0.212696i | \(0.931776\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −177.299 | −1.36761 | −0.683804 | − | 0.729666i | \(-0.739676\pi\) | ||||
−0.683804 | + | 0.729666i | \(0.739676\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 420.606 | 1.73089 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 228.019 | 0.568184 | 0.284092 | − | 0.958797i | \(-0.408308\pi\) | ||||
0.284092 | + | 0.958797i | \(0.408308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −476.072 | −0.781293 | −0.390647 | − | 0.920541i | \(-0.627749\pi\) | ||||
−0.390647 | + | 0.920541i | \(0.627749\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2814.22 | 3.22945 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1868.17 | −1.56781 | −0.783905 | − | 0.620880i | \(-0.786775\pi\) | ||||
−0.783905 | + | 0.620880i | \(0.786775\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −361.000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4567.32 | 2.26003 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1966.09 | 0.774967 | 0.387483 | − | 0.921877i | \(-0.373344\pi\) | ||||
0.387483 | + | 0.921877i | \(0.373344\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8809.50 | 2.81904 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4575.23 | −1.20782 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4201.04 | −0.927602 | −0.463801 | − | 0.885939i | \(-0.653515\pi\) | ||||
−0.463801 | + | 0.885939i | \(0.653515\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3842.27 | −0.718097 | −0.359048 | − | 0.933319i | \(-0.616899\pi\) | ||||
−0.359048 | + | 0.933319i | \(0.616899\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5873.90 | −0.938948 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 19369.1 | 2.67263 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −15414.3 | −1.85106 | −0.925528 | − | 0.378678i | \(-0.876379\pi\) | ||||
−0.925528 | + | 0.378678i | \(0.876379\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 12263.9 | 1.29112 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1927.41 | 0.179067 | 0.0895334 | − | 0.995984i | \(-0.471462\pi\) | ||||
0.0895334 | + | 0.995984i | \(0.471462\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7330.22 | −0.604569 | −0.302284 | − | 0.953218i | \(-0.597749\pi\) | ||||
−0.302284 | + | 0.953218i | \(0.597749\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −45949.2 | −3.38257 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5080.98 | 0.335508 | 0.167754 | − | 0.985829i | \(-0.446349\pi\) | ||||
0.167754 | + | 0.985829i | \(0.446349\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14628.0 | 0.870351 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 48125.0 | 2.59087 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −12616.1 | −0.616929 | −0.308465 | − | 0.951236i | \(-0.599815\pi\) | ||||
−0.308465 | + | 0.951236i | \(0.599815\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −24910.0 | −1.11037 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9299.56 | 0.379119 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7718.28 | 0.288663 | 0.144331 | − | 0.989529i | \(-0.453897\pi\) | ||||
0.144331 | + | 0.989529i | \(0.453897\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17993.0 | −0.619127 | −0.309564 | − | 0.950879i | \(-0.600183\pi\) | ||||
−0.309564 | + | 0.950879i | \(0.600183\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −74573.1 | −2.36718 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 52008.5 | 1.52683 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10746.2 | 0.292460 | 0.146230 | − | 0.989251i | \(-0.453286\pi\) | ||||
0.146230 | + | 0.989251i | \(0.453286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −50647.5 | −1.28066 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 50642.8 | 1.19226 | 0.596132 | − | 0.802887i | \(-0.296704\pi\) | ||||
0.596132 | + | 0.802887i | \(0.296704\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −58036.2 | −1.27465 | −0.637326 | − | 0.770594i | \(-0.719960\pi\) | ||||
−0.637326 | + | 0.770594i | \(0.719960\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −226938. | −4.65858 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −40427.6 | −0.777054 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 33913.4 | 0.611369 | 0.305685 | − | 0.952133i | \(-0.401115\pi\) | ||||
0.305685 | + | 0.952133i | \(0.401115\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 15653.1 | 0.265087 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 30761.3 | 0.490128 | 0.245064 | − | 0.969507i | \(-0.421191\pi\) | ||||
0.245064 | + | 0.969507i | \(0.421191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 204088. | 3.06387 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 108221. | 1.53290 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 97641.2 | 1.30665 | 0.653323 | − | 0.757079i | \(-0.273374\pi\) | ||||
0.653323 | + | 0.757079i | \(0.273374\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 84407.1 | 1.06850 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 98978.9 | 1.18668 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 39437.5 | 0.448333 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 105569. | 1.13922 | 0.569609 | − | 0.821916i | \(-0.307095\pi\) | ||||
0.569609 | + | 0.821916i | \(0.307095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 95906.1 | 0.983464 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −70055.6 | −0.683344 | −0.341672 | − | 0.939819i | \(-0.610993\pi\) | ||||
−0.341672 | + | 0.939819i | \(0.610993\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29196.8 | 0.271171 | 0.135585 | − | 0.990766i | \(-0.456709\pi\) | ||||
0.135585 | + | 0.990766i | \(0.456709\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −498958. | −4.41663 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −83750.0 | −0.707173 | −0.353586 | − | 0.935402i | \(-0.615038\pi\) | ||||
−0.353586 | + | 0.935402i | \(0.615038\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −51998.8 | −0.419206 | −0.209603 | − | 0.977787i | \(-0.567217\pi\) | ||||
−0.209603 | + | 0.977787i | \(0.567217\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 397081. | 3.05895 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 174906. | 1.28857 | 0.644287 | − | 0.764784i | \(-0.277154\pi\) | ||||
0.644287 | + | 0.764784i | \(0.277154\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −214785. | −1.51447 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −200239. | −1.35233 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 331225. | 2.14415 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −109058. | −0.677166 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −49651.2 | −0.295915 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −621005. | −3.55484 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10574.2 | −0.0581755 | −0.0290878 | − | 0.999577i | \(-0.509260\pi\) | ||||
−0.0290878 | + | 0.999577i | \(0.509260\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 188830. | 0.999074 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 38671.2 | 0.196884 | 0.0984418 | − | 0.995143i | \(-0.468614\pi\) | ||||
0.0984418 | + | 0.995143i | \(0.468614\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 64005.0 | 0.313751 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 499821. | 2.36037 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 85272.3 | 0.388156 | 0.194078 | − | 0.980986i | \(-0.437828\pi\) | ||||
0.194078 | + | 0.980986i | \(0.437828\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −198686. | −0.872230 | −0.436115 | − | 0.899891i | \(-0.643646\pi\) | ||||
−0.436115 | + | 0.899891i | \(0.643646\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −130889. | −0.554440 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −108553. | −0.443919 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 458943. | 1.81275 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −376825. | −1.43829 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −81459.5 | −0.300591 | −0.150295 | − | 0.988641i | \(-0.548023\pi\) | ||||
−0.150295 | + | 0.988641i | \(0.548023\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −517065. | −1.84545 | −0.922727 | − | 0.385455i | \(-0.874045\pi\) | ||||
−0.922727 | + | 0.385455i | \(0.874045\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −785763. | −2.71371 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 419749. | 1.40333 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 169444. | 0.548627 | 0.274314 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274314 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 324998. | 1.01950 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −348585. | −1.05985 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −116429. | −0.343234 | −0.171617 | − | 0.985164i | \(-0.554899\pi\) | ||||
−0.171617 | + | 0.985164i | \(0.554899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 641695. | 1.83493 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9810.91 | −0.0272219 | −0.0136109 | − | 0.999907i | \(-0.504333\pi\) | ||||
−0.0136109 | + | 0.999907i | \(0.504333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −144649. | −0.389581 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −151839. | −0.397093 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 191280. | 0.485908 | 0.242954 | − | 0.970038i | \(-0.421884\pi\) | ||||
0.242954 | + | 0.970038i | \(0.421884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.56192e6 | −3.85534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −198827. | −0.477027 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 631191. | 1.47241 | 0.736204 | − | 0.676759i | \(-0.236616\pi\) | ||||
0.736204 | + | 0.676759i | \(0.236616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −119770. | −0.271739 | −0.135870 | − | 0.990727i | \(-0.543383\pi\) | ||||
−0.135870 | + | 0.990727i | \(0.543383\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 463511. | 1.02313 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.68394e6 | 3.61740 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −425978. | −0.890806 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 811184. | 1.65183 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −942206. | −1.86880 | −0.934400 | − | 0.356226i | \(-0.884063\pi\) | ||||
−0.934400 | + | 0.356226i | \(0.884063\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −560559. | −1.08325 | −0.541624 | − | 0.840621i | \(-0.682190\pi\) | ||||
−0.541624 | + | 0.840621i | \(0.682190\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.33977e6 | −2.52315 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 792520. | 1.45494 | 0.727469 | − | 0.686140i | \(-0.240696\pi\) | ||||
0.727469 | + | 0.686140i | \(0.240696\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 477931. | 0.855524 | 0.427762 | − | 0.903891i | \(-0.359302\pi\) | ||||
0.427762 | + | 0.903891i | \(0.359302\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −276827. | −0.483301 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 744840. | 1.26860 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −210561. | −0.349939 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 826948. | 1.34138 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −82314.9 | −0.130350 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.09610e6 | −1.69490 | −0.847451 | − | 0.530874i | \(-0.821864\pi\) | ||||
−0.847451 | + | 0.530874i | \(0.821864\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.30459e6 | −1.97026 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 800791. | 1.18147 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 681230. | 0.982075 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.49504e6 | 2.10641 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 889382. | 1.22492 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −78676.4 | −0.105945 | −0.0529727 | − | 0.998596i | \(-0.516870\pi\) | ||||
−0.0529727 | + | 0.998596i | \(0.516870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.70533e6 | 4.87945 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −965468. | −1.24358 | −0.621789 | − | 0.783185i | \(-0.713594\pi\) | ||||
−0.621789 | + | 0.783185i | \(0.713594\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 837329. | 1.05513 | 0.527566 | − | 0.849514i | \(-0.323105\pi\) | ||||
0.527566 | + | 0.849514i | \(0.323105\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.04144e6 | 1.28411 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −881429. | −1.06365 | −0.531824 | − | 0.846855i | \(-0.678493\pi\) | ||||
−0.531824 | + | 0.846855i | \(0.678493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −555072. | −0.655662 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −873628. | −1.01031 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 298682. | 0.338232 | 0.169116 | − | 0.985596i | \(-0.445909\pi\) | ||||
0.169116 | + | 0.985596i | \(0.445909\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.04452e6 | −1.15844 | −0.579219 | − | 0.815172i | \(-0.696643\pi\) | ||||
−0.579219 | + | 0.815172i | \(0.696643\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 708547. | 0.769756 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.59804e6 | −1.70087 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 171862. | 0.179241 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −792427. | −0.809955 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.10873e6 | 1.11082 | 0.555408 | − | 0.831578i | \(-0.312562\pi\) | ||||
0.555408 | + | 0.831578i | \(0.312562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 448305. | 0.440324 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.25743e6 | −5.06317 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −83101.8 | −0.0784834 | −0.0392417 | − | 0.999230i | \(-0.512494\pi\) | ||||
−0.0392417 | + | 0.999230i | \(0.512494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.73294e6 | 2.53152 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.76698e6 | −1.60558 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.75925e6 | −1.56833 | −0.784167 | − | 0.620550i | \(-0.786909\pi\) | ||||
−0.784167 | + | 0.620550i | \(0.786909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.37825e6 | 1.20563 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.51529e6 | −2.15929 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 524521. | 0.441959 | 0.220980 | − | 0.975278i | \(-0.429075\pi\) | ||||
0.220980 | + | 0.975278i | \(0.429075\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 761057. | 0.629498 | 0.314749 | − | 0.949175i | \(-0.398080\pi\) | ||||
0.314749 | + | 0.949175i | \(0.398080\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.17437e6 | −1.76574 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00873e6 | 1.60174 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −349747. | −0.273877 | −0.136938 | − | 0.990580i | \(-0.543726\pi\) | ||||
−0.136938 | + | 0.990580i | \(0.543726\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.61608e6 | −1.24295 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.71890e6 | 1.29863 | 0.649314 | − | 0.760520i | \(-0.275056\pi\) | ||||
0.649314 | + | 0.760520i | \(0.275056\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −654088. | −0.485479 | −0.242739 | − | 0.970092i | \(-0.578046\pi\) | ||||
−0.242739 | + | 0.970092i | \(0.578046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.01593e6 | −0.740888 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −341729. | −0.244893 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.07020e6 | 1.45803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.71951e6 | −1.88260 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.93430e6 | 1.31630 | 0.658152 | − | 0.752885i | \(-0.271339\pi\) | ||||
0.658152 | + | 0.752885i | \(0.271339\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −843185. | −0.564115 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.04324e6 | −0.686266 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −935998. | −0.605476 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.29964e6 | 0.826813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.80467e6 | 1.12925 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.96565e6 | 1.20992 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.65795e6 | 1.00398 | 0.501992 | − | 0.864872i | \(-0.332601\pi\) | ||||
0.501992 | + | 0.864872i | \(0.332601\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −752126. | −0.448120 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −794581. | −0.465840 | −0.232920 | − | 0.972496i | \(-0.574828\pi\) | ||||
−0.232920 | + | 0.972496i | \(0.574828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.21582e6 | −1.27842 | −0.639211 | − | 0.769032i | \(-0.720739\pi\) | ||||
−0.639211 | + | 0.769032i | \(0.720739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8.14675e6 | 4.62602 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.59381e6 | −0.890815 | −0.445408 | − | 0.895328i | \(-0.646941\pi\) | ||||
−0.445408 | + | 0.895328i | \(0.646941\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −957916. | −0.527049 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.15745e6 | 1.16863 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 674409. | 0.359681 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.19396e6 | −2.20250 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.33952e6 | 0.692754 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −900853. | −0.458843 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.22458e6 | 1.61772 | 0.808860 | − | 0.588001i | \(-0.200085\pi\) | ||||
0.808860 | + | 0.588001i | \(0.200085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.48335e6 | −3.20397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.17397e6 | −0.571536 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.24462e6 | 0.596982 | 0.298491 | − | 0.954412i | \(-0.403517\pi\) | ||||
0.298491 | + | 0.954412i | \(0.403517\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.50568e6 | −2.12942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −876109. | −0.408012 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 386336. | 0.177309 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.53299e6 | 2.50272 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −324910. | −0.144857 | −0.0724284 | − | 0.997374i | \(-0.523075\pi\) | ||||
−0.0724284 | + | 0.997374i | \(0.523075\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 337444. | 0.148299 | 0.0741495 | − | 0.997247i | \(-0.476376\pi\) | ||||
0.0741495 | + | 0.997247i | \(0.476376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.17814e6 | 0.943663 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.80025e6 | 1.19608 | 0.598039 | − | 0.801467i | \(-0.295947\pi\) | ||||
0.598039 | + | 0.801467i | \(0.295947\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.53249e6 | −2.32997 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.53253e6 | −3.54329 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.26867e6 | −1.33855 | −0.669275 | − | 0.743015i | \(-0.733395\pi\) | ||||
−0.669275 | + | 0.743015i | \(0.733395\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.80940e6 | 1.11904 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.34017e6 | 2.49097 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.37614e6 | −1.69600 | −0.848001 | − | 0.529995i | \(-0.822194\pi\) | ||||
−0.848001 | + | 0.529995i | \(0.822194\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 810681. | 0.309945 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.23682e6 | 0.843717 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 385783. | 0.143572 | 0.0717862 | − | 0.997420i | \(-0.477130\pi\) | ||||
0.0717862 | + | 0.997420i | \(0.477130\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.59974e7 | 5.87451 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.00000e6 | 0.724729 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.75351e6 | 0.984665 | 0.492333 | − | 0.870407i | \(-0.336144\pi\) | ||||
0.492333 | + | 0.870407i | \(0.336144\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 272398. | 0.0961374 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.67232e6 | 1.97589 | 0.987947 | − | 0.154792i | \(-0.0494709\pi\) | ||||
0.987947 | + | 0.154792i | \(0.0494709\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.41652e6 | 1.51855 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.08313e6 | −1.04644 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.22486e6 | 1.41559 | 0.707797 | − | 0.706416i | \(-0.249689\pi\) | ||||
0.707797 | + | 0.706416i | \(0.249689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.67298e6 | −1.21500 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −996192. | −0.325358 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.70487e6 | −1.19476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.60192e6 | −0.510110 | −0.255055 | − | 0.966927i | \(-0.582094\pi\) | ||||
−0.255055 | + | 0.966927i | \(0.582094\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.64880e6 | −0.518486 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −584352. | −0.181474 | −0.0907369 | − | 0.995875i | \(-0.528922\pi\) | ||||
−0.0907369 | + | 0.995875i | \(0.528922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.82919e6 | 0.561044 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.71003e6 | −0.518042 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.51476e6 | −1.05174 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.70400e6 | −0.503687 | −0.251844 | − | 0.967768i | \(-0.581037\pi\) | ||||
−0.251844 | + | 0.967768i | \(0.581037\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.19666e6 | −0.641444 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.36845e6 | −0.394777 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.36052e6 | −0.957825 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.11827e6 | 1.44139 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −42813.6 | −0.0119137 | −0.00595684 | − | 0.999982i | \(-0.501896\pi\) | ||||
−0.00595684 | + | 0.999982i | \(0.501896\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.45775e6 | −1.22577 | −0.612887 | − | 0.790170i | \(-0.709992\pi\) | ||||
−0.612887 | + | 0.790170i | \(0.709992\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.13709e6 | 0.580727 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.64576e7 | −4.41972 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.19015e6 | 0.846724 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.79640e6 | 0.733593 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 127317. | 0.0330136 | 0.0165068 | − | 0.999864i | \(-0.494745\pi\) | ||||
0.0165068 | + | 0.999864i | \(0.494745\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.00930e6 | 1.79661 | 0.898307 | − | 0.439369i | \(-0.144798\pi\) | ||||
0.898307 | + | 0.439369i | \(0.144798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.18226e7 | −2.99565 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −709757. | −0.177790 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.17533e6 | 1.03402 | 0.517011 | − | 0.855979i | \(-0.327045\pi\) | ||||
0.517011 | + | 0.855979i | \(0.327045\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.15262e6 | 1.50648 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 529129. | 0.128101 | 0.0640504 | − | 0.997947i | \(-0.479598\pi\) | ||||
0.0640504 | + | 0.997947i | \(0.479598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.06668e7 | −2.55350 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.09844e6 | 0.496739 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.14414e6 | −0.501924 | −0.250962 | − | 0.967997i | \(-0.580747\pi\) | ||||
−0.250962 | + | 0.967997i | \(0.580747\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 439487. | 0.101743 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.33199e7 | 3.04969 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.22107e6 | −2.08811 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.90778e6 | −1.54721 | −0.773603 | − | 0.633670i | \(-0.781548\pi\) | ||||
−0.773603 | + | 0.633670i | \(0.781548\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.54729e6 | 1.89364 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.58026e6 | −1.44208 | −0.721042 | − | 0.692891i | \(-0.756336\pi\) | ||||
−0.721042 | + | 0.692891i | \(0.756336\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.91768e6 | 1.49971 | 0.749856 | − | 0.661601i | \(-0.230123\pi\) | ||||
0.749856 | + | 0.661601i | \(0.230123\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.08130e7 | −2.31906 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.45033e6 | 0.307734 | 0.153867 | − | 0.988092i | \(-0.450827\pi\) | ||||
0.153867 | + | 0.988092i | \(0.450827\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.90528e6 | −0.399970 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.36497e6 | −0.906629 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.67143e6 | −0.343507 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.18023e6 | −0.646732 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.30641e6 | −1.06784 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.81138e6 | 0.360720 | 0.180360 | − | 0.983601i | \(-0.442274\pi\) | ||||
0.180360 | + | 0.983601i | \(0.442274\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.33832e6 | 1.44622 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 8.97975e6 | 1.75145 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.15329e7 | −2.22630 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.19793e6 | 0.419944 | 0.209972 | − | 0.977707i | \(-0.432663\pi\) | ||||
0.209972 | + | 0.977707i | \(0.432663\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.99927e6 | 0.567209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.64236e6 | 1.43062 | 0.715310 | − | 0.698808i | \(-0.246286\pi\) | ||||
0.715310 | + | 0.698808i | \(0.246286\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.84825e6 | 1.45430 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.04773e7 | −1.92192 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.97893e6 | −1.63055 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.96363e6 | −0.353028 | −0.176514 | − | 0.984298i | \(-0.556482\pi\) | ||||
−0.176514 | + | 0.984298i | \(0.556482\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 252734. | 0.0449852 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5.51813e6 | −0.972460 | −0.486230 | − | 0.873831i | \(-0.661628\pi\) | ||||
−0.486230 | + | 0.873831i | \(0.661628\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.65323e6 | 1.33542 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.72623e6 | 0.643798 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.59852e6 | −0.444562 | −0.222281 | − | 0.974983i | \(-0.571350\pi\) | ||||
−0.222281 | + | 0.974983i | \(0.571350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.02898e7 | 1.74322 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.65166e6 | 0.277094 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.18961e6 | −0.529932 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.15856e6 | 0.190630 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.92747e6 | −0.802982 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −665007. | −0.107333 | −0.0536664 | − | 0.998559i | \(-0.517091\pi\) | ||||
−0.0536664 | + | 0.998559i | \(0.517091\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.70303e6 | −0.432113 | −0.216057 | − | 0.976381i | \(-0.569320\pi\) | ||||
−0.216057 | + | 0.976381i | \(0.569320\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.02359e7 | 6.37111 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.17800e6 | 1.12584 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.57085e6 | −0.399427 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.24636e6 | 0.499643 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −917587. | −0.139904 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.14929e6 | 1.38198 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.62598e7 | −2.43321 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.33546e6 | 0.494520 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.58822e6 | 1.40846 | 0.704230 | − | 0.709972i | \(-0.251292\pi\) | ||||
0.704230 | + | 0.709972i | \(0.251292\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.08535e6 | 0.449060 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.68062e6 | 0.819227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.05846e7 | 1.51254 | 0.756268 | − | 0.654261i | \(-0.227020\pi\) | ||||
0.756268 | + | 0.654261i | \(0.227020\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.56798e6 | −1.07164 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.51657e6 | 0.212806 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.01282e6 | −0.836113 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.33792e7 | −5.97790 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.71496e6 | −0.643932 | −0.321966 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321966 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.48971e6 | 0.472346 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.09734e7 | 1.47209 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.60502e6 | −1.27711 | −0.638554 | − | 0.769577i | \(-0.720467\pi\) | ||||
−0.638554 | + | 0.769577i | \(0.720467\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.91077e7 | −2.51818 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.77528e6 | −0.362535 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.97008e6 | −0.902521 | −0.451260 | − | 0.892392i | \(-0.649025\pi\) | ||||
−0.451260 | + | 0.892392i | \(0.649025\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.27949e6 | −0.677644 | −0.338822 | − | 0.940851i | \(-0.610028\pi\) | ||||
−0.338822 | + | 0.940851i | \(0.610028\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.42718e7 | 3.08827 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.73202e7 | 2.18466 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.01323e7 | 1.26697 | 0.633486 | − | 0.773754i | \(-0.281623\pi\) | ||||
0.633486 | + | 0.773754i | \(0.281623\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.44403e7 | 1.79011 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.45395e6 | −0.670302 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.87671e6 | −0.350530 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.18751e7 | 2.64278 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.91129e6 | 0.947659 | 0.473830 | − | 0.880617i | \(-0.342871\pi\) | ||||
0.473830 | + | 0.880617i | \(0.342871\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.38706e6 | 0.164743 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.04158e7 | −2.40434 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.98912e6 | −1.04974 | −0.524869 | − | 0.851183i | \(-0.675886\pi\) | ||||
−0.524869 | + | 0.851183i | \(0.675886\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.61847e7 | −4.19018 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.23118e7 | −1.41379 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.04333e6 | 1.02982 | 0.514910 | − | 0.857244i | \(-0.327825\pi\) | ||||
0.514910 | + | 0.857244i | \(0.327825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.48341e6 | 0.958042 | 0.479021 | − | 0.877803i | \(-0.340992\pi\) | ||||
0.479021 | + | 0.877803i | \(0.340992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.51990e6 | 0.506215 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.19141e7 | 1.32334 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.37916e7 | 1.51930 | 0.759650 | − | 0.650332i | \(-0.225370\pi\) | ||||
0.759650 | + | 0.650332i | \(0.225370\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.91875e7 | −2.09640 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.41891e6 | −0.262130 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.69314e6 | −0.934384 | −0.467192 | − | 0.884156i | \(-0.654734\pi\) | ||||
−0.467192 | + | 0.884156i | \(0.654734\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.42415e6 | 0.578288 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.63565e6 | 0.278725 | 0.139362 | − | 0.990241i | \(-0.455495\pi\) | ||||
0.139362 | + | 0.990241i | \(0.455495\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.47325e7 | −1.54543 | −0.772717 | − | 0.634751i | \(-0.781103\pi\) | ||||
−0.772717 | + | 0.634751i | \(0.781103\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.99529e6 | −0.936022 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73117e7 | −1.78698 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.03120e7 | 4.12795 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.12048e6 | 0.215409 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.87965e7 | 2.90211 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.04039e6 | 0.204005 | 0.102002 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102002 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.82362e7 | 2.80089 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.15519e6 | 0.113689 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.96397e6 | −0.679999 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.13007e7 | 2.06368 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.92090e6 | 0.569171 | 0.284585 | − | 0.958651i | \(-0.408144\pi\) | ||||
0.284585 | + | 0.958651i | \(0.408144\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.71800e6 | 0.831552 | 0.415776 | − | 0.909467i | \(-0.363510\pi\) | ||||
0.415776 | + | 0.909467i | \(0.363510\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.06288e7 | −1.95243 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.96829e7 | −1.84854 | −0.924269 | − | 0.381742i | \(-0.875324\pi\) | ||||
−0.924269 | + | 0.381742i | \(0.875324\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.75992e6 | 0.164014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.75489e7 | −1.62292 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.87843e6 | −0.447710 | −0.223855 | − | 0.974622i | \(-0.571864\pi\) | ||||
−0.223855 | + | 0.974622i | \(0.571864\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.22464e6 | −0.384757 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.44104e7 | −2.20628 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.08130e7 | 0.969908 | 0.484954 | − | 0.874540i | \(-0.338836\pi\) | ||||
0.484954 | + | 0.874540i | \(0.338836\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.22290e6 | 0.375930 | 0.187965 | − | 0.982176i | \(-0.439811\pi\) | ||||
0.187965 | + | 0.982176i | \(0.439811\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.29110e7 | −2.02423 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.99224e6 | −0.613143 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.25960e6 | −0.718860 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.02675e6 | 0.175079 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.10276e6 | −0.351779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.79237e6 | −0.407861 | −0.203931 | − | 0.978985i | \(-0.565372\pi\) | ||||
−0.203931 | + | 0.978985i | \(0.565372\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.03055e7 | −3.40490 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.20013e6 | −0.687621 | −0.343810 | − | 0.939039i | \(-0.611718\pi\) | ||||
−0.343810 | + | 0.939039i | \(0.611718\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.87173e7 | −1.55800 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.48710e7 | 2.05506 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.11848e6 | −0.0917438 | −0.0458719 | − | 0.998947i | \(-0.514607\pi\) | ||||
−0.0458719 | + | 0.998947i | \(0.514607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.31559e6 | −0.758549 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.15700e7 | −1.74365 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.00617e6 | 0.482003 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.53615e6 | −0.202060 | −0.101030 | − | 0.994883i | \(-0.532214\pi\) | ||||
−0.101030 | + | 0.994883i | \(0.532214\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.70041e7 | −1.34499 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.17055e7 | 1.70454 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.60073e6 | −0.280743 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.27061e7 | 1.75772 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.13234e7 | −1.63893 | −0.819466 | − | 0.573128i | \(-0.805730\pi\) | ||||
−0.819466 | + | 0.573128i | \(0.805730\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.56457e6 | 0.424662 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.42990e7 | 1.08351 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.24208e7 | 0.934546 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.73372e6 | 0.727216 | 0.363608 | − | 0.931552i | \(-0.381545\pi\) | ||||
0.363608 | + | 0.931552i | \(0.381545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.42642e7 | 1.05821 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.55423e6 | −0.556501 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.18589e7 | 0.867522 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.69422e6 | −0.558942 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.68007e6 | −0.121200 | −0.0606002 | − | 0.998162i | \(-0.519301\pi\) | ||||
−0.0606002 | + | 0.998162i | \(0.519301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.17657e6 | −0.370855 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.69073e7 | 1.91437 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.70091e7 | −2.61495 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.18408e7 | −0.830891 | −0.415445 | − | 0.909618i | \(-0.636374\pi\) | ||||
−0.415445 | + | 0.909618i | \(0.636374\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.20563e7 | −1.53714 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.36941e7 | 0.947850 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.38510e6 | −0.507688 | −0.253844 | − | 0.967245i | \(-0.581695\pi\) | ||||
−0.253844 | + | 0.967245i | \(0.581695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.11663e7 | 2.81076 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.45033e6 | 0.166171 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.54272e7 | 1.71272 | 0.856361 | − | 0.516377i | \(-0.172720\pi\) | ||||
0.856361 | + | 0.516377i | \(0.172720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.42726e6 | −0.296203 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.96141e7 | 1.30345 | 0.651727 | − | 0.758454i | \(-0.274045\pi\) | ||||
0.651727 | + | 0.758454i | \(0.274045\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.89905e6 | 0.587426 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.29384e7 | 0.848356 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.48488e7 | 0.967135 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.53430e6 | −0.0992685 | −0.0496342 | − | 0.998767i | \(-0.515806\pi\) | ||||
−0.0496342 | + | 0.998767i | \(0.515806\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.85615e7 | −1.83567 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.64869e7 | 3.60645 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.20770e6 | −0.0765984 | −0.0382992 | − | 0.999266i | \(-0.512194\pi\) | ||||
−0.0382992 | + | 0.999266i | \(0.512194\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.15486e7 | −0.727653 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.52116e7 | −0.952165 | −0.476082 | − | 0.879401i | \(-0.657944\pi\) | ||||
−0.476082 | + | 0.879401i | \(0.657944\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.21934e6 | 0.573309 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 8.58408e7 | 5.30322 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.67446e6 | −0.225530 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.34827e6 | −0.204176 | −0.102088 | − | 0.994775i | \(-0.532552\pi\) | ||||
−0.102088 | + | 0.994775i | \(0.532552\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.14075e6 | 0.129697 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.37017e7 | 0.824758 | 0.412379 | − | 0.911012i | \(-0.364698\pi\) | ||||
0.412379 | + | 0.911012i | \(0.364698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.38485e7 | −2.02435 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.04021e7 | −4.18344 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −695796. | −0.0410807 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.15475e7 | 0.677426 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92207e7 | 1.12038 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.85110e7 | −1.07215 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.18608e7 | 1.25814 | 0.629070 | − | 0.777349i | \(-0.283436\pi\) | ||||
0.629070 | + | 0.777349i | \(0.283436\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.53193e7 | 2.59173 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.10108e7 | −1.76226 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.56598e6 | 0.483720 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.55044e7 | −1.99234 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.36301e6 | −0.466355 | −0.233177 | − | 0.972434i | \(-0.574912\pi\) | ||||
−0.233177 | + | 0.972434i | \(0.574912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.49212e6 | −0.526013 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.10685e7 | 2.26166 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.32334e7 | −0.724238 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.80813e7 | 2.07120 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.35120e7 | −0.730355 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.37307e6 | −0.127479 | −0.0637396 | − | 0.997967i | \(-0.520303\pi\) | ||||
−0.0637396 | + | 0.997967i | \(0.520303\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.18207e7 | −1.16498 | −0.582489 | − | 0.812839i | \(-0.697921\pi\) | ||||
−0.582489 | + | 0.812839i | \(0.697921\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.96053e7 | −1.04027 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.27193e7 | 0.670761 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.64621e6 | 0.138698 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.55021e7 | 1.84946 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.63150e6 | −0.291586 | −0.145793 | − | 0.989315i | \(-0.546573\pi\) | ||||
−0.145793 | + | 0.989315i | \(0.546573\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.74886e7 | −1.41466 | −0.707331 | − | 0.706882i | \(-0.750101\pi\) | ||||
−0.707331 | + | 0.706882i | \(0.750101\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.17461e7 | −2.64693 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.53327e6 | 0.230488 | 0.115244 | − | 0.993337i | \(-0.463235\pi\) | ||||
0.115244 | + | 0.993337i | \(0.463235\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.86843e7 | −1.44963 | −0.724817 | − | 0.688942i | \(-0.758075\pi\) | ||||
−0.724817 | + | 0.688942i | \(0.758075\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.00968e6 | 0.452592 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.73276e7 | −1.36455 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.07179e6 | 0.0531980 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.75792e7 | 0.867334 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.47030e7 | 1.21156 | 0.605781 | − | 0.795632i | \(-0.292861\pi\) | ||||
0.605781 | + | 0.795632i | \(0.292861\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.86243e6 | −0.139555 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.42798e7 | −2.14604 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.58022e7 | 0.761334 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.93360e7 | 0.926098 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.68497e7 | 0.802273 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.03059e7 | −1.43451 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.47224e7 | 1.16337 | 0.581686 | − | 0.813414i | \(-0.302393\pi\) | ||||
0.581686 | + | 0.813414i | \(0.302393\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.65876e7 | 0.776014 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.44852e7 | −1.13881 | −0.569404 | − | 0.822058i | \(-0.692826\pi\) | ||||
−0.569404 | + | 0.822058i | \(0.692826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −6.62049e6 | −0.306131 | −0.153066 | − | 0.988216i | \(-0.548915\pi\) | ||||
−0.153066 | + | 0.988216i | \(0.548915\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.80312e6 | 0.404696 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.86778e6 | 0.0853687 | 0.0426843 | − | 0.999089i | \(-0.486409\pi\) | ||||
0.0426843 | + | 0.999089i | \(0.486409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.08964e7 | −0.949579 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.33294e7 | −2.40945 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.73290e6 | 0.347370 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.11594e6 | −0.228497 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.44029e7 | 1.97186 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.10104e8 | 4.86162 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.99625e7 | −1.31546 | −0.657732 | − | 0.753252i | \(-0.728484\pi\) | ||||
−0.657732 | + | 0.753252i | \(0.728484\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.98288e7 | −2.17524 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.53722e7 | 0.667261 | 0.333631 | − | 0.942704i | \(-0.391726\pi\) | ||||
0.333631 | + | 0.942704i | \(0.391726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.92079e7 | 1.69228 | 0.846139 | − | 0.532962i | \(-0.178921\pi\) | ||||
0.846139 | + | 0.532962i | \(0.178921\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.17209e7 | 0.932223 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.26437e7 | 0.539589 | 0.269795 | − | 0.962918i | \(-0.413044\pi\) | ||||
0.269795 | + | 0.962918i | \(0.413044\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.87481e6 | 0.0795613 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.56921e6 | 0.150618 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.83423e6 | −0.0769708 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.89546e7 | −2.87743 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.41118e7 | 1.00057 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.61415e7 | 0.666108 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.35690e7 | 0.967228 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.34795e7 | −1.36634 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.30843e7 | 0.531043 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.09717e7 | −0.846475 | −0.423238 | − | 0.906019i | \(-0.639106\pi\) | ||||
−0.423238 | + | 0.906019i | \(0.639106\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −2.94658e7 | −1.18279 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.60866e7 | −1.83983 | −0.919916 | − | 0.392114i | \(-0.871744\pi\) | ||||
−0.919916 | + | 0.392114i | \(0.871744\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.01416e6 | 0.278483 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.06363e7 | −1.99944 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.85637e6 | −0.269260 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.84244e6 | 0.228195 | 0.114097 | − | 0.993470i | \(-0.463602\pi\) | ||||
0.114097 | + | 0.993470i | \(0.463602\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.27098e7 | −1.65912 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.41096e7 | −0.931507 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.35792e8 | −5.21821 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.22804e7 | 0.469366 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.13555e7 | 0.811839 | 0.405919 | − | 0.913909i | \(-0.366951\pi\) | ||||
0.405919 | + | 0.913909i | \(0.366951\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.28071e6 | −0.199672 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.04688e7 | 0.769820 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.65360e7 | 1.74085 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.24265e7 | −0.462382 | −0.231191 | − | 0.972908i | \(-0.574262\pi\) | ||||
−0.231191 | + | 0.972908i | \(0.574262\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 5.70808e7 | 2.11264 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.44931e7 | 1.26987 | 0.634934 | − | 0.772566i | \(-0.281027\pi\) | ||||
0.634934 | + | 0.772566i | \(0.281027\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.78946e6 | 0.138771 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.86179e7 | −3.22806 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.32057e7 | 0.840853 | 0.420426 | − | 0.907327i | \(-0.361881\pi\) | ||||
0.420426 | + | 0.907327i | \(0.361881\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.76294e7 | 0.995877 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.10573e7 | 1.47211 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.54048e7 | −0.906116 | −0.453058 | − | 0.891481i | \(-0.649667\pi\) | ||||
−0.453058 | + | 0.891481i | \(0.649667\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.02931e8 | 3.65208 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.46765e7 | 0.870969 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.51187e7 | −0.530845 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.38662e7 | −0.484337 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.52258e7 | −1.22404 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.12384e7 | 2.11692 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.24428e6 | 0.180352 | 0.0901758 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901758 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.73731e7 | −0.594386 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.50453e7 | −1.53321 | −0.766605 | − | 0.642119i | \(-0.778055\pi\) | ||||
−0.766605 | + | 0.642119i | \(0.778055\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.52269e7 | 1.19287 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.08039e8 | 3.63972 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.97190e7 | −1.33126 | −0.665628 | − | 0.746284i | \(-0.731836\pi\) | ||||
−0.665628 | + | 0.746284i | \(0.731836\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.22641e7 | 0.742416 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.18710e7 | −0.725598 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.93498e7 | −1.95900 | −0.979502 | − | 0.201436i | \(-0.935439\pi\) | ||||
−0.979502 | + | 0.201436i | \(0.935439\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.65790e7 | −2.84329 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.32065e7 | 0.758257 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.44118e7 | −0.468521 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.53405e6 | 0.308385 | 0.154193 | − | 0.988041i | \(-0.450722\pi\) | ||||
0.154193 | + | 0.988041i | \(0.450722\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.30670e7 | −2.67335 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.22116e7 | −1.67190 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.39124e7 | 0.761878 | 0.380939 | − | 0.924600i | \(-0.375601\pi\) | ||||
0.380939 | + | 0.924600i | \(0.375601\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.05240e7 | 2.23575 |
(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 | 76.6.a.b.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 684.6.a.e.1.4 | 4 | |||
4.3 | odd | 2 | 304.6.a.k.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.a.b.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
304.6.a.k.1.4 | 4 | 4.3 | odd | 2 | |||
684.6.a.e.1.4 | 4 | 3.2 | odd | 2 |