Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,6,Mod(1,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.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: | \(72.1727189158\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 90) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −98.0000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −354.000 | −0.882108 | −0.441054 | − | 0.897481i | \(-0.645395\pi\) | ||||
−0.441054 | + | 0.897481i | \(0.645395\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −404.000 | −0.663014 | −0.331507 | − | 0.943453i | \(-0.607557\pi\) | ||||
−0.331507 | + | 0.943453i | \(0.607557\pi\) | |||||||
\(14\) | −392.000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 654.000 | 0.548852 | 0.274426 | − | 0.961608i | \(-0.411512\pi\) | ||||
0.274426 | + | 0.961608i | \(0.411512\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1796.00 | 1.14136 | 0.570680 | − | 0.821173i | \(-0.306680\pi\) | ||||
0.570680 | + | 0.821173i | \(0.306680\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1416.00 | −0.623744 | ||||||||
\(23\) | −1080.00 | −0.425701 | −0.212850 | − | 0.977085i | \(-0.568275\pi\) | ||||
−0.212850 | + | 0.977085i | \(0.568275\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1616.00 | −0.468822 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1568.00 | −0.377964 | ||||||||
\(29\) | 5754.00 | 1.27050 | 0.635250 | − | 0.772306i | \(-0.280897\pi\) | ||||
0.635250 | + | 0.772306i | \(0.280897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10196.0 | 1.90557 | 0.952787 | − | 0.303641i | \(-0.0982024\pi\) | ||||
0.952787 | + | 0.303641i | \(0.0982024\pi\) | |||||||
\(32\) | 1024.00 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2616.00 | 0.388097 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5552.00 | −0.666723 | −0.333361 | − | 0.942799i | \(-0.608183\pi\) | ||||
−0.333361 | + | 0.942799i | \(0.608183\pi\) | |||||||
\(38\) | 7184.00 | 0.807063 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12960.0 | 1.20405 | 0.602026 | − | 0.798476i | \(-0.294360\pi\) | ||||
0.602026 | + | 0.798476i | \(0.294360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8968.00 | 0.739647 | 0.369823 | − | 0.929102i | \(-0.379418\pi\) | ||||
0.369823 | + | 0.929102i | \(0.379418\pi\) | |||||||
\(44\) | −5664.00 | −0.441054 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4320.00 | −0.301016 | ||||||||
\(47\) | −5400.00 | −0.356574 | −0.178287 | − | 0.983979i | \(-0.557055\pi\) | ||||
−0.178287 | + | 0.983979i | \(0.557055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7203.00 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6464.00 | −0.331507 | ||||||||
\(53\) | 8214.00 | 0.401666 | 0.200833 | − | 0.979625i | \(-0.435635\pi\) | ||||
0.200833 | + | 0.979625i | \(0.435635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6272.00 | −0.267261 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 23016.0 | 0.898380 | ||||||||
\(59\) | −3954.00 | −0.147879 | −0.0739395 | − | 0.997263i | \(-0.523557\pi\) | ||||
−0.0739395 | + | 0.997263i | \(0.523557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 962.000 | 0.0331017 | 0.0165509 | − | 0.999863i | \(-0.494731\pi\) | ||||
0.0165509 | + | 0.999863i | \(0.494731\pi\) | |||||||
\(62\) | 40784.0 | 1.34744 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 17956.0 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 10464.0 | 0.274426 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 56148.0 | 1.32187 | 0.660935 | − | 0.750444i | \(-0.270160\pi\) | ||||
0.660935 | + | 0.750444i | \(0.270160\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 85690.0 | 1.88201 | 0.941007 | − | 0.338386i | \(-0.109881\pi\) | ||||
0.941007 | + | 0.338386i | \(0.109881\pi\) | |||||||
\(74\) | −22208.0 | −0.471444 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28736.0 | 0.570680 | ||||||||
\(77\) | 34692.0 | 0.666811 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −26044.0 | −0.469505 | −0.234752 | − | 0.972055i | \(-0.575428\pi\) | ||||
−0.234752 | + | 0.972055i | \(0.575428\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 51840.0 | 0.851394 | ||||||||
\(83\) | −93468.0 | −1.48925 | −0.744625 | − | 0.667483i | \(-0.767372\pi\) | ||||
−0.744625 | + | 0.667483i | \(0.767372\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 35872.0 | 0.523009 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −22656.0 | −0.311872 | ||||||||
\(89\) | −73428.0 | −0.982622 | −0.491311 | − | 0.870984i | \(-0.663482\pi\) | ||||
−0.491311 | + | 0.870984i | \(0.663482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 39592.0 | 0.501192 | ||||||||
\(92\) | −17280.0 | −0.212850 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −21600.0 | −0.252136 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −128978. | −1.39183 | −0.695915 | − | 0.718124i | \(-0.745001\pi\) | ||||
−0.695915 | + | 0.718124i | \(0.745001\pi\) | |||||||
\(98\) | −28812.0 | −0.303046 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 154794. | 1.50991 | 0.754954 | − | 0.655777i | \(-0.227659\pi\) | ||||
0.754954 | + | 0.655777i | \(0.227659\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −27698.0 | −0.257250 | −0.128625 | − | 0.991693i | \(-0.541056\pi\) | ||||
−0.128625 | + | 0.991693i | \(0.541056\pi\) | |||||||
\(104\) | −25856.0 | −0.234411 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 32856.0 | 0.284021 | ||||||||
\(107\) | 221172. | 1.86754 | 0.933772 | − | 0.357869i | \(-0.116497\pi\) | ||||
0.933772 | + | 0.357869i | \(0.116497\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 123122. | 0.992589 | 0.496294 | − | 0.868154i | \(-0.334694\pi\) | ||||
0.496294 | + | 0.868154i | \(0.334694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −25088.0 | −0.188982 | ||||||||
\(113\) | 220386. | 1.62363 | 0.811817 | − | 0.583913i | \(-0.198479\pi\) | ||||
0.811817 | + | 0.583913i | \(0.198479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 92064.0 | 0.635250 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15816.0 | −0.104566 | ||||||||
\(119\) | −64092.0 | −0.414893 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −35735.0 | −0.221886 | ||||||||
\(122\) | 3848.00 | 0.0234064 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 163136. | 0.952787 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −181298. | −0.997433 | −0.498716 | − | 0.866765i | \(-0.666195\pi\) | ||||
−0.498716 | + | 0.866765i | \(0.666195\pi\) | |||||||
\(128\) | 16384.0 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 254514. | 1.29579 | 0.647893 | − | 0.761731i | \(-0.275650\pi\) | ||||
0.647893 | + | 0.761731i | \(0.275650\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −176008. | −0.862786 | ||||||||
\(134\) | 71824.0 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 41856.0 | 0.194049 | ||||||||
\(137\) | 415506. | 1.89137 | 0.945684 | − | 0.325088i | \(-0.105394\pi\) | ||||
0.945684 | + | 0.325088i | \(0.105394\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −312340. | −1.37117 | −0.685584 | − | 0.727994i | \(-0.740453\pi\) | ||||
−0.685584 | + | 0.727994i | \(0.740453\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 224592. | 0.934703 | ||||||||
\(143\) | 143016. | 0.584850 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 342760. | 1.33079 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −88832.0 | −0.333361 | ||||||||
\(149\) | −300954. | −1.11054 | −0.555270 | − | 0.831670i | \(-0.687385\pi\) | ||||
−0.555270 | + | 0.831670i | \(0.687385\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −37576.0 | −0.134112 | −0.0670561 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670561 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(152\) | 114944. | 0.403531 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 138768. | 0.471506 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 378316. | 1.22491 | 0.612457 | − | 0.790504i | \(-0.290181\pi\) | ||||
0.612457 | + | 0.790504i | \(0.290181\pi\) | |||||||
\(158\) | −104176. | −0.331990 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 105840. | 0.321799 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −66980.0 | −0.197459 | −0.0987293 | − | 0.995114i | \(-0.531478\pi\) | ||||
−0.0987293 | + | 0.995114i | \(0.531478\pi\) | |||||||
\(164\) | 207360. | 0.602026 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −373872. | −1.05306 | ||||||||
\(167\) | −83424.0 | −0.231473 | −0.115736 | − | 0.993280i | \(-0.536923\pi\) | ||||
−0.115736 | + | 0.993280i | \(0.536923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −208077. | −0.560412 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 143488. | 0.369823 | ||||||||
\(173\) | 42318.0 | 0.107500 | 0.0537502 | − | 0.998554i | \(-0.482883\pi\) | ||||
0.0537502 | + | 0.998554i | \(0.482883\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −90624.0 | −0.220527 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −293712. | −0.694819 | ||||||||
\(179\) | 167406. | 0.390516 | 0.195258 | − | 0.980752i | \(-0.437446\pi\) | ||||
0.195258 | + | 0.980752i | \(0.437446\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −483118. | −1.09612 | −0.548058 | − | 0.836440i | \(-0.684633\pi\) | ||||
−0.548058 | + | 0.836440i | \(0.684633\pi\) | |||||||
\(182\) | 158368. | 0.354396 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −69120.0 | −0.150508 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −231516. | −0.484147 | ||||||||
\(188\) | −86400.0 | −0.178287 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 772572. | 1.53234 | 0.766171 | − | 0.642637i | \(-0.222160\pi\) | ||||
0.766171 | + | 0.642637i | \(0.222160\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 670570. | 1.29584 | 0.647919 | − | 0.761709i | \(-0.275639\pi\) | ||||
0.647919 | + | 0.761709i | \(0.275639\pi\) | |||||||
\(194\) | −515912. | −0.984173 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −115248. | −0.214286 | ||||||||
\(197\) | 851922. | 1.56399 | 0.781996 | − | 0.623284i | \(-0.214202\pi\) | ||||
0.781996 | + | 0.623284i | \(0.214202\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −561256. | −1.00468 | −0.502341 | − | 0.864670i | \(-0.667528\pi\) | ||||
−0.502341 | + | 0.864670i | \(0.667528\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 619176. | 1.06767 | ||||||||
\(203\) | −563892. | −0.960408 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −110792. | −0.181903 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −103424. | −0.165754 | ||||||||
\(209\) | −635784. | −1.00680 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −578764. | −0.894943 | −0.447471 | − | 0.894298i | \(-0.647675\pi\) | ||||
−0.447471 | + | 0.894298i | \(0.647675\pi\) | |||||||
\(212\) | 131424. | 0.200833 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 884688. | 1.32055 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −999208. | −1.44048 | ||||||||
\(218\) | 492488. | 0.701866 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −264216. | −0.363897 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −863114. | −1.16227 | −0.581134 | − | 0.813808i | \(-0.697391\pi\) | ||||
−0.581134 | + | 0.813808i | \(0.697391\pi\) | |||||||
\(224\) | −100352. | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 881544. | 1.14808 | ||||||||
\(227\) | −712800. | −0.918128 | −0.459064 | − | 0.888403i | \(-0.651815\pi\) | ||||
−0.459064 | + | 0.888403i | \(0.651815\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −343666. | −0.433060 | −0.216530 | − | 0.976276i | \(-0.569474\pi\) | ||||
−0.216530 | + | 0.976276i | \(0.569474\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 368256. | 0.449190 | ||||||||
\(233\) | 218814. | 0.264049 | 0.132025 | − | 0.991246i | \(-0.457852\pi\) | ||||
0.132025 | + | 0.991246i | \(0.457852\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −63264.0 | −0.0739395 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −256368. | −0.293374 | ||||||||
\(239\) | 1.02095e6 | 1.15614 | 0.578068 | − | 0.815989i | \(-0.303807\pi\) | ||||
0.578068 | + | 0.815989i | \(0.303807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.37183e6 | 1.52145 | 0.760725 | − | 0.649074i | \(-0.224844\pi\) | ||||
0.760725 | + | 0.649074i | \(0.224844\pi\) | |||||||
\(242\) | −142940. | −0.156897 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 15392.0 | 0.0165509 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −725584. | −0.756738 | ||||||||
\(248\) | 652544. | 0.673722 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 932058. | 0.933810 | 0.466905 | − | 0.884307i | \(-0.345369\pi\) | ||||
0.466905 | + | 0.884307i | \(0.345369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 382320. | 0.375514 | ||||||||
\(254\) | −725192. | −0.705292 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.26569e6 | −1.19535 | −0.597676 | − | 0.801738i | \(-0.703909\pi\) | ||||
−0.597676 | + | 0.801738i | \(0.703909\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 544096. | 0.503995 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.01806e6 | 0.916259 | ||||||||
\(263\) | −699936. | −0.623978 | −0.311989 | − | 0.950086i | \(-0.600995\pi\) | ||||
−0.311989 | + | 0.950086i | \(0.600995\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −704032. | −0.610082 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 287296. | 0.244339 | ||||||||
\(269\) | 488178. | 0.411337 | 0.205668 | − | 0.978622i | \(-0.434063\pi\) | ||||
0.205668 | + | 0.978622i | \(0.434063\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 525968. | 0.435047 | 0.217523 | − | 0.976055i | \(-0.430202\pi\) | ||||
0.217523 | + | 0.976055i | \(0.430202\pi\) | |||||||
\(272\) | 167424. | 0.137213 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.66202e6 | 1.33740 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.42931e6 | −1.90232 | −0.951161 | − | 0.308696i | \(-0.900107\pi\) | ||||
−0.951161 | + | 0.308696i | \(0.900107\pi\) | |||||||
\(278\) | −1.24936e6 | −0.969562 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.29031e6 | −1.73033 | −0.865163 | − | 0.501490i | \(-0.832785\pi\) | ||||
−0.865163 | + | 0.501490i | \(0.832785\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.09156e6 | 1.55240 | 0.776200 | − | 0.630487i | \(-0.217145\pi\) | ||||
0.776200 | + | 0.630487i | \(0.217145\pi\) | |||||||
\(284\) | 898368. | 0.660935 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 572064. | 0.413551 | ||||||||
\(287\) | −1.27008e6 | −0.910178 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −992141. | −0.698761 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.37104e6 | 0.941007 | ||||||||
\(293\) | −107118. | −0.0728943 | −0.0364471 | − | 0.999336i | \(-0.511604\pi\) | ||||
−0.0364471 | + | 0.999336i | \(0.511604\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −355328. | −0.235722 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.20382e6 | −0.785271 | ||||||||
\(299\) | 436320. | 0.282246 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −878864. | −0.559121 | ||||||||
\(302\) | −150304. | −0.0948316 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 459776. | 0.285340 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.12938e6 | −0.683900 | −0.341950 | − | 0.939718i | \(-0.611087\pi\) | ||||
−0.341950 | + | 0.939718i | \(0.611087\pi\) | |||||||
\(308\) | 555072. | 0.333405 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.06145e6 | −1.79484 | −0.897422 | − | 0.441174i | \(-0.854562\pi\) | ||||
−0.897422 | + | 0.441174i | \(0.854562\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.23025e6 | 0.709794 | 0.354897 | − | 0.934905i | \(-0.384516\pi\) | ||||
0.354897 | + | 0.934905i | \(0.384516\pi\) | |||||||
\(314\) | 1.51326e6 | 0.866145 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −416704. | −0.234752 | ||||||||
\(317\) | 679122. | 0.379577 | 0.189788 | − | 0.981825i | \(-0.439220\pi\) | ||||
0.189788 | + | 0.981825i | \(0.439220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.03692e6 | −1.12072 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 423360. | 0.227546 | ||||||||
\(323\) | 1.17458e6 | 0.626438 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −267920. | −0.139624 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 829440. | 0.425697 | ||||||||
\(329\) | 529200. | 0.269544 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 98516.0 | 0.0494239 | 0.0247119 | − | 0.999695i | \(-0.492133\pi\) | ||||
0.0247119 | + | 0.999695i | \(0.492133\pi\) | |||||||
\(332\) | −1.49549e6 | −0.744625 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −333696. | −0.163676 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.99779e6 | 0.958244 | 0.479122 | − | 0.877748i | \(-0.340955\pi\) | ||||
0.479122 | + | 0.877748i | \(0.340955\pi\) | |||||||
\(338\) | −832308. | −0.396271 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.60938e6 | −1.68092 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.35298e6 | 1.07990 | ||||||||
\(344\) | 573952. | 0.261505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 169272. | 0.0760142 | ||||||||
\(347\) | −2.65032e6 | −1.18161 | −0.590806 | − | 0.806814i | \(-0.701190\pi\) | ||||
−0.590806 | + | 0.806814i | \(0.701190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.03378e6 | −0.893801 | −0.446900 | − | 0.894584i | \(-0.647472\pi\) | ||||
−0.446900 | + | 0.894584i | \(0.647472\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −362496. | −0.155936 | ||||||||
\(353\) | 948630. | 0.405191 | 0.202596 | − | 0.979262i | \(-0.435062\pi\) | ||||
0.202596 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.17485e6 | −0.491311 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 669624. | 0.276136 | ||||||||
\(359\) | −494616. | −0.202550 | −0.101275 | − | 0.994858i | \(-0.532292\pi\) | ||||
−0.101275 | + | 0.994858i | \(0.532292\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 749517. | 0.302701 | ||||||||
\(362\) | −1.93247e6 | −0.775072 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 633472. | 0.250596 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 75046.0 | 0.0290846 | 0.0145423 | − | 0.999894i | \(-0.495371\pi\) | ||||
0.0145423 | + | 0.999894i | \(0.495371\pi\) | |||||||
\(368\) | −276480. | −0.106425 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −804972. | −0.303631 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −533468. | −0.198535 | −0.0992673 | − | 0.995061i | \(-0.531650\pi\) | ||||
−0.0992673 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(374\) | −926064. | −0.342343 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −345600. | −0.126068 | ||||||||
\(377\) | −2.32462e6 | −0.842360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −199780. | −0.0714421 | −0.0357210 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357210 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.09029e6 | 1.08353 | ||||||||
\(383\) | −869400. | −0.302847 | −0.151423 | − | 0.988469i | \(-0.548386\pi\) | ||||
−0.151423 | + | 0.988469i | \(0.548386\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.68228e6 | 0.916296 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.06365e6 | −0.695915 | ||||||||
\(389\) | 1.05190e6 | 0.352453 | 0.176227 | − | 0.984350i | \(-0.443611\pi\) | ||||
0.176227 | + | 0.984350i | \(0.443611\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −706320. | −0.233647 | ||||||||
\(392\) | −460992. | −0.151523 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.40769e6 | 1.10591 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.19262e6 | −1.33508 | −0.667542 | − | 0.744572i | \(-0.732654\pi\) | ||||
−0.667542 | + | 0.744572i | \(0.732654\pi\) | |||||||
\(398\) | −2.24502e6 | −0.710417 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.90292e6 | 0.590963 | 0.295482 | − | 0.955348i | \(-0.404520\pi\) | ||||
0.295482 | + | 0.955348i | \(0.404520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.11918e6 | −1.26342 | ||||||||
\(404\) | 2.47670e6 | 0.754954 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.25557e6 | −0.679111 | ||||||||
\(407\) | 1.96541e6 | 0.588121 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.62910e6 | 0.481547 | 0.240774 | − | 0.970581i | \(-0.422599\pi\) | ||||
0.240774 | + | 0.970581i | \(0.422599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −443168. | −0.128625 | ||||||||
\(413\) | 387492. | 0.111786 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −413696. | −0.117206 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.54314e6 | −0.711916 | ||||||||
\(419\) | 2.33027e6 | 0.648443 | 0.324222 | − | 0.945981i | \(-0.394898\pi\) | ||||
0.324222 | + | 0.945981i | \(0.394898\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 612974. | 0.168553 | 0.0842766 | − | 0.996442i | \(-0.473142\pi\) | ||||
0.0842766 | + | 0.996442i | \(0.473142\pi\) | |||||||
\(422\) | −2.31506e6 | −0.632820 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 525696. | 0.142010 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −94276.0 | −0.0250225 | ||||||||
\(428\) | 3.53875e6 | 0.933772 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.69384e6 | −1.73573 | −0.867865 | − | 0.496800i | \(-0.834508\pi\) | ||||
−0.867865 | + | 0.496800i | \(0.834508\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.20194e6 | −0.564399 | −0.282199 | − | 0.959356i | \(-0.591064\pi\) | ||||
−0.282199 | + | 0.959356i | \(0.591064\pi\) | |||||||
\(434\) | −3.99683e6 | −1.01857 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.96995e6 | 0.496294 | ||||||||
\(437\) | −1.93968e6 | −0.485877 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.10437e6 | 0.273497 | 0.136748 | − | 0.990606i | \(-0.456335\pi\) | ||||
0.136748 | + | 0.990606i | \(0.456335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.05686e6 | −0.257314 | ||||||||
\(443\) | −3.82202e6 | −0.925303 | −0.462652 | − | 0.886540i | \(-0.653102\pi\) | ||||
−0.462652 | + | 0.886540i | \(0.653102\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.45246e6 | −0.821847 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −401408. | −0.0944911 | ||||||||
\(449\) | −3.93985e6 | −0.922283 | −0.461141 | − | 0.887327i | \(-0.652560\pi\) | ||||
−0.461141 | + | 0.887327i | \(0.652560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.58784e6 | −1.06210 | ||||||||
\(452\) | 3.52618e6 | 0.811817 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.85120e6 | −0.649214 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.01753e6 | 0.227906 | 0.113953 | − | 0.993486i | \(-0.463649\pi\) | ||||
0.113953 | + | 0.993486i | \(0.463649\pi\) | |||||||
\(458\) | −1.37466e6 | −0.306220 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.80830e6 | 1.49206 | 0.746030 | − | 0.665912i | \(-0.231957\pi\) | ||||
0.746030 | + | 0.665912i | \(0.231957\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.74281e6 | −1.46180 | −0.730901 | − | 0.682483i | \(-0.760900\pi\) | ||||
−0.730901 | + | 0.682483i | \(0.760900\pi\) | |||||||
\(464\) | 1.47302e6 | 0.317625 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 875256. | 0.186711 | ||||||||
\(467\) | 3.22619e6 | 0.684538 | 0.342269 | − | 0.939602i | \(-0.388805\pi\) | ||||
0.342269 | + | 0.939602i | \(0.388805\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.75969e6 | −0.369406 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −253056. | −0.0522831 | ||||||||
\(473\) | −3.17467e6 | −0.652448 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.02547e6 | −0.207447 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.08379e6 | 0.817512 | ||||||||
\(479\) | −6.21212e6 | −1.23709 | −0.618545 | − | 0.785749i | \(-0.712278\pi\) | ||||
−0.618545 | + | 0.785749i | \(0.712278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.24301e6 | 0.442047 | ||||||||
\(482\) | 5.48732e6 | 1.07583 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −571760. | −0.110943 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.51326e6 | 0.289128 | 0.144564 | − | 0.989495i | \(-0.453822\pi\) | ||||
0.144564 | + | 0.989495i | \(0.453822\pi\) | |||||||
\(488\) | 61568.0 | 0.0117032 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.43835e6 | 0.643646 | 0.321823 | − | 0.946800i | \(-0.395704\pi\) | ||||
0.321823 | + | 0.946800i | \(0.395704\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.76312e6 | 0.697317 | ||||||||
\(494\) | −2.90234e6 | −0.535094 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.61018e6 | 0.476393 | ||||||||
\(497\) | −5.50250e6 | −0.999239 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.27340e6 | 0.948067 | 0.474033 | − | 0.880507i | \(-0.342798\pi\) | ||||
0.474033 | + | 0.880507i | \(0.342798\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.72823e6 | 0.660304 | ||||||||
\(503\) | 8.81172e6 | 1.55289 | 0.776445 | − | 0.630185i | \(-0.217021\pi\) | ||||
0.776445 | + | 0.630185i | \(0.217021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.52928e6 | 0.265528 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.90077e6 | −0.498716 | ||||||||
\(509\) | 1.03788e7 | 1.77563 | 0.887817 | − | 0.460197i | \(-0.152221\pi\) | ||||
0.887817 | + | 0.460197i | \(0.152221\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.39762e6 | −1.42267 | ||||||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.06278e6 | −0.845242 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.91160e6 | 0.314536 | ||||||||
\(518\) | 2.17638e6 | 0.356378 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.72177e6 | 0.762098 | 0.381049 | − | 0.924555i | \(-0.375563\pi\) | ||||
0.381049 | + | 0.924555i | \(0.375563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.24340e6 | 0.678359 | 0.339179 | − | 0.940722i | \(-0.389851\pi\) | ||||
0.339179 | + | 0.940722i | \(0.389851\pi\) | |||||||
\(524\) | 4.07222e6 | 0.647893 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.79974e6 | −0.441219 | ||||||||
\(527\) | 6.66818e6 | 1.04588 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.26994e6 | −0.818779 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.81613e6 | −0.431393 | ||||||||
\(533\) | −5.23584e6 | −0.798304 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.14918e6 | 0.172774 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.95271e6 | 0.290859 | ||||||||
\(539\) | 2.54986e6 | 0.378046 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.30682e6 | −0.191966 | −0.0959828 | − | 0.995383i | \(-0.530599\pi\) | ||||
−0.0959828 | + | 0.995383i | \(0.530599\pi\) | |||||||
\(542\) | 2.10387e6 | 0.307625 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 669696. | 0.0970243 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.69388e6 | 1.38525 | 0.692627 | − | 0.721296i | \(-0.256453\pi\) | ||||
0.692627 | + | 0.721296i | \(0.256453\pi\) | |||||||
\(548\) | 6.64810e6 | 0.945684 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.03342e7 | 1.45010 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.55231e6 | 0.354912 | ||||||||
\(554\) | −9.71725e6 | −1.34514 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.99744e6 | −0.685584 | ||||||||
\(557\) | 8.47666e6 | 1.15768 | 0.578838 | − | 0.815443i | \(-0.303506\pi\) | ||||
0.578838 | + | 0.815443i | \(0.303506\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.62307e6 | −0.490397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −9.16123e6 | −1.22353 | ||||||||
\(563\) | 1.15102e6 | 0.153042 | 0.0765210 | − | 0.997068i | \(-0.475619\pi\) | ||||
0.0765210 | + | 0.997068i | \(0.475619\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.36622e6 | 1.09771 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.59347e6 | 0.467351 | ||||||||
\(569\) | 45396.0 | 0.00587810 | 0.00293905 | − | 0.999996i | \(-0.499064\pi\) | ||||
0.00293905 | + | 0.999996i | \(0.499064\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.43696e6 | 0.826211 | 0.413105 | − | 0.910683i | \(-0.364444\pi\) | ||||
0.413105 | + | 0.910683i | \(0.364444\pi\) | |||||||
\(572\) | 2.28826e6 | 0.292425 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.08032e6 | −0.643593 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 578758. | 0.0723698 | 0.0361849 | − | 0.999345i | \(-0.488479\pi\) | ||||
0.0361849 | + | 0.999345i | \(0.488479\pi\) | |||||||
\(578\) | −3.96856e6 | −0.494099 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.15986e6 | 1.12577 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.90776e6 | −0.354313 | ||||||||
\(584\) | 5.48416e6 | 0.665393 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −428472. | −0.0515440 | ||||||||
\(587\) | 960804. | 0.115091 | 0.0575453 | − | 0.998343i | \(-0.481673\pi\) | ||||
0.0575453 | + | 0.998343i | \(0.481673\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.83120e7 | 2.17494 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.42131e6 | −0.166681 | ||||||||
\(593\) | 5.70220e6 | 0.665895 | 0.332948 | − | 0.942945i | \(-0.391957\pi\) | ||||
0.332948 | + | 0.942945i | \(0.391957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.81526e6 | −0.555270 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.74528e6 | 0.199578 | ||||||||
\(599\) | −1.53569e7 | −1.74879 | −0.874393 | − | 0.485219i | \(-0.838740\pi\) | ||||
−0.874393 | + | 0.485219i | \(0.838740\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.21690e7 | 1.37425 | 0.687127 | − | 0.726537i | \(-0.258872\pi\) | ||||
0.687127 | + | 0.726537i | \(0.258872\pi\) | |||||||
\(602\) | −3.51546e6 | −0.395358 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −601216. | −0.0670561 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.94630e6 | 0.324567 | 0.162284 | − | 0.986744i | \(-0.448114\pi\) | ||||
0.162284 | + | 0.986744i | \(0.448114\pi\) | |||||||
\(608\) | 1.83910e6 | 0.201766 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.18160e6 | 0.236413 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.06180e7 | 1.14128 | 0.570642 | − | 0.821199i | \(-0.306695\pi\) | ||||
0.570642 | + | 0.821199i | \(0.306695\pi\) | |||||||
\(614\) | −4.51750e6 | −0.483590 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.22029e6 | 0.235753 | ||||||||
\(617\) | 1.14174e7 | 1.20741 | 0.603706 | − | 0.797207i | \(-0.293690\pi\) | ||||
0.603706 | + | 0.797207i | \(0.293690\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.28242e6 | −0.134525 | −0.0672626 | − | 0.997735i | \(-0.521427\pi\) | ||||
−0.0672626 | + | 0.997735i | \(0.521427\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.22458e7 | −1.26915 | ||||||||
\(623\) | 7.19594e6 | 0.742793 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.92100e6 | 0.501900 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.05306e6 | 0.612457 | ||||||||
\(629\) | −3.63101e6 | −0.365932 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.37894e6 | 0.737769 | 0.368885 | − | 0.929475i | \(-0.379740\pi\) | ||||
0.368885 | + | 0.929475i | \(0.379740\pi\) | |||||||
\(632\) | −1.66682e6 | −0.165995 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.71649e6 | 0.268401 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.91001e6 | 0.284149 | ||||||||
\(638\) | −8.14766e6 | −0.792467 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.63802e6 | 0.157462 | 0.0787309 | − | 0.996896i | \(-0.474913\pi\) | ||||
0.0787309 | + | 0.996896i | \(0.474913\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.03847e7 | −1.94436 | −0.972180 | − | 0.234236i | \(-0.924741\pi\) | ||||
−0.972180 | + | 0.234236i | \(0.924741\pi\) | |||||||
\(644\) | 1.69344e6 | 0.160900 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.69834e6 | 0.442958 | ||||||||
\(647\) | 2.10318e7 | 1.97522 | 0.987608 | − | 0.156939i | \(-0.0501625\pi\) | ||||
0.987608 | + | 0.156939i | \(0.0501625\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.39972e6 | 0.130445 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.07168e6 | −0.0987293 | ||||||||
\(653\) | −7.85504e6 | −0.720884 | −0.360442 | − | 0.932782i | \(-0.617374\pi\) | ||||
−0.360442 | + | 0.932782i | \(0.617374\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.31776e6 | 0.301013 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.11680e6 | 0.190597 | ||||||||
\(659\) | −9.32727e6 | −0.836645 | −0.418322 | − | 0.908299i | \(-0.637382\pi\) | ||||
−0.418322 | + | 0.908299i | \(0.637382\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57325e7 | 1.40053 | 0.700267 | − | 0.713881i | \(-0.253064\pi\) | ||||
0.700267 | + | 0.713881i | \(0.253064\pi\) | |||||||
\(662\) | 394064. | 0.0349480 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.98195e6 | −0.526530 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.21432e6 | −0.540853 | ||||||||
\(668\) | −1.33478e6 | −0.115736 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −340548. | −0.0291993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.26562e7 | 1.07712 | 0.538562 | − | 0.842586i | \(-0.318968\pi\) | ||||
0.538562 | + | 0.842586i | \(0.318968\pi\) | |||||||
\(674\) | 7.99118e6 | 0.677581 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.32923e6 | −0.280206 | ||||||||
\(677\) | −2.65061e6 | −0.222267 | −0.111133 | − | 0.993805i | \(-0.535448\pi\) | ||||
−0.111133 | + | 0.993805i | \(0.535448\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.26398e7 | 1.05212 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.44375e7 | −1.18859 | ||||||||
\(683\) | −5.74475e6 | −0.471215 | −0.235608 | − | 0.971848i | \(-0.575708\pi\) | ||||
−0.235608 | + | 0.971848i | \(0.575708\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.41192e6 | 0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.29581e6 | 0.184912 | ||||||||
\(689\) | −3.31846e6 | −0.266310 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.43749e7 | −1.14527 | −0.572636 | − | 0.819809i | \(-0.694079\pi\) | ||||
−0.572636 | + | 0.819809i | \(0.694079\pi\) | |||||||
\(692\) | 677088. | 0.0537502 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.06013e7 | −0.835525 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.47584e6 | 0.660847 | ||||||||
\(698\) | −8.13513e6 | −0.632013 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.26164e6 | −0.327553 | −0.163776 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163776 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.97139e6 | −0.760970 | ||||||||
\(704\) | −1.44998e6 | −0.110263 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.79452e6 | 0.286514 | ||||||||
\(707\) | −1.51698e7 | −1.14138 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.97088e7 | 1.47246 | 0.736231 | − | 0.676731i | \(-0.236604\pi\) | ||||
0.736231 | + | 0.676731i | \(0.236604\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.69939e6 | −0.347409 | ||||||||
\(713\) | −1.10117e7 | −0.811203 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.67850e6 | 0.195258 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.97846e6 | −0.143224 | ||||||||
\(719\) | 1.02211e7 | 0.737353 | 0.368676 | − | 0.929558i | \(-0.379811\pi\) | ||||
0.368676 | + | 0.929558i | \(0.379811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.71440e6 | 0.194463 | ||||||||
\(722\) | 2.99807e6 | 0.214042 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7.72989e6 | −0.548058 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.32103e7 | 0.926996 | 0.463498 | − | 0.886098i | \(-0.346594\pi\) | ||||
0.463498 | + | 0.886098i | \(0.346594\pi\) | |||||||
\(728\) | 2.53389e6 | 0.177198 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.86507e6 | 0.405957 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.30586e7 | 0.897713 | 0.448857 | − | 0.893604i | \(-0.351831\pi\) | ||||
0.448857 | + | 0.893604i | \(0.351831\pi\) | |||||||
\(734\) | 300184. | 0.0205659 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.10592e6 | −0.0752539 | ||||||||
\(737\) | −6.35642e6 | −0.431066 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.53767e7 | −1.03574 | −0.517870 | − | 0.855459i | \(-0.673275\pi\) | ||||
−0.517870 | + | 0.855459i | \(0.673275\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.21989e6 | −0.214699 | ||||||||
\(743\) | 2.62537e7 | 1.74469 | 0.872346 | − | 0.488889i | \(-0.162598\pi\) | ||||
0.872346 | + | 0.488889i | \(0.162598\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.13387e6 | −0.140385 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.70426e6 | −0.242073 | ||||||||
\(749\) | −2.16749e7 | −1.41173 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.36151e7 | −0.880886 | −0.440443 | − | 0.897781i | \(-0.645179\pi\) | ||||
−0.440443 | + | 0.897781i | \(0.645179\pi\) | |||||||
\(752\) | −1.38240e6 | −0.0891434 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.29846e6 | −0.595639 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.41208e6 | −0.533536 | −0.266768 | − | 0.963761i | \(-0.585956\pi\) | ||||
−0.266768 | + | 0.963761i | \(0.585956\pi\) | |||||||
\(758\) | −799120. | −0.0505172 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −414684. | −0.0259571 | −0.0129785 | − | 0.999916i | \(-0.504131\pi\) | ||||
−0.0129785 | + | 0.999916i | \(0.504131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.20660e7 | −0.750327 | ||||||||
\(764\) | 1.23612e7 | 0.766171 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.47760e6 | −0.214145 | ||||||||
\(767\) | 1.59742e6 | 0.0980459 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.71521e6 | 0.409491 | 0.204745 | − | 0.978815i | \(-0.434363\pi\) | ||||
0.204745 | + | 0.978815i | \(0.434363\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.07291e7 | 0.647919 | ||||||||
\(773\) | 2.37237e7 | 1.42802 | 0.714009 | − | 0.700136i | \(-0.246877\pi\) | ||||
0.714009 | + | 0.700136i | \(0.246877\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.25459e6 | −0.492086 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.20761e6 | 0.249222 | ||||||||
\(779\) | 2.32762e7 | 1.37426 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.98764e7 | −1.16603 | ||||||||
\(782\) | −2.82528e6 | −0.165213 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.84397e6 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.17798e7 | 1.82900 | 0.914501 | − | 0.404585i | \(-0.132584\pi\) | ||||
0.914501 | + | 0.404585i | \(0.132584\pi\) | |||||||
\(788\) | 1.36308e7 | 0.781996 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.15978e7 | −1.22735 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −388648. | −0.0219469 | ||||||||
\(794\) | −1.67705e7 | −0.944047 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.98010e6 | −0.502341 | ||||||||
\(797\) | −7.26280e6 | −0.405003 | −0.202502 | − | 0.979282i | \(-0.564907\pi\) | ||||
−0.202502 | + | 0.979282i | \(0.564907\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.53160e6 | −0.195706 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.61170e6 | 0.417874 | ||||||||
\(803\) | −3.03343e7 | −1.66014 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.64767e7 | −0.893375 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.90682e6 | 0.533833 | ||||||||
\(809\) | 3.22769e7 | 1.73388 | 0.866942 | − | 0.498409i | \(-0.166082\pi\) | ||||
0.866942 | + | 0.498409i | \(0.166082\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.00689e7 | −0.537563 | −0.268782 | − | 0.963201i | \(-0.586621\pi\) | ||||
−0.268782 | + | 0.963201i | \(0.586621\pi\) | |||||||
\(812\) | −9.02227e6 | −0.480204 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.86163e6 | 0.415864 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.61065e7 | 0.844203 | ||||||||
\(818\) | 6.51639e6 | 0.340505 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.08671e7 | −1.08045 | −0.540224 | − | 0.841521i | \(-0.681660\pi\) | ||||
−0.540224 | + | 0.841521i | \(0.681660\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.40683e7 | −0.724005 | −0.362003 | − | 0.932177i | \(-0.617907\pi\) | ||||
−0.362003 | + | 0.932177i | \(0.617907\pi\) | |||||||
\(824\) | −1.77267e6 | −0.0909516 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.54997e6 | 0.0790447 | ||||||||
\(827\) | −2.48210e7 | −1.26199 | −0.630995 | − | 0.775787i | \(-0.717353\pi\) | ||||
−0.630995 | + | 0.775787i | \(0.717353\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.40954e7 | −0.712347 | −0.356173 | − | 0.934420i | \(-0.615919\pi\) | ||||
−0.356173 | + | 0.934420i | \(0.615919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.65478e6 | −0.0828768 | ||||||||
\(833\) | −4.71076e6 | −0.235222 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.01725e7 | −0.503401 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.32110e6 | 0.458519 | ||||||||
\(839\) | −6.47203e6 | −0.317421 | −0.158711 | − | 0.987325i | \(-0.550734\pi\) | ||||
−0.158711 | + | 0.987325i | \(0.550734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.25974e7 | 0.614172 | ||||||||
\(842\) | 2.45190e6 | 0.119185 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.26022e6 | −0.447471 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.50203e6 | 0.167730 | ||||||||
\(848\) | 2.10278e6 | 0.100416 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.99616e6 | 0.283824 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.71706e7 | −0.808002 | −0.404001 | − | 0.914758i | \(-0.632381\pi\) | ||||
−0.404001 | + | 0.914758i | \(0.632381\pi\) | |||||||
\(854\) | −377104. | −0.0176936 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.41550e7 | 0.660276 | ||||||||
\(857\) | 2.45494e6 | 0.114180 | 0.0570899 | − | 0.998369i | \(-0.481818\pi\) | ||||
0.0570899 | + | 0.998369i | \(0.481818\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.13126e6 | 0.0523094 | 0.0261547 | − | 0.999658i | \(-0.491674\pi\) | ||||
0.0261547 | + | 0.999658i | \(0.491674\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.67754e7 | −1.22735 | ||||||||
\(863\) | −1.84069e7 | −0.841305 | −0.420653 | − | 0.907222i | \(-0.638199\pi\) | ||||
−0.420653 | + | 0.907222i | \(0.638199\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.80777e6 | −0.399090 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.59873e7 | −0.720239 | ||||||||
\(869\) | 9.21958e6 | 0.414154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.25422e6 | −0.324000 | ||||||||
\(872\) | 7.87981e6 | 0.350933 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.75872e6 | −0.343567 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.61539e7 | −1.14825 | −0.574127 | − | 0.818766i | \(-0.694659\pi\) | ||||
−0.574127 | + | 0.818766i | \(0.694659\pi\) | |||||||
\(878\) | 4.41747e6 | 0.193392 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.97640e7 | −0.857898 | −0.428949 | − | 0.903329i | \(-0.641116\pi\) | ||||
−0.428949 | + | 0.903329i | \(0.641116\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.43551e7 | −1.48282 | −0.741411 | − | 0.671051i | \(-0.765843\pi\) | ||||
−0.741411 | + | 0.671051i | \(0.765843\pi\) | |||||||
\(884\) | −4.22746e6 | −0.181948 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.52881e7 | −0.654288 | ||||||||
\(887\) | −2.11254e7 | −0.901561 | −0.450780 | − | 0.892635i | \(-0.648854\pi\) | ||||
−0.450780 | + | 0.892635i | \(0.648854\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.77672e7 | 0.753988 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.38098e7 | −0.581134 | ||||||||
\(893\) | −9.69840e6 | −0.406978 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.60563e6 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.57594e7 | −0.652152 | ||||||||
\(899\) | 5.86678e7 | 2.42103 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.37196e6 | 0.220455 | ||||||||
\(902\) | −1.83514e7 | −0.751021 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.41047e7 | 0.574041 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.61308e6 | −0.105471 | −0.0527357 | − | 0.998609i | \(-0.516794\pi\) | ||||
−0.0527357 | + | 0.998609i | \(0.516794\pi\) | |||||||
\(908\) | −1.14048e7 | −0.459064 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.27046e7 | −1.30561 | −0.652803 | − | 0.757527i | \(-0.726407\pi\) | ||||
−0.652803 | + | 0.757527i | \(0.726407\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.30877e7 | 1.31368 | ||||||||
\(914\) | 4.07010e6 | 0.161154 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.49866e6 | −0.216530 | ||||||||
\(917\) | −2.49424e7 | −0.979522 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.06463e7 | 0.806406 | 0.403203 | − | 0.915111i | \(-0.367897\pi\) | ||||
0.403203 | + | 0.915111i | \(0.367897\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 2.72332e7 | 1.05505 | ||||||||
\(923\) | −2.26838e7 | −0.876418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.69713e7 | −1.03365 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.89210e6 | 0.224595 | ||||||||
\(929\) | −2.54318e7 | −0.966803 | −0.483401 | − | 0.875399i | \(-0.660599\pi\) | ||||
−0.483401 | + | 0.875399i | \(0.660599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.29366e7 | −0.489154 | ||||||||
\(932\) | 3.50102e6 | 0.132025 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.29048e7 | 0.484041 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.52800e7 | −0.940652 | −0.470326 | − | 0.882493i | \(-0.655864\pi\) | ||||
−0.470326 | + | 0.882493i | \(0.655864\pi\) | |||||||
\(938\) | −7.03875e6 | −0.261209 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.80180e7 | −0.663336 | −0.331668 | − | 0.943396i | \(-0.607611\pi\) | ||||
−0.331668 | + | 0.943396i | \(0.607611\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.39968e7 | −0.512566 | ||||||||
\(944\) | −1.01222e6 | −0.0369698 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.26987e7 | −0.461351 | ||||||||
\(947\) | −5.10485e7 | −1.84973 | −0.924864 | − | 0.380299i | \(-0.875821\pi\) | ||||
−0.924864 | + | 0.380299i | \(0.875821\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.46188e7 | −1.24780 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.10189e6 | −0.146687 | ||||||||
\(953\) | 4.53610e7 | 1.61790 | 0.808948 | − | 0.587880i | \(-0.200037\pi\) | ||||
0.808948 | + | 0.587880i | \(0.200037\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.63352e7 | 0.578068 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.48485e7 | −0.874755 | ||||||||
\(959\) | −4.07196e7 | −1.42974 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.53293e7 | 2.63121 | ||||||||
\(962\) | 8.97203e6 | 0.312574 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.19493e7 | 0.760725 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.24701e7 | 0.428847 | 0.214424 | − | 0.976741i | \(-0.431213\pi\) | ||||
0.214424 | + | 0.976741i | \(0.431213\pi\) | |||||||
\(968\) | −2.28704e6 | −0.0784486 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.13786e7 | 0.727664 | 0.363832 | − | 0.931465i | \(-0.381468\pi\) | ||||
0.363832 | + | 0.931465i | \(0.381468\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.06093e7 | 1.03651 | ||||||||
\(974\) | 6.05303e6 | 0.204445 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 246272. | 0.00827543 | ||||||||
\(977\) | 1.31824e7 | 0.441833 | 0.220917 | − | 0.975293i | \(-0.429095\pi\) | ||||
0.220917 | + | 0.975293i | \(0.429095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.59935e7 | 0.866779 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.37534e7 | 0.455126 | ||||||||
\(983\) | −2.98823e7 | −0.986349 | −0.493175 | − | 0.869930i | \(-0.664164\pi\) | ||||
−0.493175 | + | 0.869930i | \(0.664164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.50525e7 | 0.493078 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.16093e7 | −0.378369 | ||||||||
\(989\) | −9.68544e6 | −0.314868 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.76534e7 | −1.21793 | −0.608963 | − | 0.793199i | \(-0.708414\pi\) | ||||
−0.608963 | + | 0.793199i | \(0.708414\pi\) | |||||||
\(992\) | 1.04407e7 | 0.336861 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.20100e7 | −0.706569 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.53443e7 | −0.488887 | −0.244444 | − | 0.969664i | \(-0.578605\pi\) | ||||
−0.244444 | + | 0.969664i | \(0.578605\pi\) | |||||||
\(998\) | 2.10936e7 | 0.670385 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.6.a.o.1.1 | 1 | ||
3.2 | odd | 2 | 450.6.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 450.6.c.d.199.2 | 2 | |||
5.3 | odd | 4 | 450.6.c.d.199.1 | 2 | |||
5.4 | even | 2 | 90.6.a.c.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 450.6.c.l.199.1 | 2 | |||
15.8 | even | 4 | 450.6.c.l.199.2 | 2 | |||
15.14 | odd | 2 | 90.6.a.e.1.1 | yes | 1 | ||
20.19 | odd | 2 | 720.6.a.o.1.1 | 1 | |||
60.59 | even | 2 | 720.6.a.c.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
90.6.a.c.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
90.6.a.e.1.1 | yes | 1 | 15.14 | odd | 2 | ||
450.6.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
450.6.a.o.1.1 | 1 | 1.1 | even | 1 | trivial | ||
450.6.c.d.199.1 | 2 | 5.3 | odd | 4 | |||
450.6.c.d.199.2 | 2 | 5.2 | odd | 4 | |||
450.6.c.l.199.1 | 2 | 15.2 | even | 4 | |||
450.6.c.l.199.2 | 2 | 15.8 | even | 4 | |||
720.6.a.c.1.1 | 1 | 60.59 | even | 2 | |||
720.6.a.o.1.1 | 1 | 20.19 | odd | 2 |