Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,8,Mod(199,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.199");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(70.2866307339\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 3) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.199 |
Dual form | 225.8.b.f.199.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 6.00000i | − 0.530330i | −0.964203 | − | 0.265165i | \(-0.914574\pi\) | ||||
0.964203 | − | 0.265165i | \(-0.0854264\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 92.0000 | 0.718750 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 64.0000i | − 0.0705240i | −0.999378 | − | 0.0352620i | \(-0.988773\pi\) | ||||
0.999378 | − | 0.0352620i | \(-0.0112266\pi\) | |||||||
\(8\) | − 1320.00i | − 0.911505i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 948.000 | 0.214750 | 0.107375 | − | 0.994219i | \(-0.465755\pi\) | ||||
0.107375 | + | 0.994219i | \(0.465755\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5098.00i | 0.643573i | 0.946812 | + | 0.321787i | \(0.104283\pi\) | ||||
−0.946812 | + | 0.321787i | \(0.895717\pi\) | |||||||
\(14\) | −384.000 | −0.0374010 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3856.00 | 0.235352 | ||||||||
\(17\) | − 28386.0i | − 1.40131i | −0.713502 | − | 0.700653i | \(-0.752892\pi\) | ||||
0.713502 | − | 0.700653i | \(-0.247108\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8620.00 | 0.288317 | 0.144158 | − | 0.989555i | \(-0.453953\pi\) | ||||
0.144158 | + | 0.989555i | \(0.453953\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 5688.00i | − 0.113889i | ||||||||
\(23\) | − 15288.0i | − 0.262001i | −0.991382 | − | 0.131001i | \(-0.958181\pi\) | ||||
0.991382 | − | 0.131001i | \(-0.0418190\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 30588.0 | 0.341306 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 5888.00i | − 0.0506891i | ||||||||
\(29\) | 36510.0 | 0.277983 | 0.138992 | − | 0.990294i | \(-0.455614\pi\) | ||||
0.138992 | + | 0.990294i | \(0.455614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −276808. | −1.66883 | −0.834416 | − | 0.551135i | \(-0.814195\pi\) | ||||
−0.834416 | + | 0.551135i | \(0.814195\pi\) | |||||||
\(32\) | − 192096.i | − 1.03632i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −170316. | −0.743155 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 268526.i | 0.871526i | 0.900061 | + | 0.435763i | \(0.143521\pi\) | ||||
−0.900061 | + | 0.435763i | \(0.856479\pi\) | |||||||
\(38\) | − 51720.0i | − 0.152903i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 629718. | 1.42693 | 0.713465 | − | 0.700691i | \(-0.247125\pi\) | ||||
0.713465 | + | 0.700691i | \(0.247125\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 685772.i | − 1.31535i | −0.753303 | − | 0.657673i | \(-0.771541\pi\) | ||||
0.753303 | − | 0.657673i | \(-0.228459\pi\) | |||||||
\(44\) | 87216.0 | 0.154352 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −91728.0 | −0.138947 | ||||||||
\(47\) | − 583296.i | − 0.819495i | −0.912199 | − | 0.409748i | \(-0.865617\pi\) | ||||
0.912199 | − | 0.409748i | \(-0.134383\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 819447. | 0.995026 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 469016.i | 0.462568i | ||||||||
\(53\) | − 428058.i | − 0.394945i | −0.980308 | − | 0.197473i | \(-0.936727\pi\) | ||||
0.980308 | − | 0.197473i | \(-0.0632734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −84480.0 | −0.0642830 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 219060.i | − 0.147423i | ||||||||
\(59\) | 1.30638e6 | 0.828109 | 0.414054 | − | 0.910252i | \(-0.364112\pi\) | ||||
0.414054 | + | 0.910252i | \(0.364112\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 300662. | 0.169599 | 0.0847997 | − | 0.996398i | \(-0.472975\pi\) | ||||
0.0847997 | + | 0.996398i | \(0.472975\pi\) | |||||||
\(62\) | 1.66085e6i | 0.885032i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −659008. | −0.314240 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 507244.i | − 0.206042i | −0.994679 | − | 0.103021i | \(-0.967149\pi\) | ||||
0.994679 | − | 0.103021i | \(-0.0328508\pi\) | |||||||
\(68\) | − 2.61151e6i | − 1.00719i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.56063e6 | −1.84383 | −0.921913 | − | 0.387397i | \(-0.873374\pi\) | ||||
−0.921913 | + | 0.387397i | \(0.873374\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 1.36908e6i | − 0.411907i | −0.978562 | − | 0.205954i | \(-0.933970\pi\) | ||||
0.978562 | − | 0.205954i | \(-0.0660296\pi\) | |||||||
\(74\) | 1.61116e6 | 0.462196 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 793040. | 0.207228 | ||||||||
\(77\) | − 60672.0i | − 0.0151451i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.91372e6 | 1.57767 | 0.788836 | − | 0.614603i | \(-0.210684\pi\) | ||||
0.788836 | + | 0.614603i | \(0.210684\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 3.77831e6i | − 0.756744i | ||||||||
\(83\) | − 4.37675e6i | − 0.840191i | −0.907480 | − | 0.420096i | \(-0.861997\pi\) | ||||
0.907480 | − | 0.420096i | \(-0.138003\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.11463e6 | −0.697568 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 1.25136e6i | − 0.195746i | ||||||||
\(89\) | −8.52831e6 | −1.28232 | −0.641162 | − | 0.767405i | \(-0.721547\pi\) | ||||
−0.641162 | + | 0.767405i | \(0.721547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 326272. | 0.0453874 | ||||||||
\(92\) | − 1.40650e6i | − 0.188313i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.49978e6 | −0.434603 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 8.82681e6i | − 0.981981i | −0.871165 | − | 0.490990i | \(-0.836635\pi\) | ||||
0.871165 | − | 0.490990i | \(-0.163365\pi\) | |||||||
\(98\) | − 4.91668e6i | − 0.527692i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.19864e7 | −1.15762 | −0.578808 | − | 0.815464i | \(-0.696482\pi\) | ||||
−0.578808 | + | 0.815464i | \(0.696482\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 7.20939e6i | − 0.650082i | −0.945700 | − | 0.325041i | \(-0.894622\pi\) | ||||
0.945700 | − | 0.325041i | \(-0.105378\pi\) | |||||||
\(104\) | 6.72936e6 | 0.586620 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.56835e6 | −0.209451 | ||||||||
\(107\) | − 1.14261e7i | − 0.901683i | −0.892604 | − | 0.450842i | \(-0.851124\pi\) | ||||
0.892604 | − | 0.450842i | \(-0.148876\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.02095e6 | −0.297397 | −0.148698 | − | 0.988883i | \(-0.547508\pi\) | ||||
−0.148698 | + | 0.988883i | \(0.547508\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 246784.i | − 0.0165979i | ||||||||
\(113\) | − 1.77063e7i | − 1.15439i | −0.816605 | − | 0.577197i | \(-0.804147\pi\) | ||||
0.816605 | − | 0.577197i | \(-0.195853\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 3.35892e6 | 0.199801 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 7.83828e6i | − 0.439171i | ||||||||
\(119\) | −1.81670e6 | −0.0988257 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.85885e7 | −0.953882 | ||||||||
\(122\) | − 1.80397e6i | − 0.0899436i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2.54663e7 | −1.19947 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.67883e7i | 0.727267i | 0.931542 | + | 0.363633i | \(0.118464\pi\) | ||||
−0.931542 | + | 0.363633i | \(0.881536\pi\) | |||||||
\(128\) | − 2.06342e7i | − 0.869668i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.68268e7 | −0.653960 | −0.326980 | − | 0.945031i | \(-0.606031\pi\) | ||||
−0.326980 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 551680.i | − 0.0203332i | ||||||||
\(134\) | −3.04346e6 | −0.109270 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.74695e7 | −1.27730 | ||||||||
\(137\) | − 2.80449e7i | − 0.931820i | −0.884832 | − | 0.465910i | \(-0.845727\pi\) | ||||
0.884832 | − | 0.465910i | \(-0.154273\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.18273e7 | 0.373537 | 0.186769 | − | 0.982404i | \(-0.440199\pi\) | ||||
0.186769 | + | 0.982404i | \(0.440199\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.33638e7i | 0.977836i | ||||||||
\(143\) | 4.83290e6i | 0.138208i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.21449e6 | −0.218447 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.47044e7i | 0.626409i | ||||||||
\(149\) | 2.07846e7 | 0.514743 | 0.257371 | − | 0.966313i | \(-0.417144\pi\) | ||||
0.257371 | + | 0.966313i | \(0.417144\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76112.0 | 0.00179901 | 0.000899505 | − | 1.00000i | \(-0.499714\pi\) | ||||
0.000899505 | 1.00000i | \(0.499714\pi\) | ||||||||
\(152\) | − 1.13784e7i | − 0.262802i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −364032. | −0.00803188 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 3.21825e7i | − 0.663698i | −0.943332 | − | 0.331849i | \(-0.892328\pi\) | ||||
0.943332 | − | 0.331849i | \(-0.107672\pi\) | |||||||
\(158\) | − 4.14823e7i | − 0.836687i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −978432. | −0.0184774 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 5.83435e7i | − 1.05520i | −0.849492 | − | 0.527601i | \(-0.823092\pi\) | ||||
0.849492 | − | 0.527601i | \(-0.176908\pi\) | |||||||
\(164\) | 5.79341e7 | 1.02561 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.62605e7 | −0.445579 | ||||||||
\(167\) | 2.58365e7i | 0.429266i | 0.976695 | + | 0.214633i | \(0.0688555\pi\) | ||||
−0.976695 | + | 0.214633i | \(0.931145\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67589e7 | 0.585813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 6.30910e7i | − 0.945405i | ||||||||
\(173\) | 6.35201e7i | 0.932716i | 0.884596 | + | 0.466358i | \(0.154434\pi\) | ||||
−0.884596 | + | 0.466358i | \(0.845566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.65549e6 | 0.0505418 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.11699e7i | 0.680055i | ||||||||
\(179\) | −8.09559e7 | −1.05503 | −0.527513 | − | 0.849547i | \(-0.676875\pi\) | ||||
−0.527513 | + | 0.849547i | \(0.676875\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.45032e7 | 0.808549 | 0.404274 | − | 0.914638i | \(-0.367524\pi\) | ||||
0.404274 | + | 0.914638i | \(0.367524\pi\) | |||||||
\(182\) | − 1.95763e6i | − 0.0240703i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.01802e7 | −0.238815 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.69099e7i | − 0.300931i | ||||||||
\(188\) | − 5.36632e7i | − 0.589012i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.68274e7 | −0.590121 | −0.295060 | − | 0.955479i | \(-0.595340\pi\) | ||||
−0.295060 | + | 0.955479i | \(0.595340\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1.16377e8i | − 1.16524i | −0.812744 | − | 0.582621i | \(-0.802027\pi\) | ||||
0.812744 | − | 0.582621i | \(-0.197973\pi\) | |||||||
\(194\) | −5.29609e7 | −0.520774 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.53891e7 | 0.715175 | ||||||||
\(197\) | 1.18816e8i | 1.10724i | 0.832768 | + | 0.553622i | \(0.186755\pi\) | ||||
−0.832768 | + | 0.553622i | \(0.813245\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.50106e7 | 0.854646 | 0.427323 | − | 0.904099i | \(-0.359457\pi\) | ||||
0.427323 | + | 0.904099i | \(0.359457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.19185e7i | 0.613919i | ||||||||
\(203\) | − 2.33664e6i | − 0.0196045i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.32564e7 | −0.344758 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.96579e7i | 0.151466i | ||||||||
\(209\) | 8.17176e6 | 0.0619161 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.79246e8 | 1.31360 | 0.656798 | − | 0.754067i | \(-0.271910\pi\) | ||||
0.656798 | + | 0.754067i | \(0.271910\pi\) | |||||||
\(212\) | − 3.93813e7i | − 0.283867i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.85565e7 | −0.478190 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.77157e7i | 0.117693i | ||||||||
\(218\) | 2.41257e7i | 0.157718i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.44712e8 | 0.901843 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.06537e8i | 1.24718i | 0.781750 | + | 0.623592i | \(0.214327\pi\) | ||||
−0.781750 | + | 0.623592i | \(0.785673\pi\) | |||||||
\(224\) | −1.22941e7 | −0.0730853 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.06238e8 | −0.612209 | ||||||||
\(227\) | − 4.33954e7i | − 0.246237i | −0.992392 | − | 0.123118i | \(-0.960710\pi\) | ||||
0.992392 | − | 0.123118i | \(-0.0392895\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.61931e7 | 0.199160 | 0.0995799 | − | 0.995030i | \(-0.468250\pi\) | ||||
0.0995799 | + | 0.995030i | \(0.468250\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 4.81932e7i | − 0.253383i | ||||||||
\(233\) | 9.22347e7i | 0.477693i | 0.971057 | + | 0.238846i | \(0.0767692\pi\) | ||||
−0.971057 | + | 0.238846i | \(0.923231\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.20187e8 | 0.595203 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.09002e7i | 0.0524102i | ||||||||
\(239\) | 4.98468e7 | 0.236181 | 0.118090 | − | 0.993003i | \(-0.462323\pi\) | ||||
0.118090 | + | 0.993003i | \(0.462323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.99374e8 | 0.917506 | 0.458753 | − | 0.888564i | \(-0.348296\pi\) | ||||
0.458753 | + | 0.888564i | \(0.348296\pi\) | |||||||
\(242\) | 1.11531e8i | 0.505872i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.76609e7 | 0.121900 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.39448e7i | 0.185553i | ||||||||
\(248\) | 3.65387e8i | 1.52115i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.94678e8 | 1.57538 | 0.787689 | − | 0.616073i | \(-0.211277\pi\) | ||||
0.787689 | + | 0.616073i | \(0.211277\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.44930e7i | − 0.0562649i | ||||||||
\(254\) | 1.00730e8 | 0.385691 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.08158e8 | −0.775451 | ||||||||
\(257\) | 1.42885e8i | 0.525076i | 0.964922 | + | 0.262538i | \(0.0845594\pi\) | ||||
−0.964922 | + | 0.262538i | \(0.915441\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.71857e7 | 0.0614635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.00961e8i | 0.346815i | ||||||||
\(263\) | 4.40241e8i | 1.49226i | 0.665799 | + | 0.746131i | \(0.268091\pi\) | ||||
−0.665799 | + | 0.746131i | \(0.731909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.31008e6 | −0.0107833 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 4.66664e7i | − 0.148092i | ||||||||
\(269\) | 2.75405e8 | 0.862657 | 0.431329 | − | 0.902195i | \(-0.358045\pi\) | ||||
0.431329 | + | 0.902195i | \(0.358045\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.24670e8 | −1.29616 | −0.648080 | − | 0.761572i | \(-0.724428\pi\) | ||||
−0.648080 | + | 0.761572i | \(0.724428\pi\) | |||||||
\(272\) | − 1.09456e8i | − 0.329800i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.68269e8 | −0.494172 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.16158e8i | 1.45916i | 0.683894 | + | 0.729581i | \(0.260285\pi\) | ||||
−0.683894 | + | 0.729581i | \(0.739715\pi\) | |||||||
\(278\) | − 7.09638e7i | − 0.198098i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.11043e8 | 0.836273 | 0.418137 | − | 0.908384i | \(-0.362683\pi\) | ||||
0.418137 | + | 0.908384i | \(0.362683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.94308e8i | 1.55869i | 0.626596 | + | 0.779344i | \(0.284448\pi\) | ||||
−0.626596 | + | 0.779344i | \(0.715552\pi\) | |||||||
\(284\) | −5.11578e8 | −1.32525 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.89974e7 | 0.0732957 | ||||||||
\(287\) | − 4.03020e7i | − 0.100633i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.95426e8 | −0.963658 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 1.25956e8i | − 0.296058i | ||||||||
\(293\) | 1.15515e8i | 0.268288i | 0.990962 | + | 0.134144i | \(0.0428284\pi\) | ||||
−0.990962 | + | 0.134144i | \(0.957172\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.54454e8 | 0.794400 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 1.24708e8i | − 0.272984i | ||||||||
\(299\) | 7.79382e7 | 0.168617 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.38894e7 | −0.0927635 | ||||||||
\(302\) | − 456672.i | 0 0.000954070i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.32387e7 | 0.0678558 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.60600e8i | − 0.514032i | −0.966407 | − | 0.257016i | \(-0.917261\pi\) | ||||
0.966407 | − | 0.257016i | \(-0.0827392\pi\) | |||||||
\(308\) | − 5.58182e6i | − 0.0108855i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.76795e8 | −1.08733 | −0.543663 | − | 0.839303i | \(-0.682963\pi\) | ||||
−0.543663 | + | 0.839303i | \(0.682963\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.60074e8i | 0.848053i | 0.905650 | + | 0.424026i | \(0.139384\pi\) | ||||
−0.905650 | + | 0.424026i | \(0.860616\pi\) | |||||||
\(314\) | −1.93095e8 | −0.351979 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.36062e8 | 1.13395 | ||||||||
\(317\) | − 6.25561e7i | − 0.110297i | −0.998478 | − | 0.0551483i | \(-0.982437\pi\) | ||||
0.998478 | − | 0.0551483i | \(-0.0175632\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.46115e7 | 0.0596970 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.87059e6i | 0.00979910i | ||||||||
\(323\) | − 2.44687e8i | − 0.404020i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.50061e8 | −0.559606 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 8.31228e8i | − 1.30065i | ||||||||
\(329\) | −3.73309e7 | −0.0577941 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.84236e8 | 1.03707 | 0.518535 | − | 0.855057i | \(-0.326478\pi\) | ||||
0.518535 | + | 0.855057i | \(0.326478\pi\) | |||||||
\(332\) | − 4.02661e8i | − 0.603888i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.55019e8 | 0.227652 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 6.26313e8i | − 0.891429i | −0.895175 | − | 0.445714i | \(-0.852950\pi\) | ||||
0.895175 | − | 0.445714i | \(-0.147050\pi\) | |||||||
\(338\) | − 2.20553e8i | − 0.310674i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.62414e8 | −0.358382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.05151e8i | − 0.140697i | ||||||||
\(344\) | −9.05219e8 | −1.19894 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.81120e8 | 0.494647 | ||||||||
\(347\) | 1.25340e9i | 1.61041i | 0.593000 | + | 0.805203i | \(0.297943\pi\) | ||||
−0.593000 | + | 0.805203i | \(0.702057\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.65350e8 | −0.334142 | −0.167071 | − | 0.985945i | \(-0.553431\pi\) | ||||
−0.167071 | + | 0.985945i | \(0.553431\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 1.82107e8i | − 0.222550i | ||||||||
\(353\) | − 5.69636e8i | − 0.689264i | −0.938738 | − | 0.344632i | \(-0.888004\pi\) | ||||
0.938738 | − | 0.344632i | \(-0.111996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.84605e8 | −0.921671 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.85735e8i | 0.559512i | ||||||||
\(359\) | 9.32541e8 | 1.06374 | 0.531872 | − | 0.846825i | \(-0.321489\pi\) | ||||
0.531872 | + | 0.846825i | \(0.321489\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.19567e8 | −0.916874 | ||||||||
\(362\) | − 3.87019e8i | − 0.428798i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.00170e7 | 0.0326222 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 8.52565e8i | − 0.900318i | −0.892948 | − | 0.450159i | \(-0.851367\pi\) | ||||
0.892948 | − | 0.450159i | \(-0.148633\pi\) | |||||||
\(368\) | − 5.89505e7i | − 0.0616624i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.73957e7 | −0.0278531 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 3.81183e8i | − 0.380323i | −0.981753 | − | 0.190162i | \(-0.939099\pi\) | ||||
0.981753 | − | 0.190162i | \(-0.0609012\pi\) | |||||||
\(374\) | −1.61460e8 | −0.159593 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7.69951e8 | −0.746974 | ||||||||
\(377\) | 1.86128e8i | 0.178903i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.48353e9 | 1.39978 | 0.699889 | − | 0.714251i | \(-0.253233\pi\) | ||||
0.699889 | + | 0.714251i | \(0.253233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.40964e8i | 0.312959i | ||||||||
\(383\) | − 7.61930e8i | − 0.692978i | −0.938054 | − | 0.346489i | \(-0.887374\pi\) | ||||
0.938054 | − | 0.346489i | \(-0.112626\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.98262e8 | −0.617963 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 8.12067e8i | − 0.705799i | ||||||||
\(389\) | 1.60902e9 | 1.38592 | 0.692959 | − | 0.720977i | \(-0.256307\pi\) | ||||
0.692959 | + | 0.720977i | \(0.256307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.33965e8 | −0.367144 | ||||||||
\(392\) | − 1.08167e9i | − 0.906971i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 7.12896e8 | 0.587205 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.88016e9i | 1.50809i | 0.656822 | + | 0.754046i | \(0.271900\pi\) | ||||
−0.656822 | + | 0.754046i | \(0.728100\pi\) | |||||||
\(398\) | − 5.70064e8i | − 0.453245i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.68592e8 | −0.208012 | −0.104006 | − | 0.994577i | \(-0.533166\pi\) | ||||
−0.104006 | + | 0.994577i | \(0.533166\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.41117e9i | − 1.07402i | ||||||||
\(404\) | −1.10275e9 | −0.832037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.40198e7 | −0.0103969 | ||||||||
\(407\) | 2.54563e8i | 0.187161i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.99478e7 | −0.0650069 | −0.0325034 | − | 0.999472i | \(-0.510348\pi\) | ||||
−0.0325034 | + | 0.999472i | \(0.510348\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 6.63264e8i | − 0.467247i | ||||||||
\(413\) | − 8.36083e7i | − 0.0584015i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.79305e8 | 0.666947 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 4.90306e7i | − 0.0328360i | ||||||||
\(419\) | 1.69054e9 | 1.12273 | 0.561367 | − | 0.827567i | \(-0.310276\pi\) | ||||
0.561367 | + | 0.827567i | \(0.310276\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.13333e9 | −0.740232 | −0.370116 | − | 0.928985i | \(-0.620682\pi\) | ||||
−0.370116 | + | 0.928985i | \(0.620682\pi\) | |||||||
\(422\) | − 1.07548e9i | − 0.696639i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.65037e8 | −0.359995 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.92424e7i | − 0.0119608i | ||||||||
\(428\) | − 1.05120e9i | − 0.648085i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.19943e9 | −1.32324 | −0.661621 | − | 0.749839i | \(-0.730131\pi\) | ||||
−0.661621 | + | 0.749839i | \(0.730131\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.51738e8i | 0.0898227i | 0.998991 | + | 0.0449114i | \(0.0143005\pi\) | ||||
−0.998991 | + | 0.0449114i | \(0.985699\pi\) | |||||||
\(434\) | 1.06294e8 | 0.0624160 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.69927e8 | −0.213754 | ||||||||
\(437\) | − 1.31783e8i | − 0.0755393i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.90763e8 | −0.558912 | −0.279456 | − | 0.960158i | \(-0.590154\pi\) | ||||
−0.279456 | + | 0.960158i | \(0.590154\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 8.68271e8i | − 0.478275i | ||||||||
\(443\) | − 1.77376e9i | − 0.969351i | −0.874694 | − | 0.484675i | \(-0.838938\pi\) | ||||
0.874694 | − | 0.484675i | \(-0.161062\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.23922e9 | 0.661419 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.21765e7i | 0.0221614i | ||||||||
\(449\) | −2.77010e8 | −0.144422 | −0.0722110 | − | 0.997389i | \(-0.523006\pi\) | ||||
−0.0722110 | + | 0.997389i | \(0.523006\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.96973e8 | 0.306434 | ||||||||
\(452\) | − 1.62898e9i | − 0.829720i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.60372e8 | −0.130587 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.94758e9i | 1.44464i | 0.691559 | + | 0.722320i | \(0.256924\pi\) | ||||
−0.691559 | + | 0.722320i | \(0.743076\pi\) | |||||||
\(458\) | − 2.17159e8i | − 0.105620i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.76687e9 | 1.31533 | 0.657667 | − | 0.753309i | \(-0.271543\pi\) | ||||
0.657667 | + | 0.753309i | \(0.271543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.63553e8i | − 0.217053i | −0.994094 | − | 0.108527i | \(-0.965387\pi\) | ||||
0.994094 | − | 0.108527i | \(-0.0346132\pi\) | |||||||
\(464\) | 1.40783e8 | 0.0654238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.53408e8 | 0.253335 | ||||||||
\(467\) | 4.17922e8i | 0.189883i | 0.995483 | + | 0.0949415i | \(0.0302664\pi\) | ||||
−0.995483 | + | 0.0949415i | \(0.969734\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.24636e7 | −0.0145309 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 1.72442e9i | − 0.754825i | ||||||||
\(473\) | − 6.50112e8i | − 0.282471i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.67137e8 | −0.0710310 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 2.99081e8i | − 0.125254i | ||||||||
\(479\) | −1.50973e9 | −0.627660 | −0.313830 | − | 0.949479i | \(-0.601612\pi\) | ||||
−0.313830 | + | 0.949479i | \(0.601612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.36895e9 | −0.560891 | ||||||||
\(482\) | − 1.19624e9i | − 0.486581i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.71014e9 | −0.685603 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.29460e8i | 0.364653i | 0.983238 | + | 0.182326i | \(0.0583627\pi\) | ||||
−0.983238 | + | 0.182326i | \(0.941637\pi\) | |||||||
\(488\) | − 3.96874e8i | − 0.154591i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.12803e9 | −1.95508 | −0.977541 | − | 0.210743i | \(-0.932412\pi\) | ||||
−0.977541 | + | 0.210743i | \(0.932412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 1.03637e9i | − 0.389540i | ||||||||
\(494\) | 2.63669e8 | 0.0984043 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.06737e9 | −0.392762 | ||||||||
\(497\) | 3.55880e8i | 0.130034i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.10649e8 | 0.147951 | 0.0739757 | − | 0.997260i | \(-0.476431\pi\) | ||||
0.0739757 | + | 0.997260i | \(0.476431\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 2.36807e9i | − 0.835470i | ||||||||
\(503\) | 5.02041e9i | 1.75894i | 0.475954 | + | 0.879470i | \(0.342103\pi\) | ||||
−0.475954 | + | 0.879470i | \(0.657897\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.69581e7 | −0.0298389 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.54452e9i | 0.522723i | ||||||||
\(509\) | −3.24926e9 | −1.09212 | −0.546062 | − | 0.837745i | \(-0.683874\pi\) | ||||
−0.546062 | + | 0.837745i | \(0.683874\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.76212e7 | −0.0290493 | ||||||||
\(512\) | − 1.39223e9i | − 0.458423i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.57312e8 | 0.278463 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 5.52965e8i | − 0.175987i | ||||||||
\(518\) | − 1.03114e8i | − 0.0325959i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.10950e9 | 0.653503 | 0.326752 | − | 0.945110i | \(-0.394046\pi\) | ||||
0.326752 | + | 0.945110i | \(0.394046\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.28911e9i | 1.61669i | 0.588709 | + | 0.808345i | \(0.299636\pi\) | ||||
−0.588709 | + | 0.808345i | \(0.700364\pi\) | |||||||
\(524\) | −1.54806e9 | −0.470034 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.64144e9 | 0.791391 | ||||||||
\(527\) | 7.85747e9i | 2.33854i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.17110e9 | 0.931355 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 5.07546e7i | − 0.0146145i | ||||||||
\(533\) | 3.21030e9i | 0.918334i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.69562e8 | −0.187808 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 1.65243e9i | − 0.457493i | ||||||||
\(539\) | 7.76836e8 | 0.213682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.04614e9 | 0.827101 | 0.413551 | − | 0.910481i | \(-0.364288\pi\) | ||||
0.413551 | + | 0.910481i | \(0.364288\pi\) | |||||||
\(542\) | 2.54802e9i | 0.687393i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.45284e9 | −1.45220 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 4.85537e9i | − 1.26843i | −0.773157 | − | 0.634215i | \(-0.781323\pi\) | ||||
0.773157 | − | 0.634215i | \(-0.218677\pi\) | |||||||
\(548\) | − 2.58013e9i | − 0.669746i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.14716e8 | 0.0801472 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 4.42478e8i | − 0.111264i | ||||||||
\(554\) | 3.09695e9 | 0.773838 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.08811e9 | 0.268480 | ||||||||
\(557\) | − 1.27762e9i | − 0.313263i | −0.987657 | − | 0.156631i | \(-0.949937\pi\) | ||||
0.987657 | − | 0.156631i | \(-0.0500635\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.49607e9 | 0.846522 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 1.86626e9i | − 0.443501i | ||||||||
\(563\) | 4.71265e9i | 1.11297i | 0.830856 | + | 0.556487i | \(0.187851\pi\) | ||||
−0.830856 | + | 0.556487i | \(0.812149\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.56585e9 | 0.826619 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.34003e9i | 1.68066i | ||||||||
\(569\) | 4.57800e9 | 1.04180 | 0.520898 | − | 0.853619i | \(-0.325597\pi\) | ||||
0.520898 | + | 0.853619i | \(0.325597\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.95119e9 | 1.11297 | 0.556485 | − | 0.830858i | \(-0.312150\pi\) | ||||
0.556485 | + | 0.830858i | \(0.312150\pi\) | |||||||
\(572\) | 4.44627e8i | 0.0993367i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.41812e8 | −0.0533686 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.51847e9i | 1.84606i | 0.384725 | + | 0.923031i | \(0.374296\pi\) | ||||
−0.384725 | + | 0.923031i | \(0.625704\pi\) | |||||||
\(578\) | 2.37256e9i | 0.511057i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.80112e8 | −0.0592536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 4.05799e8i | − 0.0848147i | ||||||||
\(584\) | −1.80719e9 | −0.375455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.93088e8 | 0.142281 | ||||||||
\(587\) | 5.62247e8i | 0.114735i | 0.998353 | + | 0.0573673i | \(0.0182706\pi\) | ||||
−0.998353 | + | 0.0573673i | \(0.981729\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.38608e9 | −0.481152 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.03544e9i | 0.205115i | ||||||||
\(593\) | 3.62110e9i | 0.713099i | 0.934277 | + | 0.356549i | \(0.116047\pi\) | ||||
−0.934277 | + | 0.356549i | \(0.883953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.91219e9 | 0.369971 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 4.67629e8i | − 0.0894227i | ||||||||
\(599\) | −7.48104e9 | −1.42222 | −0.711112 | − | 0.703079i | \(-0.751808\pi\) | ||||
−0.711112 | + | 0.703079i | \(0.751808\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.81270e9 | −1.09224 | −0.546119 | − | 0.837707i | \(-0.683895\pi\) | ||||
−0.546119 | + | 0.837707i | \(0.683895\pi\) | |||||||
\(602\) | 2.63336e8i | 0.0491953i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 7.00230e6 | 0.00129304 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.84051e9i | 0.696993i | 0.937310 | + | 0.348497i | \(0.113308\pi\) | ||||
−0.937310 | + | 0.348497i | \(0.886692\pi\) | |||||||
\(608\) | − 1.65587e9i | − 0.298788i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.97364e9 | 0.527405 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1.70484e9i | − 0.298932i | −0.988767 | − | 0.149466i | \(-0.952245\pi\) | ||||
0.988767 | − | 0.149466i | \(-0.0477555\pi\) | |||||||
\(614\) | −1.56360e9 | −0.272606 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.00870e7 | −0.0138048 | ||||||||
\(617\) | 2.80809e9i | 0.481297i | 0.970612 | + | 0.240649i | \(0.0773601\pi\) | ||||
−0.970612 | + | 0.240649i | \(0.922640\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.54365e9 | 0.431063 | 0.215532 | − | 0.976497i | \(-0.430852\pi\) | ||||
0.215532 | + | 0.976497i | \(0.430852\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.46077e9i | 0.576642i | ||||||||
\(623\) | 5.45812e8i | 0.0904346i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.76045e9 | 0.449748 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 2.96079e9i | − 0.477033i | ||||||||
\(629\) | 7.62238e9 | 1.22127 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.51146e8 | −0.0239494 | −0.0119747 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119747 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(632\) | − 9.12611e9i | − 1.43806i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.75337e8 | −0.0584936 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.17754e9i | 0.640373i | ||||||||
\(638\) | − 2.07669e8i | − 0.0316591i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.23625e10 | 1.85397 | 0.926987 | − | 0.375094i | \(-0.122390\pi\) | ||||
0.926987 | + | 0.375094i | \(0.122390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.86744e9i | − 0.425359i | −0.977122 | − | 0.212680i | \(-0.931781\pi\) | ||||
0.977122 | − | 0.212680i | \(-0.0682191\pi\) | |||||||
\(644\) | −9.00157e7 | −0.0132806 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.46812e9 | −0.214264 | ||||||||
\(647\) | 4.10640e9i | 0.596068i | 0.954555 | + | 0.298034i | \(0.0963309\pi\) | ||||
−0.954555 | + | 0.298034i | \(0.903669\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.23845e9 | 0.177837 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 5.36760e9i | − 0.758427i | ||||||||
\(653\) | 6.91100e9i | 0.971280i | 0.874159 | + | 0.485640i | \(0.161413\pi\) | ||||
−0.874159 | + | 0.485640i | \(0.838587\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.42819e9 | 0.335830 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.23986e8i | 0.0306499i | ||||||||
\(659\) | 3.42444e9 | 0.466112 | 0.233056 | − | 0.972463i | \(-0.425127\pi\) | ||||
0.233056 | + | 0.972463i | \(0.425127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.76437e9 | −0.911008 | −0.455504 | − | 0.890234i | \(-0.650541\pi\) | ||||
−0.455504 | + | 0.890234i | \(0.650541\pi\) | |||||||
\(662\) | − 4.10541e9i | − 0.549989i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.77731e9 | −0.765839 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 5.58165e8i | − 0.0728320i | ||||||||
\(668\) | 2.37696e9i | 0.308535i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.85028e8 | 0.0364215 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.74959e9i | 0.221250i | 0.993862 | + | 0.110625i | \(0.0352853\pi\) | ||||
−0.993862 | + | 0.110625i | \(0.964715\pi\) | |||||||
\(674\) | −3.75788e9 | −0.472752 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.38182e9 | 0.421053 | ||||||||
\(677\) | − 8.30011e9i | − 1.02807i | −0.857769 | − | 0.514036i | \(-0.828150\pi\) | ||||
0.857769 | − | 0.514036i | \(-0.171850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.64916e8 | −0.0692532 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.57448e9i | 0.190061i | ||||||||
\(683\) | − 1.21232e10i | − 1.45594i | −0.685610 | − | 0.727969i | \(-0.740464\pi\) | ||||
0.685610 | − | 0.727969i | \(-0.259536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.30908e8 | −0.0746160 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 2.64434e9i | − 0.309569i | ||||||||
\(689\) | 2.18224e9 | 0.254176 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.21846e9 | 0.947583 | 0.473791 | − | 0.880637i | \(-0.342885\pi\) | ||||
0.473791 | + | 0.880637i | \(0.342885\pi\) | |||||||
\(692\) | 5.84385e9i | 0.670390i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.52038e9 | 0.854046 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.78752e10i | − 1.99957i | ||||||||
\(698\) | 1.59210e9i | 0.177205i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.72231e9 | −0.517775 | −0.258888 | − | 0.965907i | \(-0.583356\pi\) | ||||
−0.258888 | + | 0.965907i | \(0.583356\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.31469e9i | 0.251275i | ||||||||
\(704\) | −6.24740e8 | −0.0674831 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.41781e9 | −0.365537 | ||||||||
\(707\) | 7.67131e8i | 0.0816397i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.78975e9 | −0.293970 | −0.146985 | − | 0.989139i | \(-0.546957\pi\) | ||||
−0.146985 | + | 0.989139i | \(0.546957\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.12574e10i | 1.16885i | ||||||||
\(713\) | 4.23184e9i | 0.437236i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.44794e9 | −0.758299 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 5.59524e9i | − 0.564136i | ||||||||
\(719\) | 1.51985e9 | 0.152493 | 0.0762463 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762463 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.61401e8 | −0.0458464 | ||||||||
\(722\) | 4.91740e9i | 0.486246i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.93429e9 | 0.581144 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.11761e9i | − 0.783534i | −0.920065 | − | 0.391767i | \(-0.871864\pi\) | ||||
0.920065 | − | 0.391767i | \(-0.128136\pi\) | |||||||
\(728\) | − 4.30679e8i | − 0.0413708i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.94663e10 | −1.84320 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.03241e10i | 0.968249i | 0.874999 | + | 0.484124i | \(0.160862\pi\) | ||||
−0.874999 | + | 0.484124i | \(0.839138\pi\) | |||||||
\(734\) | −5.11539e9 | −0.477466 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.93676e9 | −0.271517 | ||||||||
\(737\) | − 4.80867e8i | − 0.0442475i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.35365e10 | 1.23382 | 0.616908 | − | 0.787035i | \(-0.288385\pi\) | ||||
0.616908 | + | 0.787035i | \(0.288385\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.64374e8i | 0.0147713i | ||||||||
\(743\) | − 1.71936e10i | − 1.53782i | −0.639356 | − | 0.768910i | \(-0.720799\pi\) | ||||
0.639356 | − | 0.768910i | \(-0.279201\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.28710e9 | −0.201697 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 2.47571e9i | − 0.216294i | ||||||||
\(749\) | −7.31269e8 | −0.0635903 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.12478e10 | 0.969013 | 0.484506 | − | 0.874788i | \(-0.338999\pi\) | ||||
0.484506 | + | 0.874788i | \(0.338999\pi\) | |||||||
\(752\) | − 2.24919e9i | − 0.192870i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.11677e9 | 0.0948775 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.63068e10i | 1.36626i | 0.730296 | + | 0.683131i | \(0.239382\pi\) | ||||
−0.730296 | + | 0.683131i | \(0.760618\pi\) | |||||||
\(758\) | − 8.90118e9i | − 0.742345i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.14069e9 | −0.505093 | −0.252546 | − | 0.967585i | \(-0.581268\pi\) | ||||
−0.252546 | + | 0.967585i | \(0.581268\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.57341e8i | 0.0209736i | ||||||||
\(764\) | −5.22812e9 | −0.424149 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.57158e9 | −0.367507 | ||||||||
\(767\) | 6.65993e9i | 0.532949i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.45069e10 | −1.94333 | −0.971664 | − | 0.236368i | \(-0.924043\pi\) | ||||
−0.971664 | + | 0.236368i | \(0.924043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1.07067e10i | − 0.837518i | ||||||||
\(773\) | − 1.01722e10i | − 0.792110i | −0.918227 | − | 0.396055i | \(-0.870379\pi\) | ||||
0.918227 | − | 0.396055i | \(-0.129621\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.16514e10 | −0.895080 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 9.65411e9i | − 0.734994i | ||||||||
\(779\) | 5.42817e9 | 0.411408 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.27148e9 | −0.395962 | ||||||||
\(782\) | 2.60379e9i | 0.194707i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.15979e9 | 0.234181 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 9.79135e9i | − 0.716030i | −0.933716 | − | 0.358015i | \(-0.883454\pi\) | ||||
0.933716 | − | 0.358015i | \(-0.116546\pi\) | |||||||
\(788\) | 1.09311e10i | 0.795832i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.13320e9 | −0.0814124 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.53277e9i | 0.109150i | ||||||||
\(794\) | 1.12809e10 | 0.799786 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.74098e9 | 0.614277 | ||||||||
\(797\) | 9.75782e9i | 0.682729i | 0.939931 | + | 0.341365i | \(0.110889\pi\) | ||||
−0.939931 | + | 0.341365i | \(0.889111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.65574e10 | −1.14836 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.61155e9i | 0.110315i | ||||||||
\(803\) | − 1.29789e9i | − 0.0884572i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.46700e9 | −0.569583 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.58221e10i | 1.05517i | ||||||||
\(809\) | −2.78706e9 | −0.185066 | −0.0925330 | − | 0.995710i | \(-0.529496\pi\) | ||||
−0.0925330 | + | 0.995710i | \(0.529496\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.99983e9 | −0.526633 | −0.263316 | − | 0.964710i | \(-0.584816\pi\) | ||||
−0.263316 | + | 0.964710i | \(0.584816\pi\) | |||||||
\(812\) | − 2.14971e8i | − 0.0140907i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.52738e9 | 0.0992569 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 5.91135e9i | − 0.379236i | ||||||||
\(818\) | 5.39687e8i | 0.0344751i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.02402e10 | 0.645813 | 0.322906 | − | 0.946431i | \(-0.395340\pi\) | ||||
0.322906 | + | 0.946431i | \(0.395340\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 2.78682e10i | − 1.74265i | −0.490707 | − | 0.871324i | \(-0.663262\pi\) | ||||
0.490707 | − | 0.871324i | \(-0.336738\pi\) | |||||||
\(824\) | −9.51640e9 | −0.592553 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.01650e8 | −0.0309721 | ||||||||
\(827\) | − 2.35125e10i | − 1.44554i | −0.691090 | − | 0.722769i | \(-0.742869\pi\) | ||||
0.691090 | − | 0.722769i | \(-0.257131\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.28598e10 | 0.783960 | 0.391980 | − | 0.919974i | \(-0.371790\pi\) | ||||
0.391980 | + | 0.919974i | \(0.371790\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 3.35962e9i | − 0.202236i | ||||||||
\(833\) | − 2.32608e10i | − 1.39434i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.51802e8 | 0.0445022 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 1.01433e10i | − 0.595420i | ||||||||
\(839\) | −7.99832e9 | −0.467554 | −0.233777 | − | 0.972290i | \(-0.575109\pi\) | ||||
−0.233777 | + | 0.972290i | \(0.575109\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.59169e10 | −0.922725 | ||||||||
\(842\) | 6.79996e9i | 0.392567i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.64907e10 | 0.944147 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.18966e9i | 0.0672716i | ||||||||
\(848\) | − 1.65059e9i | − 0.0929510i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.10523e9 | 0.228341 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.20827e9i | − 0.232157i | −0.993240 | − | 0.116079i | \(-0.962968\pi\) | ||||
0.993240 | − | 0.116079i | \(-0.0370324\pi\) | |||||||
\(854\) | −1.15454e8 | −0.00634318 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.50824e10 | −0.821888 | ||||||||
\(857\) | − 3.19307e10i | − 1.73291i | −0.499259 | − | 0.866453i | \(-0.666394\pi\) | ||||
0.499259 | − | 0.866453i | \(-0.333606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.18002e10 | −1.17350 | −0.586752 | − | 0.809767i | \(-0.699594\pi\) | ||||
−0.586752 | + | 0.809767i | \(0.699594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.31966e10i | 0.701755i | ||||||||
\(863\) | 1.04728e10i | 0.554657i | 0.960775 | + | 0.277329i | \(0.0894490\pi\) | ||||
−0.960775 | + | 0.277329i | \(0.910551\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.10427e8 | 0.0476357 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.62985e9i | 0.0845916i | ||||||||
\(869\) | 6.55421e9 | 0.338806 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.58593e9 | 0.132603 | ||||||||
\(872\) | 5.30765e9i | 0.271078i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.90695e8 | −0.0400608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.77787e10i | − 0.890024i | −0.895525 | − | 0.445012i | \(-0.853199\pi\) | ||||
0.895525 | − | 0.445012i | \(-0.146801\pi\) | |||||||
\(878\) | 5.94458e9i | 0.296408i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.64253e9 | 0.376549 | 0.188274 | − | 0.982116i | \(-0.439711\pi\) | ||||
0.188274 | + | 0.982116i | \(0.439711\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.76375e10i | 1.35094i | 0.737386 | + | 0.675472i | \(0.236060\pi\) | ||||
−0.737386 | + | 0.675472i | \(0.763940\pi\) | |||||||
\(884\) | 1.33135e10 | 0.648200 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.06425e10 | −0.514076 | ||||||||
\(887\) | − 3.23087e10i | − 1.55449i | −0.629200 | − | 0.777243i | \(-0.716617\pi\) | ||||
0.629200 | − | 0.777243i | \(-0.283383\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.07445e9 | 0.0512897 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.90014e10i | 0.896414i | ||||||||
\(893\) | − 5.02801e9i | − 0.236274i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.32059e9 | −0.0613325 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.66206e9i | 0.0765914i | ||||||||
\(899\) | −1.01063e10 | −0.463908 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21509e10 | −0.553439 | ||||||||
\(902\) | − 3.58184e9i | − 0.162511i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.33723e10 | −1.05223 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.27142e10i | 1.01082i | 0.862880 | + | 0.505409i | \(0.168658\pi\) | ||||
−0.862880 | + | 0.505409i | \(0.831342\pi\) | |||||||
\(908\) | − 3.99238e9i | − 0.176983i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.50925e9 | −0.329065 | −0.164533 | − | 0.986372i | \(-0.552612\pi\) | ||||
−0.164533 | + | 0.986372i | \(0.552612\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 4.14916e9i | − 0.180431i | ||||||||
\(914\) | 1.76855e10 | 0.766136 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.32976e9 | 0.143146 | ||||||||
\(917\) | 1.07691e9i | 0.0461199i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.49374e10 | 1.05986 | 0.529928 | − | 0.848043i | \(-0.322219\pi\) | ||||
0.529928 | + | 0.848043i | \(0.322219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 1.66012e10i | − 0.697561i | ||||||||
\(923\) | − 2.83481e10i | − 1.18664i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.78132e9 | −0.115110 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − 7.01342e9i | − 0.288079i | ||||||||
\(929\) | −8.66205e9 | −0.354459 | −0.177229 | − | 0.984170i | \(-0.556713\pi\) | ||||
−0.177229 | + | 0.984170i | \(0.556713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.06363e9 | 0.286883 | ||||||||
\(932\) | 8.48559e9i | 0.343342i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 2.50753e9 | 0.100701 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.82655e10i | 1.12245i | 0.827663 | + | 0.561226i | \(0.189670\pi\) | ||||
−0.827663 | + | 0.561226i | \(0.810330\pi\) | |||||||
\(938\) | 1.94782e8i | 0.00770616i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.67082e10 | 1.82738 | 0.913691 | − | 0.406410i | \(-0.133220\pi\) | ||||
0.913691 | + | 0.406410i | \(0.133220\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 9.62713e9i | − 0.373857i | ||||||||
\(944\) | 5.03740e9 | 0.194897 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.90067e9 | −0.149803 | ||||||||
\(947\) | 4.67392e10i | 1.78837i | 0.447701 | + | 0.894184i | \(0.352243\pi\) | ||||
−0.447701 | + | 0.894184i | \(0.647757\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.97958e9 | 0.265093 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.39805e9i | 0.0900801i | ||||||||
\(953\) | 3.82420e10i | 1.43125i | 0.698484 | + | 0.715625i | \(0.253858\pi\) | ||||
−0.698484 | + | 0.715625i | \(0.746142\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.58591e9 | 0.169755 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.05837e9i | 0.332867i | ||||||||
\(959\) | −1.79487e9 | −0.0657157 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.91101e10 | 1.78500 | ||||||||
\(962\) | 8.21367e9i | 0.297457i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.83424e10 | 0.659457 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 4.90012e10i | − 1.74267i | −0.490692 | − | 0.871333i | \(-0.663256\pi\) | ||||
0.490692 | − | 0.871333i | \(-0.336744\pi\) | |||||||
\(968\) | 2.45368e10i | 0.869468i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.72929e10 | −0.956713 | −0.478357 | − | 0.878166i | \(-0.658767\pi\) | ||||
−0.478357 | + | 0.878166i | \(0.658767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 7.56947e8i | − 0.0263433i | ||||||||
\(974\) | 5.57676e9 | 0.193386 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.15935e9 | 0.0399155 | ||||||||
\(977\) | − 3.94482e9i | − 0.135331i | −0.997708 | − | 0.0676653i | \(-0.978445\pi\) | ||||
0.997708 | − | 0.0676653i | \(-0.0215550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.08484e9 | −0.275380 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.07682e10i | 1.03684i | ||||||||
\(983\) | 4.74320e8i | 0.0159270i | 0.999968 | + | 0.00796351i | \(0.00253489\pi\) | ||||
−0.999968 | + | 0.00796351i | \(0.997465\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −6.21824e9 | −0.206585 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.04292e9i | 0.133366i | ||||||||
\(989\) | −1.04841e10 | −0.344622 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.22197e10 | 0.398843 | 0.199421 | − | 0.979914i | \(-0.436094\pi\) | ||||
0.199421 | + | 0.979914i | \(0.436094\pi\) | |||||||
\(992\) | 5.31737e10i | 1.72944i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.13528e9 | 0.0689609 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 3.60690e10i | − 1.15266i | −0.817217 | − | 0.576330i | \(-0.804484\pi\) | ||||
0.817217 | − | 0.576330i | \(-0.195516\pi\) | |||||||
\(998\) | − 2.46390e9i | − 0.0784631i | ||||||||
\(999\) | 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 | 225.8.b.f.199.1 | 2 | ||
3.2 | odd | 2 | 75.8.b.c.49.2 | 2 | |||
5.2 | odd | 4 | 225.8.a.i.1.1 | 1 | |||
5.3 | odd | 4 | 9.8.a.a.1.1 | 1 | |||
5.4 | even | 2 | inner | 225.8.b.f.199.2 | 2 | ||
15.2 | even | 4 | 75.8.a.a.1.1 | 1 | |||
15.8 | even | 4 | 3.8.a.a.1.1 | ✓ | 1 | ||
15.14 | odd | 2 | 75.8.b.c.49.1 | 2 | |||
20.3 | even | 4 | 144.8.a.b.1.1 | 1 | |||
35.13 | even | 4 | 441.8.a.a.1.1 | 1 | |||
40.3 | even | 4 | 576.8.a.x.1.1 | 1 | |||
40.13 | odd | 4 | 576.8.a.w.1.1 | 1 | |||
45.13 | odd | 12 | 81.8.c.c.55.1 | 2 | |||
45.23 | even | 12 | 81.8.c.a.55.1 | 2 | |||
45.38 | even | 12 | 81.8.c.a.28.1 | 2 | |||
45.43 | odd | 12 | 81.8.c.c.28.1 | 2 | |||
60.23 | odd | 4 | 48.8.a.g.1.1 | 1 | |||
105.23 | even | 12 | 147.8.e.b.67.1 | 2 | |||
105.38 | odd | 12 | 147.8.e.a.79.1 | 2 | |||
105.53 | even | 12 | 147.8.e.b.79.1 | 2 | |||
105.68 | odd | 12 | 147.8.e.a.67.1 | 2 | |||
105.83 | odd | 4 | 147.8.a.b.1.1 | 1 | |||
120.53 | even | 4 | 192.8.a.i.1.1 | 1 | |||
120.83 | odd | 4 | 192.8.a.a.1.1 | 1 | |||
165.98 | odd | 4 | 363.8.a.b.1.1 | 1 | |||
195.38 | even | 4 | 507.8.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.8.a.a.1.1 | ✓ | 1 | 15.8 | even | 4 | ||
9.8.a.a.1.1 | 1 | 5.3 | odd | 4 | |||
48.8.a.g.1.1 | 1 | 60.23 | odd | 4 | |||
75.8.a.a.1.1 | 1 | 15.2 | even | 4 | |||
75.8.b.c.49.1 | 2 | 15.14 | odd | 2 | |||
75.8.b.c.49.2 | 2 | 3.2 | odd | 2 | |||
81.8.c.a.28.1 | 2 | 45.38 | even | 12 | |||
81.8.c.a.55.1 | 2 | 45.23 | even | 12 | |||
81.8.c.c.28.1 | 2 | 45.43 | odd | 12 | |||
81.8.c.c.55.1 | 2 | 45.13 | odd | 12 | |||
144.8.a.b.1.1 | 1 | 20.3 | even | 4 | |||
147.8.a.b.1.1 | 1 | 105.83 | odd | 4 | |||
147.8.e.a.67.1 | 2 | 105.68 | odd | 12 | |||
147.8.e.a.79.1 | 2 | 105.38 | odd | 12 | |||
147.8.e.b.67.1 | 2 | 105.23 | even | 12 | |||
147.8.e.b.79.1 | 2 | 105.53 | even | 12 | |||
192.8.a.a.1.1 | 1 | 120.83 | odd | 4 | |||
192.8.a.i.1.1 | 1 | 120.53 | even | 4 | |||
225.8.a.i.1.1 | 1 | 5.2 | odd | 4 | |||
225.8.b.f.199.1 | 2 | 1.1 | even | 1 | trivial | ||
225.8.b.f.199.2 | 2 | 5.4 | even | 2 | inner | ||
363.8.a.b.1.1 | 1 | 165.98 | odd | 4 | |||
441.8.a.a.1.1 | 1 | 35.13 | even | 4 | |||
507.8.a.a.1.1 | 1 | 195.38 | even | 4 | |||
576.8.a.w.1.1 | 1 | 40.13 | odd | 4 | |||
576.8.a.x.1.1 | 1 | 40.3 | even | 4 |