Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,7,Mod(319,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.319");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(88.3407681100\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 106x^{6} - 304x^{5} + 4359x^{4} - 8216x^{3} + 73366x^{2} - 69308x + 604693 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 319.6 | ||
Root | \(2.23205 + 3.79090i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.319 |
Dual form | 384.7.b.c.319.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 85.3891i | − 0.683112i | −0.939861 | − | 0.341556i | \(-0.889046\pi\) | ||||
0.939861 | − | 0.341556i | \(-0.110954\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 511.824i | 1.49220i | 0.665834 | + | 0.746100i | \(0.268076\pi\) | ||||
−0.665834 | + | 0.746100i | \(0.731924\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1212.89 | 0.911261 | 0.455631 | − | 0.890169i | \(-0.349414\pi\) | ||||
0.455631 | + | 0.890169i | \(0.349414\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2744.91i | 1.24939i | 0.780869 | + | 0.624694i | \(0.214776\pi\) | ||||
−0.780869 | + | 0.624694i | \(0.785224\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − 1331.08i | − 0.394395i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8524.35 | −1.73506 | −0.867531 | − | 0.497384i | \(-0.834294\pi\) | ||||
−0.867531 | + | 0.497384i | \(0.834294\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10429.2 | −1.52051 | −0.760257 | − | 0.649622i | \(-0.774927\pi\) | ||||
−0.760257 | + | 0.649622i | \(0.774927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7978.55i | 0.861522i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 4300.69i | − 0.353471i | −0.984258 | − | 0.176736i | \(-0.943446\pi\) | ||||
0.984258 | − | 0.176736i | \(-0.0565538\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8333.71 | 0.533357 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42442.0i | 1.74021i | 0.492866 | + | 0.870105i | \(0.335949\pi\) | ||||
−0.492866 | + | 0.870105i | \(0.664051\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 57843.0i | − 1.94163i | −0.239839 | − | 0.970813i | \(-0.577095\pi\) | ||||
0.239839 | − | 0.970813i | \(-0.422905\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 18907.1 | 0.526117 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 43704.2 | 1.01934 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 83505.3i | − 1.64858i | −0.566171 | − | 0.824288i | \(-0.691576\pi\) | ||||
0.566171 | − | 0.824288i | \(-0.308424\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 42788.9i | 0.721335i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −70152.4 | −1.01787 | −0.508933 | − | 0.860806i | \(-0.669960\pi\) | ||||
−0.508933 | + | 0.860806i | \(0.669960\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −28701.0 | −0.360987 | −0.180494 | − | 0.983576i | \(-0.557770\pi\) | ||||
−0.180494 | + | 0.983576i | \(0.557770\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 20749.5i | − 0.227704i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 58746.6i | 0.565834i | 0.959144 | + | 0.282917i | \(0.0913021\pi\) | ||||
−0.959144 | + | 0.282917i | \(0.908698\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −144315. | −1.22666 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −132882. | −1.00174 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 111109.i | − 0.746316i | −0.927768 | − | 0.373158i | \(-0.878275\pi\) | ||||
0.927768 | − | 0.373158i | \(-0.121725\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 103567.i | − 0.622494i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −162575. | −0.877870 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −118257. | −0.575798 | −0.287899 | − | 0.957661i | \(-0.592957\pi\) | ||||
−0.287899 | + | 0.957661i | \(0.592957\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 53174.3i | − 0.234268i | −0.993116 | − | 0.117134i | \(-0.962629\pi\) | ||||
0.993116 | − | 0.117134i | \(-0.0373706\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 124373.i | 0.497400i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 234385. | 0.853473 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42166.1 | 0.140197 | 0.0700986 | − | 0.997540i | \(-0.477669\pi\) | ||||
0.0700986 | + | 0.997540i | \(0.477669\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 67041.1i | − 0.204077i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 351599.i | 0.982363i | 0.871057 | + | 0.491182i | \(0.163435\pi\) | ||||
−0.871057 | + | 0.491182i | \(0.836565\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −91202.9 | −0.234445 | −0.117222 | − | 0.993106i | \(-0.537399\pi\) | ||||
−0.117222 | + | 0.993106i | \(0.537399\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 129910. | 0.307934 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 620786.i | 1.35978i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 775208.i | − 1.57231i | −0.618032 | − | 0.786153i | \(-0.712070\pi\) | ||||
0.618032 | − | 0.786153i | \(-0.287930\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −669966. | −1.17170 | −0.585852 | − | 0.810418i | \(-0.699240\pi\) | ||||
−0.585852 | + | 0.810418i | \(0.699240\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 727887.i | 1.18524i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 661605.i | 1.00471i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −504715. | −0.715940 | −0.357970 | − | 0.933733i | \(-0.616531\pi\) | ||||
−0.357970 | + | 0.933733i | \(0.616531\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.40491e6 | −1.86434 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 901683.i | − 1.12100i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 890541.i | 1.03868i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.03116e6 | 1.12982 | 0.564911 | − | 0.825152i | \(-0.308911\pi\) | ||||
0.564911 | + | 0.825152i | \(0.308911\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 294732. | 0.303754 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 927592.i | 0.900312i | 0.892950 | + | 0.450156i | \(0.148632\pi\) | ||||
−0.892950 | + | 0.450156i | \(0.851368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 357299.i | 0.326979i | 0.986545 | + | 0.163489i | \(0.0522750\pi\) | ||||
−0.986545 | + | 0.163489i | \(0.947725\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 681281. | 0.588516 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.16196e6 | −0.948508 | −0.474254 | − | 0.880388i | \(-0.657282\pi\) | ||||
−0.474254 | + | 0.880388i | \(0.657282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 741394.i | − 0.572492i | −0.958156 | − | 0.286246i | \(-0.907593\pi\) | ||||
0.958156 | − | 0.286246i | \(-0.0924075\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.30172e6i | − 0.951805i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −190737. | −0.132190 | −0.0660952 | − | 0.997813i | \(-0.521054\pi\) | ||||
−0.0660952 | + | 0.997813i | \(0.521054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −367231. | −0.241461 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 667012.i | 0.416463i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 4.36297e6i | − 2.58906i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −300462. | −0.169603 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.09357e6 | −0.587665 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.04581e6i | − 1.04746i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 819411.i | 0.400028i | 0.979793 | + | 0.200014i | \(0.0640988\pi\) | ||||
−0.979793 | + | 0.200014i | \(0.935901\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −447405. | −0.208416 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.76018e6 | −1.67261 | −0.836306 | − | 0.548263i | \(-0.815289\pi\) | ||||
−0.836306 | + | 0.548263i | \(0.815289\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 5.33793e6i | − 2.26891i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 323453.i | − 0.131465i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.86568e6 | 0.725563 | 0.362782 | − | 0.931874i | \(-0.381827\pi\) | ||||
0.362782 | + | 0.931874i | \(0.381827\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.37311e6 | −1.25599 | −0.627995 | − | 0.778218i | \(-0.716124\pi\) | ||||
−0.627995 | + | 0.778218i | \(0.716124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 915768.i | 0.326684i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.32927e6i | 1.13852i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.62408e6 | 1.18876 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.24965e6 | −0.708212 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.35713e6i | 1.01487i | 0.861691 | + | 0.507434i | \(0.169406\pi\) | ||||
−0.861691 | + | 0.507434i | \(0.830594\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.78813e6i | 1.10026i | 0.835081 | + | 0.550128i | \(0.185421\pi\) | ||||
−0.835081 | + | 0.550128i | \(0.814579\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.07142e6 | −0.578354 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.93916e6 | −1.32635 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.81264e6i | 1.50202i | 0.660293 | + | 0.751008i | \(0.270432\pi\) | ||||
−0.660293 | + | 0.751008i | \(0.729568\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 1.73202e6i | − 0.430886i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.20120e6 | 0.527450 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.12374e6 | −1.18311 | −0.591554 | − | 0.806266i | \(-0.701485\pi\) | ||||
−0.591554 | + | 0.806266i | \(0.701485\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − 1.61446e6i | − 0.359397i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 1.27729e6i | − 0.274247i | −0.990554 | − | 0.137123i | \(-0.956214\pi\) | ||||
0.990554 | − | 0.137123i | \(-0.0437857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.70770e6 | −0.560972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.53430e6 | −0.506838 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.87446e6i | 0.555160i | 0.960703 | + | 0.277580i | \(0.0895324\pi\) | ||||
−0.960703 | + | 0.277580i | \(0.910468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.26540e6i | 0.795876i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.84344e6 | −0.332437 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.99970e6 | 1.56917 | 0.784583 | − | 0.620024i | \(-0.212877\pi\) | ||||
0.784583 | + | 0.620024i | \(0.212877\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.33395e6i | 0.562242i | 0.959672 | + | 0.281121i | \(0.0907062\pi\) | ||||
−0.959672 | + | 0.281121i | \(0.909294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 828905.i | − 0.135254i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.13044e6 | −1.12616 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.03391e7 | −1.58109 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.93879e6i | 0.287174i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 3.66531e6i | − 0.526030i | −0.964792 | − | 0.263015i | \(-0.915283\pi\) | ||||
0.964792 | − | 0.263015i | \(-0.0847168\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.58154e6 | −1.19369 | −0.596847 | − | 0.802355i | \(-0.703580\pi\) | ||||
−0.596847 | + | 0.802355i | \(0.703580\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.65370e6 | 0.492753 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.04264e7i | − 1.36375i | −0.731470 | − | 0.681874i | \(-0.761165\pi\) | ||||
0.731470 | − | 0.681874i | \(-0.238835\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.34498e6i | 0.551352i | 0.961251 | + | 0.275676i | \(0.0889017\pi\) | ||||
−0.961251 | + | 0.275676i | \(0.911098\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 657305. | 0.0809429 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.17228e7 | −2.59674 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.99024e6i | 0.695317i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.04507e6i | − 0.117824i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.26495e7 | −1.38559 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.90463e6 | −0.628558 | −0.314279 | − | 0.949331i | \(-0.601763\pi\) | ||||
−0.314279 | + | 0.949331i | \(0.601763\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.48088e6i | 0.567168i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.45075e6i | 0.246595i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.96054e7 | 2.89729 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.42171e6 | −0.135357 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 2.33986e7i | − 2.16777i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 1.48155e7i | − 1.33598i | −0.744169 | − | 0.667992i | \(-0.767154\pi\) | ||||
0.744169 | − | 0.667992i | \(-0.232846\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.02509e6 | 0.177786 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.99262e6 | −0.341334 | −0.170667 | − | 0.985329i | \(-0.554592\pi\) | ||||
−0.170667 | + | 0.985329i | \(0.554592\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 3.71868e6i | − 0.309658i | −0.987941 | − | 0.154829i | \(-0.950517\pi\) | ||||
0.987941 | − | 0.154829i | \(-0.0494826\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.67710e6i | 0.785071i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.25478e6 | −0.415419 | −0.207710 | − | 0.978191i | \(-0.566601\pi\) | ||||
−0.207710 | + | 0.978191i | \(0.566601\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.01631e6 | 0.386528 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 1.20843e7i | − 0.907771i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.96267e6i | 0.583264i | 0.956531 | + | 0.291632i | \(0.0941982\pi\) | ||||
−0.956531 | + | 0.291632i | \(0.905802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.44459e6 | 0.103203 | 0.0516017 | − | 0.998668i | \(-0.483567\pi\) | ||||
0.0516017 | + | 0.998668i | \(0.483567\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.23229e7i | 0.837946i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 2.86272e7i | − 1.89971i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.04437e7 | −0.676484 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −920323. | −0.0581995 | −0.0290998 | − | 0.999577i | \(-0.509264\pi\) | ||||
−0.0290998 | + | 0.999577i | \(0.509264\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 5.21625e6i | − 0.322105i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.13466e7i | 0.684300i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.73409e6 | 0.337804 | 0.168902 | − | 0.985633i | \(-0.445978\pi\) | ||||
0.168902 | + | 0.985633i | \(0.445978\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.27400e7 | 2.46000 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.03134e7i | 0.580070i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.36973e7i | 0.752952i | 0.926426 | + | 0.376476i | \(0.122864\pi\) | ||||
−0.926426 | + | 0.376476i | \(0.877136\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.48752e6 | −0.509818 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.86774e6 | −0.413348 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.95267e7i | 1.00317i | 0.865110 | + | 0.501583i | \(0.167249\pi\) | ||||
−0.865110 | + | 0.501583i | \(0.832751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 8.79492e6i | − 0.441900i | −0.975285 | − | 0.220950i | \(-0.929084\pi\) | ||||
0.975285 | − | 0.220950i | \(-0.0709158\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.19004e7 | −1.07638 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.01079e7 | 0.486028 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 1.32017e6i | − 0.0621142i | −0.999518 | − | 0.0310571i | \(-0.990113\pi\) | ||||
0.999518 | − | 0.0310571i | \(-0.00988737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 1.40558e7i | − 0.647208i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.77259e7 | 0.798893 | 0.399446 | − | 0.916757i | \(-0.369202\pi\) | ||||
0.399446 | + | 0.916757i | \(0.369202\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.14391e7 | −1.82832 | −0.914158 | − | 0.405358i | \(-0.867147\pi\) | ||||
−0.914158 | + | 0.405358i | \(0.867147\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.38822e7i | 0.599684i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 3.59057e7i | − 1.51886i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.85271e7 | 2.01044 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.60742e7 | 0.652303 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.93196e6i | 0.196072i | 0.995183 | + | 0.0980362i | \(0.0312561\pi\) | ||||
−0.995183 | + | 0.0980362i | \(0.968744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.00978e7i | 0.393335i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.59442e6 | 0.175372 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.18050e7 | 0.441623 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.46899e7i | − 0.538665i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.44597e7i | 0.519795i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.54050e6 | −0.160031 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.35700e7 | 1.50582 | 0.752910 | − | 0.658124i | \(-0.228650\pi\) | ||||
0.752910 | + | 0.658124i | \(0.228650\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.56974e6i | 0.188781i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.31388e7i | 1.76657i | 0.468837 | + | 0.883285i | \(0.344673\pi\) | ||||
−0.468837 | + | 0.883285i | \(0.655327\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.18652e7 | 1.03916 | 0.519582 | − | 0.854421i | \(-0.326088\pi\) | ||||
0.519582 | + | 0.854421i | \(0.326088\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.06201e7 | 0.339780 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.33162e7i | 1.04587i | 0.852372 | + | 0.522936i | \(0.175163\pi\) | ||||
−0.852372 | + | 0.522936i | \(0.824837\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.14774e7i | 1.58579i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.81132e7 | −0.547621 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.89023e7 | 2.63819 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.28753e7i | 0.666371i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 1.15572e7i | − 0.330528i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00679e7 | −0.844337 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.35633e6 | −0.0649758 | −0.0324879 | − | 0.999472i | \(-0.510343\pi\) | ||||
−0.0324879 | + | 0.999472i | \(0.510343\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 2.02918e7i | − 0.549525i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 3.60053e6i | − 0.0957705i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.61254e7 | 0.943894 | 0.471947 | − | 0.881627i | \(-0.343551\pi\) | ||||
0.471947 | + | 0.881627i | \(0.343551\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.97330e6 | −0.0763202 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 7.01571e7i | − 1.76933i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.36484e7i | − 0.338221i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.72457e6 | −0.139407 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.76051e7 | 0.421357 | 0.210679 | − | 0.977555i | \(-0.432433\pi\) | ||||
0.210679 | + | 0.977555i | \(0.432433\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.02782e6i | 0.0712285i | 0.999366 | + | 0.0356143i | \(0.0113388\pi\) | ||||
−0.999366 | + | 0.0356143i | \(0.988661\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.03977e7i | 0.240445i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.74661e7 | −0.851755 | −0.425877 | − | 0.904781i | \(-0.640034\pi\) | ||||
−0.425877 | + | 0.904781i | \(0.640034\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.00227e7 | 0.671064 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 6.80120e7i | − 1.49479i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 5.14739e7i | − 1.11251i | −0.831012 | − | 0.556254i | \(-0.812238\pi\) | ||||
0.831012 | − | 0.556254i | \(-0.187762\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.17226e7 | 1.31197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.68374e6 | −0.0979203 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.78773e6i | 0.160152i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.52811e7i | 0.309142i | 0.987982 | + | 0.154571i | \(0.0493995\pi\) | ||||
−0.987982 | + | 0.154571i | \(0.950601\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.70470e7 | −0.339289 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.68684e7 | 1.11365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 6.19317e7i | − 1.19340i | −0.802464 | − | 0.596701i | \(-0.796478\pi\) | ||||
0.802464 | − | 0.596701i | \(-0.203522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 3.18910e7i | − 0.604749i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.16499e8 | −2.17420 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.43446e7 | 0.630870 | 0.315435 | − | 0.948947i | \(-0.397849\pi\) | ||||
0.315435 | + | 0.948947i | \(0.397849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.27733e7i | 0.230956i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.34734e7i | − 0.239817i | −0.992785 | − | 0.119908i | \(-0.961740\pi\) | ||||
0.992785 | − | 0.119908i | \(-0.0382601\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.30083e7 | 0.928885 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.97435e6 | −0.120329 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.13679e8i | 1.93122i | 0.259993 | + | 0.965610i | \(0.416280\pi\) | ||||
−0.259993 | + | 0.965610i | \(0.583720\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.66606e7i | 0.613294i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.86155e7 | −0.965683 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.61943e7 | −1.07406 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.96900e6i | 0.0634322i | 0.999497 | + | 0.0317161i | \(0.0100972\pi\) | ||||
−0.999497 | + | 0.0317161i | \(0.989903\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − 8.32100e7i | − 1.30996i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.54308e6 | 0.0704558 | 0.0352279 | − | 0.999379i | \(-0.488784\pi\) | ||||
0.0352279 | + | 0.999379i | \(0.488784\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.58774e8 | 2.42584 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 5.04214e6i | − 0.0759014i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.01283e8i | − 1.50228i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.23651e7 | 0.619211 | 0.309606 | − | 0.950865i | \(-0.399803\pi\) | ||||
0.309606 | + | 0.950865i | \(0.399803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.90831e7 | 0.418904 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6.05267e7i | − 0.859206i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.72077e7i | 0.800406i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.25816e7 | −0.725146 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.16747e7 | 1.11031 | 0.555157 | − | 0.831746i | \(-0.312658\pi\) | ||||
0.555157 | + | 0.831746i | \(0.312658\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.99635e7i | 1.07163i | 0.844335 | + | 0.535816i | \(0.179996\pi\) | ||||
−0.844335 | + | 0.535816i | \(0.820004\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.42754e7i | 0.188611i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.10395e7 | −0.925408 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.72159e7 | 0.349574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.18981e7i | 0.657325i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.45512e7i | 0.931157i | 0.885007 | + | 0.465578i | \(0.154154\pi\) | ||||
−0.885007 | + | 0.465578i | \(0.845846\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.35595e7 | −0.659740 | −0.329870 | − | 0.944026i | \(-0.607005\pi\) | ||||
−0.329870 | + | 0.944026i | \(0.607005\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.64938e7 | 0.686330 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.48528e7i | 0.537458i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.84937e7i | 0.454984i | 0.973780 | + | 0.227492i | \(0.0730525\pi\) | ||||
−0.973780 | + | 0.227492i | \(0.926947\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.50686e7 | −0.408886 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.20100e7 | −0.483216 | −0.241608 | − | 0.970374i | \(-0.577675\pi\) | ||||
−0.241608 | + | 0.970374i | \(0.577675\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.30972e7i | 0.489067i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.23325e7i | 0.585934i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.46094e8 | 1.61396 | 0.806981 | − | 0.590577i | \(-0.201100\pi\) | ||||
0.806981 | + | 0.590577i | \(0.201100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.50870e7 | −0.927542 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.90510e7i | 0.635233i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.19964e8i | 1.27355i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.64317e8 | 1.72160 | 0.860802 | − | 0.508941i | \(-0.169963\pi\) | ||||
0.860802 | + | 0.508941i | \(0.169963\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.22902e7 | −0.333913 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.01392e7i | − 0.103491i | −0.998660 | − | 0.0517455i | \(-0.983522\pi\) | ||||
0.998660 | − | 0.0517455i | \(-0.0164785\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 1.91081e8i | − 1.92519i | −0.270937 | − | 0.962597i | \(-0.587333\pi\) | ||||
0.270937 | − | 0.962597i | \(-0.412667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.69938e7 | −0.765768 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.30526e8 | −1.28159 | −0.640793 | − | 0.767713i | \(-0.721394\pi\) | ||||
−0.640793 | + | 0.767713i | \(0.721394\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.15817e7i | 0.209202i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.06101e7i | 0.867189i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.48111e7 | −0.328954 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.69140e7 | −0.810978 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 2.69996e7i | − 0.248772i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 1.71231e8i | − 1.55803i | −0.627003 | − | 0.779017i | \(-0.715719\pi\) | ||||
0.627003 | − | 0.779017i | \(-0.284281\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.29214e8 | 2.05971 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.43132e7 | 0.304523 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 8.80496e7i | − 0.771795i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 6.38316e7i | − 0.552648i | −0.961065 | − | 0.276324i | \(-0.910884\pi\) | ||||
0.961065 | − | 0.276324i | \(-0.0891163\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.98712e7 | −0.683067 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.36774e8 | 1.15547 | 0.577735 | − | 0.816224i | \(-0.303937\pi\) | ||||
0.577735 | + | 0.816224i | \(0.303937\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 3.61791e8i | − 3.01937i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 2.51669e7i | − 0.207498i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.79957e8 | −1.46588 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.94124e8 | −1.56235 | −0.781175 | − | 0.624312i | \(-0.785379\pi\) | ||||
−0.781175 | + | 0.624312i | \(0.785379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 1.99110e7i | − 0.158336i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.34518e7i | 0.734317i | 0.930158 | + | 0.367159i | \(0.119669\pi\) | ||||
−0.930158 | + | 0.367159i | \(0.880331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.92062e7 | 0.615014 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.22089e7 | −0.323877 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.32104e7i | 0.479331i | 0.970856 | + | 0.239665i | \(0.0770377\pi\) | ||||
−0.970856 | + | 0.239665i | \(0.922962\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 4.66799e7i | − 0.349838i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.95058e7 | −0.292623 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.05094e7 | 0.223363 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.12530e7i | 0.515622i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.48084e7i | 0.320522i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.37718e8 | −1.68092 | −0.840462 | − | 0.541871i | \(-0.817716\pi\) | ||||
−0.840462 | + | 0.541871i | \(0.817716\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.13720e7 | 0.359105 | 0.179553 | − | 0.983748i | \(-0.442535\pi\) | ||||
0.179553 | + | 0.983748i | \(0.442535\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.64909e7i | 0.459499i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.93074e8i | 3.36884i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.29540e8 | 0.875058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.87364e7 | −0.191933 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.92562e8i | − 1.27171i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.92189e7i | 0.647938i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.40291e8 | 0.905958 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.75038e8 | −1.11781 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.82128e8i | 1.15023i | 0.818072 | + | 0.575116i | \(0.195043\pi\) | ||||
−0.818072 | + | 0.575116i | \(0.804957\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.19711e7i | 0.324610i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.33069e7 | −0.391076 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.68154e7 | 0.408239 | 0.204120 | − | 0.978946i | \(-0.434567\pi\) | ||||
0.204120 | + | 0.978946i | \(0.434567\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 1.29213e7i | − 0.0780892i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 4.42636e8i | − 2.64602i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.96770e8 | 2.34619 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.11153e8 | −0.650190 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 606923.i | − 0.00351211i | −0.999998 | − | 0.00175606i | \(-0.999441\pi\) | ||||
0.999998 | − | 0.00175606i | \(-0.000558970\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 7.87816e7i | − 0.451013i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.61171e8 | −0.912845 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.47309e8 | −1.38584 | −0.692922 | − | 0.721012i | \(-0.743677\pi\) | ||||
−0.692922 | + | 0.721012i | \(0.743677\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.62869e7i | 0.0903009i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.02227e7i | 0.165800i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.83163e8 | 0.994262 | 0.497131 | − | 0.867675i | \(-0.334387\pi\) | ||||
0.497131 | + | 0.867675i | \(0.334387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.30136e8 | −0.699021 | −0.349510 | − | 0.936933i | \(-0.613652\pi\) | ||||
−0.349510 | + | 0.936933i | \(0.613652\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 5.71365e7i | − 0.303703i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 3.58407e7i | − 0.188527i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.46187e7 | 0.128156 | 0.0640778 | − | 0.997945i | \(-0.479589\pi\) | ||||
0.0640778 | + | 0.997945i | \(0.479589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.33773e8 | −0.689180 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 3.42905e8i | − 1.74842i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 1.34763e8i | − 0.680089i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.69556e7 | 0.284491 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.56349e7 | −0.225623 | −0.112811 | − | 0.993616i | \(-0.535986\pi\) | ||||
−0.112811 | + | 0.993616i | \(0.535986\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.03257e8i | 2.95227i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − 1.62531e8i | − 0.787360i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.58370e8 | 0.759466 | 0.379733 | − | 0.925096i | \(-0.376016\pi\) | ||||
0.379733 | + | 0.925096i | \(0.376016\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.72550e8 | −1.76862 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.77316e7i | 0.318323i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.34911e8i | 1.09301i | 0.837457 | + | 0.546504i | \(0.184042\pi\) | ||||
−0.837457 | + | 0.546504i | \(0.815958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.40513e7 | 0.295056 | 0.147528 | − | 0.989058i | \(-0.452868\pi\) | ||||
0.147528 | + | 0.989058i | \(0.452868\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.02464e7 | 0.0467324 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.56562e7i | 0.115858i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 6.98586e7i | − 0.312359i | −0.987729 | − | 0.156179i | \(-0.950082\pi\) | ||||
0.987729 | − | 0.156179i | \(-0.0499178\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.38626e8 | −1.49923 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.61254e8 | −0.706946 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.62634e7i | 0.114017i | 0.998374 | + | 0.0570085i | \(0.0181562\pi\) | ||||
−0.998374 | + | 0.0570085i | \(0.981844\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.33786e7i | 0.401441i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.98936e8 | −1.27269 | −0.636345 | − | 0.771404i | \(-0.719555\pi\) | ||||
−0.636345 | + | 0.771404i | \(0.719555\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.32500e8 | −0.558657 | −0.279328 | − | 0.960196i | \(-0.590112\pi\) | ||||
−0.279328 | + | 0.960196i | \(0.590112\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 1.62910e7i | − 0.0680256i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 2.58326e8i | − 1.06833i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.44757e7 | −0.182172 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.97186e8 | −0.799969 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.11829e8i | 2.86038i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1.19185e8i | − 0.474390i | −0.971462 | − | 0.237195i | \(-0.923772\pi\) | ||||
0.971462 | − | 0.237195i | \(-0.0762280\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.20440e7 | −0.362898 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.99687e7 | 0.273264 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 3.96132e8i | − 1.53257i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.54385e7i | 0.327454i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.84005e7 | 0.297677 | 0.148838 | − | 0.988862i | \(-0.452447\pi\) | ||||
0.148838 | + | 0.988862i | \(0.452447\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.05651e8 | −0.397410 | −0.198705 | − | 0.980059i | \(-0.563674\pi\) | ||||
−0.198705 | + | 0.980059i | \(0.563674\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.82035e7i | 0.142372i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 2.37697e8i | − 0.877628i | −0.898578 | − | 0.438814i | \(-0.855399\pi\) | ||||
0.898578 | − | 0.438814i | \(-0.144601\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.43432e8 | −0.524703 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.61503e8 | 1.67275 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.71315e7i | 0.0615257i | 0.999527 | + | 0.0307628i | \(0.00979366\pi\) | ||||
−0.999527 | + | 0.0307628i | \(0.990206\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.21079e8i | 1.14258i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.21623e7 | −0.0781482 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.62898e8 | −1.26803 | −0.634013 | − | 0.773323i | \(-0.718593\pi\) | ||||
−0.634013 | + | 0.773323i | \(0.718593\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 4.90659e8i | − 1.69893i | −0.527645 | − | 0.849465i | \(-0.676925\pi\) | ||||
0.527645 | − | 0.849465i | \(-0.323075\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.64747e8i | − 1.25156i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −4.55800e8 | −1.54992 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.82530e8 | 0.615114 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − 2.30950e8i | − 0.771330i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 6.44945e7i | − 0.213479i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.66234e8 | −0.545350 | −0.272675 | − | 0.962106i | \(-0.587908\pi\) | ||||
−0.272675 | + | 0.962106i | \(0.587908\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.15681e7 | 0.102645 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.98782e8i | − 0.640635i | −0.947310 | − | 0.320318i | \(-0.896210\pi\) | ||||
0.947310 | − | 0.320318i | \(-0.103790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.27772e8i | 1.68592i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.22387e7 | −0.197070 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 795875. | 0.00249794 | 0.00124897 | − | 0.999999i | \(-0.499602\pi\) | ||||
0.00124897 | + | 0.999999i | \(0.499602\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.59309e8i | − 0.495641i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 5.79684e7i | − 0.178781i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.04985e8 | 0.932439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.26115e8 | −1.89767 | −0.948833 | − | 0.315778i | \(-0.897734\pi\) | ||||
−0.948833 | + | 0.315778i | \(0.897734\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.50851e8i | 0.453261i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.88027e8i | 0.857982i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.98004e8 | 1.76606 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.19139e7 | −0.239843 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 7.92815e7i | − 0.230154i | −0.993357 | − | 0.115077i | \(-0.963289\pi\) | ||||
0.993357 | − | 0.115077i | \(-0.0367114\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.70894e8i | 2.50668i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.81966e7 | 0.223162 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.74764e8 | −1.34344 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 6.27826e7i | − 0.176157i | −0.996114 | − | 0.0880786i | \(-0.971927\pi\) | ||||
0.996114 | − | 0.0880786i | \(-0.0280727\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 1.88376e8i | − 0.524102i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.48764e8 | −0.686309 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.84283e8 | 0.777737 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.24126e8i | 0.336747i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 3.24833e8i | − 0.873924i | −0.899480 | − | 0.436962i | \(-0.856054\pi\) | ||||
0.899480 | − | 0.436962i | \(-0.143946\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.82874e8 | −0.487918 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.25190e7 | 0.0595845 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.53699e8i | 0.928154i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 1.75113e8i | − 0.455737i | −0.973692 | − | 0.227869i | \(-0.926824\pi\) | ||||
0.973692 | − | 0.227869i | \(-0.0731757\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.44658e8 | 0.626335 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.79408e8i | − 0.709458i | −0.934969 | − | 0.354729i | \(-0.884573\pi\) | ||||
0.934969 | − | 0.354729i | \(-0.115427\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.92096e8i | 0.483789i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.11428e7 | 0.127756 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.00369e8 | 1.23981 | 0.619907 | − | 0.784675i | \(-0.287170\pi\) | ||||
0.619907 | + | 0.784675i | \(0.287170\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 4.46254e8i | − 1.09680i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.12068e8i | 1.24842i | 0.781256 | + | 0.624211i | \(0.214579\pi\) | ||||
−0.781256 | + | 0.624211i | \(0.785421\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.86662e8 | 0.693269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.62802e8 | −0.390568 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 5.94721e8i | − 1.41536i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 4.54568e8i | − 1.07319i | −0.843838 | − | 0.536597i | \(-0.819709\pi\) | ||||
0.843838 | − | 0.536597i | \(-0.180291\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.43464e7 | −0.0336015 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.23464e8 | 0.751598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.55132e8i | 0.818657i | 0.912387 | + | 0.409329i | \(0.134237\pi\) | ||||
−0.912387 | + | 0.409329i | \(0.865763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 8.13133e7i | − 0.185967i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.07962e8 | −1.60641 | −0.803204 | − | 0.595704i | \(-0.796873\pi\) | ||||
−0.803204 | + | 0.595704i | \(0.796873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.79463e8 | 0.854272 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.76876e8i | 0.395081i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 3.24604e8i | − 0.719396i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.29332e8 | −1.16399 | −0.581995 | − | 0.813193i | \(-0.697728\pi\) | ||||
−0.581995 | + | 0.813193i | \(0.697728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.93856e7 | 0.195031 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.71149e8i | 1.23655i | 0.785963 | + | 0.618274i | \(0.212168\pi\) | ||||
−0.785963 | + | 0.618274i | \(0.787832\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 4.82046e8i | − 1.03558i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.66251e8 | 1.42028 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.31634e8 | 1.54768 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.26450e8i | 0.895189i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.60770e8i | 0.334904i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.96336e8 | 1.02605 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.56385e8 | 0.320828 | 0.160414 | − | 0.987050i | \(-0.448717\pi\) | ||||
0.160414 | + | 0.987050i | \(0.448717\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.13519e8i | 0.434717i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 9.76239e7i | − 0.197254i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.45958e8 | 0.292691 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.47896e8 | −0.294343 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.02539e8i | 1.19017i | 0.803661 | + | 0.595087i | \(0.202882\pi\) | ||||
−0.803661 | + | 0.595087i | \(0.797118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 5.00777e8i | − 0.981756i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.22646e8 | −0.238647 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.10619e8 | −0.213640 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.87958e8i | − 0.360307i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.04392e8i | 0.579178i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.30938e8 | 0.436164 | 0.218082 | − | 0.975930i | \(-0.430020\pi\) | ||||
0.218082 | + | 0.975930i | \(0.430020\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.15316e8 | 0.216185 | 0.108093 | − | 0.994141i | \(-0.465526\pi\) | ||||
0.108093 | + | 0.994141i | \(0.465526\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.37099e8i | − 0.255131i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.37511e8i | 0.808195i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.99329e8 | 0.548887 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.41393e8 | −0.621446 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.70428e7i | 0.157291i | 0.996903 | + | 0.0786454i | \(0.0250595\pi\) | ||||
−0.996903 | + | 0.0786454i | \(0.974941\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.58502e8i | 0.284337i | 0.989842 | + | 0.142169i | \(0.0454076\pi\) | ||||
−0.989842 | + | 0.142169i | \(0.954592\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.57566e8 | 0.280608 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.20614e8 | 1.09725 | 0.548624 | − | 0.836069i | \(-0.315152\pi\) | ||||
0.548624 | + | 0.836069i | \(0.315152\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.05341e9i | 1.84898i | 0.381206 | + | 0.924490i | \(0.375509\pi\) | ||||
−0.381206 | + | 0.924490i | \(0.624491\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 2.05794e7i | − 0.0358617i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.23019e9 | 2.12833 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.09067e8 | −0.187341 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 2.19109e8i | − 0.373666i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.80870e8i | 0.306254i | 0.988207 | + | 0.153127i | \(0.0489343\pi\) | ||||
−0.988207 | + | 0.153127i | \(0.951066\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.20650e9 | −2.02833 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.76319e8 | 0.461241 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.31208e8i | 0.383207i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.53784e8i | − 0.253081i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.45972e8 | −1.05558 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.59130e8 | −0.582724 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 8.06034e8i | − 1.29869i | −0.760493 | − | 0.649346i | \(-0.775043\pi\) | ||||
0.760493 | − | 0.649346i | \(-0.224957\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.16401e8i | 0.346228i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −4.09751e8 | −0.650995 | −0.325497 | − | 0.945543i | \(-0.605532\pi\) | ||||
−0.325497 | + | 0.945543i | \(0.605532\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.81567e8 | 1.39084 | 0.695418 | − | 0.718606i | \(-0.255219\pi\) | ||||
0.695418 | + | 0.718606i | \(0.255219\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 5.59714e8i | − 0.876914i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 5.12988e8i | − 0.798132i | −0.916922 | − | 0.399066i | \(-0.869334\pi\) | ||||
0.916922 | − | 0.399066i | \(-0.130666\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.45448e8 | 0.379237 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.56462e8 | 1.16073 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 9.40241e8i | − 1.43278i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.15742e8i | 0.175161i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.50571e8 | 0.376607 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.04710e9 | 1.56301 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 1.12822e8i | − 0.167262i | −0.996497 | − | 0.0836308i | \(-0.973348\pi\) | ||||
0.996497 | − | 0.0836308i | \(-0.0266516\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.68816e7i | 0.113202i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.06050e9 | 1.55090 | 0.775448 | − | 0.631412i | \(-0.217524\pi\) | ||||
0.775448 | + | 0.631412i | \(0.217524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.09446e8 | −1.17573 | −0.587863 | − | 0.808961i | \(-0.700030\pi\) | ||||
−0.587863 | + | 0.808961i | \(0.700030\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.57410e8i | 0.227092i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 3.59419e6i | − 0.00515027i | −0.999997 | − | 0.00257514i | \(-0.999180\pi\) | ||||
0.999997 | − | 0.00257514i | \(-0.000819692\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.19394e8 | −0.596922 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.16199e7 | 0.101251 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 6.12680e8i | − 0.860359i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 7.68476e8i | − 1.07192i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.84021e8 | 0.254971 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.45497e9 | 3.37884 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.47135e8i | 1.29490i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 2.28993e8i | − 0.310998i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.84683e8 | 0.384074 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.63921e8 | 1.02383 | 0.511913 | − | 0.859037i | \(-0.328937\pi\) | ||||
0.511913 | + | 0.859037i | \(0.328937\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.25405e8i | 0.300104i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.16841e7i | 0.121266i | 0.998160 | + | 0.0606330i | \(0.0193119\pi\) | ||||
−0.998160 | + | 0.0606330i | \(0.980688\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.12594e8 | −1.06773 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.07794e7 | −0.0923940 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.92455e9i | − 2.49587i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 1.18709e9i | − 1.52945i | −0.644356 | − | 0.764726i | \(-0.722874\pi\) | ||||
0.644356 | − | 0.764726i | \(-0.277126\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.79190e8 | 0.869385 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.65105e8 | −1.22735 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 6.95909e8i | − 0.879280i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.68236e7i | 0.108993i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.88302e8 | 0.484309 | 0.242155 | − | 0.970238i | \(-0.422146\pi\) | ||||
0.242155 | + | 0.970238i | \(0.422146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.50509e9 | 1.86515 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.28352e8i | 1.01993i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.82845e8i | 1.08006i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.69038e8 | 0.934822 | 0.467411 | − | 0.884040i | \(-0.345187\pi\) | ||||
0.467411 | + | 0.884040i | \(0.345187\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.96730e8 | 0.599961 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.80625e8i | 0.816843i | 0.912793 | + | 0.408422i | \(0.133921\pi\) | ||||
−0.912793 | + | 0.408422i | \(0.866079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.01703e8i | 0.359787i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.65551e8 | 0.196172 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.54633e8 | −0.535317 | −0.267659 | − | 0.963514i | \(-0.586250\pi\) | ||||
−0.267659 | + | 0.963514i | \(0.586250\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − 2.50343e8i | − 0.292912i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.19349e8i | 0.603834i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.97601e8 | −0.805987 | −0.402994 | − | 0.915203i | \(-0.632030\pi\) | ||||
−0.402994 | + | 0.915203i | \(0.632030\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.12977e8 | −0.359337 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.02453e8i | 0.915554i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.54900e8i | 1.08268i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.45830e9 | −2.76991 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.82357e8 | −0.316169 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.32769e8i | 0.815428i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 3.55787e7i | − 0.0393469i | −0.999806 | − | 0.0196735i | \(-0.993737\pi\) | ||||
0.999806 | − | 0.0196735i | \(-0.00626266\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.38585e9 | 1.52316 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.23470e8 | −0.899477 | −0.449738 | − | 0.893160i | \(-0.648483\pi\) | ||||
−0.449738 | + | 0.893160i | \(0.648483\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 1.72644e9i | − 1.87419i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.56590e8i | 0.384729i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.25779e7 | 0.0456563 | 0.0228281 | − | 0.999739i | \(-0.492733\pi\) | ||||
0.0228281 | + | 0.999739i | \(0.492733\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.12164e8 | −0.652408 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.80159e8i | − 0.190831i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 1.45686e9i | − 1.53376i | −0.641793 | − | 0.766878i | \(-0.721809\pi\) | ||||
0.641793 | − | 0.766878i | \(-0.278191\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.90297e8 | −0.931593 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.68713e8 | −0.487478 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.23434e8i | 0.127599i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.26328e9i | 1.29801i | 0.760784 | + | 0.649005i | \(0.224814\pi\) | ||||
−0.760784 | + | 0.649005i | \(0.775186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.67315e7 | −0.0375138 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.71014e8 | 0.376635 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.99928e8i | 0.908076i | 0.890982 | + | 0.454038i | \(0.150017\pi\) | ||||
−0.890982 | + | 0.454038i | \(0.849983\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 3.16318e8i | − 0.317268i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.7.b.c.319.6 | yes | 8 | |
4.3 | odd | 2 | inner | 384.7.b.c.319.2 | ✓ | 8 | |
8.3 | odd | 2 | inner | 384.7.b.c.319.7 | yes | 8 | |
8.5 | even | 2 | inner | 384.7.b.c.319.3 | yes | 8 | |
16.3 | odd | 4 | 768.7.g.g.511.2 | 8 | |||
16.5 | even | 4 | 768.7.g.g.511.3 | 8 | |||
16.11 | odd | 4 | 768.7.g.g.511.7 | 8 | |||
16.13 | even | 4 | 768.7.g.g.511.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.7.b.c.319.2 | ✓ | 8 | 4.3 | odd | 2 | inner | |
384.7.b.c.319.3 | yes | 8 | 8.5 | even | 2 | inner | |
384.7.b.c.319.6 | yes | 8 | 1.1 | even | 1 | trivial | |
384.7.b.c.319.7 | yes | 8 | 8.3 | odd | 2 | inner | |
768.7.g.g.511.2 | 8 | 16.3 | odd | 4 | |||
768.7.g.g.511.3 | 8 | 16.5 | even | 4 | |||
768.7.g.g.511.6 | 8 | 16.13 | even | 4 | |||
768.7.g.g.511.7 | 8 | 16.11 | odd | 4 |