Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [800,6,Mod(449,800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("800.449");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 800 = 2^{5} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 800.c (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: | \(128.307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{70})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.2 | ||
Root | \(4.18330 + 4.18330i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 800.449 |
Dual form | 800.6.c.f.449.3 |
$q$-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 \(\left(\mathbb{Z}/800\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 12.7332i | − 0.816835i | −0.912795 | − | 0.408418i | \(-0.866081\pi\) | ||||
0.912795 | − | 0.408418i | \(-0.133919\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 68.7332i | − 0.530178i | −0.964224 | − | 0.265089i | \(-0.914599\pi\) | ||||
0.964224 | − | 0.265089i | \(-0.0854013\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 80.8656 | 0.332780 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −327.332 | −0.815655 | −0.407828 | − | 0.913059i | \(-0.633714\pi\) | ||||
−0.407828 | + | 0.913059i | \(0.633714\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 719.328i | 1.18051i | 0.807218 | + | 0.590254i | \(0.200972\pi\) | ||||
−0.807218 | + | 0.590254i | \(0.799028\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 379.328i | − 0.318341i | −0.987251 | − | 0.159171i | \(-0.949118\pi\) | ||||
0.987251 | − | 0.159171i | \(-0.0508820\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1029.33 | 0.654139 | 0.327069 | − | 0.945000i | \(-0.393939\pi\) | ||||
0.327069 | + | 0.945000i | \(0.393939\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −875.194 | −0.433068 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 779.120i | − 0.307104i | −0.988141 | − | 0.153552i | \(-0.950929\pi\) | ||||
0.988141 | − | 0.153552i | \(-0.0490712\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 4123.85i | − 1.08866i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1392.66 | −0.307503 | −0.153751 | − | 0.988110i | \(-0.549135\pi\) | ||||
−0.153751 | + | 0.988110i | \(0.549135\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2744.68 | −0.512965 | −0.256483 | − | 0.966549i | \(-0.582564\pi\) | ||||
−0.256483 | + | 0.966549i | \(0.582564\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4167.98i | 0.666256i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 12640.6i | 1.51797i | 0.651108 | + | 0.758985i | \(0.274304\pi\) | ||||
−0.651108 | + | 0.758985i | \(0.725696\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9159.35 | 0.964280 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8210.43 | 0.762792 | 0.381396 | − | 0.924412i | \(-0.375443\pi\) | ||||
0.381396 | + | 0.924412i | \(0.375443\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 22524.5i | 1.85774i | 0.370408 | + | 0.928869i | \(0.379218\pi\) | ||||
−0.370408 | + | 0.928869i | \(0.620782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 7739.18i | − 0.511035i | −0.966804 | − | 0.255517i | \(-0.917754\pi\) | ||||
0.966804 | − | 0.255517i | \(-0.0822458\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12082.7 | 0.718912 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4830.06 | −0.260032 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2401.86i | 0.117451i | 0.998274 | + | 0.0587256i | \(0.0187037\pi\) | ||||
−0.998274 | + | 0.0587256i | \(0.981296\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 13106.6i | − 0.534323i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 15734.7 | 0.588474 | 0.294237 | − | 0.955732i | \(-0.404934\pi\) | ||||
0.294237 | + | 0.955732i | \(0.404934\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 32082.1 | 1.10392 | 0.551961 | − | 0.833870i | \(-0.313880\pi\) | ||||
0.551961 | + | 0.833870i | \(0.313880\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 5558.15i | − 0.176433i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 9009.07i | − 0.245184i | −0.992457 | − | 0.122592i | \(-0.960879\pi\) | ||||
0.992457 | − | 0.122592i | \(-0.0391207\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9920.70 | −0.250853 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −43832.3 | −1.03192 | −0.515962 | − | 0.856611i | \(-0.672566\pi\) | ||||
−0.515962 | + | 0.856611i | \(0.672566\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 65837.5i | 1.44599i | 0.690852 | + | 0.722997i | \(0.257236\pi\) | ||||
−0.690852 | + | 0.722997i | \(0.742764\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22498.6i | 0.432442i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39601.3 | 0.713907 | 0.356954 | − | 0.934122i | \(-0.383815\pi\) | ||||
0.356954 | + | 0.934122i | \(0.383815\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −32859.4 | −0.556477 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 63101.4i | − 1.00541i | −0.864458 | − | 0.502706i | \(-0.832338\pi\) | ||||
0.864458 | − | 0.502706i | \(-0.167662\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 17733.0i | 0.251179i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −34510.9 | −0.461829 | −0.230915 | − | 0.972974i | \(-0.574172\pi\) | ||||
−0.230915 | + | 0.972974i | \(0.574172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 49441.7 | 0.625879 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 34948.6i | 0.419008i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 14081.3i | − 0.151955i | −0.997110 | − | 0.0759773i | \(-0.975792\pi\) | ||||
0.997110 | − | 0.0759773i | \(-0.0242076\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −26469.9 | −0.271434 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 184018. | 1.79497 | 0.897485 | − | 0.441044i | \(-0.145392\pi\) | ||||
0.897485 | + | 0.441044i | \(0.145392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 70168.0i | − 0.651697i | −0.945422 | − | 0.325849i | \(-0.894350\pi\) | ||||
0.945422 | − | 0.325849i | \(-0.105650\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7952.89i | − 0.0671530i | −0.999436 | − | 0.0335765i | \(-0.989310\pi\) | ||||
0.999436 | − | 0.0335765i | \(-0.0106897\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −168681. | −1.35988 | −0.679939 | − | 0.733269i | \(-0.737994\pi\) | ||||
−0.679939 | + | 0.733269i | \(0.737994\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 160955. | 1.23993 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 61891.3i | 0.455967i | 0.973665 | + | 0.227984i | \(0.0732133\pi\) | ||||
−0.973665 | + | 0.227984i | \(0.926787\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 58168.9i | 0.392849i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26072.4 | −0.168777 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53904.8 | −0.334706 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 104545.i | − 0.623075i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 358695.i | 1.97340i | 0.162538 | + | 0.986702i | \(0.448032\pi\) | ||||
−0.162538 | + | 0.986702i | \(0.551968\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 286809. | 1.51747 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 312592. | 1.59148 | 0.795738 | − | 0.605641i | \(-0.207083\pi\) | ||||
0.795738 | + | 0.605641i | \(0.207083\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 70749.0i | − 0.346810i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 33573.9i | − 0.152827i | −0.997076 | − | 0.0764135i | \(-0.975653\pi\) | ||||
0.997076 | − | 0.0764135i | \(-0.0243469\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 342175. | 1.50214 | 0.751072 | − | 0.660220i | \(-0.229537\pi\) | ||||
0.751072 | + | 0.660220i | \(0.229537\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −98544.6 | −0.417431 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 235459.i | − 0.962887i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 153852.i | − 0.587232i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 239318. | 0.883099 | 0.441549 | − | 0.897237i | \(-0.354429\pi\) | ||||
0.441549 | + | 0.897237i | \(0.354429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −169513. | −0.605007 | −0.302503 | − | 0.953148i | \(-0.597822\pi\) | ||||
−0.302503 | + | 0.953148i | \(0.597822\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 30674.6i | − 0.105938i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 186382.i | 0.603469i | 0.953392 | + | 0.301735i | \(0.0975656\pi\) | ||||
−0.953392 | + | 0.301735i | \(0.902434\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 30583.3 | 0.0959383 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −53551.4 | −0.162820 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 403058.i | − 1.18822i | −0.804382 | − | 0.594112i | \(-0.797504\pi\) | ||||
0.804382 | − | 0.594112i | \(-0.202496\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 167631.i | − 0.465119i | −0.972582 | − | 0.232560i | \(-0.925290\pi\) | ||||
0.972582 | − | 0.232560i | \(-0.0747101\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −146140. | −0.393597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 83237.2 | 0.217684 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 84080.4i | − 0.213589i | −0.994281 | − | 0.106795i | \(-0.965941\pi\) | ||||
0.994281 | − | 0.106795i | \(-0.0340588\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 200353.i | − 0.480686i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 741698. | 1.73019 | 0.865096 | − | 0.501607i | \(-0.167257\pi\) | ||||
0.865096 | + | 0.501607i | \(0.167257\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −343670. | −0.779732 | −0.389866 | − | 0.920872i | \(-0.627479\pi\) | ||||
−0.389866 | + | 0.920872i | \(0.627479\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 408508.i | − 0.901722i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 124166.i | 0.259657i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −283445. | −0.577184 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −631035. | −1.25161 | −0.625806 | − | 0.779978i | \(-0.715230\pi\) | ||||
−0.625806 | + | 0.779978i | \(0.715230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 847791.i | − 1.63831i | −0.573574 | − | 0.819154i | \(-0.694444\pi\) | ||||
0.573574 | − | 0.819154i | \(-0.305556\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 397282.i | − 0.729346i | −0.931136 | − | 0.364673i | \(-0.881181\pi\) | ||||
0.931136 | − | 0.364673i | \(-0.118819\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 896038. | 1.60396 | 0.801980 | − | 0.597350i | \(-0.203780\pi\) | ||||
0.801980 | + | 0.597350i | \(0.203780\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −114714. | −0.200275 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 95721.7i | 0.163031i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 63004.0i | − 0.102198i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −336932. | −0.533552 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 876761. | 1.35574 | 0.677868 | − | 0.735184i | \(-0.262904\pi\) | ||||
0.677868 | + | 0.735184i | \(0.262904\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 558125.i | 0.842913i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 188651.i | 0.271963i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 838322. | 1.18114 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 272861. | 0.375804 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 54891.1i | 0.0739162i | 0.999317 | + | 0.0369581i | \(0.0117668\pi\) | ||||
−0.999317 | + | 0.0369581i | \(0.988233\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 803329.i | − 1.03473i | −0.855764 | − | 0.517367i | \(-0.826912\pi\) | ||||
0.855764 | − | 0.517367i | \(-0.173088\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 589546. | 0.742898 | 0.371449 | − | 0.928453i | \(-0.378861\pi\) | ||||
0.371449 | + | 0.928453i | \(0.378861\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 286479. | 0.353234 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 1.02048e6i | − 1.23144i | −0.787965 | − | 0.615720i | \(-0.788865\pi\) | ||||
0.787965 | − | 0.615720i | \(-0.211135\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 504251.i | − 0.583145i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.65512e6 | 1.87428 | 0.937139 | − | 0.348956i | \(-0.113464\pi\) | ||||
0.937139 | + | 0.348956i | \(0.113464\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.19028e6 | −1.32010 | −0.660049 | − | 0.751223i | \(-0.729464\pi\) | ||||
−0.660049 | + | 0.751223i | \(0.729464\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 583689.i | − 0.634112i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 740424.i | 0.772215i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −803483. | −0.821256 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 23776.0 | 0.0238207 | 0.0119104 | − | 0.999929i | \(-0.496209\pi\) | ||||
0.0119104 | + | 0.999929i | \(0.496209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 255031.i | 0.250491i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 341681.i | − 0.322692i | −0.986898 | − | 0.161346i | \(-0.948416\pi\) | ||||
0.986898 | − | 0.161346i | \(-0.0515835\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 868828. | 0.804794 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −112618. | −0.102331 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 1.09120e6i | − 0.972782i | −0.873741 | − | 0.486391i | \(-0.838313\pi\) | ||||
0.873741 | − | 0.486391i | \(-0.161687\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 439434.i | 0.377238i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 922907. | 0.777638 | 0.388819 | − | 0.921314i | \(-0.372883\pi\) | ||||
0.388819 | + | 0.921314i | \(0.372883\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.34302e6 | 1.11086 | 0.555430 | − | 0.831564i | \(-0.312554\pi\) | ||||
0.555430 | + | 0.831564i | \(0.312554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 629551.i | − 0.511240i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 247543.i | − 0.193843i | −0.995292 | − | 0.0969217i | \(-0.969100\pi\) | ||||
0.995292 | − | 0.0969217i | \(-0.0308996\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −221951. | −0.170705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.03588e6 | 0.782604 | 0.391302 | − | 0.920262i | \(-0.372025\pi\) | ||||
0.391302 | + | 0.920262i | \(0.372025\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.39427e6i | − 1.77708i | −0.458795 | − | 0.888542i | \(-0.651719\pi\) | ||||
0.458795 | − | 0.888542i | \(-0.348281\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 564329.i | − 0.404415i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27597e6 | 0.898659 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −179300. | −0.124122 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.44817e6i | 1.66599i | 0.553280 | + | 0.832995i | \(0.313376\pi\) | ||||
−0.553280 | + | 0.832995i | \(0.686624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.34987e6i | 0.887973i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 560443. | 0.362538 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.54818e6 | 0.984931 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.34314e6i | − 1.46620i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 939476.i | 0.568905i | 0.958690 | + | 0.284453i | \(0.0918118\pi\) | ||||
−0.958690 | + | 0.284453i | \(0.908188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −893463. | −0.532329 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.13941e6 | 0.668004 | 0.334002 | − | 0.942572i | \(-0.391601\pi\) | ||||
0.334002 | + | 0.942572i | \(0.391601\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 1.51692e6i | − 0.875191i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.73484e6i | 1.52857i | 0.644880 | + | 0.764284i | \(0.276907\pi\) | ||||
−0.644880 | + | 0.764284i | \(0.723093\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 455861. | 0.250816 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −101266. | −0.0548530 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 390453.i | − 0.208239i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.14785e6i | 1.11080i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −531939. | −0.270939 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −122807. | −0.0616104 | −0.0308052 | − | 0.999525i | \(-0.509807\pi\) | ||||
−0.0308052 | + | 0.999525i | \(0.509807\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.02219e6i | 0.505150i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 1.65582e6i | − 0.794217i | −0.917772 | − | 0.397108i | \(-0.870014\pi\) | ||||
0.917772 | − | 0.397108i | \(-0.129986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 788075. | 0.372450 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 898423. | 0.418403 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 1.98568e6i | − 0.911329i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.63896e6i | 0.730711i | 0.930868 | + | 0.365355i | \(0.119052\pi\) | ||||
−0.930868 | + | 0.365355i | \(0.880948\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.07756e6 | −0.913040 | −0.456520 | − | 0.889713i | \(-0.650904\pi\) | ||||
−0.456520 | + | 0.889713i | \(0.650904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.96640e6 | 1.28517 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.87344e6i | 1.65447i | 0.561854 | + | 0.827236i | \(0.310088\pi\) | ||||
−0.561854 | + | 0.827236i | \(0.689912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 331985.i | 0.137863i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.16016e6 | 1.29411 | 0.647057 | − | 0.762441i | \(-0.275999\pi\) | ||||
0.647057 | + | 0.762441i | \(0.275999\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.41658e6 | −0.572103 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 686380.i | 0.273400i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 1.76875e6i | − 0.685491i | −0.939428 | − | 0.342745i | \(-0.888643\pi\) | ||||
0.939428 | − | 0.342745i | \(-0.111357\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 663941. | 0.253842 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 165087. | 0.0622700 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.86744e6i | 1.43930i | 0.694336 | + | 0.719651i | \(0.255698\pi\) | ||||
−0.694336 | + | 0.719651i | \(0.744302\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.00178e6i | − 0.363009i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.06193e6 | −1.81016 | −0.905082 | − | 0.425236i | \(-0.860191\pi\) | ||||
−0.905082 | + | 0.425236i | \(0.860191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.56734e6 | 1.61195 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.23524e6i | 1.47530i | 0.675181 | + | 0.737652i | \(0.264065\pi\) | ||||
−0.675181 | + | 0.737652i | \(0.735935\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.82146e6i | 0.618219i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 390940. | 0.130989 | 0.0654947 | − | 0.997853i | \(-0.479137\pi\) | ||||
0.0654947 | + | 0.997853i | \(0.479137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −295542. | −0.0977637 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 3.98030e6i | − 1.29997i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.36908e6i | 1.07284i | 0.843951 | + | 0.536421i | \(0.180224\pi\) | ||||
−0.843951 | + | 0.536421i | \(0.819776\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −900861. | −0.283286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.51542e6 | −1.71284 | −0.856422 | − | 0.516277i | \(-0.827318\pi\) | ||||
−0.856422 | + | 0.516277i | \(0.827318\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 1.97433e6i | − 0.605559i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 4.13767e6i | − 1.23814i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.29662e6 | 0.974453 | 0.487227 | − | 0.873276i | \(-0.338009\pi\) | ||||
0.487227 | + | 0.873276i | \(0.338009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −427503. | −0.124834 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 1.08149e6i | − 0.311996i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 4.35699e6i | − 1.22700i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.88088e6 | 1.91474 | 0.957368 | − | 0.288870i | \(-0.0932795\pi\) | ||||
0.957368 | + | 0.288870i | \(0.0932795\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.04971e6 | 0.838596 | 0.419298 | − | 0.907849i | \(-0.362276\pi\) | ||||
0.419298 | + | 0.907849i | \(0.362276\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 625834.i | − 0.170062i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 2.20511e6i | − 0.585275i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.99815e6 | −0.786520 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.20632e6 | −1.60931 | −0.804657 | − | 0.593740i | \(-0.797651\pi\) | ||||
−0.804657 | + | 0.593740i | \(0.797651\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 1.87723e6i | − 0.481169i | −0.970628 | − | 0.240585i | \(-0.922661\pi\) | ||||
0.970628 | − | 0.240585i | \(-0.0773392\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 801971.i | − 0.200888i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.85883e6 | 0.460341 | 0.230170 | − | 0.973150i | \(-0.426072\pi\) | ||||
0.230170 | + | 0.973150i | \(0.426072\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 977079. | 0.239240 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.39604e6i | 1.06427i | 0.846659 | + | 0.532136i | \(0.178610\pi\) | ||||
−0.846659 | + | 0.532136i | \(0.821390\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.04728e6i | − 0.721346i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 984885. | 0.230552 | 0.115276 | − | 0.993333i | \(-0.463225\pi\) | ||||
0.115276 | + | 0.993333i | \(0.463225\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.68754e6 | −0.622175 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.15844e6i | 0.494191i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 696014.i | − 0.155893i | −0.996958 | − | 0.0779466i | \(-0.975164\pi\) | ||||
0.996958 | − | 0.0779466i | \(-0.0248364\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.56429e6 | −0.346566 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.03623e6 | 1.32286 | 0.661430 | − | 0.750007i | \(-0.269950\pi\) | ||||
0.661430 | + | 0.750007i | \(0.269950\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.07793e6i | 0.450483i | 0.974303 | + | 0.225241i | \(0.0723171\pi\) | ||||
−0.974303 | + | 0.225241i | \(0.927683\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 1.81361e6i | − 0.384816i | −0.981315 | − | 0.192408i | \(-0.938370\pi\) | ||||
0.981315 | − | 0.192408i | \(-0.0616296\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −619222. | −0.129991 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.37324e6 | 0.492935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 7.37300e6i | − 1.51527i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 194228.i | 0.0390854i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.10687e6 | −1.21613 | −0.608065 | − | 0.793887i | \(-0.708054\pi\) | ||||
−0.608065 | + | 0.793887i | \(0.708054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.09273e6 | −1.79197 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 681881.i | 0.132997i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.32848e6i | 0.253823i | 0.991914 | + | 0.126912i | \(0.0405064\pi\) | ||||
−0.991914 | + | 0.126912i | \(0.959494\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5.13222e6 | −0.970583 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.72480e6 | −1.63325 | −0.816623 | − | 0.577171i | \(-0.804157\pi\) | ||||
−0.816623 | + | 0.577171i | \(0.804157\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 528273.i | 0.0978907i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.01273e6i | 0.547104i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.20143e6 | −0.935129 | −0.467564 | − | 0.883959i | \(-0.654868\pi\) | ||||
−0.467564 | + | 0.883959i | \(0.654868\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.13448e6 | −0.379926 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.44189e6i | 1.13525i | 0.823286 | + | 0.567627i | \(0.192139\pi\) | ||||
−0.823286 | + | 0.567627i | \(0.807861\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.86083e6i | 0.321504i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.31511e6 | 0.396075 | 0.198038 | − | 0.980194i | \(-0.436543\pi\) | ||||
0.198038 | + | 0.980194i | \(0.436543\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.52522e6 | 0.766633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 4.24479e6i | − 0.712136i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.53328e6i | 0.416828i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.07061e6 | −0.174467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.65617e6 | −1.55851 | −0.779257 | − | 0.626705i | \(-0.784403\pi\) | ||||
−0.779257 | + | 0.626705i | \(0.784403\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.40583e6i | 1.02405i | 0.858970 | + | 0.512025i | \(0.171105\pi\) | ||||
−0.858970 | + | 0.512025i | \(0.828895\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.04114e6i | 0.163298i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.82931e6 | 0.905687 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.27239e6 | 0.195833 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.90599e6i | 0.900481i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 9.44418e6i | − 1.41328i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.95507e6 | −0.586384 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.32300e6 | 0.194342 | 0.0971709 | − | 0.995268i | \(-0.469021\pi\) | ||||
0.0971709 | + | 0.995268i | \(0.469021\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.37602e6i | 0.636912i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.68044e6i | 0.668834i | 0.942425 | + | 0.334417i | \(0.108539\pi\) | ||||
−0.942425 | + | 0.334417i | \(0.891461\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.59434e6 | 0.367363 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.43350e6 | −0.201149 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 2.72192e6i | − 0.378498i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.58860e6i | 1.03639i | 0.855262 | + | 0.518195i | \(0.173396\pi\) | ||||
−0.855262 | + | 0.518195i | \(0.826604\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.62025e7 | −2.19307 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.58103e6 | 0.212097 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 399946.i | 0.0531777i | 0.999646 | + | 0.0265889i | \(0.00846450\pi\) | ||||
−0.999646 | + | 0.0265889i | \(0.991536\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.25853e6i | 0.295032i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.57419e6 | −0.203834 | −0.101917 | − | 0.994793i | \(-0.532498\pi\) | ||||
−0.101917 | + | 0.994793i | \(0.532498\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.11290e6 | 0.399554 | 0.199777 | − | 0.979841i | \(-0.435978\pi\) | ||||
0.199777 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.03509e6i | 1.02236i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 5.57621e6i | − 0.697267i | −0.937259 | − | 0.348634i | \(-0.886646\pi\) | ||||
0.937259 | − | 0.348634i | \(-0.113354\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.07951e7 | −1.33823 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.33716e6 | −0.533047 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 786205.i | − 0.0957997i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.11890e7i | − 1.34028i | −0.742236 | − | 0.670138i | \(-0.766235\pi\) | ||||
0.742236 | − | 0.670138i | \(-0.233765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.82518e6 | −0.335551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.05868e6 | −0.595756 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.44707e7i | − 1.68987i | −0.534871 | − | 0.844934i | \(-0.679640\pi\) | ||||
0.534871 | − | 0.844934i | \(-0.320360\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 1.14094e7i | − 1.31017i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.32734e6 | −0.265028 | −0.132514 | − | 0.991181i | \(-0.542305\pi\) | ||||
−0.132514 | + | 0.991181i | \(0.542305\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.28568e6 | 0.483987 | 0.241993 | − | 0.970278i | \(-0.422199\pi\) | ||||
0.241993 | + | 0.970278i | \(0.422199\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 728524.i | − 0.0815925i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.04310e7i | 1.14909i | 0.818471 | + | 0.574547i | \(0.194822\pi\) | ||||
−0.818471 | + | 0.574547i | \(0.805178\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.21884e6 | 0.133170 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.56701e6 | 0.603280 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 3.52495e6i | − 0.378880i | −0.981892 | − | 0.189440i | \(-0.939333\pi\) | ||||
0.981892 | − | 0.189440i | \(-0.0606673\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.16178e7i | 1.22861i | 0.789070 | + | 0.614303i | \(0.210563\pi\) | ||||
−0.789070 | + | 0.614303i | \(0.789437\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.04132e7 | −1.09234 | −0.546171 | − | 0.837673i | \(-0.683915\pi\) | ||||
−0.546171 | + | 0.837673i | \(0.683915\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.21297e6 | −0.334332 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.37204e6i | 0.244851i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.29022e6i | 0.435824i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.79493e6 | 0.483232 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.57325e6 | −0.657214 | −0.328607 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328607 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 1.11640e7i | − 1.10741i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.69146e6i | 0.848680i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.54452e6 | −0.343404 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.21768e6 | 0.693829 | 0.346914 | − | 0.937897i | \(-0.387229\pi\) | ||||
0.346914 | + | 0.937897i | \(0.387229\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 989729.i | − 0.0944036i | −0.998885 | − | 0.0472018i | \(-0.984970\pi\) | ||||
0.998885 | − | 0.0472018i | \(-0.0150304\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 4.31383e6i | − 0.405138i | −0.979268 | − | 0.202569i | \(-0.935071\pi\) | ||||
0.979268 | − | 0.202569i | \(-0.0649290\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.15046e6 | −0.479992 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.40213e6 | 0.222149 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.49637e7i | 1.37327i | 0.727004 | + | 0.686633i | \(0.240912\pi\) | ||||
−0.727004 | + | 0.686633i | \(0.759088\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.32399e6i | 0.481198i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.42210e6 | −0.396657 | −0.198328 | − | 0.980136i | \(-0.563551\pi\) | ||||
−0.198328 | + | 0.980136i | \(0.563551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.57925e7 | 1.40587 | 0.702937 | − | 0.711252i | \(-0.251872\pi\) | ||||
0.702937 | + | 0.711252i | \(0.251872\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 3.47440e6i | − 0.306970i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.08505e6i | 0.0944352i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 698939. | 0.0603773 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.05015e7 | −0.900420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.60799e6i | 0.477276i | 0.971109 | + | 0.238638i | \(0.0767009\pi\) | ||||
−0.971109 | + | 0.238638i | \(0.923299\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 7.01232e6i | − 0.588017i | −0.955803 | − | 0.294009i | \(-0.905011\pi\) | ||||
0.955803 | − | 0.294009i | \(-0.0949894\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −967853. | −0.0805629 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.02289e7 | −0.845207 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.16662e7i | 1.77718i | 0.458703 | + | 0.888590i | \(0.348314\pi\) | ||||
−0.458703 | + | 0.888590i | \(0.651686\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 7.50681e6i | − 0.606825i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.72772e6 | −0.138652 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.20276e6 | −0.334842 | −0.167421 | − | 0.985885i | \(-0.553544\pi\) | ||||
−0.167421 | + | 0.985885i | \(0.553544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.81936e6i | 0.143908i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 3.11444e6i | − 0.242828i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.29939e7 | −1.00588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.50989e6 | −0.116051 | −0.0580256 | − | 0.998315i | \(-0.518481\pi\) | ||||
−0.0580256 | + | 0.998315i | \(0.518481\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.30113e7i | 0.992963i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.26482e7i | − 0.951653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.08359e6 | −0.155667 | −0.0778336 | − | 0.996966i | \(-0.524800\pi\) | ||||
−0.0778336 | + | 0.996966i | \(0.524800\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.20238e6 | 0.237574 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.13844e6i | 0.157534i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2.10749e7i | − 1.53098i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.03357e7 | −0.745618 | −0.372809 | − | 0.927908i | \(-0.621605\pi\) | ||||
−0.372809 | + | 0.927908i | \(0.621605\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.82287e6 | −0.345515 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.51561e7i | 1.07830i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.39227e6i | 0.238042i | 0.992892 | + | 0.119021i | \(0.0379756\pi\) | ||||
−0.992892 | + | 0.119021i | \(0.962024\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.54171e7 | −1.07444 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.54418e6 | 0.591394 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.99922e7i | 1.37436i | 0.726487 | + | 0.687180i | \(0.241152\pi\) | ||||
−0.726487 | + | 0.687180i | \(0.758848\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.94896e6i | 0.199986i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.37515e7 | 1.59986 | 0.799928 | − | 0.600096i | \(-0.204871\pi\) | ||||
0.799928 | + | 0.600096i | \(0.204871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.42797e6 | 0.630773 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 768079.i | − 0.0510427i | −0.999674 | − | 0.0255214i | \(-0.991875\pi\) | ||||
0.999674 | − | 0.0255214i | \(-0.00812458\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 5.10273e6i | − 0.334581i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −546628. | −0.0356030 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.34656e7 | −1.51821 | −0.759105 | − | 0.650968i | \(-0.774363\pi\) | ||||
−0.759105 | + | 0.650968i | \(0.774363\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 302745.i | − 0.0194576i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.58118e7i | 1.63711i | 0.574425 | + | 0.818557i | \(0.305226\pi\) | ||||
−0.574425 | + | 0.818557i | \(0.694774\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.24736e6 | 0.204610 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.19501e7 | 0.748013 | 0.374006 | − | 0.927426i | \(-0.377984\pi\) | ||||
0.374006 | + | 0.927426i | \(0.377984\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.15940e7i | 0.720977i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.13184e7i | 0.694698i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.61907e7 | 0.987302 | 0.493651 | − | 0.869660i | \(-0.335662\pi\) | ||||
0.493651 | + | 0.869660i | \(0.335662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.35070e6 | −0.263586 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.40818e7i | 0.847637i | 0.905747 | + | 0.423818i | \(0.139311\pi\) | ||||
−0.905747 | + | 0.423818i | \(0.860689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 1.10630e7i | − 0.657384i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.45122e6 | 0.498972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.43477e7 | 0.841695 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.74310e6i | 0.334766i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 4.41819e6i | − 0.254277i | −0.991885 | − | 0.127139i | \(-0.959421\pi\) | ||||
0.991885 | − | 0.127139i | \(-0.0405793\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.38945e7 | −0.794602 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.25399e6 | 0.241744 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.30776e7i | 1.30319i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.04472e6i | 0.337078i | 0.985695 | + | 0.168539i | \(0.0539049\pi\) | ||||
−0.985695 | + | 0.168539i | \(0.946095\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.93569e6 | −0.162683 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.79074e6 | −0.153688 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 2.15507e7i | − 1.17943i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 1.17516e7i | − 0.635202i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.71556e7 | 0.921583 | 0.460791 | − | 0.887509i | \(-0.347566\pi\) | ||||
0.460791 | + | 0.887509i | \(0.347566\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.83020e7 | −0.977114 | −0.488557 | − | 0.872532i | \(-0.662477\pi\) | ||||
−0.488557 | + | 0.872532i | \(0.662477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 1.71009e7i | − 0.907389i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.31851e7i | 1.21522i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.99813e6 | 0.208280 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −77887.9 | −0.00403285 | −0.00201643 | − | 0.999998i | \(-0.500642\pi\) | ||||
−0.00201643 | + | 0.999998i | \(0.500642\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 423648.i | − 0.0218025i | −0.999941 | − | 0.0109012i | \(-0.996530\pi\) | ||||
0.999941 | − | 0.0109012i | \(-0.00347004\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 5.18956e6i | − 0.263856i | −0.991259 | − | 0.131928i | \(-0.957883\pi\) | ||||
0.991259 | − | 0.131928i | \(-0.0421168\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.08613e7 | 1.05428 | 0.527139 | − | 0.849779i | \(-0.323265\pi\) | ||||
0.527139 | + | 0.849779i | \(0.323265\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.15201e6 | −0.158338 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 4.58332e6i | − 0.228859i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.13187e7i | 0.558446i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.18798e6 | −0.401580 | −0.200790 | − | 0.979634i | \(-0.564351\pi\) | ||||
−0.200790 | + | 0.979634i | \(0.564351\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.85717e7 | −0.905442 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1.31900e7i | − 0.639258i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.70505e6i | 0.177454i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.04868e7 | −1.45158 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.84854e6 | 0.466174 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 3.11924e7i | − 1.46783i | −0.679241 | − | 0.733915i | \(-0.737691\pi\) | ||||
0.679241 | − | 0.733915i | \(-0.262309\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 1.88654e7i | − 0.877433i | −0.898626 | − | 0.438716i | \(-0.855433\pi\) | ||||
0.898626 | − | 0.438716i | \(-0.144567\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.30703e7 | 0.604369 | 0.302184 | − | 0.953249i | \(-0.402284\pi\) | ||||
0.302184 | + | 0.953249i | \(0.402284\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.18571e6 | −0.330341 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.58115e6i | 0.255092i | 0.991833 | + | 0.127546i | \(0.0407100\pi\) | ||||
−0.991833 | + | 0.127546i | \(0.959290\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.62471e7i | − 0.734056i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.29628e7 | −0.582302 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.48047e6 | 0.289442 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1.13869e6i | − 0.0505675i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.17437e7i | 0.954629i | 0.878732 | + | 0.477315i | \(0.158390\pi\) | ||||
−0.878732 | + | 0.477315i | \(0.841610\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.11730e7 | 1.36084 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26789e7 | 0.984425 | 0.492212 | − | 0.870475i | \(-0.336188\pi\) | ||||
0.492212 | + | 0.870475i | \(0.336188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.34145e7i | − 1.01061i | −0.862942 | − | 0.505304i | \(-0.831381\pi\) | ||||
0.862942 | − | 0.505304i | \(-0.168619\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.56731e7i | 0.668875i | 0.942418 | + | 0.334437i | \(0.108546\pi\) | ||||
−0.942418 | + | 0.334437i | \(0.891454\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.46543e7 | 1.04626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.07559e7 | 0.453894 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 7.96616e6i | − 0.334288i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 7.13624e6i | − 0.296134i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.82240e6 | 0.157738 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 911092. | 0.0373895 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.97133e7i | − 0.804527i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.67553e7i | 1.48355i | 0.670649 | + | 0.741775i | \(0.266016\pi\) | ||||
−0.670649 | + | 0.741775i | \(0.733984\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.48807e7 | 0.597331 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.11183e7 | 0.843067 | 0.421534 | − | 0.906813i | \(-0.361492\pi\) | ||||
0.421534 | + | 0.906813i | \(0.361492\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.06551e7i | 0.820070i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 2.14855e7i | − 0.843765i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.27922e6 | 0.284312 | 0.142156 | − | 0.989844i | \(-0.454596\pi\) | ||||
0.142156 | + | 0.989844i | \(0.454596\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.19625e7 | 0.464702 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 3.15298e7i | − 1.21819i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 5.67418e6i | − 0.216872i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.41165e7 | 1.29696 | 0.648478 | − | 0.761234i | \(-0.275406\pi\) | ||||
0.648478 | + | 0.761234i | \(0.275406\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.24371e7 | 0.470268 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 1.45083e7i | − 0.545649i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.73880e7i | − 1.76327i | −0.471929 | − | 0.881637i | \(-0.656442\pi\) | ||||
0.471929 | − | 0.881637i | \(-0.343558\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.93153e7 | −0.714887 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.97476e7 | −1.46331 | −0.731656 | − | 0.681674i | \(-0.761252\pi\) | ||||
−0.731656 | + | 0.681674i | \(0.761252\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 6.39691e6i | − 0.234256i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.76410e7i | 1.00156i | 0.865573 | + | 0.500782i | \(0.166954\pi\) | ||||
−0.865573 | + | 0.500782i | \(0.833046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.73588e7 | −1.70701 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.48233e7 | 1.24859 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.22977e6i | 0.186531i | 0.995641 | + | 0.0932654i | \(0.0297305\pi\) | ||||
−0.995641 | + | 0.0932654i | \(0.970269\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 5.80457e6i | − 0.204876i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.30764e6 | −0.0810255 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.10959e7 | −0.736866 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 643115.i | − 0.0223472i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.76477e7i | − 0.606905i | −0.952847 | − | 0.303453i | \(-0.901861\pi\) | ||||
0.952847 | − | 0.303453i | \(-0.0981394\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.97172e6 | −0.170097 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.66934e7 | 1.24893 | 0.624467 | − | 0.781051i | \(-0.285316\pi\) | ||||
0.624467 | + | 0.781051i | \(0.285316\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 2.35188e7i | − 0.796404i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.16023e7i | 1.05921i | 0.848244 | + | 0.529605i | \(0.177660\pi\) | ||||
−0.848244 | + | 0.529605i | \(0.822340\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12965e7 | 0.376693 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.36405e7 | −0.452540 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 3.73829e7i | − 1.23393i | −0.786992 | − | 0.616963i | \(-0.788363\pi\) | ||||
0.786992 | − | 0.616963i | \(-0.211637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.77328e6i | 0.221313i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.75493e7 | 0.570518 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.84243e7 | 0.919401 | 0.459701 | − | 0.888074i | \(-0.347957\pi\) | ||||
0.459701 | + | 0.888074i | \(0.347957\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.56373e6i | 0.0503256i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 1.70600e7i | − 0.543553i | −0.962360 | − | 0.271776i | \(-0.912389\pi\) | ||||
0.962360 | − | 0.271776i | \(-0.0876111\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.21279e7 | 1.65256 |
(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 | 800.6.c.f.449.2 | 4 | ||
4.3 | odd | 2 | 800.6.c.g.449.3 | 4 | |||
5.2 | odd | 4 | 800.6.a.l.1.1 | 2 | |||
5.3 | odd | 4 | 160.6.a.a.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 800.6.c.f.449.3 | 4 | ||
20.3 | even | 4 | 160.6.a.e.1.1 | yes | 2 | ||
20.7 | even | 4 | 800.6.a.g.1.2 | 2 | |||
20.19 | odd | 2 | 800.6.c.g.449.2 | 4 | |||
40.3 | even | 4 | 320.6.a.r.1.2 | 2 | |||
40.13 | odd | 4 | 320.6.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.a.a.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
160.6.a.e.1.1 | yes | 2 | 20.3 | even | 4 | ||
320.6.a.r.1.2 | 2 | 40.3 | even | 4 | |||
320.6.a.v.1.1 | 2 | 40.13 | odd | 4 | |||
800.6.a.g.1.2 | 2 | 20.7 | even | 4 | |||
800.6.a.l.1.1 | 2 | 5.2 | odd | 4 | |||
800.6.c.f.449.2 | 4 | 1.1 | even | 1 | trivial | ||
800.6.c.f.449.3 | 4 | 5.4 | even | 2 | inner | ||
800.6.c.g.449.2 | 4 | 20.19 | odd | 2 | |||
800.6.c.g.449.3 | 4 | 4.3 | odd | 2 |